TSTP Solution File: ITP077^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP077^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n031.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 03:18:01 EDT 2023
% Result : Theorem 0.55s 1.19s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.18 % Problem : ITP077^1 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.19 % Command : do_cvc5 %s %d
% 0.20/0.41 % Computer : n031.cluster.edu
% 0.20/0.41 % Model : x86_64 x86_64
% 0.20/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.41 % Memory : 8042.1875MB
% 0.20/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.41 % CPULimit : 300
% 0.20/0.41 % WCLimit : 300
% 0.20/0.41 % DateTime : Sun Aug 27 17:10:24 EDT 2023
% 0.20/0.41 % CPUTime :
% 0.26/0.60 %----Proving TH0
% 0.26/0.61 %------------------------------------------------------------------------------
% 0.26/0.61 % File : ITP077^1 : TPTP v8.1.2. Released v7.5.0.
% 0.26/0.61 % Domain : Interactive Theorem Proving
% 0.26/0.61 % Problem : Sledgehammer Hilbert_Function problem prob_146__11622158_1
% 0.26/0.61 % Version : Especial.
% 0.26/0.61 % English :
% 0.26/0.61
% 0.26/0.61 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.26/0.61 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.26/0.61 % Source : [Des21]
% 0.26/0.61 % Names : Hilbert_Function/prob_146__11622158_1 [Des21]
% 0.26/0.61
% 0.26/0.61 % Status : Theorem
% 0.26/0.61 % Rating : 0.15 v8.1.0, 0.18 v7.5.0
% 0.26/0.61 % Syntax : Number of formulae : 540 ( 127 unt; 186 typ; 0 def)
% 0.26/0.61 % Number of atoms : 1058 ( 380 equ; 0 cnn)
% 0.26/0.61 % Maximal formula atoms : 12 ( 2 avg)
% 0.26/0.61 % Number of connectives : 3365 ( 86 ~; 11 |; 63 &;2650 @)
% 0.26/0.61 % ( 0 <=>; 555 =>; 0 <=; 0 <~>)
% 0.26/0.61 % Maximal formula depth : 17 ( 7 avg)
% 0.26/0.61 % Number of types : 44 ( 43 usr)
% 0.26/0.61 % Number of type conns : 402 ( 402 >; 0 *; 0 +; 0 <<)
% 0.26/0.61 % Number of symbols : 146 ( 143 usr; 8 con; 0-3 aty)
% 0.26/0.61 % Number of variables : 1068 ( 87 ^; 916 !; 65 ?;1068 :)
% 0.26/0.61 % SPC : TH0_THM_EQU_NAR
% 0.26/0.61
% 0.26/0.61 % Comments : This file was generated by Sledgehammer 2021-02-23 15:37:07.615
% 0.26/0.61 %------------------------------------------------------------------------------
% 0.26/0.61 % Could-be-implicit typings (43)
% 0.26/0.61 thf(ty_n_t__Set__Oset_It__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J_J,type,
% 0.26/0.61 set_list_list_list_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Multiset__Omultiset_It__Multiset__Omultiset_It__List__Olist_Itf__a_J_J_J,type,
% 0.26/0.61 multis971982480list_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__List__Olist_It__Set__Oset_It__List__Olist_It__List__Olist_Itf__a_J_J_J_J,type,
% 0.26/0.61 list_set_list_list_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Set__Oset_It__List__Olist_It__Set__Oset_It__List__Olist_Itf__a_J_J_J_J,type,
% 0.26/0.61 set_list_set_list_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Set__Oset_It__List__Olist_It__List__Olist_It__Set__Oset_Itf__a_J_J_J_J,type,
% 0.26/0.61 set_list_list_set_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__List__Olist_It__Set__Oset_It__Set__Oset_It__List__Olist_Itf__a_J_J_J_J,type,
% 0.26/0.61 list_set_set_list_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__List__Olist_It__Set__Oset_It__List__Olist_It__Set__Oset_Itf__a_J_J_J_J,type,
% 0.26/0.61 list_set_list_set_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Set__Oset_It__List__Olist_It__Set__Oset_It__Set__Oset_Itf__a_J_J_J_J,type,
% 0.26/0.61 set_list_set_set_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__List__Olist_It__Set__Oset_It__Set__Oset_It__Set__Oset_Itf__a_J_J_J_J,type,
% 0.26/0.61 list_set_set_set_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__List__Olist_It__Multiset__Omultiset_It__List__Olist_Itf__a_J_J_J,type,
% 0.26/0.61 list_multiset_list_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Set__Oset_It__Multiset__Omultiset_It__List__Olist_Itf__a_J_J_J,type,
% 0.26/0.61 set_multiset_list_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Set__Oset_It__List__Olist_It__Multiset__Omultiset_Itf__a_J_J_J,type,
% 0.26/0.61 set_list_multiset_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Multiset__Omultiset_It__Set__Oset_It__List__Olist_Itf__a_J_J_J,type,
% 0.26/0.61 multiset_set_list_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__List__Olist_It__Set__Oset_It__Multiset__Omultiset_Itf__a_J_J_J,type,
% 0.26/0.61 list_set_multiset_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Multiset__Omultiset_It__Set__Oset_It__Set__Oset_Itf__a_J_J_J,type,
% 0.26/0.61 multiset_set_set_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.26/0.61 list_list_list_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Set__Oset_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.26/0.61 set_list_list_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Multiset__Omultiset_It__Multiset__Omultiset_Itf__a_J_J,type,
% 0.26/0.61 multiset_multiset_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__List__Olist_It__Set__Oset_It__List__Olist_Itf__a_J_J_J,type,
% 0.26/0.61 list_set_list_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__List__Olist_It__List__Olist_It__Set__Oset_Itf__a_J_J_J,type,
% 0.26/0.61 list_list_set_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Set__Oset_It__Set__Oset_It__List__Olist_Itf__a_J_J_J,type,
% 0.26/0.61 set_set_list_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Set__Oset_It__List__Olist_It__Set__Oset_Itf__a_J_J_J,type,
% 0.26/0.61 set_list_set_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__List__Olist_It__Set__Oset_It__Set__Oset_Itf__a_J_J_J,type,
% 0.26/0.61 list_set_set_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Set__Oset_Itf__a_J_J_J,type,
% 0.26/0.61 set_set_set_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Multiset__Omultiset_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 multiset_list_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__List__Olist_It__Multiset__Omultiset_Itf__a_J_J,type,
% 0.26/0.61 list_multiset_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Set__Oset_It__Multiset__Omultiset_Itf__a_J_J,type,
% 0.26/0.61 set_multiset_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Multiset__Omultiset_It__Set__Oset_Itf__a_J_J,type,
% 0.26/0.61 multiset_set_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 0.26/0.61 set_list_nat: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.26/0.61 list_set_nat: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.26/0.61 set_set_nat: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 list_list_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 set_list_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__List__Olist_It__Set__Oset_Itf__a_J_J,type,
% 0.26/0.61 list_set_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Multiset__Omultiset_It__Nat__Onat_J,type,
% 0.26/0.61 multiset_nat: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.26/0.61 set_set_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Multiset__Omultiset_Itf__a_J,type,
% 0.26/0.61 multiset_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__List__Olist_It__Nat__Onat_J,type,
% 0.26/0.61 list_nat: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.26/0.61 set_nat: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__List__Olist_Itf__a_J,type,
% 0.26/0.61 list_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Set__Oset_Itf__a_J,type,
% 0.26/0.61 set_a: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_t__Nat__Onat,type,
% 0.26/0.61 nat: $tType ).
% 0.26/0.61
% 0.26/0.61 thf(ty_n_tf__a,type,
% 0.26/0.61 a: $tType ).
% 0.26/0.61
% 0.26/0.61 % Explicit typings (143)
% 0.26/0.61 thf(sy_c_Fun_Obij__betw_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 0.26/0.61 bij_be94573046list_a: ( list_a > list_a ) > set_list_a > set_list_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Fun_Obij__betw_001t__List__Olist_Itf__a_J_001tf__a,type,
% 0.26/0.61 bij_betw_list_a_a: ( list_a > a ) > set_list_a > set_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.26/0.61 bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Fun_Obij__betw_001tf__a_001t__List__Olist_Itf__a_J,type,
% 0.26/0.61 bij_betw_a_list_a: ( a > list_a ) > set_a > set_list_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Fun_Obij__betw_001tf__a_001tf__a,type,
% 0.26/0.61 bij_betw_a_a: ( a > a ) > set_a > set_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Fun_Oinj__on_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 0.26/0.61 inj_on_list_a_list_a: ( list_a > list_a ) > set_list_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Fun_Oinj__on_001t__List__Olist_Itf__a_J_001tf__a,type,
% 0.26/0.61 inj_on_list_a_a: ( list_a > a ) > set_list_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Fun_Oinj__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.26/0.61 inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Fun_Oinj__on_001tf__a_001t__List__Olist_Itf__a_J,type,
% 0.26/0.61 inj_on_a_list_a: ( a > list_a ) > set_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Fun_Oinj__on_001tf__a_001tf__a,type,
% 0.26/0.61 inj_on_a_a: ( a > a ) > set_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Groups__List_Omonoid__add__class_Osum__list_001t__Multiset__Omultiset_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 groups1271887971list_a: list_multiset_list_a > multiset_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Groups__List_Omonoid__add__class_Osum__list_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.26/0.61 groups1592617181iset_a: list_multiset_a > multiset_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Groups__List_Omonoid__add__class_Osum__list_001t__Nat__Onat,type,
% 0.26/0.61 groups921905271st_nat: list_nat > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Groups__List_Omonoid__add__class_Osum__list_001tf__a,type,
% 0.26/0.61 groups1792256535list_a: list_a > a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Hilbert__Choice_Oinv__into_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 0.26/0.61 hilber921249868list_a: set_list_a > ( list_a > list_a ) > list_a > list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Hilbert__Choice_Oinv__into_001t__List__Olist_Itf__a_J_001tf__a,type,
% 0.26/0.61 hilber2125729734st_a_a: set_list_a > ( list_a > a ) > a > list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Hilbert__Choice_Oinv__into_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.26/0.61 hilber815131374at_nat: set_nat > ( nat > nat ) > nat > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Hilbert__Choice_Oinv__into_001tf__a_001t__List__Olist_Itf__a_J,type,
% 0.26/0.61 hilber165648082list_a: set_a > ( a > list_a ) > list_a > a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Hilbert__Choice_Oinv__into_001tf__a_001tf__a,type,
% 0.26/0.61 hilbert_inv_into_a_a: set_a > ( a > a ) > a > a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Hilbert__Function__Mirabelle__sksumwvvhs_Odirect__decomp_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.26/0.61 hilber2024005914iset_a: set_multiset_a > list_set_multiset_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Hilbert__Function__Mirabelle__sksumwvvhs_Odirect__decomp_001t__Nat__Onat,type,
% 0.26/0.61 hilber1014902394mp_nat: set_nat > list_set_nat > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Hilbert__Function__Mirabelle__sksumwvvhs_Odirect__decomp_001tf__a,type,
% 0.26/0.61 hilber2037636820comp_a: set_a > list_set_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Olist__ex_001t__Set__Oset_Itf__a_J,type,
% 0.26/0.61 list_ex_set_a: ( set_a > $o ) > list_set_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Olist__ex_001tf__a,type,
% 0.26/0.61 list_ex_a: ( a > $o ) > list_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Olist__update_001t__Set__Oset_Itf__a_J,type,
% 0.26/0.61 list_update_set_a: list_set_a > nat > set_a > list_set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Olist__update_001tf__a,type,
% 0.26/0.61 list_update_a: list_a > nat > a > list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Olistset_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 listset_list_list_a: list_set_list_list_a > set_list_list_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Olistset_001t__List__Olist_It__Set__Oset_Itf__a_J_J,type,
% 0.26/0.61 listset_list_set_a: list_set_list_set_a > set_list_list_set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Olistset_001t__List__Olist_Itf__a_J,type,
% 0.26/0.61 listset_list_a: list_set_list_a > set_list_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Olistset_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.26/0.61 listset_multiset_a: list_set_multiset_a > set_list_multiset_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Olistset_001t__Nat__Onat,type,
% 0.26/0.61 listset_nat: list_set_nat > set_list_nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Olistset_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 listset_set_list_a: list_set_set_list_a > set_list_set_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Olistset_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.26/0.61 listset_set_set_a: list_set_set_set_a > set_list_set_set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Olistset_001t__Set__Oset_Itf__a_J,type,
% 0.26/0.61 listset_set_a: list_set_set_a > set_list_set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Olistset_001tf__a,type,
% 0.26/0.61 listset_a: list_set_a > set_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Onth_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 nth_list_list_a: list_list_list_a > nat > list_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Onth_001t__List__Olist_It__Set__Oset_Itf__a_J_J,type,
% 0.26/0.61 nth_list_set_a: list_list_set_a > nat > list_set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Onth_001t__List__Olist_Itf__a_J,type,
% 0.26/0.61 nth_list_a: list_list_a > nat > list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Onth_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.26/0.61 nth_multiset_a: list_multiset_a > nat > multiset_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 0.26/0.61 nth_nat: list_nat > nat > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Onth_001t__Set__Oset_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.26/0.61 nth_set_list_list_a: list_set_list_list_a > nat > set_list_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Onth_001t__Set__Oset_It__List__Olist_It__Set__Oset_Itf__a_J_J_J,type,
% 0.26/0.61 nth_set_list_set_a: list_set_list_set_a > nat > set_list_set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Onth_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 nth_set_list_a: list_set_list_a > nat > set_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Onth_001t__Set__Oset_It__Multiset__Omultiset_Itf__a_J_J,type,
% 0.26/0.61 nth_set_multiset_a: list_set_multiset_a > nat > set_multiset_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.26/0.61 nth_set_nat: list_set_nat > nat > set_nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Onth_001t__Set__Oset_It__Set__Oset_It__List__Olist_Itf__a_J_J_J,type,
% 0.26/0.61 nth_set_set_list_a: list_set_set_list_a > nat > set_set_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Onth_001t__Set__Oset_It__Set__Oset_It__Set__Oset_Itf__a_J_J_J,type,
% 0.26/0.61 nth_set_set_set_a: list_set_set_set_a > nat > set_set_set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Onth_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.26/0.61 nth_set_set_a: list_set_set_a > nat > set_set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Onth_001t__Set__Oset_Itf__a_J,type,
% 0.26/0.61 nth_set_a: list_set_a > nat > set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Onth_001tf__a,type,
% 0.26/0.61 nth_a: list_a > nat > a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Orev_001t__List__Olist_Itf__a_J,type,
% 0.26/0.61 rev_list_a: list_list_a > list_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Orev_001t__Nat__Onat,type,
% 0.26/0.61 rev_nat: list_nat > list_nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Orev_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 rev_set_list_a: list_set_list_a > list_set_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Orev_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.26/0.61 rev_set_set_a: list_set_set_a > list_set_set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Orev_001t__Set__Oset_Itf__a_J,type,
% 0.26/0.61 rev_set_a: list_set_a > list_set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_List_Orev_001tf__a,type,
% 0.26/0.61 rev_a: list_a > list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Multiset_Ocomm__monoid__add__class_Osum__mset_001t__Multiset__Omultiset_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 comm_m324867663list_a: multis971982480list_a > multiset_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Multiset_Ocomm__monoid__add__class_Osum__mset_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.26/0.61 comm_m2145643721iset_a: multiset_multiset_a > multiset_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Multiset_Ocomm__monoid__add__class_Osum__mset_001t__Nat__Onat,type,
% 0.26/0.61 comm_m1100186507et_nat: multiset_nat > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Multiset_Ocomm__monoid__add__class_Osum__mset_001tf__a,type,
% 0.26/0.61 comm_m543484931mset_a: multiset_a > a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Multiset_Omset_001t__List__Olist_Itf__a_J,type,
% 0.26/0.61 mset_list_a: list_list_a > multiset_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Multiset_Omset_001t__Multiset__Omultiset_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 mset_multiset_list_a: list_multiset_list_a > multis971982480list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Multiset_Omset_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.26/0.61 mset_multiset_a: list_multiset_a > multiset_multiset_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Multiset_Omset_001t__Nat__Onat,type,
% 0.26/0.61 mset_nat: list_nat > multiset_nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Multiset_Omset_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 mset_set_list_a: list_set_list_a > multiset_set_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Multiset_Omset_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.26/0.61 mset_set_set_a: list_set_set_a > multiset_set_set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Multiset_Omset_001t__Set__Oset_Itf__a_J,type,
% 0.26/0.61 mset_set_a: list_set_a > multiset_set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Multiset_Omset_001tf__a,type,
% 0.26/0.61 mset_a: list_a > multiset_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Multiset_Oset__mset_001t__List__Olist_Itf__a_J,type,
% 0.26/0.61 set_mset_list_a: multiset_list_a > set_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Multiset_Oset__mset_001t__Multiset__Omultiset_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 set_ms1660427399list_a: multis971982480list_a > set_multiset_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Multiset_Oset__mset_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.26/0.61 set_mset_multiset_a: multiset_multiset_a > set_multiset_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Multiset_Oset__mset_001t__Set__Oset_Itf__a_J,type,
% 0.26/0.61 set_mset_set_a: multiset_set_a > set_set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Multiset_Oset__mset_001tf__a,type,
% 0.26/0.61 set_mset_a: multiset_a > set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.26/0.61 size_s575106428list_a: list_list_list_a > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Set__Oset_Itf__a_J_J_J,type,
% 0.26/0.61 size_s341332310_set_a: list_list_set_a > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 size_s1427607542list_a: list_list_a > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Multiset__Omultiset_Itf__a_J_J,type,
% 0.26/0.61 size_s1657263798iset_a: list_multiset_a > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 0.26/0.61 size_size_list_nat: list_nat > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__List__Olist_It__List__Olist_Itf__a_J_J_J_J,type,
% 0.26/0.61 size_s240404444list_a: list_set_list_list_a > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__List__Olist_It__Set__Oset_Itf__a_J_J_J_J,type,
% 0.26/0.61 size_s926492982_set_a: list_set_list_set_a > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__List__Olist_Itf__a_J_J_J,type,
% 0.26/0.61 size_s1635937238list_a: list_set_list_a > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Multiset__Omultiset_Itf__a_J_J_J,type,
% 0.26/0.61 size_s802269334iset_a: list_set_multiset_a > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.26/0.61 size_s577819178et_nat: list_set_nat > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Set__Oset_It__List__Olist_Itf__a_J_J_J_J,type,
% 0.26/0.61 size_s469631926list_a: list_set_set_list_a > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Set__Oset_It__Set__Oset_Itf__a_J_J_J_J,type,
% 0.26/0.61 size_s726512144_set_a: list_set_set_set_a > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Set__Oset_Itf__a_J_J_J,type,
% 0.26/0.61 size_s739728560_set_a: list_set_set_a > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_Itf__a_J_J,type,
% 0.26/0.61 size_size_list_set_a: list_set_a > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_Itf__a_J,type,
% 0.26/0.61 size_size_list_a: list_a > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Nat_Osize__class_Osize_001t__Multiset__Omultiset_It__Set__Oset_Itf__a_J_J,type,
% 0.26/0.61 size_s657334288_set_a: multiset_set_a > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Nat_Osize__class_Osize_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.26/0.61 size_size_multiset_a: multiset_a > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.26/0.61 ord_less_nat: nat > nat > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 ord_less_set_list_a: set_list_a > set_list_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.26/0.61 ord_less_set_nat: set_nat > set_nat > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_Itf__a_J,type,
% 0.26/0.61 ord_less_set_a: set_a > set_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_I_Eo_Mt__Nat__Onat_J,type,
% 0.26/0.61 ord_less_eq_o_nat: ( $o > nat ) > ( $o > nat ) > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.26/0.61 ord_less_eq_nat: nat > nat > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 ord_le1301786372list_a: set_list_a > set_list_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.26/0.61 ord_less_eq_set_nat: set_nat > set_nat > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_Itf__a_J,type,
% 0.26/0.61 ord_less_eq_set_a: set_a > set_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Permutation_Operm_001t__Set__Oset_Itf__a_J,type,
% 0.26/0.61 perm_set_a: list_set_a > list_set_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Permutation_Operm_001tf__a,type,
% 0.26/0.61 perm_a: list_a > list_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_OCollect_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 collect_list_list_a: ( list_list_a > $o ) > set_list_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_OCollect_001t__List__Olist_It__Set__Oset_Itf__a_J_J,type,
% 0.26/0.61 collect_list_set_a: ( list_set_a > $o ) > set_list_set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_OCollect_001t__List__Olist_Itf__a_J,type,
% 0.26/0.61 collect_list_a: ( list_a > $o ) > set_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_OCollect_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.26/0.61 collect_multiset_a: ( multiset_a > $o ) > set_multiset_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.26/0.61 collect_nat: ( nat > $o ) > set_nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_OCollect_001t__Set__Oset_Itf__a_J,type,
% 0.26/0.61 collect_set_a: ( set_a > $o ) > set_set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_OCollect_001tf__a,type,
% 0.26/0.61 collect_a: ( a > $o ) > set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_Oimage_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
% 0.26/0.61 image_list_nat_nat: ( list_nat > nat ) > set_list_nat > set_nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_Oimage_001t__List__Olist_Itf__a_J_001t__List__Olist_Itf__a_J,type,
% 0.26/0.61 image_list_a_list_a: ( list_a > list_a ) > set_list_a > set_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_Oimage_001t__List__Olist_Itf__a_J_001tf__a,type,
% 0.26/0.61 image_list_a_a: ( list_a > a ) > set_list_a > set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.26/0.61 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_Oimage_001tf__a_001t__List__Olist_Itf__a_J,type,
% 0.26/0.61 image_a_list_a: ( a > list_a ) > set_a > set_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set_Oimage_001tf__a_001tf__a,type,
% 0.26/0.61 image_a_a: ( a > a ) > set_a > set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 0.26/0.61 set_ord_lessThan_nat: nat > set_nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 set_or1578766727list_a: set_list_a > set_set_list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.26/0.61 set_or1597314339et_nat: set_nat > set_set_nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_Itf__a_J,type,
% 0.26/0.61 set_or1164043265_set_a: set_a > set_set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__List__Olist_It__List__Olist_It__List__Olist_Itf__a_J_J_J,type,
% 0.26/0.61 member1511395513list_a: list_list_list_a > set_list_list_list_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__List__Olist_It__List__Olist_It__Set__Oset_Itf__a_J_J_J,type,
% 0.26/0.61 member954073875_set_a: list_list_set_a > set_list_list_set_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__List__Olist_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 member_list_list_a: list_list_a > set_list_list_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__List__Olist_It__Multiset__Omultiset_Itf__a_J_J,type,
% 0.26/0.61 member518144627iset_a: list_multiset_a > set_list_multiset_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 0.26/0.61 member_list_nat: list_nat > set_list_nat > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__List__Olist_It__Set__Oset_It__List__Olist_Itf__a_J_J_J,type,
% 0.26/0.61 member101195155list_a: list_set_list_a > set_list_set_list_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__List__Olist_It__Set__Oset_It__Set__Oset_Itf__a_J_J_J,type,
% 0.26/0.61 member814963949_set_a: list_set_set_a > set_list_set_set_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__List__Olist_It__Set__Oset_Itf__a_J_J,type,
% 0.26/0.61 member_list_set_a: list_set_a > set_list_set_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__List__Olist_Itf__a_J,type,
% 0.26/0.61 member_list_a: list_a > set_list_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Multiset__Omultiset_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 member528267379list_a: multiset_list_a > set_multiset_list_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Multiset__Omultiset_Itf__a_J,type,
% 0.26/0.61 member_multiset_a: multiset_a > set_multiset_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Nat__Onat,type,
% 0.26/0.61 member_nat: nat > set_nat > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Set__Oset_It__List__Olist_Itf__a_J_J,type,
% 0.26/0.61 member_set_list_a: set_list_a > set_set_list_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.26/0.61 member_set_nat: set_nat > set_set_nat > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Set__Oset_It__Set__Oset_Itf__a_J_J,type,
% 0.26/0.61 member_set_set_a: set_set_a > set_set_set_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001t__Set__Oset_Itf__a_J,type,
% 0.26/0.61 member_set_a: set_a > set_set_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_c_member_001tf__a,type,
% 0.26/0.61 member_a: a > set_a > $o ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_A,type,
% 0.26/0.61 a2: set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_a____,type,
% 0.26/0.61 a3: a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_f____,type,
% 0.26/0.61 f: nat > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_g____,type,
% 0.26/0.61 g: nat > nat ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_qs2____,type,
% 0.26/0.61 qs2: list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_qs____,type,
% 0.26/0.61 qs: list_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_ss1,type,
% 0.26/0.61 ss1: list_set_a ).
% 0.26/0.61
% 0.26/0.61 thf(sy_v_ss2,type,
% 0.26/0.61 ss2: list_set_a ).
% 0.26/0.61
% 0.26/0.61 % Relevant facts (353)
% 0.26/0.61 thf(fact_0__092_060open_062mset_Aqs2_A_061_Amset_Aqs_092_060close_062,axiom,
% 0.26/0.61 ( ( mset_a @ qs2 )
% 0.26/0.61 = ( mset_a @ qs ) ) ).
% 0.26/0.61
% 0.26/0.61 % \<open>mset qs2 = mset qs\<close>
% 0.26/0.61 thf(fact_1__092_060open_062a_A_092_060in_062_AA_092_060close_062,axiom,
% 0.26/0.61 member_a @ a3 @ a2 ).
% 0.26/0.61
% 0.26/0.61 % \<open>a \<in> A\<close>
% 0.26/0.61 thf(fact_2_a,axiom,
% 0.26/0.61 ( a3
% 0.26/0.61 = ( groups1792256535list_a @ qs ) ) ).
% 0.26/0.61
% 0.26/0.61 % a
% 0.26/0.61 thf(fact_3_len__qs2,axiom,
% 0.26/0.61 ( ( size_size_list_a @ qs2 )
% 0.26/0.61 = ( size_size_list_a @ qs ) ) ).
% 0.26/0.61
% 0.26/0.61 % len_qs2
% 0.26/0.61 thf(fact_4__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062qs_O_A_092_060lbrakk_062a_A_061_Asum__list_Aqs_059_Aqs_A_092_060in_062_Alistset_Ass1_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.26/0.61 ~ ! [Qs: list_a] :
% 0.26/0.61 ( ( a3
% 0.26/0.61 = ( groups1792256535list_a @ Qs ) )
% 0.26/0.61 => ~ ( member_list_a @ Qs @ ( listset_a @ ss1 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % \<open>\<And>thesis. (\<And>qs. \<lbrakk>a = sum_list qs; qs \<in> listset ss1\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.26/0.61 thf(fact_5_qs2__in,axiom,
% 0.26/0.61 member_list_a @ qs2 @ ( listset_a @ ss2 ) ).
% 0.26/0.61
% 0.26/0.61 % qs2_in
% 0.26/0.61 thf(fact_6_direct__decompD_I1_J,axiom,
% 0.26/0.61 ! [A: set_multiset_a,Ss: list_set_multiset_a,Qs2: list_multiset_a] :
% 0.26/0.61 ( ( hilber2024005914iset_a @ A @ Ss )
% 0.26/0.61 => ( ( member518144627iset_a @ Qs2 @ ( listset_multiset_a @ Ss ) )
% 0.26/0.61 => ( member_multiset_a @ ( groups1592617181iset_a @ Qs2 ) @ A ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % direct_decompD(1)
% 0.26/0.61 thf(fact_7_direct__decompD_I1_J,axiom,
% 0.26/0.61 ! [A: set_nat,Ss: list_set_nat,Qs2: list_nat] :
% 0.26/0.61 ( ( hilber1014902394mp_nat @ A @ Ss )
% 0.26/0.61 => ( ( member_list_nat @ Qs2 @ ( listset_nat @ Ss ) )
% 0.26/0.61 => ( member_nat @ ( groups921905271st_nat @ Qs2 ) @ A ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % direct_decompD(1)
% 0.26/0.61 thf(fact_8_direct__decompD_I1_J,axiom,
% 0.26/0.61 ! [A: set_a,Ss: list_set_a,Qs2: list_a] :
% 0.26/0.61 ( ( hilber2037636820comp_a @ A @ Ss )
% 0.26/0.61 => ( ( member_list_a @ Qs2 @ ( listset_a @ Ss ) )
% 0.26/0.61 => ( member_a @ ( groups1792256535list_a @ Qs2 ) @ A ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % direct_decompD(1)
% 0.26/0.61 thf(fact_9_direct__decompE,axiom,
% 0.26/0.61 ! [A: set_multiset_a,Ss: list_set_multiset_a,A2: multiset_a] :
% 0.26/0.61 ( ( hilber2024005914iset_a @ A @ Ss )
% 0.26/0.61 => ( ( member_multiset_a @ A2 @ A )
% 0.26/0.61 => ~ ! [Qs: list_multiset_a] :
% 0.26/0.61 ( ( member518144627iset_a @ Qs @ ( listset_multiset_a @ Ss ) )
% 0.26/0.61 => ( A2
% 0.26/0.61 != ( groups1592617181iset_a @ Qs ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % direct_decompE
% 0.26/0.61 thf(fact_10_direct__decompE,axiom,
% 0.26/0.61 ! [A: set_nat,Ss: list_set_nat,A2: nat] :
% 0.26/0.61 ( ( hilber1014902394mp_nat @ A @ Ss )
% 0.26/0.61 => ( ( member_nat @ A2 @ A )
% 0.26/0.61 => ~ ! [Qs: list_nat] :
% 0.26/0.61 ( ( member_list_nat @ Qs @ ( listset_nat @ Ss ) )
% 0.26/0.61 => ( A2
% 0.26/0.61 != ( groups921905271st_nat @ Qs ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % direct_decompE
% 0.26/0.61 thf(fact_11_direct__decompE,axiom,
% 0.26/0.61 ! [A: set_a,Ss: list_set_a,A2: a] :
% 0.26/0.61 ( ( hilber2037636820comp_a @ A @ Ss )
% 0.26/0.61 => ( ( member_a @ A2 @ A )
% 0.26/0.61 => ~ ! [Qs: list_a] :
% 0.26/0.61 ( ( member_list_a @ Qs @ ( listset_a @ Ss ) )
% 0.26/0.61 => ( A2
% 0.26/0.61 != ( groups1792256535list_a @ Qs ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % direct_decompE
% 0.26/0.61 thf(fact_12_direct__decompI__alt,axiom,
% 0.26/0.61 ! [Ss: list_set_multiset_a,A: set_multiset_a] :
% 0.26/0.61 ( ! [Qs: list_multiset_a] :
% 0.26/0.61 ( ( member518144627iset_a @ Qs @ ( listset_multiset_a @ Ss ) )
% 0.26/0.61 => ( member_multiset_a @ ( groups1592617181iset_a @ Qs ) @ A ) )
% 0.26/0.61 => ( ! [A3: multiset_a] :
% 0.26/0.61 ( ( member_multiset_a @ A3 @ A )
% 0.26/0.61 => ? [X: list_multiset_a] :
% 0.26/0.61 ( ( member518144627iset_a @ X @ ( listset_multiset_a @ Ss ) )
% 0.26/0.61 & ( A3
% 0.26/0.61 = ( groups1592617181iset_a @ X ) )
% 0.26/0.61 & ! [Y: list_multiset_a] :
% 0.26/0.61 ( ( ( member518144627iset_a @ Y @ ( listset_multiset_a @ Ss ) )
% 0.26/0.61 & ( A3
% 0.26/0.61 = ( groups1592617181iset_a @ Y ) ) )
% 0.26/0.61 => ( Y = X ) ) ) )
% 0.26/0.61 => ( hilber2024005914iset_a @ A @ Ss ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % direct_decompI_alt
% 0.26/0.61 thf(fact_13_direct__decompI__alt,axiom,
% 0.26/0.61 ! [Ss: list_set_nat,A: set_nat] :
% 0.26/0.61 ( ! [Qs: list_nat] :
% 0.26/0.61 ( ( member_list_nat @ Qs @ ( listset_nat @ Ss ) )
% 0.26/0.61 => ( member_nat @ ( groups921905271st_nat @ Qs ) @ A ) )
% 0.26/0.61 => ( ! [A3: nat] :
% 0.26/0.61 ( ( member_nat @ A3 @ A )
% 0.26/0.61 => ? [X: list_nat] :
% 0.26/0.61 ( ( member_list_nat @ X @ ( listset_nat @ Ss ) )
% 0.26/0.61 & ( A3
% 0.26/0.61 = ( groups921905271st_nat @ X ) )
% 0.26/0.61 & ! [Y: list_nat] :
% 0.26/0.61 ( ( ( member_list_nat @ Y @ ( listset_nat @ Ss ) )
% 0.26/0.61 & ( A3
% 0.26/0.61 = ( groups921905271st_nat @ Y ) ) )
% 0.26/0.61 => ( Y = X ) ) ) )
% 0.26/0.61 => ( hilber1014902394mp_nat @ A @ Ss ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % direct_decompI_alt
% 0.26/0.61 thf(fact_14_direct__decompI__alt,axiom,
% 0.26/0.61 ! [Ss: list_set_a,A: set_a] :
% 0.26/0.61 ( ! [Qs: list_a] :
% 0.26/0.61 ( ( member_list_a @ Qs @ ( listset_a @ Ss ) )
% 0.26/0.61 => ( member_a @ ( groups1792256535list_a @ Qs ) @ A ) )
% 0.26/0.61 => ( ! [A3: a] :
% 0.26/0.61 ( ( member_a @ A3 @ A )
% 0.26/0.61 => ? [X: list_a] :
% 0.26/0.61 ( ( member_list_a @ X @ ( listset_a @ Ss ) )
% 0.26/0.61 & ( A3
% 0.26/0.61 = ( groups1792256535list_a @ X ) )
% 0.26/0.61 & ! [Y: list_a] :
% 0.26/0.61 ( ( ( member_list_a @ Y @ ( listset_a @ Ss ) )
% 0.26/0.61 & ( A3
% 0.26/0.61 = ( groups1792256535list_a @ Y ) ) )
% 0.26/0.61 => ( Y = X ) ) ) )
% 0.26/0.61 => ( hilber2037636820comp_a @ A @ Ss ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % direct_decompI_alt
% 0.26/0.61 thf(fact_15_direct__decomp__unique,axiom,
% 0.26/0.61 ! [A: set_nat,Ss: list_set_nat,Qs2: list_nat,Qs3: list_nat] :
% 0.26/0.61 ( ( hilber1014902394mp_nat @ A @ Ss )
% 0.26/0.61 => ( ( member_list_nat @ Qs2 @ ( listset_nat @ Ss ) )
% 0.26/0.61 => ( ( member_list_nat @ Qs3 @ ( listset_nat @ Ss ) )
% 0.26/0.61 => ( ( ( groups921905271st_nat @ Qs2 )
% 0.26/0.61 = ( groups921905271st_nat @ Qs3 ) )
% 0.26/0.61 => ( Qs2 = Qs3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % direct_decomp_unique
% 0.26/0.61 thf(fact_16_direct__decomp__unique,axiom,
% 0.26/0.61 ! [A: set_a,Ss: list_set_a,Qs2: list_a,Qs3: list_a] :
% 0.26/0.61 ( ( hilber2037636820comp_a @ A @ Ss )
% 0.26/0.61 => ( ( member_list_a @ Qs2 @ ( listset_a @ Ss ) )
% 0.26/0.61 => ( ( member_list_a @ Qs3 @ ( listset_a @ Ss ) )
% 0.26/0.61 => ( ( ( groups1792256535list_a @ Qs2 )
% 0.26/0.61 = ( groups1792256535list_a @ Qs3 ) )
% 0.26/0.61 => ( Qs2 = Qs3 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % direct_decomp_unique
% 0.26/0.61 thf(fact_17_sum__list_Orev,axiom,
% 0.26/0.61 ! [Xs: list_nat] :
% 0.26/0.61 ( ( groups921905271st_nat @ ( rev_nat @ Xs ) )
% 0.26/0.61 = ( groups921905271st_nat @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % sum_list.rev
% 0.26/0.61 thf(fact_18_sum__list_Orev,axiom,
% 0.26/0.61 ! [Xs: list_a] :
% 0.26/0.61 ( ( groups1792256535list_a @ ( rev_a @ Xs ) )
% 0.26/0.61 = ( groups1792256535list_a @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % sum_list.rev
% 0.26/0.61 thf(fact_19__C1_C,axiom,
% 0.26/0.61 ! [I: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I @ ( size_size_list_a @ qs ) )
% 0.26/0.61 => ( ( nth_a @ qs2 @ I )
% 0.26/0.61 = ( nth_a @ qs @ ( g @ I ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % "1"
% 0.26/0.61 thf(fact_20_g__bij2,axiom,
% 0.26/0.61 bij_betw_nat_nat @ g @ ( set_ord_lessThan_nat @ ( size_size_list_a @ qs2 ) ) @ ( set_ord_lessThan_nat @ ( size_size_list_a @ qs ) ) ).
% 0.26/0.61
% 0.26/0.61 % g_bij2
% 0.26/0.61 thf(fact_21_sum__mset__sum__list,axiom,
% 0.26/0.61 ! [Xs: list_nat] :
% 0.26/0.61 ( ( comm_m1100186507et_nat @ ( mset_nat @ Xs ) )
% 0.26/0.61 = ( groups921905271st_nat @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % sum_mset_sum_list
% 0.26/0.61 thf(fact_22_sum__mset__sum__list,axiom,
% 0.26/0.61 ! [Xs: list_multiset_list_a] :
% 0.26/0.61 ( ( comm_m324867663list_a @ ( mset_multiset_list_a @ Xs ) )
% 0.26/0.61 = ( groups1271887971list_a @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % sum_mset_sum_list
% 0.26/0.61 thf(fact_23_sum__mset__sum__list,axiom,
% 0.26/0.61 ! [Xs: list_multiset_a] :
% 0.26/0.61 ( ( comm_m2145643721iset_a @ ( mset_multiset_a @ Xs ) )
% 0.26/0.61 = ( groups1592617181iset_a @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % sum_mset_sum_list
% 0.26/0.61 thf(fact_24_sum__mset__sum__list,axiom,
% 0.26/0.61 ! [Xs: list_a] :
% 0.26/0.61 ( ( comm_m543484931mset_a @ ( mset_a @ Xs ) )
% 0.26/0.61 = ( groups1792256535list_a @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % sum_mset_sum_list
% 0.26/0.61 thf(fact_25_direct__decompD_I3_J,axiom,
% 0.26/0.61 ! [A: set_nat,Ss: list_set_nat] :
% 0.26/0.61 ( ( hilber1014902394mp_nat @ A @ Ss )
% 0.26/0.61 => ( ( image_list_nat_nat @ groups921905271st_nat @ ( listset_nat @ Ss ) )
% 0.26/0.61 = A ) ) ).
% 0.26/0.61
% 0.26/0.61 % direct_decompD(3)
% 0.26/0.61 thf(fact_26_direct__decompD_I3_J,axiom,
% 0.26/0.61 ! [A: set_a,Ss: list_set_a] :
% 0.26/0.61 ( ( hilber2037636820comp_a @ A @ Ss )
% 0.26/0.61 => ( ( image_list_a_a @ groups1792256535list_a @ ( listset_a @ Ss ) )
% 0.26/0.61 = A ) ) ).
% 0.26/0.61
% 0.26/0.61 % direct_decompD(3)
% 0.26/0.61 thf(fact_27_assms_I1_J,axiom,
% 0.26/0.61 hilber2037636820comp_a @ a2 @ ss1 ).
% 0.26/0.61
% 0.26/0.61 % assms(1)
% 0.26/0.61 thf(fact_28_qs__in,axiom,
% 0.26/0.61 member_list_a @ qs @ ( listset_a @ ss1 ) ).
% 0.26/0.61
% 0.26/0.61 % qs_in
% 0.26/0.61 thf(fact_29_mset__rev,axiom,
% 0.26/0.61 ! [Xs: list_set_a] :
% 0.26/0.61 ( ( mset_set_a @ ( rev_set_a @ Xs ) )
% 0.26/0.61 = ( mset_set_a @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % mset_rev
% 0.26/0.61 thf(fact_30_mset__rev,axiom,
% 0.26/0.61 ! [Xs: list_list_a] :
% 0.26/0.61 ( ( mset_list_a @ ( rev_list_a @ Xs ) )
% 0.26/0.61 = ( mset_list_a @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % mset_rev
% 0.26/0.61 thf(fact_31_mset__rev,axiom,
% 0.26/0.61 ! [Xs: list_a] :
% 0.26/0.61 ( ( mset_a @ ( rev_a @ Xs ) )
% 0.26/0.61 = ( mset_a @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % mset_rev
% 0.26/0.61 thf(fact_32__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062qs2_O_A_092_060lbrakk_062qs2_A_092_060in_062_Alistset_Ass2_059_Alength_Aqs2_A_061_Alength_Aqs_059_A_092_060And_062i_O_Ai_A_060_Alength_Aqs_A_092_060Longrightarrow_062_Aqs2_A_B_Ai_A_061_Aqs_A_B_Ag_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.26/0.61 ~ ! [Qs22: list_a] :
% 0.26/0.61 ( ( member_list_a @ Qs22 @ ( listset_a @ ss2 ) )
% 0.26/0.61 => ( ( ( size_size_list_a @ Qs22 )
% 0.26/0.61 = ( size_size_list_a @ qs ) )
% 0.26/0.61 => ~ ! [I2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ qs ) )
% 0.26/0.61 => ( ( nth_a @ Qs22 @ I2 )
% 0.26/0.61 = ( nth_a @ qs @ ( g @ I2 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % \<open>\<And>thesis. (\<And>qs2. \<lbrakk>qs2 \<in> listset ss2; length qs2 = length qs; \<And>i. i < length qs \<Longrightarrow> qs2 ! i = qs ! g i\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.26/0.61 thf(fact_33_assms_I2_J,axiom,
% 0.26/0.61 perm_set_a @ ss1 @ ss2 ).
% 0.26/0.61
% 0.26/0.61 % assms(2)
% 0.26/0.61 thf(fact_34_ex__mset,axiom,
% 0.26/0.61 ! [X2: multiset_set_a] :
% 0.26/0.61 ? [Xs2: list_set_a] :
% 0.26/0.61 ( ( mset_set_a @ Xs2 )
% 0.26/0.61 = X2 ) ).
% 0.26/0.61
% 0.26/0.61 % ex_mset
% 0.26/0.61 thf(fact_35_ex__mset,axiom,
% 0.26/0.61 ! [X2: multiset_list_a] :
% 0.26/0.61 ? [Xs2: list_list_a] :
% 0.26/0.61 ( ( mset_list_a @ Xs2 )
% 0.26/0.61 = X2 ) ).
% 0.26/0.61
% 0.26/0.61 % ex_mset
% 0.26/0.61 thf(fact_36_ex__mset,axiom,
% 0.26/0.61 ! [X2: multiset_a] :
% 0.26/0.61 ? [Xs2: list_a] :
% 0.26/0.61 ( ( mset_a @ Xs2 )
% 0.26/0.61 = X2 ) ).
% 0.26/0.61
% 0.26/0.61 % ex_mset
% 0.26/0.61 thf(fact_37_mset__eq__length,axiom,
% 0.26/0.61 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.26/0.61 ( ( ( mset_list_a @ Xs )
% 0.26/0.61 = ( mset_list_a @ Ys ) )
% 0.26/0.61 => ( ( size_s1427607542list_a @ Xs )
% 0.26/0.61 = ( size_s1427607542list_a @ Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % mset_eq_length
% 0.26/0.61 thf(fact_38_mset__eq__length,axiom,
% 0.26/0.61 ! [Xs: list_set_list_a,Ys: list_set_list_a] :
% 0.26/0.61 ( ( ( mset_set_list_a @ Xs )
% 0.26/0.61 = ( mset_set_list_a @ Ys ) )
% 0.26/0.61 => ( ( size_s1635937238list_a @ Xs )
% 0.26/0.61 = ( size_s1635937238list_a @ Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % mset_eq_length
% 0.26/0.61 thf(fact_39_mset__eq__length,axiom,
% 0.26/0.61 ! [Xs: list_set_set_a,Ys: list_set_set_a] :
% 0.26/0.61 ( ( ( mset_set_set_a @ Xs )
% 0.26/0.61 = ( mset_set_set_a @ Ys ) )
% 0.26/0.61 => ( ( size_s739728560_set_a @ Xs )
% 0.26/0.61 = ( size_s739728560_set_a @ Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % mset_eq_length
% 0.26/0.61 thf(fact_40_mset__eq__length,axiom,
% 0.26/0.61 ! [Xs: list_nat,Ys: list_nat] :
% 0.26/0.61 ( ( ( mset_nat @ Xs )
% 0.26/0.61 = ( mset_nat @ Ys ) )
% 0.26/0.61 => ( ( size_size_list_nat @ Xs )
% 0.26/0.61 = ( size_size_list_nat @ Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % mset_eq_length
% 0.26/0.61 thf(fact_41_mset__eq__length,axiom,
% 0.26/0.61 ! [Xs: list_a,Ys: list_a] :
% 0.26/0.61 ( ( ( mset_a @ Xs )
% 0.26/0.61 = ( mset_a @ Ys ) )
% 0.26/0.61 => ( ( size_size_list_a @ Xs )
% 0.26/0.61 = ( size_size_list_a @ Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % mset_eq_length
% 0.26/0.61 thf(fact_42_mset__eq__length,axiom,
% 0.26/0.61 ! [Xs: list_set_a,Ys: list_set_a] :
% 0.26/0.61 ( ( ( mset_set_a @ Xs )
% 0.26/0.61 = ( mset_set_a @ Ys ) )
% 0.26/0.61 => ( ( size_size_list_set_a @ Xs )
% 0.26/0.61 = ( size_size_list_set_a @ Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % mset_eq_length
% 0.26/0.61 thf(fact_43_mset__bij,axiom,
% 0.26/0.61 ! [F: nat > nat,Xs: list_list_a,Ys: list_list_a] :
% 0.26/0.61 ( ( bij_betw_nat_nat @ F @ ( set_ord_lessThan_nat @ ( size_s1427607542list_a @ Xs ) ) @ ( set_ord_lessThan_nat @ ( size_s1427607542list_a @ Ys ) ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 0.26/0.61 => ( ( nth_list_a @ Xs @ I3 )
% 0.26/0.61 = ( nth_list_a @ Ys @ ( F @ I3 ) ) ) )
% 0.26/0.61 => ( ( mset_list_a @ Xs )
% 0.26/0.61 = ( mset_list_a @ Ys ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % mset_bij
% 0.26/0.61 thf(fact_44_mset__bij,axiom,
% 0.26/0.61 ! [F: nat > nat,Xs: list_set_list_a,Ys: list_set_list_a] :
% 0.26/0.61 ( ( bij_betw_nat_nat @ F @ ( set_ord_lessThan_nat @ ( size_s1635937238list_a @ Xs ) ) @ ( set_ord_lessThan_nat @ ( size_s1635937238list_a @ Ys ) ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s1635937238list_a @ Xs ) )
% 0.26/0.61 => ( ( nth_set_list_a @ Xs @ I3 )
% 0.26/0.61 = ( nth_set_list_a @ Ys @ ( F @ I3 ) ) ) )
% 0.26/0.61 => ( ( mset_set_list_a @ Xs )
% 0.26/0.61 = ( mset_set_list_a @ Ys ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % mset_bij
% 0.26/0.61 thf(fact_45_mset__bij,axiom,
% 0.26/0.61 ! [F: nat > nat,Xs: list_set_set_a,Ys: list_set_set_a] :
% 0.26/0.61 ( ( bij_betw_nat_nat @ F @ ( set_ord_lessThan_nat @ ( size_s739728560_set_a @ Xs ) ) @ ( set_ord_lessThan_nat @ ( size_s739728560_set_a @ Ys ) ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s739728560_set_a @ Xs ) )
% 0.26/0.61 => ( ( nth_set_set_a @ Xs @ I3 )
% 0.26/0.61 = ( nth_set_set_a @ Ys @ ( F @ I3 ) ) ) )
% 0.26/0.61 => ( ( mset_set_set_a @ Xs )
% 0.26/0.61 = ( mset_set_set_a @ Ys ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % mset_bij
% 0.26/0.61 thf(fact_46_mset__bij,axiom,
% 0.26/0.61 ! [F: nat > nat,Xs: list_nat,Ys: list_nat] :
% 0.26/0.61 ( ( bij_betw_nat_nat @ F @ ( set_ord_lessThan_nat @ ( size_size_list_nat @ Xs ) ) @ ( set_ord_lessThan_nat @ ( size_size_list_nat @ Ys ) ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.26/0.61 => ( ( nth_nat @ Xs @ I3 )
% 0.26/0.61 = ( nth_nat @ Ys @ ( F @ I3 ) ) ) )
% 0.26/0.61 => ( ( mset_nat @ Xs )
% 0.26/0.61 = ( mset_nat @ Ys ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % mset_bij
% 0.26/0.61 thf(fact_47_mset__bij,axiom,
% 0.26/0.61 ! [F: nat > nat,Xs: list_a,Ys: list_a] :
% 0.26/0.61 ( ( bij_betw_nat_nat @ F @ ( set_ord_lessThan_nat @ ( size_size_list_a @ Xs ) ) @ ( set_ord_lessThan_nat @ ( size_size_list_a @ Ys ) ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 0.26/0.61 => ( ( nth_a @ Xs @ I3 )
% 0.26/0.61 = ( nth_a @ Ys @ ( F @ I3 ) ) ) )
% 0.26/0.61 => ( ( mset_a @ Xs )
% 0.26/0.61 = ( mset_a @ Ys ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % mset_bij
% 0.26/0.61 thf(fact_48_mset__bij,axiom,
% 0.26/0.61 ! [F: nat > nat,Xs: list_set_a,Ys: list_set_a] :
% 0.26/0.61 ( ( bij_betw_nat_nat @ F @ ( set_ord_lessThan_nat @ ( size_size_list_set_a @ Xs ) ) @ ( set_ord_lessThan_nat @ ( size_size_list_set_a @ Ys ) ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_size_list_set_a @ Xs ) )
% 0.26/0.61 => ( ( nth_set_a @ Xs @ I3 )
% 0.26/0.61 = ( nth_set_a @ Ys @ ( F @ I3 ) ) ) )
% 0.26/0.61 => ( ( mset_set_a @ Xs )
% 0.26/0.61 = ( mset_set_a @ Ys ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % mset_bij
% 0.26/0.61 thf(fact_49_listset__permE,axiom,
% 0.26/0.61 ! [Ys: list_set_list_a,Xs: list_set_set_list_a,F: nat > nat,Xs3: list_set_set_list_a] :
% 0.26/0.61 ( ( member101195155list_a @ Ys @ ( listset_set_list_a @ Xs ) )
% 0.26/0.61 => ( ( bij_betw_nat_nat @ F @ ( set_ord_lessThan_nat @ ( size_s469631926list_a @ Xs ) ) @ ( set_ord_lessThan_nat @ ( size_s469631926list_a @ Xs3 ) ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s469631926list_a @ Xs ) )
% 0.26/0.61 => ( ( nth_set_set_list_a @ Xs3 @ I3 )
% 0.26/0.61 = ( nth_set_set_list_a @ Xs @ ( F @ I3 ) ) ) )
% 0.26/0.61 => ~ ! [Ys2: list_set_list_a] :
% 0.26/0.61 ( ( member101195155list_a @ Ys2 @ ( listset_set_list_a @ Xs3 ) )
% 0.26/0.61 => ( ( ( size_s1635937238list_a @ Ys2 )
% 0.26/0.61 = ( size_s1635937238list_a @ Ys ) )
% 0.26/0.61 => ~ ! [I2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I2 @ ( size_s1635937238list_a @ Ys ) )
% 0.26/0.61 => ( ( nth_set_list_a @ Ys2 @ I2 )
% 0.26/0.61 = ( nth_set_list_a @ Ys @ ( F @ I2 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listset_permE
% 0.26/0.61 thf(fact_50_listset__permE,axiom,
% 0.26/0.61 ! [Ys: list_set_set_a,Xs: list_set_set_set_a,F: nat > nat,Xs3: list_set_set_set_a] :
% 0.26/0.61 ( ( member814963949_set_a @ Ys @ ( listset_set_set_a @ Xs ) )
% 0.26/0.61 => ( ( bij_betw_nat_nat @ F @ ( set_ord_lessThan_nat @ ( size_s726512144_set_a @ Xs ) ) @ ( set_ord_lessThan_nat @ ( size_s726512144_set_a @ Xs3 ) ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s726512144_set_a @ Xs ) )
% 0.26/0.61 => ( ( nth_set_set_set_a @ Xs3 @ I3 )
% 0.26/0.61 = ( nth_set_set_set_a @ Xs @ ( F @ I3 ) ) ) )
% 0.26/0.61 => ~ ! [Ys2: list_set_set_a] :
% 0.26/0.61 ( ( member814963949_set_a @ Ys2 @ ( listset_set_set_a @ Xs3 ) )
% 0.26/0.61 => ( ( ( size_s739728560_set_a @ Ys2 )
% 0.26/0.61 = ( size_s739728560_set_a @ Ys ) )
% 0.26/0.61 => ~ ! [I2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I2 @ ( size_s739728560_set_a @ Ys ) )
% 0.26/0.61 => ( ( nth_set_set_a @ Ys2 @ I2 )
% 0.26/0.61 = ( nth_set_set_a @ Ys @ ( F @ I2 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listset_permE
% 0.26/0.61 thf(fact_51_listset__permE,axiom,
% 0.26/0.61 ! [Ys: list_nat,Xs: list_set_nat,F: nat > nat,Xs3: list_set_nat] :
% 0.26/0.61 ( ( member_list_nat @ Ys @ ( listset_nat @ Xs ) )
% 0.26/0.61 => ( ( bij_betw_nat_nat @ F @ ( set_ord_lessThan_nat @ ( size_s577819178et_nat @ Xs ) ) @ ( set_ord_lessThan_nat @ ( size_s577819178et_nat @ Xs3 ) ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s577819178et_nat @ Xs ) )
% 0.26/0.61 => ( ( nth_set_nat @ Xs3 @ I3 )
% 0.26/0.61 = ( nth_set_nat @ Xs @ ( F @ I3 ) ) ) )
% 0.26/0.61 => ~ ! [Ys2: list_nat] :
% 0.26/0.61 ( ( member_list_nat @ Ys2 @ ( listset_nat @ Xs3 ) )
% 0.26/0.61 => ( ( ( size_size_list_nat @ Ys2 )
% 0.26/0.61 = ( size_size_list_nat @ Ys ) )
% 0.26/0.61 => ~ ! [I2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ys ) )
% 0.26/0.61 => ( ( nth_nat @ Ys2 @ I2 )
% 0.26/0.61 = ( nth_nat @ Ys @ ( F @ I2 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listset_permE
% 0.26/0.61 thf(fact_52_listset__permE,axiom,
% 0.26/0.61 ! [Ys: list_list_a,Xs: list_set_list_a,F: nat > nat,Xs3: list_set_list_a] :
% 0.26/0.61 ( ( member_list_list_a @ Ys @ ( listset_list_a @ Xs ) )
% 0.26/0.61 => ( ( bij_betw_nat_nat @ F @ ( set_ord_lessThan_nat @ ( size_s1635937238list_a @ Xs ) ) @ ( set_ord_lessThan_nat @ ( size_s1635937238list_a @ Xs3 ) ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s1635937238list_a @ Xs ) )
% 0.26/0.61 => ( ( nth_set_list_a @ Xs3 @ I3 )
% 0.26/0.61 = ( nth_set_list_a @ Xs @ ( F @ I3 ) ) ) )
% 0.26/0.61 => ~ ! [Ys2: list_list_a] :
% 0.26/0.61 ( ( member_list_list_a @ Ys2 @ ( listset_list_a @ Xs3 ) )
% 0.26/0.61 => ( ( ( size_s1427607542list_a @ Ys2 )
% 0.26/0.61 = ( size_s1427607542list_a @ Ys ) )
% 0.26/0.61 => ~ ! [I2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I2 @ ( size_s1427607542list_a @ Ys ) )
% 0.26/0.61 => ( ( nth_list_a @ Ys2 @ I2 )
% 0.26/0.61 = ( nth_list_a @ Ys @ ( F @ I2 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listset_permE
% 0.26/0.61 thf(fact_53_listset__permE,axiom,
% 0.26/0.61 ! [Ys: list_set_a,Xs: list_set_set_a,F: nat > nat,Xs3: list_set_set_a] :
% 0.26/0.61 ( ( member_list_set_a @ Ys @ ( listset_set_a @ Xs ) )
% 0.26/0.61 => ( ( bij_betw_nat_nat @ F @ ( set_ord_lessThan_nat @ ( size_s739728560_set_a @ Xs ) ) @ ( set_ord_lessThan_nat @ ( size_s739728560_set_a @ Xs3 ) ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s739728560_set_a @ Xs ) )
% 0.26/0.61 => ( ( nth_set_set_a @ Xs3 @ I3 )
% 0.26/0.61 = ( nth_set_set_a @ Xs @ ( F @ I3 ) ) ) )
% 0.26/0.61 => ~ ! [Ys2: list_set_a] :
% 0.26/0.61 ( ( member_list_set_a @ Ys2 @ ( listset_set_a @ Xs3 ) )
% 0.26/0.61 => ( ( ( size_size_list_set_a @ Ys2 )
% 0.26/0.61 = ( size_size_list_set_a @ Ys ) )
% 0.26/0.61 => ~ ! [I2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I2 @ ( size_size_list_set_a @ Ys ) )
% 0.26/0.61 => ( ( nth_set_a @ Ys2 @ I2 )
% 0.26/0.61 = ( nth_set_a @ Ys @ ( F @ I2 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listset_permE
% 0.26/0.61 thf(fact_54_listset__permE,axiom,
% 0.26/0.61 ! [Ys: list_a,Xs: list_set_a,F: nat > nat,Xs3: list_set_a] :
% 0.26/0.61 ( ( member_list_a @ Ys @ ( listset_a @ Xs ) )
% 0.26/0.61 => ( ( bij_betw_nat_nat @ F @ ( set_ord_lessThan_nat @ ( size_size_list_set_a @ Xs ) ) @ ( set_ord_lessThan_nat @ ( size_size_list_set_a @ Xs3 ) ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_size_list_set_a @ Xs ) )
% 0.26/0.61 => ( ( nth_set_a @ Xs3 @ I3 )
% 0.26/0.61 = ( nth_set_a @ Xs @ ( F @ I3 ) ) ) )
% 0.26/0.61 => ~ ! [Ys2: list_a] :
% 0.26/0.61 ( ( member_list_a @ Ys2 @ ( listset_a @ Xs3 ) )
% 0.26/0.61 => ( ( ( size_size_list_a @ Ys2 )
% 0.26/0.61 = ( size_size_list_a @ Ys ) )
% 0.26/0.61 => ~ ! [I2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ Ys ) )
% 0.26/0.61 => ( ( nth_a @ Ys2 @ I2 )
% 0.26/0.61 = ( nth_a @ Ys @ ( F @ I2 ) ) ) ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listset_permE
% 0.26/0.61 thf(fact_55_g__bij,axiom,
% 0.26/0.61 bij_betw_nat_nat @ g @ ( set_ord_lessThan_nat @ ( size_size_list_set_a @ ss1 ) ) @ ( set_ord_lessThan_nat @ ( size_size_list_set_a @ ss2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % g_bij
% 0.26/0.61 thf(fact_56_length__rev,axiom,
% 0.26/0.61 ! [Xs: list_list_a] :
% 0.26/0.61 ( ( size_s1427607542list_a @ ( rev_list_a @ Xs ) )
% 0.26/0.61 = ( size_s1427607542list_a @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % length_rev
% 0.26/0.61 thf(fact_57_length__rev,axiom,
% 0.26/0.61 ! [Xs: list_set_list_a] :
% 0.26/0.61 ( ( size_s1635937238list_a @ ( rev_set_list_a @ Xs ) )
% 0.26/0.61 = ( size_s1635937238list_a @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % length_rev
% 0.26/0.61 thf(fact_58_length__rev,axiom,
% 0.26/0.61 ! [Xs: list_set_set_a] :
% 0.26/0.61 ( ( size_s739728560_set_a @ ( rev_set_set_a @ Xs ) )
% 0.26/0.61 = ( size_s739728560_set_a @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % length_rev
% 0.26/0.61 thf(fact_59_length__rev,axiom,
% 0.26/0.61 ! [Xs: list_nat] :
% 0.26/0.61 ( ( size_size_list_nat @ ( rev_nat @ Xs ) )
% 0.26/0.61 = ( size_size_list_nat @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % length_rev
% 0.26/0.61 thf(fact_60_length__rev,axiom,
% 0.26/0.61 ! [Xs: list_a] :
% 0.26/0.61 ( ( size_size_list_a @ ( rev_a @ Xs ) )
% 0.26/0.61 = ( size_size_list_a @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % length_rev
% 0.26/0.61 thf(fact_61_length__rev,axiom,
% 0.26/0.61 ! [Xs: list_set_a] :
% 0.26/0.61 ( ( size_size_list_set_a @ ( rev_set_a @ Xs ) )
% 0.26/0.61 = ( size_size_list_set_a @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % length_rev
% 0.26/0.61 thf(fact_62_lessThan__iff,axiom,
% 0.26/0.61 ! [I: set_nat,K: set_nat] :
% 0.26/0.61 ( ( member_set_nat @ I @ ( set_or1597314339et_nat @ K ) )
% 0.26/0.61 = ( ord_less_set_nat @ I @ K ) ) ).
% 0.26/0.61
% 0.26/0.61 % lessThan_iff
% 0.26/0.61 thf(fact_63_lessThan__iff,axiom,
% 0.26/0.61 ! [I: set_list_a,K: set_list_a] :
% 0.26/0.61 ( ( member_set_list_a @ I @ ( set_or1578766727list_a @ K ) )
% 0.26/0.61 = ( ord_less_set_list_a @ I @ K ) ) ).
% 0.26/0.61
% 0.26/0.61 % lessThan_iff
% 0.26/0.61 thf(fact_64_lessThan__iff,axiom,
% 0.26/0.61 ! [I: set_a,K: set_a] :
% 0.26/0.61 ( ( member_set_a @ I @ ( set_or1164043265_set_a @ K ) )
% 0.26/0.61 = ( ord_less_set_a @ I @ K ) ) ).
% 0.26/0.61
% 0.26/0.61 % lessThan_iff
% 0.26/0.61 thf(fact_65_lessThan__iff,axiom,
% 0.26/0.61 ! [I: nat,K: nat] :
% 0.26/0.61 ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 0.26/0.61 = ( ord_less_nat @ I @ K ) ) ).
% 0.26/0.61
% 0.26/0.61 % lessThan_iff
% 0.26/0.61 thf(fact_66_listsetI,axiom,
% 0.26/0.61 ! [Ys: list_multiset_a,Xs: list_set_multiset_a] :
% 0.26/0.61 ( ( ( size_s1657263798iset_a @ Ys )
% 0.26/0.61 = ( size_s802269334iset_a @ Xs ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s802269334iset_a @ Xs ) )
% 0.26/0.61 => ( member_multiset_a @ ( nth_multiset_a @ Ys @ I3 ) @ ( nth_set_multiset_a @ Xs @ I3 ) ) )
% 0.26/0.61 => ( member518144627iset_a @ Ys @ ( listset_multiset_a @ Xs ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetI
% 0.26/0.61 thf(fact_67_listsetI,axiom,
% 0.26/0.61 ! [Ys: list_list_list_a,Xs: list_set_list_list_a] :
% 0.26/0.61 ( ( ( size_s575106428list_a @ Ys )
% 0.26/0.61 = ( size_s240404444list_a @ Xs ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s240404444list_a @ Xs ) )
% 0.26/0.61 => ( member_list_list_a @ ( nth_list_list_a @ Ys @ I3 ) @ ( nth_set_list_list_a @ Xs @ I3 ) ) )
% 0.26/0.61 => ( member1511395513list_a @ Ys @ ( listset_list_list_a @ Xs ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetI
% 0.26/0.61 thf(fact_68_listsetI,axiom,
% 0.26/0.61 ! [Ys: list_list_set_a,Xs: list_set_list_set_a] :
% 0.26/0.61 ( ( ( size_s341332310_set_a @ Ys )
% 0.26/0.61 = ( size_s926492982_set_a @ Xs ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s926492982_set_a @ Xs ) )
% 0.26/0.61 => ( member_list_set_a @ ( nth_list_set_a @ Ys @ I3 ) @ ( nth_set_list_set_a @ Xs @ I3 ) ) )
% 0.26/0.61 => ( member954073875_set_a @ Ys @ ( listset_list_set_a @ Xs ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetI
% 0.26/0.61 thf(fact_69_listsetI,axiom,
% 0.26/0.61 ! [Ys: list_set_list_a,Xs: list_set_set_list_a] :
% 0.26/0.61 ( ( ( size_s1635937238list_a @ Ys )
% 0.26/0.61 = ( size_s469631926list_a @ Xs ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s469631926list_a @ Xs ) )
% 0.26/0.61 => ( member_set_list_a @ ( nth_set_list_a @ Ys @ I3 ) @ ( nth_set_set_list_a @ Xs @ I3 ) ) )
% 0.26/0.61 => ( member101195155list_a @ Ys @ ( listset_set_list_a @ Xs ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetI
% 0.26/0.61 thf(fact_70_listsetI,axiom,
% 0.26/0.61 ! [Ys: list_set_set_a,Xs: list_set_set_set_a] :
% 0.26/0.61 ( ( ( size_s739728560_set_a @ Ys )
% 0.26/0.61 = ( size_s726512144_set_a @ Xs ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s726512144_set_a @ Xs ) )
% 0.26/0.61 => ( member_set_set_a @ ( nth_set_set_a @ Ys @ I3 ) @ ( nth_set_set_set_a @ Xs @ I3 ) ) )
% 0.26/0.61 => ( member814963949_set_a @ Ys @ ( listset_set_set_a @ Xs ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetI
% 0.26/0.61 thf(fact_71_listsetI,axiom,
% 0.26/0.61 ! [Ys: list_nat,Xs: list_set_nat] :
% 0.26/0.61 ( ( ( size_size_list_nat @ Ys )
% 0.26/0.61 = ( size_s577819178et_nat @ Xs ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s577819178et_nat @ Xs ) )
% 0.26/0.61 => ( member_nat @ ( nth_nat @ Ys @ I3 ) @ ( nth_set_nat @ Xs @ I3 ) ) )
% 0.26/0.61 => ( member_list_nat @ Ys @ ( listset_nat @ Xs ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetI
% 0.26/0.61 thf(fact_72_listsetI,axiom,
% 0.26/0.61 ! [Ys: list_list_a,Xs: list_set_list_a] :
% 0.26/0.61 ( ( ( size_s1427607542list_a @ Ys )
% 0.26/0.61 = ( size_s1635937238list_a @ Xs ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s1635937238list_a @ Xs ) )
% 0.26/0.61 => ( member_list_a @ ( nth_list_a @ Ys @ I3 ) @ ( nth_set_list_a @ Xs @ I3 ) ) )
% 0.26/0.61 => ( member_list_list_a @ Ys @ ( listset_list_a @ Xs ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetI
% 0.26/0.61 thf(fact_73_listsetI,axiom,
% 0.26/0.61 ! [Ys: list_a,Xs: list_set_a] :
% 0.26/0.61 ( ( ( size_size_list_a @ Ys )
% 0.26/0.61 = ( size_size_list_set_a @ Xs ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_size_list_set_a @ Xs ) )
% 0.26/0.61 => ( member_a @ ( nth_a @ Ys @ I3 ) @ ( nth_set_a @ Xs @ I3 ) ) )
% 0.26/0.61 => ( member_list_a @ Ys @ ( listset_a @ Xs ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetI
% 0.26/0.61 thf(fact_74_listsetI,axiom,
% 0.26/0.61 ! [Ys: list_set_a,Xs: list_set_set_a] :
% 0.26/0.61 ( ( ( size_size_list_set_a @ Ys )
% 0.26/0.61 = ( size_s739728560_set_a @ Xs ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s739728560_set_a @ Xs ) )
% 0.26/0.61 => ( member_set_a @ ( nth_set_a @ Ys @ I3 ) @ ( nth_set_set_a @ Xs @ I3 ) ) )
% 0.26/0.61 => ( member_list_set_a @ Ys @ ( listset_set_a @ Xs ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetI
% 0.26/0.61 thf(fact_75_len__qs,axiom,
% 0.26/0.61 ( ( size_size_list_a @ qs )
% 0.26/0.61 = ( size_size_list_set_a @ ss1 ) ) ).
% 0.26/0.61
% 0.26/0.61 % len_qs
% 0.26/0.61 thf(fact_76_f__bij,axiom,
% 0.26/0.61 bij_betw_nat_nat @ f @ ( set_ord_lessThan_nat @ ( size_size_list_set_a @ ss2 ) ) @ ( set_ord_lessThan_nat @ ( size_size_list_set_a @ ss1 ) ) ).
% 0.26/0.61
% 0.26/0.61 % f_bij
% 0.26/0.61 thf(fact_77_nth__equalityI,axiom,
% 0.26/0.61 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.26/0.61 ( ( ( size_s1427607542list_a @ Xs )
% 0.26/0.61 = ( size_s1427607542list_a @ Ys ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s1427607542list_a @ Xs ) )
% 0.26/0.61 => ( ( nth_list_a @ Xs @ I3 )
% 0.26/0.61 = ( nth_list_a @ Ys @ I3 ) ) )
% 0.26/0.61 => ( Xs = Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % nth_equalityI
% 0.26/0.61 thf(fact_78_nth__equalityI,axiom,
% 0.26/0.61 ! [Xs: list_set_list_a,Ys: list_set_list_a] :
% 0.26/0.61 ( ( ( size_s1635937238list_a @ Xs )
% 0.26/0.61 = ( size_s1635937238list_a @ Ys ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s1635937238list_a @ Xs ) )
% 0.26/0.61 => ( ( nth_set_list_a @ Xs @ I3 )
% 0.26/0.61 = ( nth_set_list_a @ Ys @ I3 ) ) )
% 0.26/0.61 => ( Xs = Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % nth_equalityI
% 0.26/0.61 thf(fact_79_nth__equalityI,axiom,
% 0.26/0.61 ! [Xs: list_set_set_a,Ys: list_set_set_a] :
% 0.26/0.61 ( ( ( size_s739728560_set_a @ Xs )
% 0.26/0.61 = ( size_s739728560_set_a @ Ys ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_s739728560_set_a @ Xs ) )
% 0.26/0.61 => ( ( nth_set_set_a @ Xs @ I3 )
% 0.26/0.61 = ( nth_set_set_a @ Ys @ I3 ) ) )
% 0.26/0.61 => ( Xs = Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % nth_equalityI
% 0.26/0.61 thf(fact_80_nth__equalityI,axiom,
% 0.26/0.61 ! [Xs: list_nat,Ys: list_nat] :
% 0.26/0.61 ( ( ( size_size_list_nat @ Xs )
% 0.26/0.61 = ( size_size_list_nat @ Ys ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 0.26/0.61 => ( ( nth_nat @ Xs @ I3 )
% 0.26/0.61 = ( nth_nat @ Ys @ I3 ) ) )
% 0.26/0.61 => ( Xs = Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % nth_equalityI
% 0.26/0.61 thf(fact_81_nth__equalityI,axiom,
% 0.26/0.61 ! [Xs: list_a,Ys: list_a] :
% 0.26/0.61 ( ( ( size_size_list_a @ Xs )
% 0.26/0.61 = ( size_size_list_a @ Ys ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_size_list_a @ Xs ) )
% 0.26/0.61 => ( ( nth_a @ Xs @ I3 )
% 0.26/0.61 = ( nth_a @ Ys @ I3 ) ) )
% 0.26/0.61 => ( Xs = Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % nth_equalityI
% 0.26/0.61 thf(fact_82_nth__equalityI,axiom,
% 0.26/0.61 ! [Xs: list_set_a,Ys: list_set_a] :
% 0.26/0.61 ( ( ( size_size_list_set_a @ Xs )
% 0.26/0.61 = ( size_size_list_set_a @ Ys ) )
% 0.26/0.61 => ( ! [I3: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I3 @ ( size_size_list_set_a @ Xs ) )
% 0.26/0.61 => ( ( nth_set_a @ Xs @ I3 )
% 0.26/0.61 = ( nth_set_a @ Ys @ I3 ) ) )
% 0.26/0.61 => ( Xs = Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % nth_equalityI
% 0.26/0.61 thf(fact_83_Skolem__list__nth,axiom,
% 0.26/0.61 ! [K: nat,P: nat > list_a > $o] :
% 0.26/0.61 ( ( ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ K )
% 0.26/0.61 => ? [X3: list_a] : ( P @ I4 @ X3 ) ) )
% 0.26/0.61 = ( ? [Xs4: list_list_a] :
% 0.26/0.61 ( ( ( size_s1427607542list_a @ Xs4 )
% 0.26/0.61 = K )
% 0.26/0.61 & ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ K )
% 0.26/0.61 => ( P @ I4 @ ( nth_list_a @ Xs4 @ I4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Skolem_list_nth
% 0.26/0.61 thf(fact_84_Skolem__list__nth,axiom,
% 0.26/0.61 ! [K: nat,P: nat > set_list_a > $o] :
% 0.26/0.61 ( ( ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ K )
% 0.26/0.61 => ? [X3: set_list_a] : ( P @ I4 @ X3 ) ) )
% 0.26/0.61 = ( ? [Xs4: list_set_list_a] :
% 0.26/0.61 ( ( ( size_s1635937238list_a @ Xs4 )
% 0.26/0.61 = K )
% 0.26/0.61 & ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ K )
% 0.26/0.61 => ( P @ I4 @ ( nth_set_list_a @ Xs4 @ I4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Skolem_list_nth
% 0.26/0.61 thf(fact_85_Skolem__list__nth,axiom,
% 0.26/0.61 ! [K: nat,P: nat > set_set_a > $o] :
% 0.26/0.61 ( ( ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ K )
% 0.26/0.61 => ? [X3: set_set_a] : ( P @ I4 @ X3 ) ) )
% 0.26/0.61 = ( ? [Xs4: list_set_set_a] :
% 0.26/0.61 ( ( ( size_s739728560_set_a @ Xs4 )
% 0.26/0.61 = K )
% 0.26/0.61 & ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ K )
% 0.26/0.61 => ( P @ I4 @ ( nth_set_set_a @ Xs4 @ I4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Skolem_list_nth
% 0.26/0.61 thf(fact_86_Skolem__list__nth,axiom,
% 0.26/0.61 ! [K: nat,P: nat > nat > $o] :
% 0.26/0.61 ( ( ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ K )
% 0.26/0.61 => ? [X3: nat] : ( P @ I4 @ X3 ) ) )
% 0.26/0.61 = ( ? [Xs4: list_nat] :
% 0.26/0.61 ( ( ( size_size_list_nat @ Xs4 )
% 0.26/0.61 = K )
% 0.26/0.61 & ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ K )
% 0.26/0.61 => ( P @ I4 @ ( nth_nat @ Xs4 @ I4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Skolem_list_nth
% 0.26/0.61 thf(fact_87_Skolem__list__nth,axiom,
% 0.26/0.61 ! [K: nat,P: nat > a > $o] :
% 0.26/0.61 ( ( ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ K )
% 0.26/0.61 => ? [X3: a] : ( P @ I4 @ X3 ) ) )
% 0.26/0.61 = ( ? [Xs4: list_a] :
% 0.26/0.61 ( ( ( size_size_list_a @ Xs4 )
% 0.26/0.61 = K )
% 0.26/0.61 & ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ K )
% 0.26/0.61 => ( P @ I4 @ ( nth_a @ Xs4 @ I4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Skolem_list_nth
% 0.26/0.61 thf(fact_88_Skolem__list__nth,axiom,
% 0.26/0.61 ! [K: nat,P: nat > set_a > $o] :
% 0.26/0.61 ( ( ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ K )
% 0.26/0.61 => ? [X3: set_a] : ( P @ I4 @ X3 ) ) )
% 0.26/0.61 = ( ? [Xs4: list_set_a] :
% 0.26/0.61 ( ( ( size_size_list_set_a @ Xs4 )
% 0.26/0.61 = K )
% 0.26/0.61 & ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ K )
% 0.26/0.61 => ( P @ I4 @ ( nth_set_a @ Xs4 @ I4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Skolem_list_nth
% 0.26/0.61 thf(fact_89_list__eq__iff__nth__eq,axiom,
% 0.26/0.61 ( ( ^ [Y2: list_list_a,Z: list_list_a] : ( Y2 = Z ) )
% 0.26/0.61 = ( ^ [Xs4: list_list_a,Ys3: list_list_a] :
% 0.26/0.61 ( ( ( size_s1427607542list_a @ Xs4 )
% 0.26/0.61 = ( size_s1427607542list_a @ Ys3 ) )
% 0.26/0.61 & ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ ( size_s1427607542list_a @ Xs4 ) )
% 0.26/0.61 => ( ( nth_list_a @ Xs4 @ I4 )
% 0.26/0.61 = ( nth_list_a @ Ys3 @ I4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % list_eq_iff_nth_eq
% 0.26/0.61 thf(fact_90_list__eq__iff__nth__eq,axiom,
% 0.26/0.61 ( ( ^ [Y2: list_set_list_a,Z: list_set_list_a] : ( Y2 = Z ) )
% 0.26/0.61 = ( ^ [Xs4: list_set_list_a,Ys3: list_set_list_a] :
% 0.26/0.61 ( ( ( size_s1635937238list_a @ Xs4 )
% 0.26/0.61 = ( size_s1635937238list_a @ Ys3 ) )
% 0.26/0.61 & ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ ( size_s1635937238list_a @ Xs4 ) )
% 0.26/0.61 => ( ( nth_set_list_a @ Xs4 @ I4 )
% 0.26/0.61 = ( nth_set_list_a @ Ys3 @ I4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % list_eq_iff_nth_eq
% 0.26/0.61 thf(fact_91_list__eq__iff__nth__eq,axiom,
% 0.26/0.61 ( ( ^ [Y2: list_set_set_a,Z: list_set_set_a] : ( Y2 = Z ) )
% 0.26/0.61 = ( ^ [Xs4: list_set_set_a,Ys3: list_set_set_a] :
% 0.26/0.61 ( ( ( size_s739728560_set_a @ Xs4 )
% 0.26/0.61 = ( size_s739728560_set_a @ Ys3 ) )
% 0.26/0.61 & ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ ( size_s739728560_set_a @ Xs4 ) )
% 0.26/0.61 => ( ( nth_set_set_a @ Xs4 @ I4 )
% 0.26/0.61 = ( nth_set_set_a @ Ys3 @ I4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % list_eq_iff_nth_eq
% 0.26/0.61 thf(fact_92_list__eq__iff__nth__eq,axiom,
% 0.26/0.61 ( ( ^ [Y2: list_nat,Z: list_nat] : ( Y2 = Z ) )
% 0.26/0.61 = ( ^ [Xs4: list_nat,Ys3: list_nat] :
% 0.26/0.61 ( ( ( size_size_list_nat @ Xs4 )
% 0.26/0.61 = ( size_size_list_nat @ Ys3 ) )
% 0.26/0.61 & ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs4 ) )
% 0.26/0.61 => ( ( nth_nat @ Xs4 @ I4 )
% 0.26/0.61 = ( nth_nat @ Ys3 @ I4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % list_eq_iff_nth_eq
% 0.26/0.61 thf(fact_93_list__eq__iff__nth__eq,axiom,
% 0.26/0.61 ( ( ^ [Y2: list_a,Z: list_a] : ( Y2 = Z ) )
% 0.26/0.61 = ( ^ [Xs4: list_a,Ys3: list_a] :
% 0.26/0.61 ( ( ( size_size_list_a @ Xs4 )
% 0.26/0.61 = ( size_size_list_a @ Ys3 ) )
% 0.26/0.61 & ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ ( size_size_list_a @ Xs4 ) )
% 0.26/0.61 => ( ( nth_a @ Xs4 @ I4 )
% 0.26/0.61 = ( nth_a @ Ys3 @ I4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % list_eq_iff_nth_eq
% 0.26/0.61 thf(fact_94_list__eq__iff__nth__eq,axiom,
% 0.26/0.61 ( ( ^ [Y2: list_set_a,Z: list_set_a] : ( Y2 = Z ) )
% 0.26/0.61 = ( ^ [Xs4: list_set_a,Ys3: list_set_a] :
% 0.26/0.61 ( ( ( size_size_list_set_a @ Xs4 )
% 0.26/0.61 = ( size_size_list_set_a @ Ys3 ) )
% 0.26/0.61 & ! [I4: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I4 @ ( size_size_list_set_a @ Xs4 ) )
% 0.26/0.61 => ( ( nth_set_a @ Xs4 @ I4 )
% 0.26/0.61 = ( nth_set_a @ Ys3 @ I4 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % list_eq_iff_nth_eq
% 0.26/0.61 thf(fact_95_lessThan__eq__iff,axiom,
% 0.26/0.61 ! [X4: nat,Y3: nat] :
% 0.26/0.61 ( ( ( set_ord_lessThan_nat @ X4 )
% 0.26/0.61 = ( set_ord_lessThan_nat @ Y3 ) )
% 0.26/0.61 = ( X4 = Y3 ) ) ).
% 0.26/0.61
% 0.26/0.61 % lessThan_eq_iff
% 0.26/0.61 thf(fact_96_rev__is__rev__conv,axiom,
% 0.26/0.61 ! [Xs: list_a,Ys: list_a] :
% 0.26/0.61 ( ( ( rev_a @ Xs )
% 0.26/0.61 = ( rev_a @ Ys ) )
% 0.26/0.61 = ( Xs = Ys ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_is_rev_conv
% 0.26/0.61 thf(fact_97_rev__is__rev__conv,axiom,
% 0.26/0.61 ! [Xs: list_set_a,Ys: list_set_a] :
% 0.26/0.61 ( ( ( rev_set_a @ Xs )
% 0.26/0.61 = ( rev_set_a @ Ys ) )
% 0.26/0.61 = ( Xs = Ys ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_is_rev_conv
% 0.26/0.61 thf(fact_98_rev__rev__ident,axiom,
% 0.26/0.61 ! [Xs: list_a] :
% 0.26/0.61 ( ( rev_a @ ( rev_a @ Xs ) )
% 0.26/0.61 = Xs ) ).
% 0.26/0.61
% 0.26/0.61 % rev_rev_ident
% 0.26/0.61 thf(fact_99_rev__rev__ident,axiom,
% 0.26/0.61 ! [Xs: list_set_a] :
% 0.26/0.61 ( ( rev_set_a @ ( rev_set_a @ Xs ) )
% 0.26/0.61 = Xs ) ).
% 0.26/0.61
% 0.26/0.61 % rev_rev_ident
% 0.26/0.61 thf(fact_100_len__ss1,axiom,
% 0.26/0.61 ( ( size_size_list_set_a @ ss1 )
% 0.26/0.61 = ( size_size_list_set_a @ ss2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % len_ss1
% 0.26/0.61 thf(fact_101_g,axiom,
% 0.26/0.61 ! [I: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I @ ( size_size_list_set_a @ ss1 ) )
% 0.26/0.61 => ( ( nth_set_a @ ss2 @ I )
% 0.26/0.61 = ( nth_set_a @ ss1 @ ( g @ I ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % g
% 0.26/0.61 thf(fact_102_f,axiom,
% 0.26/0.61 ! [I: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I @ ( size_size_list_set_a @ ss2 ) )
% 0.26/0.61 => ( ( nth_set_a @ ss1 @ I )
% 0.26/0.61 = ( nth_set_a @ ss2 @ ( f @ I ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % f
% 0.26/0.61 thf(fact_103__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062f_O_A_092_060lbrakk_062bij__betw_Af_A_123_O_O_060length_Ass2_125_A_123_O_O_060length_Ass1_125_059_A_092_060And_062i_O_Ai_A_060_Alength_Ass2_A_092_060Longrightarrow_062_Ass1_A_B_Ai_A_061_Ass2_A_B_Af_Ai_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.26/0.61 ~ ! [F2: nat > nat] :
% 0.26/0.61 ( ( bij_betw_nat_nat @ F2 @ ( set_ord_lessThan_nat @ ( size_size_list_set_a @ ss2 ) ) @ ( set_ord_lessThan_nat @ ( size_size_list_set_a @ ss1 ) ) )
% 0.26/0.61 => ~ ! [I2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I2 @ ( size_size_list_set_a @ ss2 ) )
% 0.26/0.61 => ( ( nth_set_a @ ss1 @ I2 )
% 0.26/0.61 = ( nth_set_a @ ss2 @ ( F2 @ I2 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % \<open>\<And>thesis. (\<And>f. \<lbrakk>bij_betw f {..<length ss2} {..<length ss1}; \<And>i. i < length ss2 \<Longrightarrow> ss1 ! i = ss2 ! f i\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.26/0.61 thf(fact_104__092_060open_062_092_060exists_062f_O_Abij__betw_Af_A_123_O_O_060length_Ass1_125_A_123_O_O_060length_Ass2_125_A_092_060and_062_A_I_092_060forall_062i_060length_Ass1_O_Ass1_A_B_Ai_A_061_Ass2_A_B_Af_Ai_J_092_060close_062,axiom,
% 0.26/0.61 ? [F2: nat > nat] :
% 0.26/0.61 ( ( bij_betw_nat_nat @ F2 @ ( set_ord_lessThan_nat @ ( size_size_list_set_a @ ss1 ) ) @ ( set_ord_lessThan_nat @ ( size_size_list_set_a @ ss2 ) ) )
% 0.26/0.61 & ! [I2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I2 @ ( size_size_list_set_a @ ss1 ) )
% 0.26/0.61 => ( ( nth_set_a @ ss1 @ I2 )
% 0.26/0.61 = ( nth_set_a @ ss2 @ ( F2 @ I2 ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % \<open>\<exists>f. bij_betw f {..<length ss1} {..<length ss2} \<and> (\<forall>i<length ss1. ss1 ! i = ss2 ! f i)\<close>
% 0.26/0.61 thf(fact_105_f__g,axiom,
% 0.26/0.61 ! [I: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I @ ( size_size_list_set_a @ ss1 ) )
% 0.26/0.61 => ( ( f @ ( g @ I ) )
% 0.26/0.61 = I ) ) ).
% 0.26/0.61
% 0.26/0.61 % f_g
% 0.26/0.61 thf(fact_106_g__f,axiom,
% 0.26/0.61 ! [I: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I @ ( size_size_list_set_a @ ss2 ) )
% 0.26/0.61 => ( ( g @ ( f @ I ) )
% 0.26/0.61 = I ) ) ).
% 0.26/0.61
% 0.26/0.61 % g_f
% 0.26/0.61 thf(fact_107_listsetD_I2_J,axiom,
% 0.26/0.61 ! [Ys: list_set_set_a,Xs: list_set_set_set_a,I: nat] :
% 0.26/0.61 ( ( member814963949_set_a @ Ys @ ( listset_set_set_a @ Xs ) )
% 0.26/0.61 => ( ( ord_less_nat @ I @ ( size_s726512144_set_a @ Xs ) )
% 0.26/0.61 => ( member_set_set_a @ ( nth_set_set_a @ Ys @ I ) @ ( nth_set_set_set_a @ Xs @ I ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetD(2)
% 0.26/0.61 thf(fact_108_listsetD_I2_J,axiom,
% 0.26/0.61 ! [Ys: list_set_list_a,Xs: list_set_set_list_a,I: nat] :
% 0.26/0.61 ( ( member101195155list_a @ Ys @ ( listset_set_list_a @ Xs ) )
% 0.26/0.61 => ( ( ord_less_nat @ I @ ( size_s469631926list_a @ Xs ) )
% 0.26/0.61 => ( member_set_list_a @ ( nth_set_list_a @ Ys @ I ) @ ( nth_set_set_list_a @ Xs @ I ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetD(2)
% 0.26/0.61 thf(fact_109_listsetD_I2_J,axiom,
% 0.26/0.61 ! [Ys: list_multiset_a,Xs: list_set_multiset_a,I: nat] :
% 0.26/0.61 ( ( member518144627iset_a @ Ys @ ( listset_multiset_a @ Xs ) )
% 0.26/0.61 => ( ( ord_less_nat @ I @ ( size_s802269334iset_a @ Xs ) )
% 0.26/0.61 => ( member_multiset_a @ ( nth_multiset_a @ Ys @ I ) @ ( nth_set_multiset_a @ Xs @ I ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetD(2)
% 0.26/0.61 thf(fact_110_listsetD_I2_J,axiom,
% 0.26/0.61 ! [Ys: list_list_list_a,Xs: list_set_list_list_a,I: nat] :
% 0.26/0.61 ( ( member1511395513list_a @ Ys @ ( listset_list_list_a @ Xs ) )
% 0.26/0.61 => ( ( ord_less_nat @ I @ ( size_s240404444list_a @ Xs ) )
% 0.26/0.61 => ( member_list_list_a @ ( nth_list_list_a @ Ys @ I ) @ ( nth_set_list_list_a @ Xs @ I ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetD(2)
% 0.26/0.61 thf(fact_111_listsetD_I2_J,axiom,
% 0.26/0.61 ! [Ys: list_list_set_a,Xs: list_set_list_set_a,I: nat] :
% 0.26/0.61 ( ( member954073875_set_a @ Ys @ ( listset_list_set_a @ Xs ) )
% 0.26/0.61 => ( ( ord_less_nat @ I @ ( size_s926492982_set_a @ Xs ) )
% 0.26/0.61 => ( member_list_set_a @ ( nth_list_set_a @ Ys @ I ) @ ( nth_set_list_set_a @ Xs @ I ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetD(2)
% 0.26/0.61 thf(fact_112_listsetD_I2_J,axiom,
% 0.26/0.61 ! [Ys: list_nat,Xs: list_set_nat,I: nat] :
% 0.26/0.61 ( ( member_list_nat @ Ys @ ( listset_nat @ Xs ) )
% 0.26/0.61 => ( ( ord_less_nat @ I @ ( size_s577819178et_nat @ Xs ) )
% 0.26/0.61 => ( member_nat @ ( nth_nat @ Ys @ I ) @ ( nth_set_nat @ Xs @ I ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetD(2)
% 0.26/0.61 thf(fact_113_listsetD_I2_J,axiom,
% 0.26/0.61 ! [Ys: list_set_a,Xs: list_set_set_a,I: nat] :
% 0.26/0.61 ( ( member_list_set_a @ Ys @ ( listset_set_a @ Xs ) )
% 0.26/0.61 => ( ( ord_less_nat @ I @ ( size_s739728560_set_a @ Xs ) )
% 0.26/0.61 => ( member_set_a @ ( nth_set_a @ Ys @ I ) @ ( nth_set_set_a @ Xs @ I ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetD(2)
% 0.26/0.61 thf(fact_114_listsetD_I2_J,axiom,
% 0.26/0.61 ! [Ys: list_list_a,Xs: list_set_list_a,I: nat] :
% 0.26/0.61 ( ( member_list_list_a @ Ys @ ( listset_list_a @ Xs ) )
% 0.26/0.61 => ( ( ord_less_nat @ I @ ( size_s1635937238list_a @ Xs ) )
% 0.26/0.61 => ( member_list_a @ ( nth_list_a @ Ys @ I ) @ ( nth_set_list_a @ Xs @ I ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetD(2)
% 0.26/0.61 thf(fact_115_listsetD_I2_J,axiom,
% 0.26/0.61 ! [Ys: list_a,Xs: list_set_a,I: nat] :
% 0.26/0.61 ( ( member_list_a @ Ys @ ( listset_a @ Xs ) )
% 0.26/0.61 => ( ( ord_less_nat @ I @ ( size_size_list_set_a @ Xs ) )
% 0.26/0.61 => ( member_a @ ( nth_a @ Ys @ I ) @ ( nth_set_a @ Xs @ I ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetD(2)
% 0.26/0.61 thf(fact_116_neq__if__length__neq,axiom,
% 0.26/0.61 ! [Xs: list_list_a,Ys: list_list_a] :
% 0.26/0.61 ( ( ( size_s1427607542list_a @ Xs )
% 0.26/0.61 != ( size_s1427607542list_a @ Ys ) )
% 0.26/0.61 => ( Xs != Ys ) ) ).
% 0.26/0.61
% 0.26/0.61 % neq_if_length_neq
% 0.26/0.61 thf(fact_117_neq__if__length__neq,axiom,
% 0.26/0.61 ! [Xs: list_set_list_a,Ys: list_set_list_a] :
% 0.26/0.61 ( ( ( size_s1635937238list_a @ Xs )
% 0.26/0.61 != ( size_s1635937238list_a @ Ys ) )
% 0.26/0.61 => ( Xs != Ys ) ) ).
% 0.26/0.61
% 0.26/0.61 % neq_if_length_neq
% 0.26/0.61 thf(fact_118_neq__if__length__neq,axiom,
% 0.26/0.61 ! [Xs: list_set_set_a,Ys: list_set_set_a] :
% 0.26/0.61 ( ( ( size_s739728560_set_a @ Xs )
% 0.26/0.61 != ( size_s739728560_set_a @ Ys ) )
% 0.26/0.61 => ( Xs != Ys ) ) ).
% 0.26/0.61
% 0.26/0.61 % neq_if_length_neq
% 0.26/0.61 thf(fact_119_neq__if__length__neq,axiom,
% 0.26/0.61 ! [Xs: list_nat,Ys: list_nat] :
% 0.26/0.61 ( ( ( size_size_list_nat @ Xs )
% 0.26/0.61 != ( size_size_list_nat @ Ys ) )
% 0.26/0.61 => ( Xs != Ys ) ) ).
% 0.26/0.61
% 0.26/0.61 % neq_if_length_neq
% 0.26/0.61 thf(fact_120_neq__if__length__neq,axiom,
% 0.26/0.61 ! [Xs: list_a,Ys: list_a] :
% 0.26/0.61 ( ( ( size_size_list_a @ Xs )
% 0.26/0.61 != ( size_size_list_a @ Ys ) )
% 0.26/0.61 => ( Xs != Ys ) ) ).
% 0.26/0.61
% 0.26/0.61 % neq_if_length_neq
% 0.26/0.61 thf(fact_121_neq__if__length__neq,axiom,
% 0.26/0.61 ! [Xs: list_set_a,Ys: list_set_a] :
% 0.26/0.61 ( ( ( size_size_list_set_a @ Xs )
% 0.26/0.61 != ( size_size_list_set_a @ Ys ) )
% 0.26/0.61 => ( Xs != Ys ) ) ).
% 0.26/0.61
% 0.26/0.61 % neq_if_length_neq
% 0.26/0.61 thf(fact_122_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A2: multiset_a,P: multiset_a > $o] :
% 0.26/0.61 ( ( member_multiset_a @ A2 @ ( collect_multiset_a @ P ) )
% 0.26/0.61 = ( P @ A2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_123_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A2: list_list_a,P: list_list_a > $o] :
% 0.26/0.61 ( ( member_list_list_a @ A2 @ ( collect_list_list_a @ P ) )
% 0.26/0.61 = ( P @ A2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_124_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A2: list_set_a,P: list_set_a > $o] :
% 0.26/0.61 ( ( member_list_set_a @ A2 @ ( collect_list_set_a @ P ) )
% 0.26/0.61 = ( P @ A2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_125_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A2: set_a,P: set_a > $o] :
% 0.26/0.61 ( ( member_set_a @ A2 @ ( collect_set_a @ P ) )
% 0.26/0.61 = ( P @ A2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_126_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A2: nat,P: nat > $o] :
% 0.26/0.61 ( ( member_nat @ A2 @ ( collect_nat @ P ) )
% 0.26/0.61 = ( P @ A2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_127_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A2: a,P: a > $o] :
% 0.26/0.61 ( ( member_a @ A2 @ ( collect_a @ P ) )
% 0.26/0.61 = ( P @ A2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_128_mem__Collect__eq,axiom,
% 0.26/0.61 ! [A2: list_a,P: list_a > $o] :
% 0.26/0.61 ( ( member_list_a @ A2 @ ( collect_list_a @ P ) )
% 0.26/0.61 = ( P @ A2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % mem_Collect_eq
% 0.26/0.61 thf(fact_129_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A: set_multiset_a] :
% 0.26/0.61 ( ( collect_multiset_a
% 0.26/0.61 @ ^ [X5: multiset_a] : ( member_multiset_a @ X5 @ A ) )
% 0.26/0.61 = A ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_130_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A: set_list_list_a] :
% 0.26/0.61 ( ( collect_list_list_a
% 0.26/0.61 @ ^ [X5: list_list_a] : ( member_list_list_a @ X5 @ A ) )
% 0.26/0.61 = A ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_131_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A: set_list_set_a] :
% 0.26/0.61 ( ( collect_list_set_a
% 0.26/0.61 @ ^ [X5: list_set_a] : ( member_list_set_a @ X5 @ A ) )
% 0.26/0.61 = A ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_132_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A: set_set_a] :
% 0.26/0.61 ( ( collect_set_a
% 0.26/0.61 @ ^ [X5: set_a] : ( member_set_a @ X5 @ A ) )
% 0.26/0.61 = A ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_133_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A: set_nat] :
% 0.26/0.61 ( ( collect_nat
% 0.26/0.61 @ ^ [X5: nat] : ( member_nat @ X5 @ A ) )
% 0.26/0.61 = A ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_134_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A: set_a] :
% 0.26/0.61 ( ( collect_a
% 0.26/0.61 @ ^ [X5: a] : ( member_a @ X5 @ A ) )
% 0.26/0.61 = A ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_135_Collect__mem__eq,axiom,
% 0.26/0.61 ! [A: set_list_a] :
% 0.26/0.61 ( ( collect_list_a
% 0.26/0.61 @ ^ [X5: list_a] : ( member_list_a @ X5 @ A ) )
% 0.26/0.61 = A ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_mem_eq
% 0.26/0.61 thf(fact_136_Collect__cong,axiom,
% 0.26/0.61 ! [P: list_a > $o,Q: list_a > $o] :
% 0.26/0.61 ( ! [X6: list_a] :
% 0.26/0.61 ( ( P @ X6 )
% 0.26/0.61 = ( Q @ X6 ) )
% 0.26/0.61 => ( ( collect_list_a @ P )
% 0.26/0.61 = ( collect_list_a @ Q ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_cong
% 0.26/0.61 thf(fact_137_Collect__cong,axiom,
% 0.26/0.61 ! [P: a > $o,Q: a > $o] :
% 0.26/0.61 ( ! [X6: a] :
% 0.26/0.61 ( ( P @ X6 )
% 0.26/0.61 = ( Q @ X6 ) )
% 0.26/0.61 => ( ( collect_a @ P )
% 0.26/0.61 = ( collect_a @ Q ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % Collect_cong
% 0.26/0.61 thf(fact_138_Ex__list__of__length,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ? [Xs2: list_list_a] :
% 0.26/0.61 ( ( size_s1427607542list_a @ Xs2 )
% 0.26/0.61 = N ) ).
% 0.26/0.61
% 0.26/0.61 % Ex_list_of_length
% 0.26/0.61 thf(fact_139_Ex__list__of__length,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ? [Xs2: list_set_list_a] :
% 0.26/0.61 ( ( size_s1635937238list_a @ Xs2 )
% 0.26/0.61 = N ) ).
% 0.26/0.61
% 0.26/0.61 % Ex_list_of_length
% 0.26/0.61 thf(fact_140_Ex__list__of__length,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ? [Xs2: list_set_set_a] :
% 0.26/0.61 ( ( size_s739728560_set_a @ Xs2 )
% 0.26/0.61 = N ) ).
% 0.26/0.61
% 0.26/0.61 % Ex_list_of_length
% 0.26/0.61 thf(fact_141_Ex__list__of__length,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ? [Xs2: list_nat] :
% 0.26/0.61 ( ( size_size_list_nat @ Xs2 )
% 0.26/0.61 = N ) ).
% 0.26/0.61
% 0.26/0.61 % Ex_list_of_length
% 0.26/0.61 thf(fact_142_Ex__list__of__length,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ? [Xs2: list_a] :
% 0.26/0.61 ( ( size_size_list_a @ Xs2 )
% 0.26/0.61 = N ) ).
% 0.26/0.61
% 0.26/0.61 % Ex_list_of_length
% 0.26/0.61 thf(fact_143_Ex__list__of__length,axiom,
% 0.26/0.61 ! [N: nat] :
% 0.26/0.61 ? [Xs2: list_set_a] :
% 0.26/0.61 ( ( size_size_list_set_a @ Xs2 )
% 0.26/0.61 = N ) ).
% 0.26/0.61
% 0.26/0.61 % Ex_list_of_length
% 0.26/0.61 thf(fact_144_rev__swap,axiom,
% 0.26/0.61 ! [Xs: list_a,Ys: list_a] :
% 0.26/0.61 ( ( ( rev_a @ Xs )
% 0.26/0.61 = Ys )
% 0.26/0.61 = ( Xs
% 0.26/0.61 = ( rev_a @ Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_swap
% 0.26/0.61 thf(fact_145_rev__swap,axiom,
% 0.26/0.61 ! [Xs: list_set_a,Ys: list_set_a] :
% 0.26/0.61 ( ( ( rev_set_a @ Xs )
% 0.26/0.61 = Ys )
% 0.26/0.61 = ( Xs
% 0.26/0.61 = ( rev_set_a @ Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_swap
% 0.26/0.61 thf(fact_146_lessThan__strict__subset__iff,axiom,
% 0.26/0.61 ! [M: nat,N: nat] :
% 0.26/0.61 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 0.26/0.61 = ( ord_less_nat @ M @ N ) ) ).
% 0.26/0.61
% 0.26/0.61 % lessThan_strict_subset_iff
% 0.26/0.61 thf(fact_147_length__induct,axiom,
% 0.26/0.61 ! [P: list_set_list_a > $o,Xs: list_set_list_a] :
% 0.26/0.61 ( ! [Xs2: list_set_list_a] :
% 0.26/0.61 ( ! [Ys4: list_set_list_a] :
% 0.26/0.61 ( ( ord_less_nat @ ( size_s1635937238list_a @ Ys4 ) @ ( size_s1635937238list_a @ Xs2 ) )
% 0.26/0.61 => ( P @ Ys4 ) )
% 0.26/0.61 => ( P @ Xs2 ) )
% 0.26/0.61 => ( P @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % length_induct
% 0.26/0.61 thf(fact_148_length__induct,axiom,
% 0.26/0.61 ! [P: list_set_set_a > $o,Xs: list_set_set_a] :
% 0.26/0.61 ( ! [Xs2: list_set_set_a] :
% 0.26/0.61 ( ! [Ys4: list_set_set_a] :
% 0.26/0.61 ( ( ord_less_nat @ ( size_s739728560_set_a @ Ys4 ) @ ( size_s739728560_set_a @ Xs2 ) )
% 0.26/0.61 => ( P @ Ys4 ) )
% 0.26/0.61 => ( P @ Xs2 ) )
% 0.26/0.61 => ( P @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % length_induct
% 0.26/0.61 thf(fact_149_length__induct,axiom,
% 0.26/0.61 ! [P: list_nat > $o,Xs: list_nat] :
% 0.26/0.61 ( ! [Xs2: list_nat] :
% 0.26/0.61 ( ! [Ys4: list_nat] :
% 0.26/0.61 ( ( ord_less_nat @ ( size_size_list_nat @ Ys4 ) @ ( size_size_list_nat @ Xs2 ) )
% 0.26/0.61 => ( P @ Ys4 ) )
% 0.26/0.61 => ( P @ Xs2 ) )
% 0.26/0.61 => ( P @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % length_induct
% 0.26/0.61 thf(fact_150_length__induct,axiom,
% 0.26/0.61 ! [P: list_a > $o,Xs: list_a] :
% 0.26/0.61 ( ! [Xs2: list_a] :
% 0.26/0.61 ( ! [Ys4: list_a] :
% 0.26/0.61 ( ( ord_less_nat @ ( size_size_list_a @ Ys4 ) @ ( size_size_list_a @ Xs2 ) )
% 0.26/0.61 => ( P @ Ys4 ) )
% 0.26/0.61 => ( P @ Xs2 ) )
% 0.26/0.61 => ( P @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % length_induct
% 0.26/0.61 thf(fact_151_length__induct,axiom,
% 0.26/0.61 ! [P: list_set_a > $o,Xs: list_set_a] :
% 0.26/0.61 ( ! [Xs2: list_set_a] :
% 0.26/0.61 ( ! [Ys4: list_set_a] :
% 0.26/0.61 ( ( ord_less_nat @ ( size_size_list_set_a @ Ys4 ) @ ( size_size_list_set_a @ Xs2 ) )
% 0.26/0.61 => ( P @ Ys4 ) )
% 0.26/0.61 => ( P @ Xs2 ) )
% 0.26/0.61 => ( P @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % length_induct
% 0.26/0.61 thf(fact_152_listsetD_I1_J,axiom,
% 0.26/0.61 ! [Ys: list_a,Xs: list_set_a] :
% 0.26/0.61 ( ( member_list_a @ Ys @ ( listset_a @ Xs ) )
% 0.26/0.61 => ( ( size_size_list_a @ Ys )
% 0.26/0.61 = ( size_size_list_set_a @ Xs ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetD(1)
% 0.26/0.61 thf(fact_153_listsetD_I1_J,axiom,
% 0.26/0.61 ! [Ys: list_set_a,Xs: list_set_set_a] :
% 0.26/0.61 ( ( member_list_set_a @ Ys @ ( listset_set_a @ Xs ) )
% 0.26/0.61 => ( ( size_size_list_set_a @ Ys )
% 0.26/0.61 = ( size_s739728560_set_a @ Xs ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % listsetD(1)
% 0.26/0.61 thf(fact_154_permutation__Ex__bij,axiom,
% 0.26/0.61 ! [Xs: list_a,Ys: list_a] :
% 0.26/0.61 ( ( perm_a @ Xs @ Ys )
% 0.26/0.61 => ? [F2: nat > nat] :
% 0.26/0.61 ( ( bij_betw_nat_nat @ F2 @ ( set_ord_lessThan_nat @ ( size_size_list_a @ Xs ) ) @ ( set_ord_lessThan_nat @ ( size_size_list_a @ Ys ) ) )
% 0.26/0.61 & ! [I2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I2 @ ( size_size_list_a @ Xs ) )
% 0.26/0.61 => ( ( nth_a @ Xs @ I2 )
% 0.26/0.61 = ( nth_a @ Ys @ ( F2 @ I2 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % permutation_Ex_bij
% 0.26/0.61 thf(fact_155_permutation__Ex__bij,axiom,
% 0.26/0.61 ! [Xs: list_set_a,Ys: list_set_a] :
% 0.26/0.61 ( ( perm_set_a @ Xs @ Ys )
% 0.26/0.61 => ? [F2: nat > nat] :
% 0.26/0.61 ( ( bij_betw_nat_nat @ F2 @ ( set_ord_lessThan_nat @ ( size_size_list_set_a @ Xs ) ) @ ( set_ord_lessThan_nat @ ( size_size_list_set_a @ Ys ) ) )
% 0.26/0.61 & ! [I2: nat] :
% 0.26/0.61 ( ( ord_less_nat @ I2 @ ( size_size_list_set_a @ Xs ) )
% 0.26/0.61 => ( ( nth_set_a @ Xs @ I2 )
% 0.26/0.61 = ( nth_set_a @ Ys @ ( F2 @ I2 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % permutation_Ex_bij
% 0.26/0.61 thf(fact_156_g__def,axiom,
% 0.26/0.61 ( g
% 0.26/0.61 = ( hilber815131374at_nat @ ( set_ord_lessThan_nat @ ( size_size_list_set_a @ ss2 ) ) @ f ) ) ).
% 0.26/0.61
% 0.26/0.61 % g_def
% 0.26/0.61 thf(fact_157_perm__refl,axiom,
% 0.26/0.61 ! [L: list_set_a] : ( perm_set_a @ L @ L ) ).
% 0.26/0.61
% 0.26/0.61 % perm_refl
% 0.26/0.61 thf(fact_158_image__eqI,axiom,
% 0.26/0.61 ! [B: a,F: a > a,X4: a,A: set_a] :
% 0.26/0.61 ( ( B
% 0.26/0.61 = ( F @ X4 ) )
% 0.26/0.61 => ( ( member_a @ X4 @ A )
% 0.26/0.61 => ( member_a @ B @ ( image_a_a @ F @ A ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % image_eqI
% 0.26/0.61 thf(fact_159_image__eqI,axiom,
% 0.26/0.61 ! [B: list_a,F: a > list_a,X4: a,A: set_a] :
% 0.26/0.61 ( ( B
% 0.26/0.61 = ( F @ X4 ) )
% 0.26/0.61 => ( ( member_a @ X4 @ A )
% 0.26/0.61 => ( member_list_a @ B @ ( image_a_list_a @ F @ A ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % image_eqI
% 0.26/0.61 thf(fact_160_image__eqI,axiom,
% 0.26/0.61 ! [B: a,F: list_a > a,X4: list_a,A: set_list_a] :
% 0.26/0.61 ( ( B
% 0.26/0.61 = ( F @ X4 ) )
% 0.26/0.61 => ( ( member_list_a @ X4 @ A )
% 0.26/0.61 => ( member_a @ B @ ( image_list_a_a @ F @ A ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % image_eqI
% 0.26/0.61 thf(fact_161_image__eqI,axiom,
% 0.26/0.61 ! [B: list_a,F: list_a > list_a,X4: list_a,A: set_list_a] :
% 0.26/0.61 ( ( B
% 0.26/0.61 = ( F @ X4 ) )
% 0.26/0.61 => ( ( member_list_a @ X4 @ A )
% 0.26/0.61 => ( member_list_a @ B @ ( image_list_a_list_a @ F @ A ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % image_eqI
% 0.26/0.61 thf(fact_162_mset__eq__perm,axiom,
% 0.26/0.61 ! [Xs: list_a,Ys: list_a] :
% 0.26/0.61 ( ( ( mset_a @ Xs )
% 0.26/0.61 = ( mset_a @ Ys ) )
% 0.26/0.61 = ( perm_a @ Xs @ Ys ) ) ).
% 0.26/0.61
% 0.26/0.61 % mset_eq_perm
% 0.26/0.61 thf(fact_163_mset__eq__perm,axiom,
% 0.26/0.61 ! [Xs: list_set_a,Ys: list_set_a] :
% 0.26/0.61 ( ( ( mset_set_a @ Xs )
% 0.26/0.61 = ( mset_set_a @ Ys ) )
% 0.26/0.61 = ( perm_set_a @ Xs @ Ys ) ) ).
% 0.26/0.61
% 0.26/0.61 % mset_eq_perm
% 0.26/0.61 thf(fact_164_perm__rev,axiom,
% 0.26/0.61 ! [Xs: list_set_a] : ( perm_set_a @ ( rev_set_a @ Xs ) @ Xs ) ).
% 0.26/0.61
% 0.26/0.61 % perm_rev
% 0.26/0.61 thf(fact_165_perm__length,axiom,
% 0.26/0.61 ! [Xs: list_a,Ys: list_a] :
% 0.26/0.61 ( ( perm_a @ Xs @ Ys )
% 0.26/0.61 => ( ( size_size_list_a @ Xs )
% 0.26/0.61 = ( size_size_list_a @ Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % perm_length
% 0.26/0.61 thf(fact_166_perm__length,axiom,
% 0.26/0.61 ! [Xs: list_set_a,Ys: list_set_a] :
% 0.26/0.61 ( ( perm_set_a @ Xs @ Ys )
% 0.26/0.61 => ( ( size_size_list_set_a @ Xs )
% 0.26/0.61 = ( size_size_list_set_a @ Ys ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % perm_length
% 0.26/0.61 thf(fact_167_bij__betw__imp__surj__on,axiom,
% 0.26/0.61 ! [F: nat > nat,A: set_nat,B2: set_nat] :
% 0.26/0.61 ( ( bij_betw_nat_nat @ F @ A @ B2 )
% 0.26/0.61 => ( ( image_nat_nat @ F @ A )
% 0.26/0.61 = B2 ) ) ).
% 0.26/0.61
% 0.26/0.61 % bij_betw_imp_surj_on
% 0.26/0.61 thf(fact_168_mbs_Oless__not__eq,axiom,
% 0.26/0.61 ! [X4: list_a,A: set_list_a,Y3: list_a] :
% 0.26/0.61 ( ( member_list_a @ X4 @ A )
% 0.26/0.61 => ( ( ord_less_nat @ ( size_size_list_a @ X4 ) @ ( size_size_list_a @ Y3 ) )
% 0.26/0.61 => ( X4 != Y3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % mbs.less_not_eq
% 0.26/0.61 thf(fact_169_mbs_Oless__not__eq,axiom,
% 0.26/0.61 ! [X4: list_set_a,A: set_list_set_a,Y3: list_set_a] :
% 0.26/0.61 ( ( member_list_set_a @ X4 @ A )
% 0.26/0.61 => ( ( ord_less_nat @ ( size_size_list_set_a @ X4 ) @ ( size_size_list_set_a @ Y3 ) )
% 0.26/0.61 => ( X4 != Y3 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % mbs.less_not_eq
% 0.26/0.61 thf(fact_170_size__mset,axiom,
% 0.26/0.61 ! [Xs: list_a] :
% 0.26/0.61 ( ( size_size_multiset_a @ ( mset_a @ Xs ) )
% 0.26/0.61 = ( size_size_list_a @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % size_mset
% 0.26/0.61 thf(fact_171_size__mset,axiom,
% 0.26/0.61 ! [Xs: list_set_a] :
% 0.26/0.61 ( ( size_s657334288_set_a @ ( mset_set_a @ Xs ) )
% 0.26/0.61 = ( size_size_list_set_a @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % size_mset
% 0.26/0.61 thf(fact_172_psubsetD,axiom,
% 0.26/0.61 ! [A: set_a,B2: set_a,C: a] :
% 0.26/0.61 ( ( ord_less_set_a @ A @ B2 )
% 0.26/0.61 => ( ( member_a @ C @ A )
% 0.26/0.61 => ( member_a @ C @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % psubsetD
% 0.26/0.61 thf(fact_173_psubsetD,axiom,
% 0.26/0.61 ! [A: set_list_a,B2: set_list_a,C: list_a] :
% 0.26/0.61 ( ( ord_less_set_list_a @ A @ B2 )
% 0.26/0.61 => ( ( member_list_a @ C @ A )
% 0.26/0.61 => ( member_list_a @ C @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % psubsetD
% 0.26/0.61 thf(fact_174_imageI,axiom,
% 0.26/0.61 ! [X4: a,A: set_a,F: a > a] :
% 0.26/0.61 ( ( member_a @ X4 @ A )
% 0.26/0.61 => ( member_a @ ( F @ X4 ) @ ( image_a_a @ F @ A ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageI
% 0.26/0.61 thf(fact_175_imageI,axiom,
% 0.26/0.61 ! [X4: a,A: set_a,F: a > list_a] :
% 0.26/0.61 ( ( member_a @ X4 @ A )
% 0.26/0.61 => ( member_list_a @ ( F @ X4 ) @ ( image_a_list_a @ F @ A ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageI
% 0.26/0.61 thf(fact_176_imageI,axiom,
% 0.26/0.61 ! [X4: list_a,A: set_list_a,F: list_a > a] :
% 0.26/0.61 ( ( member_list_a @ X4 @ A )
% 0.26/0.61 => ( member_a @ ( F @ X4 ) @ ( image_list_a_a @ F @ A ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageI
% 0.26/0.61 thf(fact_177_imageI,axiom,
% 0.26/0.61 ! [X4: list_a,A: set_list_a,F: list_a > list_a] :
% 0.26/0.61 ( ( member_list_a @ X4 @ A )
% 0.26/0.61 => ( member_list_a @ ( F @ X4 ) @ ( image_list_a_list_a @ F @ A ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % imageI
% 0.26/0.61 thf(fact_178_rev__image__eqI,axiom,
% 0.26/0.61 ! [X4: a,A: set_a,B: a,F: a > a] :
% 0.26/0.61 ( ( member_a @ X4 @ A )
% 0.26/0.61 => ( ( B
% 0.26/0.61 = ( F @ X4 ) )
% 0.26/0.61 => ( member_a @ B @ ( image_a_a @ F @ A ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_image_eqI
% 0.26/0.61 thf(fact_179_rev__image__eqI,axiom,
% 0.26/0.61 ! [X4: a,A: set_a,B: list_a,F: a > list_a] :
% 0.26/0.61 ( ( member_a @ X4 @ A )
% 0.26/0.61 => ( ( B
% 0.26/0.61 = ( F @ X4 ) )
% 0.26/0.61 => ( member_list_a @ B @ ( image_a_list_a @ F @ A ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_image_eqI
% 0.26/0.61 thf(fact_180_rev__image__eqI,axiom,
% 0.26/0.61 ! [X4: list_a,A: set_list_a,B: a,F: list_a > a] :
% 0.26/0.61 ( ( member_list_a @ X4 @ A )
% 0.26/0.61 => ( ( B
% 0.26/0.61 = ( F @ X4 ) )
% 0.26/0.61 => ( member_a @ B @ ( image_list_a_a @ F @ A ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_image_eqI
% 0.26/0.61 thf(fact_181_rev__image__eqI,axiom,
% 0.26/0.61 ! [X4: list_a,A: set_list_a,B: list_a,F: list_a > list_a] :
% 0.26/0.61 ( ( member_list_a @ X4 @ A )
% 0.26/0.61 => ( ( B
% 0.26/0.61 = ( F @ X4 ) )
% 0.26/0.61 => ( member_list_a @ B @ ( image_list_a_list_a @ F @ A ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % rev_image_eqI
% 0.26/0.61 thf(fact_182_direct__decomp__def,axiom,
% 0.26/0.61 ( hilber2037636820comp_a
% 0.26/0.61 = ( ^ [A4: set_a,Ss2: list_set_a] : ( bij_betw_list_a_a @ groups1792256535list_a @ ( listset_a @ Ss2 ) @ A4 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % direct_decomp_def
% 0.26/0.61 thf(fact_183_bij__betwE,axiom,
% 0.26/0.61 ! [F: nat > nat,A: set_nat,B2: set_nat] :
% 0.26/0.61 ( ( bij_betw_nat_nat @ F @ A @ B2 )
% 0.26/0.61 => ! [X: nat] :
% 0.26/0.61 ( ( member_nat @ X @ A )
% 0.26/0.61 => ( member_nat @ ( F @ X ) @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % bij_betwE
% 0.26/0.61 thf(fact_184_bij__betw__inv,axiom,
% 0.26/0.61 ! [F: nat > nat,A: set_nat,B2: set_nat] :
% 0.26/0.61 ( ( bij_betw_nat_nat @ F @ A @ B2 )
% 0.26/0.61 => ? [G: nat > nat] : ( bij_betw_nat_nat @ G @ B2 @ A ) ) ).
% 0.26/0.61
% 0.26/0.61 % bij_betw_inv
% 0.26/0.61 thf(fact_185_bij__betw__cong,axiom,
% 0.26/0.61 ! [A: set_nat,F: nat > nat,G2: nat > nat,A5: set_nat] :
% 0.26/0.61 ( ! [A3: nat] :
% 0.26/0.61 ( ( member_nat @ A3 @ A )
% 0.26/0.61 => ( ( F @ A3 )
% 0.26/0.61 = ( G2 @ A3 ) ) )
% 0.26/0.61 => ( ( bij_betw_nat_nat @ F @ A @ A5 )
% 0.26/0.61 = ( bij_betw_nat_nat @ G2 @ A @ A5 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % bij_betw_cong
% 0.26/0.61 thf(fact_186_bij__betw__apply,axiom,
% 0.26/0.61 ! [F: a > a,A: set_a,B2: set_a,A2: a] :
% 0.26/0.61 ( ( bij_betw_a_a @ F @ A @ B2 )
% 0.26/0.61 => ( ( member_a @ A2 @ A )
% 0.26/0.61 => ( member_a @ ( F @ A2 ) @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % bij_betw_apply
% 0.26/0.61 thf(fact_187_bij__betw__apply,axiom,
% 0.26/0.61 ! [F: a > list_a,A: set_a,B2: set_list_a,A2: a] :
% 0.26/0.61 ( ( bij_betw_a_list_a @ F @ A @ B2 )
% 0.26/0.61 => ( ( member_a @ A2 @ A )
% 0.26/0.61 => ( member_list_a @ ( F @ A2 ) @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % bij_betw_apply
% 0.26/0.61 thf(fact_188_bij__betw__apply,axiom,
% 0.26/0.61 ! [F: list_a > a,A: set_list_a,B2: set_a,A2: list_a] :
% 0.26/0.61 ( ( bij_betw_list_a_a @ F @ A @ B2 )
% 0.26/0.61 => ( ( member_list_a @ A2 @ A )
% 0.26/0.61 => ( member_a @ ( F @ A2 ) @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % bij_betw_apply
% 0.26/0.61 thf(fact_189_bij__betw__apply,axiom,
% 0.26/0.61 ! [F: list_a > list_a,A: set_list_a,B2: set_list_a,A2: list_a] :
% 0.26/0.61 ( ( bij_be94573046list_a @ F @ A @ B2 )
% 0.26/0.61 => ( ( member_list_a @ A2 @ A )
% 0.26/0.61 => ( member_list_a @ ( F @ A2 ) @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % bij_betw_apply
% 0.26/0.61 thf(fact_190_bij__betw__apply,axiom,
% 0.26/0.61 ! [F: nat > nat,A: set_nat,B2: set_nat,A2: nat] :
% 0.26/0.61 ( ( bij_betw_nat_nat @ F @ A @ B2 )
% 0.26/0.61 => ( ( member_nat @ A2 @ A )
% 0.26/0.61 => ( member_nat @ ( F @ A2 ) @ B2 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % bij_betw_apply
% 0.26/0.61 thf(fact_191_bij__betw__iff__bijections,axiom,
% 0.26/0.61 ( bij_betw_a_a
% 0.26/0.61 = ( ^ [F3: a > a,A4: set_a,B3: set_a] :
% 0.26/0.61 ? [G3: a > a] :
% 0.26/0.61 ( ! [X5: a] :
% 0.26/0.61 ( ( member_a @ X5 @ A4 )
% 0.26/0.61 => ( ( member_a @ ( F3 @ X5 ) @ B3 )
% 0.26/0.61 & ( ( G3 @ ( F3 @ X5 ) )
% 0.26/0.61 = X5 ) ) )
% 0.26/0.61 & ! [X5: a] :
% 0.26/0.61 ( ( member_a @ X5 @ B3 )
% 0.26/0.61 => ( ( member_a @ ( G3 @ X5 ) @ A4 )
% 0.26/0.61 & ( ( F3 @ ( G3 @ X5 ) )
% 0.26/0.61 = X5 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % bij_betw_iff_bijections
% 0.26/0.61 thf(fact_192_bij__betw__iff__bijections,axiom,
% 0.26/0.61 ( bij_betw_list_a_a
% 0.26/0.61 = ( ^ [F3: list_a > a,A4: set_list_a,B3: set_a] :
% 0.26/0.61 ? [G3: a > list_a] :
% 0.26/0.61 ( ! [X5: list_a] :
% 0.26/0.61 ( ( member_list_a @ X5 @ A4 )
% 0.26/0.61 => ( ( member_a @ ( F3 @ X5 ) @ B3 )
% 0.26/0.61 & ( ( G3 @ ( F3 @ X5 ) )
% 0.26/0.61 = X5 ) ) )
% 0.26/0.61 & ! [X5: a] :
% 0.26/0.61 ( ( member_a @ X5 @ B3 )
% 0.26/0.61 => ( ( member_list_a @ ( G3 @ X5 ) @ A4 )
% 0.26/0.61 & ( ( F3 @ ( G3 @ X5 ) )
% 0.26/0.61 = X5 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % bij_betw_iff_bijections
% 0.26/0.61 thf(fact_193_bij__betw__iff__bijections,axiom,
% 0.26/0.61 ( bij_betw_a_list_a
% 0.26/0.61 = ( ^ [F3: a > list_a,A4: set_a,B3: set_list_a] :
% 0.26/0.61 ? [G3: list_a > a] :
% 0.26/0.61 ( ! [X5: a] :
% 0.26/0.61 ( ( member_a @ X5 @ A4 )
% 0.26/0.61 => ( ( member_list_a @ ( F3 @ X5 ) @ B3 )
% 0.26/0.61 & ( ( G3 @ ( F3 @ X5 ) )
% 0.26/0.61 = X5 ) ) )
% 0.26/0.61 & ! [X5: list_a] :
% 0.26/0.61 ( ( member_list_a @ X5 @ B3 )
% 0.26/0.61 => ( ( member_a @ ( G3 @ X5 ) @ A4 )
% 0.26/0.61 & ( ( F3 @ ( G3 @ X5 ) )
% 0.26/0.61 = X5 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % bij_betw_iff_bijections
% 0.26/0.61 thf(fact_194_bij__betw__iff__bijections,axiom,
% 0.26/0.61 ( bij_be94573046list_a
% 0.26/0.61 = ( ^ [F3: list_a > list_a,A4: set_list_a,B3: set_list_a] :
% 0.26/0.61 ? [G3: list_a > list_a] :
% 0.26/0.61 ( ! [X5: list_a] :
% 0.26/0.61 ( ( member_list_a @ X5 @ A4 )
% 0.26/0.61 => ( ( member_list_a @ ( F3 @ X5 ) @ B3 )
% 0.26/0.61 & ( ( G3 @ ( F3 @ X5 ) )
% 0.26/0.61 = X5 ) ) )
% 0.26/0.61 & ! [X5: list_a] :
% 0.26/0.61 ( ( member_list_a @ X5 @ B3 )
% 0.26/0.61 => ( ( member_list_a @ ( G3 @ X5 ) @ A4 )
% 0.26/0.61 & ( ( F3 @ ( G3 @ X5 ) )
% 0.26/0.61 = X5 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % bij_betw_iff_bijections
% 0.26/0.61 thf(fact_195_bij__betw__iff__bijections,axiom,
% 0.26/0.61 ( bij_betw_nat_nat
% 0.26/0.61 = ( ^ [F3: nat > nat,A4: set_nat,B3: set_nat] :
% 0.26/0.61 ? [G3: nat > nat] :
% 0.26/0.61 ( ! [X5: nat] :
% 0.26/0.61 ( ( member_nat @ X5 @ A4 )
% 0.26/0.61 => ( ( member_nat @ ( F3 @ X5 ) @ B3 )
% 0.26/0.61 & ( ( G3 @ ( F3 @ X5 ) )
% 0.26/0.61 = X5 ) ) )
% 0.26/0.61 & ! [X5: nat] :
% 0.26/0.61 ( ( member_nat @ X5 @ B3 )
% 0.26/0.61 => ( ( member_nat @ ( G3 @ X5 ) @ A4 )
% 0.26/0.61 & ( ( F3 @ ( G3 @ X5 ) )
% 0.26/0.61 = X5 ) ) ) ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % bij_betw_iff_bijections
% 0.26/0.61 thf(fact_196_perm__sym,axiom,
% 0.26/0.61 ! [Xs: list_set_a,Ys: list_set_a] :
% 0.26/0.61 ( ( perm_set_a @ Xs @ Ys )
% 0.26/0.61 => ( perm_set_a @ Ys @ Xs ) ) ).
% 0.26/0.61
% 0.26/0.61 % perm_sym
% 0.26/0.61 thf(fact_197_perm_Otrans,axiom,
% 0.26/0.61 ! [Xs: list_set_a,Ys: list_set_a,Zs: list_set_a] :
% 0.26/0.61 ( ( perm_set_a @ Xs @ Ys )
% 0.26/0.61 => ( ( perm_set_a @ Ys @ Zs )
% 0.26/0.61 => ( perm_set_a @ Xs @ Zs ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % perm.trans
% 0.26/0.61 thf(fact_198_bij__betw__inv__into__right,axiom,
% 0.26/0.61 ! [F: nat > nat,A: set_nat,A5: set_nat,A6: nat] :
% 0.26/0.61 ( ( bij_betw_nat_nat @ F @ A @ A5 )
% 0.26/0.61 => ( ( member_nat @ A6 @ A5 )
% 0.26/0.61 => ( ( F @ ( hilber815131374at_nat @ A @ F @ A6 ) )
% 0.26/0.61 = A6 ) ) ) ).
% 0.26/0.61
% 0.26/0.61 % bij_betw_inv_into_right
% 0.26/0.61 thf(fact_199_bij__betw__inv__into__left,axiom,
% 0.26/0.61 ! [F: nat > nat,A: set_nat,A5: set_nat,A2: nat] :
% 0.26/0.61 ( ( bij_betw_nat_nat @ F @ A @ A5 )
% 0.26/0.62 => ( ( member_nat @ A2 @ A )
% 0.26/0.62 => ( ( hilber815131374at_nat @ A @ F @ ( F @ A2 ) )
% 0.26/0.62 = A2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % bij_betw_inv_into_left
% 0.26/0.62 thf(fact_200_inv__into__inv__into__eq,axiom,
% 0.26/0.62 ! [F: nat > nat,A: set_nat,A5: set_nat,A2: nat] :
% 0.26/0.62 ( ( bij_betw_nat_nat @ F @ A @ A5 )
% 0.26/0.62 => ( ( member_nat @ A2 @ A )
% 0.26/0.62 => ( ( hilber815131374at_nat @ A5 @ ( hilber815131374at_nat @ A @ F ) @ A2 )
% 0.26/0.62 = ( F @ A2 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % inv_into_inv_into_eq
% 0.26/0.62 thf(fact_201_bij__betw__inv__into,axiom,
% 0.26/0.62 ! [F: nat > nat,A: set_nat,B2: set_nat] :
% 0.26/0.62 ( ( bij_betw_nat_nat @ F @ A @ B2 )
% 0.26/0.62 => ( bij_betw_nat_nat @ ( hilber815131374at_nat @ A @ F ) @ B2 @ A ) ) ).
% 0.26/0.62
% 0.26/0.62 % bij_betw_inv_into
% 0.26/0.62 thf(fact_202_inv__into__injective,axiom,
% 0.26/0.62 ! [A: set_nat,F: nat > nat,X4: nat,Y3: nat] :
% 0.26/0.62 ( ( ( hilber815131374at_nat @ A @ F @ X4 )
% 0.26/0.62 = ( hilber815131374at_nat @ A @ F @ Y3 ) )
% 0.26/0.62 => ( ( member_nat @ X4 @ ( image_nat_nat @ F @ A ) )
% 0.26/0.62 => ( ( member_nat @ Y3 @ ( image_nat_nat @ F @ A ) )
% 0.26/0.62 => ( X4 = Y3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % inv_into_injective
% 0.26/0.62 thf(fact_203_inv__into__into,axiom,
% 0.26/0.62 ! [X4: a,F: a > a,A: set_a] :
% 0.26/0.62 ( ( member_a @ X4 @ ( image_a_a @ F @ A ) )
% 0.26/0.62 => ( member_a @ ( hilbert_inv_into_a_a @ A @ F @ X4 ) @ A ) ) ).
% 0.26/0.62
% 0.26/0.62 % inv_into_into
% 0.26/0.62 thf(fact_204_inv__into__into,axiom,
% 0.26/0.62 ! [X4: a,F: list_a > a,A: set_list_a] :
% 0.26/0.62 ( ( member_a @ X4 @ ( image_list_a_a @ F @ A ) )
% 0.26/0.62 => ( member_list_a @ ( hilber2125729734st_a_a @ A @ F @ X4 ) @ A ) ) ).
% 0.26/0.62
% 0.26/0.62 % inv_into_into
% 0.26/0.62 thf(fact_205_inv__into__into,axiom,
% 0.26/0.62 ! [X4: list_a,F: a > list_a,A: set_a] :
% 0.26/0.62 ( ( member_list_a @ X4 @ ( image_a_list_a @ F @ A ) )
% 0.26/0.62 => ( member_a @ ( hilber165648082list_a @ A @ F @ X4 ) @ A ) ) ).
% 0.26/0.62
% 0.26/0.62 % inv_into_into
% 0.26/0.62 thf(fact_206_inv__into__into,axiom,
% 0.26/0.62 ! [X4: list_a,F: list_a > list_a,A: set_list_a] :
% 0.26/0.62 ( ( member_list_a @ X4 @ ( image_list_a_list_a @ F @ A ) )
% 0.26/0.62 => ( member_list_a @ ( hilber921249868list_a @ A @ F @ X4 ) @ A ) ) ).
% 0.26/0.62
% 0.26/0.62 % inv_into_into
% 0.26/0.62 thf(fact_207_inv__into__into,axiom,
% 0.26/0.62 ! [X4: nat,F: nat > nat,A: set_nat] :
% 0.26/0.62 ( ( member_nat @ X4 @ ( image_nat_nat @ F @ A ) )
% 0.26/0.62 => ( member_nat @ ( hilber815131374at_nat @ A @ F @ X4 ) @ A ) ) ).
% 0.26/0.62
% 0.26/0.62 % inv_into_into
% 0.26/0.62 thf(fact_208_f__inv__into__f,axiom,
% 0.26/0.62 ! [Y3: nat,F: nat > nat,A: set_nat] :
% 0.26/0.62 ( ( member_nat @ Y3 @ ( image_nat_nat @ F @ A ) )
% 0.26/0.62 => ( ( F @ ( hilber815131374at_nat @ A @ F @ Y3 ) )
% 0.26/0.62 = Y3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % f_inv_into_f
% 0.26/0.62 thf(fact_209_list__ex__length,axiom,
% 0.26/0.62 ( list_ex_a
% 0.26/0.62 = ( ^ [P2: a > $o,Xs4: list_a] :
% 0.26/0.62 ? [N2: nat] :
% 0.26/0.62 ( ( ord_less_nat @ N2 @ ( size_size_list_a @ Xs4 ) )
% 0.26/0.62 & ( P2 @ ( nth_a @ Xs4 @ N2 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % list_ex_length
% 0.26/0.62 thf(fact_210_list__ex__length,axiom,
% 0.26/0.62 ( list_ex_set_a
% 0.26/0.62 = ( ^ [P2: set_a > $o,Xs4: list_set_a] :
% 0.26/0.62 ? [N2: nat] :
% 0.26/0.62 ( ( ord_less_nat @ N2 @ ( size_size_list_set_a @ Xs4 ) )
% 0.26/0.62 & ( P2 @ ( nth_set_a @ Xs4 @ N2 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % list_ex_length
% 0.26/0.62 thf(fact_211_direct__decompI,axiom,
% 0.26/0.62 ! [Ss: list_set_a,A: set_a] :
% 0.26/0.62 ( ( inj_on_list_a_a @ groups1792256535list_a @ ( listset_a @ Ss ) )
% 0.26/0.62 => ( ( ( image_list_a_a @ groups1792256535list_a @ ( listset_a @ Ss ) )
% 0.26/0.62 = A )
% 0.26/0.62 => ( hilber2037636820comp_a @ A @ Ss ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % direct_decompI
% 0.26/0.62 thf(fact_212_elem__le__sum__list,axiom,
% 0.26/0.62 ! [K: nat,Ns: list_nat] :
% 0.26/0.62 ( ( ord_less_nat @ K @ ( size_size_list_nat @ Ns ) )
% 0.26/0.62 => ( ord_less_eq_nat @ ( nth_nat @ Ns @ K ) @ ( groups921905271st_nat @ Ns ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % elem_le_sum_list
% 0.26/0.62 thf(fact_213_perm__swap,axiom,
% 0.26/0.62 ! [I: nat,Xs: list_a,J: nat] :
% 0.26/0.62 ( ( ord_less_nat @ I @ ( size_size_list_a @ Xs ) )
% 0.26/0.62 => ( ( ord_less_nat @ J @ ( size_size_list_a @ Xs ) )
% 0.26/0.62 => ( perm_a @ ( list_update_a @ ( list_update_a @ Xs @ I @ ( nth_a @ Xs @ J ) ) @ J @ ( nth_a @ Xs @ I ) ) @ Xs ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % perm_swap
% 0.26/0.62 thf(fact_214_perm__swap,axiom,
% 0.26/0.62 ! [I: nat,Xs: list_set_a,J: nat] :
% 0.26/0.62 ( ( ord_less_nat @ I @ ( size_size_list_set_a @ Xs ) )
% 0.26/0.62 => ( ( ord_less_nat @ J @ ( size_size_list_set_a @ Xs ) )
% 0.26/0.62 => ( perm_set_a @ ( list_update_set_a @ ( list_update_set_a @ Xs @ I @ ( nth_set_a @ Xs @ J ) ) @ J @ ( nth_set_a @ Xs @ I ) ) @ Xs ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % perm_swap
% 0.26/0.62 thf(fact_215_mset__swap,axiom,
% 0.26/0.62 ! [I: nat,Ls: list_a,J: nat] :
% 0.26/0.62 ( ( ord_less_nat @ I @ ( size_size_list_a @ Ls ) )
% 0.26/0.62 => ( ( ord_less_nat @ J @ ( size_size_list_a @ Ls ) )
% 0.26/0.62 => ( ( mset_a @ ( list_update_a @ ( list_update_a @ Ls @ J @ ( nth_a @ Ls @ I ) ) @ I @ ( nth_a @ Ls @ J ) ) )
% 0.26/0.62 = ( mset_a @ Ls ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mset_swap
% 0.26/0.62 thf(fact_216_mset__swap,axiom,
% 0.26/0.62 ! [I: nat,Ls: list_set_a,J: nat] :
% 0.26/0.62 ( ( ord_less_nat @ I @ ( size_size_list_set_a @ Ls ) )
% 0.26/0.62 => ( ( ord_less_nat @ J @ ( size_size_list_set_a @ Ls ) )
% 0.26/0.62 => ( ( mset_set_a @ ( list_update_set_a @ ( list_update_set_a @ Ls @ J @ ( nth_set_a @ Ls @ I ) ) @ I @ ( nth_set_a @ Ls @ J ) ) )
% 0.26/0.62 = ( mset_set_a @ Ls ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mset_swap
% 0.26/0.62 thf(fact_217_nth__mem__mset,axiom,
% 0.26/0.62 ! [I: nat,Ls: list_list_a] :
% 0.26/0.62 ( ( ord_less_nat @ I @ ( size_s1427607542list_a @ Ls ) )
% 0.26/0.62 => ( member_list_a @ ( nth_list_a @ Ls @ I ) @ ( set_mset_list_a @ ( mset_list_a @ Ls ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % nth_mem_mset
% 0.26/0.62 thf(fact_218_nth__mem__mset,axiom,
% 0.26/0.62 ! [I: nat,Ls: list_a] :
% 0.26/0.62 ( ( ord_less_nat @ I @ ( size_size_list_a @ Ls ) )
% 0.26/0.62 => ( member_a @ ( nth_a @ Ls @ I ) @ ( set_mset_a @ ( mset_a @ Ls ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % nth_mem_mset
% 0.26/0.62 thf(fact_219_nth__mem__mset,axiom,
% 0.26/0.62 ! [I: nat,Ls: list_set_a] :
% 0.26/0.62 ( ( ord_less_nat @ I @ ( size_size_list_set_a @ Ls ) )
% 0.26/0.62 => ( member_set_a @ ( nth_set_a @ Ls @ I ) @ ( set_mset_set_a @ ( mset_set_a @ Ls ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % nth_mem_mset
% 0.26/0.62 thf(fact_220_in__Union__mset__iff,axiom,
% 0.26/0.62 ! [X4: a,MM: multiset_multiset_a] :
% 0.26/0.62 ( ( member_a @ X4 @ ( set_mset_a @ ( comm_m2145643721iset_a @ MM ) ) )
% 0.26/0.62 = ( ? [M2: multiset_a] :
% 0.26/0.62 ( ( member_multiset_a @ M2 @ ( set_mset_multiset_a @ MM ) )
% 0.26/0.62 & ( member_a @ X4 @ ( set_mset_a @ M2 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_Union_mset_iff
% 0.26/0.62 thf(fact_221_in__Union__mset__iff,axiom,
% 0.26/0.62 ! [X4: list_a,MM: multis971982480list_a] :
% 0.26/0.62 ( ( member_list_a @ X4 @ ( set_mset_list_a @ ( comm_m324867663list_a @ MM ) ) )
% 0.26/0.62 = ( ? [M2: multiset_list_a] :
% 0.26/0.62 ( ( member528267379list_a @ M2 @ ( set_ms1660427399list_a @ MM ) )
% 0.26/0.62 & ( member_list_a @ X4 @ ( set_mset_list_a @ M2 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_Union_mset_iff
% 0.26/0.62 thf(fact_222_lessThan__subset__iff,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat] :
% 0.26/0.62 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X4 ) @ ( set_ord_lessThan_nat @ Y3 ) )
% 0.26/0.62 = ( ord_less_eq_nat @ X4 @ Y3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % lessThan_subset_iff
% 0.26/0.62 thf(fact_223_list__update__beyond,axiom,
% 0.26/0.62 ! [Xs: list_a,I: nat,X4: a] :
% 0.26/0.62 ( ( ord_less_eq_nat @ ( size_size_list_a @ Xs ) @ I )
% 0.26/0.62 => ( ( list_update_a @ Xs @ I @ X4 )
% 0.26/0.62 = Xs ) ) ).
% 0.26/0.62
% 0.26/0.62 % list_update_beyond
% 0.26/0.62 thf(fact_224_list__update__beyond,axiom,
% 0.26/0.62 ! [Xs: list_set_a,I: nat,X4: set_a] :
% 0.26/0.62 ( ( ord_less_eq_nat @ ( size_size_list_set_a @ Xs ) @ I )
% 0.26/0.62 => ( ( list_update_set_a @ Xs @ I @ X4 )
% 0.26/0.62 = Xs ) ) ).
% 0.26/0.62
% 0.26/0.62 % list_update_beyond
% 0.26/0.62 thf(fact_225_length__list__update,axiom,
% 0.26/0.62 ! [Xs: list_a,I: nat,X4: a] :
% 0.26/0.62 ( ( size_size_list_a @ ( list_update_a @ Xs @ I @ X4 ) )
% 0.26/0.62 = ( size_size_list_a @ Xs ) ) ).
% 0.26/0.62
% 0.26/0.62 % length_list_update
% 0.26/0.62 thf(fact_226_length__list__update,axiom,
% 0.26/0.62 ! [Xs: list_set_a,I: nat,X4: set_a] :
% 0.26/0.62 ( ( size_size_list_set_a @ ( list_update_set_a @ Xs @ I @ X4 ) )
% 0.26/0.62 = ( size_size_list_set_a @ Xs ) ) ).
% 0.26/0.62
% 0.26/0.62 % length_list_update
% 0.26/0.62 thf(fact_227_inv__into__f__f,axiom,
% 0.26/0.62 ! [F: nat > nat,A: set_nat,X4: nat] :
% 0.26/0.62 ( ( inj_on_nat_nat @ F @ A )
% 0.26/0.62 => ( ( member_nat @ X4 @ A )
% 0.26/0.62 => ( ( hilber815131374at_nat @ A @ F @ ( F @ X4 ) )
% 0.26/0.62 = X4 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % inv_into_f_f
% 0.26/0.62 thf(fact_228_list__update__id,axiom,
% 0.26/0.62 ! [Xs: list_a,I: nat] :
% 0.26/0.62 ( ( list_update_a @ Xs @ I @ ( nth_a @ Xs @ I ) )
% 0.26/0.62 = Xs ) ).
% 0.26/0.62
% 0.26/0.62 % list_update_id
% 0.26/0.62 thf(fact_229_list__update__id,axiom,
% 0.26/0.62 ! [Xs: list_set_a,I: nat] :
% 0.26/0.62 ( ( list_update_set_a @ Xs @ I @ ( nth_set_a @ Xs @ I ) )
% 0.26/0.62 = Xs ) ).
% 0.26/0.62
% 0.26/0.62 % list_update_id
% 0.26/0.62 thf(fact_230_nth__list__update__neq,axiom,
% 0.26/0.62 ! [I: nat,J: nat,Xs: list_a,X4: a] :
% 0.26/0.62 ( ( I != J )
% 0.26/0.62 => ( ( nth_a @ ( list_update_a @ Xs @ I @ X4 ) @ J )
% 0.26/0.62 = ( nth_a @ Xs @ J ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % nth_list_update_neq
% 0.26/0.62 thf(fact_231_nth__list__update__neq,axiom,
% 0.26/0.62 ! [I: nat,J: nat,Xs: list_set_a,X4: set_a] :
% 0.26/0.62 ( ( I != J )
% 0.26/0.62 => ( ( nth_set_a @ ( list_update_set_a @ Xs @ I @ X4 ) @ J )
% 0.26/0.62 = ( nth_set_a @ Xs @ J ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % nth_list_update_neq
% 0.26/0.62 thf(fact_232_inv__into__image__cancel,axiom,
% 0.26/0.62 ! [F: nat > nat,A: set_nat,S: set_nat] :
% 0.26/0.62 ( ( inj_on_nat_nat @ F @ A )
% 0.26/0.62 => ( ( ord_less_eq_set_nat @ S @ A )
% 0.26/0.62 => ( ( image_nat_nat @ ( hilber815131374at_nat @ A @ F ) @ ( image_nat_nat @ F @ S ) )
% 0.26/0.62 = S ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % inv_into_image_cancel
% 0.26/0.62 thf(fact_233_nth__list__update__eq,axiom,
% 0.26/0.62 ! [I: nat,Xs: list_a,X4: a] :
% 0.26/0.62 ( ( ord_less_nat @ I @ ( size_size_list_a @ Xs ) )
% 0.26/0.62 => ( ( nth_a @ ( list_update_a @ Xs @ I @ X4 ) @ I )
% 0.26/0.62 = X4 ) ) ).
% 0.26/0.62
% 0.26/0.62 % nth_list_update_eq
% 0.26/0.62 thf(fact_234_nth__list__update__eq,axiom,
% 0.26/0.62 ! [I: nat,Xs: list_set_a,X4: set_a] :
% 0.26/0.62 ( ( ord_less_nat @ I @ ( size_size_list_set_a @ Xs ) )
% 0.26/0.62 => ( ( nth_set_a @ ( list_update_set_a @ Xs @ I @ X4 ) @ I )
% 0.26/0.62 = X4 ) ) ).
% 0.26/0.62
% 0.26/0.62 % nth_list_update_eq
% 0.26/0.62 thf(fact_235_inj__on__inv__into,axiom,
% 0.26/0.62 ! [B2: set_nat,F: nat > nat,A: set_nat] :
% 0.26/0.62 ( ( ord_less_eq_set_nat @ B2 @ ( image_nat_nat @ F @ A ) )
% 0.26/0.62 => ( inj_on_nat_nat @ ( hilber815131374at_nat @ A @ F ) @ B2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % inj_on_inv_into
% 0.26/0.62 thf(fact_236_inj__on__image__mem__iff,axiom,
% 0.26/0.62 ! [F: a > a,B2: set_a,A2: a,A: set_a] :
% 0.26/0.62 ( ( inj_on_a_a @ F @ B2 )
% 0.26/0.62 => ( ( member_a @ A2 @ B2 )
% 0.26/0.62 => ( ( ord_less_eq_set_a @ A @ B2 )
% 0.26/0.62 => ( ( member_a @ ( F @ A2 ) @ ( image_a_a @ F @ A ) )
% 0.26/0.62 = ( member_a @ A2 @ A ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % inj_on_image_mem_iff
% 0.26/0.62 thf(fact_237_inj__on__image__mem__iff,axiom,
% 0.26/0.62 ! [F: a > list_a,B2: set_a,A2: a,A: set_a] :
% 0.26/0.62 ( ( inj_on_a_list_a @ F @ B2 )
% 0.26/0.62 => ( ( member_a @ A2 @ B2 )
% 0.26/0.62 => ( ( ord_less_eq_set_a @ A @ B2 )
% 0.26/0.62 => ( ( member_list_a @ ( F @ A2 ) @ ( image_a_list_a @ F @ A ) )
% 0.26/0.62 = ( member_a @ A2 @ A ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % inj_on_image_mem_iff
% 0.26/0.62 thf(fact_238_inj__on__image__mem__iff,axiom,
% 0.26/0.62 ! [F: list_a > a,B2: set_list_a,A2: list_a,A: set_list_a] :
% 0.26/0.62 ( ( inj_on_list_a_a @ F @ B2 )
% 0.26/0.62 => ( ( member_list_a @ A2 @ B2 )
% 0.26/0.62 => ( ( ord_le1301786372list_a @ A @ B2 )
% 0.26/0.62 => ( ( member_a @ ( F @ A2 ) @ ( image_list_a_a @ F @ A ) )
% 0.26/0.62 = ( member_list_a @ A2 @ A ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % inj_on_image_mem_iff
% 0.26/0.62 thf(fact_239_inj__on__image__mem__iff,axiom,
% 0.26/0.62 ! [F: list_a > list_a,B2: set_list_a,A2: list_a,A: set_list_a] :
% 0.26/0.62 ( ( inj_on_list_a_list_a @ F @ B2 )
% 0.26/0.62 => ( ( member_list_a @ A2 @ B2 )
% 0.26/0.62 => ( ( ord_le1301786372list_a @ A @ B2 )
% 0.26/0.62 => ( ( member_list_a @ ( F @ A2 ) @ ( image_list_a_list_a @ F @ A ) )
% 0.26/0.62 = ( member_list_a @ A2 @ A ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % inj_on_image_mem_iff
% 0.26/0.62 thf(fact_240_bij__betw__imp__inj__on,axiom,
% 0.26/0.62 ! [F: nat > nat,A: set_nat,B2: set_nat] :
% 0.26/0.62 ( ( bij_betw_nat_nat @ F @ A @ B2 )
% 0.26/0.62 => ( inj_on_nat_nat @ F @ A ) ) ).
% 0.26/0.62
% 0.26/0.62 % bij_betw_imp_inj_on
% 0.26/0.62 thf(fact_241_inv__into__f__eq,axiom,
% 0.26/0.62 ! [F: nat > nat,A: set_nat,X4: nat,Y3: nat] :
% 0.26/0.62 ( ( inj_on_nat_nat @ F @ A )
% 0.26/0.62 => ( ( member_nat @ X4 @ A )
% 0.26/0.62 => ( ( ( F @ X4 )
% 0.26/0.62 = Y3 )
% 0.26/0.62 => ( ( hilber815131374at_nat @ A @ F @ Y3 )
% 0.26/0.62 = X4 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % inv_into_f_eq
% 0.26/0.62 thf(fact_242_image__subsetI,axiom,
% 0.26/0.62 ! [A: set_a,F: a > a,B2: set_a] :
% 0.26/0.62 ( ! [X6: a] :
% 0.26/0.62 ( ( member_a @ X6 @ A )
% 0.26/0.62 => ( member_a @ ( F @ X6 ) @ B2 ) )
% 0.26/0.62 => ( ord_less_eq_set_a @ ( image_a_a @ F @ A ) @ B2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % image_subsetI
% 0.26/0.62 thf(fact_243_image__subsetI,axiom,
% 0.26/0.62 ! [A: set_a,F: a > list_a,B2: set_list_a] :
% 0.26/0.62 ( ! [X6: a] :
% 0.26/0.62 ( ( member_a @ X6 @ A )
% 0.26/0.62 => ( member_list_a @ ( F @ X6 ) @ B2 ) )
% 0.26/0.62 => ( ord_le1301786372list_a @ ( image_a_list_a @ F @ A ) @ B2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % image_subsetI
% 0.26/0.62 thf(fact_244_image__subsetI,axiom,
% 0.26/0.62 ! [A: set_list_a,F: list_a > a,B2: set_a] :
% 0.26/0.62 ( ! [X6: list_a] :
% 0.26/0.62 ( ( member_list_a @ X6 @ A )
% 0.26/0.62 => ( member_a @ ( F @ X6 ) @ B2 ) )
% 0.26/0.62 => ( ord_less_eq_set_a @ ( image_list_a_a @ F @ A ) @ B2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % image_subsetI
% 0.26/0.62 thf(fact_245_image__subsetI,axiom,
% 0.26/0.62 ! [A: set_list_a,F: list_a > list_a,B2: set_list_a] :
% 0.26/0.62 ( ! [X6: list_a] :
% 0.26/0.62 ( ( member_list_a @ X6 @ A )
% 0.26/0.62 => ( member_list_a @ ( F @ X6 ) @ B2 ) )
% 0.26/0.62 => ( ord_le1301786372list_a @ ( image_list_a_list_a @ F @ A ) @ B2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % image_subsetI
% 0.26/0.62 thf(fact_246_bij__betw__def,axiom,
% 0.26/0.62 ( bij_betw_nat_nat
% 0.26/0.62 = ( ^ [F3: nat > nat,A4: set_nat,B3: set_nat] :
% 0.26/0.62 ( ( inj_on_nat_nat @ F3 @ A4 )
% 0.26/0.62 & ( ( image_nat_nat @ F3 @ A4 )
% 0.26/0.62 = B3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % bij_betw_def
% 0.26/0.62 thf(fact_247_bij__betw__imageI,axiom,
% 0.26/0.62 ! [F: nat > nat,A: set_nat,B2: set_nat] :
% 0.26/0.62 ( ( inj_on_nat_nat @ F @ A )
% 0.26/0.62 => ( ( ( image_nat_nat @ F @ A )
% 0.26/0.62 = B2 )
% 0.26/0.62 => ( bij_betw_nat_nat @ F @ A @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % bij_betw_imageI
% 0.26/0.62 thf(fact_248_inj__on__imp__bij__betw,axiom,
% 0.26/0.62 ! [F: nat > nat,A: set_nat] :
% 0.26/0.62 ( ( inj_on_nat_nat @ F @ A )
% 0.26/0.62 => ( bij_betw_nat_nat @ F @ A @ ( image_nat_nat @ F @ A ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % inj_on_imp_bij_betw
% 0.26/0.62 thf(fact_249_mbs_Ominimal,axiom,
% 0.26/0.62 ! [X4: list_a,A: set_list_a,P: list_a > $o] :
% 0.26/0.62 ( ( member_list_a @ X4 @ A )
% 0.26/0.62 => ( ( P @ X4 )
% 0.26/0.62 => ? [X6: list_a] :
% 0.26/0.62 ( ( member_list_a @ X6 @ A )
% 0.26/0.62 & ( ord_less_eq_nat @ ( size_size_list_a @ X6 ) @ ( size_size_list_a @ X4 ) )
% 0.26/0.62 & ( P @ X6 )
% 0.26/0.62 & ! [Xa: list_a] :
% 0.26/0.62 ( ( member_list_a @ Xa @ A )
% 0.26/0.62 => ( ( ord_less_nat @ ( size_size_list_a @ Xa ) @ ( size_size_list_a @ X6 ) )
% 0.26/0.62 => ~ ( P @ Xa ) ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mbs.minimal
% 0.26/0.62 thf(fact_250_mbs_Ominimal,axiom,
% 0.26/0.62 ! [X4: list_set_a,A: set_list_set_a,P: list_set_a > $o] :
% 0.26/0.62 ( ( member_list_set_a @ X4 @ A )
% 0.26/0.62 => ( ( P @ X4 )
% 0.26/0.62 => ? [X6: list_set_a] :
% 0.26/0.62 ( ( member_list_set_a @ X6 @ A )
% 0.26/0.62 & ( ord_less_eq_nat @ ( size_size_list_set_a @ X6 ) @ ( size_size_list_set_a @ X4 ) )
% 0.26/0.62 & ( P @ X6 )
% 0.26/0.62 & ! [Xa: list_set_a] :
% 0.26/0.62 ( ( member_list_set_a @ Xa @ A )
% 0.26/0.62 => ( ( ord_less_nat @ ( size_size_list_set_a @ Xa ) @ ( size_size_list_set_a @ X6 ) )
% 0.26/0.62 => ~ ( P @ Xa ) ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % mbs.minimal
% 0.26/0.62 thf(fact_251_bij__betw__subset,axiom,
% 0.26/0.62 ! [F: nat > nat,A: set_nat,A5: set_nat,B2: set_nat,B4: set_nat] :
% 0.26/0.62 ( ( bij_betw_nat_nat @ F @ A @ A5 )
% 0.26/0.62 => ( ( ord_less_eq_set_nat @ B2 @ A )
% 0.26/0.62 => ( ( ( image_nat_nat @ F @ B2 )
% 0.26/0.62 = B4 )
% 0.26/0.62 => ( bij_betw_nat_nat @ F @ B2 @ B4 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % bij_betw_subset
% 0.26/0.62 thf(fact_252_bij__betw__byWitness,axiom,
% 0.26/0.62 ! [A: set_nat,F4: nat > nat,F: nat > nat,A5: set_nat] :
% 0.26/0.62 ( ! [X6: nat] :
% 0.26/0.62 ( ( member_nat @ X6 @ A )
% 0.26/0.62 => ( ( F4 @ ( F @ X6 ) )
% 0.26/0.62 = X6 ) )
% 0.26/0.62 => ( ! [X6: nat] :
% 0.26/0.62 ( ( member_nat @ X6 @ A5 )
% 0.26/0.62 => ( ( F @ ( F4 @ X6 ) )
% 0.26/0.62 = X6 ) )
% 0.26/0.62 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A ) @ A5 )
% 0.26/0.62 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F4 @ A5 ) @ A )
% 0.26/0.62 => ( bij_betw_nat_nat @ F @ A @ A5 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % bij_betw_byWitness
% 0.26/0.62 thf(fact_253_image__inv__into__cancel,axiom,
% 0.26/0.62 ! [F: nat > nat,A: set_nat,A5: set_nat,B4: set_nat] :
% 0.26/0.62 ( ( ( image_nat_nat @ F @ A )
% 0.26/0.62 = A5 )
% 0.26/0.62 => ( ( ord_less_eq_set_nat @ B4 @ A5 )
% 0.26/0.62 => ( ( image_nat_nat @ F @ ( image_nat_nat @ ( hilber815131374at_nat @ A @ F ) @ B4 ) )
% 0.26/0.62 = B4 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % image_inv_into_cancel
% 0.26/0.62 thf(fact_254_listset__mono,axiom,
% 0.26/0.62 ! [Xs: list_set_a,Ys: list_set_a] :
% 0.26/0.62 ( ( ( size_size_list_set_a @ Xs )
% 0.26/0.62 = ( size_size_list_set_a @ Ys ) )
% 0.26/0.62 => ( ! [I3: nat] :
% 0.26/0.62 ( ( ord_less_nat @ I3 @ ( size_size_list_set_a @ Ys ) )
% 0.26/0.62 => ( ord_less_eq_set_a @ ( nth_set_a @ Xs @ I3 ) @ ( nth_set_a @ Ys @ I3 ) ) )
% 0.26/0.62 => ( ord_le1301786372list_a @ ( listset_a @ Xs ) @ ( listset_a @ Ys ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % listset_mono
% 0.26/0.62 thf(fact_255_nth__list__update,axiom,
% 0.26/0.62 ! [I: nat,Xs: list_a,J: nat,X4: a] :
% 0.26/0.62 ( ( ord_less_nat @ I @ ( size_size_list_a @ Xs ) )
% 0.26/0.62 => ( ( ( I = J )
% 0.26/0.62 => ( ( nth_a @ ( list_update_a @ Xs @ I @ X4 ) @ J )
% 0.26/0.62 = X4 ) )
% 0.26/0.62 & ( ( I != J )
% 0.26/0.62 => ( ( nth_a @ ( list_update_a @ Xs @ I @ X4 ) @ J )
% 0.26/0.62 = ( nth_a @ Xs @ J ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % nth_list_update
% 0.26/0.62 thf(fact_256_nth__list__update,axiom,
% 0.26/0.62 ! [I: nat,Xs: list_set_a,J: nat,X4: set_a] :
% 0.26/0.62 ( ( ord_less_nat @ I @ ( size_size_list_set_a @ Xs ) )
% 0.26/0.62 => ( ( ( I = J )
% 0.26/0.62 => ( ( nth_set_a @ ( list_update_set_a @ Xs @ I @ X4 ) @ J )
% 0.26/0.62 = X4 ) )
% 0.26/0.62 & ( ( I != J )
% 0.26/0.62 => ( ( nth_set_a @ ( list_update_set_a @ Xs @ I @ X4 ) @ J )
% 0.26/0.62 = ( nth_set_a @ Xs @ J ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % nth_list_update
% 0.26/0.62 thf(fact_257_list__update__same__conv,axiom,
% 0.26/0.62 ! [I: nat,Xs: list_a,X4: a] :
% 0.26/0.62 ( ( ord_less_nat @ I @ ( size_size_list_a @ Xs ) )
% 0.26/0.62 => ( ( ( list_update_a @ Xs @ I @ X4 )
% 0.26/0.62 = Xs )
% 0.26/0.62 = ( ( nth_a @ Xs @ I )
% 0.26/0.62 = X4 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % list_update_same_conv
% 0.26/0.62 thf(fact_258_list__update__same__conv,axiom,
% 0.26/0.62 ! [I: nat,Xs: list_set_a,X4: set_a] :
% 0.26/0.62 ( ( ord_less_nat @ I @ ( size_size_list_set_a @ Xs ) )
% 0.26/0.62 => ( ( ( list_update_set_a @ Xs @ I @ X4 )
% 0.26/0.62 = Xs )
% 0.26/0.62 = ( ( nth_set_a @ Xs @ I )
% 0.26/0.62 = X4 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % list_update_same_conv
% 0.26/0.62 thf(fact_259_bij__betw__inv__into__subset,axiom,
% 0.26/0.62 ! [F: nat > nat,A: set_nat,A5: set_nat,B2: set_nat,B4: set_nat] :
% 0.26/0.62 ( ( bij_betw_nat_nat @ F @ A @ A5 )
% 0.26/0.62 => ( ( ord_less_eq_set_nat @ B2 @ A )
% 0.26/0.62 => ( ( ( image_nat_nat @ F @ B2 )
% 0.26/0.62 = B4 )
% 0.26/0.62 => ( bij_betw_nat_nat @ ( hilber815131374at_nat @ A @ F ) @ B4 @ B2 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % bij_betw_inv_into_subset
% 0.26/0.62 thf(fact_260_direct__decompD_I2_J,axiom,
% 0.26/0.62 ! [A: set_a,Ss: list_set_a] :
% 0.26/0.62 ( ( hilber2037636820comp_a @ A @ Ss )
% 0.26/0.62 => ( inj_on_list_a_a @ groups1792256535list_a @ ( listset_a @ Ss ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % direct_decompD(2)
% 0.26/0.62 thf(fact_261_Schroeder__Bernstein,axiom,
% 0.26/0.62 ! [F: nat > nat,A: set_nat,B2: set_nat,G2: nat > nat] :
% 0.26/0.62 ( ( inj_on_nat_nat @ F @ A )
% 0.26/0.62 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A ) @ B2 )
% 0.26/0.62 => ( ( inj_on_nat_nat @ G2 @ B2 )
% 0.26/0.62 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ G2 @ B2 ) @ A )
% 0.26/0.62 => ? [H: nat > nat] : ( bij_betw_nat_nat @ H @ A @ B2 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % Schroeder_Bernstein
% 0.26/0.62 thf(fact_262_order__refl,axiom,
% 0.26/0.62 ! [X4: nat] : ( ord_less_eq_nat @ X4 @ X4 ) ).
% 0.26/0.62
% 0.26/0.62 % order_refl
% 0.26/0.62 thf(fact_263_minf_I8_J,axiom,
% 0.26/0.62 ! [T: nat] :
% 0.26/0.62 ? [Z2: nat] :
% 0.26/0.62 ! [X: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X @ Z2 )
% 0.26/0.62 => ~ ( ord_less_eq_nat @ T @ X ) ) ).
% 0.26/0.62
% 0.26/0.62 % minf(8)
% 0.26/0.62 thf(fact_264_minf_I6_J,axiom,
% 0.26/0.62 ! [T: nat] :
% 0.26/0.62 ? [Z2: nat] :
% 0.26/0.62 ! [X: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X @ Z2 )
% 0.26/0.62 => ( ord_less_eq_nat @ X @ T ) ) ).
% 0.26/0.62
% 0.26/0.62 % minf(6)
% 0.26/0.62 thf(fact_265_subsetI,axiom,
% 0.26/0.62 ! [A: set_a,B2: set_a] :
% 0.26/0.62 ( ! [X6: a] :
% 0.26/0.62 ( ( member_a @ X6 @ A )
% 0.26/0.62 => ( member_a @ X6 @ B2 ) )
% 0.26/0.62 => ( ord_less_eq_set_a @ A @ B2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % subsetI
% 0.26/0.62 thf(fact_266_subsetI,axiom,
% 0.26/0.62 ! [A: set_list_a,B2: set_list_a] :
% 0.26/0.62 ( ! [X6: list_a] :
% 0.26/0.62 ( ( member_list_a @ X6 @ A )
% 0.26/0.62 => ( member_list_a @ X6 @ B2 ) )
% 0.26/0.62 => ( ord_le1301786372list_a @ A @ B2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % subsetI
% 0.26/0.62 thf(fact_267_bounded__Max__nat,axiom,
% 0.26/0.62 ! [P: nat > $o,X4: nat,M3: nat] :
% 0.26/0.62 ( ( P @ X4 )
% 0.26/0.62 => ( ! [X6: nat] :
% 0.26/0.62 ( ( P @ X6 )
% 0.26/0.62 => ( ord_less_eq_nat @ X6 @ M3 ) )
% 0.26/0.62 => ~ ! [M4: nat] :
% 0.26/0.62 ( ( P @ M4 )
% 0.26/0.62 => ~ ! [X: nat] :
% 0.26/0.62 ( ( P @ X )
% 0.26/0.62 => ( ord_less_eq_nat @ X @ M4 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % bounded_Max_nat
% 0.26/0.62 thf(fact_268_subset__iff,axiom,
% 0.26/0.62 ( ord_less_eq_set_a
% 0.26/0.62 = ( ^ [A4: set_a,B3: set_a] :
% 0.26/0.62 ! [T2: a] :
% 0.26/0.62 ( ( member_a @ T2 @ A4 )
% 0.26/0.62 => ( member_a @ T2 @ B3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_iff
% 0.26/0.62 thf(fact_269_subset__iff,axiom,
% 0.26/0.62 ( ord_le1301786372list_a
% 0.26/0.62 = ( ^ [A4: set_list_a,B3: set_list_a] :
% 0.26/0.62 ! [T2: list_a] :
% 0.26/0.62 ( ( member_list_a @ T2 @ A4 )
% 0.26/0.62 => ( member_list_a @ T2 @ B3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_iff
% 0.26/0.62 thf(fact_270_subset__eq,axiom,
% 0.26/0.62 ( ord_less_eq_set_a
% 0.26/0.62 = ( ^ [A4: set_a,B3: set_a] :
% 0.26/0.62 ! [X5: a] :
% 0.26/0.62 ( ( member_a @ X5 @ A4 )
% 0.26/0.62 => ( member_a @ X5 @ B3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_eq
% 0.26/0.62 thf(fact_271_subset__eq,axiom,
% 0.26/0.62 ( ord_le1301786372list_a
% 0.26/0.62 = ( ^ [A4: set_list_a,B3: set_list_a] :
% 0.26/0.62 ! [X5: list_a] :
% 0.26/0.62 ( ( member_list_a @ X5 @ A4 )
% 0.26/0.62 => ( member_list_a @ X5 @ B3 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subset_eq
% 0.26/0.62 thf(fact_272_subsetD,axiom,
% 0.26/0.62 ! [A: set_a,B2: set_a,C: a] :
% 0.26/0.62 ( ( ord_less_eq_set_a @ A @ B2 )
% 0.26/0.62 => ( ( member_a @ C @ A )
% 0.26/0.62 => ( member_a @ C @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subsetD
% 0.26/0.62 thf(fact_273_subsetD,axiom,
% 0.26/0.62 ! [A: set_list_a,B2: set_list_a,C: list_a] :
% 0.26/0.62 ( ( ord_le1301786372list_a @ A @ B2 )
% 0.26/0.62 => ( ( member_list_a @ C @ A )
% 0.26/0.62 => ( member_list_a @ C @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % subsetD
% 0.26/0.62 thf(fact_274_in__mono,axiom,
% 0.26/0.62 ! [A: set_a,B2: set_a,X4: a] :
% 0.26/0.62 ( ( ord_less_eq_set_a @ A @ B2 )
% 0.26/0.62 => ( ( member_a @ X4 @ A )
% 0.26/0.62 => ( member_a @ X4 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_mono
% 0.26/0.62 thf(fact_275_in__mono,axiom,
% 0.26/0.62 ! [A: set_list_a,B2: set_list_a,X4: list_a] :
% 0.26/0.62 ( ( ord_le1301786372list_a @ A @ B2 )
% 0.26/0.62 => ( ( member_list_a @ X4 @ A )
% 0.26/0.62 => ( member_list_a @ X4 @ B2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % in_mono
% 0.26/0.62 thf(fact_276_dual__order_Oantisym,axiom,
% 0.26/0.62 ! [B: nat,A2: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ B @ A2 )
% 0.26/0.62 => ( ( ord_less_eq_nat @ A2 @ B )
% 0.26/0.62 => ( A2 = B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % dual_order.antisym
% 0.26/0.62 thf(fact_277_dual__order_Oeq__iff,axiom,
% 0.26/0.62 ( ( ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
% 0.26/0.62 = ( ^ [A7: nat,B5: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ B5 @ A7 )
% 0.26/0.62 & ( ord_less_eq_nat @ A7 @ B5 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % dual_order.eq_iff
% 0.26/0.62 thf(fact_278_dual__order_Otrans,axiom,
% 0.26/0.62 ! [B: nat,A2: nat,C: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ B @ A2 )
% 0.26/0.62 => ( ( ord_less_eq_nat @ C @ B )
% 0.26/0.62 => ( ord_less_eq_nat @ C @ A2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % dual_order.trans
% 0.26/0.62 thf(fact_279_linorder__wlog,axiom,
% 0.26/0.62 ! [P: nat > nat > $o,A2: nat,B: nat] :
% 0.26/0.62 ( ! [A3: nat,B6: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ A3 @ B6 )
% 0.26/0.62 => ( P @ A3 @ B6 ) )
% 0.26/0.62 => ( ! [A3: nat,B6: nat] :
% 0.26/0.62 ( ( P @ B6 @ A3 )
% 0.26/0.62 => ( P @ A3 @ B6 ) )
% 0.26/0.62 => ( P @ A2 @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % linorder_wlog
% 0.26/0.62 thf(fact_280_dual__order_Orefl,axiom,
% 0.26/0.62 ! [A2: nat] : ( ord_less_eq_nat @ A2 @ A2 ) ).
% 0.26/0.62
% 0.26/0.62 % dual_order.refl
% 0.26/0.62 thf(fact_281_order__trans,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat,Z3: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.26/0.62 => ( ( ord_less_eq_nat @ Y3 @ Z3 )
% 0.26/0.62 => ( ord_less_eq_nat @ X4 @ Z3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % order_trans
% 0.26/0.62 thf(fact_282_order__class_Oorder_Oantisym,axiom,
% 0.26/0.62 ! [A2: nat,B: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ A2 @ B )
% 0.26/0.62 => ( ( ord_less_eq_nat @ B @ A2 )
% 0.26/0.62 => ( A2 = B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % order_class.order.antisym
% 0.26/0.62 thf(fact_283_ord__le__eq__trans,axiom,
% 0.26/0.62 ! [A2: nat,B: nat,C: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ A2 @ B )
% 0.26/0.62 => ( ( B = C )
% 0.26/0.62 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ord_le_eq_trans
% 0.26/0.62 thf(fact_284_ord__eq__le__trans,axiom,
% 0.26/0.62 ! [A2: nat,B: nat,C: nat] :
% 0.26/0.62 ( ( A2 = B )
% 0.26/0.62 => ( ( ord_less_eq_nat @ B @ C )
% 0.26/0.62 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ord_eq_le_trans
% 0.26/0.62 thf(fact_285_order__class_Oorder_Oeq__iff,axiom,
% 0.26/0.62 ( ( ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
% 0.26/0.62 = ( ^ [A7: nat,B5: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ A7 @ B5 )
% 0.26/0.62 & ( ord_less_eq_nat @ B5 @ A7 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % order_class.order.eq_iff
% 0.26/0.62 thf(fact_286_antisym__conv,axiom,
% 0.26/0.62 ! [Y3: nat,X4: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ Y3 @ X4 )
% 0.26/0.62 => ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.26/0.62 = ( X4 = Y3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % antisym_conv
% 0.26/0.62 thf(fact_287_le__cases3,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat,Z3: nat] :
% 0.26/0.62 ( ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.26/0.62 => ~ ( ord_less_eq_nat @ Y3 @ Z3 ) )
% 0.26/0.62 => ( ( ( ord_less_eq_nat @ Y3 @ X4 )
% 0.26/0.62 => ~ ( ord_less_eq_nat @ X4 @ Z3 ) )
% 0.26/0.62 => ( ( ( ord_less_eq_nat @ X4 @ Z3 )
% 0.26/0.62 => ~ ( ord_less_eq_nat @ Z3 @ Y3 ) )
% 0.26/0.62 => ( ( ( ord_less_eq_nat @ Z3 @ Y3 )
% 0.26/0.62 => ~ ( ord_less_eq_nat @ Y3 @ X4 ) )
% 0.26/0.62 => ( ( ( ord_less_eq_nat @ Y3 @ Z3 )
% 0.26/0.62 => ~ ( ord_less_eq_nat @ Z3 @ X4 ) )
% 0.26/0.62 => ~ ( ( ord_less_eq_nat @ Z3 @ X4 )
% 0.26/0.62 => ~ ( ord_less_eq_nat @ X4 @ Y3 ) ) ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % le_cases3
% 0.26/0.62 thf(fact_288_order_Otrans,axiom,
% 0.26/0.62 ! [A2: nat,B: nat,C: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ A2 @ B )
% 0.26/0.62 => ( ( ord_less_eq_nat @ B @ C )
% 0.26/0.62 => ( ord_less_eq_nat @ A2 @ C ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % order.trans
% 0.26/0.62 thf(fact_289_le__cases,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat] :
% 0.26/0.62 ( ~ ( ord_less_eq_nat @ X4 @ Y3 )
% 0.26/0.62 => ( ord_less_eq_nat @ Y3 @ X4 ) ) ).
% 0.26/0.62
% 0.26/0.62 % le_cases
% 0.26/0.62 thf(fact_290_eq__refl,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat] :
% 0.26/0.62 ( ( X4 = Y3 )
% 0.26/0.62 => ( ord_less_eq_nat @ X4 @ Y3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % eq_refl
% 0.26/0.62 thf(fact_291_linear,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.26/0.62 | ( ord_less_eq_nat @ Y3 @ X4 ) ) ).
% 0.26/0.62
% 0.26/0.62 % linear
% 0.26/0.62 thf(fact_292_antisym,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.26/0.62 => ( ( ord_less_eq_nat @ Y3 @ X4 )
% 0.26/0.62 => ( X4 = Y3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % antisym
% 0.26/0.62 thf(fact_293_le__rel__bool__arg__iff,axiom,
% 0.26/0.62 ( ord_less_eq_o_nat
% 0.26/0.62 = ( ^ [X7: $o > nat,Y4: $o > nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ ( X7 @ $false ) @ ( Y4 @ $false ) )
% 0.26/0.62 & ( ord_less_eq_nat @ ( X7 @ $true ) @ ( Y4 @ $true ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % le_rel_bool_arg_iff
% 0.26/0.62 thf(fact_294_eq__iff,axiom,
% 0.26/0.62 ( ( ^ [Y2: nat,Z: nat] : ( Y2 = Z ) )
% 0.26/0.62 = ( ^ [X5: nat,Y5: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ X5 @ Y5 )
% 0.26/0.62 & ( ord_less_eq_nat @ Y5 @ X5 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % eq_iff
% 0.26/0.62 thf(fact_295_ord__le__eq__subst,axiom,
% 0.26/0.62 ! [A2: nat,B: nat,F: nat > nat,C: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ A2 @ B )
% 0.26/0.62 => ( ( ( F @ B )
% 0.26/0.62 = C )
% 0.26/0.62 => ( ! [X6: nat,Y: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ X6 @ Y )
% 0.26/0.62 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y ) ) )
% 0.26/0.62 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ord_le_eq_subst
% 0.26/0.62 thf(fact_296_ord__eq__le__subst,axiom,
% 0.26/0.62 ! [A2: nat,F: nat > nat,B: nat,C: nat] :
% 0.26/0.62 ( ( A2
% 0.26/0.62 = ( F @ B ) )
% 0.26/0.62 => ( ( ord_less_eq_nat @ B @ C )
% 0.26/0.62 => ( ! [X6: nat,Y: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ X6 @ Y )
% 0.26/0.62 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y ) ) )
% 0.26/0.62 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ord_eq_le_subst
% 0.26/0.62 thf(fact_297_order__subst2,axiom,
% 0.26/0.62 ! [A2: nat,B: nat,F: nat > nat,C: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ A2 @ B )
% 0.26/0.62 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.26/0.62 => ( ! [X6: nat,Y: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ X6 @ Y )
% 0.26/0.62 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y ) ) )
% 0.26/0.62 => ( ord_less_eq_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % order_subst2
% 0.26/0.62 thf(fact_298_order__subst1,axiom,
% 0.26/0.62 ! [A2: nat,F: nat > nat,B: nat,C: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ A2 @ ( F @ B ) )
% 0.26/0.62 => ( ( ord_less_eq_nat @ B @ C )
% 0.26/0.62 => ( ! [X6: nat,Y: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ X6 @ Y )
% 0.26/0.62 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y ) ) )
% 0.26/0.62 => ( ord_less_eq_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % order_subst1
% 0.26/0.62 thf(fact_299_dual__order_Ostrict__implies__not__eq,axiom,
% 0.26/0.62 ! [B: nat,A2: nat] :
% 0.26/0.62 ( ( ord_less_nat @ B @ A2 )
% 0.26/0.62 => ( A2 != B ) ) ).
% 0.26/0.62
% 0.26/0.62 % dual_order.strict_implies_not_eq
% 0.26/0.62 thf(fact_300_order_Ostrict__implies__not__eq,axiom,
% 0.26/0.62 ! [A2: nat,B: nat] :
% 0.26/0.62 ( ( ord_less_nat @ A2 @ B )
% 0.26/0.62 => ( A2 != B ) ) ).
% 0.26/0.62
% 0.26/0.62 % order.strict_implies_not_eq
% 0.26/0.62 thf(fact_301_not__less__iff__gr__or__eq,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat] :
% 0.26/0.62 ( ( ~ ( ord_less_nat @ X4 @ Y3 ) )
% 0.26/0.62 = ( ( ord_less_nat @ Y3 @ X4 )
% 0.26/0.62 | ( X4 = Y3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % not_less_iff_gr_or_eq
% 0.26/0.62 thf(fact_302_dual__order_Ostrict__trans,axiom,
% 0.26/0.62 ! [B: nat,A2: nat,C: nat] :
% 0.26/0.62 ( ( ord_less_nat @ B @ A2 )
% 0.26/0.62 => ( ( ord_less_nat @ C @ B )
% 0.26/0.62 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % dual_order.strict_trans
% 0.26/0.62 thf(fact_303_linorder__less__wlog,axiom,
% 0.26/0.62 ! [P: nat > nat > $o,A2: nat,B: nat] :
% 0.26/0.62 ( ! [A3: nat,B6: nat] :
% 0.26/0.62 ( ( ord_less_nat @ A3 @ B6 )
% 0.26/0.62 => ( P @ A3 @ B6 ) )
% 0.26/0.62 => ( ! [A3: nat] : ( P @ A3 @ A3 )
% 0.26/0.62 => ( ! [A3: nat,B6: nat] :
% 0.26/0.62 ( ( P @ B6 @ A3 )
% 0.26/0.62 => ( P @ A3 @ B6 ) )
% 0.26/0.62 => ( P @ A2 @ B ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % linorder_less_wlog
% 0.26/0.62 thf(fact_304_exists__least__iff,axiom,
% 0.26/0.62 ( ( ^ [P3: nat > $o] :
% 0.26/0.62 ? [X3: nat] : ( P3 @ X3 ) )
% 0.26/0.62 = ( ^ [P2: nat > $o] :
% 0.26/0.62 ? [N2: nat] :
% 0.26/0.62 ( ( P2 @ N2 )
% 0.26/0.62 & ! [M5: nat] :
% 0.26/0.62 ( ( ord_less_nat @ M5 @ N2 )
% 0.26/0.62 => ~ ( P2 @ M5 ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % exists_least_iff
% 0.26/0.62 thf(fact_305_less__imp__not__less,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X4 @ Y3 )
% 0.26/0.62 => ~ ( ord_less_nat @ Y3 @ X4 ) ) ).
% 0.26/0.62
% 0.26/0.62 % less_imp_not_less
% 0.26/0.62 thf(fact_306_order_Ostrict__trans,axiom,
% 0.26/0.62 ! [A2: nat,B: nat,C: nat] :
% 0.26/0.62 ( ( ord_less_nat @ A2 @ B )
% 0.26/0.62 => ( ( ord_less_nat @ B @ C )
% 0.26/0.62 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % order.strict_trans
% 0.26/0.62 thf(fact_307_dual__order_Oirrefl,axiom,
% 0.26/0.62 ! [A2: nat] :
% 0.26/0.62 ~ ( ord_less_nat @ A2 @ A2 ) ).
% 0.26/0.62
% 0.26/0.62 % dual_order.irrefl
% 0.26/0.62 thf(fact_308_linorder__cases,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat] :
% 0.26/0.62 ( ~ ( ord_less_nat @ X4 @ Y3 )
% 0.26/0.62 => ( ( X4 != Y3 )
% 0.26/0.62 => ( ord_less_nat @ Y3 @ X4 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % linorder_cases
% 0.26/0.62 thf(fact_309_less__imp__triv,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat,P: $o] :
% 0.26/0.62 ( ( ord_less_nat @ X4 @ Y3 )
% 0.26/0.62 => ( ( ord_less_nat @ Y3 @ X4 )
% 0.26/0.62 => P ) ) ).
% 0.26/0.62
% 0.26/0.62 % less_imp_triv
% 0.26/0.62 thf(fact_310_less__imp__not__eq2,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X4 @ Y3 )
% 0.26/0.62 => ( Y3 != X4 ) ) ).
% 0.26/0.62
% 0.26/0.62 % less_imp_not_eq2
% 0.26/0.62 thf(fact_311_antisym__conv3,axiom,
% 0.26/0.62 ! [Y3: nat,X4: nat] :
% 0.26/0.62 ( ~ ( ord_less_nat @ Y3 @ X4 )
% 0.26/0.62 => ( ( ~ ( ord_less_nat @ X4 @ Y3 ) )
% 0.26/0.62 = ( X4 = Y3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % antisym_conv3
% 0.26/0.62 thf(fact_312_less__induct,axiom,
% 0.26/0.62 ! [P: nat > $o,A2: nat] :
% 0.26/0.62 ( ! [X6: nat] :
% 0.26/0.62 ( ! [Y6: nat] :
% 0.26/0.62 ( ( ord_less_nat @ Y6 @ X6 )
% 0.26/0.62 => ( P @ Y6 ) )
% 0.26/0.62 => ( P @ X6 ) )
% 0.26/0.62 => ( P @ A2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % less_induct
% 0.26/0.62 thf(fact_313_less__not__sym,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X4 @ Y3 )
% 0.26/0.62 => ~ ( ord_less_nat @ Y3 @ X4 ) ) ).
% 0.26/0.62
% 0.26/0.62 % less_not_sym
% 0.26/0.62 thf(fact_314_less__imp__not__eq,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X4 @ Y3 )
% 0.26/0.62 => ( X4 != Y3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % less_imp_not_eq
% 0.26/0.62 thf(fact_315_dual__order_Oasym,axiom,
% 0.26/0.62 ! [B: nat,A2: nat] :
% 0.26/0.62 ( ( ord_less_nat @ B @ A2 )
% 0.26/0.62 => ~ ( ord_less_nat @ A2 @ B ) ) ).
% 0.26/0.62
% 0.26/0.62 % dual_order.asym
% 0.26/0.62 thf(fact_316_ord__less__eq__trans,axiom,
% 0.26/0.62 ! [A2: nat,B: nat,C: nat] :
% 0.26/0.62 ( ( ord_less_nat @ A2 @ B )
% 0.26/0.62 => ( ( B = C )
% 0.26/0.62 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ord_less_eq_trans
% 0.26/0.62 thf(fact_317_ord__eq__less__trans,axiom,
% 0.26/0.62 ! [A2: nat,B: nat,C: nat] :
% 0.26/0.62 ( ( A2 = B )
% 0.26/0.62 => ( ( ord_less_nat @ B @ C )
% 0.26/0.62 => ( ord_less_nat @ A2 @ C ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ord_eq_less_trans
% 0.26/0.62 thf(fact_318_less__irrefl,axiom,
% 0.26/0.62 ! [X4: nat] :
% 0.26/0.62 ~ ( ord_less_nat @ X4 @ X4 ) ).
% 0.26/0.62
% 0.26/0.62 % less_irrefl
% 0.26/0.62 thf(fact_319_less__linear,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X4 @ Y3 )
% 0.26/0.62 | ( X4 = Y3 )
% 0.26/0.62 | ( ord_less_nat @ Y3 @ X4 ) ) ).
% 0.26/0.62
% 0.26/0.62 % less_linear
% 0.26/0.62 thf(fact_320_less__trans,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat,Z3: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X4 @ Y3 )
% 0.26/0.62 => ( ( ord_less_nat @ Y3 @ Z3 )
% 0.26/0.62 => ( ord_less_nat @ X4 @ Z3 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % less_trans
% 0.26/0.62 thf(fact_321_less__asym_H,axiom,
% 0.26/0.62 ! [A2: nat,B: nat] :
% 0.26/0.62 ( ( ord_less_nat @ A2 @ B )
% 0.26/0.62 => ~ ( ord_less_nat @ B @ A2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % less_asym'
% 0.26/0.62 thf(fact_322_less__asym,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X4 @ Y3 )
% 0.26/0.62 => ~ ( ord_less_nat @ Y3 @ X4 ) ) ).
% 0.26/0.62
% 0.26/0.62 % less_asym
% 0.26/0.62 thf(fact_323_less__imp__neq,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X4 @ Y3 )
% 0.26/0.62 => ( X4 != Y3 ) ) ).
% 0.26/0.62
% 0.26/0.62 % less_imp_neq
% 0.26/0.62 thf(fact_324_order_Oasym,axiom,
% 0.26/0.62 ! [A2: nat,B: nat] :
% 0.26/0.62 ( ( ord_less_nat @ A2 @ B )
% 0.26/0.62 => ~ ( ord_less_nat @ B @ A2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % order.asym
% 0.26/0.62 thf(fact_325_neq__iff,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat] :
% 0.26/0.62 ( ( X4 != Y3 )
% 0.26/0.62 = ( ( ord_less_nat @ X4 @ Y3 )
% 0.26/0.62 | ( ord_less_nat @ Y3 @ X4 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % neq_iff
% 0.26/0.62 thf(fact_326_neqE,axiom,
% 0.26/0.62 ! [X4: nat,Y3: nat] :
% 0.26/0.62 ( ( X4 != Y3 )
% 0.26/0.62 => ( ~ ( ord_less_nat @ X4 @ Y3 )
% 0.26/0.62 => ( ord_less_nat @ Y3 @ X4 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % neqE
% 0.26/0.62 thf(fact_327_gt__ex,axiom,
% 0.26/0.62 ! [X4: nat] :
% 0.26/0.62 ? [X_1: nat] : ( ord_less_nat @ X4 @ X_1 ) ).
% 0.26/0.62
% 0.26/0.62 % gt_ex
% 0.26/0.62 thf(fact_328_order__less__subst2,axiom,
% 0.26/0.62 ! [A2: nat,B: nat,F: nat > nat,C: nat] :
% 0.26/0.62 ( ( ord_less_nat @ A2 @ B )
% 0.26/0.62 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.26/0.62 => ( ! [X6: nat,Y: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X6 @ Y )
% 0.26/0.62 => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y ) ) )
% 0.26/0.62 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % order_less_subst2
% 0.26/0.62 thf(fact_329_order__less__subst1,axiom,
% 0.26/0.62 ! [A2: nat,F: nat > nat,B: nat,C: nat] :
% 0.26/0.62 ( ( ord_less_nat @ A2 @ ( F @ B ) )
% 0.26/0.62 => ( ( ord_less_nat @ B @ C )
% 0.26/0.62 => ( ! [X6: nat,Y: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X6 @ Y )
% 0.26/0.62 => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y ) ) )
% 0.26/0.62 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % order_less_subst1
% 0.26/0.62 thf(fact_330_ord__less__eq__subst,axiom,
% 0.26/0.62 ! [A2: nat,B: nat,F: nat > nat,C: nat] :
% 0.26/0.62 ( ( ord_less_nat @ A2 @ B )
% 0.26/0.62 => ( ( ( F @ B )
% 0.26/0.62 = C )
% 0.26/0.62 => ( ! [X6: nat,Y: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X6 @ Y )
% 0.26/0.62 => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y ) ) )
% 0.26/0.62 => ( ord_less_nat @ ( F @ A2 ) @ C ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ord_less_eq_subst
% 0.26/0.62 thf(fact_331_ord__eq__less__subst,axiom,
% 0.26/0.62 ! [A2: nat,F: nat > nat,B: nat,C: nat] :
% 0.26/0.62 ( ( A2
% 0.26/0.62 = ( F @ B ) )
% 0.26/0.62 => ( ( ord_less_nat @ B @ C )
% 0.26/0.62 => ( ! [X6: nat,Y: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X6 @ Y )
% 0.26/0.62 => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y ) ) )
% 0.26/0.62 => ( ord_less_nat @ A2 @ ( F @ C ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % ord_eq_less_subst
% 0.26/0.62 thf(fact_332_pinf_I1_J,axiom,
% 0.26/0.62 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.26/0.62 ( ? [Z4: nat] :
% 0.26/0.62 ! [X6: nat] :
% 0.26/0.62 ( ( ord_less_nat @ Z4 @ X6 )
% 0.26/0.62 => ( ( P @ X6 )
% 0.26/0.62 = ( P4 @ X6 ) ) )
% 0.26/0.62 => ( ? [Z4: nat] :
% 0.26/0.62 ! [X6: nat] :
% 0.26/0.62 ( ( ord_less_nat @ Z4 @ X6 )
% 0.26/0.62 => ( ( Q @ X6 )
% 0.26/0.62 = ( Q2 @ X6 ) ) )
% 0.26/0.62 => ? [Z2: nat] :
% 0.26/0.62 ! [X: nat] :
% 0.26/0.62 ( ( ord_less_nat @ Z2 @ X )
% 0.26/0.62 => ( ( ( P @ X )
% 0.26/0.62 & ( Q @ X ) )
% 0.26/0.62 = ( ( P4 @ X )
% 0.26/0.62 & ( Q2 @ X ) ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % pinf(1)
% 0.26/0.62 thf(fact_333_pinf_I2_J,axiom,
% 0.26/0.62 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.26/0.62 ( ? [Z4: nat] :
% 0.26/0.62 ! [X6: nat] :
% 0.26/0.62 ( ( ord_less_nat @ Z4 @ X6 )
% 0.26/0.62 => ( ( P @ X6 )
% 0.26/0.62 = ( P4 @ X6 ) ) )
% 0.26/0.62 => ( ? [Z4: nat] :
% 0.26/0.62 ! [X6: nat] :
% 0.26/0.62 ( ( ord_less_nat @ Z4 @ X6 )
% 0.26/0.62 => ( ( Q @ X6 )
% 0.26/0.62 = ( Q2 @ X6 ) ) )
% 0.26/0.62 => ? [Z2: nat] :
% 0.26/0.62 ! [X: nat] :
% 0.26/0.62 ( ( ord_less_nat @ Z2 @ X )
% 0.26/0.62 => ( ( ( P @ X )
% 0.26/0.62 | ( Q @ X ) )
% 0.26/0.62 = ( ( P4 @ X )
% 0.26/0.62 | ( Q2 @ X ) ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % pinf(2)
% 0.26/0.62 thf(fact_334_pinf_I3_J,axiom,
% 0.26/0.62 ! [T: nat] :
% 0.26/0.62 ? [Z2: nat] :
% 0.26/0.62 ! [X: nat] :
% 0.26/0.62 ( ( ord_less_nat @ Z2 @ X )
% 0.26/0.62 => ( X != T ) ) ).
% 0.26/0.62
% 0.26/0.62 % pinf(3)
% 0.26/0.62 thf(fact_335_pinf_I4_J,axiom,
% 0.26/0.62 ! [T: nat] :
% 0.26/0.62 ? [Z2: nat] :
% 0.26/0.62 ! [X: nat] :
% 0.26/0.62 ( ( ord_less_nat @ Z2 @ X )
% 0.26/0.62 => ( X != T ) ) ).
% 0.26/0.62
% 0.26/0.62 % pinf(4)
% 0.26/0.62 thf(fact_336_pinf_I5_J,axiom,
% 0.26/0.62 ! [T: nat] :
% 0.26/0.62 ? [Z2: nat] :
% 0.26/0.62 ! [X: nat] :
% 0.26/0.62 ( ( ord_less_nat @ Z2 @ X )
% 0.26/0.62 => ~ ( ord_less_nat @ X @ T ) ) ).
% 0.26/0.62
% 0.26/0.62 % pinf(5)
% 0.26/0.62 thf(fact_337_pinf_I7_J,axiom,
% 0.26/0.62 ! [T: nat] :
% 0.26/0.62 ? [Z2: nat] :
% 0.26/0.62 ! [X: nat] :
% 0.26/0.62 ( ( ord_less_nat @ Z2 @ X )
% 0.26/0.62 => ( ord_less_nat @ T @ X ) ) ).
% 0.26/0.62
% 0.26/0.62 % pinf(7)
% 0.26/0.62 thf(fact_338_minf_I1_J,axiom,
% 0.26/0.62 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.26/0.62 ( ? [Z4: nat] :
% 0.26/0.62 ! [X6: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X6 @ Z4 )
% 0.26/0.62 => ( ( P @ X6 )
% 0.26/0.62 = ( P4 @ X6 ) ) )
% 0.26/0.62 => ( ? [Z4: nat] :
% 0.26/0.62 ! [X6: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X6 @ Z4 )
% 0.26/0.62 => ( ( Q @ X6 )
% 0.26/0.62 = ( Q2 @ X6 ) ) )
% 0.26/0.62 => ? [Z2: nat] :
% 0.26/0.62 ! [X: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X @ Z2 )
% 0.26/0.62 => ( ( ( P @ X )
% 0.26/0.62 & ( Q @ X ) )
% 0.26/0.62 = ( ( P4 @ X )
% 0.26/0.62 & ( Q2 @ X ) ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % minf(1)
% 0.26/0.62 thf(fact_339_minf_I2_J,axiom,
% 0.26/0.62 ! [P: nat > $o,P4: nat > $o,Q: nat > $o,Q2: nat > $o] :
% 0.26/0.62 ( ? [Z4: nat] :
% 0.26/0.62 ! [X6: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X6 @ Z4 )
% 0.26/0.62 => ( ( P @ X6 )
% 0.26/0.62 = ( P4 @ X6 ) ) )
% 0.26/0.62 => ( ? [Z4: nat] :
% 0.26/0.62 ! [X6: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X6 @ Z4 )
% 0.26/0.62 => ( ( Q @ X6 )
% 0.26/0.62 = ( Q2 @ X6 ) ) )
% 0.26/0.62 => ? [Z2: nat] :
% 0.26/0.62 ! [X: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X @ Z2 )
% 0.26/0.62 => ( ( ( P @ X )
% 0.26/0.62 | ( Q @ X ) )
% 0.26/0.62 = ( ( P4 @ X )
% 0.26/0.62 | ( Q2 @ X ) ) ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % minf(2)
% 0.26/0.62 thf(fact_340_minf_I3_J,axiom,
% 0.26/0.62 ! [T: nat] :
% 0.26/0.62 ? [Z2: nat] :
% 0.26/0.62 ! [X: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X @ Z2 )
% 0.26/0.62 => ( X != T ) ) ).
% 0.26/0.62
% 0.26/0.62 % minf(3)
% 0.26/0.62 thf(fact_341_minf_I4_J,axiom,
% 0.26/0.62 ! [T: nat] :
% 0.26/0.62 ? [Z2: nat] :
% 0.26/0.62 ! [X: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X @ Z2 )
% 0.26/0.62 => ( X != T ) ) ).
% 0.26/0.62
% 0.26/0.62 % minf(4)
% 0.26/0.62 thf(fact_342_minf_I5_J,axiom,
% 0.26/0.62 ! [T: nat] :
% 0.26/0.62 ? [Z2: nat] :
% 0.26/0.62 ! [X: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X @ Z2 )
% 0.26/0.62 => ( ord_less_nat @ X @ T ) ) ).
% 0.26/0.62
% 0.26/0.62 % minf(5)
% 0.26/0.62 thf(fact_343_minf_I7_J,axiom,
% 0.26/0.62 ! [T: nat] :
% 0.26/0.62 ? [Z2: nat] :
% 0.26/0.62 ! [X: nat] :
% 0.26/0.62 ( ( ord_less_nat @ X @ Z2 )
% 0.26/0.62 => ~ ( ord_less_nat @ T @ X ) ) ).
% 0.26/0.62
% 0.26/0.62 % minf(7)
% 0.26/0.62 thf(fact_344_order_Onot__eq__order__implies__strict,axiom,
% 0.26/0.62 ! [A2: nat,B: nat] :
% 0.26/0.62 ( ( A2 != B )
% 0.26/0.62 => ( ( ord_less_eq_nat @ A2 @ B )
% 0.26/0.62 => ( ord_less_nat @ A2 @ B ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % order.not_eq_order_implies_strict
% 0.26/0.62 thf(fact_345_dual__order_Ostrict__implies__order,axiom,
% 0.26/0.62 ! [B: nat,A2: nat] :
% 0.26/0.62 ( ( ord_less_nat @ B @ A2 )
% 0.26/0.62 => ( ord_less_eq_nat @ B @ A2 ) ) ).
% 0.26/0.62
% 0.26/0.62 % dual_order.strict_implies_order
% 0.26/0.62 thf(fact_346_dual__order_Ostrict__iff__order,axiom,
% 0.26/0.62 ( ord_less_nat
% 0.26/0.62 = ( ^ [B5: nat,A7: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ B5 @ A7 )
% 0.26/0.62 & ( A7 != B5 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % dual_order.strict_iff_order
% 0.26/0.62 thf(fact_347_dual__order_Oorder__iff__strict,axiom,
% 0.26/0.62 ( ord_less_eq_nat
% 0.26/0.62 = ( ^ [B5: nat,A7: nat] :
% 0.26/0.62 ( ( ord_less_nat @ B5 @ A7 )
% 0.26/0.62 | ( A7 = B5 ) ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % dual_order.order_iff_strict
% 0.26/0.62 thf(fact_348_order_Ostrict__implies__order,axiom,
% 0.26/0.62 ! [A2: nat,B: nat] :
% 0.26/0.62 ( ( ord_less_nat @ A2 @ B )
% 0.26/0.62 => ( ord_less_eq_nat @ A2 @ B ) ) ).
% 0.26/0.62
% 0.26/0.62 % order.strict_implies_order
% 0.26/0.62 thf(fact_349_dual__order_Ostrict__trans2,axiom,
% 0.26/0.62 ! [B: nat,A2: nat,C: nat] :
% 0.26/0.62 ( ( ord_less_nat @ B @ A2 )
% 0.26/0.62 => ( ( ord_less_eq_nat @ C @ B )
% 0.26/0.62 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % dual_order.strict_trans2
% 0.26/0.62 thf(fact_350_dual__order_Ostrict__trans1,axiom,
% 0.26/0.62 ! [B: nat,A2: nat,C: nat] :
% 0.26/0.62 ( ( ord_less_eq_nat @ B @ A2 )
% 0.26/0.62 => ( ( ord_less_nat @ C @ B )
% 0.26/0.62 => ( ord_less_nat @ C @ A2 ) ) ) ).
% 0.26/0.62
% 0.26/0.62 % dual_order.strict_trans1
% 0.26/0.70 thf(fact_351_order_Ostrict__iff__order,axiom,
% 0.26/0.70 ( ord_less_nat
% 0.26/0.70 = ( ^ [A7: nat,B5: nat] :
% 0.26/0.70 ( ( ord_less_eq_nat @ A7 @ B5 )
% 0.26/0.70 & ( A7 != B5 ) ) ) ) ).
% 0.26/0.70
% 0.26/0.70 % order.strict_iff_order
% 0.26/0.70 thf(fact_352_order_Oorder__iff__strict,axiom,
% 0.26/0.70 ( ord_less_eq_nat
% 0.26/0.70 = ( ^ [A7: nat,B5: nat] :
% 0.26/0.70 ( ( ord_less_nat @ A7 @ B5 )
% 0.26/0.70 | ( A7 = B5 ) ) ) ) ).
% 0.26/0.70
% 0.26/0.70 % order.order_iff_strict
% 0.26/0.70
% 0.26/0.70 % Conjectures (1)
% 0.26/0.70 thf(conj_0,conjecture,
% 0.26/0.70 ( a3
% 0.26/0.70 = ( groups1792256535list_a @ qs2 ) ) ).
% 0.26/0.70
% 0.26/0.70 %------------------------------------------------------------------------------
% 0.26/0.70 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Jb0lEjBIig/cvc5---1.0.5_12410.p...
% 0.26/0.70 (declare-sort $$unsorted 0)
% 0.26/0.70 (declare-sort tptp.set_list_list_list_a 0)
% 0.26/0.70 (declare-sort tptp.multis971982480list_a 0)
% 0.26/0.70 (declare-sort tptp.list_set_list_list_a 0)
% 0.26/0.70 (declare-sort tptp.set_list_set_list_a 0)
% 0.26/0.70 (declare-sort tptp.set_list_list_set_a 0)
% 0.26/0.70 (declare-sort tptp.list_set_set_list_a 0)
% 0.26/0.70 (declare-sort tptp.list_set_list_set_a 0)
% 0.26/0.70 (declare-sort tptp.set_list_set_set_a 0)
% 0.26/0.70 (declare-sort tptp.list_set_set_set_a 0)
% 0.26/0.70 (declare-sort tptp.list_multiset_list_a 0)
% 0.26/0.70 (declare-sort tptp.set_multiset_list_a 0)
% 0.26/0.70 (declare-sort tptp.set_list_multiset_a 0)
% 0.26/0.70 (declare-sort tptp.multiset_set_list_a 0)
% 0.26/0.70 (declare-sort tptp.list_set_multiset_a 0)
% 0.26/0.70 (declare-sort tptp.multiset_set_set_a 0)
% 0.26/0.70 (declare-sort tptp.list_list_list_a 0)
% 0.26/0.70 (declare-sort tptp.set_list_list_a 0)
% 0.26/0.70 (declare-sort tptp.multiset_multiset_a 0)
% 0.26/0.70 (declare-sort tptp.list_set_list_a 0)
% 0.26/0.70 (declare-sort tptp.list_list_set_a 0)
% 0.26/0.70 (declare-sort tptp.set_set_list_a 0)
% 0.26/0.70 (declare-sort tptp.set_list_set_a 0)
% 0.26/0.70 (declare-sort tptp.list_set_set_a 0)
% 0.26/0.70 (declare-sort tptp.set_set_set_a 0)
% 0.26/0.70 (declare-sort tptp.multiset_list_a 0)
% 0.26/0.70 (declare-sort tptp.list_multiset_a 0)
% 0.26/0.70 (declare-sort tptp.set_multiset_a 0)
% 0.26/0.70 (declare-sort tptp.multiset_set_a 0)
% 0.26/0.70 (declare-sort tptp.set_list_nat 0)
% 0.26/0.70 (declare-sort tptp.list_set_nat 0)
% 0.26/0.70 (declare-sort tptp.set_set_nat 0)
% 0.26/0.70 (declare-sort tptp.list_list_a 0)
% 0.26/0.70 (declare-sort tptp.set_list_a 0)
% 0.26/0.70 (declare-sort tptp.list_set_a 0)
% 0.26/0.70 (declare-sort tptp.multiset_nat 0)
% 0.26/0.70 (declare-sort tptp.set_set_a 0)
% 0.26/0.70 (declare-sort tptp.multiset_a 0)
% 0.26/0.70 (declare-sort tptp.list_nat 0)
% 0.26/0.70 (declare-sort tptp.set_nat 0)
% 0.26/0.70 (declare-sort tptp.list_a 0)
% 0.26/0.70 (declare-sort tptp.set_a 0)
% 0.26/0.70 (declare-sort tptp.nat 0)
% 0.26/0.70 (declare-sort tptp.a 0)
% 0.26/0.70 (declare-fun tptp.bij_be94573046list_a ((-> tptp.list_a tptp.list_a) tptp.set_list_a tptp.set_list_a) Bool)
% 0.26/0.70 (declare-fun tptp.bij_betw_list_a_a ((-> tptp.list_a tptp.a) tptp.set_list_a tptp.set_a) Bool)
% 0.26/0.70 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 0.26/0.70 (declare-fun tptp.bij_betw_a_list_a ((-> tptp.a tptp.list_a) tptp.set_a tptp.set_list_a) Bool)
% 0.26/0.70 (declare-fun tptp.bij_betw_a_a ((-> tptp.a tptp.a) tptp.set_a tptp.set_a) Bool)
% 0.26/0.70 (declare-fun tptp.inj_on_list_a_list_a ((-> tptp.list_a tptp.list_a) tptp.set_list_a) Bool)
% 0.26/0.70 (declare-fun tptp.inj_on_list_a_a ((-> tptp.list_a tptp.a) tptp.set_list_a) Bool)
% 0.26/0.70 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 0.26/0.70 (declare-fun tptp.inj_on_a_list_a ((-> tptp.a tptp.list_a) tptp.set_a) Bool)
% 0.26/0.70 (declare-fun tptp.inj_on_a_a ((-> tptp.a tptp.a) tptp.set_a) Bool)
% 0.26/0.70 (declare-fun tptp.groups1271887971list_a (tptp.list_multiset_list_a) tptp.multiset_list_a)
% 0.26/0.70 (declare-fun tptp.groups1592617181iset_a (tptp.list_multiset_a) tptp.multiset_a)
% 0.26/0.70 (declare-fun tptp.groups921905271st_nat (tptp.list_nat) tptp.nat)
% 0.26/0.70 (declare-fun tptp.groups1792256535list_a (tptp.list_a) tptp.a)
% 0.26/0.70 (declare-fun tptp.hilber921249868list_a (tptp.set_list_a (-> tptp.list_a tptp.list_a) tptp.list_a) tptp.list_a)
% 0.26/0.70 (declare-fun tptp.hilber2125729734st_a_a (tptp.set_list_a (-> tptp.list_a tptp.a) tptp.a) tptp.list_a)
% 0.26/0.70 (declare-fun tptp.hilber815131374at_nat (tptp.set_nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 0.26/0.70 (declare-fun tptp.hilber165648082list_a (tptp.set_a (-> tptp.a tptp.list_a) tptp.list_a) tptp.a)
% 0.26/0.70 (declare-fun tptp.hilbert_inv_into_a_a (tptp.set_a (-> tptp.a tptp.a) tptp.a) tptp.a)
% 0.26/0.70 (declare-fun tptp.hilber2024005914iset_a (tptp.set_multiset_a tptp.list_set_multiset_a) Bool)
% 0.26/0.70 (declare-fun tptp.hilber1014902394mp_nat (tptp.set_nat tptp.list_set_nat) Bool)
% 0.26/0.70 (declare-fun tptp.hilber2037636820comp_a (tptp.set_a tptp.list_set_a) Bool)
% 0.26/0.70 (declare-fun tptp.list_ex_set_a ((-> tptp.set_a Bool) tptp.list_set_a) Bool)
% 0.26/0.70 (declare-fun tptp.list_ex_a ((-> tptp.a Bool) tptp.list_a) Bool)
% 0.26/0.70 (declare-fun tptp.list_update_set_a (tptp.list_set_a tptp.nat tptp.set_a) tptp.list_set_a)
% 0.26/0.70 (declare-fun tptp.list_update_a (tptp.list_a tptp.nat tptp.a) tptp.list_a)
% 0.26/0.70 (declare-fun tptp.listset_list_list_a (tptp.list_set_list_list_a) tptp.set_list_list_list_a)
% 0.26/0.70 (declare-fun tptp.listset_list_set_a (tptp.list_set_list_set_a) tptp.set_list_list_set_a)
% 0.26/0.70 (declare-fun tptp.listset_list_a (tptp.list_set_list_a) tptp.set_list_list_a)
% 0.26/0.70 (declare-fun tptp.listset_multiset_a (tptp.list_set_multiset_a) tptp.set_list_multiset_a)
% 0.26/0.70 (declare-fun tptp.listset_nat (tptp.list_set_nat) tptp.set_list_nat)
% 0.26/0.70 (declare-fun tptp.listset_set_list_a (tptp.list_set_set_list_a) tptp.set_list_set_list_a)
% 0.26/0.70 (declare-fun tptp.listset_set_set_a (tptp.list_set_set_set_a) tptp.set_list_set_set_a)
% 0.26/0.70 (declare-fun tptp.listset_set_a (tptp.list_set_set_a) tptp.set_list_set_a)
% 0.26/0.70 (declare-fun tptp.listset_a (tptp.list_set_a) tptp.set_list_a)
% 0.26/0.70 (declare-fun tptp.nth_list_list_a (tptp.list_list_list_a tptp.nat) tptp.list_list_a)
% 0.26/0.70 (declare-fun tptp.nth_list_set_a (tptp.list_list_set_a tptp.nat) tptp.list_set_a)
% 0.26/0.70 (declare-fun tptp.nth_list_a (tptp.list_list_a tptp.nat) tptp.list_a)
% 0.26/0.70 (declare-fun tptp.nth_multiset_a (tptp.list_multiset_a tptp.nat) tptp.multiset_a)
% 0.26/0.70 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 0.26/0.70 (declare-fun tptp.nth_set_list_list_a (tptp.list_set_list_list_a tptp.nat) tptp.set_list_list_a)
% 0.26/0.70 (declare-fun tptp.nth_set_list_set_a (tptp.list_set_list_set_a tptp.nat) tptp.set_list_set_a)
% 0.26/0.70 (declare-fun tptp.nth_set_list_a (tptp.list_set_list_a tptp.nat) tptp.set_list_a)
% 0.26/0.70 (declare-fun tptp.nth_set_multiset_a (tptp.list_set_multiset_a tptp.nat) tptp.set_multiset_a)
% 0.26/0.70 (declare-fun tptp.nth_set_nat (tptp.list_set_nat tptp.nat) tptp.set_nat)
% 0.26/0.70 (declare-fun tptp.nth_set_set_list_a (tptp.list_set_set_list_a tptp.nat) tptp.set_set_list_a)
% 0.26/0.70 (declare-fun tptp.nth_set_set_set_a (tptp.list_set_set_set_a tptp.nat) tptp.set_set_set_a)
% 0.26/0.70 (declare-fun tptp.nth_set_set_a (tptp.list_set_set_a tptp.nat) tptp.set_set_a)
% 0.26/0.70 (declare-fun tptp.nth_set_a (tptp.list_set_a tptp.nat) tptp.set_a)
% 0.26/0.70 (declare-fun tptp.nth_a (tptp.list_a tptp.nat) tptp.a)
% 0.26/0.70 (declare-fun tptp.rev_list_a (tptp.list_list_a) tptp.list_list_a)
% 0.26/0.70 (declare-fun tptp.rev_nat (tptp.list_nat) tptp.list_nat)
% 0.26/0.70 (declare-fun tptp.rev_set_list_a (tptp.list_set_list_a) tptp.list_set_list_a)
% 0.26/0.70 (declare-fun tptp.rev_set_set_a (tptp.list_set_set_a) tptp.list_set_set_a)
% 0.26/0.70 (declare-fun tptp.rev_set_a (tptp.list_set_a) tptp.list_set_a)
% 0.26/0.70 (declare-fun tptp.rev_a (tptp.list_a) tptp.list_a)
% 0.26/0.70 (declare-fun tptp.comm_m324867663list_a (tptp.multis971982480list_a) tptp.multiset_list_a)
% 0.26/0.70 (declare-fun tptp.comm_m2145643721iset_a (tptp.multiset_multiset_a) tptp.multiset_a)
% 0.26/0.70 (declare-fun tptp.comm_m1100186507et_nat (tptp.multiset_nat) tptp.nat)
% 0.26/0.70 (declare-fun tptp.comm_m543484931mset_a (tptp.multiset_a) tptp.a)
% 0.26/0.70 (declare-fun tptp.mset_list_a (tptp.list_list_a) tptp.multiset_list_a)
% 0.26/0.70 (declare-fun tptp.mset_multiset_list_a (tptp.list_multiset_list_a) tptp.multis971982480list_a)
% 0.26/0.70 (declare-fun tptp.mset_multiset_a (tptp.list_multiset_a) tptp.multiset_multiset_a)
% 0.26/0.70 (declare-fun tptp.mset_nat (tptp.list_nat) tptp.multiset_nat)
% 0.26/0.70 (declare-fun tptp.mset_set_list_a (tptp.list_set_list_a) tptp.multiset_set_list_a)
% 0.26/0.70 (declare-fun tptp.mset_set_set_a (tptp.list_set_set_a) tptp.multiset_set_set_a)
% 0.26/0.70 (declare-fun tptp.mset_set_a (tptp.list_set_a) tptp.multiset_set_a)
% 0.26/0.70 (declare-fun tptp.mset_a (tptp.list_a) tptp.multiset_a)
% 0.26/0.70 (declare-fun tptp.set_mset_list_a (tptp.multiset_list_a) tptp.set_list_a)
% 0.26/0.70 (declare-fun tptp.set_ms1660427399list_a (tptp.multis971982480list_a) tptp.set_multiset_list_a)
% 0.26/0.70 (declare-fun tptp.set_mset_multiset_a (tptp.multiset_multiset_a) tptp.set_multiset_a)
% 0.26/0.70 (declare-fun tptp.set_mset_set_a (tptp.multiset_set_a) tptp.set_set_a)
% 0.26/0.70 (declare-fun tptp.set_mset_a (tptp.multiset_a) tptp.set_a)
% 0.26/0.70 (declare-fun tptp.size_s575106428list_a (tptp.list_list_list_a) tptp.nat)
% 0.26/0.70 (declare-fun tptp.size_s341332310_set_a (tptp.list_list_set_a) tptp.nat)
% 0.26/0.70 (declare-fun tptp.size_s1427607542list_a (tptp.list_list_a) tptp.nat)
% 0.26/0.70 (declare-fun tptp.size_s1657263798iset_a (tptp.list_multiset_a) tptp.nat)
% 0.26/0.70 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 0.26/0.70 (declare-fun tptp.size_s240404444list_a (tptp.list_set_list_list_a) tptp.nat)
% 0.26/0.70 (declare-fun tptp.size_s926492982_set_a (tptp.list_set_list_set_a) tptp.nat)
% 0.26/0.70 (declare-fun tptp.size_s1635937238list_a (tptp.list_set_list_a) tptp.nat)
% 0.26/0.70 (declare-fun tptp.size_s802269334iset_a (tptp.list_set_multiset_a) tptp.nat)
% 0.26/0.70 (declare-fun tptp.size_s577819178et_nat (tptp.list_set_nat) tptp.nat)
% 0.26/0.70 (declare-fun tptp.size_s469631926list_a (tptp.list_set_set_list_a) tptp.nat)
% 0.26/0.70 (declare-fun tptp.size_s726512144_set_a (tptp.list_set_set_set_a) tptp.nat)
% 0.26/0.70 (declare-fun tptp.size_s739728560_set_a (tptp.list_set_set_a) tptp.nat)
% 0.26/0.70 (declare-fun tptp.size_size_list_set_a (tptp.list_set_a) tptp.nat)
% 0.26/0.70 (declare-fun tptp.size_size_list_a (tptp.list_a) tptp.nat)
% 0.26/0.70 (declare-fun tptp.size_s657334288_set_a (tptp.multiset_set_a) tptp.nat)
% 0.26/0.70 (declare-fun tptp.size_size_multiset_a (tptp.multiset_a) tptp.nat)
% 0.26/0.70 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.26/0.70 (declare-fun tptp.ord_less_set_list_a (tptp.set_list_a tptp.set_list_a) Bool)
% 0.26/0.70 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 0.26/0.70 (declare-fun tptp.ord_less_set_a (tptp.set_a tptp.set_a) Bool)
% 0.26/0.70 (declare-fun tptp.ord_less_eq_o_nat ((-> Bool tptp.nat) (-> Bool tptp.nat)) Bool)
% 0.26/0.70 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.26/0.70 (declare-fun tptp.ord_le1301786372list_a (tptp.set_list_a tptp.set_list_a) Bool)
% 0.26/0.70 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 0.26/0.70 (declare-fun tptp.ord_less_eq_set_a (tptp.set_a tptp.set_a) Bool)
% 0.26/0.70 (declare-fun tptp.perm_set_a (tptp.list_set_a tptp.list_set_a) Bool)
% 0.26/0.70 (declare-fun tptp.perm_a (tptp.list_a tptp.list_a) Bool)
% 0.26/0.70 (declare-fun tptp.collect_list_list_a ((-> tptp.list_list_a Bool)) tptp.set_list_list_a)
% 0.26/0.70 (declare-fun tptp.collect_list_set_a ((-> tptp.list_set_a Bool)) tptp.set_list_set_a)
% 0.26/0.70 (declare-fun tptp.collect_list_a ((-> tptp.list_a Bool)) tptp.set_list_a)
% 0.26/0.70 (declare-fun tptp.collect_multiset_a ((-> tptp.multiset_a Bool)) tptp.set_multiset_a)
% 0.26/0.70 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 0.26/0.70 (declare-fun tptp.collect_set_a ((-> tptp.set_a Bool)) tptp.set_set_a)
% 0.26/0.70 (declare-fun tptp.collect_a ((-> tptp.a Bool)) tptp.set_a)
% 0.26/0.70 (declare-fun tptp.image_list_nat_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat) tptp.set_nat)
% 0.26/0.70 (declare-fun tptp.image_list_a_list_a ((-> tptp.list_a tptp.list_a) tptp.set_list_a) tptp.set_list_a)
% 0.26/0.70 (declare-fun tptp.image_list_a_a ((-> tptp.list_a tptp.a) tptp.set_list_a) tptp.set_a)
% 0.26/0.70 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 0.26/0.70 (declare-fun tptp.image_a_list_a ((-> tptp.a tptp.list_a) tptp.set_a) tptp.set_list_a)
% 0.26/0.70 (declare-fun tptp.image_a_a ((-> tptp.a tptp.a) tptp.set_a) tptp.set_a)
% 0.26/0.70 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 0.26/0.70 (declare-fun tptp.set_or1578766727list_a (tptp.set_list_a) tptp.set_set_list_a)
% 0.26/0.70 (declare-fun tptp.set_or1597314339et_nat (tptp.set_nat) tptp.set_set_nat)
% 0.26/0.70 (declare-fun tptp.set_or1164043265_set_a (tptp.set_a) tptp.set_set_a)
% 0.26/0.70 (declare-fun tptp.member1511395513list_a (tptp.list_list_list_a tptp.set_list_list_list_a) Bool)
% 0.26/0.70 (declare-fun tptp.member954073875_set_a (tptp.list_list_set_a tptp.set_list_list_set_a) Bool)
% 0.26/0.70 (declare-fun tptp.member_list_list_a (tptp.list_list_a tptp.set_list_list_a) Bool)
% 0.26/0.70 (declare-fun tptp.member518144627iset_a (tptp.list_multiset_a tptp.set_list_multiset_a) Bool)
% 0.26/0.70 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 0.26/0.70 (declare-fun tptp.member101195155list_a (tptp.list_set_list_a tptp.set_list_set_list_a) Bool)
% 0.26/0.70 (declare-fun tptp.member814963949_set_a (tptp.list_set_set_a tptp.set_list_set_set_a) Bool)
% 0.26/0.70 (declare-fun tptp.member_list_set_a (tptp.list_set_a tptp.set_list_set_a) Bool)
% 0.26/0.70 (declare-fun tptp.member_list_a (tptp.list_a tptp.set_list_a) Bool)
% 0.26/0.70 (declare-fun tptp.member528267379list_a (tptp.multiset_list_a tptp.set_multiset_list_a) Bool)
% 0.26/0.70 (declare-fun tptp.member_multiset_a (tptp.multiset_a tptp.set_multiset_a) Bool)
% 0.26/0.70 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 0.26/0.70 (declare-fun tptp.member_set_list_a (tptp.set_list_a tptp.set_set_list_a) Bool)
% 0.26/0.70 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 0.26/0.70 (declare-fun tptp.member_set_set_a (tptp.set_set_a tptp.set_set_set_a) Bool)
% 0.26/0.70 (declare-fun tptp.member_set_a (tptp.set_a tptp.set_set_a) Bool)
% 0.26/0.70 (declare-fun tptp.member_a (tptp.a tptp.set_a) Bool)
% 0.26/0.70 (declare-fun tptp.a2 () tptp.set_a)
% 0.26/0.70 (declare-fun tptp.a3 () tptp.a)
% 0.26/0.70 (declare-fun tptp.f (tptp.nat) tptp.nat)
% 0.26/0.70 (declare-fun tptp.g (tptp.nat) tptp.nat)
% 0.26/0.70 (declare-fun tptp.qs2 () tptp.list_a)
% 0.26/0.70 (declare-fun tptp.qs () tptp.list_a)
% 0.26/0.70 (declare-fun tptp.ss1 () tptp.list_set_a)
% 0.26/0.70 (declare-fun tptp.ss2 () tptp.list_set_a)
% 0.26/0.70 (assert (= (@ tptp.mset_a tptp.qs2) (@ tptp.mset_a tptp.qs)))
% 0.26/0.70 (assert (@ (@ tptp.member_a tptp.a3) tptp.a2))
% 0.26/0.70 (assert (= tptp.a3 (@ tptp.groups1792256535list_a tptp.qs)))
% 0.26/0.70 (assert (= (@ tptp.size_size_list_a tptp.qs2) (@ tptp.size_size_list_a tptp.qs)))
% 0.26/0.70 (assert (not (forall ((Qs tptp.list_a)) (=> (= tptp.a3 (@ tptp.groups1792256535list_a Qs)) (not (@ (@ tptp.member_list_a Qs) (@ tptp.listset_a tptp.ss1)))))))
% 0.26/0.70 (assert (@ (@ tptp.member_list_a tptp.qs2) (@ tptp.listset_a tptp.ss2)))
% 0.26/0.70 (assert (forall ((A tptp.set_multiset_a) (Ss tptp.list_set_multiset_a) (Qs2 tptp.list_multiset_a)) (=> (@ (@ tptp.hilber2024005914iset_a A) Ss) (=> (@ (@ tptp.member518144627iset_a Qs2) (@ tptp.listset_multiset_a Ss)) (@ (@ tptp.member_multiset_a (@ tptp.groups1592617181iset_a Qs2)) A)))))
% 0.26/0.70 (assert (forall ((A tptp.set_nat) (Ss tptp.list_set_nat) (Qs2 tptp.list_nat)) (=> (@ (@ tptp.hilber1014902394mp_nat A) Ss) (=> (@ (@ tptp.member_list_nat Qs2) (@ tptp.listset_nat Ss)) (@ (@ tptp.member_nat (@ tptp.groups921905271st_nat Qs2)) A)))))
% 0.26/0.70 (assert (forall ((A tptp.set_a) (Ss tptp.list_set_a) (Qs2 tptp.list_a)) (=> (@ (@ tptp.hilber2037636820comp_a A) Ss) (=> (@ (@ tptp.member_list_a Qs2) (@ tptp.listset_a Ss)) (@ (@ tptp.member_a (@ tptp.groups1792256535list_a Qs2)) A)))))
% 0.26/0.70 (assert (forall ((A tptp.set_multiset_a) (Ss tptp.list_set_multiset_a) (A2 tptp.multiset_a)) (=> (@ (@ tptp.hilber2024005914iset_a A) Ss) (=> (@ (@ tptp.member_multiset_a A2) A) (not (forall ((Qs tptp.list_multiset_a)) (=> (@ (@ tptp.member518144627iset_a Qs) (@ tptp.listset_multiset_a Ss)) (not (= A2 (@ tptp.groups1592617181iset_a Qs))))))))))
% 0.26/0.70 (assert (forall ((A tptp.set_nat) (Ss tptp.list_set_nat) (A2 tptp.nat)) (=> (@ (@ tptp.hilber1014902394mp_nat A) Ss) (=> (@ (@ tptp.member_nat A2) A) (not (forall ((Qs tptp.list_nat)) (=> (@ (@ tptp.member_list_nat Qs) (@ tptp.listset_nat Ss)) (not (= A2 (@ tptp.groups921905271st_nat Qs))))))))))
% 0.26/0.70 (assert (forall ((A tptp.set_a) (Ss tptp.list_set_a) (A2 tptp.a)) (=> (@ (@ tptp.hilber2037636820comp_a A) Ss) (=> (@ (@ tptp.member_a A2) A) (not (forall ((Qs tptp.list_a)) (=> (@ (@ tptp.member_list_a Qs) (@ tptp.listset_a Ss)) (not (= A2 (@ tptp.groups1792256535list_a Qs))))))))))
% 0.26/0.70 (assert (forall ((Ss tptp.list_set_multiset_a) (A tptp.set_multiset_a)) (=> (forall ((Qs tptp.list_multiset_a)) (=> (@ (@ tptp.member518144627iset_a Qs) (@ tptp.listset_multiset_a Ss)) (@ (@ tptp.member_multiset_a (@ tptp.groups1592617181iset_a Qs)) A))) (=> (forall ((A3 tptp.multiset_a)) (=> (@ (@ tptp.member_multiset_a A3) A) (exists ((X tptp.list_multiset_a)) (and (@ (@ tptp.member518144627iset_a X) (@ tptp.listset_multiset_a Ss)) (= A3 (@ tptp.groups1592617181iset_a X)) (forall ((Y tptp.list_multiset_a)) (=> (and (@ (@ tptp.member518144627iset_a Y) (@ tptp.listset_multiset_a Ss)) (= A3 (@ tptp.groups1592617181iset_a Y))) (= Y X))))))) (@ (@ tptp.hilber2024005914iset_a A) Ss)))))
% 0.26/0.70 (assert (forall ((Ss tptp.list_set_nat) (A tptp.set_nat)) (=> (forall ((Qs tptp.list_nat)) (=> (@ (@ tptp.member_list_nat Qs) (@ tptp.listset_nat Ss)) (@ (@ tptp.member_nat (@ tptp.groups921905271st_nat Qs)) A))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A) (exists ((X tptp.list_nat)) (and (@ (@ tptp.member_list_nat X) (@ tptp.listset_nat Ss)) (= A3 (@ tptp.groups921905271st_nat X)) (forall ((Y tptp.list_nat)) (=> (and (@ (@ tptp.member_list_nat Y) (@ tptp.listset_nat Ss)) (= A3 (@ tptp.groups921905271st_nat Y))) (= Y X))))))) (@ (@ tptp.hilber1014902394mp_nat A) Ss)))))
% 0.26/0.70 (assert (forall ((Ss tptp.list_set_a) (A tptp.set_a)) (=> (forall ((Qs tptp.list_a)) (=> (@ (@ tptp.member_list_a Qs) (@ tptp.listset_a Ss)) (@ (@ tptp.member_a (@ tptp.groups1792256535list_a Qs)) A))) (=> (forall ((A3 tptp.a)) (=> (@ (@ tptp.member_a A3) A) (exists ((X tptp.list_a)) (and (@ (@ tptp.member_list_a X) (@ tptp.listset_a Ss)) (= A3 (@ tptp.groups1792256535list_a X)) (forall ((Y tptp.list_a)) (=> (and (@ (@ tptp.member_list_a Y) (@ tptp.listset_a Ss)) (= A3 (@ tptp.groups1792256535list_a Y))) (= Y X))))))) (@ (@ tptp.hilber2037636820comp_a A) Ss)))))
% 0.26/0.70 (assert (forall ((A tptp.set_nat) (Ss tptp.list_set_nat) (Qs2 tptp.list_nat) (Qs3 tptp.list_nat)) (let ((_let_1 (@ tptp.listset_nat Ss))) (=> (@ (@ tptp.hilber1014902394mp_nat A) Ss) (=> (@ (@ tptp.member_list_nat Qs2) _let_1) (=> (@ (@ tptp.member_list_nat Qs3) _let_1) (=> (= (@ tptp.groups921905271st_nat Qs2) (@ tptp.groups921905271st_nat Qs3)) (= Qs2 Qs3))))))))
% 0.26/0.70 (assert (forall ((A tptp.set_a) (Ss tptp.list_set_a) (Qs2 tptp.list_a) (Qs3 tptp.list_a)) (let ((_let_1 (@ tptp.listset_a Ss))) (=> (@ (@ tptp.hilber2037636820comp_a A) Ss) (=> (@ (@ tptp.member_list_a Qs2) _let_1) (=> (@ (@ tptp.member_list_a Qs3) _let_1) (=> (= (@ tptp.groups1792256535list_a Qs2) (@ tptp.groups1792256535list_a Qs3)) (= Qs2 Qs3))))))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.groups921905271st_nat (@ tptp.rev_nat Xs)) (@ tptp.groups921905271st_nat Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_a)) (= (@ tptp.groups1792256535list_a (@ tptp.rev_a Xs)) (@ tptp.groups1792256535list_a Xs))))
% 0.26/0.70 (assert (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_a tptp.qs)) (= (@ (@ tptp.nth_a tptp.qs2) I) (@ (@ tptp.nth_a tptp.qs) (@ tptp.g I))))))
% 0.26/0.70 (assert (@ (@ (@ tptp.bij_betw_nat_nat tptp.g) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_a tptp.qs2))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_a tptp.qs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.comm_m1100186507et_nat (@ tptp.mset_nat Xs)) (@ tptp.groups921905271st_nat Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_multiset_list_a)) (= (@ tptp.comm_m324867663list_a (@ tptp.mset_multiset_list_a Xs)) (@ tptp.groups1271887971list_a Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_multiset_a)) (= (@ tptp.comm_m2145643721iset_a (@ tptp.mset_multiset_a Xs)) (@ tptp.groups1592617181iset_a Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_a)) (= (@ tptp.comm_m543484931mset_a (@ tptp.mset_a Xs)) (@ tptp.groups1792256535list_a Xs))))
% 0.26/0.70 (assert (forall ((A tptp.set_nat) (Ss tptp.list_set_nat)) (=> (@ (@ tptp.hilber1014902394mp_nat A) Ss) (= (@ (@ tptp.image_list_nat_nat tptp.groups921905271st_nat) (@ tptp.listset_nat Ss)) A))))
% 0.26/0.70 (assert (forall ((A tptp.set_a) (Ss tptp.list_set_a)) (=> (@ (@ tptp.hilber2037636820comp_a A) Ss) (= (@ (@ tptp.image_list_a_a tptp.groups1792256535list_a) (@ tptp.listset_a Ss)) A))))
% 0.26/0.70 (assert (@ (@ tptp.hilber2037636820comp_a tptp.a2) tptp.ss1))
% 0.26/0.70 (assert (@ (@ tptp.member_list_a tptp.qs) (@ tptp.listset_a tptp.ss1)))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a)) (= (@ tptp.mset_set_a (@ tptp.rev_set_a Xs)) (@ tptp.mset_set_a Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_list_a)) (= (@ tptp.mset_list_a (@ tptp.rev_list_a Xs)) (@ tptp.mset_list_a Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_a)) (= (@ tptp.mset_a (@ tptp.rev_a Xs)) (@ tptp.mset_a Xs))))
% 0.26/0.70 (assert (not (forall ((Qs22 tptp.list_a)) (=> (@ (@ tptp.member_list_a Qs22) (@ tptp.listset_a tptp.ss2)) (=> (= (@ tptp.size_size_list_a Qs22) (@ tptp.size_size_list_a tptp.qs)) (not (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_a tptp.qs)) (= (@ (@ tptp.nth_a Qs22) I2) (@ (@ tptp.nth_a tptp.qs) (@ tptp.g I2)))))))))))
% 0.26/0.70 (assert (@ (@ tptp.perm_set_a tptp.ss1) tptp.ss2))
% 0.26/0.70 (assert (forall ((X2 tptp.multiset_set_a)) (exists ((Xs2 tptp.list_set_a)) (= (@ tptp.mset_set_a Xs2) X2))))
% 0.26/0.70 (assert (forall ((X2 tptp.multiset_list_a)) (exists ((Xs2 tptp.list_list_a)) (= (@ tptp.mset_list_a Xs2) X2))))
% 0.26/0.70 (assert (forall ((X2 tptp.multiset_a)) (exists ((Xs2 tptp.list_a)) (= (@ tptp.mset_a Xs2) X2))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (= (@ tptp.mset_list_a Xs) (@ tptp.mset_list_a Ys)) (= (@ tptp.size_s1427607542list_a Xs) (@ tptp.size_s1427607542list_a Ys)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_list_a) (Ys tptp.list_set_list_a)) (=> (= (@ tptp.mset_set_list_a Xs) (@ tptp.mset_set_list_a Ys)) (= (@ tptp.size_s1635937238list_a Xs) (@ tptp.size_s1635937238list_a Ys)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_set_a) (Ys tptp.list_set_set_a)) (=> (= (@ tptp.mset_set_set_a Xs) (@ tptp.mset_set_set_a Ys)) (= (@ tptp.size_s739728560_set_a Xs) (@ tptp.size_s739728560_set_a Ys)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.mset_nat Xs) (@ tptp.mset_nat Ys)) (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (= (@ tptp.mset_a Xs) (@ tptp.mset_a Ys)) (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (=> (= (@ tptp.mset_set_a Xs) (@ tptp.mset_set_a Ys)) (= (@ tptp.size_size_list_set_a Xs) (@ tptp.size_size_list_set_a Ys)))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s1427607542list_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s1427607542list_a Ys))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1427607542list_a Xs)) (= (@ (@ tptp.nth_list_a Xs) I3) (@ (@ tptp.nth_list_a Ys) (@ F I3))))) (= (@ tptp.mset_list_a Xs) (@ tptp.mset_list_a Ys))))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (Xs tptp.list_set_list_a) (Ys tptp.list_set_list_a)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s1635937238list_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s1635937238list_a Ys))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1635937238list_a Xs)) (= (@ (@ tptp.nth_set_list_a Xs) I3) (@ (@ tptp.nth_set_list_a Ys) (@ F I3))))) (= (@ tptp.mset_set_list_a Xs) (@ tptp.mset_set_list_a Ys))))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (Xs tptp.list_set_set_a) (Ys tptp.list_set_set_a)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s739728560_set_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s739728560_set_a Ys))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s739728560_set_a Xs)) (= (@ (@ tptp.nth_set_set_a Xs) I3) (@ (@ tptp.nth_set_set_a Ys) (@ F I3))))) (= (@ tptp.mset_set_set_a Xs) (@ tptp.mset_set_set_a Ys))))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_nat Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_nat Ys))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I3) (@ (@ tptp.nth_nat Ys) (@ F I3))))) (= (@ tptp.mset_nat Xs) (@ tptp.mset_nat Ys))))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_a Ys))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a Xs) I3) (@ (@ tptp.nth_a Ys) (@ F I3))))) (= (@ tptp.mset_a Xs) (@ tptp.mset_a Ys))))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (Xs tptp.list_set_a) (Ys tptp.list_set_a)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a Ys))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_set_a Xs)) (= (@ (@ tptp.nth_set_a Xs) I3) (@ (@ tptp.nth_set_a Ys) (@ F I3))))) (= (@ tptp.mset_set_a Xs) (@ tptp.mset_set_a Ys))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_set_list_a) (Xs tptp.list_set_set_list_a) (F (-> tptp.nat tptp.nat)) (Xs3 tptp.list_set_set_list_a)) (=> (@ (@ tptp.member101195155list_a Ys) (@ tptp.listset_set_list_a Xs)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s469631926list_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s469631926list_a Xs3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s469631926list_a Xs)) (= (@ (@ tptp.nth_set_set_list_a Xs3) I3) (@ (@ tptp.nth_set_set_list_a Xs) (@ F I3))))) (not (forall ((Ys2 tptp.list_set_list_a)) (=> (@ (@ tptp.member101195155list_a Ys2) (@ tptp.listset_set_list_a Xs3)) (=> (= (@ tptp.size_s1635937238list_a Ys2) (@ tptp.size_s1635937238list_a Ys)) (not (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1635937238list_a Ys)) (= (@ (@ tptp.nth_set_list_a Ys2) I2) (@ (@ tptp.nth_set_list_a Ys) (@ F I2)))))))))))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_set_set_a) (Xs tptp.list_set_set_set_a) (F (-> tptp.nat tptp.nat)) (Xs3 tptp.list_set_set_set_a)) (=> (@ (@ tptp.member814963949_set_a Ys) (@ tptp.listset_set_set_a Xs)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s726512144_set_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s726512144_set_a Xs3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s726512144_set_a Xs)) (= (@ (@ tptp.nth_set_set_set_a Xs3) I3) (@ (@ tptp.nth_set_set_set_a Xs) (@ F I3))))) (not (forall ((Ys2 tptp.list_set_set_a)) (=> (@ (@ tptp.member814963949_set_a Ys2) (@ tptp.listset_set_set_a Xs3)) (=> (= (@ tptp.size_s739728560_set_a Ys2) (@ tptp.size_s739728560_set_a Ys)) (not (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s739728560_set_a Ys)) (= (@ (@ tptp.nth_set_set_a Ys2) I2) (@ (@ tptp.nth_set_set_a Ys) (@ F I2)))))))))))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_nat) (Xs tptp.list_set_nat) (F (-> tptp.nat tptp.nat)) (Xs3 tptp.list_set_nat)) (=> (@ (@ tptp.member_list_nat Ys) (@ tptp.listset_nat Xs)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s577819178et_nat Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s577819178et_nat Xs3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s577819178et_nat Xs)) (= (@ (@ tptp.nth_set_nat Xs3) I3) (@ (@ tptp.nth_set_nat Xs) (@ F I3))))) (not (forall ((Ys2 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat Ys2) (@ tptp.listset_nat Xs3)) (=> (= (@ tptp.size_size_list_nat Ys2) (@ tptp.size_size_list_nat Ys)) (not (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.nth_nat Ys2) I2) (@ (@ tptp.nth_nat Ys) (@ F I2)))))))))))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_list_a) (Xs tptp.list_set_list_a) (F (-> tptp.nat tptp.nat)) (Xs3 tptp.list_set_list_a)) (=> (@ (@ tptp.member_list_list_a Ys) (@ tptp.listset_list_a Xs)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s1635937238list_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s1635937238list_a Xs3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1635937238list_a Xs)) (= (@ (@ tptp.nth_set_list_a Xs3) I3) (@ (@ tptp.nth_set_list_a Xs) (@ F I3))))) (not (forall ((Ys2 tptp.list_list_a)) (=> (@ (@ tptp.member_list_list_a Ys2) (@ tptp.listset_list_a Xs3)) (=> (= (@ tptp.size_s1427607542list_a Ys2) (@ tptp.size_s1427607542list_a Ys)) (not (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1427607542list_a Ys)) (= (@ (@ tptp.nth_list_a Ys2) I2) (@ (@ tptp.nth_list_a Ys) (@ F I2)))))))))))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_set_a) (Xs tptp.list_set_set_a) (F (-> tptp.nat tptp.nat)) (Xs3 tptp.list_set_set_a)) (=> (@ (@ tptp.member_list_set_a Ys) (@ tptp.listset_set_a Xs)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s739728560_set_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s739728560_set_a Xs3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s739728560_set_a Xs)) (= (@ (@ tptp.nth_set_set_a Xs3) I3) (@ (@ tptp.nth_set_set_a Xs) (@ F I3))))) (not (forall ((Ys2 tptp.list_set_a)) (=> (@ (@ tptp.member_list_set_a Ys2) (@ tptp.listset_set_a Xs3)) (=> (= (@ tptp.size_size_list_set_a Ys2) (@ tptp.size_size_list_set_a Ys)) (not (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_set_a Ys)) (= (@ (@ tptp.nth_set_a Ys2) I2) (@ (@ tptp.nth_set_a Ys) (@ F I2)))))))))))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_a) (Xs tptp.list_set_a) (F (-> tptp.nat tptp.nat)) (Xs3 tptp.list_set_a)) (=> (@ (@ tptp.member_list_a Ys) (@ tptp.listset_a Xs)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a Xs3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_set_a Xs)) (= (@ (@ tptp.nth_set_a Xs3) I3) (@ (@ tptp.nth_set_a Xs) (@ F I3))))) (not (forall ((Ys2 tptp.list_a)) (=> (@ (@ tptp.member_list_a Ys2) (@ tptp.listset_a Xs3)) (=> (= (@ tptp.size_size_list_a Ys2) (@ tptp.size_size_list_a Ys)) (not (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_a Ys)) (= (@ (@ tptp.nth_a Ys2) I2) (@ (@ tptp.nth_a Ys) (@ F I2)))))))))))))))
% 0.26/0.70 (assert (@ (@ (@ tptp.bij_betw_nat_nat tptp.g) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a tptp.ss1))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a tptp.ss2))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_list_a)) (= (@ tptp.size_s1427607542list_a (@ tptp.rev_list_a Xs)) (@ tptp.size_s1427607542list_a Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_list_a)) (= (@ tptp.size_s1635937238list_a (@ tptp.rev_set_list_a Xs)) (@ tptp.size_s1635937238list_a Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_set_a)) (= (@ tptp.size_s739728560_set_a (@ tptp.rev_set_set_a Xs)) (@ tptp.size_s739728560_set_a Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ tptp.rev_nat Xs)) (@ tptp.size_size_list_nat Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_a)) (= (@ tptp.size_size_list_a (@ tptp.rev_a Xs)) (@ tptp.size_size_list_a Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a)) (= (@ tptp.size_size_list_set_a (@ tptp.rev_set_a Xs)) (@ tptp.size_size_list_set_a Xs))))
% 0.26/0.70 (assert (forall ((I tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ tptp.set_or1597314339et_nat K)) (@ (@ tptp.ord_less_set_nat I) K))))
% 0.26/0.70 (assert (forall ((I tptp.set_list_a) (K tptp.set_list_a)) (= (@ (@ tptp.member_set_list_a I) (@ tptp.set_or1578766727list_a K)) (@ (@ tptp.ord_less_set_list_a I) K))))
% 0.26/0.70 (assert (forall ((I tptp.set_a) (K tptp.set_a)) (= (@ (@ tptp.member_set_a I) (@ tptp.set_or1164043265_set_a K)) (@ (@ tptp.ord_less_set_a I) K))))
% 0.26/0.70 (assert (forall ((I tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I) K))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_multiset_a) (Xs tptp.list_set_multiset_a)) (=> (= (@ tptp.size_s1657263798iset_a Ys) (@ tptp.size_s802269334iset_a Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s802269334iset_a Xs)) (@ (@ tptp.member_multiset_a (@ (@ tptp.nth_multiset_a Ys) I3)) (@ (@ tptp.nth_set_multiset_a Xs) I3)))) (@ (@ tptp.member518144627iset_a Ys) (@ tptp.listset_multiset_a Xs))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_list_list_a) (Xs tptp.list_set_list_list_a)) (=> (= (@ tptp.size_s575106428list_a Ys) (@ tptp.size_s240404444list_a Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s240404444list_a Xs)) (@ (@ tptp.member_list_list_a (@ (@ tptp.nth_list_list_a Ys) I3)) (@ (@ tptp.nth_set_list_list_a Xs) I3)))) (@ (@ tptp.member1511395513list_a Ys) (@ tptp.listset_list_list_a Xs))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_list_set_a) (Xs tptp.list_set_list_set_a)) (=> (= (@ tptp.size_s341332310_set_a Ys) (@ tptp.size_s926492982_set_a Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s926492982_set_a Xs)) (@ (@ tptp.member_list_set_a (@ (@ tptp.nth_list_set_a Ys) I3)) (@ (@ tptp.nth_set_list_set_a Xs) I3)))) (@ (@ tptp.member954073875_set_a Ys) (@ tptp.listset_list_set_a Xs))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_set_list_a) (Xs tptp.list_set_set_list_a)) (=> (= (@ tptp.size_s1635937238list_a Ys) (@ tptp.size_s469631926list_a Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s469631926list_a Xs)) (@ (@ tptp.member_set_list_a (@ (@ tptp.nth_set_list_a Ys) I3)) (@ (@ tptp.nth_set_set_list_a Xs) I3)))) (@ (@ tptp.member101195155list_a Ys) (@ tptp.listset_set_list_a Xs))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_set_set_a) (Xs tptp.list_set_set_set_a)) (=> (= (@ tptp.size_s739728560_set_a Ys) (@ tptp.size_s726512144_set_a Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s726512144_set_a Xs)) (@ (@ tptp.member_set_set_a (@ (@ tptp.nth_set_set_a Ys) I3)) (@ (@ tptp.nth_set_set_set_a Xs) I3)))) (@ (@ tptp.member814963949_set_a Ys) (@ tptp.listset_set_set_a Xs))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_nat) (Xs tptp.list_set_nat)) (=> (= (@ tptp.size_size_list_nat Ys) (@ tptp.size_s577819178et_nat Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s577819178et_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Ys) I3)) (@ (@ tptp.nth_set_nat Xs) I3)))) (@ (@ tptp.member_list_nat Ys) (@ tptp.listset_nat Xs))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_list_a) (Xs tptp.list_set_list_a)) (=> (= (@ tptp.size_s1427607542list_a Ys) (@ tptp.size_s1635937238list_a Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1635937238list_a Xs)) (@ (@ tptp.member_list_a (@ (@ tptp.nth_list_a Ys) I3)) (@ (@ tptp.nth_set_list_a Xs) I3)))) (@ (@ tptp.member_list_list_a Ys) (@ tptp.listset_list_a Xs))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_a) (Xs tptp.list_set_a)) (=> (= (@ tptp.size_size_list_a Ys) (@ tptp.size_size_list_set_a Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_set_a Xs)) (@ (@ tptp.member_a (@ (@ tptp.nth_a Ys) I3)) (@ (@ tptp.nth_set_a Xs) I3)))) (@ (@ tptp.member_list_a Ys) (@ tptp.listset_a Xs))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_set_a) (Xs tptp.list_set_set_a)) (=> (= (@ tptp.size_size_list_set_a Ys) (@ tptp.size_s739728560_set_a Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s739728560_set_a Xs)) (@ (@ tptp.member_set_a (@ (@ tptp.nth_set_a Ys) I3)) (@ (@ tptp.nth_set_set_a Xs) I3)))) (@ (@ tptp.member_list_set_a Ys) (@ tptp.listset_set_a Xs))))))
% 0.26/0.70 (assert (= (@ tptp.size_size_list_a tptp.qs) (@ tptp.size_size_list_set_a tptp.ss1)))
% 0.26/0.70 (assert (@ (@ (@ tptp.bij_betw_nat_nat tptp.f) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a tptp.ss2))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a tptp.ss1))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (= (@ tptp.size_s1427607542list_a Xs) (@ tptp.size_s1427607542list_a Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1427607542list_a Xs)) (= (@ (@ tptp.nth_list_a Xs) I3) (@ (@ tptp.nth_list_a Ys) I3)))) (= Xs Ys)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_list_a) (Ys tptp.list_set_list_a)) (=> (= (@ tptp.size_s1635937238list_a Xs) (@ tptp.size_s1635937238list_a Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1635937238list_a Xs)) (= (@ (@ tptp.nth_set_list_a Xs) I3) (@ (@ tptp.nth_set_list_a Ys) I3)))) (= Xs Ys)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_set_a) (Ys tptp.list_set_set_a)) (=> (= (@ tptp.size_s739728560_set_a Xs) (@ tptp.size_s739728560_set_a Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s739728560_set_a Xs)) (= (@ (@ tptp.nth_set_set_a Xs) I3) (@ (@ tptp.nth_set_set_a Ys) I3)))) (= Xs Ys)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I3) (@ (@ tptp.nth_nat Ys) I3)))) (= Xs Ys)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a Xs) I3) (@ (@ tptp.nth_a Ys) I3)))) (= Xs Ys)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (=> (= (@ tptp.size_size_list_set_a Xs) (@ tptp.size_size_list_set_a Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_set_a Xs)) (= (@ (@ tptp.nth_set_a Xs) I3) (@ (@ tptp.nth_set_a Ys) I3)))) (= Xs Ys)))))
% 0.26/0.70 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.list_a Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X3 tptp.list_a)) (@ (@ P I4) X3)))) (exists ((Xs4 tptp.list_list_a)) (and (= (@ tptp.size_s1427607542list_a Xs4) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_list_a Xs4) I4)))))))))
% 0.26/0.70 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.set_list_a Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X3 tptp.set_list_a)) (@ (@ P I4) X3)))) (exists ((Xs4 tptp.list_set_list_a)) (and (= (@ tptp.size_s1635937238list_a Xs4) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_set_list_a Xs4) I4)))))))))
% 0.26/0.70 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.set_set_a Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X3 tptp.set_set_a)) (@ (@ P I4) X3)))) (exists ((Xs4 tptp.list_set_set_a)) (and (= (@ tptp.size_s739728560_set_a Xs4) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_set_set_a Xs4) I4)))))))))
% 0.26/0.70 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X3 tptp.nat)) (@ (@ P I4) X3)))) (exists ((Xs4 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs4) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_nat Xs4) I4)))))))))
% 0.26/0.70 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.a Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X3 tptp.a)) (@ (@ P I4) X3)))) (exists ((Xs4 tptp.list_a)) (and (= (@ tptp.size_size_list_a Xs4) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_a Xs4) I4)))))))))
% 0.26/0.70 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.set_a Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X3 tptp.set_a)) (@ (@ P I4) X3)))) (exists ((Xs4 tptp.list_set_a)) (and (= (@ tptp.size_size_list_set_a Xs4) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_set_a Xs4) I4)))))))))
% 0.26/0.70 (assert (= (lambda ((Y2 tptp.list_list_a) (Z tptp.list_list_a)) (= Y2 Z)) (lambda ((Xs4 tptp.list_list_a) (Ys3 tptp.list_list_a)) (and (= (@ tptp.size_s1427607542list_a Xs4) (@ tptp.size_s1427607542list_a Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s1427607542list_a Xs4)) (= (@ (@ tptp.nth_list_a Xs4) I4) (@ (@ tptp.nth_list_a Ys3) I4))))))))
% 0.26/0.70 (assert (= (lambda ((Y2 tptp.list_set_list_a) (Z tptp.list_set_list_a)) (= Y2 Z)) (lambda ((Xs4 tptp.list_set_list_a) (Ys3 tptp.list_set_list_a)) (and (= (@ tptp.size_s1635937238list_a Xs4) (@ tptp.size_s1635937238list_a Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s1635937238list_a Xs4)) (= (@ (@ tptp.nth_set_list_a Xs4) I4) (@ (@ tptp.nth_set_list_a Ys3) I4))))))))
% 0.26/0.70 (assert (= (lambda ((Y2 tptp.list_set_set_a) (Z tptp.list_set_set_a)) (= Y2 Z)) (lambda ((Xs4 tptp.list_set_set_a) (Ys3 tptp.list_set_set_a)) (and (= (@ tptp.size_s739728560_set_a Xs4) (@ tptp.size_s739728560_set_a Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s739728560_set_a Xs4)) (= (@ (@ tptp.nth_set_set_a Xs4) I4) (@ (@ tptp.nth_set_set_a Ys3) I4))))))))
% 0.26/0.70 (assert (= (lambda ((Y2 tptp.list_nat) (Z tptp.list_nat)) (= Y2 Z)) (lambda ((Xs4 tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs4) (@ tptp.size_size_list_nat Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs4)) (= (@ (@ tptp.nth_nat Xs4) I4) (@ (@ tptp.nth_nat Ys3) I4))))))))
% 0.26/0.70 (assert (= (lambda ((Y2 tptp.list_a) (Z tptp.list_a)) (= Y2 Z)) (lambda ((Xs4 tptp.list_a) (Ys3 tptp.list_a)) (and (= (@ tptp.size_size_list_a Xs4) (@ tptp.size_size_list_a Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_a Xs4)) (= (@ (@ tptp.nth_a Xs4) I4) (@ (@ tptp.nth_a Ys3) I4))))))))
% 0.26/0.70 (assert (= (lambda ((Y2 tptp.list_set_a) (Z tptp.list_set_a)) (= Y2 Z)) (lambda ((Xs4 tptp.list_set_a) (Ys3 tptp.list_set_a)) (and (= (@ tptp.size_size_list_set_a Xs4) (@ tptp.size_size_list_set_a Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_set_a Xs4)) (= (@ (@ tptp.nth_set_a Xs4) I4) (@ (@ tptp.nth_set_a Ys3) I4))))))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat X4) (@ tptp.set_ord_lessThan_nat Y3)) (= X4 Y3))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= (@ tptp.rev_a Xs) (@ tptp.rev_a Ys)) (= Xs Ys))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (= (= (@ tptp.rev_set_a Xs) (@ tptp.rev_set_a Ys)) (= Xs Ys))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_a)) (= (@ tptp.rev_a (@ tptp.rev_a Xs)) Xs)))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a)) (= (@ tptp.rev_set_a (@ tptp.rev_set_a Xs)) Xs)))
% 0.26/0.70 (assert (= (@ tptp.size_size_list_set_a tptp.ss1) (@ tptp.size_size_list_set_a tptp.ss2)))
% 0.26/0.70 (assert (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a tptp.ss1)) (= (@ (@ tptp.nth_set_a tptp.ss2) I) (@ (@ tptp.nth_set_a tptp.ss1) (@ tptp.g I))))))
% 0.26/0.70 (assert (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a tptp.ss2)) (= (@ (@ tptp.nth_set_a tptp.ss1) I) (@ (@ tptp.nth_set_a tptp.ss2) (@ tptp.f I))))))
% 0.26/0.70 (assert (not (forall ((F2 (-> tptp.nat tptp.nat))) (=> (@ (@ (@ tptp.bij_betw_nat_nat F2) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a tptp.ss2))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a tptp.ss1))) (not (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_set_a tptp.ss2)) (= (@ (@ tptp.nth_set_a tptp.ss1) I2) (@ (@ tptp.nth_set_a tptp.ss2) (@ F2 I2))))))))))
% 0.26/0.70 (assert (exists ((F2 (-> tptp.nat tptp.nat))) (and (@ (@ (@ tptp.bij_betw_nat_nat F2) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a tptp.ss1))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a tptp.ss2))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_set_a tptp.ss1)) (= (@ (@ tptp.nth_set_a tptp.ss1) I2) (@ (@ tptp.nth_set_a tptp.ss2) (@ F2 I2))))))))
% 0.26/0.70 (assert (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a tptp.ss1)) (= (@ tptp.f (@ tptp.g I)) I))))
% 0.26/0.70 (assert (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a tptp.ss2)) (= (@ tptp.g (@ tptp.f I)) I))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_set_set_a) (Xs tptp.list_set_set_set_a) (I tptp.nat)) (=> (@ (@ tptp.member814963949_set_a Ys) (@ tptp.listset_set_set_a Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s726512144_set_a Xs)) (@ (@ tptp.member_set_set_a (@ (@ tptp.nth_set_set_a Ys) I)) (@ (@ tptp.nth_set_set_set_a Xs) I))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_set_list_a) (Xs tptp.list_set_set_list_a) (I tptp.nat)) (=> (@ (@ tptp.member101195155list_a Ys) (@ tptp.listset_set_list_a Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s469631926list_a Xs)) (@ (@ tptp.member_set_list_a (@ (@ tptp.nth_set_list_a Ys) I)) (@ (@ tptp.nth_set_set_list_a Xs) I))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_multiset_a) (Xs tptp.list_set_multiset_a) (I tptp.nat)) (=> (@ (@ tptp.member518144627iset_a Ys) (@ tptp.listset_multiset_a Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s802269334iset_a Xs)) (@ (@ tptp.member_multiset_a (@ (@ tptp.nth_multiset_a Ys) I)) (@ (@ tptp.nth_set_multiset_a Xs) I))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_list_list_a) (Xs tptp.list_set_list_list_a) (I tptp.nat)) (=> (@ (@ tptp.member1511395513list_a Ys) (@ tptp.listset_list_list_a Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s240404444list_a Xs)) (@ (@ tptp.member_list_list_a (@ (@ tptp.nth_list_list_a Ys) I)) (@ (@ tptp.nth_set_list_list_a Xs) I))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_list_set_a) (Xs tptp.list_set_list_set_a) (I tptp.nat)) (=> (@ (@ tptp.member954073875_set_a Ys) (@ tptp.listset_list_set_a Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s926492982_set_a Xs)) (@ (@ tptp.member_list_set_a (@ (@ tptp.nth_list_set_a Ys) I)) (@ (@ tptp.nth_set_list_set_a Xs) I))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_nat) (Xs tptp.list_set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_list_nat Ys) (@ tptp.listset_nat Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s577819178et_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Ys) I)) (@ (@ tptp.nth_set_nat Xs) I))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_set_a) (Xs tptp.list_set_set_a) (I tptp.nat)) (=> (@ (@ tptp.member_list_set_a Ys) (@ tptp.listset_set_a Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s739728560_set_a Xs)) (@ (@ tptp.member_set_a (@ (@ tptp.nth_set_a Ys) I)) (@ (@ tptp.nth_set_set_a Xs) I))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_list_a) (Xs tptp.list_set_list_a) (I tptp.nat)) (=> (@ (@ tptp.member_list_list_a Ys) (@ tptp.listset_list_a Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1635937238list_a Xs)) (@ (@ tptp.member_list_a (@ (@ tptp.nth_list_a Ys) I)) (@ (@ tptp.nth_set_list_a Xs) I))))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_a) (Xs tptp.list_set_a) (I tptp.nat)) (=> (@ (@ tptp.member_list_a Ys) (@ tptp.listset_a Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a Xs)) (@ (@ tptp.member_a (@ (@ tptp.nth_a Ys) I)) (@ (@ tptp.nth_set_a Xs) I))))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (not (= (@ tptp.size_s1427607542list_a Xs) (@ tptp.size_s1427607542list_a Ys))) (not (= Xs Ys)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_list_a) (Ys tptp.list_set_list_a)) (=> (not (= (@ tptp.size_s1635937238list_a Xs) (@ tptp.size_s1635937238list_a Ys))) (not (= Xs Ys)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_set_a) (Ys tptp.list_set_set_a)) (=> (not (= (@ tptp.size_s739728560_set_a Xs) (@ tptp.size_s739728560_set_a Ys))) (not (= Xs Ys)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys))) (not (= Xs Ys)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (not (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys))) (not (= Xs Ys)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (=> (not (= (@ tptp.size_size_list_set_a Xs) (@ tptp.size_size_list_set_a Ys))) (not (= Xs Ys)))))
% 0.26/0.70 (assert (forall ((A2 tptp.multiset_a) (P (-> tptp.multiset_a Bool))) (= (@ (@ tptp.member_multiset_a A2) (@ tptp.collect_multiset_a P)) (@ P A2))))
% 0.26/0.70 (assert (forall ((A2 tptp.list_list_a) (P (-> tptp.list_list_a Bool))) (= (@ (@ tptp.member_list_list_a A2) (@ tptp.collect_list_list_a P)) (@ P A2))))
% 0.26/0.70 (assert (forall ((A2 tptp.list_set_a) (P (-> tptp.list_set_a Bool))) (= (@ (@ tptp.member_list_set_a A2) (@ tptp.collect_list_set_a P)) (@ P A2))))
% 0.26/0.70 (assert (forall ((A2 tptp.set_a) (P (-> tptp.set_a Bool))) (= (@ (@ tptp.member_set_a A2) (@ tptp.collect_set_a P)) (@ P A2))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A2) (@ tptp.collect_nat P)) (@ P A2))))
% 0.26/0.70 (assert (forall ((A2 tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a A2) (@ tptp.collect_a P)) (@ P A2))))
% 0.26/0.70 (assert (forall ((A2 tptp.list_a) (P (-> tptp.list_a Bool))) (= (@ (@ tptp.member_list_a A2) (@ tptp.collect_list_a P)) (@ P A2))))
% 0.26/0.70 (assert (forall ((A tptp.set_multiset_a)) (= (@ tptp.collect_multiset_a (lambda ((X5 tptp.multiset_a)) (@ (@ tptp.member_multiset_a X5) A))) A)))
% 0.26/0.70 (assert (forall ((A tptp.set_list_list_a)) (= (@ tptp.collect_list_list_a (lambda ((X5 tptp.list_list_a)) (@ (@ tptp.member_list_list_a X5) A))) A)))
% 0.26/0.70 (assert (forall ((A tptp.set_list_set_a)) (= (@ tptp.collect_list_set_a (lambda ((X5 tptp.list_set_a)) (@ (@ tptp.member_list_set_a X5) A))) A)))
% 0.26/0.70 (assert (forall ((A tptp.set_set_a)) (= (@ tptp.collect_set_a (lambda ((X5 tptp.set_a)) (@ (@ tptp.member_set_a X5) A))) A)))
% 0.26/0.70 (assert (forall ((A tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X5 tptp.nat)) (@ (@ tptp.member_nat X5) A))) A)))
% 0.26/0.70 (assert (forall ((A tptp.set_a)) (= (@ tptp.collect_a (lambda ((X5 tptp.a)) (@ (@ tptp.member_a X5) A))) A)))
% 0.26/0.70 (assert (forall ((A tptp.set_list_a)) (= (@ tptp.collect_list_a (lambda ((X5 tptp.list_a)) (@ (@ tptp.member_list_a X5) A))) A)))
% 0.26/0.70 (assert (forall ((P (-> tptp.list_a Bool)) (Q (-> tptp.list_a Bool))) (=> (forall ((X6 tptp.list_a)) (= (@ P X6) (@ Q X6))) (= (@ tptp.collect_list_a P) (@ tptp.collect_list_a Q)))))
% 0.26/0.70 (assert (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X6 tptp.a)) (= (@ P X6) (@ Q X6))) (= (@ tptp.collect_a P) (@ tptp.collect_a Q)))))
% 0.26/0.70 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_list_a)) (= (@ tptp.size_s1427607542list_a Xs2) N))))
% 0.26/0.70 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_set_list_a)) (= (@ tptp.size_s1635937238list_a Xs2) N))))
% 0.26/0.70 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_set_set_a)) (= (@ tptp.size_s739728560_set_a Xs2) N))))
% 0.26/0.70 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs2) N))))
% 0.26/0.70 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_a)) (= (@ tptp.size_size_list_a Xs2) N))))
% 0.26/0.70 (assert (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_set_a)) (= (@ tptp.size_size_list_set_a Xs2) N))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= (@ tptp.rev_a Xs) Ys) (= Xs (@ tptp.rev_a Ys)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (= (= (@ tptp.rev_set_a Xs) Ys) (= Xs (@ tptp.rev_set_a Ys)))))
% 0.26/0.70 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M)) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.26/0.70 (assert (forall ((P (-> tptp.list_set_list_a Bool)) (Xs tptp.list_set_list_a)) (=> (forall ((Xs2 tptp.list_set_list_a)) (=> (forall ((Ys4 tptp.list_set_list_a)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s1635937238list_a Ys4)) (@ tptp.size_s1635937238list_a Xs2)) (@ P Ys4))) (@ P Xs2))) (@ P Xs))))
% 0.26/0.70 (assert (forall ((P (-> tptp.list_set_set_a Bool)) (Xs tptp.list_set_set_a)) (=> (forall ((Xs2 tptp.list_set_set_a)) (=> (forall ((Ys4 tptp.list_set_set_a)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s739728560_set_a Ys4)) (@ tptp.size_s739728560_set_a Xs2)) (@ P Ys4))) (@ P Xs2))) (@ P Xs))))
% 0.26/0.70 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs2 tptp.list_nat)) (=> (forall ((Ys4 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys4)) (@ tptp.size_size_list_nat Xs2)) (@ P Ys4))) (@ P Xs2))) (@ P Xs))))
% 0.26/0.70 (assert (forall ((P (-> tptp.list_a Bool)) (Xs tptp.list_a)) (=> (forall ((Xs2 tptp.list_a)) (=> (forall ((Ys4 tptp.list_a)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_a Ys4)) (@ tptp.size_size_list_a Xs2)) (@ P Ys4))) (@ P Xs2))) (@ P Xs))))
% 0.26/0.70 (assert (forall ((P (-> tptp.list_set_a Bool)) (Xs tptp.list_set_a)) (=> (forall ((Xs2 tptp.list_set_a)) (=> (forall ((Ys4 tptp.list_set_a)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_set_a Ys4)) (@ tptp.size_size_list_set_a Xs2)) (@ P Ys4))) (@ P Xs2))) (@ P Xs))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_a) (Xs tptp.list_set_a)) (=> (@ (@ tptp.member_list_a Ys) (@ tptp.listset_a Xs)) (= (@ tptp.size_size_list_a Ys) (@ tptp.size_size_list_set_a Xs)))))
% 0.26/0.70 (assert (forall ((Ys tptp.list_set_a) (Xs tptp.list_set_set_a)) (=> (@ (@ tptp.member_list_set_a Ys) (@ tptp.listset_set_a Xs)) (= (@ tptp.size_size_list_set_a Ys) (@ tptp.size_s739728560_set_a Xs)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ tptp.perm_a Xs) Ys) (exists ((F2 (-> tptp.nat tptp.nat))) (and (@ (@ (@ tptp.bij_betw_nat_nat F2) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_a Ys))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a Xs) I2) (@ (@ tptp.nth_a Ys) (@ F2 I2))))))))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (=> (@ (@ tptp.perm_set_a Xs) Ys) (exists ((F2 (-> tptp.nat tptp.nat))) (and (@ (@ (@ tptp.bij_betw_nat_nat F2) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a Ys))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_set_a Xs)) (= (@ (@ tptp.nth_set_a Xs) I2) (@ (@ tptp.nth_set_a Ys) (@ F2 I2))))))))))
% 0.26/0.70 (assert (= tptp.g (@ (@ tptp.hilber815131374at_nat (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a tptp.ss2))) tptp.f)))
% 0.26/0.70 (assert (forall ((L tptp.list_set_a)) (@ (@ tptp.perm_set_a L) L)))
% 0.26/0.70 (assert (forall ((B tptp.a) (F (-> tptp.a tptp.a)) (X4 tptp.a) (A tptp.set_a)) (=> (= B (@ F X4)) (=> (@ (@ tptp.member_a X4) A) (@ (@ tptp.member_a B) (@ (@ tptp.image_a_a F) A))))))
% 0.26/0.70 (assert (forall ((B tptp.list_a) (F (-> tptp.a tptp.list_a)) (X4 tptp.a) (A tptp.set_a)) (=> (= B (@ F X4)) (=> (@ (@ tptp.member_a X4) A) (@ (@ tptp.member_list_a B) (@ (@ tptp.image_a_list_a F) A))))))
% 0.26/0.70 (assert (forall ((B tptp.a) (F (-> tptp.list_a tptp.a)) (X4 tptp.list_a) (A tptp.set_list_a)) (=> (= B (@ F X4)) (=> (@ (@ tptp.member_list_a X4) A) (@ (@ tptp.member_a B) (@ (@ tptp.image_list_a_a F) A))))))
% 0.26/0.70 (assert (forall ((B tptp.list_a) (F (-> tptp.list_a tptp.list_a)) (X4 tptp.list_a) (A tptp.set_list_a)) (=> (= B (@ F X4)) (=> (@ (@ tptp.member_list_a X4) A) (@ (@ tptp.member_list_a B) (@ (@ tptp.image_list_a_list_a F) A))))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= (@ tptp.mset_a Xs) (@ tptp.mset_a Ys)) (@ (@ tptp.perm_a Xs) Ys))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (= (= (@ tptp.mset_set_a Xs) (@ tptp.mset_set_a Ys)) (@ (@ tptp.perm_set_a Xs) Ys))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a)) (@ (@ tptp.perm_set_a (@ tptp.rev_set_a Xs)) Xs)))
% 0.26/0.70 (assert (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ tptp.perm_a Xs) Ys) (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (=> (@ (@ tptp.perm_set_a Xs) Ys) (= (@ tptp.size_size_list_set_a Xs) (@ tptp.size_size_list_set_a Ys)))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) B2) (= (@ (@ tptp.image_nat_nat F) A) B2))))
% 0.26/0.70 (assert (forall ((X4 tptp.list_a) (A tptp.set_list_a) (Y3 tptp.list_a)) (=> (@ (@ tptp.member_list_a X4) A) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_a X4)) (@ tptp.size_size_list_a Y3)) (not (= X4 Y3))))))
% 0.26/0.70 (assert (forall ((X4 tptp.list_set_a) (A tptp.set_list_set_a) (Y3 tptp.list_set_a)) (=> (@ (@ tptp.member_list_set_a X4) A) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_set_a X4)) (@ tptp.size_size_list_set_a Y3)) (not (= X4 Y3))))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_a)) (= (@ tptp.size_size_multiset_a (@ tptp.mset_a Xs)) (@ tptp.size_size_list_a Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a)) (= (@ tptp.size_s657334288_set_a (@ tptp.mset_set_a Xs)) (@ tptp.size_size_list_set_a Xs))))
% 0.26/0.70 (assert (forall ((A tptp.set_a) (B2 tptp.set_a) (C tptp.a)) (let ((_let_1 (@ tptp.member_a C))) (=> (@ (@ tptp.ord_less_set_a A) B2) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((A tptp.set_list_a) (B2 tptp.set_list_a) (C tptp.list_a)) (let ((_let_1 (@ tptp.member_list_a C))) (=> (@ (@ tptp.ord_less_set_list_a A) B2) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((X4 tptp.a) (A tptp.set_a) (F (-> tptp.a tptp.a))) (=> (@ (@ tptp.member_a X4) A) (@ (@ tptp.member_a (@ F X4)) (@ (@ tptp.image_a_a F) A)))))
% 0.26/0.70 (assert (forall ((X4 tptp.a) (A tptp.set_a) (F (-> tptp.a tptp.list_a))) (=> (@ (@ tptp.member_a X4) A) (@ (@ tptp.member_list_a (@ F X4)) (@ (@ tptp.image_a_list_a F) A)))))
% 0.26/0.70 (assert (forall ((X4 tptp.list_a) (A tptp.set_list_a) (F (-> tptp.list_a tptp.a))) (=> (@ (@ tptp.member_list_a X4) A) (@ (@ tptp.member_a (@ F X4)) (@ (@ tptp.image_list_a_a F) A)))))
% 0.26/0.70 (assert (forall ((X4 tptp.list_a) (A tptp.set_list_a) (F (-> tptp.list_a tptp.list_a))) (=> (@ (@ tptp.member_list_a X4) A) (@ (@ tptp.member_list_a (@ F X4)) (@ (@ tptp.image_list_a_list_a F) A)))))
% 0.26/0.70 (assert (forall ((X4 tptp.a) (A tptp.set_a) (B tptp.a) (F (-> tptp.a tptp.a))) (=> (@ (@ tptp.member_a X4) A) (=> (= B (@ F X4)) (@ (@ tptp.member_a B) (@ (@ tptp.image_a_a F) A))))))
% 0.26/0.70 (assert (forall ((X4 tptp.a) (A tptp.set_a) (B tptp.list_a) (F (-> tptp.a tptp.list_a))) (=> (@ (@ tptp.member_a X4) A) (=> (= B (@ F X4)) (@ (@ tptp.member_list_a B) (@ (@ tptp.image_a_list_a F) A))))))
% 0.26/0.70 (assert (forall ((X4 tptp.list_a) (A tptp.set_list_a) (B tptp.a) (F (-> tptp.list_a tptp.a))) (=> (@ (@ tptp.member_list_a X4) A) (=> (= B (@ F X4)) (@ (@ tptp.member_a B) (@ (@ tptp.image_list_a_a F) A))))))
% 0.26/0.70 (assert (forall ((X4 tptp.list_a) (A tptp.set_list_a) (B tptp.list_a) (F (-> tptp.list_a tptp.list_a))) (=> (@ (@ tptp.member_list_a X4) A) (=> (= B (@ F X4)) (@ (@ tptp.member_list_a B) (@ (@ tptp.image_list_a_list_a F) A))))))
% 0.26/0.70 (assert (= tptp.hilber2037636820comp_a (lambda ((A4 tptp.set_a) (Ss2 tptp.list_set_a)) (@ (@ (@ tptp.bij_betw_list_a_a tptp.groups1792256535list_a) (@ tptp.listset_a Ss2)) A4))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) B2) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.member_nat (@ F X)) B2))))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) B2) (exists ((G (-> tptp.nat tptp.nat))) (@ (@ (@ tptp.bij_betw_nat_nat G) B2) A)))))
% 0.26/0.70 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G2 (-> tptp.nat tptp.nat)) (A5 tptp.set_nat)) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A) (= (@ F A3) (@ G2 A3)))) (= (@ (@ (@ tptp.bij_betw_nat_nat F) A) A5) (@ (@ (@ tptp.bij_betw_nat_nat G2) A) A5)))))
% 0.26/0.70 (assert (forall ((F (-> tptp.a tptp.a)) (A tptp.set_a) (B2 tptp.set_a) (A2 tptp.a)) (=> (@ (@ (@ tptp.bij_betw_a_a F) A) B2) (=> (@ (@ tptp.member_a A2) A) (@ (@ tptp.member_a (@ F A2)) B2)))))
% 0.26/0.70 (assert (forall ((F (-> tptp.a tptp.list_a)) (A tptp.set_a) (B2 tptp.set_list_a) (A2 tptp.a)) (=> (@ (@ (@ tptp.bij_betw_a_list_a F) A) B2) (=> (@ (@ tptp.member_a A2) A) (@ (@ tptp.member_list_a (@ F A2)) B2)))))
% 0.26/0.70 (assert (forall ((F (-> tptp.list_a tptp.a)) (A tptp.set_list_a) (B2 tptp.set_a) (A2 tptp.list_a)) (=> (@ (@ (@ tptp.bij_betw_list_a_a F) A) B2) (=> (@ (@ tptp.member_list_a A2) A) (@ (@ tptp.member_a (@ F A2)) B2)))))
% 0.26/0.70 (assert (forall ((F (-> tptp.list_a tptp.list_a)) (A tptp.set_list_a) (B2 tptp.set_list_a) (A2 tptp.list_a)) (=> (@ (@ (@ tptp.bij_be94573046list_a F) A) B2) (=> (@ (@ tptp.member_list_a A2) A) (@ (@ tptp.member_list_a (@ F A2)) B2)))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B2 tptp.set_nat) (A2 tptp.nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) B2) (=> (@ (@ tptp.member_nat A2) A) (@ (@ tptp.member_nat (@ F A2)) B2)))))
% 0.26/0.70 (assert (= tptp.bij_betw_a_a (lambda ((F3 (-> tptp.a tptp.a)) (A4 tptp.set_a) (B3 tptp.set_a)) (exists ((G3 (-> tptp.a tptp.a))) (and (forall ((X5 tptp.a)) (let ((_let_1 (@ F3 X5))) (=> (@ (@ tptp.member_a X5) A4) (and (@ (@ tptp.member_a _let_1) B3) (= (@ G3 _let_1) X5))))) (forall ((X5 tptp.a)) (let ((_let_1 (@ G3 X5))) (=> (@ (@ tptp.member_a X5) B3) (and (@ (@ tptp.member_a _let_1) A4) (= (@ F3 _let_1) X5))))))))))
% 0.26/0.70 (assert (= tptp.bij_betw_list_a_a (lambda ((F3 (-> tptp.list_a tptp.a)) (A4 tptp.set_list_a) (B3 tptp.set_a)) (exists ((G3 (-> tptp.a tptp.list_a))) (and (forall ((X5 tptp.list_a)) (let ((_let_1 (@ F3 X5))) (=> (@ (@ tptp.member_list_a X5) A4) (and (@ (@ tptp.member_a _let_1) B3) (= (@ G3 _let_1) X5))))) (forall ((X5 tptp.a)) (let ((_let_1 (@ G3 X5))) (=> (@ (@ tptp.member_a X5) B3) (and (@ (@ tptp.member_list_a _let_1) A4) (= (@ F3 _let_1) X5))))))))))
% 0.26/0.70 (assert (= tptp.bij_betw_a_list_a (lambda ((F3 (-> tptp.a tptp.list_a)) (A4 tptp.set_a) (B3 tptp.set_list_a)) (exists ((G3 (-> tptp.list_a tptp.a))) (and (forall ((X5 tptp.a)) (let ((_let_1 (@ F3 X5))) (=> (@ (@ tptp.member_a X5) A4) (and (@ (@ tptp.member_list_a _let_1) B3) (= (@ G3 _let_1) X5))))) (forall ((X5 tptp.list_a)) (let ((_let_1 (@ G3 X5))) (=> (@ (@ tptp.member_list_a X5) B3) (and (@ (@ tptp.member_a _let_1) A4) (= (@ F3 _let_1) X5))))))))))
% 0.26/0.70 (assert (= tptp.bij_be94573046list_a (lambda ((F3 (-> tptp.list_a tptp.list_a)) (A4 tptp.set_list_a) (B3 tptp.set_list_a)) (exists ((G3 (-> tptp.list_a tptp.list_a))) (and (forall ((X5 tptp.list_a)) (let ((_let_1 (@ F3 X5))) (=> (@ (@ tptp.member_list_a X5) A4) (and (@ (@ tptp.member_list_a _let_1) B3) (= (@ G3 _let_1) X5))))) (forall ((X5 tptp.list_a)) (let ((_let_1 (@ G3 X5))) (=> (@ (@ tptp.member_list_a X5) B3) (and (@ (@ tptp.member_list_a _let_1) A4) (= (@ F3 _let_1) X5))))))))))
% 0.26/0.70 (assert (= tptp.bij_betw_nat_nat (lambda ((F3 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (B3 tptp.set_nat)) (exists ((G3 (-> tptp.nat tptp.nat))) (and (forall ((X5 tptp.nat)) (let ((_let_1 (@ F3 X5))) (=> (@ (@ tptp.member_nat X5) A4) (and (@ (@ tptp.member_nat _let_1) B3) (= (@ G3 _let_1) X5))))) (forall ((X5 tptp.nat)) (let ((_let_1 (@ G3 X5))) (=> (@ (@ tptp.member_nat X5) B3) (and (@ (@ tptp.member_nat _let_1) A4) (= (@ F3 _let_1) X5))))))))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (=> (@ (@ tptp.perm_set_a Xs) Ys) (@ (@ tptp.perm_set_a Ys) Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a) (Zs tptp.list_set_a)) (let ((_let_1 (@ tptp.perm_set_a Xs))) (=> (@ _let_1 Ys) (=> (@ (@ tptp.perm_set_a Ys) Zs) (@ _let_1 Zs))))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (A5 tptp.set_nat) (A6 tptp.nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) A5) (=> (@ (@ tptp.member_nat A6) A5) (= (@ F (@ (@ (@ tptp.hilber815131374at_nat A) F) A6)) A6)))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (A5 tptp.set_nat) (A2 tptp.nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) A5) (=> (@ (@ tptp.member_nat A2) A) (= (@ (@ (@ tptp.hilber815131374at_nat A) F) (@ F A2)) A2)))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (A5 tptp.set_nat) (A2 tptp.nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) A5) (=> (@ (@ tptp.member_nat A2) A) (= (@ (@ (@ tptp.hilber815131374at_nat A5) (@ (@ tptp.hilber815131374at_nat A) F)) A2) (@ F A2))))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) B2) (@ (@ (@ tptp.bij_betw_nat_nat (@ (@ tptp.hilber815131374at_nat A) F)) B2) A))))
% 0.26/0.70 (assert (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat)) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.image_nat_nat F) A))) (let ((_let_2 (@ (@ tptp.hilber815131374at_nat A) F))) (=> (= (@ _let_2 X4) (@ _let_2 Y3)) (=> (@ (@ tptp.member_nat X4) _let_1) (=> (@ (@ tptp.member_nat Y3) _let_1) (= X4 Y3))))))))
% 0.26/0.70 (assert (forall ((X4 tptp.a) (F (-> tptp.a tptp.a)) (A tptp.set_a)) (=> (@ (@ tptp.member_a X4) (@ (@ tptp.image_a_a F) A)) (@ (@ tptp.member_a (@ (@ (@ tptp.hilbert_inv_into_a_a A) F) X4)) A))))
% 0.26/0.70 (assert (forall ((X4 tptp.a) (F (-> tptp.list_a tptp.a)) (A tptp.set_list_a)) (=> (@ (@ tptp.member_a X4) (@ (@ tptp.image_list_a_a F) A)) (@ (@ tptp.member_list_a (@ (@ (@ tptp.hilber2125729734st_a_a A) F) X4)) A))))
% 0.26/0.70 (assert (forall ((X4 tptp.list_a) (F (-> tptp.a tptp.list_a)) (A tptp.set_a)) (=> (@ (@ tptp.member_list_a X4) (@ (@ tptp.image_a_list_a F) A)) (@ (@ tptp.member_a (@ (@ (@ tptp.hilber165648082list_a A) F) X4)) A))))
% 0.26/0.70 (assert (forall ((X4 tptp.list_a) (F (-> tptp.list_a tptp.list_a)) (A tptp.set_list_a)) (=> (@ (@ tptp.member_list_a X4) (@ (@ tptp.image_list_a_list_a F) A)) (@ (@ tptp.member_list_a (@ (@ (@ tptp.hilber921249868list_a A) F) X4)) A))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.image_nat_nat F) A)) (@ (@ tptp.member_nat (@ (@ (@ tptp.hilber815131374at_nat A) F) X4)) A))))
% 0.26/0.70 (assert (forall ((Y3 tptp.nat) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat Y3) (@ (@ tptp.image_nat_nat F) A)) (= (@ F (@ (@ (@ tptp.hilber815131374at_nat A) F) Y3)) Y3))))
% 0.26/0.70 (assert (= tptp.list_ex_a (lambda ((P2 (-> tptp.a Bool)) (Xs4 tptp.list_a)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_a Xs4)) (@ P2 (@ (@ tptp.nth_a Xs4) N2)))))))
% 0.26/0.70 (assert (= tptp.list_ex_set_a (lambda ((P2 (-> tptp.set_a Bool)) (Xs4 tptp.list_set_a)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_set_a Xs4)) (@ P2 (@ (@ tptp.nth_set_a Xs4) N2)))))))
% 0.26/0.70 (assert (forall ((Ss tptp.list_set_a) (A tptp.set_a)) (let ((_let_1 (@ tptp.listset_a Ss))) (=> (@ (@ tptp.inj_on_list_a_a tptp.groups1792256535list_a) _let_1) (=> (= (@ (@ tptp.image_list_a_a tptp.groups1792256535list_a) _let_1) A) (@ (@ tptp.hilber2037636820comp_a A) Ss))))))
% 0.26/0.70 (assert (forall ((K tptp.nat) (Ns tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat K) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.nth_nat Ns) K)) (@ tptp.groups921905271st_nat Ns)))))
% 0.26/0.70 (assert (forall ((I tptp.nat) (Xs tptp.list_a) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_a Xs))) (let ((_let_2 (@ tptp.size_size_list_a Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (@ (@ tptp.perm_a (@ (@ (@ tptp.list_update_a (@ (@ (@ tptp.list_update_a Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) Xs)))))))
% 0.26/0.70 (assert (forall ((I tptp.nat) (Xs tptp.list_set_a) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_set_a Xs))) (let ((_let_2 (@ tptp.size_size_list_set_a Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (@ (@ tptp.perm_set_a (@ (@ (@ tptp.list_update_set_a (@ (@ (@ tptp.list_update_set_a Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) Xs)))))))
% 0.26/0.70 (assert (forall ((I tptp.nat) (Ls tptp.list_a) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_a Ls))) (let ((_let_2 (@ tptp.size_size_list_a Ls))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.mset_a (@ (@ (@ tptp.list_update_a (@ (@ (@ tptp.list_update_a Ls) J) (@ _let_1 I))) I) (@ _let_1 J))) (@ tptp.mset_a Ls))))))))
% 0.26/0.70 (assert (forall ((I tptp.nat) (Ls tptp.list_set_a) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_set_a Ls))) (let ((_let_2 (@ tptp.size_size_list_set_a Ls))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.mset_set_a (@ (@ (@ tptp.list_update_set_a (@ (@ (@ tptp.list_update_set_a Ls) J) (@ _let_1 I))) I) (@ _let_1 J))) (@ tptp.mset_set_a Ls))))))))
% 0.26/0.70 (assert (forall ((I tptp.nat) (Ls tptp.list_list_a)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1427607542list_a Ls)) (@ (@ tptp.member_list_a (@ (@ tptp.nth_list_a Ls) I)) (@ tptp.set_mset_list_a (@ tptp.mset_list_a Ls))))))
% 0.26/0.70 (assert (forall ((I tptp.nat) (Ls tptp.list_a)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_a Ls)) (@ (@ tptp.member_a (@ (@ tptp.nth_a Ls) I)) (@ tptp.set_mset_a (@ tptp.mset_a Ls))))))
% 0.26/0.70 (assert (forall ((I tptp.nat) (Ls tptp.list_set_a)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a Ls)) (@ (@ tptp.member_set_a (@ (@ tptp.nth_set_a Ls) I)) (@ tptp.set_mset_set_a (@ tptp.mset_set_a Ls))))))
% 0.26/0.70 (assert (forall ((X4 tptp.a) (MM tptp.multiset_multiset_a)) (= (@ (@ tptp.member_a X4) (@ tptp.set_mset_a (@ tptp.comm_m2145643721iset_a MM))) (exists ((M2 tptp.multiset_a)) (and (@ (@ tptp.member_multiset_a M2) (@ tptp.set_mset_multiset_a MM)) (@ (@ tptp.member_a X4) (@ tptp.set_mset_a M2)))))))
% 0.26/0.70 (assert (forall ((X4 tptp.list_a) (MM tptp.multis971982480list_a)) (= (@ (@ tptp.member_list_a X4) (@ tptp.set_mset_list_a (@ tptp.comm_m324867663list_a MM))) (exists ((M2 tptp.multiset_list_a)) (and (@ (@ tptp.member528267379list_a M2) (@ tptp.set_ms1660427399list_a MM)) (@ (@ tptp.member_list_a X4) (@ tptp.set_mset_list_a M2)))))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X4)) (@ tptp.set_ord_lessThan_nat Y3)) (@ (@ tptp.ord_less_eq_nat X4) Y3))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_a) (I tptp.nat) (X4 tptp.a)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_a Xs)) I) (= (@ (@ (@ tptp.list_update_a Xs) I) X4) Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a) (I tptp.nat) (X4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_set_a Xs)) I) (= (@ (@ (@ tptp.list_update_set_a Xs) I) X4) Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_a) (I tptp.nat) (X4 tptp.a)) (= (@ tptp.size_size_list_a (@ (@ (@ tptp.list_update_a Xs) I) X4)) (@ tptp.size_size_list_a Xs))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a) (I tptp.nat) (X4 tptp.set_a)) (= (@ tptp.size_size_list_set_a (@ (@ (@ tptp.list_update_set_a Xs) I) X4)) (@ tptp.size_size_list_set_a Xs))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (X4 tptp.nat)) (=> (@ (@ tptp.inj_on_nat_nat F) A) (=> (@ (@ tptp.member_nat X4) A) (= (@ (@ (@ tptp.hilber815131374at_nat A) F) (@ F X4)) X4)))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_a) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_a Xs) I) (@ (@ tptp.nth_a Xs) I)) Xs)))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_set_a Xs) I) (@ (@ tptp.nth_set_a Xs) I)) Xs)))
% 0.26/0.70 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_a) (X4 tptp.a)) (=> (not (= I J)) (= (@ (@ tptp.nth_a (@ (@ (@ tptp.list_update_a Xs) I) X4)) J) (@ (@ tptp.nth_a Xs) J)))))
% 0.26/0.70 (assert (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_set_a) (X4 tptp.set_a)) (=> (not (= I J)) (= (@ (@ tptp.nth_set_a (@ (@ (@ tptp.list_update_set_a Xs) I) X4)) J) (@ (@ tptp.nth_set_a Xs) J)))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (S tptp.set_nat)) (=> (@ (@ tptp.inj_on_nat_nat F) A) (=> (@ (@ tptp.ord_less_eq_set_nat S) A) (= (@ (@ tptp.image_nat_nat (@ (@ tptp.hilber815131374at_nat A) F)) (@ (@ tptp.image_nat_nat F) S)) S)))))
% 0.26/0.70 (assert (forall ((I tptp.nat) (Xs tptp.list_a) (X4 tptp.a)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a (@ (@ (@ tptp.list_update_a Xs) I) X4)) I) X4))))
% 0.26/0.70 (assert (forall ((I tptp.nat) (Xs tptp.list_set_a) (X4 tptp.set_a)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a Xs)) (= (@ (@ tptp.nth_set_a (@ (@ (@ tptp.list_update_set_a Xs) I) X4)) I) X4))))
% 0.26/0.70 (assert (forall ((B2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) (@ (@ tptp.image_nat_nat F) A)) (@ (@ tptp.inj_on_nat_nat (@ (@ tptp.hilber815131374at_nat A) F)) B2))))
% 0.26/0.70 (assert (forall ((F (-> tptp.a tptp.a)) (B2 tptp.set_a) (A2 tptp.a) (A tptp.set_a)) (let ((_let_1 (@ tptp.member_a A2))) (=> (@ (@ tptp.inj_on_a_a F) B2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_a A) B2) (= (@ (@ tptp.member_a (@ F A2)) (@ (@ tptp.image_a_a F) A)) (@ _let_1 A))))))))
% 0.26/0.70 (assert (forall ((F (-> tptp.a tptp.list_a)) (B2 tptp.set_a) (A2 tptp.a) (A tptp.set_a)) (let ((_let_1 (@ tptp.member_a A2))) (=> (@ (@ tptp.inj_on_a_list_a F) B2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_a A) B2) (= (@ (@ tptp.member_list_a (@ F A2)) (@ (@ tptp.image_a_list_a F) A)) (@ _let_1 A))))))))
% 0.26/0.70 (assert (forall ((F (-> tptp.list_a tptp.a)) (B2 tptp.set_list_a) (A2 tptp.list_a) (A tptp.set_list_a)) (let ((_let_1 (@ tptp.member_list_a A2))) (=> (@ (@ tptp.inj_on_list_a_a F) B2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le1301786372list_a A) B2) (= (@ (@ tptp.member_a (@ F A2)) (@ (@ tptp.image_list_a_a F) A)) (@ _let_1 A))))))))
% 0.26/0.70 (assert (forall ((F (-> tptp.list_a tptp.list_a)) (B2 tptp.set_list_a) (A2 tptp.list_a) (A tptp.set_list_a)) (let ((_let_1 (@ tptp.member_list_a A2))) (=> (@ (@ tptp.inj_on_list_a_list_a F) B2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le1301786372list_a A) B2) (= (@ (@ tptp.member_list_a (@ F A2)) (@ (@ tptp.image_list_a_list_a F) A)) (@ _let_1 A))))))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) B2) (@ (@ tptp.inj_on_nat_nat F) A))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.inj_on_nat_nat F) A) (=> (@ (@ tptp.member_nat X4) A) (=> (= (@ F X4) Y3) (= (@ (@ (@ tptp.hilber815131374at_nat A) F) Y3) X4))))))
% 0.26/0.70 (assert (forall ((A tptp.set_a) (F (-> tptp.a tptp.a)) (B2 tptp.set_a)) (=> (forall ((X6 tptp.a)) (=> (@ (@ tptp.member_a X6) A) (@ (@ tptp.member_a (@ F X6)) B2))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_a_a F) A)) B2))))
% 0.26/0.70 (assert (forall ((A tptp.set_a) (F (-> tptp.a tptp.list_a)) (B2 tptp.set_list_a)) (=> (forall ((X6 tptp.a)) (=> (@ (@ tptp.member_a X6) A) (@ (@ tptp.member_list_a (@ F X6)) B2))) (@ (@ tptp.ord_le1301786372list_a (@ (@ tptp.image_a_list_a F) A)) B2))))
% 0.26/0.70 (assert (forall ((A tptp.set_list_a) (F (-> tptp.list_a tptp.a)) (B2 tptp.set_a)) (=> (forall ((X6 tptp.list_a)) (=> (@ (@ tptp.member_list_a X6) A) (@ (@ tptp.member_a (@ F X6)) B2))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_list_a_a F) A)) B2))))
% 0.26/0.70 (assert (forall ((A tptp.set_list_a) (F (-> tptp.list_a tptp.list_a)) (B2 tptp.set_list_a)) (=> (forall ((X6 tptp.list_a)) (=> (@ (@ tptp.member_list_a X6) A) (@ (@ tptp.member_list_a (@ F X6)) B2))) (@ (@ tptp.ord_le1301786372list_a (@ (@ tptp.image_list_a_list_a F) A)) B2))))
% 0.26/0.70 (assert (= tptp.bij_betw_nat_nat (lambda ((F3 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.inj_on_nat_nat F3) A4) (= (@ (@ tptp.image_nat_nat F3) A4) B3)))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.inj_on_nat_nat F) A) (=> (= (@ (@ tptp.image_nat_nat F) A) B2) (@ (@ (@ tptp.bij_betw_nat_nat F) A) B2)))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ (@ tptp.inj_on_nat_nat F) A) (@ (@ (@ tptp.bij_betw_nat_nat F) A) (@ (@ tptp.image_nat_nat F) A)))))
% 0.26/0.70 (assert (forall ((X4 tptp.list_a) (A tptp.set_list_a) (P (-> tptp.list_a Bool))) (=> (@ (@ tptp.member_list_a X4) A) (=> (@ P X4) (exists ((X6 tptp.list_a)) (and (@ (@ tptp.member_list_a X6) A) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_a X6)) (@ tptp.size_size_list_a X4)) (@ P X6) (forall ((Xa tptp.list_a)) (=> (@ (@ tptp.member_list_a Xa) A) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_a Xa)) (@ tptp.size_size_list_a X6)) (not (@ P Xa)))))))))))
% 0.26/0.70 (assert (forall ((X4 tptp.list_set_a) (A tptp.set_list_set_a) (P (-> tptp.list_set_a Bool))) (=> (@ (@ tptp.member_list_set_a X4) A) (=> (@ P X4) (exists ((X6 tptp.list_set_a)) (and (@ (@ tptp.member_list_set_a X6) A) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_set_a X6)) (@ tptp.size_size_list_set_a X4)) (@ P X6) (forall ((Xa tptp.list_set_a)) (=> (@ (@ tptp.member_list_set_a Xa) A) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_set_a Xa)) (@ tptp.size_size_list_set_a X6)) (not (@ P Xa)))))))))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (A5 tptp.set_nat) (B2 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.bij_betw_nat_nat F))) (=> (@ (@ _let_1 A) A5) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A) (=> (= (@ (@ tptp.image_nat_nat F) B2) B4) (@ (@ _let_1 B2) B4)))))))
% 0.26/0.70 (assert (forall ((A tptp.set_nat) (F4 (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat)) (A5 tptp.set_nat)) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A) (= (@ F4 (@ F X6)) X6))) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A5) (= (@ F (@ F4 X6)) X6))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat F) A)) A5) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat F4) A5)) A) (@ (@ (@ tptp.bij_betw_nat_nat F) A) A5)))))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (A5 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat F))) (=> (= (@ _let_1 A) A5) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A5) (= (@ _let_1 (@ (@ tptp.image_nat_nat (@ (@ tptp.hilber815131374at_nat A) F)) B4)) B4))))))
% 0.26/0.70 (assert (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (=> (= (@ tptp.size_size_list_set_a Xs) (@ tptp.size_size_list_set_a Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_set_a Ys)) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.nth_set_a Xs) I3)) (@ (@ tptp.nth_set_a Ys) I3)))) (@ (@ tptp.ord_le1301786372list_a (@ tptp.listset_a Xs)) (@ tptp.listset_a Ys))))))
% 0.26/0.70 (assert (forall ((I tptp.nat) (Xs tptp.list_a) (J tptp.nat) (X4 tptp.a)) (let ((_let_1 (@ (@ tptp.nth_a (@ (@ (@ tptp.list_update_a Xs) I) X4)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_a Xs)) (and (=> _let_2 (= _let_1 X4)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_a Xs) J)))))))))
% 0.26/0.70 (assert (forall ((I tptp.nat) (Xs tptp.list_set_a) (J tptp.nat) (X4 tptp.set_a)) (let ((_let_1 (@ (@ tptp.nth_set_a (@ (@ (@ tptp.list_update_set_a Xs) I) X4)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a Xs)) (and (=> _let_2 (= _let_1 X4)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_set_a Xs) J)))))))))
% 0.26/0.70 (assert (forall ((I tptp.nat) (Xs tptp.list_a) (X4 tptp.a)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_a Xs)) (= (= (@ (@ (@ tptp.list_update_a Xs) I) X4) Xs) (= (@ (@ tptp.nth_a Xs) I) X4)))))
% 0.26/0.70 (assert (forall ((I tptp.nat) (Xs tptp.list_set_a) (X4 tptp.set_a)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a Xs)) (= (= (@ (@ (@ tptp.list_update_set_a Xs) I) X4) Xs) (= (@ (@ tptp.nth_set_a Xs) I) X4)))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (A5 tptp.set_nat) (B2 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) A5) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A) (=> (= (@ (@ tptp.image_nat_nat F) B2) B4) (@ (@ (@ tptp.bij_betw_nat_nat (@ (@ tptp.hilber815131374at_nat A) F)) B4) B2))))))
% 0.26/0.70 (assert (forall ((A tptp.set_a) (Ss tptp.list_set_a)) (=> (@ (@ tptp.hilber2037636820comp_a A) Ss) (@ (@ tptp.inj_on_list_a_a tptp.groups1792256535list_a) (@ tptp.listset_a Ss)))))
% 0.26/0.70 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B2 tptp.set_nat) (G2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.inj_on_nat_nat F) A) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat F) A)) B2) (=> (@ (@ tptp.inj_on_nat_nat G2) B2) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat G2) B2)) A) (exists ((H (-> tptp.nat tptp.nat))) (@ (@ (@ tptp.bij_betw_nat_nat H) A) B2))))))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X4) X4)))
% 0.26/0.70 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (not (@ (@ tptp.ord_less_eq_nat T) X)))))))
% 0.26/0.70 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (@ (@ tptp.ord_less_eq_nat X) T))))))
% 0.26/0.70 (assert (forall ((A tptp.set_a) (B2 tptp.set_a)) (=> (forall ((X6 tptp.a)) (let ((_let_1 (@ tptp.member_a X6))) (=> (@ _let_1 A) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_a A) B2))))
% 0.26/0.70 (assert (forall ((A tptp.set_list_a) (B2 tptp.set_list_a)) (=> (forall ((X6 tptp.list_a)) (let ((_let_1 (@ tptp.member_list_a X6))) (=> (@ _let_1 A) (@ _let_1 B2)))) (@ (@ tptp.ord_le1301786372list_a A) B2))))
% 0.26/0.70 (assert (forall ((P (-> tptp.nat Bool)) (X4 tptp.nat) (M3 tptp.nat)) (=> (@ P X4) (=> (forall ((X6 tptp.nat)) (=> (@ P X6) (@ (@ tptp.ord_less_eq_nat X6) M3))) (not (forall ((M4 tptp.nat)) (=> (@ P M4) (not (forall ((X tptp.nat)) (=> (@ P X) (@ (@ tptp.ord_less_eq_nat X) M4)))))))))))
% 0.26/0.70 (assert (= tptp.ord_less_eq_set_a (lambda ((A4 tptp.set_a) (B3 tptp.set_a)) (forall ((T2 tptp.a)) (let ((_let_1 (@ tptp.member_a T2))) (=> (@ _let_1 A4) (@ _let_1 B3)))))))
% 0.26/0.70 (assert (= tptp.ord_le1301786372list_a (lambda ((A4 tptp.set_list_a) (B3 tptp.set_list_a)) (forall ((T2 tptp.list_a)) (let ((_let_1 (@ tptp.member_list_a T2))) (=> (@ _let_1 A4) (@ _let_1 B3)))))))
% 0.26/0.70 (assert (= tptp.ord_less_eq_set_a (lambda ((A4 tptp.set_a) (B3 tptp.set_a)) (forall ((X5 tptp.a)) (let ((_let_1 (@ tptp.member_a X5))) (=> (@ _let_1 A4) (@ _let_1 B3)))))))
% 0.26/0.70 (assert (= tptp.ord_le1301786372list_a (lambda ((A4 tptp.set_list_a) (B3 tptp.set_list_a)) (forall ((X5 tptp.list_a)) (let ((_let_1 (@ tptp.member_list_a X5))) (=> (@ _let_1 A4) (@ _let_1 B3)))))))
% 0.26/0.70 (assert (forall ((A tptp.set_a) (B2 tptp.set_a) (C tptp.a)) (let ((_let_1 (@ tptp.member_a C))) (=> (@ (@ tptp.ord_less_eq_set_a A) B2) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((A tptp.set_list_a) (B2 tptp.set_list_a) (C tptp.list_a)) (let ((_let_1 (@ tptp.member_list_a C))) (=> (@ (@ tptp.ord_le1301786372list_a A) B2) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((A tptp.set_a) (B2 tptp.set_a) (X4 tptp.a)) (let ((_let_1 (@ tptp.member_a X4))) (=> (@ (@ tptp.ord_less_eq_set_a A) B2) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((A tptp.set_list_a) (B2 tptp.set_list_a) (X4 tptp.list_a)) (let ((_let_1 (@ tptp.member_list_a X4))) (=> (@ (@ tptp.ord_le1301786372list_a A) B2) (=> (@ _let_1 A) (@ _let_1 B2))))))
% 0.26/0.70 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (= A2 B)))))
% 0.26/0.70 (assert (= (lambda ((Y2 tptp.nat) (Z tptp.nat)) (= Y2 Z)) (lambda ((A7 tptp.nat) (B5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B5) A7) (@ (@ tptp.ord_less_eq_nat A7) B5)))))
% 0.26/0.70 (assert (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A3) B6) (@ (@ P A3) B6))) (=> (forall ((A3 tptp.nat) (B6 tptp.nat)) (=> (@ (@ P B6) A3) (@ (@ P A3) B6))) (@ (@ P A2) B)))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) A2)))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_nat Y3) Z3) (@ _let_1 Z3))))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_eq_nat B) A2) (= A2 B)))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A2 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A2) C)))))
% 0.26/0.70 (assert (= (lambda ((Y2 tptp.nat) (Z tptp.nat)) (= Y2 Z)) (lambda ((A7 tptp.nat) (B5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A7) B5) (@ (@ tptp.ord_less_eq_nat B5) A7)))))
% 0.26/0.70 (assert (forall ((Y3 tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X4) (= (@ (@ tptp.ord_less_eq_nat X4) Y3) (= X4 Y3)))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X4))) (let ((_let_2 (@ _let_1 Y3))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z3))) (let ((_let_4 (@ _let_3 X4))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y3))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X4))) (let ((_let_8 (@ _let_3 Y3))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X4) Y3)) (@ (@ tptp.ord_less_eq_nat Y3) X4))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= X4 Y3) (@ (@ tptp.ord_less_eq_nat X4) Y3))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_nat Y3) X4))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (=> (@ (@ tptp.ord_less_eq_nat Y3) X4) (= X4 Y3)))))
% 0.26/0.70 (assert (= tptp.ord_less_eq_o_nat (lambda ((X7 (-> Bool tptp.nat)) (Y4 (-> Bool tptp.nat))) (and (@ (@ tptp.ord_less_eq_nat (@ X7 false)) (@ Y4 false)) (@ (@ tptp.ord_less_eq_nat (@ X7 true)) (@ Y4 true))))))
% 0.26/0.70 (assert (= (lambda ((Y2 tptp.nat) (Z tptp.nat)) (= Y2 Z)) (lambda ((X5 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_nat Y5) X5)))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X6) Y) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X6 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X6) Y) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F C)))))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X6 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X6) Y) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X6 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X6) Y) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 0.26/0.70 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A2) (not (= A2 B)))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (not (= A2 B)))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X4) Y3)) (or (@ (@ tptp.ord_less_nat Y3) X4) (= X4 Y3)))))
% 0.26/0.70 (assert (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B6) (@ (@ P A3) B6))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.nat) (B6 tptp.nat)) (=> (@ (@ P B6) A3) (@ (@ P A3) B6))) (@ (@ P A2) B))))))
% 0.26/0.70 (assert (= (lambda ((P3 (-> tptp.nat Bool))) (exists ((X3 tptp.nat)) (@ P3 X3))) (lambda ((P2 (-> tptp.nat Bool))) (exists ((N2 tptp.nat)) (and (@ P2 N2) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N2) (not (@ P2 M5)))))))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (@ (@ tptp.ord_less_nat Y3) X4)))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) A2))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X4) Y3)) (=> (not (= X4 Y3)) (@ (@ tptp.ord_less_nat Y3) X4)))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (=> (@ (@ tptp.ord_less_nat Y3) X4) P))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (= Y3 X4)))))
% 0.26/0.70 (assert (forall ((Y3 tptp.nat) (X4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y3) X4)) (= (not (@ (@ tptp.ord_less_nat X4) Y3)) (= X4 Y3)))))
% 0.26/0.70 (assert (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat)) (=> (forall ((X6 tptp.nat)) (=> (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y6) X6) (@ P Y6))) (@ P X6))) (@ P A2))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (@ (@ tptp.ord_less_nat Y3) X4)))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (= X4 Y3)))))
% 0.26/0.70 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A2) (not (@ (@ tptp.ord_less_nat A2) B)))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A2 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A2) C)))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat)) (not (@ (@ tptp.ord_less_nat X4) X4))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_nat X4) Y3) (= X4 Y3) (@ (@ tptp.ord_less_nat Y3) X4))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_nat Y3) Z3) (@ _let_1 Z3))))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (not (@ (@ tptp.ord_less_nat B) A2)))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (@ (@ tptp.ord_less_nat Y3) X4)))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (= X4 Y3)))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (not (@ (@ tptp.ord_less_nat B) A2)))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (not (= X4 Y3)) (or (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_nat Y3) X4)))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (not (= X4 Y3)) (=> (not (@ (@ tptp.ord_less_nat X4) Y3)) (@ (@ tptp.ord_less_nat Y3) X4)))))
% 0.26/0.70 (assert (forall ((X4 tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X4) X_1))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X6 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Y) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F Y)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X6 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Y) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F Y)))) (@ _let_1 (@ F C))))))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Y) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F Y)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))))
% 0.26/0.70 (assert (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X6 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Y) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F Y)))) (@ (@ tptp.ord_less_nat A2) (@ F C)))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X6) (= (@ P X6) (@ P4 X6))))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X6) (= (@ Q X6) (@ Q2 X6))))) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (= (and (@ P X) (@ Q X)) (and (@ P4 X) (@ Q2 X))))))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X6) (= (@ P X6) (@ P4 X6))))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X6) (= (@ Q X6) (@ Q2 X6))))) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (= (or (@ P X) (@ Q X)) (or (@ P4 X) (@ Q2 X))))))))))
% 0.26/0.70 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (not (= X T)))))))
% 0.26/0.70 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (not (= X T)))))))
% 0.26/0.70 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (not (@ (@ tptp.ord_less_nat X) T)))))))
% 0.26/0.70 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (@ (@ tptp.ord_less_nat T) X))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z4) (= (@ P X6) (@ P4 X6))))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z4) (= (@ Q X6) (@ Q2 X6))))) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (= (and (@ P X) (@ Q X)) (and (@ P4 X) (@ Q2 X))))))))))
% 0.26/0.70 (assert (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z4) (= (@ P X6) (@ P4 X6))))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z4) (= (@ Q X6) (@ Q2 X6))))) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (= (or (@ P X) (@ Q X)) (or (@ P4 X) (@ Q2 X))))))))))
% 0.26/0.70 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (not (= X T)))))))
% 0.26/0.70 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (not (= X T)))))))
% 0.26/0.70 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Z2) (@ _let_1 T)))))))
% 0.55/1.19 (assert (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (not (@ (@ tptp.ord_less_nat T) X)))))))
% 0.55/1.19 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (not (= A2 B)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (@ (@ tptp.ord_less_nat A2) B)))))
% 0.55/1.19 (assert (forall ((B tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A2) (@ (@ tptp.ord_less_eq_nat B) A2))))
% 0.55/1.19 (assert (= tptp.ord_less_nat (lambda ((B5 tptp.nat) (A7 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B5) A7) (not (= A7 B5))))))
% 0.55/1.19 (assert (= tptp.ord_less_eq_nat (lambda ((B5 tptp.nat) (A7 tptp.nat)) (or (@ (@ tptp.ord_less_nat B5) A7) (= A7 B5)))))
% 0.55/1.19 (assert (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (@ (@ tptp.ord_less_eq_nat A2) B))))
% 0.55/1.19 (assert (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A2) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_nat C) A2)))))
% 0.55/1.19 (assert (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))))
% 0.55/1.19 (assert (= tptp.ord_less_nat (lambda ((A7 tptp.nat) (B5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A7) B5) (not (= A7 B5))))))
% 0.55/1.19 (assert (= tptp.ord_less_eq_nat (lambda ((A7 tptp.nat) (B5 tptp.nat)) (or (@ (@ tptp.ord_less_nat A7) B5) (= A7 B5)))))
% 0.55/1.19 (assert (not (= tptp.a3 (@ tptp.groups1792256535list_a tptp.qs2))))
% 0.55/1.19 (set-info :filename cvc5---1.0.5_12410)
% 0.55/1.19 (check-sat-assuming ( true ))
% 0.55/1.19 ------- get file name : TPTP file name is ITP077^1
% 0.55/1.19 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12410.smt2...
% 0.55/1.19 --- Run --ho-elim --full-saturate-quant at 10...
% 0.55/1.19 % SZS status Theorem for ITP077^1
% 0.55/1.19 % SZS output start Proof for ITP077^1
% 0.55/1.19 (
% 0.55/1.19 (let ((_let_1 (@ tptp.groups1792256535list_a tptp.qs2))) (let ((_let_2 (not (= tptp.a3 _let_1)))) (let ((_let_3 (= tptp.ord_less_nat (lambda ((B5 tptp.nat) (A7 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B5) A7) (not (= A7 B5))))))) (let ((_let_4 (= tptp.ord_less_eq_o_nat (lambda ((X7 (-> Bool tptp.nat)) (Y4 (-> Bool tptp.nat))) (and (@ (@ tptp.ord_less_eq_nat (@ X7 false)) (@ Y4 false)) (@ (@ tptp.ord_less_eq_nat (@ X7 true)) (@ Y4 true))))))) (let ((_let_5 (= tptp.ord_le1301786372list_a (lambda ((A4 tptp.set_list_a) (B3 tptp.set_list_a)) (forall ((T2 tptp.list_a)) (let ((_let_1 (@ tptp.member_list_a T2))) (=> (@ _let_1 A4) (@ _let_1 B3)))))))) (let ((_let_6 (= tptp.ord_less_eq_set_a (lambda ((A4 tptp.set_a) (B3 tptp.set_a)) (forall ((T2 tptp.a)) (let ((_let_1 (@ tptp.member_a T2))) (=> (@ _let_1 A4) (@ _let_1 B3)))))))) (let ((_let_7 (= tptp.list_ex_set_a (lambda ((P2 (-> tptp.set_a Bool)) (Xs4 tptp.list_set_a)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_set_a Xs4)) (@ P2 (@ (@ tptp.nth_set_a Xs4) N2)))))))) (let ((_let_8 (= tptp.list_ex_a (lambda ((P2 (-> tptp.a Bool)) (Xs4 tptp.list_a)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_a Xs4)) (@ P2 (@ (@ tptp.nth_a Xs4) N2)))))))) (let ((_let_9 (= tptp.bij_betw_nat_nat (lambda ((F3 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (B3 tptp.set_nat)) (exists ((G3 (-> tptp.nat tptp.nat))) (and (forall ((X5 tptp.nat)) (let ((_let_1 (@ F3 X5))) (=> (@ (@ tptp.member_nat X5) A4) (and (@ (@ tptp.member_nat _let_1) B3) (= (@ G3 _let_1) X5))))) (forall ((X5 tptp.nat)) (let ((_let_1 (@ G3 X5))) (=> (@ (@ tptp.member_nat X5) B3) (and (@ (@ tptp.member_nat _let_1) A4) (= (@ F3 _let_1) X5))))))))))) (let ((_let_10 (= tptp.bij_be94573046list_a (lambda ((F3 (-> tptp.list_a tptp.list_a)) (A4 tptp.set_list_a) (B3 tptp.set_list_a)) (exists ((G3 (-> tptp.list_a tptp.list_a))) (and (forall ((X5 tptp.list_a)) (let ((_let_1 (@ F3 X5))) (=> (@ (@ tptp.member_list_a X5) A4) (and (@ (@ tptp.member_list_a _let_1) B3) (= (@ G3 _let_1) X5))))) (forall ((X5 tptp.list_a)) (let ((_let_1 (@ G3 X5))) (=> (@ (@ tptp.member_list_a X5) B3) (and (@ (@ tptp.member_list_a _let_1) A4) (= (@ F3 _let_1) X5))))))))))) (let ((_let_11 (= tptp.bij_betw_a_list_a (lambda ((F3 (-> tptp.a tptp.list_a)) (A4 tptp.set_a) (B3 tptp.set_list_a)) (exists ((G3 (-> tptp.list_a tptp.a))) (and (forall ((X5 tptp.a)) (let ((_let_1 (@ F3 X5))) (=> (@ (@ tptp.member_a X5) A4) (and (@ (@ tptp.member_list_a _let_1) B3) (= (@ G3 _let_1) X5))))) (forall ((X5 tptp.list_a)) (let ((_let_1 (@ G3 X5))) (=> (@ (@ tptp.member_list_a X5) B3) (and (@ (@ tptp.member_a _let_1) A4) (= (@ F3 _let_1) X5))))))))))) (let ((_let_12 (= tptp.bij_betw_list_a_a (lambda ((F3 (-> tptp.list_a tptp.a)) (A4 tptp.set_list_a) (B3 tptp.set_a)) (exists ((G3 (-> tptp.a tptp.list_a))) (and (forall ((X5 tptp.list_a)) (let ((_let_1 (@ F3 X5))) (=> (@ (@ tptp.member_list_a X5) A4) (and (@ (@ tptp.member_a _let_1) B3) (= (@ G3 _let_1) X5))))) (forall ((X5 tptp.a)) (let ((_let_1 (@ G3 X5))) (=> (@ (@ tptp.member_a X5) B3) (and (@ (@ tptp.member_list_a _let_1) A4) (= (@ F3 _let_1) X5))))))))))) (let ((_let_13 (= tptp.bij_betw_a_a (lambda ((F3 (-> tptp.a tptp.a)) (A4 tptp.set_a) (B3 tptp.set_a)) (exists ((G3 (-> tptp.a tptp.a))) (and (forall ((X5 tptp.a)) (let ((_let_1 (@ F3 X5))) (=> (@ (@ tptp.member_a X5) A4) (and (@ (@ tptp.member_a _let_1) B3) (= (@ G3 _let_1) X5))))) (forall ((X5 tptp.a)) (let ((_let_1 (@ G3 X5))) (=> (@ (@ tptp.member_a X5) B3) (and (@ (@ tptp.member_a _let_1) A4) (= (@ F3 _let_1) X5))))))))))) (let ((_let_14 (= tptp.hilber2037636820comp_a (lambda ((A4 tptp.set_a) (Ss2 tptp.list_set_a)) (@ (@ (@ tptp.bij_betw_list_a_a tptp.groups1792256535list_a) (@ tptp.listset_a Ss2)) A4))))) (let ((_let_15 (@ tptp.size_size_list_set_a tptp.ss2))) (let ((_let_16 (@ tptp.set_ord_lessThan_nat _let_15))) (let ((_let_17 (= tptp.g (@ (@ tptp.hilber815131374at_nat _let_16) tptp.f)))) (let ((_let_18 (@ tptp.size_size_list_set_a tptp.ss1))) (let ((_let_19 (@ tptp.set_ord_lessThan_nat _let_18))) (let ((_let_20 (@ tptp.size_size_list_a tptp.qs))) (let ((_let_21 (@ tptp.bij_betw_nat_nat tptp.g))) (let ((_let_22 (forall ((Xs tptp.list_a)) (= (@ tptp.comm_m543484931mset_a (@ tptp.mset_a Xs)) (@ tptp.groups1792256535list_a Xs))))) (let ((_let_23 (@ tptp.size_size_list_a tptp.qs2))) (let ((_let_24 (@ tptp.groups1792256535list_a tptp.qs))) (let ((_let_25 (= tptp.a3 _let_24))) (let ((_let_26 (= (@ tptp.mset_a tptp.qs2) (@ tptp.mset_a tptp.qs)))) (let ((_let_27 (ho_162 k_161 tptp.qs2))) (let ((_let_28 (ho_162 k_161 tptp.qs))) (let ((_let_29 (= _let_28 _let_27))) (let ((_let_30 (ho_164 k_163 tptp.qs2))) (let ((_let_31 (ho_164 k_163 tptp.qs))) (let ((_let_32 (= _let_31 _let_30))) (let ((_let_33 (= _let_30 (ho_212 k_211 _let_27)))) (let ((_let_34 (= _let_31 (ho_212 k_211 _let_28)))) (let ((_let_35 (forall ((u |u_(-> tptp.set_a tptp.set_set_a)|) (e tptp.set_set_a) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_set_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_278 v ii) (ite (= i ii) e (ho_278 u ii)))))))))) (let ((_let_36 (forall ((x |u_(-> tptp.set_a tptp.set_set_a)|) (y |u_(-> tptp.set_a tptp.set_set_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_278 x z) (ho_278 y z)))) (= x y))))) (let ((_let_37 (forall ((u |u_(-> tptp.set_list_a tptp.set_set_list_a)|) (e tptp.set_set_list_a) (i tptp.set_list_a)) (not (forall ((v |u_(-> tptp.set_list_a tptp.set_set_list_a)|)) (not (forall ((ii tptp.set_list_a)) (= (ho_272 v ii) (ite (= i ii) e (ho_272 u ii)))))))))) (let ((_let_38 (forall ((x |u_(-> tptp.set_list_a tptp.set_set_list_a)|) (y |u_(-> tptp.set_list_a tptp.set_set_list_a)|)) (or (not (forall ((z tptp.set_list_a)) (= (ho_272 x z) (ho_272 y z)))) (= x y))))) (let ((_let_39 (forall ((u |u_(-> tptp.set_a tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_84 v ii) (ite (= i ii) e (ho_84 u ii)))))))))) (let ((_let_40 (forall ((x |u_(-> tptp.set_a tptp.a Bool)|) (y |u_(-> tptp.set_a tptp.a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_84 x z) (ho_84 y z)))) (= x y))))) (let ((_let_41 (forall ((u |u_(-> tptp.list_set_set_a tptp.list_set_set_a)|) (e tptp.list_set_set_a) (i tptp.list_set_set_a)) (not (forall ((v |u_(-> tptp.list_set_set_a tptp.list_set_set_a)|)) (not (forall ((ii tptp.list_set_set_a)) (= (ho_263 v ii) (ite (= i ii) e (ho_263 u ii)))))))))) (let ((_let_42 (forall ((x |u_(-> tptp.list_set_set_a tptp.list_set_set_a)|) (y |u_(-> tptp.list_set_set_a tptp.list_set_set_a)|)) (or (not (forall ((z tptp.list_set_set_a)) (= (ho_263 x z) (ho_263 y z)))) (= x y))))) (let ((_let_43 (forall ((u |u_(-> tptp.list_set_list_a tptp.list_set_list_a)|) (e tptp.list_set_list_a) (i tptp.list_set_list_a)) (not (forall ((v |u_(-> tptp.list_set_list_a tptp.list_set_list_a)|)) (not (forall ((ii tptp.list_set_list_a)) (= (ho_261 v ii) (ite (= i ii) e (ho_261 u ii)))))))))) (let ((_let_44 (forall ((x |u_(-> tptp.list_set_list_a tptp.list_set_list_a)|) (y |u_(-> tptp.list_set_list_a tptp.list_set_list_a)|)) (or (not (forall ((z tptp.list_set_list_a)) (= (ho_261 x z) (ho_261 y z)))) (= x y))))) (let ((_let_45 (forall ((u |u_(-> tptp.list_set_nat tptp.nat tptp.set_nat)|) (e |u_(-> tptp.nat tptp.set_nat)|) (i tptp.list_set_nat)) (not (forall ((v |u_(-> tptp.list_set_nat tptp.nat tptp.set_nat)|)) (not (forall ((ii tptp.list_set_nat)) (= (ho_255 v ii) (ite (= i ii) e (ho_255 u ii)))))))))) (let ((_let_46 (forall ((x |u_(-> tptp.list_set_nat tptp.nat tptp.set_nat)|) (y |u_(-> tptp.list_set_nat tptp.nat tptp.set_nat)|)) (or (not (forall ((z tptp.list_set_nat)) (= (ho_255 x z) (ho_255 y z)))) (= x y))))) (let ((_let_47 (forall ((u |u_(-> tptp.list_set_set_set_a tptp.nat tptp.set_set_set_a)|) (e |u_(-> tptp.nat tptp.set_set_set_a)|) (i tptp.list_set_set_set_a)) (not (forall ((v |u_(-> tptp.list_set_set_set_a tptp.nat tptp.set_set_set_a)|)) (not (forall ((ii tptp.list_set_set_set_a)) (= (ho_250 v ii) (ite (= i ii) e (ho_250 u ii)))))))))) (let ((_let_48 (forall ((x |u_(-> tptp.list_set_set_set_a tptp.nat tptp.set_set_set_a)|) (y |u_(-> tptp.list_set_set_set_a tptp.nat tptp.set_set_set_a)|)) (or (not (forall ((z tptp.list_set_set_set_a)) (= (ho_250 x z) (ho_250 y z)))) (= x y))))) (let ((_let_49 (forall ((u |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a tptp.list_a)|) (e |u_(-> tptp.list_a tptp.list_a)|) (i |u_(-> tptp.list_a tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a tptp.list_a)|)) (not (forall ((ii |u_(-> tptp.list_a tptp.list_a)|)) (= (ho_367 v ii) (ite (= i ii) e (ho_367 u ii)))))))))) (let ((_let_50 (forall ((x |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a tptp.list_a)|) (y |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a tptp.list_a)|)) (or (not (forall ((z |u_(-> tptp.list_a tptp.list_a)|)) (= (ho_367 x z) (ho_367 y z)))) (= x y))))) (let ((_let_51 (forall ((u |u_(-> tptp.list_set_set_set_a tptp.nat)|) (e tptp.nat) (i tptp.list_set_set_set_a)) (not (forall ((v |u_(-> tptp.list_set_set_set_a tptp.nat)|)) (not (forall ((ii tptp.list_set_set_set_a)) (= (ho_243 v ii) (ite (= i ii) e (ho_243 u ii)))))))))) (let ((_let_52 (forall ((x |u_(-> tptp.list_set_set_set_a tptp.nat)|) (y |u_(-> tptp.list_set_set_set_a tptp.nat)|)) (or (not (forall ((z tptp.list_set_set_set_a)) (= (ho_243 x z) (ho_243 y z)))) (= x y))))) (let ((_let_53 (forall ((u |u_(-> tptp.set_nat tptp.set_set_nat)|) (e tptp.set_set_nat) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat tptp.set_set_nat)|)) (not (forall ((ii tptp.set_nat)) (= (ho_266 v ii) (ite (= i ii) e (ho_266 u ii)))))))))) (let ((_let_54 (forall ((x |u_(-> tptp.set_nat tptp.set_set_nat)|) (y |u_(-> tptp.set_nat tptp.set_set_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_266 x z) (ho_266 y z)))) (= x y))))) (let ((_let_55 (forall ((u |u_(-> tptp.nat tptp.set_set_list_a)|) (e tptp.set_set_list_a) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_set_list_a)|)) (not (forall ((ii tptp.nat)) (= (ho_241 v ii) (ite (= i ii) e (ho_241 u ii)))))))))) (let ((_let_56 (forall ((x |u_(-> tptp.nat tptp.set_set_list_a)|) (y |u_(-> tptp.nat tptp.set_set_list_a)|)) (or (not (forall ((z tptp.nat)) (= (ho_241 x z) (ho_241 y z)))) (= x y))))) (let ((_let_57 (forall ((u |u_(-> _u_(-> tptp.list_a tptp.a)_ tptp.set_list_a tptp.set_a)|) (e |u_(-> tptp.set_list_a tptp.set_a)|) (i |u_(-> tptp.list_a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a tptp.a)_ tptp.set_list_a tptp.set_a)|)) (not (forall ((ii |u_(-> tptp.list_a tptp.a)|)) (= (ho_217 v ii) (ite (= i ii) e (ho_217 u ii)))))))))) (let ((_let_58 (forall ((x |u_(-> _u_(-> tptp.list_a tptp.a)_ tptp.set_list_a tptp.set_a)|) (y |u_(-> _u_(-> tptp.list_a tptp.a)_ tptp.set_list_a tptp.set_a)|)) (or (not (forall ((z |u_(-> tptp.list_a tptp.a)|)) (= (ho_217 x z) (ho_217 y z)))) (= x y))))) (let ((_let_59 (forall ((u |u_(-> tptp.nat tptp.set_a tptp.list_set_a)|) (e |u_(-> tptp.set_a tptp.list_set_a)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_a tptp.list_set_a)|)) (not (forall ((ii tptp.nat)) (= (ho_375 v ii) (ite (= i ii) e (ho_375 u ii)))))))))) (let ((_let_60 (forall ((x |u_(-> tptp.nat tptp.set_a tptp.list_set_a)|) (y |u_(-> tptp.nat tptp.set_a tptp.list_set_a)|)) (or (not (forall ((z tptp.nat)) (= (ho_375 x z) (ho_375 y z)))) (= x y))))) (let ((_let_61 (forall ((u |u_(-> tptp.list_set_set_list_a tptp.nat tptp.set_set_list_a)|) (e |u_(-> tptp.nat tptp.set_set_list_a)|) (i tptp.list_set_set_list_a)) (not (forall ((v |u_(-> tptp.list_set_set_list_a tptp.nat tptp.set_set_list_a)|)) (not (forall ((ii tptp.list_set_set_list_a)) (= (ho_240 v ii) (ite (= i ii) e (ho_240 u ii)))))))))) (let ((_let_62 (forall ((x |u_(-> tptp.list_set_set_list_a tptp.nat tptp.set_set_list_a)|) (y |u_(-> tptp.list_set_set_list_a tptp.nat tptp.set_set_list_a)|)) (or (not (forall ((z tptp.list_set_set_list_a)) (= (ho_240 x z) (ho_240 y z)))) (= x y))))) (let ((_let_63 (forall ((u |u_(-> tptp.set_set_list_a Bool)|) (e Bool) (i tptp.set_set_list_a)) (not (forall ((v |u_(-> tptp.set_set_list_a Bool)|)) (not (forall ((ii tptp.set_set_list_a)) (= (ho_275 v ii) (ite (= i ii) e (ho_275 u ii)))))))))) (let ((_let_64 (forall ((x |u_(-> tptp.set_set_list_a Bool)|) (y |u_(-> tptp.set_set_list_a Bool)|)) (or (not (forall ((z tptp.set_set_list_a)) (= (ho_275 x z) (ho_275 y z)))) (= x y))))) (let ((_let_65 (forall ((u |u_(-> tptp.nat tptp.a Bool)|) (e |u_(-> tptp.a Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.a Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_325 v ii) (ite (= i ii) e (ho_325 u ii)))))))))) (let ((_let_66 (forall ((x |u_(-> tptp.nat tptp.a Bool)|) (y |u_(-> tptp.nat tptp.a Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_325 x z) (ho_325 y z)))) (= x y))))) (let ((_let_67 (forall ((u |u_(-> tptp.set_list_set_list_a Bool)|) (e Bool) (i tptp.set_list_set_list_a)) (not (forall ((v |u_(-> tptp.set_list_set_list_a Bool)|)) (not (forall ((ii tptp.set_list_set_list_a)) (= (ho_238 v ii) (ite (= i ii) e (ho_238 u ii)))))))))) (let ((_let_68 (forall ((x |u_(-> tptp.set_list_set_list_a Bool)|) (y |u_(-> tptp.set_list_set_list_a Bool)|)) (or (not (forall ((z tptp.set_list_set_list_a)) (= (ho_238 x z) (ho_238 y z)))) (= x y))))) (let ((_let_69 (forall ((u |u_(-> tptp.list_set_set_list_a tptp.set_list_set_list_a)|) (e tptp.set_list_set_list_a) (i tptp.list_set_set_list_a)) (not (forall ((v |u_(-> tptp.list_set_set_list_a tptp.set_list_set_list_a)|)) (not (forall ((ii tptp.list_set_set_list_a)) (= (ho_235 v ii) (ite (= i ii) e (ho_235 u ii)))))))))) (let ((_let_70 (forall ((x |u_(-> tptp.list_set_set_list_a tptp.set_list_set_list_a)|) (y |u_(-> tptp.list_set_set_list_a tptp.set_list_set_list_a)|)) (or (not (forall ((z tptp.list_set_set_list_a)) (= (ho_235 x z) (ho_235 y z)))) (= x y))))) (let ((_let_71 (forall ((u |u_(-> tptp.list_set_set_list_a tptp.nat)|) (e tptp.nat) (i tptp.list_set_set_list_a)) (not (forall ((v |u_(-> tptp.list_set_set_list_a tptp.nat)|)) (not (forall ((ii tptp.list_set_set_list_a)) (= (ho_233 v ii) (ite (= i ii) e (ho_233 u ii)))))))))) (let ((_let_72 (forall ((x |u_(-> tptp.list_set_set_list_a tptp.nat)|) (y |u_(-> tptp.list_set_set_list_a tptp.nat)|)) (or (not (forall ((z tptp.list_set_set_list_a)) (= (ho_233 x z) (ho_233 y z)))) (= x y))))) (let ((_let_73 (forall ((u |u_(-> tptp.list_list_a tptp.list_list_a)|) (e tptp.list_list_a) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a tptp.list_list_a)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_226 v ii) (ite (= i ii) e (ho_226 u ii)))))))))) (let ((_let_74 (forall ((x |u_(-> tptp.list_list_a tptp.list_list_a)|) (y |u_(-> tptp.list_list_a tptp.list_list_a)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_226 x z) (ho_226 y z)))) (= x y))))) (let ((_let_75 (forall ((u |u_(-> tptp.list_set_a tptp.list_set_a)|) (e tptp.list_set_a) (i tptp.list_set_a)) (not (forall ((v |u_(-> tptp.list_set_a tptp.list_set_a)|)) (not (forall ((ii tptp.list_set_a)) (= (ho_222 v ii) (ite (= i ii) e (ho_222 u ii)))))))))) (let ((_let_76 (forall ((x |u_(-> tptp.list_set_a tptp.list_set_a)|) (y |u_(-> tptp.list_set_a tptp.list_set_a)|)) (or (not (forall ((z tptp.list_set_a)) (= (ho_222 x z) (ho_222 y z)))) (= x y))))) (let ((_let_77 (forall ((u |u_(-> tptp.set_list_a tptp.set_a)|) (e tptp.set_a) (i tptp.set_list_a)) (not (forall ((v |u_(-> tptp.set_list_a tptp.set_a)|)) (not (forall ((ii tptp.set_list_a)) (= (ho_218 v ii) (ite (= i ii) e (ho_218 u ii)))))))))) (let ((_let_78 (forall ((x |u_(-> tptp.set_list_a tptp.set_a)|) (y |u_(-> tptp.set_list_a tptp.set_a)|)) (or (not (forall ((z tptp.set_list_a)) (= (ho_218 x z) (ho_218 y z)))) (= x y))))) (let ((_let_79 (forall ((u |u_(-> tptp.list_a tptp.multiset_a)|) (e tptp.multiset_a) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.multiset_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_162 v ii) (ite (= i ii) e (ho_162 u ii)))))))))) (let ((_let_80 (forall ((x |u_(-> tptp.list_a tptp.multiset_a)|) (y |u_(-> tptp.list_a tptp.multiset_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_162 x z) (ho_162 y z)))) (= x y))))) (let ((_let_81 (forall ((u |u_(-> tptp.nat tptp.set_multiset_a)|) (e tptp.set_multiset_a) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_multiset_a)|)) (not (forall ((ii tptp.nat)) (= (ho_281 v ii) (ite (= i ii) e (ho_281 u ii)))))))))) (let ((_let_82 (forall ((x |u_(-> tptp.nat tptp.set_multiset_a)|) (y |u_(-> tptp.nat tptp.set_multiset_a)|)) (or (not (forall ((z tptp.nat)) (= (ho_281 x z) (ho_281 y z)))) (= x y))))) (let ((_let_83 (forall ((u |u_(-> _u_(-> tptp.list_nat tptp.nat)_ tptp.set_list_nat tptp.set_nat)|) (e |u_(-> tptp.set_list_nat tptp.set_nat)|) (i |u_(-> tptp.list_nat tptp.nat)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_nat tptp.nat)_ tptp.set_list_nat tptp.set_nat)|)) (not (forall ((ii |u_(-> tptp.list_nat tptp.nat)|)) (= (ho_214 v ii) (ite (= i ii) e (ho_214 u ii)))))))))) (let ((_let_84 (forall ((x |u_(-> _u_(-> tptp.list_nat tptp.nat)_ tptp.set_list_nat tptp.set_nat)|) (y |u_(-> _u_(-> tptp.list_nat tptp.nat)_ tptp.set_list_nat tptp.set_nat)|)) (or (not (forall ((z |u_(-> tptp.list_nat tptp.nat)|)) (= (ho_214 x z) (ho_214 y z)))) (= x y))))) (let ((_let_85 (forall ((u |u_(-> tptp.nat tptp.list_a Bool)|) (e |u_(-> tptp.list_a Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.list_a Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_322 v ii) (ite (= i ii) e (ho_322 u ii)))))))))) (let ((_let_86 (forall ((x |u_(-> tptp.nat tptp.list_a Bool)|) (y |u_(-> tptp.nat tptp.list_a Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_322 x z) (ho_322 y z)))) (= x y))))) (let ((_let_87 (forall ((u |u_(-> tptp.multis971982480list_a tptp.multiset_list_a)|) (e tptp.multiset_list_a) (i tptp.multis971982480list_a)) (not (forall ((v |u_(-> tptp.multis971982480list_a tptp.multiset_list_a)|)) (not (forall ((ii tptp.multis971982480list_a)) (= (ho_206 v ii) (ite (= i ii) e (ho_206 u ii)))))))))) (let ((_let_88 (forall ((x |u_(-> tptp.multis971982480list_a tptp.multiset_list_a)|) (y |u_(-> tptp.multis971982480list_a tptp.multiset_list_a)|)) (or (not (forall ((z tptp.multis971982480list_a)) (= (ho_206 x z) (ho_206 y z)))) (= x y))))) (let ((_let_89 (forall ((u |u_(-> tptp.list_multiset_list_a tptp.multiset_list_a)|) (e tptp.multiset_list_a) (i tptp.list_multiset_list_a)) (not (forall ((v |u_(-> tptp.list_multiset_list_a tptp.multiset_list_a)|)) (not (forall ((ii tptp.list_multiset_list_a)) (= (ho_202 v ii) (ite (= i ii) e (ho_202 u ii)))))))))) (let ((_let_90 (forall ((x |u_(-> tptp.list_multiset_list_a tptp.multiset_list_a)|) (y |u_(-> tptp.list_multiset_list_a tptp.multiset_list_a)|)) (or (not (forall ((z tptp.list_multiset_list_a)) (= (ho_202 x z) (ho_202 y z)))) (= x y))))) (let ((_let_91 (forall ((u |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (e |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|)) (not (forall ((ii tptp.set_nat)) (= (ho_195 v ii) (ite (= i ii) e (ho_195 u ii)))))))))) (let ((_let_92 (forall ((x |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (y |u_(-> tptp.set_nat _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_195 x z) (ho_195 y z)))) (= x y))))) (let ((_let_93 (forall ((u |u_(-> tptp.nat tptp.set_nat)|) (e tptp.set_nat) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_nat)|)) (not (forall ((ii tptp.nat)) (= (ho_193 v ii) (ite (= i ii) e (ho_193 u ii)))))))))) (let ((_let_94 (forall ((x |u_(-> tptp.nat tptp.set_nat)|) (y |u_(-> tptp.nat tptp.set_nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_193 x z) (ho_193 y z)))) (= x y))))) (let ((_let_95 (forall ((u |u_(-> tptp.list_nat tptp.list_nat)|) (e tptp.list_nat) (i tptp.list_nat)) (not (forall ((v |u_(-> tptp.list_nat tptp.list_nat)|)) (not (forall ((ii tptp.list_nat)) (= (ho_188 v ii) (ite (= i ii) e (ho_188 u ii)))))))))) (let ((_let_96 (forall ((x |u_(-> tptp.list_nat tptp.list_nat)|) (y |u_(-> tptp.list_nat tptp.list_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_188 x z) (ho_188 y z)))) (= x y))))) (let ((_let_97 (forall ((u |u_(-> tptp.set_list_nat tptp.set_nat)|) (e tptp.set_nat) (i tptp.set_list_nat)) (not (forall ((v |u_(-> tptp.set_list_nat tptp.set_nat)|)) (not (forall ((ii tptp.set_list_nat)) (= (ho_215 v ii) (ite (= i ii) e (ho_215 u ii)))))))))) (let ((_let_98 (forall ((x |u_(-> tptp.set_list_nat tptp.set_nat)|) (y |u_(-> tptp.set_list_nat tptp.set_nat)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_215 x z) (ho_215 y z)))) (= x y))))) (let ((_let_99 (forall ((u |u_(-> tptp.list_multiset_list_a tptp.multis971982480list_a)|) (e tptp.multis971982480list_a) (i tptp.list_multiset_list_a)) (not (forall ((v |u_(-> tptp.list_multiset_list_a tptp.multis971982480list_a)|)) (not (forall ((ii tptp.list_multiset_list_a)) (= (ho_204 v ii) (ite (= i ii) e (ho_204 u ii)))))))))) (let ((_let_100 (forall ((x |u_(-> tptp.list_multiset_list_a tptp.multis971982480list_a)|) (y |u_(-> tptp.list_multiset_list_a tptp.multis971982480list_a)|)) (or (not (forall ((z tptp.list_multiset_list_a)) (= (ho_204 x z) (ho_204 y z)))) (= x y))))) (let ((_let_101 (forall ((u |u_(-> tptp.a tptp.list_a)|) (e tptp.list_a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.list_a)|)) (not (forall ((ii tptp.a)) (= (ho_186 v ii) (ite (= i ii) e (ho_186 u ii)))))))))) (let ((_let_102 (forall ((x |u_(-> tptp.a tptp.list_a)|) (y |u_(-> tptp.a tptp.list_a)|)) (or (not (forall ((z tptp.a)) (= (ho_186 x z) (ho_186 y z)))) (= x y))))) (let ((_let_103 (forall ((u |u_(-> tptp.set_list_a tptp.set_set_list_a Bool)|) (e |u_(-> tptp.set_set_list_a Bool)|) (i tptp.set_list_a)) (not (forall ((v |u_(-> tptp.set_list_a tptp.set_set_list_a Bool)|)) (not (forall ((ii tptp.set_list_a)) (= (ho_274 v ii) (ite (= i ii) e (ho_274 u ii)))))))))) (let ((_let_104 (forall ((x |u_(-> tptp.set_list_a tptp.set_set_list_a Bool)|) (y |u_(-> tptp.set_list_a tptp.set_set_list_a Bool)|)) (or (not (forall ((z tptp.set_list_a)) (= (ho_274 x z) (ho_274 y z)))) (= x y))))) (let ((_let_105 (forall ((u |u_(-> tptp.list_set_list_a tptp.set_list_list_a)|) (e tptp.set_list_list_a) (i tptp.list_set_list_a)) (not (forall ((v |u_(-> tptp.list_set_list_a tptp.set_list_list_a)|)) (not (forall ((ii tptp.list_set_list_a)) (= (ho_257 v ii) (ite (= i ii) e (ho_257 u ii)))))))))) (let ((_let_106 (forall ((x |u_(-> tptp.list_set_list_a tptp.set_list_list_a)|) (y |u_(-> tptp.list_set_list_a tptp.set_list_list_a)|)) (or (not (forall ((z tptp.list_set_list_a)) (= (ho_257 x z) (ho_257 y z)))) (= x y))))) (let ((_let_107 (forall ((u |u_(-> tptp.list_set_nat Bool)|) (e Bool) (i tptp.list_set_nat)) (not (forall ((v |u_(-> tptp.list_set_nat Bool)|)) (not (forall ((ii tptp.list_set_nat)) (= (ho_185 v ii) (ite (= i ii) e (ho_185 u ii)))))))))) (let ((_let_108 (forall ((x |u_(-> tptp.list_set_nat Bool)|) (y |u_(-> tptp.list_set_nat Bool)|)) (or (not (forall ((z tptp.list_set_nat)) (= (ho_185 x z) (ho_185 y z)))) (= x y))))) (let ((_let_109 (forall ((u |u_(-> tptp.list_a tptp.nat tptp.a tptp.list_a)|) (e |u_(-> tptp.nat tptp.a tptp.list_a)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.nat tptp.a tptp.list_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_371 v ii) (ite (= i ii) e (ho_371 u ii)))))))))) (let ((_let_110 (forall ((x |u_(-> tptp.list_a tptp.nat tptp.a tptp.list_a)|) (y |u_(-> tptp.list_a tptp.nat tptp.a tptp.list_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_371 x z) (ho_371 y z)))) (= x y))))) (let ((_let_111 (forall ((u |u_(-> tptp.multiset_a tptp.a)|) (e tptp.a) (i tptp.multiset_a)) (not (forall ((v |u_(-> tptp.multiset_a tptp.a)|)) (not (forall ((ii tptp.multiset_a)) (= (ho_212 v ii) (ite (= i ii) e (ho_212 u ii)))))))))) (let ((_let_112 (forall ((x |u_(-> tptp.multiset_a tptp.a)|) (y |u_(-> tptp.multiset_a tptp.a)|)) (or (not (forall ((z tptp.multiset_a)) (= (ho_212 x z) (ho_212 y z)))) (= x y))))) (let ((_let_113 (forall ((u |u_(-> tptp.list_nat tptp.set_list_nat Bool)|) (e |u_(-> tptp.set_list_nat Bool)|) (i tptp.list_nat)) (not (forall ((v |u_(-> tptp.list_nat tptp.set_list_nat Bool)|)) (not (forall ((ii tptp.list_nat)) (= (ho_181 v ii) (ite (= i ii) e (ho_181 u ii)))))))))) (let ((_let_114 (forall ((x |u_(-> tptp.list_nat tptp.set_list_nat Bool)|) (y |u_(-> tptp.list_nat tptp.set_list_nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_181 x z) (ho_181 y z)))) (= x y))))) (let ((_let_115 (forall ((u |u_(-> tptp.set_list_nat Bool)|) (e Bool) (i tptp.set_list_nat)) (not (forall ((v |u_(-> tptp.set_list_nat Bool)|)) (not (forall ((ii tptp.set_list_nat)) (= (ho_182 v ii) (ite (= i ii) e (ho_182 u ii)))))))))) (let ((_let_116 (forall ((x |u_(-> tptp.set_list_nat Bool)|) (y |u_(-> tptp.set_list_nat Bool)|)) (or (not (forall ((z tptp.set_list_nat)) (= (ho_182 x z) (ho_182 y z)))) (= x y))))) (let ((_let_117 (forall ((u |u_(-> tptp.list_set_nat tptp.set_list_nat)|) (e tptp.set_list_nat) (i tptp.list_set_nat)) (not (forall ((v |u_(-> tptp.list_set_nat tptp.set_list_nat)|)) (not (forall ((ii tptp.list_set_nat)) (= (ho_179 v ii) (ite (= i ii) e (ho_179 u ii)))))))))) (let ((_let_118 (forall ((x |u_(-> tptp.list_set_nat tptp.set_list_nat)|) (y |u_(-> tptp.list_set_nat tptp.set_list_nat)|)) (or (not (forall ((z tptp.list_set_nat)) (= (ho_179 x z) (ho_179 y z)))) (= x y))))) (let ((_let_119 (forall ((u |u_(-> _u_(-> tptp.list_a tptp.a)_ tptp.a tptp.list_a)|) (e |u_(-> tptp.a tptp.list_a)|) (i |u_(-> tptp.list_a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a tptp.a)_ tptp.a tptp.list_a)|)) (not (forall ((ii |u_(-> tptp.list_a tptp.a)|)) (= (ho_361 v ii) (ite (= i ii) e (ho_361 u ii)))))))))) (let ((_let_120 (forall ((x |u_(-> _u_(-> tptp.list_a tptp.a)_ tptp.a tptp.list_a)|) (y |u_(-> _u_(-> tptp.list_a tptp.a)_ tptp.a tptp.list_a)|)) (or (not (forall ((z |u_(-> tptp.list_a tptp.a)|)) (= (ho_361 x z) (ho_361 y z)))) (= x y))))) (let ((_let_121 (forall ((u |u_(-> tptp.set_nat tptp.list_set_nat Bool)|) (e |u_(-> tptp.list_set_nat Bool)|) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat tptp.list_set_nat Bool)|)) (not (forall ((ii tptp.set_nat)) (= (ho_184 v ii) (ite (= i ii) e (ho_184 u ii)))))))))) (let ((_let_122 (forall ((x |u_(-> tptp.set_nat tptp.list_set_nat Bool)|) (y |u_(-> tptp.set_nat tptp.list_set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_184 x z) (ho_184 y z)))) (= x y))))) (let ((_let_123 (forall ((u |u_(-> tptp.list_set_multiset_a Bool)|) (e Bool) (i tptp.list_set_multiset_a)) (not (forall ((v |u_(-> tptp.list_set_multiset_a Bool)|)) (not (forall ((ii tptp.list_set_multiset_a)) (= (ho_176 v ii) (ite (= i ii) e (ho_176 u ii)))))))))) (let ((_let_124 (forall ((x |u_(-> tptp.list_set_multiset_a Bool)|) (y |u_(-> tptp.list_set_multiset_a Bool)|)) (or (not (forall ((z tptp.list_set_multiset_a)) (= (ho_176 x z) (ho_176 y z)))) (= x y))))) (let ((_let_125 (forall ((u |u_(-> tptp.set_a _u_(-> tptp.a tptp.list_a)_ tptp.list_a tptp.a)|) (e |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a tptp.a)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a _u_(-> tptp.a tptp.list_a)_ tptp.list_a tptp.a)|)) (not (forall ((ii tptp.set_a)) (= (ho_363 v ii) (ite (= i ii) e (ho_363 u ii)))))))))) (let ((_let_126 (forall ((x |u_(-> tptp.set_a _u_(-> tptp.a tptp.list_a)_ tptp.list_a tptp.a)|) (y |u_(-> tptp.set_a _u_(-> tptp.a tptp.list_a)_ tptp.list_a tptp.a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_363 x z) (ho_363 y z)))) (= x y))))) (let ((_let_127 (forall ((u |u_(-> tptp.multiset_nat tptp.nat)|) (e tptp.nat) (i tptp.multiset_nat)) (not (forall ((v |u_(-> tptp.multiset_nat tptp.nat)|)) (not (forall ((ii tptp.multiset_nat)) (= (ho_200 v ii) (ite (= i ii) e (ho_200 u ii)))))))))) (let ((_let_128 (forall ((x |u_(-> tptp.multiset_nat tptp.nat)|) (y |u_(-> tptp.multiset_nat tptp.nat)|)) (or (not (forall ((z tptp.multiset_nat)) (= (ho_200 x z) (ho_200 y z)))) (= x y))))) (let ((_let_129 (forall ((u |u_(-> tptp.list_multiset_a tptp.set_list_multiset_a Bool)|) (e |u_(-> tptp.set_list_multiset_a Bool)|) (i tptp.list_multiset_a)) (not (forall ((v |u_(-> tptp.list_multiset_a tptp.set_list_multiset_a Bool)|)) (not (forall ((ii tptp.list_multiset_a)) (= (ho_172 v ii) (ite (= i ii) e (ho_172 u ii)))))))))) (let ((_let_130 (forall ((x |u_(-> tptp.list_multiset_a tptp.set_list_multiset_a Bool)|) (y |u_(-> tptp.list_multiset_a tptp.set_list_multiset_a Bool)|)) (or (not (forall ((z tptp.list_multiset_a)) (= (ho_172 x z) (ho_172 y z)))) (= x y))))) (let ((_let_131 (forall ((u |u_(-> tptp.set_list_set_set_a Bool)|) (e Bool) (i tptp.set_list_set_set_a)) (not (forall ((v |u_(-> tptp.set_list_set_set_a Bool)|)) (not (forall ((ii tptp.set_list_set_set_a)) (= (ho_248 v ii) (ite (= i ii) e (ho_248 u ii)))))))))) (let ((_let_132 (forall ((x |u_(-> tptp.set_list_set_set_a Bool)|) (y |u_(-> tptp.set_list_set_set_a Bool)|)) (or (not (forall ((z tptp.set_list_set_set_a)) (= (ho_248 x z) (ho_248 y z)))) (= x y))))) (let ((_let_133 (forall ((u |u_(-> tptp.a tptp.a)|) (e tptp.a) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.a)|)) (not (forall ((ii tptp.a)) (= (ho_342 v ii) (ite (= i ii) e (ho_342 u ii)))))))))) (let ((_let_134 (forall ((x |u_(-> tptp.a tptp.a)|) (y |u_(-> tptp.a tptp.a)|)) (or (not (forall ((z tptp.a)) (= (ho_342 x z) (ho_342 y z)))) (= x y))))) (let ((_let_135 (forall ((u |u_(-> tptp.list_multiset_a tptp.multiset_a)|) (e tptp.multiset_a) (i tptp.list_multiset_a)) (not (forall ((v |u_(-> tptp.list_multiset_a tptp.multiset_a)|)) (not (forall ((ii tptp.list_multiset_a)) (= (ho_168 v ii) (ite (= i ii) e (ho_168 u ii)))))))))) (let ((_let_136 (forall ((x |u_(-> tptp.list_multiset_a tptp.multiset_a)|) (y |u_(-> tptp.list_multiset_a tptp.multiset_a)|)) (or (not (forall ((z tptp.list_multiset_a)) (= (ho_168 x z) (ho_168 y z)))) (= x y))))) (let ((_let_137 (forall ((u |u_(-> tptp.nat tptp.set_set_set_a)|) (e tptp.set_set_set_a) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_set_set_a)|)) (not (forall ((ii tptp.nat)) (= (ho_251 v ii) (ite (= i ii) e (ho_251 u ii)))))))))) (let ((_let_138 (forall ((x |u_(-> tptp.nat tptp.set_set_set_a)|) (y |u_(-> tptp.nat tptp.set_set_set_a)|)) (or (not (forall ((z tptp.nat)) (= (ho_251 x z) (ho_251 y z)))) (= x y))))) (let ((_let_139 (forall ((u |u_(-> tptp.list_a tptp.a)|) (e tptp.a) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.a)|)) (not (forall ((ii tptp.list_a)) (= (ho_164 v ii) (ite (= i ii) e (ho_164 u ii)))))))))) (let ((_let_140 (forall ((x |u_(-> tptp.list_a tptp.a)|) (y |u_(-> tptp.list_a tptp.a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_164 x z) (ho_164 y z)))) (= x y))))) (let ((_let_141 (forall ((u |u_(-> tptp.multiset_list_a tptp.set_multiset_list_a Bool)|) (e |u_(-> tptp.set_multiset_list_a Bool)|) (i tptp.multiset_list_a)) (not (forall ((v |u_(-> tptp.multiset_list_a tptp.set_multiset_list_a Bool)|)) (not (forall ((ii tptp.multiset_list_a)) (= (ho_388 v ii) (ite (= i ii) e (ho_388 u ii)))))))))) (let ((_let_142 (forall ((x |u_(-> tptp.multiset_list_a tptp.set_multiset_list_a Bool)|) (y |u_(-> tptp.multiset_list_a tptp.set_multiset_list_a Bool)|)) (or (not (forall ((z tptp.multiset_list_a)) (= (ho_388 x z) (ho_388 y z)))) (= x y))))) (let ((_let_143 (forall ((u |u_(-> tptp.list_list_a tptp.nat)|) (e tptp.nat) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a tptp.nat)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_159 v ii) (ite (= i ii) e (ho_159 u ii)))))))))) (let ((_let_144 (forall ((x |u_(-> tptp.list_list_a tptp.nat)|) (y |u_(-> tptp.list_list_a tptp.nat)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_159 x z) (ho_159 y z)))) (= x y))))) (let ((_let_145 (forall ((u |u_(-> tptp.list_list_a tptp.nat tptp.list_a)|) (e |u_(-> tptp.nat tptp.list_a)|) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a tptp.nat tptp.list_a)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_156 v ii) (ite (= i ii) e (ho_156 u ii)))))))))) (let ((_let_146 (forall ((x |u_(-> tptp.list_list_a tptp.nat tptp.list_a)|) (y |u_(-> tptp.list_list_a tptp.nat tptp.list_a)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_156 x z) (ho_156 y z)))) (= x y))))) (let ((_let_147 (forall ((u |u_(-> tptp.nat tptp.a)|) (e tptp.a) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.a)|)) (not (forall ((ii tptp.nat)) (= (ho_123 v ii) (ite (= i ii) e (ho_123 u ii)))))))))) (let ((_let_148 (forall ((x |u_(-> tptp.nat tptp.a)|) (y |u_(-> tptp.nat tptp.a)|)) (or (not (forall ((z tptp.nat)) (= (ho_123 x z) (ho_123 y z)))) (= x y))))) (let ((_let_149 (forall ((u |u_(-> tptp.nat tptp.list_a)|) (e tptp.list_a) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.list_a)|)) (not (forall ((ii tptp.nat)) (= (ho_157 v ii) (ite (= i ii) e (ho_157 u ii)))))))))) (let ((_let_150 (forall ((x |u_(-> tptp.nat tptp.list_a)|) (y |u_(-> tptp.nat tptp.list_a)|)) (or (not (forall ((z tptp.nat)) (= (ho_157 x z) (ho_157 y z)))) (= x y))))) (let ((_let_151 (forall ((u |u_(-> tptp.list_set_multiset_a tptp.set_list_multiset_a)|) (e tptp.set_list_multiset_a) (i tptp.list_set_multiset_a)) (not (forall ((v |u_(-> tptp.list_set_multiset_a tptp.set_list_multiset_a)|)) (not (forall ((ii tptp.list_set_multiset_a)) (= (ho_170 v ii) (ite (= i ii) e (ho_170 u ii)))))))))) (let ((_let_152 (forall ((x |u_(-> tptp.list_set_multiset_a tptp.set_list_multiset_a)|) (y |u_(-> tptp.list_set_multiset_a tptp.set_list_multiset_a)|)) (or (not (forall ((z tptp.list_set_multiset_a)) (= (ho_170 x z) (ho_170 y z)))) (= x y))))) (let ((_let_153 (forall ((u |u_(-> tptp.set_nat Bool)|) (e Bool) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat Bool)|)) (not (forall ((ii tptp.set_nat)) (= (ho_71 v ii) (ite (= i ii) e (ho_71 u ii)))))))))) (let ((_let_154 (forall ((x |u_(-> tptp.set_nat Bool)|) (y |u_(-> tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_71 x z) (ho_71 y z)))) (= x y))))) (let ((_let_155 (forall ((u |u_(-> tptp.list_list_a tptp.list_list_a Bool)|) (e |u_(-> tptp.list_list_a Bool)|) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a tptp.list_list_a Bool)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_154 v ii) (ite (= i ii) e (ho_154 u ii)))))))))) (let ((_let_156 (forall ((x |u_(-> tptp.list_list_a tptp.list_list_a Bool)|) (y |u_(-> tptp.list_list_a tptp.list_list_a Bool)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_154 x z) (ho_154 y z)))) (= x y))))) (let ((_let_157 (forall ((u |u_(-> tptp.list_multiset_a tptp.multiset_multiset_a)|) (e tptp.multiset_multiset_a) (i tptp.list_multiset_a)) (not (forall ((v |u_(-> tptp.list_multiset_a tptp.multiset_multiset_a)|)) (not (forall ((ii tptp.list_multiset_a)) (= (ho_208 v ii) (ite (= i ii) e (ho_208 u ii)))))))))) (let ((_let_158 (forall ((x |u_(-> tptp.list_multiset_a tptp.multiset_multiset_a)|) (y |u_(-> tptp.list_multiset_a tptp.multiset_multiset_a)|)) (or (not (forall ((z tptp.list_multiset_a)) (= (ho_208 x z) (ho_208 y z)))) (= x y))))) (let ((_let_159 (forall ((u |u_(-> tptp.nat tptp.set_a Bool)|) (e |u_(-> tptp.set_a Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_a Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_326 v ii) (ite (= i ii) e (ho_326 u ii)))))))))) (let ((_let_160 (forall ((x |u_(-> tptp.nat tptp.set_a Bool)|) (y |u_(-> tptp.nat tptp.set_a Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_326 x z) (ho_326 y z)))) (= x y))))) (let ((_let_161 (forall ((u |u_(-> tptp.list_set_a tptp.set_list_set_a Bool)|) (e |u_(-> tptp.set_list_set_a Bool)|) (i tptp.list_set_a)) (not (forall ((v |u_(-> tptp.list_set_a tptp.set_list_set_a Bool)|)) (not (forall ((ii tptp.list_set_a)) (= (ho_97 v ii) (ite (= i ii) e (ho_97 u ii)))))))))) (let ((_let_162 (forall ((x |u_(-> tptp.list_set_a tptp.set_list_set_a Bool)|) (y |u_(-> tptp.list_set_a tptp.set_list_set_a Bool)|)) (or (not (forall ((z tptp.list_set_a)) (= (ho_97 x z) (ho_97 y z)))) (= x y))))) (let ((_let_163 (forall ((u |u_(-> tptp.set_list_set_a Bool)|) (e Bool) (i tptp.set_list_set_a)) (not (forall ((v |u_(-> tptp.set_list_set_a Bool)|)) (not (forall ((ii tptp.set_list_set_a)) (= (ho_98 v ii) (ite (= i ii) e (ho_98 u ii)))))))))) (let ((_let_164 (forall ((x |u_(-> tptp.set_list_set_a Bool)|) (y |u_(-> tptp.set_list_set_a Bool)|)) (or (not (forall ((z tptp.set_list_set_a)) (= (ho_98 x z) (ho_98 y z)))) (= x y))))) (let ((_let_165 (forall ((u |u_(-> tptp.set_a tptp.set_set_a Bool)|) (e |u_(-> tptp.set_set_a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_set_a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_91 v ii) (ite (= i ii) e (ho_91 u ii)))))))))) (let ((_let_166 (forall ((x |u_(-> tptp.set_a tptp.set_set_a Bool)|) (y |u_(-> tptp.set_a tptp.set_set_a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_91 x z) (ho_91 y z)))) (= x y))))) (let ((_let_167 (forall ((u |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.set_list_a Bool)|) (e |u_(-> tptp.set_list_a Bool)|) (i |u_(-> tptp.list_a tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.set_list_a Bool)|)) (not (forall ((ii |u_(-> tptp.list_a tptp.list_a)|)) (= (ho_396 v ii) (ite (= i ii) e (ho_396 u ii)))))))))) (let ((_let_168 (forall ((x |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.set_list_a Bool)|) (y |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.set_list_a Bool)|)) (or (not (forall ((z |u_(-> tptp.list_a tptp.list_a)|)) (= (ho_396 x z) (ho_396 y z)))) (= x y))))) (let ((_let_169 (forall ((u |u_(-> tptp.list_set_a tptp.nat)|) (e tptp.nat) (i tptp.list_set_a)) (not (forall ((v |u_(-> tptp.list_set_a tptp.nat)|)) (not (forall ((ii tptp.list_set_a)) (= (ho_117 v ii) (ite (= i ii) e (ho_117 u ii)))))))))) (let ((_let_170 (forall ((x |u_(-> tptp.list_set_a tptp.nat)|) (y |u_(-> tptp.list_set_a tptp.nat)|)) (or (not (forall ((z tptp.list_set_a)) (= (ho_117 x z) (ho_117 y z)))) (= x y))))) (let ((_let_171 (forall ((u |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (e |u_(-> tptp.nat tptp.nat)|) (i |u_(-> tptp.nat tptp.nat)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|)) (not (forall ((ii |u_(-> tptp.nat tptp.nat)|)) (= (ho_196 v ii) (ite (= i ii) e (ho_196 u ii)))))))))) (let ((_let_172 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.nat tptp.nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_196 x z) (ho_196 y z)))) (= x y))))) (let ((_let_173 (forall ((u |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.set_nat)|) (e |u_(-> tptp.set_nat tptp.set_nat)|) (i |u_(-> tptp.nat tptp.nat)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.set_nat)|)) (not (forall ((ii |u_(-> tptp.nat tptp.nat)|)) (= (ho_76 v ii) (ite (= i ii) e (ho_76 u ii)))))))))) (let ((_let_174 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.set_nat)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.set_nat)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_76 x z) (ho_76 y z)))) (= x y))))) (let ((_let_175 (forall ((u |u_(-> tptp.set_a tptp.list_set_a)|) (e tptp.list_set_a) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.list_set_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_376 v ii) (ite (= i ii) e (ho_376 u ii)))))))))) (let ((_let_176 (forall ((x |u_(-> tptp.set_a tptp.list_set_a)|) (y |u_(-> tptp.set_a tptp.list_set_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_376 x z) (ho_376 y z)))) (= x y))))) (let ((_let_177 (forall ((u |u_(-> tptp.list_set_list_a tptp.set_list_set_list_a Bool)|) (e |u_(-> tptp.set_list_set_list_a Bool)|) (i tptp.list_set_list_a)) (not (forall ((v |u_(-> tptp.list_set_list_a tptp.set_list_set_list_a Bool)|)) (not (forall ((ii tptp.list_set_list_a)) (= (ho_237 v ii) (ite (= i ii) e (ho_237 u ii)))))))))) (let ((_let_178 (forall ((x |u_(-> tptp.list_set_list_a tptp.set_list_set_list_a Bool)|) (y |u_(-> tptp.list_set_list_a tptp.set_list_set_list_a Bool)|)) (or (not (forall ((z tptp.list_set_list_a)) (= (ho_237 x z) (ho_237 y z)))) (= x y))))) (let ((_let_179 (forall ((u |u_(-> tptp.list_list_a tptp.multiset_list_a)|) (e tptp.multiset_list_a) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a tptp.multiset_list_a)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_224 v ii) (ite (= i ii) e (ho_224 u ii)))))))))) (let ((_let_180 (forall ((x |u_(-> tptp.list_list_a tptp.multiset_list_a)|) (y |u_(-> tptp.list_list_a tptp.multiset_list_a)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_224 x z) (ho_224 y z)))) (= x y))))) (let ((_let_181 (forall ((u |u_(-> tptp.set_set_a Bool)|) (e Bool) (i tptp.set_set_a)) (not (forall ((v |u_(-> tptp.set_set_a Bool)|)) (not (forall ((ii tptp.set_set_a)) (= (ho_92 v ii) (ite (= i ii) e (ho_92 u ii)))))))))) (let ((_let_182 (forall ((x |u_(-> tptp.set_set_a Bool)|) (y |u_(-> tptp.set_set_a Bool)|)) (or (not (forall ((z tptp.set_set_a)) (= (ho_92 x z) (ho_92 y z)))) (= x y))))) (let ((_let_183 (forall ((u |u_(-> tptp.set_list_multiset_a Bool)|) (e Bool) (i tptp.set_list_multiset_a)) (not (forall ((v |u_(-> tptp.set_list_multiset_a Bool)|)) (not (forall ((ii tptp.set_list_multiset_a)) (= (ho_173 v ii) (ite (= i ii) e (ho_173 u ii)))))))))) (let ((_let_184 (forall ((x |u_(-> tptp.set_list_multiset_a Bool)|) (y |u_(-> tptp.set_list_multiset_a Bool)|)) (or (not (forall ((z tptp.set_list_multiset_a)) (= (ho_173 x z) (ho_173 y z)))) (= x y))))) (let ((_let_185 (forall ((u |u_(-> tptp.list_set_set_a tptp.nat)|) (e tptp.nat) (i tptp.list_set_set_a)) (not (forall ((v |u_(-> tptp.list_set_set_a tptp.nat)|)) (not (forall ((ii tptp.list_set_set_a)) (= (ho_142 v ii) (ite (= i ii) e (ho_142 u ii)))))))))) (let ((_let_186 (forall ((x |u_(-> tptp.list_set_set_a tptp.nat)|) (y |u_(-> tptp.list_set_set_a tptp.nat)|)) (or (not (forall ((z tptp.list_set_set_a)) (= (ho_142 x z) (ho_142 y z)))) (= x y))))) (let ((_let_187 (forall ((u |u_(-> tptp.set_set_nat Bool)|) (e Bool) (i tptp.set_set_nat)) (not (forall ((v |u_(-> tptp.set_set_nat Bool)|)) (not (forall ((ii tptp.set_set_nat)) (= (ho_269 v ii) (ite (= i ii) e (ho_269 u ii)))))))))) (let ((_let_188 (forall ((x |u_(-> tptp.set_set_nat Bool)|) (y |u_(-> tptp.set_set_nat Bool)|)) (or (not (forall ((z tptp.set_set_nat)) (= (ho_269 x z) (ho_269 y z)))) (= x y))))) (let ((_let_189 (forall ((u |u_(-> tptp.set_nat tptp.set_nat)|) (e tptp.set_nat) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat tptp.set_nat)|)) (not (forall ((ii tptp.set_nat)) (= (ho_77 v ii) (ite (= i ii) e (ho_77 u ii)))))))))) (let ((_let_190 (forall ((x |u_(-> tptp.set_nat tptp.set_nat)|) (y |u_(-> tptp.set_nat tptp.set_nat)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_77 x z) (ho_77 y z)))) (= x y))))) (let ((_let_191 (forall ((u |u_(-> tptp.list_set_set_a tptp.list_set_set_a Bool)|) (e |u_(-> tptp.list_set_set_a Bool)|) (i tptp.list_set_set_a)) (not (forall ((v |u_(-> tptp.list_set_set_a tptp.list_set_set_a Bool)|)) (not (forall ((ii tptp.list_set_set_a)) (= (ho_136 v ii) (ite (= i ii) e (ho_136 u ii)))))))))) (let ((_let_192 (forall ((x |u_(-> tptp.list_set_set_a tptp.list_set_set_a Bool)|) (y |u_(-> tptp.list_set_set_a tptp.list_set_set_a Bool)|)) (or (not (forall ((z tptp.list_set_set_a)) (= (ho_136 x z) (ho_136 y z)))) (= x y))))) (let ((_let_193 (forall ((u |u_(-> tptp.list_set_a Bool)|) (e Bool) (i tptp.list_set_a)) (not (forall ((v |u_(-> tptp.list_set_a Bool)|)) (not (forall ((ii tptp.list_set_a)) (= (ho_95 v ii) (ite (= i ii) e (ho_95 u ii)))))))))) (let ((_let_194 (forall ((x |u_(-> tptp.list_set_a Bool)|) (y |u_(-> tptp.list_set_a Bool)|)) (or (not (forall ((z tptp.list_set_a)) (= (ho_95 x z) (ho_95 y z)))) (= x y))))) (let ((_let_195 (forall ((u |u_(-> tptp.set_set_a tptp.set_a Bool)|) (e |u_(-> tptp.set_a Bool)|) (i tptp.set_set_a)) (not (forall ((v |u_(-> tptp.set_set_a tptp.set_a Bool)|)) (not (forall ((ii tptp.set_set_a)) (= (ho_89 v ii) (ite (= i ii) e (ho_89 u ii)))))))))) (let ((_let_196 (forall ((x |u_(-> tptp.set_set_a tptp.set_a Bool)|) (y |u_(-> tptp.set_set_a tptp.set_a Bool)|)) (or (not (forall ((z tptp.set_set_a)) (= (ho_89 x z) (ho_89 y z)))) (= x y))))) (let ((_let_197 (forall ((u |u_(-> tptp.set_multiset_a Bool)|) (e Bool) (i tptp.set_multiset_a)) (not (forall ((v |u_(-> tptp.set_multiset_a Bool)|)) (not (forall ((ii tptp.set_multiset_a)) (= (ho_110 v ii) (ite (= i ii) e (ho_110 u ii)))))))))) (let ((_let_198 (forall ((x |u_(-> tptp.set_multiset_a Bool)|) (y |u_(-> tptp.set_multiset_a Bool)|)) (or (not (forall ((z tptp.set_multiset_a)) (= (ho_110 x z) (ho_110 y z)))) (= x y))))) (let ((_let_199 (forall ((u |u_(-> tptp.list_set_a tptp.multiset_set_a)|) (e tptp.multiset_set_a) (i tptp.list_set_a)) (not (forall ((v |u_(-> tptp.list_set_a tptp.multiset_set_a)|)) (not (forall ((ii tptp.list_set_a)) (= (ho_220 v ii) (ite (= i ii) e (ho_220 u ii)))))))))) (let ((_let_200 (forall ((x |u_(-> tptp.list_set_a tptp.multiset_set_a)|) (y |u_(-> tptp.list_set_a tptp.multiset_set_a)|)) (or (not (forall ((z tptp.list_set_a)) (= (ho_220 x z) (ho_220 y z)))) (= x y))))) (let ((_let_201 (forall ((u |u_(-> tptp.nat tptp.set_nat Bool)|) (e |u_(-> tptp.set_nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_73 v ii) (ite (= i ii) e (ho_73 u ii)))))))))) (let ((_let_202 (forall ((x |u_(-> tptp.nat tptp.set_nat Bool)|) (y |u_(-> tptp.nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_73 x z) (ho_73 y z)))) (= x y))))) (let ((_let_203 (forall ((u |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.set_nat Bool)|) (e |u_(-> tptp.set_nat tptp.set_nat Bool)|) (i |u_(-> tptp.nat tptp.nat)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.set_nat Bool)|)) (not (forall ((ii |u_(-> tptp.nat tptp.nat)|)) (= (ho_69 v ii) (ite (= i ii) e (ho_69 u ii)))))))))) (let ((_let_204 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.set_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat tptp.set_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_69 x z) (ho_69 y z)))) (= x y))))) (let ((_let_205 (forall ((u |u_(-> tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_40 v ii) (ite (= i ii) e (ho_40 u ii)))))))))) (let ((_let_206 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_40 x z) (ho_40 y z)))) (= x y))))) (let ((_let_207 (forall ((u |u_(-> tptp.list_set_set_set_a tptp.set_list_set_set_a)|) (e tptp.set_list_set_set_a) (i tptp.list_set_set_set_a)) (not (forall ((v |u_(-> tptp.list_set_set_set_a tptp.set_list_set_set_a)|)) (not (forall ((ii tptp.list_set_set_set_a)) (= (ho_245 v ii) (ite (= i ii) e (ho_245 u ii)))))))))) (let ((_let_208 (forall ((x |u_(-> tptp.list_set_set_set_a tptp.set_list_set_set_a)|) (y |u_(-> tptp.list_set_set_set_a tptp.set_list_set_set_a)|)) (or (not (forall ((z tptp.list_set_set_set_a)) (= (ho_245 x z) (ho_245 y z)))) (= x y))))) (let ((_let_209 (forall ((u |u_(-> tptp.list_set_set_a tptp.set_list_set_set_a Bool)|) (e |u_(-> tptp.set_list_set_set_a Bool)|) (i tptp.list_set_set_a)) (not (forall ((v |u_(-> tptp.list_set_set_a tptp.set_list_set_set_a Bool)|)) (not (forall ((ii tptp.list_set_set_a)) (= (ho_247 v ii) (ite (= i ii) e (ho_247 u ii)))))))))) (let ((_let_210 (forall ((x |u_(-> tptp.list_set_set_a tptp.set_list_set_set_a Bool)|) (y |u_(-> tptp.list_set_set_a tptp.set_list_set_set_a Bool)|)) (or (not (forall ((z tptp.list_set_set_a)) (= (ho_247 x z) (ho_247 y z)))) (= x y))))) (let ((_let_211 (forall ((u |u_(-> tptp.list_a tptp.list_a)|) (e tptp.list_a) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_a)|)) (not (forall ((ii tptp.list_a)) (= (ho_190 v ii) (ite (= i ii) e (ho_190 u ii)))))))))) (let ((_let_212 (forall ((x |u_(-> tptp.list_a tptp.list_a)|) (y |u_(-> tptp.list_a tptp.list_a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_190 x z) (ho_190 y z)))) (= x y))))) (let ((_let_213 (forall ((u |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.nat Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_47 v ii) (ite (= i ii) e (ho_47 u ii)))))))))) (let ((_let_214 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_47 x z) (ho_47 y z)))) (= x y))))) (let ((_let_215 (forall ((u |u_(-> tptp.nat tptp.set_a)|) (e tptp.set_a) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_a)|)) (not (forall ((ii tptp.nat)) (= (ho_115 v ii) (ite (= i ii) e (ho_115 u ii)))))))))) (let ((_let_216 (forall ((x |u_(-> tptp.nat tptp.set_a)|) (y |u_(-> tptp.nat tptp.set_a)|)) (or (not (forall ((z tptp.nat)) (= (ho_115 x z) (ho_115 y z)))) (= x y))))) (let ((_let_217 (forall ((u |u_(-> tptp.list_nat tptp.multiset_nat)|) (e tptp.multiset_nat) (i tptp.list_nat)) (not (forall ((v |u_(-> tptp.list_nat tptp.multiset_nat)|)) (not (forall ((ii tptp.list_nat)) (= (ho_198 v ii) (ite (= i ii) e (ho_198 u ii)))))))))) (let ((_let_218 (forall ((x |u_(-> tptp.list_nat tptp.multiset_nat)|) (y |u_(-> tptp.list_nat tptp.multiset_nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_198 x z) (ho_198 y z)))) (= x y))))) (let ((_let_219 (forall ((u |u_(-> tptp.list_a tptp.set_list_a Bool)|) (e |u_(-> tptp.set_list_a Bool)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.set_list_a Bool)|)) (not (forall ((ii tptp.list_a)) (= (ho_59 v ii) (ite (= i ii) e (ho_59 u ii)))))))))) (let ((_let_220 (forall ((x |u_(-> tptp.list_a tptp.set_list_a Bool)|) (y |u_(-> tptp.list_a tptp.set_list_a Bool)|)) (or (not (forall ((z tptp.list_a)) (= (ho_59 x z) (ho_59 y z)))) (= x y))))) (let ((_let_221 (forall ((u |u_(-> tptp.list_set_set_a tptp.set_list_set_a)|) (e tptp.set_list_set_a) (i tptp.list_set_set_a)) (not (forall ((v |u_(-> tptp.list_set_set_a tptp.set_list_set_a)|)) (not (forall ((ii tptp.list_set_set_a)) (= (ho_259 v ii) (ite (= i ii) e (ho_259 u ii)))))))))) (let ((_let_222 (forall ((x |u_(-> tptp.list_set_set_a tptp.set_list_set_a)|) (y |u_(-> tptp.list_set_set_a tptp.set_list_set_a)|)) (or (not (forall ((z tptp.list_set_set_a)) (= (ho_259 x z) (ho_259 y z)))) (= x y))))) (let ((_let_223 (forall ((u |u_(-> tptp.list_set_a tptp.list_set_a Bool)|) (e |u_(-> tptp.list_set_a Bool)|) (i tptp.list_set_a)) (not (forall ((v |u_(-> tptp.list_set_a tptp.list_set_a Bool)|)) (not (forall ((ii tptp.list_set_a)) (= (ho_112 v ii) (ite (= i ii) e (ho_112 u ii)))))))))) (let ((_let_224 (forall ((x |u_(-> tptp.list_set_a tptp.list_set_a Bool)|) (y |u_(-> tptp.list_set_a tptp.list_set_a Bool)|)) (or (not (forall ((z tptp.list_set_a)) (= (ho_112 x z) (ho_112 y z)))) (= x y))))) (let ((_let_225 (forall ((u |u_(-> tptp.list_nat tptp.nat)|) (e tptp.nat) (i tptp.list_nat)) (not (forall ((v |u_(-> tptp.list_nat tptp.nat)|)) (not (forall ((ii tptp.list_nat)) (= (ho_133 v ii) (ite (= i ii) e (ho_133 u ii)))))))))) (let ((_let_226 (forall ((x |u_(-> tptp.list_nat tptp.nat)|) (y |u_(-> tptp.list_nat tptp.nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_133 x z) (ho_133 y z)))) (= x y))))) (let ((_let_227 (forall ((u |u_(-> tptp.set_list_a Bool)|) (e Bool) (i tptp.set_list_a)) (not (forall ((v |u_(-> tptp.set_list_a Bool)|)) (not (forall ((ii tptp.set_list_a)) (= (ho_57 v ii) (ite (= i ii) e (ho_57 u ii)))))))))) (let ((_let_228 (forall ((x |u_(-> tptp.set_list_a Bool)|) (y |u_(-> tptp.set_list_a Bool)|)) (or (not (forall ((z tptp.set_list_a)) (= (ho_57 x z) (ho_57 y z)))) (= x y))))) (let ((_let_229 (forall ((u |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_a Bool)|) (e |u_(-> tptp.set_a Bool)|) (i |u_(-> tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_a Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.a)|)) (= (ho_392 v ii) (ite (= i ii) e (ho_392 u ii)))))))))) (let ((_let_230 (forall ((x |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_a Bool)|) (y |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_a Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a)|)) (= (ho_392 x z) (ho_392 y z)))) (= x y))))) (let ((_let_231 (forall ((u |u_(-> tptp.list_set_list_a tptp.multiset_set_list_a)|) (e tptp.multiset_set_list_a) (i tptp.list_set_list_a)) (not (forall ((v |u_(-> tptp.list_set_list_a tptp.multiset_set_list_a)|)) (not (forall ((ii tptp.list_set_list_a)) (= (ho_229 v ii) (ite (= i ii) e (ho_229 u ii)))))))))) (let ((_let_232 (forall ((x |u_(-> tptp.list_set_list_a tptp.multiset_set_list_a)|) (y |u_(-> tptp.list_set_list_a tptp.multiset_set_list_a)|)) (or (not (forall ((z tptp.list_set_list_a)) (= (ho_229 x z) (ho_229 y z)))) (= x y))))) (let ((_let_233 (forall ((u |u_(-> tptp.nat tptp.nat)|) (e tptp.nat) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_67 v ii) (ite (= i ii) e (ho_67 u ii)))))))))) (let ((_let_234 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_67 x z) (ho_67 y z)))) (= x y))))) (let ((_let_235 (forall ((u |u_(-> tptp.nat Bool)|) (e Bool) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_41 v ii) (ite (= i ii) e (ho_41 u ii)))))))))) (let ((_let_236 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_41 x z) (ho_41 y z)))) (= x y))))) (let ((_let_237 (forall ((u |u_(-> tptp.a tptp.set_a Bool)|) (e |u_(-> tptp.set_a Bool)|) (i tptp.a)) (not (forall ((v |u_(-> tptp.a tptp.set_a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_65 v ii) (ite (= i ii) e (ho_65 u ii)))))))))) (let ((_let_238 (forall ((x |u_(-> tptp.a tptp.set_a Bool)|) (y |u_(-> tptp.a tptp.set_a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_65 x z) (ho_65 y z)))) (= x y))))) (let ((_let_239 (forall ((u |u_(-> _u_(-> tptp.list_a tptp.a)_ tptp.set_list_a Bool)|) (e |u_(-> tptp.set_list_a Bool)|) (i |u_(-> tptp.list_a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a tptp.a)_ tptp.set_list_a Bool)|)) (not (forall ((ii |u_(-> tptp.list_a tptp.a)|)) (= (ho_369 v ii) (ite (= i ii) e (ho_369 u ii)))))))))) (let ((_let_240 (forall ((x |u_(-> _u_(-> tptp.list_a tptp.a)_ tptp.set_list_a Bool)|) (y |u_(-> _u_(-> tptp.list_a tptp.a)_ tptp.set_list_a Bool)|)) (or (not (forall ((z |u_(-> tptp.list_a tptp.a)|)) (= (ho_369 x z) (ho_369 y z)))) (= x y))))) (let ((_let_241 (forall ((u |u_(-> tptp.set_list_a tptp.set_list_a Bool)|) (e |u_(-> tptp.set_list_a Bool)|) (i tptp.set_list_a)) (not (forall ((v |u_(-> tptp.set_list_a tptp.set_list_a Bool)|)) (not (forall ((ii tptp.set_list_a)) (= (ho_56 v ii) (ite (= i ii) e (ho_56 u ii)))))))))) (let ((_let_242 (forall ((x |u_(-> tptp.set_list_a tptp.set_list_a Bool)|) (y |u_(-> tptp.set_list_a tptp.set_list_a Bool)|)) (or (not (forall ((z tptp.set_list_a)) (= (ho_56 x z) (ho_56 y z)))) (= x y))))) (let ((_let_243 (forall ((u |u_(-> tptp.set_a Bool)|) (e Bool) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_63 v ii) (ite (= i ii) e (ho_63 u ii)))))))))) (let ((_let_244 (forall ((x |u_(-> tptp.set_a Bool)|) (y |u_(-> tptp.set_a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_63 x z) (ho_63 y z)))) (= x y))))) (let ((_let_245 (forall ((u |u_(-> tptp.set_multiset_a tptp.list_set_multiset_a Bool)|) (e |u_(-> tptp.list_set_multiset_a Bool)|) (i tptp.set_multiset_a)) (not (forall ((v |u_(-> tptp.set_multiset_a tptp.list_set_multiset_a Bool)|)) (not (forall ((ii tptp.set_multiset_a)) (= (ho_175 v ii) (ite (= i ii) e (ho_175 u ii)))))))))) (let ((_let_246 (forall ((x |u_(-> tptp.set_multiset_a tptp.list_set_multiset_a Bool)|) (y |u_(-> tptp.set_multiset_a tptp.list_set_multiset_a Bool)|)) (or (not (forall ((z tptp.set_multiset_a)) (= (ho_175 x z) (ho_175 y z)))) (= x y))))) (let ((_let_247 (forall ((u |u_(-> tptp.list_set_list_a Bool)|) (e Bool) (i tptp.list_set_list_a)) (not (forall ((v |u_(-> tptp.list_set_list_a Bool)|)) (not (forall ((ii tptp.list_set_list_a)) (= (ho_146 v ii) (ite (= i ii) e (ho_146 u ii)))))))))) (let ((_let_248 (forall ((x |u_(-> tptp.list_set_list_a Bool)|) (y |u_(-> tptp.list_set_list_a Bool)|)) (or (not (forall ((z tptp.list_set_list_a)) (= (ho_146 x z) (ho_146 y z)))) (= x y))))) (let ((_let_249 (forall ((u |u_(-> tptp.multiset_multiset_a tptp.multiset_a)|) (e tptp.multiset_a) (i tptp.multiset_multiset_a)) (not (forall ((v |u_(-> tptp.multiset_multiset_a tptp.multiset_a)|)) (not (forall ((ii tptp.multiset_multiset_a)) (= (ho_210 v ii) (ite (= i ii) e (ho_210 u ii)))))))))) (let ((_let_250 (forall ((x |u_(-> tptp.multiset_multiset_a tptp.multiset_a)|) (y |u_(-> tptp.multiset_multiset_a tptp.multiset_a)|)) (or (not (forall ((z tptp.multiset_multiset_a)) (= (ho_210 x z) (ho_210 y z)))) (= x y))))) (let ((_let_251 (forall ((u |u_(-> tptp.list_list_a tptp.set_list_list_a Bool)|) (e |u_(-> tptp.set_list_list_a Bool)|) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a tptp.set_list_list_a Bool)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_103 v ii) (ite (= i ii) e (ho_103 u ii)))))))))) (let ((_let_252 (forall ((x |u_(-> tptp.list_list_a tptp.set_list_list_a Bool)|) (y |u_(-> tptp.list_list_a tptp.set_list_list_a Bool)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_103 x z) (ho_103 y z)))) (= x y))))) (let ((_let_253 (forall ((u |u_(-> tptp.nat tptp.set_set_a)|) (e tptp.set_set_a) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_set_a)|)) (not (forall ((ii tptp.nat)) (= (ho_140 v ii) (ite (= i ii) e (ho_140 u ii)))))))))) (let ((_let_254 (forall ((x |u_(-> tptp.nat tptp.set_set_a)|) (y |u_(-> tptp.nat tptp.set_set_a)|)) (or (not (forall ((z tptp.nat)) (= (ho_140 x z) (ho_140 y z)))) (= x y))))) (let ((_let_255 (forall ((u |u_(-> tptp.list_set_nat tptp.nat)|) (e tptp.nat) (i tptp.list_set_nat)) (not (forall ((v |u_(-> tptp.list_set_nat tptp.nat)|)) (not (forall ((ii tptp.list_set_nat)) (= (ho_253 v ii) (ite (= i ii) e (ho_253 u ii)))))))))) (let ((_let_256 (forall ((x |u_(-> tptp.list_set_nat tptp.nat)|) (y |u_(-> tptp.list_set_nat tptp.nat)|)) (or (not (forall ((z tptp.list_set_nat)) (= (ho_253 x z) (ho_253 y z)))) (= x y))))) (let ((_let_257 (forall ((u |u_(-> tptp.set_list_set_a tptp.list_set_a Bool)|) (e |u_(-> tptp.list_set_a Bool)|) (i tptp.set_list_set_a)) (not (forall ((v |u_(-> tptp.set_list_set_a tptp.list_set_a Bool)|)) (not (forall ((ii tptp.set_list_set_a)) (= (ho_94 v ii) (ite (= i ii) e (ho_94 u ii)))))))))) (let ((_let_258 (forall ((x |u_(-> tptp.set_list_set_a tptp.list_set_a Bool)|) (y |u_(-> tptp.set_list_set_a tptp.list_set_a Bool)|)) (or (not (forall ((z tptp.set_list_set_a)) (= (ho_94 x z) (ho_94 y z)))) (= x y))))) (let ((_let_259 (forall ((u |u_(-> tptp.list_list_a Bool)|) (e Bool) (i tptp.list_list_a)) (not (forall ((v |u_(-> tptp.list_list_a Bool)|)) (not (forall ((ii tptp.list_list_a)) (= (ho_101 v ii) (ite (= i ii) e (ho_101 u ii)))))))))) (let ((_let_260 (forall ((x |u_(-> tptp.list_list_a Bool)|) (y |u_(-> tptp.list_list_a Bool)|)) (or (not (forall ((z tptp.list_list_a)) (= (ho_101 x z) (ho_101 y z)))) (= x y))))) (let ((_let_261 (forall ((u |u_(-> tptp.set_nat tptp.set_nat Bool)|) (e |u_(-> tptp.set_nat Bool)|) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat tptp.set_nat Bool)|)) (not (forall ((ii tptp.set_nat)) (= (ho_70 v ii) (ite (= i ii) e (ho_70 u ii)))))))))) (let ((_let_262 (forall ((x |u_(-> tptp.set_nat tptp.set_nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_70 x z) (ho_70 y z)))) (= x y))))) (let ((_let_263 (forall ((u |u_(-> tptp.nat tptp.list_set_a)|) (e tptp.list_set_a) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.list_set_a)|)) (not (forall ((ii tptp.nat)) (= (ho_314 v ii) (ite (= i ii) e (ho_314 u ii)))))))))) (let ((_let_264 (forall ((x |u_(-> tptp.nat tptp.list_set_a)|) (y |u_(-> tptp.nat tptp.list_set_a)|)) (or (not (forall ((z tptp.nat)) (= (ho_314 x z) (ho_314 y z)))) (= x y))))) (let ((_let_265 (forall ((u |u_(-> tptp.list_a Bool)|) (e Bool) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a Bool)|)) (not (forall ((ii tptp.list_a)) (= (ho_82 v ii) (ite (= i ii) e (ho_82 u ii)))))))))) (let ((_let_266 (forall ((x |u_(-> tptp.list_a Bool)|) (y |u_(-> tptp.list_a Bool)|)) (or (not (forall ((z tptp.list_a)) (= (ho_82 x z) (ho_82 y z)))) (= x y))))) (let ((_let_267 (forall ((u |u_(-> tptp.list_set_set_a tptp.multiset_set_set_a)|) (e tptp.multiset_set_set_a) (i tptp.list_set_set_a)) (not (forall ((v |u_(-> tptp.list_set_set_a tptp.multiset_set_set_a)|)) (not (forall ((ii tptp.list_set_set_a)) (= (ho_231 v ii) (ite (= i ii) e (ho_231 u ii)))))))))) (let ((_let_268 (forall ((x |u_(-> tptp.list_set_set_a tptp.multiset_set_set_a)|) (y |u_(-> tptp.list_set_set_a tptp.multiset_set_set_a)|)) (or (not (forall ((z tptp.list_set_set_a)) (= (ho_231 x z) (ho_231 y z)))) (= x y))))) (let ((_let_269 (forall ((u |u_(-> tptp.nat tptp.multiset_a)|) (e tptp.multiset_a) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.multiset_a)|)) (not (forall ((ii tptp.nat)) (= (ho_284 v ii) (ite (= i ii) e (ho_284 u ii)))))))))) (let ((_let_270 (forall ((x |u_(-> tptp.nat tptp.multiset_a)|) (y |u_(-> tptp.nat tptp.multiset_a)|)) (or (not (forall ((z tptp.nat)) (= (ho_284 x z) (ho_284 y z)))) (= x y))))) (let ((_let_271 (forall ((u |u_(-> tptp.multiset_a tptp.set_multiset_a Bool)|) (e |u_(-> tptp.set_multiset_a Bool)|) (i tptp.multiset_a)) (not (forall ((v |u_(-> tptp.multiset_a tptp.set_multiset_a Bool)|)) (not (forall ((ii tptp.multiset_a)) (= (ho_109 v ii) (ite (= i ii) e (ho_109 u ii)))))))))) (let ((_let_272 (forall ((x |u_(-> tptp.multiset_a tptp.set_multiset_a Bool)|) (y |u_(-> tptp.multiset_a tptp.set_multiset_a Bool)|)) (or (not (forall ((z tptp.multiset_a)) (= (ho_109 x z) (ho_109 y z)))) (= x y))))) (let ((_let_273 (forall ((u |u_(-> tptp.set_list_list_a tptp.list_list_a Bool)|) (e |u_(-> tptp.list_list_a Bool)|) (i tptp.set_list_list_a)) (not (forall ((v |u_(-> tptp.set_list_list_a tptp.list_list_a Bool)|)) (not (forall ((ii tptp.set_list_list_a)) (= (ho_100 v ii) (ite (= i ii) e (ho_100 u ii)))))))))) (let ((_let_274 (forall ((x |u_(-> tptp.set_list_list_a tptp.list_list_a Bool)|) (y |u_(-> tptp.set_list_list_a tptp.list_list_a Bool)|)) (or (not (forall ((z tptp.set_list_list_a)) (= (ho_100 x z) (ho_100 y z)))) (= x y))))) (let ((_let_275 (forall ((u |u_(-> tptp.nat tptp.set_list_set_a)|) (e tptp.set_list_set_a) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_list_set_a)|)) (not (forall ((ii tptp.nat)) (= (ho_311 v ii) (ite (= i ii) e (ho_311 u ii)))))))))) (let ((_let_276 (forall ((x |u_(-> tptp.nat tptp.set_list_set_a)|) (y |u_(-> tptp.nat tptp.set_list_set_a)|)) (or (not (forall ((z tptp.nat)) (= (ho_311 x z) (ho_311 y z)))) (= x y))))) (let ((_let_277 (forall ((u |u_(-> tptp.set_nat tptp.set_set_nat Bool)|) (e |u_(-> tptp.set_set_nat Bool)|) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat tptp.set_set_nat Bool)|)) (not (forall ((ii tptp.set_nat)) (= (ho_268 v ii) (ite (= i ii) e (ho_268 u ii)))))))))) (let ((_let_278 (forall ((x |u_(-> tptp.set_nat tptp.set_set_nat Bool)|) (y |u_(-> tptp.set_nat tptp.set_set_nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_268 x z) (ho_268 y z)))) (= x y))))) (let ((_let_279 (forall ((u |u_(-> tptp.set_list_list_a Bool)|) (e Bool) (i tptp.set_list_list_a)) (not (forall ((v |u_(-> tptp.set_list_list_a Bool)|)) (not (forall ((ii tptp.set_list_list_a)) (= (ho_104 v ii) (ite (= i ii) e (ho_104 u ii)))))))))) (let ((_let_280 (forall ((x |u_(-> tptp.set_list_list_a Bool)|) (y |u_(-> tptp.set_list_list_a Bool)|)) (or (not (forall ((z tptp.set_list_list_a)) (= (ho_104 x z) (ho_104 y z)))) (= x y))))) (let ((_let_281 (forall ((u |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat Bool)|) (e |u_(-> tptp.set_nat Bool)|) (i |u_(-> tptp.nat tptp.nat)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat Bool)|)) (not (forall ((ii |u_(-> tptp.nat tptp.nat)|)) (= (ho_79 v ii) (ite (= i ii) e (ho_79 u ii)))))))))) (let ((_let_282 (forall ((x |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat Bool)|) (y |u_(-> _u_(-> tptp.nat tptp.nat)_ tptp.set_nat Bool)|)) (or (not (forall ((z |u_(-> tptp.nat tptp.nat)|)) (= (ho_79 x z) (ho_79 y z)))) (= x y))))) (let ((_let_283 (forall ((u |u_(-> tptp.set_multiset_a tptp.multiset_a Bool)|) (e |u_(-> tptp.multiset_a Bool)|) (i tptp.set_multiset_a)) (not (forall ((v |u_(-> tptp.set_multiset_a tptp.multiset_a Bool)|)) (not (forall ((ii tptp.set_multiset_a)) (= (ho_106 v ii) (ite (= i ii) e (ho_106 u ii)))))))))) (let ((_let_284 (forall ((x |u_(-> tptp.set_multiset_a tptp.multiset_a Bool)|) (y |u_(-> tptp.set_multiset_a tptp.multiset_a Bool)|)) (or (not (forall ((z tptp.set_multiset_a)) (= (ho_106 x z) (ho_106 y z)))) (= x y))))) (let ((_let_285 (forall ((u |u_(-> tptp.set_list_a tptp.list_a Bool)|) (e |u_(-> tptp.list_a Bool)|) (i tptp.set_list_a)) (not (forall ((v |u_(-> tptp.set_list_a tptp.list_a Bool)|)) (not (forall ((ii tptp.set_list_a)) (= (ho_81 v ii) (ite (= i ii) e (ho_81 u ii)))))))))) (let ((_let_286 (forall ((x |u_(-> tptp.set_list_a tptp.list_a Bool)|) (y |u_(-> tptp.set_list_a tptp.list_a Bool)|)) (or (not (forall ((z tptp.set_list_a)) (= (ho_81 x z) (ho_81 y z)))) (= x y))))) (let ((_let_287 (forall ((u |u_(-> tptp.multiset_a Bool)|) (e Bool) (i tptp.multiset_a)) (not (forall ((v |u_(-> tptp.multiset_a Bool)|)) (not (forall ((ii tptp.multiset_a)) (= (ho_107 v ii) (ite (= i ii) e (ho_107 u ii)))))))))) (let ((_let_288 (forall ((x |u_(-> tptp.multiset_a Bool)|) (y |u_(-> tptp.multiset_a Bool)|)) (or (not (forall ((z tptp.multiset_a)) (= (ho_107 x z) (ho_107 y z)))) (= x y))))) (let ((_let_289 (forall ((u |u_(-> tptp.nat tptp.set_list_a)|) (e tptp.set_list_a) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_list_a)|)) (not (forall ((ii tptp.nat)) (= (ho_149 v ii) (ite (= i ii) e (ho_149 u ii)))))))))) (let ((_let_290 (forall ((x |u_(-> tptp.nat tptp.set_list_a)|) (y |u_(-> tptp.nat tptp.set_list_a)|)) (or (not (forall ((z tptp.nat)) (= (ho_149 x z) (ho_149 y z)))) (= x y))))) (let ((_let_291 (forall ((u |u_(-> tptp.list_set_a tptp.nat tptp.set_a)|) (e |u_(-> tptp.nat tptp.set_a)|) (i tptp.list_set_a)) (not (forall ((v |u_(-> tptp.list_set_a tptp.nat tptp.set_a)|)) (not (forall ((ii tptp.list_set_a)) (= (ho_114 v ii) (ite (= i ii) e (ho_114 u ii)))))))))) (let ((_let_292 (forall ((x |u_(-> tptp.list_set_a tptp.nat tptp.set_a)|) (y |u_(-> tptp.list_set_a tptp.nat tptp.set_a)|)) (or (not (forall ((z tptp.list_set_a)) (= (ho_114 x z) (ho_114 y z)))) (= x y))))) (let ((_let_293 (forall ((u |u_(-> tptp.list_set_a tptp.set_list_a)|) (e tptp.set_list_a) (i tptp.list_set_a)) (not (forall ((v |u_(-> tptp.list_set_a tptp.set_list_a)|)) (not (forall ((ii tptp.list_set_a)) (= (ho_166 v ii) (ite (= i ii) e (ho_166 u ii)))))))))) (let ((_let_294 (forall ((x |u_(-> tptp.list_set_a tptp.set_list_a)|) (y |u_(-> tptp.list_set_a tptp.set_list_a)|)) (or (not (forall ((z tptp.list_set_a)) (= (ho_166 x z) (ho_166 y z)))) (= x y))))) (let ((_let_295 (forall ((u |u_(-> tptp.list_a tptp.list_a Bool)|) (e |u_(-> tptp.list_a Bool)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.list_a Bool)|)) (not (forall ((ii tptp.list_a)) (= (ho_120 v ii) (ite (= i ii) e (ho_120 u ii)))))))))) (let ((_let_296 (forall ((x |u_(-> tptp.list_a tptp.list_a Bool)|) (y |u_(-> tptp.list_a tptp.list_a Bool)|)) (or (not (forall ((z tptp.list_a)) (= (ho_120 x z) (ho_120 y z)))) (= x y))))) (let ((_let_297 (forall ((u |u_(-> tptp.list_a tptp.nat tptp.a)|) (e |u_(-> tptp.nat tptp.a)|) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.nat tptp.a)|)) (not (forall ((ii tptp.list_a)) (= (ho_122 v ii) (ite (= i ii) e (ho_122 u ii)))))))))) (let ((_let_298 (forall ((x |u_(-> tptp.list_a tptp.nat tptp.a)|) (y |u_(-> tptp.list_a tptp.nat tptp.a)|)) (or (not (forall ((z tptp.list_a)) (= (ho_122 x z) (ho_122 y z)))) (= x y))))) (let ((_let_299 (forall ((u |u_(-> tptp.a Bool)|) (e Bool) (i tptp.a)) (not (forall ((v |u_(-> tptp.a Bool)|)) (not (forall ((ii tptp.a)) (= (ho_85 v ii) (ite (= i ii) e (ho_85 u ii)))))))))) (let ((_let_300 (forall ((x |u_(-> tptp.a Bool)|) (y |u_(-> tptp.a Bool)|)) (or (not (forall ((z tptp.a)) (= (ho_85 x z) (ho_85 y z)))) (= x y))))) (let ((_let_301 (forall ((u |u_(-> tptp.list_a tptp.nat)|) (e tptp.nat) (i tptp.list_a)) (not (forall ((v |u_(-> tptp.list_a tptp.nat)|)) (not (forall ((ii tptp.list_a)) (= (ho_125 v ii) (ite (= i ii) e (ho_125 u ii)))))))))) (let ((_let_302 (forall ((x |u_(-> tptp.list_a tptp.nat)|) (y |u_(-> tptp.list_a tptp.nat)|)) (or (not (forall ((z tptp.list_a)) (= (ho_125 x z) (ho_125 y z)))) (= x y))))) (let ((_let_303 (forall ((u |u_(-> tptp.list_nat Bool)|) (e Bool) (i tptp.list_nat)) (not (forall ((v |u_(-> tptp.list_nat Bool)|)) (not (forall ((ii tptp.list_nat)) (= (ho_129 v ii) (ite (= i ii) e (ho_129 u ii)))))))))) (let ((_let_304 (forall ((x |u_(-> tptp.list_nat Bool)|) (y |u_(-> tptp.list_nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_129 x z) (ho_129 y z)))) (= x y))))) (let ((_let_305 (forall ((u |u_(-> tptp.list_nat tptp.nat tptp.nat)|) (e |u_(-> tptp.nat tptp.nat)|) (i tptp.list_nat)) (not (forall ((v |u_(-> tptp.list_nat tptp.nat tptp.nat)|)) (not (forall ((ii tptp.list_nat)) (= (ho_131 v ii) (ite (= i ii) e (ho_131 u ii)))))))))) (let ((_let_306 (forall ((x |u_(-> tptp.list_nat tptp.nat tptp.nat)|) (y |u_(-> tptp.list_nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_131 x z) (ho_131 y z)))) (= x y))))) (let ((_let_307 (forall ((u |u_(-> tptp.set_a tptp.set_a)|) (e tptp.set_a) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_345 v ii) (ite (= i ii) e (ho_345 u ii)))))))))) (let ((_let_308 (forall ((x |u_(-> tptp.set_a tptp.set_a)|) (y |u_(-> tptp.set_a tptp.set_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_345 x z) (ho_345 y z)))) (= x y))))) (let ((_let_309 (forall ((u |u_(-> tptp.list_nat tptp.list_nat Bool)|) (e |u_(-> tptp.list_nat Bool)|) (i tptp.list_nat)) (not (forall ((v |u_(-> tptp.list_nat tptp.list_nat Bool)|)) (not (forall ((ii tptp.list_nat)) (= (ho_128 v ii) (ite (= i ii) e (ho_128 u ii)))))))))) (let ((_let_310 (forall ((x |u_(-> tptp.list_nat tptp.list_nat Bool)|) (y |u_(-> tptp.list_nat tptp.list_nat Bool)|)) (or (not (forall ((z tptp.list_nat)) (= (ho_128 x z) (ho_128 y z)))) (= x y))))) (let ((_let_311 (forall ((u |u_(-> tptp.set_nat tptp.nat Bool)|) (e |u_(-> tptp.nat Bool)|) (i tptp.set_nat)) (not (forall ((v |u_(-> tptp.set_nat tptp.nat Bool)|)) (not (forall ((ii tptp.set_nat)) (= (ho_87 v ii) (ite (= i ii) e (ho_87 u ii)))))))))) (let ((_let_312 (forall ((x |u_(-> tptp.set_nat tptp.nat Bool)|) (y |u_(-> tptp.set_nat tptp.nat Bool)|)) (or (not (forall ((z tptp.set_nat)) (= (ho_87 x z) (ho_87 y z)))) (= x y))))) (let ((_let_313 (forall ((u |u_(-> tptp.set_a tptp.set_a Bool)|) (e |u_(-> tptp.set_a Bool)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_a Bool)|)) (not (forall ((ii tptp.set_a)) (= (ho_62 v ii) (ite (= i ii) e (ho_62 u ii)))))))))) (let ((_let_314 (forall ((x |u_(-> tptp.set_a tptp.set_a Bool)|) (y |u_(-> tptp.set_a tptp.set_a Bool)|)) (or (not (forall ((z tptp.set_a)) (= (ho_62 x z) (ho_62 y z)))) (= x y))))) (let ((_let_315 (forall ((u |u_(-> tptp.list_set_set_a Bool)|) (e Bool) (i tptp.list_set_set_a)) (not (forall ((v |u_(-> tptp.list_set_set_a Bool)|)) (not (forall ((ii tptp.list_set_set_a)) (= (ho_137 v ii) (ite (= i ii) e (ho_137 u ii)))))))))) (let ((_let_316 (forall ((x |u_(-> tptp.list_set_set_a Bool)|) (y |u_(-> tptp.list_set_set_a Bool)|)) (or (not (forall ((z tptp.list_set_set_a)) (= (ho_137 x z) (ho_137 y z)))) (= x y))))) (let ((_let_317 (forall ((u |u_(-> tptp.list_multiset_a tptp.nat)|) (e tptp.nat) (i tptp.list_multiset_a)) (not (forall ((v |u_(-> tptp.list_multiset_a tptp.nat)|)) (not (forall ((ii tptp.list_multiset_a)) (= (ho_288 v ii) (ite (= i ii) e (ho_288 u ii)))))))))) (let ((_let_318 (forall ((x |u_(-> tptp.list_multiset_a tptp.nat)|) (y |u_(-> tptp.list_multiset_a tptp.nat)|)) (or (not (forall ((z tptp.list_multiset_a)) (= (ho_288 x z) (ho_288 y z)))) (= x y))))) (let ((_let_319 (forall ((u |u_(-> tptp.list_set_set_a tptp.nat tptp.set_set_a)|) (e |u_(-> tptp.nat tptp.set_set_a)|) (i tptp.list_set_set_a)) (not (forall ((v |u_(-> tptp.list_set_set_a tptp.nat tptp.set_set_a)|)) (not (forall ((ii tptp.list_set_set_a)) (= (ho_139 v ii) (ite (= i ii) e (ho_139 u ii)))))))))) (let ((_let_320 (forall ((x |u_(-> tptp.list_set_set_a tptp.nat tptp.set_set_a)|) (y |u_(-> tptp.list_set_set_a tptp.nat tptp.set_set_a)|)) (or (not (forall ((z tptp.list_set_set_a)) (= (ho_139 x z) (ho_139 y z)))) (= x y))))) (let ((_let_321 (forall ((u |u_(-> tptp.list_set_list_a tptp.list_set_list_a Bool)|) (e |u_(-> tptp.list_set_list_a Bool)|) (i tptp.list_set_list_a)) (not (forall ((v |u_(-> tptp.list_set_list_a tptp.list_set_list_a Bool)|)) (not (forall ((ii tptp.list_set_list_a)) (= (ho_145 v ii) (ite (= i ii) e (ho_145 u ii)))))))))) (let ((_let_322 (forall ((x |u_(-> tptp.list_set_list_a tptp.list_set_list_a Bool)|) (y |u_(-> tptp.list_set_list_a tptp.list_set_list_a Bool)|)) (or (not (forall ((z tptp.list_set_list_a)) (= (ho_145 x z) (ho_145 y z)))) (= x y))))) (let ((_let_323 (forall ((u |u_(-> tptp.list_set_list_a tptp.nat tptp.set_list_a)|) (e |u_(-> tptp.nat tptp.set_list_a)|) (i tptp.list_set_list_a)) (not (forall ((v |u_(-> tptp.list_set_list_a tptp.nat tptp.set_list_a)|)) (not (forall ((ii tptp.list_set_list_a)) (= (ho_148 v ii) (ite (= i ii) e (ho_148 u ii)))))))))) (let ((_let_324 (forall ((x |u_(-> tptp.list_set_list_a tptp.nat tptp.set_list_a)|) (y |u_(-> tptp.list_set_list_a tptp.nat tptp.set_list_a)|)) (or (not (forall ((z tptp.list_set_list_a)) (= (ho_148 x z) (ho_148 y z)))) (= x y))))) (let ((_let_325 (forall ((u |u_(-> tptp.list_set_list_a tptp.nat)|) (e tptp.nat) (i tptp.list_set_list_a)) (not (forall ((v |u_(-> tptp.list_set_list_a tptp.nat)|)) (not (forall ((ii tptp.list_set_list_a)) (= (ho_151 v ii) (ite (= i ii) e (ho_151 u ii)))))))))) (let ((_let_326 (forall ((x |u_(-> tptp.list_set_list_a tptp.nat)|) (y |u_(-> tptp.list_set_list_a tptp.nat)|)) (or (not (forall ((z tptp.list_set_list_a)) (= (ho_151 x z) (ho_151 y z)))) (= x y))))) (let ((_let_327 (forall ((u |u_(-> tptp.list_set_multiset_a tptp.nat tptp.set_multiset_a)|) (e |u_(-> tptp.nat tptp.set_multiset_a)|) (i tptp.list_set_multiset_a)) (not (forall ((v |u_(-> tptp.list_set_multiset_a tptp.nat tptp.set_multiset_a)|)) (not (forall ((ii tptp.list_set_multiset_a)) (= (ho_280 v ii) (ite (= i ii) e (ho_280 u ii)))))))))) (let ((_let_328 (forall ((x |u_(-> tptp.list_set_multiset_a tptp.nat tptp.set_multiset_a)|) (y |u_(-> tptp.list_set_multiset_a tptp.nat tptp.set_multiset_a)|)) (or (not (forall ((z tptp.list_set_multiset_a)) (= (ho_280 x z) (ho_280 y z)))) (= x y))))) (let ((_let_329 (forall ((u |u_(-> tptp.list_multiset_a tptp.nat tptp.multiset_a)|) (e |u_(-> tptp.nat tptp.multiset_a)|) (i tptp.list_multiset_a)) (not (forall ((v |u_(-> tptp.list_multiset_a tptp.nat tptp.multiset_a)|)) (not (forall ((ii tptp.list_multiset_a)) (= (ho_283 v ii) (ite (= i ii) e (ho_283 u ii)))))))))) (let ((_let_330 (forall ((x |u_(-> tptp.list_multiset_a tptp.nat tptp.multiset_a)|) (y |u_(-> tptp.list_multiset_a tptp.nat tptp.multiset_a)|)) (or (not (forall ((z tptp.list_multiset_a)) (= (ho_283 x z) (ho_283 y z)))) (= x y))))) (let ((_let_331 (forall ((u |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a tptp.a)|) (e |u_(-> tptp.list_a tptp.a)|) (i |u_(-> tptp.a tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a tptp.a)|)) (not (forall ((ii |u_(-> tptp.a tptp.list_a)|)) (= (ho_364 v ii) (ite (= i ii) e (ho_364 u ii)))))))))) (let ((_let_332 (forall ((x |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a tptp.a)|) (y |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.list_a tptp.a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.list_a)|)) (= (ho_364 x z) (ho_364 y z)))) (= x y))))) (let ((_let_333 (forall ((u |u_(-> tptp.list_set_multiset_a tptp.nat)|) (e tptp.nat) (i tptp.list_set_multiset_a)) (not (forall ((v |u_(-> tptp.list_set_multiset_a tptp.nat)|)) (not (forall ((ii tptp.list_set_multiset_a)) (= (ho_286 v ii) (ite (= i ii) e (ho_286 u ii)))))))))) (let ((_let_334 (forall ((x |u_(-> tptp.list_set_multiset_a tptp.nat)|) (y |u_(-> tptp.list_set_multiset_a tptp.nat)|)) (or (not (forall ((z tptp.list_set_multiset_a)) (= (ho_286 x z) (ho_286 y z)))) (= x y))))) (let ((_let_335 (forall ((u |u_(-> tptp.list_set_list_list_a tptp.set_list_list_list_a)|) (e tptp.set_list_list_list_a) (i tptp.list_set_list_list_a)) (not (forall ((v |u_(-> tptp.list_set_list_list_a tptp.set_list_list_list_a)|)) (not (forall ((ii tptp.list_set_list_list_a)) (= (ho_290 v ii) (ite (= i ii) e (ho_290 u ii)))))))))) (let ((_let_336 (forall ((x |u_(-> tptp.list_set_list_list_a tptp.set_list_list_list_a)|) (y |u_(-> tptp.list_set_list_list_a tptp.set_list_list_list_a)|)) (or (not (forall ((z tptp.list_set_list_list_a)) (= (ho_290 x z) (ho_290 y z)))) (= x y))))) (let ((_let_337 (forall ((u |u_(-> tptp.set_list_list_list_a Bool)|) (e Bool) (i tptp.set_list_list_list_a)) (not (forall ((v |u_(-> tptp.set_list_list_list_a Bool)|)) (not (forall ((ii tptp.set_list_list_list_a)) (= (ho_293 v ii) (ite (= i ii) e (ho_293 u ii)))))))))) (let ((_let_338 (forall ((x |u_(-> tptp.set_list_list_list_a Bool)|) (y |u_(-> tptp.set_list_list_list_a Bool)|)) (or (not (forall ((z tptp.set_list_list_list_a)) (= (ho_293 x z) (ho_293 y z)))) (= x y))))) (let ((_let_339 (forall ((u |u_(-> tptp.list_list_list_a tptp.set_list_list_list_a Bool)|) (e |u_(-> tptp.set_list_list_list_a Bool)|) (i tptp.list_list_list_a)) (not (forall ((v |u_(-> tptp.list_list_list_a tptp.set_list_list_list_a Bool)|)) (not (forall ((ii tptp.list_list_list_a)) (= (ho_292 v ii) (ite (= i ii) e (ho_292 u ii)))))))))) (let ((_let_340 (forall ((x |u_(-> tptp.list_list_list_a tptp.set_list_list_list_a Bool)|) (y |u_(-> tptp.list_list_list_a tptp.set_list_list_list_a Bool)|)) (or (not (forall ((z tptp.list_list_list_a)) (= (ho_292 x z) (ho_292 y z)))) (= x y))))) (let ((_let_341 (forall ((u |u_(-> tptp.nat tptp.set_list_list_a)|) (e tptp.set_list_list_a) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_list_list_a)|)) (not (forall ((ii tptp.nat)) (= (ho_296 v ii) (ite (= i ii) e (ho_296 u ii)))))))))) (let ((_let_342 (forall ((x |u_(-> tptp.nat tptp.set_list_list_a)|) (y |u_(-> tptp.nat tptp.set_list_list_a)|)) (or (not (forall ((z tptp.nat)) (= (ho_296 x z) (ho_296 y z)))) (= x y))))) (let ((_let_343 (forall ((u |u_(-> tptp.list_set_list_list_a tptp.nat tptp.set_list_list_a)|) (e |u_(-> tptp.nat tptp.set_list_list_a)|) (i tptp.list_set_list_list_a)) (not (forall ((v |u_(-> tptp.list_set_list_list_a tptp.nat tptp.set_list_list_a)|)) (not (forall ((ii tptp.list_set_list_list_a)) (= (ho_295 v ii) (ite (= i ii) e (ho_295 u ii)))))))))) (let ((_let_344 (forall ((x |u_(-> tptp.list_set_list_list_a tptp.nat tptp.set_list_list_a)|) (y |u_(-> tptp.list_set_list_list_a tptp.nat tptp.set_list_list_a)|)) (or (not (forall ((z tptp.list_set_list_list_a)) (= (ho_295 x z) (ho_295 y z)))) (= x y))))) (let ((_let_345 (forall ((u |u_(-> tptp.nat tptp.list_list_a)|) (e tptp.list_list_a) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.list_list_a)|)) (not (forall ((ii tptp.nat)) (= (ho_299 v ii) (ite (= i ii) e (ho_299 u ii)))))))))) (let ((_let_346 (forall ((x |u_(-> tptp.nat tptp.list_list_a)|) (y |u_(-> tptp.nat tptp.list_list_a)|)) (or (not (forall ((z tptp.nat)) (= (ho_299 x z) (ho_299 y z)))) (= x y))))) (let ((_let_347 (forall ((u |u_(-> tptp.list_list_list_a tptp.nat tptp.list_list_a)|) (e |u_(-> tptp.nat tptp.list_list_a)|) (i tptp.list_list_list_a)) (not (forall ((v |u_(-> tptp.list_list_list_a tptp.nat tptp.list_list_a)|)) (not (forall ((ii tptp.list_list_list_a)) (= (ho_298 v ii) (ite (= i ii) e (ho_298 u ii)))))))))) (let ((_let_348 (forall ((x |u_(-> tptp.list_list_list_a tptp.nat tptp.list_list_a)|) (y |u_(-> tptp.list_list_list_a tptp.nat tptp.list_list_a)|)) (or (not (forall ((z tptp.list_list_list_a)) (= (ho_298 x z) (ho_298 y z)))) (= x y))))) (let ((_let_349 (forall ((u |u_(-> tptp.list_set_list_list_a tptp.nat)|) (e tptp.nat) (i tptp.list_set_list_list_a)) (not (forall ((v |u_(-> tptp.list_set_list_list_a tptp.nat)|)) (not (forall ((ii tptp.list_set_list_list_a)) (= (ho_301 v ii) (ite (= i ii) e (ho_301 u ii)))))))))) (let ((_let_350 (forall ((x |u_(-> tptp.list_set_list_list_a tptp.nat)|) (y |u_(-> tptp.list_set_list_list_a tptp.nat)|)) (or (not (forall ((z tptp.list_set_list_list_a)) (= (ho_301 x z) (ho_301 y z)))) (= x y))))) (let ((_let_351 (forall ((u |u_(-> tptp.list_list_list_a tptp.nat)|) (e tptp.nat) (i tptp.list_list_list_a)) (not (forall ((v |u_(-> tptp.list_list_list_a tptp.nat)|)) (not (forall ((ii tptp.list_list_list_a)) (= (ho_303 v ii) (ite (= i ii) e (ho_303 u ii)))))))))) (let ((_let_352 (forall ((x |u_(-> tptp.list_list_list_a tptp.nat)|) (y |u_(-> tptp.list_list_list_a tptp.nat)|)) (or (not (forall ((z tptp.list_list_list_a)) (= (ho_303 x z) (ho_303 y z)))) (= x y))))) (let ((_let_353 (forall ((u |u_(-> tptp.list_set_list_set_a tptp.set_list_list_set_a)|) (e tptp.set_list_list_set_a) (i tptp.list_set_list_set_a)) (not (forall ((v |u_(-> tptp.list_set_list_set_a tptp.set_list_list_set_a)|)) (not (forall ((ii tptp.list_set_list_set_a)) (= (ho_305 v ii) (ite (= i ii) e (ho_305 u ii)))))))))) (let ((_let_354 (forall ((x |u_(-> tptp.list_set_list_set_a tptp.set_list_list_set_a)|) (y |u_(-> tptp.list_set_list_set_a tptp.set_list_list_set_a)|)) (or (not (forall ((z tptp.list_set_list_set_a)) (= (ho_305 x z) (ho_305 y z)))) (= x y))))) (let ((_let_355 (forall ((u |u_(-> tptp.set_list_list_set_a Bool)|) (e Bool) (i tptp.set_list_list_set_a)) (not (forall ((v |u_(-> tptp.set_list_list_set_a Bool)|)) (not (forall ((ii tptp.set_list_list_set_a)) (= (ho_308 v ii) (ite (= i ii) e (ho_308 u ii)))))))))) (let ((_let_356 (forall ((x |u_(-> tptp.set_list_list_set_a Bool)|) (y |u_(-> tptp.set_list_list_set_a Bool)|)) (or (not (forall ((z tptp.set_list_list_set_a)) (= (ho_308 x z) (ho_308 y z)))) (= x y))))) (let ((_let_357 (forall ((u |u_(-> tptp.list_list_set_a tptp.set_list_list_set_a Bool)|) (e |u_(-> tptp.set_list_list_set_a Bool)|) (i tptp.list_list_set_a)) (not (forall ((v |u_(-> tptp.list_list_set_a tptp.set_list_list_set_a Bool)|)) (not (forall ((ii tptp.list_list_set_a)) (= (ho_307 v ii) (ite (= i ii) e (ho_307 u ii)))))))))) (let ((_let_358 (forall ((x |u_(-> tptp.list_list_set_a tptp.set_list_list_set_a Bool)|) (y |u_(-> tptp.list_list_set_a tptp.set_list_list_set_a Bool)|)) (or (not (forall ((z tptp.list_list_set_a)) (= (ho_307 x z) (ho_307 y z)))) (= x y))))) (let ((_let_359 (forall ((u |u_(-> tptp.list_set_list_set_a tptp.nat tptp.set_list_set_a)|) (e |u_(-> tptp.nat tptp.set_list_set_a)|) (i tptp.list_set_list_set_a)) (not (forall ((v |u_(-> tptp.list_set_list_set_a tptp.nat tptp.set_list_set_a)|)) (not (forall ((ii tptp.list_set_list_set_a)) (= (ho_310 v ii) (ite (= i ii) e (ho_310 u ii)))))))))) (let ((_let_360 (forall ((x |u_(-> tptp.list_set_list_set_a tptp.nat tptp.set_list_set_a)|) (y |u_(-> tptp.list_set_list_set_a tptp.nat tptp.set_list_set_a)|)) (or (not (forall ((z tptp.list_set_list_set_a)) (= (ho_310 x z) (ho_310 y z)))) (= x y))))) (let ((_let_361 (forall ((u |u_(-> tptp.list_list_set_a tptp.nat tptp.list_set_a)|) (e |u_(-> tptp.nat tptp.list_set_a)|) (i tptp.list_list_set_a)) (not (forall ((v |u_(-> tptp.list_list_set_a tptp.nat tptp.list_set_a)|)) (not (forall ((ii tptp.list_list_set_a)) (= (ho_313 v ii) (ite (= i ii) e (ho_313 u ii)))))))))) (let ((_let_362 (forall ((x |u_(-> tptp.list_list_set_a tptp.nat tptp.list_set_a)|) (y |u_(-> tptp.list_list_set_a tptp.nat tptp.list_set_a)|)) (or (not (forall ((z tptp.list_list_set_a)) (= (ho_313 x z) (ho_313 y z)))) (= x y))))) (let ((_let_363 (forall ((u |u_(-> tptp.list_set_list_set_a tptp.nat)|) (e tptp.nat) (i tptp.list_set_list_set_a)) (not (forall ((v |u_(-> tptp.list_set_list_set_a tptp.nat)|)) (not (forall ((ii tptp.list_set_list_set_a)) (= (ho_316 v ii) (ite (= i ii) e (ho_316 u ii)))))))))) (let ((_let_364 (forall ((x |u_(-> tptp.list_set_list_set_a tptp.nat)|) (y |u_(-> tptp.list_set_list_set_a tptp.nat)|)) (or (not (forall ((z tptp.list_set_list_set_a)) (= (ho_316 x z) (ho_316 y z)))) (= x y))))) (let ((_let_365 (forall ((u |u_(-> tptp.list_list_set_a tptp.nat)|) (e tptp.nat) (i tptp.list_list_set_a)) (not (forall ((v |u_(-> tptp.list_list_set_a tptp.nat)|)) (not (forall ((ii tptp.list_list_set_a)) (= (ho_318 v ii) (ite (= i ii) e (ho_318 u ii)))))))))) (let ((_let_366 (forall ((x |u_(-> tptp.list_list_set_a tptp.nat)|) (y |u_(-> tptp.list_list_set_a tptp.nat)|)) (or (not (forall ((z tptp.list_list_set_a)) (= (ho_318 x z) (ho_318 y z)))) (= x y))))) (let ((_let_367 (forall ((u |u_(-> tptp.set_set_set_a Bool)|) (e Bool) (i tptp.set_set_set_a)) (not (forall ((v |u_(-> tptp.set_set_set_a Bool)|)) (not (forall ((ii tptp.set_set_set_a)) (= (ho_321 v ii) (ite (= i ii) e (ho_321 u ii)))))))))) (let ((_let_368 (forall ((x |u_(-> tptp.set_set_set_a Bool)|) (y |u_(-> tptp.set_set_set_a Bool)|)) (or (not (forall ((z tptp.set_set_set_a)) (= (ho_321 x z) (ho_321 y z)))) (= x y))))) (let ((_let_369 (forall ((u |u_(-> tptp.set_set_a tptp.set_set_set_a Bool)|) (e |u_(-> tptp.set_set_set_a Bool)|) (i tptp.set_set_a)) (not (forall ((v |u_(-> tptp.set_set_a tptp.set_set_set_a Bool)|)) (not (forall ((ii tptp.set_set_a)) (= (ho_320 v ii) (ite (= i ii) e (ho_320 u ii)))))))))) (let ((_let_370 (forall ((x |u_(-> tptp.set_set_a tptp.set_set_set_a Bool)|) (y |u_(-> tptp.set_set_a tptp.set_set_set_a Bool)|)) (or (not (forall ((z tptp.set_set_a)) (= (ho_320 x z) (ho_320 y z)))) (= x y))))) (let ((_let_371 (forall ((u |u_(-> tptp.nat tptp.set_list_a Bool)|) (e |u_(-> tptp.set_list_a Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_list_a Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_323 v ii) (ite (= i ii) e (ho_323 u ii)))))))))) (let ((_let_372 (forall ((x |u_(-> tptp.nat tptp.set_list_a Bool)|) (y |u_(-> tptp.nat tptp.set_list_a Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_323 x z) (ho_323 y z)))) (= x y))))) (let ((_let_373 (forall ((u |u_(-> tptp.nat tptp.set_set_a Bool)|) (e |u_(-> tptp.set_set_a Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_set_a Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_324 v ii) (ite (= i ii) e (ho_324 u ii)))))))))) (let ((_let_374 (forall ((x |u_(-> tptp.nat tptp.set_set_a Bool)|) (y |u_(-> tptp.nat tptp.set_set_a Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_324 x z) (ho_324 y z)))) (= x y))))) (let ((_let_375 (forall ((u |u_(-> _u_(-> tptp.multiset_a Bool)_ tptp.set_multiset_a)|) (e tptp.set_multiset_a) (i |u_(-> tptp.multiset_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.multiset_a Bool)_ tptp.set_multiset_a)|)) (not (forall ((ii |u_(-> tptp.multiset_a Bool)|)) (= (ho_328 v ii) (ite (= i ii) e (ho_328 u ii)))))))))) (let ((_let_376 (forall ((x |u_(-> _u_(-> tptp.multiset_a Bool)_ tptp.set_multiset_a)|) (y |u_(-> _u_(-> tptp.multiset_a Bool)_ tptp.set_multiset_a)|)) (or (not (forall ((z |u_(-> tptp.multiset_a Bool)|)) (= (ho_328 x z) (ho_328 y z)))) (= x y))))) (let ((_let_377 (forall ((u |u_(-> _u_(-> tptp.list_list_a Bool)_ tptp.set_list_list_a)|) (e tptp.set_list_list_a) (i |u_(-> tptp.list_list_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_list_a Bool)_ tptp.set_list_list_a)|)) (not (forall ((ii |u_(-> tptp.list_list_a Bool)|)) (= (ho_330 v ii) (ite (= i ii) e (ho_330 u ii)))))))))) (let ((_let_378 (forall ((x |u_(-> _u_(-> tptp.list_list_a Bool)_ tptp.set_list_list_a)|) (y |u_(-> _u_(-> tptp.list_list_a Bool)_ tptp.set_list_list_a)|)) (or (not (forall ((z |u_(-> tptp.list_list_a Bool)|)) (= (ho_330 x z) (ho_330 y z)))) (= x y))))) (let ((_let_379 (forall ((u |u_(-> _u_(-> tptp.list_set_a Bool)_ tptp.set_list_set_a)|) (e tptp.set_list_set_a) (i |u_(-> tptp.list_set_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_set_a Bool)_ tptp.set_list_set_a)|)) (not (forall ((ii |u_(-> tptp.list_set_a Bool)|)) (= (ho_332 v ii) (ite (= i ii) e (ho_332 u ii)))))))))) (let ((_let_380 (forall ((x |u_(-> _u_(-> tptp.list_set_a Bool)_ tptp.set_list_set_a)|) (y |u_(-> _u_(-> tptp.list_set_a Bool)_ tptp.set_list_set_a)|)) (or (not (forall ((z |u_(-> tptp.list_set_a Bool)|)) (= (ho_332 x z) (ho_332 y z)))) (= x y))))) (let ((_let_381 (forall ((u |u_(-> _u_(-> tptp.set_a Bool)_ tptp.set_set_a)|) (e tptp.set_set_a) (i |u_(-> tptp.set_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.set_a Bool)_ tptp.set_set_a)|)) (not (forall ((ii |u_(-> tptp.set_a Bool)|)) (= (ho_334 v ii) (ite (= i ii) e (ho_334 u ii)))))))))) (let ((_let_382 (forall ((x |u_(-> _u_(-> tptp.set_a Bool)_ tptp.set_set_a)|) (y |u_(-> _u_(-> tptp.set_a Bool)_ tptp.set_set_a)|)) (or (not (forall ((z |u_(-> tptp.set_a Bool)|)) (= (ho_334 x z) (ho_334 y z)))) (= x y))))) (let ((_let_383 (forall ((u |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat)|) (e tptp.set_nat) (i |u_(-> tptp.nat Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_336 v ii) (ite (= i ii) e (ho_336 u ii)))))))))) (let ((_let_384 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat)|) (y |u_(-> _u_(-> tptp.nat Bool)_ tptp.set_nat)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_336 x z) (ho_336 y z)))) (= x y))))) (let ((_let_385 (forall ((u |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|) (e tptp.set_a) (i |u_(-> tptp.a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|)) (not (forall ((ii |u_(-> tptp.a Bool)|)) (= (ho_338 v ii) (ite (= i ii) e (ho_338 u ii)))))))))) (let ((_let_386 (forall ((x |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|) (y |u_(-> _u_(-> tptp.a Bool)_ tptp.set_a)|)) (or (not (forall ((z |u_(-> tptp.a Bool)|)) (= (ho_338 x z) (ho_338 y z)))) (= x y))))) (let ((_let_387 (forall ((u |u_(-> _u_(-> tptp.list_a Bool)_ tptp.set_list_a)|) (e tptp.set_list_a) (i |u_(-> tptp.list_a Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a Bool)_ tptp.set_list_a)|)) (not (forall ((ii |u_(-> tptp.list_a Bool)|)) (= (ho_340 v ii) (ite (= i ii) e (ho_340 u ii)))))))))) (let ((_let_388 (forall ((x |u_(-> _u_(-> tptp.list_a Bool)_ tptp.set_list_a)|) (y |u_(-> _u_(-> tptp.list_a Bool)_ tptp.set_list_a)|)) (or (not (forall ((z |u_(-> tptp.list_a Bool)|)) (= (ho_340 x z) (ho_340 y z)))) (= x y))))) (let ((_let_389 (forall ((u |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_a tptp.set_a)|) (e |u_(-> tptp.set_a tptp.set_a)|) (i |u_(-> tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_a tptp.set_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.a)|)) (= (ho_344 v ii) (ite (= i ii) e (ho_344 u ii)))))))))) (let ((_let_390 (forall ((x |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_a tptp.set_a)|) (y |u_(-> _u_(-> tptp.a tptp.a)_ tptp.set_a tptp.set_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a)|)) (= (ho_344 x z) (ho_344 y z)))) (= x y))))) (let ((_let_391 (forall ((u |u_(-> tptp.set_a tptp.set_list_a)|) (e tptp.set_list_a) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a tptp.set_list_a)|)) (not (forall ((ii tptp.set_a)) (= (ho_348 v ii) (ite (= i ii) e (ho_348 u ii)))))))))) (let ((_let_392 (forall ((x |u_(-> tptp.set_a tptp.set_list_a)|) (y |u_(-> tptp.set_a tptp.set_list_a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_348 x z) (ho_348 y z)))) (= x y))))) (let ((_let_393 (forall ((u |u_(-> tptp.set_multiset_list_a Bool)|) (e Bool) (i tptp.set_multiset_list_a)) (not (forall ((v |u_(-> tptp.set_multiset_list_a Bool)|)) (not (forall ((ii tptp.set_multiset_list_a)) (= (ho_389 v ii) (ite (= i ii) e (ho_389 u ii)))))))))) (let ((_let_394 (forall ((x |u_(-> tptp.set_multiset_list_a Bool)|) (y |u_(-> tptp.set_multiset_list_a Bool)|)) (or (not (forall ((z tptp.set_multiset_list_a)) (= (ho_389 x z) (ho_389 y z)))) (= x y))))) (let ((_let_395 (forall ((u |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.set_a tptp.set_list_a)|) (e |u_(-> tptp.set_a tptp.set_list_a)|) (i |u_(-> tptp.a tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.set_a tptp.set_list_a)|)) (not (forall ((ii |u_(-> tptp.a tptp.list_a)|)) (= (ho_347 v ii) (ite (= i ii) e (ho_347 u ii)))))))))) (let ((_let_396 (forall ((x |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.set_a tptp.set_list_a)|) (y |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.set_a tptp.set_list_a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.list_a)|)) (= (ho_347 x z) (ho_347 y z)))) (= x y))))) (let ((_let_397 (forall ((u |u_(-> tptp.set_list_a tptp.set_list_a)|) (e tptp.set_list_a) (i tptp.set_list_a)) (not (forall ((v |u_(-> tptp.set_list_a tptp.set_list_a)|)) (not (forall ((ii tptp.set_list_a)) (= (ho_351 v ii) (ite (= i ii) e (ho_351 u ii)))))))))) (let ((_let_398 (forall ((x |u_(-> tptp.set_list_a tptp.set_list_a)|) (y |u_(-> tptp.set_list_a tptp.set_list_a)|)) (or (not (forall ((z tptp.set_list_a)) (= (ho_351 x z) (ho_351 y z)))) (= x y))))) (let ((_let_399 (forall ((u |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.set_list_a tptp.set_list_a)|) (e |u_(-> tptp.set_list_a tptp.set_list_a)|) (i |u_(-> tptp.list_a tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.set_list_a tptp.set_list_a)|)) (not (forall ((ii |u_(-> tptp.list_a tptp.list_a)|)) (= (ho_350 v ii) (ite (= i ii) e (ho_350 u ii)))))))))) (let ((_let_400 (forall ((x |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.set_list_a tptp.set_list_a)|) (y |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.set_list_a tptp.set_list_a)|)) (or (not (forall ((z |u_(-> tptp.list_a tptp.list_a)|)) (= (ho_350 x z) (ho_350 y z)))) (= x y))))) (let ((_let_401 (forall ((u |u_(-> tptp.multiset_a tptp.nat)|) (e tptp.nat) (i tptp.multiset_a)) (not (forall ((v |u_(-> tptp.multiset_a tptp.nat)|)) (not (forall ((ii tptp.multiset_a)) (= (ho_353 v ii) (ite (= i ii) e (ho_353 u ii)))))))))) (let ((_let_402 (forall ((x |u_(-> tptp.multiset_a tptp.nat)|) (y |u_(-> tptp.multiset_a tptp.nat)|)) (or (not (forall ((z tptp.multiset_a)) (= (ho_353 x z) (ho_353 y z)))) (= x y))))) (let ((_let_403 (forall ((u |u_(-> tptp.multiset_set_a tptp.nat)|) (e tptp.nat) (i tptp.multiset_set_a)) (not (forall ((v |u_(-> tptp.multiset_set_a tptp.nat)|)) (not (forall ((ii tptp.multiset_set_a)) (= (ho_355 v ii) (ite (= i ii) e (ho_355 u ii)))))))))) (let ((_let_404 (forall ((x |u_(-> tptp.multiset_set_a tptp.nat)|) (y |u_(-> tptp.multiset_set_a tptp.nat)|)) (or (not (forall ((z tptp.multiset_set_a)) (= (ho_355 x z) (ho_355 y z)))) (= x y))))) (let ((_let_405 (forall ((u |u_(-> _u_(-> tptp.a tptp.a)_ tptp.a tptp.a)|) (e |u_(-> tptp.a tptp.a)|) (i |u_(-> tptp.a tptp.a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.a)_ tptp.a tptp.a)|)) (not (forall ((ii |u_(-> tptp.a tptp.a)|)) (= (ho_358 v ii) (ite (= i ii) e (ho_358 u ii)))))))))) (let ((_let_406 (forall ((x |u_(-> _u_(-> tptp.a tptp.a)_ tptp.a tptp.a)|) (y |u_(-> _u_(-> tptp.a tptp.a)_ tptp.a tptp.a)|)) (or (not (forall ((z |u_(-> tptp.a tptp.a)|)) (= (ho_358 x z) (ho_358 y z)))) (= x y))))) (let ((_let_407 (forall ((u |u_(-> tptp.set_a _u_(-> tptp.a tptp.a)_ tptp.a tptp.a)|) (e |u_(-> _u_(-> tptp.a tptp.a)_ tptp.a tptp.a)|) (i tptp.set_a)) (not (forall ((v |u_(-> tptp.set_a _u_(-> tptp.a tptp.a)_ tptp.a tptp.a)|)) (not (forall ((ii tptp.set_a)) (= (ho_357 v ii) (ite (= i ii) e (ho_357 u ii)))))))))) (let ((_let_408 (forall ((x |u_(-> tptp.set_a _u_(-> tptp.a tptp.a)_ tptp.a tptp.a)|) (y |u_(-> tptp.set_a _u_(-> tptp.a tptp.a)_ tptp.a tptp.a)|)) (or (not (forall ((z tptp.set_a)) (= (ho_357 x z) (ho_357 y z)))) (= x y))))) (let ((_let_409 (forall ((u |u_(-> tptp.set_list_a _u_(-> tptp.list_a tptp.a)_ tptp.a tptp.list_a)|) (e |u_(-> _u_(-> tptp.list_a tptp.a)_ tptp.a tptp.list_a)|) (i tptp.set_list_a)) (not (forall ((v |u_(-> tptp.set_list_a _u_(-> tptp.list_a tptp.a)_ tptp.a tptp.list_a)|)) (not (forall ((ii tptp.set_list_a)) (= (ho_360 v ii) (ite (= i ii) e (ho_360 u ii)))))))))) (let ((_let_410 (forall ((x |u_(-> tptp.set_list_a _u_(-> tptp.list_a tptp.a)_ tptp.a tptp.list_a)|) (y |u_(-> tptp.set_list_a _u_(-> tptp.list_a tptp.a)_ tptp.a tptp.list_a)|)) (or (not (forall ((z tptp.set_list_a)) (= (ho_360 x z) (ho_360 y z)))) (= x y))))) (let ((_let_411 (forall ((u |u_(-> tptp.set_list_a _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a tptp.list_a)|) (e |u_(-> _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a tptp.list_a)|) (i tptp.set_list_a)) (not (forall ((v |u_(-> tptp.set_list_a _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a tptp.list_a)|)) (not (forall ((ii tptp.set_list_a)) (= (ho_366 v ii) (ite (= i ii) e (ho_366 u ii)))))))))) (let ((_let_412 (forall ((x |u_(-> tptp.set_list_a _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a tptp.list_a)|) (y |u_(-> tptp.set_list_a _u_(-> tptp.list_a tptp.list_a)_ tptp.list_a tptp.list_a)|)) (or (not (forall ((z tptp.set_list_a)) (= (ho_366 x z) (ho_366 y z)))) (= x y))))) (let ((_let_413 (forall ((u |u_(-> tptp.nat tptp.a tptp.list_a)|) (e |u_(-> tptp.a tptp.list_a)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.a tptp.list_a)|)) (not (forall ((ii tptp.nat)) (= (ho_372 v ii) (ite (= i ii) e (ho_372 u ii)))))))))) (let ((_let_414 (forall ((x |u_(-> tptp.nat tptp.a tptp.list_a)|) (y |u_(-> tptp.nat tptp.a tptp.list_a)|)) (or (not (forall ((z tptp.nat)) (= (ho_372 x z) (ho_372 y z)))) (= x y))))) (let ((_let_415 (forall ((u |u_(-> tptp.list_set_a tptp.nat tptp.set_a tptp.list_set_a)|) (e |u_(-> tptp.nat tptp.set_a tptp.list_set_a)|) (i tptp.list_set_a)) (not (forall ((v |u_(-> tptp.list_set_a tptp.nat tptp.set_a tptp.list_set_a)|)) (not (forall ((ii tptp.list_set_a)) (= (ho_374 v ii) (ite (= i ii) e (ho_374 u ii)))))))))) (let ((_let_416 (forall ((x |u_(-> tptp.list_set_a tptp.nat tptp.set_a tptp.list_set_a)|) (y |u_(-> tptp.list_set_a tptp.nat tptp.set_a tptp.list_set_a)|)) (or (not (forall ((z tptp.list_set_a)) (= (ho_374 x z) (ho_374 y z)))) (= x y))))) (let ((_let_417 (forall ((u |u_(-> tptp.multiset_list_a tptp.set_list_a)|) (e tptp.set_list_a) (i tptp.multiset_list_a)) (not (forall ((v |u_(-> tptp.multiset_list_a tptp.set_list_a)|)) (not (forall ((ii tptp.multiset_list_a)) (= (ho_378 v ii) (ite (= i ii) e (ho_378 u ii)))))))))) (let ((_let_418 (forall ((x |u_(-> tptp.multiset_list_a tptp.set_list_a)|) (y |u_(-> tptp.multiset_list_a tptp.set_list_a)|)) (or (not (forall ((z tptp.multiset_list_a)) (= (ho_378 x z) (ho_378 y z)))) (= x y))))) (let ((_let_419 (forall ((u |u_(-> tptp.multiset_a tptp.set_a)|) (e tptp.set_a) (i tptp.multiset_a)) (not (forall ((v |u_(-> tptp.multiset_a tptp.set_a)|)) (not (forall ((ii tptp.multiset_a)) (= (ho_380 v ii) (ite (= i ii) e (ho_380 u ii)))))))))) (let ((_let_420 (forall ((x |u_(-> tptp.multiset_a tptp.set_a)|) (y |u_(-> tptp.multiset_a tptp.set_a)|)) (or (not (forall ((z tptp.multiset_a)) (= (ho_380 x z) (ho_380 y z)))) (= x y))))) (let ((_let_421 (forall ((u |u_(-> tptp.multiset_set_a tptp.set_set_a)|) (e tptp.set_set_a) (i tptp.multiset_set_a)) (not (forall ((v |u_(-> tptp.multiset_set_a tptp.set_set_a)|)) (not (forall ((ii tptp.multiset_set_a)) (= (ho_382 v ii) (ite (= i ii) e (ho_382 u ii)))))))))) (let ((_let_422 (forall ((x |u_(-> tptp.multiset_set_a tptp.set_set_a)|) (y |u_(-> tptp.multiset_set_a tptp.set_set_a)|)) (or (not (forall ((z tptp.multiset_set_a)) (= (ho_382 x z) (ho_382 y z)))) (= x y))))) (let ((_let_423 (forall ((u |u_(-> tptp.multiset_multiset_a tptp.set_multiset_a)|) (e tptp.set_multiset_a) (i tptp.multiset_multiset_a)) (not (forall ((v |u_(-> tptp.multiset_multiset_a tptp.set_multiset_a)|)) (not (forall ((ii tptp.multiset_multiset_a)) (= (ho_384 v ii) (ite (= i ii) e (ho_384 u ii)))))))))) (let ((_let_424 (forall ((x |u_(-> tptp.multiset_multiset_a tptp.set_multiset_a)|) (y |u_(-> tptp.multiset_multiset_a tptp.set_multiset_a)|)) (or (not (forall ((z tptp.multiset_multiset_a)) (= (ho_384 x z) (ho_384 y z)))) (= x y))))) (let ((_let_425 (forall ((u |u_(-> tptp.multis971982480list_a tptp.set_multiset_list_a)|) (e tptp.set_multiset_list_a) (i tptp.multis971982480list_a)) (not (forall ((v |u_(-> tptp.multis971982480list_a tptp.set_multiset_list_a)|)) (not (forall ((ii tptp.multis971982480list_a)) (= (ho_386 v ii) (ite (= i ii) e (ho_386 u ii)))))))))) (let ((_let_426 (forall ((x |u_(-> tptp.multis971982480list_a tptp.set_multiset_list_a)|) (y |u_(-> tptp.multis971982480list_a tptp.set_multiset_list_a)|)) (or (not (forall ((z tptp.multis971982480list_a)) (= (ho_386 x z) (ho_386 y z)))) (= x y))))) (let ((_let_427 (forall ((u |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.set_a Bool)|) (e |u_(-> tptp.set_a Bool)|) (i |u_(-> tptp.a tptp.list_a)|)) (not (forall ((v |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.set_a Bool)|)) (not (forall ((ii |u_(-> tptp.a tptp.list_a)|)) (= (ho_394 v ii) (ite (= i ii) e (ho_394 u ii)))))))))) (let ((_let_428 (forall ((x |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.set_a Bool)|) (y |u_(-> _u_(-> tptp.a tptp.list_a)_ tptp.set_a Bool)|)) (or (not (forall ((z |u_(-> tptp.a tptp.list_a)|)) (= (ho_394 x z) (ho_394 y z)))) (= x y))))) (let ((_let_429 (forall ((BOUND_VARIABLE_19854 tptp.nat) (BOUND_VARIABLE_19855 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_19854 BOUND_VARIABLE_19855))) (= (ho_41 (ho_40 k_39 BOUND_VARIABLE_19854) BOUND_VARIABLE_19855) (or (and (ho_41 (ho_40 k_42 BOUND_VARIABLE_19854) BOUND_VARIABLE_19855) (not _let_1)) _let_1)))))) (let ((_let_430 (forall ((BOUND_VARIABLE_19843 tptp.nat) (BOUND_VARIABLE_19844 tptp.nat)) (= (ho_41 (ho_40 k_43 BOUND_VARIABLE_19843) BOUND_VARIABLE_19844) (and (ho_41 (ho_40 k_42 BOUND_VARIABLE_19843) BOUND_VARIABLE_19844) (not (= BOUND_VARIABLE_19843 BOUND_VARIABLE_19844))))))) (let ((_let_431 (forall ((BOUND_VARIABLE_19832 tptp.nat) (BOUND_VARIABLE_19833 tptp.nat)) (= (ho_41 (ho_40 k_44 BOUND_VARIABLE_19832) BOUND_VARIABLE_19833) (and (ho_41 (ho_40 k_42 BOUND_VARIABLE_19832) BOUND_VARIABLE_19833) (not (= BOUND_VARIABLE_19832 BOUND_VARIABLE_19833))))))) (let ((_let_432 (forall ((BOUND_VARIABLE_19820 tptp.nat) (BOUND_VARIABLE_19821 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_19820 BOUND_VARIABLE_19821))) (= (ho_41 (ho_40 k_45 BOUND_VARIABLE_19820) BOUND_VARIABLE_19821) (or (and (ho_41 (ho_40 k_42 BOUND_VARIABLE_19820) BOUND_VARIABLE_19821) (not _let_1)) _let_1)))))) (let ((_let_433 (forall ((BOUND_VARIABLE_20031 |u_(-> tptp.nat Bool)|)) (= (ho_47 k_46 BOUND_VARIABLE_20031) (not (forall ((X3 tptp.nat)) (not (ho_41 BOUND_VARIABLE_20031 X3)))))))) (let ((_let_434 (forall ((BOUND_VARIABLE_20046 |u_(-> tptp.nat Bool)|)) (= (ho_47 k_48 BOUND_VARIABLE_20046) (not (forall ((N2 tptp.nat)) (or (not (ho_41 BOUND_VARIABLE_20046 N2)) (not (forall ((M5 tptp.nat)) (or (not (ho_41 (ho_40 k_42 M5) N2)) (= N2 M5) (not (ho_41 BOUND_VARIABLE_20046 M5)))))))))))) (let ((_let_435 (forall ((BOUND_VARIABLE_19789 tptp.nat) (BOUND_VARIABLE_19790 tptp.nat)) (= (= BOUND_VARIABLE_19789 BOUND_VARIABLE_19790) (ho_41 (ho_40 k_49 BOUND_VARIABLE_19789) BOUND_VARIABLE_19790))))) (let ((_let_436 (forall ((BOUND_VARIABLE_19778 tptp.nat) (BOUND_VARIABLE_19779 tptp.nat)) (= (ho_41 (ho_40 k_50 BOUND_VARIABLE_19778) BOUND_VARIABLE_19779) (and (ho_41 (ho_40 k_42 BOUND_VARIABLE_19778) BOUND_VARIABLE_19779) (ho_41 (ho_40 k_42 BOUND_VARIABLE_19779) BOUND_VARIABLE_19778)))))) (let ((_let_437 (forall ((BOUND_VARIABLE_19771 tptp.nat) (BOUND_VARIABLE_19772 tptp.nat)) (= (= BOUND_VARIABLE_19771 BOUND_VARIABLE_19772) (ho_41 (ho_40 k_51 BOUND_VARIABLE_19771) BOUND_VARIABLE_19772))))) (let ((_let_438 (forall ((BOUND_VARIABLE_19760 tptp.nat) (BOUND_VARIABLE_19761 tptp.nat)) (= (ho_41 (ho_40 k_52 BOUND_VARIABLE_19760) BOUND_VARIABLE_19761) (and (ho_41 (ho_40 k_42 BOUND_VARIABLE_19760) BOUND_VARIABLE_19761) (ho_41 (ho_40 k_42 BOUND_VARIABLE_19761) BOUND_VARIABLE_19760)))))) (let ((_let_439 (forall ((BOUND_VARIABLE_19753 tptp.nat) (BOUND_VARIABLE_19754 tptp.nat)) (= (= BOUND_VARIABLE_19753 BOUND_VARIABLE_19754) (ho_41 (ho_40 k_53 BOUND_VARIABLE_19753) BOUND_VARIABLE_19754))))) (let ((_let_440 (forall ((BOUND_VARIABLE_19742 tptp.nat) (BOUND_VARIABLE_19743 tptp.nat)) (= (ho_41 (ho_40 k_54 BOUND_VARIABLE_19742) BOUND_VARIABLE_19743) (and (ho_41 (ho_40 k_42 BOUND_VARIABLE_19743) BOUND_VARIABLE_19742) (ho_41 (ho_40 k_42 BOUND_VARIABLE_19742) BOUND_VARIABLE_19743)))))) (let ((_let_441 (forall ((BOUND_VARIABLE_19731 tptp.set_list_a) (BOUND_VARIABLE_19732 tptp.set_list_a)) (= (ho_57 (ho_56 k_55 BOUND_VARIABLE_19731) BOUND_VARIABLE_19732) (forall ((T2 tptp.list_a)) (let ((_let_1 (ho_59 k_58 T2))) (or (not (ho_57 _let_1 BOUND_VARIABLE_19731)) (ho_57 _let_1 BOUND_VARIABLE_19732)))))))) (let ((_let_442 (forall ((BOUND_VARIABLE_19720 tptp.set_list_a) (BOUND_VARIABLE_19721 tptp.set_list_a)) (= (ho_57 (ho_56 k_60 BOUND_VARIABLE_19720) BOUND_VARIABLE_19721) (forall ((X5 tptp.list_a)) (let ((_let_1 (ho_59 k_58 X5))) (or (not (ho_57 _let_1 BOUND_VARIABLE_19720)) (ho_57 _let_1 BOUND_VARIABLE_19721)))))))) (let ((_let_443 (forall ((BOUND_VARIABLE_19709 tptp.set_a) (BOUND_VARIABLE_19710 tptp.set_a)) (= (ho_63 (ho_62 k_61 BOUND_VARIABLE_19709) BOUND_VARIABLE_19710) (forall ((T2 tptp.a)) (let ((_let_1 (ho_65 k_64 T2))) (or (not (ho_63 _let_1 BOUND_VARIABLE_19709)) (ho_63 _let_1 BOUND_VARIABLE_19710)))))))) (let ((_let_444 (forall ((BOUND_VARIABLE_19698 tptp.set_a) (BOUND_VARIABLE_19699 tptp.set_a)) (= (ho_63 (ho_62 k_66 BOUND_VARIABLE_19698) BOUND_VARIABLE_19699) (forall ((X5 tptp.a)) (let ((_let_1 (ho_65 k_64 X5))) (or (not (ho_63 _let_1 BOUND_VARIABLE_19698)) (ho_63 _let_1 BOUND_VARIABLE_19699)))))))) (let ((_let_445 (forall ((BOUND_VARIABLE_20198 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_19669 tptp.set_nat) (BOUND_VARIABLE_19670 tptp.set_nat)) (= (ho_71 (ho_70 (ho_69 k_68 BOUND_VARIABLE_20198) BOUND_VARIABLE_19669) BOUND_VARIABLE_19670) (not (forall ((BOUND_VARIABLE_20215 |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((X5 tptp.nat)) (let ((_let_1 (ho_67 BOUND_VARIABLE_20198 X5))) (or (not (ho_71 (ho_73 k_72 X5) BOUND_VARIABLE_19669)) (and (ho_71 (ho_73 k_72 _let_1) BOUND_VARIABLE_19670) (= X5 (ho_67 BOUND_VARIABLE_20215 _let_1))))))) (not (forall ((X5 tptp.nat)) (let ((_let_1 (ho_67 BOUND_VARIABLE_20215 X5))) (or (not (ho_71 (ho_73 k_72 X5) BOUND_VARIABLE_19670)) (and (ho_71 (ho_73 k_72 _let_1) BOUND_VARIABLE_19669) (= X5 (ho_67 BOUND_VARIABLE_20198 _let_1)))))))))))))) (let ((_let_446 (forall ((BOUND_VARIABLE_20254 |u_(-> tptp.nat tptp.nat)|) (BOUND_VARIABLE_19656 tptp.set_nat) (BOUND_VARIABLE_19657 tptp.set_nat)) (= (ho_71 (ho_70 (ho_69 k_74 BOUND_VARIABLE_20254) BOUND_VARIABLE_19656) BOUND_VARIABLE_19657) (and (ho_71 (ho_79 k_78 BOUND_VARIABLE_20254) BOUND_VARIABLE_19656) (= BOUND_VARIABLE_19657 (ho_77 (ho_76 k_75 BOUND_VARIABLE_20254) BOUND_VARIABLE_19656))))))) (let ((_let_447 (forall ((BOUND_VARIABLE_19647 tptp.set_list_a) (BOUND_VARIABLE_19648 tptp.list_a)) (= (ho_82 (ho_81 k_80 BOUND_VARIABLE_19647) BOUND_VARIABLE_19648) (ho_57 (ho_59 k_58 BOUND_VARIABLE_19648) BOUND_VARIABLE_19647))))) (let ((_let_448 (forall ((BOUND_VARIABLE_19639 tptp.set_a) (BOUND_VARIABLE_19640 tptp.a)) (= (ho_85 (ho_84 k_83 BOUND_VARIABLE_19639) BOUND_VARIABLE_19640) (ho_63 (ho_65 k_64 BOUND_VARIABLE_19640) BOUND_VARIABLE_19639))))) (let ((_let_449 (forall ((BOUND_VARIABLE_19631 tptp.set_nat) (BOUND_VARIABLE_19632 tptp.nat)) (= (ho_41 (ho_87 k_86 BOUND_VARIABLE_19631) BOUND_VARIABLE_19632) (ho_71 (ho_73 k_72 BOUND_VARIABLE_19632) BOUND_VARIABLE_19631))))) (let ((_let_450 (forall ((BOUND_VARIABLE_19623 tptp.set_set_a) (BOUND_VARIABLE_19624 tptp.set_a)) (= (ho_63 (ho_89 k_88 BOUND_VARIABLE_19623) BOUND_VARIABLE_19624) (ho_92 (ho_91 k_90 BOUND_VARIABLE_19624) BOUND_VARIABLE_19623))))) (let ((_let_451 (forall ((BOUND_VARIABLE_19615 tptp.set_list_set_a) (BOUND_VARIABLE_19616 tptp.list_set_a)) (= (ho_95 (ho_94 k_93 BOUND_VARIABLE_19615) BOUND_VARIABLE_19616) (ho_98 (ho_97 k_96 BOUND_VARIABLE_19616) BOUND_VARIABLE_19615))))) (let ((_let_452 (forall ((BOUND_VARIABLE_19607 tptp.set_list_list_a) (BOUND_VARIABLE_19608 tptp.list_list_a)) (= (ho_101 (ho_100 k_99 BOUND_VARIABLE_19607) BOUND_VARIABLE_19608) (ho_104 (ho_103 k_102 BOUND_VARIABLE_19608) BOUND_VARIABLE_19607))))) (let ((_let_453 (forall ((BOUND_VARIABLE_19599 tptp.set_multiset_a) (BOUND_VARIABLE_19600 tptp.multiset_a)) (= (ho_107 (ho_106 k_105 BOUND_VARIABLE_19599) BOUND_VARIABLE_19600) (ho_110 (ho_109 k_108 BOUND_VARIABLE_19600) BOUND_VARIABLE_19599))))) (let ((_let_454 (forall ((BOUND_VARIABLE_19592 tptp.list_set_a) (BOUND_VARIABLE_19593 tptp.list_set_a)) (= (= BOUND_VARIABLE_19592 BOUND_VARIABLE_19593) (ho_95 (ho_112 k_111 BOUND_VARIABLE_19592) BOUND_VARIABLE_19593))))) (let ((_let_455 (forall ((BOUND_VARIABLE_19572 tptp.list_set_a) (BOUND_VARIABLE_19573 tptp.list_set_a)) (= (ho_95 (ho_112 k_118 BOUND_VARIABLE_19572) BOUND_VARIABLE_19573) (and (= (ho_117 k_116 BOUND_VARIABLE_19572) (ho_117 k_116 BOUND_VARIABLE_19573)) (forall ((I4 tptp.nat)) (let ((_let_1 (ho_117 k_116 BOUND_VARIABLE_19572))) (or (not (ho_41 (ho_40 k_42 I4) _let_1)) (= I4 _let_1) (= (ho_115 (ho_114 k_113 BOUND_VARIABLE_19573) I4) (ho_115 (ho_114 k_113 BOUND_VARIABLE_19572) I4)))))))))) (let ((_let_456 (forall ((BOUND_VARIABLE_19565 tptp.list_a) (BOUND_VARIABLE_19566 tptp.list_a)) (= (= BOUND_VARIABLE_19565 BOUND_VARIABLE_19566) (ho_82 (ho_120 k_119 BOUND_VARIABLE_19565) BOUND_VARIABLE_19566))))) (let ((_let_457 (forall ((BOUND_VARIABLE_19545 tptp.list_a) (BOUND_VARIABLE_19546 tptp.list_a)) (= (ho_82 (ho_120 k_126 BOUND_VARIABLE_19545) BOUND_VARIABLE_19546) (and (= (ho_125 k_124 BOUND_VARIABLE_19545) (ho_125 k_124 BOUND_VARIABLE_19546)) (forall ((I4 tptp.nat)) (let ((_let_1 (ho_125 k_124 BOUND_VARIABLE_19545))) (or (not (ho_41 (ho_40 k_42 I4) _let_1)) (= I4 _let_1) (= (ho_123 (ho_122 k_121 BOUND_VARIABLE_19546) I4) (ho_123 (ho_122 k_121 BOUND_VARIABLE_19545) I4)))))))))) (let ((_let_458 (forall ((BOUND_VARIABLE_19538 tptp.list_nat) (BOUND_VARIABLE_19539 tptp.list_nat)) (= (= BOUND_VARIABLE_19538 BOUND_VARIABLE_19539) (ho_129 (ho_128 k_127 BOUND_VARIABLE_19538) BOUND_VARIABLE_19539))))) (let ((_let_459 (forall ((BOUND_VARIABLE_19518 tptp.list_nat) (BOUND_VARIABLE_19519 tptp.list_nat)) (= (ho_129 (ho_128 k_134 BOUND_VARIABLE_19518) BOUND_VARIABLE_19519) (and (= (ho_133 k_132 BOUND_VARIABLE_19518) (ho_133 k_132 BOUND_VARIABLE_19519)) (forall ((I4 tptp.nat)) (let ((_let_1 (ho_133 k_132 BOUND_VARIABLE_19518))) (or (not (ho_41 (ho_40 k_42 I4) _let_1)) (= I4 _let_1) (= (ho_67 (ho_131 k_130 BOUND_VARIABLE_19519) I4) (ho_67 (ho_131 k_130 BOUND_VARIABLE_19518) I4)))))))))) (let ((_let_460 (forall ((BOUND_VARIABLE_19511 tptp.list_set_set_a) (BOUND_VARIABLE_19512 tptp.list_set_set_a)) (= (= BOUND_VARIABLE_19511 BOUND_VARIABLE_19512) (ho_137 (ho_136 k_135 BOUND_VARIABLE_19511) BOUND_VARIABLE_19512))))) (let ((_let_461 (forall ((BOUND_VARIABLE_19491 tptp.list_set_set_a) (BOUND_VARIABLE_19492 tptp.list_set_set_a)) (= (ho_137 (ho_136 k_143 BOUND_VARIABLE_19491) BOUND_VARIABLE_19492) (and (= (ho_142 k_141 BOUND_VARIABLE_19491) (ho_142 k_141 BOUND_VARIABLE_19492)) (forall ((I4 tptp.nat)) (let ((_let_1 (ho_142 k_141 BOUND_VARIABLE_19491))) (or (not (ho_41 (ho_40 k_42 I4) _let_1)) (= I4 _let_1) (= (ho_140 (ho_139 k_138 BOUND_VARIABLE_19492) I4) (ho_140 (ho_139 k_138 BOUND_VARIABLE_19491) I4)))))))))) (let ((_let_462 (forall ((BOUND_VARIABLE_19484 tptp.list_set_list_a) (BOUND_VARIABLE_19485 tptp.list_set_list_a)) (= (= BOUND_VARIABLE_19484 BOUND_VARIABLE_19485) (ho_146 (ho_145 k_144 BOUND_VARIABLE_19484) BOUND_VARIABLE_19485))))) (let ((_let_463 (forall ((BOUND_VARIABLE_19464 tptp.list_set_list_a) (BOUND_VARIABLE_19465 tptp.list_set_list_a)) (= (ho_146 (ho_145 k_152 BOUND_VARIABLE_19464) BOUND_VARIABLE_19465) (and (= (ho_151 k_150 BOUND_VARIABLE_19464) (ho_151 k_150 BOUND_VARIABLE_19465)) (forall ((I4 tptp.nat)) (let ((_let_1 (ho_151 k_150 BOUND_VARIABLE_19464))) (or (not (ho_41 (ho_40 k_42 I4) _let_1)) (= I4 _let_1) (= (ho_149 (ho_148 k_147 BOUND_VARIABLE_19465) I4) (ho_149 (ho_148 k_147 BOUND_VARIABLE_19464) I4)))))))))) (let ((_let_464 (forall ((BOUND_VARIABLE_19457 tptp.list_list_a) (BOUND_VARIABLE_19458 tptp.list_list_a)) (= (= BOUND_VARIABLE_19457 BOUND_VARIABLE_19458) (ho_101 (ho_154 k_153 BOUND_VARIABLE_19457) BOUND_VARIABLE_19458))))) (let ((_let_465 (forall ((BOUND_VARIABLE_19437 tptp.list_list_a) (BOUND_VARIABLE_19438 tptp.list_list_a)) (= (ho_101 (ho_154 k_160 BOUND_VARIABLE_19437) BOUND_VARIABLE_19438) (and (= (ho_159 k_158 BOUND_VARIABLE_19437) (ho_159 k_158 BOUND_VARIABLE_19438)) (forall ((I4 tptp.nat)) (let ((_let_1 (ho_159 k_158 BOUND_VARIABLE_19437))) (or (not (ho_41 (ho_40 k_42 I4) _let_1)) (= I4 _let_1) (= (ho_157 (ho_156 k_155 BOUND_VARIABLE_19438) I4) (ho_157 (ho_156 k_155 BOUND_VARIABLE_19437) I4)))))))))) (let ((_let_466 (forall ((BOUND_VARIABLE_19854 tptp.nat) (BOUND_VARIABLE_19855 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_19854 BOUND_VARIABLE_19855))) (= (or (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_19854) BOUND_VARIABLE_19855) (not _let_1)) _let_1) (ll_38 BOUND_VARIABLE_19854 BOUND_VARIABLE_19855)))))) (let ((_let_467 (forall ((BOUND_VARIABLE_19843 tptp.nat) (BOUND_VARIABLE_19844 tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_19843) BOUND_VARIABLE_19844) (not (= BOUND_VARIABLE_19843 BOUND_VARIABLE_19844))) (ll_37 BOUND_VARIABLE_19843 BOUND_VARIABLE_19844))))) (let ((_let_468 (forall ((BOUND_VARIABLE_19832 tptp.nat) (BOUND_VARIABLE_19833 tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_19832) BOUND_VARIABLE_19833) (not (= BOUND_VARIABLE_19832 BOUND_VARIABLE_19833))) (ll_36 BOUND_VARIABLE_19832 BOUND_VARIABLE_19833))))) (let ((_let_469 (forall ((BOUND_VARIABLE_19820 tptp.nat) (BOUND_VARIABLE_19821 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_19820 BOUND_VARIABLE_19821))) (= (or (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_19820) BOUND_VARIABLE_19821) (not _let_1)) _let_1) (ll_35 BOUND_VARIABLE_19820 BOUND_VARIABLE_19821)))))) (let ((_let_470 (forall ((BOUND_VARIABLE_19811 (-> tptp.nat Bool))) (= (not (forall ((X3 tptp.nat)) (not (@ BOUND_VARIABLE_19811 X3)))) (ll_34 BOUND_VARIABLE_19811))))) (let ((_let_471 (forall ((BOUND_VARIABLE_19796 (-> tptp.nat Bool))) (= (not (forall ((N2 tptp.nat)) (or (not (@ BOUND_VARIABLE_19796 N2)) (not (forall ((M5 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M5) N2)) (= N2 M5) (not (@ BOUND_VARIABLE_19796 M5)))))))) (ll_33 BOUND_VARIABLE_19796))))) (let ((_let_472 (forall ((BOUND_VARIABLE_19789 tptp.nat) (BOUND_VARIABLE_19790 tptp.nat)) (= (= BOUND_VARIABLE_19789 BOUND_VARIABLE_19790) (ll_32 BOUND_VARIABLE_19789 BOUND_VARIABLE_19790))))) (let ((_let_473 (forall ((BOUND_VARIABLE_19778 tptp.nat) (BOUND_VARIABLE_19779 tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_19778) BOUND_VARIABLE_19779) (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_19779) BOUND_VARIABLE_19778)) (ll_31 BOUND_VARIABLE_19778 BOUND_VARIABLE_19779))))) (let ((_let_474 (forall ((BOUND_VARIABLE_19771 tptp.nat) (BOUND_VARIABLE_19772 tptp.nat)) (= (= BOUND_VARIABLE_19771 BOUND_VARIABLE_19772) (ll_30 BOUND_VARIABLE_19771 BOUND_VARIABLE_19772))))) (let ((_let_475 (forall ((BOUND_VARIABLE_19760 tptp.nat) (BOUND_VARIABLE_19761 tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_19760) BOUND_VARIABLE_19761) (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_19761) BOUND_VARIABLE_19760)) (ll_29 BOUND_VARIABLE_19760 BOUND_VARIABLE_19761))))) (let ((_let_476 (forall ((BOUND_VARIABLE_19753 tptp.nat) (BOUND_VARIABLE_19754 tptp.nat)) (= (= BOUND_VARIABLE_19753 BOUND_VARIABLE_19754) (ll_28 BOUND_VARIABLE_19753 BOUND_VARIABLE_19754))))) (let ((_let_477 (forall ((BOUND_VARIABLE_19742 tptp.nat) (BOUND_VARIABLE_19743 tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_19743) BOUND_VARIABLE_19742) (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_19742) BOUND_VARIABLE_19743)) (ll_27 BOUND_VARIABLE_19742 BOUND_VARIABLE_19743))))) (let ((_let_478 (forall ((BOUND_VARIABLE_19731 tptp.set_list_a) (BOUND_VARIABLE_19732 tptp.set_list_a)) (= (forall ((T2 tptp.list_a)) (let ((_let_1 (@ tptp.member_list_a T2))) (or (not (@ _let_1 BOUND_VARIABLE_19731)) (@ _let_1 BOUND_VARIABLE_19732)))) (ll_26 BOUND_VARIABLE_19731 BOUND_VARIABLE_19732))))) (let ((_let_479 (forall ((BOUND_VARIABLE_19720 tptp.set_list_a) (BOUND_VARIABLE_19721 tptp.set_list_a)) (= (forall ((X5 tptp.list_a)) (let ((_let_1 (@ tptp.member_list_a X5))) (or (not (@ _let_1 BOUND_VARIABLE_19720)) (@ _let_1 BOUND_VARIABLE_19721)))) (ll_25 BOUND_VARIABLE_19720 BOUND_VARIABLE_19721))))) (let ((_let_480 (forall ((BOUND_VARIABLE_19709 tptp.set_a) (BOUND_VARIABLE_19710 tptp.set_a)) (= (forall ((T2 tptp.a)) (let ((_let_1 (@ tptp.member_a T2))) (or (not (@ _let_1 BOUND_VARIABLE_19709)) (@ _let_1 BOUND_VARIABLE_19710)))) (ll_24 BOUND_VARIABLE_19709 BOUND_VARIABLE_19710))))) (let ((_let_481 (forall ((BOUND_VARIABLE_19698 tptp.set_a) (BOUND_VARIABLE_19699 tptp.set_a)) (= (forall ((X5 tptp.a)) (let ((_let_1 (@ tptp.member_a X5))) (or (not (@ _let_1 BOUND_VARIABLE_19698)) (@ _let_1 BOUND_VARIABLE_19699)))) (ll_23 BOUND_VARIABLE_19698 BOUND_VARIABLE_19699))))) (let ((_let_482 (forall ((BOUND_VARIABLE_19668 (-> tptp.nat tptp.nat)) (BOUND_VARIABLE_19669 tptp.set_nat) (BOUND_VARIABLE_19670 tptp.set_nat)) (= (not (forall ((G3 (-> tptp.nat tptp.nat))) (or (not (forall ((X5 tptp.nat)) (let ((_let_1 (@ BOUND_VARIABLE_19668 X5))) (or (not (@ (@ tptp.member_nat X5) BOUND_VARIABLE_19669)) (and (@ (@ tptp.member_nat _let_1) BOUND_VARIABLE_19670) (= X5 (@ G3 _let_1))))))) (not (forall ((X5 tptp.nat)) (let ((_let_1 (@ G3 X5))) (or (not (@ (@ tptp.member_nat X5) BOUND_VARIABLE_19670)) (and (@ (@ tptp.member_nat _let_1) BOUND_VARIABLE_19669) (= X5 (@ BOUND_VARIABLE_19668 _let_1)))))))))) (ll_22 BOUND_VARIABLE_19668 BOUND_VARIABLE_19669 BOUND_VARIABLE_19670))))) (let ((_let_483 (forall ((BOUND_VARIABLE_19655 (-> tptp.nat tptp.nat)) (BOUND_VARIABLE_19656 tptp.set_nat) (BOUND_VARIABLE_19657 tptp.set_nat)) (= (and (@ (@ tptp.inj_on_nat_nat BOUND_VARIABLE_19655) BOUND_VARIABLE_19656) (= BOUND_VARIABLE_19657 (@ (@ tptp.image_nat_nat BOUND_VARIABLE_19655) BOUND_VARIABLE_19656))) (ll_21 BOUND_VARIABLE_19655 BOUND_VARIABLE_19656 BOUND_VARIABLE_19657))))) (let ((_let_484 (forall ((BOUND_VARIABLE_19647 tptp.set_list_a) (BOUND_VARIABLE_19648 tptp.list_a)) (= (@ (@ tptp.member_list_a BOUND_VARIABLE_19648) BOUND_VARIABLE_19647) (ll_20 BOUND_VARIABLE_19647 BOUND_VARIABLE_19648))))) (let ((_let_485 (forall ((BOUND_VARIABLE_19639 tptp.set_a) (BOUND_VARIABLE_19640 tptp.a)) (= (@ (@ tptp.member_a BOUND_VARIABLE_19640) BOUND_VARIABLE_19639) (ll_19 BOUND_VARIABLE_19639 BOUND_VARIABLE_19640))))) (let ((_let_486 (forall ((BOUND_VARIABLE_19631 tptp.set_nat) (BOUND_VARIABLE_19632 tptp.nat)) (= (@ (@ tptp.member_nat BOUND_VARIABLE_19632) BOUND_VARIABLE_19631) (ll_18 BOUND_VARIABLE_19631 BOUND_VARIABLE_19632))))) (let ((_let_487 (forall ((BOUND_VARIABLE_19623 tptp.set_set_a) (BOUND_VARIABLE_19624 tptp.set_a)) (= (@ (@ tptp.member_set_a BOUND_VARIABLE_19624) BOUND_VARIABLE_19623) (ll_17 BOUND_VARIABLE_19623 BOUND_VARIABLE_19624))))) (let ((_let_488 (forall ((BOUND_VARIABLE_19615 tptp.set_list_set_a) (BOUND_VARIABLE_19616 tptp.list_set_a)) (= (@ (@ tptp.member_list_set_a BOUND_VARIABLE_19616) BOUND_VARIABLE_19615) (ll_16 BOUND_VARIABLE_19615 BOUND_VARIABLE_19616))))) (let ((_let_489 (forall ((BOUND_VARIABLE_19607 tptp.set_list_list_a) (BOUND_VARIABLE_19608 tptp.list_list_a)) (= (@ (@ tptp.member_list_list_a BOUND_VARIABLE_19608) BOUND_VARIABLE_19607) (ll_15 BOUND_VARIABLE_19607 BOUND_VARIABLE_19608))))) (let ((_let_490 (forall ((BOUND_VARIABLE_19599 tptp.set_multiset_a) (BOUND_VARIABLE_19600 tptp.multiset_a)) (= (@ (@ tptp.member_multiset_a BOUND_VARIABLE_19600) BOUND_VARIABLE_19599) (ll_14 BOUND_VARIABLE_19599 BOUND_VARIABLE_19600))))) (let ((_let_491 (forall ((BOUND_VARIABLE_19592 tptp.list_set_a) (BOUND_VARIABLE_19593 tptp.list_set_a)) (= (= BOUND_VARIABLE_19592 BOUND_VARIABLE_19593) (ll_13 BOUND_VARIABLE_19592 BOUND_VARIABLE_19593))))) (let ((_let_492 (forall ((BOUND_VARIABLE_19572 tptp.list_set_a) (BOUND_VARIABLE_19573 tptp.list_set_a)) (= (ll_12 BOUND_VARIABLE_19572 BOUND_VARIABLE_19573) (and (= (@ tptp.size_size_list_set_a BOUND_VARIABLE_19572) (@ tptp.size_size_list_set_a BOUND_VARIABLE_19573)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_set_a BOUND_VARIABLE_19572))) (or (not (@ (@ tptp.ord_less_eq_nat I4) _let_1)) (= I4 _let_1) (= (@ (@ tptp.nth_set_a BOUND_VARIABLE_19572) I4) (@ (@ tptp.nth_set_a BOUND_VARIABLE_19573) I4)))))))))) (let ((_let_493 (forall ((BOUND_VARIABLE_19565 tptp.list_a) (BOUND_VARIABLE_19566 tptp.list_a)) (= (= BOUND_VARIABLE_19565 BOUND_VARIABLE_19566) (ll_11 BOUND_VARIABLE_19565 BOUND_VARIABLE_19566))))) (let ((_let_494 (forall ((BOUND_VARIABLE_19545 tptp.list_a) (BOUND_VARIABLE_19546 tptp.list_a)) (= (ll_10 BOUND_VARIABLE_19545 BOUND_VARIABLE_19546) (and (= (@ tptp.size_size_list_a BOUND_VARIABLE_19545) (@ tptp.size_size_list_a BOUND_VARIABLE_19546)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_a BOUND_VARIABLE_19545))) (or (not (@ (@ tptp.ord_less_eq_nat I4) _let_1)) (= I4 _let_1) (= (@ (@ tptp.nth_a BOUND_VARIABLE_19545) I4) (@ (@ tptp.nth_a BOUND_VARIABLE_19546) I4)))))))))) (let ((_let_495 (forall ((BOUND_VARIABLE_19538 tptp.list_nat) (BOUND_VARIABLE_19539 tptp.list_nat)) (= (= BOUND_VARIABLE_19538 BOUND_VARIABLE_19539) (ll_9 BOUND_VARIABLE_19538 BOUND_VARIABLE_19539))))) (let ((_let_496 (forall ((BOUND_VARIABLE_19518 tptp.list_nat) (BOUND_VARIABLE_19519 tptp.list_nat)) (= (ll_8 BOUND_VARIABLE_19518 BOUND_VARIABLE_19519) (and (= (@ tptp.size_size_list_nat BOUND_VARIABLE_19518) (@ tptp.size_size_list_nat BOUND_VARIABLE_19519)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.size_size_list_nat BOUND_VARIABLE_19518))) (or (not (@ (@ tptp.ord_less_eq_nat I4) _let_1)) (= I4 _let_1) (= (@ (@ tptp.nth_nat BOUND_VARIABLE_19518) I4) (@ (@ tptp.nth_nat BOUND_VARIABLE_19519) I4)))))))))) (let ((_let_497 (forall ((BOUND_VARIABLE_19511 tptp.list_set_set_a) (BOUND_VARIABLE_19512 tptp.list_set_set_a)) (= (= BOUND_VARIABLE_19511 BOUND_VARIABLE_19512) (ll_7 BOUND_VARIABLE_19511 BOUND_VARIABLE_19512))))) (let ((_let_498 (forall ((BOUND_VARIABLE_19491 tptp.list_set_set_a) (BOUND_VARIABLE_19492 tptp.list_set_set_a)) (= (ll_6 BOUND_VARIABLE_19491 BOUND_VARIABLE_19492) (and (= (@ tptp.size_s739728560_set_a BOUND_VARIABLE_19491) (@ tptp.size_s739728560_set_a BOUND_VARIABLE_19492)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.size_s739728560_set_a BOUND_VARIABLE_19491))) (or (not (@ (@ tptp.ord_less_eq_nat I4) _let_1)) (= I4 _let_1) (= (@ (@ tptp.nth_set_set_a BOUND_VARIABLE_19491) I4) (@ (@ tptp.nth_set_set_a BOUND_VARIABLE_19492) I4)))))))))) (let ((_let_499 (forall ((BOUND_VARIABLE_19484 tptp.list_set_list_a) (BOUND_VARIABLE_19485 tptp.list_set_list_a)) (= (= BOUND_VARIABLE_19484 BOUND_VARIABLE_19485) (ll_5 BOUND_VARIABLE_19484 BOUND_VARIABLE_19485))))) (let ((_let_500 (forall ((BOUND_VARIABLE_19464 tptp.list_set_list_a) (BOUND_VARIABLE_19465 tptp.list_set_list_a)) (= (ll_4 BOUND_VARIABLE_19464 BOUND_VARIABLE_19465) (and (= (@ tptp.size_s1635937238list_a BOUND_VARIABLE_19464) (@ tptp.size_s1635937238list_a BOUND_VARIABLE_19465)) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.size_s1635937238list_a BOUND_VARIABLE_19464))) (or (not (@ (@ tptp.ord_less_eq_nat I4) _let_1)) (= I4 _let_1) (= (@ (@ tptp.nth_set_list_a BOUND_VARIABLE_19464) I4) (@ (@ tptp.nth_set_list_a BOUND_VARIABLE_19465) I4)))))))))) (let ((_let_501 (forall ((BOUND_VARIABLE_19457 tptp.list_list_a) (BOUND_VARIABLE_19458 tptp.list_list_a)) (= (= BOUND_VARIABLE_19457 BOUND_VARIABLE_19458) (ll_3 BOUND_VARIABLE_19457 BOUND_VARIABLE_19458))))) (let ((_let_502 (forall ((BOUND_VARIABLE_19437 tptp.list_list_a) (BOUND_VARIABLE_19438 tptp.list_list_a)) (= (ll_2 BOUND_VARIABLE_19437 BOUND_VARIABLE_19438) (and (= (@ tptp.size_s1427607542list_a BOUND_VARIABLE_19437) (@ 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tptp.hilber2024005914iset_a A) Ss) (=> (@ (@ tptp.member_multiset_a A2) A) (not (forall ((Qs tptp.list_multiset_a)) (=> (@ (@ tptp.member518144627iset_a Qs) (@ tptp.listset_multiset_a Ss)) (not (= A2 (@ tptp.groups1592617181iset_a Qs))))))))) (forall ((A tptp.set_nat) (Ss tptp.list_set_nat) (A2 tptp.nat)) (=> (@ (@ tptp.hilber1014902394mp_nat A) Ss) (=> (@ (@ tptp.member_nat A2) A) (not (forall ((Qs tptp.list_nat)) (=> (@ (@ tptp.member_list_nat Qs) (@ tptp.listset_nat Ss)) (not (= A2 (@ tptp.groups921905271st_nat Qs))))))))) (forall ((A tptp.set_a) (Ss tptp.list_set_a) (A2 tptp.a)) (=> (@ (@ tptp.hilber2037636820comp_a A) Ss) (=> (@ (@ tptp.member_a A2) A) (not (forall ((Qs tptp.list_a)) (=> (@ (@ tptp.member_list_a Qs) (@ tptp.listset_a Ss)) (not (= A2 (@ tptp.groups1792256535list_a Qs))))))))) (forall ((Ss tptp.list_set_multiset_a) (A tptp.set_multiset_a)) (=> (forall ((Qs tptp.list_multiset_a)) (=> (@ (@ tptp.member518144627iset_a Qs) (@ tptp.listset_multiset_a Ss)) (@ (@ tptp.member_multiset_a (@ tptp.groups1592617181iset_a Qs)) A))) (=> (forall ((A3 tptp.multiset_a)) (=> (@ (@ tptp.member_multiset_a A3) A) (exists ((X tptp.list_multiset_a)) (and (@ (@ tptp.member518144627iset_a X) (@ tptp.listset_multiset_a Ss)) (= A3 (@ tptp.groups1592617181iset_a X)) (forall ((Y tptp.list_multiset_a)) (=> (and (@ (@ tptp.member518144627iset_a Y) (@ tptp.listset_multiset_a Ss)) (= A3 (@ tptp.groups1592617181iset_a Y))) (= Y X))))))) (@ (@ tptp.hilber2024005914iset_a A) Ss)))) (forall ((Ss tptp.list_set_nat) (A tptp.set_nat)) (=> (forall ((Qs tptp.list_nat)) (=> (@ (@ tptp.member_list_nat Qs) (@ tptp.listset_nat Ss)) (@ (@ tptp.member_nat (@ tptp.groups921905271st_nat Qs)) A))) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A) (exists ((X tptp.list_nat)) (and (@ (@ tptp.member_list_nat X) (@ tptp.listset_nat Ss)) (= A3 (@ tptp.groups921905271st_nat X)) (forall ((Y tptp.list_nat)) (=> (and (@ (@ tptp.member_list_nat Y) (@ tptp.listset_nat Ss)) (= A3 (@ tptp.groups921905271st_nat Y))) (= Y X))))))) (@ (@ tptp.hilber1014902394mp_nat A) Ss)))) (forall ((Ss tptp.list_set_a) (A tptp.set_a)) (=> (forall ((Qs tptp.list_a)) (=> (@ (@ tptp.member_list_a Qs) (@ tptp.listset_a Ss)) (@ (@ tptp.member_a (@ tptp.groups1792256535list_a Qs)) A))) (=> (forall ((A3 tptp.a)) (=> (@ (@ tptp.member_a A3) A) (exists ((X tptp.list_a)) (and (@ (@ tptp.member_list_a X) (@ tptp.listset_a Ss)) (= A3 (@ tptp.groups1792256535list_a X)) (forall ((Y tptp.list_a)) (=> (and (@ (@ tptp.member_list_a Y) (@ tptp.listset_a Ss)) (= A3 (@ tptp.groups1792256535list_a Y))) (= Y X))))))) (@ (@ tptp.hilber2037636820comp_a A) Ss)))) (forall ((A tptp.set_nat) (Ss tptp.list_set_nat) (Qs2 tptp.list_nat) (Qs3 tptp.list_nat)) (let ((_let_1 (@ tptp.listset_nat Ss))) (=> (@ (@ tptp.hilber1014902394mp_nat A) Ss) (=> (@ (@ tptp.member_list_nat Qs2) _let_1) (=> (@ (@ tptp.member_list_nat Qs3) _let_1) (=> (= (@ tptp.groups921905271st_nat Qs2) (@ tptp.groups921905271st_nat Qs3)) (= Qs2 Qs3))))))) (forall ((A tptp.set_a) (Ss tptp.list_set_a) (Qs2 tptp.list_a) (Qs3 tptp.list_a)) (let ((_let_1 (@ tptp.listset_a Ss))) (=> (@ (@ tptp.hilber2037636820comp_a A) Ss) (=> (@ (@ tptp.member_list_a Qs2) _let_1) (=> (@ (@ tptp.member_list_a Qs3) _let_1) (=> (= (@ tptp.groups1792256535list_a Qs2) (@ tptp.groups1792256535list_a Qs3)) (= Qs2 Qs3))))))) (forall ((Xs tptp.list_nat)) (= (@ tptp.groups921905271st_nat (@ tptp.rev_nat Xs)) (@ tptp.groups921905271st_nat Xs))) (forall ((Xs tptp.list_a)) (= (@ tptp.groups1792256535list_a (@ tptp.rev_a Xs)) (@ tptp.groups1792256535list_a Xs))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_a tptp.qs)) (= (@ (@ tptp.nth_a tptp.qs2) I) (@ (@ tptp.nth_a tptp.qs) (@ tptp.g I))))) (@ (@ _let_21 (@ tptp.set_ord_lessThan_nat _let_23)) (@ tptp.set_ord_lessThan_nat _let_20)) (forall ((Xs tptp.list_nat)) (= (@ tptp.comm_m1100186507et_nat (@ tptp.mset_nat Xs)) (@ tptp.groups921905271st_nat Xs))) (forall ((Xs tptp.list_multiset_list_a)) (= (@ tptp.comm_m324867663list_a (@ tptp.mset_multiset_list_a Xs)) (@ tptp.groups1271887971list_a Xs))) (forall ((Xs tptp.list_multiset_a)) (= (@ tptp.comm_m2145643721iset_a (@ tptp.mset_multiset_a Xs)) (@ tptp.groups1592617181iset_a Xs))) _let_22 (forall ((A tptp.set_nat) (Ss tptp.list_set_nat)) (=> (@ (@ tptp.hilber1014902394mp_nat A) Ss) (= (@ (@ tptp.image_list_nat_nat tptp.groups921905271st_nat) (@ tptp.listset_nat Ss)) A))) (forall ((A tptp.set_a) (Ss tptp.list_set_a)) (=> (@ (@ tptp.hilber2037636820comp_a A) Ss) (= (@ (@ tptp.image_list_a_a tptp.groups1792256535list_a) (@ tptp.listset_a Ss)) A))) (@ (@ tptp.hilber2037636820comp_a tptp.a2) tptp.ss1) (@ (@ tptp.member_list_a tptp.qs) (@ tptp.listset_a tptp.ss1)) (forall ((Xs tptp.list_set_a)) (= (@ tptp.mset_set_a (@ tptp.rev_set_a Xs)) (@ tptp.mset_set_a Xs))) (forall ((Xs tptp.list_list_a)) (= (@ tptp.mset_list_a (@ tptp.rev_list_a Xs)) (@ tptp.mset_list_a Xs))) (forall ((Xs tptp.list_a)) (= (@ tptp.mset_a (@ tptp.rev_a Xs)) (@ tptp.mset_a Xs))) (not (forall ((Qs22 tptp.list_a)) (=> (@ (@ tptp.member_list_a Qs22) (@ tptp.listset_a tptp.ss2)) (=> (= (@ tptp.size_size_list_a Qs22) (@ tptp.size_size_list_a tptp.qs)) (not (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_a tptp.qs)) (= (@ (@ tptp.nth_a Qs22) I2) (@ (@ tptp.nth_a tptp.qs) (@ tptp.g I2)))))))))) (@ (@ tptp.perm_set_a tptp.ss1) tptp.ss2) (forall ((X2 tptp.multiset_set_a)) (exists ((Xs2 tptp.list_set_a)) (= (@ tptp.mset_set_a Xs2) X2))) (forall ((X2 tptp.multiset_list_a)) (exists ((Xs2 tptp.list_list_a)) (= (@ tptp.mset_list_a Xs2) X2))) (forall ((X2 tptp.multiset_a)) (exists ((Xs2 tptp.list_a)) (= (@ tptp.mset_a Xs2) X2))) (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (= (@ tptp.mset_list_a Xs) (@ tptp.mset_list_a Ys)) (= (@ tptp.size_s1427607542list_a Xs) (@ tptp.size_s1427607542list_a Ys)))) (forall ((Xs tptp.list_set_list_a) (Ys tptp.list_set_list_a)) (=> (= (@ tptp.mset_set_list_a Xs) (@ tptp.mset_set_list_a Ys)) (= (@ tptp.size_s1635937238list_a Xs) (@ tptp.size_s1635937238list_a Ys)))) (forall ((Xs tptp.list_set_set_a) (Ys tptp.list_set_set_a)) (=> (= (@ tptp.mset_set_set_a Xs) (@ tptp.mset_set_set_a Ys)) (= (@ tptp.size_s739728560_set_a Xs) (@ tptp.size_s739728560_set_a Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.mset_nat Xs) (@ tptp.mset_nat Ys)) (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (= (@ tptp.mset_a Xs) (@ tptp.mset_a Ys)) (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys)))) (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (=> (= (@ tptp.mset_set_a Xs) (@ tptp.mset_set_a Ys)) (= (@ tptp.size_size_list_set_a Xs) (@ tptp.size_size_list_set_a Ys)))) (forall ((F (-> tptp.nat tptp.nat)) (Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s1427607542list_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s1427607542list_a Ys))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1427607542list_a Xs)) (= (@ (@ tptp.nth_list_a Xs) I3) (@ (@ tptp.nth_list_a Ys) (@ F I3))))) (= (@ tptp.mset_list_a Xs) (@ tptp.mset_list_a Ys))))) (forall ((F (-> tptp.nat tptp.nat)) (Xs tptp.list_set_list_a) (Ys tptp.list_set_list_a)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s1635937238list_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s1635937238list_a Ys))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1635937238list_a Xs)) (= (@ (@ tptp.nth_set_list_a Xs) I3) (@ (@ tptp.nth_set_list_a Ys) (@ F I3))))) (= (@ tptp.mset_set_list_a Xs) (@ tptp.mset_set_list_a Ys))))) (forall ((F (-> tptp.nat tptp.nat)) (Xs tptp.list_set_set_a) (Ys tptp.list_set_set_a)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s739728560_set_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s739728560_set_a Ys))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s739728560_set_a Xs)) (= (@ (@ tptp.nth_set_set_a Xs) I3) (@ (@ tptp.nth_set_set_a Ys) (@ F I3))))) (= (@ tptp.mset_set_set_a Xs) (@ tptp.mset_set_set_a Ys))))) (forall ((F (-> tptp.nat tptp.nat)) (Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_nat Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_nat Ys))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I3) (@ (@ tptp.nth_nat Ys) (@ F I3))))) (= (@ tptp.mset_nat Xs) (@ tptp.mset_nat Ys))))) (forall ((F (-> tptp.nat tptp.nat)) (Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_a Ys))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a Xs) I3) (@ (@ tptp.nth_a Ys) (@ F I3))))) (= (@ tptp.mset_a Xs) (@ tptp.mset_a Ys))))) (forall ((F (-> tptp.nat tptp.nat)) (Xs tptp.list_set_a) (Ys tptp.list_set_a)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a Ys))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_set_a Xs)) (= (@ (@ tptp.nth_set_a Xs) I3) (@ (@ tptp.nth_set_a Ys) (@ F I3))))) (= (@ tptp.mset_set_a Xs) (@ tptp.mset_set_a Ys))))) (forall ((Ys tptp.list_set_list_a) (Xs tptp.list_set_set_list_a) (F (-> tptp.nat tptp.nat)) (Xs3 tptp.list_set_set_list_a)) (=> (@ (@ tptp.member101195155list_a Ys) (@ tptp.listset_set_list_a Xs)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s469631926list_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s469631926list_a Xs3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s469631926list_a Xs)) (= (@ (@ tptp.nth_set_set_list_a Xs3) I3) (@ (@ tptp.nth_set_set_list_a Xs) (@ F I3))))) (not (forall ((Ys2 tptp.list_set_list_a)) (=> (@ (@ tptp.member101195155list_a Ys2) (@ tptp.listset_set_list_a Xs3)) (=> (= (@ tptp.size_s1635937238list_a Ys2) (@ tptp.size_s1635937238list_a Ys)) (not (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1635937238list_a Ys)) (= (@ (@ tptp.nth_set_list_a Ys2) I2) (@ (@ tptp.nth_set_list_a Ys) (@ F I2)))))))))))))) (forall ((Ys tptp.list_set_set_a) (Xs tptp.list_set_set_set_a) (F (-> tptp.nat tptp.nat)) (Xs3 tptp.list_set_set_set_a)) (=> (@ (@ tptp.member814963949_set_a Ys) (@ tptp.listset_set_set_a Xs)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s726512144_set_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s726512144_set_a Xs3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s726512144_set_a Xs)) (= (@ (@ tptp.nth_set_set_set_a Xs3) I3) (@ (@ tptp.nth_set_set_set_a Xs) (@ F I3))))) (not (forall ((Ys2 tptp.list_set_set_a)) (=> (@ (@ tptp.member814963949_set_a Ys2) (@ tptp.listset_set_set_a Xs3)) (=> (= (@ tptp.size_s739728560_set_a Ys2) (@ tptp.size_s739728560_set_a Ys)) (not (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s739728560_set_a Ys)) (= (@ (@ tptp.nth_set_set_a Ys2) I2) (@ (@ tptp.nth_set_set_a Ys) (@ F I2)))))))))))))) (forall ((Ys tptp.list_nat) (Xs tptp.list_set_nat) (F (-> tptp.nat tptp.nat)) (Xs3 tptp.list_set_nat)) (=> (@ (@ tptp.member_list_nat Ys) (@ tptp.listset_nat Xs)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s577819178et_nat Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s577819178et_nat Xs3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s577819178et_nat Xs)) (= (@ (@ tptp.nth_set_nat Xs3) I3) (@ (@ tptp.nth_set_nat Xs) (@ F I3))))) (not (forall ((Ys2 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat Ys2) (@ tptp.listset_nat Xs3)) (=> (= (@ tptp.size_size_list_nat Ys2) (@ tptp.size_size_list_nat Ys)) (not (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Ys)) (= (@ (@ tptp.nth_nat Ys2) I2) (@ (@ tptp.nth_nat Ys) (@ F I2)))))))))))))) (forall ((Ys tptp.list_list_a) (Xs tptp.list_set_list_a) (F (-> tptp.nat tptp.nat)) (Xs3 tptp.list_set_list_a)) (=> (@ (@ tptp.member_list_list_a Ys) (@ tptp.listset_list_a Xs)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s1635937238list_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s1635937238list_a Xs3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1635937238list_a Xs)) (= (@ (@ tptp.nth_set_list_a Xs3) I3) (@ (@ tptp.nth_set_list_a Xs) (@ F I3))))) (not (forall ((Ys2 tptp.list_list_a)) (=> (@ (@ tptp.member_list_list_a Ys2) (@ tptp.listset_list_a Xs3)) (=> (= (@ tptp.size_s1427607542list_a Ys2) (@ tptp.size_s1427607542list_a Ys)) (not (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1427607542list_a Ys)) (= (@ (@ tptp.nth_list_a Ys2) I2) (@ (@ tptp.nth_list_a Ys) (@ F I2)))))))))))))) (forall ((Ys tptp.list_set_a) (Xs tptp.list_set_set_a) (F (-> tptp.nat tptp.nat)) (Xs3 tptp.list_set_set_a)) (=> (@ (@ tptp.member_list_set_a Ys) (@ tptp.listset_set_a Xs)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s739728560_set_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_s739728560_set_a Xs3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s739728560_set_a Xs)) (= (@ (@ tptp.nth_set_set_a Xs3) I3) (@ (@ tptp.nth_set_set_a Xs) (@ F I3))))) (not (forall ((Ys2 tptp.list_set_a)) (=> (@ (@ tptp.member_list_set_a Ys2) (@ tptp.listset_set_a Xs3)) (=> (= (@ tptp.size_size_list_set_a Ys2) (@ tptp.size_size_list_set_a Ys)) (not (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_set_a Ys)) (= (@ (@ tptp.nth_set_a Ys2) I2) (@ (@ tptp.nth_set_a Ys) (@ F I2)))))))))))))) (forall ((Ys tptp.list_a) (Xs tptp.list_set_a) (F (-> tptp.nat tptp.nat)) (Xs3 tptp.list_set_a)) (=> (@ (@ tptp.member_list_a Ys) (@ tptp.listset_a Xs)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a Xs3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_set_a Xs)) (= (@ (@ tptp.nth_set_a Xs3) I3) (@ (@ tptp.nth_set_a Xs) (@ F I3))))) (not (forall ((Ys2 tptp.list_a)) (=> (@ (@ tptp.member_list_a Ys2) (@ tptp.listset_a Xs3)) (=> (= (@ tptp.size_size_list_a Ys2) (@ tptp.size_size_list_a Ys)) (not (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_a Ys)) (= (@ (@ tptp.nth_a Ys2) I2) (@ (@ tptp.nth_a Ys) (@ F I2)))))))))))))) (@ (@ _let_21 _let_19) _let_16) (forall ((Xs tptp.list_list_a)) (= (@ tptp.size_s1427607542list_a (@ tptp.rev_list_a Xs)) (@ tptp.size_s1427607542list_a Xs))) (forall ((Xs tptp.list_set_list_a)) (= (@ tptp.size_s1635937238list_a (@ tptp.rev_set_list_a Xs)) (@ tptp.size_s1635937238list_a Xs))) (forall ((Xs tptp.list_set_set_a)) (= (@ tptp.size_s739728560_set_a (@ tptp.rev_set_set_a Xs)) (@ tptp.size_s739728560_set_a Xs))) (forall ((Xs tptp.list_nat)) (= (@ tptp.size_size_list_nat (@ tptp.rev_nat Xs)) (@ tptp.size_size_list_nat Xs))) (forall ((Xs tptp.list_a)) (= (@ tptp.size_size_list_a (@ tptp.rev_a Xs)) (@ tptp.size_size_list_a Xs))) (forall ((Xs tptp.list_set_a)) (= (@ tptp.size_size_list_set_a (@ tptp.rev_set_a Xs)) (@ tptp.size_size_list_set_a Xs))) (forall ((I tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ tptp.set_or1597314339et_nat K)) (@ (@ tptp.ord_less_set_nat I) K))) (forall ((I tptp.set_list_a) (K tptp.set_list_a)) (= (@ (@ tptp.member_set_list_a I) (@ tptp.set_or1578766727list_a K)) (@ (@ tptp.ord_less_set_list_a I) K))) (forall ((I tptp.set_a) (K tptp.set_a)) (= (@ (@ tptp.member_set_a I) (@ tptp.set_or1164043265_set_a K)) (@ (@ tptp.ord_less_set_a I) K))) (forall ((I tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I) K))) (forall ((Ys tptp.list_multiset_a) (Xs tptp.list_set_multiset_a)) (=> (= (@ tptp.size_s1657263798iset_a Ys) (@ tptp.size_s802269334iset_a Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s802269334iset_a Xs)) (@ (@ tptp.member_multiset_a (@ (@ tptp.nth_multiset_a Ys) I3)) (@ (@ tptp.nth_set_multiset_a Xs) I3)))) (@ (@ tptp.member518144627iset_a Ys) (@ tptp.listset_multiset_a Xs))))) (forall ((Ys tptp.list_list_list_a) (Xs tptp.list_set_list_list_a)) (=> (= (@ tptp.size_s575106428list_a Ys) (@ tptp.size_s240404444list_a Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s240404444list_a Xs)) (@ (@ tptp.member_list_list_a (@ (@ tptp.nth_list_list_a Ys) I3)) (@ (@ tptp.nth_set_list_list_a Xs) I3)))) (@ (@ tptp.member1511395513list_a Ys) (@ tptp.listset_list_list_a Xs))))) (forall ((Ys tptp.list_list_set_a) (Xs tptp.list_set_list_set_a)) (=> (= (@ tptp.size_s341332310_set_a Ys) (@ tptp.size_s926492982_set_a Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s926492982_set_a Xs)) (@ (@ tptp.member_list_set_a (@ (@ tptp.nth_list_set_a Ys) I3)) (@ (@ tptp.nth_set_list_set_a Xs) I3)))) (@ (@ tptp.member954073875_set_a Ys) (@ tptp.listset_list_set_a Xs))))) (forall ((Ys tptp.list_set_list_a) (Xs tptp.list_set_set_list_a)) (=> (= (@ tptp.size_s1635937238list_a Ys) (@ tptp.size_s469631926list_a Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s469631926list_a Xs)) (@ (@ tptp.member_set_list_a (@ (@ tptp.nth_set_list_a Ys) I3)) (@ (@ tptp.nth_set_set_list_a Xs) I3)))) (@ (@ tptp.member101195155list_a Ys) (@ tptp.listset_set_list_a Xs))))) (forall ((Ys tptp.list_set_set_a) (Xs tptp.list_set_set_set_a)) (=> (= (@ tptp.size_s739728560_set_a Ys) (@ tptp.size_s726512144_set_a Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s726512144_set_a Xs)) (@ (@ tptp.member_set_set_a (@ (@ tptp.nth_set_set_a Ys) I3)) (@ (@ tptp.nth_set_set_set_a Xs) I3)))) (@ (@ tptp.member814963949_set_a Ys) (@ tptp.listset_set_set_a Xs))))) (forall ((Ys tptp.list_nat) (Xs tptp.list_set_nat)) (=> (= (@ tptp.size_size_list_nat Ys) (@ tptp.size_s577819178et_nat Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s577819178et_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Ys) I3)) (@ (@ tptp.nth_set_nat Xs) I3)))) (@ (@ tptp.member_list_nat Ys) (@ tptp.listset_nat Xs))))) (forall ((Ys tptp.list_list_a) (Xs tptp.list_set_list_a)) (=> (= (@ tptp.size_s1427607542list_a Ys) (@ tptp.size_s1635937238list_a Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1635937238list_a Xs)) (@ (@ tptp.member_list_a (@ (@ tptp.nth_list_a Ys) I3)) (@ (@ tptp.nth_set_list_a Xs) I3)))) (@ (@ tptp.member_list_list_a Ys) (@ tptp.listset_list_a Xs))))) (forall ((Ys tptp.list_a) (Xs tptp.list_set_a)) (=> (= (@ tptp.size_size_list_a Ys) (@ tptp.size_size_list_set_a Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_set_a Xs)) (@ (@ tptp.member_a (@ (@ tptp.nth_a Ys) I3)) (@ (@ tptp.nth_set_a Xs) I3)))) (@ (@ tptp.member_list_a Ys) (@ tptp.listset_a Xs))))) (forall ((Ys tptp.list_set_a) (Xs tptp.list_set_set_a)) (=> (= (@ tptp.size_size_list_set_a Ys) (@ tptp.size_s739728560_set_a Xs)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s739728560_set_a Xs)) (@ (@ tptp.member_set_a (@ (@ tptp.nth_set_a Ys) I3)) (@ (@ tptp.nth_set_set_a Xs) I3)))) (@ (@ tptp.member_list_set_a Ys) (@ tptp.listset_set_a Xs))))) (= _let_20 _let_18) (@ (@ (@ tptp.bij_betw_nat_nat tptp.f) _let_16) _let_19) (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (= (@ tptp.size_s1427607542list_a Xs) (@ tptp.size_s1427607542list_a Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1427607542list_a Xs)) (= (@ (@ tptp.nth_list_a Xs) I3) (@ (@ tptp.nth_list_a Ys) I3)))) (= Xs Ys)))) (forall ((Xs tptp.list_set_list_a) (Ys tptp.list_set_list_a)) (=> (= (@ tptp.size_s1635937238list_a Xs) (@ tptp.size_s1635937238list_a Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1635937238list_a Xs)) (= (@ (@ tptp.nth_set_list_a Xs) I3) (@ (@ tptp.nth_set_list_a Ys) I3)))) (= Xs Ys)))) (forall ((Xs tptp.list_set_set_a) (Ys tptp.list_set_set_a)) (=> (= (@ tptp.size_s739728560_set_a Xs) (@ tptp.size_s739728560_set_a Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s739728560_set_a Xs)) (= (@ (@ tptp.nth_set_set_a Xs) I3) (@ (@ tptp.nth_set_set_a Ys) I3)))) (= Xs Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I3) (@ (@ tptp.nth_nat Ys) I3)))) (= Xs Ys)))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a Xs) I3) (@ (@ tptp.nth_a Ys) I3)))) (= Xs Ys)))) (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (=> (= (@ tptp.size_size_list_set_a Xs) (@ tptp.size_size_list_set_a Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_set_a Xs)) (= (@ (@ tptp.nth_set_a Xs) I3) (@ (@ tptp.nth_set_a Ys) I3)))) (= Xs Ys)))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.list_a Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X3 tptp.list_a)) (@ (@ P I4) X3)))) (exists ((Xs4 tptp.list_list_a)) (and (= (@ tptp.size_s1427607542list_a Xs4) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_list_a Xs4) I4)))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.set_list_a Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X3 tptp.set_list_a)) (@ (@ P I4) X3)))) (exists ((Xs4 tptp.list_set_list_a)) (and (= (@ tptp.size_s1635937238list_a Xs4) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_set_list_a Xs4) I4)))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.set_set_a Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X3 tptp.set_set_a)) (@ (@ P I4) X3)))) (exists ((Xs4 tptp.list_set_set_a)) (and (= (@ tptp.size_s739728560_set_a Xs4) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_set_set_a Xs4) I4)))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X3 tptp.nat)) (@ (@ P I4) X3)))) (exists ((Xs4 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs4) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_nat Xs4) I4)))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.a Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X3 tptp.a)) (@ (@ P I4) X3)))) (exists ((Xs4 tptp.list_a)) (and (= (@ tptp.size_size_list_a Xs4) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_a Xs4) I4)))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.set_a Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X3 tptp.set_a)) (@ (@ P I4) X3)))) (exists ((Xs4 tptp.list_set_a)) (and (= (@ tptp.size_size_list_set_a Xs4) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_set_a Xs4) I4)))))))) (= (lambda ((Y2 tptp.list_list_a) (Z tptp.list_list_a)) (= Y2 Z)) (lambda ((Xs4 tptp.list_list_a) (Ys3 tptp.list_list_a)) (and (= (@ tptp.size_s1427607542list_a Xs4) (@ tptp.size_s1427607542list_a Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s1427607542list_a Xs4)) (= (@ (@ tptp.nth_list_a Xs4) I4) (@ (@ tptp.nth_list_a Ys3) I4))))))) (= (lambda ((Y2 tptp.list_set_list_a) (Z tptp.list_set_list_a)) (= Y2 Z)) (lambda ((Xs4 tptp.list_set_list_a) (Ys3 tptp.list_set_list_a)) (and (= (@ tptp.size_s1635937238list_a Xs4) (@ tptp.size_s1635937238list_a Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s1635937238list_a Xs4)) (= (@ (@ tptp.nth_set_list_a Xs4) I4) (@ (@ tptp.nth_set_list_a Ys3) I4))))))) (= (lambda ((Y2 tptp.list_set_set_a) (Z tptp.list_set_set_a)) (= Y2 Z)) (lambda ((Xs4 tptp.list_set_set_a) (Ys3 tptp.list_set_set_a)) (and (= (@ tptp.size_s739728560_set_a Xs4) (@ tptp.size_s739728560_set_a Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s739728560_set_a Xs4)) (= (@ (@ tptp.nth_set_set_a Xs4) I4) (@ (@ tptp.nth_set_set_a Ys3) I4))))))) (= (lambda ((Y2 tptp.list_nat) (Z tptp.list_nat)) (= Y2 Z)) (lambda ((Xs4 tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs4) (@ tptp.size_size_list_nat Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs4)) (= (@ (@ tptp.nth_nat Xs4) I4) (@ (@ tptp.nth_nat Ys3) I4))))))) (= (lambda ((Y2 tptp.list_a) (Z tptp.list_a)) (= Y2 Z)) (lambda ((Xs4 tptp.list_a) (Ys3 tptp.list_a)) (and (= (@ tptp.size_size_list_a Xs4) (@ tptp.size_size_list_a Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_a Xs4)) (= (@ (@ tptp.nth_a Xs4) I4) (@ (@ tptp.nth_a Ys3) I4))))))) (= (lambda ((Y2 tptp.list_set_a) (Z tptp.list_set_a)) (= Y2 Z)) (lambda ((Xs4 tptp.list_set_a) (Ys3 tptp.list_set_a)) (and (= (@ tptp.size_size_list_set_a Xs4) (@ tptp.size_size_list_set_a Ys3)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_set_a Xs4)) (= (@ (@ tptp.nth_set_a Xs4) I4) (@ (@ tptp.nth_set_a Ys3) I4))))))) (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat X4) (@ tptp.set_ord_lessThan_nat Y3)) (= X4 Y3))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= (@ tptp.rev_a Xs) (@ tptp.rev_a Ys)) (= Xs Ys))) (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (= (= (@ tptp.rev_set_a Xs) (@ tptp.rev_set_a Ys)) (= Xs Ys))) (forall ((Xs tptp.list_a)) (= (@ tptp.rev_a (@ tptp.rev_a Xs)) Xs)) (forall ((Xs tptp.list_set_a)) (= (@ tptp.rev_set_a (@ tptp.rev_set_a Xs)) Xs)) (= _let_18 _let_15) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a tptp.ss1)) (= (@ (@ tptp.nth_set_a tptp.ss2) I) (@ (@ tptp.nth_set_a tptp.ss1) (@ tptp.g I))))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a tptp.ss2)) (= (@ (@ tptp.nth_set_a tptp.ss1) I) (@ (@ tptp.nth_set_a tptp.ss2) (@ tptp.f I))))) (not (forall ((F2 (-> tptp.nat tptp.nat))) (=> (@ (@ (@ tptp.bij_betw_nat_nat F2) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a tptp.ss2))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a tptp.ss1))) (not (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_set_a tptp.ss2)) (= (@ (@ tptp.nth_set_a tptp.ss1) I2) (@ (@ tptp.nth_set_a tptp.ss2) (@ F2 I2))))))))) (exists ((F2 (-> tptp.nat tptp.nat))) (and (@ (@ (@ tptp.bij_betw_nat_nat F2) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a tptp.ss1))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_set_a tptp.ss2))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_set_a tptp.ss1)) (= (@ (@ tptp.nth_set_a tptp.ss1) I2) (@ (@ tptp.nth_set_a tptp.ss2) (@ F2 I2))))))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a tptp.ss1)) (= (@ tptp.f (@ tptp.g I)) I))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a tptp.ss2)) (= (@ tptp.g (@ tptp.f I)) I))) (forall ((Ys tptp.list_set_set_a) (Xs tptp.list_set_set_set_a) (I tptp.nat)) (=> (@ (@ tptp.member814963949_set_a Ys) (@ tptp.listset_set_set_a Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s726512144_set_a Xs)) (@ (@ tptp.member_set_set_a (@ (@ tptp.nth_set_set_a Ys) I)) (@ (@ tptp.nth_set_set_set_a Xs) I))))) (forall ((Ys tptp.list_set_list_a) (Xs tptp.list_set_set_list_a) (I tptp.nat)) (=> (@ (@ tptp.member101195155list_a Ys) (@ tptp.listset_set_list_a Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s469631926list_a Xs)) (@ (@ tptp.member_set_list_a (@ (@ tptp.nth_set_list_a Ys) I)) (@ (@ tptp.nth_set_set_list_a Xs) I))))) (forall ((Ys tptp.list_multiset_a) (Xs tptp.list_set_multiset_a) (I tptp.nat)) (=> (@ (@ tptp.member518144627iset_a Ys) (@ tptp.listset_multiset_a Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s802269334iset_a Xs)) (@ (@ tptp.member_multiset_a (@ (@ tptp.nth_multiset_a Ys) I)) (@ (@ tptp.nth_set_multiset_a Xs) I))))) (forall ((Ys tptp.list_list_list_a) (Xs tptp.list_set_list_list_a) (I tptp.nat)) (=> (@ (@ tptp.member1511395513list_a Ys) (@ tptp.listset_list_list_a Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s240404444list_a Xs)) (@ (@ tptp.member_list_list_a (@ (@ tptp.nth_list_list_a Ys) I)) (@ (@ tptp.nth_set_list_list_a Xs) I))))) (forall ((Ys tptp.list_list_set_a) (Xs tptp.list_set_list_set_a) (I tptp.nat)) (=> (@ (@ tptp.member954073875_set_a Ys) (@ tptp.listset_list_set_a Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s926492982_set_a Xs)) (@ (@ tptp.member_list_set_a (@ (@ tptp.nth_list_set_a Ys) I)) (@ (@ tptp.nth_set_list_set_a Xs) I))))) (forall ((Ys tptp.list_nat) (Xs tptp.list_set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_list_nat Ys) (@ tptp.listset_nat Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s577819178et_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Ys) I)) (@ (@ tptp.nth_set_nat Xs) I))))) (forall ((Ys tptp.list_set_a) (Xs tptp.list_set_set_a) (I tptp.nat)) (=> (@ (@ tptp.member_list_set_a Ys) (@ tptp.listset_set_a Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s739728560_set_a Xs)) (@ (@ tptp.member_set_a (@ (@ tptp.nth_set_a Ys) I)) (@ (@ tptp.nth_set_set_a Xs) I))))) (forall ((Ys tptp.list_list_a) (Xs tptp.list_set_list_a) (I tptp.nat)) (=> (@ (@ tptp.member_list_list_a Ys) (@ tptp.listset_list_a Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1635937238list_a Xs)) (@ (@ tptp.member_list_a (@ (@ tptp.nth_list_a Ys) I)) (@ (@ tptp.nth_set_list_a Xs) I))))) (forall ((Ys tptp.list_a) (Xs tptp.list_set_a) (I tptp.nat)) (=> (@ (@ tptp.member_list_a Ys) (@ tptp.listset_a Xs)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a Xs)) (@ (@ tptp.member_a (@ (@ tptp.nth_a Ys) I)) (@ (@ tptp.nth_set_a Xs) I))))) (forall ((Xs tptp.list_list_a) (Ys tptp.list_list_a)) (=> (not (= (@ tptp.size_s1427607542list_a Xs) (@ tptp.size_s1427607542list_a Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_set_list_a) (Ys tptp.list_set_list_a)) (=> (not (= (@ tptp.size_s1635937238list_a Xs) (@ tptp.size_s1635937238list_a Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_set_set_a) (Ys tptp.list_set_set_a)) (=> (not (= (@ tptp.size_s739728560_set_a Xs) (@ tptp.size_s739728560_set_a Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (not (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (=> (not (= (@ tptp.size_size_list_set_a Xs) (@ tptp.size_size_list_set_a Ys))) (not (= Xs Ys)))) (forall ((A2 tptp.multiset_a) (P (-> tptp.multiset_a Bool))) (= (@ (@ tptp.member_multiset_a A2) (@ tptp.collect_multiset_a P)) (@ P A2))) (forall ((A2 tptp.list_list_a) (P (-> tptp.list_list_a Bool))) (= (@ (@ tptp.member_list_list_a A2) (@ tptp.collect_list_list_a P)) (@ P A2))) (forall ((A2 tptp.list_set_a) (P (-> tptp.list_set_a Bool))) (= (@ (@ tptp.member_list_set_a A2) (@ tptp.collect_list_set_a P)) (@ P A2))) (forall ((A2 tptp.set_a) (P (-> tptp.set_a Bool))) (= (@ (@ tptp.member_set_a A2) (@ tptp.collect_set_a P)) (@ P A2))) (forall ((A2 tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A2) (@ tptp.collect_nat P)) (@ P A2))) (forall ((A2 tptp.a) (P (-> tptp.a Bool))) (= (@ (@ tptp.member_a A2) (@ tptp.collect_a P)) (@ P A2))) (forall ((A2 tptp.list_a) (P (-> tptp.list_a Bool))) (= (@ (@ tptp.member_list_a A2) (@ tptp.collect_list_a P)) (@ P A2))) (forall ((A tptp.set_multiset_a)) (= (@ tptp.collect_multiset_a (lambda ((X5 tptp.multiset_a)) (@ (@ tptp.member_multiset_a X5) A))) A)) (forall ((A tptp.set_list_list_a)) (= (@ tptp.collect_list_list_a (lambda ((X5 tptp.list_list_a)) (@ (@ tptp.member_list_list_a X5) A))) A)) (forall ((A tptp.set_list_set_a)) (= (@ tptp.collect_list_set_a (lambda ((X5 tptp.list_set_a)) (@ (@ tptp.member_list_set_a X5) A))) A)) (forall ((A tptp.set_set_a)) (= (@ tptp.collect_set_a (lambda ((X5 tptp.set_a)) (@ (@ tptp.member_set_a X5) A))) A)) (forall ((A tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X5 tptp.nat)) (@ (@ tptp.member_nat X5) A))) A)) (forall ((A tptp.set_a)) (= (@ tptp.collect_a (lambda ((X5 tptp.a)) (@ (@ tptp.member_a X5) A))) A)) (forall ((A tptp.set_list_a)) (= (@ tptp.collect_list_a (lambda ((X5 tptp.list_a)) (@ (@ tptp.member_list_a X5) A))) A)) (forall ((P (-> tptp.list_a Bool)) (Q (-> tptp.list_a Bool))) (=> (forall ((X6 tptp.list_a)) (= (@ P X6) (@ Q X6))) (= (@ tptp.collect_list_a P) (@ tptp.collect_list_a Q)))) (forall ((P (-> tptp.a Bool)) (Q (-> tptp.a Bool))) (=> (forall ((X6 tptp.a)) (= (@ P X6) (@ Q X6))) (= (@ tptp.collect_a P) (@ tptp.collect_a Q)))) (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_list_a)) (= (@ tptp.size_s1427607542list_a Xs2) N))) (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_set_list_a)) (= (@ tptp.size_s1635937238list_a Xs2) N))) (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_set_set_a)) (= (@ tptp.size_s739728560_set_a Xs2) N))) (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs2) N))) (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_a)) (= (@ tptp.size_size_list_a Xs2) N))) (forall ((N tptp.nat)) (exists ((Xs2 tptp.list_set_a)) (= (@ tptp.size_size_list_set_a Xs2) N))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= (@ tptp.rev_a Xs) Ys) (= Xs (@ tptp.rev_a Ys)))) (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (= (= (@ tptp.rev_set_a Xs) Ys) (= Xs (@ tptp.rev_set_a Ys)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M)) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((P (-> tptp.list_set_list_a Bool)) (Xs tptp.list_set_list_a)) (=> (forall ((Xs2 tptp.list_set_list_a)) (=> (forall ((Ys4 tptp.list_set_list_a)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s1635937238list_a Ys4)) (@ tptp.size_s1635937238list_a Xs2)) (@ P Ys4))) (@ P Xs2))) (@ P Xs))) (forall ((P (-> tptp.list_set_set_a Bool)) (Xs tptp.list_set_set_a)) (=> (forall ((Xs2 tptp.list_set_set_a)) (=> (forall ((Ys4 tptp.list_set_set_a)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s739728560_set_a Ys4)) (@ tptp.size_s739728560_set_a Xs2)) (@ P Ys4))) (@ P Xs2))) (@ P Xs))) (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs2 tptp.list_nat)) (=> (forall ((Ys4 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys4)) (@ tptp.size_size_list_nat Xs2)) (@ P Ys4))) (@ P Xs2))) (@ P Xs))) (forall ((P (-> tptp.list_a Bool)) (Xs tptp.list_a)) (=> (forall ((Xs2 tptp.list_a)) (=> (forall ((Ys4 tptp.list_a)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_a Ys4)) (@ tptp.size_size_list_a Xs2)) (@ P Ys4))) (@ P Xs2))) (@ P Xs))) (forall ((P (-> tptp.list_set_a Bool)) (Xs tptp.list_set_a)) (=> (forall ((Xs2 tptp.list_set_a)) (=> (forall ((Ys4 tptp.list_set_a)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_set_a Ys4)) (@ tptp.size_size_list_set_a Xs2)) (@ P Ys4))) (@ P Xs2))) (@ P Xs))) (forall ((Ys tptp.list_a) (Xs tptp.list_set_a)) (=> (@ (@ tptp.member_list_a Ys) (@ tptp.listset_a Xs)) (= (@ tptp.size_size_list_a Ys) (@ tptp.size_size_list_set_a Xs)))) (forall ((Ys tptp.list_set_a) (Xs tptp.list_set_set_a)) (=> (@ (@ tptp.member_list_set_a Ys) (@ tptp.listset_set_a Xs)) (= (@ tptp.size_size_list_set_a Ys) (@ tptp.size_s739728560_set_a Xs)))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ tptp.perm_a Xs) Ys) (exists ((F2 (-> tptp.nat tptp.nat))) (and (@ (@ (@ tptp.bij_betw_nat_nat F2) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_a Xs))) (@ tptp.set_ord_lessThan_nat (@ tptp.size_size_list_a Ys))) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a Xs) I2) (@ (@ tptp.nth_a Ys) (@ F2 I2))))))))) (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (=> (@ (@ tptp.perm_set_a Xs) Ys) (exists ((F2 (-> tptp.nat tptp.nat))) (and (@ (@ (@ tptp.bij_betw_nat_nat F2) (@ 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tptp.list_a) (A tptp.set_list_a)) (=> (= B (@ F X4)) (=> (@ (@ tptp.member_list_a X4) A) (@ (@ tptp.member_list_a B) (@ (@ tptp.image_list_a_list_a F) A))))) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (= (= (@ tptp.mset_a Xs) (@ tptp.mset_a Ys)) (@ (@ tptp.perm_a Xs) Ys))) (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (= (= (@ tptp.mset_set_a Xs) (@ tptp.mset_set_a Ys)) (@ (@ tptp.perm_set_a Xs) Ys))) (forall ((Xs tptp.list_set_a)) (@ (@ tptp.perm_set_a (@ tptp.rev_set_a Xs)) Xs)) (forall ((Xs tptp.list_a) (Ys tptp.list_a)) (=> (@ (@ tptp.perm_a Xs) Ys) (= (@ tptp.size_size_list_a Xs) (@ tptp.size_size_list_a Ys)))) (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (=> (@ (@ tptp.perm_set_a Xs) Ys) (= (@ tptp.size_size_list_set_a Xs) (@ tptp.size_size_list_set_a Ys)))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) B2) (= (@ (@ tptp.image_nat_nat F) A) B2))) (forall ((X4 tptp.list_a) (A tptp.set_list_a) (Y3 tptp.list_a)) (=> (@ (@ tptp.member_list_a X4) A) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_a X4)) (@ tptp.size_size_list_a Y3)) (not (= X4 Y3))))) (forall ((X4 tptp.list_set_a) (A tptp.set_list_set_a) (Y3 tptp.list_set_a)) (=> (@ (@ tptp.member_list_set_a X4) A) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_set_a X4)) (@ tptp.size_size_list_set_a Y3)) (not (= X4 Y3))))) (forall ((Xs tptp.list_a)) (= (@ tptp.size_size_multiset_a (@ tptp.mset_a Xs)) (@ tptp.size_size_list_a Xs))) (forall ((Xs tptp.list_set_a)) (= (@ tptp.size_s657334288_set_a (@ tptp.mset_set_a Xs)) (@ tptp.size_size_list_set_a Xs))) (forall ((A tptp.set_a) (B2 tptp.set_a) (C tptp.a)) (let ((_let_1 (@ tptp.member_a C))) (=> (@ (@ tptp.ord_less_set_a A) B2) (=> (@ _let_1 A) (@ _let_1 B2))))) (forall ((A tptp.set_list_a) (B2 tptp.set_list_a) (C tptp.list_a)) (let ((_let_1 (@ tptp.member_list_a C))) (=> (@ (@ tptp.ord_less_set_list_a A) B2) (=> (@ _let_1 A) (@ _let_1 B2))))) (forall ((X4 tptp.a) (A tptp.set_a) (F (-> tptp.a tptp.a))) (=> (@ (@ tptp.member_a X4) A) (@ (@ tptp.member_a (@ F X4)) (@ (@ tptp.image_a_a F) A)))) (forall ((X4 tptp.a) (A tptp.set_a) (F (-> tptp.a tptp.list_a))) (=> (@ (@ tptp.member_a X4) A) (@ (@ tptp.member_list_a (@ F X4)) (@ (@ tptp.image_a_list_a F) A)))) (forall ((X4 tptp.list_a) (A tptp.set_list_a) (F (-> tptp.list_a tptp.a))) (=> (@ (@ tptp.member_list_a X4) A) (@ (@ tptp.member_a (@ F X4)) (@ (@ tptp.image_list_a_a F) A)))) (forall ((X4 tptp.list_a) (A tptp.set_list_a) (F (-> tptp.list_a tptp.list_a))) (=> (@ (@ tptp.member_list_a X4) A) (@ (@ tptp.member_list_a (@ F X4)) (@ (@ tptp.image_list_a_list_a F) A)))) (forall ((X4 tptp.a) (A tptp.set_a) (B tptp.a) (F (-> tptp.a tptp.a))) (=> (@ (@ tptp.member_a X4) A) (=> (= B (@ F X4)) (@ (@ tptp.member_a B) (@ (@ tptp.image_a_a F) A))))) (forall ((X4 tptp.a) (A tptp.set_a) (B tptp.list_a) (F (-> tptp.a tptp.list_a))) (=> (@ (@ tptp.member_a X4) A) (=> (= B (@ F X4)) (@ (@ tptp.member_list_a B) (@ (@ tptp.image_a_list_a F) A))))) (forall ((X4 tptp.list_a) (A tptp.set_list_a) (B tptp.a) (F (-> tptp.list_a tptp.a))) (=> (@ (@ tptp.member_list_a X4) A) (=> (= B (@ F X4)) (@ (@ tptp.member_a B) (@ (@ tptp.image_list_a_a F) A))))) (forall ((X4 tptp.list_a) (A tptp.set_list_a) (B tptp.list_a) (F (-> tptp.list_a tptp.list_a))) (=> (@ (@ tptp.member_list_a X4) A) (=> (= B (@ F X4)) (@ (@ tptp.member_list_a B) (@ (@ tptp.image_list_a_list_a F) A))))) _let_14 (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) B2) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) A) (@ (@ tptp.member_nat (@ F X)) B2))))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) B2) (exists ((G (-> tptp.nat tptp.nat))) (@ (@ (@ tptp.bij_betw_nat_nat G) B2) A)))) (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G2 (-> tptp.nat tptp.nat)) (A5 tptp.set_nat)) (=> (forall ((A3 tptp.nat)) (=> (@ (@ tptp.member_nat A3) A) (= (@ F A3) (@ G2 A3)))) (= (@ (@ (@ tptp.bij_betw_nat_nat F) A) A5) (@ (@ (@ tptp.bij_betw_nat_nat G2) A) A5)))) (forall ((F (-> tptp.a tptp.a)) (A tptp.set_a) (B2 tptp.set_a) (A2 tptp.a)) (=> (@ (@ (@ tptp.bij_betw_a_a F) A) B2) (=> (@ (@ tptp.member_a A2) A) (@ (@ tptp.member_a (@ F A2)) B2)))) (forall ((F (-> tptp.a tptp.list_a)) (A tptp.set_a) (B2 tptp.set_list_a) (A2 tptp.a)) (=> (@ (@ (@ tptp.bij_betw_a_list_a F) A) B2) (=> (@ (@ tptp.member_a A2) A) (@ (@ tptp.member_list_a (@ F A2)) B2)))) (forall ((F (-> tptp.list_a tptp.a)) (A tptp.set_list_a) (B2 tptp.set_a) (A2 tptp.list_a)) (=> (@ (@ (@ tptp.bij_betw_list_a_a F) A) B2) (=> (@ (@ tptp.member_list_a A2) A) (@ (@ tptp.member_a (@ F A2)) B2)))) (forall ((F (-> tptp.list_a tptp.list_a)) (A tptp.set_list_a) (B2 tptp.set_list_a) (A2 tptp.list_a)) (=> (@ (@ (@ tptp.bij_be94573046list_a F) A) B2) (=> (@ (@ tptp.member_list_a A2) A) (@ (@ tptp.member_list_a (@ F A2)) B2)))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B2 tptp.set_nat) (A2 tptp.nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) B2) (=> (@ (@ tptp.member_nat A2) A) (@ (@ tptp.member_nat (@ F A2)) B2)))) _let_13 _let_12 _let_11 _let_10 _let_9 (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (=> (@ (@ tptp.perm_set_a Xs) Ys) (@ (@ tptp.perm_set_a Ys) Xs))) (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a) (Zs tptp.list_set_a)) (let ((_let_1 (@ tptp.perm_set_a Xs))) (=> (@ _let_1 Ys) (=> (@ (@ tptp.perm_set_a Ys) Zs) (@ _let_1 Zs))))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (A5 tptp.set_nat) (A6 tptp.nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) A5) (=> (@ (@ tptp.member_nat A6) A5) (= (@ F (@ (@ (@ tptp.hilber815131374at_nat A) F) A6)) A6)))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (A5 tptp.set_nat) (A2 tptp.nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) A5) (=> (@ (@ tptp.member_nat A2) A) (= (@ (@ (@ tptp.hilber815131374at_nat A) F) (@ F A2)) A2)))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (A5 tptp.set_nat) (A2 tptp.nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) A5) (=> (@ (@ tptp.member_nat A2) A) (= (@ (@ (@ tptp.hilber815131374at_nat A5) (@ (@ tptp.hilber815131374at_nat A) F)) A2) (@ F A2))))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) B2) (@ (@ (@ tptp.bij_betw_nat_nat (@ (@ tptp.hilber815131374at_nat A) F)) B2) A))) (forall ((A tptp.set_nat) (F (-> tptp.nat tptp.nat)) (X4 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.image_nat_nat F) A))) (let ((_let_2 (@ (@ tptp.hilber815131374at_nat A) F))) (=> (= (@ _let_2 X4) (@ _let_2 Y3)) (=> (@ (@ tptp.member_nat X4) _let_1) (=> (@ (@ tptp.member_nat Y3) _let_1) (= X4 Y3))))))) (forall ((X4 tptp.a) (F (-> tptp.a tptp.a)) (A tptp.set_a)) (=> (@ (@ tptp.member_a X4) (@ (@ tptp.image_a_a F) A)) (@ (@ tptp.member_a (@ (@ (@ tptp.hilbert_inv_into_a_a A) F) X4)) A))) (forall ((X4 tptp.a) (F (-> tptp.list_a tptp.a)) (A tptp.set_list_a)) (=> (@ (@ tptp.member_a X4) (@ (@ tptp.image_list_a_a F) A)) (@ (@ tptp.member_list_a (@ (@ (@ tptp.hilber2125729734st_a_a A) F) X4)) A))) (forall ((X4 tptp.list_a) (F (-> tptp.a tptp.list_a)) (A tptp.set_a)) (=> (@ (@ tptp.member_list_a X4) (@ (@ tptp.image_a_list_a F) A)) (@ (@ tptp.member_a (@ (@ (@ tptp.hilber165648082list_a A) F) X4)) A))) (forall ((X4 tptp.list_a) (F (-> tptp.list_a tptp.list_a)) (A tptp.set_list_a)) (=> (@ (@ tptp.member_list_a X4) (@ (@ tptp.image_list_a_list_a F) A)) (@ (@ tptp.member_list_a (@ (@ (@ tptp.hilber921249868list_a A) F) X4)) A))) (forall ((X4 tptp.nat) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.image_nat_nat F) A)) (@ (@ tptp.member_nat (@ (@ (@ tptp.hilber815131374at_nat A) F) X4)) A))) (forall ((Y3 tptp.nat) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ (@ tptp.member_nat Y3) (@ (@ tptp.image_nat_nat F) A)) (= (@ F (@ (@ (@ tptp.hilber815131374at_nat A) F) Y3)) Y3))) _let_8 _let_7 (forall ((Ss tptp.list_set_a) (A tptp.set_a)) (let ((_let_1 (@ tptp.listset_a Ss))) (=> (@ (@ tptp.inj_on_list_a_a tptp.groups1792256535list_a) _let_1) (=> (= (@ (@ tptp.image_list_a_a tptp.groups1792256535list_a) _let_1) A) (@ (@ tptp.hilber2037636820comp_a A) Ss))))) (forall ((K tptp.nat) (Ns tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat K) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.nth_nat Ns) K)) (@ tptp.groups921905271st_nat Ns)))) (forall ((I tptp.nat) (Xs tptp.list_a) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_a Xs))) (let ((_let_2 (@ tptp.size_size_list_a Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (@ (@ tptp.perm_a (@ (@ (@ tptp.list_update_a (@ (@ (@ tptp.list_update_a Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) Xs)))))) (forall ((I tptp.nat) (Xs tptp.list_set_a) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_set_a Xs))) (let ((_let_2 (@ tptp.size_size_list_set_a Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (@ (@ tptp.perm_set_a (@ (@ (@ tptp.list_update_set_a (@ (@ (@ tptp.list_update_set_a Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) Xs)))))) (forall ((I tptp.nat) (Ls tptp.list_a) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_a Ls))) (let ((_let_2 (@ tptp.size_size_list_a Ls))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.mset_a (@ (@ (@ tptp.list_update_a (@ (@ (@ tptp.list_update_a Ls) J) (@ _let_1 I))) I) (@ _let_1 J))) (@ tptp.mset_a Ls))))))) (forall ((I tptp.nat) (Ls tptp.list_set_a) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_set_a Ls))) (let ((_let_2 (@ tptp.size_size_list_set_a Ls))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.mset_set_a (@ (@ (@ tptp.list_update_set_a (@ (@ (@ tptp.list_update_set_a Ls) J) (@ _let_1 I))) I) (@ _let_1 J))) (@ tptp.mset_set_a Ls))))))) (forall ((I tptp.nat) (Ls tptp.list_list_a)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_s1427607542list_a Ls)) (@ (@ tptp.member_list_a (@ (@ tptp.nth_list_a Ls) I)) (@ tptp.set_mset_list_a (@ tptp.mset_list_a Ls))))) (forall ((I tptp.nat) (Ls tptp.list_a)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_a Ls)) (@ (@ tptp.member_a (@ (@ tptp.nth_a Ls) I)) (@ tptp.set_mset_a (@ tptp.mset_a Ls))))) (forall ((I tptp.nat) (Ls tptp.list_set_a)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a Ls)) (@ (@ tptp.member_set_a (@ (@ tptp.nth_set_a Ls) I)) (@ tptp.set_mset_set_a (@ tptp.mset_set_a Ls))))) (forall ((X4 tptp.a) (MM tptp.multiset_multiset_a)) (= (@ (@ tptp.member_a X4) (@ tptp.set_mset_a (@ tptp.comm_m2145643721iset_a MM))) (exists ((M2 tptp.multiset_a)) (and (@ (@ tptp.member_multiset_a M2) (@ tptp.set_mset_multiset_a MM)) (@ (@ tptp.member_a X4) (@ tptp.set_mset_a M2)))))) (forall ((X4 tptp.list_a) (MM tptp.multis971982480list_a)) (= (@ (@ tptp.member_list_a X4) (@ tptp.set_mset_list_a (@ tptp.comm_m324867663list_a MM))) (exists ((M2 tptp.multiset_list_a)) (and (@ (@ tptp.member528267379list_a M2) (@ tptp.set_ms1660427399list_a MM)) (@ (@ tptp.member_list_a X4) (@ tptp.set_mset_list_a M2)))))) (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X4)) (@ tptp.set_ord_lessThan_nat Y3)) (@ (@ tptp.ord_less_eq_nat X4) Y3))) (forall ((Xs tptp.list_a) (I tptp.nat) (X4 tptp.a)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_a Xs)) I) (= (@ (@ (@ tptp.list_update_a Xs) I) X4) Xs))) (forall ((Xs tptp.list_set_a) (I tptp.nat) (X4 tptp.set_a)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_set_a Xs)) I) (= (@ (@ (@ tptp.list_update_set_a Xs) I) X4) Xs))) (forall ((Xs tptp.list_a) (I tptp.nat) (X4 tptp.a)) (= (@ tptp.size_size_list_a (@ (@ (@ tptp.list_update_a Xs) I) X4)) (@ tptp.size_size_list_a Xs))) (forall ((Xs tptp.list_set_a) (I tptp.nat) (X4 tptp.set_a)) (= (@ tptp.size_size_list_set_a (@ (@ (@ tptp.list_update_set_a Xs) I) X4)) (@ tptp.size_size_list_set_a Xs))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (X4 tptp.nat)) (=> (@ (@ tptp.inj_on_nat_nat F) A) (=> (@ (@ tptp.member_nat X4) A) (= (@ (@ (@ tptp.hilber815131374at_nat A) F) (@ F X4)) X4)))) (forall ((Xs tptp.list_a) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_a Xs) I) (@ (@ tptp.nth_a Xs) I)) Xs)) (forall ((Xs tptp.list_set_a) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_set_a Xs) I) (@ (@ tptp.nth_set_a Xs) I)) Xs)) (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_a) (X4 tptp.a)) (=> (not (= I J)) (= (@ (@ tptp.nth_a (@ (@ (@ tptp.list_update_a Xs) I) X4)) J) (@ (@ tptp.nth_a Xs) J)))) (forall ((I tptp.nat) (J tptp.nat) (Xs tptp.list_set_a) (X4 tptp.set_a)) (=> (not (= I J)) (= (@ (@ tptp.nth_set_a (@ (@ (@ tptp.list_update_set_a Xs) I) X4)) J) (@ (@ tptp.nth_set_a Xs) J)))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (S tptp.set_nat)) (=> (@ (@ tptp.inj_on_nat_nat F) A) (=> (@ (@ tptp.ord_less_eq_set_nat S) A) (= (@ (@ tptp.image_nat_nat (@ (@ tptp.hilber815131374at_nat A) F)) (@ (@ tptp.image_nat_nat F) S)) S)))) (forall ((I tptp.nat) (Xs tptp.list_a) (X4 tptp.a)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_a Xs)) (= (@ (@ tptp.nth_a (@ (@ (@ tptp.list_update_a Xs) I) X4)) I) X4))) (forall ((I tptp.nat) (Xs tptp.list_set_a) (X4 tptp.set_a)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a Xs)) (= (@ (@ tptp.nth_set_a (@ (@ (@ tptp.list_update_set_a Xs) I) X4)) I) X4))) (forall ((B2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B2) (@ (@ tptp.image_nat_nat F) A)) (@ (@ tptp.inj_on_nat_nat (@ (@ tptp.hilber815131374at_nat A) F)) B2))) (forall ((F (-> tptp.a tptp.a)) (B2 tptp.set_a) (A2 tptp.a) (A tptp.set_a)) (let ((_let_1 (@ tptp.member_a A2))) (=> (@ (@ tptp.inj_on_a_a F) B2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_a A) B2) (= (@ (@ tptp.member_a (@ F A2)) (@ (@ tptp.image_a_a F) A)) (@ _let_1 A))))))) (forall ((F (-> tptp.a tptp.list_a)) (B2 tptp.set_a) (A2 tptp.a) (A tptp.set_a)) (let ((_let_1 (@ tptp.member_a A2))) (=> (@ (@ tptp.inj_on_a_list_a F) B2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_less_eq_set_a A) B2) (= (@ (@ tptp.member_list_a (@ F A2)) (@ (@ tptp.image_a_list_a F) A)) (@ _let_1 A))))))) (forall ((F (-> tptp.list_a tptp.a)) (B2 tptp.set_list_a) (A2 tptp.list_a) (A tptp.set_list_a)) (let ((_let_1 (@ tptp.member_list_a A2))) (=> (@ (@ tptp.inj_on_list_a_a F) B2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le1301786372list_a A) B2) (= (@ (@ tptp.member_a (@ F A2)) (@ (@ tptp.image_list_a_a F) A)) (@ _let_1 A))))))) (forall ((F (-> tptp.list_a tptp.list_a)) (B2 tptp.set_list_a) (A2 tptp.list_a) (A tptp.set_list_a)) (let ((_let_1 (@ tptp.member_list_a A2))) (=> (@ (@ tptp.inj_on_list_a_list_a F) B2) (=> (@ _let_1 B2) (=> (@ (@ tptp.ord_le1301786372list_a A) B2) (= (@ (@ tptp.member_list_a (@ F A2)) (@ (@ tptp.image_list_a_list_a F) A)) (@ _let_1 A))))))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) B2) (@ (@ tptp.inj_on_nat_nat F) A))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.inj_on_nat_nat F) A) (=> (@ (@ tptp.member_nat X4) A) (=> (= (@ F X4) Y3) (= (@ (@ (@ tptp.hilber815131374at_nat A) F) Y3) X4))))) (forall ((A tptp.set_a) (F (-> tptp.a tptp.a)) (B2 tptp.set_a)) (=> (forall ((X6 tptp.a)) (=> (@ (@ tptp.member_a X6) A) (@ (@ tptp.member_a (@ F X6)) B2))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_a_a F) A)) B2))) (forall ((A tptp.set_a) (F (-> tptp.a tptp.list_a)) (B2 tptp.set_list_a)) (=> (forall ((X6 tptp.a)) (=> (@ (@ tptp.member_a X6) A) (@ (@ tptp.member_list_a (@ F X6)) B2))) (@ (@ tptp.ord_le1301786372list_a (@ (@ tptp.image_a_list_a F) A)) B2))) (forall ((A tptp.set_list_a) (F (-> tptp.list_a tptp.a)) (B2 tptp.set_a)) (=> (forall ((X6 tptp.list_a)) (=> (@ (@ tptp.member_list_a X6) A) (@ (@ tptp.member_a (@ F X6)) B2))) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.image_list_a_a F) A)) B2))) (forall ((A tptp.set_list_a) (F (-> tptp.list_a tptp.list_a)) (B2 tptp.set_list_a)) (=> (forall ((X6 tptp.list_a)) (=> (@ (@ tptp.member_list_a X6) A) (@ (@ tptp.member_list_a (@ F X6)) B2))) (@ (@ tptp.ord_le1301786372list_a (@ (@ tptp.image_list_a_list_a F) A)) B2))) (= tptp.bij_betw_nat_nat (lambda ((F3 (-> tptp.nat tptp.nat)) (A4 tptp.set_nat) (B3 tptp.set_nat)) (and (@ (@ tptp.inj_on_nat_nat F3) A4) (= (@ (@ tptp.image_nat_nat F3) A4) B3)))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.inj_on_nat_nat F) A) (=> (= (@ (@ tptp.image_nat_nat F) A) B2) (@ (@ (@ tptp.bij_betw_nat_nat F) A) B2)))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat)) (=> (@ (@ tptp.inj_on_nat_nat F) A) (@ (@ (@ tptp.bij_betw_nat_nat F) A) (@ (@ tptp.image_nat_nat F) A)))) (forall ((X4 tptp.list_a) (A tptp.set_list_a) (P (-> tptp.list_a Bool))) (=> (@ (@ tptp.member_list_a X4) A) (=> (@ P X4) (exists ((X6 tptp.list_a)) (and (@ (@ tptp.member_list_a X6) A) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_a X6)) (@ tptp.size_size_list_a X4)) (@ P X6) (forall ((Xa tptp.list_a)) (=> (@ (@ tptp.member_list_a Xa) A) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_a Xa)) (@ tptp.size_size_list_a X6)) (not (@ P Xa)))))))))) (forall ((X4 tptp.list_set_a) (A tptp.set_list_set_a) (P (-> tptp.list_set_a Bool))) (=> (@ (@ tptp.member_list_set_a X4) A) (=> (@ P X4) (exists ((X6 tptp.list_set_a)) (and (@ (@ tptp.member_list_set_a X6) A) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_set_a X6)) (@ tptp.size_size_list_set_a X4)) (@ P X6) (forall ((Xa tptp.list_set_a)) (=> (@ (@ tptp.member_list_set_a Xa) A) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_set_a Xa)) (@ tptp.size_size_list_set_a X6)) (not (@ P Xa)))))))))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (A5 tptp.set_nat) (B2 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.bij_betw_nat_nat F))) (=> (@ (@ _let_1 A) A5) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A) (=> (= (@ (@ tptp.image_nat_nat F) B2) B4) (@ (@ _let_1 B2) B4)))))) (forall ((A tptp.set_nat) (F4 (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat)) (A5 tptp.set_nat)) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A) (= (@ F4 (@ F X6)) X6))) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A5) (= (@ F (@ F4 X6)) X6))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat F) A)) A5) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat F4) A5)) A) (@ (@ (@ tptp.bij_betw_nat_nat F) A) A5)))))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (A5 tptp.set_nat) (B4 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat F))) (=> (= (@ _let_1 A) A5) (=> (@ (@ tptp.ord_less_eq_set_nat B4) A5) (= (@ _let_1 (@ (@ tptp.image_nat_nat (@ (@ tptp.hilber815131374at_nat A) F)) B4)) B4))))) (forall ((Xs tptp.list_set_a) (Ys tptp.list_set_a)) (=> (= (@ tptp.size_size_list_set_a Xs) (@ tptp.size_size_list_set_a Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_set_a Ys)) (@ (@ tptp.ord_less_eq_set_a (@ (@ tptp.nth_set_a Xs) I3)) (@ (@ tptp.nth_set_a Ys) I3)))) (@ (@ tptp.ord_le1301786372list_a (@ tptp.listset_a Xs)) (@ tptp.listset_a Ys))))) (forall ((I tptp.nat) (Xs tptp.list_a) (J tptp.nat) (X4 tptp.a)) (let ((_let_1 (@ (@ tptp.nth_a (@ (@ (@ tptp.list_update_a Xs) I) X4)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_a Xs)) (and (=> _let_2 (= _let_1 X4)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_a Xs) J)))))))) (forall ((I tptp.nat) (Xs tptp.list_set_a) (J tptp.nat) (X4 tptp.set_a)) (let ((_let_1 (@ (@ tptp.nth_set_a (@ (@ (@ tptp.list_update_set_a Xs) I) X4)) J))) (let ((_let_2 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a Xs)) (and (=> _let_2 (= _let_1 X4)) (=> (not _let_2) (= _let_1 (@ (@ tptp.nth_set_a Xs) J)))))))) (forall ((I tptp.nat) (Xs tptp.list_a) (X4 tptp.a)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_a Xs)) (= (= (@ (@ (@ tptp.list_update_a Xs) I) X4) Xs) (= (@ (@ tptp.nth_a Xs) I) X4)))) (forall ((I tptp.nat) (Xs tptp.list_set_a) (X4 tptp.set_a)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_set_a Xs)) (= (= (@ (@ (@ tptp.list_update_set_a Xs) I) X4) Xs) (= (@ (@ tptp.nth_set_a Xs) I) X4)))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (A5 tptp.set_nat) (B2 tptp.set_nat) (B4 tptp.set_nat)) (=> (@ (@ (@ tptp.bij_betw_nat_nat F) A) A5) (=> (@ (@ tptp.ord_less_eq_set_nat B2) A) (=> (= (@ (@ tptp.image_nat_nat F) B2) B4) (@ (@ (@ tptp.bij_betw_nat_nat (@ (@ tptp.hilber815131374at_nat A) F)) B4) B2))))) (forall ((A tptp.set_a) (Ss tptp.list_set_a)) (=> (@ (@ tptp.hilber2037636820comp_a A) Ss) (@ (@ tptp.inj_on_list_a_a tptp.groups1792256535list_a) (@ tptp.listset_a Ss)))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.set_nat) (B2 tptp.set_nat) (G2 (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.inj_on_nat_nat F) A) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat F) A)) B2) (=> (@ (@ tptp.inj_on_nat_nat G2) B2) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat G2) B2)) A) (exists ((H (-> tptp.nat tptp.nat))) (@ (@ (@ tptp.bij_betw_nat_nat H) A) B2))))))) (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X4) X4)) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (not (@ (@ tptp.ord_less_eq_nat T) X)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (@ (@ tptp.ord_less_eq_nat X) T))))) (forall ((A tptp.set_a) (B2 tptp.set_a)) (=> (forall ((X6 tptp.a)) (let ((_let_1 (@ tptp.member_a X6))) (=> (@ _let_1 A) (@ _let_1 B2)))) (@ (@ tptp.ord_less_eq_set_a A) B2))) (forall ((A tptp.set_list_a) (B2 tptp.set_list_a)) (=> (forall ((X6 tptp.list_a)) (let ((_let_1 (@ tptp.member_list_a X6))) (=> (@ _let_1 A) (@ _let_1 B2)))) (@ (@ tptp.ord_le1301786372list_a A) B2))) (forall ((P (-> tptp.nat Bool)) (X4 tptp.nat) (M3 tptp.nat)) (=> (@ P X4) (=> (forall ((X6 tptp.nat)) (=> (@ P X6) (@ (@ tptp.ord_less_eq_nat X6) M3))) (not (forall ((M4 tptp.nat)) (=> (@ P M4) (not (forall ((X tptp.nat)) (=> (@ P X) (@ (@ tptp.ord_less_eq_nat X) M4)))))))))) _let_6 _let_5 (= tptp.ord_less_eq_set_a (lambda ((A4 tptp.set_a) (B3 tptp.set_a)) (forall ((X5 tptp.a)) (let ((_let_1 (@ tptp.member_a X5))) (=> (@ _let_1 A4) (@ _let_1 B3)))))) (= tptp.ord_le1301786372list_a (lambda ((A4 tptp.set_list_a) (B3 tptp.set_list_a)) (forall ((X5 tptp.list_a)) (let ((_let_1 (@ tptp.member_list_a X5))) (=> (@ _let_1 A4) (@ _let_1 B3)))))) (forall ((A tptp.set_a) (B2 tptp.set_a) (C tptp.a)) (let ((_let_1 (@ tptp.member_a C))) (=> (@ (@ tptp.ord_less_eq_set_a A) B2) (=> (@ _let_1 A) (@ _let_1 B2))))) (forall ((A tptp.set_list_a) (B2 tptp.set_list_a) (C tptp.list_a)) (let ((_let_1 (@ tptp.member_list_a C))) (=> (@ (@ tptp.ord_le1301786372list_a A) B2) (=> (@ _let_1 A) (@ _let_1 B2))))) (forall ((A tptp.set_a) (B2 tptp.set_a) (X4 tptp.a)) (let ((_let_1 (@ tptp.member_a X4))) (=> (@ (@ tptp.ord_less_eq_set_a A) B2) (=> (@ _let_1 A) (@ _let_1 B2))))) (forall ((A tptp.set_list_a) (B2 tptp.set_list_a) (X4 tptp.list_a)) (let ((_let_1 (@ tptp.member_list_a X4))) (=> (@ (@ tptp.ord_le1301786372list_a A) B2) (=> (@ _let_1 A) (@ _let_1 B2))))) (forall ((B tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A2) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (= A2 B)))) (= (lambda ((Y2 tptp.nat) (Z tptp.nat)) (= Y2 Z)) (lambda ((A7 tptp.nat) (B5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B5) A7) (@ (@ tptp.ord_less_eq_nat A7) B5)))) (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A3) B6) (@ (@ P A3) B6))) (=> (forall ((A3 tptp.nat) (B6 tptp.nat)) (=> (@ (@ P B6) A3) (@ (@ P A3) B6))) (@ (@ P A2) B)))) (forall ((A2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat A2) A2)) (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_eq_nat Y3) Z3) (@ _let_1 Z3))))) (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_eq_nat B) A2) (= A2 B)))) (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A2 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A2) C)))) (= (lambda ((Y2 tptp.nat) (Z tptp.nat)) (= Y2 Z)) (lambda ((A7 tptp.nat) (B5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A7) B5) (@ (@ tptp.ord_less_eq_nat B5) A7)))) (forall ((Y3 tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X4) (= (@ (@ tptp.ord_less_eq_nat X4) Y3) (= X4 Y3)))) (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X4))) (let ((_let_2 (@ _let_1 Y3))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z3))) (let ((_let_4 (@ _let_3 X4))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y3))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X4))) (let ((_let_8 (@ _let_3 Y3))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))) (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X4) Y3)) (@ (@ tptp.ord_less_eq_nat Y3) X4))) (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (= X4 Y3) (@ (@ tptp.ord_less_eq_nat X4) Y3))) (forall ((X4 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_nat Y3) X4))) (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (=> (@ (@ tptp.ord_less_eq_nat Y3) X4) (= X4 Y3)))) _let_4 (= (lambda ((Y2 tptp.nat) (Z tptp.nat)) (= Y2 Z)) (lambda ((X5 tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X5) Y5) (@ (@ tptp.ord_less_eq_nat Y5) X5)))) (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X6) Y) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))) (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X6 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X6) Y) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat A2) (@ F C)))))) (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X6 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X6) Y) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y)))) (@ (@ tptp.ord_less_eq_nat (@ F A2)) C))))) (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X6 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X6) Y) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y)))) (@ _let_1 (@ F C))))))) (forall ((B tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A2) (not (= A2 B)))) (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (not (= A2 B)))) (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X4) Y3)) (or (@ (@ tptp.ord_less_nat Y3) X4) (= X4 Y3)))) (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A2 tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B6) (@ (@ P A3) B6))) (=> (forall ((A3 tptp.nat)) (@ (@ P A3) A3)) (=> (forall ((A3 tptp.nat) (B6 tptp.nat)) (=> (@ (@ P B6) A3) (@ (@ P A3) B6))) (@ (@ P A2) B))))) (= (lambda ((P3 (-> tptp.nat Bool))) (exists ((X3 tptp.nat)) (@ P3 X3))) (lambda ((P2 (-> tptp.nat Bool))) (exists ((N2 tptp.nat)) (and (@ P2 N2) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N2) (not (@ P2 M5)))))))) (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (@ (@ tptp.ord_less_nat Y3) X4)))) (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))) (forall ((A2 tptp.nat)) (not (@ (@ tptp.ord_less_nat A2) A2))) (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X4) Y3)) (=> (not (= X4 Y3)) (@ (@ tptp.ord_less_nat Y3) X4)))) (forall ((X4 tptp.nat) (Y3 tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (=> (@ (@ tptp.ord_less_nat Y3) X4) P))) (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (= Y3 X4)))) (forall ((Y3 tptp.nat) (X4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y3) X4)) (= (not (@ (@ tptp.ord_less_nat X4) Y3)) (= X4 Y3)))) (forall ((P (-> tptp.nat Bool)) (A2 tptp.nat)) (=> (forall ((X6 tptp.nat)) (=> (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y6) X6) (@ P Y6))) (@ P X6))) (@ P A2))) (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (@ (@ tptp.ord_less_nat Y3) X4)))) (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (= X4 Y3)))) (forall ((B tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A2) (not (@ (@ tptp.ord_less_nat A2) B)))) (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A2 tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A2 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A2) C)))) (forall ((X4 tptp.nat)) (not (@ (@ tptp.ord_less_nat X4) X4))) (forall ((X4 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_nat X4) Y3) (= X4 Y3) (@ (@ tptp.ord_less_nat Y3) X4))) (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X4))) (=> (@ _let_1 Y3) (=> (@ (@ tptp.ord_less_nat Y3) Z3) (@ _let_1 Z3))))) (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (not (@ (@ tptp.ord_less_nat B) A2)))) (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (@ (@ tptp.ord_less_nat Y3) X4)))) (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (not (= X4 Y3)))) (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (not (@ (@ tptp.ord_less_nat B) A2)))) (forall ((X4 tptp.nat) (Y3 tptp.nat)) (= (not (= X4 Y3)) (or (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_nat Y3) X4)))) (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (not (= X4 Y3)) (=> (not (@ (@ tptp.ord_less_nat X4) Y3)) (@ (@ tptp.ord_less_nat Y3) X4)))) (forall ((X4 tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X4) X_1))) (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X6 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Y) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F Y)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))) (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A2))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X6 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Y) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F Y)))) (@ _let_1 (@ F C))))))) (forall ((A2 tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Y) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F Y)))) (@ (@ tptp.ord_less_nat (@ F A2)) C))))) (forall ((A2 tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A2 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X6 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Y) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F Y)))) (@ (@ tptp.ord_less_nat A2) (@ F C)))))) (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X6) (= (@ P X6) (@ P4 X6))))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X6) (= (@ Q X6) (@ Q2 X6))))) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (= (and (@ P X) (@ Q X)) (and (@ P4 X) (@ Q2 X))))))))) (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X6) (= (@ P X6) (@ P4 X6))))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X6) (= (@ Q X6) (@ Q2 X6))))) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (= (or (@ P X) (@ Q X)) (or (@ P4 X) (@ Q2 X))))))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (not (= X T)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (not (= X T)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (not (@ (@ tptp.ord_less_nat X) T)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X) (@ (@ tptp.ord_less_nat T) X))))) (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z4) (= (@ P X6) (@ P4 X6))))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z4) (= (@ Q X6) (@ Q2 X6))))) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (= (and (@ P X) (@ Q X)) (and (@ P4 X) (@ Q2 X))))))))) (forall ((P (-> tptp.nat Bool)) (P4 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q2 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z4) (= (@ P X6) (@ P4 X6))))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z4) (= (@ Q X6) (@ Q2 X6))))) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (= (or (@ P X) (@ Q X)) (or (@ P4 X) (@ Q2 X))))))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (not (= X T)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (not (= X T)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Z2) (@ _let_1 T)))))) (forall ((T tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Z2) (not (@ (@ tptp.ord_less_nat T) X)))))) (forall ((A2 tptp.nat) (B tptp.nat)) (=> (not (= A2 B)) (=> (@ (@ tptp.ord_less_eq_nat A2) B) (@ (@ tptp.ord_less_nat A2) B)))) (forall ((B tptp.nat) (A2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A2) (@ (@ tptp.ord_less_eq_nat B) A2))) _let_3 (= tptp.ord_less_eq_nat (lambda ((B5 tptp.nat) (A7 tptp.nat)) (or (@ (@ tptp.ord_less_nat B5) A7) (= A7 B5)))) (forall ((A2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B) (@ (@ tptp.ord_less_eq_nat A2) B))) (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A2) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_nat C) A2)))) (forall ((B tptp.nat) (A2 tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A2) (=> (@ _let_1 B) (@ _let_1 A2))))) (= tptp.ord_less_nat (lambda ((A7 tptp.nat) (B5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A7) B5) (not (= A7 B5))))) (= tptp.ord_less_eq_nat (lambda ((A7 tptp.nat) (B5 tptp.nat)) (or (@ (@ tptp.ord_less_nat A7) B5) (= A7 B5)))) _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.55/1.20 )
% 0.55/1.20 % SZS output end Proof for ITP077^1
% 0.55/1.20 % cvc5---1.0.5 exiting
% 0.55/1.20 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------