TSTP Solution File: ITP055^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP055^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n021.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 03:17:50 EDT 2023
% Result : Theorem 0.58s 0.79s
% Output : Proof 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.17 % Problem : ITP055^1 : TPTP v8.1.2. Released v7.5.0.
% 0.18/0.18 % Command : do_cvc5 %s %d
% 0.18/0.39 % Computer : n021.cluster.edu
% 0.18/0.39 % Model : x86_64 x86_64
% 0.18/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39 % Memory : 8042.1875MB
% 0.18/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39 % CPULimit : 300
% 0.18/0.39 % WCLimit : 300
% 0.18/0.39 % DateTime : Sun Aug 27 11:25:43 EDT 2023
% 0.18/0.39 % CPUTime :
% 0.25/0.57 %----Proving TH0
% 0.25/0.58 %------------------------------------------------------------------------------
% 0.25/0.58 % File : ITP055^1 : TPTP v8.1.2. Released v7.5.0.
% 0.25/0.58 % Domain : Interactive Theorem Proving
% 0.25/0.58 % Problem : Sledgehammer FLPTheorem problem prob_1231__3305662_1
% 0.25/0.58 % Version : Especial.
% 0.25/0.58 % English :
% 0.25/0.58
% 0.25/0.58 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.25/0.58 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.25/0.58 % Source : [Des21]
% 0.25/0.58 % Names : FLPTheorem/prob_1231__3305662_1 [Des21]
% 0.25/0.58
% 0.25/0.58 % Status : Theorem
% 0.25/0.58 % Rating : 0.15 v8.1.0, 0.18 v7.5.0
% 0.25/0.58 % Syntax : Number of formulae : 414 ( 186 unt; 72 typ; 0 def)
% 0.25/0.58 % Number of atoms : 741 ( 451 equ; 0 cnn)
% 0.25/0.58 % Maximal formula atoms : 6 ( 2 avg)
% 0.25/0.58 % Number of connectives : 3000 ( 179 ~; 10 |; 38 &;2297 @)
% 0.25/0.58 % ( 0 <=>; 476 =>; 0 <=; 0 <~>)
% 0.25/0.58 % Maximal formula depth : 23 ( 7 avg)
% 0.25/0.58 % Number of types : 15 ( 14 usr)
% 0.25/0.58 % Number of type conns : 520 ( 520 >; 0 *; 0 +; 0 <<)
% 0.25/0.58 % Number of symbols : 59 ( 58 usr; 14 con; 0-4 aty)
% 0.25/0.58 % Number of variables : 1101 ( 11 ^;1046 !; 44 ?;1101 :)
% 0.25/0.58 % SPC : TH0_THM_EQU_NAR
% 0.25/0.58
% 0.25/0.58 % Comments : This file was generated by Sledgehammer 2021-02-23 15:32:18.186
% 0.25/0.58 %------------------------------------------------------------------------------
% 0.25/0.58 % Could-be-implicit typings (14)
% 0.25/0.58 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J_J,type,
% 0.25/0.58 list_l1584713811t_unit: $tType ).
% 0.25/0.58
% 0.25/0.58 thf(ty_n_t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
% 0.25/0.58 list_l611321411t_unit: $tType ).
% 0.25/0.58
% 0.25/0.58 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.25/0.58 list_c1059388851t_unit: $tType ).
% 0.25/0.58
% 0.25/0.58 thf(ty_n_t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.25/0.58 config256849571t_unit: $tType ).
% 0.25/0.58
% 0.25/0.58 thf(ty_n_t__List__Olist_It__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J_J,type,
% 0.25/0.58 list_l1341496881ge_p_v: $tType ).
% 0.25/0.58
% 0.25/0.58 thf(ty_n_t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
% 0.25/0.58 list_l1619404459ge_p_v: $tType ).
% 0.25/0.58
% 0.25/0.58 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.25/0.58 list_message_p_v: $tType ).
% 0.25/0.58
% 0.25/0.58 thf(ty_n_t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.25/0.58 message_p_v: $tType ).
% 0.25/0.58
% 0.25/0.58 thf(ty_n_t__AsynchronousSystem__OmessageValue_Itf__v_J,type,
% 0.25/0.58 messageValue_v: $tType ).
% 0.25/0.58
% 0.25/0.58 thf(ty_n_t__Set__Oset_It__Nat__Onat_J,type,
% 0.25/0.58 set_nat: $tType ).
% 0.25/0.58
% 0.25/0.58 thf(ty_n_t__Nat__Onat,type,
% 0.25/0.58 nat: $tType ).
% 0.25/0.58
% 0.25/0.58 thf(ty_n_t__Int__Oint,type,
% 0.25/0.58 int: $tType ).
% 0.25/0.58
% 0.25/0.58 thf(ty_n_tf__s,type,
% 0.25/0.58 s: $tType ).
% 0.25/0.58
% 0.25/0.58 thf(ty_n_tf__p,type,
% 0.25/0.58 p: $tType ).
% 0.25/0.58
% 0.25/0.58 % Explicit typings (58)
% 0.25/0.58 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_001tf__p_001tf__s_001tf__v,type,
% 0.25/0.58 fLPThe9398366_p_s_v: ( p > s > messageValue_v > s ) > ( p > s > messageValue_v > message_p_v > nat ) > ( p > s ) > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionCfg_001tf__p_001tf__v_001tf__s,type,
% 0.25/0.58 fLPThe1519354920_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_c1059388851t_unit ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_FLPTheorem__Mirabelle__bncobrwgic_OflpPseudoConsensus_OinfiniteExecutionMsg_001tf__p_001tf__v_001tf__s,type,
% 0.25/0.58 fLPThe536531371_p_v_s: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > list_message_p_v ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Groups_Oone__class_Oone_001t__Int__Oint,type,
% 0.25/0.58 one_one_int: int ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.25/0.58 one_one_nat: nat ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Groups_Ouminus__class_Ouminus_001t__Int__Oint,type,
% 0.25/0.58 uminus_uminus_int: int > int ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Groups_Ozero__class_Ozero_001t__Int__Oint,type,
% 0.25/0.58 zero_zero_int: int ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat,type,
% 0.25/0.58 zero_zero_nat: nat ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Int_Onat,type,
% 0.25/0.58 nat2: int > nat ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 0.25/0.58 ring_1_of_int_int: int > int ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.25/0.58 prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.25/0.58 prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_ListUtilities_OprefixList_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.25/0.58 prefix747844452t_unit: list_l611321411t_unit > list_l611321411t_unit > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_ListUtilities_OprefixList_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.25/0.58 prefix1465223476ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Ogen__length_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.25/0.58 gen_le193291088t_unit: nat > list_c1059388851t_unit > nat ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Ogen__length_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.25/0.58 gen_le697204914ge_p_v: nat > list_message_p_v > nat ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Oinsert_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.25/0.58 insert1308755079t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Oinsert_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.25/0.58 insert_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Olist_OCons_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.25/0.58 cons_c1162654829t_unit: config256849571t_unit > list_c1059388851t_unit > list_c1059388851t_unit ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Olist_OCons_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.25/0.58 cons_message_p_v: message_p_v > list_message_p_v > list_message_p_v ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.25/0.58 cons_l1083444861t_unit: list_c1059388851t_unit > list_l611321411t_unit > list_l611321411t_unit ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.25/0.58 cons_l233104475ge_p_v: list_message_p_v > list_l1619404459ge_p_v > list_l1619404459ge_p_v ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
% 0.25/0.58 cons_l1777019405t_unit: list_l611321411t_unit > list_l1584713811t_unit > list_l1584713811t_unit ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Olist_OCons_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
% 0.25/0.58 cons_l1383421281ge_p_v: list_l1619404459ge_p_v > list_l1341496881ge_p_v > list_l1341496881ge_p_v ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.25/0.58 nil_co1338500125t_unit: list_c1059388851t_unit ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.25/0.58 nil_message_p_v: list_message_p_v ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.25/0.58 nil_li307996205t_unit: list_l611321411t_unit ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.25/0.58 nil_list_message_p_v: list_l1619404459ge_p_v ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
% 0.25/0.58 nil_li2108369341t_unit: list_l1584713811t_unit ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Olist_ONil_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
% 0.25/0.58 nil_li835338673ge_p_v: list_l1341496881ge_p_v ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Olist__ex1_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.25/0.58 list_e1598815642t_unit: ( config256849571t_unit > $o ) > list_c1059388851t_unit > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Olist__ex1_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.25/0.58 list_ex1_message_p_v: ( message_p_v > $o ) > list_message_p_v > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_On__lists_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.25/0.58 n_list1987762709t_unit: nat > list_c1059388851t_unit > list_l611321411t_unit ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_On__lists_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.25/0.58 n_lists_message_p_v: nat > list_message_p_v > list_l1619404459ge_p_v ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Onths_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.25/0.58 nths_c890550943t_unit: list_c1059388851t_unit > set_nat > list_c1059388851t_unit ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Onths_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.25/0.58 nths_message_p_v: list_message_p_v > set_nat > list_message_p_v ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Oproduct__lists_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.25/0.58 produc663212148t_unit: list_l611321411t_unit > list_l611321411t_unit ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Oproduct__lists_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.25/0.58 produc1505827982ge_p_v: list_l1619404459ge_p_v > list_l1619404459ge_p_v ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Osubseqs_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.25/0.58 subseq1144048270t_unit: list_c1059388851t_unit > list_l611321411t_unit ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_List_Osubseqs_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.25/0.58 subseqs_message_p_v: list_message_p_v > list_l1619404459ge_p_v ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Nat_OSuc,type,
% 0.25/0.58 suc: nat > nat ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 0.25/0.58 semiri2019852685at_int: nat > int ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 0.25/0.58 semiri1382578993at_nat: nat > nat ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.25/0.58 size_s1406904903t_unit: list_c1059388851t_unit > nat ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.25/0.58 size_s1168481041ge_p_v: list_message_p_v > nat ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J_J,type,
% 0.25/0.58 size_s503142615t_unit: list_l611321411t_unit > nat ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J_J,type,
% 0.25/0.58 size_s1809856791ge_p_v: list_l1619404459ge_p_v > nat ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 0.25/0.58 ord_less_int: int > int > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.25/0.58 ord_less_nat: nat > nat > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
% 0.25/0.58 ord_less_eq_int: int > int > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.25/0.58 ord_less_eq_nat: nat > nat > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_Set_OCollect_001t__Nat__Onat,type,
% 0.25/0.58 collect_nat: ( nat > $o ) > set_nat ).
% 0.25/0.58
% 0.25/0.58 thf(sy_c_member_001t__Nat__Onat,type,
% 0.25/0.58 member_nat: nat > set_nat > $o ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_cfg____,type,
% 0.25/0.58 cfg: config256849571t_unit ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_fe____,type,
% 0.25/0.58 fe: nat > list_c1059388851t_unit ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_m____,type,
% 0.25/0.58 m: nat ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_n____,type,
% 0.25/0.58 n: nat ).
% 0.25/0.58
% 0.25/0.58 thf(sy_v_na____,type,
% 0.25/0.58 na: nat ).
% 0.25/0.58
% 0.25/0.58 % Relevant facts (341)
% 0.25/0.58 thf(fact_0__092_060open_062m_A_060_An_092_060close_062,axiom,
% 0.25/0.58 ord_less_nat @ m @ na ).
% 0.25/0.58
% 0.25/0.58 % \<open>m < n\<close>
% 0.25/0.58 thf(fact_1_MLessN,axiom,
% 0.25/0.58 ord_less_nat @ m @ n ).
% 0.25/0.58
% 0.25/0.58 % MLessN
% 0.25/0.58 thf(fact_2_IA_I1_J,axiom,
% 0.25/0.58 ( ( ord_less_nat @ m @ na )
% 0.25/0.58 => ( prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % IA(1)
% 0.25/0.58 thf(fact_3__092_060open_062m_A_061_An_A_092_060or_062_Am_A_060_An_092_060close_062,axiom,
% 0.25/0.58 ( ( m = na )
% 0.25/0.58 | ( ord_less_nat @ m @ na ) ) ).
% 0.25/0.58
% 0.25/0.58 % \<open>m = n \<or> m < n\<close>
% 0.25/0.58 thf(fact_4_IA_I2_J,axiom,
% 0.25/0.58 ord_less_nat @ m @ ( suc @ na ) ).
% 0.25/0.58
% 0.25/0.58 % IA(2)
% 0.25/0.58 thf(fact_5_PrefixListTransitive,axiom,
% 0.25/0.58 ! [L1: list_message_p_v,L2: list_message_p_v,L3: list_message_p_v] :
% 0.25/0.58 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.25/0.58 => ( ( prefix47729710ge_p_v @ L2 @ L3 )
% 0.25/0.58 => ( prefix47729710ge_p_v @ L1 @ L3 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % PrefixListTransitive
% 0.25/0.58 thf(fact_6_PrefixListTransitive,axiom,
% 0.25/0.58 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit,L3: list_c1059388851t_unit] :
% 0.25/0.58 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.25/0.58 => ( ( prefix1615116500t_unit @ L2 @ L3 )
% 0.25/0.58 => ( prefix1615116500t_unit @ L1 @ L3 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % PrefixListTransitive
% 0.25/0.58 thf(fact_7_FE_I1_J,axiom,
% 0.25/0.58 ( ( fe @ zero_zero_nat )
% 0.25/0.58 = ( cons_c1162654829t_unit @ cfg @ nil_co1338500125t_unit ) ) ).
% 0.25/0.58
% 0.25/0.58 % FE(1)
% 0.25/0.58 thf(fact_8_prefixList_Ointros_I2_J,axiom,
% 0.25/0.58 ! [Xa: list_l611321411t_unit,Xb: list_l611321411t_unit,X: list_c1059388851t_unit] :
% 0.25/0.58 ( ( prefix747844452t_unit @ Xa @ Xb )
% 0.25/0.58 => ( prefix747844452t_unit @ ( cons_l1083444861t_unit @ X @ Xa ) @ ( cons_l1083444861t_unit @ X @ Xb ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.intros(2)
% 0.25/0.58 thf(fact_9_prefixList_Ointros_I2_J,axiom,
% 0.25/0.58 ! [Xa: list_l1619404459ge_p_v,Xb: list_l1619404459ge_p_v,X: list_message_p_v] :
% 0.25/0.58 ( ( prefix1465223476ge_p_v @ Xa @ Xb )
% 0.25/0.58 => ( prefix1465223476ge_p_v @ ( cons_l233104475ge_p_v @ X @ Xa ) @ ( cons_l233104475ge_p_v @ X @ Xb ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.intros(2)
% 0.25/0.58 thf(fact_10_prefixList_Ointros_I2_J,axiom,
% 0.25/0.58 ! [Xa: list_message_p_v,Xb: list_message_p_v,X: message_p_v] :
% 0.25/0.58 ( ( prefix47729710ge_p_v @ Xa @ Xb )
% 0.25/0.58 => ( prefix47729710ge_p_v @ ( cons_message_p_v @ X @ Xa ) @ ( cons_message_p_v @ X @ Xb ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.intros(2)
% 0.25/0.58 thf(fact_11_prefixList_Ointros_I2_J,axiom,
% 0.25/0.58 ! [Xa: list_c1059388851t_unit,Xb: list_c1059388851t_unit,X: config256849571t_unit] :
% 0.25/0.58 ( ( prefix1615116500t_unit @ Xa @ Xb )
% 0.25/0.58 => ( prefix1615116500t_unit @ ( cons_c1162654829t_unit @ X @ Xa ) @ ( cons_c1162654829t_unit @ X @ Xb ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.intros(2)
% 0.25/0.58 thf(fact_12_PrefixListMonotonicity,axiom,
% 0.25/0.58 ! [L1: list_message_p_v,L2: list_message_p_v] :
% 0.25/0.58 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.25/0.58 => ( ord_less_nat @ ( size_s1168481041ge_p_v @ L1 ) @ ( size_s1168481041ge_p_v @ L2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % PrefixListMonotonicity
% 0.25/0.58 thf(fact_13_PrefixListMonotonicity,axiom,
% 0.25/0.58 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
% 0.25/0.58 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.25/0.58 => ( ord_less_nat @ ( size_s1406904903t_unit @ L1 ) @ ( size_s1406904903t_unit @ L2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % PrefixListMonotonicity
% 0.25/0.58 thf(fact_14_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 0.25/0.58 ! [P: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,Q: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,A4: config256849571t_unit,A5: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,A6: list_c1059388851t_unit > list_message_p_v > list_message_p_v,A7: nat] :
% 0.25/0.58 ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.25/0.58 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 0.25/0.58 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.25/0.58 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.25/0.58 => ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.25/0.58 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.25/0.58 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 0.25/0.58 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.25/0.58 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.25/0.58 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.25/0.58 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % infiniteExecutionCfg_infiniteExecutionMsg.induct(2)
% 0.25/0.58 thf(fact_15_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 0.25/0.58 ! [P: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,Q: config256849571t_unit > ( list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit ) > ( list_c1059388851t_unit > list_message_p_v > list_message_p_v ) > nat > $o,A0: config256849571t_unit,A1: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,A2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,A3: nat] :
% 0.25/0.58 ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( P @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.25/0.58 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 0.25/0.58 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.25/0.58 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.25/0.58 => ( P @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.25/0.58 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ zero_zero_nat )
% 0.25/0.58 => ( ! [Cfg: config256849571t_unit,FStepCfg: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N: nat] :
% 0.25/0.58 ( ( P @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.25/0.58 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.25/0.58 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.25/0.58 => ( P @ A0 @ A1 @ A2 @ A3 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % infiniteExecutionCfg_infiniteExecutionMsg.induct(1)
% 0.25/0.58 thf(fact_16_prefixList_Ointros_I1_J,axiom,
% 0.25/0.58 ! [X: list_c1059388851t_unit,Xs: list_l611321411t_unit] : ( prefix747844452t_unit @ nil_li307996205t_unit @ ( cons_l1083444861t_unit @ X @ Xs ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.intros(1)
% 0.25/0.58 thf(fact_17_prefixList_Ointros_I1_J,axiom,
% 0.25/0.58 ! [X: list_message_p_v,Xs: list_l1619404459ge_p_v] : ( prefix1465223476ge_p_v @ nil_list_message_p_v @ ( cons_l233104475ge_p_v @ X @ Xs ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.intros(1)
% 0.25/0.58 thf(fact_18_prefixList_Ointros_I1_J,axiom,
% 0.25/0.58 ! [X: message_p_v,Xs: list_message_p_v] : ( prefix47729710ge_p_v @ nil_message_p_v @ ( cons_message_p_v @ X @ Xs ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.intros(1)
% 0.25/0.58 thf(fact_19_prefixList_Ointros_I1_J,axiom,
% 0.25/0.58 ! [X: config256849571t_unit,Xs: list_c1059388851t_unit] : ( prefix1615116500t_unit @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ X @ Xs ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.intros(1)
% 0.25/0.58 thf(fact_20_prefixList_Ocases,axiom,
% 0.25/0.58 ! [A1: list_l611321411t_unit,A2: list_l611321411t_unit] :
% 0.25/0.58 ( ( prefix747844452t_unit @ A1 @ A2 )
% 0.25/0.58 => ( ( ( A1 = nil_li307996205t_unit )
% 0.25/0.58 => ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 0.25/0.58 ( A2
% 0.25/0.58 != ( cons_l1083444861t_unit @ X2 @ Xs2 ) ) )
% 0.25/0.58 => ~ ! [Xa2: list_l611321411t_unit,Xb2: list_l611321411t_unit,X2: list_c1059388851t_unit] :
% 0.25/0.58 ( ( A1
% 0.25/0.58 = ( cons_l1083444861t_unit @ X2 @ Xa2 ) )
% 0.25/0.58 => ( ( A2
% 0.25/0.58 = ( cons_l1083444861t_unit @ X2 @ Xb2 ) )
% 0.25/0.58 => ~ ( prefix747844452t_unit @ Xa2 @ Xb2 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.cases
% 0.25/0.58 thf(fact_21_prefixList_Ocases,axiom,
% 0.25/0.58 ! [A1: list_l1619404459ge_p_v,A2: list_l1619404459ge_p_v] :
% 0.25/0.58 ( ( prefix1465223476ge_p_v @ A1 @ A2 )
% 0.25/0.58 => ( ( ( A1 = nil_list_message_p_v )
% 0.25/0.58 => ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 0.25/0.58 ( A2
% 0.25/0.58 != ( cons_l233104475ge_p_v @ X2 @ Xs2 ) ) )
% 0.25/0.58 => ~ ! [Xa2: list_l1619404459ge_p_v,Xb2: list_l1619404459ge_p_v,X2: list_message_p_v] :
% 0.25/0.58 ( ( A1
% 0.25/0.58 = ( cons_l233104475ge_p_v @ X2 @ Xa2 ) )
% 0.25/0.58 => ( ( A2
% 0.25/0.58 = ( cons_l233104475ge_p_v @ X2 @ Xb2 ) )
% 0.25/0.58 => ~ ( prefix1465223476ge_p_v @ Xa2 @ Xb2 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.cases
% 0.25/0.58 thf(fact_22_prefixList_Ocases,axiom,
% 0.25/0.58 ! [A1: list_message_p_v,A2: list_message_p_v] :
% 0.25/0.58 ( ( prefix47729710ge_p_v @ A1 @ A2 )
% 0.25/0.58 => ( ( ( A1 = nil_message_p_v )
% 0.25/0.58 => ! [X2: message_p_v,Xs2: list_message_p_v] :
% 0.25/0.58 ( A2
% 0.25/0.58 != ( cons_message_p_v @ X2 @ Xs2 ) ) )
% 0.25/0.58 => ~ ! [Xa2: list_message_p_v,Xb2: list_message_p_v,X2: message_p_v] :
% 0.25/0.58 ( ( A1
% 0.25/0.58 = ( cons_message_p_v @ X2 @ Xa2 ) )
% 0.25/0.58 => ( ( A2
% 0.25/0.58 = ( cons_message_p_v @ X2 @ Xb2 ) )
% 0.25/0.58 => ~ ( prefix47729710ge_p_v @ Xa2 @ Xb2 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.cases
% 0.25/0.58 thf(fact_23_prefixList_Ocases,axiom,
% 0.25/0.58 ! [A1: list_c1059388851t_unit,A2: list_c1059388851t_unit] :
% 0.25/0.58 ( ( prefix1615116500t_unit @ A1 @ A2 )
% 0.25/0.58 => ( ( ( A1 = nil_co1338500125t_unit )
% 0.25/0.58 => ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 0.25/0.58 ( A2
% 0.25/0.58 != ( cons_c1162654829t_unit @ X2 @ Xs2 ) ) )
% 0.25/0.58 => ~ ! [Xa2: list_c1059388851t_unit,Xb2: list_c1059388851t_unit,X2: config256849571t_unit] :
% 0.25/0.58 ( ( A1
% 0.25/0.58 = ( cons_c1162654829t_unit @ X2 @ Xa2 ) )
% 0.25/0.58 => ( ( A2
% 0.25/0.58 = ( cons_c1162654829t_unit @ X2 @ Xb2 ) )
% 0.25/0.58 => ~ ( prefix1615116500t_unit @ Xa2 @ Xb2 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.cases
% 0.25/0.58 thf(fact_24_prefixList_Osimps,axiom,
% 0.25/0.58 ( prefix747844452t_unit
% 0.25/0.58 = ( ^ [A12: list_l611321411t_unit,A22: list_l611321411t_unit] :
% 0.25/0.58 ( ? [X3: list_c1059388851t_unit,Xs3: list_l611321411t_unit] :
% 0.25/0.58 ( ( A12 = nil_li307996205t_unit )
% 0.25/0.58 & ( A22
% 0.25/0.58 = ( cons_l1083444861t_unit @ X3 @ Xs3 ) ) )
% 0.25/0.58 | ? [Xa3: list_l611321411t_unit,Xb3: list_l611321411t_unit,X3: list_c1059388851t_unit] :
% 0.25/0.58 ( ( A12
% 0.25/0.58 = ( cons_l1083444861t_unit @ X3 @ Xa3 ) )
% 0.25/0.58 & ( A22
% 0.25/0.58 = ( cons_l1083444861t_unit @ X3 @ Xb3 ) )
% 0.25/0.58 & ( prefix747844452t_unit @ Xa3 @ Xb3 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.simps
% 0.25/0.58 thf(fact_25_prefixList_Osimps,axiom,
% 0.25/0.58 ( prefix1465223476ge_p_v
% 0.25/0.58 = ( ^ [A12: list_l1619404459ge_p_v,A22: list_l1619404459ge_p_v] :
% 0.25/0.58 ( ? [X3: list_message_p_v,Xs3: list_l1619404459ge_p_v] :
% 0.25/0.58 ( ( A12 = nil_list_message_p_v )
% 0.25/0.58 & ( A22
% 0.25/0.58 = ( cons_l233104475ge_p_v @ X3 @ Xs3 ) ) )
% 0.25/0.58 | ? [Xa3: list_l1619404459ge_p_v,Xb3: list_l1619404459ge_p_v,X3: list_message_p_v] :
% 0.25/0.58 ( ( A12
% 0.25/0.58 = ( cons_l233104475ge_p_v @ X3 @ Xa3 ) )
% 0.25/0.58 & ( A22
% 0.25/0.58 = ( cons_l233104475ge_p_v @ X3 @ Xb3 ) )
% 0.25/0.58 & ( prefix1465223476ge_p_v @ Xa3 @ Xb3 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.simps
% 0.25/0.58 thf(fact_26_prefixList_Osimps,axiom,
% 0.25/0.58 ( prefix47729710ge_p_v
% 0.25/0.58 = ( ^ [A12: list_message_p_v,A22: list_message_p_v] :
% 0.25/0.58 ( ? [X3: message_p_v,Xs3: list_message_p_v] :
% 0.25/0.58 ( ( A12 = nil_message_p_v )
% 0.25/0.58 & ( A22
% 0.25/0.58 = ( cons_message_p_v @ X3 @ Xs3 ) ) )
% 0.25/0.58 | ? [Xa3: list_message_p_v,Xb3: list_message_p_v,X3: message_p_v] :
% 0.25/0.58 ( ( A12
% 0.25/0.58 = ( cons_message_p_v @ X3 @ Xa3 ) )
% 0.25/0.58 & ( A22
% 0.25/0.58 = ( cons_message_p_v @ X3 @ Xb3 ) )
% 0.25/0.58 & ( prefix47729710ge_p_v @ Xa3 @ Xb3 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.simps
% 0.25/0.58 thf(fact_27_prefixList_Osimps,axiom,
% 0.25/0.58 ( prefix1615116500t_unit
% 0.25/0.58 = ( ^ [A12: list_c1059388851t_unit,A22: list_c1059388851t_unit] :
% 0.25/0.58 ( ? [X3: config256849571t_unit,Xs3: list_c1059388851t_unit] :
% 0.25/0.58 ( ( A12 = nil_co1338500125t_unit )
% 0.25/0.58 & ( A22
% 0.25/0.58 = ( cons_c1162654829t_unit @ X3 @ Xs3 ) ) )
% 0.25/0.58 | ? [Xa3: list_c1059388851t_unit,Xb3: list_c1059388851t_unit,X3: config256849571t_unit] :
% 0.25/0.58 ( ( A12
% 0.25/0.58 = ( cons_c1162654829t_unit @ X3 @ Xa3 ) )
% 0.25/0.58 & ( A22
% 0.25/0.58 = ( cons_c1162654829t_unit @ X3 @ Xb3 ) )
% 0.25/0.58 & ( prefix1615116500t_unit @ Xa3 @ Xb3 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.simps
% 0.25/0.58 thf(fact_28_prefixList_Oinducts,axiom,
% 0.25/0.58 ! [X1: list_l611321411t_unit,X22: list_l611321411t_unit,P: list_l611321411t_unit > list_l611321411t_unit > $o] :
% 0.25/0.58 ( ( prefix747844452t_unit @ X1 @ X22 )
% 0.25/0.58 => ( ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit] : ( P @ nil_li307996205t_unit @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) )
% 0.25/0.58 => ( ! [Xa2: list_l611321411t_unit,Xb2: list_l611321411t_unit,X2: list_c1059388851t_unit] :
% 0.25/0.58 ( ( prefix747844452t_unit @ Xa2 @ Xb2 )
% 0.25/0.58 => ( ( P @ Xa2 @ Xb2 )
% 0.25/0.58 => ( P @ ( cons_l1083444861t_unit @ X2 @ Xa2 ) @ ( cons_l1083444861t_unit @ X2 @ Xb2 ) ) ) )
% 0.25/0.58 => ( P @ X1 @ X22 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.inducts
% 0.25/0.58 thf(fact_29_prefixList_Oinducts,axiom,
% 0.25/0.58 ! [X1: list_l1619404459ge_p_v,X22: list_l1619404459ge_p_v,P: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o] :
% 0.25/0.58 ( ( prefix1465223476ge_p_v @ X1 @ X22 )
% 0.25/0.58 => ( ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v] : ( P @ nil_list_message_p_v @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) )
% 0.25/0.58 => ( ! [Xa2: list_l1619404459ge_p_v,Xb2: list_l1619404459ge_p_v,X2: list_message_p_v] :
% 0.25/0.58 ( ( prefix1465223476ge_p_v @ Xa2 @ Xb2 )
% 0.25/0.58 => ( ( P @ Xa2 @ Xb2 )
% 0.25/0.58 => ( P @ ( cons_l233104475ge_p_v @ X2 @ Xa2 ) @ ( cons_l233104475ge_p_v @ X2 @ Xb2 ) ) ) )
% 0.25/0.58 => ( P @ X1 @ X22 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.inducts
% 0.25/0.58 thf(fact_30_prefixList_Oinducts,axiom,
% 0.25/0.58 ! [X1: list_message_p_v,X22: list_message_p_v,P: list_message_p_v > list_message_p_v > $o] :
% 0.25/0.58 ( ( prefix47729710ge_p_v @ X1 @ X22 )
% 0.25/0.58 => ( ! [X2: message_p_v,Xs2: list_message_p_v] : ( P @ nil_message_p_v @ ( cons_message_p_v @ X2 @ Xs2 ) )
% 0.25/0.58 => ( ! [Xa2: list_message_p_v,Xb2: list_message_p_v,X2: message_p_v] :
% 0.25/0.58 ( ( prefix47729710ge_p_v @ Xa2 @ Xb2 )
% 0.25/0.58 => ( ( P @ Xa2 @ Xb2 )
% 0.25/0.58 => ( P @ ( cons_message_p_v @ X2 @ Xa2 ) @ ( cons_message_p_v @ X2 @ Xb2 ) ) ) )
% 0.25/0.58 => ( P @ X1 @ X22 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.inducts
% 0.25/0.58 thf(fact_31_prefixList_Oinducts,axiom,
% 0.25/0.58 ! [X1: list_c1059388851t_unit,X22: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 0.25/0.58 ( ( prefix1615116500t_unit @ X1 @ X22 )
% 0.25/0.58 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) )
% 0.25/0.58 => ( ! [Xa2: list_c1059388851t_unit,Xb2: list_c1059388851t_unit,X2: config256849571t_unit] :
% 0.25/0.58 ( ( prefix1615116500t_unit @ Xa2 @ Xb2 )
% 0.25/0.58 => ( ( P @ Xa2 @ Xb2 )
% 0.25/0.58 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xa2 ) @ ( cons_c1162654829t_unit @ X2 @ Xb2 ) ) ) )
% 0.25/0.58 => ( P @ X1 @ X22 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % prefixList.inducts
% 0.25/0.58 thf(fact_32_NatPredicateTippingPoint,axiom,
% 0.25/0.58 ! [N2: nat,Pr: nat > $o] :
% 0.25/0.58 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 0.25/0.58 => ( ( Pr @ zero_zero_nat )
% 0.25/0.58 => ( ~ ( Pr @ N2 )
% 0.25/0.58 => ? [N: nat] :
% 0.25/0.58 ( ( ord_less_nat @ N @ N2 )
% 0.25/0.58 & ( Pr @ N )
% 0.25/0.58 & ~ ( Pr @ ( suc @ N ) ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % NatPredicateTippingPoint
% 0.25/0.58 thf(fact_33_infiniteExecutionCfg_Osimps_I1_J,axiom,
% 0.25/0.58 ! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
% 0.25/0.58 ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 0.25/0.58 = ( cons_c1162654829t_unit @ Cfg2 @ nil_co1338500125t_unit ) ) ).
% 0.25/0.58
% 0.25/0.58 % infiniteExecutionCfg.simps(1)
% 0.25/0.58 thf(fact_34_length__greater__0__conv,axiom,
% 0.25/0.58 ! [Xs: list_l611321411t_unit] :
% 0.25/0.58 ( ( ord_less_nat @ zero_zero_nat @ ( size_s503142615t_unit @ Xs ) )
% 0.25/0.58 = ( Xs != nil_li307996205t_unit ) ) ).
% 0.25/0.58
% 0.25/0.58 % length_greater_0_conv
% 0.25/0.58 thf(fact_35_length__greater__0__conv,axiom,
% 0.25/0.58 ! [Xs: list_l1619404459ge_p_v] :
% 0.25/0.58 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1809856791ge_p_v @ Xs ) )
% 0.25/0.58 = ( Xs != nil_list_message_p_v ) ) ).
% 0.25/0.58
% 0.25/0.58 % length_greater_0_conv
% 0.25/0.58 thf(fact_36_length__greater__0__conv,axiom,
% 0.25/0.58 ! [Xs: list_message_p_v] :
% 0.25/0.58 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1168481041ge_p_v @ Xs ) )
% 0.25/0.58 = ( Xs != nil_message_p_v ) ) ).
% 0.25/0.58
% 0.25/0.58 % length_greater_0_conv
% 0.25/0.58 thf(fact_37_length__greater__0__conv,axiom,
% 0.25/0.58 ! [Xs: list_c1059388851t_unit] :
% 0.25/0.58 ( ( ord_less_nat @ zero_zero_nat @ ( size_s1406904903t_unit @ Xs ) )
% 0.25/0.58 = ( Xs != nil_co1338500125t_unit ) ) ).
% 0.25/0.58
% 0.25/0.58 % length_greater_0_conv
% 0.25/0.58 thf(fact_38_length__0__conv,axiom,
% 0.25/0.58 ! [Xs: list_l611321411t_unit] :
% 0.25/0.58 ( ( ( size_s503142615t_unit @ Xs )
% 0.25/0.58 = zero_zero_nat )
% 0.25/0.58 = ( Xs = nil_li307996205t_unit ) ) ).
% 0.25/0.58
% 0.25/0.58 % length_0_conv
% 0.25/0.58 thf(fact_39_length__0__conv,axiom,
% 0.25/0.58 ! [Xs: list_l1619404459ge_p_v] :
% 0.25/0.58 ( ( ( size_s1809856791ge_p_v @ Xs )
% 0.25/0.58 = zero_zero_nat )
% 0.25/0.58 = ( Xs = nil_list_message_p_v ) ) ).
% 0.25/0.58
% 0.25/0.58 % length_0_conv
% 0.25/0.58 thf(fact_40_length__0__conv,axiom,
% 0.25/0.58 ! [Xs: list_message_p_v] :
% 0.25/0.58 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.25/0.58 = zero_zero_nat )
% 0.25/0.58 = ( Xs = nil_message_p_v ) ) ).
% 0.25/0.58
% 0.25/0.58 % length_0_conv
% 0.25/0.58 thf(fact_41_length__0__conv,axiom,
% 0.25/0.58 ! [Xs: list_c1059388851t_unit] :
% 0.25/0.58 ( ( ( size_s1406904903t_unit @ Xs )
% 0.25/0.58 = zero_zero_nat )
% 0.25/0.58 = ( Xs = nil_co1338500125t_unit ) ) ).
% 0.25/0.58
% 0.25/0.58 % length_0_conv
% 0.25/0.58 thf(fact_42_less__Suc0,axiom,
% 0.25/0.58 ! [N3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ N3 @ ( suc @ zero_zero_nat ) )
% 0.25/0.58 = ( N3 = zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_Suc0
% 0.25/0.58 thf(fact_43_zero__less__Suc,axiom,
% 0.25/0.58 ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % zero_less_Suc
% 0.25/0.58 thf(fact_44_lessI,axiom,
% 0.25/0.58 ! [N3: nat] : ( ord_less_nat @ N3 @ ( suc @ N3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % lessI
% 0.25/0.58 thf(fact_45_Suc__mono,axiom,
% 0.25/0.58 ! [M: nat,N3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ M @ N3 )
% 0.25/0.58 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N3 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Suc_mono
% 0.25/0.58 thf(fact_46_Suc__less__eq,axiom,
% 0.25/0.58 ! [M: nat,N3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N3 ) )
% 0.25/0.58 = ( ord_less_nat @ M @ N3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % Suc_less_eq
% 0.25/0.58 thf(fact_47_neq0__conv,axiom,
% 0.25/0.58 ! [N3: nat] :
% 0.25/0.58 ( ( N3 != zero_zero_nat )
% 0.25/0.58 = ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % neq0_conv
% 0.25/0.58 thf(fact_48_less__nat__zero__code,axiom,
% 0.25/0.58 ! [N3: nat] :
% 0.25/0.58 ~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).
% 0.25/0.58
% 0.25/0.58 % less_nat_zero_code
% 0.25/0.58 thf(fact_49_bot__nat__0_Onot__eq__extremum,axiom,
% 0.25/0.58 ! [A: nat] :
% 0.25/0.58 ( ( A != zero_zero_nat )
% 0.25/0.58 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.25/0.58
% 0.25/0.58 % bot_nat_0.not_eq_extremum
% 0.25/0.58 thf(fact_50_list_Oinject,axiom,
% 0.25/0.58 ! [X21: message_p_v,X222: list_message_p_v,Y21: message_p_v,Y22: list_message_p_v] :
% 0.25/0.58 ( ( ( cons_message_p_v @ X21 @ X222 )
% 0.25/0.58 = ( cons_message_p_v @ Y21 @ Y22 ) )
% 0.25/0.58 = ( ( X21 = Y21 )
% 0.25/0.58 & ( X222 = Y22 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % list.inject
% 0.25/0.58 thf(fact_51_list_Oinject,axiom,
% 0.25/0.58 ! [X21: list_c1059388851t_unit,X222: list_l611321411t_unit,Y21: list_c1059388851t_unit,Y22: list_l611321411t_unit] :
% 0.25/0.58 ( ( ( cons_l1083444861t_unit @ X21 @ X222 )
% 0.25/0.58 = ( cons_l1083444861t_unit @ Y21 @ Y22 ) )
% 0.25/0.58 = ( ( X21 = Y21 )
% 0.25/0.58 & ( X222 = Y22 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % list.inject
% 0.25/0.58 thf(fact_52_list_Oinject,axiom,
% 0.25/0.58 ! [X21: list_message_p_v,X222: list_l1619404459ge_p_v,Y21: list_message_p_v,Y22: list_l1619404459ge_p_v] :
% 0.25/0.58 ( ( ( cons_l233104475ge_p_v @ X21 @ X222 )
% 0.25/0.58 = ( cons_l233104475ge_p_v @ Y21 @ Y22 ) )
% 0.25/0.58 = ( ( X21 = Y21 )
% 0.25/0.58 & ( X222 = Y22 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % list.inject
% 0.25/0.58 thf(fact_53_list_Oinject,axiom,
% 0.25/0.58 ! [X21: config256849571t_unit,X222: list_c1059388851t_unit,Y21: config256849571t_unit,Y22: list_c1059388851t_unit] :
% 0.25/0.58 ( ( ( cons_c1162654829t_unit @ X21 @ X222 )
% 0.25/0.58 = ( cons_c1162654829t_unit @ Y21 @ Y22 ) )
% 0.25/0.58 = ( ( X21 = Y21 )
% 0.25/0.58 & ( X222 = Y22 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % list.inject
% 0.25/0.58 thf(fact_54_old_Onat_Oinject,axiom,
% 0.25/0.58 ! [Nat: nat,Nat2: nat] :
% 0.25/0.58 ( ( ( suc @ Nat )
% 0.25/0.58 = ( suc @ Nat2 ) )
% 0.25/0.58 = ( Nat = Nat2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.nat.inject
% 0.25/0.58 thf(fact_55_nat_Oinject,axiom,
% 0.25/0.58 ! [X22: nat,Y2: nat] :
% 0.25/0.58 ( ( ( suc @ X22 )
% 0.25/0.58 = ( suc @ Y2 ) )
% 0.25/0.58 = ( X22 = Y2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % nat.inject
% 0.25/0.58 thf(fact_56_not__Cons__self2,axiom,
% 0.25/0.58 ! [X: message_p_v,Xs: list_message_p_v] :
% 0.25/0.58 ( ( cons_message_p_v @ X @ Xs )
% 0.25/0.58 != Xs ) ).
% 0.25/0.58
% 0.25/0.58 % not_Cons_self2
% 0.25/0.58 thf(fact_57_not__Cons__self2,axiom,
% 0.25/0.58 ! [X: list_c1059388851t_unit,Xs: list_l611321411t_unit] :
% 0.25/0.58 ( ( cons_l1083444861t_unit @ X @ Xs )
% 0.25/0.58 != Xs ) ).
% 0.25/0.58
% 0.25/0.58 % not_Cons_self2
% 0.25/0.58 thf(fact_58_not__Cons__self2,axiom,
% 0.25/0.58 ! [X: list_message_p_v,Xs: list_l1619404459ge_p_v] :
% 0.25/0.58 ( ( cons_l233104475ge_p_v @ X @ Xs )
% 0.25/0.58 != Xs ) ).
% 0.25/0.58
% 0.25/0.58 % not_Cons_self2
% 0.25/0.58 thf(fact_59_not__Cons__self2,axiom,
% 0.25/0.58 ! [X: config256849571t_unit,Xs: list_c1059388851t_unit] :
% 0.25/0.58 ( ( cons_c1162654829t_unit @ X @ Xs )
% 0.25/0.58 != Xs ) ).
% 0.25/0.58
% 0.25/0.58 % not_Cons_self2
% 0.25/0.58 thf(fact_60_n__not__Suc__n,axiom,
% 0.25/0.58 ! [N3: nat] :
% 0.25/0.58 ( N3
% 0.25/0.58 != ( suc @ N3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % n_not_Suc_n
% 0.25/0.58 thf(fact_61_Suc__inject,axiom,
% 0.25/0.58 ! [X: nat,Y: nat] :
% 0.25/0.58 ( ( ( suc @ X )
% 0.25/0.58 = ( suc @ Y ) )
% 0.25/0.58 => ( X = Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % Suc_inject
% 0.25/0.58 thf(fact_62_linorder__neqE__nat,axiom,
% 0.25/0.58 ! [X: nat,Y: nat] :
% 0.25/0.58 ( ( X != Y )
% 0.25/0.58 => ( ~ ( ord_less_nat @ X @ Y )
% 0.25/0.58 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % linorder_neqE_nat
% 0.25/0.58 thf(fact_63_infinite__descent,axiom,
% 0.25/0.58 ! [P: nat > $o,N3: nat] :
% 0.25/0.58 ( ! [N: nat] :
% 0.25/0.58 ( ~ ( P @ N )
% 0.25/0.58 => ? [M2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ M2 @ N )
% 0.25/0.58 & ~ ( P @ M2 ) ) )
% 0.25/0.58 => ( P @ N3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % infinite_descent
% 0.25/0.58 thf(fact_64_nat__less__induct,axiom,
% 0.25/0.58 ! [P: nat > $o,N3: nat] :
% 0.25/0.58 ( ! [N: nat] :
% 0.25/0.58 ( ! [M2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ M2 @ N )
% 0.25/0.58 => ( P @ M2 ) )
% 0.25/0.58 => ( P @ N ) )
% 0.25/0.58 => ( P @ N3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % nat_less_induct
% 0.25/0.58 thf(fact_65_less__irrefl__nat,axiom,
% 0.25/0.58 ! [N3: nat] :
% 0.25/0.58 ~ ( ord_less_nat @ N3 @ N3 ) ).
% 0.25/0.58
% 0.25/0.58 % less_irrefl_nat
% 0.25/0.58 thf(fact_66_less__not__refl3,axiom,
% 0.25/0.58 ! [S: nat,T: nat] :
% 0.25/0.58 ( ( ord_less_nat @ S @ T )
% 0.25/0.58 => ( S != T ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_not_refl3
% 0.25/0.58 thf(fact_67_less__not__refl2,axiom,
% 0.25/0.58 ! [N3: nat,M: nat] :
% 0.25/0.58 ( ( ord_less_nat @ N3 @ M )
% 0.25/0.58 => ( M != N3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_not_refl2
% 0.25/0.58 thf(fact_68_mem__Collect__eq,axiom,
% 0.25/0.58 ! [A: nat,P: nat > $o] :
% 0.25/0.58 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 0.25/0.58 = ( P @ A ) ) ).
% 0.25/0.58
% 0.25/0.58 % mem_Collect_eq
% 0.25/0.58 thf(fact_69_Collect__mem__eq,axiom,
% 0.25/0.58 ! [A8: set_nat] :
% 0.25/0.58 ( ( collect_nat
% 0.25/0.58 @ ^ [X3: nat] : ( member_nat @ X3 @ A8 ) )
% 0.25/0.58 = A8 ) ).
% 0.25/0.58
% 0.25/0.58 % Collect_mem_eq
% 0.25/0.58 thf(fact_70_less__not__refl,axiom,
% 0.25/0.58 ! [N3: nat] :
% 0.25/0.58 ~ ( ord_less_nat @ N3 @ N3 ) ).
% 0.25/0.58
% 0.25/0.58 % less_not_refl
% 0.25/0.58 thf(fact_71_nat__neq__iff,axiom,
% 0.25/0.58 ! [M: nat,N3: nat] :
% 0.25/0.58 ( ( M != N3 )
% 0.25/0.58 = ( ( ord_less_nat @ M @ N3 )
% 0.25/0.58 | ( ord_less_nat @ N3 @ M ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % nat_neq_iff
% 0.25/0.58 thf(fact_72_size__neq__size__imp__neq,axiom,
% 0.25/0.58 ! [X: list_message_p_v,Y: list_message_p_v] :
% 0.25/0.58 ( ( ( size_s1168481041ge_p_v @ X )
% 0.25/0.58 != ( size_s1168481041ge_p_v @ Y ) )
% 0.25/0.58 => ( X != Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % size_neq_size_imp_neq
% 0.25/0.58 thf(fact_73_size__neq__size__imp__neq,axiom,
% 0.25/0.58 ! [X: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
% 0.25/0.58 ( ( ( size_s1406904903t_unit @ X )
% 0.25/0.58 != ( size_s1406904903t_unit @ Y ) )
% 0.25/0.58 => ( X != Y ) ) ).
% 0.25/0.58
% 0.25/0.58 % size_neq_size_imp_neq
% 0.25/0.58 thf(fact_74_neq__if__length__neq,axiom,
% 0.25/0.58 ! [Xs: list_message_p_v,Ys: list_message_p_v] :
% 0.25/0.58 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.25/0.58 != ( size_s1168481041ge_p_v @ Ys ) )
% 0.25/0.58 => ( Xs != Ys ) ) ).
% 0.25/0.58
% 0.25/0.58 % neq_if_length_neq
% 0.25/0.58 thf(fact_75_neq__if__length__neq,axiom,
% 0.25/0.58 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 0.25/0.58 ( ( ( size_s1406904903t_unit @ Xs )
% 0.25/0.58 != ( size_s1406904903t_unit @ Ys ) )
% 0.25/0.58 => ( Xs != Ys ) ) ).
% 0.25/0.58
% 0.25/0.58 % neq_if_length_neq
% 0.25/0.58 thf(fact_76_Ex__list__of__length,axiom,
% 0.25/0.58 ! [N3: nat] :
% 0.25/0.58 ? [Xs2: list_message_p_v] :
% 0.25/0.58 ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.25/0.58 = N3 ) ).
% 0.25/0.58
% 0.25/0.58 % Ex_list_of_length
% 0.25/0.58 thf(fact_77_Ex__list__of__length,axiom,
% 0.25/0.58 ! [N3: nat] :
% 0.25/0.58 ? [Xs2: list_c1059388851t_unit] :
% 0.25/0.58 ( ( size_s1406904903t_unit @ Xs2 )
% 0.25/0.58 = N3 ) ).
% 0.25/0.58
% 0.25/0.58 % Ex_list_of_length
% 0.25/0.58 thf(fact_78_not0__implies__Suc,axiom,
% 0.25/0.58 ! [N3: nat] :
% 0.25/0.58 ( ( N3 != zero_zero_nat )
% 0.25/0.58 => ? [M3: nat] :
% 0.25/0.58 ( N3
% 0.25/0.58 = ( suc @ M3 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % not0_implies_Suc
% 0.25/0.58 thf(fact_79_old_Onat_Oinducts,axiom,
% 0.25/0.58 ! [P: nat > $o,Nat: nat] :
% 0.25/0.58 ( ( P @ zero_zero_nat )
% 0.25/0.58 => ( ! [Nat3: nat] :
% 0.25/0.58 ( ( P @ Nat3 )
% 0.25/0.58 => ( P @ ( suc @ Nat3 ) ) )
% 0.25/0.58 => ( P @ Nat ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.nat.inducts
% 0.25/0.58 thf(fact_80_old_Onat_Oexhaust,axiom,
% 0.25/0.58 ! [Y: nat] :
% 0.25/0.58 ( ( Y != zero_zero_nat )
% 0.25/0.58 => ~ ! [Nat3: nat] :
% 0.25/0.58 ( Y
% 0.25/0.58 != ( suc @ Nat3 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.nat.exhaust
% 0.25/0.58 thf(fact_81_Zero__not__Suc,axiom,
% 0.25/0.58 ! [M: nat] :
% 0.25/0.58 ( zero_zero_nat
% 0.25/0.58 != ( suc @ M ) ) ).
% 0.25/0.58
% 0.25/0.58 % Zero_not_Suc
% 0.25/0.58 thf(fact_82_Zero__neq__Suc,axiom,
% 0.25/0.58 ! [M: nat] :
% 0.25/0.58 ( zero_zero_nat
% 0.25/0.58 != ( suc @ M ) ) ).
% 0.25/0.58
% 0.25/0.58 % Zero_neq_Suc
% 0.25/0.58 thf(fact_83_Suc__neq__Zero,axiom,
% 0.25/0.58 ! [M: nat] :
% 0.25/0.58 ( ( suc @ M )
% 0.25/0.58 != zero_zero_nat ) ).
% 0.25/0.58
% 0.25/0.58 % Suc_neq_Zero
% 0.25/0.58 thf(fact_84_zero__induct,axiom,
% 0.25/0.58 ! [P: nat > $o,K: nat] :
% 0.25/0.58 ( ( P @ K )
% 0.25/0.58 => ( ! [N: nat] :
% 0.25/0.58 ( ( P @ ( suc @ N ) )
% 0.25/0.58 => ( P @ N ) )
% 0.25/0.58 => ( P @ zero_zero_nat ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % zero_induct
% 0.25/0.58 thf(fact_85_diff__induct,axiom,
% 0.25/0.58 ! [P: nat > nat > $o,M: nat,N3: nat] :
% 0.25/0.58 ( ! [X2: nat] : ( P @ X2 @ zero_zero_nat )
% 0.25/0.58 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 0.25/0.58 => ( ! [X2: nat,Y3: nat] :
% 0.25/0.58 ( ( P @ X2 @ Y3 )
% 0.25/0.58 => ( P @ ( suc @ X2 ) @ ( suc @ Y3 ) ) )
% 0.25/0.58 => ( P @ M @ N3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % diff_induct
% 0.25/0.58 thf(fact_86_nat__induct,axiom,
% 0.25/0.58 ! [P: nat > $o,N3: nat] :
% 0.25/0.58 ( ( P @ zero_zero_nat )
% 0.25/0.58 => ( ! [N: nat] :
% 0.25/0.58 ( ( P @ N )
% 0.25/0.58 => ( P @ ( suc @ N ) ) )
% 0.25/0.58 => ( P @ N3 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % nat_induct
% 0.25/0.58 thf(fact_87_nat_OdiscI,axiom,
% 0.25/0.58 ! [Nat: nat,X22: nat] :
% 0.25/0.58 ( ( Nat
% 0.25/0.58 = ( suc @ X22 ) )
% 0.25/0.58 => ( Nat != zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % nat.discI
% 0.25/0.58 thf(fact_88_old_Onat_Odistinct_I1_J,axiom,
% 0.25/0.58 ! [Nat2: nat] :
% 0.25/0.58 ( zero_zero_nat
% 0.25/0.58 != ( suc @ Nat2 ) ) ).
% 0.25/0.58
% 0.25/0.58 % old.nat.distinct(1)
% 0.25/0.58 thf(fact_89_old_Onat_Odistinct_I2_J,axiom,
% 0.25/0.58 ! [Nat2: nat] :
% 0.25/0.58 ( ( suc @ Nat2 )
% 0.25/0.58 != zero_zero_nat ) ).
% 0.25/0.58
% 0.25/0.58 % old.nat.distinct(2)
% 0.25/0.58 thf(fact_90_nat_Odistinct_I1_J,axiom,
% 0.25/0.58 ! [X22: nat] :
% 0.25/0.58 ( zero_zero_nat
% 0.25/0.58 != ( suc @ X22 ) ) ).
% 0.25/0.58
% 0.25/0.58 % nat.distinct(1)
% 0.25/0.58 thf(fact_91_bot__nat__0_Oextremum__strict,axiom,
% 0.25/0.58 ! [A: nat] :
% 0.25/0.58 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.25/0.58
% 0.25/0.58 % bot_nat_0.extremum_strict
% 0.25/0.58 thf(fact_92_infinite__descent0,axiom,
% 0.25/0.58 ! [P: nat > $o,N3: nat] :
% 0.25/0.58 ( ( P @ zero_zero_nat )
% 0.25/0.58 => ( ! [N: nat] :
% 0.25/0.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.25/0.58 => ( ~ ( P @ N )
% 0.25/0.58 => ? [M2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ M2 @ N )
% 0.25/0.58 & ~ ( P @ M2 ) ) ) )
% 0.25/0.58 => ( P @ N3 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % infinite_descent0
% 0.25/0.58 thf(fact_93_gr__implies__not0,axiom,
% 0.25/0.58 ! [M: nat,N3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ M @ N3 )
% 0.25/0.58 => ( N3 != zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % gr_implies_not0
% 0.25/0.58 thf(fact_94_less__zeroE,axiom,
% 0.25/0.58 ! [N3: nat] :
% 0.25/0.58 ~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).
% 0.25/0.58
% 0.25/0.58 % less_zeroE
% 0.25/0.58 thf(fact_95_not__less0,axiom,
% 0.25/0.58 ! [N3: nat] :
% 0.25/0.58 ~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).
% 0.25/0.58
% 0.25/0.58 % not_less0
% 0.25/0.58 thf(fact_96_not__gr0,axiom,
% 0.25/0.58 ! [N3: nat] :
% 0.25/0.58 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 0.25/0.58 = ( N3 = zero_zero_nat ) ) ).
% 0.25/0.58
% 0.25/0.58 % not_gr0
% 0.25/0.58 thf(fact_97_gr0I,axiom,
% 0.25/0.58 ! [N3: nat] :
% 0.25/0.58 ( ( N3 != zero_zero_nat )
% 0.25/0.58 => ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % gr0I
% 0.25/0.58 thf(fact_98_not__less__less__Suc__eq,axiom,
% 0.25/0.58 ! [N3: nat,M: nat] :
% 0.25/0.58 ( ~ ( ord_less_nat @ N3 @ M )
% 0.25/0.58 => ( ( ord_less_nat @ N3 @ ( suc @ M ) )
% 0.25/0.58 = ( N3 = M ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % not_less_less_Suc_eq
% 0.25/0.58 thf(fact_99_strict__inc__induct,axiom,
% 0.25/0.58 ! [I: nat,J: nat,P: nat > $o] :
% 0.25/0.58 ( ( ord_less_nat @ I @ J )
% 0.25/0.58 => ( ! [I2: nat] :
% 0.25/0.58 ( ( J
% 0.25/0.58 = ( suc @ I2 ) )
% 0.25/0.58 => ( P @ I2 ) )
% 0.25/0.58 => ( ! [I2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I2 @ J )
% 0.25/0.58 => ( ( P @ ( suc @ I2 ) )
% 0.25/0.58 => ( P @ I2 ) ) )
% 0.25/0.58 => ( P @ I ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % strict_inc_induct
% 0.25/0.58 thf(fact_100_less__Suc__induct,axiom,
% 0.25/0.58 ! [I: nat,J: nat,P: nat > nat > $o] :
% 0.25/0.58 ( ( ord_less_nat @ I @ J )
% 0.25/0.58 => ( ! [I2: nat] : ( P @ I2 @ ( suc @ I2 ) )
% 0.25/0.58 => ( ! [I2: nat,J2: nat,K2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I2 @ J2 )
% 0.25/0.58 => ( ( ord_less_nat @ J2 @ K2 )
% 0.25/0.58 => ( ( P @ I2 @ J2 )
% 0.25/0.58 => ( ( P @ J2 @ K2 )
% 0.25/0.58 => ( P @ I2 @ K2 ) ) ) ) )
% 0.25/0.58 => ( P @ I @ J ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_Suc_induct
% 0.25/0.58 thf(fact_101_less__trans__Suc,axiom,
% 0.25/0.58 ! [I: nat,J: nat,K: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I @ J )
% 0.25/0.58 => ( ( ord_less_nat @ J @ K )
% 0.25/0.58 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_trans_Suc
% 0.25/0.58 thf(fact_102_Suc__less__SucD,axiom,
% 0.25/0.58 ! [M: nat,N3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N3 ) )
% 0.25/0.58 => ( ord_less_nat @ M @ N3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % Suc_less_SucD
% 0.25/0.58 thf(fact_103_less__antisym,axiom,
% 0.25/0.58 ! [N3: nat,M: nat] :
% 0.25/0.58 ( ~ ( ord_less_nat @ N3 @ M )
% 0.25/0.58 => ( ( ord_less_nat @ N3 @ ( suc @ M ) )
% 0.25/0.58 => ( M = N3 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_antisym
% 0.25/0.58 thf(fact_104_Suc__less__eq2,axiom,
% 0.25/0.58 ! [N3: nat,M: nat] :
% 0.25/0.58 ( ( ord_less_nat @ ( suc @ N3 ) @ M )
% 0.25/0.58 = ( ? [M4: nat] :
% 0.25/0.58 ( ( M
% 0.25/0.58 = ( suc @ M4 ) )
% 0.25/0.58 & ( ord_less_nat @ N3 @ M4 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Suc_less_eq2
% 0.25/0.58 thf(fact_105_All__less__Suc,axiom,
% 0.25/0.58 ! [N3: nat,P: nat > $o] :
% 0.25/0.58 ( ( ! [I3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
% 0.25/0.58 => ( P @ I3 ) ) )
% 0.25/0.58 = ( ( P @ N3 )
% 0.25/0.58 & ! [I3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I3 @ N3 )
% 0.25/0.58 => ( P @ I3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % All_less_Suc
% 0.25/0.58 thf(fact_106_not__less__eq,axiom,
% 0.25/0.58 ! [M: nat,N3: nat] :
% 0.25/0.58 ( ( ~ ( ord_less_nat @ M @ N3 ) )
% 0.25/0.58 = ( ord_less_nat @ N3 @ ( suc @ M ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % not_less_eq
% 0.25/0.58 thf(fact_107_less__Suc__eq,axiom,
% 0.25/0.58 ! [M: nat,N3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ M @ ( suc @ N3 ) )
% 0.25/0.58 = ( ( ord_less_nat @ M @ N3 )
% 0.25/0.58 | ( M = N3 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_Suc_eq
% 0.25/0.58 thf(fact_108_Ex__less__Suc,axiom,
% 0.25/0.58 ! [N3: nat,P: nat > $o] :
% 0.25/0.58 ( ( ? [I3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
% 0.25/0.58 & ( P @ I3 ) ) )
% 0.25/0.58 = ( ( P @ N3 )
% 0.25/0.58 | ? [I3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I3 @ N3 )
% 0.25/0.58 & ( P @ I3 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Ex_less_Suc
% 0.25/0.58 thf(fact_109_less__SucI,axiom,
% 0.25/0.58 ! [M: nat,N3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ M @ N3 )
% 0.25/0.58 => ( ord_less_nat @ M @ ( suc @ N3 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_SucI
% 0.25/0.58 thf(fact_110_less__SucE,axiom,
% 0.25/0.58 ! [M: nat,N3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ M @ ( suc @ N3 ) )
% 0.25/0.58 => ( ~ ( ord_less_nat @ M @ N3 )
% 0.25/0.58 => ( M = N3 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % less_SucE
% 0.25/0.58 thf(fact_111_Suc__lessI,axiom,
% 0.25/0.58 ! [M: nat,N3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ M @ N3 )
% 0.25/0.58 => ( ( ( suc @ M )
% 0.25/0.58 != N3 )
% 0.25/0.58 => ( ord_less_nat @ ( suc @ M ) @ N3 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Suc_lessI
% 0.25/0.58 thf(fact_112_Suc__lessE,axiom,
% 0.25/0.58 ! [I: nat,K: nat] :
% 0.25/0.58 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 0.25/0.58 => ~ ! [J2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I @ J2 )
% 0.25/0.58 => ( K
% 0.25/0.58 != ( suc @ J2 ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Suc_lessE
% 0.25/0.58 thf(fact_113_Suc__lessD,axiom,
% 0.25/0.58 ! [M: nat,N3: nat] :
% 0.25/0.58 ( ( ord_less_nat @ ( suc @ M ) @ N3 )
% 0.25/0.58 => ( ord_less_nat @ M @ N3 ) ) ).
% 0.25/0.58
% 0.25/0.58 % Suc_lessD
% 0.25/0.58 thf(fact_114_Nat_OlessE,axiom,
% 0.25/0.58 ! [I: nat,K: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I @ K )
% 0.25/0.58 => ( ( K
% 0.25/0.58 != ( suc @ I ) )
% 0.25/0.58 => ~ ! [J2: nat] :
% 0.25/0.58 ( ( ord_less_nat @ I @ J2 )
% 0.25/0.58 => ( K
% 0.25/0.58 != ( suc @ J2 ) ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % Nat.lessE
% 0.25/0.58 thf(fact_115_map__tailrec__rev_Oinduct,axiom,
% 0.25/0.58 ! [P: ( message_p_v > config256849571t_unit ) > list_message_p_v > list_c1059388851t_unit > $o,A0: message_p_v > config256849571t_unit,A1: list_message_p_v,A2: list_c1059388851t_unit] :
% 0.25/0.58 ( ! [F: message_p_v > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_message_p_v @ X_1 )
% 0.25/0.58 => ( ! [F: message_p_v > config256849571t_unit,A9: message_p_v,As: list_message_p_v,Bs: list_c1059388851t_unit] :
% 0.25/0.58 ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A9 ) @ Bs ) )
% 0.25/0.58 => ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
% 0.25/0.58 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % map_tailrec_rev.induct
% 0.25/0.58 thf(fact_116_map__tailrec__rev_Oinduct,axiom,
% 0.25/0.58 ! [P: ( config256849571t_unit > config256849571t_unit ) > list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit,A1: list_c1059388851t_unit,A2: list_c1059388851t_unit] :
% 0.25/0.58 ( ! [F: config256849571t_unit > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_co1338500125t_unit @ X_1 )
% 0.25/0.58 => ( ! [F: config256849571t_unit > config256849571t_unit,A9: config256849571t_unit,As: list_c1059388851t_unit,Bs: list_c1059388851t_unit] :
% 0.25/0.58 ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A9 ) @ Bs ) )
% 0.25/0.58 => ( P @ F @ ( cons_c1162654829t_unit @ A9 @ As ) @ Bs ) )
% 0.25/0.58 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % map_tailrec_rev.induct
% 0.25/0.58 thf(fact_117_map__tailrec__rev_Oinduct,axiom,
% 0.25/0.58 ! [P: ( message_p_v > message_p_v ) > list_message_p_v > list_message_p_v > $o,A0: message_p_v > message_p_v,A1: list_message_p_v,A2: list_message_p_v] :
% 0.25/0.58 ( ! [F: message_p_v > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_message_p_v @ X_1 )
% 0.25/0.58 => ( ! [F: message_p_v > message_p_v,A9: message_p_v,As: list_message_p_v,Bs: list_message_p_v] :
% 0.25/0.58 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
% 0.25/0.58 => ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
% 0.25/0.58 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % map_tailrec_rev.induct
% 0.25/0.58 thf(fact_118_map__tailrec__rev_Oinduct,axiom,
% 0.25/0.58 ! [P: ( list_message_p_v > message_p_v ) > list_l1619404459ge_p_v > list_message_p_v > $o,A0: list_message_p_v > message_p_v,A1: list_l1619404459ge_p_v,A2: list_message_p_v] :
% 0.25/0.58 ( ! [F: list_message_p_v > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_list_message_p_v @ X_1 )
% 0.25/0.58 => ( ! [F: list_message_p_v > message_p_v,A9: list_message_p_v,As: list_l1619404459ge_p_v,Bs: list_message_p_v] :
% 0.25/0.58 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
% 0.25/0.58 => ( P @ F @ ( cons_l233104475ge_p_v @ A9 @ As ) @ Bs ) )
% 0.25/0.58 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % map_tailrec_rev.induct
% 0.25/0.58 thf(fact_119_map__tailrec__rev_Oinduct,axiom,
% 0.25/0.58 ! [P: ( message_p_v > list_message_p_v ) > list_message_p_v > list_l1619404459ge_p_v > $o,A0: message_p_v > list_message_p_v,A1: list_message_p_v,A2: list_l1619404459ge_p_v] :
% 0.25/0.58 ( ! [F: message_p_v > list_message_p_v,X_1: list_l1619404459ge_p_v] : ( P @ F @ nil_message_p_v @ X_1 )
% 0.25/0.58 => ( ! [F: message_p_v > list_message_p_v,A9: message_p_v,As: list_message_p_v,Bs: list_l1619404459ge_p_v] :
% 0.25/0.58 ( ( P @ F @ As @ ( cons_l233104475ge_p_v @ ( F @ A9 ) @ Bs ) )
% 0.25/0.58 => ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
% 0.25/0.58 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % map_tailrec_rev.induct
% 0.25/0.58 thf(fact_120_map__tailrec__rev_Oinduct,axiom,
% 0.25/0.58 ! [P: ( config256849571t_unit > message_p_v ) > list_c1059388851t_unit > list_message_p_v > $o,A0: config256849571t_unit > message_p_v,A1: list_c1059388851t_unit,A2: list_message_p_v] :
% 0.25/0.58 ( ! [F: config256849571t_unit > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_co1338500125t_unit @ X_1 )
% 0.25/0.58 => ( ! [F: config256849571t_unit > message_p_v,A9: config256849571t_unit,As: list_c1059388851t_unit,Bs: list_message_p_v] :
% 0.25/0.58 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
% 0.25/0.58 => ( P @ F @ ( cons_c1162654829t_unit @ A9 @ As ) @ Bs ) )
% 0.25/0.58 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % map_tailrec_rev.induct
% 0.25/0.58 thf(fact_121_map__tailrec__rev_Oinduct,axiom,
% 0.25/0.58 ! [P: ( list_message_p_v > list_message_p_v ) > list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o,A0: list_message_p_v > list_message_p_v,A1: list_l1619404459ge_p_v,A2: list_l1619404459ge_p_v] :
% 0.25/0.58 ( ! [F: list_message_p_v > list_message_p_v,X_1: list_l1619404459ge_p_v] : ( P @ F @ nil_list_message_p_v @ X_1 )
% 0.25/0.58 => ( ! [F: list_message_p_v > list_message_p_v,A9: list_message_p_v,As: list_l1619404459ge_p_v,Bs: list_l1619404459ge_p_v] :
% 0.25/0.58 ( ( P @ F @ As @ ( cons_l233104475ge_p_v @ ( F @ A9 ) @ Bs ) )
% 0.25/0.58 => ( P @ F @ ( cons_l233104475ge_p_v @ A9 @ As ) @ Bs ) )
% 0.25/0.58 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % map_tailrec_rev.induct
% 0.25/0.58 thf(fact_122_map__tailrec__rev_Oinduct,axiom,
% 0.25/0.58 ! [P: ( list_message_p_v > config256849571t_unit ) > list_l1619404459ge_p_v > list_c1059388851t_unit > $o,A0: list_message_p_v > config256849571t_unit,A1: list_l1619404459ge_p_v,A2: list_c1059388851t_unit] :
% 0.25/0.58 ( ! [F: list_message_p_v > config256849571t_unit,X_1: list_c1059388851t_unit] : ( P @ F @ nil_list_message_p_v @ X_1 )
% 0.25/0.58 => ( ! [F: list_message_p_v > config256849571t_unit,A9: list_message_p_v,As: list_l1619404459ge_p_v,Bs: list_c1059388851t_unit] :
% 0.25/0.58 ( ( P @ F @ As @ ( cons_c1162654829t_unit @ ( F @ A9 ) @ Bs ) )
% 0.25/0.58 => ( P @ F @ ( cons_l233104475ge_p_v @ A9 @ As ) @ Bs ) )
% 0.25/0.58 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % map_tailrec_rev.induct
% 0.25/0.58 thf(fact_123_map__tailrec__rev_Oinduct,axiom,
% 0.25/0.58 ! [P: ( list_c1059388851t_unit > message_p_v ) > list_l611321411t_unit > list_message_p_v > $o,A0: list_c1059388851t_unit > message_p_v,A1: list_l611321411t_unit,A2: list_message_p_v] :
% 0.25/0.58 ( ! [F: list_c1059388851t_unit > message_p_v,X_1: list_message_p_v] : ( P @ F @ nil_li307996205t_unit @ X_1 )
% 0.25/0.58 => ( ! [F: list_c1059388851t_unit > message_p_v,A9: list_c1059388851t_unit,As: list_l611321411t_unit,Bs: list_message_p_v] :
% 0.25/0.58 ( ( P @ F @ As @ ( cons_message_p_v @ ( F @ A9 ) @ Bs ) )
% 0.25/0.58 => ( P @ F @ ( cons_l1083444861t_unit @ A9 @ As ) @ Bs ) )
% 0.25/0.58 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % map_tailrec_rev.induct
% 0.25/0.58 thf(fact_124_map__tailrec__rev_Oinduct,axiom,
% 0.25/0.58 ! [P: ( message_p_v > list_c1059388851t_unit ) > list_message_p_v > list_l611321411t_unit > $o,A0: message_p_v > list_c1059388851t_unit,A1: list_message_p_v,A2: list_l611321411t_unit] :
% 0.25/0.58 ( ! [F: message_p_v > list_c1059388851t_unit,X_1: list_l611321411t_unit] : ( P @ F @ nil_message_p_v @ X_1 )
% 0.25/0.58 => ( ! [F: message_p_v > list_c1059388851t_unit,A9: message_p_v,As: list_message_p_v,Bs: list_l611321411t_unit] :
% 0.25/0.58 ( ( P @ F @ As @ ( cons_l1083444861t_unit @ ( F @ A9 ) @ Bs ) )
% 0.25/0.58 => ( P @ F @ ( cons_message_p_v @ A9 @ As ) @ Bs ) )
% 0.25/0.58 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % map_tailrec_rev.induct
% 0.25/0.58 thf(fact_125_list__nonempty__induct,axiom,
% 0.25/0.58 ! [Xs: list_l611321411t_unit,P: list_l611321411t_unit > $o] :
% 0.25/0.58 ( ( Xs != nil_li307996205t_unit )
% 0.25/0.58 => ( ! [X2: list_c1059388851t_unit] : ( P @ ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
% 0.25/0.58 => ( ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 0.25/0.58 ( ( Xs2 != nil_li307996205t_unit )
% 0.25/0.58 => ( ( P @ Xs2 )
% 0.25/0.58 => ( P @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) ) ) )
% 0.25/0.58 => ( P @ Xs ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % list_nonempty_induct
% 0.25/0.58 thf(fact_126_list__nonempty__induct,axiom,
% 0.25/0.58 ! [Xs: list_l1619404459ge_p_v,P: list_l1619404459ge_p_v > $o] :
% 0.25/0.58 ( ( Xs != nil_list_message_p_v )
% 0.25/0.58 => ( ! [X2: list_message_p_v] : ( P @ ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
% 0.25/0.58 => ( ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 0.25/0.58 ( ( Xs2 != nil_list_message_p_v )
% 0.25/0.58 => ( ( P @ Xs2 )
% 0.25/0.58 => ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) ) ) )
% 0.25/0.58 => ( P @ Xs ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % list_nonempty_induct
% 0.25/0.58 thf(fact_127_list__nonempty__induct,axiom,
% 0.25/0.58 ! [Xs: list_message_p_v,P: list_message_p_v > $o] :
% 0.25/0.58 ( ( Xs != nil_message_p_v )
% 0.25/0.58 => ( ! [X2: message_p_v] : ( P @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
% 0.25/0.58 => ( ! [X2: message_p_v,Xs2: list_message_p_v] :
% 0.25/0.58 ( ( Xs2 != nil_message_p_v )
% 0.25/0.58 => ( ( P @ Xs2 )
% 0.25/0.58 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) ) ) )
% 0.25/0.58 => ( P @ Xs ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % list_nonempty_induct
% 0.25/0.58 thf(fact_128_list__nonempty__induct,axiom,
% 0.25/0.58 ! [Xs: list_c1059388851t_unit,P: list_c1059388851t_unit > $o] :
% 0.25/0.58 ( ( Xs != nil_co1338500125t_unit )
% 0.25/0.58 => ( ! [X2: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
% 0.25/0.58 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 0.25/0.58 ( ( Xs2 != nil_co1338500125t_unit )
% 0.25/0.58 => ( ( P @ Xs2 )
% 0.25/0.58 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) ) ) )
% 0.25/0.58 => ( P @ Xs ) ) ) ) ).
% 0.25/0.58
% 0.25/0.58 % list_nonempty_induct
% 0.25/0.58 thf(fact_129_successively_Oinduct,axiom,
% 0.25/0.58 ! [P: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_l611321411t_unit > $o,A0: list_c1059388851t_unit > list_c1059388851t_unit > $o,A1: list_l611321411t_unit] :
% 0.25/0.58 ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o] : ( P @ P2 @ nil_li307996205t_unit )
% 0.25/0.58 => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X2: list_c1059388851t_unit] : ( P @ P2 @ ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
% 0.25/0.58 => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X2: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 0.25/0.58 ( ( P @ P2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) )
% 0.25/0.59 => ( P @ P2 @ ( cons_l1083444861t_unit @ X2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % successively.induct
% 0.25/0.59 thf(fact_130_successively_Oinduct,axiom,
% 0.25/0.59 ! [P: ( list_message_p_v > list_message_p_v > $o ) > list_l1619404459ge_p_v > $o,A0: list_message_p_v > list_message_p_v > $o,A1: list_l1619404459ge_p_v] :
% 0.25/0.59 ( ! [P2: list_message_p_v > list_message_p_v > $o] : ( P @ P2 @ nil_list_message_p_v )
% 0.25/0.59 => ( ! [P2: list_message_p_v > list_message_p_v > $o,X2: list_message_p_v] : ( P @ P2 @ ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
% 0.25/0.59 => ( ! [P2: list_message_p_v > list_message_p_v > $o,X2: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 0.25/0.59 ( ( P @ P2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) )
% 0.25/0.59 => ( P @ P2 @ ( cons_l233104475ge_p_v @ X2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % successively.induct
% 0.25/0.59 thf(fact_131_successively_Oinduct,axiom,
% 0.25/0.59 ! [P: ( message_p_v > message_p_v > $o ) > list_message_p_v > $o,A0: message_p_v > message_p_v > $o,A1: list_message_p_v] :
% 0.25/0.59 ( ! [P2: message_p_v > message_p_v > $o] : ( P @ P2 @ nil_message_p_v )
% 0.25/0.59 => ( ! [P2: message_p_v > message_p_v > $o,X2: message_p_v] : ( P @ P2 @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
% 0.25/0.59 => ( ! [P2: message_p_v > message_p_v > $o,X2: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 0.25/0.59 ( ( P @ P2 @ ( cons_message_p_v @ Y3 @ Xs2 ) )
% 0.25/0.59 => ( P @ P2 @ ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % successively.induct
% 0.25/0.59 thf(fact_132_successively_Oinduct,axiom,
% 0.25/0.59 ! [P: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit] :
% 0.25/0.59 ( ! [P2: config256849571t_unit > config256849571t_unit > $o] : ( P @ P2 @ nil_co1338500125t_unit )
% 0.25/0.59 => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X2: config256849571t_unit] : ( P @ P2 @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
% 0.25/0.59 => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X2: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 0.25/0.59 ( ( P @ P2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) )
% 0.25/0.59 => ( P @ P2 @ ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % successively.induct
% 0.25/0.59 thf(fact_133_remdups__adj_Oinduct,axiom,
% 0.25/0.59 ! [P: list_l611321411t_unit > $o,A0: list_l611321411t_unit] :
% 0.25/0.59 ( ( P @ nil_li307996205t_unit )
% 0.25/0.59 => ( ! [X2: list_c1059388851t_unit] : ( P @ ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
% 0.25/0.59 => ( ! [X2: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 0.25/0.59 ( ( ( X2 = Y3 )
% 0.25/0.59 => ( P @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) ) )
% 0.25/0.59 => ( ( ( X2 != Y3 )
% 0.25/0.59 => ( P @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) )
% 0.25/0.59 => ( P @ ( cons_l1083444861t_unit @ X2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) ) )
% 0.25/0.59 => ( P @ A0 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % remdups_adj.induct
% 0.25/0.59 thf(fact_134_remdups__adj_Oinduct,axiom,
% 0.25/0.59 ! [P: list_l1619404459ge_p_v > $o,A0: list_l1619404459ge_p_v] :
% 0.25/0.59 ( ( P @ nil_list_message_p_v )
% 0.25/0.59 => ( ! [X2: list_message_p_v] : ( P @ ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
% 0.25/0.59 => ( ! [X2: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 0.25/0.59 ( ( ( X2 = Y3 )
% 0.25/0.59 => ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) ) )
% 0.25/0.59 => ( ( ( X2 != Y3 )
% 0.25/0.59 => ( P @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) )
% 0.25/0.59 => ( P @ ( cons_l233104475ge_p_v @ X2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) ) )
% 0.25/0.59 => ( P @ A0 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % remdups_adj.induct
% 0.25/0.59 thf(fact_135_remdups__adj_Oinduct,axiom,
% 0.25/0.59 ! [P: list_message_p_v > $o,A0: list_message_p_v] :
% 0.25/0.59 ( ( P @ nil_message_p_v )
% 0.25/0.59 => ( ! [X2: message_p_v] : ( P @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
% 0.25/0.59 => ( ! [X2: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 0.25/0.59 ( ( ( X2 = Y3 )
% 0.25/0.59 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) ) )
% 0.25/0.59 => ( ( ( X2 != Y3 )
% 0.25/0.59 => ( P @ ( cons_message_p_v @ Y3 @ Xs2 ) ) )
% 0.25/0.59 => ( P @ ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) ) )
% 0.25/0.59 => ( P @ A0 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % remdups_adj.induct
% 0.25/0.59 thf(fact_136_remdups__adj_Oinduct,axiom,
% 0.25/0.59 ! [P: list_c1059388851t_unit > $o,A0: list_c1059388851t_unit] :
% 0.25/0.59 ( ( P @ nil_co1338500125t_unit )
% 0.25/0.59 => ( ! [X2: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
% 0.25/0.59 => ( ! [X2: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 0.25/0.59 ( ( ( X2 = Y3 )
% 0.25/0.59 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) ) )
% 0.25/0.59 => ( ( ( X2 != Y3 )
% 0.25/0.59 => ( P @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) )
% 0.25/0.59 => ( P @ ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) ) )
% 0.25/0.59 => ( P @ A0 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % remdups_adj.induct
% 0.25/0.59 thf(fact_137_sorted__wrt_Oinduct,axiom,
% 0.25/0.59 ! [P: ( list_c1059388851t_unit > list_c1059388851t_unit > $o ) > list_l611321411t_unit > $o,A0: list_c1059388851t_unit > list_c1059388851t_unit > $o,A1: list_l611321411t_unit] :
% 0.25/0.59 ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o] : ( P @ P2 @ nil_li307996205t_unit )
% 0.25/0.59 => ( ! [P2: list_c1059388851t_unit > list_c1059388851t_unit > $o,X2: list_c1059388851t_unit,Ys2: list_l611321411t_unit] :
% 0.25/0.59 ( ( P @ P2 @ Ys2 )
% 0.25/0.59 => ( P @ P2 @ ( cons_l1083444861t_unit @ X2 @ Ys2 ) ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sorted_wrt.induct
% 0.25/0.59 thf(fact_138_sorted__wrt_Oinduct,axiom,
% 0.25/0.59 ! [P: ( list_message_p_v > list_message_p_v > $o ) > list_l1619404459ge_p_v > $o,A0: list_message_p_v > list_message_p_v > $o,A1: list_l1619404459ge_p_v] :
% 0.25/0.59 ( ! [P2: list_message_p_v > list_message_p_v > $o] : ( P @ P2 @ nil_list_message_p_v )
% 0.25/0.59 => ( ! [P2: list_message_p_v > list_message_p_v > $o,X2: list_message_p_v,Ys2: list_l1619404459ge_p_v] :
% 0.25/0.59 ( ( P @ P2 @ Ys2 )
% 0.25/0.59 => ( P @ P2 @ ( cons_l233104475ge_p_v @ X2 @ Ys2 ) ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sorted_wrt.induct
% 0.25/0.59 thf(fact_139_sorted__wrt_Oinduct,axiom,
% 0.25/0.59 ! [P: ( message_p_v > message_p_v > $o ) > list_message_p_v > $o,A0: message_p_v > message_p_v > $o,A1: list_message_p_v] :
% 0.25/0.59 ( ! [P2: message_p_v > message_p_v > $o] : ( P @ P2 @ nil_message_p_v )
% 0.25/0.59 => ( ! [P2: message_p_v > message_p_v > $o,X2: message_p_v,Ys2: list_message_p_v] :
% 0.25/0.59 ( ( P @ P2 @ Ys2 )
% 0.25/0.59 => ( P @ P2 @ ( cons_message_p_v @ X2 @ Ys2 ) ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sorted_wrt.induct
% 0.25/0.59 thf(fact_140_sorted__wrt_Oinduct,axiom,
% 0.25/0.59 ! [P: ( config256849571t_unit > config256849571t_unit > $o ) > list_c1059388851t_unit > $o,A0: config256849571t_unit > config256849571t_unit > $o,A1: list_c1059388851t_unit] :
% 0.25/0.59 ( ! [P2: config256849571t_unit > config256849571t_unit > $o] : ( P @ P2 @ nil_co1338500125t_unit )
% 0.25/0.59 => ( ! [P2: config256849571t_unit > config256849571t_unit > $o,X2: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 0.25/0.59 ( ( P @ P2 @ Ys2 )
% 0.25/0.59 => ( P @ P2 @ ( cons_c1162654829t_unit @ X2 @ Ys2 ) ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % sorted_wrt.induct
% 0.25/0.59 thf(fact_141_remdups__adj_Ocases,axiom,
% 0.25/0.59 ! [X: list_l611321411t_unit] :
% 0.25/0.59 ( ( X != nil_li307996205t_unit )
% 0.25/0.59 => ( ! [X2: list_c1059388851t_unit] :
% 0.25/0.59 ( X
% 0.25/0.59 != ( cons_l1083444861t_unit @ X2 @ nil_li307996205t_unit ) )
% 0.25/0.59 => ~ ! [X2: list_c1059388851t_unit,Y3: list_c1059388851t_unit,Xs2: list_l611321411t_unit] :
% 0.25/0.59 ( X
% 0.25/0.59 != ( cons_l1083444861t_unit @ X2 @ ( cons_l1083444861t_unit @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % remdups_adj.cases
% 0.25/0.59 thf(fact_142_remdups__adj_Ocases,axiom,
% 0.25/0.59 ! [X: list_l1619404459ge_p_v] :
% 0.25/0.59 ( ( X != nil_list_message_p_v )
% 0.25/0.59 => ( ! [X2: list_message_p_v] :
% 0.25/0.59 ( X
% 0.25/0.59 != ( cons_l233104475ge_p_v @ X2 @ nil_list_message_p_v ) )
% 0.25/0.59 => ~ ! [X2: list_message_p_v,Y3: list_message_p_v,Xs2: list_l1619404459ge_p_v] :
% 0.25/0.59 ( X
% 0.25/0.59 != ( cons_l233104475ge_p_v @ X2 @ ( cons_l233104475ge_p_v @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % remdups_adj.cases
% 0.25/0.59 thf(fact_143_remdups__adj_Ocases,axiom,
% 0.25/0.59 ! [X: list_message_p_v] :
% 0.25/0.59 ( ( X != nil_message_p_v )
% 0.25/0.59 => ( ! [X2: message_p_v] :
% 0.25/0.59 ( X
% 0.25/0.59 != ( cons_message_p_v @ X2 @ nil_message_p_v ) )
% 0.25/0.59 => ~ ! [X2: message_p_v,Y3: message_p_v,Xs2: list_message_p_v] :
% 0.25/0.59 ( X
% 0.25/0.59 != ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % remdups_adj.cases
% 0.25/0.59 thf(fact_144_remdups__adj_Ocases,axiom,
% 0.25/0.59 ! [X: list_c1059388851t_unit] :
% 0.25/0.59 ( ( X != nil_co1338500125t_unit )
% 0.25/0.59 => ( ! [X2: config256849571t_unit] :
% 0.25/0.59 ( X
% 0.25/0.59 != ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
% 0.25/0.59 => ~ ! [X2: config256849571t_unit,Y3: config256849571t_unit,Xs2: list_c1059388851t_unit] :
% 0.25/0.59 ( X
% 0.25/0.59 != ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % remdups_adj.cases
% 0.25/0.59 thf(fact_145_transpose_Ocases,axiom,
% 0.25/0.59 ! [X: list_l1584713811t_unit] :
% 0.25/0.59 ( ( X != nil_li2108369341t_unit )
% 0.25/0.59 => ( ! [Xss: list_l1584713811t_unit] :
% 0.25/0.59 ( X
% 0.25/0.59 != ( cons_l1777019405t_unit @ nil_li307996205t_unit @ Xss ) )
% 0.25/0.59 => ~ ! [X2: list_c1059388851t_unit,Xs2: list_l611321411t_unit,Xss: list_l1584713811t_unit] :
% 0.25/0.59 ( X
% 0.25/0.59 != ( cons_l1777019405t_unit @ ( cons_l1083444861t_unit @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % transpose.cases
% 0.25/0.59 thf(fact_146_transpose_Ocases,axiom,
% 0.25/0.59 ! [X: list_l1341496881ge_p_v] :
% 0.25/0.59 ( ( X != nil_li835338673ge_p_v )
% 0.25/0.59 => ( ! [Xss: list_l1341496881ge_p_v] :
% 0.25/0.59 ( X
% 0.25/0.59 != ( cons_l1383421281ge_p_v @ nil_list_message_p_v @ Xss ) )
% 0.25/0.59 => ~ ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v,Xss: list_l1341496881ge_p_v] :
% 0.25/0.59 ( X
% 0.25/0.59 != ( cons_l1383421281ge_p_v @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % transpose.cases
% 0.25/0.59 thf(fact_147_transpose_Ocases,axiom,
% 0.25/0.59 ! [X: list_l1619404459ge_p_v] :
% 0.25/0.59 ( ( X != nil_list_message_p_v )
% 0.25/0.59 => ( ! [Xss: list_l1619404459ge_p_v] :
% 0.25/0.59 ( X
% 0.25/0.59 != ( cons_l233104475ge_p_v @ nil_message_p_v @ Xss ) )
% 0.25/0.59 => ~ ! [X2: message_p_v,Xs2: list_message_p_v,Xss: list_l1619404459ge_p_v] :
% 0.25/0.59 ( X
% 0.25/0.59 != ( cons_l233104475ge_p_v @ ( cons_message_p_v @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % transpose.cases
% 0.25/0.59 thf(fact_148_transpose_Ocases,axiom,
% 0.25/0.59 ! [X: list_l611321411t_unit] :
% 0.25/0.59 ( ( X != nil_li307996205t_unit )
% 0.25/0.59 => ( ! [Xss: list_l611321411t_unit] :
% 0.25/0.59 ( X
% 0.25/0.59 != ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ Xss ) )
% 0.25/0.59 => ~ ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Xss: list_l611321411t_unit] :
% 0.25/0.59 ( X
% 0.25/0.59 != ( cons_l1083444861t_unit @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % transpose.cases
% 0.25/0.59 thf(fact_149_shuffles_Oinduct,axiom,
% 0.25/0.59 ! [P: list_l1619404459ge_p_v > list_l1619404459ge_p_v > $o,A0: list_l1619404459ge_p_v,A1: list_l1619404459ge_p_v] :
% 0.25/0.59 ( ! [X_1: list_l1619404459ge_p_v] : ( P @ nil_list_message_p_v @ X_1 )
% 0.25/0.59 => ( ! [Xs2: list_l1619404459ge_p_v] : ( P @ Xs2 @ nil_list_message_p_v )
% 0.25/0.59 => ( ! [X2: list_message_p_v,Xs2: list_l1619404459ge_p_v,Y3: list_message_p_v,Ys2: list_l1619404459ge_p_v] :
% 0.25/0.59 ( ( P @ Xs2 @ ( cons_l233104475ge_p_v @ Y3 @ Ys2 ) )
% 0.25/0.59 => ( ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) @ Ys2 )
% 0.25/0.59 => ( P @ ( cons_l233104475ge_p_v @ X2 @ Xs2 ) @ ( cons_l233104475ge_p_v @ Y3 @ Ys2 ) ) ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % shuffles.induct
% 0.25/0.59 thf(fact_150_shuffles_Oinduct,axiom,
% 0.25/0.59 ! [P: list_message_p_v > list_message_p_v > $o,A0: list_message_p_v,A1: list_message_p_v] :
% 0.25/0.59 ( ! [X_1: list_message_p_v] : ( P @ nil_message_p_v @ X_1 )
% 0.25/0.59 => ( ! [Xs2: list_message_p_v] : ( P @ Xs2 @ nil_message_p_v )
% 0.25/0.59 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v] :
% 0.25/0.59 ( ( P @ Xs2 @ ( cons_message_p_v @ Y3 @ Ys2 ) )
% 0.25/0.59 => ( ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ Ys2 )
% 0.25/0.59 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % shuffles.induct
% 0.25/0.59 thf(fact_151_shuffles_Oinduct,axiom,
% 0.25/0.59 ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: list_c1059388851t_unit,A1: list_c1059388851t_unit] :
% 0.25/0.59 ( ! [X_1: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ X_1 )
% 0.25/0.59 => ( ! [Xs2: list_c1059388851t_unit] : ( P @ Xs2 @ nil_co1338500125t_unit )
% 0.25/0.59 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 0.25/0.59 ( ( P @ Xs2 @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) )
% 0.25/0.59 => ( ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ Ys2 )
% 0.25/0.59 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % shuffles.induct
% 0.25/0.59 thf(fact_152_induct__list012,axiom,
% 0.25/0.59 ! [P: list_message_p_v > $o,Xs: list_message_p_v] :
% 0.25/0.59 ( ( P @ nil_message_p_v )
% 0.25/0.59 => ( ! [X2: message_p_v] : ( P @ ( cons_message_p_v @ X2 @ nil_message_p_v ) )
% 0.25/0.59 => ( ! [X2: message_p_v,Y3: message_p_v,Zs: list_message_p_v] :
% 0.25/0.59 ( ( P @ Zs )
% 0.25/0.59 => ( ( P @ ( cons_message_p_v @ Y3 @ Zs ) )
% 0.25/0.59 => ( P @ ( cons_message_p_v @ X2 @ ( cons_message_p_v @ Y3 @ Zs ) ) ) ) )
% 0.25/0.59 => ( P @ Xs ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % induct_list012
% 0.25/0.59 thf(fact_153_induct__list012,axiom,
% 0.25/0.59 ! [P: list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit] :
% 0.25/0.59 ( ( P @ nil_co1338500125t_unit )
% 0.25/0.59 => ( ! [X2: config256849571t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ nil_co1338500125t_unit ) )
% 0.25/0.59 => ( ! [X2: config256849571t_unit,Y3: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 0.25/0.59 ( ( P @ Zs )
% 0.25/0.59 => ( ( P @ ( cons_c1162654829t_unit @ Y3 @ Zs ) )
% 0.25/0.59 => ( P @ ( cons_c1162654829t_unit @ X2 @ ( cons_c1162654829t_unit @ Y3 @ Zs ) ) ) ) )
% 0.25/0.59 => ( P @ Xs ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % induct_list012
% 0.25/0.59 thf(fact_154_splice_Oinduct,axiom,
% 0.25/0.59 ! [P: list_message_p_v > list_message_p_v > $o,A0: list_message_p_v,A1: list_message_p_v] :
% 0.25/0.59 ( ! [X_1: list_message_p_v] : ( P @ nil_message_p_v @ X_1 )
% 0.25/0.59 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Ys2: list_message_p_v] :
% 0.25/0.59 ( ( P @ Ys2 @ Xs2 )
% 0.25/0.59 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ Ys2 ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % splice.induct
% 0.25/0.59 thf(fact_155_splice_Oinduct,axiom,
% 0.25/0.59 ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,A0: list_c1059388851t_unit,A1: list_c1059388851t_unit] :
% 0.25/0.59 ( ! [X_1: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ X_1 )
% 0.25/0.59 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Ys2: list_c1059388851t_unit] :
% 0.25/0.59 ( ( P @ Ys2 @ Xs2 )
% 0.25/0.59 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ Ys2 ) )
% 0.25/0.59 => ( P @ A0 @ A1 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % splice.induct
% 0.25/0.59 thf(fact_156_list__induct2_H,axiom,
% 0.25/0.59 ! [P: list_message_p_v > list_message_p_v > $o,Xs: list_message_p_v,Ys: list_message_p_v] :
% 0.25/0.59 ( ( P @ nil_message_p_v @ nil_message_p_v )
% 0.25/0.59 => ( ! [X2: message_p_v,Xs2: list_message_p_v] : ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ nil_message_p_v )
% 0.25/0.59 => ( ! [Y3: message_p_v,Ys2: list_message_p_v] : ( P @ nil_message_p_v @ ( cons_message_p_v @ Y3 @ Ys2 ) )
% 0.25/0.59 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v] :
% 0.25/0.59 ( ( P @ Xs2 @ Ys2 )
% 0.25/0.59 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct2'
% 0.25/0.59 thf(fact_157_list__induct2_H,axiom,
% 0.25/0.59 ! [P: list_message_p_v > list_c1059388851t_unit > $o,Xs: list_message_p_v,Ys: list_c1059388851t_unit] :
% 0.25/0.59 ( ( P @ nil_message_p_v @ nil_co1338500125t_unit )
% 0.25/0.59 => ( ! [X2: message_p_v,Xs2: list_message_p_v] : ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ nil_co1338500125t_unit )
% 0.25/0.59 => ( ! [Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] : ( P @ nil_message_p_v @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) )
% 0.25/0.59 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 0.25/0.59 ( ( P @ Xs2 @ Ys2 )
% 0.25/0.59 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct2'
% 0.25/0.59 thf(fact_158_list__induct2_H,axiom,
% 0.25/0.59 ! [P: list_c1059388851t_unit > list_message_p_v > $o,Xs: list_c1059388851t_unit,Ys: list_message_p_v] :
% 0.25/0.59 ( ( P @ nil_co1338500125t_unit @ nil_message_p_v )
% 0.25/0.59 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ nil_message_p_v )
% 0.25/0.59 => ( ! [Y3: message_p_v,Ys2: list_message_p_v] : ( P @ nil_co1338500125t_unit @ ( cons_message_p_v @ Y3 @ Ys2 ) )
% 0.25/0.59 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v] :
% 0.25/0.59 ( ( P @ Xs2 @ Ys2 )
% 0.25/0.59 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct2'
% 0.25/0.59 thf(fact_159_list__induct2_H,axiom,
% 0.25/0.59 ! [P: list_c1059388851t_unit > list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 0.25/0.59 ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 0.25/0.59 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit] : ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ nil_co1338500125t_unit )
% 0.25/0.59 => ( ! [Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] : ( P @ nil_co1338500125t_unit @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) )
% 0.25/0.59 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 0.25/0.59 ( ( P @ Xs2 @ Ys2 )
% 0.25/0.59 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct2'
% 0.25/0.59 thf(fact_160_neq__Nil__conv,axiom,
% 0.25/0.59 ! [Xs: list_message_p_v] :
% 0.25/0.59 ( ( Xs != nil_message_p_v )
% 0.25/0.59 = ( ? [Y4: message_p_v,Ys3: list_message_p_v] :
% 0.25/0.59 ( Xs
% 0.25/0.59 = ( cons_message_p_v @ Y4 @ Ys3 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % neq_Nil_conv
% 0.25/0.59 thf(fact_161_neq__Nil__conv,axiom,
% 0.25/0.59 ! [Xs: list_c1059388851t_unit] :
% 0.25/0.59 ( ( Xs != nil_co1338500125t_unit )
% 0.25/0.59 = ( ? [Y4: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 0.25/0.59 ( Xs
% 0.25/0.59 = ( cons_c1162654829t_unit @ Y4 @ Ys3 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % neq_Nil_conv
% 0.25/0.59 thf(fact_162_list_Oinducts,axiom,
% 0.25/0.59 ! [P: list_message_p_v > $o,List: list_message_p_v] :
% 0.25/0.59 ( ( P @ nil_message_p_v )
% 0.25/0.59 => ( ! [X12: message_p_v,X23: list_message_p_v] :
% 0.25/0.59 ( ( P @ X23 )
% 0.25/0.59 => ( P @ ( cons_message_p_v @ X12 @ X23 ) ) )
% 0.25/0.59 => ( P @ List ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.inducts
% 0.25/0.59 thf(fact_163_list_Oinducts,axiom,
% 0.25/0.59 ! [P: list_c1059388851t_unit > $o,List: list_c1059388851t_unit] :
% 0.25/0.59 ( ( P @ nil_co1338500125t_unit )
% 0.25/0.59 => ( ! [X12: config256849571t_unit,X23: list_c1059388851t_unit] :
% 0.25/0.59 ( ( P @ X23 )
% 0.25/0.59 => ( P @ ( cons_c1162654829t_unit @ X12 @ X23 ) ) )
% 0.25/0.59 => ( P @ List ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.inducts
% 0.25/0.59 thf(fact_164_list_Oexhaust,axiom,
% 0.25/0.59 ! [Y: list_message_p_v] :
% 0.25/0.59 ( ( Y != nil_message_p_v )
% 0.25/0.59 => ~ ! [X212: message_p_v,X223: list_message_p_v] :
% 0.25/0.59 ( Y
% 0.25/0.59 != ( cons_message_p_v @ X212 @ X223 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.exhaust
% 0.25/0.59 thf(fact_165_list_Oexhaust,axiom,
% 0.25/0.59 ! [Y: list_c1059388851t_unit] :
% 0.25/0.59 ( ( Y != nil_co1338500125t_unit )
% 0.25/0.59 => ~ ! [X212: config256849571t_unit,X223: list_c1059388851t_unit] :
% 0.25/0.59 ( Y
% 0.25/0.59 != ( cons_c1162654829t_unit @ X212 @ X223 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.exhaust
% 0.25/0.59 thf(fact_166_list_OdiscI,axiom,
% 0.25/0.59 ! [List: list_message_p_v,X21: message_p_v,X222: list_message_p_v] :
% 0.25/0.59 ( ( List
% 0.25/0.59 = ( cons_message_p_v @ X21 @ X222 ) )
% 0.25/0.59 => ( List != nil_message_p_v ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.discI
% 0.25/0.59 thf(fact_167_list_OdiscI,axiom,
% 0.25/0.59 ! [List: list_c1059388851t_unit,X21: config256849571t_unit,X222: list_c1059388851t_unit] :
% 0.25/0.59 ( ( List
% 0.25/0.59 = ( cons_c1162654829t_unit @ X21 @ X222 ) )
% 0.25/0.59 => ( List != nil_co1338500125t_unit ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.discI
% 0.25/0.59 thf(fact_168_list_Odistinct_I1_J,axiom,
% 0.25/0.59 ! [X21: message_p_v,X222: list_message_p_v] :
% 0.25/0.59 ( nil_message_p_v
% 0.25/0.59 != ( cons_message_p_v @ X21 @ X222 ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.distinct(1)
% 0.25/0.59 thf(fact_169_list_Odistinct_I1_J,axiom,
% 0.25/0.59 ! [X21: config256849571t_unit,X222: list_c1059388851t_unit] :
% 0.25/0.59 ( nil_co1338500125t_unit
% 0.25/0.59 != ( cons_c1162654829t_unit @ X21 @ X222 ) ) ).
% 0.25/0.59
% 0.25/0.59 % list.distinct(1)
% 0.25/0.59 thf(fact_170_length__induct,axiom,
% 0.25/0.59 ! [P: list_c1059388851t_unit > $o,Xs: list_c1059388851t_unit] :
% 0.25/0.59 ( ! [Xs2: list_c1059388851t_unit] :
% 0.25/0.59 ( ! [Ys4: list_c1059388851t_unit] :
% 0.25/0.59 ( ( ord_less_nat @ ( size_s1406904903t_unit @ Ys4 ) @ ( size_s1406904903t_unit @ Xs2 ) )
% 0.25/0.59 => ( P @ Ys4 ) )
% 0.25/0.59 => ( P @ Xs2 ) )
% 0.25/0.59 => ( P @ Xs ) ) ).
% 0.25/0.59
% 0.25/0.59 % length_induct
% 0.25/0.59 thf(fact_171_lift__Suc__mono__less__iff,axiom,
% 0.25/0.59 ! [F2: nat > nat,N3: nat,M: nat] :
% 0.25/0.59 ( ! [N: nat] : ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 0.25/0.59 => ( ( ord_less_nat @ ( F2 @ N3 ) @ ( F2 @ M ) )
% 0.25/0.59 = ( ord_less_nat @ N3 @ M ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % lift_Suc_mono_less_iff
% 0.25/0.59 thf(fact_172_lift__Suc__mono__less__iff,axiom,
% 0.25/0.59 ! [F2: nat > int,N3: nat,M: nat] :
% 0.25/0.59 ( ! [N: nat] : ( ord_less_int @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 0.25/0.59 => ( ( ord_less_int @ ( F2 @ N3 ) @ ( F2 @ M ) )
% 0.25/0.59 = ( ord_less_nat @ N3 @ M ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % lift_Suc_mono_less_iff
% 0.25/0.59 thf(fact_173_lift__Suc__mono__less,axiom,
% 0.25/0.59 ! [F2: nat > nat,N3: nat,N4: nat] :
% 0.25/0.59 ( ! [N: nat] : ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 0.25/0.59 => ( ( ord_less_nat @ N3 @ N4 )
% 0.25/0.59 => ( ord_less_nat @ ( F2 @ N3 ) @ ( F2 @ N4 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % lift_Suc_mono_less
% 0.25/0.59 thf(fact_174_lift__Suc__mono__less,axiom,
% 0.25/0.59 ! [F2: nat > int,N3: nat,N4: nat] :
% 0.25/0.59 ( ! [N: nat] : ( ord_less_int @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 0.25/0.59 => ( ( ord_less_nat @ N3 @ N4 )
% 0.25/0.59 => ( ord_less_int @ ( F2 @ N3 ) @ ( F2 @ N4 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % lift_Suc_mono_less
% 0.25/0.59 thf(fact_175_less__Suc__eq__0__disj,axiom,
% 0.25/0.59 ! [M: nat,N3: nat] :
% 0.25/0.59 ( ( ord_less_nat @ M @ ( suc @ N3 ) )
% 0.25/0.59 = ( ( M = zero_zero_nat )
% 0.25/0.59 | ? [J3: nat] :
% 0.25/0.59 ( ( M
% 0.25/0.59 = ( suc @ J3 ) )
% 0.25/0.59 & ( ord_less_nat @ J3 @ N3 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % less_Suc_eq_0_disj
% 0.25/0.59 thf(fact_176_gr0__implies__Suc,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.25/0.59 => ? [M3: nat] :
% 0.25/0.59 ( N3
% 0.25/0.59 = ( suc @ M3 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % gr0_implies_Suc
% 0.25/0.59 thf(fact_177_All__less__Suc2,axiom,
% 0.25/0.59 ! [N3: nat,P: nat > $o] :
% 0.25/0.59 ( ( ! [I3: nat] :
% 0.25/0.59 ( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
% 0.25/0.59 => ( P @ I3 ) ) )
% 0.25/0.59 = ( ( P @ zero_zero_nat )
% 0.25/0.59 & ! [I3: nat] :
% 0.25/0.59 ( ( ord_less_nat @ I3 @ N3 )
% 0.25/0.59 => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % All_less_Suc2
% 0.25/0.59 thf(fact_178_gr0__conv__Suc,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.25/0.59 = ( ? [M5: nat] :
% 0.25/0.59 ( N3
% 0.25/0.59 = ( suc @ M5 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % gr0_conv_Suc
% 0.25/0.59 thf(fact_179_Ex__less__Suc2,axiom,
% 0.25/0.59 ! [N3: nat,P: nat > $o] :
% 0.25/0.59 ( ( ? [I3: nat] :
% 0.25/0.59 ( ( ord_less_nat @ I3 @ ( suc @ N3 ) )
% 0.25/0.59 & ( P @ I3 ) ) )
% 0.25/0.59 = ( ( P @ zero_zero_nat )
% 0.25/0.59 | ? [I3: nat] :
% 0.25/0.59 ( ( ord_less_nat @ I3 @ N3 )
% 0.25/0.59 & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Ex_less_Suc2
% 0.25/0.59 thf(fact_180_length__Suc__conv,axiom,
% 0.25/0.59 ! [Xs: list_c1059388851t_unit,N3: nat] :
% 0.25/0.59 ( ( ( size_s1406904903t_unit @ Xs )
% 0.25/0.59 = ( suc @ N3 ) )
% 0.25/0.59 = ( ? [Y4: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 0.25/0.59 ( ( Xs
% 0.25/0.59 = ( cons_c1162654829t_unit @ Y4 @ Ys3 ) )
% 0.25/0.59 & ( ( size_s1406904903t_unit @ Ys3 )
% 0.25/0.59 = N3 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % length_Suc_conv
% 0.25/0.59 thf(fact_181_Suc__length__conv,axiom,
% 0.25/0.59 ! [N3: nat,Xs: list_c1059388851t_unit] :
% 0.25/0.59 ( ( ( suc @ N3 )
% 0.25/0.59 = ( size_s1406904903t_unit @ Xs ) )
% 0.25/0.59 = ( ? [Y4: config256849571t_unit,Ys3: list_c1059388851t_unit] :
% 0.25/0.59 ( ( Xs
% 0.25/0.59 = ( cons_c1162654829t_unit @ Y4 @ Ys3 ) )
% 0.25/0.59 & ( ( size_s1406904903t_unit @ Ys3 )
% 0.25/0.59 = N3 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % Suc_length_conv
% 0.25/0.59 thf(fact_182_list_Osize_I3_J,axiom,
% 0.25/0.59 ( ( size_s1168481041ge_p_v @ nil_message_p_v )
% 0.25/0.59 = zero_zero_nat ) ).
% 0.25/0.59
% 0.25/0.59 % list.size(3)
% 0.25/0.59 thf(fact_183_list_Osize_I3_J,axiom,
% 0.25/0.59 ( ( size_s1406904903t_unit @ nil_co1338500125t_unit )
% 0.25/0.59 = zero_zero_nat ) ).
% 0.25/0.59
% 0.25/0.59 % list.size(3)
% 0.25/0.59 thf(fact_184_list__induct3,axiom,
% 0.25/0.59 ! [Xs: list_message_p_v,Ys: list_message_p_v,Zs2: list_message_p_v,P: list_message_p_v > list_message_p_v > list_message_p_v > $o] :
% 0.25/0.59 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Ys ) )
% 0.25/0.59 => ( ( ( size_s1168481041ge_p_v @ Ys )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 0.25/0.59 => ( ( P @ nil_message_p_v @ nil_message_p_v @ nil_message_p_v )
% 0.25/0.59 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v,Z: message_p_v,Zs: list_message_p_v] :
% 0.25/0.59 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.25/0.59 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Zs ) )
% 0.25/0.59 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.25/0.59 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct3
% 0.25/0.59 thf(fact_185_list__induct3,axiom,
% 0.25/0.59 ! [Xs: list_message_p_v,Ys: list_message_p_v,Zs2: list_c1059388851t_unit,P: list_message_p_v > list_message_p_v > list_c1059388851t_unit > $o] :
% 0.25/0.59 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Ys ) )
% 0.25/0.59 => ( ( ( size_s1168481041ge_p_v @ Ys )
% 0.25/0.59 = ( size_s1406904903t_unit @ Zs2 ) )
% 0.25/0.59 => ( ( P @ nil_message_p_v @ nil_message_p_v @ nil_co1338500125t_unit )
% 0.25/0.59 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 0.25/0.59 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.25/0.59 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 0.25/0.59 = ( size_s1406904903t_unit @ Zs ) )
% 0.25/0.59 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.25/0.59 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct3
% 0.25/0.59 thf(fact_186_list__induct3,axiom,
% 0.25/0.59 ! [Xs: list_message_p_v,Ys: list_c1059388851t_unit,Zs2: list_message_p_v,P: list_message_p_v > list_c1059388851t_unit > list_message_p_v > $o] :
% 0.25/0.59 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.25/0.59 = ( size_s1406904903t_unit @ Ys ) )
% 0.25/0.59 => ( ( ( size_s1406904903t_unit @ Ys )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 0.25/0.59 => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit @ nil_message_p_v )
% 0.25/0.59 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: message_p_v,Zs: list_message_p_v] :
% 0.25/0.59 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.25/0.59 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.25/0.59 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Zs ) )
% 0.25/0.59 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.25/0.59 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct3
% 0.25/0.59 thf(fact_187_list__induct3,axiom,
% 0.25/0.59 ! [Xs: list_message_p_v,Ys: list_c1059388851t_unit,Zs2: list_c1059388851t_unit,P: list_message_p_v > list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 0.25/0.59 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.25/0.59 = ( size_s1406904903t_unit @ Ys ) )
% 0.25/0.59 => ( ( ( size_s1406904903t_unit @ Ys )
% 0.25/0.59 = ( size_s1406904903t_unit @ Zs2 ) )
% 0.25/0.59 => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 0.25/0.59 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 0.25/0.59 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.25/0.59 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.25/0.59 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 0.25/0.59 = ( size_s1406904903t_unit @ Zs ) )
% 0.25/0.59 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.25/0.59 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct3
% 0.25/0.59 thf(fact_188_list__induct3,axiom,
% 0.25/0.59 ! [Xs: list_c1059388851t_unit,Ys: list_message_p_v,Zs2: list_message_p_v,P: list_c1059388851t_unit > list_message_p_v > list_message_p_v > $o] :
% 0.25/0.59 ( ( ( size_s1406904903t_unit @ Xs )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Ys ) )
% 0.25/0.59 => ( ( ( size_s1168481041ge_p_v @ Ys )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 0.25/0.59 => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v @ nil_message_p_v )
% 0.25/0.59 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v,Z: message_p_v,Zs: list_message_p_v] :
% 0.25/0.59 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.25/0.59 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Zs ) )
% 0.25/0.59 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.25/0.59 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct3
% 0.25/0.59 thf(fact_189_list__induct3,axiom,
% 0.25/0.59 ! [Xs: list_c1059388851t_unit,Ys: list_message_p_v,Zs2: list_c1059388851t_unit,P: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit > $o] :
% 0.25/0.59 ( ( ( size_s1406904903t_unit @ Xs )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Ys ) )
% 0.25/0.59 => ( ( ( size_s1168481041ge_p_v @ Ys )
% 0.25/0.59 = ( size_s1406904903t_unit @ Zs2 ) )
% 0.25/0.59 => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v @ nil_co1338500125t_unit )
% 0.25/0.59 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 0.25/0.59 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.25/0.59 => ( ( ( size_s1168481041ge_p_v @ Ys2 )
% 0.25/0.59 = ( size_s1406904903t_unit @ Zs ) )
% 0.25/0.59 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.25/0.59 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct3
% 0.25/0.59 thf(fact_190_list__induct3,axiom,
% 0.25/0.59 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit,Zs2: list_message_p_v,P: list_c1059388851t_unit > list_c1059388851t_unit > list_message_p_v > $o] :
% 0.25/0.59 ( ( ( size_s1406904903t_unit @ Xs )
% 0.25/0.59 = ( size_s1406904903t_unit @ Ys ) )
% 0.25/0.59 => ( ( ( size_s1406904903t_unit @ Ys )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Zs2 ) )
% 0.25/0.59 => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit @ nil_message_p_v )
% 0.25/0.59 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: message_p_v,Zs: list_message_p_v] :
% 0.25/0.59 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.25/0.59 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.25/0.59 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Zs ) )
% 0.25/0.59 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.25/0.59 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_message_p_v @ Z @ Zs ) ) ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct3
% 0.25/0.59 thf(fact_191_list__induct3,axiom,
% 0.25/0.59 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit,Zs2: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 0.25/0.59 ( ( ( size_s1406904903t_unit @ Xs )
% 0.25/0.59 = ( size_s1406904903t_unit @ Ys ) )
% 0.25/0.59 => ( ( ( size_s1406904903t_unit @ Ys )
% 0.25/0.59 = ( size_s1406904903t_unit @ Zs2 ) )
% 0.25/0.59 => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 0.25/0.59 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit,Z: config256849571t_unit,Zs: list_c1059388851t_unit] :
% 0.25/0.59 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.25/0.59 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.25/0.59 => ( ( ( size_s1406904903t_unit @ Ys2 )
% 0.25/0.59 = ( size_s1406904903t_unit @ Zs ) )
% 0.25/0.59 => ( ( P @ Xs2 @ Ys2 @ Zs )
% 0.25/0.59 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) @ ( cons_c1162654829t_unit @ Z @ Zs ) ) ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct3
% 0.25/0.59 thf(fact_192_list__induct2,axiom,
% 0.25/0.59 ! [Xs: list_message_p_v,Ys: list_message_p_v,P: list_message_p_v > list_message_p_v > $o] :
% 0.25/0.59 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Ys ) )
% 0.25/0.59 => ( ( P @ nil_message_p_v @ nil_message_p_v )
% 0.25/0.59 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: message_p_v,Ys2: list_message_p_v] :
% 0.25/0.59 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.25/0.59 => ( ( P @ Xs2 @ Ys2 )
% 0.25/0.59 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct2
% 0.25/0.59 thf(fact_193_list__induct2,axiom,
% 0.25/0.59 ! [Xs: list_message_p_v,Ys: list_c1059388851t_unit,P: list_message_p_v > list_c1059388851t_unit > $o] :
% 0.25/0.59 ( ( ( size_s1168481041ge_p_v @ Xs )
% 0.25/0.59 = ( size_s1406904903t_unit @ Ys ) )
% 0.25/0.59 => ( ( P @ nil_message_p_v @ nil_co1338500125t_unit )
% 0.25/0.59 => ( ! [X2: message_p_v,Xs2: list_message_p_v,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 0.25/0.59 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.25/0.59 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.25/0.59 => ( ( P @ Xs2 @ Ys2 )
% 0.25/0.59 => ( P @ ( cons_message_p_v @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct2
% 0.25/0.59 thf(fact_194_list__induct2,axiom,
% 0.25/0.59 ! [Xs: list_c1059388851t_unit,Ys: list_message_p_v,P: list_c1059388851t_unit > list_message_p_v > $o] :
% 0.25/0.59 ( ( ( size_s1406904903t_unit @ Xs )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Ys ) )
% 0.25/0.59 => ( ( P @ nil_co1338500125t_unit @ nil_message_p_v )
% 0.25/0.59 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: message_p_v,Ys2: list_message_p_v] :
% 0.25/0.59 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.25/0.59 = ( size_s1168481041ge_p_v @ Ys2 ) )
% 0.25/0.59 => ( ( P @ Xs2 @ Ys2 )
% 0.25/0.59 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_message_p_v @ Y3 @ Ys2 ) ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct2
% 0.25/0.59 thf(fact_195_list__induct2,axiom,
% 0.25/0.59 ! [Xs: list_c1059388851t_unit,Ys: list_c1059388851t_unit,P: list_c1059388851t_unit > list_c1059388851t_unit > $o] :
% 0.25/0.59 ( ( ( size_s1406904903t_unit @ Xs )
% 0.25/0.59 = ( size_s1406904903t_unit @ Ys ) )
% 0.25/0.59 => ( ( P @ nil_co1338500125t_unit @ nil_co1338500125t_unit )
% 0.25/0.59 => ( ! [X2: config256849571t_unit,Xs2: list_c1059388851t_unit,Y3: config256849571t_unit,Ys2: list_c1059388851t_unit] :
% 0.25/0.59 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.25/0.59 = ( size_s1406904903t_unit @ Ys2 ) )
% 0.25/0.59 => ( ( P @ Xs2 @ Ys2 )
% 0.25/0.59 => ( P @ ( cons_c1162654829t_unit @ X2 @ Xs2 ) @ ( cons_c1162654829t_unit @ Y3 @ Ys2 ) ) ) )
% 0.25/0.59 => ( P @ Xs @ Ys ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % list_induct2
% 0.25/0.59 thf(fact_196_infiniteExecutionCfg_Oelims,axiom,
% 0.25/0.59 ! [X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_c1059388851t_unit] :
% 0.25/0.59 ( ( ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ Xc )
% 0.25/0.59 = Y )
% 0.25/0.59 => ( ( ( Xc = zero_zero_nat )
% 0.25/0.59 => ( Y
% 0.25/0.59 != ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) )
% 0.25/0.59 => ~ ! [N: nat] :
% 0.25/0.59 ( ( Xc
% 0.25/0.59 = ( suc @ N ) )
% 0.25/0.59 => ( Y
% 0.25/0.59 != ( Xa @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % infiniteExecutionCfg.elims
% 0.25/0.59 thf(fact_197_infiniteExecutionMsg_Oelims,axiom,
% 0.25/0.59 ! [X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_message_p_v] :
% 0.25/0.59 ( ( ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ Xc )
% 0.25/0.59 = Y )
% 0.25/0.59 => ( ( ( Xc = zero_zero_nat )
% 0.25/0.59 => ( Y != nil_message_p_v ) )
% 0.25/0.59 => ~ ! [N: nat] :
% 0.25/0.59 ( ( Xc
% 0.25/0.59 = ( suc @ N ) )
% 0.25/0.59 => ( Y
% 0.25/0.59 != ( Xb @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % infiniteExecutionMsg.elims
% 0.25/0.59 thf(fact_198_infiniteExecutionMsg_Osimps_I2_J,axiom,
% 0.25/0.59 ! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
% 0.25/0.59 ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 0.25/0.59 = ( FStepMsg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % infiniteExecutionMsg.simps(2)
% 0.25/0.59 thf(fact_199_infiniteExecutionCfg_Osimps_I2_J,axiom,
% 0.25/0.59 ! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
% 0.25/0.59 ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 0.25/0.59 = ( FStepCfg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % infiniteExecutionCfg.simps(2)
% 0.25/0.59 thf(fact_200_infiniteExecutionMsg_Osimps_I1_J,axiom,
% 0.25/0.59 ! [Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
% 0.25/0.59 ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 0.25/0.59 = nil_message_p_v ) ).
% 0.25/0.59
% 0.25/0.59 % infiniteExecutionMsg.simps(1)
% 0.25/0.59 thf(fact_201_not__gr__zero,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 0.25/0.59 = ( N3 = zero_zero_nat ) ) ).
% 0.25/0.59
% 0.25/0.59 % not_gr_zero
% 0.25/0.59 thf(fact_202_length__Cons,axiom,
% 0.25/0.59 ! [X: config256849571t_unit,Xs: list_c1059388851t_unit] :
% 0.25/0.59 ( ( size_s1406904903t_unit @ ( cons_c1162654829t_unit @ X @ Xs ) )
% 0.25/0.59 = ( suc @ ( size_s1406904903t_unit @ Xs ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % length_Cons
% 0.25/0.59 thf(fact_203_zero__reorient,axiom,
% 0.25/0.59 ! [X: nat] :
% 0.25/0.59 ( ( zero_zero_nat = X )
% 0.25/0.59 = ( X = zero_zero_nat ) ) ).
% 0.25/0.59
% 0.25/0.59 % zero_reorient
% 0.25/0.59 thf(fact_204_zero__reorient,axiom,
% 0.25/0.59 ! [X: int] :
% 0.25/0.59 ( ( zero_zero_int = X )
% 0.25/0.59 = ( X = zero_zero_int ) ) ).
% 0.25/0.59
% 0.25/0.59 % zero_reorient
% 0.25/0.59 thf(fact_205_gr__zeroI,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( N3 != zero_zero_nat )
% 0.25/0.59 => ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % gr_zeroI
% 0.25/0.59 thf(fact_206_not__less__zero,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ~ ( ord_less_nat @ N3 @ zero_zero_nat ) ).
% 0.25/0.59
% 0.25/0.59 % not_less_zero
% 0.25/0.59 thf(fact_207_gr__implies__not__zero,axiom,
% 0.25/0.59 ! [M: nat,N3: nat] :
% 0.25/0.59 ( ( ord_less_nat @ M @ N3 )
% 0.25/0.59 => ( N3 != zero_zero_nat ) ) ).
% 0.25/0.59
% 0.25/0.59 % gr_implies_not_zero
% 0.25/0.59 thf(fact_208_zero__less__iff__neq__zero,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.25/0.59 = ( N3 != zero_zero_nat ) ) ).
% 0.25/0.59
% 0.25/0.59 % zero_less_iff_neq_zero
% 0.25/0.59 thf(fact_209_n__lists__Nil,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( ( N3 = zero_zero_nat )
% 0.25/0.59 => ( ( n_list1987762709t_unit @ N3 @ nil_co1338500125t_unit )
% 0.25/0.59 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) )
% 0.25/0.59 & ( ( N3 != zero_zero_nat )
% 0.25/0.59 => ( ( n_list1987762709t_unit @ N3 @ nil_co1338500125t_unit )
% 0.25/0.59 = nil_li307996205t_unit ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % n_lists_Nil
% 0.25/0.59 thf(fact_210_n__lists__Nil,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( ( N3 = zero_zero_nat )
% 0.25/0.59 => ( ( n_lists_message_p_v @ N3 @ nil_message_p_v )
% 0.25/0.59 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) )
% 0.25/0.59 & ( ( N3 != zero_zero_nat )
% 0.25/0.59 => ( ( n_lists_message_p_v @ N3 @ nil_message_p_v )
% 0.25/0.59 = nil_list_message_p_v ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % n_lists_Nil
% 0.25/0.59 thf(fact_211_flpPseudoConsensus_OinfiniteExecutionCfg_Oelims,axiom,
% 0.25/0.59 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_c1059388851t_unit] :
% 0.25/0.59 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.25/0.59 => ( ( ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ Xc )
% 0.25/0.59 = Y )
% 0.25/0.59 => ( ( ( Xc = zero_zero_nat )
% 0.25/0.59 => ( Y
% 0.25/0.59 != ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) )
% 0.25/0.59 => ~ ! [N: nat] :
% 0.25/0.59 ( ( Xc
% 0.25/0.59 = ( suc @ N ) )
% 0.25/0.59 => ( Y
% 0.25/0.59 != ( Xa @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % flpPseudoConsensus.infiniteExecutionCfg.elims
% 0.25/0.59 thf(fact_212_n__lists_Osimps_I1_J,axiom,
% 0.25/0.59 ! [Xs: list_c1059388851t_unit] :
% 0.25/0.59 ( ( n_list1987762709t_unit @ zero_zero_nat @ Xs )
% 0.25/0.59 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% 0.25/0.59
% 0.25/0.59 % n_lists.simps(1)
% 0.25/0.59 thf(fact_213_n__lists_Osimps_I1_J,axiom,
% 0.25/0.59 ! [Xs: list_message_p_v] :
% 0.25/0.59 ( ( n_lists_message_p_v @ zero_zero_nat @ Xs )
% 0.25/0.59 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% 0.25/0.59
% 0.25/0.59 % n_lists.simps(1)
% 0.25/0.59 thf(fact_214_flpPseudoConsensus_OinfiniteExecutionMsg_Oelims,axiom,
% 0.25/0.59 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,X: config256849571t_unit,Xa: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,Xb: list_c1059388851t_unit > list_message_p_v > list_message_p_v,Xc: nat,Y: list_message_p_v] :
% 0.25/0.59 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.25/0.59 => ( ( ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ Xc )
% 0.25/0.59 = Y )
% 0.25/0.59 => ( ( ( Xc = zero_zero_nat )
% 0.25/0.59 => ( Y != nil_message_p_v ) )
% 0.25/0.59 => ~ ! [N: nat] :
% 0.25/0.59 ( ( Xc
% 0.25/0.59 = ( suc @ N ) )
% 0.25/0.59 => ( Y
% 0.25/0.59 != ( Xb @ ( fLPThe1519354920_p_v_s @ X @ Xa @ Xb @ N ) @ ( fLPThe536531371_p_v_s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % flpPseudoConsensus.infiniteExecutionMsg.elims
% 0.25/0.59 thf(fact_215_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I2_J,axiom,
% 0.25/0.59 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
% 0.25/0.59 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.25/0.59 => ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 0.25/0.59 = ( FStepMsg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % flpPseudoConsensus.infiniteExecutionMsg.simps(2)
% 0.25/0.59 thf(fact_216_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I2_J,axiom,
% 0.25/0.59 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v,N3: nat] :
% 0.25/0.59 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.25/0.59 => ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 0.25/0.59 = ( FStepCfg2 @ ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % flpPseudoConsensus.infiniteExecutionCfg.simps(2)
% 0.25/0.59 thf(fact_217_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I1_J,axiom,
% 0.25/0.59 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
% 0.25/0.59 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.25/0.59 => ( ( fLPThe536531371_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 0.25/0.59 = nil_message_p_v ) ) ).
% 0.25/0.59
% 0.25/0.59 % flpPseudoConsensus.infiniteExecutionMsg.simps(1)
% 0.25/0.59 thf(fact_218_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I1_J,axiom,
% 0.25/0.59 ! [Trans: p > s > messageValue_v > s,Sends: p > s > messageValue_v > message_p_v > nat,Start: p > s,Cfg2: config256849571t_unit,FStepCfg2: list_c1059388851t_unit > list_message_p_v > list_c1059388851t_unit,FStepMsg2: list_c1059388851t_unit > list_message_p_v > list_message_p_v] :
% 0.25/0.59 ( ( fLPThe9398366_p_s_v @ Trans @ Sends @ Start )
% 0.25/0.59 => ( ( fLPThe1519354920_p_v_s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ zero_zero_nat )
% 0.25/0.59 = ( cons_c1162654829t_unit @ Cfg2 @ nil_co1338500125t_unit ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % flpPseudoConsensus.infiniteExecutionCfg.simps(1)
% 0.25/0.59 thf(fact_219_less__numeral__extra_I3_J,axiom,
% 0.25/0.59 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.25/0.59
% 0.25/0.59 % less_numeral_extra(3)
% 0.25/0.59 thf(fact_220_less__numeral__extra_I3_J,axiom,
% 0.25/0.59 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.25/0.59
% 0.25/0.59 % less_numeral_extra(3)
% 0.25/0.59 thf(fact_221_product__lists_Osimps_I1_J,axiom,
% 0.25/0.59 ( ( produc663212148t_unit @ nil_li307996205t_unit )
% 0.25/0.59 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% 0.25/0.59
% 0.25/0.59 % product_lists.simps(1)
% 0.25/0.59 thf(fact_222_product__lists_Osimps_I1_J,axiom,
% 0.25/0.59 ( ( produc1505827982ge_p_v @ nil_list_message_p_v )
% 0.25/0.59 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% 0.25/0.59
% 0.25/0.59 % product_lists.simps(1)
% 0.25/0.59 thf(fact_223_subseqs_Osimps_I1_J,axiom,
% 0.25/0.59 ( ( subseq1144048270t_unit @ nil_co1338500125t_unit )
% 0.25/0.59 = ( cons_l1083444861t_unit @ nil_co1338500125t_unit @ nil_li307996205t_unit ) ) ).
% 0.25/0.59
% 0.25/0.59 % subseqs.simps(1)
% 0.25/0.59 thf(fact_224_subseqs_Osimps_I1_J,axiom,
% 0.25/0.59 ( ( subseqs_message_p_v @ nil_message_p_v )
% 0.25/0.59 = ( cons_l233104475ge_p_v @ nil_message_p_v @ nil_list_message_p_v ) ) ).
% 0.25/0.59
% 0.25/0.59 % subseqs.simps(1)
% 0.25/0.59 thf(fact_225_length__code,axiom,
% 0.25/0.59 ( size_s1406904903t_unit
% 0.25/0.59 = ( gen_le193291088t_unit @ zero_zero_nat ) ) ).
% 0.25/0.59
% 0.25/0.59 % length_code
% 0.25/0.59 thf(fact_226_gen__length__code_I2_J,axiom,
% 0.25/0.59 ! [N3: nat,X: config256849571t_unit,Xs: list_c1059388851t_unit] :
% 0.25/0.59 ( ( gen_le193291088t_unit @ N3 @ ( cons_c1162654829t_unit @ X @ Xs ) )
% 0.25/0.59 = ( gen_le193291088t_unit @ ( suc @ N3 ) @ Xs ) ) ).
% 0.25/0.59
% 0.25/0.59 % gen_length_code(2)
% 0.25/0.59 thf(fact_227_gen__length__code_I1_J,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( gen_le193291088t_unit @ N3 @ nil_co1338500125t_unit )
% 0.25/0.59 = N3 ) ).
% 0.25/0.59
% 0.25/0.59 % gen_length_code(1)
% 0.25/0.59 thf(fact_228_gen__length__code_I1_J,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( gen_le697204914ge_p_v @ N3 @ nil_message_p_v )
% 0.25/0.59 = N3 ) ).
% 0.25/0.59
% 0.25/0.59 % gen_length_code(1)
% 0.25/0.59 thf(fact_229_insert__Nil,axiom,
% 0.25/0.59 ! [X: message_p_v] :
% 0.25/0.59 ( ( insert_message_p_v @ X @ nil_message_p_v )
% 0.25/0.59 = ( cons_message_p_v @ X @ nil_message_p_v ) ) ).
% 0.25/0.59
% 0.25/0.59 % insert_Nil
% 0.25/0.59 thf(fact_230_insert__Nil,axiom,
% 0.25/0.59 ! [X: config256849571t_unit] :
% 0.25/0.59 ( ( insert1308755079t_unit @ X @ nil_co1338500125t_unit )
% 0.25/0.59 = ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) ).
% 0.25/0.59
% 0.25/0.59 % insert_Nil
% 0.25/0.59 thf(fact_231_nths__singleton,axiom,
% 0.25/0.59 ! [A8: set_nat,X: message_p_v] :
% 0.25/0.59 ( ( ( member_nat @ zero_zero_nat @ A8 )
% 0.25/0.59 => ( ( nths_message_p_v @ ( cons_message_p_v @ X @ nil_message_p_v ) @ A8 )
% 0.25/0.59 = ( cons_message_p_v @ X @ nil_message_p_v ) ) )
% 0.25/0.59 & ( ~ ( member_nat @ zero_zero_nat @ A8 )
% 0.25/0.59 => ( ( nths_message_p_v @ ( cons_message_p_v @ X @ nil_message_p_v ) @ A8 )
% 0.25/0.59 = nil_message_p_v ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % nths_singleton
% 0.25/0.59 thf(fact_232_nths__singleton,axiom,
% 0.25/0.59 ! [A8: set_nat,X: config256849571t_unit] :
% 0.25/0.59 ( ( ( member_nat @ zero_zero_nat @ A8 )
% 0.25/0.59 => ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) @ A8 )
% 0.25/0.59 = ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) ) )
% 0.25/0.59 & ( ~ ( member_nat @ zero_zero_nat @ A8 )
% 0.25/0.59 => ( ( nths_c890550943t_unit @ ( cons_c1162654829t_unit @ X @ nil_co1338500125t_unit ) @ A8 )
% 0.25/0.59 = nil_co1338500125t_unit ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % nths_singleton
% 0.25/0.59 thf(fact_233_of__nat__0__less__iff,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1382578993at_nat @ N3 ) )
% 0.25/0.59 = ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_0_less_iff
% 0.25/0.59 thf(fact_234_of__nat__0__less__iff,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( ord_less_int @ zero_zero_int @ ( semiri2019852685at_int @ N3 ) )
% 0.25/0.59 = ( ord_less_nat @ zero_zero_nat @ N3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_0_less_iff
% 0.25/0.59 thf(fact_235_of__nat__eq__iff,axiom,
% 0.25/0.59 ! [M: nat,N3: nat] :
% 0.25/0.59 ( ( ( semiri2019852685at_int @ M )
% 0.25/0.59 = ( semiri2019852685at_int @ N3 ) )
% 0.25/0.59 = ( M = N3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_eq_iff
% 0.25/0.59 thf(fact_236_nths__nil,axiom,
% 0.25/0.59 ! [A8: set_nat] :
% 0.25/0.59 ( ( nths_c890550943t_unit @ nil_co1338500125t_unit @ A8 )
% 0.25/0.59 = nil_co1338500125t_unit ) ).
% 0.25/0.59
% 0.25/0.59 % nths_nil
% 0.25/0.59 thf(fact_237_nths__nil,axiom,
% 0.25/0.59 ! [A8: set_nat] :
% 0.25/0.59 ( ( nths_message_p_v @ nil_message_p_v @ A8 )
% 0.25/0.59 = nil_message_p_v ) ).
% 0.25/0.59
% 0.25/0.59 % nths_nil
% 0.25/0.59 thf(fact_238_of__nat__0,axiom,
% 0.25/0.59 ( ( semiri1382578993at_nat @ zero_zero_nat )
% 0.25/0.59 = zero_zero_nat ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_0
% 0.25/0.59 thf(fact_239_of__nat__0,axiom,
% 0.25/0.59 ( ( semiri2019852685at_int @ zero_zero_nat )
% 0.25/0.59 = zero_zero_int ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_0
% 0.25/0.59 thf(fact_240_of__nat__0__eq__iff,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( zero_zero_nat
% 0.25/0.59 = ( semiri1382578993at_nat @ N3 ) )
% 0.25/0.59 = ( zero_zero_nat = N3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_0_eq_iff
% 0.25/0.59 thf(fact_241_of__nat__0__eq__iff,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( zero_zero_int
% 0.25/0.59 = ( semiri2019852685at_int @ N3 ) )
% 0.25/0.59 = ( zero_zero_nat = N3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_0_eq_iff
% 0.25/0.59 thf(fact_242_of__nat__eq__0__iff,axiom,
% 0.25/0.59 ! [M: nat] :
% 0.25/0.59 ( ( ( semiri1382578993at_nat @ M )
% 0.25/0.59 = zero_zero_nat )
% 0.25/0.59 = ( M = zero_zero_nat ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_eq_0_iff
% 0.25/0.59 thf(fact_243_of__nat__eq__0__iff,axiom,
% 0.25/0.59 ! [M: nat] :
% 0.25/0.59 ( ( ( semiri2019852685at_int @ M )
% 0.25/0.59 = zero_zero_int )
% 0.25/0.59 = ( M = zero_zero_nat ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_eq_0_iff
% 0.25/0.59 thf(fact_244_of__nat__less__iff,axiom,
% 0.25/0.59 ! [M: nat,N3: nat] :
% 0.25/0.59 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N3 ) )
% 0.25/0.59 = ( ord_less_nat @ M @ N3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_less_iff
% 0.25/0.59 thf(fact_245_of__nat__less__iff,axiom,
% 0.25/0.59 ! [M: nat,N3: nat] :
% 0.25/0.59 ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) )
% 0.25/0.59 = ( ord_less_nat @ M @ N3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_less_iff
% 0.25/0.59 thf(fact_246_of__nat__less__0__iff,axiom,
% 0.25/0.59 ! [M: nat] :
% 0.25/0.59 ~ ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_less_0_iff
% 0.25/0.59 thf(fact_247_of__nat__less__0__iff,axiom,
% 0.25/0.59 ! [M: nat] :
% 0.25/0.59 ~ ( ord_less_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_less_0_iff
% 0.25/0.59 thf(fact_248_of__nat__neq__0,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( semiri1382578993at_nat @ ( suc @ N3 ) )
% 0.25/0.59 != zero_zero_nat ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_neq_0
% 0.25/0.59 thf(fact_249_of__nat__neq__0,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( semiri2019852685at_int @ ( suc @ N3 ) )
% 0.25/0.59 != zero_zero_int ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_neq_0
% 0.25/0.59 thf(fact_250_less__imp__of__nat__less,axiom,
% 0.25/0.59 ! [M: nat,N3: nat] :
% 0.25/0.59 ( ( ord_less_nat @ M @ N3 )
% 0.25/0.59 => ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N3 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % less_imp_of_nat_less
% 0.25/0.59 thf(fact_251_less__imp__of__nat__less,axiom,
% 0.25/0.59 ! [M: nat,N3: nat] :
% 0.25/0.59 ( ( ord_less_nat @ M @ N3 )
% 0.25/0.59 => ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % less_imp_of_nat_less
% 0.25/0.59 thf(fact_252_of__nat__less__imp__less,axiom,
% 0.25/0.59 ! [M: nat,N3: nat] :
% 0.25/0.59 ( ( ord_less_nat @ ( semiri1382578993at_nat @ M ) @ ( semiri1382578993at_nat @ N3 ) )
% 0.25/0.59 => ( ord_less_nat @ M @ N3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_less_imp_less
% 0.25/0.59 thf(fact_253_of__nat__less__imp__less,axiom,
% 0.25/0.59 ! [M: nat,N3: nat] :
% 0.25/0.59 ( ( ord_less_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) )
% 0.25/0.59 => ( ord_less_nat @ M @ N3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_less_imp_less
% 0.25/0.59 thf(fact_254_nths__all,axiom,
% 0.25/0.59 ! [Xs: list_c1059388851t_unit,I4: set_nat] :
% 0.25/0.59 ( ! [I2: nat] :
% 0.25/0.59 ( ( ord_less_nat @ I2 @ ( size_s1406904903t_unit @ Xs ) )
% 0.25/0.59 => ( member_nat @ I2 @ I4 ) )
% 0.25/0.59 => ( ( nths_c890550943t_unit @ Xs @ I4 )
% 0.25/0.59 = Xs ) ) ).
% 0.25/0.59
% 0.25/0.59 % nths_all
% 0.25/0.59 thf(fact_255_pos__int__cases,axiom,
% 0.25/0.59 ! [K: int] :
% 0.25/0.59 ( ( ord_less_int @ zero_zero_int @ K )
% 0.25/0.59 => ~ ! [N: nat] :
% 0.25/0.59 ( ( K
% 0.25/0.59 = ( semiri2019852685at_int @ N ) )
% 0.25/0.59 => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % pos_int_cases
% 0.25/0.59 thf(fact_256_zero__less__imp__eq__int,axiom,
% 0.25/0.59 ! [K: int] :
% 0.25/0.59 ( ( ord_less_int @ zero_zero_int @ K )
% 0.25/0.59 => ? [N: nat] :
% 0.25/0.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.25/0.59 & ( K
% 0.25/0.59 = ( semiri2019852685at_int @ N ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % zero_less_imp_eq_int
% 0.25/0.59 thf(fact_257_list__ex1__simps_I1_J,axiom,
% 0.25/0.59 ! [P: config256849571t_unit > $o] :
% 0.25/0.59 ~ ( list_e1598815642t_unit @ P @ nil_co1338500125t_unit ) ).
% 0.25/0.59
% 0.25/0.59 % list_ex1_simps(1)
% 0.25/0.59 thf(fact_258_list__ex1__simps_I1_J,axiom,
% 0.25/0.59 ! [P: message_p_v > $o] :
% 0.25/0.59 ~ ( list_ex1_message_p_v @ P @ nil_message_p_v ) ).
% 0.25/0.59
% 0.25/0.59 % list_ex1_simps(1)
% 0.25/0.59 thf(fact_259_nat__int__comparison_I2_J,axiom,
% 0.25/0.59 ( ord_less_nat
% 0.25/0.59 = ( ^ [A10: nat,B: nat] : ( ord_less_int @ ( semiri2019852685at_int @ A10 ) @ ( semiri2019852685at_int @ B ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % nat_int_comparison(2)
% 0.25/0.59 thf(fact_260_int__ops_I1_J,axiom,
% 0.25/0.59 ( ( semiri2019852685at_int @ zero_zero_nat )
% 0.25/0.59 = zero_zero_int ) ).
% 0.25/0.59
% 0.25/0.59 % int_ops(1)
% 0.25/0.59 thf(fact_261_neg__int__cases,axiom,
% 0.25/0.59 ! [K: int] :
% 0.25/0.59 ( ( ord_less_int @ K @ zero_zero_int )
% 0.25/0.59 => ~ ! [N: nat] :
% 0.25/0.59 ( ( K
% 0.25/0.59 = ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) )
% 0.25/0.59 => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % neg_int_cases
% 0.25/0.59 thf(fact_262_neg__equal__iff__equal,axiom,
% 0.25/0.59 ! [A: int,B2: int] :
% 0.25/0.59 ( ( ( uminus_uminus_int @ A )
% 0.25/0.59 = ( uminus_uminus_int @ B2 ) )
% 0.25/0.59 = ( A = B2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % neg_equal_iff_equal
% 0.25/0.59 thf(fact_263_add_Oinverse__inverse,axiom,
% 0.25/0.59 ! [A: int] :
% 0.25/0.59 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 0.25/0.59 = A ) ).
% 0.25/0.59
% 0.25/0.59 % add.inverse_inverse
% 0.25/0.59 thf(fact_264_add_Oinverse__neutral,axiom,
% 0.25/0.59 ( ( uminus_uminus_int @ zero_zero_int )
% 0.25/0.59 = zero_zero_int ) ).
% 0.25/0.59
% 0.25/0.59 % add.inverse_neutral
% 0.25/0.59 thf(fact_265_neg__0__equal__iff__equal,axiom,
% 0.25/0.59 ! [A: int] :
% 0.25/0.59 ( ( zero_zero_int
% 0.25/0.59 = ( uminus_uminus_int @ A ) )
% 0.25/0.59 = ( zero_zero_int = A ) ) ).
% 0.25/0.59
% 0.25/0.59 % neg_0_equal_iff_equal
% 0.25/0.59 thf(fact_266_neg__equal__0__iff__equal,axiom,
% 0.25/0.59 ! [A: int] :
% 0.25/0.59 ( ( ( uminus_uminus_int @ A )
% 0.25/0.59 = zero_zero_int )
% 0.25/0.59 = ( A = zero_zero_int ) ) ).
% 0.25/0.59
% 0.25/0.59 % neg_equal_0_iff_equal
% 0.25/0.59 thf(fact_267_equal__neg__zero,axiom,
% 0.25/0.59 ! [A: int] :
% 0.25/0.59 ( ( A
% 0.25/0.59 = ( uminus_uminus_int @ A ) )
% 0.25/0.59 = ( A = zero_zero_int ) ) ).
% 0.25/0.59
% 0.25/0.59 % equal_neg_zero
% 0.25/0.59 thf(fact_268_neg__equal__zero,axiom,
% 0.25/0.59 ! [A: int] :
% 0.25/0.59 ( ( ( uminus_uminus_int @ A )
% 0.25/0.59 = A )
% 0.25/0.59 = ( A = zero_zero_int ) ) ).
% 0.25/0.59
% 0.25/0.59 % neg_equal_zero
% 0.25/0.59 thf(fact_269_neg__less__iff__less,axiom,
% 0.25/0.59 ! [B2: int,A: int] :
% 0.25/0.59 ( ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) )
% 0.25/0.59 = ( ord_less_int @ A @ B2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % neg_less_iff_less
% 0.25/0.59 thf(fact_270_less__neg__neg,axiom,
% 0.25/0.59 ! [A: int] :
% 0.25/0.59 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 0.25/0.59 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.25/0.59
% 0.25/0.59 % less_neg_neg
% 0.25/0.59 thf(fact_271_neg__less__pos,axiom,
% 0.25/0.59 ! [A: int] :
% 0.25/0.59 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 0.25/0.59 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.25/0.59
% 0.25/0.59 % neg_less_pos
% 0.25/0.59 thf(fact_272_neg__0__less__iff__less,axiom,
% 0.25/0.59 ! [A: int] :
% 0.25/0.59 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.25/0.59 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.25/0.59
% 0.25/0.59 % neg_0_less_iff_less
% 0.25/0.59 thf(fact_273_neg__less__0__iff__less,axiom,
% 0.25/0.59 ! [A: int] :
% 0.25/0.59 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.25/0.59 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.25/0.59
% 0.25/0.59 % neg_less_0_iff_less
% 0.25/0.59 thf(fact_274_negative__eq__positive,axiom,
% 0.25/0.59 ! [N3: nat,M: nat] :
% 0.25/0.59 ( ( ( uminus_uminus_int @ ( semiri2019852685at_int @ N3 ) )
% 0.25/0.59 = ( semiri2019852685at_int @ M ) )
% 0.25/0.59 = ( ( N3 = zero_zero_nat )
% 0.25/0.59 & ( M = zero_zero_nat ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % negative_eq_positive
% 0.25/0.59 thf(fact_275_negative__zless,axiom,
% 0.25/0.59 ! [N3: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N3 ) ) ) @ ( semiri2019852685at_int @ M ) ) ).
% 0.25/0.59
% 0.25/0.59 % negative_zless
% 0.25/0.59 thf(fact_276_minus__less__iff,axiom,
% 0.25/0.59 ! [A: int,B2: int] :
% 0.25/0.59 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B2 )
% 0.25/0.59 = ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ A ) ) ).
% 0.25/0.59
% 0.25/0.59 % minus_less_iff
% 0.25/0.59 thf(fact_277_less__minus__iff,axiom,
% 0.25/0.59 ! [A: int,B2: int] :
% 0.25/0.59 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B2 ) )
% 0.25/0.59 = ( ord_less_int @ B2 @ ( uminus_uminus_int @ A ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % less_minus_iff
% 0.25/0.59 thf(fact_278_verit__negate__coefficient_I2_J,axiom,
% 0.25/0.59 ! [A: int,B2: int] :
% 0.25/0.59 ( ( ord_less_int @ A @ B2 )
% 0.25/0.59 => ( ord_less_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % verit_negate_coefficient(2)
% 0.25/0.59 thf(fact_279_minus__equation__iff,axiom,
% 0.25/0.59 ! [A: int,B2: int] :
% 0.25/0.59 ( ( ( uminus_uminus_int @ A )
% 0.25/0.59 = B2 )
% 0.25/0.59 = ( ( uminus_uminus_int @ B2 )
% 0.25/0.59 = A ) ) ).
% 0.25/0.59
% 0.25/0.59 % minus_equation_iff
% 0.25/0.59 thf(fact_280_equation__minus__iff,axiom,
% 0.25/0.59 ! [A: int,B2: int] :
% 0.25/0.59 ( ( A
% 0.25/0.59 = ( uminus_uminus_int @ B2 ) )
% 0.25/0.59 = ( B2
% 0.25/0.59 = ( uminus_uminus_int @ A ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % equation_minus_iff
% 0.25/0.59 thf(fact_281_int__cases,axiom,
% 0.25/0.59 ! [Z2: int] :
% 0.25/0.59 ( ! [N: nat] :
% 0.25/0.59 ( Z2
% 0.25/0.59 != ( semiri2019852685at_int @ N ) )
% 0.25/0.59 => ~ ! [N: nat] :
% 0.25/0.59 ( Z2
% 0.25/0.59 != ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % int_cases
% 0.25/0.59 thf(fact_282_int__of__nat__induct,axiom,
% 0.25/0.59 ! [P: int > $o,Z2: int] :
% 0.25/0.59 ( ! [N: nat] : ( P @ ( semiri2019852685at_int @ N ) )
% 0.25/0.59 => ( ! [N: nat] : ( P @ ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N ) ) ) )
% 0.25/0.59 => ( P @ Z2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % int_of_nat_induct
% 0.25/0.59 thf(fact_283_int__cases4,axiom,
% 0.25/0.59 ! [M: int] :
% 0.25/0.59 ( ! [N: nat] :
% 0.25/0.59 ( M
% 0.25/0.59 != ( semiri2019852685at_int @ N ) )
% 0.25/0.59 => ~ ! [N: nat] :
% 0.25/0.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.25/0.59 => ( M
% 0.25/0.59 != ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % int_cases4
% 0.25/0.59 thf(fact_284_verit__comp__simplify1_I1_J,axiom,
% 0.25/0.59 ! [A: nat] :
% 0.25/0.59 ~ ( ord_less_nat @ A @ A ) ).
% 0.25/0.59
% 0.25/0.59 % verit_comp_simplify1(1)
% 0.25/0.59 thf(fact_285_verit__comp__simplify1_I1_J,axiom,
% 0.25/0.59 ! [A: int] :
% 0.25/0.59 ~ ( ord_less_int @ A @ A ) ).
% 0.25/0.59
% 0.25/0.59 % verit_comp_simplify1(1)
% 0.25/0.59 thf(fact_286_int__cases3,axiom,
% 0.25/0.59 ! [K: int] :
% 0.25/0.59 ( ( K != zero_zero_int )
% 0.25/0.59 => ( ! [N: nat] :
% 0.25/0.59 ( ( K
% 0.25/0.59 = ( semiri2019852685at_int @ N ) )
% 0.25/0.59 => ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.25/0.59 => ~ ! [N: nat] :
% 0.25/0.59 ( ( K
% 0.25/0.59 = ( uminus_uminus_int @ ( semiri2019852685at_int @ N ) ) )
% 0.25/0.59 => ~ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % int_cases3
% 0.25/0.59 thf(fact_287_negative__zless__0,axiom,
% 0.25/0.59 ! [N3: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N3 ) ) ) @ zero_zero_int ) ).
% 0.25/0.59
% 0.25/0.59 % negative_zless_0
% 0.25/0.59 thf(fact_288_negD,axiom,
% 0.25/0.59 ! [X: int] :
% 0.25/0.59 ( ( ord_less_int @ X @ zero_zero_int )
% 0.25/0.59 => ? [N: nat] :
% 0.25/0.59 ( X
% 0.25/0.59 = ( uminus_uminus_int @ ( semiri2019852685at_int @ ( suc @ N ) ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % negD
% 0.25/0.59 thf(fact_289_zero__less__nat__eq,axiom,
% 0.25/0.59 ! [Z2: int] :
% 0.25/0.59 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z2 ) )
% 0.25/0.59 = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % zero_less_nat_eq
% 0.25/0.59 thf(fact_290_of__int__0__less__iff,axiom,
% 0.25/0.59 ! [Z2: int] :
% 0.25/0.59 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 0.25/0.59 = ( ord_less_int @ zero_zero_int @ Z2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_int_0_less_iff
% 0.25/0.59 thf(fact_291_of__int__0,axiom,
% 0.25/0.59 ( ( ring_1_of_int_int @ zero_zero_int )
% 0.25/0.59 = zero_zero_int ) ).
% 0.25/0.59
% 0.25/0.59 % of_int_0
% 0.25/0.59 thf(fact_292_of__int__0__eq__iff,axiom,
% 0.25/0.59 ! [Z2: int] :
% 0.25/0.59 ( ( zero_zero_int
% 0.25/0.59 = ( ring_1_of_int_int @ Z2 ) )
% 0.25/0.59 = ( Z2 = zero_zero_int ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_int_0_eq_iff
% 0.25/0.59 thf(fact_293_of__int__eq__0__iff,axiom,
% 0.25/0.59 ! [Z2: int] :
% 0.25/0.59 ( ( ( ring_1_of_int_int @ Z2 )
% 0.25/0.59 = zero_zero_int )
% 0.25/0.59 = ( Z2 = zero_zero_int ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_int_eq_0_iff
% 0.25/0.59 thf(fact_294_of__int__less__iff,axiom,
% 0.25/0.59 ! [W: int,Z2: int] :
% 0.25/0.59 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z2 ) )
% 0.25/0.59 = ( ord_less_int @ W @ Z2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_int_less_iff
% 0.25/0.59 thf(fact_295_zless__nat__conj,axiom,
% 0.25/0.59 ! [W: int,Z2: int] :
% 0.25/0.59 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
% 0.25/0.59 = ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.25/0.59 & ( ord_less_int @ W @ Z2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % zless_nat_conj
% 0.25/0.59 thf(fact_296_nat__zminus__int,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( nat2 @ ( uminus_uminus_int @ ( semiri2019852685at_int @ N3 ) ) )
% 0.25/0.59 = zero_zero_nat ) ).
% 0.25/0.59
% 0.25/0.59 % nat_zminus_int
% 0.25/0.59 thf(fact_297_of__int__less__0__iff,axiom,
% 0.25/0.59 ! [Z2: int] :
% 0.25/0.59 ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 0.25/0.59 = ( ord_less_int @ Z2 @ zero_zero_int ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_int_less_0_iff
% 0.25/0.59 thf(fact_298_nat__zero__as__int,axiom,
% 0.25/0.59 ( zero_zero_nat
% 0.25/0.59 = ( nat2 @ zero_zero_int ) ) ).
% 0.25/0.59
% 0.25/0.59 % nat_zero_as_int
% 0.25/0.59 thf(fact_299_nat__mono__iff,axiom,
% 0.25/0.59 ! [Z2: int,W: int] :
% 0.25/0.59 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.25/0.59 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
% 0.25/0.59 = ( ord_less_int @ W @ Z2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % nat_mono_iff
% 0.25/0.59 thf(fact_300_zless__nat__eq__int__zless,axiom,
% 0.25/0.59 ! [M: nat,Z2: int] :
% 0.25/0.59 ( ( ord_less_nat @ M @ ( nat2 @ Z2 ) )
% 0.25/0.59 = ( ord_less_int @ ( semiri2019852685at_int @ M ) @ Z2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % zless_nat_eq_int_zless
% 0.25/0.59 thf(fact_301_of__int__pos,axiom,
% 0.25/0.59 ! [Z2: int] :
% 0.25/0.59 ( ( ord_less_int @ zero_zero_int @ Z2 )
% 0.25/0.59 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_int_pos
% 0.25/0.59 thf(fact_302_of__nat__less__of__int__iff,axiom,
% 0.25/0.59 ! [N3: nat,X: int] :
% 0.25/0.59 ( ( ord_less_int @ ( semiri2019852685at_int @ N3 ) @ ( ring_1_of_int_int @ X ) )
% 0.25/0.59 = ( ord_less_int @ ( semiri2019852685at_int @ N3 ) @ X ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_less_of_int_iff
% 0.25/0.59 thf(fact_303_split__nat,axiom,
% 0.25/0.59 ! [P: nat > $o,I: int] :
% 0.25/0.59 ( ( P @ ( nat2 @ I ) )
% 0.25/0.59 = ( ! [N5: nat] :
% 0.25/0.59 ( ( I
% 0.25/0.59 = ( semiri2019852685at_int @ N5 ) )
% 0.25/0.59 => ( P @ N5 ) )
% 0.25/0.59 & ( ( ord_less_int @ I @ zero_zero_int )
% 0.25/0.59 => ( P @ zero_zero_nat ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % split_nat
% 0.25/0.59 thf(fact_304_one__less__nat__eq,axiom,
% 0.25/0.59 ! [Z2: int] :
% 0.25/0.59 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z2 ) )
% 0.25/0.59 = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % one_less_nat_eq
% 0.25/0.59 thf(fact_305_nat__less__iff,axiom,
% 0.25/0.59 ! [W: int,M: nat] :
% 0.25/0.59 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.25/0.59 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 0.25/0.59 = ( ord_less_int @ W @ ( semiri2019852685at_int @ M ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % nat_less_iff
% 0.25/0.59 thf(fact_306_le__zero__eq,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( ord_less_eq_nat @ N3 @ zero_zero_nat )
% 0.25/0.59 = ( N3 = zero_zero_nat ) ) ).
% 0.25/0.59
% 0.25/0.59 % le_zero_eq
% 0.25/0.59 thf(fact_307_neg__le__iff__le,axiom,
% 0.25/0.59 ! [B2: int,A: int] :
% 0.25/0.59 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B2 ) @ ( uminus_uminus_int @ A ) )
% 0.25/0.59 = ( ord_less_eq_int @ A @ B2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % neg_le_iff_le
% 0.25/0.59 thf(fact_308_of__nat__le__iff,axiom,
% 0.25/0.59 ! [M: nat,N3: nat] :
% 0.25/0.59 ( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ ( semiri2019852685at_int @ N3 ) )
% 0.25/0.59 = ( ord_less_eq_nat @ M @ N3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_le_iff
% 0.25/0.59 thf(fact_309_of__nat__1,axiom,
% 0.25/0.59 ( ( semiri2019852685at_int @ one_one_nat )
% 0.25/0.59 = one_one_int ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_1
% 0.25/0.59 thf(fact_310_of__nat__1__eq__iff,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( one_one_int
% 0.25/0.59 = ( semiri2019852685at_int @ N3 ) )
% 0.25/0.59 = ( N3 = one_one_nat ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_1_eq_iff
% 0.25/0.59 thf(fact_311_of__nat__eq__1__iff,axiom,
% 0.25/0.59 ! [N3: nat] :
% 0.25/0.59 ( ( ( semiri2019852685at_int @ N3 )
% 0.25/0.59 = one_one_int )
% 0.25/0.59 = ( N3 = one_one_nat ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_eq_1_iff
% 0.25/0.59 thf(fact_312_neg__0__le__iff__le,axiom,
% 0.25/0.59 ! [A: int] :
% 0.25/0.59 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.25/0.59 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.25/0.59
% 0.25/0.59 % neg_0_le_iff_le
% 0.25/0.59 thf(fact_313_neg__le__0__iff__le,axiom,
% 0.25/0.59 ! [A: int] :
% 0.25/0.59 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.25/0.59 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.25/0.59
% 0.25/0.59 % neg_le_0_iff_le
% 0.25/0.59 thf(fact_314_less__eq__neg__nonpos,axiom,
% 0.25/0.59 ! [A: int] :
% 0.25/0.59 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 0.25/0.59 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.25/0.59
% 0.25/0.59 % less_eq_neg_nonpos
% 0.25/0.59 thf(fact_315_neg__less__eq__nonneg,axiom,
% 0.25/0.59 ! [A: int] :
% 0.25/0.59 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 0.25/0.59 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.25/0.59
% 0.25/0.59 % neg_less_eq_nonneg
% 0.25/0.59 thf(fact_316_of__nat__le__0__iff,axiom,
% 0.25/0.59 ! [M: nat] :
% 0.25/0.59 ( ( ord_less_eq_nat @ ( semiri1382578993at_nat @ M ) @ zero_zero_nat )
% 0.25/0.59 = ( M = zero_zero_nat ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_le_0_iff
% 0.25/0.59 thf(fact_317_of__nat__le__0__iff,axiom,
% 0.25/0.59 ! [M: nat] :
% 0.25/0.59 ( ( ord_less_eq_int @ ( semiri2019852685at_int @ M ) @ zero_zero_int )
% 0.25/0.59 = ( M = zero_zero_nat ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_nat_le_0_iff
% 0.25/0.59 thf(fact_318_nat__1,axiom,
% 0.25/0.59 ( ( nat2 @ one_one_int )
% 0.25/0.59 = ( suc @ zero_zero_nat ) ) ).
% 0.25/0.59
% 0.25/0.59 % nat_1
% 0.25/0.59 thf(fact_319_nat__le__0,axiom,
% 0.25/0.59 ! [Z2: int] :
% 0.25/0.59 ( ( ord_less_eq_int @ Z2 @ zero_zero_int )
% 0.25/0.59 => ( ( nat2 @ Z2 )
% 0.25/0.59 = zero_zero_nat ) ) ).
% 0.25/0.59
% 0.25/0.59 % nat_le_0
% 0.25/0.59 thf(fact_320_nat__0__iff,axiom,
% 0.25/0.59 ! [I: int] :
% 0.25/0.59 ( ( ( nat2 @ I )
% 0.25/0.59 = zero_zero_nat )
% 0.25/0.59 = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 0.25/0.59
% 0.25/0.59 % nat_0_iff
% 0.25/0.59 thf(fact_321_of__int__le__0__iff,axiom,
% 0.25/0.59 ! [Z2: int] :
% 0.25/0.59 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z2 ) @ zero_zero_int )
% 0.25/0.59 = ( ord_less_eq_int @ Z2 @ zero_zero_int ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_int_le_0_iff
% 0.25/0.59 thf(fact_322_of__int__0__le__iff,axiom,
% 0.25/0.59 ! [Z2: int] :
% 0.25/0.59 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) )
% 0.25/0.59 = ( ord_less_eq_int @ zero_zero_int @ Z2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_int_0_le_iff
% 0.25/0.59 thf(fact_323_of__int__less__1__iff,axiom,
% 0.25/0.59 ! [Z2: int] :
% 0.25/0.59 ( ( ord_less_int @ ( ring_1_of_int_int @ Z2 ) @ one_one_int )
% 0.25/0.59 = ( ord_less_int @ Z2 @ one_one_int ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_int_less_1_iff
% 0.25/0.59 thf(fact_324_of__int__1__less__iff,axiom,
% 0.25/0.59 ! [Z2: int] :
% 0.25/0.59 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z2 ) )
% 0.25/0.59 = ( ord_less_int @ one_one_int @ Z2 ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_int_1_less_iff
% 0.25/0.59 thf(fact_325_of__int__nonneg,axiom,
% 0.25/0.59 ! [Z2: int] :
% 0.25/0.59 ( ( ord_less_eq_int @ zero_zero_int @ Z2 )
% 0.25/0.59 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z2 ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % of_int_nonneg
% 0.25/0.59 thf(fact_326_verit__comp__simplify1_I3_J,axiom,
% 0.25/0.59 ! [B3: nat,A11: nat] :
% 0.25/0.59 ( ( ~ ( ord_less_eq_nat @ B3 @ A11 ) )
% 0.25/0.59 = ( ord_less_nat @ A11 @ B3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % verit_comp_simplify1(3)
% 0.25/0.59 thf(fact_327_verit__comp__simplify1_I3_J,axiom,
% 0.25/0.59 ! [B3: int,A11: int] :
% 0.25/0.59 ( ( ~ ( ord_less_eq_int @ B3 @ A11 ) )
% 0.25/0.59 = ( ord_less_int @ A11 @ B3 ) ) ).
% 0.25/0.59
% 0.25/0.59 % verit_comp_simplify1(3)
% 0.25/0.59 thf(fact_328_le__numeral__extra_I4_J,axiom,
% 0.25/0.59 ord_less_eq_int @ one_one_int @ one_one_int ).
% 0.25/0.59
% 0.25/0.59 % le_numeral_extra(4)
% 0.25/0.59 thf(fact_329_one__reorient,axiom,
% 0.25/0.59 ! [X: int] :
% 0.25/0.59 ( ( one_one_int = X )
% 0.25/0.59 = ( X = one_one_int ) ) ).
% 0.25/0.59
% 0.25/0.59 % one_reorient
% 0.25/0.59 thf(fact_330_lift__Suc__antimono__le,axiom,
% 0.25/0.59 ! [F2: nat > int,N3: nat,N4: nat] :
% 0.25/0.59 ( ! [N: nat] : ( ord_less_eq_int @ ( F2 @ ( suc @ N ) ) @ ( F2 @ N ) )
% 0.25/0.59 => ( ( ord_less_eq_nat @ N3 @ N4 )
% 0.25/0.59 => ( ord_less_eq_int @ ( F2 @ N4 ) @ ( F2 @ N3 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % lift_Suc_antimono_le
% 0.25/0.59 thf(fact_331_lift__Suc__mono__le,axiom,
% 0.25/0.59 ! [F2: nat > int,N3: nat,N4: nat] :
% 0.25/0.59 ( ! [N: nat] : ( ord_less_eq_int @ ( F2 @ N ) @ ( F2 @ ( suc @ N ) ) )
% 0.25/0.59 => ( ( ord_less_eq_nat @ N3 @ N4 )
% 0.25/0.59 => ( ord_less_eq_int @ ( F2 @ N3 ) @ ( F2 @ N4 ) ) ) ) ).
% 0.25/0.59
% 0.25/0.59 % lift_Suc_mono_le
% 0.25/0.59 thf(fact_332_zero__le,axiom,
% 0.25/0.59 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 0.25/0.59
% 0.25/0.59 % zero_le
% 0.25/0.59 thf(fact_333_le__numeral__extra_I3_J,axiom,
% 0.25/0.59 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 0.25/0.59
% 0.25/0.59 % le_numeral_extra(3)
% 0.25/0.67 thf(fact_334_le__numeral__extra_I3_J,axiom,
% 0.25/0.67 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.25/0.67
% 0.25/0.67 % le_numeral_extra(3)
% 0.25/0.67 thf(fact_335_less__numeral__extra_I4_J,axiom,
% 0.25/0.67 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.25/0.67
% 0.25/0.67 % less_numeral_extra(4)
% 0.25/0.67 thf(fact_336_less__numeral__extra_I4_J,axiom,
% 0.25/0.67 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 0.25/0.67
% 0.25/0.67 % less_numeral_extra(4)
% 0.25/0.67 thf(fact_337_of__nat__mono,axiom,
% 0.25/0.67 ! [I: nat,J: nat] :
% 0.25/0.67 ( ( ord_less_eq_nat @ I @ J )
% 0.25/0.67 => ( ord_less_eq_int @ ( semiri2019852685at_int @ I ) @ ( semiri2019852685at_int @ J ) ) ) ).
% 0.25/0.67
% 0.25/0.67 % of_nat_mono
% 0.25/0.67 thf(fact_338_less__minus__one__simps_I4_J,axiom,
% 0.25/0.67 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.25/0.67
% 0.25/0.67 % less_minus_one_simps(4)
% 0.25/0.67 thf(fact_339_less__minus__one__simps_I2_J,axiom,
% 0.25/0.67 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.25/0.67
% 0.25/0.67 % less_minus_one_simps(2)
% 0.25/0.67 thf(fact_340_zero__neq__neg__one,axiom,
% 0.25/0.67 ( zero_zero_int
% 0.25/0.67 != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.25/0.67
% 0.25/0.67 % zero_neq_neg_one
% 0.25/0.67
% 0.25/0.67 % Conjectures (1)
% 0.25/0.67 thf(conj_0,conjecture,
% 0.25/0.67 prefix1615116500t_unit @ ( fe @ m ) @ ( fe @ na ) ).
% 0.25/0.67
% 0.25/0.67 %------------------------------------------------------------------------------
% 0.25/0.67 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.I8IbewYdi0/cvc5---1.0.5_26401.p...
% 0.25/0.67 (declare-sort $$unsorted 0)
% 0.25/0.67 (declare-sort tptp.list_l1584713811t_unit 0)
% 0.25/0.67 (declare-sort tptp.list_l611321411t_unit 0)
% 0.25/0.67 (declare-sort tptp.list_c1059388851t_unit 0)
% 0.25/0.67 (declare-sort tptp.config256849571t_unit 0)
% 0.25/0.67 (declare-sort tptp.list_l1341496881ge_p_v 0)
% 0.25/0.67 (declare-sort tptp.list_l1619404459ge_p_v 0)
% 0.25/0.67 (declare-sort tptp.list_message_p_v 0)
% 0.25/0.67 (declare-sort tptp.message_p_v 0)
% 0.25/0.67 (declare-sort tptp.messageValue_v 0)
% 0.25/0.67 (declare-sort tptp.set_nat 0)
% 0.25/0.67 (declare-sort tptp.nat 0)
% 0.25/0.67 (declare-sort tptp.int 0)
% 0.25/0.67 (declare-sort tptp.s 0)
% 0.25/0.67 (declare-sort tptp.p 0)
% 0.25/0.67 (declare-fun tptp.fLPThe9398366_p_s_v ((-> tptp.p tptp.s tptp.messageValue_v tptp.s) (-> tptp.p tptp.s tptp.messageValue_v tptp.message_p_v tptp.nat) (-> tptp.p tptp.s)) Bool)
% 0.25/0.67 (declare-fun tptp.fLPThe1519354920_p_v_s (tptp.config256849571t_unit (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit) (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v) tptp.nat) tptp.list_c1059388851t_unit)
% 0.25/0.67 (declare-fun tptp.fLPThe536531371_p_v_s (tptp.config256849571t_unit (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit) (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v) tptp.nat) tptp.list_message_p_v)
% 0.25/0.67 (declare-fun tptp.one_one_int () tptp.int)
% 0.25/0.67 (declare-fun tptp.one_one_nat () tptp.nat)
% 0.25/0.67 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 0.25/0.67 (declare-fun tptp.zero_zero_int () tptp.int)
% 0.25/0.67 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.25/0.67 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 0.25/0.67 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 0.25/0.67 (declare-fun tptp.prefix1615116500t_unit (tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit) Bool)
% 0.25/0.67 (declare-fun tptp.prefix47729710ge_p_v (tptp.list_message_p_v tptp.list_message_p_v) Bool)
% 0.25/0.67 (declare-fun tptp.prefix747844452t_unit (tptp.list_l611321411t_unit tptp.list_l611321411t_unit) Bool)
% 0.25/0.67 (declare-fun tptp.prefix1465223476ge_p_v (tptp.list_l1619404459ge_p_v tptp.list_l1619404459ge_p_v) Bool)
% 0.25/0.67 (declare-fun tptp.gen_le193291088t_unit (tptp.nat tptp.list_c1059388851t_unit) tptp.nat)
% 0.25/0.67 (declare-fun tptp.gen_le697204914ge_p_v (tptp.nat tptp.list_message_p_v) tptp.nat)
% 0.25/0.67 (declare-fun tptp.insert1308755079t_unit (tptp.config256849571t_unit tptp.list_c1059388851t_unit) tptp.list_c1059388851t_unit)
% 0.25/0.67 (declare-fun tptp.insert_message_p_v (tptp.message_p_v tptp.list_message_p_v) tptp.list_message_p_v)
% 0.25/0.67 (declare-fun tptp.cons_c1162654829t_unit (tptp.config256849571t_unit tptp.list_c1059388851t_unit) tptp.list_c1059388851t_unit)
% 0.25/0.67 (declare-fun tptp.cons_message_p_v (tptp.message_p_v tptp.list_message_p_v) tptp.list_message_p_v)
% 0.25/0.67 (declare-fun tptp.cons_l1083444861t_unit (tptp.list_c1059388851t_unit tptp.list_l611321411t_unit) tptp.list_l611321411t_unit)
% 0.25/0.67 (declare-fun tptp.cons_l233104475ge_p_v (tptp.list_message_p_v tptp.list_l1619404459ge_p_v) tptp.list_l1619404459ge_p_v)
% 0.25/0.67 (declare-fun tptp.cons_l1777019405t_unit (tptp.list_l611321411t_unit tptp.list_l1584713811t_unit) tptp.list_l1584713811t_unit)
% 0.25/0.67 (declare-fun tptp.cons_l1383421281ge_p_v (tptp.list_l1619404459ge_p_v tptp.list_l1341496881ge_p_v) tptp.list_l1341496881ge_p_v)
% 0.25/0.67 (declare-fun tptp.nil_co1338500125t_unit () tptp.list_c1059388851t_unit)
% 0.25/0.67 (declare-fun tptp.nil_message_p_v () tptp.list_message_p_v)
% 0.25/0.67 (declare-fun tptp.nil_li307996205t_unit () tptp.list_l611321411t_unit)
% 0.25/0.67 (declare-fun tptp.nil_list_message_p_v () tptp.list_l1619404459ge_p_v)
% 0.25/0.67 (declare-fun tptp.nil_li2108369341t_unit () tptp.list_l1584713811t_unit)
% 0.25/0.67 (declare-fun tptp.nil_li835338673ge_p_v () tptp.list_l1341496881ge_p_v)
% 0.25/0.67 (declare-fun tptp.list_e1598815642t_unit ((-> tptp.config256849571t_unit Bool) tptp.list_c1059388851t_unit) Bool)
% 0.25/0.67 (declare-fun tptp.list_ex1_message_p_v ((-> tptp.message_p_v Bool) tptp.list_message_p_v) Bool)
% 0.25/0.67 (declare-fun tptp.n_list1987762709t_unit (tptp.nat tptp.list_c1059388851t_unit) tptp.list_l611321411t_unit)
% 0.25/0.67 (declare-fun tptp.n_lists_message_p_v (tptp.nat tptp.list_message_p_v) tptp.list_l1619404459ge_p_v)
% 0.25/0.67 (declare-fun tptp.nths_c890550943t_unit (tptp.list_c1059388851t_unit tptp.set_nat) tptp.list_c1059388851t_unit)
% 0.25/0.67 (declare-fun tptp.nths_message_p_v (tptp.list_message_p_v tptp.set_nat) tptp.list_message_p_v)
% 0.25/0.67 (declare-fun tptp.produc663212148t_unit (tptp.list_l611321411t_unit) tptp.list_l611321411t_unit)
% 0.25/0.67 (declare-fun tptp.produc1505827982ge_p_v (tptp.list_l1619404459ge_p_v) tptp.list_l1619404459ge_p_v)
% 0.25/0.67 (declare-fun tptp.subseq1144048270t_unit (tptp.list_c1059388851t_unit) tptp.list_l611321411t_unit)
% 0.25/0.67 (declare-fun tptp.subseqs_message_p_v (tptp.list_message_p_v) tptp.list_l1619404459ge_p_v)
% 0.25/0.67 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 0.25/0.67 (declare-fun tptp.semiri2019852685at_int (tptp.nat) tptp.int)
% 0.25/0.67 (declare-fun tptp.semiri1382578993at_nat (tptp.nat) tptp.nat)
% 0.25/0.67 (declare-fun tptp.size_s1406904903t_unit (tptp.list_c1059388851t_unit) tptp.nat)
% 0.25/0.67 (declare-fun tptp.size_s1168481041ge_p_v (tptp.list_message_p_v) tptp.nat)
% 0.25/0.67 (declare-fun tptp.size_s503142615t_unit (tptp.list_l611321411t_unit) tptp.nat)
% 0.25/0.67 (declare-fun tptp.size_s1809856791ge_p_v (tptp.list_l1619404459ge_p_v) tptp.nat)
% 0.25/0.67 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 0.25/0.67 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.25/0.67 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 0.25/0.67 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.25/0.67 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 0.25/0.67 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 0.25/0.67 (declare-fun tptp.cfg () tptp.config256849571t_unit)
% 0.25/0.67 (declare-fun tptp.fe (tptp.nat) tptp.list_c1059388851t_unit)
% 0.25/0.67 (declare-fun tptp.m () tptp.nat)
% 0.25/0.67 (declare-fun tptp.n () tptp.nat)
% 0.25/0.67 (declare-fun tptp.na () tptp.nat)
% 0.25/0.67 (assert (@ (@ tptp.ord_less_nat tptp.m) tptp.na))
% 0.25/0.67 (assert (@ (@ tptp.ord_less_nat tptp.m) tptp.n))
% 0.25/0.67 (assert (=> (@ (@ tptp.ord_less_nat tptp.m) tptp.na) (@ (@ tptp.prefix1615116500t_unit (@ tptp.fe tptp.m)) (@ tptp.fe tptp.na))))
% 0.25/0.67 (assert (or (= tptp.m tptp.na) (@ (@ tptp.ord_less_nat tptp.m) tptp.na)))
% 0.25/0.67 (assert (@ (@ tptp.ord_less_nat tptp.m) (@ tptp.suc tptp.na)))
% 0.25/0.67 (assert (forall ((L1 tptp.list_message_p_v) (L2 tptp.list_message_p_v) (L3 tptp.list_message_p_v)) (let ((_let_1 (@ tptp.prefix47729710ge_p_v L1))) (=> (@ _let_1 L2) (=> (@ (@ tptp.prefix47729710ge_p_v L2) L3) (@ _let_1 L3))))))
% 0.25/0.67 (assert (forall ((L1 tptp.list_c1059388851t_unit) (L2 tptp.list_c1059388851t_unit) (L3 tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.prefix1615116500t_unit L1))) (=> (@ _let_1 L2) (=> (@ (@ tptp.prefix1615116500t_unit L2) L3) (@ _let_1 L3))))))
% 0.25/0.67 (assert (= (@ tptp.fe tptp.zero_zero_nat) (@ (@ tptp.cons_c1162654829t_unit tptp.cfg) tptp.nil_co1338500125t_unit)))
% 0.25/0.67 (assert (forall ((Xa tptp.list_l611321411t_unit) (Xb tptp.list_l611321411t_unit) (X tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.cons_l1083444861t_unit X))) (=> (@ (@ tptp.prefix747844452t_unit Xa) Xb) (@ (@ tptp.prefix747844452t_unit (@ _let_1 Xa)) (@ _let_1 Xb))))))
% 0.25/0.67 (assert (forall ((Xa tptp.list_l1619404459ge_p_v) (Xb tptp.list_l1619404459ge_p_v) (X tptp.list_message_p_v)) (let ((_let_1 (@ tptp.cons_l233104475ge_p_v X))) (=> (@ (@ tptp.prefix1465223476ge_p_v Xa) Xb) (@ (@ tptp.prefix1465223476ge_p_v (@ _let_1 Xa)) (@ _let_1 Xb))))))
% 0.25/0.67 (assert (forall ((Xa tptp.list_message_p_v) (Xb tptp.list_message_p_v) (X tptp.message_p_v)) (let ((_let_1 (@ tptp.cons_message_p_v X))) (=> (@ (@ tptp.prefix47729710ge_p_v Xa) Xb) (@ (@ tptp.prefix47729710ge_p_v (@ _let_1 Xa)) (@ _let_1 Xb))))))
% 0.25/0.67 (assert (forall ((Xa tptp.list_c1059388851t_unit) (Xb tptp.list_c1059388851t_unit) (X tptp.config256849571t_unit)) (let ((_let_1 (@ tptp.cons_c1162654829t_unit X))) (=> (@ (@ tptp.prefix1615116500t_unit Xa) Xb) (@ (@ tptp.prefix1615116500t_unit (@ _let_1 Xa)) (@ _let_1 Xb))))))
% 0.25/0.67 (assert (forall ((L1 tptp.list_message_p_v) (L2 tptp.list_message_p_v)) (=> (@ (@ tptp.prefix47729710ge_p_v L1) L2) (@ (@ tptp.ord_less_nat (@ tptp.size_s1168481041ge_p_v L1)) (@ tptp.size_s1168481041ge_p_v L2)))))
% 0.25/0.67 (assert (forall ((L1 tptp.list_c1059388851t_unit) (L2 tptp.list_c1059388851t_unit)) (=> (@ (@ tptp.prefix1615116500t_unit L1) L2) (@ (@ tptp.ord_less_nat (@ tptp.size_s1406904903t_unit L1)) (@ tptp.size_s1406904903t_unit L2)))))
% 0.25/0.67 (assert (forall ((P (-> tptp.config256849571t_unit (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit) (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v) tptp.nat Bool)) (Q (-> tptp.config256849571t_unit (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit) (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v) tptp.nat Bool)) (A4 tptp.config256849571t_unit) (A5 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (A6 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (A7 tptp.nat)) (=> (forall ((Cfg tptp.config256849571t_unit) (FStepCfg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v))) (@ (@ (@ (@ P Cfg) FStepCfg) FStepMsg) tptp.zero_zero_nat)) (=> (forall ((Cfg tptp.config256849571t_unit) (FStepCfg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (N tptp.nat)) (let ((_let_1 (@ (@ (@ P Cfg) FStepCfg) FStepMsg))) (=> (@ _let_1 N) (=> (@ (@ (@ (@ Q Cfg) FStepCfg) FStepMsg) N) (@ _let_1 (@ tptp.suc N)))))) (=> (forall ((Cfg tptp.config256849571t_unit) (FStepCfg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v))) (@ (@ (@ (@ Q Cfg) FStepCfg) FStepMsg) tptp.zero_zero_nat)) (=> (forall ((Cfg tptp.config256849571t_unit) (FStepCfg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (N tptp.nat)) (let ((_let_1 (@ (@ (@ Q Cfg) FStepCfg) FStepMsg))) (=> (@ (@ (@ (@ P Cfg) FStepCfg) FStepMsg) N) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N)))))) (@ (@ (@ (@ Q A4) A5) A6) A7)))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.config256849571t_unit (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit) (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v) tptp.nat Bool)) (Q (-> tptp.config256849571t_unit (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit) (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v) tptp.nat Bool)) (A0 tptp.config256849571t_unit) (A1 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (A2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (A3 tptp.nat)) (=> (forall ((Cfg tptp.config256849571t_unit) (FStepCfg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v))) (@ (@ (@ (@ P Cfg) FStepCfg) FStepMsg) tptp.zero_zero_nat)) (=> (forall ((Cfg tptp.config256849571t_unit) (FStepCfg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (N tptp.nat)) (let ((_let_1 (@ (@ (@ P Cfg) FStepCfg) FStepMsg))) (=> (@ _let_1 N) (=> (@ (@ (@ (@ Q Cfg) FStepCfg) FStepMsg) N) (@ _let_1 (@ tptp.suc N)))))) (=> (forall ((Cfg tptp.config256849571t_unit) (FStepCfg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v))) (@ (@ (@ (@ Q Cfg) FStepCfg) FStepMsg) tptp.zero_zero_nat)) (=> (forall ((Cfg tptp.config256849571t_unit) (FStepCfg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (N tptp.nat)) (let ((_let_1 (@ (@ (@ Q Cfg) FStepCfg) FStepMsg))) (=> (@ (@ (@ (@ P Cfg) FStepCfg) FStepMsg) N) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N)))))) (@ (@ (@ (@ P A0) A1) A2) A3)))))))
% 0.25/0.67 (assert (forall ((X tptp.list_c1059388851t_unit) (Xs tptp.list_l611321411t_unit)) (@ (@ tptp.prefix747844452t_unit tptp.nil_li307996205t_unit) (@ (@ tptp.cons_l1083444861t_unit X) Xs))))
% 0.25/0.67 (assert (forall ((X tptp.list_message_p_v) (Xs tptp.list_l1619404459ge_p_v)) (@ (@ tptp.prefix1465223476ge_p_v tptp.nil_list_message_p_v) (@ (@ tptp.cons_l233104475ge_p_v X) Xs))))
% 0.25/0.67 (assert (forall ((X tptp.message_p_v) (Xs tptp.list_message_p_v)) (@ (@ tptp.prefix47729710ge_p_v tptp.nil_message_p_v) (@ (@ tptp.cons_message_p_v X) Xs))))
% 0.25/0.67 (assert (forall ((X tptp.config256849571t_unit) (Xs tptp.list_c1059388851t_unit)) (@ (@ tptp.prefix1615116500t_unit tptp.nil_co1338500125t_unit) (@ (@ tptp.cons_c1162654829t_unit X) Xs))))
% 0.25/0.67 (assert (forall ((A1 tptp.list_l611321411t_unit) (A2 tptp.list_l611321411t_unit)) (=> (@ (@ tptp.prefix747844452t_unit A1) A2) (=> (=> (= A1 tptp.nil_li307996205t_unit) (forall ((X2 tptp.list_c1059388851t_unit) (Xs2 tptp.list_l611321411t_unit)) (not (= A2 (@ (@ tptp.cons_l1083444861t_unit X2) Xs2))))) (not (forall ((Xa2 tptp.list_l611321411t_unit) (Xb2 tptp.list_l611321411t_unit) (X2 tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.cons_l1083444861t_unit X2))) (=> (= A1 (@ _let_1 Xa2)) (=> (= A2 (@ _let_1 Xb2)) (not (@ (@ tptp.prefix747844452t_unit Xa2) Xb2)))))))))))
% 0.25/0.67 (assert (forall ((A1 tptp.list_l1619404459ge_p_v) (A2 tptp.list_l1619404459ge_p_v)) (=> (@ (@ tptp.prefix1465223476ge_p_v A1) A2) (=> (=> (= A1 tptp.nil_list_message_p_v) (forall ((X2 tptp.list_message_p_v) (Xs2 tptp.list_l1619404459ge_p_v)) (not (= A2 (@ (@ tptp.cons_l233104475ge_p_v X2) Xs2))))) (not (forall ((Xa2 tptp.list_l1619404459ge_p_v) (Xb2 tptp.list_l1619404459ge_p_v) (X2 tptp.list_message_p_v)) (let ((_let_1 (@ tptp.cons_l233104475ge_p_v X2))) (=> (= A1 (@ _let_1 Xa2)) (=> (= A2 (@ _let_1 Xb2)) (not (@ (@ tptp.prefix1465223476ge_p_v Xa2) Xb2)))))))))))
% 0.25/0.67 (assert (forall ((A1 tptp.list_message_p_v) (A2 tptp.list_message_p_v)) (=> (@ (@ tptp.prefix47729710ge_p_v A1) A2) (=> (=> (= A1 tptp.nil_message_p_v) (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v)) (not (= A2 (@ (@ tptp.cons_message_p_v X2) Xs2))))) (not (forall ((Xa2 tptp.list_message_p_v) (Xb2 tptp.list_message_p_v) (X2 tptp.message_p_v)) (let ((_let_1 (@ tptp.cons_message_p_v X2))) (=> (= A1 (@ _let_1 Xa2)) (=> (= A2 (@ _let_1 Xb2)) (not (@ (@ tptp.prefix47729710ge_p_v Xa2) Xb2)))))))))))
% 0.25/0.67 (assert (forall ((A1 tptp.list_c1059388851t_unit) (A2 tptp.list_c1059388851t_unit)) (=> (@ (@ tptp.prefix1615116500t_unit A1) A2) (=> (=> (= A1 tptp.nil_co1338500125t_unit) (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit)) (not (= A2 (@ (@ tptp.cons_c1162654829t_unit X2) Xs2))))) (not (forall ((Xa2 tptp.list_c1059388851t_unit) (Xb2 tptp.list_c1059388851t_unit) (X2 tptp.config256849571t_unit)) (let ((_let_1 (@ tptp.cons_c1162654829t_unit X2))) (=> (= A1 (@ _let_1 Xa2)) (=> (= A2 (@ _let_1 Xb2)) (not (@ (@ tptp.prefix1615116500t_unit Xa2) Xb2)))))))))))
% 0.25/0.67 (assert (= tptp.prefix747844452t_unit (lambda ((A12 tptp.list_l611321411t_unit) (A22 tptp.list_l611321411t_unit)) (or (exists ((X3 tptp.list_c1059388851t_unit) (Xs3 tptp.list_l611321411t_unit)) (and (= A12 tptp.nil_li307996205t_unit) (= A22 (@ (@ tptp.cons_l1083444861t_unit X3) Xs3)))) (exists ((Xa3 tptp.list_l611321411t_unit) (Xb3 tptp.list_l611321411t_unit) (X3 tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.cons_l1083444861t_unit X3))) (and (= A12 (@ _let_1 Xa3)) (= A22 (@ _let_1 Xb3)) (@ (@ tptp.prefix747844452t_unit Xa3) Xb3))))))))
% 0.25/0.67 (assert (= tptp.prefix1465223476ge_p_v (lambda ((A12 tptp.list_l1619404459ge_p_v) (A22 tptp.list_l1619404459ge_p_v)) (or (exists ((X3 tptp.list_message_p_v) (Xs3 tptp.list_l1619404459ge_p_v)) (and (= A12 tptp.nil_list_message_p_v) (= A22 (@ (@ tptp.cons_l233104475ge_p_v X3) Xs3)))) (exists ((Xa3 tptp.list_l1619404459ge_p_v) (Xb3 tptp.list_l1619404459ge_p_v) (X3 tptp.list_message_p_v)) (let ((_let_1 (@ tptp.cons_l233104475ge_p_v X3))) (and (= A12 (@ _let_1 Xa3)) (= A22 (@ _let_1 Xb3)) (@ (@ tptp.prefix1465223476ge_p_v Xa3) Xb3))))))))
% 0.25/0.67 (assert (= tptp.prefix47729710ge_p_v (lambda ((A12 tptp.list_message_p_v) (A22 tptp.list_message_p_v)) (or (exists ((X3 tptp.message_p_v) (Xs3 tptp.list_message_p_v)) (and (= A12 tptp.nil_message_p_v) (= A22 (@ (@ tptp.cons_message_p_v X3) Xs3)))) (exists ((Xa3 tptp.list_message_p_v) (Xb3 tptp.list_message_p_v) (X3 tptp.message_p_v)) (let ((_let_1 (@ tptp.cons_message_p_v X3))) (and (= A12 (@ _let_1 Xa3)) (= A22 (@ _let_1 Xb3)) (@ (@ tptp.prefix47729710ge_p_v Xa3) Xb3))))))))
% 0.25/0.67 (assert (= tptp.prefix1615116500t_unit (lambda ((A12 tptp.list_c1059388851t_unit) (A22 tptp.list_c1059388851t_unit)) (or (exists ((X3 tptp.config256849571t_unit) (Xs3 tptp.list_c1059388851t_unit)) (and (= A12 tptp.nil_co1338500125t_unit) (= A22 (@ (@ tptp.cons_c1162654829t_unit X3) Xs3)))) (exists ((Xa3 tptp.list_c1059388851t_unit) (Xb3 tptp.list_c1059388851t_unit) (X3 tptp.config256849571t_unit)) (let ((_let_1 (@ tptp.cons_c1162654829t_unit X3))) (and (= A12 (@ _let_1 Xa3)) (= A22 (@ _let_1 Xb3)) (@ (@ tptp.prefix1615116500t_unit Xa3) Xb3))))))))
% 0.25/0.67 (assert (forall ((X1 tptp.list_l611321411t_unit) (X22 tptp.list_l611321411t_unit) (P (-> tptp.list_l611321411t_unit tptp.list_l611321411t_unit Bool))) (=> (@ (@ tptp.prefix747844452t_unit X1) X22) (=> (forall ((X2 tptp.list_c1059388851t_unit) (Xs2 tptp.list_l611321411t_unit)) (@ (@ P tptp.nil_li307996205t_unit) (@ (@ tptp.cons_l1083444861t_unit X2) Xs2))) (=> (forall ((Xa2 tptp.list_l611321411t_unit) (Xb2 tptp.list_l611321411t_unit) (X2 tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.cons_l1083444861t_unit X2))) (=> (@ (@ tptp.prefix747844452t_unit Xa2) Xb2) (=> (@ (@ P Xa2) Xb2) (@ (@ P (@ _let_1 Xa2)) (@ _let_1 Xb2)))))) (@ (@ P X1) X22))))))
% 0.25/0.67 (assert (forall ((X1 tptp.list_l1619404459ge_p_v) (X22 tptp.list_l1619404459ge_p_v) (P (-> tptp.list_l1619404459ge_p_v tptp.list_l1619404459ge_p_v Bool))) (=> (@ (@ tptp.prefix1465223476ge_p_v X1) X22) (=> (forall ((X2 tptp.list_message_p_v) (Xs2 tptp.list_l1619404459ge_p_v)) (@ (@ P tptp.nil_list_message_p_v) (@ (@ tptp.cons_l233104475ge_p_v X2) Xs2))) (=> (forall ((Xa2 tptp.list_l1619404459ge_p_v) (Xb2 tptp.list_l1619404459ge_p_v) (X2 tptp.list_message_p_v)) (let ((_let_1 (@ tptp.cons_l233104475ge_p_v X2))) (=> (@ (@ tptp.prefix1465223476ge_p_v Xa2) Xb2) (=> (@ (@ P Xa2) Xb2) (@ (@ P (@ _let_1 Xa2)) (@ _let_1 Xb2)))))) (@ (@ P X1) X22))))))
% 0.25/0.67 (assert (forall ((X1 tptp.list_message_p_v) (X22 tptp.list_message_p_v) (P (-> tptp.list_message_p_v tptp.list_message_p_v Bool))) (=> (@ (@ tptp.prefix47729710ge_p_v X1) X22) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v)) (@ (@ P tptp.nil_message_p_v) (@ (@ tptp.cons_message_p_v X2) Xs2))) (=> (forall ((Xa2 tptp.list_message_p_v) (Xb2 tptp.list_message_p_v) (X2 tptp.message_p_v)) (let ((_let_1 (@ tptp.cons_message_p_v X2))) (=> (@ (@ tptp.prefix47729710ge_p_v Xa2) Xb2) (=> (@ (@ P Xa2) Xb2) (@ (@ P (@ _let_1 Xa2)) (@ _let_1 Xb2)))))) (@ (@ P X1) X22))))))
% 0.25/0.67 (assert (forall ((X1 tptp.list_c1059388851t_unit) (X22 tptp.list_c1059388851t_unit) (P (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool))) (=> (@ (@ tptp.prefix1615116500t_unit X1) X22) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit)) (@ (@ P tptp.nil_co1338500125t_unit) (@ (@ tptp.cons_c1162654829t_unit X2) Xs2))) (=> (forall ((Xa2 tptp.list_c1059388851t_unit) (Xb2 tptp.list_c1059388851t_unit) (X2 tptp.config256849571t_unit)) (let ((_let_1 (@ tptp.cons_c1162654829t_unit X2))) (=> (@ (@ tptp.prefix1615116500t_unit Xa2) Xb2) (=> (@ (@ P Xa2) Xb2) (@ (@ P (@ _let_1 Xa2)) (@ _let_1 Xb2)))))) (@ (@ P X1) X22))))))
% 0.25/0.67 (assert (forall ((N2 tptp.nat) (Pr (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ Pr tptp.zero_zero_nat) (=> (not (@ Pr N2)) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_nat N) N2) (@ Pr N) (not (@ Pr (@ tptp.suc N))))))))))
% 0.25/0.67 (assert (forall ((Cfg2 tptp.config256849571t_unit) (FStepCfg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v))) (= (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s Cfg2) FStepCfg2) FStepMsg2) tptp.zero_zero_nat) (@ (@ tptp.cons_c1162654829t_unit Cfg2) tptp.nil_co1338500125t_unit))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_l611321411t_unit)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s503142615t_unit Xs)) (not (= Xs tptp.nil_li307996205t_unit)))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_l1619404459ge_p_v)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s1809856791ge_p_v Xs)) (not (= Xs tptp.nil_list_message_p_v)))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_message_p_v)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s1168481041ge_p_v Xs)) (not (= Xs tptp.nil_message_p_v)))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_c1059388851t_unit)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s1406904903t_unit Xs)) (not (= Xs tptp.nil_co1338500125t_unit)))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_l611321411t_unit)) (= (= (@ tptp.size_s503142615t_unit Xs) tptp.zero_zero_nat) (= Xs tptp.nil_li307996205t_unit))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_l1619404459ge_p_v)) (= (= (@ tptp.size_s1809856791ge_p_v Xs) tptp.zero_zero_nat) (= Xs tptp.nil_list_message_p_v))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_message_p_v)) (= (= (@ tptp.size_s1168481041ge_p_v Xs) tptp.zero_zero_nat) (= Xs tptp.nil_message_p_v))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_c1059388851t_unit)) (= (= (@ tptp.size_s1406904903t_unit Xs) tptp.zero_zero_nat) (= Xs tptp.nil_co1338500125t_unit))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (= (@ (@ tptp.ord_less_nat N3) (@ tptp.suc tptp.zero_zero_nat)) (= N3 tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N3))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat N3) (@ tptp.suc N3))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N3) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N3)))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N3)) (@ (@ tptp.ord_less_nat M) N3))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (= (not (= N3 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_nat N3) tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 0.25/0.67 (assert (forall ((X21 tptp.message_p_v) (X222 tptp.list_message_p_v) (Y21 tptp.message_p_v) (Y22 tptp.list_message_p_v)) (= (= (@ (@ tptp.cons_message_p_v X21) X222) (@ (@ tptp.cons_message_p_v Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))))
% 0.25/0.67 (assert (forall ((X21 tptp.list_c1059388851t_unit) (X222 tptp.list_l611321411t_unit) (Y21 tptp.list_c1059388851t_unit) (Y22 tptp.list_l611321411t_unit)) (= (= (@ (@ tptp.cons_l1083444861t_unit X21) X222) (@ (@ tptp.cons_l1083444861t_unit Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))))
% 0.25/0.67 (assert (forall ((X21 tptp.list_message_p_v) (X222 tptp.list_l1619404459ge_p_v) (Y21 tptp.list_message_p_v) (Y22 tptp.list_l1619404459ge_p_v)) (= (= (@ (@ tptp.cons_l233104475ge_p_v X21) X222) (@ (@ tptp.cons_l233104475ge_p_v Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))))
% 0.25/0.67 (assert (forall ((X21 tptp.config256849571t_unit) (X222 tptp.list_c1059388851t_unit) (Y21 tptp.config256849571t_unit) (Y22 tptp.list_c1059388851t_unit)) (= (= (@ (@ tptp.cons_c1162654829t_unit X21) X222) (@ (@ tptp.cons_c1162654829t_unit Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))))
% 0.25/0.67 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 0.25/0.67 (assert (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y2)) (= X22 Y2))))
% 0.25/0.67 (assert (forall ((X tptp.message_p_v) (Xs tptp.list_message_p_v)) (not (= (@ (@ tptp.cons_message_p_v X) Xs) Xs))))
% 0.25/0.67 (assert (forall ((X tptp.list_c1059388851t_unit) (Xs tptp.list_l611321411t_unit)) (not (= (@ (@ tptp.cons_l1083444861t_unit X) Xs) Xs))))
% 0.25/0.67 (assert (forall ((X tptp.list_message_p_v) (Xs tptp.list_l1619404459ge_p_v)) (not (= (@ (@ tptp.cons_l233104475ge_p_v X) Xs) Xs))))
% 0.25/0.67 (assert (forall ((X tptp.config256849571t_unit) (Xs tptp.list_c1059388851t_unit)) (not (= (@ (@ tptp.cons_c1162654829t_unit X) Xs) Xs))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (not (= N3 (@ tptp.suc N3)))))
% 0.25/0.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))))
% 0.25/0.67 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 0.25/0.67 (assert (forall ((P (-> tptp.nat Bool)) (N3 tptp.nat)) (=> (forall ((N tptp.nat)) (=> (not (@ P N)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N) (not (@ P M2)))))) (@ P N3))))
% 0.25/0.67 (assert (forall ((P (-> tptp.nat Bool)) (N3 tptp.nat)) (=> (forall ((N tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ P M2))) (@ P N))) (@ P N3))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_nat N3) N3))))
% 0.25/0.67 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) M) (not (= M N3)))))
% 0.25/0.67 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 0.25/0.67 (assert (forall ((A8 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A8))) A8)))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_nat N3) N3))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (= (not (= M N3)) (or (@ (@ tptp.ord_less_nat M) N3) (@ (@ tptp.ord_less_nat N3) M)))))
% 0.25/0.67 (assert (forall ((X tptp.list_message_p_v) (Y tptp.list_message_p_v)) (=> (not (= (@ tptp.size_s1168481041ge_p_v X) (@ tptp.size_s1168481041ge_p_v Y))) (not (= X Y)))))
% 0.25/0.67 (assert (forall ((X tptp.list_c1059388851t_unit) (Y tptp.list_c1059388851t_unit)) (=> (not (= (@ tptp.size_s1406904903t_unit X) (@ tptp.size_s1406904903t_unit Y))) (not (= X Y)))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_message_p_v) (Ys tptp.list_message_p_v)) (=> (not (= (@ tptp.size_s1168481041ge_p_v Xs) (@ tptp.size_s1168481041ge_p_v Ys))) (not (= Xs Ys)))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_c1059388851t_unit) (Ys tptp.list_c1059388851t_unit)) (=> (not (= (@ tptp.size_s1406904903t_unit Xs) (@ tptp.size_s1406904903t_unit Ys))) (not (= Xs Ys)))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (exists ((Xs2 tptp.list_message_p_v)) (= (@ tptp.size_s1168481041ge_p_v Xs2) N3))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (exists ((Xs2 tptp.list_c1059388851t_unit)) (= (@ tptp.size_s1406904903t_unit Xs2) N3))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (exists ((M3 tptp.nat)) (= N3 (@ tptp.suc M3))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.nat Bool)) (Nat tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((Nat3 tptp.nat)) (=> (@ P Nat3) (@ P (@ tptp.suc Nat3)))) (@ P Nat)))))
% 0.25/0.67 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))))
% 0.25/0.67 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.25/0.67 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 0.25/0.67 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N tptp.nat)) (=> (@ P (@ tptp.suc N)) (@ P N))) (@ P tptp.zero_zero_nat)))))
% 0.25/0.67 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N3 tptp.nat)) (=> (forall ((X2 tptp.nat)) (@ (@ P X2) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X2) Y3) (@ (@ P (@ tptp.suc X2)) (@ tptp.suc Y3)))) (@ (@ P M) N3))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.nat Bool)) (N3 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N tptp.nat)) (=> (@ P N) (@ P (@ tptp.suc N)))) (@ P N3)))))
% 0.25/0.67 (assert (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))))
% 0.25/0.67 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 0.25/0.67 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))))
% 0.25/0.67 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((P (-> tptp.nat Bool)) (N3 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (@ P N)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N) (not (@ P M2))))))) (@ P N3)))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N3) (not (= N3 tptp.zero_zero_nat)))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_nat N3) tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_nat N3) tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)) (= N3 tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N3))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N3 M))))))
% 0.25/0.67 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I2 tptp.nat)) (=> (= J (@ tptp.suc I2)) (@ P I2))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ P (@ tptp.suc I2)) (@ P I2)))) (@ P I))))))
% 0.25/0.67 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I2 tptp.nat)) (@ (@ P I2) (@ tptp.suc I2))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I2))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (=> (@ _let_1 J2) (=> (@ (@ P J2) K2) (@ _let_1 K2))))))) (@ (@ P I) J))))))
% 0.25/0.67 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K)))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N3)) (@ (@ tptp.ord_less_nat M) N3))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N3))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N3))))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N3)) M) (exists ((M4 tptp.nat)) (and (= M (@ tptp.suc M4)) (@ (@ tptp.ord_less_nat N3) M4))))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N3)) (@ P I3))) (and (@ P N3) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N3) (@ P I3)))))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N3)) (@ (@ tptp.ord_less_nat N3) (@ tptp.suc M)))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N3)) (or (@ _let_1 N3) (= M N3))))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N3)) (@ P I3))) (or (@ P N3) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N3) (@ P I3)))))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N3) (@ _let_1 (@ tptp.suc N3))))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N3)) (=> (not (@ _let_1 N3)) (= M N3))))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N3) (=> (not (= _let_1 N3)) (@ (@ tptp.ord_less_nat _let_1) N3))))))
% 0.25/0.67 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2)))))))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N3) (@ (@ tptp.ord_less_nat M) N3))))
% 0.25/0.67 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K) (=> (not (= K (@ tptp.suc I))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2))))))))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.message_p_v tptp.config256849571t_unit) tptp.list_message_p_v tptp.list_c1059388851t_unit Bool)) (A0 (-> tptp.message_p_v tptp.config256849571t_unit)) (A1 tptp.list_message_p_v) (A2 tptp.list_c1059388851t_unit)) (=> (forall ((F (-> tptp.message_p_v tptp.config256849571t_unit)) (X_1 tptp.list_c1059388851t_unit)) (@ (@ (@ P F) tptp.nil_message_p_v) X_1)) (=> (forall ((F (-> tptp.message_p_v tptp.config256849571t_unit)) (A9 tptp.message_p_v) (As tptp.list_message_p_v) (Bs tptp.list_c1059388851t_unit)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_c1162654829t_unit (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_message_p_v A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.config256849571t_unit tptp.config256849571t_unit) tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (A0 (-> tptp.config256849571t_unit tptp.config256849571t_unit)) (A1 tptp.list_c1059388851t_unit) (A2 tptp.list_c1059388851t_unit)) (=> (forall ((F (-> tptp.config256849571t_unit tptp.config256849571t_unit)) (X_1 tptp.list_c1059388851t_unit)) (@ (@ (@ P F) tptp.nil_co1338500125t_unit) X_1)) (=> (forall ((F (-> tptp.config256849571t_unit tptp.config256849571t_unit)) (A9 tptp.config256849571t_unit) (As tptp.list_c1059388851t_unit) (Bs tptp.list_c1059388851t_unit)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_c1162654829t_unit (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_c1162654829t_unit A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.message_p_v tptp.message_p_v) tptp.list_message_p_v tptp.list_message_p_v Bool)) (A0 (-> tptp.message_p_v tptp.message_p_v)) (A1 tptp.list_message_p_v) (A2 tptp.list_message_p_v)) (=> (forall ((F (-> tptp.message_p_v tptp.message_p_v)) (X_1 tptp.list_message_p_v)) (@ (@ (@ P F) tptp.nil_message_p_v) X_1)) (=> (forall ((F (-> tptp.message_p_v tptp.message_p_v)) (A9 tptp.message_p_v) (As tptp.list_message_p_v) (Bs tptp.list_message_p_v)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_message_p_v (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_message_p_v A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.list_message_p_v tptp.message_p_v) tptp.list_l1619404459ge_p_v tptp.list_message_p_v Bool)) (A0 (-> tptp.list_message_p_v tptp.message_p_v)) (A1 tptp.list_l1619404459ge_p_v) (A2 tptp.list_message_p_v)) (=> (forall ((F (-> tptp.list_message_p_v tptp.message_p_v)) (X_1 tptp.list_message_p_v)) (@ (@ (@ P F) tptp.nil_list_message_p_v) X_1)) (=> (forall ((F (-> tptp.list_message_p_v tptp.message_p_v)) (A9 tptp.list_message_p_v) (As tptp.list_l1619404459ge_p_v) (Bs tptp.list_message_p_v)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_message_p_v (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_l233104475ge_p_v A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.message_p_v tptp.list_message_p_v) tptp.list_message_p_v tptp.list_l1619404459ge_p_v Bool)) (A0 (-> tptp.message_p_v tptp.list_message_p_v)) (A1 tptp.list_message_p_v) (A2 tptp.list_l1619404459ge_p_v)) (=> (forall ((F (-> tptp.message_p_v tptp.list_message_p_v)) (X_1 tptp.list_l1619404459ge_p_v)) (@ (@ (@ P F) tptp.nil_message_p_v) X_1)) (=> (forall ((F (-> tptp.message_p_v tptp.list_message_p_v)) (A9 tptp.message_p_v) (As tptp.list_message_p_v) (Bs tptp.list_l1619404459ge_p_v)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_l233104475ge_p_v (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_message_p_v A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.config256849571t_unit tptp.message_p_v) tptp.list_c1059388851t_unit tptp.list_message_p_v Bool)) (A0 (-> tptp.config256849571t_unit tptp.message_p_v)) (A1 tptp.list_c1059388851t_unit) (A2 tptp.list_message_p_v)) (=> (forall ((F (-> tptp.config256849571t_unit tptp.message_p_v)) (X_1 tptp.list_message_p_v)) (@ (@ (@ P F) tptp.nil_co1338500125t_unit) X_1)) (=> (forall ((F (-> tptp.config256849571t_unit tptp.message_p_v)) (A9 tptp.config256849571t_unit) (As tptp.list_c1059388851t_unit) (Bs tptp.list_message_p_v)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_message_p_v (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_c1162654829t_unit A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.list_message_p_v tptp.list_message_p_v) tptp.list_l1619404459ge_p_v tptp.list_l1619404459ge_p_v Bool)) (A0 (-> tptp.list_message_p_v tptp.list_message_p_v)) (A1 tptp.list_l1619404459ge_p_v) (A2 tptp.list_l1619404459ge_p_v)) (=> (forall ((F (-> tptp.list_message_p_v tptp.list_message_p_v)) (X_1 tptp.list_l1619404459ge_p_v)) (@ (@ (@ P F) tptp.nil_list_message_p_v) X_1)) (=> (forall ((F (-> tptp.list_message_p_v tptp.list_message_p_v)) (A9 tptp.list_message_p_v) (As tptp.list_l1619404459ge_p_v) (Bs tptp.list_l1619404459ge_p_v)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_l233104475ge_p_v (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_l233104475ge_p_v A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.list_message_p_v tptp.config256849571t_unit) tptp.list_l1619404459ge_p_v tptp.list_c1059388851t_unit Bool)) (A0 (-> tptp.list_message_p_v tptp.config256849571t_unit)) (A1 tptp.list_l1619404459ge_p_v) (A2 tptp.list_c1059388851t_unit)) (=> (forall ((F (-> tptp.list_message_p_v tptp.config256849571t_unit)) (X_1 tptp.list_c1059388851t_unit)) (@ (@ (@ P F) tptp.nil_list_message_p_v) X_1)) (=> (forall ((F (-> tptp.list_message_p_v tptp.config256849571t_unit)) (A9 tptp.list_message_p_v) (As tptp.list_l1619404459ge_p_v) (Bs tptp.list_c1059388851t_unit)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_c1162654829t_unit (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_l233104475ge_p_v A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.list_c1059388851t_unit tptp.message_p_v) tptp.list_l611321411t_unit tptp.list_message_p_v Bool)) (A0 (-> tptp.list_c1059388851t_unit tptp.message_p_v)) (A1 tptp.list_l611321411t_unit) (A2 tptp.list_message_p_v)) (=> (forall ((F (-> tptp.list_c1059388851t_unit tptp.message_p_v)) (X_1 tptp.list_message_p_v)) (@ (@ (@ P F) tptp.nil_li307996205t_unit) X_1)) (=> (forall ((F (-> tptp.list_c1059388851t_unit tptp.message_p_v)) (A9 tptp.list_c1059388851t_unit) (As tptp.list_l611321411t_unit) (Bs tptp.list_message_p_v)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_message_p_v (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_l1083444861t_unit A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.message_p_v tptp.list_c1059388851t_unit) tptp.list_message_p_v tptp.list_l611321411t_unit Bool)) (A0 (-> tptp.message_p_v tptp.list_c1059388851t_unit)) (A1 tptp.list_message_p_v) (A2 tptp.list_l611321411t_unit)) (=> (forall ((F (-> tptp.message_p_v tptp.list_c1059388851t_unit)) (X_1 tptp.list_l611321411t_unit)) (@ (@ (@ P F) tptp.nil_message_p_v) X_1)) (=> (forall ((F (-> tptp.message_p_v tptp.list_c1059388851t_unit)) (A9 tptp.message_p_v) (As tptp.list_message_p_v) (Bs tptp.list_l611321411t_unit)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_l1083444861t_unit (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_message_p_v A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_l611321411t_unit) (P (-> tptp.list_l611321411t_unit Bool))) (=> (not (= Xs tptp.nil_li307996205t_unit)) (=> (forall ((X2 tptp.list_c1059388851t_unit)) (@ P (@ (@ tptp.cons_l1083444861t_unit X2) tptp.nil_li307996205t_unit))) (=> (forall ((X2 tptp.list_c1059388851t_unit) (Xs2 tptp.list_l611321411t_unit)) (=> (not (= Xs2 tptp.nil_li307996205t_unit)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_l1083444861t_unit X2) Xs2))))) (@ P Xs))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_l1619404459ge_p_v) (P (-> tptp.list_l1619404459ge_p_v Bool))) (=> (not (= Xs tptp.nil_list_message_p_v)) (=> (forall ((X2 tptp.list_message_p_v)) (@ P (@ (@ tptp.cons_l233104475ge_p_v X2) tptp.nil_list_message_p_v))) (=> (forall ((X2 tptp.list_message_p_v) (Xs2 tptp.list_l1619404459ge_p_v)) (=> (not (= Xs2 tptp.nil_list_message_p_v)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_l233104475ge_p_v X2) Xs2))))) (@ P Xs))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_message_p_v) (P (-> tptp.list_message_p_v Bool))) (=> (not (= Xs tptp.nil_message_p_v)) (=> (forall ((X2 tptp.message_p_v)) (@ P (@ (@ tptp.cons_message_p_v X2) tptp.nil_message_p_v))) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v)) (=> (not (= Xs2 tptp.nil_message_p_v)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_message_p_v X2) Xs2))))) (@ P Xs))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_c1059388851t_unit) (P (-> tptp.list_c1059388851t_unit Bool))) (=> (not (= Xs tptp.nil_co1338500125t_unit)) (=> (forall ((X2 tptp.config256849571t_unit)) (@ P (@ (@ tptp.cons_c1162654829t_unit X2) tptp.nil_co1338500125t_unit))) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit)) (=> (not (= Xs2 tptp.nil_co1338500125t_unit)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2))))) (@ P Xs))))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool) tptp.list_l611321411t_unit Bool)) (A0 (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (A1 tptp.list_l611321411t_unit)) (=> (forall ((P2 (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool))) (@ (@ P P2) tptp.nil_li307996205t_unit)) (=> (forall ((P2 (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (X2 tptp.list_c1059388851t_unit)) (@ (@ P P2) (@ (@ tptp.cons_l1083444861t_unit X2) tptp.nil_li307996205t_unit))) (=> (forall ((P2 (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (X2 tptp.list_c1059388851t_unit) (Y3 tptp.list_c1059388851t_unit) (Xs2 tptp.list_l611321411t_unit)) (let ((_let_1 (@ (@ tptp.cons_l1083444861t_unit Y3) Xs2))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_l1083444861t_unit X2) _let_1)))))) (@ (@ P A0) A1))))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.list_message_p_v tptp.list_message_p_v Bool) tptp.list_l1619404459ge_p_v Bool)) (A0 (-> tptp.list_message_p_v tptp.list_message_p_v Bool)) (A1 tptp.list_l1619404459ge_p_v)) (=> (forall ((P2 (-> tptp.list_message_p_v tptp.list_message_p_v Bool))) (@ (@ P P2) tptp.nil_list_message_p_v)) (=> (forall ((P2 (-> tptp.list_message_p_v tptp.list_message_p_v Bool)) (X2 tptp.list_message_p_v)) (@ (@ P P2) (@ (@ tptp.cons_l233104475ge_p_v X2) tptp.nil_list_message_p_v))) (=> (forall ((P2 (-> tptp.list_message_p_v tptp.list_message_p_v Bool)) (X2 tptp.list_message_p_v) (Y3 tptp.list_message_p_v) (Xs2 tptp.list_l1619404459ge_p_v)) (let ((_let_1 (@ (@ tptp.cons_l233104475ge_p_v Y3) Xs2))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_l233104475ge_p_v X2) _let_1)))))) (@ (@ P A0) A1))))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.message_p_v tptp.message_p_v Bool) tptp.list_message_p_v Bool)) (A0 (-> tptp.message_p_v tptp.message_p_v Bool)) (A1 tptp.list_message_p_v)) (=> (forall ((P2 (-> tptp.message_p_v tptp.message_p_v Bool))) (@ (@ P P2) tptp.nil_message_p_v)) (=> (forall ((P2 (-> tptp.message_p_v tptp.message_p_v Bool)) (X2 tptp.message_p_v)) (@ (@ P P2) (@ (@ tptp.cons_message_p_v X2) tptp.nil_message_p_v))) (=> (forall ((P2 (-> tptp.message_p_v tptp.message_p_v Bool)) (X2 tptp.message_p_v) (Y3 tptp.message_p_v) (Xs2 tptp.list_message_p_v)) (let ((_let_1 (@ (@ tptp.cons_message_p_v Y3) Xs2))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_message_p_v X2) _let_1)))))) (@ (@ P A0) A1))))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool) tptp.list_c1059388851t_unit Bool)) (A0 (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool)) (A1 tptp.list_c1059388851t_unit)) (=> (forall ((P2 (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool))) (@ (@ P P2) tptp.nil_co1338500125t_unit)) (=> (forall ((P2 (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool)) (X2 tptp.config256849571t_unit)) (@ (@ P P2) (@ (@ tptp.cons_c1162654829t_unit X2) tptp.nil_co1338500125t_unit))) (=> (forall ((P2 (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool)) (X2 tptp.config256849571t_unit) (Y3 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit)) (let ((_let_1 (@ (@ tptp.cons_c1162654829t_unit Y3) Xs2))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_c1162654829t_unit X2) _let_1)))))) (@ (@ P A0) A1))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_l611321411t_unit Bool)) (A0 tptp.list_l611321411t_unit)) (=> (@ P tptp.nil_li307996205t_unit) (=> (forall ((X2 tptp.list_c1059388851t_unit)) (@ P (@ (@ tptp.cons_l1083444861t_unit X2) tptp.nil_li307996205t_unit))) (=> (forall ((X2 tptp.list_c1059388851t_unit) (Y3 tptp.list_c1059388851t_unit) (Xs2 tptp.list_l611321411t_unit)) (let ((_let_1 (@ (@ tptp.cons_l1083444861t_unit Y3) Xs2))) (let ((_let_2 (@ tptp.cons_l1083444861t_unit X2))) (let ((_let_3 (= X2 Y3))) (=> (=> _let_3 (@ P (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_l1619404459ge_p_v Bool)) (A0 tptp.list_l1619404459ge_p_v)) (=> (@ P tptp.nil_list_message_p_v) (=> (forall ((X2 tptp.list_message_p_v)) (@ P (@ (@ tptp.cons_l233104475ge_p_v X2) tptp.nil_list_message_p_v))) (=> (forall ((X2 tptp.list_message_p_v) (Y3 tptp.list_message_p_v) (Xs2 tptp.list_l1619404459ge_p_v)) (let ((_let_1 (@ (@ tptp.cons_l233104475ge_p_v Y3) Xs2))) (let ((_let_2 (@ tptp.cons_l233104475ge_p_v X2))) (let ((_let_3 (= X2 Y3))) (=> (=> _let_3 (@ P (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_message_p_v Bool)) (A0 tptp.list_message_p_v)) (=> (@ P tptp.nil_message_p_v) (=> (forall ((X2 tptp.message_p_v)) (@ P (@ (@ tptp.cons_message_p_v X2) tptp.nil_message_p_v))) (=> (forall ((X2 tptp.message_p_v) (Y3 tptp.message_p_v) (Xs2 tptp.list_message_p_v)) (let ((_let_1 (@ (@ tptp.cons_message_p_v Y3) Xs2))) (let ((_let_2 (@ tptp.cons_message_p_v X2))) (let ((_let_3 (= X2 Y3))) (=> (=> _let_3 (@ P (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_c1059388851t_unit Bool)) (A0 tptp.list_c1059388851t_unit)) (=> (@ P tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.config256849571t_unit)) (@ P (@ (@ tptp.cons_c1162654829t_unit X2) tptp.nil_co1338500125t_unit))) (=> (forall ((X2 tptp.config256849571t_unit) (Y3 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit)) (let ((_let_1 (@ (@ tptp.cons_c1162654829t_unit Y3) Xs2))) (let ((_let_2 (@ tptp.cons_c1162654829t_unit X2))) (let ((_let_3 (= X2 Y3))) (=> (=> _let_3 (@ P (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool) tptp.list_l611321411t_unit Bool)) (A0 (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (A1 tptp.list_l611321411t_unit)) (=> (forall ((P2 (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool))) (@ (@ P P2) tptp.nil_li307996205t_unit)) (=> (forall ((P2 (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (X2 tptp.list_c1059388851t_unit) (Ys2 tptp.list_l611321411t_unit)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_l1083444861t_unit X2) Ys2))))) (@ (@ P A0) A1)))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.list_message_p_v tptp.list_message_p_v Bool) tptp.list_l1619404459ge_p_v Bool)) (A0 (-> tptp.list_message_p_v tptp.list_message_p_v Bool)) (A1 tptp.list_l1619404459ge_p_v)) (=> (forall ((P2 (-> tptp.list_message_p_v tptp.list_message_p_v Bool))) (@ (@ P P2) tptp.nil_list_message_p_v)) (=> (forall ((P2 (-> tptp.list_message_p_v tptp.list_message_p_v Bool)) (X2 tptp.list_message_p_v) (Ys2 tptp.list_l1619404459ge_p_v)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_l233104475ge_p_v X2) Ys2))))) (@ (@ P A0) A1)))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.message_p_v tptp.message_p_v Bool) tptp.list_message_p_v Bool)) (A0 (-> tptp.message_p_v tptp.message_p_v Bool)) (A1 tptp.list_message_p_v)) (=> (forall ((P2 (-> tptp.message_p_v tptp.message_p_v Bool))) (@ (@ P P2) tptp.nil_message_p_v)) (=> (forall ((P2 (-> tptp.message_p_v tptp.message_p_v Bool)) (X2 tptp.message_p_v) (Ys2 tptp.list_message_p_v)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_message_p_v X2) Ys2))))) (@ (@ P A0) A1)))))
% 0.25/0.67 (assert (forall ((P (-> (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool) tptp.list_c1059388851t_unit Bool)) (A0 (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool)) (A1 tptp.list_c1059388851t_unit)) (=> (forall ((P2 (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool))) (@ (@ P P2) tptp.nil_co1338500125t_unit)) (=> (forall ((P2 (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool)) (X2 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_c1162654829t_unit X2) Ys2))))) (@ (@ P A0) A1)))))
% 0.25/0.67 (assert (forall ((X tptp.list_l611321411t_unit)) (=> (not (= X tptp.nil_li307996205t_unit)) (=> (forall ((X2 tptp.list_c1059388851t_unit)) (not (= X (@ (@ tptp.cons_l1083444861t_unit X2) tptp.nil_li307996205t_unit)))) (not (forall ((X2 tptp.list_c1059388851t_unit) (Y3 tptp.list_c1059388851t_unit) (Xs2 tptp.list_l611321411t_unit)) (not (= X (@ (@ tptp.cons_l1083444861t_unit X2) (@ (@ tptp.cons_l1083444861t_unit Y3) Xs2))))))))))
% 0.25/0.67 (assert (forall ((X tptp.list_l1619404459ge_p_v)) (=> (not (= X tptp.nil_list_message_p_v)) (=> (forall ((X2 tptp.list_message_p_v)) (not (= X (@ (@ tptp.cons_l233104475ge_p_v X2) tptp.nil_list_message_p_v)))) (not (forall ((X2 tptp.list_message_p_v) (Y3 tptp.list_message_p_v) (Xs2 tptp.list_l1619404459ge_p_v)) (not (= X (@ (@ tptp.cons_l233104475ge_p_v X2) (@ (@ tptp.cons_l233104475ge_p_v Y3) Xs2))))))))))
% 0.25/0.67 (assert (forall ((X tptp.list_message_p_v)) (=> (not (= X tptp.nil_message_p_v)) (=> (forall ((X2 tptp.message_p_v)) (not (= X (@ (@ tptp.cons_message_p_v X2) tptp.nil_message_p_v)))) (not (forall ((X2 tptp.message_p_v) (Y3 tptp.message_p_v) (Xs2 tptp.list_message_p_v)) (not (= X (@ (@ tptp.cons_message_p_v X2) (@ (@ tptp.cons_message_p_v Y3) Xs2))))))))))
% 0.25/0.67 (assert (forall ((X tptp.list_c1059388851t_unit)) (=> (not (= X tptp.nil_co1338500125t_unit)) (=> (forall ((X2 tptp.config256849571t_unit)) (not (= X (@ (@ tptp.cons_c1162654829t_unit X2) tptp.nil_co1338500125t_unit)))) (not (forall ((X2 tptp.config256849571t_unit) (Y3 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit)) (not (= X (@ (@ tptp.cons_c1162654829t_unit X2) (@ (@ tptp.cons_c1162654829t_unit Y3) Xs2))))))))))
% 0.25/0.67 (assert (forall ((X tptp.list_l1584713811t_unit)) (=> (not (= X tptp.nil_li2108369341t_unit)) (=> (forall ((Xss tptp.list_l1584713811t_unit)) (not (= X (@ (@ tptp.cons_l1777019405t_unit tptp.nil_li307996205t_unit) Xss)))) (not (forall ((X2 tptp.list_c1059388851t_unit) (Xs2 tptp.list_l611321411t_unit) (Xss tptp.list_l1584713811t_unit)) (not (= X (@ (@ tptp.cons_l1777019405t_unit (@ (@ tptp.cons_l1083444861t_unit X2) Xs2)) Xss)))))))))
% 0.25/0.67 (assert (forall ((X tptp.list_l1341496881ge_p_v)) (=> (not (= X tptp.nil_li835338673ge_p_v)) (=> (forall ((Xss tptp.list_l1341496881ge_p_v)) (not (= X (@ (@ tptp.cons_l1383421281ge_p_v tptp.nil_list_message_p_v) Xss)))) (not (forall ((X2 tptp.list_message_p_v) (Xs2 tptp.list_l1619404459ge_p_v) (Xss tptp.list_l1341496881ge_p_v)) (not (= X (@ (@ tptp.cons_l1383421281ge_p_v (@ (@ tptp.cons_l233104475ge_p_v X2) Xs2)) Xss)))))))))
% 0.25/0.67 (assert (forall ((X tptp.list_l1619404459ge_p_v)) (=> (not (= X tptp.nil_list_message_p_v)) (=> (forall ((Xss tptp.list_l1619404459ge_p_v)) (not (= X (@ (@ tptp.cons_l233104475ge_p_v tptp.nil_message_p_v) Xss)))) (not (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Xss tptp.list_l1619404459ge_p_v)) (not (= X (@ (@ tptp.cons_l233104475ge_p_v (@ (@ tptp.cons_message_p_v X2) Xs2)) Xss)))))))))
% 0.25/0.67 (assert (forall ((X tptp.list_l611321411t_unit)) (=> (not (= X tptp.nil_li307996205t_unit)) (=> (forall ((Xss tptp.list_l611321411t_unit)) (not (= X (@ (@ tptp.cons_l1083444861t_unit tptp.nil_co1338500125t_unit) Xss)))) (not (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Xss tptp.list_l611321411t_unit)) (not (= X (@ (@ tptp.cons_l1083444861t_unit (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) Xss)))))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_l1619404459ge_p_v tptp.list_l1619404459ge_p_v Bool)) (A0 tptp.list_l1619404459ge_p_v) (A1 tptp.list_l1619404459ge_p_v)) (=> (forall ((X_1 tptp.list_l1619404459ge_p_v)) (@ (@ P tptp.nil_list_message_p_v) X_1)) (=> (forall ((Xs2 tptp.list_l1619404459ge_p_v)) (@ (@ P Xs2) tptp.nil_list_message_p_v)) (=> (forall ((X2 tptp.list_message_p_v) (Xs2 tptp.list_l1619404459ge_p_v) (Y3 tptp.list_message_p_v) (Ys2 tptp.list_l1619404459ge_p_v)) (let ((_let_1 (@ (@ tptp.cons_l233104475ge_p_v Y3) Ys2))) (let ((_let_2 (@ P (@ (@ tptp.cons_l233104475ge_p_v X2) Xs2)))) (=> (@ (@ P Xs2) _let_1) (=> (@ _let_2 Ys2) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_message_p_v tptp.list_message_p_v Bool)) (A0 tptp.list_message_p_v) (A1 tptp.list_message_p_v)) (=> (forall ((X_1 tptp.list_message_p_v)) (@ (@ P tptp.nil_message_p_v) X_1)) (=> (forall ((Xs2 tptp.list_message_p_v)) (@ (@ P Xs2) tptp.nil_message_p_v)) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v)) (let ((_let_1 (@ (@ tptp.cons_message_p_v Y3) Ys2))) (let ((_let_2 (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)))) (=> (@ (@ P Xs2) _let_1) (=> (@ _let_2 Ys2) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (A0 tptp.list_c1059388851t_unit) (A1 tptp.list_c1059388851t_unit)) (=> (forall ((X_1 tptp.list_c1059388851t_unit)) (@ (@ P tptp.nil_co1338500125t_unit) X_1)) (=> (forall ((Xs2 tptp.list_c1059388851t_unit)) (@ (@ P Xs2) tptp.nil_co1338500125t_unit)) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit)) (let ((_let_1 (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2))) (let ((_let_2 (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)))) (=> (@ (@ P Xs2) _let_1) (=> (@ _let_2 Ys2) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_message_p_v Bool)) (Xs tptp.list_message_p_v)) (=> (@ P tptp.nil_message_p_v) (=> (forall ((X2 tptp.message_p_v)) (@ P (@ (@ tptp.cons_message_p_v X2) tptp.nil_message_p_v))) (=> (forall ((X2 tptp.message_p_v) (Y3 tptp.message_p_v) (Zs tptp.list_message_p_v)) (let ((_let_1 (@ (@ tptp.cons_message_p_v Y3) Zs))) (=> (@ P Zs) (=> (@ P _let_1) (@ P (@ (@ tptp.cons_message_p_v X2) _let_1)))))) (@ P Xs))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_c1059388851t_unit Bool)) (Xs tptp.list_c1059388851t_unit)) (=> (@ P tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.config256849571t_unit)) (@ P (@ (@ tptp.cons_c1162654829t_unit X2) tptp.nil_co1338500125t_unit))) (=> (forall ((X2 tptp.config256849571t_unit) (Y3 tptp.config256849571t_unit) (Zs tptp.list_c1059388851t_unit)) (let ((_let_1 (@ (@ tptp.cons_c1162654829t_unit Y3) Zs))) (=> (@ P Zs) (=> (@ P _let_1) (@ P (@ (@ tptp.cons_c1162654829t_unit X2) _let_1)))))) (@ P Xs))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_message_p_v tptp.list_message_p_v Bool)) (A0 tptp.list_message_p_v) (A1 tptp.list_message_p_v)) (=> (forall ((X_1 tptp.list_message_p_v)) (@ (@ P tptp.nil_message_p_v) X_1)) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Ys2 tptp.list_message_p_v)) (=> (@ (@ P Ys2) Xs2) (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) Ys2))) (@ (@ P A0) A1)))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (A0 tptp.list_c1059388851t_unit) (A1 tptp.list_c1059388851t_unit)) (=> (forall ((X_1 tptp.list_c1059388851t_unit)) (@ (@ P tptp.nil_co1338500125t_unit) X_1)) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Ys2 tptp.list_c1059388851t_unit)) (=> (@ (@ P Ys2) Xs2) (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) Ys2))) (@ (@ P A0) A1)))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_message_p_v tptp.list_message_p_v Bool)) (Xs tptp.list_message_p_v) (Ys tptp.list_message_p_v)) (=> (@ (@ P tptp.nil_message_p_v) tptp.nil_message_p_v) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v)) (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) tptp.nil_message_p_v)) (=> (forall ((Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v)) (@ (@ P tptp.nil_message_p_v) (@ (@ tptp.cons_message_p_v Y3) Ys2))) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) (@ (@ tptp.cons_message_p_v Y3) Ys2)))) (@ (@ P Xs) Ys)))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_message_p_v tptp.list_c1059388851t_unit Bool)) (Xs tptp.list_message_p_v) (Ys tptp.list_c1059388851t_unit)) (=> (@ (@ P tptp.nil_message_p_v) tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v)) (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) tptp.nil_co1338500125t_unit)) (=> (forall ((Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit)) (@ (@ P tptp.nil_message_p_v) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2))) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2)))) (@ (@ P Xs) Ys)))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_c1059388851t_unit tptp.list_message_p_v Bool)) (Xs tptp.list_c1059388851t_unit) (Ys tptp.list_message_p_v)) (=> (@ (@ P tptp.nil_co1338500125t_unit) tptp.nil_message_p_v) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit)) (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) tptp.nil_message_p_v)) (=> (forall ((Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v)) (@ (@ P tptp.nil_co1338500125t_unit) (@ (@ tptp.cons_message_p_v Y3) Ys2))) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) (@ (@ tptp.cons_message_p_v Y3) Ys2)))) (@ (@ P Xs) Ys)))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (Xs tptp.list_c1059388851t_unit) (Ys tptp.list_c1059388851t_unit)) (=> (@ (@ P tptp.nil_co1338500125t_unit) tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit)) (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) tptp.nil_co1338500125t_unit)) (=> (forall ((Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit)) (@ (@ P tptp.nil_co1338500125t_unit) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2))) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2)))) (@ (@ P Xs) Ys)))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_message_p_v)) (= (not (= Xs tptp.nil_message_p_v)) (exists ((Y4 tptp.message_p_v) (Ys3 tptp.list_message_p_v)) (= Xs (@ (@ tptp.cons_message_p_v Y4) Ys3))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_c1059388851t_unit)) (= (not (= Xs tptp.nil_co1338500125t_unit)) (exists ((Y4 tptp.config256849571t_unit) (Ys3 tptp.list_c1059388851t_unit)) (= Xs (@ (@ tptp.cons_c1162654829t_unit Y4) Ys3))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_message_p_v Bool)) (List tptp.list_message_p_v)) (=> (@ P tptp.nil_message_p_v) (=> (forall ((X12 tptp.message_p_v) (X23 tptp.list_message_p_v)) (=> (@ P X23) (@ P (@ (@ tptp.cons_message_p_v X12) X23)))) (@ P List)))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_c1059388851t_unit Bool)) (List tptp.list_c1059388851t_unit)) (=> (@ P tptp.nil_co1338500125t_unit) (=> (forall ((X12 tptp.config256849571t_unit) (X23 tptp.list_c1059388851t_unit)) (=> (@ P X23) (@ P (@ (@ tptp.cons_c1162654829t_unit X12) X23)))) (@ P List)))))
% 0.25/0.67 (assert (forall ((Y tptp.list_message_p_v)) (=> (not (= Y tptp.nil_message_p_v)) (not (forall ((X212 tptp.message_p_v) (X223 tptp.list_message_p_v)) (not (= Y (@ (@ tptp.cons_message_p_v X212) X223))))))))
% 0.25/0.67 (assert (forall ((Y tptp.list_c1059388851t_unit)) (=> (not (= Y tptp.nil_co1338500125t_unit)) (not (forall ((X212 tptp.config256849571t_unit) (X223 tptp.list_c1059388851t_unit)) (not (= Y (@ (@ tptp.cons_c1162654829t_unit X212) X223))))))))
% 0.25/0.67 (assert (forall ((List tptp.list_message_p_v) (X21 tptp.message_p_v) (X222 tptp.list_message_p_v)) (=> (= List (@ (@ tptp.cons_message_p_v X21) X222)) (not (= List tptp.nil_message_p_v)))))
% 0.25/0.67 (assert (forall ((List tptp.list_c1059388851t_unit) (X21 tptp.config256849571t_unit) (X222 tptp.list_c1059388851t_unit)) (=> (= List (@ (@ tptp.cons_c1162654829t_unit X21) X222)) (not (= List tptp.nil_co1338500125t_unit)))))
% 0.25/0.67 (assert (forall ((X21 tptp.message_p_v) (X222 tptp.list_message_p_v)) (not (= tptp.nil_message_p_v (@ (@ tptp.cons_message_p_v X21) X222)))))
% 0.25/0.67 (assert (forall ((X21 tptp.config256849571t_unit) (X222 tptp.list_c1059388851t_unit)) (not (= tptp.nil_co1338500125t_unit (@ (@ tptp.cons_c1162654829t_unit X21) X222)))))
% 0.25/0.67 (assert (forall ((P (-> tptp.list_c1059388851t_unit Bool)) (Xs tptp.list_c1059388851t_unit)) (=> (forall ((Xs2 tptp.list_c1059388851t_unit)) (=> (forall ((Ys4 tptp.list_c1059388851t_unit)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s1406904903t_unit Ys4)) (@ tptp.size_s1406904903t_unit Xs2)) (@ P Ys4))) (@ P Xs2))) (@ P Xs))))
% 0.25/0.67 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (N3 tptp.nat) (M tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ F2 N)) (@ F2 (@ tptp.suc N)))) (= (@ (@ tptp.ord_less_nat (@ F2 N3)) (@ F2 M)) (@ (@ tptp.ord_less_nat N3) M)))))
% 0.25/0.67 (assert (forall ((F2 (-> tptp.nat tptp.int)) (N3 tptp.nat) (M tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ F2 N)) (@ F2 (@ tptp.suc N)))) (= (@ (@ tptp.ord_less_int (@ F2 N3)) (@ F2 M)) (@ (@ tptp.ord_less_nat N3) M)))))
% 0.25/0.67 (assert (forall ((F2 (-> tptp.nat tptp.nat)) (N3 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ F2 N)) (@ F2 (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_nat N3) N4) (@ (@ tptp.ord_less_nat (@ F2 N3)) (@ F2 N4))))))
% 0.25/0.67 (assert (forall ((F2 (-> tptp.nat tptp.int)) (N3 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ F2 N)) (@ F2 (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_nat N3) N4) (@ (@ tptp.ord_less_int (@ F2 N3)) (@ F2 N4))))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N3)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N3)))))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (exists ((M3 tptp.nat)) (= N3 (@ tptp.suc M3))))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N3)) (@ P I3))) (and (@ P tptp.zero_zero_nat) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N3) (@ P (@ tptp.suc I3))))))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (exists ((M5 tptp.nat)) (= N3 (@ tptp.suc M5))))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N3)) (@ P I3))) (or (@ P tptp.zero_zero_nat) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N3) (@ P (@ tptp.suc I3))))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_c1059388851t_unit) (N3 tptp.nat)) (= (= (@ tptp.size_s1406904903t_unit Xs) (@ tptp.suc N3)) (exists ((Y4 tptp.config256849571t_unit) (Ys3 tptp.list_c1059388851t_unit)) (and (= Xs (@ (@ tptp.cons_c1162654829t_unit Y4) Ys3)) (= (@ tptp.size_s1406904903t_unit Ys3) N3))))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat) (Xs tptp.list_c1059388851t_unit)) (= (= (@ tptp.suc N3) (@ tptp.size_s1406904903t_unit Xs)) (exists ((Y4 tptp.config256849571t_unit) (Ys3 tptp.list_c1059388851t_unit)) (and (= Xs (@ (@ tptp.cons_c1162654829t_unit Y4) Ys3)) (= (@ tptp.size_s1406904903t_unit Ys3) N3))))))
% 0.25/0.67 (assert (= (@ tptp.size_s1168481041ge_p_v tptp.nil_message_p_v) tptp.zero_zero_nat))
% 0.25/0.67 (assert (= (@ tptp.size_s1406904903t_unit tptp.nil_co1338500125t_unit) tptp.zero_zero_nat))
% 0.25/0.67 (assert (forall ((Xs tptp.list_message_p_v) (Ys tptp.list_message_p_v) (Zs2 tptp.list_message_p_v) (P (-> tptp.list_message_p_v tptp.list_message_p_v tptp.list_message_p_v Bool))) (let ((_let_1 (@ tptp.size_s1168481041ge_p_v Ys))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs) _let_1) (=> (= _let_1 (@ tptp.size_s1168481041ge_p_v Zs2)) (=> (@ (@ (@ P tptp.nil_message_p_v) tptp.nil_message_p_v) tptp.nil_message_p_v) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v) (Z tptp.message_p_v) (Zs tptp.list_message_p_v)) (let ((_let_1 (@ tptp.size_s1168481041ge_p_v Ys2))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s1168481041ge_p_v Zs)) (=> (@ (@ (@ P Xs2) Ys2) Zs) (@ (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) (@ (@ tptp.cons_message_p_v Y3) Ys2)) (@ (@ tptp.cons_message_p_v Z) Zs))))))) (@ (@ (@ P Xs) Ys) Zs2))))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_message_p_v) (Ys tptp.list_message_p_v) (Zs2 tptp.list_c1059388851t_unit) (P (-> tptp.list_message_p_v tptp.list_message_p_v tptp.list_c1059388851t_unit Bool))) (let ((_let_1 (@ tptp.size_s1168481041ge_p_v Ys))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs) _let_1) (=> (= _let_1 (@ tptp.size_s1406904903t_unit Zs2)) (=> (@ (@ (@ P tptp.nil_message_p_v) tptp.nil_message_p_v) tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v) (Z tptp.config256849571t_unit) (Zs tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.size_s1168481041ge_p_v Ys2))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s1406904903t_unit Zs)) (=> (@ (@ (@ P Xs2) Ys2) Zs) (@ (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) (@ (@ tptp.cons_message_p_v Y3) Ys2)) (@ (@ tptp.cons_c1162654829t_unit Z) Zs))))))) (@ (@ (@ P Xs) Ys) Zs2))))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_message_p_v) (Ys tptp.list_c1059388851t_unit) (Zs2 tptp.list_message_p_v) (P (-> tptp.list_message_p_v tptp.list_c1059388851t_unit tptp.list_message_p_v Bool))) (let ((_let_1 (@ tptp.size_s1406904903t_unit Ys))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs) _let_1) (=> (= _let_1 (@ tptp.size_s1168481041ge_p_v Zs2)) (=> (@ (@ (@ P tptp.nil_message_p_v) tptp.nil_co1338500125t_unit) tptp.nil_message_p_v) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit) (Z tptp.message_p_v) (Zs tptp.list_message_p_v)) (let ((_let_1 (@ tptp.size_s1406904903t_unit Ys2))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s1168481041ge_p_v Zs)) (=> (@ (@ (@ P Xs2) Ys2) Zs) (@ (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2)) (@ (@ tptp.cons_message_p_v Z) Zs))))))) (@ (@ (@ P Xs) Ys) Zs2))))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_message_p_v) (Ys tptp.list_c1059388851t_unit) (Zs2 tptp.list_c1059388851t_unit) (P (-> tptp.list_message_p_v tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool))) (let ((_let_1 (@ tptp.size_s1406904903t_unit Ys))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs) _let_1) (=> (= _let_1 (@ tptp.size_s1406904903t_unit Zs2)) (=> (@ (@ (@ P tptp.nil_message_p_v) tptp.nil_co1338500125t_unit) tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit) (Z tptp.config256849571t_unit) (Zs tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.size_s1406904903t_unit Ys2))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s1406904903t_unit Zs)) (=> (@ (@ (@ P Xs2) Ys2) Zs) (@ (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2)) (@ (@ tptp.cons_c1162654829t_unit Z) Zs))))))) (@ (@ (@ P Xs) Ys) Zs2))))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_c1059388851t_unit) (Ys tptp.list_message_p_v) (Zs2 tptp.list_message_p_v) (P (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v Bool))) (let ((_let_1 (@ tptp.size_s1168481041ge_p_v Ys))) (=> (= (@ tptp.size_s1406904903t_unit Xs) _let_1) (=> (= _let_1 (@ tptp.size_s1168481041ge_p_v Zs2)) (=> (@ (@ (@ P tptp.nil_co1338500125t_unit) tptp.nil_message_p_v) tptp.nil_message_p_v) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v) (Z tptp.message_p_v) (Zs tptp.list_message_p_v)) (let ((_let_1 (@ tptp.size_s1168481041ge_p_v Ys2))) (=> (= (@ tptp.size_s1406904903t_unit Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s1168481041ge_p_v Zs)) (=> (@ (@ (@ P Xs2) Ys2) Zs) (@ (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) (@ (@ tptp.cons_message_p_v Y3) Ys2)) (@ (@ tptp.cons_message_p_v Z) Zs))))))) (@ (@ (@ P Xs) Ys) Zs2))))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_c1059388851t_unit) (Ys tptp.list_message_p_v) (Zs2 tptp.list_c1059388851t_unit) (P (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit Bool))) (let ((_let_1 (@ tptp.size_s1168481041ge_p_v Ys))) (=> (= (@ tptp.size_s1406904903t_unit Xs) _let_1) (=> (= _let_1 (@ tptp.size_s1406904903t_unit Zs2)) (=> (@ (@ (@ P tptp.nil_co1338500125t_unit) tptp.nil_message_p_v) tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v) (Z tptp.config256849571t_unit) (Zs tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.size_s1168481041ge_p_v Ys2))) (=> (= (@ tptp.size_s1406904903t_unit Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s1406904903t_unit Zs)) (=> (@ (@ (@ P Xs2) Ys2) Zs) (@ (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) (@ (@ tptp.cons_message_p_v Y3) Ys2)) (@ (@ tptp.cons_c1162654829t_unit Z) Zs))))))) (@ (@ (@ P Xs) Ys) Zs2))))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_c1059388851t_unit) (Ys tptp.list_c1059388851t_unit) (Zs2 tptp.list_message_p_v) (P (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit tptp.list_message_p_v Bool))) (let ((_let_1 (@ tptp.size_s1406904903t_unit Ys))) (=> (= (@ tptp.size_s1406904903t_unit Xs) _let_1) (=> (= _let_1 (@ tptp.size_s1168481041ge_p_v Zs2)) (=> (@ (@ (@ P tptp.nil_co1338500125t_unit) tptp.nil_co1338500125t_unit) tptp.nil_message_p_v) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit) (Z tptp.message_p_v) (Zs tptp.list_message_p_v)) (let ((_let_1 (@ tptp.size_s1406904903t_unit Ys2))) (=> (= (@ tptp.size_s1406904903t_unit Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s1168481041ge_p_v Zs)) (=> (@ (@ (@ P Xs2) Ys2) Zs) (@ (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2)) (@ (@ tptp.cons_message_p_v Z) Zs))))))) (@ (@ (@ P Xs) Ys) Zs2))))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_c1059388851t_unit) (Ys tptp.list_c1059388851t_unit) (Zs2 tptp.list_c1059388851t_unit) (P (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool))) (let ((_let_1 (@ tptp.size_s1406904903t_unit Ys))) (=> (= (@ tptp.size_s1406904903t_unit Xs) _let_1) (=> (= _let_1 (@ tptp.size_s1406904903t_unit Zs2)) (=> (@ (@ (@ P tptp.nil_co1338500125t_unit) tptp.nil_co1338500125t_unit) tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit) (Z tptp.config256849571t_unit) (Zs tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.size_s1406904903t_unit Ys2))) (=> (= (@ tptp.size_s1406904903t_unit Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s1406904903t_unit Zs)) (=> (@ (@ (@ P Xs2) Ys2) Zs) (@ (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2)) (@ (@ tptp.cons_c1162654829t_unit Z) Zs))))))) (@ (@ (@ P Xs) Ys) Zs2))))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_message_p_v) (Ys tptp.list_message_p_v) (P (-> tptp.list_message_p_v tptp.list_message_p_v Bool))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs) (@ tptp.size_s1168481041ge_p_v Ys)) (=> (@ (@ P tptp.nil_message_p_v) tptp.nil_message_p_v) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v)) (=> (= (@ tptp.size_s1168481041ge_p_v Xs2) (@ tptp.size_s1168481041ge_p_v Ys2)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) (@ (@ tptp.cons_message_p_v Y3) Ys2))))) (@ (@ P Xs) Ys))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_message_p_v) (Ys tptp.list_c1059388851t_unit) (P (-> tptp.list_message_p_v tptp.list_c1059388851t_unit Bool))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs) (@ tptp.size_s1406904903t_unit Ys)) (=> (@ (@ P tptp.nil_message_p_v) tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit)) (=> (= (@ tptp.size_s1168481041ge_p_v Xs2) (@ tptp.size_s1406904903t_unit Ys2)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2))))) (@ (@ P Xs) Ys))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_c1059388851t_unit) (Ys tptp.list_message_p_v) (P (-> tptp.list_c1059388851t_unit tptp.list_message_p_v Bool))) (=> (= (@ tptp.size_s1406904903t_unit Xs) (@ tptp.size_s1168481041ge_p_v Ys)) (=> (@ (@ P tptp.nil_co1338500125t_unit) tptp.nil_message_p_v) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v)) (=> (= (@ tptp.size_s1406904903t_unit Xs2) (@ tptp.size_s1168481041ge_p_v Ys2)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) (@ (@ tptp.cons_message_p_v Y3) Ys2))))) (@ (@ P Xs) Ys))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_c1059388851t_unit) (Ys tptp.list_c1059388851t_unit) (P (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool))) (=> (= (@ tptp.size_s1406904903t_unit Xs) (@ tptp.size_s1406904903t_unit Ys)) (=> (@ (@ P tptp.nil_co1338500125t_unit) tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit)) (=> (= (@ tptp.size_s1406904903t_unit Xs2) (@ tptp.size_s1406904903t_unit Ys2)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2))))) (@ (@ P Xs) Ys))))))
% 0.25/0.67 (assert (forall ((X tptp.config256849571t_unit) (Xa (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (Xb (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (Xc tptp.nat) (Y tptp.list_c1059388851t_unit)) (=> (= (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s X) Xa) Xb) Xc) Y) (=> (=> (= Xc tptp.zero_zero_nat) (not (= Y (@ (@ tptp.cons_c1162654829t_unit X) tptp.nil_co1338500125t_unit)))) (not (forall ((N tptp.nat)) (=> (= Xc (@ tptp.suc N)) (not (= Y (@ (@ Xa (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s X) Xa) Xb) N)) (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s X) Xa) Xb) N)))))))))))
% 0.25/0.67 (assert (forall ((X tptp.config256849571t_unit) (Xa (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (Xb (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (Xc tptp.nat) (Y tptp.list_message_p_v)) (=> (= (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s X) Xa) Xb) Xc) Y) (=> (=> (= Xc tptp.zero_zero_nat) (not (= Y tptp.nil_message_p_v))) (not (forall ((N tptp.nat)) (=> (= Xc (@ tptp.suc N)) (not (= Y (@ (@ Xb (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s X) Xa) Xb) N)) (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s X) Xa) Xb) N)))))))))))
% 0.25/0.67 (assert (forall ((Cfg2 tptp.config256849571t_unit) (FStepCfg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (N3 tptp.nat)) (let ((_let_1 (@ (@ (@ tptp.fLPThe536531371_p_v_s Cfg2) FStepCfg2) FStepMsg2))) (= (@ _let_1 (@ tptp.suc N3)) (@ (@ FStepMsg2 (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s Cfg2) FStepCfg2) FStepMsg2) N3)) (@ _let_1 N3))))))
% 0.25/0.67 (assert (forall ((Cfg2 tptp.config256849571t_unit) (FStepCfg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (N3 tptp.nat)) (let ((_let_1 (@ (@ (@ tptp.fLPThe1519354920_p_v_s Cfg2) FStepCfg2) FStepMsg2))) (= (@ _let_1 (@ tptp.suc N3)) (@ (@ FStepCfg2 (@ _let_1 N3)) (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s Cfg2) FStepCfg2) FStepMsg2) N3))))))
% 0.25/0.67 (assert (forall ((Cfg2 tptp.config256849571t_unit) (FStepCfg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v))) (= (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s Cfg2) FStepCfg2) FStepMsg2) tptp.zero_zero_nat) tptp.nil_message_p_v)))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)) (= N3 tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((X tptp.config256849571t_unit) (Xs tptp.list_c1059388851t_unit)) (= (@ tptp.size_s1406904903t_unit (@ (@ tptp.cons_c1162654829t_unit X) Xs)) (@ tptp.suc (@ tptp.size_s1406904903t_unit Xs)))))
% 0.25/0.67 (assert (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_nat N3) tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N3) (not (= N3 tptp.zero_zero_nat)))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (not (= N3 tptp.zero_zero_nat)))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (let ((_let_1 (@ (@ tptp.n_list1987762709t_unit N3) tptp.nil_co1338500125t_unit))) (let ((_let_2 (= N3 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_l1083444861t_unit tptp.nil_co1338500125t_unit) tptp.nil_li307996205t_unit))) (=> (not _let_2) (= _let_1 tptp.nil_li307996205t_unit)))))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (let ((_let_1 (@ (@ tptp.n_lists_message_p_v N3) tptp.nil_message_p_v))) (let ((_let_2 (= N3 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_l233104475ge_p_v tptp.nil_message_p_v) tptp.nil_list_message_p_v))) (=> (not _let_2) (= _let_1 tptp.nil_list_message_p_v)))))))
% 0.25/0.67 (assert (forall ((Trans (-> tptp.p tptp.s tptp.messageValue_v tptp.s)) (Sends (-> tptp.p tptp.s tptp.messageValue_v tptp.message_p_v tptp.nat)) (Start (-> tptp.p tptp.s)) (X tptp.config256849571t_unit) (Xa (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (Xb (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (Xc tptp.nat) (Y tptp.list_c1059388851t_unit)) (=> (@ (@ (@ tptp.fLPThe9398366_p_s_v Trans) Sends) Start) (=> (= (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s X) Xa) Xb) Xc) Y) (=> (=> (= Xc tptp.zero_zero_nat) (not (= Y (@ (@ tptp.cons_c1162654829t_unit X) tptp.nil_co1338500125t_unit)))) (not (forall ((N tptp.nat)) (=> (= Xc (@ tptp.suc N)) (not (= Y (@ (@ Xa (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s X) Xa) Xb) N)) (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s X) Xa) Xb) N))))))))))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_c1059388851t_unit)) (= (@ (@ tptp.n_list1987762709t_unit tptp.zero_zero_nat) Xs) (@ (@ tptp.cons_l1083444861t_unit tptp.nil_co1338500125t_unit) tptp.nil_li307996205t_unit))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_message_p_v)) (= (@ (@ tptp.n_lists_message_p_v tptp.zero_zero_nat) Xs) (@ (@ tptp.cons_l233104475ge_p_v tptp.nil_message_p_v) tptp.nil_list_message_p_v))))
% 0.25/0.67 (assert (forall ((Trans (-> tptp.p tptp.s tptp.messageValue_v tptp.s)) (Sends (-> tptp.p tptp.s tptp.messageValue_v tptp.message_p_v tptp.nat)) (Start (-> tptp.p tptp.s)) (X tptp.config256849571t_unit) (Xa (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (Xb (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (Xc tptp.nat) (Y tptp.list_message_p_v)) (=> (@ (@ (@ tptp.fLPThe9398366_p_s_v Trans) Sends) Start) (=> (= (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s X) Xa) Xb) Xc) Y) (=> (=> (= Xc tptp.zero_zero_nat) (not (= Y tptp.nil_message_p_v))) (not (forall ((N tptp.nat)) (=> (= Xc (@ tptp.suc N)) (not (= Y (@ (@ Xb (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s X) Xa) Xb) N)) (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s X) Xa) Xb) N))))))))))))
% 0.25/0.67 (assert (forall ((Trans (-> tptp.p tptp.s tptp.messageValue_v tptp.s)) (Sends (-> tptp.p tptp.s tptp.messageValue_v tptp.message_p_v tptp.nat)) (Start (-> tptp.p tptp.s)) (Cfg2 tptp.config256849571t_unit) (FStepCfg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (N3 tptp.nat)) (let ((_let_1 (@ (@ (@ tptp.fLPThe536531371_p_v_s Cfg2) FStepCfg2) FStepMsg2))) (=> (@ (@ (@ tptp.fLPThe9398366_p_s_v Trans) Sends) Start) (= (@ _let_1 (@ tptp.suc N3)) (@ (@ FStepMsg2 (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s Cfg2) FStepCfg2) FStepMsg2) N3)) (@ _let_1 N3)))))))
% 0.25/0.67 (assert (forall ((Trans (-> tptp.p tptp.s tptp.messageValue_v tptp.s)) (Sends (-> tptp.p tptp.s tptp.messageValue_v tptp.message_p_v tptp.nat)) (Start (-> tptp.p tptp.s)) (Cfg2 tptp.config256849571t_unit) (FStepCfg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (N3 tptp.nat)) (let ((_let_1 (@ (@ (@ tptp.fLPThe1519354920_p_v_s Cfg2) FStepCfg2) FStepMsg2))) (=> (@ (@ (@ tptp.fLPThe9398366_p_s_v Trans) Sends) Start) (= (@ _let_1 (@ tptp.suc N3)) (@ (@ FStepCfg2 (@ _let_1 N3)) (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s Cfg2) FStepCfg2) FStepMsg2) N3)))))))
% 0.25/0.67 (assert (forall ((Trans (-> tptp.p tptp.s tptp.messageValue_v tptp.s)) (Sends (-> tptp.p tptp.s tptp.messageValue_v tptp.message_p_v tptp.nat)) (Start (-> tptp.p tptp.s)) (Cfg2 tptp.config256849571t_unit) (FStepCfg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v))) (=> (@ (@ (@ tptp.fLPThe9398366_p_s_v Trans) Sends) Start) (= (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s Cfg2) FStepCfg2) FStepMsg2) tptp.zero_zero_nat) tptp.nil_message_p_v))))
% 0.25/0.67 (assert (forall ((Trans (-> tptp.p tptp.s tptp.messageValue_v tptp.s)) (Sends (-> tptp.p tptp.s tptp.messageValue_v tptp.message_p_v tptp.nat)) (Start (-> tptp.p tptp.s)) (Cfg2 tptp.config256849571t_unit) (FStepCfg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v))) (=> (@ (@ (@ tptp.fLPThe9398366_p_s_v Trans) Sends) Start) (= (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s Cfg2) FStepCfg2) FStepMsg2) tptp.zero_zero_nat) (@ (@ tptp.cons_c1162654829t_unit Cfg2) tptp.nil_co1338500125t_unit)))))
% 0.25/0.67 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 0.25/0.67 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 0.25/0.67 (assert (= (@ tptp.produc663212148t_unit tptp.nil_li307996205t_unit) (@ (@ tptp.cons_l1083444861t_unit tptp.nil_co1338500125t_unit) tptp.nil_li307996205t_unit)))
% 0.25/0.67 (assert (= (@ tptp.produc1505827982ge_p_v tptp.nil_list_message_p_v) (@ (@ tptp.cons_l233104475ge_p_v tptp.nil_message_p_v) tptp.nil_list_message_p_v)))
% 0.25/0.67 (assert (= (@ tptp.subseq1144048270t_unit tptp.nil_co1338500125t_unit) (@ (@ tptp.cons_l1083444861t_unit tptp.nil_co1338500125t_unit) tptp.nil_li307996205t_unit)))
% 0.25/0.67 (assert (= (@ tptp.subseqs_message_p_v tptp.nil_message_p_v) (@ (@ tptp.cons_l233104475ge_p_v tptp.nil_message_p_v) tptp.nil_list_message_p_v)))
% 0.25/0.67 (assert (= tptp.size_s1406904903t_unit (@ tptp.gen_le193291088t_unit tptp.zero_zero_nat)))
% 0.25/0.67 (assert (forall ((N3 tptp.nat) (X tptp.config256849571t_unit) (Xs tptp.list_c1059388851t_unit)) (= (@ (@ tptp.gen_le193291088t_unit N3) (@ (@ tptp.cons_c1162654829t_unit X) Xs)) (@ (@ tptp.gen_le193291088t_unit (@ tptp.suc N3)) Xs))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (= (@ (@ tptp.gen_le193291088t_unit N3) tptp.nil_co1338500125t_unit) N3)))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (= (@ (@ tptp.gen_le697204914ge_p_v N3) tptp.nil_message_p_v) N3)))
% 0.25/0.67 (assert (forall ((X tptp.message_p_v)) (= (@ (@ tptp.insert_message_p_v X) tptp.nil_message_p_v) (@ (@ tptp.cons_message_p_v X) tptp.nil_message_p_v))))
% 0.25/0.67 (assert (forall ((X tptp.config256849571t_unit)) (= (@ (@ tptp.insert1308755079t_unit X) tptp.nil_co1338500125t_unit) (@ (@ tptp.cons_c1162654829t_unit X) tptp.nil_co1338500125t_unit))))
% 0.25/0.67 (assert (forall ((A8 tptp.set_nat) (X tptp.message_p_v)) (let ((_let_1 (@ (@ tptp.cons_message_p_v X) tptp.nil_message_p_v))) (let ((_let_2 (@ (@ tptp.nths_message_p_v _let_1) A8))) (let ((_let_3 (@ (@ tptp.member_nat tptp.zero_zero_nat) A8))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.nil_message_p_v))))))))
% 0.25/0.67 (assert (forall ((A8 tptp.set_nat) (X tptp.config256849571t_unit)) (let ((_let_1 (@ (@ tptp.cons_c1162654829t_unit X) tptp.nil_co1338500125t_unit))) (let ((_let_2 (@ (@ tptp.nths_c890550943t_unit _let_1) A8))) (let ((_let_3 (@ (@ tptp.member_nat tptp.zero_zero_nat) A8))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.nil_co1338500125t_unit))))))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1382578993at_nat N3)) (@ _let_1 N3)))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri2019852685at_int N3)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (= (= (@ tptp.semiri2019852685at_int M) (@ tptp.semiri2019852685at_int N3)) (= M N3))))
% 0.25/0.67 (assert (forall ((A8 tptp.set_nat)) (= (@ (@ tptp.nths_c890550943t_unit tptp.nil_co1338500125t_unit) A8) tptp.nil_co1338500125t_unit)))
% 0.25/0.67 (assert (forall ((A8 tptp.set_nat)) (= (@ (@ tptp.nths_message_p_v tptp.nil_message_p_v) A8) tptp.nil_message_p_v)))
% 0.25/0.67 (assert (= (@ tptp.semiri1382578993at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 0.25/0.67 (assert (= (@ tptp.semiri2019852685at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1382578993at_nat N3)) (= tptp.zero_zero_nat N3))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri2019852685at_int N3)) (= tptp.zero_zero_nat N3))))
% 0.25/0.67 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1382578993at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri2019852685at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1382578993at_nat M)) (@ tptp.semiri1382578993at_nat N3)) (@ (@ tptp.ord_less_nat M) N3))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int M)) (@ tptp.semiri2019852685at_int N3)) (@ (@ tptp.ord_less_nat M) N3))))
% 0.25/0.67 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1382578993at_nat M)) tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int M)) tptp.zero_zero_int))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (not (= (@ tptp.semiri1382578993at_nat (@ tptp.suc N3)) tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (not (= (@ tptp.semiri2019852685at_int (@ tptp.suc N3)) tptp.zero_zero_int))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N3) (@ (@ tptp.ord_less_nat (@ tptp.semiri1382578993at_nat M)) (@ tptp.semiri1382578993at_nat N3)))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N3) (@ (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int M)) (@ tptp.semiri2019852685at_int N3)))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1382578993at_nat M)) (@ tptp.semiri1382578993at_nat N3)) (@ (@ tptp.ord_less_nat M) N3))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int M)) (@ tptp.semiri2019852685at_int N3)) (@ (@ tptp.ord_less_nat M) N3))))
% 0.25/0.67 (assert (forall ((Xs tptp.list_c1059388851t_unit) (I4 tptp.set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1406904903t_unit Xs)) (@ (@ tptp.member_nat I2) I4))) (= (@ (@ tptp.nths_c890550943t_unit Xs) I4) Xs))))
% 0.25/0.67 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N tptp.nat)) (=> (= K (@ tptp.semiri2019852685at_int N)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))))
% 0.25/0.67 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= K (@ tptp.semiri2019852685at_int N)))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.config256849571t_unit Bool))) (not (@ (@ tptp.list_e1598815642t_unit P) tptp.nil_co1338500125t_unit))))
% 0.25/0.67 (assert (forall ((P (-> tptp.message_p_v Bool))) (not (@ (@ tptp.list_ex1_message_p_v P) tptp.nil_message_p_v))))
% 0.25/0.67 (assert (= tptp.ord_less_nat (lambda ((A10 tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int A10)) (@ tptp.semiri2019852685at_int B)))))
% 0.25/0.67 (assert (= (@ tptp.semiri2019852685at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 0.25/0.67 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int N))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))))
% 0.25/0.67 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B2)) (= A B2))))
% 0.25/0.67 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 0.25/0.67 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 0.25/0.67 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 0.25/0.67 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 0.25/0.67 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 0.25/0.67 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 0.25/0.67 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) B2))))
% 0.25/0.67 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))))
% 0.25/0.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 0.25/0.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 0.25/0.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat) (M tptp.nat)) (= (= (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int N3)) (@ tptp.semiri2019852685at_int M)) (and (= N3 tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int (@ tptp.suc N3)))) (@ tptp.semiri2019852685at_int M))))
% 0.25/0.67 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B2)) A))))
% 0.25/0.67 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.ord_less_int B2) (@ tptp.uminus_uminus_int A)))))
% 0.25/0.67 (assert (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)))))
% 0.25/0.67 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B2) (= (@ tptp.uminus_uminus_int B2) A))))
% 0.25/0.67 (assert (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ tptp.uminus_uminus_int B2)) (= B2 (@ tptp.uminus_uminus_int A)))))
% 0.25/0.67 (assert (forall ((Z2 tptp.int)) (=> (forall ((N tptp.nat)) (not (= Z2 (@ tptp.semiri2019852685at_int N)))) (not (forall ((N tptp.nat)) (not (= Z2 (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int (@ tptp.suc N))))))))))
% 0.25/0.67 (assert (forall ((P (-> tptp.int Bool)) (Z2 tptp.int)) (=> (forall ((N tptp.nat)) (@ P (@ tptp.semiri2019852685at_int N))) (=> (forall ((N tptp.nat)) (@ P (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int (@ tptp.suc N))))) (@ P Z2)))))
% 0.25/0.67 (assert (forall ((M tptp.int)) (=> (forall ((N tptp.nat)) (not (= M (@ tptp.semiri2019852685at_int N)))) (not (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int N))))))))))
% 0.25/0.67 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 0.25/0.67 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 0.25/0.67 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N tptp.nat)) (=> (= K (@ tptp.semiri2019852685at_int N)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (not (forall ((N tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int N))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int (@ tptp.suc N3)))) tptp.zero_zero_int)))
% 0.25/0.67 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (exists ((N tptp.nat)) (= X (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int (@ tptp.suc N))))))))
% 0.25/0.67 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2))))
% 0.25/0.67 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))))
% 0.25/0.67 (assert (= (@ tptp.ring_1_of_int_int tptp.zero_zero_int) tptp.zero_zero_int))
% 0.25/0.67 (assert (forall ((Z2 tptp.int)) (= (= tptp.zero_zero_int (@ tptp.ring_1_of_int_int Z2)) (= Z2 tptp.zero_zero_int))))
% 0.25/0.67 (assert (forall ((Z2 tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z2) tptp.zero_zero_int) (= Z2 tptp.zero_zero_int))))
% 0.25/0.67 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z2)) (@ (@ tptp.ord_less_int W) Z2))))
% 0.25/0.67 (assert (forall ((W tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z2)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (@ (@ tptp.ord_less_int W) Z2)))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int N3))) tptp.zero_zero_nat)))
% 0.25/0.67 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z2) tptp.zero_zero_int))))
% 0.25/0.67 (assert (= tptp.zero_zero_nat (@ tptp.nat2 tptp.zero_zero_int)))
% 0.25/0.67 (assert (forall ((Z2 tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int W) Z2)))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int M)) Z2))))
% 0.25/0.67 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 Z2) (@ _let_1 (@ tptp.ring_1_of_int_int Z2))))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int N3)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X)) (@ _let_1 X)))))
% 0.25/0.67 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.int)) (= (@ P (@ tptp.nat2 I)) (and (forall ((N5 tptp.nat)) (=> (= I (@ tptp.semiri2019852685at_int N5)) (@ P N5))) (=> (@ (@ tptp.ord_less_int I) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))))
% 0.25/0.67 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z2))))
% 0.25/0.67 (assert (forall ((W tptp.int) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) M) (@ (@ tptp.ord_less_int W) (@ tptp.semiri2019852685at_int M))))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N3) tptp.zero_zero_nat) (= N3 tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) B2))))
% 0.25/0.67 (assert (forall ((M tptp.nat) (N3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri2019852685at_int M)) (@ tptp.semiri2019852685at_int N3)) (@ (@ tptp.ord_less_eq_nat M) N3))))
% 0.25/0.67 (assert (= (@ tptp.semiri2019852685at_int tptp.one_one_nat) tptp.one_one_int))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri2019852685at_int N3)) (= N3 tptp.one_one_nat))))
% 0.25/0.67 (assert (forall ((N3 tptp.nat)) (= (= (@ tptp.semiri2019852685at_int N3) tptp.one_one_int) (= N3 tptp.one_one_nat))))
% 0.25/0.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 0.25/0.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 0.25/0.67 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))))
% 0.25/0.67 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 0.25/0.67 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1382578993at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri2019852685at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 0.25/0.67 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 0.25/0.67 (assert (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z2) tptp.zero_zero_int) (= (@ tptp.nat2 Z2) tptp.zero_zero_nat))))
% 0.25/0.67 (assert (forall ((I tptp.int)) (= (= (@ tptp.nat2 I) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int))))
% 0.25/0.67 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int Z2) tptp.zero_zero_int))))
% 0.25/0.67 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))))
% 0.25/0.67 (assert (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z2)) tptp.one_one_int) (@ (@ tptp.ord_less_int Z2) tptp.one_one_int))))
% 0.25/0.67 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))))
% 0.25/0.67 (assert (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z2) (@ _let_1 (@ tptp.ring_1_of_int_int Z2))))))
% 0.25/0.67 (assert (forall ((B3 tptp.nat) (A11 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B3) A11)) (@ (@ tptp.ord_less_nat A11) B3))))
% 0.25/0.67 (assert (forall ((B3 tptp.int) (A11 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B3) A11)) (@ (@ tptp.ord_less_int A11) B3))))
% 0.25/0.67 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 0.25/0.67 (assert (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))))
% 0.25/0.67 (assert (forall ((F2 (-> tptp.nat tptp.int)) (N3 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F2 (@ tptp.suc N))) (@ F2 N))) (=> (@ (@ tptp.ord_less_eq_nat N3) N4) (@ (@ tptp.ord_less_eq_int (@ F2 N4)) (@ F2 N3))))))
% 0.25/0.67 (assert (forall ((F2 (-> tptp.nat tptp.int)) (N3 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F2 N)) (@ F2 (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_eq_nat N3) N4) (@ (@ tptp.ord_less_eq_int (@ F2 N3)) (@ F2 N4))))))
% 0.58/0.79 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 0.58/0.79 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 0.58/0.79 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 0.58/0.79 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 0.58/0.79 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 0.58/0.79 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri2019852685at_int I)) (@ tptp.semiri2019852685at_int J)))))
% 0.58/0.79 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 0.58/0.79 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 0.58/0.79 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 0.58/0.79 (assert (not (@ (@ tptp.prefix1615116500t_unit (@ tptp.fe tptp.m)) (@ tptp.fe tptp.na))))
% 0.58/0.79 (set-info :filename cvc5---1.0.5_26401)
% 0.58/0.79 (check-sat-assuming ( true ))
% 0.58/0.79 ------- get file name : TPTP file name is ITP055^1
% 0.58/0.79 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_26401.smt2...
% 0.58/0.79 --- Run --ho-elim --full-saturate-quant at 10...
% 0.58/0.79 % SZS status Theorem for ITP055^1
% 0.58/0.79 % SZS output start Proof for ITP055^1
% 0.58/0.79 (
% 0.58/0.79 (let ((_let_1 (@ (@ tptp.prefix1615116500t_unit (@ tptp.fe tptp.m)) (@ tptp.fe tptp.na)))) (let ((_let_2 (not _let_1))) (let ((_let_3 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_4 (@ tptp.ord_less_int tptp.one_one_int))) (let ((_let_5 (= (@ tptp.semiri2019852685at_int tptp.zero_zero_nat) tptp.zero_zero_int))) (let ((_let_6 (@ (@ tptp.cons_l233104475ge_p_v tptp.nil_message_p_v) tptp.nil_list_message_p_v))) (let ((_let_7 (@ (@ tptp.cons_l1083444861t_unit tptp.nil_co1338500125t_unit) tptp.nil_li307996205t_unit))) (let ((_let_8 (@ tptp.ord_less_nat tptp.m))) (let ((_let_9 (@ _let_8 tptp.na))) (let ((_let_10 (=> _let_9 _let_1))) (SCOPE (SCOPE (CONTRA (RESOLUTION (IMPLIES_ELIM (ASSUME :args (_let_10))) (ASSUME :args (_let_9)) :args (false _let_9)) (ASSUME :args (_let_2))) :args (_let_9 (@ _let_8 tptp.n) _let_10 (or (= tptp.m tptp.na) _let_9) (@ _let_8 (@ tptp.suc tptp.na)) (forall ((L1 tptp.list_message_p_v) (L2 tptp.list_message_p_v) (L3 tptp.list_message_p_v)) (let ((_let_1 (@ tptp.prefix47729710ge_p_v L1))) (=> (@ _let_1 L2) (=> (@ (@ tptp.prefix47729710ge_p_v L2) L3) (@ _let_1 L3))))) (forall ((L1 tptp.list_c1059388851t_unit) (L2 tptp.list_c1059388851t_unit) (L3 tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.prefix1615116500t_unit L1))) (=> (@ _let_1 L2) (=> (@ (@ tptp.prefix1615116500t_unit L2) L3) (@ _let_1 L3))))) (= (@ tptp.fe tptp.zero_zero_nat) (@ (@ tptp.cons_c1162654829t_unit tptp.cfg) tptp.nil_co1338500125t_unit)) (forall ((Xa tptp.list_l611321411t_unit) (Xb tptp.list_l611321411t_unit) (X tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.cons_l1083444861t_unit X))) (=> (@ (@ tptp.prefix747844452t_unit Xa) Xb) (@ (@ tptp.prefix747844452t_unit (@ _let_1 Xa)) (@ _let_1 Xb))))) (forall ((Xa tptp.list_l1619404459ge_p_v) (Xb tptp.list_l1619404459ge_p_v) (X tptp.list_message_p_v)) (let ((_let_1 (@ tptp.cons_l233104475ge_p_v X))) (=> (@ (@ tptp.prefix1465223476ge_p_v Xa) Xb) (@ (@ tptp.prefix1465223476ge_p_v (@ _let_1 Xa)) (@ _let_1 Xb))))) (forall ((Xa tptp.list_message_p_v) (Xb tptp.list_message_p_v) (X tptp.message_p_v)) (let ((_let_1 (@ tptp.cons_message_p_v X))) (=> (@ (@ tptp.prefix47729710ge_p_v Xa) Xb) (@ (@ tptp.prefix47729710ge_p_v (@ _let_1 Xa)) (@ _let_1 Xb))))) (forall ((Xa tptp.list_c1059388851t_unit) (Xb tptp.list_c1059388851t_unit) (X tptp.config256849571t_unit)) (let ((_let_1 (@ tptp.cons_c1162654829t_unit X))) (=> (@ (@ tptp.prefix1615116500t_unit Xa) Xb) (@ (@ tptp.prefix1615116500t_unit (@ _let_1 Xa)) (@ _let_1 Xb))))) (forall ((L1 tptp.list_message_p_v) (L2 tptp.list_message_p_v)) (=> (@ (@ tptp.prefix47729710ge_p_v L1) L2) (@ (@ tptp.ord_less_nat (@ tptp.size_s1168481041ge_p_v L1)) (@ tptp.size_s1168481041ge_p_v L2)))) (forall ((L1 tptp.list_c1059388851t_unit) (L2 tptp.list_c1059388851t_unit)) (=> (@ (@ tptp.prefix1615116500t_unit L1) L2) (@ (@ tptp.ord_less_nat (@ tptp.size_s1406904903t_unit L1)) (@ tptp.size_s1406904903t_unit L2)))) (forall ((P (-> tptp.config256849571t_unit (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit) (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v) tptp.nat Bool)) (Q (-> tptp.config256849571t_unit (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit) (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v) tptp.nat Bool)) (A4 tptp.config256849571t_unit) (A5 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (A6 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (A7 tptp.nat)) (=> (forall ((Cfg tptp.config256849571t_unit) (FStepCfg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v))) (@ (@ (@ (@ P Cfg) FStepCfg) FStepMsg) tptp.zero_zero_nat)) (=> (forall ((Cfg tptp.config256849571t_unit) (FStepCfg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (N tptp.nat)) (let ((_let_1 (@ (@ (@ P Cfg) FStepCfg) FStepMsg))) (=> (@ _let_1 N) (=> (@ (@ (@ (@ Q Cfg) FStepCfg) FStepMsg) N) (@ _let_1 (@ tptp.suc N)))))) (=> (forall ((Cfg tptp.config256849571t_unit) (FStepCfg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v))) (@ (@ (@ (@ Q Cfg) FStepCfg) FStepMsg) tptp.zero_zero_nat)) (=> (forall ((Cfg tptp.config256849571t_unit) (FStepCfg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (N tptp.nat)) (let ((_let_1 (@ (@ (@ Q Cfg) FStepCfg) FStepMsg))) (=> (@ (@ (@ (@ P Cfg) FStepCfg) FStepMsg) N) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N)))))) (@ (@ (@ (@ Q A4) A5) A6) A7)))))) (forall ((P (-> tptp.config256849571t_unit (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit) (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v) tptp.nat Bool)) (Q (-> tptp.config256849571t_unit (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit) (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v) tptp.nat Bool)) (A0 tptp.config256849571t_unit) (A1 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (A2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (A3 tptp.nat)) (=> (forall ((Cfg tptp.config256849571t_unit) (FStepCfg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v))) (@ (@ (@ (@ P Cfg) FStepCfg) FStepMsg) tptp.zero_zero_nat)) (=> (forall ((Cfg tptp.config256849571t_unit) (FStepCfg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (N tptp.nat)) (let ((_let_1 (@ (@ (@ P Cfg) FStepCfg) FStepMsg))) (=> (@ _let_1 N) (=> (@ (@ (@ (@ Q Cfg) FStepCfg) FStepMsg) N) (@ _let_1 (@ tptp.suc N)))))) (=> (forall ((Cfg tptp.config256849571t_unit) (FStepCfg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v))) (@ (@ (@ (@ Q Cfg) FStepCfg) FStepMsg) tptp.zero_zero_nat)) (=> (forall ((Cfg tptp.config256849571t_unit) (FStepCfg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (N tptp.nat)) (let ((_let_1 (@ (@ (@ Q Cfg) FStepCfg) FStepMsg))) (=> (@ (@ (@ (@ P Cfg) FStepCfg) FStepMsg) N) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N)))))) (@ (@ (@ (@ P A0) A1) A2) A3)))))) (forall ((X tptp.list_c1059388851t_unit) (Xs tptp.list_l611321411t_unit)) (@ (@ tptp.prefix747844452t_unit tptp.nil_li307996205t_unit) (@ (@ tptp.cons_l1083444861t_unit X) Xs))) (forall ((X tptp.list_message_p_v) (Xs tptp.list_l1619404459ge_p_v)) (@ (@ tptp.prefix1465223476ge_p_v tptp.nil_list_message_p_v) (@ (@ tptp.cons_l233104475ge_p_v X) Xs))) (forall ((X tptp.message_p_v) (Xs tptp.list_message_p_v)) (@ (@ tptp.prefix47729710ge_p_v tptp.nil_message_p_v) (@ (@ tptp.cons_message_p_v X) Xs))) (forall ((X tptp.config256849571t_unit) (Xs tptp.list_c1059388851t_unit)) (@ (@ tptp.prefix1615116500t_unit tptp.nil_co1338500125t_unit) (@ (@ tptp.cons_c1162654829t_unit X) Xs))) (forall ((A1 tptp.list_l611321411t_unit) (A2 tptp.list_l611321411t_unit)) (=> (@ (@ tptp.prefix747844452t_unit A1) A2) (=> (=> (= A1 tptp.nil_li307996205t_unit) (forall ((X2 tptp.list_c1059388851t_unit) (Xs2 tptp.list_l611321411t_unit)) (not (= A2 (@ (@ tptp.cons_l1083444861t_unit X2) Xs2))))) (not (forall ((Xa2 tptp.list_l611321411t_unit) (Xb2 tptp.list_l611321411t_unit) (X2 tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.cons_l1083444861t_unit X2))) (=> (= A1 (@ _let_1 Xa2)) (=> (= A2 (@ _let_1 Xb2)) (not (@ (@ tptp.prefix747844452t_unit Xa2) Xb2)))))))))) (forall ((A1 tptp.list_l1619404459ge_p_v) (A2 tptp.list_l1619404459ge_p_v)) (=> (@ (@ tptp.prefix1465223476ge_p_v A1) A2) (=> (=> (= A1 tptp.nil_list_message_p_v) (forall ((X2 tptp.list_message_p_v) (Xs2 tptp.list_l1619404459ge_p_v)) (not (= A2 (@ (@ tptp.cons_l233104475ge_p_v X2) Xs2))))) (not (forall ((Xa2 tptp.list_l1619404459ge_p_v) (Xb2 tptp.list_l1619404459ge_p_v) (X2 tptp.list_message_p_v)) (let ((_let_1 (@ tptp.cons_l233104475ge_p_v X2))) (=> (= A1 (@ _let_1 Xa2)) (=> (= A2 (@ _let_1 Xb2)) (not (@ (@ tptp.prefix1465223476ge_p_v Xa2) Xb2)))))))))) (forall ((A1 tptp.list_message_p_v) (A2 tptp.list_message_p_v)) (=> (@ (@ tptp.prefix47729710ge_p_v A1) A2) (=> (=> (= A1 tptp.nil_message_p_v) (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v)) (not (= A2 (@ (@ tptp.cons_message_p_v X2) Xs2))))) (not (forall ((Xa2 tptp.list_message_p_v) (Xb2 tptp.list_message_p_v) (X2 tptp.message_p_v)) (let ((_let_1 (@ tptp.cons_message_p_v X2))) (=> (= A1 (@ _let_1 Xa2)) (=> (= A2 (@ _let_1 Xb2)) (not (@ (@ tptp.prefix47729710ge_p_v Xa2) Xb2)))))))))) (forall ((A1 tptp.list_c1059388851t_unit) (A2 tptp.list_c1059388851t_unit)) (=> (@ (@ tptp.prefix1615116500t_unit A1) A2) (=> (=> (= A1 tptp.nil_co1338500125t_unit) (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit)) (not (= A2 (@ (@ tptp.cons_c1162654829t_unit X2) Xs2))))) (not (forall ((Xa2 tptp.list_c1059388851t_unit) (Xb2 tptp.list_c1059388851t_unit) (X2 tptp.config256849571t_unit)) (let ((_let_1 (@ tptp.cons_c1162654829t_unit X2))) (=> (= A1 (@ _let_1 Xa2)) (=> (= A2 (@ _let_1 Xb2)) (not (@ (@ tptp.prefix1615116500t_unit Xa2) Xb2)))))))))) (= tptp.prefix747844452t_unit (lambda ((A12 tptp.list_l611321411t_unit) (A22 tptp.list_l611321411t_unit)) (or (exists ((X3 tptp.list_c1059388851t_unit) (Xs3 tptp.list_l611321411t_unit)) (and (= A12 tptp.nil_li307996205t_unit) (= A22 (@ (@ tptp.cons_l1083444861t_unit X3) Xs3)))) (exists ((Xa3 tptp.list_l611321411t_unit) (Xb3 tptp.list_l611321411t_unit) (X3 tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.cons_l1083444861t_unit X3))) (and (= A12 (@ _let_1 Xa3)) (= A22 (@ _let_1 Xb3)) (@ (@ tptp.prefix747844452t_unit Xa3) Xb3))))))) (= tptp.prefix1465223476ge_p_v (lambda ((A12 tptp.list_l1619404459ge_p_v) (A22 tptp.list_l1619404459ge_p_v)) (or (exists ((X3 tptp.list_message_p_v) (Xs3 tptp.list_l1619404459ge_p_v)) (and (= A12 tptp.nil_list_message_p_v) (= A22 (@ (@ tptp.cons_l233104475ge_p_v X3) Xs3)))) (exists ((Xa3 tptp.list_l1619404459ge_p_v) (Xb3 tptp.list_l1619404459ge_p_v) (X3 tptp.list_message_p_v)) (let ((_let_1 (@ tptp.cons_l233104475ge_p_v X3))) (and (= A12 (@ _let_1 Xa3)) (= A22 (@ _let_1 Xb3)) (@ (@ tptp.prefix1465223476ge_p_v Xa3) Xb3))))))) (= tptp.prefix47729710ge_p_v (lambda ((A12 tptp.list_message_p_v) (A22 tptp.list_message_p_v)) (or (exists ((X3 tptp.message_p_v) (Xs3 tptp.list_message_p_v)) (and (= A12 tptp.nil_message_p_v) (= A22 (@ (@ tptp.cons_message_p_v X3) Xs3)))) (exists ((Xa3 tptp.list_message_p_v) (Xb3 tptp.list_message_p_v) (X3 tptp.message_p_v)) (let ((_let_1 (@ tptp.cons_message_p_v X3))) (and (= A12 (@ _let_1 Xa3)) (= A22 (@ _let_1 Xb3)) (@ (@ tptp.prefix47729710ge_p_v Xa3) Xb3))))))) (= tptp.prefix1615116500t_unit (lambda ((A12 tptp.list_c1059388851t_unit) (A22 tptp.list_c1059388851t_unit)) (or (exists ((X3 tptp.config256849571t_unit) (Xs3 tptp.list_c1059388851t_unit)) (and (= A12 tptp.nil_co1338500125t_unit) (= A22 (@ (@ tptp.cons_c1162654829t_unit X3) Xs3)))) (exists ((Xa3 tptp.list_c1059388851t_unit) (Xb3 tptp.list_c1059388851t_unit) (X3 tptp.config256849571t_unit)) (let ((_let_1 (@ tptp.cons_c1162654829t_unit X3))) (and (= A12 (@ _let_1 Xa3)) (= A22 (@ _let_1 Xb3)) (@ (@ tptp.prefix1615116500t_unit Xa3) Xb3))))))) (forall ((X1 tptp.list_l611321411t_unit) (X22 tptp.list_l611321411t_unit) (P (-> tptp.list_l611321411t_unit tptp.list_l611321411t_unit Bool))) (=> (@ (@ tptp.prefix747844452t_unit X1) X22) (=> (forall ((X2 tptp.list_c1059388851t_unit) (Xs2 tptp.list_l611321411t_unit)) (@ (@ P tptp.nil_li307996205t_unit) (@ (@ tptp.cons_l1083444861t_unit X2) Xs2))) (=> (forall ((Xa2 tptp.list_l611321411t_unit) (Xb2 tptp.list_l611321411t_unit) (X2 tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.cons_l1083444861t_unit X2))) (=> (@ (@ tptp.prefix747844452t_unit Xa2) Xb2) (=> (@ (@ P Xa2) Xb2) (@ (@ P (@ _let_1 Xa2)) (@ _let_1 Xb2)))))) (@ (@ P X1) X22))))) (forall ((X1 tptp.list_l1619404459ge_p_v) (X22 tptp.list_l1619404459ge_p_v) (P (-> tptp.list_l1619404459ge_p_v tptp.list_l1619404459ge_p_v Bool))) (=> (@ (@ tptp.prefix1465223476ge_p_v X1) X22) (=> (forall ((X2 tptp.list_message_p_v) (Xs2 tptp.list_l1619404459ge_p_v)) (@ (@ P tptp.nil_list_message_p_v) (@ (@ tptp.cons_l233104475ge_p_v X2) Xs2))) (=> (forall ((Xa2 tptp.list_l1619404459ge_p_v) (Xb2 tptp.list_l1619404459ge_p_v) (X2 tptp.list_message_p_v)) (let ((_let_1 (@ tptp.cons_l233104475ge_p_v X2))) (=> (@ (@ tptp.prefix1465223476ge_p_v Xa2) Xb2) (=> (@ (@ P Xa2) Xb2) (@ (@ P (@ _let_1 Xa2)) (@ _let_1 Xb2)))))) (@ (@ P X1) X22))))) (forall ((X1 tptp.list_message_p_v) (X22 tptp.list_message_p_v) (P (-> tptp.list_message_p_v tptp.list_message_p_v Bool))) (=> (@ (@ tptp.prefix47729710ge_p_v X1) X22) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v)) (@ (@ P tptp.nil_message_p_v) (@ (@ tptp.cons_message_p_v X2) Xs2))) (=> (forall ((Xa2 tptp.list_message_p_v) (Xb2 tptp.list_message_p_v) (X2 tptp.message_p_v)) (let ((_let_1 (@ tptp.cons_message_p_v X2))) (=> (@ (@ tptp.prefix47729710ge_p_v Xa2) Xb2) (=> (@ (@ P Xa2) Xb2) (@ (@ P (@ _let_1 Xa2)) (@ _let_1 Xb2)))))) (@ (@ P X1) X22))))) (forall ((X1 tptp.list_c1059388851t_unit) (X22 tptp.list_c1059388851t_unit) (P (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool))) (=> (@ (@ tptp.prefix1615116500t_unit X1) X22) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit)) (@ (@ P tptp.nil_co1338500125t_unit) (@ (@ tptp.cons_c1162654829t_unit X2) Xs2))) (=> (forall ((Xa2 tptp.list_c1059388851t_unit) (Xb2 tptp.list_c1059388851t_unit) (X2 tptp.config256849571t_unit)) (let ((_let_1 (@ tptp.cons_c1162654829t_unit X2))) (=> (@ (@ tptp.prefix1615116500t_unit Xa2) Xb2) (=> (@ (@ P Xa2) Xb2) (@ (@ P (@ _let_1 Xa2)) (@ _let_1 Xb2)))))) (@ (@ P X1) X22))))) (forall ((N2 tptp.nat) (Pr (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ Pr tptp.zero_zero_nat) (=> (not (@ Pr N2)) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_nat N) N2) (@ Pr N) (not (@ Pr (@ tptp.suc N))))))))) (forall ((Cfg2 tptp.config256849571t_unit) (FStepCfg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v))) (= (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s Cfg2) FStepCfg2) FStepMsg2) tptp.zero_zero_nat) (@ (@ tptp.cons_c1162654829t_unit Cfg2) tptp.nil_co1338500125t_unit))) (forall ((Xs tptp.list_l611321411t_unit)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s503142615t_unit Xs)) (not (= Xs tptp.nil_li307996205t_unit)))) (forall ((Xs tptp.list_l1619404459ge_p_v)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s1809856791ge_p_v Xs)) (not (= Xs tptp.nil_list_message_p_v)))) (forall ((Xs tptp.list_message_p_v)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s1168481041ge_p_v Xs)) (not (= Xs tptp.nil_message_p_v)))) (forall ((Xs tptp.list_c1059388851t_unit)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s1406904903t_unit Xs)) (not (= Xs tptp.nil_co1338500125t_unit)))) (forall ((Xs tptp.list_l611321411t_unit)) (= (= (@ tptp.size_s503142615t_unit Xs) tptp.zero_zero_nat) (= Xs tptp.nil_li307996205t_unit))) (forall ((Xs tptp.list_l1619404459ge_p_v)) (= (= (@ tptp.size_s1809856791ge_p_v Xs) tptp.zero_zero_nat) (= Xs tptp.nil_list_message_p_v))) (forall ((Xs tptp.list_message_p_v)) (= (= (@ tptp.size_s1168481041ge_p_v Xs) tptp.zero_zero_nat) (= Xs tptp.nil_message_p_v))) (forall ((Xs tptp.list_c1059388851t_unit)) (= (= (@ tptp.size_s1406904903t_unit Xs) tptp.zero_zero_nat) (= Xs tptp.nil_co1338500125t_unit))) (forall ((N3 tptp.nat)) (= (@ (@ tptp.ord_less_nat N3) (@ tptp.suc tptp.zero_zero_nat)) (= N3 tptp.zero_zero_nat))) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N3))) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat N3) (@ tptp.suc N3))) (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N3) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N3)))) (forall ((M tptp.nat) (N3 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N3)) (@ (@ tptp.ord_less_nat M) N3))) (forall ((N3 tptp.nat)) (= (not (= N3 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))) (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_nat N3) tptp.zero_zero_nat))) (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))) (forall ((X21 tptp.message_p_v) (X222 tptp.list_message_p_v) (Y21 tptp.message_p_v) (Y22 tptp.list_message_p_v)) (= (= (@ (@ tptp.cons_message_p_v X21) X222) (@ (@ tptp.cons_message_p_v Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))) (forall ((X21 tptp.list_c1059388851t_unit) (X222 tptp.list_l611321411t_unit) (Y21 tptp.list_c1059388851t_unit) (Y22 tptp.list_l611321411t_unit)) (= (= (@ (@ tptp.cons_l1083444861t_unit X21) X222) (@ (@ tptp.cons_l1083444861t_unit Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))) (forall ((X21 tptp.list_message_p_v) (X222 tptp.list_l1619404459ge_p_v) (Y21 tptp.list_message_p_v) (Y22 tptp.list_l1619404459ge_p_v)) (= (= (@ (@ tptp.cons_l233104475ge_p_v X21) X222) (@ (@ tptp.cons_l233104475ge_p_v Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))) (forall ((X21 tptp.config256849571t_unit) (X222 tptp.list_c1059388851t_unit) (Y21 tptp.config256849571t_unit) (Y22 tptp.list_c1059388851t_unit)) (= (= (@ (@ tptp.cons_c1162654829t_unit X21) X222) (@ (@ tptp.cons_c1162654829t_unit Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))) (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))) (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y2)) (= X22 Y2))) (forall ((X tptp.message_p_v) (Xs tptp.list_message_p_v)) (not (= (@ (@ tptp.cons_message_p_v X) Xs) Xs))) (forall ((X tptp.list_c1059388851t_unit) (Xs tptp.list_l611321411t_unit)) (not (= (@ (@ tptp.cons_l1083444861t_unit X) Xs) Xs))) (forall ((X tptp.list_message_p_v) (Xs tptp.list_l1619404459ge_p_v)) (not (= (@ (@ tptp.cons_l233104475ge_p_v X) Xs) Xs))) (forall ((X tptp.config256849571t_unit) (Xs tptp.list_c1059388851t_unit)) (not (= (@ (@ tptp.cons_c1162654829t_unit X) Xs) Xs))) (forall ((N3 tptp.nat)) (not (= N3 (@ tptp.suc N3)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))) (forall ((P (-> tptp.nat Bool)) (N3 tptp.nat)) (=> (forall ((N tptp.nat)) (=> (not (@ P N)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N) (not (@ P M2)))))) (@ P N3))) (forall ((P (-> tptp.nat Bool)) (N3 tptp.nat)) (=> (forall ((N tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N) (@ P M2))) (@ P N))) (@ P N3))) (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_nat N3) N3))) (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))) (forall ((N3 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) M) (not (= M N3)))) (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))) (forall ((A8 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A8))) A8)) (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_nat N3) N3))) (forall ((M tptp.nat) (N3 tptp.nat)) (= (not (= M N3)) (or (@ (@ tptp.ord_less_nat M) N3) (@ (@ tptp.ord_less_nat N3) M)))) (forall ((X tptp.list_message_p_v) (Y tptp.list_message_p_v)) (=> (not (= (@ tptp.size_s1168481041ge_p_v X) (@ tptp.size_s1168481041ge_p_v Y))) (not (= X Y)))) (forall ((X tptp.list_c1059388851t_unit) (Y tptp.list_c1059388851t_unit)) (=> (not (= (@ tptp.size_s1406904903t_unit X) (@ tptp.size_s1406904903t_unit Y))) (not (= X Y)))) (forall ((Xs tptp.list_message_p_v) (Ys tptp.list_message_p_v)) (=> (not (= (@ tptp.size_s1168481041ge_p_v Xs) (@ tptp.size_s1168481041ge_p_v Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_c1059388851t_unit) (Ys tptp.list_c1059388851t_unit)) (=> (not (= (@ tptp.size_s1406904903t_unit Xs) (@ tptp.size_s1406904903t_unit Ys))) (not (= Xs Ys)))) (forall ((N3 tptp.nat)) (exists ((Xs2 tptp.list_message_p_v)) (= (@ tptp.size_s1168481041ge_p_v Xs2) N3))) (forall ((N3 tptp.nat)) (exists ((Xs2 tptp.list_c1059388851t_unit)) (= (@ tptp.size_s1406904903t_unit Xs2) N3))) (forall ((N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (exists ((M3 tptp.nat)) (= N3 (@ tptp.suc M3))))) (forall ((P (-> tptp.nat Bool)) (Nat tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((Nat3 tptp.nat)) (=> (@ P Nat3) (@ P (@ tptp.suc Nat3)))) (@ P Nat)))) (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))) (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))) (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N tptp.nat)) (=> (@ P (@ tptp.suc N)) (@ P N))) (@ P tptp.zero_zero_nat)))) (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N3 tptp.nat)) (=> (forall ((X2 tptp.nat)) (@ (@ P X2) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X2 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X2) Y3) (@ (@ P (@ tptp.suc X2)) (@ tptp.suc Y3)))) (@ (@ P M) N3))))) (forall ((P (-> tptp.nat Bool)) (N3 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N tptp.nat)) (=> (@ P N) (@ P (@ tptp.suc N)))) (@ P N3)))) (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))) (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))) (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))) (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))) (forall ((P (-> tptp.nat Bool)) (N3 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (@ P N)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N) (not (@ P M2))))))) (@ P N3)))) (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N3) (not (= N3 tptp.zero_zero_nat)))) (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_nat N3) tptp.zero_zero_nat))) (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_nat N3) tptp.zero_zero_nat))) (forall ((N3 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)) (= N3 tptp.zero_zero_nat))) (forall ((N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))) (forall ((N3 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N3))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N3 M))))) (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I2 tptp.nat)) (=> (= J (@ tptp.suc I2)) (@ P I2))) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ P (@ tptp.suc I2)) (@ P I2)))) (@ P I))))) (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I2 tptp.nat)) (@ (@ P I2) (@ tptp.suc I2))) (=> (forall ((I2 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I2))) (=> (@ (@ tptp.ord_less_nat I2) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (=> (@ _let_1 J2) (=> (@ (@ P J2) K2) (@ _let_1 K2))))))) (@ (@ P I) J))))) (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K)))) (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N3)) (@ (@ tptp.ord_less_nat M) N3))) (forall ((N3 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N3))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N3))))) (forall ((N3 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N3)) M) (exists ((M4 tptp.nat)) (and (= M (@ tptp.suc M4)) (@ (@ tptp.ord_less_nat N3) M4))))) (forall ((N3 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N3)) (@ P I3))) (and (@ P N3) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N3) (@ P I3)))))) (forall ((M tptp.nat) (N3 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N3)) (@ (@ tptp.ord_less_nat N3) (@ tptp.suc M)))) (forall ((M tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N3)) (or (@ _let_1 N3) (= M N3))))) (forall ((N3 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N3)) (@ P I3))) (or (@ P N3) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N3) (@ P I3)))))) (forall ((M tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N3) (@ _let_1 (@ tptp.suc N3))))) (forall ((M tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N3)) (=> (not (@ _let_1 N3)) (= M N3))))) (forall ((M tptp.nat) (N3 tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N3) (=> (not (= _let_1 N3)) (@ (@ tptp.ord_less_nat _let_1) N3))))) (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2)))))))) (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N3) (@ (@ tptp.ord_less_nat M) N3))) (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K) (=> (not (= K (@ tptp.suc I))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2))))))))) (forall ((P (-> (-> tptp.message_p_v tptp.config256849571t_unit) tptp.list_message_p_v tptp.list_c1059388851t_unit Bool)) (A0 (-> tptp.message_p_v tptp.config256849571t_unit)) (A1 tptp.list_message_p_v) (A2 tptp.list_c1059388851t_unit)) (=> (forall ((F (-> tptp.message_p_v tptp.config256849571t_unit)) (X_1 tptp.list_c1059388851t_unit)) (@ (@ (@ P F) tptp.nil_message_p_v) X_1)) (=> (forall ((F (-> tptp.message_p_v tptp.config256849571t_unit)) (A9 tptp.message_p_v) (As tptp.list_message_p_v) (Bs tptp.list_c1059388851t_unit)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_c1162654829t_unit (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_message_p_v A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))) (forall ((P (-> (-> tptp.config256849571t_unit tptp.config256849571t_unit) tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (A0 (-> tptp.config256849571t_unit tptp.config256849571t_unit)) (A1 tptp.list_c1059388851t_unit) (A2 tptp.list_c1059388851t_unit)) (=> (forall ((F (-> tptp.config256849571t_unit tptp.config256849571t_unit)) (X_1 tptp.list_c1059388851t_unit)) (@ (@ (@ P F) tptp.nil_co1338500125t_unit) X_1)) (=> (forall ((F (-> tptp.config256849571t_unit tptp.config256849571t_unit)) (A9 tptp.config256849571t_unit) (As tptp.list_c1059388851t_unit) (Bs tptp.list_c1059388851t_unit)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_c1162654829t_unit (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_c1162654829t_unit A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))) (forall ((P (-> (-> tptp.message_p_v tptp.message_p_v) tptp.list_message_p_v tptp.list_message_p_v Bool)) (A0 (-> tptp.message_p_v tptp.message_p_v)) (A1 tptp.list_message_p_v) (A2 tptp.list_message_p_v)) (=> (forall ((F (-> tptp.message_p_v tptp.message_p_v)) (X_1 tptp.list_message_p_v)) (@ (@ (@ P F) tptp.nil_message_p_v) X_1)) (=> (forall ((F (-> tptp.message_p_v tptp.message_p_v)) (A9 tptp.message_p_v) (As tptp.list_message_p_v) (Bs tptp.list_message_p_v)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_message_p_v (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_message_p_v A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))) (forall ((P (-> (-> tptp.list_message_p_v tptp.message_p_v) tptp.list_l1619404459ge_p_v tptp.list_message_p_v Bool)) (A0 (-> tptp.list_message_p_v tptp.message_p_v)) (A1 tptp.list_l1619404459ge_p_v) (A2 tptp.list_message_p_v)) (=> (forall ((F (-> tptp.list_message_p_v tptp.message_p_v)) (X_1 tptp.list_message_p_v)) (@ (@ (@ P F) tptp.nil_list_message_p_v) X_1)) (=> (forall ((F (-> tptp.list_message_p_v tptp.message_p_v)) (A9 tptp.list_message_p_v) (As tptp.list_l1619404459ge_p_v) (Bs tptp.list_message_p_v)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_message_p_v (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_l233104475ge_p_v A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))) (forall ((P (-> (-> tptp.message_p_v tptp.list_message_p_v) tptp.list_message_p_v tptp.list_l1619404459ge_p_v Bool)) (A0 (-> tptp.message_p_v tptp.list_message_p_v)) (A1 tptp.list_message_p_v) (A2 tptp.list_l1619404459ge_p_v)) (=> (forall ((F (-> tptp.message_p_v tptp.list_message_p_v)) (X_1 tptp.list_l1619404459ge_p_v)) (@ (@ (@ P F) tptp.nil_message_p_v) X_1)) (=> (forall ((F (-> tptp.message_p_v tptp.list_message_p_v)) (A9 tptp.message_p_v) (As tptp.list_message_p_v) (Bs tptp.list_l1619404459ge_p_v)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_l233104475ge_p_v (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_message_p_v A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))) (forall ((P (-> (-> tptp.config256849571t_unit tptp.message_p_v) tptp.list_c1059388851t_unit tptp.list_message_p_v Bool)) (A0 (-> tptp.config256849571t_unit tptp.message_p_v)) (A1 tptp.list_c1059388851t_unit) (A2 tptp.list_message_p_v)) (=> (forall ((F (-> tptp.config256849571t_unit tptp.message_p_v)) (X_1 tptp.list_message_p_v)) (@ (@ (@ P F) tptp.nil_co1338500125t_unit) X_1)) (=> (forall ((F (-> tptp.config256849571t_unit tptp.message_p_v)) (A9 tptp.config256849571t_unit) (As tptp.list_c1059388851t_unit) (Bs tptp.list_message_p_v)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_message_p_v (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_c1162654829t_unit A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))) (forall ((P (-> (-> tptp.list_message_p_v tptp.list_message_p_v) tptp.list_l1619404459ge_p_v tptp.list_l1619404459ge_p_v Bool)) (A0 (-> tptp.list_message_p_v tptp.list_message_p_v)) (A1 tptp.list_l1619404459ge_p_v) (A2 tptp.list_l1619404459ge_p_v)) (=> (forall ((F (-> tptp.list_message_p_v tptp.list_message_p_v)) (X_1 tptp.list_l1619404459ge_p_v)) (@ (@ (@ P F) tptp.nil_list_message_p_v) X_1)) (=> (forall ((F (-> tptp.list_message_p_v tptp.list_message_p_v)) (A9 tptp.list_message_p_v) (As tptp.list_l1619404459ge_p_v) (Bs tptp.list_l1619404459ge_p_v)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_l233104475ge_p_v (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_l233104475ge_p_v A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))) (forall ((P (-> (-> tptp.list_message_p_v tptp.config256849571t_unit) tptp.list_l1619404459ge_p_v tptp.list_c1059388851t_unit Bool)) (A0 (-> tptp.list_message_p_v tptp.config256849571t_unit)) (A1 tptp.list_l1619404459ge_p_v) (A2 tptp.list_c1059388851t_unit)) (=> (forall ((F (-> tptp.list_message_p_v tptp.config256849571t_unit)) (X_1 tptp.list_c1059388851t_unit)) (@ (@ (@ P F) tptp.nil_list_message_p_v) X_1)) (=> (forall ((F (-> tptp.list_message_p_v tptp.config256849571t_unit)) (A9 tptp.list_message_p_v) (As tptp.list_l1619404459ge_p_v) (Bs tptp.list_c1059388851t_unit)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_c1162654829t_unit (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_l233104475ge_p_v A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))) (forall ((P (-> (-> tptp.list_c1059388851t_unit tptp.message_p_v) tptp.list_l611321411t_unit tptp.list_message_p_v Bool)) (A0 (-> tptp.list_c1059388851t_unit tptp.message_p_v)) (A1 tptp.list_l611321411t_unit) (A2 tptp.list_message_p_v)) (=> (forall ((F (-> tptp.list_c1059388851t_unit tptp.message_p_v)) (X_1 tptp.list_message_p_v)) (@ (@ (@ P F) tptp.nil_li307996205t_unit) X_1)) (=> (forall ((F (-> tptp.list_c1059388851t_unit tptp.message_p_v)) (A9 tptp.list_c1059388851t_unit) (As tptp.list_l611321411t_unit) (Bs tptp.list_message_p_v)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_message_p_v (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_l1083444861t_unit A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))) (forall ((P (-> (-> tptp.message_p_v tptp.list_c1059388851t_unit) tptp.list_message_p_v tptp.list_l611321411t_unit Bool)) (A0 (-> tptp.message_p_v tptp.list_c1059388851t_unit)) (A1 tptp.list_message_p_v) (A2 tptp.list_l611321411t_unit)) (=> (forall ((F (-> tptp.message_p_v tptp.list_c1059388851t_unit)) (X_1 tptp.list_l611321411t_unit)) (@ (@ (@ P F) tptp.nil_message_p_v) X_1)) (=> (forall ((F (-> tptp.message_p_v tptp.list_c1059388851t_unit)) (A9 tptp.message_p_v) (As tptp.list_message_p_v) (Bs tptp.list_l611321411t_unit)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_l1083444861t_unit (@ F A9)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_message_p_v A9) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))) (forall ((Xs tptp.list_l611321411t_unit) (P (-> tptp.list_l611321411t_unit Bool))) (=> (not (= Xs tptp.nil_li307996205t_unit)) (=> (forall ((X2 tptp.list_c1059388851t_unit)) (@ P (@ (@ tptp.cons_l1083444861t_unit X2) tptp.nil_li307996205t_unit))) (=> (forall ((X2 tptp.list_c1059388851t_unit) (Xs2 tptp.list_l611321411t_unit)) (=> (not (= Xs2 tptp.nil_li307996205t_unit)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_l1083444861t_unit X2) Xs2))))) (@ P Xs))))) (forall ((Xs tptp.list_l1619404459ge_p_v) (P (-> tptp.list_l1619404459ge_p_v Bool))) (=> (not (= Xs tptp.nil_list_message_p_v)) (=> (forall ((X2 tptp.list_message_p_v)) (@ P (@ (@ tptp.cons_l233104475ge_p_v X2) tptp.nil_list_message_p_v))) (=> (forall ((X2 tptp.list_message_p_v) (Xs2 tptp.list_l1619404459ge_p_v)) (=> (not (= Xs2 tptp.nil_list_message_p_v)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_l233104475ge_p_v X2) Xs2))))) (@ P Xs))))) (forall ((Xs tptp.list_message_p_v) (P (-> tptp.list_message_p_v Bool))) (=> (not (= Xs tptp.nil_message_p_v)) (=> (forall ((X2 tptp.message_p_v)) (@ P (@ (@ tptp.cons_message_p_v X2) tptp.nil_message_p_v))) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v)) (=> (not (= Xs2 tptp.nil_message_p_v)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_message_p_v X2) Xs2))))) (@ P Xs))))) (forall ((Xs tptp.list_c1059388851t_unit) (P (-> tptp.list_c1059388851t_unit Bool))) (=> (not (= Xs tptp.nil_co1338500125t_unit)) (=> (forall ((X2 tptp.config256849571t_unit)) (@ P (@ (@ tptp.cons_c1162654829t_unit X2) tptp.nil_co1338500125t_unit))) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit)) (=> (not (= Xs2 tptp.nil_co1338500125t_unit)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2))))) (@ P Xs))))) (forall ((P (-> (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool) tptp.list_l611321411t_unit Bool)) (A0 (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (A1 tptp.list_l611321411t_unit)) (=> (forall ((P2 (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool))) (@ (@ P P2) tptp.nil_li307996205t_unit)) (=> (forall ((P2 (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (X2 tptp.list_c1059388851t_unit)) (@ (@ P P2) (@ (@ tptp.cons_l1083444861t_unit X2) tptp.nil_li307996205t_unit))) (=> (forall ((P2 (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (X2 tptp.list_c1059388851t_unit) (Y3 tptp.list_c1059388851t_unit) (Xs2 tptp.list_l611321411t_unit)) (let ((_let_1 (@ (@ tptp.cons_l1083444861t_unit Y3) Xs2))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_l1083444861t_unit X2) _let_1)))))) (@ (@ P A0) A1))))) (forall ((P (-> (-> tptp.list_message_p_v tptp.list_message_p_v Bool) tptp.list_l1619404459ge_p_v Bool)) (A0 (-> tptp.list_message_p_v tptp.list_message_p_v Bool)) (A1 tptp.list_l1619404459ge_p_v)) (=> (forall ((P2 (-> tptp.list_message_p_v tptp.list_message_p_v Bool))) (@ (@ P P2) tptp.nil_list_message_p_v)) (=> (forall ((P2 (-> tptp.list_message_p_v tptp.list_message_p_v Bool)) (X2 tptp.list_message_p_v)) (@ (@ P P2) (@ (@ tptp.cons_l233104475ge_p_v X2) tptp.nil_list_message_p_v))) (=> (forall ((P2 (-> tptp.list_message_p_v tptp.list_message_p_v Bool)) (X2 tptp.list_message_p_v) (Y3 tptp.list_message_p_v) (Xs2 tptp.list_l1619404459ge_p_v)) (let ((_let_1 (@ (@ tptp.cons_l233104475ge_p_v Y3) Xs2))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_l233104475ge_p_v X2) _let_1)))))) (@ (@ P A0) A1))))) (forall ((P (-> (-> tptp.message_p_v tptp.message_p_v Bool) tptp.list_message_p_v Bool)) (A0 (-> tptp.message_p_v tptp.message_p_v Bool)) (A1 tptp.list_message_p_v)) (=> (forall ((P2 (-> tptp.message_p_v tptp.message_p_v Bool))) (@ (@ P P2) tptp.nil_message_p_v)) (=> (forall ((P2 (-> tptp.message_p_v tptp.message_p_v Bool)) (X2 tptp.message_p_v)) (@ (@ P P2) (@ (@ tptp.cons_message_p_v X2) tptp.nil_message_p_v))) (=> (forall ((P2 (-> tptp.message_p_v tptp.message_p_v Bool)) (X2 tptp.message_p_v) (Y3 tptp.message_p_v) (Xs2 tptp.list_message_p_v)) (let ((_let_1 (@ (@ tptp.cons_message_p_v Y3) Xs2))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_message_p_v X2) _let_1)))))) (@ (@ P A0) A1))))) (forall ((P (-> (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool) tptp.list_c1059388851t_unit Bool)) (A0 (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool)) (A1 tptp.list_c1059388851t_unit)) (=> (forall ((P2 (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool))) (@ (@ P P2) tptp.nil_co1338500125t_unit)) (=> (forall ((P2 (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool)) (X2 tptp.config256849571t_unit)) (@ (@ P P2) (@ (@ tptp.cons_c1162654829t_unit X2) tptp.nil_co1338500125t_unit))) (=> (forall ((P2 (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool)) (X2 tptp.config256849571t_unit) (Y3 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit)) (let ((_let_1 (@ (@ tptp.cons_c1162654829t_unit Y3) Xs2))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_c1162654829t_unit X2) _let_1)))))) (@ (@ P A0) A1))))) (forall ((P (-> tptp.list_l611321411t_unit Bool)) (A0 tptp.list_l611321411t_unit)) (=> (@ P tptp.nil_li307996205t_unit) (=> (forall ((X2 tptp.list_c1059388851t_unit)) (@ P (@ (@ tptp.cons_l1083444861t_unit X2) tptp.nil_li307996205t_unit))) (=> (forall ((X2 tptp.list_c1059388851t_unit) (Y3 tptp.list_c1059388851t_unit) (Xs2 tptp.list_l611321411t_unit)) (let ((_let_1 (@ (@ tptp.cons_l1083444861t_unit Y3) Xs2))) (let ((_let_2 (@ tptp.cons_l1083444861t_unit X2))) (let ((_let_3 (= X2 Y3))) (=> (=> _let_3 (@ P (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))) (forall ((P (-> tptp.list_l1619404459ge_p_v Bool)) (A0 tptp.list_l1619404459ge_p_v)) (=> (@ P tptp.nil_list_message_p_v) (=> (forall ((X2 tptp.list_message_p_v)) (@ P (@ (@ tptp.cons_l233104475ge_p_v X2) tptp.nil_list_message_p_v))) (=> (forall ((X2 tptp.list_message_p_v) (Y3 tptp.list_message_p_v) (Xs2 tptp.list_l1619404459ge_p_v)) (let ((_let_1 (@ (@ tptp.cons_l233104475ge_p_v Y3) Xs2))) (let ((_let_2 (@ tptp.cons_l233104475ge_p_v X2))) (let ((_let_3 (= X2 Y3))) (=> (=> _let_3 (@ P (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))) (forall ((P (-> tptp.list_message_p_v Bool)) (A0 tptp.list_message_p_v)) (=> (@ P tptp.nil_message_p_v) (=> (forall ((X2 tptp.message_p_v)) (@ P (@ (@ tptp.cons_message_p_v X2) tptp.nil_message_p_v))) (=> (forall ((X2 tptp.message_p_v) (Y3 tptp.message_p_v) (Xs2 tptp.list_message_p_v)) (let ((_let_1 (@ (@ tptp.cons_message_p_v Y3) Xs2))) (let ((_let_2 (@ tptp.cons_message_p_v X2))) (let ((_let_3 (= X2 Y3))) (=> (=> _let_3 (@ P (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))) (forall ((P (-> tptp.list_c1059388851t_unit Bool)) (A0 tptp.list_c1059388851t_unit)) (=> (@ P tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.config256849571t_unit)) (@ P (@ (@ tptp.cons_c1162654829t_unit X2) tptp.nil_co1338500125t_unit))) (=> (forall ((X2 tptp.config256849571t_unit) (Y3 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit)) (let ((_let_1 (@ (@ tptp.cons_c1162654829t_unit Y3) Xs2))) (let ((_let_2 (@ tptp.cons_c1162654829t_unit X2))) (let ((_let_3 (= X2 Y3))) (=> (=> _let_3 (@ P (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))) (forall ((P (-> (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool) tptp.list_l611321411t_unit Bool)) (A0 (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (A1 tptp.list_l611321411t_unit)) (=> (forall ((P2 (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool))) (@ (@ P P2) tptp.nil_li307996205t_unit)) (=> (forall ((P2 (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (X2 tptp.list_c1059388851t_unit) (Ys2 tptp.list_l611321411t_unit)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_l1083444861t_unit X2) Ys2))))) (@ (@ P A0) A1)))) (forall ((P (-> (-> tptp.list_message_p_v tptp.list_message_p_v Bool) tptp.list_l1619404459ge_p_v Bool)) (A0 (-> tptp.list_message_p_v tptp.list_message_p_v Bool)) (A1 tptp.list_l1619404459ge_p_v)) (=> (forall ((P2 (-> tptp.list_message_p_v tptp.list_message_p_v Bool))) (@ (@ P P2) tptp.nil_list_message_p_v)) (=> (forall ((P2 (-> tptp.list_message_p_v tptp.list_message_p_v Bool)) (X2 tptp.list_message_p_v) (Ys2 tptp.list_l1619404459ge_p_v)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_l233104475ge_p_v X2) Ys2))))) (@ (@ P A0) A1)))) (forall ((P (-> (-> tptp.message_p_v tptp.message_p_v Bool) tptp.list_message_p_v Bool)) (A0 (-> tptp.message_p_v tptp.message_p_v Bool)) (A1 tptp.list_message_p_v)) (=> (forall ((P2 (-> tptp.message_p_v tptp.message_p_v Bool))) (@ (@ P P2) tptp.nil_message_p_v)) (=> (forall ((P2 (-> tptp.message_p_v tptp.message_p_v Bool)) (X2 tptp.message_p_v) (Ys2 tptp.list_message_p_v)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_message_p_v X2) Ys2))))) (@ (@ P A0) A1)))) (forall ((P (-> (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool) tptp.list_c1059388851t_unit Bool)) (A0 (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool)) (A1 tptp.list_c1059388851t_unit)) (=> (forall ((P2 (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool))) (@ (@ P P2) tptp.nil_co1338500125t_unit)) (=> (forall ((P2 (-> tptp.config256849571t_unit tptp.config256849571t_unit Bool)) (X2 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys2) (@ _let_1 (@ (@ tptp.cons_c1162654829t_unit X2) Ys2))))) (@ (@ P A0) A1)))) (forall ((X tptp.list_l611321411t_unit)) (=> (not (= X tptp.nil_li307996205t_unit)) (=> (forall ((X2 tptp.list_c1059388851t_unit)) (not (= X (@ (@ tptp.cons_l1083444861t_unit X2) tptp.nil_li307996205t_unit)))) (not (forall ((X2 tptp.list_c1059388851t_unit) (Y3 tptp.list_c1059388851t_unit) (Xs2 tptp.list_l611321411t_unit)) (not (= X (@ (@ tptp.cons_l1083444861t_unit X2) (@ (@ tptp.cons_l1083444861t_unit Y3) Xs2))))))))) (forall ((X tptp.list_l1619404459ge_p_v)) (=> (not (= X tptp.nil_list_message_p_v)) (=> (forall ((X2 tptp.list_message_p_v)) (not (= X (@ (@ tptp.cons_l233104475ge_p_v X2) tptp.nil_list_message_p_v)))) (not (forall ((X2 tptp.list_message_p_v) (Y3 tptp.list_message_p_v) (Xs2 tptp.list_l1619404459ge_p_v)) (not (= X (@ (@ tptp.cons_l233104475ge_p_v X2) (@ (@ tptp.cons_l233104475ge_p_v Y3) Xs2))))))))) (forall ((X tptp.list_message_p_v)) (=> (not (= X tptp.nil_message_p_v)) (=> (forall ((X2 tptp.message_p_v)) (not (= X (@ (@ tptp.cons_message_p_v X2) tptp.nil_message_p_v)))) (not (forall ((X2 tptp.message_p_v) (Y3 tptp.message_p_v) (Xs2 tptp.list_message_p_v)) (not (= X (@ (@ tptp.cons_message_p_v X2) (@ (@ tptp.cons_message_p_v Y3) Xs2))))))))) (forall ((X tptp.list_c1059388851t_unit)) (=> (not (= X tptp.nil_co1338500125t_unit)) (=> (forall ((X2 tptp.config256849571t_unit)) (not (= X (@ (@ tptp.cons_c1162654829t_unit X2) tptp.nil_co1338500125t_unit)))) (not (forall ((X2 tptp.config256849571t_unit) (Y3 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit)) (not (= X (@ (@ tptp.cons_c1162654829t_unit X2) (@ (@ tptp.cons_c1162654829t_unit Y3) Xs2))))))))) (forall ((X tptp.list_l1584713811t_unit)) (=> (not (= X tptp.nil_li2108369341t_unit)) (=> (forall ((Xss tptp.list_l1584713811t_unit)) (not (= X (@ (@ tptp.cons_l1777019405t_unit tptp.nil_li307996205t_unit) Xss)))) (not (forall ((X2 tptp.list_c1059388851t_unit) (Xs2 tptp.list_l611321411t_unit) (Xss tptp.list_l1584713811t_unit)) (not (= X (@ (@ tptp.cons_l1777019405t_unit (@ (@ tptp.cons_l1083444861t_unit X2) Xs2)) Xss)))))))) (forall ((X tptp.list_l1341496881ge_p_v)) (=> (not (= X tptp.nil_li835338673ge_p_v)) (=> (forall ((Xss tptp.list_l1341496881ge_p_v)) (not (= X (@ (@ tptp.cons_l1383421281ge_p_v tptp.nil_list_message_p_v) Xss)))) (not (forall ((X2 tptp.list_message_p_v) (Xs2 tptp.list_l1619404459ge_p_v) (Xss tptp.list_l1341496881ge_p_v)) (not (= X (@ (@ tptp.cons_l1383421281ge_p_v (@ (@ tptp.cons_l233104475ge_p_v X2) Xs2)) Xss)))))))) (forall ((X tptp.list_l1619404459ge_p_v)) (=> (not (= X tptp.nil_list_message_p_v)) (=> (forall ((Xss tptp.list_l1619404459ge_p_v)) (not (= X (@ (@ tptp.cons_l233104475ge_p_v tptp.nil_message_p_v) Xss)))) (not (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Xss tptp.list_l1619404459ge_p_v)) (not (= X (@ (@ tptp.cons_l233104475ge_p_v (@ (@ tptp.cons_message_p_v X2) Xs2)) Xss)))))))) (forall ((X tptp.list_l611321411t_unit)) (=> (not (= X tptp.nil_li307996205t_unit)) (=> (forall ((Xss tptp.list_l611321411t_unit)) (not (= X (@ (@ tptp.cons_l1083444861t_unit tptp.nil_co1338500125t_unit) Xss)))) (not (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Xss tptp.list_l611321411t_unit)) (not (= X (@ (@ tptp.cons_l1083444861t_unit (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) Xss)))))))) (forall ((P (-> tptp.list_l1619404459ge_p_v tptp.list_l1619404459ge_p_v Bool)) (A0 tptp.list_l1619404459ge_p_v) (A1 tptp.list_l1619404459ge_p_v)) (=> (forall ((X_1 tptp.list_l1619404459ge_p_v)) (@ (@ P tptp.nil_list_message_p_v) X_1)) (=> (forall ((Xs2 tptp.list_l1619404459ge_p_v)) (@ (@ P Xs2) tptp.nil_list_message_p_v)) (=> (forall ((X2 tptp.list_message_p_v) (Xs2 tptp.list_l1619404459ge_p_v) (Y3 tptp.list_message_p_v) (Ys2 tptp.list_l1619404459ge_p_v)) (let ((_let_1 (@ (@ tptp.cons_l233104475ge_p_v Y3) Ys2))) (let ((_let_2 (@ P (@ (@ tptp.cons_l233104475ge_p_v X2) Xs2)))) (=> (@ (@ P Xs2) _let_1) (=> (@ _let_2 Ys2) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))) (forall ((P (-> tptp.list_message_p_v tptp.list_message_p_v Bool)) (A0 tptp.list_message_p_v) (A1 tptp.list_message_p_v)) (=> (forall ((X_1 tptp.list_message_p_v)) (@ (@ P tptp.nil_message_p_v) X_1)) (=> (forall ((Xs2 tptp.list_message_p_v)) (@ (@ P Xs2) tptp.nil_message_p_v)) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v)) (let ((_let_1 (@ (@ tptp.cons_message_p_v Y3) Ys2))) (let ((_let_2 (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)))) (=> (@ (@ P Xs2) _let_1) (=> (@ _let_2 Ys2) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))) (forall ((P (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (A0 tptp.list_c1059388851t_unit) (A1 tptp.list_c1059388851t_unit)) (=> (forall ((X_1 tptp.list_c1059388851t_unit)) (@ (@ P tptp.nil_co1338500125t_unit) X_1)) (=> (forall ((Xs2 tptp.list_c1059388851t_unit)) (@ (@ P Xs2) tptp.nil_co1338500125t_unit)) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit)) (let ((_let_1 (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2))) (let ((_let_2 (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)))) (=> (@ (@ P Xs2) _let_1) (=> (@ _let_2 Ys2) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))) (forall ((P (-> tptp.list_message_p_v Bool)) (Xs tptp.list_message_p_v)) (=> (@ P tptp.nil_message_p_v) (=> (forall ((X2 tptp.message_p_v)) (@ P (@ (@ tptp.cons_message_p_v X2) tptp.nil_message_p_v))) (=> (forall ((X2 tptp.message_p_v) (Y3 tptp.message_p_v) (Zs tptp.list_message_p_v)) (let ((_let_1 (@ (@ tptp.cons_message_p_v Y3) Zs))) (=> (@ P Zs) (=> (@ P _let_1) (@ P (@ (@ tptp.cons_message_p_v X2) _let_1)))))) (@ P Xs))))) (forall ((P (-> tptp.list_c1059388851t_unit Bool)) (Xs tptp.list_c1059388851t_unit)) (=> (@ P tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.config256849571t_unit)) (@ P (@ (@ tptp.cons_c1162654829t_unit X2) tptp.nil_co1338500125t_unit))) (=> (forall ((X2 tptp.config256849571t_unit) (Y3 tptp.config256849571t_unit) (Zs tptp.list_c1059388851t_unit)) (let ((_let_1 (@ (@ tptp.cons_c1162654829t_unit Y3) Zs))) (=> (@ P Zs) (=> (@ P _let_1) (@ P (@ (@ tptp.cons_c1162654829t_unit X2) _let_1)))))) (@ P Xs))))) (forall ((P (-> tptp.list_message_p_v tptp.list_message_p_v Bool)) (A0 tptp.list_message_p_v) (A1 tptp.list_message_p_v)) (=> (forall ((X_1 tptp.list_message_p_v)) (@ (@ P tptp.nil_message_p_v) X_1)) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Ys2 tptp.list_message_p_v)) (=> (@ (@ P Ys2) Xs2) (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) Ys2))) (@ (@ P A0) A1)))) (forall ((P (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (A0 tptp.list_c1059388851t_unit) (A1 tptp.list_c1059388851t_unit)) (=> (forall ((X_1 tptp.list_c1059388851t_unit)) (@ (@ P tptp.nil_co1338500125t_unit) X_1)) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Ys2 tptp.list_c1059388851t_unit)) (=> (@ (@ P Ys2) Xs2) (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) Ys2))) (@ (@ P A0) A1)))) (forall ((P (-> tptp.list_message_p_v tptp.list_message_p_v Bool)) (Xs tptp.list_message_p_v) (Ys tptp.list_message_p_v)) (=> (@ (@ P tptp.nil_message_p_v) tptp.nil_message_p_v) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v)) (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) tptp.nil_message_p_v)) (=> (forall ((Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v)) (@ (@ P tptp.nil_message_p_v) (@ (@ tptp.cons_message_p_v Y3) Ys2))) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) (@ (@ tptp.cons_message_p_v Y3) Ys2)))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_message_p_v tptp.list_c1059388851t_unit Bool)) (Xs tptp.list_message_p_v) (Ys tptp.list_c1059388851t_unit)) (=> (@ (@ P tptp.nil_message_p_v) tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v)) (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) tptp.nil_co1338500125t_unit)) (=> (forall ((Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit)) (@ (@ P tptp.nil_message_p_v) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2))) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2)))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_c1059388851t_unit tptp.list_message_p_v Bool)) (Xs tptp.list_c1059388851t_unit) (Ys tptp.list_message_p_v)) (=> (@ (@ P tptp.nil_co1338500125t_unit) tptp.nil_message_p_v) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit)) (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) tptp.nil_message_p_v)) (=> (forall ((Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v)) (@ (@ P tptp.nil_co1338500125t_unit) (@ (@ tptp.cons_message_p_v Y3) Ys2))) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) (@ (@ tptp.cons_message_p_v Y3) Ys2)))) (@ (@ P Xs) Ys)))))) (forall ((P (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)) (Xs tptp.list_c1059388851t_unit) (Ys tptp.list_c1059388851t_unit)) (=> (@ (@ P tptp.nil_co1338500125t_unit) tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit)) (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) tptp.nil_co1338500125t_unit)) (=> (forall ((Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit)) (@ (@ P tptp.nil_co1338500125t_unit) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2))) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2)))) (@ (@ P Xs) Ys)))))) (forall ((Xs tptp.list_message_p_v)) (= (not (= Xs tptp.nil_message_p_v)) (exists ((Y4 tptp.message_p_v) (Ys3 tptp.list_message_p_v)) (= Xs (@ (@ tptp.cons_message_p_v Y4) Ys3))))) (forall ((Xs tptp.list_c1059388851t_unit)) (= (not (= Xs tptp.nil_co1338500125t_unit)) (exists ((Y4 tptp.config256849571t_unit) (Ys3 tptp.list_c1059388851t_unit)) (= Xs (@ (@ tptp.cons_c1162654829t_unit Y4) Ys3))))) (forall ((P (-> tptp.list_message_p_v Bool)) (List tptp.list_message_p_v)) (=> (@ P tptp.nil_message_p_v) (=> (forall ((X12 tptp.message_p_v) (X23 tptp.list_message_p_v)) (=> (@ P X23) (@ P (@ (@ tptp.cons_message_p_v X12) X23)))) (@ P List)))) (forall ((P (-> tptp.list_c1059388851t_unit Bool)) (List tptp.list_c1059388851t_unit)) (=> (@ P tptp.nil_co1338500125t_unit) (=> (forall ((X12 tptp.config256849571t_unit) (X23 tptp.list_c1059388851t_unit)) (=> (@ P X23) (@ P (@ (@ tptp.cons_c1162654829t_unit X12) X23)))) (@ P List)))) (forall ((Y tptp.list_message_p_v)) (=> (not (= Y tptp.nil_message_p_v)) (not (forall ((X212 tptp.message_p_v) (X223 tptp.list_message_p_v)) (not (= Y (@ (@ tptp.cons_message_p_v X212) X223))))))) (forall ((Y tptp.list_c1059388851t_unit)) (=> (not (= Y tptp.nil_co1338500125t_unit)) (not (forall ((X212 tptp.config256849571t_unit) (X223 tptp.list_c1059388851t_unit)) (not (= Y (@ (@ tptp.cons_c1162654829t_unit X212) X223))))))) (forall ((List tptp.list_message_p_v) (X21 tptp.message_p_v) (X222 tptp.list_message_p_v)) (=> (= List (@ (@ tptp.cons_message_p_v X21) X222)) (not (= List tptp.nil_message_p_v)))) (forall ((List tptp.list_c1059388851t_unit) (X21 tptp.config256849571t_unit) (X222 tptp.list_c1059388851t_unit)) (=> (= List (@ (@ tptp.cons_c1162654829t_unit X21) X222)) (not (= List tptp.nil_co1338500125t_unit)))) (forall ((X21 tptp.message_p_v) (X222 tptp.list_message_p_v)) (not (= tptp.nil_message_p_v (@ (@ tptp.cons_message_p_v X21) X222)))) (forall ((X21 tptp.config256849571t_unit) (X222 tptp.list_c1059388851t_unit)) (not (= tptp.nil_co1338500125t_unit (@ (@ tptp.cons_c1162654829t_unit X21) X222)))) (forall ((P (-> tptp.list_c1059388851t_unit Bool)) (Xs tptp.list_c1059388851t_unit)) (=> (forall ((Xs2 tptp.list_c1059388851t_unit)) (=> (forall ((Ys4 tptp.list_c1059388851t_unit)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s1406904903t_unit Ys4)) (@ tptp.size_s1406904903t_unit Xs2)) (@ P Ys4))) (@ P Xs2))) (@ P Xs))) (forall ((F2 (-> tptp.nat tptp.nat)) (N3 tptp.nat) (M tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ F2 N)) (@ F2 (@ tptp.suc N)))) (= (@ (@ tptp.ord_less_nat (@ F2 N3)) (@ F2 M)) (@ (@ tptp.ord_less_nat N3) M)))) (forall ((F2 (-> tptp.nat tptp.int)) (N3 tptp.nat) (M tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ F2 N)) (@ F2 (@ tptp.suc N)))) (= (@ (@ tptp.ord_less_int (@ F2 N3)) (@ F2 M)) (@ (@ tptp.ord_less_nat N3) M)))) (forall ((F2 (-> tptp.nat tptp.nat)) (N3 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ F2 N)) (@ F2 (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_nat N3) N4) (@ (@ tptp.ord_less_nat (@ F2 N3)) (@ F2 N4))))) (forall ((F2 (-> tptp.nat tptp.int)) (N3 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ F2 N)) (@ F2 (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_nat N3) N4) (@ (@ tptp.ord_less_int (@ F2 N3)) (@ F2 N4))))) (forall ((M tptp.nat) (N3 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N3)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N3)))))) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (exists ((M3 tptp.nat)) (= N3 (@ tptp.suc M3))))) (forall ((N3 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N3)) (@ P I3))) (and (@ P tptp.zero_zero_nat) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N3) (@ P (@ tptp.suc I3))))))) (forall ((N3 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (exists ((M5 tptp.nat)) (= N3 (@ tptp.suc M5))))) (forall ((N3 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N3)) (@ P I3))) (or (@ P tptp.zero_zero_nat) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N3) (@ P (@ tptp.suc I3))))))) (forall ((Xs tptp.list_c1059388851t_unit) (N3 tptp.nat)) (= (= (@ tptp.size_s1406904903t_unit Xs) (@ tptp.suc N3)) (exists ((Y4 tptp.config256849571t_unit) (Ys3 tptp.list_c1059388851t_unit)) (and (= Xs (@ (@ tptp.cons_c1162654829t_unit Y4) Ys3)) (= (@ tptp.size_s1406904903t_unit Ys3) N3))))) (forall ((N3 tptp.nat) (Xs tptp.list_c1059388851t_unit)) (= (= (@ tptp.suc N3) (@ tptp.size_s1406904903t_unit Xs)) (exists ((Y4 tptp.config256849571t_unit) (Ys3 tptp.list_c1059388851t_unit)) (and (= Xs (@ (@ tptp.cons_c1162654829t_unit Y4) Ys3)) (= (@ tptp.size_s1406904903t_unit Ys3) N3))))) (= (@ tptp.size_s1168481041ge_p_v tptp.nil_message_p_v) tptp.zero_zero_nat) (= (@ tptp.size_s1406904903t_unit tptp.nil_co1338500125t_unit) tptp.zero_zero_nat) (forall ((Xs tptp.list_message_p_v) (Ys tptp.list_message_p_v) (Zs2 tptp.list_message_p_v) (P (-> tptp.list_message_p_v tptp.list_message_p_v tptp.list_message_p_v Bool))) (let ((_let_1 (@ tptp.size_s1168481041ge_p_v Ys))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs) _let_1) (=> (= _let_1 (@ tptp.size_s1168481041ge_p_v Zs2)) (=> (@ (@ (@ P tptp.nil_message_p_v) tptp.nil_message_p_v) tptp.nil_message_p_v) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v) (Z tptp.message_p_v) (Zs tptp.list_message_p_v)) (let ((_let_1 (@ tptp.size_s1168481041ge_p_v Ys2))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s1168481041ge_p_v Zs)) (=> (@ (@ (@ P Xs2) Ys2) Zs) (@ (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) (@ (@ tptp.cons_message_p_v Y3) Ys2)) (@ (@ tptp.cons_message_p_v Z) Zs))))))) (@ (@ (@ P Xs) Ys) Zs2))))))) (forall ((Xs tptp.list_message_p_v) (Ys tptp.list_message_p_v) (Zs2 tptp.list_c1059388851t_unit) (P (-> tptp.list_message_p_v tptp.list_message_p_v tptp.list_c1059388851t_unit Bool))) (let ((_let_1 (@ tptp.size_s1168481041ge_p_v Ys))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs) _let_1) (=> (= _let_1 (@ tptp.size_s1406904903t_unit Zs2)) (=> (@ (@ (@ P tptp.nil_message_p_v) tptp.nil_message_p_v) tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v) (Z tptp.config256849571t_unit) (Zs tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.size_s1168481041ge_p_v Ys2))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s1406904903t_unit Zs)) (=> (@ (@ (@ P Xs2) Ys2) Zs) (@ (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) (@ (@ tptp.cons_message_p_v Y3) Ys2)) (@ (@ tptp.cons_c1162654829t_unit Z) Zs))))))) (@ (@ (@ P Xs) Ys) Zs2))))))) (forall ((Xs tptp.list_message_p_v) (Ys tptp.list_c1059388851t_unit) (Zs2 tptp.list_message_p_v) (P (-> tptp.list_message_p_v tptp.list_c1059388851t_unit tptp.list_message_p_v Bool))) (let ((_let_1 (@ tptp.size_s1406904903t_unit Ys))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs) _let_1) (=> (= _let_1 (@ tptp.size_s1168481041ge_p_v Zs2)) (=> (@ (@ (@ P tptp.nil_message_p_v) tptp.nil_co1338500125t_unit) tptp.nil_message_p_v) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit) (Z tptp.message_p_v) (Zs tptp.list_message_p_v)) (let ((_let_1 (@ tptp.size_s1406904903t_unit Ys2))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s1168481041ge_p_v Zs)) (=> (@ (@ (@ P Xs2) Ys2) Zs) (@ (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2)) (@ (@ tptp.cons_message_p_v Z) Zs))))))) (@ (@ (@ P Xs) Ys) Zs2))))))) (forall ((Xs tptp.list_message_p_v) (Ys tptp.list_c1059388851t_unit) (Zs2 tptp.list_c1059388851t_unit) (P (-> tptp.list_message_p_v tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool))) (let ((_let_1 (@ tptp.size_s1406904903t_unit Ys))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs) _let_1) (=> (= _let_1 (@ tptp.size_s1406904903t_unit Zs2)) (=> (@ (@ (@ P tptp.nil_message_p_v) tptp.nil_co1338500125t_unit) tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit) (Z tptp.config256849571t_unit) (Zs tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.size_s1406904903t_unit Ys2))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s1406904903t_unit Zs)) (=> (@ (@ (@ P Xs2) Ys2) Zs) (@ (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2)) (@ (@ tptp.cons_c1162654829t_unit Z) Zs))))))) (@ (@ (@ P Xs) Ys) Zs2))))))) (forall ((Xs tptp.list_c1059388851t_unit) (Ys tptp.list_message_p_v) (Zs2 tptp.list_message_p_v) (P (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v Bool))) (let ((_let_1 (@ tptp.size_s1168481041ge_p_v Ys))) (=> (= (@ tptp.size_s1406904903t_unit Xs) _let_1) (=> (= _let_1 (@ tptp.size_s1168481041ge_p_v Zs2)) (=> (@ (@ (@ P tptp.nil_co1338500125t_unit) tptp.nil_message_p_v) tptp.nil_message_p_v) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v) (Z tptp.message_p_v) (Zs tptp.list_message_p_v)) (let ((_let_1 (@ tptp.size_s1168481041ge_p_v Ys2))) (=> (= (@ tptp.size_s1406904903t_unit Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s1168481041ge_p_v Zs)) (=> (@ (@ (@ P Xs2) Ys2) Zs) (@ (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) (@ (@ tptp.cons_message_p_v Y3) Ys2)) (@ (@ tptp.cons_message_p_v Z) Zs))))))) (@ (@ (@ P Xs) Ys) Zs2))))))) (forall ((Xs tptp.list_c1059388851t_unit) (Ys tptp.list_message_p_v) (Zs2 tptp.list_c1059388851t_unit) (P (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit Bool))) (let ((_let_1 (@ tptp.size_s1168481041ge_p_v Ys))) (=> (= (@ tptp.size_s1406904903t_unit Xs) _let_1) (=> (= _let_1 (@ tptp.size_s1406904903t_unit Zs2)) (=> (@ (@ (@ P tptp.nil_co1338500125t_unit) tptp.nil_message_p_v) tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v) (Z tptp.config256849571t_unit) (Zs tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.size_s1168481041ge_p_v Ys2))) (=> (= (@ tptp.size_s1406904903t_unit Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s1406904903t_unit Zs)) (=> (@ (@ (@ P Xs2) Ys2) Zs) (@ (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) (@ (@ tptp.cons_message_p_v Y3) Ys2)) (@ (@ tptp.cons_c1162654829t_unit Z) Zs))))))) (@ (@ (@ P Xs) Ys) Zs2))))))) (forall ((Xs tptp.list_c1059388851t_unit) (Ys tptp.list_c1059388851t_unit) (Zs2 tptp.list_message_p_v) (P (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit tptp.list_message_p_v Bool))) (let ((_let_1 (@ tptp.size_s1406904903t_unit Ys))) (=> (= (@ tptp.size_s1406904903t_unit Xs) _let_1) (=> (= _let_1 (@ tptp.size_s1168481041ge_p_v Zs2)) (=> (@ (@ (@ P tptp.nil_co1338500125t_unit) tptp.nil_co1338500125t_unit) tptp.nil_message_p_v) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit) (Z tptp.message_p_v) (Zs tptp.list_message_p_v)) (let ((_let_1 (@ tptp.size_s1406904903t_unit Ys2))) (=> (= (@ tptp.size_s1406904903t_unit Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s1168481041ge_p_v Zs)) (=> (@ (@ (@ P Xs2) Ys2) Zs) (@ (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2)) (@ (@ tptp.cons_message_p_v Z) Zs))))))) (@ (@ (@ P Xs) Ys) Zs2))))))) (forall ((Xs tptp.list_c1059388851t_unit) (Ys tptp.list_c1059388851t_unit) (Zs2 tptp.list_c1059388851t_unit) (P (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool))) (let ((_let_1 (@ tptp.size_s1406904903t_unit Ys))) (=> (= (@ tptp.size_s1406904903t_unit Xs) _let_1) (=> (= _let_1 (@ tptp.size_s1406904903t_unit Zs2)) (=> (@ (@ (@ P tptp.nil_co1338500125t_unit) tptp.nil_co1338500125t_unit) tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit) (Z tptp.config256849571t_unit) (Zs tptp.list_c1059388851t_unit)) (let ((_let_1 (@ tptp.size_s1406904903t_unit Ys2))) (=> (= (@ tptp.size_s1406904903t_unit Xs2) _let_1) (=> (= _let_1 (@ tptp.size_s1406904903t_unit Zs)) (=> (@ (@ (@ P Xs2) Ys2) Zs) (@ (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2)) (@ (@ tptp.cons_c1162654829t_unit Z) Zs))))))) (@ (@ (@ P Xs) Ys) Zs2))))))) (forall ((Xs tptp.list_message_p_v) (Ys tptp.list_message_p_v) (P (-> tptp.list_message_p_v tptp.list_message_p_v Bool))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs) (@ tptp.size_s1168481041ge_p_v Ys)) (=> (@ (@ P tptp.nil_message_p_v) tptp.nil_message_p_v) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v)) (=> (= (@ tptp.size_s1168481041ge_p_v Xs2) (@ tptp.size_s1168481041ge_p_v Ys2)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) (@ (@ tptp.cons_message_p_v Y3) Ys2))))) (@ (@ P Xs) Ys))))) (forall ((Xs tptp.list_message_p_v) (Ys tptp.list_c1059388851t_unit) (P (-> tptp.list_message_p_v tptp.list_c1059388851t_unit Bool))) (=> (= (@ tptp.size_s1168481041ge_p_v Xs) (@ tptp.size_s1406904903t_unit Ys)) (=> (@ (@ P tptp.nil_message_p_v) tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.message_p_v) (Xs2 tptp.list_message_p_v) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit)) (=> (= (@ tptp.size_s1168481041ge_p_v Xs2) (@ tptp.size_s1406904903t_unit Ys2)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.cons_message_p_v X2) Xs2)) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2))))) (@ (@ P Xs) Ys))))) (forall ((Xs tptp.list_c1059388851t_unit) (Ys tptp.list_message_p_v) (P (-> tptp.list_c1059388851t_unit tptp.list_message_p_v Bool))) (=> (= (@ tptp.size_s1406904903t_unit Xs) (@ tptp.size_s1168481041ge_p_v Ys)) (=> (@ (@ P tptp.nil_co1338500125t_unit) tptp.nil_message_p_v) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.message_p_v) (Ys2 tptp.list_message_p_v)) (=> (= (@ tptp.size_s1406904903t_unit Xs2) (@ tptp.size_s1168481041ge_p_v Ys2)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) (@ (@ tptp.cons_message_p_v Y3) Ys2))))) (@ (@ P Xs) Ys))))) (forall ((Xs tptp.list_c1059388851t_unit) (Ys tptp.list_c1059388851t_unit) (P (-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool))) (=> (= (@ tptp.size_s1406904903t_unit Xs) (@ tptp.size_s1406904903t_unit Ys)) (=> (@ (@ P tptp.nil_co1338500125t_unit) tptp.nil_co1338500125t_unit) (=> (forall ((X2 tptp.config256849571t_unit) (Xs2 tptp.list_c1059388851t_unit) (Y3 tptp.config256849571t_unit) (Ys2 tptp.list_c1059388851t_unit)) (=> (= (@ tptp.size_s1406904903t_unit Xs2) (@ tptp.size_s1406904903t_unit Ys2)) (=> (@ (@ P Xs2) Ys2) (@ (@ P (@ (@ tptp.cons_c1162654829t_unit X2) Xs2)) (@ (@ tptp.cons_c1162654829t_unit Y3) Ys2))))) (@ (@ P Xs) Ys))))) (forall ((X tptp.config256849571t_unit) (Xa (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (Xb (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (Xc tptp.nat) (Y tptp.list_c1059388851t_unit)) (=> (= (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s X) Xa) Xb) Xc) Y) (=> (=> (= Xc tptp.zero_zero_nat) (not (= Y (@ (@ tptp.cons_c1162654829t_unit X) tptp.nil_co1338500125t_unit)))) (not (forall ((N tptp.nat)) (=> (= Xc (@ tptp.suc N)) (not (= Y (@ (@ Xa (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s X) Xa) Xb) N)) (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s X) Xa) Xb) N)))))))))) (forall ((X tptp.config256849571t_unit) (Xa (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (Xb (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (Xc tptp.nat) (Y tptp.list_message_p_v)) (=> (= (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s X) Xa) Xb) Xc) Y) (=> (=> (= Xc tptp.zero_zero_nat) (not (= Y tptp.nil_message_p_v))) (not (forall ((N tptp.nat)) (=> (= Xc (@ tptp.suc N)) (not (= Y (@ (@ Xb (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s X) Xa) Xb) N)) (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s X) Xa) Xb) N)))))))))) (forall ((Cfg2 tptp.config256849571t_unit) (FStepCfg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (N3 tptp.nat)) (let ((_let_1 (@ (@ (@ tptp.fLPThe536531371_p_v_s Cfg2) FStepCfg2) FStepMsg2))) (= (@ _let_1 (@ tptp.suc N3)) (@ (@ FStepMsg2 (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s Cfg2) FStepCfg2) FStepMsg2) N3)) (@ _let_1 N3))))) (forall ((Cfg2 tptp.config256849571t_unit) (FStepCfg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (N3 tptp.nat)) (let ((_let_1 (@ (@ (@ tptp.fLPThe1519354920_p_v_s Cfg2) FStepCfg2) FStepMsg2))) (= (@ _let_1 (@ tptp.suc N3)) (@ (@ FStepCfg2 (@ _let_1 N3)) (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s Cfg2) FStepCfg2) FStepMsg2) N3))))) (forall ((Cfg2 tptp.config256849571t_unit) (FStepCfg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v))) (= (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s Cfg2) FStepCfg2) FStepMsg2) tptp.zero_zero_nat) tptp.nil_message_p_v)) (forall ((N3 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)) (= N3 tptp.zero_zero_nat))) (forall ((X tptp.config256849571t_unit) (Xs tptp.list_c1059388851t_unit)) (= (@ tptp.size_s1406904903t_unit (@ (@ tptp.cons_c1162654829t_unit X) Xs)) (@ tptp.suc (@ tptp.size_s1406904903t_unit Xs)))) (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))) (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))) (forall ((N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))) (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_nat N3) tptp.zero_zero_nat))) (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N3) (not (= N3 tptp.zero_zero_nat)))) (forall ((N3 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (not (= N3 tptp.zero_zero_nat)))) (forall ((N3 tptp.nat)) (let ((_let_1 (@ (@ tptp.n_list1987762709t_unit N3) tptp.nil_co1338500125t_unit))) (let ((_let_2 (= N3 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_l1083444861t_unit tptp.nil_co1338500125t_unit) tptp.nil_li307996205t_unit))) (=> (not _let_2) (= _let_1 tptp.nil_li307996205t_unit)))))) (forall ((N3 tptp.nat)) (let ((_let_1 (@ (@ tptp.n_lists_message_p_v N3) tptp.nil_message_p_v))) (let ((_let_2 (= N3 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_l233104475ge_p_v tptp.nil_message_p_v) tptp.nil_list_message_p_v))) (=> (not _let_2) (= _let_1 tptp.nil_list_message_p_v)))))) (forall ((Trans (-> tptp.p tptp.s tptp.messageValue_v tptp.s)) (Sends (-> tptp.p tptp.s tptp.messageValue_v tptp.message_p_v tptp.nat)) (Start (-> tptp.p tptp.s)) (X tptp.config256849571t_unit) (Xa (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (Xb (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (Xc tptp.nat) (Y tptp.list_c1059388851t_unit)) (=> (@ (@ (@ tptp.fLPThe9398366_p_s_v Trans) Sends) Start) (=> (= (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s X) Xa) Xb) Xc) Y) (=> (=> (= Xc tptp.zero_zero_nat) (not (= Y (@ (@ tptp.cons_c1162654829t_unit X) tptp.nil_co1338500125t_unit)))) (not (forall ((N tptp.nat)) (=> (= Xc (@ tptp.suc N)) (not (= Y (@ (@ Xa (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s X) Xa) Xb) N)) (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s X) Xa) Xb) N))))))))))) (forall ((Xs tptp.list_c1059388851t_unit)) (= (@ (@ tptp.n_list1987762709t_unit tptp.zero_zero_nat) Xs) (@ (@ tptp.cons_l1083444861t_unit tptp.nil_co1338500125t_unit) tptp.nil_li307996205t_unit))) (forall ((Xs tptp.list_message_p_v)) (= (@ (@ tptp.n_lists_message_p_v tptp.zero_zero_nat) Xs) (@ (@ tptp.cons_l233104475ge_p_v tptp.nil_message_p_v) tptp.nil_list_message_p_v))) (forall ((Trans (-> tptp.p tptp.s tptp.messageValue_v tptp.s)) (Sends (-> tptp.p tptp.s tptp.messageValue_v tptp.message_p_v tptp.nat)) (Start (-> tptp.p tptp.s)) (X tptp.config256849571t_unit) (Xa (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (Xb (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (Xc tptp.nat) (Y tptp.list_message_p_v)) (=> (@ (@ (@ tptp.fLPThe9398366_p_s_v Trans) Sends) Start) (=> (= (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s X) Xa) Xb) Xc) Y) (=> (=> (= Xc tptp.zero_zero_nat) (not (= Y tptp.nil_message_p_v))) (not (forall ((N tptp.nat)) (=> (= Xc (@ tptp.suc N)) (not (= Y (@ (@ Xb (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s X) Xa) Xb) N)) (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s X) Xa) Xb) N))))))))))) (forall ((Trans (-> tptp.p tptp.s tptp.messageValue_v tptp.s)) (Sends (-> tptp.p tptp.s tptp.messageValue_v tptp.message_p_v tptp.nat)) (Start (-> tptp.p tptp.s)) (Cfg2 tptp.config256849571t_unit) (FStepCfg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (N3 tptp.nat)) (let ((_let_1 (@ (@ (@ tptp.fLPThe536531371_p_v_s Cfg2) FStepCfg2) FStepMsg2))) (=> (@ (@ (@ tptp.fLPThe9398366_p_s_v Trans) Sends) Start) (= (@ _let_1 (@ tptp.suc N3)) (@ (@ FStepMsg2 (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s Cfg2) FStepCfg2) FStepMsg2) N3)) (@ _let_1 N3)))))) (forall ((Trans (-> tptp.p tptp.s tptp.messageValue_v tptp.s)) (Sends (-> tptp.p tptp.s tptp.messageValue_v tptp.message_p_v tptp.nat)) (Start (-> tptp.p tptp.s)) (Cfg2 tptp.config256849571t_unit) (FStepCfg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v)) (N3 tptp.nat)) (let ((_let_1 (@ (@ (@ tptp.fLPThe1519354920_p_v_s Cfg2) FStepCfg2) FStepMsg2))) (=> (@ (@ (@ tptp.fLPThe9398366_p_s_v Trans) Sends) Start) (= (@ _let_1 (@ tptp.suc N3)) (@ (@ FStepCfg2 (@ _let_1 N3)) (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s Cfg2) FStepCfg2) FStepMsg2) N3)))))) (forall ((Trans (-> tptp.p tptp.s tptp.messageValue_v tptp.s)) (Sends (-> tptp.p tptp.s tptp.messageValue_v tptp.message_p_v tptp.nat)) (Start (-> tptp.p tptp.s)) (Cfg2 tptp.config256849571t_unit) (FStepCfg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v))) (=> (@ (@ (@ tptp.fLPThe9398366_p_s_v Trans) Sends) Start) (= (@ (@ (@ (@ tptp.fLPThe536531371_p_v_s Cfg2) FStepCfg2) FStepMsg2) tptp.zero_zero_nat) tptp.nil_message_p_v))) (forall ((Trans (-> tptp.p tptp.s tptp.messageValue_v tptp.s)) (Sends (-> tptp.p tptp.s tptp.messageValue_v tptp.message_p_v tptp.nat)) (Start (-> tptp.p tptp.s)) (Cfg2 tptp.config256849571t_unit) (FStepCfg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_c1059388851t_unit)) (FStepMsg2 (-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.list_message_p_v))) (=> (@ (@ (@ tptp.fLPThe9398366_p_s_v Trans) Sends) Start) (= (@ (@ (@ (@ tptp.fLPThe1519354920_p_v_s Cfg2) FStepCfg2) FStepMsg2) tptp.zero_zero_nat) (@ (@ tptp.cons_c1162654829t_unit Cfg2) tptp.nil_co1338500125t_unit)))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)) (= (@ tptp.produc663212148t_unit tptp.nil_li307996205t_unit) _let_7) (= (@ tptp.produc1505827982ge_p_v tptp.nil_list_message_p_v) _let_6) (= (@ tptp.subseq1144048270t_unit tptp.nil_co1338500125t_unit) _let_7) (= (@ tptp.subseqs_message_p_v tptp.nil_message_p_v) _let_6) (= tptp.size_s1406904903t_unit (@ tptp.gen_le193291088t_unit tptp.zero_zero_nat)) (forall ((N3 tptp.nat) (X tptp.config256849571t_unit) (Xs tptp.list_c1059388851t_unit)) (= (@ (@ tptp.gen_le193291088t_unit N3) (@ (@ tptp.cons_c1162654829t_unit X) Xs)) (@ (@ tptp.gen_le193291088t_unit (@ tptp.suc N3)) Xs))) (forall ((N3 tptp.nat)) (= (@ (@ tptp.gen_le193291088t_unit N3) tptp.nil_co1338500125t_unit) N3)) (forall ((N3 tptp.nat)) (= (@ (@ tptp.gen_le697204914ge_p_v N3) tptp.nil_message_p_v) N3)) (forall ((X tptp.message_p_v)) (= (@ (@ tptp.insert_message_p_v X) tptp.nil_message_p_v) (@ (@ tptp.cons_message_p_v X) tptp.nil_message_p_v))) (forall ((X tptp.config256849571t_unit)) (= (@ (@ tptp.insert1308755079t_unit X) tptp.nil_co1338500125t_unit) (@ (@ tptp.cons_c1162654829t_unit X) tptp.nil_co1338500125t_unit))) (forall ((A8 tptp.set_nat) (X tptp.message_p_v)) (let ((_let_1 (@ (@ tptp.cons_message_p_v X) tptp.nil_message_p_v))) (let ((_let_2 (@ (@ tptp.nths_message_p_v _let_1) A8))) (let ((_let_3 (@ (@ tptp.member_nat tptp.zero_zero_nat) A8))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.nil_message_p_v))))))) (forall ((A8 tptp.set_nat) (X tptp.config256849571t_unit)) (let ((_let_1 (@ (@ tptp.cons_c1162654829t_unit X) tptp.nil_co1338500125t_unit))) (let ((_let_2 (@ (@ tptp.nths_c890550943t_unit _let_1) A8))) (let ((_let_3 (@ (@ tptp.member_nat tptp.zero_zero_nat) A8))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 tptp.nil_co1338500125t_unit))))))) (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1382578993at_nat N3)) (@ _let_1 N3)))) (forall ((N3 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri2019852685at_int N3)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))) (forall ((M tptp.nat) (N3 tptp.nat)) (= (= (@ tptp.semiri2019852685at_int M) (@ tptp.semiri2019852685at_int N3)) (= M N3))) (forall ((A8 tptp.set_nat)) (= (@ (@ tptp.nths_c890550943t_unit tptp.nil_co1338500125t_unit) A8) tptp.nil_co1338500125t_unit)) (forall ((A8 tptp.set_nat)) (= (@ (@ tptp.nths_message_p_v tptp.nil_message_p_v) A8) tptp.nil_message_p_v)) (= (@ tptp.semiri1382578993at_nat tptp.zero_zero_nat) tptp.zero_zero_nat) _let_5 (forall ((N3 tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1382578993at_nat N3)) (= tptp.zero_zero_nat N3))) (forall ((N3 tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri2019852685at_int N3)) (= tptp.zero_zero_nat N3))) (forall ((M tptp.nat)) (= (= (@ tptp.semiri1382578993at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (@ tptp.semiri2019852685at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat) (N3 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1382578993at_nat M)) (@ tptp.semiri1382578993at_nat N3)) (@ (@ tptp.ord_less_nat M) N3))) (forall ((M tptp.nat) (N3 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int M)) (@ tptp.semiri2019852685at_int N3)) (@ (@ tptp.ord_less_nat M) N3))) (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1382578993at_nat M)) tptp.zero_zero_nat))) (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int M)) tptp.zero_zero_int))) (forall ((N3 tptp.nat)) (not (= (@ tptp.semiri1382578993at_nat (@ tptp.suc N3)) tptp.zero_zero_nat))) (forall ((N3 tptp.nat)) (not (= (@ tptp.semiri2019852685at_int (@ tptp.suc N3)) tptp.zero_zero_int))) (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N3) (@ (@ tptp.ord_less_nat (@ tptp.semiri1382578993at_nat M)) (@ tptp.semiri1382578993at_nat N3)))) (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N3) (@ (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int M)) (@ tptp.semiri2019852685at_int N3)))) (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1382578993at_nat M)) (@ tptp.semiri1382578993at_nat N3)) (@ (@ tptp.ord_less_nat M) N3))) (forall ((M tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int M)) (@ tptp.semiri2019852685at_int N3)) (@ (@ tptp.ord_less_nat M) N3))) (forall ((Xs tptp.list_c1059388851t_unit) (I4 tptp.set_nat)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1406904903t_unit Xs)) (@ (@ tptp.member_nat I2) I4))) (= (@ (@ tptp.nths_c890550943t_unit Xs) I4) Xs))) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N tptp.nat)) (=> (= K (@ tptp.semiri2019852685at_int N)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= K (@ tptp.semiri2019852685at_int N)))))) (forall ((P (-> tptp.config256849571t_unit Bool))) (not (@ (@ tptp.list_e1598815642t_unit P) tptp.nil_co1338500125t_unit))) (forall ((P (-> tptp.message_p_v Bool))) (not (@ (@ tptp.list_ex1_message_p_v P) tptp.nil_message_p_v))) (= tptp.ord_less_nat (lambda ((A10 tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int A10)) (@ tptp.semiri2019852685at_int B)))) _let_5 (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int N))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B2)) (= A B2))) (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)) (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int) (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))) (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))) (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))) (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) B2))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))) (forall ((N3 tptp.nat) (M tptp.nat)) (= (= (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int N3)) (@ tptp.semiri2019852685at_int M)) (and (= N3 tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))) (forall ((N3 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int (@ tptp.suc N3)))) (@ tptp.semiri2019852685at_int M))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B2) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B2)) A))) (forall ((A tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ tptp.uminus_uminus_int B2)) (@ (@ tptp.ord_less_int B2) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.int) (B2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B2) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.int) (B2 tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B2) (= (@ tptp.uminus_uminus_int B2) A))) (forall ((A tptp.int) (B2 tptp.int)) (= (= A (@ tptp.uminus_uminus_int B2)) (= B2 (@ tptp.uminus_uminus_int A)))) (forall ((Z2 tptp.int)) (=> (forall ((N tptp.nat)) (not (= Z2 (@ tptp.semiri2019852685at_int N)))) (not (forall ((N tptp.nat)) (not (= Z2 (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int (@ tptp.suc N))))))))) (forall ((P (-> tptp.int Bool)) (Z2 tptp.int)) (=> (forall ((N tptp.nat)) (@ P (@ tptp.semiri2019852685at_int N))) (=> (forall ((N tptp.nat)) (@ P (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int (@ tptp.suc N))))) (@ P Z2)))) (forall ((M tptp.int)) (=> (forall ((N tptp.nat)) (not (= M (@ tptp.semiri2019852685at_int N)))) (not (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int N))))))))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))) (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))) (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N tptp.nat)) (=> (= K (@ tptp.semiri2019852685at_int N)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))) (not (forall ((N tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int N))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))))) (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int (@ tptp.suc N3)))) tptp.zero_zero_int)) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (exists ((N tptp.nat)) (= X (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int (@ tptp.suc N))))))) (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2))) (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))) (= (@ tptp.ring_1_of_int_int tptp.zero_zero_int) tptp.zero_zero_int) (forall ((Z2 tptp.int)) (= (= tptp.zero_zero_int (@ tptp.ring_1_of_int_int Z2)) (= Z2 tptp.zero_zero_int))) (forall ((Z2 tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z2) tptp.zero_zero_int) (= Z2 tptp.zero_zero_int))) (forall ((W tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z2)) (@ (@ tptp.ord_less_int W) Z2))) (forall ((W tptp.int) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z2)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (@ (@ tptp.ord_less_int W) Z2)))) (forall ((N3 tptp.nat)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.semiri2019852685at_int N3))) tptp.zero_zero_nat)) (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z2) tptp.zero_zero_int))) (= tptp.zero_zero_nat (@ tptp.nat2 tptp.zero_zero_int)) (forall ((Z2 tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z2) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int W) Z2)))) (forall ((M tptp.nat) (Z2 tptp.int)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int M)) Z2))) (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 Z2) (@ _let_1 (@ tptp.ring_1_of_int_int Z2))))) (forall ((N3 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri2019852685at_int N3)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X)) (@ _let_1 X)))) (forall ((P (-> tptp.nat Bool)) (I tptp.int)) (= (@ P (@ tptp.nat2 I)) (and (forall ((N5 tptp.nat)) (=> (= I (@ tptp.semiri2019852685at_int N5)) (@ P N5))) (=> (@ (@ tptp.ord_less_int I) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))) (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z2)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z2))) (forall ((W tptp.int) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) M) (@ (@ tptp.ord_less_int W) (@ tptp.semiri2019852685at_int M))))) (forall ((N3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N3) tptp.zero_zero_nat) (= N3 tptp.zero_zero_nat))) (forall ((B2 tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B2)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) B2))) (forall ((M tptp.nat) (N3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri2019852685at_int M)) (@ tptp.semiri2019852685at_int N3)) (@ (@ tptp.ord_less_eq_nat M) N3))) (= (@ tptp.semiri2019852685at_int tptp.one_one_nat) tptp.one_one_int) (forall ((N3 tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri2019852685at_int N3)) (= N3 tptp.one_one_nat))) (forall ((N3 tptp.nat)) (= (= (@ tptp.semiri2019852685at_int N3) tptp.one_one_int) (= N3 tptp.one_one_nat))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))) (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1382578993at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri2019852685at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))) (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z2) tptp.zero_zero_int) (= (@ tptp.nat2 Z2) tptp.zero_zero_nat))) (forall ((I tptp.int)) (= (= (@ tptp.nat2 I) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int))) (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int Z2) tptp.zero_zero_int))) (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))) (forall ((Z2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z2)) tptp.one_one_int) (@ (@ tptp.ord_less_int Z2) tptp.one_one_int))) (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z2)) (@ _let_1 Z2)))) (forall ((Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z2) (@ _let_1 (@ tptp.ring_1_of_int_int Z2))))) (forall ((B3 tptp.nat) (A11 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B3) A11)) (@ (@ tptp.ord_less_nat A11) B3))) (forall ((B3 tptp.int) (A11 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B3) A11)) (@ (@ tptp.ord_less_int A11) B3))) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int) (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))) (forall ((F2 (-> tptp.nat tptp.int)) (N3 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F2 (@ tptp.suc N))) (@ F2 N))) (=> (@ (@ tptp.ord_less_eq_nat N3) N4) (@ (@ tptp.ord_less_eq_int (@ F2 N4)) (@ F2 N3))))) (forall ((F2 (-> tptp.nat tptp.int)) (N3 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F2 N)) (@ F2 (@ tptp.suc N)))) (=> (@ (@ tptp.ord_less_eq_nat N3) N4) (@ (@ tptp.ord_less_eq_int (@ F2 N3)) (@ F2 N4))))) (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int) (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)) (not (@ _let_4 tptp.one_one_int)) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri2019852685at_int I)) (@ tptp.semiri2019852685at_int J)))) (not (@ _let_4 _let_3)) (@ (@ tptp.ord_less_int _let_3) tptp.one_one_int) (not (= tptp.zero_zero_int _let_3)) _let_2 true)))))))))))))
% 0.58/0.79 )
% 0.58/0.79 % SZS output end Proof for ITP055^1
% 0.58/0.79 % cvc5---1.0.5 exiting
% 0.58/0.80 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------