TSTP Solution File: ITP061^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP061^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.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 03:17:53 EDT 2023
% Result : Theorem 1.03s 1.21s
% Output : Proof 1.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15 % Problem : ITP061^1 : TPTP v8.1.2. Released v7.5.0.
% 0.15/0.16 % Command : do_cvc5 %s %d
% 0.17/0.37 % Computer : n015.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Sun Aug 27 15:51:24 EDT 2023
% 0.17/0.37 % CPUTime :
% 0.23/0.53 %----Proving TH0
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 % File : ITP061^1 : TPTP v8.1.2. Released v7.5.0.
% 0.23/0.54 % Domain : Interactive Theorem Proving
% 0.23/0.54 % Problem : Sledgehammer FLPTheorem problem prob_979__3303242_1
% 0.23/0.54 % Version : Especial.
% 0.23/0.54 % English :
% 0.23/0.54
% 0.23/0.54 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.23/0.54 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.23/0.54 % Source : [Des21]
% 0.23/0.54 % Names : FLPTheorem/prob_979__3303242_1 [Des21]
% 0.23/0.54
% 0.23/0.54 % Status : Theorem
% 0.23/0.54 % Rating : 0.38 v8.1.0, 0.36 v7.5.0
% 0.23/0.54 % Syntax : Number of formulae : 274 ( 94 unt; 38 typ; 0 def)
% 0.23/0.54 % Number of atoms : 616 ( 172 equ; 0 cnn)
% 0.23/0.54 % Maximal formula atoms : 12 ( 2 avg)
% 0.23/0.54 % Number of connectives : 1864 ( 84 ~; 18 |; 27 &;1410 @)
% 0.23/0.54 % ( 0 <=>; 325 =>; 0 <=; 0 <~>)
% 0.23/0.54 % Maximal formula depth : 16 ( 7 avg)
% 0.23/0.54 % Number of types : 8 ( 7 usr)
% 0.23/0.54 % Number of type conns : 87 ( 87 >; 0 *; 0 +; 0 <<)
% 0.23/0.54 % Number of symbols : 32 ( 31 usr; 12 con; 0-4 aty)
% 0.23/0.54 % Number of variables : 600 ( 42 ^; 537 !; 21 ?; 600 :)
% 0.23/0.54 % SPC : TH0_THM_EQU_NAR
% 0.23/0.54
% 0.23/0.54 % Comments : This file was generated by Sledgehammer 2021-02-23 15:31:50.858
% 0.23/0.54 %------------------------------------------------------------------------------
% 0.23/0.54 % Could-be-implicit typings (7)
% 0.23/0.54 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J_J,type,
% 0.23/0.54 list_c1059388851t_unit: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(ty_n_t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.23/0.54 config256849571t_unit: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(ty_n_t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.23/0.54 list_message_p_v: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(ty_n_t__Set__Oset_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.23/0.54 set_message_p_v: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(ty_n_t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.23/0.54 message_p_v: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(ty_n_t__Nat__Onat,type,
% 0.23/0.54 nat: $tType ).
% 0.23/0.54
% 0.23/0.54 thf(ty_n_tf__p,type,
% 0.23/0.54 p: $tType ).
% 0.23/0.54
% 0.23/0.54 % Explicit typings (31)
% 0.23/0.54 thf(sy_c_AsynchronousSystem_Oenabled_001tf__p_001tf__v_001tf__s,type,
% 0.23/0.54 enabled_p_v_s: config256849571t_unit > message_p_v > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_AsynchronousSystem_OisReceiverOf_001tf__p_001tf__v,type,
% 0.23/0.54 isReceiverOf_p_v: p > message_p_v > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Execution_Oexecution_OfirstOccurrence_001tf__p_001tf__v_001tf__s,type,
% 0.23/0.54 firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Execution_Oexecution_OminimalEnabled_001tf__p_001tf__v_001tf__s,type,
% 0.23/0.54 minimalEnabled_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
% 0.23/0.54 minus_minus_nat: nat > nat > nat ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Groups_Oone__class_Oone_001t__Nat__Onat,type,
% 0.23/0.54 one_one_nat: nat ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.23/0.54 prefix1615116500t_unit: list_c1059388851t_unit > list_c1059388851t_unit > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_ListUtilities_OprefixList_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.23/0.54 prefix47729710ge_p_v: list_message_p_v > list_message_p_v > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_List_Olist_ONil_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.23/0.54 nil_co1338500125t_unit: list_c1059388851t_unit ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_List_Onth_001t__AsynchronousSystem__Oconfiguration__Oconfiguration____ext_Itf__p_Mtf__v_Mtf__s_Mt__Product____Type__Ounit_J,type,
% 0.23/0.54 nth_co1649820636t_unit: list_c1059388851t_unit > nat > config256849571t_unit ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_List_Onth_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.23/0.54 nth_message_p_v: list_message_p_v > nat > message_p_v ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Nat_OSuc,type,
% 0.23/0.54 suc: nat > nat ).
% 0.23/0.54
% 0.23/0.54 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,
% 0.23/0.54 size_s1406904903t_unit: list_c1059388851t_unit > nat ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J_J,type,
% 0.23/0.54 size_s1168481041ge_p_v: list_message_p_v > nat ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 0.23/0.54 ord_less_nat: nat > nat > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
% 0.23/0.54 ord_less_eq_nat: nat > nat > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_Set_OCollect_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.23/0.54 collect_message_p_v: ( message_p_v > $o ) > set_message_p_v ).
% 0.23/0.54
% 0.23/0.54 thf(sy_c_member_001t__AsynchronousSystem__Omessage_Itf__p_Mtf__v_J,type,
% 0.23/0.54 member_message_p_v: message_p_v > set_message_p_v > $o ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_OccM_H____,type,
% 0.23/0.54 occM: nat ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_OccM____,type,
% 0.23/0.54 occM2: nat ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_consumedMsg____,type,
% 0.23/0.54 consumedMsg: message_p_v ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_fe____,type,
% 0.23/0.54 fe: nat > list_c1059388851t_unit ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_firstOccSet____,type,
% 0.23/0.54 firstOccSet: nat > set_message_p_v ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_ft____,type,
% 0.23/0.54 ft: nat > list_message_p_v ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_index____,type,
% 0.23/0.54 index: nat ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_msg_H____,type,
% 0.23/0.54 msg: message_p_v ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_msg____,type,
% 0.23/0.54 msg2: message_p_v ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_msga____,type,
% 0.23/0.54 msga: message_p_v ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_n0____,type,
% 0.23/0.54 n0: nat ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_n____,type,
% 0.23/0.54 n: nat ).
% 0.23/0.54
% 0.23/0.54 thf(sy_v_p____,type,
% 0.23/0.54 p2: p ).
% 0.23/0.54
% 0.23/0.54 % Relevant facts (235)
% 0.23/0.54 thf(fact_0_AssumpOccMFirstOccurrence_I3_J,axiom,
% 0.23/0.54 ord_less_nat @ occM2 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ).
% 0.23/0.54
% 0.23/0.54 % AssumpOccMFirstOccurrence(3)
% 0.23/0.54 thf(fact_1__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_AOccM_092_060close_062,axiom,
% 0.23/0.54 ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ occM2 ).
% 0.23/0.54
% 0.23/0.54 % \<open>length (fe index) - 1 \<le> OccM\<close>
% 0.23/0.54 thf(fact_2_OccM_H_I3_J,axiom,
% 0.23/0.54 ord_less_nat @ occM @ ( size_s1406904903t_unit @ ( fe @ index ) ) ).
% 0.23/0.54
% 0.23/0.54 % OccM'(3)
% 0.23/0.54 thf(fact_3__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Alength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_092_060close_062,axiom,
% 0.23/0.54 ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) ).
% 0.23/0.54
% 0.23/0.54 % \<open>length (fe index) - 1 \<le> length (fe (Suc index)) - 1\<close>
% 0.23/0.54 thf(fact_4_NotEmpty_I2_J,axiom,
% 0.23/0.54 ( ( fe @ index )
% 0.23/0.54 != nil_co1338500125t_unit ) ).
% 0.23/0.54
% 0.23/0.54 % NotEmpty(2)
% 0.23/0.54 thf(fact_5_AssumptionFair_I2_J,axiom,
% 0.23/0.54 ord_less_nat @ n0 @ ( size_s1406904903t_unit @ ( fe @ n ) ) ).
% 0.23/0.54
% 0.23/0.54 % AssumptionFair(2)
% 0.23/0.54 thf(fact_6_one__natural_Orsp,axiom,
% 0.23/0.54 one_one_nat = one_one_nat ).
% 0.23/0.54
% 0.23/0.54 % one_natural.rsp
% 0.23/0.54 thf(fact_7_diff__commute,axiom,
% 0.23/0.54 ! [I: nat,J: nat,K: nat] :
% 0.23/0.54 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 0.23/0.54 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 0.23/0.54
% 0.23/0.54 % diff_commute
% 0.23/0.54 thf(fact_8_Ex__list__of__length,axiom,
% 0.23/0.54 ! [N: nat] :
% 0.23/0.54 ? [Xs: list_c1059388851t_unit] :
% 0.23/0.54 ( ( size_s1406904903t_unit @ Xs )
% 0.23/0.54 = N ) ).
% 0.23/0.54
% 0.23/0.54 % Ex_list_of_length
% 0.23/0.54 thf(fact_9_Ex__list__of__length,axiom,
% 0.23/0.54 ! [N: nat] :
% 0.23/0.54 ? [Xs: list_message_p_v] :
% 0.23/0.54 ( ( size_s1168481041ge_p_v @ Xs )
% 0.23/0.54 = N ) ).
% 0.23/0.54
% 0.23/0.54 % Ex_list_of_length
% 0.23/0.54 thf(fact_10_neq__if__length__neq,axiom,
% 0.23/0.54 ! [Xs2: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 0.23/0.54 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.23/0.54 != ( size_s1406904903t_unit @ Ys ) )
% 0.23/0.54 => ( Xs2 != Ys ) ) ).
% 0.23/0.54
% 0.23/0.54 % neq_if_length_neq
% 0.23/0.54 thf(fact_11_neq__if__length__neq,axiom,
% 0.23/0.54 ! [Xs2: list_message_p_v,Ys: list_message_p_v] :
% 0.23/0.54 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.23/0.54 != ( size_s1168481041ge_p_v @ Ys ) )
% 0.23/0.54 => ( Xs2 != Ys ) ) ).
% 0.23/0.54
% 0.23/0.54 % neq_if_length_neq
% 0.23/0.54 thf(fact_12_size__neq__size__imp__neq,axiom,
% 0.23/0.54 ! [X: list_c1059388851t_unit,Y: list_c1059388851t_unit] :
% 0.23/0.54 ( ( ( size_s1406904903t_unit @ X )
% 0.23/0.54 != ( size_s1406904903t_unit @ Y ) )
% 0.23/0.54 => ( X != Y ) ) ).
% 0.23/0.54
% 0.23/0.54 % size_neq_size_imp_neq
% 0.23/0.54 thf(fact_13_size__neq__size__imp__neq,axiom,
% 0.23/0.54 ! [X: list_message_p_v,Y: list_message_p_v] :
% 0.23/0.54 ( ( ( size_s1168481041ge_p_v @ X )
% 0.23/0.54 != ( size_s1168481041ge_p_v @ Y ) )
% 0.23/0.54 => ( X != Y ) ) ).
% 0.23/0.54
% 0.23/0.54 % size_neq_size_imp_neq
% 0.23/0.54 thf(fact_14_nat_Oinject,axiom,
% 0.23/0.54 ! [X2: nat,Y2: nat] :
% 0.23/0.54 ( ( ( suc @ X2 )
% 0.23/0.54 = ( suc @ Y2 ) )
% 0.23/0.54 = ( X2 = Y2 ) ) ).
% 0.23/0.54
% 0.23/0.54 % nat.inject
% 0.23/0.54 thf(fact_15_old_Onat_Oinject,axiom,
% 0.23/0.54 ! [Nat: nat,Nat2: nat] :
% 0.23/0.54 ( ( ( suc @ Nat )
% 0.23/0.54 = ( suc @ Nat2 ) )
% 0.23/0.54 = ( Nat = Nat2 ) ) ).
% 0.23/0.54
% 0.23/0.54 % old.nat.inject
% 0.23/0.54 thf(fact_16_NotEmpty_I1_J,axiom,
% 0.23/0.54 ( ( fe @ ( suc @ index ) )
% 0.23/0.54 != nil_co1338500125t_unit ) ).
% 0.23/0.54
% 0.23/0.54 % NotEmpty(1)
% 0.23/0.54 thf(fact_17_lessI,axiom,
% 0.23/0.54 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % lessI
% 0.23/0.54 thf(fact_18_Suc__mono,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_nat @ M @ N )
% 0.23/0.54 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_mono
% 0.23/0.54 thf(fact_19_Suc__less__eq,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.23/0.54 = ( ord_less_nat @ M @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_less_eq
% 0.23/0.54 thf(fact_20_Suc__le__mono,axiom,
% 0.23/0.54 ! [N: nat,M: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.23/0.54 = ( ord_less_eq_nat @ N @ M ) ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_le_mono
% 0.23/0.54 thf(fact_21_Suc__diff__diff,axiom,
% 0.23/0.54 ! [M: nat,N: nat,K: nat] :
% 0.23/0.54 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 0.23/0.54 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_diff_diff
% 0.23/0.54 thf(fact_22_diff__Suc__Suc,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.23/0.54 = ( minus_minus_nat @ M @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % diff_Suc_Suc
% 0.23/0.54 thf(fact_23_diff__diff__cancel,axiom,
% 0.23/0.54 ! [I: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ I @ N )
% 0.23/0.54 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 0.23/0.54 = I ) ) ).
% 0.23/0.54
% 0.23/0.54 % diff_diff_cancel
% 0.23/0.54 thf(fact_24_diff__Suc__1,axiom,
% 0.23/0.54 ! [N: nat] :
% 0.23/0.54 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 0.23/0.54 = N ) ).
% 0.23/0.54
% 0.23/0.54 % diff_Suc_1
% 0.23/0.54 thf(fact_25_Nat_OlessE,axiom,
% 0.23/0.54 ! [I: nat,K: nat] :
% 0.23/0.54 ( ( ord_less_nat @ I @ K )
% 0.23/0.54 => ( ( K
% 0.23/0.54 != ( suc @ I ) )
% 0.23/0.54 => ~ ! [J2: nat] :
% 0.23/0.54 ( ( ord_less_nat @ I @ J2 )
% 0.23/0.54 => ( K
% 0.23/0.54 != ( suc @ J2 ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Nat.lessE
% 0.23/0.54 thf(fact_26_Suc__leD,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.23/0.54 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_leD
% 0.23/0.54 thf(fact_27_Suc__leI,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_nat @ M @ N )
% 0.23/0.54 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_leI
% 0.23/0.54 thf(fact_28_le__SucE,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.23/0.54 => ( ~ ( ord_less_eq_nat @ M @ N )
% 0.23/0.54 => ( M
% 0.23/0.54 = ( suc @ N ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_SucE
% 0.23/0.54 thf(fact_29_le__SucI,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ M @ N )
% 0.23/0.54 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_SucI
% 0.23/0.54 thf(fact_30_le__refl,axiom,
% 0.23/0.54 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.23/0.54
% 0.23/0.54 % le_refl
% 0.23/0.54 thf(fact_31_Suc__le__D,axiom,
% 0.23/0.54 ! [N: nat,M2: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ ( suc @ N ) @ M2 )
% 0.23/0.54 => ? [M3: nat] :
% 0.23/0.54 ( M2
% 0.23/0.54 = ( suc @ M3 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_le_D
% 0.23/0.54 thf(fact_32_le__trans,axiom,
% 0.23/0.54 ! [I: nat,J: nat,K: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ I @ J )
% 0.23/0.54 => ( ( ord_less_eq_nat @ J @ K )
% 0.23/0.54 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_trans
% 0.23/0.54 thf(fact_33_Suc__le__eq,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.23/0.54 = ( ord_less_nat @ M @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_le_eq
% 0.23/0.54 thf(fact_34_Suc__lessD,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 0.23/0.54 => ( ord_less_nat @ M @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_lessD
% 0.23/0.54 thf(fact_35_Suc__lessE,axiom,
% 0.23/0.54 ! [I: nat,K: nat] :
% 0.23/0.54 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 0.23/0.54 => ~ ! [J2: nat] :
% 0.23/0.54 ( ( ord_less_nat @ I @ J2 )
% 0.23/0.54 => ( K
% 0.23/0.54 != ( suc @ J2 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_lessE
% 0.23/0.54 thf(fact_36_Suc__lessI,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_nat @ M @ N )
% 0.23/0.54 => ( ( ( suc @ M )
% 0.23/0.54 != N )
% 0.23/0.54 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_lessI
% 0.23/0.54 thf(fact_37_eq__imp__le,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( M = N )
% 0.23/0.54 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % eq_imp_le
% 0.23/0.54 thf(fact_38_le__Suc__eq,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 0.23/0.54 = ( ( ord_less_eq_nat @ M @ N )
% 0.23/0.54 | ( M
% 0.23/0.54 = ( suc @ N ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_Suc_eq
% 0.23/0.54 thf(fact_39_less__SucE,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.23/0.54 => ( ~ ( ord_less_nat @ M @ N )
% 0.23/0.54 => ( M = N ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % less_SucE
% 0.23/0.54 thf(fact_40_less__SucI,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_nat @ M @ N )
% 0.23/0.54 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % less_SucI
% 0.23/0.54 thf(fact_41_Suc__inject,axiom,
% 0.23/0.54 ! [X: nat,Y: nat] :
% 0.23/0.54 ( ( ( suc @ X )
% 0.23/0.54 = ( suc @ Y ) )
% 0.23/0.54 => ( X = Y ) ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_inject
% 0.23/0.54 thf(fact_42_dec__induct,axiom,
% 0.23/0.54 ! [I: nat,J: nat,P: nat > $o] :
% 0.23/0.54 ( ( ord_less_eq_nat @ I @ J )
% 0.23/0.54 => ( ( P @ I )
% 0.23/0.54 => ( ! [N2: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ I @ N2 )
% 0.23/0.54 => ( ( ord_less_nat @ N2 @ J )
% 0.23/0.54 => ( ( P @ N2 )
% 0.23/0.54 => ( P @ ( suc @ N2 ) ) ) ) )
% 0.23/0.54 => ( P @ J ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % dec_induct
% 0.23/0.54 thf(fact_43_mem__Collect__eq,axiom,
% 0.23/0.54 ! [A: message_p_v,P: message_p_v > $o] :
% 0.23/0.54 ( ( member_message_p_v @ A @ ( collect_message_p_v @ P ) )
% 0.23/0.54 = ( P @ A ) ) ).
% 0.23/0.54
% 0.23/0.54 % mem_Collect_eq
% 0.23/0.54 thf(fact_44_Collect__mem__eq,axiom,
% 0.23/0.54 ! [A2: set_message_p_v] :
% 0.23/0.54 ( ( collect_message_p_v
% 0.23/0.54 @ ^ [X3: message_p_v] : ( member_message_p_v @ X3 @ A2 ) )
% 0.23/0.54 = A2 ) ).
% 0.23/0.54
% 0.23/0.54 % Collect_mem_eq
% 0.23/0.54 thf(fact_45_Collect__cong,axiom,
% 0.23/0.54 ! [P: message_p_v > $o,Q: message_p_v > $o] :
% 0.23/0.54 ( ! [X4: message_p_v] :
% 0.23/0.54 ( ( P @ X4 )
% 0.23/0.54 = ( Q @ X4 ) )
% 0.23/0.54 => ( ( collect_message_p_v @ P )
% 0.23/0.54 = ( collect_message_p_v @ Q ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Collect_cong
% 0.23/0.54 thf(fact_46_inc__induct,axiom,
% 0.23/0.54 ! [I: nat,J: nat,P: nat > $o] :
% 0.23/0.54 ( ( ord_less_eq_nat @ I @ J )
% 0.23/0.54 => ( ( P @ J )
% 0.23/0.54 => ( ! [N2: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ I @ N2 )
% 0.23/0.54 => ( ( ord_less_nat @ N2 @ J )
% 0.23/0.54 => ( ( P @ ( suc @ N2 ) )
% 0.23/0.54 => ( P @ N2 ) ) ) )
% 0.23/0.54 => ( P @ I ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % inc_induct
% 0.23/0.54 thf(fact_47_le__antisym,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ M @ N )
% 0.23/0.54 => ( ( ord_less_eq_nat @ N @ M )
% 0.23/0.54 => ( M = N ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_antisym
% 0.23/0.54 thf(fact_48_Ex__less__Suc,axiom,
% 0.23/0.54 ! [N: nat,P: nat > $o] :
% 0.23/0.54 ( ( ? [I2: nat] :
% 0.23/0.54 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 0.23/0.54 & ( P @ I2 ) ) )
% 0.23/0.54 = ( ( P @ N )
% 0.23/0.54 | ? [I2: nat] :
% 0.23/0.54 ( ( ord_less_nat @ I2 @ N )
% 0.23/0.54 & ( P @ I2 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Ex_less_Suc
% 0.23/0.54 thf(fact_49_less__Suc__eq,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.23/0.54 = ( ( ord_less_nat @ M @ N )
% 0.23/0.54 | ( M = N ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % less_Suc_eq
% 0.23/0.54 thf(fact_50_n__not__Suc__n,axiom,
% 0.23/0.54 ! [N: nat] :
% 0.23/0.54 ( N
% 0.23/0.54 != ( suc @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % n_not_Suc_n
% 0.23/0.54 thf(fact_51_nat__less__le,axiom,
% 0.23/0.54 ( ord_less_nat
% 0.23/0.54 = ( ^ [M4: nat,N3: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ M4 @ N3 )
% 0.23/0.54 & ( M4 != N3 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % nat_less_le
% 0.23/0.54 thf(fact_52_nat__neq__iff,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( M != N )
% 0.23/0.54 = ( ( ord_less_nat @ M @ N )
% 0.23/0.54 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % nat_neq_iff
% 0.23/0.54 thf(fact_53_not__less__eq,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ~ ( ord_less_nat @ M @ N ) )
% 0.23/0.54 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % not_less_eq
% 0.23/0.54 thf(fact_54_All__less__Suc,axiom,
% 0.23/0.54 ! [N: nat,P: nat > $o] :
% 0.23/0.54 ( ( ! [I2: nat] :
% 0.23/0.54 ( ( ord_less_nat @ I2 @ ( suc @ N ) )
% 0.23/0.54 => ( P @ I2 ) ) )
% 0.23/0.54 = ( ( P @ N )
% 0.23/0.54 & ! [I2: nat] :
% 0.23/0.54 ( ( ord_less_nat @ I2 @ N )
% 0.23/0.54 => ( P @ I2 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % All_less_Suc
% 0.23/0.54 thf(fact_55_Suc__le__lessD,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 0.23/0.54 => ( ord_less_nat @ M @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_le_lessD
% 0.23/0.54 thf(fact_56_Suc__less__eq2,axiom,
% 0.23/0.54 ! [N: nat,M: nat] :
% 0.23/0.54 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 0.23/0.54 = ( ? [M5: nat] :
% 0.23/0.54 ( ( M
% 0.23/0.54 = ( suc @ M5 ) )
% 0.23/0.54 & ( ord_less_nat @ N @ M5 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_less_eq2
% 0.23/0.54 thf(fact_57_less__antisym,axiom,
% 0.23/0.54 ! [N: nat,M: nat] :
% 0.23/0.54 ( ~ ( ord_less_nat @ N @ M )
% 0.23/0.54 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.23/0.54 => ( M = N ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % less_antisym
% 0.23/0.54 thf(fact_58_Suc__less__SucD,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.23/0.54 => ( ord_less_nat @ M @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_less_SucD
% 0.23/0.54 thf(fact_59_less__not__refl,axiom,
% 0.23/0.54 ! [N: nat] :
% 0.23/0.54 ~ ( ord_less_nat @ N @ N ) ).
% 0.23/0.54
% 0.23/0.54 % less_not_refl
% 0.23/0.54 thf(fact_60_nat__le__linear,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ M @ N )
% 0.23/0.54 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.23/0.54
% 0.23/0.54 % nat_le_linear
% 0.23/0.54 thf(fact_61_Suc__n__not__le__n,axiom,
% 0.23/0.54 ! [N: nat] :
% 0.23/0.54 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_n_not_le_n
% 0.23/0.54 thf(fact_62_le__less__Suc__eq,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ M @ N )
% 0.23/0.54 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.23/0.54 = ( N = M ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_less_Suc_eq
% 0.23/0.54 thf(fact_63_less__Suc__eq__le,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 0.23/0.54 = ( ord_less_eq_nat @ M @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % less_Suc_eq_le
% 0.23/0.54 thf(fact_64_less__eq__Suc__le,axiom,
% 0.23/0.54 ( ord_less_nat
% 0.23/0.54 = ( ^ [N3: nat] : ( ord_less_eq_nat @ ( suc @ N3 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % less_eq_Suc_le
% 0.23/0.54 thf(fact_65_less__not__refl2,axiom,
% 0.23/0.54 ! [N: nat,M: nat] :
% 0.23/0.54 ( ( ord_less_nat @ N @ M )
% 0.23/0.54 => ( M != N ) ) ).
% 0.23/0.54
% 0.23/0.54 % less_not_refl2
% 0.23/0.54 thf(fact_66_less__not__refl3,axiom,
% 0.23/0.54 ! [S: nat,T: nat] :
% 0.23/0.54 ( ( ord_less_nat @ S @ T )
% 0.23/0.54 => ( S != T ) ) ).
% 0.23/0.54
% 0.23/0.54 % less_not_refl3
% 0.23/0.54 thf(fact_67_less__trans__Suc,axiom,
% 0.23/0.54 ! [I: nat,J: nat,K: nat] :
% 0.23/0.54 ( ( ord_less_nat @ I @ J )
% 0.23/0.54 => ( ( ord_less_nat @ J @ K )
% 0.23/0.54 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % less_trans_Suc
% 0.23/0.54 thf(fact_68_not__less__eq__eq,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 0.23/0.54 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 0.23/0.54
% 0.23/0.54 % not_less_eq_eq
% 0.23/0.54 thf(fact_69_full__nat__induct,axiom,
% 0.23/0.54 ! [P: nat > $o,N: nat] :
% 0.23/0.54 ( ! [N2: nat] :
% 0.23/0.54 ( ! [M6: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ ( suc @ M6 ) @ N2 )
% 0.23/0.54 => ( P @ M6 ) )
% 0.23/0.54 => ( P @ N2 ) )
% 0.23/0.54 => ( P @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % full_nat_induct
% 0.23/0.54 thf(fact_70_le__imp__less__Suc,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ M @ N )
% 0.23/0.54 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_imp_less_Suc
% 0.23/0.54 thf(fact_71_less__Suc__induct,axiom,
% 0.23/0.54 ! [I: nat,J: nat,P: nat > nat > $o] :
% 0.23/0.54 ( ( ord_less_nat @ I @ J )
% 0.23/0.54 => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 0.23/0.54 => ( ! [I3: nat,J2: nat,K2: nat] :
% 0.23/0.54 ( ( ord_less_nat @ I3 @ J2 )
% 0.23/0.54 => ( ( ord_less_nat @ J2 @ K2 )
% 0.23/0.54 => ( ( P @ I3 @ J2 )
% 0.23/0.54 => ( ( P @ J2 @ K2 )
% 0.23/0.54 => ( P @ I3 @ K2 ) ) ) ) )
% 0.23/0.54 => ( P @ I @ J ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % less_Suc_induct
% 0.23/0.54 thf(fact_72_less__imp__le__nat,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_nat @ M @ N )
% 0.23/0.54 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % less_imp_le_nat
% 0.23/0.54 thf(fact_73_less__irrefl__nat,axiom,
% 0.23/0.54 ! [N: nat] :
% 0.23/0.54 ~ ( ord_less_nat @ N @ N ) ).
% 0.23/0.54
% 0.23/0.54 % less_irrefl_nat
% 0.23/0.54 thf(fact_74_nat__less__induct,axiom,
% 0.23/0.54 ! [P: nat > $o,N: nat] :
% 0.23/0.54 ( ! [N2: nat] :
% 0.23/0.54 ( ! [M6: nat] :
% 0.23/0.54 ( ( ord_less_nat @ M6 @ N2 )
% 0.23/0.54 => ( P @ M6 ) )
% 0.23/0.54 => ( P @ N2 ) )
% 0.23/0.54 => ( P @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % nat_less_induct
% 0.23/0.54 thf(fact_75_infinite__descent,axiom,
% 0.23/0.54 ! [P: nat > $o,N: nat] :
% 0.23/0.54 ( ! [N2: nat] :
% 0.23/0.54 ( ~ ( P @ N2 )
% 0.23/0.54 => ? [M6: nat] :
% 0.23/0.54 ( ( ord_less_nat @ M6 @ N2 )
% 0.23/0.54 & ~ ( P @ M6 ) ) )
% 0.23/0.54 => ( P @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % infinite_descent
% 0.23/0.54 thf(fact_76_le__eq__less__or__eq,axiom,
% 0.23/0.54 ( ord_less_eq_nat
% 0.23/0.54 = ( ^ [M4: nat,N3: nat] :
% 0.23/0.54 ( ( ord_less_nat @ M4 @ N3 )
% 0.23/0.54 | ( M4 = N3 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_eq_less_or_eq
% 0.23/0.54 thf(fact_77_less__or__eq__imp__le,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ( ord_less_nat @ M @ N )
% 0.23/0.54 | ( M = N ) )
% 0.23/0.54 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % less_or_eq_imp_le
% 0.23/0.54 thf(fact_78_linorder__neqE__nat,axiom,
% 0.23/0.54 ! [X: nat,Y: nat] :
% 0.23/0.54 ( ( X != Y )
% 0.23/0.54 => ( ~ ( ord_less_nat @ X @ Y )
% 0.23/0.54 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % linorder_neqE_nat
% 0.23/0.54 thf(fact_79_strict__inc__induct,axiom,
% 0.23/0.54 ! [I: nat,J: nat,P: nat > $o] :
% 0.23/0.54 ( ( ord_less_nat @ I @ J )
% 0.23/0.54 => ( ! [I3: nat] :
% 0.23/0.54 ( ( J
% 0.23/0.54 = ( suc @ I3 ) )
% 0.23/0.54 => ( P @ I3 ) )
% 0.23/0.54 => ( ! [I3: nat] :
% 0.23/0.54 ( ( ord_less_nat @ I3 @ J )
% 0.23/0.54 => ( ( P @ ( suc @ I3 ) )
% 0.23/0.54 => ( P @ I3 ) ) )
% 0.23/0.54 => ( P @ I ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % strict_inc_induct
% 0.23/0.54 thf(fact_80_Nat_Oex__has__greatest__nat,axiom,
% 0.23/0.54 ! [P: nat > $o,K: nat,B: nat] :
% 0.23/0.54 ( ( P @ K )
% 0.23/0.54 => ( ! [Y3: nat] :
% 0.23/0.54 ( ( P @ Y3 )
% 0.23/0.54 => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.23/0.54 => ? [X4: nat] :
% 0.23/0.54 ( ( P @ X4 )
% 0.23/0.54 & ! [Y4: nat] :
% 0.23/0.54 ( ( P @ Y4 )
% 0.23/0.54 => ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Nat.ex_has_greatest_nat
% 0.23/0.54 thf(fact_81_le__neq__implies__less,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ M @ N )
% 0.23/0.54 => ( ( M != N )
% 0.23/0.54 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_neq_implies_less
% 0.23/0.54 thf(fact_82_nat__induct__at__least,axiom,
% 0.23/0.54 ! [M: nat,N: nat,P: nat > $o] :
% 0.23/0.54 ( ( ord_less_eq_nat @ M @ N )
% 0.23/0.54 => ( ( P @ M )
% 0.23/0.54 => ( ! [N2: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ M @ N2 )
% 0.23/0.54 => ( ( P @ N2 )
% 0.23/0.54 => ( P @ ( suc @ N2 ) ) ) )
% 0.23/0.54 => ( P @ N ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % nat_induct_at_least
% 0.23/0.54 thf(fact_83_not__less__less__Suc__eq,axiom,
% 0.23/0.54 ! [N: nat,M: nat] :
% 0.23/0.54 ( ~ ( ord_less_nat @ N @ M )
% 0.23/0.54 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 0.23/0.54 = ( N = M ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % not_less_less_Suc_eq
% 0.23/0.54 thf(fact_84_less__mono__imp__le__mono,axiom,
% 0.23/0.54 ! [F: nat > nat,I: nat,J: nat] :
% 0.23/0.54 ( ! [I3: nat,J2: nat] :
% 0.23/0.54 ( ( ord_less_nat @ I3 @ J2 )
% 0.23/0.54 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 0.23/0.54 => ( ( ord_less_eq_nat @ I @ J )
% 0.23/0.54 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % less_mono_imp_le_mono
% 0.23/0.54 thf(fact_85_transitive__stepwise__le,axiom,
% 0.23/0.54 ! [M: nat,N: nat,R: nat > nat > $o] :
% 0.23/0.54 ( ( ord_less_eq_nat @ M @ N )
% 0.23/0.54 => ( ! [X4: nat] : ( R @ X4 @ X4 )
% 0.23/0.54 => ( ! [X4: nat,Y3: nat,Z: nat] :
% 0.23/0.54 ( ( R @ X4 @ Y3 )
% 0.23/0.54 => ( ( R @ Y3 @ Z )
% 0.23/0.54 => ( R @ X4 @ Z ) ) )
% 0.23/0.54 => ( ! [N2: nat] : ( R @ N2 @ ( suc @ N2 ) )
% 0.23/0.54 => ( R @ M @ N ) ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % transitive_stepwise_le
% 0.23/0.54 thf(fact_86_lift__Suc__mono__le,axiom,
% 0.23/0.54 ! [F: nat > nat,N: nat,N4: nat] :
% 0.23/0.54 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.23/0.54 => ( ( ord_less_eq_nat @ N @ N4 )
% 0.23/0.54 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % lift_Suc_mono_le
% 0.23/0.54 thf(fact_87_lift__Suc__mono__less,axiom,
% 0.23/0.54 ! [F: nat > nat,N: nat,N4: nat] :
% 0.23/0.54 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.23/0.54 => ( ( ord_less_nat @ N @ N4 )
% 0.23/0.54 => ( ord_less_nat @ ( F @ N ) @ ( F @ N4 ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % lift_Suc_mono_less
% 0.23/0.54 thf(fact_88_lift__Suc__antimono__le,axiom,
% 0.23/0.54 ! [F: nat > nat,N: nat,N4: nat] :
% 0.23/0.54 ( ! [N2: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.23/0.54 => ( ( ord_less_eq_nat @ N @ N4 )
% 0.23/0.54 => ( ord_less_eq_nat @ ( F @ N4 ) @ ( F @ N ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % lift_Suc_antimono_le
% 0.23/0.54 thf(fact_89_lift__Suc__mono__less__iff,axiom,
% 0.23/0.54 ! [F: nat > nat,N: nat,M: nat] :
% 0.23/0.54 ( ! [N2: nat] : ( ord_less_nat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.23/0.54 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 0.23/0.54 = ( ord_less_nat @ N @ M ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % lift_Suc_mono_less_iff
% 0.23/0.54 thf(fact_90_diff__less__Suc,axiom,
% 0.23/0.54 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 0.23/0.54
% 0.23/0.54 % diff_less_Suc
% 0.23/0.54 thf(fact_91_Suc__diff__Suc,axiom,
% 0.23/0.54 ! [N: nat,M: nat] :
% 0.23/0.54 ( ( ord_less_nat @ N @ M )
% 0.23/0.54 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 0.23/0.54 = ( minus_minus_nat @ M @ N ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_diff_Suc
% 0.23/0.54 thf(fact_92_Suc__diff__le,axiom,
% 0.23/0.54 ! [N: nat,M: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ N @ M )
% 0.23/0.54 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 0.23/0.54 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Suc_diff_le
% 0.23/0.54 thf(fact_93_zero__induct__lemma,axiom,
% 0.23/0.54 ! [P: nat > $o,K: nat,I: nat] :
% 0.23/0.54 ( ( P @ K )
% 0.23/0.54 => ( ! [N2: nat] :
% 0.23/0.54 ( ( P @ ( suc @ N2 ) )
% 0.23/0.54 => ( P @ N2 ) )
% 0.23/0.54 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % zero_induct_lemma
% 0.23/0.54 thf(fact_94_diff__less__mono,axiom,
% 0.23/0.54 ! [A: nat,B: nat,C: nat] :
% 0.23/0.54 ( ( ord_less_nat @ A @ B )
% 0.23/0.54 => ( ( ord_less_eq_nat @ C @ A )
% 0.23/0.54 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % diff_less_mono
% 0.23/0.54 thf(fact_95_less__diff__iff,axiom,
% 0.23/0.54 ! [K: nat,M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ K @ M )
% 0.23/0.54 => ( ( ord_less_eq_nat @ K @ N )
% 0.23/0.54 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.23/0.54 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % less_diff_iff
% 0.23/0.54 thf(fact_96_diff__Suc__eq__diff__pred,axiom,
% 0.23/0.54 ! [M: nat,N: nat] :
% 0.23/0.54 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 0.23/0.54 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 0.23/0.54
% 0.23/0.54 % diff_Suc_eq_diff_pred
% 0.23/0.54 thf(fact_97_length__induct,axiom,
% 0.23/0.54 ! [P: list_c1059388851t_unit > $o,Xs2: list_c1059388851t_unit] :
% 0.23/0.54 ( ! [Xs: list_c1059388851t_unit] :
% 0.23/0.54 ( ! [Ys2: list_c1059388851t_unit] :
% 0.23/0.54 ( ( ord_less_nat @ ( size_s1406904903t_unit @ Ys2 ) @ ( size_s1406904903t_unit @ Xs ) )
% 0.23/0.54 => ( P @ Ys2 ) )
% 0.23/0.54 => ( P @ Xs ) )
% 0.23/0.54 => ( P @ Xs2 ) ) ).
% 0.23/0.54
% 0.23/0.54 % length_induct
% 0.23/0.54 thf(fact_98_length__induct,axiom,
% 0.23/0.54 ! [P: list_message_p_v > $o,Xs2: list_message_p_v] :
% 0.23/0.54 ( ! [Xs: list_message_p_v] :
% 0.23/0.54 ( ! [Ys2: list_message_p_v] :
% 0.23/0.54 ( ( ord_less_nat @ ( size_s1168481041ge_p_v @ Ys2 ) @ ( size_s1168481041ge_p_v @ Xs ) )
% 0.23/0.54 => ( P @ Ys2 ) )
% 0.23/0.54 => ( P @ Xs ) )
% 0.23/0.54 => ( P @ Xs2 ) ) ).
% 0.23/0.54
% 0.23/0.54 % length_induct
% 0.23/0.54 thf(fact_99_less__imp__diff__less,axiom,
% 0.23/0.54 ! [J: nat,K: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_nat @ J @ K )
% 0.23/0.54 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 0.23/0.54
% 0.23/0.54 % less_imp_diff_less
% 0.23/0.54 thf(fact_100_diff__less__mono2,axiom,
% 0.23/0.54 ! [M: nat,N: nat,L: nat] :
% 0.23/0.54 ( ( ord_less_nat @ M @ N )
% 0.23/0.54 => ( ( ord_less_nat @ M @ L )
% 0.23/0.54 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % diff_less_mono2
% 0.23/0.54 thf(fact_101_diff__le__mono2,axiom,
% 0.23/0.54 ! [M: nat,N: nat,L: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ M @ N )
% 0.23/0.54 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % diff_le_mono2
% 0.23/0.54 thf(fact_102_le__diff__iff_H,axiom,
% 0.23/0.54 ! [A: nat,C: nat,B: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ A @ C )
% 0.23/0.54 => ( ( ord_less_eq_nat @ B @ C )
% 0.23/0.54 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 0.23/0.54 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_diff_iff'
% 0.23/0.54 thf(fact_103_diff__le__self,axiom,
% 0.23/0.54 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 0.23/0.54
% 0.23/0.54 % diff_le_self
% 0.23/0.54 thf(fact_104_diff__le__mono,axiom,
% 0.23/0.54 ! [M: nat,N: nat,L: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ M @ N )
% 0.23/0.54 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % diff_le_mono
% 0.23/0.54 thf(fact_105_Nat_Odiff__diff__eq,axiom,
% 0.23/0.54 ! [K: nat,M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ K @ M )
% 0.23/0.54 => ( ( ord_less_eq_nat @ K @ N )
% 0.23/0.54 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.23/0.54 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Nat.diff_diff_eq
% 0.23/0.54 thf(fact_106_le__diff__iff,axiom,
% 0.23/0.54 ! [K: nat,M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ K @ M )
% 0.23/0.54 => ( ( ord_less_eq_nat @ K @ N )
% 0.23/0.54 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.23/0.54 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % le_diff_iff
% 0.23/0.54 thf(fact_107_eq__diff__iff,axiom,
% 0.23/0.54 ! [K: nat,M: nat,N: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ K @ M )
% 0.23/0.54 => ( ( ord_less_eq_nat @ K @ N )
% 0.23/0.54 => ( ( ( minus_minus_nat @ M @ K )
% 0.23/0.54 = ( minus_minus_nat @ N @ K ) )
% 0.23/0.54 = ( M = N ) ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % eq_diff_iff
% 0.23/0.54 thf(fact_108_one__reorient,axiom,
% 0.23/0.54 ! [X: nat] :
% 0.23/0.54 ( ( one_one_nat = X )
% 0.23/0.54 = ( X = one_one_nat ) ) ).
% 0.23/0.54
% 0.23/0.54 % one_reorient
% 0.23/0.54 thf(fact_109_diff__right__commute,axiom,
% 0.23/0.54 ! [A: nat,C: nat,B: nat] :
% 0.23/0.54 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 0.23/0.54 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 0.23/0.54
% 0.23/0.54 % diff_right_commute
% 0.23/0.54 thf(fact_110_Subset,axiom,
% 0.23/0.54 ! [MsgInSet: message_p_v] :
% 0.23/0.54 ( ( member_message_p_v @ MsgInSet @ ( firstOccSet @ ( suc @ index ) ) )
% 0.23/0.54 => ( member_message_p_v @ MsgInSet @ ( firstOccSet @ index ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % Subset
% 0.23/0.54 thf(fact_111_SameCfgOnLow,axiom,
% 0.23/0.54 ! [I4: nat] :
% 0.23/0.54 ( ( ord_less_nat @ I4 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
% 0.23/0.54 => ( ( nth_co1649820636t_unit @ ( fe @ index ) @ I4 )
% 0.23/0.54 = ( nth_co1649820636t_unit @ ( fe @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % SameCfgOnLow
% 0.23/0.54 thf(fact_112__092_060open_062_092_060not_062_AOccM_A_060_Alength_A_Ift_Aindex_J_092_060close_062,axiom,
% 0.23/0.54 ~ ( ord_less_nat @ occM2 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % \<open>\<not> OccM < length (ft index)\<close>
% 0.23/0.54 thf(fact_113_IPrefixListEx,axiom,
% 0.23/0.54 ! [I4: nat] : ( prefix1615116500t_unit @ ( fe @ I4 ) @ ( fe @ ( suc @ I4 ) ) ) ).
% 0.23/0.54
% 0.23/0.54 % IPrefixListEx
% 0.23/0.54 thf(fact_114_order__refl,axiom,
% 0.23/0.54 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 0.23/0.54
% 0.23/0.54 % order_refl
% 0.23/0.54 thf(fact_115_nat__descend__induct,axiom,
% 0.23/0.54 ! [N: nat,P: nat > $o,M: nat] :
% 0.23/0.54 ( ! [K2: nat] :
% 0.23/0.54 ( ( ord_less_nat @ N @ K2 )
% 0.23/0.54 => ( P @ K2 ) )
% 0.23/0.54 => ( ! [K2: nat] :
% 0.23/0.54 ( ( ord_less_eq_nat @ K2 @ N )
% 0.23/0.55 => ( ! [I4: nat] :
% 0.23/0.55 ( ( ord_less_nat @ K2 @ I4 )
% 0.23/0.55 => ( P @ I4 ) )
% 0.23/0.55 => ( P @ K2 ) ) )
% 0.23/0.55 => ( P @ M ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % nat_descend_induct
% 0.23/0.55 thf(fact_116_KeepProperty,axiom,
% 0.23/0.55 ! [Low: nat,P: nat > $o,Q: nat > $o] :
% 0.23/0.55 ( ! [I3: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ Low @ I3 )
% 0.23/0.55 => ( ( P @ I3 )
% 0.23/0.55 => ( ( P @ ( suc @ I3 ) )
% 0.23/0.55 & ( Q @ I3 ) ) ) )
% 0.23/0.55 => ( ( P @ Low )
% 0.23/0.55 => ! [I4: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ Low @ I4 )
% 0.23/0.55 => ( Q @ I4 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % KeepProperty
% 0.23/0.55 thf(fact_117_less__numeral__extra_I4_J,axiom,
% 0.23/0.55 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.23/0.55
% 0.23/0.55 % less_numeral_extra(4)
% 0.23/0.55 thf(fact_118_le__numeral__extra_I4_J,axiom,
% 0.23/0.55 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 0.23/0.55
% 0.23/0.55 % le_numeral_extra(4)
% 0.23/0.55 thf(fact_119_LengthStep,axiom,
% 0.23/0.55 ord_less_nat @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) @ ( size_s1168481041ge_p_v @ ( ft @ ( suc @ index ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % LengthStep
% 0.23/0.55 thf(fact_120_ConsumedMsg_I1_J,axiom,
% 0.23/0.55 minimalEnabled_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ consumedMsg ).
% 0.23/0.55
% 0.23/0.55 % ConsumedMsg(1)
% 0.23/0.55 thf(fact_121_PrefixListTransitive,axiom,
% 0.23/0.55 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit,L3: list_c1059388851t_unit] :
% 0.23/0.55 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.23/0.55 => ( ( prefix1615116500t_unit @ L2 @ L3 )
% 0.23/0.55 => ( prefix1615116500t_unit @ L1 @ L3 ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % PrefixListTransitive
% 0.23/0.55 thf(fact_122_PrefixListTransitive,axiom,
% 0.23/0.55 ! [L1: list_message_p_v,L2: list_message_p_v,L3: list_message_p_v] :
% 0.23/0.55 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.23/0.55 => ( ( prefix47729710ge_p_v @ L2 @ L3 )
% 0.23/0.55 => ( prefix47729710ge_p_v @ L1 @ L3 ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % PrefixListTransitive
% 0.23/0.55 thf(fact_123_PrefixSameOnLow,axiom,
% 0.23/0.55 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
% 0.23/0.55 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.23/0.55 => ! [Index: nat] :
% 0.23/0.55 ( ( ord_less_nat @ Index @ ( size_s1406904903t_unit @ L1 ) )
% 0.23/0.55 => ( ( nth_co1649820636t_unit @ L1 @ Index )
% 0.23/0.55 = ( nth_co1649820636t_unit @ L2 @ Index ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % PrefixSameOnLow
% 0.23/0.55 thf(fact_124_PrefixSameOnLow,axiom,
% 0.23/0.55 ! [L1: list_message_p_v,L2: list_message_p_v] :
% 0.23/0.55 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.23/0.55 => ! [Index: nat] :
% 0.23/0.55 ( ( ord_less_nat @ Index @ ( size_s1168481041ge_p_v @ L1 ) )
% 0.23/0.55 => ( ( nth_message_p_v @ L1 @ Index )
% 0.23/0.55 = ( nth_message_p_v @ L2 @ Index ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % PrefixSameOnLow
% 0.23/0.55 thf(fact_125_PrefixListMonotonicity,axiom,
% 0.23/0.55 ! [L1: list_c1059388851t_unit,L2: list_c1059388851t_unit] :
% 0.23/0.55 ( ( prefix1615116500t_unit @ L1 @ L2 )
% 0.23/0.55 => ( ord_less_nat @ ( size_s1406904903t_unit @ L1 ) @ ( size_s1406904903t_unit @ L2 ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % PrefixListMonotonicity
% 0.23/0.55 thf(fact_126_PrefixListMonotonicity,axiom,
% 0.23/0.55 ! [L1: list_message_p_v,L2: list_message_p_v] :
% 0.23/0.55 ( ( prefix47729710ge_p_v @ L1 @ L2 )
% 0.23/0.55 => ( ord_less_nat @ ( size_s1168481041ge_p_v @ L1 ) @ ( size_s1168481041ge_p_v @ L2 ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % PrefixListMonotonicity
% 0.23/0.55 thf(fact_127_nth__equalityI,axiom,
% 0.23/0.55 ! [Xs2: list_c1059388851t_unit,Ys: list_c1059388851t_unit] :
% 0.23/0.55 ( ( ( size_s1406904903t_unit @ Xs2 )
% 0.23/0.55 = ( size_s1406904903t_unit @ Ys ) )
% 0.23/0.55 => ( ! [I3: nat] :
% 0.23/0.55 ( ( ord_less_nat @ I3 @ ( size_s1406904903t_unit @ Xs2 ) )
% 0.23/0.55 => ( ( nth_co1649820636t_unit @ Xs2 @ I3 )
% 0.23/0.55 = ( nth_co1649820636t_unit @ Ys @ I3 ) ) )
% 0.23/0.55 => ( Xs2 = Ys ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % nth_equalityI
% 0.23/0.55 thf(fact_128_nth__equalityI,axiom,
% 0.23/0.55 ! [Xs2: list_message_p_v,Ys: list_message_p_v] :
% 0.23/0.55 ( ( ( size_s1168481041ge_p_v @ Xs2 )
% 0.23/0.55 = ( size_s1168481041ge_p_v @ Ys ) )
% 0.23/0.55 => ( ! [I3: nat] :
% 0.23/0.55 ( ( ord_less_nat @ I3 @ ( size_s1168481041ge_p_v @ Xs2 ) )
% 0.23/0.55 => ( ( nth_message_p_v @ Xs2 @ I3 )
% 0.23/0.55 = ( nth_message_p_v @ Ys @ I3 ) ) )
% 0.23/0.55 => ( Xs2 = Ys ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % nth_equalityI
% 0.23/0.55 thf(fact_129_Skolem__list__nth,axiom,
% 0.23/0.55 ! [K: nat,P: nat > config256849571t_unit > $o] :
% 0.23/0.55 ( ( ! [I2: nat] :
% 0.23/0.55 ( ( ord_less_nat @ I2 @ K )
% 0.23/0.55 => ? [X5: config256849571t_unit] : ( P @ I2 @ X5 ) ) )
% 0.23/0.55 = ( ? [Xs3: list_c1059388851t_unit] :
% 0.23/0.55 ( ( ( size_s1406904903t_unit @ Xs3 )
% 0.23/0.55 = K )
% 0.23/0.55 & ! [I2: nat] :
% 0.23/0.55 ( ( ord_less_nat @ I2 @ K )
% 0.23/0.55 => ( P @ I2 @ ( nth_co1649820636t_unit @ Xs3 @ I2 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % Skolem_list_nth
% 0.23/0.55 thf(fact_130_Skolem__list__nth,axiom,
% 0.23/0.55 ! [K: nat,P: nat > message_p_v > $o] :
% 0.23/0.55 ( ( ! [I2: nat] :
% 0.23/0.55 ( ( ord_less_nat @ I2 @ K )
% 0.23/0.55 => ? [X5: message_p_v] : ( P @ I2 @ X5 ) ) )
% 0.23/0.55 = ( ? [Xs3: list_message_p_v] :
% 0.23/0.55 ( ( ( size_s1168481041ge_p_v @ Xs3 )
% 0.23/0.55 = K )
% 0.23/0.55 & ! [I2: nat] :
% 0.23/0.55 ( ( ord_less_nat @ I2 @ K )
% 0.23/0.55 => ( P @ I2 @ ( nth_message_p_v @ Xs3 @ I2 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % Skolem_list_nth
% 0.23/0.55 thf(fact_131_list__eq__iff__nth__eq,axiom,
% 0.23/0.55 ( ( ^ [Y5: list_c1059388851t_unit,Z2: list_c1059388851t_unit] : ( Y5 = Z2 ) )
% 0.23/0.55 = ( ^ [Xs3: list_c1059388851t_unit,Ys3: list_c1059388851t_unit] :
% 0.23/0.55 ( ( ( size_s1406904903t_unit @ Xs3 )
% 0.23/0.55 = ( size_s1406904903t_unit @ Ys3 ) )
% 0.23/0.55 & ! [I2: nat] :
% 0.23/0.55 ( ( ord_less_nat @ I2 @ ( size_s1406904903t_unit @ Xs3 ) )
% 0.23/0.55 => ( ( nth_co1649820636t_unit @ Xs3 @ I2 )
% 0.23/0.55 = ( nth_co1649820636t_unit @ Ys3 @ I2 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % list_eq_iff_nth_eq
% 0.23/0.55 thf(fact_132_list__eq__iff__nth__eq,axiom,
% 0.23/0.55 ( ( ^ [Y5: list_message_p_v,Z2: list_message_p_v] : ( Y5 = Z2 ) )
% 0.23/0.55 = ( ^ [Xs3: list_message_p_v,Ys3: list_message_p_v] :
% 0.23/0.55 ( ( ( size_s1168481041ge_p_v @ Xs3 )
% 0.23/0.55 = ( size_s1168481041ge_p_v @ Ys3 ) )
% 0.23/0.55 & ! [I2: nat] :
% 0.23/0.55 ( ( ord_less_nat @ I2 @ ( size_s1168481041ge_p_v @ Xs3 ) )
% 0.23/0.55 => ( ( nth_message_p_v @ Xs3 @ I2 )
% 0.23/0.55 = ( nth_message_p_v @ Ys3 @ I2 ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % list_eq_iff_nth_eq
% 0.23/0.55 thf(fact_133_dual__order_Oantisym,axiom,
% 0.23/0.55 ! [B: nat,A: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ B @ A )
% 0.23/0.55 => ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.55 => ( A = B ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % dual_order.antisym
% 0.23/0.55 thf(fact_134_dual__order_Oeq__iff,axiom,
% 0.23/0.55 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 0.23/0.55 = ( ^ [A3: nat,B2: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ B2 @ A3 )
% 0.23/0.55 & ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % dual_order.eq_iff
% 0.23/0.55 thf(fact_135_dual__order_Otrans,axiom,
% 0.23/0.55 ! [B: nat,A: nat,C: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ B @ A )
% 0.23/0.55 => ( ( ord_less_eq_nat @ C @ B )
% 0.23/0.55 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % dual_order.trans
% 0.23/0.55 thf(fact_136_linorder__wlog,axiom,
% 0.23/0.55 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.23/0.55 ( ! [A4: nat,B3: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ A4 @ B3 )
% 0.23/0.55 => ( P @ A4 @ B3 ) )
% 0.23/0.55 => ( ! [A4: nat,B3: nat] :
% 0.23/0.55 ( ( P @ B3 @ A4 )
% 0.23/0.55 => ( P @ A4 @ B3 ) )
% 0.23/0.55 => ( P @ A @ B ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % linorder_wlog
% 0.23/0.55 thf(fact_137_dual__order_Orefl,axiom,
% 0.23/0.55 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.23/0.55
% 0.23/0.55 % dual_order.refl
% 0.23/0.55 thf(fact_138_order__trans,axiom,
% 0.23/0.55 ! [X: nat,Y: nat,Z3: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ X @ Y )
% 0.23/0.55 => ( ( ord_less_eq_nat @ Y @ Z3 )
% 0.23/0.55 => ( ord_less_eq_nat @ X @ Z3 ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order_trans
% 0.23/0.55 thf(fact_139_order__class_Oorder_Oantisym,axiom,
% 0.23/0.55 ! [A: nat,B: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.55 => ( ( ord_less_eq_nat @ B @ A )
% 0.23/0.55 => ( A = B ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order_class.order.antisym
% 0.23/0.55 thf(fact_140_ord__le__eq__trans,axiom,
% 0.23/0.55 ! [A: nat,B: nat,C: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.55 => ( ( B = C )
% 0.23/0.55 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % ord_le_eq_trans
% 0.23/0.55 thf(fact_141_ord__eq__le__trans,axiom,
% 0.23/0.55 ! [A: nat,B: nat,C: nat] :
% 0.23/0.55 ( ( A = B )
% 0.23/0.55 => ( ( ord_less_eq_nat @ B @ C )
% 0.23/0.55 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % ord_eq_le_trans
% 0.23/0.55 thf(fact_142_order__class_Oorder_Oeq__iff,axiom,
% 0.23/0.55 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 0.23/0.55 = ( ^ [A3: nat,B2: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ A3 @ B2 )
% 0.23/0.55 & ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order_class.order.eq_iff
% 0.23/0.55 thf(fact_143_antisym__conv,axiom,
% 0.23/0.55 ! [Y: nat,X: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ Y @ X )
% 0.23/0.55 => ( ( ord_less_eq_nat @ X @ Y )
% 0.23/0.55 = ( X = Y ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % antisym_conv
% 0.23/0.55 thf(fact_144_le__cases3,axiom,
% 0.23/0.55 ! [X: nat,Y: nat,Z3: nat] :
% 0.23/0.55 ( ( ( ord_less_eq_nat @ X @ Y )
% 0.23/0.55 => ~ ( ord_less_eq_nat @ Y @ Z3 ) )
% 0.23/0.55 => ( ( ( ord_less_eq_nat @ Y @ X )
% 0.23/0.55 => ~ ( ord_less_eq_nat @ X @ Z3 ) )
% 0.23/0.55 => ( ( ( ord_less_eq_nat @ X @ Z3 )
% 0.23/0.55 => ~ ( ord_less_eq_nat @ Z3 @ Y ) )
% 0.23/0.55 => ( ( ( ord_less_eq_nat @ Z3 @ Y )
% 0.23/0.55 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 0.23/0.55 => ( ( ( ord_less_eq_nat @ Y @ Z3 )
% 0.23/0.55 => ~ ( ord_less_eq_nat @ Z3 @ X ) )
% 0.23/0.55 => ~ ( ( ord_less_eq_nat @ Z3 @ X )
% 0.23/0.55 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % le_cases3
% 0.23/0.55 thf(fact_145_order_Otrans,axiom,
% 0.23/0.55 ! [A: nat,B: nat,C: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.55 => ( ( ord_less_eq_nat @ B @ C )
% 0.23/0.55 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order.trans
% 0.23/0.55 thf(fact_146_le__cases,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ~ ( ord_less_eq_nat @ X @ Y )
% 0.23/0.55 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.23/0.55
% 0.23/0.55 % le_cases
% 0.23/0.55 thf(fact_147_eq__refl,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( X = Y )
% 0.23/0.55 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.23/0.55
% 0.23/0.55 % eq_refl
% 0.23/0.55 thf(fact_148_linear,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ X @ Y )
% 0.23/0.55 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.23/0.55
% 0.23/0.55 % linear
% 0.23/0.55 thf(fact_149_antisym,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ X @ Y )
% 0.23/0.55 => ( ( ord_less_eq_nat @ Y @ X )
% 0.23/0.55 => ( X = Y ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % antisym
% 0.23/0.55 thf(fact_150_eq__iff,axiom,
% 0.23/0.55 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 0.23/0.55 = ( ^ [X3: nat,Y6: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ X3 @ Y6 )
% 0.23/0.55 & ( ord_less_eq_nat @ Y6 @ X3 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % eq_iff
% 0.23/0.55 thf(fact_151_ord__le__eq__subst,axiom,
% 0.23/0.55 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.55 => ( ( ( F @ B )
% 0.23/0.55 = C )
% 0.23/0.55 => ( ! [X4: nat,Y3: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.23/0.55 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.23/0.55 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % ord_le_eq_subst
% 0.23/0.55 thf(fact_152_ord__eq__le__subst,axiom,
% 0.23/0.55 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.23/0.55 ( ( A
% 0.23/0.55 = ( F @ B ) )
% 0.23/0.55 => ( ( ord_less_eq_nat @ B @ C )
% 0.23/0.55 => ( ! [X4: nat,Y3: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.23/0.55 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.23/0.55 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % ord_eq_le_subst
% 0.23/0.55 thf(fact_153_order__subst2,axiom,
% 0.23/0.55 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.55 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.23/0.55 => ( ! [X4: nat,Y3: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.23/0.55 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.23/0.55 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order_subst2
% 0.23/0.55 thf(fact_154_order__subst1,axiom,
% 0.23/0.55 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.23/0.55 => ( ( ord_less_eq_nat @ B @ C )
% 0.23/0.55 => ( ! [X4: nat,Y3: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.23/0.55 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.23/0.55 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order_subst1
% 0.23/0.55 thf(fact_155_dual__order_Ostrict__implies__not__eq,axiom,
% 0.23/0.55 ! [B: nat,A: nat] :
% 0.23/0.55 ( ( ord_less_nat @ B @ A )
% 0.23/0.55 => ( A != B ) ) ).
% 0.23/0.55
% 0.23/0.55 % dual_order.strict_implies_not_eq
% 0.23/0.55 thf(fact_156_order_Ostrict__implies__not__eq,axiom,
% 0.23/0.55 ! [A: nat,B: nat] :
% 0.23/0.55 ( ( ord_less_nat @ A @ B )
% 0.23/0.55 => ( A != B ) ) ).
% 0.23/0.55
% 0.23/0.55 % order.strict_implies_not_eq
% 0.23/0.55 thf(fact_157_not__less__iff__gr__or__eq,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.23/0.55 = ( ( ord_less_nat @ Y @ X )
% 0.23/0.55 | ( X = Y ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % not_less_iff_gr_or_eq
% 0.23/0.55 thf(fact_158_dual__order_Ostrict__trans,axiom,
% 0.23/0.55 ! [B: nat,A: nat,C: nat] :
% 0.23/0.55 ( ( ord_less_nat @ B @ A )
% 0.23/0.55 => ( ( ord_less_nat @ C @ B )
% 0.23/0.55 => ( ord_less_nat @ C @ A ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % dual_order.strict_trans
% 0.23/0.55 thf(fact_159_linorder__less__wlog,axiom,
% 0.23/0.55 ! [P: nat > nat > $o,A: nat,B: nat] :
% 0.23/0.55 ( ! [A4: nat,B3: nat] :
% 0.23/0.55 ( ( ord_less_nat @ A4 @ B3 )
% 0.23/0.55 => ( P @ A4 @ B3 ) )
% 0.23/0.55 => ( ! [A4: nat] : ( P @ A4 @ A4 )
% 0.23/0.55 => ( ! [A4: nat,B3: nat] :
% 0.23/0.55 ( ( P @ B3 @ A4 )
% 0.23/0.55 => ( P @ A4 @ B3 ) )
% 0.23/0.55 => ( P @ A @ B ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % linorder_less_wlog
% 0.23/0.55 thf(fact_160_exists__least__iff,axiom,
% 0.23/0.55 ( ( ^ [P2: nat > $o] :
% 0.23/0.55 ? [X5: nat] : ( P2 @ X5 ) )
% 0.23/0.55 = ( ^ [P3: nat > $o] :
% 0.23/0.55 ? [N3: nat] :
% 0.23/0.55 ( ( P3 @ N3 )
% 0.23/0.55 & ! [M4: nat] :
% 0.23/0.55 ( ( ord_less_nat @ M4 @ N3 )
% 0.23/0.55 => ~ ( P3 @ M4 ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % exists_least_iff
% 0.23/0.55 thf(fact_161_less__imp__not__less,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( ord_less_nat @ X @ Y )
% 0.23/0.55 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_imp_not_less
% 0.23/0.55 thf(fact_162_order_Ostrict__trans,axiom,
% 0.23/0.55 ! [A: nat,B: nat,C: nat] :
% 0.23/0.55 ( ( ord_less_nat @ A @ B )
% 0.23/0.55 => ( ( ord_less_nat @ B @ C )
% 0.23/0.55 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order.strict_trans
% 0.23/0.55 thf(fact_163_dual__order_Oirrefl,axiom,
% 0.23/0.55 ! [A: nat] :
% 0.23/0.55 ~ ( ord_less_nat @ A @ A ) ).
% 0.23/0.55
% 0.23/0.55 % dual_order.irrefl
% 0.23/0.55 thf(fact_164_linorder__cases,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ~ ( ord_less_nat @ X @ Y )
% 0.23/0.55 => ( ( X != Y )
% 0.23/0.55 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % linorder_cases
% 0.23/0.55 thf(fact_165_less__imp__triv,axiom,
% 0.23/0.55 ! [X: nat,Y: nat,P: $o] :
% 0.23/0.55 ( ( ord_less_nat @ X @ Y )
% 0.23/0.55 => ( ( ord_less_nat @ Y @ X )
% 0.23/0.55 => P ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_imp_triv
% 0.23/0.55 thf(fact_166_less__imp__not__eq2,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( ord_less_nat @ X @ Y )
% 0.23/0.55 => ( Y != X ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_imp_not_eq2
% 0.23/0.55 thf(fact_167_antisym__conv3,axiom,
% 0.23/0.55 ! [Y: nat,X: nat] :
% 0.23/0.55 ( ~ ( ord_less_nat @ Y @ X )
% 0.23/0.55 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.23/0.55 = ( X = Y ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % antisym_conv3
% 0.23/0.55 thf(fact_168_less__induct,axiom,
% 0.23/0.55 ! [P: nat > $o,A: nat] :
% 0.23/0.55 ( ! [X4: nat] :
% 0.23/0.55 ( ! [Y4: nat] :
% 0.23/0.55 ( ( ord_less_nat @ Y4 @ X4 )
% 0.23/0.55 => ( P @ Y4 ) )
% 0.23/0.55 => ( P @ X4 ) )
% 0.23/0.55 => ( P @ A ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_induct
% 0.23/0.55 thf(fact_169_less__not__sym,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( ord_less_nat @ X @ Y )
% 0.23/0.55 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_not_sym
% 0.23/0.55 thf(fact_170_less__imp__not__eq,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( ord_less_nat @ X @ Y )
% 0.23/0.55 => ( X != Y ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_imp_not_eq
% 0.23/0.55 thf(fact_171_dual__order_Oasym,axiom,
% 0.23/0.55 ! [B: nat,A: nat] :
% 0.23/0.55 ( ( ord_less_nat @ B @ A )
% 0.23/0.55 => ~ ( ord_less_nat @ A @ B ) ) ).
% 0.23/0.55
% 0.23/0.55 % dual_order.asym
% 0.23/0.55 thf(fact_172_ord__less__eq__trans,axiom,
% 0.23/0.55 ! [A: nat,B: nat,C: nat] :
% 0.23/0.55 ( ( ord_less_nat @ A @ B )
% 0.23/0.55 => ( ( B = C )
% 0.23/0.55 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % ord_less_eq_trans
% 0.23/0.55 thf(fact_173_ord__eq__less__trans,axiom,
% 0.23/0.55 ! [A: nat,B: nat,C: nat] :
% 0.23/0.55 ( ( A = B )
% 0.23/0.55 => ( ( ord_less_nat @ B @ C )
% 0.23/0.55 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % ord_eq_less_trans
% 0.23/0.55 thf(fact_174_less__irrefl,axiom,
% 0.23/0.55 ! [X: nat] :
% 0.23/0.55 ~ ( ord_less_nat @ X @ X ) ).
% 0.23/0.55
% 0.23/0.55 % less_irrefl
% 0.23/0.55 thf(fact_175_less__linear,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( ord_less_nat @ X @ Y )
% 0.23/0.55 | ( X = Y )
% 0.23/0.55 | ( ord_less_nat @ Y @ X ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_linear
% 0.23/0.55 thf(fact_176_less__trans,axiom,
% 0.23/0.55 ! [X: nat,Y: nat,Z3: nat] :
% 0.23/0.55 ( ( ord_less_nat @ X @ Y )
% 0.23/0.55 => ( ( ord_less_nat @ Y @ Z3 )
% 0.23/0.55 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_trans
% 0.23/0.55 thf(fact_177_less__asym_H,axiom,
% 0.23/0.55 ! [A: nat,B: nat] :
% 0.23/0.55 ( ( ord_less_nat @ A @ B )
% 0.23/0.55 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_asym'
% 0.23/0.55 thf(fact_178_less__asym,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( ord_less_nat @ X @ Y )
% 0.23/0.55 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_asym
% 0.23/0.55 thf(fact_179_less__imp__neq,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( ord_less_nat @ X @ Y )
% 0.23/0.55 => ( X != Y ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_imp_neq
% 0.23/0.55 thf(fact_180_order_Oasym,axiom,
% 0.23/0.55 ! [A: nat,B: nat] :
% 0.23/0.55 ( ( ord_less_nat @ A @ B )
% 0.23/0.55 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.23/0.55
% 0.23/0.55 % order.asym
% 0.23/0.55 thf(fact_181_neq__iff,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( X != Y )
% 0.23/0.55 = ( ( ord_less_nat @ X @ Y )
% 0.23/0.55 | ( ord_less_nat @ Y @ X ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % neq_iff
% 0.23/0.55 thf(fact_182_neqE,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( X != Y )
% 0.23/0.55 => ( ~ ( ord_less_nat @ X @ Y )
% 0.23/0.55 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % neqE
% 0.23/0.55 thf(fact_183_gt__ex,axiom,
% 0.23/0.55 ! [X: nat] :
% 0.23/0.55 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 0.23/0.55
% 0.23/0.55 % gt_ex
% 0.23/0.55 thf(fact_184_order__less__subst2,axiom,
% 0.23/0.55 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.23/0.55 ( ( ord_less_nat @ A @ B )
% 0.23/0.55 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.23/0.55 => ( ! [X4: nat,Y3: nat] :
% 0.23/0.55 ( ( ord_less_nat @ X4 @ Y3 )
% 0.23/0.55 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.23/0.55 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order_less_subst2
% 0.23/0.55 thf(fact_185_order__less__subst1,axiom,
% 0.23/0.55 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.23/0.55 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.23/0.55 => ( ( ord_less_nat @ B @ C )
% 0.23/0.55 => ( ! [X4: nat,Y3: nat] :
% 0.23/0.55 ( ( ord_less_nat @ X4 @ Y3 )
% 0.23/0.55 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.23/0.55 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order_less_subst1
% 0.23/0.55 thf(fact_186_ord__less__eq__subst,axiom,
% 0.23/0.55 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.23/0.55 ( ( ord_less_nat @ A @ B )
% 0.23/0.55 => ( ( ( F @ B )
% 0.23/0.55 = C )
% 0.23/0.55 => ( ! [X4: nat,Y3: nat] :
% 0.23/0.55 ( ( ord_less_nat @ X4 @ Y3 )
% 0.23/0.55 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.23/0.55 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % ord_less_eq_subst
% 0.23/0.55 thf(fact_187_ord__eq__less__subst,axiom,
% 0.23/0.55 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.23/0.55 ( ( A
% 0.23/0.55 = ( F @ B ) )
% 0.23/0.55 => ( ( ord_less_nat @ B @ C )
% 0.23/0.55 => ( ! [X4: nat,Y3: nat] :
% 0.23/0.55 ( ( ord_less_nat @ X4 @ Y3 )
% 0.23/0.55 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.23/0.55 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % ord_eq_less_subst
% 0.23/0.55 thf(fact_188_MinPredicate,axiom,
% 0.23/0.55 ! [P: nat > $o] :
% 0.23/0.55 ( ? [X_12: nat] : ( P @ X_12 )
% 0.23/0.55 => ? [N0: nat] :
% 0.23/0.55 ( ( P @ N0 )
% 0.23/0.55 & ! [N5: nat] :
% 0.23/0.55 ( ( P @ N5 )
% 0.23/0.55 => ( ord_less_eq_nat @ N0 @ N5 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % MinPredicate
% 0.23/0.55 thf(fact_189_order_Onot__eq__order__implies__strict,axiom,
% 0.23/0.55 ! [A: nat,B: nat] :
% 0.23/0.55 ( ( A != B )
% 0.23/0.55 => ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.55 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order.not_eq_order_implies_strict
% 0.23/0.55 thf(fact_190_dual__order_Ostrict__implies__order,axiom,
% 0.23/0.55 ! [B: nat,A: nat] :
% 0.23/0.55 ( ( ord_less_nat @ B @ A )
% 0.23/0.55 => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.23/0.55
% 0.23/0.55 % dual_order.strict_implies_order
% 0.23/0.55 thf(fact_191_dual__order_Ostrict__iff__order,axiom,
% 0.23/0.55 ( ord_less_nat
% 0.23/0.55 = ( ^ [B2: nat,A3: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ B2 @ A3 )
% 0.23/0.55 & ( A3 != B2 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % dual_order.strict_iff_order
% 0.23/0.55 thf(fact_192_dual__order_Oorder__iff__strict,axiom,
% 0.23/0.55 ( ord_less_eq_nat
% 0.23/0.55 = ( ^ [B2: nat,A3: nat] :
% 0.23/0.55 ( ( ord_less_nat @ B2 @ A3 )
% 0.23/0.55 | ( A3 = B2 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % dual_order.order_iff_strict
% 0.23/0.55 thf(fact_193_order_Ostrict__implies__order,axiom,
% 0.23/0.55 ! [A: nat,B: nat] :
% 0.23/0.55 ( ( ord_less_nat @ A @ B )
% 0.23/0.55 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.23/0.55
% 0.23/0.55 % order.strict_implies_order
% 0.23/0.55 thf(fact_194_dual__order_Ostrict__trans2,axiom,
% 0.23/0.55 ! [B: nat,A: nat,C: nat] :
% 0.23/0.55 ( ( ord_less_nat @ B @ A )
% 0.23/0.55 => ( ( ord_less_eq_nat @ C @ B )
% 0.23/0.55 => ( ord_less_nat @ C @ A ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % dual_order.strict_trans2
% 0.23/0.55 thf(fact_195_dual__order_Ostrict__trans1,axiom,
% 0.23/0.55 ! [B: nat,A: nat,C: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ B @ A )
% 0.23/0.55 => ( ( ord_less_nat @ C @ B )
% 0.23/0.55 => ( ord_less_nat @ C @ A ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % dual_order.strict_trans1
% 0.23/0.55 thf(fact_196_order_Ostrict__iff__order,axiom,
% 0.23/0.55 ( ord_less_nat
% 0.23/0.55 = ( ^ [A3: nat,B2: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ A3 @ B2 )
% 0.23/0.55 & ( A3 != B2 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order.strict_iff_order
% 0.23/0.55 thf(fact_197_order_Oorder__iff__strict,axiom,
% 0.23/0.55 ( ord_less_eq_nat
% 0.23/0.55 = ( ^ [A3: nat,B2: nat] :
% 0.23/0.55 ( ( ord_less_nat @ A3 @ B2 )
% 0.23/0.55 | ( A3 = B2 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order.order_iff_strict
% 0.23/0.55 thf(fact_198_order_Ostrict__trans2,axiom,
% 0.23/0.55 ! [A: nat,B: nat,C: nat] :
% 0.23/0.55 ( ( ord_less_nat @ A @ B )
% 0.23/0.55 => ( ( ord_less_eq_nat @ B @ C )
% 0.23/0.55 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order.strict_trans2
% 0.23/0.55 thf(fact_199_order_Ostrict__trans1,axiom,
% 0.23/0.55 ! [A: nat,B: nat,C: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.55 => ( ( ord_less_nat @ B @ C )
% 0.23/0.55 => ( ord_less_nat @ A @ C ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order.strict_trans1
% 0.23/0.55 thf(fact_200_not__le__imp__less,axiom,
% 0.23/0.55 ! [Y: nat,X: nat] :
% 0.23/0.55 ( ~ ( ord_less_eq_nat @ Y @ X )
% 0.23/0.55 => ( ord_less_nat @ X @ Y ) ) ).
% 0.23/0.55
% 0.23/0.55 % not_le_imp_less
% 0.23/0.55 thf(fact_201_less__le__not__le,axiom,
% 0.23/0.55 ( ord_less_nat
% 0.23/0.55 = ( ^ [X3: nat,Y6: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ X3 @ Y6 )
% 0.23/0.55 & ~ ( ord_less_eq_nat @ Y6 @ X3 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_le_not_le
% 0.23/0.55 thf(fact_202_le__imp__less__or__eq,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ X @ Y )
% 0.23/0.55 => ( ( ord_less_nat @ X @ Y )
% 0.23/0.55 | ( X = Y ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % le_imp_less_or_eq
% 0.23/0.55 thf(fact_203_le__less__linear,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ X @ Y )
% 0.23/0.55 | ( ord_less_nat @ Y @ X ) ) ).
% 0.23/0.55
% 0.23/0.55 % le_less_linear
% 0.23/0.55 thf(fact_204_less__le__trans,axiom,
% 0.23/0.55 ! [X: nat,Y: nat,Z3: nat] :
% 0.23/0.55 ( ( ord_less_nat @ X @ Y )
% 0.23/0.55 => ( ( ord_less_eq_nat @ Y @ Z3 )
% 0.23/0.55 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_le_trans
% 0.23/0.55 thf(fact_205_le__less__trans,axiom,
% 0.23/0.55 ! [X: nat,Y: nat,Z3: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ X @ Y )
% 0.23/0.55 => ( ( ord_less_nat @ Y @ Z3 )
% 0.23/0.55 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % le_less_trans
% 0.23/0.55 thf(fact_206_less__imp__le,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( ord_less_nat @ X @ Y )
% 0.23/0.55 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_imp_le
% 0.23/0.55 thf(fact_207_antisym__conv2,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ X @ Y )
% 0.23/0.55 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.23/0.55 = ( X = Y ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % antisym_conv2
% 0.23/0.55 thf(fact_208_antisym__conv1,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ~ ( ord_less_nat @ X @ Y )
% 0.23/0.55 => ( ( ord_less_eq_nat @ X @ Y )
% 0.23/0.55 = ( X = Y ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % antisym_conv1
% 0.23/0.55 thf(fact_209_le__neq__trans,axiom,
% 0.23/0.55 ! [A: nat,B: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.55 => ( ( A != B )
% 0.23/0.55 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % le_neq_trans
% 0.23/0.55 thf(fact_210_not__less,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.23/0.55 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.23/0.55
% 0.23/0.55 % not_less
% 0.23/0.55 thf(fact_211_not__le,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 0.23/0.55 = ( ord_less_nat @ Y @ X ) ) ).
% 0.23/0.55
% 0.23/0.55 % not_le
% 0.23/0.55 thf(fact_212_order__less__le__subst2,axiom,
% 0.23/0.55 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.23/0.55 ( ( ord_less_nat @ A @ B )
% 0.23/0.55 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 0.23/0.55 => ( ! [X4: nat,Y3: nat] :
% 0.23/0.55 ( ( ord_less_nat @ X4 @ Y3 )
% 0.23/0.55 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.23/0.55 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order_less_le_subst2
% 0.23/0.55 thf(fact_213_order__less__le__subst1,axiom,
% 0.23/0.55 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.23/0.55 ( ( ord_less_nat @ A @ ( F @ B ) )
% 0.23/0.55 => ( ( ord_less_eq_nat @ B @ C )
% 0.23/0.55 => ( ! [X4: nat,Y3: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.23/0.55 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.23/0.55 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order_less_le_subst1
% 0.23/0.55 thf(fact_214_order__le__less__subst2,axiom,
% 0.23/0.55 ! [A: nat,B: nat,F: nat > nat,C: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.23/0.55 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 0.23/0.55 => ( ! [X4: nat,Y3: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ X4 @ Y3 )
% 0.23/0.55 => ( ord_less_eq_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.23/0.55 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order_le_less_subst2
% 0.23/0.55 thf(fact_215_order__le__less__subst1,axiom,
% 0.23/0.55 ! [A: nat,F: nat > nat,B: nat,C: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 0.23/0.55 => ( ( ord_less_nat @ B @ C )
% 0.23/0.55 => ( ! [X4: nat,Y3: nat] :
% 0.23/0.55 ( ( ord_less_nat @ X4 @ Y3 )
% 0.23/0.55 => ( ord_less_nat @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 0.23/0.55 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % order_le_less_subst1
% 0.23/0.55 thf(fact_216_less__le,axiom,
% 0.23/0.55 ( ord_less_nat
% 0.23/0.55 = ( ^ [X3: nat,Y6: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ X3 @ Y6 )
% 0.23/0.55 & ( X3 != Y6 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % less_le
% 0.23/0.55 thf(fact_217_le__less,axiom,
% 0.23/0.55 ( ord_less_eq_nat
% 0.23/0.55 = ( ^ [X3: nat,Y6: nat] :
% 0.23/0.55 ( ( ord_less_nat @ X3 @ Y6 )
% 0.23/0.55 | ( X3 = Y6 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % le_less
% 0.23/0.55 thf(fact_218_leI,axiom,
% 0.23/0.55 ! [X: nat,Y: nat] :
% 0.23/0.55 ( ~ ( ord_less_nat @ X @ Y )
% 0.23/0.55 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.23/0.55
% 0.23/0.55 % leI
% 0.23/0.55 thf(fact_219_leD,axiom,
% 0.23/0.55 ! [Y: nat,X: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ Y @ X )
% 0.23/0.55 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 0.23/0.55
% 0.23/0.55 % leD
% 0.23/0.55 thf(fact_220_AssumpMinImplAllBigger,axiom,
% 0.23/0.55 minimalEnabled_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ msg ).
% 0.23/0.55
% 0.23/0.55 % AssumpMinImplAllBigger
% 0.23/0.55 thf(fact_221__092_060open_062execution_OfirstOccurrence_A_Ife_Aindex_J_A_Ift_Aindex_J_Amsg_AOccM_092_060close_062,axiom,
% 0.23/0.55 firstO1414030372_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ msga @ occM2 ).
% 0.23/0.55
% 0.23/0.55 % \<open>execution.firstOccurrence (fe index) (ft index) msg OccM\<close>
% 0.23/0.55 thf(fact_222_SameMsgOnLow,axiom,
% 0.23/0.55 ! [I4: nat] :
% 0.23/0.55 ( ( ord_less_nat @ I4 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 0.23/0.55 => ( ( nth_message_p_v @ ( ft @ index ) @ I4 )
% 0.23/0.55 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % SameMsgOnLow
% 0.23/0.55 thf(fact_223_OccM_H_I5_J,axiom,
% 0.23/0.55 ! [N5: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ occM @ N5 )
% 0.23/0.55 => ( ( ord_less_nat @ N5 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 0.23/0.55 => ( msg
% 0.23/0.55 != ( nth_message_p_v @ ( ft @ index ) @ N5 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % OccM'(5)
% 0.23/0.55 thf(fact_224_IPrefixList,axiom,
% 0.23/0.55 ! [I4: nat] : ( prefix47729710ge_p_v @ ( ft @ I4 ) @ ( ft @ ( suc @ I4 ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % IPrefixList
% 0.23/0.55 thf(fact_225_OccM_H_I1_J,axiom,
% 0.23/0.55 ? [P4: p] : ( isReceiverOf_p_v @ P4 @ msg ) ).
% 0.23/0.55
% 0.23/0.55 % OccM'(1)
% 0.23/0.55 thf(fact_226_FirstOccMsg_H,axiom,
% 0.23/0.55 firstO1414030372_p_v_s @ ( fe @ index ) @ ( ft @ index ) @ msg @ occM ).
% 0.23/0.55
% 0.23/0.55 % FirstOccMsg'
% 0.23/0.55 thf(fact_227_AssumpOccMFirstOccurrence_I5_J,axiom,
% 0.23/0.55 ! [N5: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ occM2 @ N5 )
% 0.23/0.55 => ( ( ord_less_nat @ N5 @ ( size_s1168481041ge_p_v @ ( ft @ index ) ) )
% 0.23/0.55 => ( msga
% 0.23/0.55 != ( nth_message_p_v @ ( ft @ index ) @ N5 ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % AssumpOccMFirstOccurrence(5)
% 0.23/0.55 thf(fact_228_OccM_H_I4_J,axiom,
% 0.23/0.55 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ index ) @ occM ) @ msg ).
% 0.23/0.55
% 0.23/0.55 % OccM'(4)
% 0.23/0.55 thf(fact_229_AssumptionFairContr,axiom,
% 0.23/0.55 ! [N5: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ n @ N5 )
% 0.23/0.55 => ! [N02: nat] :
% 0.23/0.55 ( ( ord_less_nat @ N02 @ ( size_s1168481041ge_p_v @ ( ft @ N5 ) ) )
% 0.23/0.55 => ( ( ord_less_eq_nat @ ( size_s1168481041ge_p_v @ ( ft @ n ) ) @ N02 )
% 0.23/0.55 => ( msg2
% 0.23/0.55 != ( nth_message_p_v @ ( ft @ N5 ) @ N02 ) ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % AssumptionFairContr
% 0.23/0.55 thf(fact_230_MessageStaysOrConsumed,axiom,
% 0.23/0.55 ! [N1: nat,N22: nat,N: nat,Msg: message_p_v] :
% 0.23/0.55 ( ( ( ord_less_eq_nat @ N1 @ N22 )
% 0.23/0.55 & ( ord_less_nat @ N22 @ ( size_s1406904903t_unit @ ( fe @ N ) ) )
% 0.23/0.55 & ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ N ) @ N1 ) @ Msg ) )
% 0.23/0.55 => ( ( enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ N ) @ N22 ) @ Msg )
% 0.23/0.55 | ? [N03: nat] :
% 0.23/0.55 ( ( ord_less_eq_nat @ N1 @ N03 )
% 0.23/0.55 & ( ord_less_nat @ N03 @ ( size_s1168481041ge_p_v @ ( ft @ N ) ) )
% 0.23/0.55 & ( ( nth_message_p_v @ ( ft @ N ) @ N03 )
% 0.23/0.55 = Msg ) ) ) ) ).
% 0.23/0.55
% 0.23/0.55 % MessageStaysOrConsumed
% 0.23/0.55 thf(fact_231__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_O_Alength_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Ai_A_092_060and_062_Amsg_____A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062,axiom,
% 0.23/0.55 ~ ? [I4: nat] :
% 0.23/0.55 ( ( ord_less_nat @ I4 @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ ( suc @ index ) ) ) @ one_one_nat ) )
% 0.23/0.55 & ( ord_less_eq_nat @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) @ I4 )
% 0.23/0.60 & ( msg2
% 0.23/0.60 = ( nth_message_p_v @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.23/0.60
% 0.23/0.60 % \<open>\<not> (\<exists>i<length (fe (Suc index)) - 1. length (fe index) - 1 \<le> i \<and> msg__ = ft (Suc index) ! i)\<close>
% 0.23/0.60 thf(fact_232_AssumptionFair_I4_J,axiom,
% 0.23/0.60 isReceiverOf_p_v @ p2 @ msg2 ).
% 0.23/0.60
% 0.23/0.60 % AssumptionFair(4)
% 0.23/0.60 thf(fact_233_AssumpOccMFirstOccurrence_I1_J,axiom,
% 0.23/0.60 ? [P4: p] : ( isReceiverOf_p_v @ P4 @ msga ) ).
% 0.23/0.60
% 0.23/0.60 % AssumpOccMFirstOccurrence(1)
% 0.23/0.60 thf(fact_234_AssumptionFair_I3_J,axiom,
% 0.23/0.60 enabled_p_v_s @ ( nth_co1649820636t_unit @ ( fe @ n ) @ n0 ) @ msg2 ).
% 0.23/0.60
% 0.23/0.60 % AssumptionFair(3)
% 0.23/0.60
% 0.23/0.60 % Conjectures (1)
% 0.23/0.60 thf(conj_0,conjecture,
% 0.23/0.60 ( occM2
% 0.23/0.60 = ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ one_one_nat ) ) ).
% 0.23/0.60
% 0.23/0.60 %------------------------------------------------------------------------------
% 0.23/0.60 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.YaIekxt7gr/cvc5---1.0.5_29467.p...
% 0.23/0.60 (declare-sort $$unsorted 0)
% 0.23/0.60 (declare-sort tptp.list_c1059388851t_unit 0)
% 0.23/0.60 (declare-sort tptp.config256849571t_unit 0)
% 0.23/0.60 (declare-sort tptp.list_message_p_v 0)
% 0.23/0.60 (declare-sort tptp.set_message_p_v 0)
% 0.23/0.60 (declare-sort tptp.message_p_v 0)
% 0.23/0.60 (declare-sort tptp.nat 0)
% 0.23/0.60 (declare-sort tptp.p 0)
% 0.23/0.60 (declare-fun tptp.enabled_p_v_s (tptp.config256849571t_unit tptp.message_p_v) Bool)
% 0.23/0.60 (declare-fun tptp.isReceiverOf_p_v (tptp.p tptp.message_p_v) Bool)
% 0.23/0.60 (declare-fun tptp.firstO1414030372_p_v_s (tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.message_p_v tptp.nat) Bool)
% 0.23/0.60 (declare-fun tptp.minimalEnabled_p_v_s (tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.message_p_v) Bool)
% 0.23/0.60 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.23/0.60 (declare-fun tptp.one_one_nat () tptp.nat)
% 0.23/0.60 (declare-fun tptp.prefix1615116500t_unit (tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit) Bool)
% 0.23/0.60 (declare-fun tptp.prefix47729710ge_p_v (tptp.list_message_p_v tptp.list_message_p_v) Bool)
% 0.23/0.60 (declare-fun tptp.nil_co1338500125t_unit () tptp.list_c1059388851t_unit)
% 0.23/0.60 (declare-fun tptp.nth_co1649820636t_unit (tptp.list_c1059388851t_unit tptp.nat) tptp.config256849571t_unit)
% 0.23/0.60 (declare-fun tptp.nth_message_p_v (tptp.list_message_p_v tptp.nat) tptp.message_p_v)
% 0.23/0.60 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 0.23/0.60 (declare-fun tptp.size_s1406904903t_unit (tptp.list_c1059388851t_unit) tptp.nat)
% 0.23/0.60 (declare-fun tptp.size_s1168481041ge_p_v (tptp.list_message_p_v) tptp.nat)
% 0.23/0.60 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.23/0.60 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.23/0.60 (declare-fun tptp.collect_message_p_v ((-> tptp.message_p_v Bool)) tptp.set_message_p_v)
% 0.23/0.60 (declare-fun tptp.member_message_p_v (tptp.message_p_v tptp.set_message_p_v) Bool)
% 0.23/0.60 (declare-fun tptp.occM () tptp.nat)
% 0.23/0.60 (declare-fun tptp.occM2 () tptp.nat)
% 0.23/0.60 (declare-fun tptp.consumedMsg () tptp.message_p_v)
% 0.23/0.60 (declare-fun tptp.fe (tptp.nat) tptp.list_c1059388851t_unit)
% 0.23/0.60 (declare-fun tptp.firstOccSet (tptp.nat) tptp.set_message_p_v)
% 0.23/0.60 (declare-fun tptp.ft (tptp.nat) tptp.list_message_p_v)
% 0.23/0.60 (declare-fun tptp.index () tptp.nat)
% 0.23/0.60 (declare-fun tptp.msg () tptp.message_p_v)
% 0.23/0.60 (declare-fun tptp.msg2 () tptp.message_p_v)
% 0.23/0.60 (declare-fun tptp.msga () tptp.message_p_v)
% 0.23/0.60 (declare-fun tptp.n0 () tptp.nat)
% 0.23/0.60 (declare-fun tptp.n () tptp.nat)
% 0.23/0.60 (declare-fun tptp.p2 () tptp.p)
% 0.23/0.60 (assert (@ (@ tptp.ord_less_nat tptp.occM2) (@ tptp.size_s1406904903t_unit (@ tptp.fe tptp.index))))
% 0.23/0.60 (assert (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.size_s1406904903t_unit (@ tptp.fe tptp.index))) tptp.one_one_nat)) tptp.occM2))
% 0.23/0.60 (assert (@ (@ tptp.ord_less_nat tptp.occM) (@ tptp.size_s1406904903t_unit (@ tptp.fe tptp.index))))
% 0.23/0.60 (assert (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.size_s1406904903t_unit (@ tptp.fe tptp.index))) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat (@ tptp.size_s1406904903t_unit (@ tptp.fe (@ tptp.suc tptp.index)))) tptp.one_one_nat)))
% 0.23/0.60 (assert (not (= (@ tptp.fe tptp.index) tptp.nil_co1338500125t_unit)))
% 0.23/0.60 (assert (@ (@ tptp.ord_less_nat tptp.n0) (@ tptp.size_s1406904903t_unit (@ tptp.fe tptp.n))))
% 0.23/0.60 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 0.23/0.60 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 0.23/0.60 (assert (forall ((N tptp.nat)) (exists ((Xs tptp.list_c1059388851t_unit)) (= (@ tptp.size_s1406904903t_unit Xs) N))))
% 0.23/0.60 (assert (forall ((N tptp.nat)) (exists ((Xs tptp.list_message_p_v)) (= (@ tptp.size_s1168481041ge_p_v Xs) N))))
% 0.23/0.60 (assert (forall ((Xs2 tptp.list_c1059388851t_unit) (Ys tptp.list_c1059388851t_unit)) (=> (not (= (@ tptp.size_s1406904903t_unit Xs2) (@ tptp.size_s1406904903t_unit Ys))) (not (= Xs2 Ys)))))
% 0.23/0.60 (assert (forall ((Xs2 tptp.list_message_p_v) (Ys tptp.list_message_p_v)) (=> (not (= (@ tptp.size_s1168481041ge_p_v Xs2) (@ tptp.size_s1168481041ge_p_v Ys))) (not (= Xs2 Ys)))))
% 0.23/0.60 (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)))))
% 0.23/0.60 (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)))))
% 0.23/0.60 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X2) (@ tptp.suc Y2)) (= X2 Y2))))
% 0.23/0.60 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 0.23/0.60 (assert (not (= (@ tptp.fe (@ tptp.suc tptp.index)) tptp.nil_co1338500125t_unit)))
% 0.23/0.60 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.23/0.60 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N) M))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N)) K))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 0.23/0.60 (assert (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ _let_1 (@ _let_1 I)) I)))))
% 0.23/0.60 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 0.23/0.60 (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))))))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M _let_1)))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 0.23/0.60 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 0.23/0.60 (assert (forall ((N tptp.nat) (M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M2) (exists ((M3 tptp.nat)) (= M2 (@ tptp.suc M3))))))
% 0.23/0.60 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 0.23/0.60 (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)))))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M _let_1)))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M N))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))))
% 0.23/0.60 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P I) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (=> (@ (@ tptp.ord_less_nat N2) J) (=> (@ P N2) (@ P (@ tptp.suc N2)))))) (@ P J))))))
% 0.23/0.60 (assert (forall ((A tptp.message_p_v) (P (-> tptp.message_p_v Bool))) (= (@ (@ tptp.member_message_p_v A) (@ tptp.collect_message_p_v P)) (@ P A))))
% 0.23/0.60 (assert (forall ((A2 tptp.set_message_p_v)) (= (@ tptp.collect_message_p_v (lambda ((X3 tptp.message_p_v)) (@ (@ tptp.member_message_p_v X3) A2))) A2)))
% 0.23/0.60 (assert (forall ((P (-> tptp.message_p_v Bool)) (Q (-> tptp.message_p_v Bool))) (=> (forall ((X4 tptp.message_p_v)) (= (@ P X4) (@ Q X4))) (= (@ tptp.collect_message_p_v P) (@ tptp.collect_message_p_v Q)))))
% 0.23/0.60 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ P J) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) N2) (=> (@ (@ tptp.ord_less_nat N2) J) (=> (@ P (@ tptp.suc N2)) (@ P N2))))) (@ P I))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 0.23/0.60 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (or (@ P N) (exists ((I2 tptp.nat)) (and (@ (@ tptp.ord_less_nat I2) N) (@ P I2)))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M N))))))
% 0.23/0.60 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 0.23/0.60 (assert (= tptp.ord_less_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M4) N3) (not (= M4 N3))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 0.23/0.60 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.suc N)) (@ P I2))) (and (@ P N) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N) (@ P I2)))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 0.23/0.60 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M5 tptp.nat)) (and (= M (@ tptp.suc M5)) (@ (@ tptp.ord_less_nat N) M5))))))
% 0.23/0.60 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.23/0.60 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 0.23/0.60 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)) (= N M)))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.23/0.60 (assert (= tptp.ord_less_nat (lambda ((N3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N3)) __flatten_var_0))))
% 0.23/0.60 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 0.23/0.60 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 0.23/0.60 (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)))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))))
% 0.23/0.60 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M6)) N2) (@ P M6))) (@ P N2))) (@ P N))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 0.23/0.60 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I3 tptp.nat)) (@ (@ P I3) (@ tptp.suc I3))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I3))) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (=> (@ _let_1 J2) (=> (@ (@ P J2) K2) (@ _let_1 K2))))))) (@ (@ P I) J))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.23/0.60 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.23/0.60 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N2) (@ P M6))) (@ P N2))) (@ P N))))
% 0.23/0.60 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N2 tptp.nat)) (=> (not (@ P N2)) (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N2) (not (@ P M6)))))) (@ P N))))
% 0.23/0.60 (assert (= tptp.ord_less_eq_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (or (@ (@ tptp.ord_less_nat M4) N3) (= M4 N3)))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 0.23/0.60 (assert (forall ((I tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I) J) (=> (forall ((I3 tptp.nat)) (=> (= J (@ tptp.suc I3)) (@ P I3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J) (=> (@ P (@ tptp.suc I3)) (@ P I3)))) (@ P I))))))
% 0.23/0.60 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X4 tptp.nat)) (and (@ P X4) (forall ((Y4 tptp.nat)) (=> (@ P Y4) (@ (@ tptp.ord_less_eq_nat Y4) X4)))))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ P M) (=> (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ P N2) (@ P (@ tptp.suc N2))))) (@ P N))))))
% 0.23/0.60 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N M))))))
% 0.23/0.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J2) (@ (@ tptp.ord_less_nat (@ F I3)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (forall ((X4 tptp.nat)) (@ (@ R X4) X4)) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ R X4))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z) (@ _let_1 Z))))) (=> (forall ((N2 tptp.nat)) (@ (@ R N2) (@ tptp.suc N2))) (@ (@ R M) N)))))))
% 0.23/0.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N4))))))
% 0.23/0.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (=> (@ (@ tptp.ord_less_nat N) N4) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N4))))))
% 0.23/0.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ F N))))))
% 0.23/0.60 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 0.23/0.60 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))))
% 0.23/0.60 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N))))))
% 0.23/0.60 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I tptp.nat)) (=> (@ P K) (=> (forall ((N2 tptp.nat)) (=> (@ P (@ tptp.suc N2)) (@ P N2))) (@ P (@ (@ tptp.minus_minus_nat K) I))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B) C))))))
% 0.23/0.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_nat M) N)))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))))
% 0.23/0.60 (assert (forall ((P (-> tptp.list_c1059388851t_unit Bool)) (Xs2 tptp.list_c1059388851t_unit)) (=> (forall ((Xs tptp.list_c1059388851t_unit)) (=> (forall ((Ys2 tptp.list_c1059388851t_unit)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s1406904903t_unit Ys2)) (@ tptp.size_s1406904903t_unit Xs)) (@ P Ys2))) (@ P Xs))) (@ P Xs2))))
% 0.23/0.60 (assert (forall ((P (-> tptp.list_message_p_v Bool)) (Xs2 tptp.list_message_p_v)) (=> (forall ((Xs tptp.list_message_p_v)) (=> (forall ((Ys2 tptp.list_message_p_v)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s1168481041ge_p_v Ys2)) (@ tptp.size_s1168481041ge_p_v Xs)) (@ P Ys2))) (@ P Xs))) (@ P Xs2))))
% 0.23/0.60 (assert (forall ((J tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N)) K))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 0.23/0.60 (assert (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N) L)))))
% 0.23/0.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))))
% 0.23/0.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 0.23/0.60 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N) K)) (= M N)))))))
% 0.23/0.60 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C)))))
% 0.23/0.60 (assert (forall ((MsgInSet tptp.message_p_v)) (let ((_let_1 (@ tptp.member_message_p_v MsgInSet))) (=> (@ _let_1 (@ tptp.firstOccSet (@ tptp.suc tptp.index))) (@ _let_1 (@ tptp.firstOccSet tptp.index))))))
% 0.23/0.60 (assert (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.fe tptp.index))) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s1406904903t_unit _let_1)) (= (@ (@ tptp.nth_co1649820636t_unit _let_1) I4) (@ (@ tptp.nth_co1649820636t_unit (@ tptp.fe (@ tptp.suc tptp.index))) I4))))))
% 0.23/0.60 (assert (not (@ (@ tptp.ord_less_nat tptp.occM2) (@ tptp.size_s1168481041ge_p_v (@ tptp.ft tptp.index)))))
% 0.23/0.60 (assert (forall ((I4 tptp.nat)) (@ (@ tptp.prefix1615116500t_unit (@ tptp.fe I4)) (@ tptp.fe (@ tptp.suc I4)))))
% 0.23/0.60 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)))
% 0.23/0.60 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (@ P K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I4) (@ P I4))) (@ P K2)))) (@ P M)))))
% 0.23/0.60 (assert (forall ((Low tptp.nat) (P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Low) I3) (=> (@ P I3) (and (@ P (@ tptp.suc I3)) (@ Q I3))))) (=> (@ P Low) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Low) I4) (@ Q I4)))))))
% 0.23/0.60 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 0.23/0.60 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 0.23/0.60 (assert (@ (@ tptp.ord_less_nat (@ tptp.size_s1168481041ge_p_v (@ tptp.ft tptp.index))) (@ tptp.size_s1168481041ge_p_v (@ tptp.ft (@ tptp.suc tptp.index)))))
% 0.23/0.60 (assert (@ (@ (@ tptp.minimalEnabled_p_v_s (@ tptp.fe tptp.index)) (@ tptp.ft tptp.index)) tptp.consumedMsg))
% 0.23/0.60 (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))))))
% 0.23/0.60 (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))))))
% 0.23/0.60 (assert (forall ((L1 tptp.list_c1059388851t_unit) (L2 tptp.list_c1059388851t_unit)) (=> (@ (@ tptp.prefix1615116500t_unit L1) L2) (forall ((Index tptp.nat)) (=> (@ (@ tptp.ord_less_nat Index) (@ tptp.size_s1406904903t_unit L1)) (= (@ (@ tptp.nth_co1649820636t_unit L1) Index) (@ (@ tptp.nth_co1649820636t_unit L2) Index)))))))
% 0.23/0.60 (assert (forall ((L1 tptp.list_message_p_v) (L2 tptp.list_message_p_v)) (=> (@ (@ tptp.prefix47729710ge_p_v L1) L2) (forall ((Index tptp.nat)) (=> (@ (@ tptp.ord_less_nat Index) (@ tptp.size_s1168481041ge_p_v L1)) (= (@ (@ tptp.nth_message_p_v L1) Index) (@ (@ tptp.nth_message_p_v L2) Index)))))))
% 0.23/0.60 (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)))))
% 0.23/0.60 (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)))))
% 0.23/0.60 (assert (forall ((Xs2 tptp.list_c1059388851t_unit) (Ys tptp.list_c1059388851t_unit)) (=> (= (@ tptp.size_s1406904903t_unit Xs2) (@ tptp.size_s1406904903t_unit Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1406904903t_unit Xs2)) (= (@ (@ tptp.nth_co1649820636t_unit Xs2) I3) (@ (@ tptp.nth_co1649820636t_unit Ys) I3)))) (= Xs2 Ys)))))
% 0.23/0.60 (assert (forall ((Xs2 tptp.list_message_p_v) (Ys tptp.list_message_p_v)) (=> (= (@ tptp.size_s1168481041ge_p_v Xs2) (@ tptp.size_s1168481041ge_p_v Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1168481041ge_p_v Xs2)) (= (@ (@ tptp.nth_message_p_v Xs2) I3) (@ (@ tptp.nth_message_p_v Ys) I3)))) (= Xs2 Ys)))))
% 0.23/0.60 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.config256849571t_unit Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X5 tptp.config256849571t_unit)) (@ (@ P I2) X5)))) (exists ((Xs3 tptp.list_c1059388851t_unit)) (and (= (@ tptp.size_s1406904903t_unit Xs3) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_co1649820636t_unit Xs3) I2)))))))))
% 0.23/0.60 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.message_p_v Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X5 tptp.message_p_v)) (@ (@ P I2) X5)))) (exists ((Xs3 tptp.list_message_p_v)) (and (= (@ tptp.size_s1168481041ge_p_v Xs3) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_message_p_v Xs3) I2)))))))))
% 0.23/0.60 (assert (= (lambda ((Y5 tptp.list_c1059388851t_unit) (Z2 tptp.list_c1059388851t_unit)) (= Y5 Z2)) (lambda ((Xs3 tptp.list_c1059388851t_unit) (Ys3 tptp.list_c1059388851t_unit)) (and (= (@ tptp.size_s1406904903t_unit Xs3) (@ tptp.size_s1406904903t_unit Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1406904903t_unit Xs3)) (= (@ (@ tptp.nth_co1649820636t_unit Xs3) I2) (@ (@ tptp.nth_co1649820636t_unit Ys3) I2))))))))
% 0.23/0.60 (assert (= (lambda ((Y5 tptp.list_message_p_v) (Z2 tptp.list_message_p_v)) (= Y5 Z2)) (lambda ((Xs3 tptp.list_message_p_v) (Ys3 tptp.list_message_p_v)) (and (= (@ tptp.size_s1168481041ge_p_v Xs3) (@ tptp.size_s1168481041ge_p_v Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1168481041ge_p_v Xs3)) (= (@ (@ tptp.nth_message_p_v Xs3) I2) (@ (@ tptp.nth_message_p_v Ys3) I2))))))))
% 0.23/0.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 0.23/0.60 (assert (= (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (@ (@ tptp.ord_less_eq_nat A3) B2)))))
% 0.23/0.60 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.23/0.60 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B)))))
% 0.23/0.60 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z3) (@ _let_1 Z3))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A) C)))))
% 0.23/0.60 (assert (= (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (@ (@ tptp.ord_less_eq_nat B2) A3)))))
% 0.23/0.60 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z3))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= X Y)))))
% 0.23/0.60 (assert (= (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2)) (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y6) (@ (@ tptp.ord_less_eq_nat Y6) X3)))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 0.23/0.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (or (@ (@ tptp.ord_less_nat Y) X) (= X Y)))))
% 0.23/0.60 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.23/0.60 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.nat)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B))))))
% 0.23/0.60 (assert (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X5 tptp.nat)) (@ P2 X5))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((N3 tptp.nat)) (and (@ P3 N3) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N3) (not (@ P3 M4)))))))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))))
% 0.23/0.60 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= Y X)))))
% 0.23/0.60 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 0.23/0.60 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y4) X4) (@ P Y4))) (@ P X4))) (@ P A))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 0.23/0.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 0.23/0.60 (assert (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z3) (@ _let_1 Z3))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat Y) X)))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 0.23/0.60 (assert (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_1))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 0.23/0.60 (assert (forall ((P (-> tptp.nat Bool))) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (exists ((N0 tptp.nat)) (and (@ P N0) (forall ((N5 tptp.nat)) (=> (@ P N5) (@ (@ tptp.ord_less_eq_nat N0) N5))))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 0.23/0.60 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 0.23/0.60 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (not (= A3 B2))))))
% 0.23/0.60 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (or (@ (@ tptp.ord_less_nat B2) A3) (= A3 B2)))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 0.23/0.60 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_nat C) A)))))
% 0.23/0.60 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 0.23/0.60 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (not (= A3 B2))))))
% 0.23/0.60 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (or (@ (@ tptp.ord_less_nat A3) B2) (= A3 B2)))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 0.23/0.60 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))))
% 0.23/0.60 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y6) (not (@ (@ tptp.ord_less_eq_nat Y6) X3))))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_nat Y) X))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z3) (@ _let_1 Z3))))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z3) (@ (@ tptp.ord_less_nat X) Z3)))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 0.23/0.60 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 0.23/0.60 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y6) (not (= X3 Y6))))))
% 0.23/0.60 (assert (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (or (@ (@ tptp.ord_less_nat X3) Y6) (= X3 Y6)))))
% 0.23/0.60 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 0.23/0.60 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))))
% 0.23/0.60 (assert (@ (@ (@ tptp.minimalEnabled_p_v_s (@ tptp.fe tptp.index)) (@ tptp.ft tptp.index)) tptp.msg))
% 0.23/0.60 (assert (@ (@ (@ (@ tptp.firstO1414030372_p_v_s (@ tptp.fe tptp.index)) (@ tptp.ft tptp.index)) tptp.msga) tptp.occM2))
% 0.23/0.60 (assert (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.ft tptp.index))) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s1168481041ge_p_v _let_1)) (= (@ (@ tptp.nth_message_p_v _let_1) I4) (@ (@ tptp.nth_message_p_v (@ tptp.ft (@ tptp.suc tptp.index))) I4))))))
% 0.23/0.60 (assert (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.ft tptp.index))) (=> (@ (@ tptp.ord_less_eq_nat tptp.occM) N5) (=> (@ (@ tptp.ord_less_nat N5) (@ tptp.size_s1168481041ge_p_v _let_1)) (not (= tptp.msg (@ (@ tptp.nth_message_p_v _let_1) N5))))))))
% 0.23/0.60 (assert (forall ((I4 tptp.nat)) (@ (@ tptp.prefix47729710ge_p_v (@ tptp.ft I4)) (@ tptp.ft (@ tptp.suc I4)))))
% 0.23/0.60 (assert (exists ((P4 tptp.p)) (@ (@ tptp.isReceiverOf_p_v P4) tptp.msg)))
% 0.23/0.60 (assert (@ (@ (@ (@ tptp.firstO1414030372_p_v_s (@ tptp.fe tptp.index)) (@ tptp.ft tptp.index)) tptp.msg) tptp.occM))
% 0.23/0.60 (assert (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.ft tptp.index))) (=> (@ (@ tptp.ord_less_eq_nat tptp.occM2) N5) (=> (@ (@ tptp.ord_less_nat N5) (@ tptp.size_s1168481041ge_p_v _let_1)) (not (= tptp.msga (@ (@ tptp.nth_message_p_v _let_1) N5))))))))
% 0.23/0.60 (assert (@ (@ tptp.enabled_p_v_s (@ (@ tptp.nth_co1649820636t_unit (@ tptp.fe tptp.index)) tptp.occM)) tptp.msg))
% 0.23/0.60 (assert (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.n) N5) (forall ((N02 tptp.nat)) (let ((_let_1 (@ tptp.ft N5))) (=> (@ (@ tptp.ord_less_nat N02) (@ tptp.size_s1168481041ge_p_v _let_1)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s1168481041ge_p_v (@ tptp.ft tptp.n))) N02) (not (= tptp.msg2 (@ (@ tptp.nth_message_p_v _let_1) N02))))))))))
% 0.23/0.60 (assert (forall ((N1 tptp.nat) (N22 tptp.nat) (N tptp.nat) (Msg tptp.message_p_v)) (let ((_let_1 (@ tptp.fe N))) (let ((_let_2 (@ tptp.nth_co1649820636t_unit _let_1))) (=> (and (@ (@ tptp.ord_less_eq_nat N1) N22) (@ (@ tptp.ord_less_nat N22) (@ tptp.size_s1406904903t_unit _let_1)) (@ (@ tptp.enabled_p_v_s (@ _let_2 N1)) Msg)) (or (@ (@ tptp.enabled_p_v_s (@ _let_2 N22)) Msg) (exists ((N03 tptp.nat)) (let ((_let_1 (@ tptp.ft N))) (and (@ (@ tptp.ord_less_eq_nat N1) N03) (@ (@ tptp.ord_less_nat N03) (@ tptp.size_s1168481041ge_p_v _let_1)) (= (@ (@ tptp.nth_message_p_v _let_1) N03) Msg))))))))))
% 0.23/0.60 (assert (not (exists ((I4 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.index))) (and (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.minus_minus_nat (@ tptp.size_s1406904903t_unit (@ tptp.fe _let_1))) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.size_s1406904903t_unit (@ tptp.fe tptp.index))) tptp.one_one_nat)) I4) (= tptp.msg2 (@ (@ tptp.nth_message_p_v (@ tptp.ft _let_1)) I4)))))))
% 0.23/0.60 (assert (@ (@ tptp.isReceiverOf_p_v tptp.p2) tptp.msg2))
% 0.23/0.60 (assert (exists ((P4 tptp.p)) (@ (@ tptp.isReceiverOf_p_v P4) tptp.msga)))
% 0.23/0.60 (assert (@ (@ tptp.enabled_p_v_s (@ (@ tptp.nth_co1649820636t_unit (@ tptp.fe tptp.n)) tptp.n0)) tptp.msg2))
% 0.23/0.60 (assert (not (= tptp.occM2 (@ (@ tptp.minus_minus_nat (@ tptp.size_s1406904903t_unit (@ tptp.fe tptp.index))) tptp.one_one_nat))))
% 0.23/0.60 (set-info :filename cvc5---1.0.5_29467)
% 0.23/0.60 (check-sat-assuming ( true ))
% 0.23/0.60 ------- get file name : TPTP file name is ITP061^1
% 1.03/1.21 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_29467.smt2...
% 1.03/1.21 --- Run --ho-elim --full-saturate-quant at 10...
% 1.03/1.21 % SZS status Theorem for ITP061^1
% 1.03/1.21 % SZS output start Proof for ITP061^1
% 1.03/1.21 (
% 1.03/1.21 (let ((_let_1 (@ tptp.fe tptp.index))) (let ((_let_2 (@ tptp.size_s1406904903t_unit _let_1))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) tptp.one_one_nat))) (let ((_let_4 (not (= tptp.occM2 _let_3)))) (let ((_let_5 (@ tptp.fe tptp.n))) (let ((_let_6 (@ tptp.ft tptp.index))) (let ((_let_7 (@ (@ tptp.firstO1414030372_p_v_s _let_1) _let_6))) (let ((_let_8 (@ (@ tptp.minimalEnabled_p_v_s _let_1) _let_6))) (let ((_let_9 (@ tptp.suc tptp.index))) (let ((_let_10 (@ tptp.size_s1168481041ge_p_v _let_6))) (let ((_let_11 (@ tptp.ord_less_nat tptp.occM2))) (let ((_let_12 (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)))))) (let ((_let_13 (= tptp.ord_less_nat (lambda ((M4 tptp.nat) (N3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M4) N3) (not (= M4 N3))))))) (let ((_let_14 (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))))))))))) (let ((_let_15 (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))) (let ((_let_16 (@ tptp.fe _let_9))) (let ((_let_17 (@ tptp.ord_less_eq_nat _let_3))) (let ((_let_18 (@ (@ tptp.ord_less_nat tptp.occM) _let_2))) (let ((_let_19 (@ _let_17 tptp.occM2))) (let ((_let_20 (@ _let_11 _let_2))) (let ((_let_21 (ho_60 k_59 (ho_74 k_73 tptp.index)))) (let ((_let_22 (ho_66 (ho_76 k_75 _let_21) tptp.one_one_nat))) (let ((_let_23 (ho_66 k_65 _let_22))) (let ((_let_24 (= _let_21 _let_23))) (let ((_let_25 (ho_66 k_65 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_138))) (let ((_let_26 (= _let_21 _let_25))) (let ((_let_27 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_138 (ho_66 (ho_76 k_75 _let_25) tptp.one_one_nat)))) (let ((_let_28 (not _let_24))) (let ((_let_29 (and (ho_27 (ho_26 k_28 _let_23) _let_21) _let_28))) (let ((_let_30 (= tptp.occM2 _let_21))) (let ((_let_31 (ho_27 (ho_26 k_28 tptp.occM2) _let_21))) (let ((_let_32 (not _let_31))) (let ((_let_33 (= tptp.occM2 _let_22))) (let ((_let_34 (ho_27 (ho_26 k_28 _let_22) tptp.occM2))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33 _let_32 _let_30 _let_29))) (let ((_let_37 (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (ho_66 k_65 I))) (or (not (ho_27 (ho_26 k_28 I) J)) (= I J) (not (ho_27 (ho_26 k_28 J) K)) (= J K) (and (ho_27 (ho_26 k_28 _let_1) K) (not (= K _let_1)))))))) (let ((_let_38 (ASSUME :args (_let_13)))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_12)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_38 :args ((forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (or (not (@ (@ tptp.ord_less_nat I) J)) (not (@ (@ tptp.ord_less_nat J) K)) (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc I))) (or (not (@ (@ tptp.ord_less_eq_nat I) J)) (= I J) (not (@ (@ tptp.ord_less_eq_nat J) K)) (= J K) (and (@ (@ tptp.ord_less_eq_nat _let_1) K) (not (= K _let_1)))))) _let_37))))))) (let ((_let_40 (0))) (let ((_let_41 (forall ((u |u_(-> tptp.nat tptp.message_p_v Bool)|) (e |u_(-> tptp.message_p_v Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.message_p_v Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_90 v ii) (ite (= i ii) e (ho_90 u ii)))))))))) (let ((_let_42 (forall ((x |u_(-> tptp.nat tptp.message_p_v Bool)|) (y |u_(-> tptp.nat tptp.message_p_v Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_90 x z) (ho_90 y z)))) (= x y))))) (let ((_let_43 (forall ((u |u_(-> tptp.config256849571t_unit Bool)|) (e Bool) (i tptp.config256849571t_unit)) (not (forall ((v |u_(-> tptp.config256849571t_unit Bool)|)) (not (forall ((ii tptp.config256849571t_unit)) (= (ho_89 v ii) (ite (= i ii) e (ho_89 u ii)))))))))) (let ((_let_44 (forall ((x |u_(-> tptp.config256849571t_unit Bool)|) (y |u_(-> tptp.config256849571t_unit Bool)|)) (or (not (forall ((z tptp.config256849571t_unit)) (= (ho_89 x z) (ho_89 y z)))) (= x y))))) (let ((_let_45 (forall ((u |u_(-> tptp.set_message_p_v Bool)|) (e Bool) (i tptp.set_message_p_v)) (not (forall ((v |u_(-> tptp.set_message_p_v Bool)|)) (not (forall ((ii tptp.set_message_p_v)) (= (ho_72 v ii) (ite (= i ii) e (ho_72 u ii)))))))))) (let ((_let_46 (forall ((x |u_(-> tptp.set_message_p_v Bool)|) (y |u_(-> tptp.set_message_p_v Bool)|)) (or (not (forall ((z tptp.set_message_p_v)) (= (ho_72 x z) (ho_72 y z)))) (= x y))))) (let ((_let_47 (forall ((u |u_(-> tptp.config256849571t_unit tptp.message_p_v Bool)|) (e |u_(-> tptp.message_p_v Bool)|) (i tptp.config256849571t_unit)) (not (forall ((v |u_(-> tptp.config256849571t_unit tptp.message_p_v Bool)|)) (not (forall ((ii tptp.config256849571t_unit)) (= (ho_98 v ii) (ite (= i ii) e (ho_98 u ii)))))))))) (let ((_let_48 (forall ((x |u_(-> tptp.config256849571t_unit tptp.message_p_v Bool)|) (y |u_(-> tptp.config256849571t_unit tptp.message_p_v Bool)|)) (or (not (forall ((z tptp.config256849571t_unit)) (= (ho_98 x z) (ho_98 y z)))) (= x y))))) (let ((_let_49 (forall ((u |u_(-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.message_p_v Bool)|) (e |u_(-> tptp.list_message_p_v tptp.message_p_v Bool)|) (i tptp.list_c1059388851t_unit)) (not (forall ((v |u_(-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.message_p_v Bool)|)) (not (forall ((ii tptp.list_c1059388851t_unit)) (= (ho_85 v ii) (ite (= i ii) e (ho_85 u ii)))))))))) (let ((_let_50 (forall ((x |u_(-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.message_p_v Bool)|) (y |u_(-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.message_p_v Bool)|)) (or (not (forall ((z tptp.list_c1059388851t_unit)) (= (ho_85 x z) (ho_85 y z)))) (= x y))))) (let ((_let_51 (forall ((u |u_(-> tptp.nat tptp.set_message_p_v)|) (e tptp.set_message_p_v) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.set_message_p_v)|)) (not (forall ((ii tptp.nat)) (= (ho_80 v ii) (ite (= i ii) e (ho_80 u ii)))))))))) (let ((_let_52 (forall ((x |u_(-> tptp.nat tptp.set_message_p_v)|) (y |u_(-> tptp.nat tptp.set_message_p_v)|)) (or (not (forall ((z tptp.nat)) (= (ho_80 x z) (ho_80 y z)))) (= x y))))) (let ((_let_53 (forall ((u |u_(-> _u_(-> tptp.message_p_v Bool)_ tptp.set_message_p_v)|) (e tptp.set_message_p_v) (i |u_(-> tptp.message_p_v Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.message_p_v Bool)_ tptp.set_message_p_v)|)) (not (forall ((ii |u_(-> tptp.message_p_v Bool)|)) (= (ho_78 v ii) (ite (= i ii) e (ho_78 u ii)))))))))) (let ((_let_54 (forall ((x |u_(-> _u_(-> tptp.message_p_v Bool)_ tptp.set_message_p_v)|) (y |u_(-> _u_(-> tptp.message_p_v Bool)_ tptp.set_message_p_v)|)) (or (not (forall ((z |u_(-> tptp.message_p_v Bool)|)) (= (ho_78 x z) (ho_78 y z)))) (= x y))))) (let ((_let_55 (forall ((u |u_(-> tptp.list_message_p_v tptp.message_p_v tptp.nat Bool)|) (e |u_(-> tptp.message_p_v tptp.nat Bool)|) (i tptp.list_message_p_v)) (not (forall ((v |u_(-> tptp.list_message_p_v tptp.message_p_v tptp.nat Bool)|)) (not (forall ((ii tptp.list_message_p_v)) (= (ho_93 v ii) (ite (= i ii) e (ho_93 u ii)))))))))) (let ((_let_56 (forall ((x |u_(-> tptp.list_message_p_v tptp.message_p_v tptp.nat Bool)|) (y |u_(-> tptp.list_message_p_v tptp.message_p_v tptp.nat Bool)|)) (or (not (forall ((z tptp.list_message_p_v)) (= (ho_93 x z) (ho_93 y z)))) (= x y))))) (let ((_let_57 (forall ((u |u_(-> tptp.list_message_p_v tptp.message_p_v Bool)|) (e |u_(-> tptp.message_p_v Bool)|) (i tptp.list_message_p_v)) (not (forall ((v |u_(-> tptp.list_message_p_v tptp.message_p_v Bool)|)) (not (forall ((ii tptp.list_message_p_v)) (= (ho_86 v ii) (ite (= i ii) e (ho_86 u ii)))))))))) (let ((_let_58 (forall ((x |u_(-> tptp.list_message_p_v tptp.message_p_v Bool)|) (y |u_(-> tptp.list_message_p_v tptp.message_p_v Bool)|)) (or (not (forall ((z tptp.list_message_p_v)) (= (ho_86 x z) (ho_86 y z)))) (= x y))))) (let ((_let_59 (forall ((u |u_(-> tptp.nat tptp.nat tptp.nat)|) (e |u_(-> tptp.nat tptp.nat)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_76 v ii) (ite (= i ii) e (ho_76 u ii)))))))))) (let ((_let_60 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_76 x z) (ho_76 y z)))) (= x y))))) (let ((_let_61 (forall ((u |u_(-> tptp.nat tptp.list_c1059388851t_unit)|) (e tptp.list_c1059388851t_unit) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.list_c1059388851t_unit)|)) (not (forall ((ii tptp.nat)) (= (ho_74 v ii) (ite (= i ii) e (ho_74 u ii)))))))))) (let ((_let_62 (forall ((x |u_(-> tptp.nat tptp.list_c1059388851t_unit)|) (y |u_(-> tptp.nat tptp.list_c1059388851t_unit)|)) (or (not (forall ((z tptp.nat)) (= (ho_74 x z) (ho_74 y z)))) (= x y))))) (let ((_let_63 (forall ((u |u_(-> tptp.message_p_v tptp.set_message_p_v Bool)|) (e |u_(-> tptp.set_message_p_v Bool)|) (i tptp.message_p_v)) (not (forall ((v |u_(-> tptp.message_p_v tptp.set_message_p_v Bool)|)) (not (forall ((ii tptp.message_p_v)) (= (ho_71 v ii) (ite (= i ii) e (ho_71 u ii)))))))))) (let ((_let_64 (forall ((x |u_(-> tptp.message_p_v tptp.set_message_p_v Bool)|) (y |u_(-> tptp.message_p_v tptp.set_message_p_v Bool)|)) (or (not (forall ((z tptp.message_p_v)) (= (ho_71 x z) (ho_71 y z)))) (= x y))))) (let ((_let_65 (forall ((u |u_(-> tptp.message_p_v tptp.nat Bool)|) (e |u_(-> tptp.nat Bool)|) (i tptp.message_p_v)) (not (forall ((v |u_(-> tptp.message_p_v tptp.nat Bool)|)) (not (forall ((ii tptp.message_p_v)) (= (ho_94 v ii) (ite (= i ii) e (ho_94 u ii)))))))))) (let ((_let_66 (forall ((x |u_(-> tptp.message_p_v tptp.nat Bool)|) (y |u_(-> tptp.message_p_v tptp.nat Bool)|)) (or (not (forall ((z tptp.message_p_v)) (= (ho_94 x z) (ho_94 y z)))) (= x y))))) (let ((_let_67 (forall ((u |u_(-> tptp.list_c1059388851t_unit Bool)|) (e Bool) (i tptp.list_c1059388851t_unit)) (not (forall ((v |u_(-> tptp.list_c1059388851t_unit Bool)|)) (not (forall ((ii tptp.list_c1059388851t_unit)) (= (ho_55 v ii) (ite (= i ii) e (ho_55 u ii)))))))))) (let ((_let_68 (forall ((x |u_(-> tptp.list_c1059388851t_unit Bool)|) (y |u_(-> tptp.list_c1059388851t_unit Bool)|)) (or (not (forall ((z tptp.list_c1059388851t_unit)) (= (ho_55 x z) (ho_55 y z)))) (= x y))))) (let ((_let_69 (forall ((u |u_(-> tptp.nat tptp.list_message_p_v)|) (e tptp.list_message_p_v) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.list_message_p_v)|)) (not (forall ((ii tptp.nat)) (= (ho_82 v ii) (ite (= i ii) e (ho_82 u ii)))))))))) (let ((_let_70 (forall ((x |u_(-> tptp.nat tptp.list_message_p_v)|) (y |u_(-> tptp.nat tptp.list_message_p_v)|)) (or (not (forall ((z tptp.nat)) (= (ho_82 x z) (ho_82 y z)))) (= x y))))) (let ((_let_71 (forall ((u |u_(-> tptp.message_p_v Bool)|) (e Bool) (i tptp.message_p_v)) (not (forall ((v |u_(-> tptp.message_p_v Bool)|)) (not (forall ((ii tptp.message_p_v)) (= (ho_69 v ii) (ite (= i ii) e (ho_69 u ii)))))))))) (let ((_let_72 (forall ((x |u_(-> tptp.message_p_v Bool)|) (y |u_(-> tptp.message_p_v Bool)|)) (or (not (forall ((z tptp.message_p_v)) (= (ho_69 x z) (ho_69 y z)))) (= x y))))) (let ((_let_73 (forall ((u |u_(-> tptp.set_message_p_v tptp.message_p_v Bool)|) (e |u_(-> tptp.message_p_v Bool)|) (i tptp.set_message_p_v)) (not (forall ((v |u_(-> tptp.set_message_p_v tptp.message_p_v Bool)|)) (not (forall ((ii tptp.set_message_p_v)) (= (ho_68 v ii) (ite (= i ii) e (ho_68 u ii)))))))))) (let ((_let_74 (forall ((x |u_(-> tptp.set_message_p_v tptp.message_p_v Bool)|) (y |u_(-> tptp.set_message_p_v tptp.message_p_v Bool)|)) (or (not (forall ((z tptp.set_message_p_v)) (= (ho_68 x z) (ho_68 y z)))) (= x y))))) (let ((_let_75 (forall ((u |u_(-> tptp.list_c1059388851t_unit tptp.nat tptp.config256849571t_unit)|) (e |u_(-> tptp.nat tptp.config256849571t_unit)|) (i tptp.list_c1059388851t_unit)) (not (forall ((v |u_(-> tptp.list_c1059388851t_unit tptp.nat tptp.config256849571t_unit)|)) (not (forall ((ii tptp.list_c1059388851t_unit)) (= (ho_57 v ii) (ite (= i ii) e (ho_57 u ii)))))))))) (let ((_let_76 (forall ((x |u_(-> tptp.list_c1059388851t_unit tptp.nat tptp.config256849571t_unit)|) (y |u_(-> tptp.list_c1059388851t_unit tptp.nat tptp.config256849571t_unit)|)) (or (not (forall ((z tptp.list_c1059388851t_unit)) (= (ho_57 x z) (ho_57 y z)))) (= x y))))) (let ((_let_77 (forall ((u |u_(-> tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_26 v ii) (ite (= i ii) e (ho_26 u ii)))))))))) (let ((_let_78 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_26 x z) (ho_26 y z)))) (= x y))))) (let ((_let_79 (forall ((u |u_(-> tptp.list_message_p_v tptp.list_message_p_v Bool)|) (e |u_(-> tptp.list_message_p_v Bool)|) (i tptp.list_message_p_v)) (not (forall ((v |u_(-> tptp.list_message_p_v tptp.list_message_p_v Bool)|)) (not (forall ((ii tptp.list_message_p_v)) (= (ho_45 v ii) (ite (= i ii) e (ho_45 u ii)))))))))) (let ((_let_80 (forall ((x |u_(-> tptp.list_message_p_v tptp.list_message_p_v Bool)|) (y |u_(-> tptp.list_message_p_v tptp.list_message_p_v Bool)|)) (or (not (forall ((z tptp.list_message_p_v)) (= (ho_45 x z) (ho_45 y z)))) (= x y))))) (let ((_let_81 (forall ((u |u_(-> tptp.nat tptp.config256849571t_unit)|) (e tptp.config256849571t_unit) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.config256849571t_unit)|)) (not (forall ((ii tptp.nat)) (= (ho_58 v ii) (ite (= i ii) e (ho_58 u ii)))))))))) (let ((_let_82 (forall ((x |u_(-> tptp.nat tptp.config256849571t_unit)|) (y |u_(-> tptp.nat tptp.config256849571t_unit)|)) (or (not (forall ((z tptp.nat)) (= (ho_58 x z) (ho_58 y z)))) (= x y))))) (let ((_let_83 (forall ((u |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.nat Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_36 v ii) (ite (= i ii) e (ho_36 u ii)))))))))) (let ((_let_84 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_36 x z) (ho_36 y z)))) (= x y))))) (let ((_let_85 (forall ((u |u_(-> tptp.nat tptp.nat)|) (e tptp.nat) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_66 v ii) (ite (= i ii) e (ho_66 u ii)))))))))) (let ((_let_86 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_66 x z) (ho_66 y z)))) (= x y))))) (let ((_let_87 (forall ((u |u_(-> tptp.list_message_p_v Bool)|) (e Bool) (i tptp.list_message_p_v)) (not (forall ((v |u_(-> tptp.list_message_p_v Bool)|)) (not (forall ((ii tptp.list_message_p_v)) (= (ho_46 v ii) (ite (= i ii) e (ho_46 u ii)))))))))) (let ((_let_88 (forall ((x |u_(-> tptp.list_message_p_v Bool)|) (y |u_(-> tptp.list_message_p_v Bool)|)) (or (not (forall ((z tptp.list_message_p_v)) (= (ho_46 x z) (ho_46 y z)))) (= x y))))) (let ((_let_89 (forall ((u |u_(-> tptp.nat tptp.message_p_v)|) (e tptp.message_p_v) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.message_p_v)|)) (not (forall ((ii tptp.nat)) (= (ho_49 v ii) (ite (= i ii) e (ho_49 u ii)))))))))) (let ((_let_90 (forall ((x |u_(-> tptp.nat tptp.message_p_v)|) (y |u_(-> tptp.nat tptp.message_p_v)|)) (or (not (forall ((z tptp.nat)) (= (ho_49 x z) (ho_49 y z)))) (= x y))))) (let ((_let_91 (forall ((u |u_(-> tptp.list_message_p_v tptp.nat tptp.message_p_v)|) (e |u_(-> tptp.nat tptp.message_p_v)|) (i tptp.list_message_p_v)) (not (forall ((v |u_(-> tptp.list_message_p_v tptp.nat tptp.message_p_v)|)) (not (forall ((ii tptp.list_message_p_v)) (= (ho_48 v ii) (ite (= i ii) e (ho_48 u ii)))))))))) (let ((_let_92 (forall ((x |u_(-> tptp.list_message_p_v tptp.nat tptp.message_p_v)|) (y |u_(-> tptp.list_message_p_v tptp.nat tptp.message_p_v)|)) (or (not (forall ((z tptp.list_message_p_v)) (= (ho_48 x z) (ho_48 y z)))) (= x y))))) (let ((_let_93 (forall ((u |u_(-> tptp.list_message_p_v tptp.nat)|) (e tptp.nat) (i tptp.list_message_p_v)) (not (forall ((v |u_(-> tptp.list_message_p_v tptp.nat)|)) (not (forall ((ii tptp.list_message_p_v)) (= (ho_51 v ii) (ite (= i ii) e (ho_51 u ii)))))))))) (let ((_let_94 (forall ((x |u_(-> tptp.list_message_p_v tptp.nat)|) (y |u_(-> tptp.list_message_p_v tptp.nat)|)) (or (not (forall ((z tptp.list_message_p_v)) (= (ho_51 x z) (ho_51 y z)))) (= x y))))) (let ((_let_95 (forall ((u |u_(-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)|) (e |u_(-> tptp.list_c1059388851t_unit Bool)|) (i tptp.list_c1059388851t_unit)) (not (forall ((v |u_(-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)|)) (not (forall ((ii tptp.list_c1059388851t_unit)) (= (ho_54 v ii) (ite (= i ii) e (ho_54 u ii)))))))))) (let ((_let_96 (forall ((x |u_(-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)|) (y |u_(-> tptp.list_c1059388851t_unit tptp.list_c1059388851t_unit Bool)|)) (or (not (forall ((z tptp.list_c1059388851t_unit)) (= (ho_54 x z) (ho_54 y z)))) (= x y))))) (let ((_let_97 (forall ((u |u_(-> tptp.nat tptp.config256849571t_unit Bool)|) (e |u_(-> tptp.config256849571t_unit Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.config256849571t_unit Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_88 v ii) (ite (= i ii) e (ho_88 u ii)))))))))) (let ((_let_98 (forall ((x |u_(-> tptp.nat tptp.config256849571t_unit Bool)|) (y |u_(-> tptp.nat tptp.config256849571t_unit Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_88 x z) (ho_88 y z)))) (= x y))))) (let ((_let_99 (forall ((u |u_(-> tptp.nat Bool)|) (e Bool) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_27 v ii) (ite (= i ii) e (ho_27 u ii)))))))))) (let ((_let_100 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_27 x z) (ho_27 y z)))) (= x y))))) (let ((_let_101 (forall ((u |u_(-> tptp.list_c1059388851t_unit tptp.nat)|) (e tptp.nat) (i tptp.list_c1059388851t_unit)) (not (forall ((v |u_(-> tptp.list_c1059388851t_unit tptp.nat)|)) (not (forall ((ii tptp.list_c1059388851t_unit)) (= (ho_60 v ii) (ite (= i ii) e (ho_60 u ii)))))))))) (let ((_let_102 (forall ((x |u_(-> tptp.list_c1059388851t_unit tptp.nat)|) (y |u_(-> tptp.list_c1059388851t_unit tptp.nat)|)) (or (not (forall ((z tptp.list_c1059388851t_unit)) (= (ho_60 x z) (ho_60 y z)))) (= x y))))) (let ((_let_103 (forall ((u |u_(-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.message_p_v tptp.nat Bool)|) (e |u_(-> tptp.list_message_p_v tptp.message_p_v tptp.nat Bool)|) (i tptp.list_c1059388851t_unit)) (not (forall ((v |u_(-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.message_p_v tptp.nat Bool)|)) (not (forall ((ii tptp.list_c1059388851t_unit)) (= (ho_92 v ii) (ite (= i ii) e (ho_92 u ii)))))))))) (let ((_let_104 (forall ((x |u_(-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.message_p_v tptp.nat Bool)|) (y |u_(-> tptp.list_c1059388851t_unit tptp.list_message_p_v tptp.message_p_v tptp.nat Bool)|)) (or (not (forall ((z tptp.list_c1059388851t_unit)) (= (ho_92 x z) (ho_92 y z)))) (= x y))))) (let ((_let_105 (forall ((u |u_(-> tptp.p tptp.message_p_v Bool)|) (e |u_(-> tptp.message_p_v Bool)|) (i tptp.p)) (not (forall ((v |u_(-> tptp.p tptp.message_p_v Bool)|)) (not (forall ((ii tptp.p)) (= (ho_96 v ii) (ite (= i ii) e (ho_96 u ii)))))))))) (let ((_let_106 (forall ((x |u_(-> tptp.p tptp.message_p_v Bool)|) (y |u_(-> tptp.p tptp.message_p_v Bool)|)) (or (not (forall ((z tptp.p)) (= (ho_96 x z) (ho_96 y z)))) (= x y))))) (let ((_let_107 (forall ((BOUND_VARIABLE_11519 tptp.nat) (BOUND_VARIABLE_11520 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_11519 BOUND_VARIABLE_11520))) (= (ho_27 (ho_26 k_25 BOUND_VARIABLE_11519) BOUND_VARIABLE_11520) (or (and (ho_27 (ho_26 k_28 BOUND_VARIABLE_11519) BOUND_VARIABLE_11520) (not _let_1)) _let_1)))))) (let ((_let_108 (forall ((BOUND_VARIABLE_11508 tptp.nat) (BOUND_VARIABLE_11509 tptp.nat)) (= (ho_27 (ho_26 k_29 BOUND_VARIABLE_11508) BOUND_VARIABLE_11509) (and (ho_27 (ho_26 k_28 BOUND_VARIABLE_11508) BOUND_VARIABLE_11509) (not (= BOUND_VARIABLE_11508 BOUND_VARIABLE_11509))))))) (let ((_let_109 (forall ((BOUND_VARIABLE_11496 tptp.nat) (BOUND_VARIABLE_11497 tptp.nat)) (= (ho_27 (ho_26 k_30 BOUND_VARIABLE_11496) BOUND_VARIABLE_11497) (and (ho_27 (ho_26 k_28 BOUND_VARIABLE_11496) BOUND_VARIABLE_11497) (not (ho_27 (ho_26 k_28 BOUND_VARIABLE_11497) BOUND_VARIABLE_11496))))))) (let ((_let_110 (forall ((BOUND_VARIABLE_11484 tptp.nat) (BOUND_VARIABLE_11485 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_11484 BOUND_VARIABLE_11485))) (= (ho_27 (ho_26 k_31 BOUND_VARIABLE_11484) BOUND_VARIABLE_11485) (or (and (ho_27 (ho_26 k_28 BOUND_VARIABLE_11484) BOUND_VARIABLE_11485) (not _let_1)) _let_1)))))) (let ((_let_111 (forall ((BOUND_VARIABLE_11473 tptp.nat) (BOUND_VARIABLE_11474 tptp.nat)) (= (ho_27 (ho_26 k_32 BOUND_VARIABLE_11473) BOUND_VARIABLE_11474) (and (ho_27 (ho_26 k_28 BOUND_VARIABLE_11473) BOUND_VARIABLE_11474) (not (= BOUND_VARIABLE_11473 BOUND_VARIABLE_11474))))))) (let ((_let_112 (forall ((BOUND_VARIABLE_11461 tptp.nat) (BOUND_VARIABLE_11462 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_11461 BOUND_VARIABLE_11462))) (= (ho_27 (ho_26 k_33 BOUND_VARIABLE_11461) BOUND_VARIABLE_11462) (or (and (ho_27 (ho_26 k_28 BOUND_VARIABLE_11461) BOUND_VARIABLE_11462) (not _let_1)) _let_1)))))) (let ((_let_113 (forall ((BOUND_VARIABLE_11450 tptp.nat) (BOUND_VARIABLE_11451 tptp.nat)) (= (ho_27 (ho_26 k_34 BOUND_VARIABLE_11450) BOUND_VARIABLE_11451) (and (ho_27 (ho_26 k_28 BOUND_VARIABLE_11450) BOUND_VARIABLE_11451) (not (= BOUND_VARIABLE_11450 BOUND_VARIABLE_11451))))))) (let ((_let_114 (forall ((BOUND_VARIABLE_11677 |u_(-> tptp.nat Bool)|)) (= (ho_36 k_35 BOUND_VARIABLE_11677) (not (forall ((X5 tptp.nat)) (not (ho_27 BOUND_VARIABLE_11677 X5)))))))) (let ((_let_115 (forall ((BOUND_VARIABLE_11692 |u_(-> tptp.nat Bool)|)) (= (ho_36 k_37 BOUND_VARIABLE_11692) (not (forall ((N3 tptp.nat)) (or (not (ho_27 BOUND_VARIABLE_11692 N3)) (not (forall ((M4 tptp.nat)) (or (not (ho_27 (ho_26 k_28 M4) N3)) (= N3 M4) (not (ho_27 BOUND_VARIABLE_11692 M4)))))))))))) (let ((_let_116 (forall ((BOUND_VARIABLE_11419 tptp.nat) (BOUND_VARIABLE_11420 tptp.nat)) (= (= BOUND_VARIABLE_11419 BOUND_VARIABLE_11420) (ho_27 (ho_26 k_38 BOUND_VARIABLE_11419) BOUND_VARIABLE_11420))))) (let ((_let_117 (forall ((BOUND_VARIABLE_11408 tptp.nat) (BOUND_VARIABLE_11409 tptp.nat)) (= (ho_27 (ho_26 k_39 BOUND_VARIABLE_11408) BOUND_VARIABLE_11409) (and (ho_27 (ho_26 k_28 BOUND_VARIABLE_11408) BOUND_VARIABLE_11409) (ho_27 (ho_26 k_28 BOUND_VARIABLE_11409) BOUND_VARIABLE_11408)))))) (let ((_let_118 (forall ((BOUND_VARIABLE_11401 tptp.nat) (BOUND_VARIABLE_11402 tptp.nat)) (= (= BOUND_VARIABLE_11401 BOUND_VARIABLE_11402) (ho_27 (ho_26 k_40 BOUND_VARIABLE_11401) BOUND_VARIABLE_11402))))) (let ((_let_119 (forall ((BOUND_VARIABLE_11390 tptp.nat) (BOUND_VARIABLE_11391 tptp.nat)) (= (ho_27 (ho_26 k_41 BOUND_VARIABLE_11390) BOUND_VARIABLE_11391) (and (ho_27 (ho_26 k_28 BOUND_VARIABLE_11390) BOUND_VARIABLE_11391) (ho_27 (ho_26 k_28 BOUND_VARIABLE_11391) BOUND_VARIABLE_11390)))))) (let ((_let_120 (forall ((BOUND_VARIABLE_11383 tptp.nat) (BOUND_VARIABLE_11384 tptp.nat)) (= (= BOUND_VARIABLE_11383 BOUND_VARIABLE_11384) (ho_27 (ho_26 k_42 BOUND_VARIABLE_11383) BOUND_VARIABLE_11384))))) (let ((_let_121 (forall ((BOUND_VARIABLE_11372 tptp.nat) (BOUND_VARIABLE_11373 tptp.nat)) (= (ho_27 (ho_26 k_43 BOUND_VARIABLE_11372) BOUND_VARIABLE_11373) (and (ho_27 (ho_26 k_28 BOUND_VARIABLE_11373) BOUND_VARIABLE_11372) (ho_27 (ho_26 k_28 BOUND_VARIABLE_11372) BOUND_VARIABLE_11373)))))) (let ((_let_122 (forall ((BOUND_VARIABLE_11365 tptp.list_message_p_v) (BOUND_VARIABLE_11366 tptp.list_message_p_v)) (= (= BOUND_VARIABLE_11365 BOUND_VARIABLE_11366) (ho_46 (ho_45 k_44 BOUND_VARIABLE_11365) BOUND_VARIABLE_11366))))) (let ((_let_123 (forall ((BOUND_VARIABLE_11345 tptp.list_message_p_v) (BOUND_VARIABLE_11346 tptp.list_message_p_v)) (= (ho_46 (ho_45 k_52 BOUND_VARIABLE_11345) BOUND_VARIABLE_11346) (and (= (ho_51 k_50 BOUND_VARIABLE_11345) (ho_51 k_50 BOUND_VARIABLE_11346)) (forall ((I2 tptp.nat)) (let ((_let_1 (ho_51 k_50 BOUND_VARIABLE_11345))) (or (not (ho_27 (ho_26 k_28 I2) _let_1)) (= I2 _let_1) (= (ho_49 (ho_48 k_47 BOUND_VARIABLE_11346) I2) (ho_49 (ho_48 k_47 BOUND_VARIABLE_11345) I2)))))))))) (let ((_let_124 (forall ((BOUND_VARIABLE_11338 tptp.list_c1059388851t_unit) (BOUND_VARIABLE_11339 tptp.list_c1059388851t_unit)) (= (= BOUND_VARIABLE_11338 BOUND_VARIABLE_11339) (ho_55 (ho_54 k_53 BOUND_VARIABLE_11338) BOUND_VARIABLE_11339))))) (let ((_let_125 (forall ((BOUND_VARIABLE_11318 tptp.list_c1059388851t_unit) (BOUND_VARIABLE_11319 tptp.list_c1059388851t_unit)) (= (ho_55 (ho_54 k_61 BOUND_VARIABLE_11318) BOUND_VARIABLE_11319) (and (= (ho_60 k_59 BOUND_VARIABLE_11318) (ho_60 k_59 BOUND_VARIABLE_11319)) (forall ((I2 tptp.nat)) (let ((_let_1 (ho_60 k_59 BOUND_VARIABLE_11318))) (or (not (ho_27 (ho_26 k_28 I2) _let_1)) (= I2 _let_1) (= (ho_58 (ho_57 k_56 BOUND_VARIABLE_11319) I2) (ho_58 (ho_57 k_56 BOUND_VARIABLE_11318) I2)))))))))) (let ((_let_126 (forall ((BOUND_VARIABLE_11306 tptp.nat) (BOUND_VARIABLE_11307 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_11306 BOUND_VARIABLE_11307))) (= (ho_27 (ho_26 k_62 BOUND_VARIABLE_11306) BOUND_VARIABLE_11307) (or (and (ho_27 (ho_26 k_28 BOUND_VARIABLE_11306) BOUND_VARIABLE_11307) (not _let_1)) _let_1)))))) (let ((_let_127 (forall ((BOUND_VARIABLE_11295 tptp.nat) (BOUND_VARIABLE_11296 tptp.nat)) (= (ho_27 (ho_26 k_63 BOUND_VARIABLE_11295) BOUND_VARIABLE_11296) (and (ho_27 (ho_26 k_28 BOUND_VARIABLE_11295) BOUND_VARIABLE_11296) (not (= BOUND_VARIABLE_11295 BOUND_VARIABLE_11296))))))) (let ((_let_128 (forall ((BOUND_VARIABLE_11286 tptp.nat) (BOUND_VARIABLE_11287 tptp.nat)) (= (ho_27 (ho_26 k_64 BOUND_VARIABLE_11286) BOUND_VARIABLE_11287) (ho_27 (ho_26 k_28 (ho_66 k_65 BOUND_VARIABLE_11286)) BOUND_VARIABLE_11287))))) (let ((_let_129 (forall ((BOUND_VARIABLE_11278 tptp.set_message_p_v) (BOUND_VARIABLE_11279 tptp.message_p_v)) (= (ho_69 (ho_68 k_67 BOUND_VARIABLE_11278) BOUND_VARIABLE_11279) (ho_72 (ho_71 k_70 BOUND_VARIABLE_11279) BOUND_VARIABLE_11278))))) (let ((_let_130 (not _let_30))) (let ((_let_131 (forall ((BOUND_VARIABLE_11519 tptp.nat) (BOUND_VARIABLE_11520 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_11519 BOUND_VARIABLE_11520))) (= (or (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_11519) BOUND_VARIABLE_11520) (not _let_1)) _let_1) (ll_24 BOUND_VARIABLE_11519 BOUND_VARIABLE_11520)))))) (let ((_let_132 (forall ((BOUND_VARIABLE_11508 tptp.nat) (BOUND_VARIABLE_11509 tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_11508) BOUND_VARIABLE_11509) (not (= BOUND_VARIABLE_11508 BOUND_VARIABLE_11509))) (ll_23 BOUND_VARIABLE_11508 BOUND_VARIABLE_11509))))) (let ((_let_133 (forall ((BOUND_VARIABLE_11496 tptp.nat) (BOUND_VARIABLE_11497 tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_11496) BOUND_VARIABLE_11497) (not (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_11497) BOUND_VARIABLE_11496))) (ll_22 BOUND_VARIABLE_11496 BOUND_VARIABLE_11497))))) (let ((_let_134 (forall ((BOUND_VARIABLE_11484 tptp.nat) (BOUND_VARIABLE_11485 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_11484 BOUND_VARIABLE_11485))) (= (or (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_11484) BOUND_VARIABLE_11485) (not _let_1)) _let_1) (ll_21 BOUND_VARIABLE_11484 BOUND_VARIABLE_11485)))))) (let ((_let_135 (forall ((BOUND_VARIABLE_11473 tptp.nat) (BOUND_VARIABLE_11474 tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_11473) BOUND_VARIABLE_11474) (not (= BOUND_VARIABLE_11473 BOUND_VARIABLE_11474))) (ll_20 BOUND_VARIABLE_11473 BOUND_VARIABLE_11474))))) (let ((_let_136 (forall ((BOUND_VARIABLE_11461 tptp.nat) (BOUND_VARIABLE_11462 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_11461 BOUND_VARIABLE_11462))) (= (or (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_11461) BOUND_VARIABLE_11462) (not _let_1)) _let_1) (ll_19 BOUND_VARIABLE_11461 BOUND_VARIABLE_11462)))))) (let ((_let_137 (forall ((BOUND_VARIABLE_11450 tptp.nat) (BOUND_VARIABLE_11451 tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_11450) BOUND_VARIABLE_11451) (not (= BOUND_VARIABLE_11450 BOUND_VARIABLE_11451))) (ll_18 BOUND_VARIABLE_11450 BOUND_VARIABLE_11451))))) (let ((_let_138 (forall ((BOUND_VARIABLE_11441 (-> tptp.nat Bool))) (= (not (forall ((X5 tptp.nat)) (not (@ BOUND_VARIABLE_11441 X5)))) (ll_17 BOUND_VARIABLE_11441))))) (let ((_let_139 (forall ((BOUND_VARIABLE_11426 (-> tptp.nat Bool))) (= (not (forall ((N3 tptp.nat)) (or (not (@ BOUND_VARIABLE_11426 N3)) (not (forall ((M4 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M4) N3)) (= N3 M4) (not (@ BOUND_VARIABLE_11426 M4)))))))) (ll_16 BOUND_VARIABLE_11426))))) (let ((_let_140 (forall ((BOUND_VARIABLE_11419 tptp.nat) (BOUND_VARIABLE_11420 tptp.nat)) (= (= BOUND_VARIABLE_11419 BOUND_VARIABLE_11420) (ll_15 BOUND_VARIABLE_11419 BOUND_VARIABLE_11420))))) (let ((_let_141 (forall ((BOUND_VARIABLE_11408 tptp.nat) (BOUND_VARIABLE_11409 tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_11408) BOUND_VARIABLE_11409) (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_11409) BOUND_VARIABLE_11408)) (ll_14 BOUND_VARIABLE_11408 BOUND_VARIABLE_11409))))) (let ((_let_142 (forall ((BOUND_VARIABLE_11401 tptp.nat) (BOUND_VARIABLE_11402 tptp.nat)) (= (= BOUND_VARIABLE_11401 BOUND_VARIABLE_11402) (ll_13 BOUND_VARIABLE_11401 BOUND_VARIABLE_11402))))) (let ((_let_143 (forall ((BOUND_VARIABLE_11390 tptp.nat) (BOUND_VARIABLE_11391 tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_11390) BOUND_VARIABLE_11391) (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_11391) BOUND_VARIABLE_11390)) (ll_12 BOUND_VARIABLE_11390 BOUND_VARIABLE_11391))))) (let ((_let_144 (forall ((BOUND_VARIABLE_11383 tptp.nat) (BOUND_VARIABLE_11384 tptp.nat)) (= (= BOUND_VARIABLE_11383 BOUND_VARIABLE_11384) (ll_11 BOUND_VARIABLE_11383 BOUND_VARIABLE_11384))))) (let ((_let_145 (forall ((BOUND_VARIABLE_11372 tptp.nat) (BOUND_VARIABLE_11373 tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_11373) BOUND_VARIABLE_11372) (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_11372) BOUND_VARIABLE_11373)) (ll_10 BOUND_VARIABLE_11372 BOUND_VARIABLE_11373))))) (let ((_let_146 (forall ((BOUND_VARIABLE_11365 tptp.list_message_p_v) (BOUND_VARIABLE_11366 tptp.list_message_p_v)) (= (= BOUND_VARIABLE_11365 BOUND_VARIABLE_11366) (ll_9 BOUND_VARIABLE_11365 BOUND_VARIABLE_11366))))) (let ((_let_147 (forall ((BOUND_VARIABLE_11345 tptp.list_message_p_v) (BOUND_VARIABLE_11346 tptp.list_message_p_v)) (= (ll_8 BOUND_VARIABLE_11345 BOUND_VARIABLE_11346) (and (= (@ tptp.size_s1168481041ge_p_v BOUND_VARIABLE_11345) (@ tptp.size_s1168481041ge_p_v BOUND_VARIABLE_11346)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.size_s1168481041ge_p_v BOUND_VARIABLE_11345))) (or (not (@ (@ tptp.ord_less_eq_nat I2) _let_1)) (= I2 _let_1) (= (@ (@ tptp.nth_message_p_v BOUND_VARIABLE_11345) I2) (@ (@ tptp.nth_message_p_v BOUND_VARIABLE_11346) I2)))))))))) (let ((_let_148 (forall ((BOUND_VARIABLE_11338 tptp.list_c1059388851t_unit) (BOUND_VARIABLE_11339 tptp.list_c1059388851t_unit)) (= (= BOUND_VARIABLE_11338 BOUND_VARIABLE_11339) (ll_7 BOUND_VARIABLE_11338 BOUND_VARIABLE_11339))))) (let ((_let_149 (forall ((BOUND_VARIABLE_11318 tptp.list_c1059388851t_unit) (BOUND_VARIABLE_11319 tptp.list_c1059388851t_unit)) (= (ll_6 BOUND_VARIABLE_11318 BOUND_VARIABLE_11319) (and (= (@ tptp.size_s1406904903t_unit BOUND_VARIABLE_11318) (@ tptp.size_s1406904903t_unit BOUND_VARIABLE_11319)) (forall ((I2 tptp.nat)) (let ((_let_1 (@ tptp.size_s1406904903t_unit BOUND_VARIABLE_11318))) (or (not (@ (@ tptp.ord_less_eq_nat I2) _let_1)) (= I2 _let_1) (= (@ (@ tptp.nth_co1649820636t_unit BOUND_VARIABLE_11318) I2) (@ (@ tptp.nth_co1649820636t_unit BOUND_VARIABLE_11319) I2)))))))))) (let ((_let_150 (forall ((BOUND_VARIABLE_11306 tptp.nat) (BOUND_VARIABLE_11307 tptp.nat)) (let ((_let_1 (= BOUND_VARIABLE_11306 BOUND_VARIABLE_11307))) (= (or (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_11306) BOUND_VARIABLE_11307) (not _let_1)) _let_1) (ll_5 BOUND_VARIABLE_11306 BOUND_VARIABLE_11307)))))) (let ((_let_151 (forall ((BOUND_VARIABLE_11295 tptp.nat) (BOUND_VARIABLE_11296 tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat BOUND_VARIABLE_11295) BOUND_VARIABLE_11296) (not (= BOUND_VARIABLE_11295 BOUND_VARIABLE_11296))) (ll_4 BOUND_VARIABLE_11295 BOUND_VARIABLE_11296))))) (let ((_let_152 (forall ((BOUND_VARIABLE_11286 tptp.nat) (BOUND_VARIABLE_11287 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc BOUND_VARIABLE_11286)) BOUND_VARIABLE_11287) (ll_3 BOUND_VARIABLE_11286 BOUND_VARIABLE_11287))))) (let ((_let_153 (forall ((BOUND_VARIABLE_11278 tptp.set_message_p_v) (BOUND_VARIABLE_11279 tptp.message_p_v)) (= (@ (@ tptp.member_message_p_v BOUND_VARIABLE_11279) BOUND_VARIABLE_11278) (ll_2 BOUND_VARIABLE_11278 BOUND_VARIABLE_11279))))) (let ((_let_154 (and (@ (@ tptp.ord_less_eq_nat tptp.occM2) _let_2) (not (= tptp.occM2 _let_2)) _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131))) (let ((_let_155 (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO _let_38 :args (_let_20 SB_DEFAULT SBA_FIXPOINT))) (PREPROCESS :args ((and _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131)))) :args (_let_154)) (PREPROCESS :args ((= _let_154 (and _let_31 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107))))) (PREPROCESS :args ((and _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41)))) :args ((and _let_31 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41))))) (let ((_let_156 (1))) (let ((_let_157 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_29 1)) :args ((or _let_28 (not _let_29)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_30 _let_33 _let_32 _let_35 _let_29 (not _let_36)))) (AND_ELIM _let_155 :args _let_156) (EQ_RESOLVE (ASSUME :args (_let_4)) (PREPROCESS :args ((= _let_4 (not _let_33))))) (AND_ELIM _let_155 :args _let_40) (EQ_RESOLVE (ASSUME :args (_let_19)) (PREPROCESS :args ((= _let_19 _let_34)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_39 :args (_let_22 tptp.occM2 _let_21 QUANTIFIERS_INST_E_MATCHING ((not (= (ho_27 (ho_26 k_28 I) J) false)) (not (= (ho_27 (ho_26 k_28 J) K) false))))) :args (_let_37)))) _let_39 :args (_let_36 false _let_37)) :args (_let_29 true _let_30 true _let_33 false _let_31 false _let_34 false _let_36)) :args (_let_28 false _let_29)))) (let ((_let_158 (not _let_26))) (let ((_let_159 (ho_26 k_28 tptp.occM))) (let ((_let_160 (or (not (ho_27 _let_159 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_138)) (= tptp.occM SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_138) _let_158))) (let ((_let_161 (forall ((J2 tptp.nat)) (or (not (ho_27 (ho_26 k_28 tptp.occM) J2)) (= tptp.occM J2) (not (= (ho_60 k_59 (ho_74 k_73 tptp.index)) (ho_66 k_65 J2))))))) (let ((_let_162 (not _let_160))) (let ((_let_163 (not _let_161))) (let ((_let_164 (ho_66 k_65 tptp.occM))) (let ((_let_165 (= _let_21 _let_164))) (let ((_let_166 (= tptp.occM _let_21))) (let ((_let_167 (ho_27 _let_159 _let_21))) (let ((_let_168 (not _let_167))) (let ((_let_169 (or _let_168 _let_166 _let_165 _let_163))) (let ((_let_170 (forall ((I tptp.nat) (K tptp.nat)) (or (not (ho_27 (ho_26 k_28 I) K)) (= I K) (= K (ho_66 k_65 I)) (not (forall ((J2 tptp.nat)) (or (not (ho_27 (ho_26 k_28 I) J2)) (= I J2) (not (= K (ho_66 k_65 J2)))))))))) (let ((_let_171 (EQ_RESOLVE (ASSUME :args (_let_14)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_38 :args ((forall ((I tptp.nat) (K tptp.nat)) (or (not (@ (@ tptp.ord_less_nat I) K)) (= K (@ tptp.suc I)) (not (forall ((J2 tptp.nat)) (or (not (@ (@ tptp.ord_less_nat I) J2)) (not (= K (@ tptp.suc J2)))))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((I tptp.nat) (K tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat I) K)) (= I K) (= K (@ tptp.suc I)) (not (forall ((J2 tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat I) J2)) (= I J2) (not (= K (@ tptp.suc J2)))))))) _let_170))))))) (let ((_let_172 (= tptp.occM _let_22))) (let ((_let_173 (= tptp.occM (ho_66 (ho_76 k_75 _let_164) tptp.one_one_nat)))) (let ((_let_174 (not _let_165))) (let ((_let_175 (and _let_165 _let_172))) (let ((_let_176 (APPLY_UF ho_66))) (let ((_let_177 (ASSUME :args (_let_172)))) (let ((_let_178 (REFL :args (k_65)))) (let ((_let_179 (ASSUME :args (_let_165)))) (let ((_let_180 (SYMM _let_179))) (let ((_let_181 (forall ((N tptp.nat)) (= N (ho_66 (ho_76 k_75 (ho_66 k_65 N)) tptp.one_one_nat))))) (let ((_let_182 (EQ_RESOLVE (ASSUME :args (_let_15)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((N tptp.nat)) (= N (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat))) _let_181))))))) (let ((_let_183 (_let_181))) (let ((_let_184 (and _let_165 _let_173))) (let ((_let_185 (_let_165 _let_173))) (let ((_let_186 (REFL :args (tptp.one_one_nat)))) (let ((_let_187 (APPLY_UF ho_76))) (let ((_let_188 (REFL :args (k_75)))) (let ((_let_189 (ASSUME :args 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tptp.nat) (N4 tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N2))) (@ F N2))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (@ (@ tptp.ord_less_eq_nat (@ F N4)) (@ F N))))) (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F (@ tptp.suc N2)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N))))) (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I tptp.nat)) (=> (@ P K) (=> (forall ((N2 tptp.nat)) (=> (@ P (@ 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Ys2))) (@ P Xs))) (@ P Xs2))) (forall ((P (-> tptp.list_message_p_v Bool)) (Xs2 tptp.list_message_p_v)) (=> (forall ((Xs tptp.list_message_p_v)) (=> (forall ((Ys2 tptp.list_message_p_v)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s1168481041ge_p_v Ys2)) (@ tptp.size_s1168481041ge_p_v Xs)) (@ P Ys2))) (@ P Xs))) (@ P Xs2))) (forall ((J tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N)) K))) (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))) (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)) (forall ((M tptp.nat) (N tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N) L)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M) N)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N) K)) (= M N)))))) (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C)))) (forall ((MsgInSet tptp.message_p_v)) (let ((_let_1 (@ tptp.member_message_p_v MsgInSet))) (=> (@ _let_1 (@ tptp.firstOccSet (@ tptp.suc tptp.index))) (@ _let_1 (@ tptp.firstOccSet tptp.index))))) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.fe tptp.index))) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s1406904903t_unit _let_1)) (= (@ (@ tptp.nth_co1649820636t_unit _let_1) I4) (@ (@ tptp.nth_co1649820636t_unit (@ tptp.fe (@ tptp.suc tptp.index))) I4))))) (not (@ _let_11 _let_10)) (forall ((I4 tptp.nat)) (@ (@ tptp.prefix1615116500t_unit (@ tptp.fe I4)) (@ tptp.fe (@ tptp.suc I4)))) (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)) (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K2) (@ P K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I4) (@ P I4))) (@ P K2)))) (@ P M)))) (forall ((Low tptp.nat) (P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Low) I3) (=> (@ P I3) (and (@ P (@ tptp.suc I3)) (@ Q I3))))) (=> (@ P Low) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Low) I4) (@ Q I4)))))) (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat) (@ (@ tptp.ord_less_nat _let_10) (@ tptp.size_s1168481041ge_p_v (@ tptp.ft _let_9))) (@ _let_8 tptp.consumedMsg) (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))))) (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)) (=> (@ (@ tptp.prefix1615116500t_unit L1) L2) (forall ((Index tptp.nat)) (=> (@ (@ tptp.ord_less_nat Index) (@ tptp.size_s1406904903t_unit L1)) (= (@ (@ tptp.nth_co1649820636t_unit L1) Index) (@ (@ tptp.nth_co1649820636t_unit L2) Index)))))) (forall ((L1 tptp.list_message_p_v) (L2 tptp.list_message_p_v)) (=> (@ (@ tptp.prefix47729710ge_p_v L1) L2) (forall ((Index tptp.nat)) (=> (@ (@ tptp.ord_less_nat Index) (@ tptp.size_s1168481041ge_p_v L1)) (= (@ (@ tptp.nth_message_p_v L1) Index) (@ (@ tptp.nth_message_p_v L2) Index)))))) (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 ((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 ((Xs2 tptp.list_c1059388851t_unit) (Ys tptp.list_c1059388851t_unit)) (=> (= (@ tptp.size_s1406904903t_unit Xs2) (@ tptp.size_s1406904903t_unit Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1406904903t_unit Xs2)) (= (@ (@ tptp.nth_co1649820636t_unit Xs2) I3) (@ (@ tptp.nth_co1649820636t_unit Ys) I3)))) (= Xs2 Ys)))) (forall ((Xs2 tptp.list_message_p_v) (Ys tptp.list_message_p_v)) (=> (= (@ tptp.size_s1168481041ge_p_v Xs2) (@ tptp.size_s1168481041ge_p_v Ys)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s1168481041ge_p_v Xs2)) (= (@ (@ tptp.nth_message_p_v Xs2) I3) (@ (@ tptp.nth_message_p_v Ys) I3)))) (= Xs2 Ys)))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.config256849571t_unit Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X5 tptp.config256849571t_unit)) (@ (@ P I2) X5)))) (exists ((Xs3 tptp.list_c1059388851t_unit)) (and (= (@ tptp.size_s1406904903t_unit Xs3) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_co1649820636t_unit Xs3) I2)))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.message_p_v Bool))) (= (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (exists ((X5 tptp.message_p_v)) (@ (@ P I2) X5)))) (exists ((Xs3 tptp.list_message_p_v)) (and (= (@ tptp.size_s1168481041ge_p_v Xs3) K) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (@ (@ P I2) (@ (@ tptp.nth_message_p_v Xs3) I2)))))))) (= (lambda ((Y5 tptp.list_c1059388851t_unit) (Z2 tptp.list_c1059388851t_unit)) (= Y5 Z2)) (lambda ((Xs3 tptp.list_c1059388851t_unit) (Ys3 tptp.list_c1059388851t_unit)) (and (= (@ tptp.size_s1406904903t_unit Xs3) (@ tptp.size_s1406904903t_unit Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1406904903t_unit Xs3)) (= (@ (@ tptp.nth_co1649820636t_unit Xs3) I2) (@ (@ tptp.nth_co1649820636t_unit Ys3) I2))))))) (= (lambda ((Y5 tptp.list_message_p_v) (Z2 tptp.list_message_p_v)) (= Y5 Z2)) (lambda ((Xs3 tptp.list_message_p_v) (Ys3 tptp.list_message_p_v)) (and (= (@ tptp.size_s1168481041ge_p_v Xs3) (@ tptp.size_s1168481041ge_p_v Ys3)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_s1168481041ge_p_v Xs3)) (= (@ (@ tptp.nth_message_p_v Xs3) I2) (@ (@ tptp.nth_message_p_v Ys3) I2))))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))) (= (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (@ (@ tptp.ord_less_eq_nat A3) B2)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B)))) (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z3) (@ _let_1 Z3))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A) C)))) (= (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (@ (@ tptp.ord_less_eq_nat B2) A3)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z3))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z3))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z3))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= X Y)))) (= (lambda ((Y5 tptp.nat) (Z2 tptp.nat)) (= Y5 Z2)) (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y6) (@ (@ tptp.ord_less_eq_nat Y6) X3)))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (or (@ (@ tptp.ord_less_nat Y) X) (= X Y)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B3) (@ (@ P A4) B3))) (=> (forall ((A4 tptp.nat)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.nat) (B3 tptp.nat)) (=> (@ (@ P B3) A4) (@ (@ P A4) B3))) (@ (@ P A) B))))) (= (lambda ((P2 (-> tptp.nat Bool))) (exists ((X5 tptp.nat)) (@ P2 X5))) (lambda ((P3 (-> tptp.nat Bool))) (exists ((N3 tptp.nat)) (and (@ P3 N3) (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N3) (not (@ P3 M4)))))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= Y X)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))) (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X4 tptp.nat)) (=> (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y4) X4) (@ P Y4))) (@ P X4))) (@ P A))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))) (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))) (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z3) (@ _let_1 Z3))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))) (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_1))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (= (@ F B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))) (forall ((P (-> tptp.nat Bool))) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (exists ((N0 tptp.nat)) (and (@ P N0) (forall ((N5 tptp.nat)) (=> (@ P N5) (@ (@ tptp.ord_less_eq_nat N0) N5))))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))) (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (not (= A3 B2))))) (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (or (@ (@ tptp.ord_less_nat B2) A3) (= A3 B2)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_nat C) A)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))) (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (not (= A3 B2))))) (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (or (@ (@ tptp.ord_less_nat A3) B2) (= A3 B2)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))) (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y6) (not (@ (@ tptp.ord_less_eq_nat Y6) X3))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_nat Y) X))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z3) (@ _let_1 Z3))))) (forall ((X tptp.nat) (Y tptp.nat) (Z3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z3) (@ (@ tptp.ord_less_nat X) Z3)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ _let_1 (@ F C))))))) (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))) (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X4 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y3) (@ (@ tptp.ord_less_nat (@ F X4)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))) (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y6) (not (= X3 Y6))))) (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y6 tptp.nat)) (or (@ (@ tptp.ord_less_nat X3) Y6) (= X3 Y6)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))) (@ _let_8 tptp.msg) (@ (@ _let_7 tptp.msga) tptp.occM2) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.ft tptp.index))) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s1168481041ge_p_v _let_1)) (= (@ (@ tptp.nth_message_p_v _let_1) I4) (@ (@ tptp.nth_message_p_v (@ tptp.ft (@ tptp.suc tptp.index))) I4))))) (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.ft tptp.index))) (=> (@ (@ tptp.ord_less_eq_nat tptp.occM) N5) (=> (@ (@ tptp.ord_less_nat N5) (@ tptp.size_s1168481041ge_p_v _let_1)) (not (= tptp.msg (@ (@ tptp.nth_message_p_v _let_1) N5))))))) (forall ((I4 tptp.nat)) (@ (@ tptp.prefix47729710ge_p_v (@ tptp.ft I4)) (@ tptp.ft (@ tptp.suc I4)))) (exists ((P4 tptp.p)) (@ (@ tptp.isReceiverOf_p_v P4) tptp.msg)) (@ (@ _let_7 tptp.msg) tptp.occM) (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.ft tptp.index))) (=> (@ (@ tptp.ord_less_eq_nat tptp.occM2) N5) (=> (@ (@ tptp.ord_less_nat N5) (@ tptp.size_s1168481041ge_p_v _let_1)) (not (= tptp.msga (@ (@ tptp.nth_message_p_v _let_1) N5))))))) (@ (@ tptp.enabled_p_v_s (@ (@ tptp.nth_co1649820636t_unit _let_1) tptp.occM)) tptp.msg) (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.n) N5) (forall ((N02 tptp.nat)) (let ((_let_1 (@ tptp.ft N5))) (=> (@ (@ tptp.ord_less_nat N02) (@ tptp.size_s1168481041ge_p_v _let_1)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s1168481041ge_p_v (@ tptp.ft tptp.n))) N02) (not (= tptp.msg2 (@ (@ tptp.nth_message_p_v _let_1) N02))))))))) (forall ((N1 tptp.nat) (N22 tptp.nat) (N tptp.nat) (Msg tptp.message_p_v)) (let ((_let_1 (@ tptp.fe N))) (let ((_let_2 (@ tptp.nth_co1649820636t_unit _let_1))) (=> (and (@ (@ tptp.ord_less_eq_nat N1) N22) (@ (@ tptp.ord_less_nat N22) (@ tptp.size_s1406904903t_unit _let_1)) (@ (@ tptp.enabled_p_v_s (@ _let_2 N1)) Msg)) (or (@ (@ tptp.enabled_p_v_s (@ _let_2 N22)) Msg) (exists ((N03 tptp.nat)) (let ((_let_1 (@ tptp.ft N))) (and (@ (@ tptp.ord_less_eq_nat N1) N03) (@ (@ tptp.ord_less_nat N03) (@ tptp.size_s1168481041ge_p_v _let_1)) (= (@ (@ tptp.nth_message_p_v _let_1) N03) Msg))))))))) (not (exists ((I4 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.index))) (and (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.minus_minus_nat (@ tptp.size_s1406904903t_unit (@ tptp.fe _let_1))) tptp.one_one_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat (@ tptp.size_s1406904903t_unit (@ tptp.fe tptp.index))) tptp.one_one_nat)) I4) (= tptp.msg2 (@ (@ tptp.nth_message_p_v (@ tptp.ft _let_1)) I4)))))) (@ (@ tptp.isReceiverOf_p_v tptp.p2) tptp.msg2) (exists ((P4 tptp.p)) (@ (@ tptp.isReceiverOf_p_v P4) tptp.msga)) (@ (@ tptp.enabled_p_v_s (@ (@ tptp.nth_co1649820636t_unit _let_5) tptp.n0)) tptp.msg2) _let_4 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.03/1.22 )
% 1.03/1.22 % SZS output end Proof for ITP061^1
% 1.03/1.22 % cvc5---1.0.5 exiting
% 1.03/1.22 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------