%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP054^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n025.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 : Wed Feb 25 08:55:11 AM UTC 2026
% Result : Theorem 20.43s 4.29s
% Output : Refutation 20.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP054^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n025.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:24:57 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.49 ---- Original DTF file ---
% 0.29/0.49 thf(spec,logic,$$dhol).
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 % File : ITP054^2 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.49 % Domain : Interactive Theorem Proving
% 0.29/0.49 % Problem : Sledgehammer FLPTheorem problem prob_1046__3303610_1
% 0.29/0.49 % Version : Especial.
% 0.29/0.49 % English :
% 0.29/0.49
% 0.29/0.49 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.49 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.49 % Source : [Des21]
% 0.29/0.49 % Names : FLPTheorem/prob_1046__3303610_1 [Des21]
% 0.29/0.49
% 0.29/0.49 % Status : Theorem
% 0.29/0.49 % Rating : 0.33 v9.1.0, 0.00 v7.5.0
% 0.29/0.49 % Syntax : Number of formulae : 325 ( 125 unt; 54 typ; 0 def)
% 0.29/0.49 % Number of atoms : 612 ( 218 equ; 0 cnn)
% 0.29/0.49 % Maximal formula atoms : 7 ( 2 avg)
% 0.29/0.49 % Number of connectives : 3563 ( 81 ~; 15 |; 44 &;3121 @)
% 0.29/0.49 % ( 0 <=>; 302 =>; 0 <=; 0 <~>)
% 0.29/0.49 % Maximal formula depth : 21 ( 7 avg)
% 0.29/0.49 % Number of types : 6 ( 5 usr)
% 0.29/0.49 % Number of type conns : 176 ( 176 >; 0 *; 0 +; 0 <<)
% 0.29/0.49 % Number of symbols : 52 ( 49 usr; 9 con; 0-7 aty)
% 0.29/0.49 % Number of variables : 692 ( 23 ^; 591 !; 35 ?; 692 :)
% 0.29/0.49 % ( 43 !>; 0 ?*; 0 @-; 0 @+)
% 0.29/0.49 % SPC : TH1_THM_EQU_NAR
% 0.29/0.49
% 0.29/0.49 % Comments : This file was generated by Sledgehammer 2021-02-23 16:17:16.937
% 0.29/0.49 %------------------------------------------------------------------------------
% 0.29/0.49 % Could-be-implicit typings (9)
% 0.29/0.49 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext,type,
% 0.29/0.49 configuration_ext: $tType > $tType > $tType > $tType > $tType ).
% 0.29/0.49
% 0.29/0.49 thf(ty_t_AsynchronousSystem_Omessage,type,
% 0.29/0.49 message: $tType > $tType > $tType ).
% 0.29/0.49
% 0.29/0.49 thf(ty_t_Product__Type_Ounit,type,
% 0.29/0.49 product_unit: $tType ).
% 0.29/0.49
% 0.29/0.49 thf(ty_t_List_Olist,type,
% 0.29/0.49 list: $tType > $tType ).
% 0.29/0.49
% 0.29/0.49 thf(ty_t_Set_Oset,type,
% 0.29/0.49 set: $tType > $tType ).
% 0.29/0.49
% 0.29/0.49 thf(ty_t_Nat_Onat,type,
% 0.29/0.49 nat: $tType ).
% 0.29/0.49
% 0.29/0.49 thf(ty_tf_v,type,
% 0.29/0.49 v: $tType ).
% 0.29/0.49
% 0.29/0.49 thf(ty_tf_s,type,
% 0.29/0.49 s: $tType ).
% 0.29/0.49
% 0.29/0.49 thf(ty_tf_p,type,
% 0.29/0.49 p: $tType ).
% 0.29/0.49
% 0.29/0.49 % Explicit typings (45)
% 0.29/0.49 thf(sy_cl_HOL_Otype,type,
% 0.29/0.49 type:
% 0.29/0.49 !>[A: $tType] : $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_cl_Nat_Osize,type,
% 0.29/0.49 size:
% 0.29/0.49 !>[A: $tType] : $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_cl_Groups_Oone,type,
% 0.29/0.49 one:
% 0.29/0.49 !>[A: $tType] : $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_cl_Groups_Ozero,type,
% 0.29/0.49 zero:
% 0.29/0.49 !>[A: $tType] : $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_cl_Num_Oneg__numeral,type,
% 0.29/0.49 neg_numeral:
% 0.29/0.49 !>[A: $tType] : $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_cl_Orderings_Oorder,type,
% 0.29/0.49 order:
% 0.29/0.49 !>[A: $tType] : $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_cl_Groups_Ogroup__add,type,
% 0.29/0.49 group_add:
% 0.29/0.49 !>[A: $tType] : $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_cl_Orderings_Owellorder,type,
% 0.29/0.49 wellorder:
% 0.29/0.49 !>[A: $tType] : $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_cl_Groups_Ocomm__monoid__diff,type,
% 0.29/0.49 comm_monoid_diff:
% 0.29/0.49 !>[A: $tType] : $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.29/0.49 ordered_ab_group_add:
% 0.29/0.49 !>[A: $tType] : $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.29/0.49 cancel1352612707id_add:
% 0.29/0.49 !>[A: $tType] : $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.29/0.49 cancel146912293up_add:
% 0.29/0.49 !>[A: $tType] : $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.29/0.49 canoni770627133id_add:
% 0.29/0.49 !>[A: $tType] : $o ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_AsynchronousSystem_Oconfiguration_Omsgs,type,
% 0.29/0.49 msgs:
% 0.29/0.49 !>[P: $tType,V: $tType,S: $tType,Z: $tType] : ( ( configuration_ext @ P @ V @ S @ Z ) > ( message @ P @ V ) > nat ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_AsynchronousSystem_Oenabled,type,
% 0.29/0.49 enabled:
% 0.29/0.49 !>[P: $tType,V: $tType,S: $tType] : ( ( configuration_ext @ P @ V @ S @ product_unit ) > ( message @ P @ V ) > $o ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Execution_Oexecution_OfirstOccurrence,type,
% 0.29/0.49 firstOccurrence:
% 0.29/0.49 !>[P: $tType,V: $tType,S: $tType] : ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( message @ P @ V ) > nat > $o ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Execution_Oexecution_OminimalEnabled,type,
% 0.29/0.49 minimalEnabled:
% 0.29/0.49 !>[P: $tType,V: $tType,S: $tType] : ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( message @ P @ V ) > $o ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.29/0.49 minus_minus:
% 0.29/0.49 !>[A: $tType] : ( A > A > A ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.29/0.49 one_one:
% 0.29/0.49 !>[A: $tType] : A ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.29/0.49 zero_zero:
% 0.29/0.49 !>[A: $tType] : A ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_If,type,
% 0.29/0.49 if:
% 0.29/0.49 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_ListUtilities_OprefixList,type,
% 0.29/0.49 prefixList:
% 0.29/0.49 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_List_Olast,type,
% 0.29/0.49 last:
% 0.29/0.49 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_List_Olist_ONil,type,
% 0.29/0.49 nil:
% 0.29/0.49 !>[A: $tType] : ( list @ A ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_List_Olist_Otl,type,
% 0.29/0.49 tl:
% 0.29/0.49 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_List_Olist__ex,type,
% 0.29/0.49 list_ex:
% 0.29/0.49 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_List_Olist__ex1,type,
% 0.29/0.49 list_ex1:
% 0.29/0.49 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_List_Onth,type,
% 0.29/0.49 nth:
% 0.29/0.49 !>[A: $tType] : ( ( list @ A ) > nat > A ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_List_Oremdups__adj,type,
% 0.29/0.49 remdups_adj:
% 0.29/0.49 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Nat_OSuc,type,
% 0.29/0.49 suc: nat > nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.29/0.49 size_size:
% 0.29/0.49 !>[A: $tType] : ( A > nat ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.29/0.49 ord_less:
% 0.29/0.49 !>[A: $tType] : ( A > A > $o ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.29/0.49 ord_less_eq:
% 0.29/0.49 !>[A: $tType] : ( A > A > $o ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_Set_OCollect,type,
% 0.29/0.49 collect:
% 0.29/0.49 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_c_member,type,
% 0.29/0.49 member:
% 0.29/0.49 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_v_consumedMsg____,type,
% 0.29/0.49 consumedMsg: message @ p @ v ).
% 0.29/0.49
% 0.29/0.49 thf(sy_v_fe____,type,
% 0.29/0.49 fe: nat > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_v_firstOccSet____,type,
% 0.29/0.49 firstOccSet: nat > ( set @ ( message @ p @ v ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_v_ft____,type,
% 0.29/0.49 ft: nat > ( list @ ( message @ p @ v ) ) ).
% 0.29/0.49
% 0.29/0.49 thf(sy_v_index____,type,
% 0.29/0.49 index: nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_v_msg____,type,
% 0.29/0.49 msg: message @ p @ v ).
% 0.29/0.49
% 0.29/0.49 thf(sy_v_n0____,type,
% 0.29/0.49 n0: nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_v_n1____,type,
% 0.29/0.49 n1: nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_v_nMsg____,type,
% 0.29/0.49 nMsg: nat ).
% 0.29/0.49
% 0.29/0.49 thf(sy_v_n____,type,
% 0.29/0.49 n: nat ).
% 0.29/0.49
% 0.29/0.49 % Relevant facts (251)
% 0.29/0.49 thf(fact_0_AssumpGreaterOccurrence_I1_J,axiom,
% 0.29/0.49 ~ ( ord_less @ nat @ nMsg @ n1 ) ).
% 0.29/0.49
% 0.29/0.49 % AssumpGreaterOccurrence(1)
% 0.29/0.49 thf(fact_1__092_060open_062nMsg_A_060_Alength_A_Ife_Aindex_J_092_060close_062,axiom,
% 0.29/0.49 ord_less @ nat @ nMsg @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ).
% 0.29/0.49
% 0.29/0.49 % \<open>nMsg < length (fe index)\<close>
% 0.29/0.49 thf(fact_2_NotEmpty_I2_J,axiom,
% 0.29/0.49 ( ( fe @ index )
% 0.29/0.49 != ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % NotEmpty(2)
% 0.29/0.49 thf(fact_3_AssumptionFair_I2_J,axiom,
% 0.29/0.49 ord_less @ nat @ n0 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ) ).
% 0.29/0.49
% 0.29/0.49 % AssumptionFair(2)
% 0.29/0.49 thf(fact_4_length__induct,axiom,
% 0.29/0.49 ! [A: $tType,P2: ( list @ A ) > $o,Xs: list @ A] :
% 0.29/0.49 ( ! [Xs2: list @ A] :
% 0.29/0.49 ( ! [Ys: list @ A] :
% 0.29/0.49 ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ys ) @ ( size_size @ ( list @ A ) @ Xs2 ) )
% 0.29/0.49 => ( P2 @ Ys ) )
% 0.29/0.49 => ( P2 @ Xs2 ) )
% 0.29/0.49 => ( P2 @ Xs ) ) ).
% 0.29/0.49
% 0.29/0.49 % length_induct
% 0.29/0.49 thf(fact_5_SameCfgOnLow,axiom,
% 0.29/0.49 ! [I: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) )
% 0.29/0.49 => ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ I )
% 0.29/0.49 = ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ I ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % SameCfgOnLow
% 0.29/0.49 thf(fact_6_Ex__list__of__length,axiom,
% 0.29/0.49 ! [A: $tType,N: nat] :
% 0.29/0.49 ? [Xs2: list @ A] :
% 0.29/0.49 ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.29/0.49 = N ) ).
% 0.29/0.49
% 0.29/0.49 % Ex_list_of_length
% 0.29/0.49 thf(fact_7_neq__if__length__neq,axiom,
% 0.29/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.29/0.49 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.29/0.49 != ( size_size @ ( list @ A ) @ Ys2 ) )
% 0.29/0.49 => ( Xs != Ys2 ) ) ).
% 0.29/0.49
% 0.29/0.49 % neq_if_length_neq
% 0.29/0.49 thf(fact_8_size__neq__size__imp__neq,axiom,
% 0.29/0.49 ! [A: $tType] :
% 0.29/0.49 ( ( size @ A )
% 0.29/0.49 => ! [X: A,Y: A] :
% 0.29/0.49 ( ( ( size_size @ A @ X )
% 0.29/0.49 != ( size_size @ A @ Y ) )
% 0.29/0.49 => ( X != Y ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % size_neq_size_imp_neq
% 0.29/0.49 thf(fact_9_nat__neq__iff,axiom,
% 0.29/0.49 ! [M: nat,N: nat] :
% 0.29/0.49 ( ( M != N )
% 0.29/0.49 = ( ( ord_less @ nat @ M @ N )
% 0.29/0.49 | ( ord_less @ nat @ N @ M ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % nat_neq_iff
% 0.29/0.49 thf(fact_10_less__not__refl,axiom,
% 0.29/0.49 ! [N: nat] :
% 0.29/0.49 ~ ( ord_less @ nat @ N @ N ) ).
% 0.29/0.49
% 0.29/0.49 % less_not_refl
% 0.29/0.49 thf(fact_11_less__not__refl2,axiom,
% 0.29/0.49 ! [N: nat,M: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ N @ M )
% 0.29/0.49 => ( M != N ) ) ).
% 0.29/0.49
% 0.29/0.49 % less_not_refl2
% 0.29/0.49 thf(fact_12_less__not__refl3,axiom,
% 0.29/0.49 ! [S2: nat,T: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ S2 @ T )
% 0.29/0.49 => ( S2 != T ) ) ).
% 0.29/0.49
% 0.29/0.49 % less_not_refl3
% 0.29/0.49 thf(fact_13_less__irrefl__nat,axiom,
% 0.29/0.49 ! [N: nat] :
% 0.29/0.49 ~ ( ord_less @ nat @ N @ N ) ).
% 0.29/0.49
% 0.29/0.49 % less_irrefl_nat
% 0.29/0.49 thf(fact_14_nat_Oinject,axiom,
% 0.29/0.49 ! [X2: nat,Y2: nat] :
% 0.29/0.49 ( ( ( suc @ X2 )
% 0.29/0.49 = ( suc @ Y2 ) )
% 0.29/0.49 = ( X2 = Y2 ) ) ).
% 0.29/0.49
% 0.29/0.49 % nat.inject
% 0.29/0.49 thf(fact_15_old_Onat_Oinject,axiom,
% 0.29/0.49 ! [Nat: nat,Nat2: nat] :
% 0.29/0.49 ( ( ( suc @ Nat )
% 0.29/0.49 = ( suc @ Nat2 ) )
% 0.29/0.49 = ( Nat = Nat2 ) ) ).
% 0.29/0.49
% 0.29/0.49 % old.nat.inject
% 0.29/0.49 thf(fact_16_NotEmpty_I1_J,axiom,
% 0.29/0.49 ( ( fe @ ( suc @ index ) )
% 0.29/0.49 != ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % NotEmpty(1)
% 0.29/0.49 thf(fact_17_Suc__less__eq,axiom,
% 0.29/0.49 ! [M: nat,N: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.29/0.49 = ( ord_less @ nat @ M @ N ) ) ).
% 0.29/0.49
% 0.29/0.49 % Suc_less_eq
% 0.29/0.49 thf(fact_18_Suc__mono,axiom,
% 0.29/0.49 ! [M: nat,N: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ M @ N )
% 0.29/0.49 => ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % Suc_mono
% 0.29/0.49 thf(fact_19_lessI,axiom,
% 0.29/0.49 ! [N: nat] : ( ord_less @ nat @ N @ ( suc @ N ) ) ).
% 0.29/0.49
% 0.29/0.49 % lessI
% 0.29/0.49 thf(fact_20_Suc__inject,axiom,
% 0.29/0.49 ! [X: nat,Y: nat] :
% 0.29/0.49 ( ( ( suc @ X )
% 0.29/0.49 = ( suc @ Y ) )
% 0.29/0.49 => ( X = Y ) ) ).
% 0.29/0.49
% 0.29/0.49 % Suc_inject
% 0.29/0.49 thf(fact_21_n__not__Suc__n,axiom,
% 0.29/0.49 ! [N: nat] :
% 0.29/0.49 ( N
% 0.29/0.49 != ( suc @ N ) ) ).
% 0.29/0.49
% 0.29/0.49 % n_not_Suc_n
% 0.29/0.49 thf(fact_22_not__less__less__Suc__eq,axiom,
% 0.29/0.49 ! [N: nat,M: nat] :
% 0.29/0.49 ( ~ ( ord_less @ nat @ N @ M )
% 0.29/0.49 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 0.29/0.49 = ( N = M ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % not_less_less_Suc_eq
% 0.29/0.49 thf(fact_23_strict__inc__induct,axiom,
% 0.29/0.49 ! [I2: nat,J: nat,P2: nat > $o] :
% 0.29/0.49 ( ( ord_less @ nat @ I2 @ J )
% 0.29/0.49 => ( ! [I3: nat] :
% 0.29/0.49 ( ( J
% 0.29/0.49 = ( suc @ I3 ) )
% 0.29/0.49 => ( P2 @ I3 ) )
% 0.29/0.49 => ( ! [I3: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ I3 @ J )
% 0.29/0.49 => ( ( P2 @ ( suc @ I3 ) )
% 0.29/0.49 => ( P2 @ I3 ) ) )
% 0.29/0.49 => ( P2 @ I2 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % strict_inc_induct
% 0.29/0.49 thf(fact_24_less__Suc__induct,axiom,
% 0.29/0.49 ! [I2: nat,J: nat,P2: nat > nat > $o] :
% 0.29/0.49 ( ( ord_less @ nat @ I2 @ J )
% 0.29/0.49 => ( ! [I3: nat] : ( P2 @ I3 @ ( suc @ I3 ) )
% 0.29/0.49 => ( ! [I3: nat,J2: nat,K: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ I3 @ J2 )
% 0.29/0.49 => ( ( ord_less @ nat @ J2 @ K )
% 0.29/0.49 => ( ( P2 @ I3 @ J2 )
% 0.29/0.49 => ( ( P2 @ J2 @ K )
% 0.29/0.49 => ( P2 @ I3 @ K ) ) ) ) )
% 0.29/0.49 => ( P2 @ I2 @ J ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % less_Suc_induct
% 0.29/0.49 thf(fact_25_less__trans__Suc,axiom,
% 0.29/0.49 ! [I2: nat,J: nat,K2: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ I2 @ J )
% 0.29/0.49 => ( ( ord_less @ nat @ J @ K2 )
% 0.29/0.49 => ( ord_less @ nat @ ( suc @ I2 ) @ K2 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % less_trans_Suc
% 0.29/0.49 thf(fact_26_Suc__less__SucD,axiom,
% 0.29/0.49 ! [M: nat,N: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.29/0.49 => ( ord_less @ nat @ M @ N ) ) ).
% 0.29/0.49
% 0.29/0.49 % Suc_less_SucD
% 0.29/0.49 thf(fact_27_less__antisym,axiom,
% 0.29/0.49 ! [N: nat,M: nat] :
% 0.29/0.49 ( ~ ( ord_less @ nat @ N @ M )
% 0.29/0.49 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 0.29/0.49 => ( M = N ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % less_antisym
% 0.29/0.49 thf(fact_28_Suc__less__eq2,axiom,
% 0.29/0.49 ! [N: nat,M: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ ( suc @ N ) @ M )
% 0.29/0.49 = ( ? [M2: nat] :
% 0.29/0.49 ( ( M
% 0.29/0.49 = ( suc @ M2 ) )
% 0.29/0.49 & ( ord_less @ nat @ N @ M2 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % Suc_less_eq2
% 0.29/0.49 thf(fact_29_All__less__Suc,axiom,
% 0.29/0.49 ! [N: nat,P2: nat > $o] :
% 0.29/0.49 ( ( ! [I4: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ I4 @ ( suc @ N ) )
% 0.29/0.49 => ( P2 @ I4 ) ) )
% 0.29/0.49 = ( ( P2 @ N )
% 0.29/0.49 & ! [I4: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ I4 @ N )
% 0.29/0.49 => ( P2 @ I4 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % All_less_Suc
% 0.29/0.49 thf(fact_30_not__less__eq,axiom,
% 0.29/0.49 ! [M: nat,N: nat] :
% 0.29/0.49 ( ( ~ ( ord_less @ nat @ M @ N ) )
% 0.29/0.49 = ( ord_less @ nat @ N @ ( suc @ M ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % not_less_eq
% 0.29/0.49 thf(fact_31_less__Suc__eq,axiom,
% 0.29/0.49 ! [M: nat,N: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.29/0.49 = ( ( ord_less @ nat @ M @ N )
% 0.29/0.49 | ( M = N ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % less_Suc_eq
% 0.29/0.49 thf(fact_32_Ex__less__Suc,axiom,
% 0.29/0.49 ! [N: nat,P2: nat > $o] :
% 0.29/0.49 ( ( ? [I4: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ I4 @ ( suc @ N ) )
% 0.29/0.49 & ( P2 @ I4 ) ) )
% 0.29/0.49 = ( ( P2 @ N )
% 0.29/0.49 | ? [I4: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ I4 @ N )
% 0.29/0.49 & ( P2 @ I4 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % Ex_less_Suc
% 0.29/0.49 thf(fact_33_less__SucI,axiom,
% 0.29/0.49 ! [M: nat,N: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ M @ N )
% 0.29/0.49 => ( ord_less @ nat @ M @ ( suc @ N ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % less_SucI
% 0.29/0.49 thf(fact_34_less__SucE,axiom,
% 0.29/0.49 ! [M: nat,N: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.29/0.49 => ( ~ ( ord_less @ nat @ M @ N )
% 0.29/0.49 => ( M = N ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % less_SucE
% 0.29/0.49 thf(fact_35_Suc__lessI,axiom,
% 0.29/0.49 ! [M: nat,N: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ M @ N )
% 0.29/0.49 => ( ( ( suc @ M )
% 0.29/0.49 != N )
% 0.29/0.49 => ( ord_less @ nat @ ( suc @ M ) @ N ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % Suc_lessI
% 0.29/0.49 thf(fact_36_Suc__lessE,axiom,
% 0.29/0.49 ! [I2: nat,K2: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ ( suc @ I2 ) @ K2 )
% 0.29/0.49 => ~ ! [J2: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ I2 @ J2 )
% 0.29/0.49 => ( K2
% 0.29/0.49 != ( suc @ J2 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % Suc_lessE
% 0.29/0.49 thf(fact_37_Suc__lessD,axiom,
% 0.29/0.49 ! [M: nat,N: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ ( suc @ M ) @ N )
% 0.29/0.49 => ( ord_less @ nat @ M @ N ) ) ).
% 0.29/0.49
% 0.29/0.49 % Suc_lessD
% 0.29/0.49 thf(fact_38_Nat_OlessE,axiom,
% 0.29/0.49 ! [I2: nat,K2: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ I2 @ K2 )
% 0.29/0.49 => ( ( K2
% 0.29/0.49 != ( suc @ I2 ) )
% 0.29/0.49 => ~ ! [J2: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ I2 @ J2 )
% 0.29/0.49 => ( K2
% 0.29/0.49 != ( suc @ J2 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % Nat.lessE
% 0.29/0.49 thf(fact_39_list__eq__iff__nth__eq,axiom,
% 0.29/0.49 ! [A: $tType] :
% 0.29/0.49 ( ( ^ [Y3: list @ A,Z2: list @ A] : ( Y3 = Z2 ) )
% 0.29/0.49 = ( ^ [Xs3: list @ A,Ys3: list @ A] :
% 0.29/0.49 ( ( ( size_size @ ( list @ A ) @ Xs3 )
% 0.29/0.49 = ( size_size @ ( list @ A ) @ Ys3 ) )
% 0.29/0.49 & ! [I4: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ A ) @ Xs3 ) )
% 0.29/0.49 => ( ( nth @ A @ Xs3 @ I4 )
% 0.29/0.49 = ( nth @ A @ Ys3 @ I4 ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % list_eq_iff_nth_eq
% 0.29/0.49 thf(fact_40_Skolem__list__nth,axiom,
% 0.29/0.49 ! [A: $tType,K2: nat,P2: nat > A > $o] :
% 0.29/0.49 ( ( ! [I4: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ I4 @ K2 )
% 0.29/0.49 => ? [X3: A] : ( P2 @ I4 @ X3 ) ) )
% 0.29/0.49 = ( ? [Xs3: list @ A] :
% 0.29/0.49 ( ( ( size_size @ ( list @ A ) @ Xs3 )
% 0.29/0.49 = K2 )
% 0.29/0.49 & ! [I4: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ I4 @ K2 )
% 0.29/0.49 => ( P2 @ I4 @ ( nth @ A @ Xs3 @ I4 ) ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % Skolem_list_nth
% 0.29/0.49 thf(fact_41_nth__equalityI,axiom,
% 0.29/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.29/0.49 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.29/0.49 = ( size_size @ ( list @ A ) @ Ys2 ) )
% 0.29/0.49 => ( ! [I3: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ I3 @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.29/0.49 => ( ( nth @ A @ Xs @ I3 )
% 0.29/0.49 = ( nth @ A @ Ys2 @ I3 ) ) )
% 0.29/0.49 => ( Xs = Ys2 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % nth_equalityI
% 0.29/0.49 thf(fact_42_lift__Suc__mono__less__iff,axiom,
% 0.29/0.49 ! [A: $tType] :
% 0.29/0.49 ( ( order @ A )
% 0.29/0.49 => ! [F: nat > A,N: nat,M: nat] :
% 0.29/0.49 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.49 => ( ( ord_less @ A @ ( F @ N ) @ ( F @ M ) )
% 0.29/0.49 = ( ord_less @ nat @ N @ M ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % lift_Suc_mono_less_iff
% 0.29/0.49 thf(fact_43_mem__Collect__eq,axiom,
% 0.29/0.49 ! [A: $tType,A2: A,P2: A > $o] :
% 0.29/0.49 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 0.29/0.49 = ( P2 @ A2 ) ) ).
% 0.29/0.49
% 0.29/0.49 % mem_Collect_eq
% 0.29/0.49 thf(fact_44_Collect__mem__eq,axiom,
% 0.29/0.49 ! [A: $tType,A3: set @ A] :
% 0.29/0.49 ( ( collect @ A
% 0.29/0.49 @ ^ [X4: A] : ( member @ A @ X4 @ A3 ) )
% 0.29/0.49 = A3 ) ).
% 0.29/0.49
% 0.29/0.49 % Collect_mem_eq
% 0.29/0.49 thf(fact_45_Collect__cong,axiom,
% 0.29/0.49 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.29/0.49 ( ! [X5: A] :
% 0.29/0.49 ( ( P2 @ X5 )
% 0.29/0.49 = ( Q @ X5 ) )
% 0.29/0.49 => ( ( collect @ A @ P2 )
% 0.29/0.49 = ( collect @ A @ Q ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % Collect_cong
% 0.29/0.49 thf(fact_46_lift__Suc__mono__less,axiom,
% 0.29/0.49 ! [A: $tType] :
% 0.29/0.49 ( ( order @ A )
% 0.29/0.49 => ! [F: nat > A,N: nat,N3: nat] :
% 0.29/0.49 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.49 => ( ( ord_less @ nat @ N @ N3 )
% 0.29/0.49 => ( ord_less @ A @ ( F @ N ) @ ( F @ N3 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % lift_Suc_mono_less
% 0.29/0.49 thf(fact_47_measure__induct__rule,axiom,
% 0.29/0.49 ! [B: $tType,A: $tType] :
% 0.29/0.49 ( ( wellorder @ B )
% 0.29/0.49 => ! [F: A > B,P2: A > $o,A2: A] :
% 0.29/0.49 ( ! [X5: A] :
% 0.29/0.49 ( ! [Y4: A] :
% 0.29/0.49 ( ( ord_less @ B @ ( F @ Y4 ) @ ( F @ X5 ) )
% 0.29/0.49 => ( P2 @ Y4 ) )
% 0.29/0.49 => ( P2 @ X5 ) )
% 0.29/0.49 => ( P2 @ A2 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % measure_induct_rule
% 0.29/0.49 thf(fact_48_measure__induct,axiom,
% 0.29/0.49 ! [B: $tType,A: $tType] :
% 0.29/0.49 ( ( wellorder @ B )
% 0.29/0.49 => ! [F: A > B,P2: A > $o,A2: A] :
% 0.29/0.49 ( ! [X5: A] :
% 0.29/0.49 ( ! [Y4: A] :
% 0.29/0.49 ( ( ord_less @ B @ ( F @ Y4 ) @ ( F @ X5 ) )
% 0.29/0.49 => ( P2 @ Y4 ) )
% 0.29/0.49 => ( P2 @ X5 ) )
% 0.29/0.49 => ( P2 @ A2 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % measure_induct
% 0.29/0.49 thf(fact_49_infinite__descent__measure,axiom,
% 0.29/0.49 ! [A: $tType,P2: A > $o,V2: A > nat,X: A] :
% 0.29/0.49 ( ! [X5: A] :
% 0.29/0.49 ( ~ ( P2 @ X5 )
% 0.29/0.49 => ? [Y4: A] :
% 0.29/0.49 ( ( ord_less @ nat @ ( V2 @ Y4 ) @ ( V2 @ X5 ) )
% 0.29/0.49 & ~ ( P2 @ Y4 ) ) )
% 0.29/0.49 => ( P2 @ X ) ) ).
% 0.29/0.49
% 0.29/0.49 % infinite_descent_measure
% 0.29/0.49 thf(fact_50_linorder__neqE__nat,axiom,
% 0.29/0.49 ! [X: nat,Y: nat] :
% 0.29/0.49 ( ( X != Y )
% 0.29/0.49 => ( ~ ( ord_less @ nat @ X @ Y )
% 0.29/0.49 => ( ord_less @ nat @ Y @ X ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % linorder_neqE_nat
% 0.29/0.49 thf(fact_51_infinite__descent,axiom,
% 0.29/0.49 ! [P2: nat > $o,N: nat] :
% 0.29/0.49 ( ! [N2: nat] :
% 0.29/0.49 ( ~ ( P2 @ N2 )
% 0.29/0.49 => ? [M3: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ M3 @ N2 )
% 0.29/0.49 & ~ ( P2 @ M3 ) ) )
% 0.29/0.49 => ( P2 @ N ) ) ).
% 0.29/0.49
% 0.29/0.49 % infinite_descent
% 0.29/0.49 thf(fact_52_nat__less__induct,axiom,
% 0.29/0.49 ! [P2: nat > $o,N: nat] :
% 0.29/0.49 ( ! [N2: nat] :
% 0.29/0.49 ( ! [M3: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ M3 @ N2 )
% 0.29/0.49 => ( P2 @ M3 ) )
% 0.29/0.49 => ( P2 @ N2 ) )
% 0.29/0.49 => ( P2 @ N ) ) ).
% 0.29/0.49
% 0.29/0.49 % nat_less_induct
% 0.29/0.49 thf(fact_53_Subset,axiom,
% 0.29/0.49 ! [MsgInSet: message @ p @ v] :
% 0.29/0.49 ( ( member @ ( message @ p @ v ) @ MsgInSet @ ( firstOccSet @ ( suc @ index ) ) )
% 0.29/0.49 => ( member @ ( message @ p @ v ) @ MsgInSet @ ( firstOccSet @ index ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % Subset
% 0.29/0.49 thf(fact_54_IPrefixListEx,axiom,
% 0.29/0.49 ! [I: nat] : ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ I ) @ ( fe @ ( suc @ I ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % IPrefixListEx
% 0.29/0.49 thf(fact_55_AssumptionFair_I3_J,axiom,
% 0.29/0.49 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ n0 ) @ msg ).
% 0.29/0.49
% 0.29/0.49 % AssumptionFair(3)
% 0.29/0.49 thf(fact_56_list__ex__length,axiom,
% 0.29/0.49 ! [A: $tType] :
% 0.29/0.49 ( ( list_ex @ A )
% 0.29/0.49 = ( ^ [P3: A > $o,Xs3: list @ A] :
% 0.29/0.49 ? [N4: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ N4 @ ( size_size @ ( list @ A ) @ Xs3 ) )
% 0.29/0.49 & ( P3 @ ( nth @ A @ Xs3 @ N4 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % list_ex_length
% 0.29/0.49 thf(fact_57_AssumpGreaterOccurrence_I2_J,axiom,
% 0.29/0.49 firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ consumedMsg @ n1 ).
% 0.29/0.49
% 0.29/0.49 % AssumpGreaterOccurrence(2)
% 0.29/0.49 thf(fact_58_list__ex1__simps_I1_J,axiom,
% 0.29/0.49 ! [A: $tType,P2: A > $o] :
% 0.29/0.49 ~ ( list_ex1 @ A @ P2 @ ( nil @ A ) ) ).
% 0.29/0.49
% 0.29/0.49 % list_ex1_simps(1)
% 0.29/0.49 thf(fact_59_LengthStep,axiom,
% 0.29/0.49 ord_less @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % LengthStep
% 0.29/0.49 thf(fact_60_remdups__adj__adjacent,axiom,
% 0.29/0.49 ! [A: $tType,I2: nat,Xs: list @ A] :
% 0.29/0.49 ( ( ord_less @ nat @ ( suc @ I2 ) @ ( size_size @ ( list @ A ) @ ( remdups_adj @ A @ Xs ) ) )
% 0.29/0.49 => ( ( nth @ A @ ( remdups_adj @ A @ Xs ) @ I2 )
% 0.29/0.49 != ( nth @ A @ ( remdups_adj @ A @ Xs ) @ ( suc @ I2 ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % remdups_adj_adjacent
% 0.29/0.49 thf(fact_61_nth__tl,axiom,
% 0.29/0.49 ! [A: $tType,N: nat,Xs: list @ A] :
% 0.29/0.49 ( ( ord_less @ nat @ N @ ( size_size @ ( list @ A ) @ ( tl @ A @ Xs ) ) )
% 0.29/0.49 => ( ( nth @ A @ ( tl @ A @ Xs ) @ N )
% 0.29/0.49 = ( nth @ A @ Xs @ ( suc @ N ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % nth_tl
% 0.29/0.49 thf(fact_62_length__greater__0__conv,axiom,
% 0.29/0.49 ! [A: $tType,Xs: list @ A] :
% 0.29/0.49 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.29/0.49 = ( Xs
% 0.29/0.49 != ( nil @ A ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % length_greater_0_conv
% 0.29/0.49 thf(fact_63_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 0.29/0.49 ! [P2: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,Q: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,A4: configuration_ext @ p @ v @ s @ product_unit,A5: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),A6: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),A7: nat] :
% 0.29/0.49 ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 0.29/0.49 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N2: nat] :
% 0.29/0.49 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.29/0.49 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.29/0.49 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 0.29/0.49 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 0.29/0.49 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N2: nat] :
% 0.29/0.49 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.29/0.49 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.29/0.49 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 0.29/0.49 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % infiniteExecutionCfg_infiniteExecutionMsg.induct(2)
% 0.29/0.49 thf(fact_64_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 0.29/0.49 ! [P2: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,Q: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,A0: configuration_ext @ p @ v @ s @ product_unit,A1: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),A22: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),A32: nat] :
% 0.29/0.49 ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 0.29/0.49 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N2: nat] :
% 0.29/0.49 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.29/0.49 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.29/0.49 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 0.29/0.49 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 0.29/0.49 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N2: nat] :
% 0.29/0.49 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.29/0.49 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.29/0.49 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 0.29/0.49 => ( P2 @ A0 @ A1 @ A22 @ A32 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % infiniteExecutionCfg_infiniteExecutionMsg.induct(1)
% 0.29/0.49 thf(fact_65_AssumpGreaterOccurrence_I3_J,axiom,
% 0.29/0.49 firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg ).
% 0.29/0.49
% 0.29/0.49 % AssumpGreaterOccurrence(3)
% 0.29/0.49 thf(fact_66_ConsumedInSet,axiom,
% 0.29/0.49 member @ ( message @ p @ v ) @ consumedMsg @ ( firstOccSet @ index ) ).
% 0.29/0.49
% 0.29/0.49 % ConsumedInSet
% 0.29/0.49 thf(fact_67_SameMsgOnLow,axiom,
% 0.29/0.49 ! [I: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 0.29/0.49 => ( ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ I )
% 0.29/0.49 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % SameMsgOnLow
% 0.29/0.49 thf(fact_68_neq0__conv,axiom,
% 0.29/0.49 ! [N: nat] :
% 0.29/0.49 ( ( N
% 0.29/0.49 != ( zero_zero @ nat ) )
% 0.29/0.49 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 0.29/0.49
% 0.29/0.49 % neq0_conv
% 0.29/0.49 thf(fact_69_less__nat__zero__code,axiom,
% 0.29/0.49 ! [N: nat] :
% 0.29/0.49 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.29/0.49
% 0.29/0.49 % less_nat_zero_code
% 0.29/0.49 thf(fact_70_bot__nat__0_Onot__eq__extremum,axiom,
% 0.29/0.49 ! [A2: nat] :
% 0.29/0.49 ( ( A2
% 0.29/0.49 != ( zero_zero @ nat ) )
% 0.29/0.49 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A2 ) ) ).
% 0.29/0.49
% 0.29/0.49 % bot_nat_0.not_eq_extremum
% 0.29/0.49 thf(fact_71_ConsumedMsg_I1_J,axiom,
% 0.29/0.49 minimalEnabled @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ consumedMsg ).
% 0.29/0.49
% 0.29/0.49 % ConsumedMsg(1)
% 0.29/0.49 thf(fact_72_remdups__adj__Nil__iff,axiom,
% 0.29/0.49 ! [A: $tType,Xs: list @ A] :
% 0.29/0.49 ( ( ( remdups_adj @ A @ Xs )
% 0.29/0.49 = ( nil @ A ) )
% 0.29/0.49 = ( Xs
% 0.29/0.49 = ( nil @ A ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % remdups_adj_Nil_iff
% 0.29/0.49 thf(fact_73_list__ex__simps_I2_J,axiom,
% 0.29/0.49 ! [A: $tType,P2: A > $o] :
% 0.29/0.49 ~ ( list_ex @ A @ P2 @ ( nil @ A ) ) ).
% 0.29/0.49
% 0.29/0.49 % list_ex_simps(2)
% 0.29/0.49 thf(fact_74_SmallIndex,axiom,
% 0.29/0.49 ! [NMsg: nat] :
% 0.29/0.49 ( ( firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ NMsg )
% 0.29/0.49 => ( ord_less @ nat @ NMsg @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % SmallIndex
% 0.29/0.49 thf(fact_75_zero__less__Suc,axiom,
% 0.29/0.49 ! [N: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ N ) ) ).
% 0.29/0.49
% 0.29/0.49 % zero_less_Suc
% 0.29/0.49 thf(fact_76_less__Suc0,axiom,
% 0.29/0.49 ! [N: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ N @ ( suc @ ( zero_zero @ nat ) ) )
% 0.29/0.49 = ( N
% 0.29/0.49 = ( zero_zero @ nat ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % less_Suc0
% 0.29/0.49 thf(fact_77_length__0__conv,axiom,
% 0.29/0.49 ! [A: $tType,Xs: list @ A] :
% 0.29/0.49 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.29/0.49 = ( zero_zero @ nat ) )
% 0.29/0.49 = ( Xs
% 0.29/0.49 = ( nil @ A ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % length_0_conv
% 0.29/0.49 thf(fact_78_AssumptionFairContr,axiom,
% 0.29/0.49 ! [N5: nat] :
% 0.29/0.49 ( ( ord_less_eq @ nat @ n @ N5 )
% 0.29/0.49 => ! [N0: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ N0 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N5 ) ) )
% 0.29/0.49 => ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) @ N0 )
% 0.29/0.49 => ( msg
% 0.29/0.49 != ( nth @ ( message @ p @ v ) @ ( ft @ N5 ) @ N0 ) ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % AssumptionFairContr
% 0.29/0.49 thf(fact_79_AssumptionFirstOccSetDecrOrConsumed_I1_J,axiom,
% 0.29/0.49 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) @ msg ).
% 0.29/0.49
% 0.29/0.49 % AssumptionFirstOccSetDecrOrConsumed(1)
% 0.29/0.49 thf(fact_80_AssumptionCase1ImplThesis_H,axiom,
% 0.29/0.49 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg ).
% 0.29/0.49
% 0.29/0.49 % AssumptionCase1ImplThesis'
% 0.29/0.49 thf(fact_81_remdups__adj_Osimps_I1_J,axiom,
% 0.29/0.49 ! [A: $tType] :
% 0.29/0.49 ( ( remdups_adj @ A @ ( nil @ A ) )
% 0.29/0.49 = ( nil @ A ) ) ).
% 0.29/0.49
% 0.29/0.49 % remdups_adj.simps(1)
% 0.29/0.49 thf(fact_82_list_Osel_I2_J,axiom,
% 0.29/0.49 ! [A: $tType] :
% 0.29/0.49 ( ( tl @ A @ ( nil @ A ) )
% 0.29/0.49 = ( nil @ A ) ) ).
% 0.29/0.49
% 0.29/0.49 % list.sel(2)
% 0.29/0.49 thf(fact_83_not0__implies__Suc,axiom,
% 0.29/0.49 ! [N: nat] :
% 0.29/0.49 ( ( N
% 0.29/0.49 != ( zero_zero @ nat ) )
% 0.29/0.49 => ? [M4: nat] :
% 0.29/0.49 ( N
% 0.29/0.49 = ( suc @ M4 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % not0_implies_Suc
% 0.29/0.49 thf(fact_84_old_Onat_Oinducts,axiom,
% 0.29/0.49 ! [P2: nat > $o,Nat: nat] :
% 0.29/0.49 ( ( P2 @ ( zero_zero @ nat ) )
% 0.29/0.49 => ( ! [Nat3: nat] :
% 0.29/0.49 ( ( P2 @ Nat3 )
% 0.29/0.49 => ( P2 @ ( suc @ Nat3 ) ) )
% 0.29/0.49 => ( P2 @ Nat ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % old.nat.inducts
% 0.29/0.49 thf(fact_85_old_Onat_Oexhaust,axiom,
% 0.29/0.49 ! [Y: nat] :
% 0.29/0.49 ( ( Y
% 0.29/0.49 != ( zero_zero @ nat ) )
% 0.29/0.49 => ~ ! [Nat3: nat] :
% 0.29/0.49 ( Y
% 0.29/0.49 != ( suc @ Nat3 ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % old.nat.exhaust
% 0.29/0.49 thf(fact_86_Zero__not__Suc,axiom,
% 0.29/0.49 ! [M: nat] :
% 0.29/0.49 ( ( zero_zero @ nat )
% 0.29/0.49 != ( suc @ M ) ) ).
% 0.29/0.49
% 0.29/0.49 % Zero_not_Suc
% 0.29/0.49 thf(fact_87_Zero__neq__Suc,axiom,
% 0.29/0.49 ! [M: nat] :
% 0.29/0.49 ( ( zero_zero @ nat )
% 0.29/0.49 != ( suc @ M ) ) ).
% 0.29/0.49
% 0.29/0.49 % Zero_neq_Suc
% 0.29/0.49 thf(fact_88_Suc__neq__Zero,axiom,
% 0.29/0.49 ! [M: nat] :
% 0.29/0.49 ( ( suc @ M )
% 0.29/0.49 != ( zero_zero @ nat ) ) ).
% 0.29/0.49
% 0.29/0.49 % Suc_neq_Zero
% 0.29/0.49 thf(fact_89_zero__induct,axiom,
% 0.29/0.49 ! [P2: nat > $o,K2: nat] :
% 0.29/0.49 ( ( P2 @ K2 )
% 0.29/0.49 => ( ! [N2: nat] :
% 0.29/0.49 ( ( P2 @ ( suc @ N2 ) )
% 0.29/0.49 => ( P2 @ N2 ) )
% 0.29/0.49 => ( P2 @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % zero_induct
% 0.29/0.49 thf(fact_90_diff__induct,axiom,
% 0.29/0.49 ! [P2: nat > nat > $o,M: nat,N: nat] :
% 0.29/0.49 ( ! [X5: nat] : ( P2 @ X5 @ ( zero_zero @ nat ) )
% 0.29/0.49 => ( ! [Y5: nat] : ( P2 @ ( zero_zero @ nat ) @ ( suc @ Y5 ) )
% 0.29/0.49 => ( ! [X5: nat,Y5: nat] :
% 0.29/0.49 ( ( P2 @ X5 @ Y5 )
% 0.29/0.49 => ( P2 @ ( suc @ X5 ) @ ( suc @ Y5 ) ) )
% 0.29/0.49 => ( P2 @ M @ N ) ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % diff_induct
% 0.29/0.49 thf(fact_91_nat__induct,axiom,
% 0.29/0.49 ! [P2: nat > $o,N: nat] :
% 0.29/0.49 ( ( P2 @ ( zero_zero @ nat ) )
% 0.29/0.49 => ( ! [N2: nat] :
% 0.29/0.49 ( ( P2 @ N2 )
% 0.29/0.49 => ( P2 @ ( suc @ N2 ) ) )
% 0.29/0.49 => ( P2 @ N ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % nat_induct
% 0.29/0.49 thf(fact_92_nat_OdiscI,axiom,
% 0.29/0.49 ! [Nat: nat,X2: nat] :
% 0.29/0.49 ( ( Nat
% 0.29/0.49 = ( suc @ X2 ) )
% 0.29/0.49 => ( Nat
% 0.29/0.49 != ( zero_zero @ nat ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % nat.discI
% 0.29/0.49 thf(fact_93_old_Onat_Odistinct_I1_J,axiom,
% 0.29/0.49 ! [Nat2: nat] :
% 0.29/0.49 ( ( zero_zero @ nat )
% 0.29/0.49 != ( suc @ Nat2 ) ) ).
% 0.29/0.49
% 0.29/0.49 % old.nat.distinct(1)
% 0.29/0.49 thf(fact_94_old_Onat_Odistinct_I2_J,axiom,
% 0.29/0.49 ! [Nat4: nat] :
% 0.29/0.49 ( ( suc @ Nat4 )
% 0.29/0.49 != ( zero_zero @ nat ) ) ).
% 0.29/0.49
% 0.29/0.49 % old.nat.distinct(2)
% 0.29/0.49 thf(fact_95_nat_Odistinct_I1_J,axiom,
% 0.29/0.49 ! [X2: nat] :
% 0.29/0.49 ( ( zero_zero @ nat )
% 0.29/0.49 != ( suc @ X2 ) ) ).
% 0.29/0.49
% 0.29/0.49 % nat.distinct(1)
% 0.29/0.49 thf(fact_96_gr0I,axiom,
% 0.29/0.49 ! [N: nat] :
% 0.29/0.49 ( ( N
% 0.29/0.49 != ( zero_zero @ nat ) )
% 0.29/0.49 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 0.29/0.49
% 0.29/0.49 % gr0I
% 0.29/0.49 thf(fact_97_not__gr0,axiom,
% 0.29/0.49 ! [N: nat] :
% 0.29/0.49 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) )
% 0.29/0.49 = ( N
% 0.29/0.49 = ( zero_zero @ nat ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % not_gr0
% 0.29/0.49 thf(fact_98_not__less0,axiom,
% 0.29/0.49 ! [N: nat] :
% 0.29/0.49 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.29/0.49
% 0.29/0.49 % not_less0
% 0.29/0.49 thf(fact_99_less__zeroE,axiom,
% 0.29/0.49 ! [N: nat] :
% 0.29/0.49 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.29/0.49
% 0.29/0.49 % less_zeroE
% 0.29/0.49 thf(fact_100_gr__implies__not0,axiom,
% 0.29/0.49 ! [M: nat,N: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ M @ N )
% 0.29/0.49 => ( N
% 0.29/0.49 != ( zero_zero @ nat ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % gr_implies_not0
% 0.29/0.49 thf(fact_101_infinite__descent0,axiom,
% 0.29/0.49 ! [P2: nat > $o,N: nat] :
% 0.29/0.49 ( ( P2 @ ( zero_zero @ nat ) )
% 0.29/0.49 => ( ! [N2: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.29/0.49 => ( ~ ( P2 @ N2 )
% 0.29/0.49 => ? [M3: nat] :
% 0.29/0.49 ( ( ord_less @ nat @ M3 @ N2 )
% 0.29/0.49 & ~ ( P2 @ M3 ) ) ) )
% 0.29/0.49 => ( P2 @ N ) ) ) ).
% 0.29/0.49
% 0.29/0.49 % infinite_descent0
% 0.29/0.49 thf(fact_102_bot__nat__0_Oextremum__strict,axiom,
% 0.29/0.49 ! [A2: nat] :
% 0.29/0.49 ~ ( ord_less @ nat @ A2 @ ( zero_zero @ nat ) ) ).
% 0.29/0.49
% 0.29/0.49 % bot_nat_0.extremum_strict
% 0.29/0.49 thf(fact_103_infinite__descent0__measure,axiom,
% 0.29/0.49 ! [A: $tType,V2: A > nat,P2: A > $o,X: A] :
% 0.29/0.49 ( ! [X5: A] :
% 0.29/0.49 ( ( ( V2 @ X5 )
% 0.29/0.49 = ( zero_zero @ nat ) )
% 0.29/0.49 => ( P2 @ X5 ) )
% 0.29/0.49 => ( ! [X5: A] :
% 0.29/0.49 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V2 @ X5 ) )
% 0.29/0.49 => ( ~ ( P2 @ X5 )
% 0.29/0.49 => ? [Y4: A] :
% 0.29/0.49 ( ( ord_less @ nat @ ( V2 @ Y4 ) @ ( V2 @ X5 ) )
% 0.29/0.50 & ~ ( P2 @ Y4 ) ) ) )
% 0.29/0.50 => ( P2 @ X ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % infinite_descent0_measure
% 0.29/0.50 thf(fact_104_less__Suc__eq__0__disj,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.29/0.50 = ( ( M
% 0.29/0.50 = ( zero_zero @ nat ) )
% 0.29/0.50 | ? [J3: nat] :
% 0.29/0.50 ( ( M
% 0.29/0.50 = ( suc @ J3 ) )
% 0.29/0.50 & ( ord_less @ nat @ J3 @ N ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % less_Suc_eq_0_disj
% 0.29/0.50 thf(fact_105_gr0__implies__Suc,axiom,
% 0.29/0.50 ! [N: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.29/0.50 => ? [M4: nat] :
% 0.29/0.50 ( N
% 0.29/0.50 = ( suc @ M4 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % gr0_implies_Suc
% 0.29/0.50 thf(fact_106_All__less__Suc2,axiom,
% 0.29/0.50 ! [N: nat,P2: nat > $o] :
% 0.29/0.50 ( ( ! [I4: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ I4 @ ( suc @ N ) )
% 0.29/0.50 => ( P2 @ I4 ) ) )
% 0.29/0.50 = ( ( P2 @ ( zero_zero @ nat ) )
% 0.29/0.50 & ! [I4: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ I4 @ N )
% 0.29/0.50 => ( P2 @ ( suc @ I4 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % All_less_Suc2
% 0.29/0.50 thf(fact_107_gr0__conv__Suc,axiom,
% 0.29/0.50 ! [N: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.29/0.50 = ( ? [M5: nat] :
% 0.29/0.50 ( N
% 0.29/0.50 = ( suc @ M5 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % gr0_conv_Suc
% 0.29/0.50 thf(fact_108_Ex__less__Suc2,axiom,
% 0.29/0.50 ! [N: nat,P2: nat > $o] :
% 0.29/0.50 ( ( ? [I4: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ I4 @ ( suc @ N ) )
% 0.29/0.50 & ( P2 @ I4 ) ) )
% 0.29/0.50 = ( ( P2 @ ( zero_zero @ nat ) )
% 0.29/0.50 | ? [I4: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ I4 @ N )
% 0.29/0.50 & ( P2 @ ( suc @ I4 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Ex_less_Suc2
% 0.29/0.50 thf(fact_109_list_Osize_I3_J,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( size_size @ ( list @ A ) @ ( nil @ A ) )
% 0.29/0.50 = ( zero_zero @ nat ) ) ).
% 0.29/0.50
% 0.29/0.50 % list.size(3)
% 0.29/0.50 thf(fact_110_MinImplFirstOcc,axiom,
% 0.29/0.50 ! [Msg: message @ p @ v] :
% 0.29/0.50 ( ( minimalEnabled @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ Msg )
% 0.29/0.50 => ( member @ ( message @ p @ v ) @ Msg @ ( firstOccSet @ index ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % MinImplFirstOcc
% 0.29/0.50 thf(fact_111_Case2ImplThesis,axiom,
% 0.29/0.50 ( ? [N0: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ n0 @ N0 )
% 0.29/0.50 & ( ord_less @ nat @ N0 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
% 0.29/0.50 & ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ N0 )
% 0.29/0.50 = msg ) )
% 0.29/0.50 => ? [N6: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ n @ N6 )
% 0.29/0.50 & ? [N02: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ n0 @ N02 )
% 0.29/0.50 & ( ord_less @ nat @ N02 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N6 ) ) )
% 0.29/0.50 & ( msg
% 0.29/0.50 = ( nth @ ( message @ p @ v ) @ ( ft @ N6 ) @ N02 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Case2ImplThesis
% 0.29/0.50 thf(fact_112_MessageStaysOrConsumed,axiom,
% 0.29/0.50 ! [N1: nat,N22: nat,N: nat,Msg2: message @ p @ v] :
% 0.29/0.50 ( ( ( ord_less_eq @ nat @ N1 @ N22 )
% 0.29/0.50 & ( ord_less @ nat @ N22 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ N ) ) )
% 0.29/0.50 & ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N ) @ N1 ) @ Msg2 ) )
% 0.29/0.50 => ( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N ) @ N22 ) @ Msg2 )
% 0.29/0.50 | ? [N02: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ N1 @ N02 )
% 0.29/0.50 & ( ord_less @ nat @ N02 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N ) ) )
% 0.29/0.50 & ( ( nth @ ( message @ p @ v ) @ ( ft @ N ) @ N02 )
% 0.29/0.50 = Msg2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % MessageStaysOrConsumed
% 0.29/0.50 thf(fact_113_NotConsumedIntermediate,axiom,
% 0.29/0.50 ! [I: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 0.29/0.50 => ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ I )
% 0.29/0.50 => ( ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I )
% 0.29/0.50 != msg ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NotConsumedIntermediate
% 0.29/0.50 thf(fact_114__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ift_A_ISuc_Aindex_J_J_O_Alength_A_Ift_Aindex_J_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,
% 0.29/0.50 ~ ? [I: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 0.29/0.50 & ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ I )
% 0.29/0.50 & ( msg
% 0.29/0.50 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % \<open>\<not> (\<exists>i<length (ft (Suc index)). length (ft index) \<le> i \<and> msg = ft (Suc index) ! i)\<close>
% 0.29/0.50 thf(fact_115_Nitpick_Osize__list__simp_I2_J,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( size_size @ ( list @ A ) )
% 0.29/0.50 = ( ^ [Xs3: list @ A] :
% 0.29/0.50 ( if @ nat
% 0.29/0.50 @ ( Xs3
% 0.29/0.50 = ( nil @ A ) )
% 0.29/0.50 @ ( zero_zero @ nat )
% 0.29/0.50 @ ( suc @ ( size_size @ ( list @ A ) @ ( tl @ A @ Xs3 ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Nitpick.size_list_simp(2)
% 0.29/0.50 thf(fact_116_not__gr__zero,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( canoni770627133id_add @ A )
% 0.29/0.50 => ! [N: A] :
% 0.29/0.50 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 0.29/0.50 = ( N
% 0.29/0.50 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % not_gr_zero
% 0.29/0.50 thf(fact_117_le__zero__eq,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( canoni770627133id_add @ A )
% 0.29/0.50 => ! [N: A] :
% 0.29/0.50 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 0.29/0.50 = ( N
% 0.29/0.50 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_zero_eq
% 0.29/0.50 thf(fact_118_bot__nat__0_Oextremum,axiom,
% 0.29/0.50 ! [A2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A2 ) ).
% 0.29/0.50
% 0.29/0.50 % bot_nat_0.extremum
% 0.29/0.50 thf(fact_119_le0,axiom,
% 0.29/0.50 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 0.29/0.50
% 0.29/0.50 % le0
% 0.29/0.50 thf(fact_120_Suc__le__mono,axiom,
% 0.29/0.50 ! [N: nat,M: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.29/0.50 = ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.29/0.50
% 0.29/0.50 % Suc_le_mono
% 0.29/0.50 thf(fact_121_EnabledInSuc,axiom,
% 0.29/0.50 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) ) @ msg ).
% 0.29/0.50
% 0.29/0.50 % EnabledInSuc
% 0.29/0.50 thf(fact_122_MinImplAllBigger,axiom,
% 0.29/0.50 ! [Msg: message @ p @ v] :
% 0.29/0.50 ( ( minimalEnabled @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ Msg )
% 0.29/0.50 => ? [OccM: nat] :
% 0.29/0.50 ( ( firstOccurrence @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ Msg @ OccM )
% 0.29/0.50 & ! [Msg3: message @ p @ v,OccM2: nat] :
% 0.29/0.50 ( ( firstOccurrence @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ Msg3 @ OccM2 )
% 0.29/0.50 => ( ord_less_eq @ nat @ OccM @ OccM2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % MinImplAllBigger
% 0.29/0.50 thf(fact_123_last__remdups__adj,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A] :
% 0.29/0.50 ( ( last @ A @ ( remdups_adj @ A @ Xs ) )
% 0.29/0.50 = ( last @ A @ Xs ) ) ).
% 0.29/0.50
% 0.29/0.50 % last_remdups_adj
% 0.29/0.50 thf(fact_124_EnabledOrConsumedAtLast,axiom,
% 0.29/0.50 ( ( enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg )
% 0.29/0.50 | ? [N02: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ n0 @ N02 )
% 0.29/0.50 & ( ord_less @ nat @ N02 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
% 0.29/0.50 & ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ N02 )
% 0.29/0.50 = msg ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % EnabledOrConsumedAtLast
% 0.29/0.50 thf(fact_125_zero__le,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( canoni770627133id_add @ A )
% 0.29/0.50 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 0.29/0.50
% 0.29/0.50 % zero_le
% 0.29/0.50 thf(fact_126_lift__Suc__antimono__le,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( order @ A )
% 0.29/0.50 => ! [F: nat > A,N: nat,N3: nat] :
% 0.29/0.50 ( ! [N2: nat] : ( ord_less_eq @ A @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.29/0.50 => ( ( ord_less_eq @ nat @ N @ N3 )
% 0.29/0.50 => ( ord_less_eq @ A @ ( F @ N3 ) @ ( F @ N ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % lift_Suc_antimono_le
% 0.29/0.50 thf(fact_127_lift__Suc__mono__le,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( order @ A )
% 0.29/0.50 => ! [F: nat > A,N: nat,N3: nat] :
% 0.29/0.50 ( ! [N2: nat] : ( ord_less_eq @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.29/0.50 => ( ( ord_less_eq @ nat @ N @ N3 )
% 0.29/0.50 => ( ord_less_eq @ A @ ( F @ N ) @ ( F @ N3 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % lift_Suc_mono_le
% 0.29/0.50 thf(fact_128_Nat_Oex__has__greatest__nat,axiom,
% 0.29/0.50 ! [P2: nat > $o,K2: nat,B2: nat] :
% 0.29/0.50 ( ( P2 @ K2 )
% 0.29/0.50 => ( ! [Y5: nat] :
% 0.29/0.50 ( ( P2 @ Y5 )
% 0.29/0.50 => ( ord_less_eq @ nat @ Y5 @ B2 ) )
% 0.29/0.50 => ? [X5: nat] :
% 0.29/0.50 ( ( P2 @ X5 )
% 0.29/0.50 & ! [Y4: nat] :
% 0.29/0.50 ( ( P2 @ Y4 )
% 0.29/0.50 => ( ord_less_eq @ nat @ Y4 @ X5 ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Nat.ex_has_greatest_nat
% 0.29/0.50 thf(fact_129_nat__le__linear,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ M @ N )
% 0.29/0.50 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.29/0.50
% 0.29/0.50 % nat_le_linear
% 0.29/0.50 thf(fact_130_le__antisym,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ M @ N )
% 0.29/0.50 => ( ( ord_less_eq @ nat @ N @ M )
% 0.29/0.50 => ( M = N ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_antisym
% 0.29/0.50 thf(fact_131_eq__imp__le,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( M = N )
% 0.29/0.50 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.29/0.50
% 0.29/0.50 % eq_imp_le
% 0.29/0.50 thf(fact_132_le__trans,axiom,
% 0.29/0.50 ! [I2: nat,J: nat,K2: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ I2 @ J )
% 0.29/0.50 => ( ( ord_less_eq @ nat @ J @ K2 )
% 0.29/0.50 => ( ord_less_eq @ nat @ I2 @ K2 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_trans
% 0.29/0.50 thf(fact_133_le__refl,axiom,
% 0.29/0.50 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 0.29/0.50
% 0.29/0.50 % le_refl
% 0.29/0.50 thf(fact_134_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.29/0.50 ! [A2: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 0.29/0.50 => ( A2
% 0.29/0.50 = ( zero_zero @ nat ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % bot_nat_0.extremum_uniqueI
% 0.29/0.50 thf(fact_135_bot__nat__0_Oextremum__unique,axiom,
% 0.29/0.50 ! [A2: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 0.29/0.50 = ( A2
% 0.29/0.50 = ( zero_zero @ nat ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % bot_nat_0.extremum_unique
% 0.29/0.50 thf(fact_136_le__0__eq,axiom,
% 0.29/0.50 ! [N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ N @ ( zero_zero @ nat ) )
% 0.29/0.50 = ( N
% 0.29/0.50 = ( zero_zero @ nat ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_0_eq
% 0.29/0.50 thf(fact_137_less__eq__nat_Osimps_I1_J,axiom,
% 0.29/0.50 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 0.29/0.50
% 0.29/0.50 % less_eq_nat.simps(1)
% 0.29/0.50 thf(fact_138_Suc__leD,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 0.29/0.50 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.29/0.50
% 0.29/0.50 % Suc_leD
% 0.29/0.50 thf(fact_139_le__SucE,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ M @ ( suc @ N ) )
% 0.29/0.50 => ( ~ ( ord_less_eq @ nat @ M @ N )
% 0.29/0.50 => ( M
% 0.29/0.50 = ( suc @ N ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_SucE
% 0.29/0.50 thf(fact_140_le__SucI,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ M @ N )
% 0.29/0.50 => ( ord_less_eq @ nat @ M @ ( suc @ N ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_SucI
% 0.29/0.50 thf(fact_141_Suc__le__D,axiom,
% 0.29/0.50 ! [N: nat,M6: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ ( suc @ N ) @ M6 )
% 0.29/0.50 => ? [M4: nat] :
% 0.29/0.50 ( M6
% 0.29/0.50 = ( suc @ M4 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Suc_le_D
% 0.29/0.50 thf(fact_142_le__Suc__eq,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ M @ ( suc @ N ) )
% 0.29/0.50 = ( ( ord_less_eq @ nat @ M @ N )
% 0.29/0.50 | ( M
% 0.29/0.50 = ( suc @ N ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_Suc_eq
% 0.29/0.50 thf(fact_143_Suc__n__not__le__n,axiom,
% 0.29/0.50 ! [N: nat] :
% 0.29/0.50 ~ ( ord_less_eq @ nat @ ( suc @ N ) @ N ) ).
% 0.29/0.50
% 0.29/0.50 % Suc_n_not_le_n
% 0.29/0.50 thf(fact_144_not__less__eq__eq,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ~ ( ord_less_eq @ nat @ M @ N ) )
% 0.29/0.50 = ( ord_less_eq @ nat @ ( suc @ N ) @ M ) ) ).
% 0.29/0.50
% 0.29/0.50 % not_less_eq_eq
% 0.29/0.50 thf(fact_145_full__nat__induct,axiom,
% 0.29/0.50 ! [P2: nat > $o,N: nat] :
% 0.29/0.50 ( ! [N2: nat] :
% 0.29/0.50 ( ! [M3: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ ( suc @ M3 ) @ N2 )
% 0.29/0.50 => ( P2 @ M3 ) )
% 0.29/0.50 => ( P2 @ N2 ) )
% 0.29/0.50 => ( P2 @ N ) ) ).
% 0.29/0.50
% 0.29/0.50 % full_nat_induct
% 0.29/0.50 thf(fact_146_nat__induct__at__least,axiom,
% 0.29/0.50 ! [M: nat,N: nat,P2: nat > $o] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ M @ N )
% 0.29/0.50 => ( ( P2 @ M )
% 0.29/0.50 => ( ! [N2: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.29/0.50 => ( ( P2 @ N2 )
% 0.29/0.50 => ( P2 @ ( suc @ N2 ) ) ) )
% 0.29/0.50 => ( P2 @ N ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % nat_induct_at_least
% 0.29/0.50 thf(fact_147_transitive__stepwise__le,axiom,
% 0.29/0.50 ! [M: nat,N: nat,R: nat > nat > $o] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ M @ N )
% 0.29/0.50 => ( ! [X5: nat] : ( R @ X5 @ X5 )
% 0.29/0.50 => ( ! [X5: nat,Y5: nat,Z3: nat] :
% 0.29/0.50 ( ( R @ X5 @ Y5 )
% 0.29/0.50 => ( ( R @ Y5 @ Z3 )
% 0.29/0.50 => ( R @ X5 @ Z3 ) ) )
% 0.29/0.50 => ( ! [N2: nat] : ( R @ N2 @ ( suc @ N2 ) )
% 0.29/0.50 => ( R @ M @ N ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % transitive_stepwise_le
% 0.29/0.50 thf(fact_148_less__mono__imp__le__mono,axiom,
% 0.29/0.50 ! [F: nat > nat,I2: nat,J: nat] :
% 0.29/0.50 ( ! [I3: nat,J2: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ I3 @ J2 )
% 0.29/0.50 => ( ord_less @ nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 0.29/0.50 => ( ( ord_less_eq @ nat @ I2 @ J )
% 0.29/0.50 => ( ord_less_eq @ nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % less_mono_imp_le_mono
% 0.29/0.50 thf(fact_149_le__neq__implies__less,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ M @ N )
% 0.29/0.50 => ( ( M != N )
% 0.29/0.50 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_neq_implies_less
% 0.29/0.50 thf(fact_150_less__or__eq__imp__le,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ( ord_less @ nat @ M @ N )
% 0.29/0.50 | ( M = N ) )
% 0.29/0.50 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.29/0.50
% 0.29/0.50 % less_or_eq_imp_le
% 0.29/0.50 thf(fact_151_le__eq__less__or__eq,axiom,
% 0.29/0.50 ( ( ord_less_eq @ nat )
% 0.29/0.50 = ( ^ [M5: nat,N4: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ M5 @ N4 )
% 0.29/0.50 | ( M5 = N4 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_eq_less_or_eq
% 0.29/0.50 thf(fact_152_less__imp__le__nat,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ M @ N )
% 0.29/0.50 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.29/0.50
% 0.29/0.50 % less_imp_le_nat
% 0.29/0.50 thf(fact_153_nat__less__le,axiom,
% 0.29/0.50 ( ( ord_less @ nat )
% 0.29/0.50 = ( ^ [M5: nat,N4: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ M5 @ N4 )
% 0.29/0.50 & ( M5 != N4 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % nat_less_le
% 0.29/0.50 thf(fact_154_ex__least__nat__le,axiom,
% 0.29/0.50 ! [P2: nat > $o,N: nat] :
% 0.29/0.50 ( ( P2 @ N )
% 0.29/0.50 => ( ~ ( P2 @ ( zero_zero @ nat ) )
% 0.29/0.50 => ? [K: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ K @ N )
% 0.29/0.50 & ! [I: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ I @ K )
% 0.29/0.50 => ~ ( P2 @ I ) )
% 0.29/0.50 & ( P2 @ K ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ex_least_nat_le
% 0.29/0.50 thf(fact_155_Suc__leI,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ M @ N )
% 0.29/0.50 => ( ord_less_eq @ nat @ ( suc @ M ) @ N ) ) ).
% 0.29/0.50
% 0.29/0.50 % Suc_leI
% 0.29/0.50 thf(fact_156_Suc__le__eq,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 0.29/0.50 = ( ord_less @ nat @ M @ N ) ) ).
% 0.29/0.50
% 0.29/0.50 % Suc_le_eq
% 0.29/0.50 thf(fact_157_dec__induct,axiom,
% 0.29/0.50 ! [I2: nat,J: nat,P2: nat > $o] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ I2 @ J )
% 0.29/0.50 => ( ( P2 @ I2 )
% 0.29/0.50 => ( ! [N2: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ I2 @ N2 )
% 0.29/0.50 => ( ( ord_less @ nat @ N2 @ J )
% 0.29/0.50 => ( ( P2 @ N2 )
% 0.29/0.50 => ( P2 @ ( suc @ N2 ) ) ) ) )
% 0.29/0.50 => ( P2 @ J ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % dec_induct
% 0.29/0.50 thf(fact_158_inc__induct,axiom,
% 0.29/0.50 ! [I2: nat,J: nat,P2: nat > $o] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ I2 @ J )
% 0.29/0.50 => ( ( P2 @ J )
% 0.29/0.50 => ( ! [N2: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ I2 @ N2 )
% 0.29/0.50 => ( ( ord_less @ nat @ N2 @ J )
% 0.29/0.50 => ( ( P2 @ ( suc @ N2 ) )
% 0.29/0.50 => ( P2 @ N2 ) ) ) )
% 0.29/0.50 => ( P2 @ I2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % inc_induct
% 0.29/0.50 thf(fact_159_Suc__le__lessD,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 0.29/0.50 => ( ord_less @ nat @ M @ N ) ) ).
% 0.29/0.50
% 0.29/0.50 % Suc_le_lessD
% 0.29/0.50 thf(fact_160_le__less__Suc__eq,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ M @ N )
% 0.29/0.50 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 0.29/0.50 = ( N = M ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_less_Suc_eq
% 0.29/0.50 thf(fact_161_less__Suc__eq__le,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.29/0.50 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.29/0.50
% 0.29/0.50 % less_Suc_eq_le
% 0.29/0.50 thf(fact_162_less__eq__Suc__le,axiom,
% 0.29/0.50 ( ( ord_less @ nat )
% 0.29/0.50 = ( ^ [N4: nat] : ( ord_less_eq @ nat @ ( suc @ N4 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % less_eq_Suc_le
% 0.29/0.50 thf(fact_163_le__imp__less__Suc,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ M @ N )
% 0.29/0.50 => ( ord_less @ nat @ M @ ( suc @ N ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_imp_less_Suc
% 0.29/0.50 thf(fact_164_remdups__adj__length,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A] : ( ord_less_eq @ nat @ ( size_size @ ( list @ A ) @ ( remdups_adj @ A @ Xs ) ) @ ( size_size @ ( list @ A ) @ Xs ) ) ).
% 0.29/0.50
% 0.29/0.50 % remdups_adj_length
% 0.29/0.50 thf(fact_165_last__tl,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A] :
% 0.29/0.50 ( ( ( Xs
% 0.29/0.50 = ( nil @ A ) )
% 0.29/0.50 | ( ( tl @ A @ Xs )
% 0.29/0.50 != ( nil @ A ) ) )
% 0.29/0.50 => ( ( last @ A @ ( tl @ A @ Xs ) )
% 0.29/0.50 = ( last @ A @ Xs ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % last_tl
% 0.29/0.50 thf(fact_166_ex__least__nat__less,axiom,
% 0.29/0.50 ! [P2: nat > $o,N: nat] :
% 0.29/0.50 ( ( P2 @ N )
% 0.29/0.50 => ( ~ ( P2 @ ( zero_zero @ nat ) )
% 0.29/0.50 => ? [K: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ K @ N )
% 0.29/0.50 & ! [I: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ I @ K )
% 0.29/0.50 => ~ ( P2 @ I ) )
% 0.29/0.50 & ( P2 @ ( suc @ K ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % ex_least_nat_less
% 0.29/0.50 thf(fact_167_zero__reorient,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( zero @ A )
% 0.29/0.50 => ! [X: A] :
% 0.29/0.50 ( ( ( zero_zero @ A )
% 0.29/0.50 = X )
% 0.29/0.50 = ( X
% 0.29/0.50 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % zero_reorient
% 0.29/0.50 thf(fact_168_remdups__adj__length__ge1,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A] :
% 0.29/0.50 ( ( Xs
% 0.29/0.50 != ( nil @ A ) )
% 0.29/0.50 => ( ord_less_eq @ nat @ ( suc @ ( zero_zero @ nat ) ) @ ( size_size @ ( list @ A ) @ ( remdups_adj @ A @ Xs ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % remdups_adj_length_ge1
% 0.29/0.50 thf(fact_169_zero__less__iff__neq__zero,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( canoni770627133id_add @ A )
% 0.29/0.50 => ! [N: A] :
% 0.29/0.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 0.29/0.50 = ( N
% 0.29/0.50 != ( zero_zero @ A ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % zero_less_iff_neq_zero
% 0.29/0.50 thf(fact_170_gr__implies__not__zero,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( canoni770627133id_add @ A )
% 0.29/0.50 => ! [M: A,N: A] :
% 0.29/0.50 ( ( ord_less @ A @ M @ N )
% 0.29/0.50 => ( N
% 0.29/0.50 != ( zero_zero @ A ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % gr_implies_not_zero
% 0.29/0.50 thf(fact_171_not__less__zero,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( canoni770627133id_add @ A )
% 0.29/0.50 => ! [N: A] :
% 0.29/0.50 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % not_less_zero
% 0.29/0.50 thf(fact_172_gr__zeroI,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( canoni770627133id_add @ A )
% 0.29/0.50 => ! [N: A] :
% 0.29/0.50 ( ( N
% 0.29/0.50 != ( zero_zero @ A ) )
% 0.29/0.50 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % gr_zeroI
% 0.29/0.50 thf(fact_173_LastOfIndex,axiom,
% 0.29/0.50 ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( suc @ ( zero_zero @ nat ) ) ) )
% 0.29/0.50 = ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % LastOfIndex
% 0.29/0.50 thf(fact_174__092_060open_062_092_060And_062n0_Amsg_O_A_092_060forall_062n_O_Aexecution_OfirstOccurrence_A_Ife_An_J_A_Ift_An_J_Amsg_An0_A_092_060longrightarrow_062_Amsg_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062,axiom,
% 0.29/0.50 ! [Msg2: message @ p @ v,N03: nat,N7: nat] :
% 0.29/0.50 ( ( firstOccurrence @ p @ v @ s @ ( fe @ N7 ) @ ( ft @ N7 ) @ Msg2 @ N03 )
% 0.29/0.50 => ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N7 ) ) @ Msg2 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % \<open>\<And>n0 msg. \<forall>n. execution.firstOccurrence (fe n) (ft n) msg n0 \<longrightarrow> msg \<in># msgs (last (fe n))\<close>
% 0.29/0.50 thf(fact_175__092_060open_062_092_060forall_062n_O_A_092_060forall_062msg_H_092_060in_062firstOccSet_An_O_Amsg_H_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062,axiom,
% 0.29/0.50 ! [N7: nat,X6: message @ p @ v] :
% 0.29/0.50 ( ( member @ ( message @ p @ v ) @ X6 @ ( firstOccSet @ N7 ) )
% 0.29/0.50 => ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N7 ) ) @ X6 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % \<open>\<forall>n. \<forall>msg'\<in>firstOccSet n. msg' \<in># msgs (last (fe n))\<close>
% 0.29/0.50 thf(fact_176_PrefixSameOnLow,axiom,
% 0.29/0.50 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 0.29/0.50 ( ( prefixList @ A @ L1 @ L2 )
% 0.29/0.50 => ! [Index: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ Index @ ( size_size @ ( list @ A ) @ L1 ) )
% 0.29/0.50 => ( ( nth @ A @ L1 @ Index )
% 0.29/0.50 = ( nth @ A @ L2 @ Index ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % PrefixSameOnLow
% 0.29/0.50 thf(fact_177_IPrefixList,axiom,
% 0.29/0.50 ! [I: nat] : ( prefixList @ ( message @ p @ v ) @ ( ft @ I ) @ ( ft @ ( suc @ I ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % IPrefixList
% 0.29/0.50 thf(fact_178_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( cancel1352612707id_add @ A )
% 0.29/0.50 => ! [A2: A] :
% 0.29/0.50 ( ( minus_minus @ A @ A2 @ A2 )
% 0.29/0.50 = ( zero_zero @ A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % cancel_comm_monoid_add_class.diff_cancel
% 0.29/0.50 thf(fact_179_diff__zero,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( cancel1352612707id_add @ A )
% 0.29/0.50 => ! [A2: A] :
% 0.29/0.50 ( ( minus_minus @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.50 = A2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_zero
% 0.29/0.50 thf(fact_180_zero__diff,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( comm_monoid_diff @ A )
% 0.29/0.50 => ! [A2: A] :
% 0.29/0.50 ( ( minus_minus @ A @ ( zero_zero @ A ) @ A2 )
% 0.29/0.50 = ( zero_zero @ A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % zero_diff
% 0.29/0.50 thf(fact_181_diff__0__right,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( group_add @ A )
% 0.29/0.50 => ! [A2: A] :
% 0.29/0.50 ( ( minus_minus @ A @ A2 @ ( zero_zero @ A ) )
% 0.29/0.50 = A2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_0_right
% 0.29/0.50 thf(fact_182_diff__self,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( group_add @ A )
% 0.29/0.50 => ! [A2: A] :
% 0.29/0.50 ( ( minus_minus @ A @ A2 @ A2 )
% 0.29/0.50 = ( zero_zero @ A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_self
% 0.29/0.50 thf(fact_183_diff__0__eq__0,axiom,
% 0.29/0.50 ! [N: nat] :
% 0.29/0.50 ( ( minus_minus @ nat @ ( zero_zero @ nat ) @ N )
% 0.29/0.50 = ( zero_zero @ nat ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_0_eq_0
% 0.29/0.50 thf(fact_184_diff__self__eq__0,axiom,
% 0.29/0.50 ! [M: nat] :
% 0.29/0.50 ( ( minus_minus @ nat @ M @ M )
% 0.29/0.50 = ( zero_zero @ nat ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_self_eq_0
% 0.29/0.50 thf(fact_185_Suc__diff__diff,axiom,
% 0.29/0.50 ! [M: nat,N: nat,K2: nat] :
% 0.29/0.50 ( ( minus_minus @ nat @ ( minus_minus @ nat @ ( suc @ M ) @ N ) @ ( suc @ K2 ) )
% 0.29/0.50 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ N ) @ K2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % Suc_diff_diff
% 0.29/0.50 thf(fact_186_diff__Suc__Suc,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( minus_minus @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.29/0.50 = ( minus_minus @ nat @ M @ N ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_Suc_Suc
% 0.29/0.50 thf(fact_187_diff__diff__cancel,axiom,
% 0.29/0.50 ! [I2: nat,N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ I2 @ N )
% 0.29/0.50 => ( ( minus_minus @ nat @ N @ ( minus_minus @ nat @ N @ I2 ) )
% 0.29/0.50 = I2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_diff_cancel
% 0.29/0.50 thf(fact_188_diff__ge__0__iff__ge,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( ordered_ab_group_add @ A )
% 0.29/0.50 => ! [A2: A,B2: A] :
% 0.29/0.50 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A2 @ B2 ) )
% 0.29/0.50 = ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_ge_0_iff_ge
% 0.29/0.50 thf(fact_189_diff__gt__0__iff__gt,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( ordered_ab_group_add @ A )
% 0.29/0.50 => ! [A2: A,B2: A] :
% 0.29/0.50 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A2 @ B2 ) )
% 0.29/0.50 = ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_gt_0_iff_gt
% 0.29/0.50 thf(fact_190_zero__less__diff,axiom,
% 0.29/0.50 ! [N: nat,M: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( minus_minus @ nat @ N @ M ) )
% 0.29/0.50 = ( ord_less @ nat @ M @ N ) ) ).
% 0.29/0.50
% 0.29/0.50 % zero_less_diff
% 0.29/0.50 thf(fact_191_diff__is__0__eq_H,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ M @ N )
% 0.29/0.50 => ( ( minus_minus @ nat @ M @ N )
% 0.29/0.50 = ( zero_zero @ nat ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_is_0_eq'
% 0.29/0.50 thf(fact_192_diff__is__0__eq,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ( minus_minus @ nat @ M @ N )
% 0.29/0.50 = ( zero_zero @ nat ) )
% 0.29/0.50 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_is_0_eq
% 0.29/0.50 thf(fact_193_Suc__pred,axiom,
% 0.29/0.50 ! [N: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.29/0.50 => ( ( suc @ ( minus_minus @ nat @ N @ ( suc @ ( zero_zero @ nat ) ) ) )
% 0.29/0.50 = N ) ) ).
% 0.29/0.50
% 0.29/0.50 % Suc_pred
% 0.29/0.50 thf(fact_194_eq__iff__diff__eq__0,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( group_add @ A )
% 0.29/0.50 => ( ( ^ [Y3: A,Z2: A] : ( Y3 = Z2 ) )
% 0.29/0.50 = ( ^ [A8: A,B3: A] :
% 0.29/0.50 ( ( minus_minus @ A @ A8 @ B3 )
% 0.29/0.50 = ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % eq_iff_diff_eq_0
% 0.29/0.50 thf(fact_195_diff__strict__mono,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( ordered_ab_group_add @ A )
% 0.29/0.50 => ! [A2: A,B2: A,D: A,C: A] :
% 0.29/0.50 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/0.50 => ( ( ord_less @ A @ D @ C )
% 0.29/0.50 => ( ord_less @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B2 @ D ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_strict_mono
% 0.29/0.50 thf(fact_196_diff__eq__diff__less,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( ordered_ab_group_add @ A )
% 0.29/0.50 => ! [A2: A,B2: A,C: A,D: A] :
% 0.29/0.50 ( ( ( minus_minus @ A @ A2 @ B2 )
% 0.29/0.50 = ( minus_minus @ A @ C @ D ) )
% 0.29/0.50 => ( ( ord_less @ A @ A2 @ B2 )
% 0.29/0.50 = ( ord_less @ A @ C @ D ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_eq_diff_less
% 0.29/0.50 thf(fact_197_diff__strict__left__mono,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( ordered_ab_group_add @ A )
% 0.29/0.50 => ! [B2: A,A2: A,C: A] :
% 0.29/0.50 ( ( ord_less @ A @ B2 @ A2 )
% 0.29/0.50 => ( ord_less @ A @ ( minus_minus @ A @ C @ A2 ) @ ( minus_minus @ A @ C @ B2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_strict_left_mono
% 0.29/0.50 thf(fact_198_diff__strict__right__mono,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( ordered_ab_group_add @ A )
% 0.29/0.50 => ! [A2: A,B2: A,C: A] :
% 0.29/0.50 ( ( ord_less @ A @ A2 @ B2 )
% 0.29/0.50 => ( ord_less @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B2 @ C ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_strict_right_mono
% 0.29/0.50 thf(fact_199_diff__eq__diff__eq,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( group_add @ A )
% 0.29/0.50 => ! [A2: A,B2: A,C: A,D: A] :
% 0.29/0.50 ( ( ( minus_minus @ A @ A2 @ B2 )
% 0.29/0.50 = ( minus_minus @ A @ C @ D ) )
% 0.29/0.50 => ( ( A2 = B2 )
% 0.29/0.50 = ( C = D ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_eq_diff_eq
% 0.29/0.50 thf(fact_200_diff__mono,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( ordered_ab_group_add @ A )
% 0.29/0.50 => ! [A2: A,B2: A,D: A,C: A] :
% 0.29/0.50 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.50 => ( ( ord_less_eq @ A @ D @ C )
% 0.29/0.50 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B2 @ D ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_mono
% 0.29/0.50 thf(fact_201_diff__left__mono,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( ordered_ab_group_add @ A )
% 0.29/0.50 => ! [B2: A,A2: A,C: A] :
% 0.29/0.50 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.29/0.50 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A2 ) @ ( minus_minus @ A @ C @ B2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_left_mono
% 0.29/0.50 thf(fact_202_diff__right__mono,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( ordered_ab_group_add @ A )
% 0.29/0.50 => ! [A2: A,B2: A,C: A] :
% 0.29/0.50 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.50 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B2 @ C ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_right_mono
% 0.29/0.50 thf(fact_203_diff__eq__diff__less__eq,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( ordered_ab_group_add @ A )
% 0.29/0.50 => ! [A2: A,B2: A,C: A,D: A] :
% 0.29/0.50 ( ( ( minus_minus @ A @ A2 @ B2 )
% 0.29/0.50 = ( minus_minus @ A @ C @ D ) )
% 0.29/0.50 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.29/0.50 = ( ord_less_eq @ A @ C @ D ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_eq_diff_less_eq
% 0.29/0.50 thf(fact_204_diff__right__commute,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( cancel146912293up_add @ A )
% 0.29/0.50 => ! [A2: A,C: A,B2: A] :
% 0.29/0.50 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C ) @ B2 )
% 0.29/0.50 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B2 ) @ C ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_right_commute
% 0.29/0.50 thf(fact_205_diff__le__mono2,axiom,
% 0.29/0.50 ! [M: nat,N: nat,L: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ M @ N )
% 0.29/0.50 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ L @ N ) @ ( minus_minus @ nat @ L @ M ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_le_mono2
% 0.29/0.50 thf(fact_206_le__diff__iff_H,axiom,
% 0.29/0.50 ! [A2: nat,C: nat,B2: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ A2 @ C )
% 0.29/0.50 => ( ( ord_less_eq @ nat @ B2 @ C )
% 0.29/0.50 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ A2 ) @ ( minus_minus @ nat @ C @ B2 ) )
% 0.29/0.50 = ( ord_less_eq @ nat @ B2 @ A2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_diff_iff'
% 0.29/0.50 thf(fact_207_diff__le__self,axiom,
% 0.29/0.50 ! [M: nat,N: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ N ) @ M ) ).
% 0.29/0.50
% 0.29/0.50 % diff_le_self
% 0.29/0.50 thf(fact_208_diff__le__mono,axiom,
% 0.29/0.50 ! [M: nat,N: nat,L: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ M @ N )
% 0.29/0.50 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ L ) @ ( minus_minus @ nat @ N @ L ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_le_mono
% 0.29/0.50 thf(fact_209_Nat_Odiff__diff__eq,axiom,
% 0.29/0.50 ! [K2: nat,M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ K2 @ M )
% 0.29/0.50 => ( ( ord_less_eq @ nat @ K2 @ N )
% 0.29/0.50 => ( ( minus_minus @ nat @ ( minus_minus @ nat @ M @ K2 ) @ ( minus_minus @ nat @ N @ K2 ) )
% 0.29/0.50 = ( minus_minus @ nat @ M @ N ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Nat.diff_diff_eq
% 0.29/0.50 thf(fact_210_le__diff__iff,axiom,
% 0.29/0.50 ! [K2: nat,M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ K2 @ M )
% 0.29/0.50 => ( ( ord_less_eq @ nat @ K2 @ N )
% 0.29/0.50 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ K2 ) @ ( minus_minus @ nat @ N @ K2 ) )
% 0.29/0.50 = ( ord_less_eq @ nat @ M @ N ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_diff_iff
% 0.29/0.50 thf(fact_211_eq__diff__iff,axiom,
% 0.29/0.50 ! [K2: nat,M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ K2 @ M )
% 0.29/0.50 => ( ( ord_less_eq @ nat @ K2 @ N )
% 0.29/0.50 => ( ( ( minus_minus @ nat @ M @ K2 )
% 0.29/0.50 = ( minus_minus @ nat @ N @ K2 ) )
% 0.29/0.50 = ( M = N ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % eq_diff_iff
% 0.29/0.50 thf(fact_212_minus__nat_Odiff__0,axiom,
% 0.29/0.50 ! [M: nat] :
% 0.29/0.50 ( ( minus_minus @ nat @ M @ ( zero_zero @ nat ) )
% 0.29/0.50 = M ) ).
% 0.29/0.50
% 0.29/0.50 % minus_nat.diff_0
% 0.29/0.50 thf(fact_213_diffs0__imp__equal,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( ( minus_minus @ nat @ M @ N )
% 0.29/0.50 = ( zero_zero @ nat ) )
% 0.29/0.50 => ( ( ( minus_minus @ nat @ N @ M )
% 0.29/0.50 = ( zero_zero @ nat ) )
% 0.29/0.50 => ( M = N ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diffs0_imp_equal
% 0.29/0.50 thf(fact_214_zero__induct__lemma,axiom,
% 0.29/0.50 ! [P2: nat > $o,K2: nat,I2: nat] :
% 0.29/0.50 ( ( P2 @ K2 )
% 0.29/0.50 => ( ! [N2: nat] :
% 0.29/0.50 ( ( P2 @ ( suc @ N2 ) )
% 0.29/0.50 => ( P2 @ N2 ) )
% 0.29/0.50 => ( P2 @ ( minus_minus @ nat @ K2 @ I2 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % zero_induct_lemma
% 0.29/0.50 thf(fact_215_less__imp__diff__less,axiom,
% 0.29/0.50 ! [J: nat,K2: nat,N: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ J @ K2 )
% 0.29/0.50 => ( ord_less @ nat @ ( minus_minus @ nat @ J @ N ) @ K2 ) ) ).
% 0.29/0.50
% 0.29/0.50 % less_imp_diff_less
% 0.29/0.50 thf(fact_216_diff__less__mono2,axiom,
% 0.29/0.50 ! [M: nat,N: nat,L: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ M @ N )
% 0.29/0.50 => ( ( ord_less @ nat @ M @ L )
% 0.29/0.50 => ( ord_less @ nat @ ( minus_minus @ nat @ L @ N ) @ ( minus_minus @ nat @ L @ M ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_less_mono2
% 0.29/0.50 thf(fact_217_diff__commute,axiom,
% 0.29/0.50 ! [I2: nat,J: nat,K2: nat] :
% 0.29/0.50 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I2 @ J ) @ K2 )
% 0.29/0.50 = ( minus_minus @ nat @ ( minus_minus @ nat @ I2 @ K2 ) @ J ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_commute
% 0.29/0.50 thf(fact_218_le__iff__diff__le__0,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( ordered_ab_group_add @ A )
% 0.29/0.50 => ( ( ord_less_eq @ A )
% 0.29/0.50 = ( ^ [A8: A,B3: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ A8 @ B3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % le_iff_diff_le_0
% 0.29/0.50 thf(fact_219_less__iff__diff__less__0,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( ordered_ab_group_add @ A )
% 0.29/0.50 => ( ( ord_less @ A )
% 0.29/0.50 = ( ^ [A8: A,B3: A] : ( ord_less @ A @ ( minus_minus @ A @ A8 @ B3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % less_iff_diff_less_0
% 0.29/0.50 thf(fact_220_diff__less,axiom,
% 0.29/0.50 ! [N: nat,M: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.29/0.50 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 0.29/0.50 => ( ord_less @ nat @ ( minus_minus @ nat @ M @ N ) @ M ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_less
% 0.29/0.50 thf(fact_221_diff__less__Suc,axiom,
% 0.29/0.50 ! [M: nat,N: nat] : ( ord_less @ nat @ ( minus_minus @ nat @ M @ N ) @ ( suc @ M ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_less_Suc
% 0.29/0.50 thf(fact_222_Suc__diff__Suc,axiom,
% 0.29/0.50 ! [N: nat,M: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ N @ M )
% 0.29/0.50 => ( ( suc @ ( minus_minus @ nat @ M @ ( suc @ N ) ) )
% 0.29/0.50 = ( minus_minus @ nat @ M @ N ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Suc_diff_Suc
% 0.29/0.50 thf(fact_223_Suc__diff__le,axiom,
% 0.29/0.50 ! [N: nat,M: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ N @ M )
% 0.29/0.50 => ( ( minus_minus @ nat @ ( suc @ M ) @ N )
% 0.29/0.50 = ( suc @ ( minus_minus @ nat @ M @ N ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Suc_diff_le
% 0.29/0.50 thf(fact_224_less__diff__iff,axiom,
% 0.29/0.50 ! [K2: nat,M: nat,N: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ K2 @ M )
% 0.29/0.50 => ( ( ord_less_eq @ nat @ K2 @ N )
% 0.29/0.50 => ( ( ord_less @ nat @ ( minus_minus @ nat @ M @ K2 ) @ ( minus_minus @ nat @ N @ K2 ) )
% 0.29/0.50 = ( ord_less @ nat @ M @ N ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % less_diff_iff
% 0.29/0.50 thf(fact_225_diff__less__mono,axiom,
% 0.29/0.50 ! [A2: nat,B2: nat,C: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ A2 @ B2 )
% 0.29/0.50 => ( ( ord_less_eq @ nat @ C @ A2 )
% 0.29/0.50 => ( ord_less @ nat @ ( minus_minus @ nat @ A2 @ C ) @ ( minus_minus @ nat @ B2 @ C ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_less_mono
% 0.29/0.50 thf(fact_226_diff__Suc__less,axiom,
% 0.29/0.50 ! [N: nat,I2: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.29/0.50 => ( ord_less @ nat @ ( minus_minus @ nat @ N @ ( suc @ I2 ) ) @ N ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_Suc_less
% 0.29/0.50 thf(fact_227_MinPredicate,axiom,
% 0.29/0.50 ! [P2: nat > $o] :
% 0.29/0.50 ( ? [X_1: nat] : ( P2 @ X_1 )
% 0.29/0.50 => ? [N04: nat] :
% 0.29/0.50 ( ( P2 @ N04 )
% 0.29/0.50 & ! [N5: nat] :
% 0.29/0.50 ( ( P2 @ N5 )
% 0.29/0.50 => ( ord_less_eq @ nat @ N04 @ N5 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % MinPredicate
% 0.29/0.50 thf(fact_228_PrefixListTransitive,axiom,
% 0.29/0.50 ! [A: $tType,L1: list @ A,L2: list @ A,L3: list @ A] :
% 0.29/0.50 ( ( prefixList @ A @ L1 @ L2 )
% 0.29/0.50 => ( ( prefixList @ A @ L2 @ L3 )
% 0.29/0.50 => ( prefixList @ A @ L1 @ L3 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % PrefixListTransitive
% 0.29/0.50 thf(fact_229_KeepProperty,axiom,
% 0.29/0.50 ! [Low: nat,P2: nat > $o,Q: nat > $o] :
% 0.29/0.50 ( ! [I3: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ Low @ I3 )
% 0.29/0.50 => ( ( P2 @ I3 )
% 0.29/0.50 => ( ( P2 @ ( suc @ I3 ) )
% 0.29/0.50 & ( Q @ I3 ) ) ) )
% 0.29/0.50 => ( ( P2 @ Low )
% 0.29/0.50 => ! [I: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ Low @ I )
% 0.29/0.50 => ( Q @ I ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % KeepProperty
% 0.29/0.50 thf(fact_230_NatPredicateTippingPoint,axiom,
% 0.29/0.50 ! [N22: nat,Pr: nat > $o] :
% 0.29/0.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N22 )
% 0.29/0.50 => ( ( Pr @ ( zero_zero @ nat ) )
% 0.29/0.50 => ( ~ ( Pr @ N22 )
% 0.29/0.50 => ? [N2: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ N2 @ N22 )
% 0.29/0.50 & ( Pr @ N2 )
% 0.29/0.50 & ~ ( Pr @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % NatPredicateTippingPoint
% 0.29/0.50 thf(fact_231_PrefixListMonotonicity,axiom,
% 0.29/0.50 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 0.29/0.50 ( ( prefixList @ A @ L1 @ L2 )
% 0.29/0.50 => ( ord_less @ nat @ ( size_size @ ( list @ A ) @ L1 ) @ ( size_size @ ( list @ A ) @ L2 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % PrefixListMonotonicity
% 0.29/0.50 thf(fact_232_EnabledOrConsumed,axiom,
% 0.29/0.50 ( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ) @ ( one_one @ nat ) ) ) @ msg )
% 0.29/0.50 | ? [N02: nat] :
% 0.29/0.50 ( ( ord_less_eq @ nat @ n0 @ N02 )
% 0.29/0.50 & ( ord_less @ nat @ N02 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
% 0.29/0.50 & ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ N02 )
% 0.29/0.50 = msg ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % EnabledOrConsumed
% 0.29/0.50 thf(fact_233__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,
% 0.29/0.50 ~ ? [I: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ I @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) )
% 0.29/0.50 & ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ I )
% 0.29/0.50 & ( msg
% 0.29/0.50 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % \<open>\<not> (\<exists>i<length (fe (Suc index)) - 1. length (fe index) - 1 \<le> i \<and> msg = ft (Suc index) ! i)\<close>
% 0.29/0.50 thf(fact_234_EnabledIntermediate,axiom,
% 0.29/0.50 ! [I: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) )
% 0.29/0.50 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ I )
% 0.29/0.50 => ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ I ) @ msg ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % EnabledIntermediate
% 0.29/0.50 thf(fact_235__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,
% 0.29/0.50 ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) ).
% 0.29/0.50
% 0.29/0.50 % \<open>length (fe index) - 1 \<le> length (fe (Suc index)) - 1\<close>
% 0.29/0.50 thf(fact_236_less__one,axiom,
% 0.29/0.50 ! [N: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ N @ ( one_one @ nat ) )
% 0.29/0.50 = ( N
% 0.29/0.50 = ( zero_zero @ nat ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % less_one
% 0.29/0.50 thf(fact_237__092_060open_062enabled_A_Ife_A_ISuc_Aindex_J_A_B_A_Ilength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_J_J_Amsg_092_060close_062,axiom,
% 0.29/0.50 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) ) @ msg ).
% 0.29/0.50
% 0.29/0.50 % \<open>enabled (fe (Suc index) ! (length (fe (Suc index)) - 1)) msg\<close>
% 0.29/0.50 thf(fact_238_diff__Suc__1,axiom,
% 0.29/0.50 ! [N: nat] :
% 0.29/0.50 ( ( minus_minus @ nat @ ( suc @ N ) @ ( one_one @ nat ) )
% 0.29/0.50 = N ) ).
% 0.29/0.50
% 0.29/0.50 % diff_Suc_1
% 0.29/0.50 thf(fact_239_length__tl,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A] :
% 0.29/0.50 ( ( size_size @ ( list @ A ) @ ( tl @ A @ Xs ) )
% 0.29/0.50 = ( minus_minus @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( one_one @ nat ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % length_tl
% 0.29/0.50 thf(fact_240_Suc__diff__1,axiom,
% 0.29/0.50 ! [N: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.29/0.50 => ( ( suc @ ( minus_minus @ nat @ N @ ( one_one @ nat ) ) )
% 0.29/0.50 = N ) ) ).
% 0.29/0.50
% 0.29/0.50 % Suc_diff_1
% 0.29/0.50 thf(fact_241_one__reorient,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( one @ A )
% 0.29/0.50 => ! [X: A] :
% 0.29/0.50 ( ( ( one_one @ A )
% 0.29/0.50 = X )
% 0.29/0.50 = ( X
% 0.29/0.50 = ( one_one @ A ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % one_reorient
% 0.29/0.50 thf(fact_242_One__nat__def,axiom,
% 0.29/0.50 ( ( one_one @ nat )
% 0.29/0.50 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % One_nat_def
% 0.29/0.50 thf(fact_243_MinPredicate2,axiom,
% 0.29/0.50 ! [P2: nat > $o] :
% 0.29/0.50 ( ? [X_1: nat] : ( P2 @ X_1 )
% 0.29/0.50 => ? [N04: nat] :
% 0.29/0.50 ( ( P2 @ N04 )
% 0.29/0.50 & ( ( N04
% 0.29/0.50 = ( zero_zero @ nat ) )
% 0.29/0.50 | ~ ( P2 @ ( minus_minus @ nat @ N04 @ ( one_one @ nat ) ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % MinPredicate2
% 0.29/0.50 thf(fact_244_diff__Suc__eq__diff__pred,axiom,
% 0.29/0.50 ! [M: nat,N: nat] :
% 0.29/0.50 ( ( minus_minus @ nat @ M @ ( suc @ N ) )
% 0.29/0.50 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ ( one_one @ nat ) ) @ N ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_Suc_eq_diff_pred
% 0.29/0.50 thf(fact_245_nat__induct__non__zero,axiom,
% 0.29/0.50 ! [N: nat,P2: nat > $o] :
% 0.29/0.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.29/0.50 => ( ( P2 @ ( one_one @ nat ) )
% 0.29/0.50 => ( ! [N2: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.29/0.50 => ( ( P2 @ N2 )
% 0.29/0.50 => ( P2 @ ( suc @ N2 ) ) ) )
% 0.29/0.50 => ( P2 @ N ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % nat_induct_non_zero
% 0.29/0.50 thf(fact_246_Suc__pred_H,axiom,
% 0.29/0.50 ! [N: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.29/0.50 => ( N
% 0.29/0.50 = ( suc @ ( minus_minus @ nat @ N @ ( one_one @ nat ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Suc_pred'
% 0.29/0.50 thf(fact_247_Suc__diff__eq__diff__pred,axiom,
% 0.29/0.50 ! [N: nat,M: nat] :
% 0.29/0.50 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.29/0.50 => ( ( minus_minus @ nat @ ( suc @ M ) @ N )
% 0.29/0.50 = ( minus_minus @ nat @ M @ ( minus_minus @ nat @ N @ ( one_one @ nat ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % Suc_diff_eq_diff_pred
% 0.29/0.50 thf(fact_248_last__conv__nth,axiom,
% 0.29/0.50 ! [A: $tType,Xs: list @ A] :
% 0.29/0.50 ( ( Xs
% 0.29/0.50 != ( nil @ A ) )
% 0.29/0.50 => ( ( last @ A @ Xs )
% 0.29/0.50 = ( nth @ A @ Xs @ ( minus_minus @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( one_one @ nat ) ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % last_conv_nth
% 0.29/0.50 thf(fact_249_diff__numeral__special_I9_J,axiom,
% 0.29/0.50 ! [A: $tType] :
% 0.29/0.50 ( ( neg_numeral @ A )
% 0.29/0.50 => ( ( minus_minus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
% 0.29/0.50 = ( zero_zero @ A ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % diff_numeral_special(9)
% 0.29/0.50 thf(fact_250_enabled__def,axiom,
% 0.29/0.50 ! [S: $tType,V: $tType,P: $tType] :
% 0.29/0.50 ( ( enabled @ P @ V @ S )
% 0.29/0.50 = ( ^ [Cfg2: configuration_ext @ P @ V @ S @ product_unit,Msg4: message @ P @ V] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ P @ V @ S @ product_unit @ Cfg2 @ Msg4 ) ) ) ) ).
% 0.29/0.50
% 0.29/0.50 % enabled_def
% 0.29/0.50
% 0.29/0.50 % Type constructors (16)
% 0.29/0.50 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.29/0.50 ! [A9: $tType,A10: $tType] :
% 0.29/0.50 ( ( order @ A10 )
% 0.29/0.50 => ( order @ ( A9 > A10 ) ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.29/0.50 canoni770627133id_add @ nat ).
% 0.29/0.50
% 0.29/0.50 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 0.29/0.50 cancel146912293up_add @ nat ).
% 0.29/0.50
% 0.29/0.50 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 0.29/0.50 cancel1352612707id_add @ nat ).
% 0.29/0.50
% 0.29/0.50 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff,axiom,
% 0.29/0.50 comm_monoid_diff @ nat ).
% 0.29/0.50
% 0.29/0.50 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.29/0.50 wellorder @ nat ).
% 0.29/0.50
% 0.29/0.50 thf(tcon_Nat_Onat___Orderings_Oorder_1,axiom,
% 0.29/0.50 order @ nat ).
% 0.29/0.50
% 0.29/0.50 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.29/0.50 zero @ nat ).
% 0.29/0.50
% 0.29/0.50 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.29/0.50 one @ nat ).
% 0.29/0.50
% 0.29/0.50 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 0.29/0.50 size @ nat ).
% 0.29/0.50
% 0.29/0.50 thf(tcon_Set_Oset___Orderings_Oorder_2,axiom,
% 0.29/0.50 ! [A9: $tType] : ( order @ ( set @ A9 ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(tcon_HOL_Obool___Orderings_Oorder_3,axiom,
% 0.29/0.50 order @ $o ).
% 0.29/0.50
% 0.29/0.50 thf(tcon_List_Olist___Nat_Osize_4,axiom,
% 0.29/0.50 ! [A9: $tType] : ( size @ ( list @ A9 ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_5,axiom,
% 0.29/0.50 wellorder @ product_unit ).
% 0.29/0.50
% 0.29/0.50 thf(tcon_Product__Type_Ounit___Orderings_Oorder_6,axiom,
% 0.29/0.50 order @ product_unit ).
% 0.29/0.50
% 0.29/0.50 thf(tcon_AsynchronousSystem_Omessage___Nat_Osize_7,axiom,
% 0.29/0.50 ! [A9: $tType,A10: $tType] : ( size @ ( message @ A9 @ A10 ) ) ).
% 0.29/0.50
% 0.29/0.50 % Helper facts (3)
% 0.29/0.50 thf(help_If_3_1_T,axiom,
% 0.29/0.50 ! [P2: $o] :
% 0.29/0.50 ( ( P2 = $true )
% 0.29/0.50 | ( P2 = $false ) ) ).
% 0.29/0.50
% 0.29/0.50 thf(help_If_2_1_T,axiom,
% 0.29/0.50 ! [A: $tType,X: A,Y: A] :
% 0.29/0.50 ( ( if @ A @ $false @ X @ Y )
% 0.29/0.50 = Y ) ).
% 0.29/0.50
% 0.29/0.50 thf(help_If_1_1_T,axiom,
% 0.29/0.50 ! [A: $tType,X: A,Y: A] :
% 0.29/0.50 ( ( if @ A @ $true @ X @ Y )
% 0.29/0.50 = X ) ).
% 0.29/0.50
% 0.29/0.50 % Conjectures (1)
% 0.29/0.50 thf(conj_0,conjecture,
% 0.29/0.50 ord_less @ nat @ n1 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ).
% 0.29/0.50
% 0.29/0.50 %------------------------------------------------------------------------------
% 0.29/0.50 ------------------------
% 2.44/1.57 ---- Embedded in THF ---
% 2.44/1.58 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.44/1.58 %%% Generated on Tue Feb 24 08:24:59 EST 2026
% 2.44/1.58 %%% using '$$dhol' embedding, version 1.3.0.
% 2.44/1.58 %%% Logic specification used:
% 2.44/1.58 %%% thf(spec, logic, $$dhol).
% 2.44/1.58
% 2.44/1.58 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.6wC2JEysVn/DTF2DTF4609.p
% 2.44/1.58 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext, type, configuration_ext: ($tType > ($tType > ($tType > ($tType > $tType))))).
% 2.44/1.58 thf(ty_t_AsynchronousSystem_Omessage, type, message: ($tType > ($tType > $tType))).
% 2.44/1.58 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 2.44/1.58 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.44/1.58 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.44/1.58 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.44/1.58 thf(ty_tf_v, type, v: $tType).
% 2.44/1.58 thf(ty_tf_s, type, s: $tType).
% 2.44/1.58 thf(ty_tf_p, type, p: $tType).
% 2.44/1.58 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.44/1.58 thf(sy_cl_Nat_Osize, type, size: (!> [A:$tType]: ($o))).
% 2.44/1.58 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: ($o))).
% 2.44/1.58 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 2.44/1.58 thf(sy_cl_Num_Oneg__numeral, type, neg_numeral: (!> [A:$tType]: ($o))).
% 2.44/1.58 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.44/1.58 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 2.44/1.58 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 2.44/1.58 thf(sy_cl_Groups_Ocomm__monoid__diff, type, comm_monoid_diff: (!> [A:$tType]: ($o))).
% 2.44/1.58 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: ($o))).
% 2.44/1.58 thf(sy_cl_Groups_Ocancel__comm__monoid__add, type, cancel1352612707id_add: (!> [A:$tType]: ($o))).
% 2.44/1.58 thf(sy_cl_Groups_Ocancel__ab__semigroup__add, type, cancel146912293up_add: (!> [A:$tType]: ($o))).
% 2.44/1.58 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 2.44/1.58 thf(sy_c_AsynchronousSystem_Oconfiguration_Omsgs, type, msgs: (!> [P:$tType,V:$tType,S:$tType,Z:$tType]: ((((((configuration_ext @ P) @ V) @ S) @ Z) > (((message @ P) @ V) > nat))))).
% 2.44/1.58 thf(sy_c_AsynchronousSystem_Oenabled, type, enabled: (!> [P:$tType,V:$tType,S:$tType]: ((((((configuration_ext @ P) @ V) @ S) @ product_unit) > (((message @ P) @ V) > $o))))).
% 2.44/1.58 thf(sy_c_Execution_Oexecution_OfirstOccurrence, type, firstOccurrence: (!> [P:$tType,V:$tType,S:$tType]: (((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (((message @ P) @ V) > (nat > $o))))))).
% 2.44/1.58 thf(sy_c_Execution_Oexecution_OminimalEnabled, type, minimalEnabled: (!> [P:$tType,V:$tType,S:$tType]: (((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (((message @ P) @ V) > $o)))))).
% 2.44/1.58 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 2.44/1.58 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 2.44/1.58 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.44/1.58 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.44/1.58 thf(sy_c_ListUtilities_OprefixList, type, prefixList: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.44/1.58 thf(sy_c_List_Olast, type, last: (!> [A:$tType]: (((list @ A) > A)))).
% 2.44/1.58 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.44/1.58 thf(sy_c_List_Olist_Otl, type, tl: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.44/1.58 thf(sy_c_List_Olist__ex, type, list_ex: (!> [A:$tType]: (((A > $o) > ((list @ A) > $o))))).
% 2.44/1.58 thf(sy_c_List_Olist__ex1, type, list_ex1: (!> [A:$tType]: (((A > $o) > ((list @ A) > $o))))).
% 2.44/1.58 thf(sy_c_List_Onth, type, nth: (!> [A:$tType]: (((list @ A) > (nat > A))))).
% 2.44/1.58 thf(sy_c_List_Oremdups__adj, type, remdups_adj: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.44/1.58 thf(sy_c_Nat_OSuc, type, suc: (nat > nat)).
% 2.44/1.58 thf(sy_c_Nat_Osize__class_Osize, type, size_size: (!> [A:$tType]: ((A > nat)))).
% 2.44/1.58 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.44/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.44/1.58 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.44/1.58 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.44/1.58 thf(sy_v_consumedMsg____, type, consumedMsg: ((message @ p) @ v)).
% 2.44/1.58 thf(sy_v_fe____, type, fe: (nat > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))).
% 2.44/1.58 thf(sy_v_firstOccSet____, type, firstOccSet: (nat > (set @ ((message @ p) @ v)))).
% 2.44/1.58 thf(sy_v_ft____, type, ft: (nat > (list @ ((message @ p) @ v)))).
% 2.44/1.58 thf(sy_v_index____, type, index: nat).
% 2.44/1.58 thf(sy_v_msg____, type, msg: ((message @ p) @ v)).
% 2.44/1.58 thf(sy_v_n0____, type, n0: nat).
% 2.44/1.58 thf(sy_v_n1____, type, n1: nat).
% 2.44/1.58 thf(sy_v_nMsg____, type, nMsg: nat).
% 2.44/1.58 thf(sy_v_n____, type, n: nat).
% 2.44/1.58 thf(fact_0_AssumpGreaterOccurrence_I1_J, axiom, (~ ((((ord_less @ nat) @ nMsg) @ n1)))).
% 2.44/1.58 thf(fact_1__092_060open_062nMsg_A_060_Alength_A_Ife_Aindex_J_092_060close_062, axiom, (((ord_less @ nat) @ nMsg) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index)))).
% 2.44/1.58 thf(fact_2_NotEmpty_I2_J, axiom, ((fe @ index) != (nil @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))).
% 2.44/1.58 thf(fact_3_AssumptionFair_I2_J, axiom, (((ord_less @ nat) @ n0) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ n)))).
% 2.44/1.58 thf(fact_4_length__induct, axiom, (! [A:$tType,P2:((list @ A) > $o),Xs:(list @ A)]: (((! [Xs2:(list @ A)]: (((! [Ys:(list @ A)]: (((((ord_less @ nat) @ ((size_size @ (list @ A)) @ Ys)) @ ((size_size @ (list @ A)) @ Xs2)) => (P2 @ Ys)))) => (P2 @ Xs2)))) => (P2 @ Xs))))).
% 2.44/1.58 thf(fact_5_SameCfgOnLow, axiom, (! [I:nat]: (((((ord_less @ nat) @ I) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) => ((((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index)) @ I) = (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ I)))))).
% 2.44/1.58 thf(fact_6_Ex__list__of__length, axiom, (! [A:$tType,N:nat]: ((? [Xs2:(list @ A)]: ((((size_size @ (list @ A)) @ Xs2) = N)))))).
% 2.44/1.58 thf(fact_7_neq__if__length__neq, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((((size_size @ (list @ A)) @ Xs) != ((size_size @ (list @ A)) @ Ys2)) => (Xs != Ys2))))).
% 2.44/1.58 thf(fact_8_size__neq__size__imp__neq, axiom, (! [A:$tType]: (((size @ A) => (! [X:A,Y:A]: (((((size_size @ A) @ X) != ((size_size @ A) @ Y)) => (X != Y)))))))).
% 2.44/1.58 thf(fact_9_nat__neq__iff, axiom, (! [M:nat,N:nat]: (((M != N) = ((((ord_less @ nat) @ M) @ N) | (((ord_less @ nat) @ N) @ M)))))).
% 2.44/1.58 thf(fact_10_less__not__refl, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.44/1.58 thf(fact_11_less__not__refl2, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ N) @ M) => (M != N))))).
% 2.44/1.58 thf(fact_12_less__not__refl3, axiom, (! [S2:nat,T:nat]: (((((ord_less @ nat) @ S2) @ T) => (S2 != T))))).
% 2.44/1.58 thf(fact_13_less__irrefl__nat, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.44/1.58 thf(fact_14_nat_Oinject, axiom, (! [X2:nat,Y2:nat]: ((((suc @ X2) = (suc @ Y2)) = (X2 = Y2))))).
% 2.44/1.58 thf(fact_15_old_Onat_Oinject, axiom, (! [Nat:nat,Nat2:nat]: ((((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))).
% 2.44/1.58 thf(fact_16_NotEmpty_I1_J, axiom, ((fe @ (suc @ index)) != (nil @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))).
% 2.44/1.58 thf(fact_17_Suc__less__eq, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (suc @ M)) @ (suc @ N)) = (((ord_less @ nat) @ M) @ N))))).
% 2.44/1.58 thf(fact_18_Suc__mono, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less @ nat) @ (suc @ M)) @ (suc @ N)))))).
% 2.44/1.58 thf(fact_19_lessI, axiom, (! [N:nat]: ((((ord_less @ nat) @ N) @ (suc @ N))))).
% 2.44/1.58 thf(fact_20_Suc__inject, axiom, (! [X:nat,Y:nat]: ((((suc @ X) = (suc @ Y)) => (X = Y))))).
% 2.44/1.58 thf(fact_21_n__not__Suc__n, axiom, (! [N:nat]: ((N != (suc @ N))))).
% 2.44/1.58 thf(fact_22_not__less__less__Suc__eq, axiom, (! [N:nat,M:nat]: (((~ ((((ord_less @ nat) @ N) @ M))) => ((((ord_less @ nat) @ N) @ (suc @ M)) = (N = M)))))).
% 2.44/1.58 thf(fact_23_strict__inc__induct, axiom, (! [I2:nat,J:nat,P2:(nat > $o)]: (((((ord_less @ nat) @ I2) @ J) => ((! [I3:nat]: (((J = (suc @ I3)) => (P2 @ I3)))) => ((! [I3:nat]: (((((ord_less @ nat) @ I3) @ J) => ((P2 @ (suc @ I3)) => (P2 @ I3))))) => (P2 @ I2))))))).
% 2.44/1.58 thf(fact_24_less__Suc__induct, axiom, (! [I2:nat,J:nat,P2:(nat > (nat > $o))]: (((((ord_less @ nat) @ I2) @ J) => ((! [I3:nat]: (((P2 @ I3) @ (suc @ I3)))) => ((! [I3:nat,J2:nat,K:nat]: (((((ord_less @ nat) @ I3) @ J2) => ((((ord_less @ nat) @ J2) @ K) => (((P2 @ I3) @ J2) => (((P2 @ J2) @ K) => ((P2 @ I3) @ K))))))) => ((P2 @ I2) @ J))))))).
% 2.44/1.58 thf(fact_25_less__trans__Suc, axiom, (! [I2:nat,J:nat,K2:nat]: (((((ord_less @ nat) @ I2) @ J) => ((((ord_less @ nat) @ J) @ K2) => (((ord_less @ nat) @ (suc @ I2)) @ K2)))))).
% 2.44/1.58 thf(fact_26_Suc__less__SucD, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (suc @ M)) @ (suc @ N)) => (((ord_less @ nat) @ M) @ N))))).
% 2.44/1.58 thf(fact_27_less__antisym, axiom, (! [N:nat,M:nat]: (((~ ((((ord_less @ nat) @ N) @ M))) => ((((ord_less @ nat) @ N) @ (suc @ M)) => (M = N)))))).
% 2.44/1.58 thf(fact_28_Suc__less__eq2, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ (suc @ N)) @ M) = (? [M2:nat]: (((M = (suc @ M2)) & (((ord_less @ nat) @ N) @ M2)))))))).
% 2.44/1.58 thf(fact_29_All__less__Suc, axiom, (! [N:nat,P2:(nat > $o)]: (((! [I4:nat]: (((((ord_less @ nat) @ I4) @ (suc @ N)) => (P2 @ I4)))) = ((P2 @ N) & (! [I4:nat]: (((((ord_less @ nat) @ I4) @ N) => (P2 @ I4))))))))).
% 2.44/1.58 thf(fact_30_not__less__eq, axiom, (! [M:nat,N:nat]: (((~ ((((ord_less @ nat) @ M) @ N))) = (((ord_less @ nat) @ N) @ (suc @ M)))))).
% 2.44/1.58 thf(fact_31_less__Suc__eq, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ (suc @ N)) = ((((ord_less @ nat) @ M) @ N) | (M = N)))))).
% 2.44/1.58 thf(fact_32_Ex__less__Suc, axiom, (! [N:nat,P2:(nat > $o)]: (((? [I4:nat]: (((((ord_less @ nat) @ I4) @ (suc @ N)) & (P2 @ I4)))) = ((P2 @ N) | (? [I4:nat]: (((((ord_less @ nat) @ I4) @ N) & (P2 @ I4))))))))).
% 2.44/1.58 thf(fact_33_less__SucI, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less @ nat) @ M) @ (suc @ N)))))).
% 2.44/1.58 thf(fact_34_less__SucE, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ (suc @ N)) => ((~ ((((ord_less @ nat) @ M) @ N))) => (M = N)))))).
% 2.44/1.58 thf(fact_35_Suc__lessI, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((suc @ M) != N) => (((ord_less @ nat) @ (suc @ M)) @ N)))))).
% 2.44/1.58 thf(fact_36_Suc__lessE, axiom, (! [I2:nat,K2:nat]: (((((ord_less @ nat) @ (suc @ I2)) @ K2) => (~ ((! [J2:nat]: (((((ord_less @ nat) @ I2) @ J2) => (K2 != (suc @ J2))))))))))).
% 2.44/1.58 thf(fact_37_Suc__lessD, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (suc @ M)) @ N) => (((ord_less @ nat) @ M) @ N))))).
% 2.44/1.58 thf(fact_38_Nat_OlessE, axiom, (! [I2:nat,K2:nat]: (((((ord_less @ nat) @ I2) @ K2) => ((K2 != (suc @ I2)) => (~ ((! [J2:nat]: (((((ord_less @ nat) @ I2) @ J2) => (K2 != (suc @ J2)))))))))))).
% 2.44/1.58 thf(fact_39_list__eq__iff__nth__eq, axiom, (! [A:$tType]: (((^ [Y3:(list @ A),Z2:(list @ A)]: ((Y3 = Z2))) = (^ [Xs3:(list @ A),Ys3:(list @ A)]: (((((size_size @ (list @ A)) @ Xs3) = ((size_size @ (list @ A)) @ Ys3)) & (! [I4:nat]: (((((ord_less @ nat) @ I4) @ ((size_size @ (list @ A)) @ Xs3)) => ((((nth @ A) @ Xs3) @ I4) = (((nth @ A) @ Ys3) @ I4)))))))))))).
% 2.44/1.58 thf(fact_40_Skolem__list__nth, axiom, (! [A:$tType,K2:nat,P2:(nat > (A > $o))]: (((! [I4:nat]: (((((ord_less @ nat) @ I4) @ K2) => (? [X3:A]: (((P2 @ I4) @ X3)))))) = (? [Xs3:(list @ A)]: (((((size_size @ (list @ A)) @ Xs3) = K2) & (! [I4:nat]: (((((ord_less @ nat) @ I4) @ K2) => ((P2 @ I4) @ (((nth @ A) @ Xs3) @ I4)))))))))))).
% 2.44/1.58 thf(fact_41_nth__equalityI, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ A)) @ Ys2)) => ((! [I3:nat]: (((((ord_less @ nat) @ I3) @ ((size_size @ (list @ A)) @ Xs)) => ((((nth @ A) @ Xs) @ I3) = (((nth @ A) @ Ys2) @ I3))))) => (Xs = Ys2)))))).
% 2.44/1.58 thf(fact_42_lift__Suc__mono__less__iff, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N:nat,M:nat]: (((! [N2:nat]: ((((ord_less @ A) @ (F @ N2)) @ (F @ (suc @ N2))))) => ((((ord_less @ A) @ (F @ N)) @ (F @ M)) = (((ord_less @ nat) @ N) @ M))))))))).
% 2.44/1.58 thf(fact_43_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P2:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P2)) = (P2 @ A2))))).
% 2.44/1.58 thf(fact_44_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member @ A) @ X4) @ A3)))) = A3)))).
% 2.44/1.58 thf(fact_45_Collect__cong, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P2 @ X5) = (Q @ X5)))) => (((collect @ A) @ P2) = ((collect @ A) @ Q)))))).
% 2.44/1.58 thf(fact_46_lift__Suc__mono__less, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N:nat,N3:nat]: (((! [N2:nat]: ((((ord_less @ A) @ (F @ N2)) @ (F @ (suc @ N2))))) => ((((ord_less @ nat) @ N) @ N3) => (((ord_less @ A) @ (F @ N)) @ (F @ N3)))))))))).
% 2.44/1.58 thf(fact_47_measure__induct__rule, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F:(A > B),P2:(A > $o),A2:A]: (((! [X5:A]: (((! [Y4:A]: (((((ord_less @ B) @ (F @ Y4)) @ (F @ X5)) => (P2 @ Y4)))) => (P2 @ X5)))) => (P2 @ A2)))))))).
% 2.44/1.58 thf(fact_48_measure__induct, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F:(A > B),P2:(A > $o),A2:A]: (((! [X5:A]: (((! [Y4:A]: (((((ord_less @ B) @ (F @ Y4)) @ (F @ X5)) => (P2 @ Y4)))) => (P2 @ X5)))) => (P2 @ A2)))))))).
% 2.44/1.58 thf(fact_49_infinite__descent__measure, axiom, (! [A:$tType,P2:(A > $o),V2:(A > nat),X:A]: (((! [X5:A]: (((~ ((P2 @ X5))) => (? [Y4:A]: (((((ord_less @ nat) @ (V2 @ Y4)) @ (V2 @ X5)) & (~ ((P2 @ Y4))))))))) => (P2 @ X))))).
% 2.44/1.58 thf(fact_50_linorder__neqE__nat, axiom, (! [X:nat,Y:nat]: (((X != Y) => ((~ ((((ord_less @ nat) @ X) @ Y))) => (((ord_less @ nat) @ Y) @ X)))))).
% 2.44/1.58 thf(fact_51_infinite__descent, axiom, (! [P2:(nat > $o),N:nat]: (((! [N2:nat]: (((~ ((P2 @ N2))) => (? [M3:nat]: (((((ord_less @ nat) @ M3) @ N2) & (~ ((P2 @ M3))))))))) => (P2 @ N))))).
% 2.44/1.58 thf(fact_52_nat__less__induct, axiom, (! [P2:(nat > $o),N:nat]: (((! [N2:nat]: (((! [M3:nat]: (((((ord_less @ nat) @ M3) @ N2) => (P2 @ M3)))) => (P2 @ N2)))) => (P2 @ N))))).
% 2.44/1.58 thf(fact_53_Subset, axiom, (! [MsgInSet:((message @ p) @ v)]: (((((member @ ((message @ p) @ v)) @ MsgInSet) @ (firstOccSet @ (suc @ index))) => (((member @ ((message @ p) @ v)) @ MsgInSet) @ (firstOccSet @ index)))))).
% 2.44/1.58 thf(fact_54_IPrefixListEx, axiom, (! [I:nat]: ((((prefixList @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ I)) @ (fe @ (suc @ I)))))).
% 2.44/1.58 thf(fact_55_AssumptionFair_I3_J, axiom, (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ n)) @ n0)) @ msg)).
% 2.44/1.58 thf(fact_56_list__ex__length, axiom, (! [A:$tType]: (((list_ex @ A) = (^ [P3:(A > $o),Xs3:(list @ A)]: ((? [N4:nat]: (((((ord_less @ nat) @ N4) @ ((size_size @ (list @ A)) @ Xs3)) & (P3 @ (((nth @ A) @ Xs3) @ N4))))))))))).
% 2.44/1.58 thf(fact_57_AssumpGreaterOccurrence_I2_J, axiom, (((((((firstOccurrence @ p) @ v) @ s) @ (fe @ (suc @ index))) @ (ft @ (suc @ index))) @ consumedMsg) @ n1)).
% 2.44/1.58 thf(fact_58_list__ex1__simps_I1_J, axiom, (! [A:$tType,P2:(A > $o)]: ((~ ((((list_ex1 @ A) @ P2) @ (nil @ A))))))).
% 2.44/1.58 thf(fact_59_LengthStep, axiom, (((ord_less @ nat) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ (suc @ index))))).
% 2.44/1.58 thf(fact_60_remdups__adj__adjacent, axiom, (! [A:$tType,I2:nat,Xs:(list @ A)]: (((((ord_less @ nat) @ (suc @ I2)) @ ((size_size @ (list @ A)) @ ((remdups_adj @ A) @ Xs))) => ((((nth @ A) @ ((remdups_adj @ A) @ Xs)) @ I2) != (((nth @ A) @ ((remdups_adj @ A) @ Xs)) @ (suc @ I2))))))).
% 2.44/1.58 thf(fact_61_nth__tl, axiom, (! [A:$tType,N:nat,Xs:(list @ A)]: (((((ord_less @ nat) @ N) @ ((size_size @ (list @ A)) @ ((tl @ A) @ Xs))) => ((((nth @ A) @ ((tl @ A) @ Xs)) @ N) = (((nth @ A) @ Xs) @ (suc @ N))))))).
% 2.44/1.58 thf(fact_62_length__greater__0__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ ((size_size @ (list @ A)) @ Xs)) = (Xs != (nil @ A)))))).
% 2.44/1.58 thf(fact_63_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J, axiom, (! [P2:(((((configuration_ext @ p) @ v) @ s) @ product_unit) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))) > (nat > $o)))),Q:(((((configuration_ext @ p) @ v) @ s) @ product_unit) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))) > (nat > $o)))),A4:((((configuration_ext @ p) @ v) @ s) @ product_unit),A5:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),A6:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),A7:nat]: (((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v))))]: (((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ (zero_zero @ nat)))) => ((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),N2:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N2) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N2) => ((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N2)))))) => ((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v))))]: (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (zero_zero @ nat)))) => ((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),N2:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N2) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N2) => ((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N2)))))) => ((((Q @ A4) @ A5) @ A6) @ A7)))))))).
% 2.44/1.58 thf(fact_64_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J, axiom, (! [P2:(((((configuration_ext @ p) @ v) @ s) @ product_unit) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))) > (nat > $o)))),Q:(((((configuration_ext @ p) @ v) @ s) @ product_unit) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))) > (nat > $o)))),A0:((((configuration_ext @ p) @ v) @ s) @ product_unit),A1:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),A22:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),A32:nat]: (((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v))))]: (((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ (zero_zero @ nat)))) => ((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),N2:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N2) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N2) => ((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N2)))))) => ((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v))))]: (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (zero_zero @ nat)))) => ((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),N2:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N2) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N2) => ((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N2)))))) => ((((P2 @ A0) @ A1) @ A22) @ A32)))))))).
% 2.44/1.58 thf(fact_65_AssumpGreaterOccurrence_I3_J, axiom, (((((((firstOccurrence @ p) @ v) @ s) @ (fe @ (suc @ index))) @ (ft @ (suc @ index))) @ msg) @ nMsg)).
% 2.44/1.58 thf(fact_66_ConsumedInSet, axiom, (((member @ ((message @ p) @ v)) @ consumedMsg) @ (firstOccSet @ index))).
% 2.44/1.58 thf(fact_67_SameMsgOnLow, axiom, (! [I:nat]: (((((ord_less @ nat) @ I) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) => ((((nth @ ((message @ p) @ v)) @ (ft @ index)) @ I) = (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ I)))))).
% 2.44/1.58 thf(fact_68_neq0__conv, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ N))))).
% 2.44/1.58 thf(fact_69_less__nat__zero__code, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.44/1.58 thf(fact_70_bot__nat__0_Onot__eq__extremum, axiom, (! [A2:nat]: (((A2 != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ A2))))).
% 2.44/1.58 thf(fact_71_ConsumedMsg_I1_J, axiom, ((((((minimalEnabled @ p) @ v) @ s) @ (fe @ index)) @ (ft @ index)) @ consumedMsg)).
% 2.44/1.58 thf(fact_72_remdups__adj__Nil__iff, axiom, (! [A:$tType,Xs:(list @ A)]: (((((remdups_adj @ A) @ Xs) = (nil @ A)) = (Xs = (nil @ A)))))).
% 2.44/1.58 thf(fact_73_list__ex__simps_I2_J, axiom, (! [A:$tType,P2:(A > $o)]: ((~ ((((list_ex @ A) @ P2) @ (nil @ A))))))).
% 2.44/1.58 thf(fact_74_SmallIndex, axiom, (! [NMsg:nat]: (((((((((firstOccurrence @ p) @ v) @ s) @ (fe @ (suc @ index))) @ (ft @ (suc @ index))) @ msg) @ NMsg) => (((ord_less @ nat) @ NMsg) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))))))).
% 2.44/1.58 thf(fact_75_zero__less__Suc, axiom, (! [N:nat]: ((((ord_less @ nat) @ (zero_zero @ nat)) @ (suc @ N))))).
% 2.44/1.58 thf(fact_76_less__Suc0, axiom, (! [N:nat]: (((((ord_less @ nat) @ N) @ (suc @ (zero_zero @ nat))) = (N = (zero_zero @ nat)))))).
% 2.44/1.58 thf(fact_77_length__0__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((size_size @ (list @ A)) @ Xs) = (zero_zero @ nat)) = (Xs = (nil @ A)))))).
% 2.44/1.58 thf(fact_78_AssumptionFairContr, axiom, (! [N5:nat]: (((((ord_less_eq @ nat) @ n) @ N5) => (! [N0:nat]: (((((ord_less @ nat) @ N0) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ N5))) => ((((ord_less_eq @ nat) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ n))) @ N0) => (msg != (((nth @ ((message @ p) @ v)) @ (ft @ N5)) @ N0)))))))))).
% 2.44/1.58 thf(fact_79_AssumptionFirstOccSetDecrOrConsumed_I1_J, axiom, (((((enabled @ p) @ v) @ s) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index))) @ msg)).
% 2.44/1.58 thf(fact_80_AssumptionCase1ImplThesis_H, axiom, (((((enabled @ p) @ v) @ s) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ n))) @ msg)).
% 2.44/1.58 thf(fact_81_remdups__adj_Osimps_I1_J, axiom, (! [A:$tType]: ((((remdups_adj @ A) @ (nil @ A)) = (nil @ A))))).
% 2.44/1.58 thf(fact_82_list_Osel_I2_J, axiom, (! [A:$tType]: ((((tl @ A) @ (nil @ A)) = (nil @ A))))).
% 2.44/1.58 thf(fact_83_not0__implies__Suc, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) => (? [M4:nat]: ((N = (suc @ M4)))))))).
% 2.44/1.58 thf(fact_84_old_Onat_Oinducts, axiom, (! [P2:(nat > $o),Nat:nat]: (((P2 @ (zero_zero @ nat)) => ((! [Nat3:nat]: (((P2 @ Nat3) => (P2 @ (suc @ Nat3))))) => (P2 @ Nat)))))).
% 2.44/1.58 thf(fact_85_old_Onat_Oexhaust, axiom, (! [Y:nat]: (((Y != (zero_zero @ nat)) => (~ ((! [Nat3:nat]: ((Y != (suc @ Nat3)))))))))).
% 2.44/1.58 thf(fact_86_Zero__not__Suc, axiom, (! [M:nat]: (((zero_zero @ nat) != (suc @ M))))).
% 2.44/1.58 thf(fact_87_Zero__neq__Suc, axiom, (! [M:nat]: (((zero_zero @ nat) != (suc @ M))))).
% 2.44/1.58 thf(fact_88_Suc__neq__Zero, axiom, (! [M:nat]: (((suc @ M) != (zero_zero @ nat))))).
% 2.44/1.58 thf(fact_89_zero__induct, axiom, (! [P2:(nat > $o),K2:nat]: (((P2 @ K2) => ((! [N2:nat]: (((P2 @ (suc @ N2)) => (P2 @ N2)))) => (P2 @ (zero_zero @ nat))))))).
% 2.44/1.58 thf(fact_90_diff__induct, axiom, (! [P2:(nat > (nat > $o)),M:nat,N:nat]: (((! [X5:nat]: (((P2 @ X5) @ (zero_zero @ nat)))) => ((! [Y5:nat]: (((P2 @ (zero_zero @ nat)) @ (suc @ Y5)))) => ((! [X5:nat,Y5:nat]: ((((P2 @ X5) @ Y5) => ((P2 @ (suc @ X5)) @ (suc @ Y5))))) => ((P2 @ M) @ N))))))).
% 2.44/1.58 thf(fact_91_nat__induct, axiom, (! [P2:(nat > $o),N:nat]: (((P2 @ (zero_zero @ nat)) => ((! [N2:nat]: (((P2 @ N2) => (P2 @ (suc @ N2))))) => (P2 @ N)))))).
% 2.44/1.58 thf(fact_92_nat_OdiscI, axiom, (! [Nat:nat,X2:nat]: (((Nat = (suc @ X2)) => (Nat != (zero_zero @ nat)))))).
% 2.44/1.58 thf(fact_93_old_Onat_Odistinct_I1_J, axiom, (! [Nat2:nat]: (((zero_zero @ nat) != (suc @ Nat2))))).
% 2.44/1.58 thf(fact_94_old_Onat_Odistinct_I2_J, axiom, (! [Nat4:nat]: (((suc @ Nat4) != (zero_zero @ nat))))).
% 2.44/1.58 thf(fact_95_nat_Odistinct_I1_J, axiom, (! [X2:nat]: (((zero_zero @ nat) != (suc @ X2))))).
% 2.44/1.58 thf(fact_96_gr0I, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) => (((ord_less @ nat) @ (zero_zero @ nat)) @ N))))).
% 2.44/1.58 thf(fact_97_not__gr0, axiom, (! [N:nat]: (((~ ((((ord_less @ nat) @ (zero_zero @ nat)) @ N))) = (N = (zero_zero @ nat)))))).
% 2.44/1.58 thf(fact_98_not__less0, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.44/1.58 thf(fact_99_less__zeroE, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.44/1.58 thf(fact_100_gr__implies__not0, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (N != (zero_zero @ nat)))))).
% 2.44/1.58 thf(fact_101_infinite__descent0, axiom, (! [P2:(nat > $o),N:nat]: (((P2 @ (zero_zero @ nat)) => ((! [N2:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) => ((~ ((P2 @ N2))) => (? [M3:nat]: (((((ord_less @ nat) @ M3) @ N2) & (~ ((P2 @ M3)))))))))) => (P2 @ N)))))).
% 2.44/1.58 thf(fact_102_bot__nat__0_Oextremum__strict, axiom, (! [A2:nat]: ((~ ((((ord_less @ nat) @ A2) @ (zero_zero @ nat))))))).
% 2.44/1.58 thf(fact_103_infinite__descent0__measure, axiom, (! [A:$tType,V2:(A > nat),P2:(A > $o),X:A]: (((! [X5:A]: ((((V2 @ X5) = (zero_zero @ nat)) => (P2 @ X5)))) => ((! [X5:A]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (V2 @ X5)) => ((~ ((P2 @ X5))) => (? [Y4:A]: (((((ord_less @ nat) @ (V2 @ Y4)) @ (V2 @ X5)) & (~ ((P2 @ Y4)))))))))) => (P2 @ X)))))).
% 2.44/1.58 thf(fact_104_less__Suc__eq__0__disj, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ (suc @ N)) = ((M = (zero_zero @ nat)) | (? [J3:nat]: (((M = (suc @ J3)) & (((ord_less @ nat) @ J3) @ N))))))))).
% 2.44/1.58 thf(fact_105_gr0__implies__Suc, axiom, (! [N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => (? [M4:nat]: ((N = (suc @ M4)))))))).
% 2.44/1.58 thf(fact_106_All__less__Suc2, axiom, (! [N:nat,P2:(nat > $o)]: (((! [I4:nat]: (((((ord_less @ nat) @ I4) @ (suc @ N)) => (P2 @ I4)))) = ((P2 @ (zero_zero @ nat)) & (! [I4:nat]: (((((ord_less @ nat) @ I4) @ N) => (P2 @ (suc @ I4)))))))))).
% 2.44/1.58 thf(fact_107_gr0__conv__Suc, axiom, (! [N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) = (? [M5:nat]: ((N = (suc @ M5)))))))).
% 2.44/1.58 thf(fact_108_Ex__less__Suc2, axiom, (! [N:nat,P2:(nat > $o)]: (((? [I4:nat]: (((((ord_less @ nat) @ I4) @ (suc @ N)) & (P2 @ I4)))) = ((P2 @ (zero_zero @ nat)) | (? [I4:nat]: (((((ord_less @ nat) @ I4) @ N) & (P2 @ (suc @ I4)))))))))).
% 2.44/1.58 thf(fact_109_list_Osize_I3_J, axiom, (! [A:$tType]: ((((size_size @ (list @ A)) @ (nil @ A)) = (zero_zero @ nat))))).
% 2.44/1.58 thf(fact_110_MinImplFirstOcc, axiom, (! [Msg:((message @ p) @ v)]: ((((((((minimalEnabled @ p) @ v) @ s) @ (fe @ index)) @ (ft @ index)) @ Msg) => (((member @ ((message @ p) @ v)) @ Msg) @ (firstOccSet @ index)))))).
% 2.44/1.58 thf(fact_111_Case2ImplThesis, axiom, ((? [N0:nat]: (((((ord_less_eq @ nat) @ n0) @ N0) & ((((ord_less @ nat) @ N0) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ n))) & ((((nth @ ((message @ p) @ v)) @ (ft @ n)) @ N0) = msg))))) => (? [N6:nat]: (((((ord_less_eq @ nat) @ n) @ N6) & (? [N02:nat]: (((((ord_less_eq @ nat) @ n0) @ N02) & ((((ord_less @ nat) @ N02) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ N6))) & (msg = (((nth @ ((message @ p) @ v)) @ (ft @ N6)) @ N02))))))))))).
% 2.44/1.58 thf(fact_112_MessageStaysOrConsumed, axiom, (! [N1:nat,N22:nat,N:nat,Msg2:((message @ p) @ v)]: ((((((ord_less_eq @ nat) @ N1) @ N22) & ((((ord_less @ nat) @ N22) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ N))) & (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ N)) @ N1)) @ Msg2))) => ((((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ N)) @ N22)) @ Msg2) | (? [N02:nat]: (((((ord_less_eq @ nat) @ N1) @ N02) & ((((ord_less @ nat) @ N02) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ N))) & ((((nth @ ((message @ p) @ v)) @ (ft @ N)) @ N02) = Msg2)))))))))).
% 2.44/1.58 thf(fact_113_NotConsumedIntermediate, axiom, (! [I:nat]: (((((ord_less @ nat) @ I) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ (suc @ index)))) => ((((ord_less_eq @ nat) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) @ I) => ((((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ I) != msg)))))).
% 2.44/1.58 thf(fact_114__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ift_A_ISuc_Aindex_J_J_O_Alength_A_Ift_Aindex_J_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, (~ ((? [I:nat]: (((((ord_less @ nat) @ I) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ (suc @ index)))) & ((((ord_less_eq @ nat) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) @ I) & (msg = (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ I))))))))).
% 2.44/1.58 thf(fact_115_Nitpick_Osize__list__simp_I2_J, axiom, (! [A:$tType]: (((size_size @ (list @ A)) = (^ [Xs3:(list @ A)]: (((((if @ nat) @ (Xs3 = (nil @ A))) @ (zero_zero @ nat)) @ (suc @ ((size_size @ (list @ A)) @ ((tl @ A) @ Xs3)))))))))).
% 2.44/1.58 thf(fact_116_not__gr__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((~ ((((ord_less @ A) @ (zero_zero @ A)) @ N))) = (N = (zero_zero @ A))))))))).
% 2.44/1.58 thf(fact_117_le__zero__eq, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less_eq @ A) @ N) @ (zero_zero @ A)) = (N = (zero_zero @ A))))))))).
% 2.44/1.58 thf(fact_118_bot__nat__0_Oextremum, axiom, (! [A2:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ A2)))).
% 2.44/1.58 thf(fact_119_le0, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N)))).
% 2.44/1.58 thf(fact_120_Suc__le__mono, axiom, (! [N:nat,M:nat]: (((((ord_less_eq @ nat) @ (suc @ N)) @ (suc @ M)) = (((ord_less_eq @ nat) @ N) @ M))))).
% 2.44/1.58 thf(fact_121_EnabledInSuc, axiom, (((((enabled @ p) @ v) @ s) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index)))) @ msg)).
% 2.44/1.58 thf(fact_122_MinImplAllBigger, axiom, (! [Msg:((message @ p) @ v)]: ((((((((minimalEnabled @ p) @ v) @ s) @ (fe @ index)) @ (ft @ index)) @ Msg) => (? [OccM:nat]: (((((((((firstOccurrence @ p) @ v) @ s) @ (fe @ index)) @ (ft @ index)) @ Msg) @ OccM) & (! [Msg3:((message @ p) @ v),OccM2:nat]: (((((((((firstOccurrence @ p) @ v) @ s) @ (fe @ index)) @ (ft @ index)) @ Msg3) @ OccM2) => (((ord_less_eq @ nat) @ OccM) @ OccM2))))))))))).
% 2.44/1.58 thf(fact_123_last__remdups__adj, axiom, (! [A:$tType,Xs:(list @ A)]: ((((last @ A) @ ((remdups_adj @ A) @ Xs)) = ((last @ A) @ Xs))))).
% 2.44/1.58 thf(fact_124_EnabledOrConsumedAtLast, axiom, ((((((enabled @ p) @ v) @ s) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ n))) @ msg) | (? [N02:nat]: (((((ord_less_eq @ nat) @ n0) @ N02) & ((((ord_less @ nat) @ N02) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ n))) & ((((nth @ ((message @ p) @ v)) @ (ft @ n)) @ N02) = msg))))))).
% 2.44/1.58 thf(fact_125_zero__le, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X))))))).
% 2.44/1.58 thf(fact_126_lift__Suc__antimono__le, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N:nat,N3:nat]: (((! [N2:nat]: ((((ord_less_eq @ A) @ (F @ (suc @ N2))) @ (F @ N2)))) => ((((ord_less_eq @ nat) @ N) @ N3) => (((ord_less_eq @ A) @ (F @ N3)) @ (F @ N)))))))))).
% 2.44/1.58 thf(fact_127_lift__Suc__mono__le, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N:nat,N3:nat]: (((! [N2:nat]: ((((ord_less_eq @ A) @ (F @ N2)) @ (F @ (suc @ N2))))) => ((((ord_less_eq @ nat) @ N) @ N3) => (((ord_less_eq @ A) @ (F @ N)) @ (F @ N3)))))))))).
% 2.44/1.58 thf(fact_128_Nat_Oex__has__greatest__nat, axiom, (! [P2:(nat > $o),K2:nat,B2:nat]: (((P2 @ K2) => ((! [Y5:nat]: (((P2 @ Y5) => (((ord_less_eq @ nat) @ Y5) @ B2)))) => (? [X5:nat]: (((P2 @ X5) & (! [Y4:nat]: (((P2 @ Y4) => (((ord_less_eq @ nat) @ Y4) @ X5)))))))))))).
% 2.44/1.58 thf(fact_129_nat__le__linear, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) | (((ord_less_eq @ nat) @ N) @ M))))).
% 2.44/1.58 thf(fact_130_le__antisym, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((ord_less_eq @ nat) @ N) @ M) => (M = N)))))).
% 2.44/1.58 thf(fact_131_eq__imp__le, axiom, (! [M:nat,N:nat]: (((M = N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.44/1.58 thf(fact_132_le__trans, axiom, (! [I2:nat,J:nat,K2:nat]: (((((ord_less_eq @ nat) @ I2) @ J) => ((((ord_less_eq @ nat) @ J) @ K2) => (((ord_less_eq @ nat) @ I2) @ K2)))))).
% 2.44/1.58 thf(fact_133_le__refl, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ N) @ N)))).
% 2.44/1.58 thf(fact_134_bot__nat__0_Oextremum__uniqueI, axiom, (! [A2:nat]: (((((ord_less_eq @ nat) @ A2) @ (zero_zero @ nat)) => (A2 = (zero_zero @ nat)))))).
% 2.44/1.58 thf(fact_135_bot__nat__0_Oextremum__unique, axiom, (! [A2:nat]: (((((ord_less_eq @ nat) @ A2) @ (zero_zero @ nat)) = (A2 = (zero_zero @ nat)))))).
% 2.44/1.58 thf(fact_136_le__0__eq, axiom, (! [N:nat]: (((((ord_less_eq @ nat) @ N) @ (zero_zero @ nat)) = (N = (zero_zero @ nat)))))).
% 2.44/1.58 thf(fact_137_less__eq__nat_Osimps_I1_J, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N)))).
% 2.44/1.58 thf(fact_138_Suc__leD, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ (suc @ M)) @ N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.44/1.58 thf(fact_139_le__SucE, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ (suc @ N)) => ((~ ((((ord_less_eq @ nat) @ M) @ N))) => (M = (suc @ N))))))).
% 2.44/1.58 thf(fact_140_le__SucI, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ M) @ (suc @ N)))))).
% 2.44/1.58 thf(fact_141_Suc__le__D, axiom, (! [N:nat,M6:nat]: (((((ord_less_eq @ nat) @ (suc @ N)) @ M6) => (? [M4:nat]: ((M6 = (suc @ M4)))))))).
% 2.44/1.58 thf(fact_142_le__Suc__eq, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ (suc @ N)) = ((((ord_less_eq @ nat) @ M) @ N) | (M = (suc @ N))))))).
% 2.44/1.58 thf(fact_143_Suc__n__not__le__n, axiom, (! [N:nat]: ((~ ((((ord_less_eq @ nat) @ (suc @ N)) @ N)))))).
% 2.44/1.58 thf(fact_144_not__less__eq__eq, axiom, (! [M:nat,N:nat]: (((~ ((((ord_less_eq @ nat) @ M) @ N))) = (((ord_less_eq @ nat) @ (suc @ N)) @ M))))).
% 2.44/1.58 thf(fact_145_full__nat__induct, axiom, (! [P2:(nat > $o),N:nat]: (((! [N2:nat]: (((! [M3:nat]: (((((ord_less_eq @ nat) @ (suc @ M3)) @ N2) => (P2 @ M3)))) => (P2 @ N2)))) => (P2 @ N))))).
% 2.44/1.58 thf(fact_146_nat__induct__at__least, axiom, (! [M:nat,N:nat,P2:(nat > $o)]: (((((ord_less_eq @ nat) @ M) @ N) => ((P2 @ M) => ((! [N2:nat]: (((((ord_less_eq @ nat) @ M) @ N2) => ((P2 @ N2) => (P2 @ (suc @ N2)))))) => (P2 @ N))))))).
% 2.44/1.58 thf(fact_147_transitive__stepwise__le, axiom, (! [M:nat,N:nat,R:(nat > (nat > $o))]: (((((ord_less_eq @ nat) @ M) @ N) => ((! [X5:nat]: (((R @ X5) @ X5))) => ((! [X5:nat,Y5:nat,Z3:nat]: ((((R @ X5) @ Y5) => (((R @ Y5) @ Z3) => ((R @ X5) @ Z3))))) => ((! [N2:nat]: (((R @ N2) @ (suc @ N2)))) => ((R @ M) @ N)))))))).
% 2.44/1.58 thf(fact_148_less__mono__imp__le__mono, axiom, (! [F:(nat > nat),I2:nat,J:nat]: (((! [I3:nat,J2:nat]: (((((ord_less @ nat) @ I3) @ J2) => (((ord_less @ nat) @ (F @ I3)) @ (F @ J2))))) => ((((ord_less_eq @ nat) @ I2) @ J) => (((ord_less_eq @ nat) @ (F @ I2)) @ (F @ J))))))).
% 2.44/1.58 thf(fact_149_le__neq__implies__less, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((M != N) => (((ord_less @ nat) @ M) @ N)))))).
% 2.44/1.58 thf(fact_150_less__or__eq__imp__le, axiom, (! [M:nat,N:nat]: ((((((ord_less @ nat) @ M) @ N) | (M = N)) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.44/1.58 thf(fact_151_le__eq__less__or__eq, axiom, ((ord_less_eq @ nat) = (^ [M5:nat,N4:nat]: (((((ord_less @ nat) @ M5) @ N4) | (M5 = N4)))))).
% 2.44/1.58 thf(fact_152_less__imp__le__nat, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.44/1.58 thf(fact_153_nat__less__le, axiom, ((ord_less @ nat) = (^ [M5:nat,N4:nat]: (((((ord_less_eq @ nat) @ M5) @ N4) & (M5 != N4)))))).
% 2.44/1.58 thf(fact_154_ex__least__nat__le, axiom, (! [P2:(nat > $o),N:nat]: (((P2 @ N) => ((~ ((P2 @ (zero_zero @ nat)))) => (? [K:nat]: (((((ord_less_eq @ nat) @ K) @ N) & ((! [I:nat]: (((((ord_less @ nat) @ I) @ K) => (~ ((P2 @ I)))))) & (P2 @ K)))))))))).
% 2.44/1.58 thf(fact_155_Suc__leI, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ (suc @ M)) @ N))))).
% 2.44/1.58 thf(fact_156_Suc__le__eq, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ (suc @ M)) @ N) = (((ord_less @ nat) @ M) @ N))))).
% 2.44/1.58 thf(fact_157_dec__induct, axiom, (! [I2:nat,J:nat,P2:(nat > $o)]: (((((ord_less_eq @ nat) @ I2) @ J) => ((P2 @ I2) => ((! [N2:nat]: (((((ord_less_eq @ nat) @ I2) @ N2) => ((((ord_less @ nat) @ N2) @ J) => ((P2 @ N2) => (P2 @ (suc @ N2))))))) => (P2 @ J))))))).
% 2.44/1.58 thf(fact_158_inc__induct, axiom, (! [I2:nat,J:nat,P2:(nat > $o)]: (((((ord_less_eq @ nat) @ I2) @ J) => ((P2 @ J) => ((! [N2:nat]: (((((ord_less_eq @ nat) @ I2) @ N2) => ((((ord_less @ nat) @ N2) @ J) => ((P2 @ (suc @ N2)) => (P2 @ N2)))))) => (P2 @ I2))))))).
% 2.44/1.58 thf(fact_159_Suc__le__lessD, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ (suc @ M)) @ N) => (((ord_less @ nat) @ M) @ N))))).
% 2.44/1.58 thf(fact_160_le__less__Suc__eq, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((ord_less @ nat) @ N) @ (suc @ M)) = (N = M)))))).
% 2.44/1.58 thf(fact_161_less__Suc__eq__le, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ (suc @ N)) = (((ord_less_eq @ nat) @ M) @ N))))).
% 2.44/1.58 thf(fact_162_less__eq__Suc__le, axiom, ((ord_less @ nat) = (^ [N4:nat]: (((ord_less_eq @ nat) @ (suc @ N4)))))).
% 2.44/1.58 thf(fact_163_le__imp__less__Suc, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => (((ord_less @ nat) @ M) @ (suc @ N)))))).
% 2.44/1.58 thf(fact_164_remdups__adj__length, axiom, (! [A:$tType,Xs:(list @ A)]: ((((ord_less_eq @ nat) @ ((size_size @ (list @ A)) @ ((remdups_adj @ A) @ Xs))) @ ((size_size @ (list @ A)) @ Xs))))).
% 2.44/1.58 thf(fact_165_last__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((Xs = (nil @ A)) | (((tl @ A) @ Xs) != (nil @ A))) => (((last @ A) @ ((tl @ A) @ Xs)) = ((last @ A) @ Xs)))))).
% 2.44/1.58 thf(fact_166_ex__least__nat__less, axiom, (! [P2:(nat > $o),N:nat]: (((P2 @ N) => ((~ ((P2 @ (zero_zero @ nat)))) => (? [K:nat]: (((((ord_less @ nat) @ K) @ N) & ((! [I:nat]: (((((ord_less_eq @ nat) @ I) @ K) => (~ ((P2 @ I)))))) & (P2 @ (suc @ K))))))))))).
% 2.44/1.58 thf(fact_167_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X:A]: ((((zero_zero @ A) = X) = (X = (zero_zero @ A))))))))).
% 2.44/1.58 thf(fact_168_remdups__adj__length__ge1, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((ord_less_eq @ nat) @ (suc @ (zero_zero @ nat))) @ ((size_size @ (list @ A)) @ ((remdups_adj @ A) @ Xs))))))).
% 2.44/1.58 thf(fact_169_zero__less__iff__neq__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ N) = (N != (zero_zero @ A))))))))).
% 2.44/1.58 thf(fact_170_gr__implies__not__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [M:A,N:A]: (((((ord_less @ A) @ M) @ N) => (N != (zero_zero @ A))))))))).
% 2.44/1.58 thf(fact_171_not__less__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: ((~ ((((ord_less @ A) @ N) @ (zero_zero @ A)))))))))).
% 2.44/1.58 thf(fact_172_gr__zeroI, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((N != (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ N)))))))).
% 2.44/1.58 thf(fact_173_LastOfIndex, axiom, ((((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) @ (suc @ (zero_zero @ nat)))) = ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index)))).
% 2.44/1.58 thf(fact_174__092_060open_062_092_060And_062n0_Amsg_O_A_092_060forall_062n_O_Aexecution_OfirstOccurrence_A_Ife_An_J_A_Ift_An_J_Amsg_An0_A_092_060longrightarrow_062_Amsg_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062, axiom, (! [Msg2:((message @ p) @ v),N03:nat,N7:nat]: (((((((((firstOccurrence @ p) @ v) @ s) @ (fe @ N7)) @ (ft @ N7)) @ Msg2) @ N03) => (((ord_less @ nat) @ (zero_zero @ nat)) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ N7))) @ Msg2)))))).
% 2.44/1.58 thf(fact_175__092_060open_062_092_060forall_062n_O_A_092_060forall_062msg_H_092_060in_062firstOccSet_An_O_Amsg_H_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062, axiom, (! [N7:nat,X6:((message @ p) @ v)]: (((((member @ ((message @ p) @ v)) @ X6) @ (firstOccSet @ N7)) => (((ord_less @ nat) @ (zero_zero @ nat)) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ N7))) @ X6)))))).
% 2.44/1.58 thf(fact_176_PrefixSameOnLow, axiom, (! [A:$tType,L1:(list @ A),L2:(list @ A)]: (((((prefixList @ A) @ L1) @ L2) => (! [Index:nat]: (((((ord_less @ nat) @ Index) @ ((size_size @ (list @ A)) @ L1)) => ((((nth @ A) @ L1) @ Index) = (((nth @ A) @ L2) @ Index))))))))).
% 2.44/1.58 thf(fact_177_IPrefixList, axiom, (! [I:nat]: ((((prefixList @ ((message @ p) @ v)) @ (ft @ I)) @ (ft @ (suc @ I)))))).
% 2.44/1.58 thf(fact_178_cancel__comm__monoid__add__class_Odiff__cancel, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A]: (((((minus_minus @ A) @ A2) @ A2) = (zero_zero @ A)))))))).
% 2.44/1.58 thf(fact_179_diff__zero, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A2:A]: (((((minus_minus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.44/1.58 thf(fact_180_zero__diff, axiom, (! [A:$tType]: (((comm_monoid_diff @ A) => (! [A2:A]: (((((minus_minus @ A) @ (zero_zero @ A)) @ A2) = (zero_zero @ A)))))))).
% 2.44/1.58 thf(fact_181_diff__0__right, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A]: (((((minus_minus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 2.44/1.58 thf(fact_182_diff__self, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A]: (((((minus_minus @ A) @ A2) @ A2) = (zero_zero @ A)))))))).
% 2.44/1.58 thf(fact_183_diff__0__eq__0, axiom, (! [N:nat]: (((((minus_minus @ nat) @ (zero_zero @ nat)) @ N) = (zero_zero @ nat))))).
% 2.44/1.58 thf(fact_184_diff__self__eq__0, axiom, (! [M:nat]: (((((minus_minus @ nat) @ M) @ M) = (zero_zero @ nat))))).
% 2.44/1.58 thf(fact_185_Suc__diff__diff, axiom, (! [M:nat,N:nat,K2:nat]: (((((minus_minus @ nat) @ (((minus_minus @ nat) @ (suc @ M)) @ N)) @ (suc @ K2)) = (((minus_minus @ nat) @ (((minus_minus @ nat) @ M) @ N)) @ K2))))).
% 2.44/1.58 thf(fact_186_diff__Suc__Suc, axiom, (! [M:nat,N:nat]: (((((minus_minus @ nat) @ (suc @ M)) @ (suc @ N)) = (((minus_minus @ nat) @ M) @ N))))).
% 2.44/1.58 thf(fact_187_diff__diff__cancel, axiom, (! [I2:nat,N:nat]: (((((ord_less_eq @ nat) @ I2) @ N) => ((((minus_minus @ nat) @ N) @ (((minus_minus @ nat) @ N) @ I2)) = I2))))).
% 2.44/1.58 thf(fact_188_diff__ge__0__iff__ge, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((minus_minus @ A) @ A2) @ B2)) = (((ord_less_eq @ A) @ B2) @ A2)))))))).
% 2.44/1.58 thf(fact_189_diff__gt__0__iff__gt, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((minus_minus @ A) @ A2) @ B2)) = (((ord_less @ A) @ B2) @ A2)))))))).
% 2.44/1.58 thf(fact_190_zero__less__diff, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (((minus_minus @ nat) @ N) @ M)) = (((ord_less @ nat) @ M) @ N))))).
% 2.44/1.58 thf(fact_191_diff__is__0__eq_H, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((minus_minus @ nat) @ M) @ N) = (zero_zero @ nat)))))).
% 2.44/1.58 thf(fact_192_diff__is__0__eq, axiom, (! [M:nat,N:nat]: ((((((minus_minus @ nat) @ M) @ N) = (zero_zero @ nat)) = (((ord_less_eq @ nat) @ M) @ N))))).
% 2.44/1.58 thf(fact_193_Suc__pred, axiom, (! [N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => ((suc @ (((minus_minus @ nat) @ N) @ (suc @ (zero_zero @ nat)))) = N))))).
% 2.44/1.58 thf(fact_194_eq__iff__diff__eq__0, axiom, (! [A:$tType]: (((group_add @ A) => ((^ [Y3:A,Z2:A]: ((Y3 = Z2))) = (^ [A8:A,B3:A]: (((((minus_minus @ A) @ A8) @ B3) = (zero_zero @ A))))))))).
% 2.44/1.58 thf(fact_195_diff__strict__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B2:A,D:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ D) @ C) => (((ord_less @ A) @ (((minus_minus @ A) @ A2) @ C)) @ (((minus_minus @ A) @ B2) @ D)))))))))).
% 2.44/1.58 thf(fact_196_diff__eq__diff__less, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B2:A,C:A,D:A]: ((((((minus_minus @ A) @ A2) @ B2) = (((minus_minus @ A) @ C) @ D)) => ((((ord_less @ A) @ A2) @ B2) = (((ord_less @ A) @ C) @ D))))))))).
% 2.44/1.58 thf(fact_197_diff__strict__left__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less @ A) @ B2) @ A2) => (((ord_less @ A) @ (((minus_minus @ A) @ C) @ A2)) @ (((minus_minus @ A) @ C) @ B2))))))))).
% 2.44/1.58 thf(fact_198_diff__strict__right__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less @ A) @ (((minus_minus @ A) @ A2) @ C)) @ (((minus_minus @ A) @ B2) @ C))))))))).
% 2.44/1.58 thf(fact_199_diff__eq__diff__eq, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B2:A,C:A,D:A]: ((((((minus_minus @ A) @ A2) @ B2) = (((minus_minus @ A) @ C) @ D)) => ((A2 = B2) = (C = D))))))))).
% 2.44/1.58 thf(fact_200_diff__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B2:A,D:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ D) @ C) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A2) @ C)) @ (((minus_minus @ A) @ B2) @ D)))))))))).
% 2.44/1.58 thf(fact_201_diff__left__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B2:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A2) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ C) @ A2)) @ (((minus_minus @ A) @ C) @ B2))))))))).
% 2.44/1.58 thf(fact_202_diff__right__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A2) @ C)) @ (((minus_minus @ A) @ B2) @ C))))))))).
% 2.44/1.58 thf(fact_203_diff__eq__diff__less__eq, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A2:A,B2:A,C:A,D:A]: ((((((minus_minus @ A) @ A2) @ B2) = (((minus_minus @ A) @ C) @ D)) => ((((ord_less_eq @ A) @ A2) @ B2) = (((ord_less_eq @ A) @ C) @ D))))))))).
% 2.44/1.58 thf(fact_204_diff__right__commute, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [A2:A,C:A,B2:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ C)) @ B2) = (((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ B2)) @ C)))))))).
% 2.44/1.58 thf(fact_205_diff__le__mono2, axiom, (! [M:nat,N:nat,L:nat]: (((((ord_less_eq @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ (((minus_minus @ nat) @ L) @ N)) @ (((minus_minus @ nat) @ L) @ M)))))).
% 2.44/1.58 thf(fact_206_le__diff__iff_H, axiom, (! [A2:nat,C:nat,B2:nat]: (((((ord_less_eq @ nat) @ A2) @ C) => ((((ord_less_eq @ nat) @ B2) @ C) => ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ C) @ A2)) @ (((minus_minus @ nat) @ C) @ B2)) = (((ord_less_eq @ nat) @ B2) @ A2))))))).
% 2.44/1.58 thf(fact_207_diff__le__self, axiom, (! [M:nat,N:nat]: ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ M) @ N)) @ M)))).
% 2.44/1.58 thf(fact_208_diff__le__mono, axiom, (! [M:nat,N:nat,L:nat]: (((((ord_less_eq @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ (((minus_minus @ nat) @ M) @ L)) @ (((minus_minus @ nat) @ N) @ L)))))).
% 2.44/1.58 thf(fact_209_Nat_Odiff__diff__eq, axiom, (! [K2:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ K2) @ M) => ((((ord_less_eq @ nat) @ K2) @ N) => ((((minus_minus @ nat) @ (((minus_minus @ nat) @ M) @ K2)) @ (((minus_minus @ nat) @ N) @ K2)) = (((minus_minus @ nat) @ M) @ N))))))).
% 2.44/1.58 thf(fact_210_le__diff__iff, axiom, (! [K2:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ K2) @ M) => ((((ord_less_eq @ nat) @ K2) @ N) => ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ M) @ K2)) @ (((minus_minus @ nat) @ N) @ K2)) = (((ord_less_eq @ nat) @ M) @ N))))))).
% 2.44/1.58 thf(fact_211_eq__diff__iff, axiom, (! [K2:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ K2) @ M) => ((((ord_less_eq @ nat) @ K2) @ N) => (((((minus_minus @ nat) @ M) @ K2) = (((minus_minus @ nat) @ N) @ K2)) = (M = N))))))).
% 2.44/1.58 thf(fact_212_minus__nat_Odiff__0, axiom, (! [M:nat]: (((((minus_minus @ nat) @ M) @ (zero_zero @ nat)) = M)))).
% 2.44/1.58 thf(fact_213_diffs0__imp__equal, axiom, (! [M:nat,N:nat]: ((((((minus_minus @ nat) @ M) @ N) = (zero_zero @ nat)) => (((((minus_minus @ nat) @ N) @ M) = (zero_zero @ nat)) => (M = N)))))).
% 2.44/1.58 thf(fact_214_zero__induct__lemma, axiom, (! [P2:(nat > $o),K2:nat,I2:nat]: (((P2 @ K2) => ((! [N2:nat]: (((P2 @ (suc @ N2)) => (P2 @ N2)))) => (P2 @ (((minus_minus @ nat) @ K2) @ I2))))))).
% 2.44/1.58 thf(fact_215_less__imp__diff__less, axiom, (! [J:nat,K2:nat,N:nat]: (((((ord_less @ nat) @ J) @ K2) => (((ord_less @ nat) @ (((minus_minus @ nat) @ J) @ N)) @ K2))))).
% 2.44/1.58 thf(fact_216_diff__less__mono2, axiom, (! [M:nat,N:nat,L:nat]: (((((ord_less @ nat) @ M) @ N) => ((((ord_less @ nat) @ M) @ L) => (((ord_less @ nat) @ (((minus_minus @ nat) @ L) @ N)) @ (((minus_minus @ nat) @ L) @ M))))))).
% 2.44/1.58 thf(fact_217_diff__commute, axiom, (! [I2:nat,J:nat,K2:nat]: (((((minus_minus @ nat) @ (((minus_minus @ nat) @ I2) @ J)) @ K2) = (((minus_minus @ nat) @ (((minus_minus @ nat) @ I2) @ K2)) @ J))))).
% 2.44/1.58 thf(fact_218_le__iff__diff__le__0, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => ((ord_less_eq @ A) = (^ [A8:A,B3:A]: ((((ord_less_eq @ A) @ (((minus_minus @ A) @ A8) @ B3)) @ (zero_zero @ A))))))))).
% 2.44/1.58 thf(fact_219_less__iff__diff__less__0, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => ((ord_less @ A) = (^ [A8:A,B3:A]: ((((ord_less @ A) @ (((minus_minus @ A) @ A8) @ B3)) @ (zero_zero @ A))))))))).
% 2.44/1.58 thf(fact_220_diff__less, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => ((((ord_less @ nat) @ (zero_zero @ nat)) @ M) => (((ord_less @ nat) @ (((minus_minus @ nat) @ M) @ N)) @ M)))))).
% 2.44/1.58 thf(fact_221_diff__less__Suc, axiom, (! [M:nat,N:nat]: ((((ord_less @ nat) @ (((minus_minus @ nat) @ M) @ N)) @ (suc @ M))))).
% 2.44/1.58 thf(fact_222_Suc__diff__Suc, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ N) @ M) => ((suc @ (((minus_minus @ nat) @ M) @ (suc @ N))) = (((minus_minus @ nat) @ M) @ N)))))).
% 2.44/1.58 thf(fact_223_Suc__diff__le, axiom, (! [N:nat,M:nat]: (((((ord_less_eq @ nat) @ N) @ M) => ((((minus_minus @ nat) @ (suc @ M)) @ N) = (suc @ (((minus_minus @ nat) @ M) @ N))))))).
% 2.44/1.58 thf(fact_224_less__diff__iff, axiom, (! [K2:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ K2) @ M) => ((((ord_less_eq @ nat) @ K2) @ N) => ((((ord_less @ nat) @ (((minus_minus @ nat) @ M) @ K2)) @ (((minus_minus @ nat) @ N) @ K2)) = (((ord_less @ nat) @ M) @ N))))))).
% 2.44/1.58 thf(fact_225_diff__less__mono, axiom, (! [A2:nat,B2:nat,C:nat]: (((((ord_less @ nat) @ A2) @ B2) => ((((ord_less_eq @ nat) @ C) @ A2) => (((ord_less @ nat) @ (((minus_minus @ nat) @ A2) @ C)) @ (((minus_minus @ nat) @ B2) @ C))))))).
% 2.44/1.58 thf(fact_226_diff__Suc__less, axiom, (! [N:nat,I2:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => (((ord_less @ nat) @ (((minus_minus @ nat) @ N) @ (suc @ I2))) @ N))))).
% 2.44/1.58 thf(fact_227_MinPredicate, axiom, (! [P2:(nat > $o)]: (((? [X_1:nat]: ((P2 @ X_1))) => (? [N04:nat]: (((P2 @ N04) & (! [N5:nat]: (((P2 @ N5) => (((ord_less_eq @ nat) @ N04) @ N5))))))))))).
% 2.44/1.58 thf(fact_228_PrefixListTransitive, axiom, (! [A:$tType,L1:(list @ A),L2:(list @ A),L3:(list @ A)]: (((((prefixList @ A) @ L1) @ L2) => ((((prefixList @ A) @ L2) @ L3) => (((prefixList @ A) @ L1) @ L3)))))).
% 2.44/1.58 thf(fact_229_KeepProperty, axiom, (! [Low:nat,P2:(nat > $o),Q:(nat > $o)]: (((! [I3:nat]: (((((ord_less_eq @ nat) @ Low) @ I3) => ((P2 @ I3) => ((P2 @ (suc @ I3)) & (Q @ I3)))))) => ((P2 @ Low) => (! [I:nat]: (((((ord_less_eq @ nat) @ Low) @ I) => (Q @ I))))))))).
% 2.44/1.58 thf(fact_230_NatPredicateTippingPoint, axiom, (! [N22:nat,Pr:(nat > $o)]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N22) => ((Pr @ (zero_zero @ nat)) => ((~ ((Pr @ N22))) => (? [N2:nat]: (((((ord_less @ nat) @ N2) @ N22) & ((Pr @ N2) & (~ ((Pr @ (suc @ N2)))))))))))))).
% 2.44/1.58 thf(fact_231_PrefixListMonotonicity, axiom, (! [A:$tType,L1:(list @ A),L2:(list @ A)]: (((((prefixList @ A) @ L1) @ L2) => (((ord_less @ nat) @ ((size_size @ (list @ A)) @ L1)) @ ((size_size @ (list @ A)) @ L2)))))).
% 2.44/1.58 thf(fact_232_EnabledOrConsumed, axiom, ((((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ n)) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ n))) @ (one_one @ nat)))) @ msg) | (? [N02:nat]: (((((ord_less_eq @ nat) @ n0) @ N02) & ((((ord_less @ nat) @ N02) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ n))) & ((((nth @ ((message @ p) @ v)) @ (ft @ n)) @ N02) = msg))))))).
% 2.44/1.58 thf(fact_233__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, (~ ((? [I:nat]: (((((ord_less @ nat) @ I) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ (suc @ index)))) @ (one_one @ nat))) & ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) @ (one_one @ nat))) @ I) & (msg = (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ I))))))))).
% 2.44/1.58 thf(fact_234_EnabledIntermediate, axiom, (! [I:nat]: (((((ord_less @ nat) @ I) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ (suc @ index)))) => ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) @ (one_one @ nat))) @ I) => (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ I)) @ msg)))))).
% 2.44/1.58 thf(fact_235__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, (((ord_less_eq @ nat) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) @ (one_one @ nat))) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ (suc @ index)))) @ (one_one @ nat)))).
% 2.44/1.58 thf(fact_236_less__one, axiom, (! [N:nat]: (((((ord_less @ nat) @ N) @ (one_one @ nat)) = (N = (zero_zero @ nat)))))).
% 2.44/1.58 thf(fact_237__092_060open_062enabled_A_Ife_A_ISuc_Aindex_J_A_B_A_Ilength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_J_J_Amsg_092_060close_062, axiom, (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ (suc @ index)))) @ (one_one @ nat)))) @ msg)).
% 2.44/1.58 thf(fact_238_diff__Suc__1, axiom, (! [N:nat]: (((((minus_minus @ nat) @ (suc @ N)) @ (one_one @ nat)) = N)))).
% 2.44/1.58 thf(fact_239_length__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((size_size @ (list @ A)) @ ((tl @ A) @ Xs)) = (((minus_minus @ nat) @ ((size_size @ (list @ A)) @ Xs)) @ (one_one @ nat)))))).
% 2.44/1.58 thf(fact_240_Suc__diff__1, axiom, (! [N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => ((suc @ (((minus_minus @ nat) @ N) @ (one_one @ nat))) = N))))).
% 2.44/1.58 thf(fact_241_one__reorient, axiom, (! [A:$tType]: (((one @ A) => (! [X:A]: ((((one_one @ A) = X) = (X = (one_one @ A))))))))).
% 2.44/1.58 thf(fact_242_One__nat__def, axiom, ((one_one @ nat) = (suc @ (zero_zero @ nat)))).
% 2.44/1.58 thf(fact_243_MinPredicate2, axiom, (! [P2:(nat > $o)]: (((? [X_1:nat]: ((P2 @ X_1))) => (? [N04:nat]: (((P2 @ N04) & ((N04 = (zero_zero @ nat)) | (~ ((P2 @ (((minus_minus @ nat) @ N04) @ (one_one @ nat))))))))))))).
% 2.44/1.58 thf(fact_244_diff__Suc__eq__diff__pred, axiom, (! [M:nat,N:nat]: (((((minus_minus @ nat) @ M) @ (suc @ N)) = (((minus_minus @ nat) @ (((minus_minus @ nat) @ M) @ (one_one @ nat))) @ N))))).
% 2.44/1.58 thf(fact_245_nat__induct__non__zero, axiom, (! [N:nat,P2:(nat > $o)]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => ((P2 @ (one_one @ nat)) => ((! [N2:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) => ((P2 @ N2) => (P2 @ (suc @ N2)))))) => (P2 @ N))))))).
% 2.44/1.58 thf(fact_246_Suc__pred_H, axiom, (! [N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => (N = (suc @ (((minus_minus @ nat) @ N) @ (one_one @ nat)))))))).
% 2.44/1.58 thf(fact_247_Suc__diff__eq__diff__pred, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => ((((minus_minus @ nat) @ (suc @ M)) @ N) = (((minus_minus @ nat) @ M) @ (((minus_minus @ nat) @ N) @ (one_one @ nat)))))))).
% 2.44/1.58 thf(fact_248_last__conv__nth, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((last @ A) @ Xs) = (((nth @ A) @ Xs) @ (((minus_minus @ nat) @ ((size_size @ (list @ A)) @ Xs)) @ (one_one @ nat)))))))).
% 2.44/1.58 thf(fact_249_diff__numeral__special_I9_J, axiom, (! [A:$tType]: (((neg_numeral @ A) => ((((minus_minus @ A) @ (one_one @ A)) @ (one_one @ A)) = (zero_zero @ A)))))).
% 2.44/1.58 thf(fact_250_enabled__def, axiom, (! [S:$tType,V:$tType,P:$tType]: (((((enabled @ P) @ V) @ S) = (^ [Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit),Msg4:((message @ P) @ V)]: ((((ord_less @ nat) @ (zero_zero @ nat)) @ ((((((msgs @ P) @ V) @ S) @ product_unit) @ Cfg2) @ Msg4)))))))).
% 2.44/1.58 thf(tcon_fun___Orderings_Oorder, axiom, (! [A9:$tType,A10:$tType]: (((order @ A10) => (order @ (A9 > A10)))))).
% 2.44/1.58 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 2.44/1.58 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add, axiom, (cancel146912293up_add @ nat)).
% 2.44/1.58 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add, axiom, (cancel1352612707id_add @ nat)).
% 2.44/1.58 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff, axiom, (comm_monoid_diff @ nat)).
% 2.44/1.58 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, (wellorder @ nat)).
% 2.44/1.58 thf(tcon_Nat_Onat___Orderings_Oorder_1, axiom, (order @ nat)).
% 2.44/1.58 thf(tcon_Nat_Onat___Groups_Ozero, axiom, (zero @ nat)).
% 2.44/1.58 thf(tcon_Nat_Onat___Groups_Oone, axiom, (one @ nat)).
% 2.44/1.58 thf(tcon_Nat_Onat___Nat_Osize, axiom, (size @ nat)).
% 2.44/1.58 thf(tcon_Set_Oset___Orderings_Oorder_2, axiom, (! [A9:$tType]: ((order @ (set @ A9))))).
% 2.44/1.58 thf(tcon_HOL_Obool___Orderings_Oorder_3, axiom, (order @ $o)).
% 2.44/1.58 thf(tcon_List_Olist___Nat_Osize_4, axiom, (! [A9:$tType]: ((size @ (list @ A9))))).
% 2.44/1.58 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_5, axiom, (wellorder @ product_unit)).
% 2.44/1.58 thf(tcon_Product__Type_Ounit___Orderings_Oorder_6, axiom, (order @ product_unit)).
% 2.44/1.58 thf(tcon_AsynchronousSystem_Omessage___Nat_Osize_7, axiom, (! [A9:$tType,A10:$tType]: ((size @ ((message @ A9) @ A10))))).
% 2.44/1.58 thf(help_If_3_1_T, axiom, (! [P2:$o]: (((P2 = $true) | (P2 = $false))))).
% 2.44/1.58 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.44/1.58 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.44/1.58 thf(conj_0, conjecture, (((ord_less @ nat) @ n1) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index)))).
% 2.44/1.58 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.6wC2JEysVn/DTF2DTF4609.p
% 2.44/1.58 ------------------------
% 2.65/1.60 ---- Cleaned THF ---
% 2.65/1.60 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext,type,
% 2.65/1.60 configuration_ext: $tType > $tType > $tType > $tType > $tType ).
% 2.65/1.60
% 2.65/1.60 thf(ty_t_AsynchronousSystem_Omessage,type,
% 2.65/1.60 message: $tType > $tType > $tType ).
% 2.65/1.60
% 2.65/1.60 thf(ty_t_Product__Type_Ounit,type,
% 2.65/1.60 product_unit: $tType ).
% 2.65/1.60
% 2.65/1.60 thf(ty_t_List_Olist,type,
% 2.65/1.60 list: $tType > $tType ).
% 2.65/1.60
% 2.65/1.60 thf(ty_t_Set_Oset,type,
% 2.65/1.60 set: $tType > $tType ).
% 2.65/1.60
% 2.65/1.60 thf(ty_t_Nat_Onat,type,
% 2.65/1.60 nat: $tType ).
% 2.65/1.60
% 2.65/1.60 thf(ty_tf_v,type,
% 2.65/1.60 v: $tType ).
% 2.65/1.60
% 2.65/1.60 thf(ty_tf_s,type,
% 2.65/1.60 s: $tType ).
% 2.65/1.60
% 2.65/1.60 thf(ty_tf_p,type,
% 2.65/1.60 p: $tType ).
% 2.65/1.60
% 2.65/1.60 thf(sy_cl_HOL_Otype,type,
% 2.65/1.60 type:
% 2.65/1.60 !>[A: $tType] : $o ).
% 2.65/1.60
% 2.65/1.60 thf(sy_cl_Nat_Osize,type,
% 2.65/1.60 size:
% 2.65/1.60 !>[A: $tType] : $o ).
% 2.65/1.60
% 2.65/1.60 thf(sy_cl_Groups_Oone,type,
% 2.65/1.60 one:
% 2.65/1.60 !>[A: $tType] : $o ).
% 2.65/1.60
% 2.65/1.60 thf(sy_cl_Groups_Ozero,type,
% 2.65/1.60 zero:
% 2.65/1.60 !>[A: $tType] : $o ).
% 2.65/1.60
% 2.65/1.60 thf(sy_cl_Num_Oneg__numeral,type,
% 2.65/1.60 neg_numeral:
% 2.65/1.60 !>[A: $tType] : $o ).
% 2.65/1.60
% 2.65/1.60 thf(sy_cl_Orderings_Oorder,type,
% 2.65/1.60 order:
% 2.65/1.60 !>[A: $tType] : $o ).
% 2.65/1.60
% 2.65/1.60 thf(sy_cl_Groups_Ogroup__add,type,
% 2.65/1.60 group_add:
% 2.65/1.60 !>[A: $tType] : $o ).
% 2.65/1.60
% 2.65/1.60 thf(sy_cl_Orderings_Owellorder,type,
% 2.65/1.60 wellorder:
% 2.65/1.60 !>[A: $tType] : $o ).
% 2.65/1.60
% 2.65/1.60 thf(sy_cl_Groups_Ocomm__monoid__diff,type,
% 2.65/1.60 comm_monoid_diff:
% 2.65/1.60 !>[A: $tType] : $o ).
% 2.65/1.60
% 2.65/1.60 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 2.65/1.60 ordered_ab_group_add:
% 2.65/1.60 !>[A: $tType] : $o ).
% 2.65/1.60
% 2.65/1.60 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 2.65/1.60 cancel1352612707id_add:
% 2.65/1.60 !>[A: $tType] : $o ).
% 2.65/1.60
% 2.65/1.60 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 2.65/1.60 cancel146912293up_add:
% 2.65/1.60 !>[A: $tType] : $o ).
% 2.65/1.60
% 2.65/1.60 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.65/1.60 canoni770627133id_add:
% 2.65/1.60 !>[A: $tType] : $o ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_AsynchronousSystem_Oconfiguration_Omsgs,type,
% 2.65/1.60 msgs:
% 2.65/1.60 !>[P: $tType,V: $tType,S: $tType,Z: $tType] : ( ( configuration_ext @ P @ V @ S @ Z ) > ( message @ P @ V ) > nat ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_AsynchronousSystem_Oenabled,type,
% 2.65/1.60 enabled:
% 2.65/1.60 !>[P: $tType,V: $tType,S: $tType] : ( ( configuration_ext @ P @ V @ S @ product_unit ) > ( message @ P @ V ) > $o ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_Execution_Oexecution_OfirstOccurrence,type,
% 2.65/1.60 firstOccurrence:
% 2.65/1.60 !>[P: $tType,V: $tType,S: $tType] : ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( message @ P @ V ) > nat > $o ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_Execution_Oexecution_OminimalEnabled,type,
% 2.65/1.60 minimalEnabled:
% 2.65/1.60 !>[P: $tType,V: $tType,S: $tType] : ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( message @ P @ V ) > $o ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 2.65/1.60 minus_minus:
% 2.65/1.60 !>[A: $tType] : ( A > A > A ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_Groups_Oone__class_Oone,type,
% 2.65/1.60 one_one:
% 2.65/1.60 !>[A: $tType] : A ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.65/1.60 zero_zero:
% 2.65/1.60 !>[A: $tType] : A ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_If,type,
% 2.65/1.60 if:
% 2.65/1.60 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_ListUtilities_OprefixList,type,
% 2.65/1.60 prefixList:
% 2.65/1.60 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_List_Olast,type,
% 2.65/1.60 last:
% 2.65/1.60 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_List_Olist_ONil,type,
% 2.65/1.60 nil:
% 2.65/1.60 !>[A: $tType] : ( list @ A ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_List_Olist_Otl,type,
% 2.65/1.60 tl:
% 2.65/1.60 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_List_Olist__ex,type,
% 2.65/1.60 list_ex:
% 2.65/1.60 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_List_Olist__ex1,type,
% 2.65/1.60 list_ex1:
% 2.65/1.60 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_List_Onth,type,
% 2.65/1.60 nth:
% 2.65/1.60 !>[A: $tType] : ( ( list @ A ) > nat > A ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_List_Oremdups__adj,type,
% 2.65/1.60 remdups_adj:
% 2.65/1.60 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_Nat_OSuc,type,
% 2.65/1.60 suc: nat > nat ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_Nat_Osize__class_Osize,type,
% 2.65/1.60 size_size:
% 2.65/1.60 !>[A: $tType] : ( A > nat ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.65/1.60 ord_less:
% 2.65/1.60 !>[A: $tType] : ( A > A > $o ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.65/1.60 ord_less_eq:
% 2.65/1.60 !>[A: $tType] : ( A > A > $o ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_Set_OCollect,type,
% 2.65/1.60 collect:
% 2.65/1.60 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_c_member,type,
% 2.65/1.60 member:
% 2.65/1.60 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_v_consumedMsg____,type,
% 2.65/1.60 consumedMsg: message @ p @ v ).
% 2.65/1.60
% 2.65/1.60 thf(sy_v_fe____,type,
% 2.65/1.60 fe: nat > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_v_firstOccSet____,type,
% 2.65/1.60 firstOccSet: nat > ( set @ ( message @ p @ v ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_v_ft____,type,
% 2.65/1.60 ft: nat > ( list @ ( message @ p @ v ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(sy_v_index____,type,
% 2.65/1.60 index: nat ).
% 2.65/1.60
% 2.65/1.60 thf(sy_v_msg____,type,
% 2.65/1.60 msg: message @ p @ v ).
% 2.65/1.60
% 2.65/1.60 thf(sy_v_n0____,type,
% 2.65/1.60 n0: nat ).
% 2.65/1.60
% 2.65/1.60 thf(sy_v_n1____,type,
% 2.65/1.60 n1: nat ).
% 2.65/1.60
% 2.65/1.60 thf(sy_v_nMsg____,type,
% 2.65/1.60 nMsg: nat ).
% 2.65/1.60
% 2.65/1.60 thf(sy_v_n____,type,
% 2.65/1.60 n: nat ).
% 2.65/1.60
% 2.65/1.60 thf(fact_0_AssumpGreaterOccurrence_I1_J,axiom,
% 2.65/1.60 ~ ( ord_less @ nat @ nMsg @ n1 ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_1__092_060open_062nMsg_A_060_Alength_A_Ife_Aindex_J_092_060close_062,axiom,
% 2.65/1.60 ord_less @ nat @ nMsg @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_2_NotEmpty_I2_J,axiom,
% 2.65/1.60 ( ( fe @ index )
% 2.65/1.60 != ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_3_AssumptionFair_I2_J,axiom,
% 2.65/1.60 ord_less @ nat @ n0 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_4_length__induct,axiom,
% 2.65/1.60 ! [A: $tType,P2: ( list @ A ) > $o,Xs: list @ A] :
% 2.65/1.60 ( ! [Xs2: list @ A] :
% 2.65/1.60 ( ! [Ys: list @ A] :
% 2.65/1.60 ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ys ) @ ( size_size @ ( list @ A ) @ Xs2 ) )
% 2.65/1.60 => ( P2 @ Ys ) )
% 2.65/1.60 => ( P2 @ Xs2 ) )
% 2.65/1.60 => ( P2 @ Xs ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_5_SameCfgOnLow,axiom,
% 2.65/1.60 ! [I: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) )
% 2.65/1.60 => ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ I )
% 2.65/1.60 = ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ I ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_6_Ex__list__of__length,axiom,
% 2.65/1.60 ! [A: $tType,N: nat] :
% 2.65/1.60 ? [Xs2: list @ A] :
% 2.65/1.60 ( ( size_size @ ( list @ A ) @ Xs2 )
% 2.65/1.60 = N ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_7_neq__if__length__neq,axiom,
% 2.65/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.60 ( ( ( size_size @ ( list @ A ) @ Xs )
% 2.65/1.60 != ( size_size @ ( list @ A ) @ Ys2 ) )
% 2.65/1.60 => ( Xs != Ys2 ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_8_size__neq__size__imp__neq,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( size @ A )
% 2.65/1.60 => ! [X: A,Y: A] :
% 2.65/1.60 ( ( ( size_size @ A @ X )
% 2.65/1.60 != ( size_size @ A @ Y ) )
% 2.65/1.60 => ( X != Y ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_9_nat__neq__iff,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( M != N )
% 2.65/1.60 = ( ( ord_less @ nat @ M @ N )
% 2.65/1.60 | ( ord_less @ nat @ N @ M ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_10_less__not__refl,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ~ ( ord_less @ nat @ N @ N ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_11_less__not__refl2,axiom,
% 2.65/1.60 ! [N: nat,M: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ N @ M )
% 2.65/1.60 => ( M != N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_12_less__not__refl3,axiom,
% 2.65/1.60 ! [S2: nat,T: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ S2 @ T )
% 2.65/1.60 => ( S2 != T ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_13_less__irrefl__nat,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ~ ( ord_less @ nat @ N @ N ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_14_nat_Oinject,axiom,
% 2.65/1.60 ! [X2: nat,Y2: nat] :
% 2.65/1.60 ( ( ( suc @ X2 )
% 2.65/1.60 = ( suc @ Y2 ) )
% 2.65/1.60 = ( X2 = Y2 ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_15_old_Onat_Oinject,axiom,
% 2.65/1.60 ! [Nat: nat,Nat2: nat] :
% 2.65/1.60 ( ( ( suc @ Nat )
% 2.65/1.60 = ( suc @ Nat2 ) )
% 2.65/1.60 = ( Nat = Nat2 ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_16_NotEmpty_I1_J,axiom,
% 2.65/1.60 ( ( fe @ ( suc @ index ) )
% 2.65/1.60 != ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_17_Suc__less__eq,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 2.65/1.60 = ( ord_less @ nat @ M @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_18_Suc__mono,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ M @ N )
% 2.65/1.60 => ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_19_lessI,axiom,
% 2.65/1.60 ! [N: nat] : ( ord_less @ nat @ N @ ( suc @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_20_Suc__inject,axiom,
% 2.65/1.60 ! [X: nat,Y: nat] :
% 2.65/1.60 ( ( ( suc @ X )
% 2.65/1.60 = ( suc @ Y ) )
% 2.65/1.60 => ( X = Y ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_21_n__not__Suc__n,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ( N
% 2.65/1.60 != ( suc @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_22_not__less__less__Suc__eq,axiom,
% 2.65/1.60 ! [N: nat,M: nat] :
% 2.65/1.60 ( ~ ( ord_less @ nat @ N @ M )
% 2.65/1.60 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 2.65/1.60 = ( N = M ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_23_strict__inc__induct,axiom,
% 2.65/1.60 ! [I2: nat,J: nat,P2: nat > $o] :
% 2.65/1.60 ( ( ord_less @ nat @ I2 @ J )
% 2.65/1.60 => ( ! [I3: nat] :
% 2.65/1.60 ( ( J
% 2.65/1.60 = ( suc @ I3 ) )
% 2.65/1.60 => ( P2 @ I3 ) )
% 2.65/1.60 => ( ! [I3: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I3 @ J )
% 2.65/1.60 => ( ( P2 @ ( suc @ I3 ) )
% 2.65/1.60 => ( P2 @ I3 ) ) )
% 2.65/1.60 => ( P2 @ I2 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_24_less__Suc__induct,axiom,
% 2.65/1.60 ! [I2: nat,J: nat,P2: nat > nat > $o] :
% 2.65/1.60 ( ( ord_less @ nat @ I2 @ J )
% 2.65/1.60 => ( ! [I3: nat] : ( P2 @ I3 @ ( suc @ I3 ) )
% 2.65/1.60 => ( ! [I3: nat,J2: nat,K: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I3 @ J2 )
% 2.65/1.60 => ( ( ord_less @ nat @ J2 @ K )
% 2.65/1.60 => ( ( P2 @ I3 @ J2 )
% 2.65/1.60 => ( ( P2 @ J2 @ K )
% 2.65/1.60 => ( P2 @ I3 @ K ) ) ) ) )
% 2.65/1.60 => ( P2 @ I2 @ J ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_25_less__trans__Suc,axiom,
% 2.65/1.60 ! [I2: nat,J: nat,K2: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I2 @ J )
% 2.65/1.60 => ( ( ord_less @ nat @ J @ K2 )
% 2.65/1.60 => ( ord_less @ nat @ ( suc @ I2 ) @ K2 ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_26_Suc__less__SucD,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 2.65/1.60 => ( ord_less @ nat @ M @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_27_less__antisym,axiom,
% 2.65/1.60 ! [N: nat,M: nat] :
% 2.65/1.60 ( ~ ( ord_less @ nat @ N @ M )
% 2.65/1.60 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 2.65/1.60 => ( M = N ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_28_Suc__less__eq2,axiom,
% 2.65/1.60 ! [N: nat,M: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ ( suc @ N ) @ M )
% 2.65/1.60 = ( ? [M2: nat] :
% 2.65/1.60 ( ( M
% 2.65/1.60 = ( suc @ M2 ) )
% 2.65/1.60 & ( ord_less @ nat @ N @ M2 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_29_All__less__Suc,axiom,
% 2.65/1.60 ! [N: nat,P2: nat > $o] :
% 2.65/1.60 ( ( ! [I4: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I4 @ ( suc @ N ) )
% 2.65/1.60 => ( P2 @ I4 ) ) )
% 2.65/1.60 = ( ( P2 @ N )
% 2.65/1.60 & ! [I4: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I4 @ N )
% 2.65/1.60 => ( P2 @ I4 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_30_not__less__eq,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ~ ( ord_less @ nat @ M @ N ) )
% 2.65/1.60 = ( ord_less @ nat @ N @ ( suc @ M ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_31_less__Suc__eq,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 2.65/1.60 = ( ( ord_less @ nat @ M @ N )
% 2.65/1.60 | ( M = N ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_32_Ex__less__Suc,axiom,
% 2.65/1.60 ! [N: nat,P2: nat > $o] :
% 2.65/1.60 ( ( ? [I4: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I4 @ ( suc @ N ) )
% 2.65/1.60 & ( P2 @ I4 ) ) )
% 2.65/1.60 = ( ( P2 @ N )
% 2.65/1.60 | ? [I4: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I4 @ N )
% 2.65/1.60 & ( P2 @ I4 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_33_less__SucI,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ M @ N )
% 2.65/1.60 => ( ord_less @ nat @ M @ ( suc @ N ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_34_less__SucE,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 2.65/1.60 => ( ~ ( ord_less @ nat @ M @ N )
% 2.65/1.60 => ( M = N ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_35_Suc__lessI,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ M @ N )
% 2.65/1.60 => ( ( ( suc @ M )
% 2.65/1.60 != N )
% 2.65/1.60 => ( ord_less @ nat @ ( suc @ M ) @ N ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_36_Suc__lessE,axiom,
% 2.65/1.60 ! [I2: nat,K2: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ ( suc @ I2 ) @ K2 )
% 2.65/1.60 => ~ ! [J2: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I2 @ J2 )
% 2.65/1.60 => ( K2
% 2.65/1.60 != ( suc @ J2 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_37_Suc__lessD,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ ( suc @ M ) @ N )
% 2.65/1.60 => ( ord_less @ nat @ M @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_38_Nat_OlessE,axiom,
% 2.65/1.60 ! [I2: nat,K2: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I2 @ K2 )
% 2.65/1.60 => ( ( K2
% 2.65/1.60 != ( suc @ I2 ) )
% 2.65/1.60 => ~ ! [J2: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I2 @ J2 )
% 2.65/1.60 => ( K2
% 2.65/1.60 != ( suc @ J2 ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_39_list__eq__iff__nth__eq,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( ^ [Y3: list @ A,Z2: list @ A] : ( Y3 = Z2 ) )
% 2.65/1.60 = ( ^ [Xs3: list @ A,Ys3: list @ A] :
% 2.65/1.60 ( ( ( size_size @ ( list @ A ) @ Xs3 )
% 2.65/1.60 = ( size_size @ ( list @ A ) @ Ys3 ) )
% 2.65/1.60 & ! [I4: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ A ) @ Xs3 ) )
% 2.65/1.60 => ( ( nth @ A @ Xs3 @ I4 )
% 2.65/1.60 = ( nth @ A @ Ys3 @ I4 ) ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_40_Skolem__list__nth,axiom,
% 2.65/1.60 ! [A: $tType,K2: nat,P2: nat > A > $o] :
% 2.65/1.60 ( ( ! [I4: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I4 @ K2 )
% 2.65/1.60 => ? [X3: A] : ( P2 @ I4 @ X3 ) ) )
% 2.65/1.60 = ( ? [Xs3: list @ A] :
% 2.65/1.60 ( ( ( size_size @ ( list @ A ) @ Xs3 )
% 2.65/1.60 = K2 )
% 2.65/1.60 & ! [I4: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I4 @ K2 )
% 2.65/1.60 => ( P2 @ I4 @ ( nth @ A @ Xs3 @ I4 ) ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_41_nth__equalityI,axiom,
% 2.65/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.60 ( ( ( size_size @ ( list @ A ) @ Xs )
% 2.65/1.60 = ( size_size @ ( list @ A ) @ Ys2 ) )
% 2.65/1.60 => ( ! [I3: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I3 @ ( size_size @ ( list @ A ) @ Xs ) )
% 2.65/1.60 => ( ( nth @ A @ Xs @ I3 )
% 2.65/1.60 = ( nth @ A @ Ys2 @ I3 ) ) )
% 2.65/1.60 => ( Xs = Ys2 ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_42_lift__Suc__mono__less__iff,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( order @ A )
% 2.65/1.60 => ! [F: nat > A,N: nat,M: nat] :
% 2.65/1.60 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 2.65/1.60 => ( ( ord_less @ A @ ( F @ N ) @ ( F @ M ) )
% 2.65/1.60 = ( ord_less @ nat @ N @ M ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_43_mem__Collect__eq,axiom,
% 2.65/1.60 ! [A: $tType,A2: A,P2: A > $o] :
% 2.65/1.60 ( ( member @ A @ A2 @ ( collect @ A @ P2 ) )
% 2.65/1.60 = ( P2 @ A2 ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_44_Collect__mem__eq,axiom,
% 2.65/1.60 ! [A: $tType,A3: set @ A] :
% 2.65/1.60 ( ( collect @ A
% 2.65/1.60 @ ^ [X4: A] : ( member @ A @ X4 @ A3 ) )
% 2.65/1.60 = A3 ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_45_Collect__cong,axiom,
% 2.65/1.60 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 2.65/1.60 ( ! [X5: A] :
% 2.65/1.60 ( ( P2 @ X5 )
% 2.65/1.60 = ( Q @ X5 ) )
% 2.65/1.60 => ( ( collect @ A @ P2 )
% 2.65/1.60 = ( collect @ A @ Q ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_46_lift__Suc__mono__less,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( order @ A )
% 2.65/1.60 => ! [F: nat > A,N: nat,N3: nat] :
% 2.65/1.60 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 2.65/1.60 => ( ( ord_less @ nat @ N @ N3 )
% 2.65/1.60 => ( ord_less @ A @ ( F @ N ) @ ( F @ N3 ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_47_measure__induct__rule,axiom,
% 2.65/1.60 ! [B: $tType,A: $tType] :
% 2.65/1.60 ( ( wellorder @ B )
% 2.65/1.60 => ! [F: A > B,P2: A > $o,A2: A] :
% 2.65/1.60 ( ! [X5: A] :
% 2.65/1.60 ( ! [Y4: A] :
% 2.65/1.60 ( ( ord_less @ B @ ( F @ Y4 ) @ ( F @ X5 ) )
% 2.65/1.60 => ( P2 @ Y4 ) )
% 2.65/1.60 => ( P2 @ X5 ) )
% 2.65/1.60 => ( P2 @ A2 ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_48_measure__induct,axiom,
% 2.65/1.60 ! [B: $tType,A: $tType] :
% 2.65/1.60 ( ( wellorder @ B )
% 2.65/1.60 => ! [F: A > B,P2: A > $o,A2: A] :
% 2.65/1.60 ( ! [X5: A] :
% 2.65/1.60 ( ! [Y4: A] :
% 2.65/1.60 ( ( ord_less @ B @ ( F @ Y4 ) @ ( F @ X5 ) )
% 2.65/1.60 => ( P2 @ Y4 ) )
% 2.65/1.60 => ( P2 @ X5 ) )
% 2.65/1.60 => ( P2 @ A2 ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_49_infinite__descent__measure,axiom,
% 2.65/1.60 ! [A: $tType,P2: A > $o,V2: A > nat,X: A] :
% 2.65/1.60 ( ! [X5: A] :
% 2.65/1.60 ( ~ ( P2 @ X5 )
% 2.65/1.60 => ? [Y4: A] :
% 2.65/1.60 ( ( ord_less @ nat @ ( V2 @ Y4 ) @ ( V2 @ X5 ) )
% 2.65/1.60 & ~ ( P2 @ Y4 ) ) )
% 2.65/1.60 => ( P2 @ X ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_50_linorder__neqE__nat,axiom,
% 2.65/1.60 ! [X: nat,Y: nat] :
% 2.65/1.60 ( ( X != Y )
% 2.65/1.60 => ( ~ ( ord_less @ nat @ X @ Y )
% 2.65/1.60 => ( ord_less @ nat @ Y @ X ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_51_infinite__descent,axiom,
% 2.65/1.60 ! [P2: nat > $o,N: nat] :
% 2.65/1.60 ( ! [N2: nat] :
% 2.65/1.60 ( ~ ( P2 @ N2 )
% 2.65/1.60 => ? [M3: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ M3 @ N2 )
% 2.65/1.60 & ~ ( P2 @ M3 ) ) )
% 2.65/1.60 => ( P2 @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_52_nat__less__induct,axiom,
% 2.65/1.60 ! [P2: nat > $o,N: nat] :
% 2.65/1.60 ( ! [N2: nat] :
% 2.65/1.60 ( ! [M3: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ M3 @ N2 )
% 2.65/1.60 => ( P2 @ M3 ) )
% 2.65/1.60 => ( P2 @ N2 ) )
% 2.65/1.60 => ( P2 @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_53_Subset,axiom,
% 2.65/1.60 ! [MsgInSet: message @ p @ v] :
% 2.65/1.60 ( ( member @ ( message @ p @ v ) @ MsgInSet @ ( firstOccSet @ ( suc @ index ) ) )
% 2.65/1.60 => ( member @ ( message @ p @ v ) @ MsgInSet @ ( firstOccSet @ index ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_54_IPrefixListEx,axiom,
% 2.65/1.60 ! [I: nat] : ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ I ) @ ( fe @ ( suc @ I ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_55_AssumptionFair_I3_J,axiom,
% 2.65/1.60 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ n0 ) @ msg ).
% 2.65/1.60
% 2.65/1.60 thf(fact_56_list__ex__length,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( list_ex @ A )
% 2.65/1.60 = ( ^ [P3: A > $o,Xs3: list @ A] :
% 2.65/1.60 ? [N4: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ N4 @ ( size_size @ ( list @ A ) @ Xs3 ) )
% 2.65/1.60 & ( P3 @ ( nth @ A @ Xs3 @ N4 ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_57_AssumpGreaterOccurrence_I2_J,axiom,
% 2.65/1.60 firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ consumedMsg @ n1 ).
% 2.65/1.60
% 2.65/1.60 thf(fact_58_list__ex1__simps_I1_J,axiom,
% 2.65/1.60 ! [A: $tType,P2: A > $o] :
% 2.65/1.60 ~ ( list_ex1 @ A @ P2 @ ( nil @ A ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_59_LengthStep,axiom,
% 2.65/1.60 ord_less @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_60_remdups__adj__adjacent,axiom,
% 2.65/1.60 ! [A: $tType,I2: nat,Xs: list @ A] :
% 2.65/1.60 ( ( ord_less @ nat @ ( suc @ I2 ) @ ( size_size @ ( list @ A ) @ ( remdups_adj @ A @ Xs ) ) )
% 2.65/1.60 => ( ( nth @ A @ ( remdups_adj @ A @ Xs ) @ I2 )
% 2.65/1.60 != ( nth @ A @ ( remdups_adj @ A @ Xs ) @ ( suc @ I2 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_61_nth__tl,axiom,
% 2.65/1.60 ! [A: $tType,N: nat,Xs: list @ A] :
% 2.65/1.60 ( ( ord_less @ nat @ N @ ( size_size @ ( list @ A ) @ ( tl @ A @ Xs ) ) )
% 2.65/1.60 => ( ( nth @ A @ ( tl @ A @ Xs ) @ N )
% 2.65/1.60 = ( nth @ A @ Xs @ ( suc @ N ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_62_length__greater__0__conv,axiom,
% 2.65/1.60 ! [A: $tType,Xs: list @ A] :
% 2.65/1.60 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ A ) @ Xs ) )
% 2.65/1.60 = ( Xs
% 2.65/1.60 != ( nil @ A ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_63_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 2.65/1.60 ! [P2: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,Q: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,A4: configuration_ext @ p @ v @ s @ product_unit,A5: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),A6: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),A7: nat] :
% 2.65/1.60 ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 2.65/1.60 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N2: nat] :
% 2.65/1.60 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 2.65/1.60 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 2.65/1.60 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 2.65/1.60 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 2.65/1.60 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N2: nat] :
% 2.65/1.60 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 2.65/1.60 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 2.65/1.60 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 2.65/1.60 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_64_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 2.65/1.60 ! [P2: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,Q: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,A0: configuration_ext @ p @ v @ s @ product_unit,A1: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),A22: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),A32: nat] :
% 2.65/1.60 ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 2.65/1.60 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N2: nat] :
% 2.65/1.60 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 2.65/1.60 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 2.65/1.60 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 2.65/1.60 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 2.65/1.60 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N2: nat] :
% 2.65/1.60 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 2.65/1.60 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 2.65/1.60 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 2.65/1.60 => ( P2 @ A0 @ A1 @ A22 @ A32 ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_65_AssumpGreaterOccurrence_I3_J,axiom,
% 2.65/1.60 firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg ).
% 2.65/1.60
% 2.65/1.60 thf(fact_66_ConsumedInSet,axiom,
% 2.65/1.60 member @ ( message @ p @ v ) @ consumedMsg @ ( firstOccSet @ index ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_67_SameMsgOnLow,axiom,
% 2.65/1.60 ! [I: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 2.65/1.60 => ( ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ I )
% 2.65/1.60 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_68_neq0__conv,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ( ( N
% 2.65/1.60 != ( zero_zero @ nat ) )
% 2.65/1.60 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_69_less__nat__zero__code,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_70_bot__nat__0_Onot__eq__extremum,axiom,
% 2.65/1.60 ! [A2: nat] :
% 2.65/1.60 ( ( A2
% 2.65/1.60 != ( zero_zero @ nat ) )
% 2.65/1.60 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A2 ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_71_ConsumedMsg_I1_J,axiom,
% 2.65/1.60 minimalEnabled @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ consumedMsg ).
% 2.65/1.60
% 2.65/1.60 thf(fact_72_remdups__adj__Nil__iff,axiom,
% 2.65/1.60 ! [A: $tType,Xs: list @ A] :
% 2.65/1.60 ( ( ( remdups_adj @ A @ Xs )
% 2.65/1.60 = ( nil @ A ) )
% 2.65/1.60 = ( Xs
% 2.65/1.60 = ( nil @ A ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_73_list__ex__simps_I2_J,axiom,
% 2.65/1.60 ! [A: $tType,P2: A > $o] :
% 2.65/1.60 ~ ( list_ex @ A @ P2 @ ( nil @ A ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_74_SmallIndex,axiom,
% 2.65/1.60 ! [NMsg: nat] :
% 2.65/1.60 ( ( firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ NMsg )
% 2.65/1.60 => ( ord_less @ nat @ NMsg @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_75_zero__less__Suc,axiom,
% 2.65/1.60 ! [N: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_76_less__Suc0,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ N @ ( suc @ ( zero_zero @ nat ) ) )
% 2.65/1.60 = ( N
% 2.65/1.60 = ( zero_zero @ nat ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_77_length__0__conv,axiom,
% 2.65/1.60 ! [A: $tType,Xs: list @ A] :
% 2.65/1.60 ( ( ( size_size @ ( list @ A ) @ Xs )
% 2.65/1.60 = ( zero_zero @ nat ) )
% 2.65/1.60 = ( Xs
% 2.65/1.60 = ( nil @ A ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_78_AssumptionFairContr,axiom,
% 2.65/1.60 ! [N5: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ n @ N5 )
% 2.65/1.60 => ! [N0: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ N0 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N5 ) ) )
% 2.65/1.60 => ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) @ N0 )
% 2.65/1.60 => ( msg
% 2.65/1.60 != ( nth @ ( message @ p @ v ) @ ( ft @ N5 ) @ N0 ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_79_AssumptionFirstOccSetDecrOrConsumed_I1_J,axiom,
% 2.65/1.60 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) @ msg ).
% 2.65/1.60
% 2.65/1.60 thf(fact_80_AssumptionCase1ImplThesis_H,axiom,
% 2.65/1.60 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg ).
% 2.65/1.60
% 2.65/1.60 thf(fact_81_remdups__adj_Osimps_I1_J,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( remdups_adj @ A @ ( nil @ A ) )
% 2.65/1.60 = ( nil @ A ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_82_list_Osel_I2_J,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( tl @ A @ ( nil @ A ) )
% 2.65/1.60 = ( nil @ A ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_83_not0__implies__Suc,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ( ( N
% 2.65/1.60 != ( zero_zero @ nat ) )
% 2.65/1.60 => ? [M4: nat] :
% 2.65/1.60 ( N
% 2.65/1.60 = ( suc @ M4 ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_84_old_Onat_Oinducts,axiom,
% 2.65/1.60 ! [P2: nat > $o,Nat: nat] :
% 2.65/1.60 ( ( P2 @ ( zero_zero @ nat ) )
% 2.65/1.60 => ( ! [Nat3: nat] :
% 2.65/1.60 ( ( P2 @ Nat3 )
% 2.65/1.60 => ( P2 @ ( suc @ Nat3 ) ) )
% 2.65/1.60 => ( P2 @ Nat ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_85_old_Onat_Oexhaust,axiom,
% 2.65/1.60 ! [Y: nat] :
% 2.65/1.60 ( ( Y
% 2.65/1.60 != ( zero_zero @ nat ) )
% 2.65/1.60 => ~ ! [Nat3: nat] :
% 2.65/1.60 ( Y
% 2.65/1.60 != ( suc @ Nat3 ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_86_Zero__not__Suc,axiom,
% 2.65/1.60 ! [M: nat] :
% 2.65/1.60 ( ( zero_zero @ nat )
% 2.65/1.60 != ( suc @ M ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_87_Zero__neq__Suc,axiom,
% 2.65/1.60 ! [M: nat] :
% 2.65/1.60 ( ( zero_zero @ nat )
% 2.65/1.60 != ( suc @ M ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_88_Suc__neq__Zero,axiom,
% 2.65/1.60 ! [M: nat] :
% 2.65/1.60 ( ( suc @ M )
% 2.65/1.60 != ( zero_zero @ nat ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_89_zero__induct,axiom,
% 2.65/1.60 ! [P2: nat > $o,K2: nat] :
% 2.65/1.60 ( ( P2 @ K2 )
% 2.65/1.60 => ( ! [N2: nat] :
% 2.65/1.60 ( ( P2 @ ( suc @ N2 ) )
% 2.65/1.60 => ( P2 @ N2 ) )
% 2.65/1.60 => ( P2 @ ( zero_zero @ nat ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_90_diff__induct,axiom,
% 2.65/1.60 ! [P2: nat > nat > $o,M: nat,N: nat] :
% 2.65/1.60 ( ! [X5: nat] : ( P2 @ X5 @ ( zero_zero @ nat ) )
% 2.65/1.60 => ( ! [Y5: nat] : ( P2 @ ( zero_zero @ nat ) @ ( suc @ Y5 ) )
% 2.65/1.60 => ( ! [X5: nat,Y5: nat] :
% 2.65/1.60 ( ( P2 @ X5 @ Y5 )
% 2.65/1.60 => ( P2 @ ( suc @ X5 ) @ ( suc @ Y5 ) ) )
% 2.65/1.60 => ( P2 @ M @ N ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_91_nat__induct,axiom,
% 2.65/1.60 ! [P2: nat > $o,N: nat] :
% 2.65/1.60 ( ( P2 @ ( zero_zero @ nat ) )
% 2.65/1.60 => ( ! [N2: nat] :
% 2.65/1.60 ( ( P2 @ N2 )
% 2.65/1.60 => ( P2 @ ( suc @ N2 ) ) )
% 2.65/1.60 => ( P2 @ N ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_92_nat_OdiscI,axiom,
% 2.65/1.60 ! [Nat: nat,X2: nat] :
% 2.65/1.60 ( ( Nat
% 2.65/1.60 = ( suc @ X2 ) )
% 2.65/1.60 => ( Nat
% 2.65/1.60 != ( zero_zero @ nat ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_93_old_Onat_Odistinct_I1_J,axiom,
% 2.65/1.60 ! [Nat2: nat] :
% 2.65/1.60 ( ( zero_zero @ nat )
% 2.65/1.60 != ( suc @ Nat2 ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_94_old_Onat_Odistinct_I2_J,axiom,
% 2.65/1.60 ! [Nat4: nat] :
% 2.65/1.60 ( ( suc @ Nat4 )
% 2.65/1.60 != ( zero_zero @ nat ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_95_nat_Odistinct_I1_J,axiom,
% 2.65/1.60 ! [X2: nat] :
% 2.65/1.60 ( ( zero_zero @ nat )
% 2.65/1.60 != ( suc @ X2 ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_96_gr0I,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ( ( N
% 2.65/1.60 != ( zero_zero @ nat ) )
% 2.65/1.60 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_97_not__gr0,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) )
% 2.65/1.60 = ( N
% 2.65/1.60 = ( zero_zero @ nat ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_98_not__less0,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_99_less__zeroE,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_100_gr__implies__not0,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ M @ N )
% 2.65/1.60 => ( N
% 2.65/1.60 != ( zero_zero @ nat ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_101_infinite__descent0,axiom,
% 2.65/1.60 ! [P2: nat > $o,N: nat] :
% 2.65/1.60 ( ( P2 @ ( zero_zero @ nat ) )
% 2.65/1.60 => ( ! [N2: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 2.65/1.60 => ( ~ ( P2 @ N2 )
% 2.65/1.60 => ? [M3: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ M3 @ N2 )
% 2.65/1.60 & ~ ( P2 @ M3 ) ) ) )
% 2.65/1.60 => ( P2 @ N ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_102_bot__nat__0_Oextremum__strict,axiom,
% 2.65/1.60 ! [A2: nat] :
% 2.65/1.60 ~ ( ord_less @ nat @ A2 @ ( zero_zero @ nat ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_103_infinite__descent0__measure,axiom,
% 2.65/1.60 ! [A: $tType,V2: A > nat,P2: A > $o,X: A] :
% 2.65/1.60 ( ! [X5: A] :
% 2.65/1.60 ( ( ( V2 @ X5 )
% 2.65/1.60 = ( zero_zero @ nat ) )
% 2.65/1.60 => ( P2 @ X5 ) )
% 2.65/1.60 => ( ! [X5: A] :
% 2.65/1.60 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V2 @ X5 ) )
% 2.65/1.60 => ( ~ ( P2 @ X5 )
% 2.65/1.60 => ? [Y4: A] :
% 2.65/1.60 ( ( ord_less @ nat @ ( V2 @ Y4 ) @ ( V2 @ X5 ) )
% 2.65/1.60 & ~ ( P2 @ Y4 ) ) ) )
% 2.65/1.60 => ( P2 @ X ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_104_less__Suc__eq__0__disj,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 2.65/1.60 = ( ( M
% 2.65/1.60 = ( zero_zero @ nat ) )
% 2.65/1.60 | ? [J3: nat] :
% 2.65/1.60 ( ( M
% 2.65/1.60 = ( suc @ J3 ) )
% 2.65/1.60 & ( ord_less @ nat @ J3 @ N ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_105_gr0__implies__Suc,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.65/1.60 => ? [M4: nat] :
% 2.65/1.60 ( N
% 2.65/1.60 = ( suc @ M4 ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_106_All__less__Suc2,axiom,
% 2.65/1.60 ! [N: nat,P2: nat > $o] :
% 2.65/1.60 ( ( ! [I4: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I4 @ ( suc @ N ) )
% 2.65/1.60 => ( P2 @ I4 ) ) )
% 2.65/1.60 = ( ( P2 @ ( zero_zero @ nat ) )
% 2.65/1.60 & ! [I4: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I4 @ N )
% 2.65/1.60 => ( P2 @ ( suc @ I4 ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_107_gr0__conv__Suc,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.65/1.60 = ( ? [M5: nat] :
% 2.65/1.60 ( N
% 2.65/1.60 = ( suc @ M5 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_108_Ex__less__Suc2,axiom,
% 2.65/1.60 ! [N: nat,P2: nat > $o] :
% 2.65/1.60 ( ( ? [I4: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I4 @ ( suc @ N ) )
% 2.65/1.60 & ( P2 @ I4 ) ) )
% 2.65/1.60 = ( ( P2 @ ( zero_zero @ nat ) )
% 2.65/1.60 | ? [I4: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I4 @ N )
% 2.65/1.60 & ( P2 @ ( suc @ I4 ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_109_list_Osize_I3_J,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( size_size @ ( list @ A ) @ ( nil @ A ) )
% 2.65/1.60 = ( zero_zero @ nat ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_110_MinImplFirstOcc,axiom,
% 2.65/1.60 ! [Msg: message @ p @ v] :
% 2.65/1.60 ( ( minimalEnabled @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ Msg )
% 2.65/1.60 => ( member @ ( message @ p @ v ) @ Msg @ ( firstOccSet @ index ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_111_Case2ImplThesis,axiom,
% 2.65/1.60 ( ? [N0: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ n0 @ N0 )
% 2.65/1.60 & ( ord_less @ nat @ N0 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
% 2.65/1.60 & ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ N0 )
% 2.65/1.60 = msg ) )
% 2.65/1.60 => ? [N6: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ n @ N6 )
% 2.65/1.60 & ? [N02: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ n0 @ N02 )
% 2.65/1.60 & ( ord_less @ nat @ N02 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N6 ) ) )
% 2.65/1.60 & ( msg
% 2.65/1.60 = ( nth @ ( message @ p @ v ) @ ( ft @ N6 ) @ N02 ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_112_MessageStaysOrConsumed,axiom,
% 2.65/1.60 ! [N1: nat,N22: nat,N: nat,Msg2: message @ p @ v] :
% 2.65/1.60 ( ( ( ord_less_eq @ nat @ N1 @ N22 )
% 2.65/1.60 & ( ord_less @ nat @ N22 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ N ) ) )
% 2.65/1.60 & ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N ) @ N1 ) @ Msg2 ) )
% 2.65/1.60 => ( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N ) @ N22 ) @ Msg2 )
% 2.65/1.60 | ? [N02: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ N1 @ N02 )
% 2.65/1.60 & ( ord_less @ nat @ N02 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N ) ) )
% 2.65/1.60 & ( ( nth @ ( message @ p @ v ) @ ( ft @ N ) @ N02 )
% 2.65/1.60 = Msg2 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_113_NotConsumedIntermediate,axiom,
% 2.65/1.60 ! [I: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 2.65/1.60 => ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ I )
% 2.65/1.60 => ( ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I )
% 2.65/1.60 != msg ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_114__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ift_A_ISuc_Aindex_J_J_O_Alength_A_Ift_Aindex_J_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,
% 2.65/1.60 ~ ? [I: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 2.65/1.60 & ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ I )
% 2.65/1.60 & ( msg
% 2.65/1.60 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_115_Nitpick_Osize__list__simp_I2_J,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( size_size @ ( list @ A ) )
% 2.65/1.60 = ( ^ [Xs3: list @ A] :
% 2.65/1.60 ( if @ nat
% 2.65/1.60 @ ( Xs3
% 2.65/1.60 = ( nil @ A ) )
% 2.65/1.60 @ ( zero_zero @ nat )
% 2.65/1.60 @ ( suc @ ( size_size @ ( list @ A ) @ ( tl @ A @ Xs3 ) ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_116_not__gr__zero,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( canoni770627133id_add @ A )
% 2.65/1.60 => ! [N: A] :
% 2.65/1.60 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 2.65/1.60 = ( N
% 2.65/1.60 = ( zero_zero @ A ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_117_le__zero__eq,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( canoni770627133id_add @ A )
% 2.65/1.60 => ! [N: A] :
% 2.65/1.60 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 2.65/1.60 = ( N
% 2.65/1.60 = ( zero_zero @ A ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_118_bot__nat__0_Oextremum,axiom,
% 2.65/1.60 ! [A2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A2 ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_119_le0,axiom,
% 2.65/1.60 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_120_Suc__le__mono,axiom,
% 2.65/1.60 ! [N: nat,M: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ ( suc @ N ) @ ( suc @ M ) )
% 2.65/1.60 = ( ord_less_eq @ nat @ N @ M ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_121_EnabledInSuc,axiom,
% 2.65/1.60 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) ) @ msg ).
% 2.65/1.60
% 2.65/1.60 thf(fact_122_MinImplAllBigger,axiom,
% 2.65/1.60 ! [Msg: message @ p @ v] :
% 2.65/1.60 ( ( minimalEnabled @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ Msg )
% 2.65/1.60 => ? [OccM: nat] :
% 2.65/1.60 ( ( firstOccurrence @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ Msg @ OccM )
% 2.65/1.60 & ! [Msg3: message @ p @ v,OccM2: nat] :
% 2.65/1.60 ( ( firstOccurrence @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ Msg3 @ OccM2 )
% 2.65/1.60 => ( ord_less_eq @ nat @ OccM @ OccM2 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_123_last__remdups__adj,axiom,
% 2.65/1.60 ! [A: $tType,Xs: list @ A] :
% 2.65/1.60 ( ( last @ A @ ( remdups_adj @ A @ Xs ) )
% 2.65/1.60 = ( last @ A @ Xs ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_124_EnabledOrConsumedAtLast,axiom,
% 2.65/1.60 ( ( enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg )
% 2.65/1.60 | ? [N02: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ n0 @ N02 )
% 2.65/1.60 & ( ord_less @ nat @ N02 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
% 2.65/1.60 & ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ N02 )
% 2.65/1.60 = msg ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_125_zero__le,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( canoni770627133id_add @ A )
% 2.65/1.60 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_126_lift__Suc__antimono__le,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( order @ A )
% 2.65/1.60 => ! [F: nat > A,N: nat,N3: nat] :
% 2.65/1.60 ( ! [N2: nat] : ( ord_less_eq @ A @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 2.65/1.60 => ( ( ord_less_eq @ nat @ N @ N3 )
% 2.65/1.60 => ( ord_less_eq @ A @ ( F @ N3 ) @ ( F @ N ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_127_lift__Suc__mono__le,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( order @ A )
% 2.65/1.60 => ! [F: nat > A,N: nat,N3: nat] :
% 2.65/1.60 ( ! [N2: nat] : ( ord_less_eq @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 2.65/1.60 => ( ( ord_less_eq @ nat @ N @ N3 )
% 2.65/1.60 => ( ord_less_eq @ A @ ( F @ N ) @ ( F @ N3 ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_128_Nat_Oex__has__greatest__nat,axiom,
% 2.65/1.60 ! [P2: nat > $o,K2: nat,B2: nat] :
% 2.65/1.60 ( ( P2 @ K2 )
% 2.65/1.60 => ( ! [Y5: nat] :
% 2.65/1.60 ( ( P2 @ Y5 )
% 2.65/1.60 => ( ord_less_eq @ nat @ Y5 @ B2 ) )
% 2.65/1.60 => ? [X5: nat] :
% 2.65/1.60 ( ( P2 @ X5 )
% 2.65/1.60 & ! [Y4: nat] :
% 2.65/1.60 ( ( P2 @ Y4 )
% 2.65/1.60 => ( ord_less_eq @ nat @ Y4 @ X5 ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_129_nat__le__linear,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ M @ N )
% 2.65/1.60 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_130_le__antisym,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ M @ N )
% 2.65/1.60 => ( ( ord_less_eq @ nat @ N @ M )
% 2.65/1.60 => ( M = N ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_131_eq__imp__le,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( M = N )
% 2.65/1.60 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_132_le__trans,axiom,
% 2.65/1.60 ! [I2: nat,J: nat,K2: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ I2 @ J )
% 2.65/1.60 => ( ( ord_less_eq @ nat @ J @ K2 )
% 2.65/1.60 => ( ord_less_eq @ nat @ I2 @ K2 ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_133_le__refl,axiom,
% 2.65/1.60 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_134_bot__nat__0_Oextremum__uniqueI,axiom,
% 2.65/1.60 ! [A2: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 2.65/1.60 => ( A2
% 2.65/1.60 = ( zero_zero @ nat ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_135_bot__nat__0_Oextremum__unique,axiom,
% 2.65/1.60 ! [A2: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ A2 @ ( zero_zero @ nat ) )
% 2.65/1.60 = ( A2
% 2.65/1.60 = ( zero_zero @ nat ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_136_le__0__eq,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ N @ ( zero_zero @ nat ) )
% 2.65/1.60 = ( N
% 2.65/1.60 = ( zero_zero @ nat ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_137_less__eq__nat_Osimps_I1_J,axiom,
% 2.65/1.60 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_138_Suc__leD,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 2.65/1.60 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_139_le__SucE,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ M @ ( suc @ N ) )
% 2.65/1.60 => ( ~ ( ord_less_eq @ nat @ M @ N )
% 2.65/1.60 => ( M
% 2.65/1.60 = ( suc @ N ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_140_le__SucI,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ M @ N )
% 2.65/1.60 => ( ord_less_eq @ nat @ M @ ( suc @ N ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_141_Suc__le__D,axiom,
% 2.65/1.60 ! [N: nat,M6: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ ( suc @ N ) @ M6 )
% 2.65/1.60 => ? [M4: nat] :
% 2.65/1.60 ( M6
% 2.65/1.60 = ( suc @ M4 ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_142_le__Suc__eq,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ M @ ( suc @ N ) )
% 2.65/1.60 = ( ( ord_less_eq @ nat @ M @ N )
% 2.65/1.60 | ( M
% 2.65/1.60 = ( suc @ N ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_143_Suc__n__not__le__n,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ~ ( ord_less_eq @ nat @ ( suc @ N ) @ N ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_144_not__less__eq__eq,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ~ ( ord_less_eq @ nat @ M @ N ) )
% 2.65/1.60 = ( ord_less_eq @ nat @ ( suc @ N ) @ M ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_145_full__nat__induct,axiom,
% 2.65/1.60 ! [P2: nat > $o,N: nat] :
% 2.65/1.60 ( ! [N2: nat] :
% 2.65/1.60 ( ! [M3: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ ( suc @ M3 ) @ N2 )
% 2.65/1.60 => ( P2 @ M3 ) )
% 2.65/1.60 => ( P2 @ N2 ) )
% 2.65/1.60 => ( P2 @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_146_nat__induct__at__least,axiom,
% 2.65/1.60 ! [M: nat,N: nat,P2: nat > $o] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ M @ N )
% 2.65/1.60 => ( ( P2 @ M )
% 2.65/1.60 => ( ! [N2: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ M @ N2 )
% 2.65/1.60 => ( ( P2 @ N2 )
% 2.65/1.60 => ( P2 @ ( suc @ N2 ) ) ) )
% 2.65/1.60 => ( P2 @ N ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_147_transitive__stepwise__le,axiom,
% 2.65/1.60 ! [M: nat,N: nat,R: nat > nat > $o] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ M @ N )
% 2.65/1.60 => ( ! [X5: nat] : ( R @ X5 @ X5 )
% 2.65/1.60 => ( ! [X5: nat,Y5: nat,Z3: nat] :
% 2.65/1.60 ( ( R @ X5 @ Y5 )
% 2.65/1.60 => ( ( R @ Y5 @ Z3 )
% 2.65/1.60 => ( R @ X5 @ Z3 ) ) )
% 2.65/1.60 => ( ! [N2: nat] : ( R @ N2 @ ( suc @ N2 ) )
% 2.65/1.60 => ( R @ M @ N ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_148_less__mono__imp__le__mono,axiom,
% 2.65/1.60 ! [F: nat > nat,I2: nat,J: nat] :
% 2.65/1.60 ( ! [I3: nat,J2: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I3 @ J2 )
% 2.65/1.60 => ( ord_less @ nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 2.65/1.60 => ( ( ord_less_eq @ nat @ I2 @ J )
% 2.65/1.60 => ( ord_less_eq @ nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_149_le__neq__implies__less,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ M @ N )
% 2.65/1.60 => ( ( M != N )
% 2.65/1.60 => ( ord_less @ nat @ M @ N ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_150_less__or__eq__imp__le,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ( ord_less @ nat @ M @ N )
% 2.65/1.60 | ( M = N ) )
% 2.65/1.60 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_151_le__eq__less__or__eq,axiom,
% 2.65/1.60 ( ( ord_less_eq @ nat )
% 2.65/1.60 = ( ^ [M5: nat,N4: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ M5 @ N4 )
% 2.65/1.60 | ( M5 = N4 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_152_less__imp__le__nat,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ M @ N )
% 2.65/1.60 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_153_nat__less__le,axiom,
% 2.65/1.60 ( ( ord_less @ nat )
% 2.65/1.60 = ( ^ [M5: nat,N4: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ M5 @ N4 )
% 2.65/1.60 & ( M5 != N4 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_154_ex__least__nat__le,axiom,
% 2.65/1.60 ! [P2: nat > $o,N: nat] :
% 2.65/1.60 ( ( P2 @ N )
% 2.65/1.60 => ( ~ ( P2 @ ( zero_zero @ nat ) )
% 2.65/1.60 => ? [K: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ K @ N )
% 2.65/1.60 & ! [I: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I @ K )
% 2.65/1.60 => ~ ( P2 @ I ) )
% 2.65/1.60 & ( P2 @ K ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_155_Suc__leI,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ M @ N )
% 2.65/1.60 => ( ord_less_eq @ nat @ ( suc @ M ) @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_156_Suc__le__eq,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 2.65/1.60 = ( ord_less @ nat @ M @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_157_dec__induct,axiom,
% 2.65/1.60 ! [I2: nat,J: nat,P2: nat > $o] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ I2 @ J )
% 2.65/1.60 => ( ( P2 @ I2 )
% 2.65/1.60 => ( ! [N2: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ I2 @ N2 )
% 2.65/1.60 => ( ( ord_less @ nat @ N2 @ J )
% 2.65/1.60 => ( ( P2 @ N2 )
% 2.65/1.60 => ( P2 @ ( suc @ N2 ) ) ) ) )
% 2.65/1.60 => ( P2 @ J ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_158_inc__induct,axiom,
% 2.65/1.60 ! [I2: nat,J: nat,P2: nat > $o] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ I2 @ J )
% 2.65/1.60 => ( ( P2 @ J )
% 2.65/1.60 => ( ! [N2: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ I2 @ N2 )
% 2.65/1.60 => ( ( ord_less @ nat @ N2 @ J )
% 2.65/1.60 => ( ( P2 @ ( suc @ N2 ) )
% 2.65/1.60 => ( P2 @ N2 ) ) ) )
% 2.65/1.60 => ( P2 @ I2 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_159_Suc__le__lessD,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 2.65/1.60 => ( ord_less @ nat @ M @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_160_le__less__Suc__eq,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ M @ N )
% 2.65/1.60 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 2.65/1.60 = ( N = M ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_161_less__Suc__eq__le,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 2.65/1.60 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_162_less__eq__Suc__le,axiom,
% 2.65/1.60 ( ( ord_less @ nat )
% 2.65/1.60 = ( ^ [N4: nat] : ( ord_less_eq @ nat @ ( suc @ N4 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_163_le__imp__less__Suc,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ M @ N )
% 2.65/1.60 => ( ord_less @ nat @ M @ ( suc @ N ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_164_remdups__adj__length,axiom,
% 2.65/1.60 ! [A: $tType,Xs: list @ A] : ( ord_less_eq @ nat @ ( size_size @ ( list @ A ) @ ( remdups_adj @ A @ Xs ) ) @ ( size_size @ ( list @ A ) @ Xs ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_165_last__tl,axiom,
% 2.65/1.60 ! [A: $tType,Xs: list @ A] :
% 2.65/1.60 ( ( ( Xs
% 2.65/1.60 = ( nil @ A ) )
% 2.65/1.60 | ( ( tl @ A @ Xs )
% 2.65/1.60 != ( nil @ A ) ) )
% 2.65/1.60 => ( ( last @ A @ ( tl @ A @ Xs ) )
% 2.65/1.60 = ( last @ A @ Xs ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_166_ex__least__nat__less,axiom,
% 2.65/1.60 ! [P2: nat > $o,N: nat] :
% 2.65/1.60 ( ( P2 @ N )
% 2.65/1.60 => ( ~ ( P2 @ ( zero_zero @ nat ) )
% 2.65/1.60 => ? [K: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ K @ N )
% 2.65/1.60 & ! [I: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ I @ K )
% 2.65/1.60 => ~ ( P2 @ I ) )
% 2.65/1.60 & ( P2 @ ( suc @ K ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_167_zero__reorient,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( zero @ A )
% 2.65/1.60 => ! [X: A] :
% 2.65/1.60 ( ( ( zero_zero @ A )
% 2.65/1.60 = X )
% 2.65/1.60 = ( X
% 2.65/1.60 = ( zero_zero @ A ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_168_remdups__adj__length__ge1,axiom,
% 2.65/1.60 ! [A: $tType,Xs: list @ A] :
% 2.65/1.60 ( ( Xs
% 2.65/1.60 != ( nil @ A ) )
% 2.65/1.60 => ( ord_less_eq @ nat @ ( suc @ ( zero_zero @ nat ) ) @ ( size_size @ ( list @ A ) @ ( remdups_adj @ A @ Xs ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_169_zero__less__iff__neq__zero,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( canoni770627133id_add @ A )
% 2.65/1.60 => ! [N: A] :
% 2.65/1.60 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 2.65/1.60 = ( N
% 2.65/1.60 != ( zero_zero @ A ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_170_gr__implies__not__zero,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( canoni770627133id_add @ A )
% 2.65/1.60 => ! [M: A,N: A] :
% 2.65/1.60 ( ( ord_less @ A @ M @ N )
% 2.65/1.60 => ( N
% 2.65/1.60 != ( zero_zero @ A ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_171_not__less__zero,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( canoni770627133id_add @ A )
% 2.65/1.60 => ! [N: A] :
% 2.65/1.60 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_172_gr__zeroI,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( canoni770627133id_add @ A )
% 2.65/1.60 => ! [N: A] :
% 2.65/1.60 ( ( N
% 2.65/1.60 != ( zero_zero @ A ) )
% 2.65/1.60 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_173_LastOfIndex,axiom,
% 2.65/1.60 ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( suc @ ( zero_zero @ nat ) ) ) )
% 2.65/1.60 = ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_174__092_060open_062_092_060And_062n0_Amsg_O_A_092_060forall_062n_O_Aexecution_OfirstOccurrence_A_Ife_An_J_A_Ift_An_J_Amsg_An0_A_092_060longrightarrow_062_Amsg_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062,axiom,
% 2.65/1.60 ! [Msg2: message @ p @ v,N03: nat,N7: nat] :
% 2.65/1.60 ( ( firstOccurrence @ p @ v @ s @ ( fe @ N7 ) @ ( ft @ N7 ) @ Msg2 @ N03 )
% 2.65/1.60 => ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N7 ) ) @ Msg2 ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_175__092_060open_062_092_060forall_062n_O_A_092_060forall_062msg_H_092_060in_062firstOccSet_An_O_Amsg_H_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062,axiom,
% 2.65/1.60 ! [N7: nat,X6: message @ p @ v] :
% 2.65/1.60 ( ( member @ ( message @ p @ v ) @ X6 @ ( firstOccSet @ N7 ) )
% 2.65/1.60 => ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N7 ) ) @ X6 ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_176_PrefixSameOnLow,axiom,
% 2.65/1.60 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 2.65/1.60 ( ( prefixList @ A @ L1 @ L2 )
% 2.65/1.60 => ! [Index: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ Index @ ( size_size @ ( list @ A ) @ L1 ) )
% 2.65/1.60 => ( ( nth @ A @ L1 @ Index )
% 2.65/1.60 = ( nth @ A @ L2 @ Index ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_177_IPrefixList,axiom,
% 2.65/1.60 ! [I: nat] : ( prefixList @ ( message @ p @ v ) @ ( ft @ I ) @ ( ft @ ( suc @ I ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_178_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( cancel1352612707id_add @ A )
% 2.65/1.60 => ! [A2: A] :
% 2.65/1.60 ( ( minus_minus @ A @ A2 @ A2 )
% 2.65/1.60 = ( zero_zero @ A ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_179_diff__zero,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( cancel1352612707id_add @ A )
% 2.65/1.60 => ! [A2: A] :
% 2.65/1.60 ( ( minus_minus @ A @ A2 @ ( zero_zero @ A ) )
% 2.65/1.60 = A2 ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_180_zero__diff,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( comm_monoid_diff @ A )
% 2.65/1.60 => ! [A2: A] :
% 2.65/1.60 ( ( minus_minus @ A @ ( zero_zero @ A ) @ A2 )
% 2.65/1.60 = ( zero_zero @ A ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_181_diff__0__right,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( group_add @ A )
% 2.65/1.60 => ! [A2: A] :
% 2.65/1.60 ( ( minus_minus @ A @ A2 @ ( zero_zero @ A ) )
% 2.65/1.60 = A2 ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_182_diff__self,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( group_add @ A )
% 2.65/1.60 => ! [A2: A] :
% 2.65/1.60 ( ( minus_minus @ A @ A2 @ A2 )
% 2.65/1.60 = ( zero_zero @ A ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_183_diff__0__eq__0,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ( ( minus_minus @ nat @ ( zero_zero @ nat ) @ N )
% 2.65/1.60 = ( zero_zero @ nat ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_184_diff__self__eq__0,axiom,
% 2.65/1.60 ! [M: nat] :
% 2.65/1.60 ( ( minus_minus @ nat @ M @ M )
% 2.65/1.60 = ( zero_zero @ nat ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_185_Suc__diff__diff,axiom,
% 2.65/1.60 ! [M: nat,N: nat,K2: nat] :
% 2.65/1.60 ( ( minus_minus @ nat @ ( minus_minus @ nat @ ( suc @ M ) @ N ) @ ( suc @ K2 ) )
% 2.65/1.60 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ N ) @ K2 ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_186_diff__Suc__Suc,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( minus_minus @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 2.65/1.60 = ( minus_minus @ nat @ M @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_187_diff__diff__cancel,axiom,
% 2.65/1.60 ! [I2: nat,N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ I2 @ N )
% 2.65/1.60 => ( ( minus_minus @ nat @ N @ ( minus_minus @ nat @ N @ I2 ) )
% 2.65/1.60 = I2 ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_188_diff__ge__0__iff__ge,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( ordered_ab_group_add @ A )
% 2.65/1.60 => ! [A2: A,B2: A] :
% 2.65/1.60 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A2 @ B2 ) )
% 2.65/1.60 = ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_189_diff__gt__0__iff__gt,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( ordered_ab_group_add @ A )
% 2.65/1.60 => ! [A2: A,B2: A] :
% 2.65/1.60 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A2 @ B2 ) )
% 2.65/1.60 = ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_190_zero__less__diff,axiom,
% 2.65/1.60 ! [N: nat,M: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( minus_minus @ nat @ N @ M ) )
% 2.65/1.60 = ( ord_less @ nat @ M @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_191_diff__is__0__eq_H,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ M @ N )
% 2.65/1.60 => ( ( minus_minus @ nat @ M @ N )
% 2.65/1.60 = ( zero_zero @ nat ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_192_diff__is__0__eq,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ( minus_minus @ nat @ M @ N )
% 2.65/1.60 = ( zero_zero @ nat ) )
% 2.65/1.60 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_193_Suc__pred,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.65/1.60 => ( ( suc @ ( minus_minus @ nat @ N @ ( suc @ ( zero_zero @ nat ) ) ) )
% 2.65/1.60 = N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_194_eq__iff__diff__eq__0,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( group_add @ A )
% 2.65/1.60 => ( ( ^ [Y3: A,Z2: A] : ( Y3 = Z2 ) )
% 2.65/1.60 = ( ^ [A8: A,B3: A] :
% 2.65/1.60 ( ( minus_minus @ A @ A8 @ B3 )
% 2.65/1.60 = ( zero_zero @ A ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_195_diff__strict__mono,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( ordered_ab_group_add @ A )
% 2.65/1.60 => ! [A2: A,B2: A,D: A,C: A] :
% 2.65/1.60 ( ( ord_less @ A @ A2 @ B2 )
% 2.65/1.60 => ( ( ord_less @ A @ D @ C )
% 2.65/1.60 => ( ord_less @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B2 @ D ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_196_diff__eq__diff__less,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( ordered_ab_group_add @ A )
% 2.65/1.60 => ! [A2: A,B2: A,C: A,D: A] :
% 2.65/1.60 ( ( ( minus_minus @ A @ A2 @ B2 )
% 2.65/1.60 = ( minus_minus @ A @ C @ D ) )
% 2.65/1.60 => ( ( ord_less @ A @ A2 @ B2 )
% 2.65/1.60 = ( ord_less @ A @ C @ D ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_197_diff__strict__left__mono,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( ordered_ab_group_add @ A )
% 2.65/1.60 => ! [B2: A,A2: A,C: A] :
% 2.65/1.60 ( ( ord_less @ A @ B2 @ A2 )
% 2.65/1.60 => ( ord_less @ A @ ( minus_minus @ A @ C @ A2 ) @ ( minus_minus @ A @ C @ B2 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_198_diff__strict__right__mono,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( ordered_ab_group_add @ A )
% 2.65/1.60 => ! [A2: A,B2: A,C: A] :
% 2.65/1.60 ( ( ord_less @ A @ A2 @ B2 )
% 2.65/1.60 => ( ord_less @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B2 @ C ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_199_diff__eq__diff__eq,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( group_add @ A )
% 2.65/1.60 => ! [A2: A,B2: A,C: A,D: A] :
% 2.65/1.60 ( ( ( minus_minus @ A @ A2 @ B2 )
% 2.65/1.60 = ( minus_minus @ A @ C @ D ) )
% 2.65/1.60 => ( ( A2 = B2 )
% 2.65/1.60 = ( C = D ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_200_diff__mono,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( ordered_ab_group_add @ A )
% 2.65/1.60 => ! [A2: A,B2: A,D: A,C: A] :
% 2.65/1.60 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.65/1.60 => ( ( ord_less_eq @ A @ D @ C )
% 2.65/1.60 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B2 @ D ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_201_diff__left__mono,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( ordered_ab_group_add @ A )
% 2.65/1.60 => ! [B2: A,A2: A,C: A] :
% 2.65/1.60 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.65/1.60 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A2 ) @ ( minus_minus @ A @ C @ B2 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_202_diff__right__mono,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( ordered_ab_group_add @ A )
% 2.65/1.60 => ! [A2: A,B2: A,C: A] :
% 2.65/1.60 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.65/1.60 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B2 @ C ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_203_diff__eq__diff__less__eq,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( ordered_ab_group_add @ A )
% 2.65/1.60 => ! [A2: A,B2: A,C: A,D: A] :
% 2.65/1.60 ( ( ( minus_minus @ A @ A2 @ B2 )
% 2.65/1.60 = ( minus_minus @ A @ C @ D ) )
% 2.65/1.60 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.65/1.60 = ( ord_less_eq @ A @ C @ D ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_204_diff__right__commute,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( cancel146912293up_add @ A )
% 2.65/1.60 => ! [A2: A,C: A,B2: A] :
% 2.65/1.60 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C ) @ B2 )
% 2.65/1.60 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B2 ) @ C ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_205_diff__le__mono2,axiom,
% 2.65/1.60 ! [M: nat,N: nat,L: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ M @ N )
% 2.65/1.60 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ L @ N ) @ ( minus_minus @ nat @ L @ M ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_206_le__diff__iff_H,axiom,
% 2.65/1.60 ! [A2: nat,C: nat,B2: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ A2 @ C )
% 2.65/1.60 => ( ( ord_less_eq @ nat @ B2 @ C )
% 2.65/1.60 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ A2 ) @ ( minus_minus @ nat @ C @ B2 ) )
% 2.65/1.60 = ( ord_less_eq @ nat @ B2 @ A2 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_207_diff__le__self,axiom,
% 2.65/1.60 ! [M: nat,N: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ N ) @ M ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_208_diff__le__mono,axiom,
% 2.65/1.60 ! [M: nat,N: nat,L: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ M @ N )
% 2.65/1.60 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ L ) @ ( minus_minus @ nat @ N @ L ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_209_Nat_Odiff__diff__eq,axiom,
% 2.65/1.60 ! [K2: nat,M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ K2 @ M )
% 2.65/1.60 => ( ( ord_less_eq @ nat @ K2 @ N )
% 2.65/1.60 => ( ( minus_minus @ nat @ ( minus_minus @ nat @ M @ K2 ) @ ( minus_minus @ nat @ N @ K2 ) )
% 2.65/1.60 = ( minus_minus @ nat @ M @ N ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_210_le__diff__iff,axiom,
% 2.65/1.60 ! [K2: nat,M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ K2 @ M )
% 2.65/1.60 => ( ( ord_less_eq @ nat @ K2 @ N )
% 2.65/1.60 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ K2 ) @ ( minus_minus @ nat @ N @ K2 ) )
% 2.65/1.60 = ( ord_less_eq @ nat @ M @ N ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_211_eq__diff__iff,axiom,
% 2.65/1.60 ! [K2: nat,M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ K2 @ M )
% 2.65/1.60 => ( ( ord_less_eq @ nat @ K2 @ N )
% 2.65/1.60 => ( ( ( minus_minus @ nat @ M @ K2 )
% 2.65/1.60 = ( minus_minus @ nat @ N @ K2 ) )
% 2.65/1.60 = ( M = N ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_212_minus__nat_Odiff__0,axiom,
% 2.65/1.60 ! [M: nat] :
% 2.65/1.60 ( ( minus_minus @ nat @ M @ ( zero_zero @ nat ) )
% 2.65/1.60 = M ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_213_diffs0__imp__equal,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( ( minus_minus @ nat @ M @ N )
% 2.65/1.60 = ( zero_zero @ nat ) )
% 2.65/1.60 => ( ( ( minus_minus @ nat @ N @ M )
% 2.65/1.60 = ( zero_zero @ nat ) )
% 2.65/1.60 => ( M = N ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_214_zero__induct__lemma,axiom,
% 2.65/1.60 ! [P2: nat > $o,K2: nat,I2: nat] :
% 2.65/1.60 ( ( P2 @ K2 )
% 2.65/1.60 => ( ! [N2: nat] :
% 2.65/1.60 ( ( P2 @ ( suc @ N2 ) )
% 2.65/1.60 => ( P2 @ N2 ) )
% 2.65/1.60 => ( P2 @ ( minus_minus @ nat @ K2 @ I2 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_215_less__imp__diff__less,axiom,
% 2.65/1.60 ! [J: nat,K2: nat,N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ J @ K2 )
% 2.65/1.60 => ( ord_less @ nat @ ( minus_minus @ nat @ J @ N ) @ K2 ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_216_diff__less__mono2,axiom,
% 2.65/1.60 ! [M: nat,N: nat,L: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ M @ N )
% 2.65/1.60 => ( ( ord_less @ nat @ M @ L )
% 2.65/1.60 => ( ord_less @ nat @ ( minus_minus @ nat @ L @ N ) @ ( minus_minus @ nat @ L @ M ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_217_diff__commute,axiom,
% 2.65/1.60 ! [I2: nat,J: nat,K2: nat] :
% 2.65/1.60 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I2 @ J ) @ K2 )
% 2.65/1.60 = ( minus_minus @ nat @ ( minus_minus @ nat @ I2 @ K2 ) @ J ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_218_le__iff__diff__le__0,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( ordered_ab_group_add @ A )
% 2.65/1.60 => ( ( ord_less_eq @ A )
% 2.65/1.60 = ( ^ [A8: A,B3: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ A8 @ B3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_219_less__iff__diff__less__0,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( ordered_ab_group_add @ A )
% 2.65/1.60 => ( ( ord_less @ A )
% 2.65/1.60 = ( ^ [A8: A,B3: A] : ( ord_less @ A @ ( minus_minus @ A @ A8 @ B3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_220_diff__less,axiom,
% 2.65/1.60 ! [N: nat,M: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.65/1.60 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 2.65/1.60 => ( ord_less @ nat @ ( minus_minus @ nat @ M @ N ) @ M ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_221_diff__less__Suc,axiom,
% 2.65/1.60 ! [M: nat,N: nat] : ( ord_less @ nat @ ( minus_minus @ nat @ M @ N ) @ ( suc @ M ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_222_Suc__diff__Suc,axiom,
% 2.65/1.60 ! [N: nat,M: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ N @ M )
% 2.65/1.60 => ( ( suc @ ( minus_minus @ nat @ M @ ( suc @ N ) ) )
% 2.65/1.60 = ( minus_minus @ nat @ M @ N ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_223_Suc__diff__le,axiom,
% 2.65/1.60 ! [N: nat,M: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ N @ M )
% 2.65/1.60 => ( ( minus_minus @ nat @ ( suc @ M ) @ N )
% 2.65/1.60 = ( suc @ ( minus_minus @ nat @ M @ N ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_224_less__diff__iff,axiom,
% 2.65/1.60 ! [K2: nat,M: nat,N: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ K2 @ M )
% 2.65/1.60 => ( ( ord_less_eq @ nat @ K2 @ N )
% 2.65/1.60 => ( ( ord_less @ nat @ ( minus_minus @ nat @ M @ K2 ) @ ( minus_minus @ nat @ N @ K2 ) )
% 2.65/1.60 = ( ord_less @ nat @ M @ N ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_225_diff__less__mono,axiom,
% 2.65/1.60 ! [A2: nat,B2: nat,C: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ A2 @ B2 )
% 2.65/1.60 => ( ( ord_less_eq @ nat @ C @ A2 )
% 2.65/1.60 => ( ord_less @ nat @ ( minus_minus @ nat @ A2 @ C ) @ ( minus_minus @ nat @ B2 @ C ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_226_diff__Suc__less,axiom,
% 2.65/1.60 ! [N: nat,I2: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.65/1.60 => ( ord_less @ nat @ ( minus_minus @ nat @ N @ ( suc @ I2 ) ) @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_227_MinPredicate,axiom,
% 2.65/1.60 ! [P2: nat > $o] :
% 2.65/1.60 ( ? [X_1: nat] : ( P2 @ X_1 )
% 2.65/1.60 => ? [N04: nat] :
% 2.65/1.60 ( ( P2 @ N04 )
% 2.65/1.60 & ! [N5: nat] :
% 2.65/1.60 ( ( P2 @ N5 )
% 2.65/1.60 => ( ord_less_eq @ nat @ N04 @ N5 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_228_PrefixListTransitive,axiom,
% 2.65/1.60 ! [A: $tType,L1: list @ A,L2: list @ A,L3: list @ A] :
% 2.65/1.60 ( ( prefixList @ A @ L1 @ L2 )
% 2.65/1.60 => ( ( prefixList @ A @ L2 @ L3 )
% 2.65/1.60 => ( prefixList @ A @ L1 @ L3 ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_229_KeepProperty,axiom,
% 2.65/1.60 ! [Low: nat,P2: nat > $o,Q: nat > $o] :
% 2.65/1.60 ( ! [I3: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ Low @ I3 )
% 2.65/1.60 => ( ( P2 @ I3 )
% 2.65/1.60 => ( ( P2 @ ( suc @ I3 ) )
% 2.65/1.60 & ( Q @ I3 ) ) ) )
% 2.65/1.60 => ( ( P2 @ Low )
% 2.65/1.60 => ! [I: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ Low @ I )
% 2.65/1.60 => ( Q @ I ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_230_NatPredicateTippingPoint,axiom,
% 2.65/1.60 ! [N22: nat,Pr: nat > $o] :
% 2.65/1.60 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N22 )
% 2.65/1.60 => ( ( Pr @ ( zero_zero @ nat ) )
% 2.65/1.60 => ( ~ ( Pr @ N22 )
% 2.65/1.60 => ? [N2: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ N2 @ N22 )
% 2.65/1.60 & ( Pr @ N2 )
% 2.65/1.60 & ~ ( Pr @ ( suc @ N2 ) ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_231_PrefixListMonotonicity,axiom,
% 2.65/1.60 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 2.65/1.60 ( ( prefixList @ A @ L1 @ L2 )
% 2.65/1.60 => ( ord_less @ nat @ ( size_size @ ( list @ A ) @ L1 ) @ ( size_size @ ( list @ A ) @ L2 ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_232_EnabledOrConsumed,axiom,
% 2.65/1.60 ( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ) @ ( one_one @ nat ) ) ) @ msg )
% 2.65/1.60 | ? [N02: nat] :
% 2.65/1.60 ( ( ord_less_eq @ nat @ n0 @ N02 )
% 2.65/1.60 & ( ord_less @ nat @ N02 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
% 2.65/1.60 & ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ N02 )
% 2.65/1.60 = msg ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_233__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,
% 2.65/1.60 ~ ? [I: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) )
% 2.65/1.60 & ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ I )
% 2.65/1.60 & ( msg
% 2.65/1.60 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_234_EnabledIntermediate,axiom,
% 2.65/1.60 ! [I: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) )
% 2.65/1.60 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ I )
% 2.65/1.60 => ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ I ) @ msg ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_235__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,
% 2.65/1.60 ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_236_less__one,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ N @ ( one_one @ nat ) )
% 2.65/1.60 = ( N
% 2.65/1.60 = ( zero_zero @ nat ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_237__092_060open_062enabled_A_Ife_A_ISuc_Aindex_J_A_B_A_Ilength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_J_J_Amsg_092_060close_062,axiom,
% 2.65/1.60 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) ) @ msg ).
% 2.65/1.60
% 2.65/1.60 thf(fact_238_diff__Suc__1,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ( ( minus_minus @ nat @ ( suc @ N ) @ ( one_one @ nat ) )
% 2.65/1.60 = N ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_239_length__tl,axiom,
% 2.65/1.60 ! [A: $tType,Xs: list @ A] :
% 2.65/1.60 ( ( size_size @ ( list @ A ) @ ( tl @ A @ Xs ) )
% 2.65/1.60 = ( minus_minus @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( one_one @ nat ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_240_Suc__diff__1,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.65/1.60 => ( ( suc @ ( minus_minus @ nat @ N @ ( one_one @ nat ) ) )
% 2.65/1.60 = N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_241_one__reorient,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( one @ A )
% 2.65/1.60 => ! [X: A] :
% 2.65/1.60 ( ( ( one_one @ A )
% 2.65/1.60 = X )
% 2.65/1.60 = ( X
% 2.65/1.60 = ( one_one @ A ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_242_One__nat__def,axiom,
% 2.65/1.60 ( ( one_one @ nat )
% 2.65/1.60 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_243_MinPredicate2,axiom,
% 2.65/1.60 ! [P2: nat > $o] :
% 2.65/1.60 ( ? [X_1: nat] : ( P2 @ X_1 )
% 2.65/1.60 => ? [N04: nat] :
% 2.65/1.60 ( ( P2 @ N04 )
% 2.65/1.60 & ( ( N04
% 2.65/1.60 = ( zero_zero @ nat ) )
% 2.65/1.60 | ~ ( P2 @ ( minus_minus @ nat @ N04 @ ( one_one @ nat ) ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_244_diff__Suc__eq__diff__pred,axiom,
% 2.65/1.60 ! [M: nat,N: nat] :
% 2.65/1.60 ( ( minus_minus @ nat @ M @ ( suc @ N ) )
% 2.65/1.60 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ ( one_one @ nat ) ) @ N ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_245_nat__induct__non__zero,axiom,
% 2.65/1.60 ! [N: nat,P2: nat > $o] :
% 2.65/1.60 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.65/1.60 => ( ( P2 @ ( one_one @ nat ) )
% 2.65/1.60 => ( ! [N2: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 2.65/1.60 => ( ( P2 @ N2 )
% 2.65/1.60 => ( P2 @ ( suc @ N2 ) ) ) )
% 2.65/1.60 => ( P2 @ N ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_246_Suc__pred_H,axiom,
% 2.65/1.60 ! [N: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.65/1.60 => ( N
% 2.65/1.60 = ( suc @ ( minus_minus @ nat @ N @ ( one_one @ nat ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_247_Suc__diff__eq__diff__pred,axiom,
% 2.65/1.60 ! [N: nat,M: nat] :
% 2.65/1.60 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.65/1.60 => ( ( minus_minus @ nat @ ( suc @ M ) @ N )
% 2.65/1.60 = ( minus_minus @ nat @ M @ ( minus_minus @ nat @ N @ ( one_one @ nat ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_248_last__conv__nth,axiom,
% 2.65/1.60 ! [A: $tType,Xs: list @ A] :
% 2.65/1.60 ( ( Xs
% 2.65/1.60 != ( nil @ A ) )
% 2.65/1.60 => ( ( last @ A @ Xs )
% 2.65/1.60 = ( nth @ A @ Xs @ ( minus_minus @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( one_one @ nat ) ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_249_diff__numeral__special_I9_J,axiom,
% 2.65/1.60 ! [A: $tType] :
% 2.65/1.60 ( ( neg_numeral @ A )
% 2.65/1.60 => ( ( minus_minus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
% 2.65/1.60 = ( zero_zero @ A ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(fact_250_enabled__def,axiom,
% 2.65/1.60 ! [S: $tType,V: $tType,P: $tType] :
% 2.65/1.60 ( ( enabled @ P @ V @ S )
% 2.65/1.60 = ( ^ [Cfg2: configuration_ext @ P @ V @ S @ product_unit,Msg4: message @ P @ V] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ P @ V @ S @ product_unit @ Cfg2 @ Msg4 ) ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.65/1.60 ! [A9: $tType,A10: $tType] :
% 2.65/1.60 ( ( order @ A10 )
% 2.65/1.60 => ( order @ ( A9 > A10 ) ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 2.65/1.60 canoni770627133id_add @ nat ).
% 2.65/1.60
% 2.65/1.60 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 2.65/1.60 cancel146912293up_add @ nat ).
% 2.65/1.60
% 2.65/1.60 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 2.65/1.60 cancel1352612707id_add @ nat ).
% 2.65/1.60
% 2.65/1.60 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff,axiom,
% 2.65/1.60 comm_monoid_diff @ nat ).
% 2.65/1.60
% 2.65/1.60 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 2.65/1.60 wellorder @ nat ).
% 2.65/1.60
% 2.65/1.60 thf(tcon_Nat_Onat___Orderings_Oorder_1,axiom,
% 2.65/1.60 order @ nat ).
% 2.65/1.60
% 2.65/1.60 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 2.65/1.60 zero @ nat ).
% 2.65/1.60
% 2.65/1.60 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 2.65/1.60 one @ nat ).
% 2.65/1.60
% 2.65/1.60 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 2.65/1.60 size @ nat ).
% 2.65/1.60
% 2.65/1.60 thf(tcon_Set_Oset___Orderings_Oorder_2,axiom,
% 2.65/1.60 ! [A9: $tType] : ( order @ ( set @ A9 ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(tcon_HOL_Obool___Orderings_Oorder_3,axiom,
% 2.65/1.60 order @ $o ).
% 2.65/1.60
% 2.65/1.60 thf(tcon_List_Olist___Nat_Osize_4,axiom,
% 2.65/1.60 ! [A9: $tType] : ( size @ ( list @ A9 ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_5,axiom,
% 2.65/1.60 wellorder @ product_unit ).
% 2.65/1.60
% 2.65/1.60 thf(tcon_Product__Type_Ounit___Orderings_Oorder_6,axiom,
% 2.65/1.60 order @ product_unit ).
% 2.65/1.60
% 2.65/1.60 thf(tcon_AsynchronousSystem_Omessage___Nat_Osize_7,axiom,
% 2.65/1.60 ! [A9: $tType,A10: $tType] : ( size @ ( message @ A9 @ A10 ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(help_If_3_1_T,axiom,
% 2.65/1.60 ! [P2: $o] :
% 2.65/1.60 ( ( P2 = $true )
% 2.65/1.60 | ( P2 = $false ) ) ).
% 2.65/1.60
% 2.65/1.60 thf(help_If_2_1_T,axiom,
% 2.65/1.60 ! [A: $tType,X: A,Y: A] :
% 2.65/1.60 ( ( if @ A @ $false @ X @ Y )
% 2.65/1.60 = Y ) ).
% 2.65/1.60
% 2.65/1.60 thf(help_If_1_1_T,axiom,
% 2.65/1.60 ! [A: $tType,X: A,Y: A] :
% 2.65/1.60 ( ( if @ A @ $true @ X @ Y )
% 2.65/1.60 = X ) ).
% 2.65/1.60
% 2.65/1.60 thf(conj_0,conjecture,
% 2.65/1.60 ord_less @ nat @ n1 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ).
% 2.65/1.60 ------------------------
% 2.65/1.62 % (4719)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/2Mi)
% 2.65/1.62 % (4718)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/27Mi)
% 2.65/1.62 % (4721)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/275Mi)
% 2.65/1.62 % (4719)Instruction limit reached!
% 2.65/1.62 % (4719)------------------------------
% 2.65/1.62 % (4719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.62 % (4719)Termination reason: Unknown
% 2.65/1.62 % (4719)Termination phase: shuffling
% 2.65/1.62
% 2.65/1.62 % (4719)Memory used [KB]: 1279
% 2.65/1.62 % (4720)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/2Mi)
% 2.65/1.62 % (4719)Time elapsed: 0.002 s
% 2.65/1.62 % (4719)Instructions burned: 2 (million)
% 2.65/1.62 % (4719)------------------------------
% 2.65/1.62 % (4719)------------------------------
% 2.65/1.62 % (4720)Instruction limit reached!
% 2.65/1.62 % (4720)------------------------------
% 2.65/1.62 % (4720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.62 % (4720)Termination reason: Unknown
% 2.65/1.62 % (4720)Termination phase: shuffling
% 2.65/1.62
% 2.65/1.62 % (4720)Memory used [KB]: 1407
% 2.65/1.62 % (4720)Time elapsed: 0.002 s
% 2.65/1.62 % (4720)Instructions burned: 3 (million)
% 2.65/1.62 % (4720)------------------------------
% 2.65/1.62 % (4720)------------------------------
% 2.65/1.63 % (4722)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/18Mi)
% 2.65/1.63 % (4717)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/4Mi)
% 2.65/1.63 % (4718)Instruction limit reached!
% 2.65/1.63 % (4718)------------------------------
% 2.65/1.63 % (4718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.63 % (4718)Termination reason: Unknown
% 2.65/1.63 % (4718)Termination phase: Property scanning
% 2.65/1.63
% 2.65/1.63 % (4718)Memory used [KB]: 1663
% 2.65/1.63 % (4718)Time elapsed: 0.010 s
% 2.65/1.63 % (4718)Instructions burned: 28 (million)
% 2.65/1.63 % (4718)------------------------------
% 2.65/1.63 % (4718)------------------------------
% 2.65/1.63 % (4717)Instruction limit reached!
% 2.65/1.63 % (4717)------------------------------
% 2.65/1.63 % (4717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.63 % (4717)Termination reason: Unknown
% 2.65/1.63 % (4717)Termination phase: shuffling
% 2.65/1.63
% 2.65/1.63 % (4717)Memory used [KB]: 1407
% 2.65/1.63 % (4717)Time elapsed: 0.003 s
% 2.65/1.63 % (4717)Instructions burned: 6 (million)
% 2.65/1.63 % (4717)------------------------------
% 2.65/1.63 % (4717)------------------------------
% 2.65/1.63 % (4716)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/183Mi)
% 2.65/1.63 % (4724)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/37Mi)
% 2.65/1.64 % (4722)Instruction limit reached!
% 2.65/1.64 % (4722)------------------------------
% 2.65/1.64 % (4722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.64 % (4722)Termination reason: Unknown
% 2.65/1.64 % (4722)Termination phase: shuffling
% 2.65/1.64
% 2.65/1.64 % (4722)Memory used [KB]: 1535
% 2.65/1.64 % (4722)Time elapsed: 0.010 s
% 2.65/1.64 % (4722)Instructions burned: 18 (million)
% 2.65/1.64 % (4722)------------------------------
% 2.65/1.64 % (4722)------------------------------
% 2.65/1.64 % (4723)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/3Mi)
% 2.65/1.64 % (4725)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/15Mi)
% 2.65/1.64 % (4726)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/3Mi)
% 2.65/1.64 % (4723)Instruction limit reached!
% 2.65/1.64 % (4723)------------------------------
% 2.65/1.64 % (4723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.64 % (4723)Termination reason: Unknown
% 2.65/1.64 % (4723)Termination phase: shuffling
% 2.65/1.64
% 2.65/1.64 % (4723)Memory used [KB]: 1407
% 2.65/1.64 % (4723)Time elapsed: 0.004 s
% 2.65/1.64 % (4723)Instructions burned: 4 (million)
% 2.65/1.64 % (4723)------------------------------
% 2.65/1.64 % (4723)------------------------------
% 2.65/1.64 % (4726)Instruction limit reached!
% 2.65/1.64 % (4726)------------------------------
% 2.65/1.64 % (4726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.64 % (4726)Termination reason: Unknown
% 2.65/1.64 % (4726)Termination phase: shuffling
% 2.65/1.64
% 2.65/1.64 % (4726)Memory used [KB]: 1279
% 2.65/1.64 % (4726)Time elapsed: 0.002 s
% 2.65/1.64 % (4726)Instructions burned: 3 (million)
% 2.65/1.64 % (4726)------------------------------
% 2.65/1.64 % (4726)------------------------------
% 2.65/1.64 % (4721)Refutation not found, incomplete strategy
% 2.65/1.64 % (4721)------------------------------
% 2.65/1.64 % (4721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.64 % (4721)Termination reason: Refutation not found, incomplete strategy
% 2.65/1.64
% 2.65/1.64
% 2.65/1.64 % (4721)Memory used [KB]: 6524
% 2.65/1.64 % (4721)Time elapsed: 0.022 s
% 2.65/1.64 % (4721)Instructions burned: 69 (million)
% 2.65/1.64 % (4721)------------------------------
% 2.65/1.64 % (4721)------------------------------
% 2.65/1.64 % (4724)Instruction limit reached!
% 2.65/1.64 % (4724)------------------------------
% 2.65/1.64 % (4724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.64 % (4724)Termination reason: Unknown
% 2.65/1.64 % (4724)Termination phase: Property scanning
% 2.65/1.64
% 2.65/1.64 % (4724)Memory used [KB]: 2046
% 2.65/1.64 % (4724)Time elapsed: 0.012 s
% 2.65/1.64 % (4724)Instructions burned: 40 (million)
% 2.65/1.64 % (4724)------------------------------
% 2.65/1.64 % (4724)------------------------------
% 2.65/1.64 % (4725)Instruction limit reached!
% 2.65/1.64 % (4725)------------------------------
% 2.65/1.64 % (4725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.64 % (4725)Termination reason: Unknown
% 2.65/1.64 % (4725)Termination phase: shuffling
% 2.65/1.64
% 2.65/1.64 % (4725)Memory used [KB]: 1535
% 2.65/1.64 % (4725)Time elapsed: 0.006 s
% 2.65/1.64 % (4725)Instructions burned: 15 (million)
% 2.65/1.64 % (4725)------------------------------
% 2.65/1.64 % (4725)------------------------------
% 2.65/1.65 % (4729)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/16Mi)
% 2.65/1.65 % (4730)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/3Mi)
% 2.65/1.65 % (4731)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/3Mi)
% 2.65/1.65 % (4727)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/1041Mi)
% 2.65/1.65 % (4732)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/7Mi)
% 2.65/1.65 % (4730)Instruction limit reached!
% 2.65/1.65 % (4730)------------------------------
% 2.65/1.65 % (4730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.65 % (4730)Termination reason: Unknown
% 2.65/1.65 % (4730)Termination phase: shuffling
% 2.65/1.65
% 2.65/1.65 % (4730)Memory used [KB]: 1279
% 2.65/1.65 % (4730)Time elapsed: 0.002 s
% 2.65/1.65 % (4730)Instructions burned: 3 (million)
% 2.65/1.65 % (4730)------------------------------
% 2.65/1.65 % (4730)------------------------------
% 2.65/1.65 % (4731)Instruction limit reached!
% 2.65/1.65 % (4731)------------------------------
% 2.65/1.65 % (4731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.65 % (4731)Termination reason: Unknown
% 2.65/1.65 % (4731)Termination phase: shuffling
% 2.65/1.65
% 2.65/1.65 % (4731)Memory used [KB]: 1279
% 2.65/1.65 % (4731)Time elapsed: 0.002 s
% 2.65/1.65 % (4731)Instructions burned: 3 (million)
% 2.65/1.65 % (4731)------------------------------
% 2.65/1.65 % (4731)------------------------------
% 2.65/1.66 % (4729)Instruction limit reached!
% 2.65/1.66 % (4729)------------------------------
% 2.65/1.66 % (4729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.66 % (4729)Termination reason: Unknown
% 2.65/1.66 % (4729)Termination phase: shuffling
% 2.65/1.66
% 2.65/1.66 % (4729)Memory used [KB]: 1535
% 2.65/1.66 % (4729)Time elapsed: 0.007 s
% 2.65/1.66 % (4729)Instructions burned: 18 (million)
% 2.65/1.66 % (4729)------------------------------
% 2.65/1.66 % (4729)------------------------------
% 2.65/1.66 % (4732)Instruction limit reached!
% 2.65/1.66 % (4732)------------------------------
% 2.65/1.66 % (4732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.66 % (4732)Termination reason: Unknown
% 2.65/1.66 % (4732)Termination phase: shuffling
% 2.65/1.66
% 2.65/1.66 % (4732)Memory used [KB]: 1407
% 2.65/1.66 % (4732)Time elapsed: 0.004 s
% 2.65/1.66 % (4732)Instructions burned: 9 (million)
% 2.65/1.66 % (4732)------------------------------
% 2.65/1.66 % (4732)------------------------------
% 2.65/1.66 % (4733)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/3Mi)
% 2.65/1.66 % (4734)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/4Mi)
% 2.65/1.66 % (4728)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/7Mi)
% 2.65/1.66 % (4733)Instruction limit reached!
% 2.65/1.66 % (4733)------------------------------
% 2.65/1.66 % (4733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.66 % (4733)Termination reason: Unknown
% 2.65/1.66 % (4733)Termination phase: shuffling
% 2.65/1.66
% 2.65/1.66 % (4733)Memory used [KB]: 1407
% 2.65/1.66 % (4733)Time elapsed: 0.002 s
% 2.65/1.66 % (4733)Instructions burned: 4 (million)
% 2.65/1.66 % (4733)------------------------------
% 2.65/1.66 % (4733)------------------------------
% 2.65/1.66 % (4734)Instruction limit reached!
% 2.65/1.66 % (4734)------------------------------
% 2.65/1.66 % (4734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.66 % (4734)Termination reason: Unknown
% 2.65/1.66 % (4734)Termination phase: shuffling
% 2.65/1.66
% 2.65/1.66 % (4734)Memory used [KB]: 1407
% 2.65/1.66 % (4734)Time elapsed: 0.003 s
% 2.65/1.66 % (4734)Instructions burned: 6 (million)
% 2.65/1.66 % (4734)------------------------------
% 2.65/1.66 % (4734)------------------------------
% 2.65/1.67 % (4735)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/18Mi)
% 2.65/1.67 % (4736)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/710Mi)
% 2.65/1.67 % (4728)Instruction limit reached!
% 2.65/1.67 % (4728)------------------------------
% 2.65/1.67 % (4728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.67 % (4728)Termination reason: Unknown
% 2.65/1.67 % (4728)Termination phase: shuffling
% 2.65/1.67
% 2.65/1.67 % (4728)Memory used [KB]: 1407
% 2.65/1.67 % (4728)Time elapsed: 0.006 s
% 2.65/1.67 % (4728)Instructions burned: 8 (million)
% 2.65/1.67 % (4728)------------------------------
% 2.65/1.67 % (4728)------------------------------
% 2.65/1.67 % (4735)Instruction limit reached!
% 2.65/1.67 % (4735)------------------------------
% 2.65/1.67 % (4735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.67 % (4735)Termination reason: Unknown
% 2.65/1.67 % (4735)Termination phase: shuffling
% 2.65/1.67
% 2.65/1.67 % (4735)Memory used [KB]: 1535
% 2.65/1.67 % (4735)Time elapsed: 0.007 s
% 2.65/1.67 % (4735)Instructions burned: 19 (million)
% 2.65/1.67 % (4735)------------------------------
% 2.65/1.67 % (4735)------------------------------
% 2.65/1.67 % (4737)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/6Mi)
% 2.65/1.67 % (4738)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/902Mi)
% 2.65/1.67 % (4737)Instruction limit reached!
% 2.65/1.67 % (4737)------------------------------
% 2.65/1.67 % (4737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.67 % (4737)Termination reason: Unknown
% 2.65/1.67 % (4737)Termination phase: shuffling
% 2.65/1.67
% 2.65/1.67 % (4737)Memory used [KB]: 1407
% 2.65/1.67 % (4737)Time elapsed: 0.003 s
% 2.65/1.67 % (4737)Instructions burned: 7 (million)
% 2.65/1.67 % (4737)------------------------------
% 2.65/1.67 % (4737)------------------------------
% 2.65/1.68 % (4740)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/5Mi)
% 2.65/1.68 % (4740)Instruction limit reached!
% 2.65/1.68 % (4740)------------------------------
% 2.65/1.68 % (4740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.68 % (4740)Termination reason: Unknown
% 2.65/1.68 % (4740)Termination phase: shuffling
% 2.65/1.68
% 2.65/1.68 % (4740)Memory used [KB]: 1407
% 2.65/1.68 % (4740)Time elapsed: 0.003 s
% 2.65/1.68 % (4740)Instructions burned: 7 (million)
% 2.65/1.68 % (4740)------------------------------
% 2.65/1.68 % (4740)------------------------------
% 2.65/1.68 % (4739)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/21Mi)
% 2.65/1.68 % (4741)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/6Mi)
% 2.65/1.69 % (4716)Instruction limit reached!
% 2.65/1.69 % (4716)------------------------------
% 2.65/1.69 % (4716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.69 % (4716)Termination reason: Unknown
% 2.65/1.69 % (4716)Termination phase: Saturation
% 2.65/1.69
% 2.65/1.69 % (4716)Memory used [KB]: 7036
% 2.65/1.69 % (4716)Time elapsed: 0.057 s
% 2.65/1.69 % (4716)Instructions burned: 183 (million)
% 2.65/1.69 % (4716)------------------------------
% 2.65/1.69 % (4716)------------------------------
% 2.65/1.69 % (4741)Instruction limit reached!
% 2.65/1.69 % (4741)------------------------------
% 2.65/1.69 % (4741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.69 % (4741)Termination reason: Unknown
% 2.65/1.69 % (4741)Termination phase: shuffling
% 2.65/1.69
% 2.65/1.69 % (4741)Memory used [KB]: 1407
% 2.65/1.69 % (4741)Time elapsed: 0.003 s
% 2.65/1.69 % (4741)Instructions burned: 8 (million)
% 2.65/1.69 % (4741)------------------------------
% 2.65/1.69 % (4741)------------------------------
% 2.65/1.69 % (4742)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/377Mi)
% 2.65/1.69 % (4743)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/779Mi)
% 2.65/1.69 % (4739)Instruction limit reached!
% 2.65/1.69 % (4739)------------------------------
% 2.65/1.69 % (4739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.69 % (4739)Termination reason: Unknown
% 2.65/1.69 % (4739)Termination phase: shuffling
% 2.65/1.69
% 2.65/1.69 % (4739)Memory used [KB]: 1663
% 2.65/1.69 % (4739)Time elapsed: 0.013 s
% 2.65/1.69 % (4739)Instructions burned: 22 (million)
% 2.65/1.69 % (4739)------------------------------
% 2.65/1.69 % (4739)------------------------------
% 2.65/1.70 % (4744)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/19Mi)
% 2.68/1.70 % (4744)Instruction limit reached!
% 2.68/1.70 % (4744)------------------------------
% 2.68/1.70 % (4744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.70 % (4744)Termination reason: Unknown
% 2.68/1.70 % (4744)Termination phase: shuffling
% 2.68/1.70
% 2.68/1.70 % (4744)Memory used [KB]: 1791
% 2.68/1.70 % (4744)Time elapsed: 0.007 s
% 2.68/1.70 % (4744)Instructions burned: 22 (million)
% 2.68/1.70 % (4744)------------------------------
% 2.68/1.70 % (4744)------------------------------
% 2.68/1.71 % (4746)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_4609 for (2998ds/17Mi)
% 2.68/1.71 % (4745)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_4609 for (2999ds/879Mi)
% 2.68/1.72 % (4746)Instruction limit reached!
% 2.68/1.72 % (4746)------------------------------
% 2.68/1.72 % (4746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.72 % (4746)Termination reason: Unknown
% 2.68/1.72 % (4746)Termination phase: shuffling
% 2.68/1.72
% 2.68/1.72 % (4746)Memory used [KB]: 1535
% 2.68/1.72 % (4746)Time elapsed: 0.007 s
% 2.68/1.72 % (4746)Instructions burned: 18 (million)
% 2.68/1.72 % (4746)------------------------------
% 2.68/1.72 % (4746)------------------------------
% 2.68/1.73 % (4747)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_4609 for (2998ds/3Mi)
% 2.68/1.73 % (4747)Instruction limit reached!
% 2.68/1.73 % (4747)------------------------------
% 2.68/1.73 % (4747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.73 % (4747)Termination reason: Unknown
% 2.68/1.73 % (4747)Termination phase: shuffling
% 2.68/1.73
% 2.68/1.73 % (4747)Memory used [KB]: 1279
% 2.68/1.73 % (4747)Time elapsed: 0.002 s
% 2.68/1.73 % (4747)Instructions burned: 3 (million)
% 2.68/1.73 % (4747)------------------------------
% 2.68/1.73 % (4747)------------------------------
% 2.68/1.74 % (4748)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_4609 for (2998ds/30Mi)
% 2.68/1.75 % (4748)Instruction limit reached!
% 2.68/1.75 % (4748)------------------------------
% 2.68/1.75 % (4748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.75 % (4748)Termination reason: Unknown
% 2.68/1.75 % (4748)Termination phase: Property scanning
% 2.68/1.75
% 2.68/1.75 % (4748)Memory used [KB]: 1663
% 2.68/1.75 % (4748)Time elapsed: 0.011 s
% 2.68/1.75 % (4748)Instructions burned: 33 (million)
% 2.68/1.75 % (4748)------------------------------
% 2.68/1.75 % (4748)------------------------------
% 2.68/1.76 % (4749)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_4609 for (2998ds/127Mi)
% 2.68/1.79 % (4749)Instruction limit reached!
% 2.68/1.79 % (4749)------------------------------
% 2.68/1.79 % (4749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.79 % (4749)Termination reason: Unknown
% 2.68/1.79 % (4749)Termination phase: Saturation
% 2.68/1.79
% 2.68/1.79 % (4749)Memory used [KB]: 6780
% 2.68/1.79 % (4749)Time elapsed: 0.039 s
% 2.68/1.79 % (4749)Instructions burned: 127 (million)
% 2.68/1.79 % (4749)------------------------------
% 2.68/1.79 % (4749)------------------------------
% 2.68/1.80 % (4750)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_4609 for (2998ds/100Mi)
% 2.68/1.81 % (4742)Instruction limit reached!
% 2.68/1.81 % (4742)------------------------------
% 2.68/1.81 % (4742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.81 % (4742)Termination reason: Unknown
% 2.68/1.81 % (4742)Termination phase: Saturation
% 2.68/1.81
% 2.68/1.81 % (4742)Memory used [KB]: 7547
% 2.68/1.81 % (4742)Time elapsed: 0.119 s
% 2.68/1.81 % (4742)Instructions burned: 377 (million)
% 2.68/1.81 % (4742)------------------------------
% 2.68/1.81 % (4742)------------------------------
% 2.68/1.82 % (4751)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_4609 for (2997ds/3Mi)
% 2.68/1.82 % (4751)Instruction limit reached!
% 2.68/1.82 % (4751)------------------------------
% 2.68/1.82 % (4751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.82 % (4751)Termination reason: Unknown
% 2.68/1.82 % (4751)Termination phase: shuffling
% 2.68/1.82
% 2.68/1.82 % (4751)Memory used [KB]: 1279
% 2.68/1.82 % (4751)Time elapsed: 0.002 s
% 2.68/1.82 % (4751)Instructions burned: 3 (million)
% 2.68/1.82 % (4751)------------------------------
% 2.68/1.82 % (4751)------------------------------
% 2.68/1.83 % (4752)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_4609 for (2997ds/20Mi)
% 2.68/1.83 % (4750)Instruction limit reached!
% 2.68/1.83 % (4750)------------------------------
% 2.68/1.83 % (4750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.83 % (4750)Termination reason: Unknown
% 2.68/1.83 % (4750)Termination phase: Saturation
% 2.68/1.83
% 2.68/1.83 % (4750)Memory used [KB]: 6652
% 2.68/1.83 % (4750)Time elapsed: 0.028 s
% 2.68/1.83 % (4750)Instructions burned: 100 (million)
% 2.68/1.83 % (4750)------------------------------
% 2.68/1.83 % (4750)------------------------------
% 2.68/1.84 % (4752)Instruction limit reached!
% 2.68/1.84 % (4752)------------------------------
% 2.68/1.84 % (4752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.84 % (4752)Termination reason: Unknown
% 2.68/1.84 % (4752)Termination phase: Property scanning
% 2.68/1.84
% 2.68/1.84 % (4752)Memory used [KB]: 1663
% 2.68/1.84 % (4752)Time elapsed: 0.008 s
% 2.68/1.84 % (4752)Instructions burned: 22 (million)
% 2.68/1.84 % (4752)------------------------------
% 2.68/1.84 % (4752)------------------------------
% 2.68/1.84 % (4753)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_4609 for (2997ds/86Mi)
% 2.68/1.85 % (4754)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_4609 for (2997ds/107Mi)
% 2.68/1.86 % (4753)Instruction limit reached!
% 2.68/1.86 % (4753)------------------------------
% 2.68/1.86 % (4753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.86 % (4753)Termination reason: Unknown
% 2.68/1.86 % (4753)Termination phase: Saturation
% 2.68/1.86
% 2.68/1.86 % (4753)Memory used [KB]: 6652
% 2.68/1.86 % (4753)Time elapsed: 0.025 s
% 2.68/1.86 % (4753)Instructions burned: 86 (million)
% 2.68/1.86 % (4753)------------------------------
% 2.68/1.86 % (4753)------------------------------
% 2.68/1.87 % (4736)Instruction limit reached!
% 2.68/1.87 % (4736)------------------------------
% 2.68/1.87 % (4736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.87 % (4736)Termination reason: Unknown
% 2.68/1.87 % (4736)Termination phase: Saturation
% 2.68/1.87
% 2.68/1.87 % (4736)Memory used [KB]: 8059
% 2.68/1.87 % (4736)Time elapsed: 0.207 s
% 2.68/1.87 % (4736)Instructions burned: 712 (million)
% 2.68/1.87 % (4736)------------------------------
% 2.68/1.87 % (4736)------------------------------
% 2.68/1.87 % (4755)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_4609 for (2997ds/39Mi)
% 2.68/1.88 % (4754)Instruction limit reached!
% 2.68/1.88 % (4754)------------------------------
% 2.68/1.88 % (4754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.88 % (4754)Termination reason: Unknown
% 2.68/1.88 % (4754)Termination phase: Saturation
% 2.68/1.88
% 2.68/1.88 % (4754)Memory used [KB]: 6780
% 2.68/1.88 % (4754)Time elapsed: 0.033 s
% 2.68/1.88 % (4754)Instructions burned: 109 (million)
% 2.68/1.88 % (4754)------------------------------
% 2.68/1.88 % (4754)------------------------------
% 2.68/1.88 % (4756)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_4609 for (2997ds/448Mi)
% 2.68/1.88 % (4755)Instruction limit reached!
% 2.68/1.88 % (4755)------------------------------
% 2.68/1.88 % (4755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.88 % (4755)Termination reason: Unknown
% 2.68/1.88 % (4755)Termination phase: Property scanning
% 2.68/1.88
% 2.68/1.88 % (4755)Memory used [KB]: 2046
% 2.68/1.88 % (4755)Time elapsed: 0.012 s
% 2.68/1.88 % (4755)Instructions burned: 41 (million)
% 2.68/1.88 % (4755)------------------------------
% 2.68/1.88 % (4755)------------------------------
% 2.68/1.89 % (4757)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_4609 for (2997ds/46Mi)
% 2.68/1.89 % (4758)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_4609 for (2997ds/98Mi)
% 2.68/1.90 % (4757)Instruction limit reached!
% 2.68/1.90 % (4757)------------------------------
% 2.68/1.90 % (4757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.90 % (4757)Termination reason: Unknown
% 2.68/1.90 % (4757)Termination phase: Preprocessing 3
% 2.68/1.90
% 2.68/1.90 % (4757)Memory used [KB]: 1791
% 2.68/1.90 % (4757)Time elapsed: 0.015 s
% 2.68/1.90 % (4757)Instructions burned: 46 (million)
% 2.68/1.90 % (4757)------------------------------
% 2.68/1.90 % (4757)------------------------------
% 2.68/1.91 % (4759)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_4609 for (2996ds/507Mi)
% 2.68/1.92 % (4758)Instruction limit reached!
% 2.68/1.92 % (4758)------------------------------
% 2.68/1.92 % (4758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.92 % (4758)Termination reason: Unknown
% 2.68/1.92 % (4758)Termination phase: Saturation
% 2.68/1.92
% 2.68/1.92 % (4758)Memory used [KB]: 2174
% 2.68/1.92 % (4758)Time elapsed: 0.028 s
% 2.68/1.92 % (4758)Instructions burned: 101 (million)
% 2.68/1.92 % (4758)------------------------------
% 2.68/1.92 % (4758)------------------------------
% 2.68/1.93 % (4760)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_4609 for (2996ds/149Mi)
% 2.68/1.93 % (4743)Instruction limit reached!
% 2.68/1.93 % (4743)------------------------------
% 2.68/1.93 % (4743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.93 % (4743)Termination reason: Unknown
% 2.68/1.93 % (4743)Termination phase: Saturation
% 2.68/1.93
% 2.68/1.93 % (4743)Memory used [KB]: 7803
% 2.68/1.93 % (4743)Time elapsed: 0.260 s
% 2.68/1.93 % (4743)Instructions burned: 781 (million)
% 2.68/1.93 % (4743)------------------------------
% 2.68/1.93 % (4743)------------------------------
% 2.68/1.94 % (4761)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_4609 for (2996ds/39Mi)
% 2.68/1.95 % (4738)Instruction limit reached!
% 2.68/1.95 % (4738)------------------------------
% 2.68/1.95 % (4738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.95 % (4738)Termination reason: Unknown
% 2.68/1.95 % (4738)Termination phase: Saturation
% 2.68/1.95
% 2.68/1.95 % (4738)Memory used [KB]: 8955
% 2.68/1.95 % (4738)Time elapsed: 0.273 s
% 2.68/1.95 % (4738)Instructions burned: 902 (million)
% 2.68/1.95 % (4738)------------------------------
% 2.68/1.95 % (4738)------------------------------
% 2.68/1.95 % (4761)Instruction limit reached!
% 2.68/1.95 % (4761)------------------------------
% 2.68/1.95 % (4761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.95 % (4761)Termination reason: Unknown
% 2.68/1.95 % (4761)Termination phase: Preprocessing 3
% 2.68/1.95
% 2.68/1.95 % (4761)Memory used [KB]: 1791
% 2.68/1.95 % (4761)Time elapsed: 0.013 s
% 2.68/1.95 % (4761)Instructions burned: 39 (million)
% 2.68/1.95 % (4761)------------------------------
% 2.68/1.95 % (4761)------------------------------
% 2.68/1.96 % (4762)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_4609 for (2996ds/6Mi)
% 2.68/1.96 % (4762)Instruction limit reached!
% 2.68/1.96 % (4762)------------------------------
% 2.68/1.96 % (4762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.96 % (4762)Termination reason: Unknown
% 2.68/1.96 % (4762)Termination phase: shuffling
% 2.68/1.96
% 2.68/1.96 % (4762)Memory used [KB]: 1407
% 2.68/1.96 % (4762)Time elapsed: 0.003 s
% 2.68/1.96 % (4762)Instructions burned: 6 (million)
% 2.68/1.96 % (4762)------------------------------
% 2.68/1.96 % (4762)------------------------------
% 2.68/1.96 % (4763)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_4609 for (2996ds/1087Mi)
% 2.68/1.97 % (4764)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_4609 for (2996ds/47Mi)
% 2.68/1.97 % (4727)Instruction limit reached!
% 2.68/1.97 % (4727)------------------------------
% 2.68/1.97 % (4727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.97 % (4727)Termination reason: Unknown
% 2.68/1.97 % (4727)Termination phase: Saturation
% 2.68/1.97
% 2.68/1.97 % (4727)Memory used [KB]: 8827
% 2.68/1.97 % (4727)Time elapsed: 0.321 s
% 2.68/1.97 % (4727)Instructions burned: 1043 (million)
% 2.68/1.97 % (4727)------------------------------
% 2.68/1.97 % (4727)------------------------------
% 2.68/1.98 % (4760)Instruction limit reached!
% 2.68/1.98 % (4760)------------------------------
% 2.68/1.98 % (4760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.98 % (4760)Termination reason: Unknown
% 2.68/1.98 % (4760)Termination phase: Saturation
% 2.68/1.98
% 2.68/1.98 % (4760)Memory used [KB]: 6780
% 2.68/1.98 % (4760)Time elapsed: 0.046 s
% 2.68/1.98 % (4760)Instructions burned: 150 (million)
% 2.68/1.98 % (4760)------------------------------
% 2.68/1.98 % (4760)------------------------------
% 2.68/1.98 % (4765)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_4609 for (2996ds/44Mi)
% 2.68/1.98 % (4764)Instruction limit reached!
% 2.68/1.98 % (4764)------------------------------
% 2.68/1.98 % (4764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.98 % (4764)Termination reason: Unknown
% 2.68/1.98 % (4764)Termination phase: Property scanning
% 2.68/1.98
% 2.68/1.98 % (4764)Memory used [KB]: 1918
% 2.68/1.98 % (4764)Time elapsed: 0.017 s
% 2.68/1.98 % (4764)Instructions burned: 51 (million)
% 2.68/1.98 % (4764)------------------------------
% 2.68/1.98 % (4764)------------------------------
% 2.68/1.99 % (4766)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_4609 for (2996ds/432Mi)
% 2.68/1.99 % (4767)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_4609 for (2996ds/62Mi)
% 2.68/1.99 % (4765)Instruction limit reached!
% 2.68/1.99 % (4765)------------------------------
% 2.68/1.99 % (4765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.99 % (4765)Termination reason: Unknown
% 2.68/1.99 % (4765)Termination phase: Property scanning
% 2.68/1.99
% 2.68/1.99 % (4765)Memory used [KB]: 2046
% 2.68/1.99 % (4765)Time elapsed: 0.014 s
% 2.68/1.99 % (4765)Instructions burned: 46 (million)
% 2.68/1.99 % (4765)------------------------------
% 2.68/1.99 % (4765)------------------------------
% 2.68/2.00 % (4768)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_4609 for (2996ds/31Mi)
% 2.68/2.01 % (4767)Instruction limit reached!
% 2.68/2.01 % (4767)------------------------------
% 2.68/2.01 % (4767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/2.01 % (4767)Termination reason: Unknown
% 2.68/2.01 % (4767)Termination phase: Property scanning
% 2.68/2.01
% 2.68/2.01 % (4767)Memory used [KB]: 2046
% 2.68/2.01 % (4767)Time elapsed: 0.018 s
% 2.68/2.01 % (4767)Instructions burned: 65 (million)
% 2.68/2.01 % (4767)------------------------------
% 2.68/2.01 % (4767)------------------------------
% 2.68/2.01 % (4768)Instruction limit reached!
% 2.68/2.01 % (4768)------------------------------
% 2.68/2.01 % (4768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/2.01 % (4768)Termination reason: Unknown
% 2.68/2.01 % (4768)Termination phase: Preprocessing 1
% 2.68/2.01
% 2.68/2.01 % (4768)Memory used [KB]: 1663
% 2.68/2.01 % (4768)Time elapsed: 0.011 s
% 2.68/2.01 % (4768)Instructions burned: 33 (million)
% 2.68/2.01 % (4768)------------------------------
% 2.68/2.01 % (4768)------------------------------
% 2.68/2.02 % (4756)Instruction limit reached!
% 2.68/2.02 % (4756)------------------------------
% 2.68/2.02 % (4756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/2.02 % (4756)Termination reason: Unknown
% 2.68/2.02 % (4756)Termination phase: Saturation
% 2.68/2.02
% 2.68/2.02 % (4756)Memory used [KB]: 7803
% 2.68/2.02 % (4756)Time elapsed: 0.137 s
% 2.68/2.02 % (4756)Instructions burned: 449 (million)
% 2.68/2.02 % (4756)------------------------------
% 2.68/2.02 % (4756)------------------------------
% 2.68/2.02 % (4769)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_4609 for (2995ds/96Mi)
% 5.37/2.02 % (4770)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_4609 for (2995ds/453Mi)
% 5.37/2.03 % (4771)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_4609 for (2995ds/71Mi)
% 5.37/2.05 % (4769)Instruction limit reached!
% 5.37/2.05 % (4769)------------------------------
% 5.37/2.05 % (4769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.37/2.05 % (4769)Termination reason: Unknown
% 5.37/2.05 % (4769)Termination phase: Saturation
% 5.37/2.05
% 5.37/2.05 % (4769)Memory used [KB]: 6524
% 5.37/2.05 % (4769)Time elapsed: 0.030 s
% 5.37/2.05 % (4769)Instructions burned: 98 (million)
% 5.37/2.05 % (4769)------------------------------
% 5.37/2.05 % (4769)------------------------------
% 5.37/2.05 % (4771)Instruction limit reached!
% 5.37/2.05 % (4771)------------------------------
% 5.37/2.05 % (4771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.37/2.05 % (4771)Termination reason: Unknown
% 5.37/2.05 % (4771)Termination phase: Property scanning
% 5.37/2.05
% 5.37/2.05 % (4771)Memory used [KB]: 2046
% 5.37/2.05 % (4771)Time elapsed: 0.023 s
% 5.37/2.05 % (4771)Instructions burned: 74 (million)
% 5.37/2.05 % (4771)------------------------------
% 5.37/2.05 % (4771)------------------------------
% 5.37/2.06 % (4772)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_4609 for (2995ds/83Mi)
% 5.37/2.06 % (4773)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_4609 for (2995ds/11Mi)
% 5.37/2.06 % (4773)Instruction limit reached!
% 5.37/2.06 % (4773)------------------------------
% 5.37/2.06 % (4773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.37/2.06 % (4773)Termination reason: Unknown
% 5.37/2.06 % (4773)Termination phase: shuffling
% 5.37/2.06
% 5.37/2.06 % (4773)Memory used [KB]: 1535
% 5.37/2.06 % (4773)Time elapsed: 0.004 s
% 5.37/2.06 % (4773)Instructions burned: 11 (million)
% 5.37/2.06 % (4773)------------------------------
% 5.37/2.06 % (4773)------------------------------
% 5.37/2.07 % (4774)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_4609 for (2995ds/41Mi)
% 5.37/2.08 % (4772)Instruction limit reached!
% 5.37/2.08 % (4772)------------------------------
% 5.37/2.08 % (4772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.37/2.08 % (4772)Termination reason: Unknown
% 5.37/2.08 % (4772)Termination phase: Saturation
% 5.37/2.08
% 5.37/2.08 % (4772)Memory used [KB]: 6396
% 5.37/2.08 % (4772)Time elapsed: 0.025 s
% 5.37/2.08 % (4772)Instructions burned: 84 (million)
% 5.37/2.08 % (4772)------------------------------
% 5.37/2.08 % (4772)------------------------------
% 5.37/2.08 % (4774)Instruction limit reached!
% 5.37/2.08 % (4774)------------------------------
% 5.37/2.08 % (4774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.37/2.08 % (4774)Termination reason: Unknown
% 5.37/2.08 % (4774)Termination phase: Property scanning
% 5.37/2.08
% 5.37/2.08 % (4774)Memory used [KB]: 2046
% 5.37/2.08 % (4774)Time elapsed: 0.012 s
% 5.37/2.08 % (4774)Instructions burned: 41 (million)
% 5.37/2.08 % (4774)------------------------------
% 5.37/2.08 % (4774)------------------------------
% 5.37/2.09 % (4775)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_4609 for (2995ds/6Mi)
% 5.37/2.09 % (4776)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_4609 for (2995ds/150Mi)
% 5.37/2.09 % (4775)Instruction limit reached!
% 5.37/2.09 % (4775)------------------------------
% 5.37/2.09 % (4775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.37/2.09 % (4775)Termination reason: Unknown
% 5.37/2.09 % (4775)Termination phase: shuffling
% 5.37/2.09
% 5.37/2.09 % (4775)Memory used [KB]: 1407
% 5.37/2.09 % (4775)Time elapsed: 0.004 s
% 5.37/2.09 % (4775)Instructions burned: 8 (million)
% 5.37/2.09 % (4775)------------------------------
% 5.37/2.09 % (4775)------------------------------
% 5.37/2.10 % (4745)Instruction limit reached!
% 5.37/2.10 % (4745)------------------------------
% 5.37/2.10 % (4745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.37/2.10 % (4745)Termination reason: Unknown
% 5.37/2.10 % (4745)Termination phase: Saturation
% 5.37/2.10
% 5.37/2.10 % (4745)Memory used [KB]: 7931
% 5.37/2.10 % (4745)Time elapsed: 0.389 s
% 5.37/2.10 % (4745)Instructions burned: 881 (million)
% 5.37/2.10 % (4745)------------------------------
% 5.37/2.10 % (4745)------------------------------
% 5.37/2.10 % (4777)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_4609 for (2995ds/343Mi)
% 5.37/2.11 % (4778)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_4609 for (2995ds/109Mi)
% 5.98/2.14 % (4776)Instruction limit reached!
% 5.98/2.14 % (4776)------------------------------
% 5.98/2.14 % (4776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.14 % (4776)Termination reason: Unknown
% 5.98/2.14 % (4776)Termination phase: Saturation
% 5.98/2.14
% 5.98/2.14 % (4776)Memory used [KB]: 6908
% 5.98/2.14 % (4776)Time elapsed: 0.047 s
% 5.98/2.14 % (4776)Instructions burned: 152 (million)
% 5.98/2.14 % (4776)------------------------------
% 5.98/2.14 % (4776)------------------------------
% 5.98/2.14 % (4778)Instruction limit reached!
% 5.98/2.14 % (4778)------------------------------
% 5.98/2.14 % (4778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.14 % (4778)Termination reason: Unknown
% 5.98/2.14 % (4778)Termination phase: Saturation
% 5.98/2.14
% 5.98/2.14 % (4778)Memory used [KB]: 6652
% 5.98/2.14 % (4778)Time elapsed: 0.032 s
% 5.98/2.14 % (4778)Instructions burned: 109 (million)
% 5.98/2.14 % (4778)------------------------------
% 5.98/2.14 % (4778)------------------------------
% 5.98/2.15 % (4779)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_4609 for (2994ds/253Mi)
% 5.98/2.15 % (4780)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_4609 for (2994ds/140Mi)
% 5.98/2.15 % (4766)Instruction limit reached!
% 5.98/2.15 % (4766)------------------------------
% 5.98/2.15 % (4766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.15 % (4766)Termination reason: Unknown
% 5.98/2.15 % (4766)Termination phase: Saturation
% 5.98/2.15
% 5.98/2.15 % (4766)Memory used [KB]: 3965
% 5.98/2.15 % (4766)Time elapsed: 0.174 s
% 5.98/2.15 % (4766)Instructions burned: 432 (million)
% 5.98/2.15 % (4766)------------------------------
% 5.98/2.15 % (4766)------------------------------
% 5.98/2.16 % (4770)Instruction limit reached!
% 5.98/2.16 % (4770)------------------------------
% 5.98/2.16 % (4770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.16 % (4770)Termination reason: Unknown
% 5.98/2.16 % (4770)Termination phase: Saturation
% 5.98/2.16
% 5.98/2.16 % (4770)Memory used [KB]: 7291
% 5.98/2.16 % (4770)Time elapsed: 0.135 s
% 5.98/2.16 % (4770)Instructions burned: 453 (million)
% 5.98/2.16 % (4770)------------------------------
% 5.98/2.16 % (4770)------------------------------
% 5.98/2.16 % (4781)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_4609 for (2994ds/614Mi)
% 5.98/2.16 % (4759)Instruction limit reached!
% 5.98/2.16 % (4759)------------------------------
% 5.98/2.16 % (4759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.16 % (4759)Termination reason: Unknown
% 5.98/2.16 % (4759)Termination phase: Saturation
% 5.98/2.16
% 5.98/2.16 % (4759)Memory used [KB]: 7803
% 5.98/2.16 % (4759)Time elapsed: 0.254 s
% 5.98/2.16 % (4759)Instructions burned: 508 (million)
% 5.98/2.16 % (4759)------------------------------
% 5.98/2.16 % (4759)------------------------------
% 5.98/2.17 % (4782)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_4609 for (2994ds/202Mi)
% 5.98/2.17 % (4783)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_4609 for (2994ds/339Mi)
% 5.98/2.19 % (4780)Instruction limit reached!
% 5.98/2.19 % (4780)------------------------------
% 5.98/2.19 % (4780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.98/2.19 % (4780)Termination reason: Unknown
% 5.98/2.19 % (4780)Termination phase: Saturation
% 5.98/2.19
% 5.98/2.19 % (4780)Memory used [KB]: 6908
% 5.98/2.19 % (4780)Time elapsed: 0.046 s
% 5.98/2.19 % (4780)Instructions burned: 141 (million)
% 5.98/2.19 % (4780)------------------------------
% 5.98/2.19 % (4780)------------------------------
% 6.42/2.20 % (4782)Refutation not found, incomplete strategy
% 6.42/2.20 % (4782)------------------------------
% 6.42/2.20 % (4782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.20 % (4782)Termination reason: Refutation not found, incomplete strategy
% 6.42/2.20
% 6.42/2.20
% 6.42/2.20 % (4782)Memory used [KB]: 6908
% 6.42/2.20 % (4782)Time elapsed: 0.034 s
% 6.42/2.20 % (4782)Instructions burned: 107 (million)
% 6.42/2.20 % (4782)------------------------------
% 6.42/2.20 % (4782)------------------------------
% 6.42/2.20 % (4784)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_4609 for (2994ds/283Mi)
% 6.42/2.21 % (4785)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_4609 for (2994ds/134Mi)
% 6.42/2.21 % (4777)Instruction limit reached!
% 6.42/2.21 % (4777)------------------------------
% 6.42/2.21 % (4777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.21 % (4777)Termination reason: Unknown
% 6.42/2.21 % (4777)Termination phase: Saturation
% 6.42/2.21
% 6.42/2.21 % (4777)Memory used [KB]: 7547
% 6.42/2.21 % (4777)Time elapsed: 0.110 s
% 6.42/2.21 % (4777)Instructions burned: 344 (million)
% 6.42/2.21 % (4777)------------------------------
% 6.42/2.21 % (4777)------------------------------
% 6.42/2.22 % (4786)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_4609 for (2994ds/298Mi)
% 6.42/2.23 % (4779)Instruction limit reached!
% 6.42/2.23 % (4779)------------------------------
% 6.42/2.23 % (4779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.23 % (4779)Termination reason: Unknown
% 6.42/2.23 % (4779)Termination phase: Saturation
% 6.42/2.23
% 6.42/2.23 % (4779)Memory used [KB]: 7675
% 6.42/2.23 % (4779)Time elapsed: 0.080 s
% 6.42/2.23 % (4779)Instructions burned: 254 (million)
% 6.42/2.23 % (4779)------------------------------
% 6.42/2.23 % (4779)------------------------------
% 6.42/2.24 % (4787)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_4609 for (2993ds/192Mi)
% 6.42/2.25 % (4785)Instruction limit reached!
% 6.42/2.25 % (4785)------------------------------
% 6.42/2.25 % (4785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.25 % (4785)Termination reason: Unknown
% 6.42/2.25 % (4785)Termination phase: Saturation
% 6.42/2.25
% 6.42/2.25 % (4785)Memory used [KB]: 6780
% 6.42/2.25 % (4785)Time elapsed: 0.043 s
% 6.42/2.25 % (4785)Instructions burned: 136 (million)
% 6.42/2.25 % (4785)------------------------------
% 6.42/2.25 % (4785)------------------------------
% 6.42/2.26 % (4788)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_4609 for (2993ds/258Mi)
% 6.42/2.28 % (4783)Instruction limit reached!
% 6.42/2.28 % (4783)------------------------------
% 6.42/2.28 % (4783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.28 % (4783)Termination reason: Unknown
% 6.42/2.28 % (4783)Termination phase: Saturation
% 6.42/2.28
% 6.42/2.28 % (4783)Memory used [KB]: 7675
% 6.42/2.28 % (4783)Time elapsed: 0.111 s
% 6.42/2.28 % (4783)Instructions burned: 341 (million)
% 6.42/2.28 % (4783)------------------------------
% 6.42/2.28 % (4783)------------------------------
% 6.42/2.29 % (4784)Instruction limit reached!
% 6.42/2.29 % (4784)------------------------------
% 6.42/2.29 % (4784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.29 % (4784)Termination reason: Unknown
% 6.42/2.29 % (4784)Termination phase: Saturation
% 6.42/2.29
% 6.42/2.29 % (4784)Memory used [KB]: 7291
% 6.42/2.29 % (4784)Time elapsed: 0.089 s
% 6.42/2.29 % (4784)Instructions burned: 285 (million)
% 6.42/2.29 % (4784)------------------------------
% 6.42/2.29 % (4784)------------------------------
% 6.42/2.29 % (4787)Instruction limit reached!
% 6.42/2.29 % (4787)------------------------------
% 6.42/2.29 % (4787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.29 % (4787)Termination reason: Unknown
% 6.42/2.29 % (4787)Termination phase: Saturation
% 6.42/2.29
% 6.42/2.29 % (4787)Memory used [KB]: 7547
% 6.42/2.29 % (4787)Time elapsed: 0.058 s
% 6.42/2.29 % (4787)Instructions burned: 192 (million)
% 6.42/2.29 % (4787)------------------------------
% 6.42/2.29 % (4787)------------------------------
% 6.42/2.29 % (4789)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_4609 for (2993ds/90Mi)
% 7.11/2.30 % (4792)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_4609 for (2993ds/231Mi)
% 7.11/2.30 % (4793)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_4609 for (2993ds/458Mi)
% 7.11/2.31 % (4786)Instruction limit reached!
% 7.11/2.31 % (4786)------------------------------
% 7.11/2.31 % (4786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.31 % (4786)Termination reason: Unknown
% 7.11/2.31 % (4786)Termination phase: Saturation
% 7.11/2.31
% 7.11/2.31 % (4786)Memory used [KB]: 7675
% 7.11/2.31 % (4786)Time elapsed: 0.110 s
% 7.11/2.31 % (4786)Instructions burned: 300 (million)
% 7.11/2.31 % (4786)------------------------------
% 7.11/2.31 % (4786)------------------------------
% 7.11/2.32 % (4763)Instruction limit reached!
% 7.11/2.32 % (4763)------------------------------
% 7.11/2.32 % (4763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.32 % (4763)Termination reason: Unknown
% 7.11/2.32 % (4763)Termination phase: Saturation
% 7.11/2.32
% 7.11/2.32 % (4763)Memory used [KB]: 8443
% 7.11/2.32 % (4763)Time elapsed: 0.354 s
% 7.11/2.32 % (4763)Instructions burned: 1089 (million)
% 7.11/2.32 % (4763)------------------------------
% 7.11/2.32 % (4763)------------------------------
% 7.11/2.32 % (4801)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_4609 for (2992ds/31Mi)
% 7.11/2.32 % (4789)Instruction limit reached!
% 7.11/2.32 % (4789)------------------------------
% 7.11/2.32 % (4789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.32 % (4789)Termination reason: Unknown
% 7.11/2.32 % (4789)Termination phase: Saturation
% 7.11/2.32
% 7.11/2.32 % (4789)Memory used [KB]: 6524
% 7.11/2.32 % (4789)Time elapsed: 0.027 s
% 7.11/2.32 % (4789)Instructions burned: 91 (million)
% 7.11/2.32 % (4789)------------------------------
% 7.11/2.32 % (4789)------------------------------
% 7.11/2.33 % (4804)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_4609 for (2992ds/297Mi)
% 7.11/2.33 % (4801)Instruction limit reached!
% 7.11/2.33 % (4801)------------------------------
% 7.11/2.33 % (4801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.33 % (4801)Termination reason: Unknown
% 7.11/2.33 % (4801)Termination phase: Property scanning
% 7.11/2.33
% 7.11/2.33 % (4801)Memory used [KB]: 1663
% 7.11/2.33 % (4801)Time elapsed: 0.011 s
% 7.11/2.33 % (4801)Instructions burned: 32 (million)
% 7.11/2.33 % (4801)------------------------------
% 7.11/2.33 % (4801)------------------------------
% 7.11/2.33 % (4806)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_4609 for (2992ds/987Mi)
% 7.11/2.34 % (4788)Instruction limit reached!
% 7.11/2.34 % (4788)------------------------------
% 7.11/2.34 % (4788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.34 % (4788)Termination reason: Unknown
% 7.11/2.34 % (4788)Termination phase: Saturation
% 7.11/2.34
% 7.11/2.34 % (4788)Memory used [KB]: 7419
% 7.11/2.34 % (4788)Time elapsed: 0.099 s
% 7.11/2.34 % (4788)Instructions burned: 261 (million)
% 7.11/2.34 % (4788)------------------------------
% 7.11/2.34 % (4788)------------------------------
% 7.11/2.34 % (4811)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_4609 for (2992ds/182Mi)
% 7.11/2.35 % (4816)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_4609 for (2992ds/182Mi)
% 7.11/2.35 % (4781)Instruction limit reached!
% 7.11/2.35 % (4781)------------------------------
% 7.11/2.35 % (4781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.35 % (4781)Termination reason: Unknown
% 7.11/2.35 % (4781)Termination phase: Saturation
% 7.11/2.35
% 7.11/2.35 % (4781)Memory used [KB]: 8699
% 7.11/2.35 % (4781)Time elapsed: 0.193 s
% 7.11/2.35 % (4781)Instructions burned: 614 (million)
% 7.11/2.35 % (4781)------------------------------
% 7.11/2.35 % (4781)------------------------------
% 7.11/2.36 % (4822)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_4609 for (2992ds/154Mi)
% 7.11/2.37 % (4792)Instruction limit reached!
% 7.11/2.37 % (4792)------------------------------
% 7.11/2.37 % (4792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.37 % (4792)Termination reason: Unknown
% 7.11/2.37 % (4792)Termination phase: Saturation
% 7.11/2.37
% 7.11/2.37 % (4792)Memory used [KB]: 7036
% 7.11/2.37 % (4792)Time elapsed: 0.069 s
% 7.11/2.37 % (4792)Instructions burned: 233 (million)
% 7.11/2.37 % (4792)------------------------------
% 7.11/2.37 % (4792)------------------------------
% 7.11/2.38 % (4831)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_4609 for (2992ds/79Mi)
% 7.11/2.39 % (4811)Instruction limit reached!
% 7.11/2.39 % (4811)------------------------------
% 7.11/2.39 % (4811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.11/2.39 % (4811)Termination reason: Unknown
% 7.11/2.39 % (4811)Termination phase: Saturation
% 7.11/2.39
% 7.11/2.39 % (4811)Memory used [KB]: 6908
% 7.11/2.39 % (4811)Time elapsed: 0.055 s
% 7.11/2.39 % (4811)Instructions burned: 183 (million)
% 7.11/2.39 % (4811)------------------------------
% 7.11/2.39 % (4811)------------------------------
% 7.72/2.40 % (4822)Refutation not found, incomplete strategy
% 7.72/2.40 % (4822)------------------------------
% 7.72/2.40 % (4822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.40 % (4822)Termination reason: Refutation not found, incomplete strategy
% 7.72/2.40
% 7.72/2.40
% 7.72/2.40 % (4822)Memory used [KB]: 7164
% 7.72/2.40 % (4822)Time elapsed: 0.038 s
% 7.72/2.40 % (4822)Instructions burned: 130 (million)
% 7.72/2.40 % (4822)------------------------------
% 7.72/2.40 % (4822)------------------------------
% 7.72/2.40 % (4831)Instruction limit reached!
% 7.72/2.40 % (4831)------------------------------
% 7.72/2.40 % (4831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.40 % (4831)Termination reason: Unknown
% 7.72/2.40 % (4831)Termination phase: Saturation
% 7.72/2.40
% 7.72/2.40 % (4831)Memory used [KB]: 2046
% 7.72/2.40 % (4831)Time elapsed: 0.024 s
% 7.72/2.40 % (4831)Instructions burned: 81 (million)
% 7.72/2.40 % (4831)------------------------------
% 7.72/2.40 % (4831)------------------------------
% 7.72/2.40 % (4840)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_4609 for (2992ds/216Mi)
% 7.72/2.40 % (4816)Instruction limit reached!
% 7.72/2.40 % (4816)------------------------------
% 7.72/2.40 % (4816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.40 % (4816)Termination reason: Unknown
% 7.72/2.40 % (4816)Termination phase: Saturation
% 7.72/2.40
% 7.72/2.40 % (4816)Memory used [KB]: 6908
% 7.72/2.40 % (4816)Time elapsed: 0.058 s
% 7.72/2.40 % (4816)Instructions burned: 182 (million)
% 7.72/2.40 % (4816)------------------------------
% 7.72/2.40 % (4816)------------------------------
% 7.72/2.41 % (4844)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_4609 for (2992ds/114Mi)
% 7.72/2.41 % (4845)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_4609 for (2992ds/922Mi)
% 7.72/2.41 % (4848)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_4609 for (2991ds/182Mi)
% 7.72/2.42 % (4804)Instruction limit reached!
% 7.72/2.42 % (4804)------------------------------
% 7.72/2.42 % (4804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.42 % (4804)Termination reason: Unknown
% 7.72/2.42 % (4804)Termination phase: Saturation
% 7.72/2.42
% 7.72/2.42 % (4804)Memory used [KB]: 7164
% 7.72/2.42 % (4804)Time elapsed: 0.091 s
% 7.72/2.42 % (4804)Instructions burned: 299 (million)
% 7.72/2.42 % (4804)------------------------------
% 7.72/2.42 % (4804)------------------------------
% 7.72/2.43 % (4854)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_4609 for (2991ds/164Mi)
% 7.72/2.44 % (4844)Instruction limit reached!
% 7.72/2.44 % (4844)------------------------------
% 7.72/2.44 % (4844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.44 % (4844)Termination reason: Unknown
% 7.72/2.44 % (4844)Termination phase: Saturation
% 7.72/2.44
% 7.72/2.44 % (4844)Memory used [KB]: 6780
% 7.72/2.44 % (4844)Time elapsed: 0.035 s
% 7.72/2.44 % (4844)Instructions burned: 115 (million)
% 7.72/2.44 % (4844)------------------------------
% 7.72/2.44 % (4844)------------------------------
% 7.72/2.45 % (4793)Instruction limit reached!
% 7.72/2.45 % (4793)------------------------------
% 7.72/2.45 % (4793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.45 % (4793)Termination reason: Unknown
% 7.72/2.45 % (4793)Termination phase: Saturation
% 7.72/2.45
% 7.72/2.45 % (4793)Memory used [KB]: 7675
% 7.72/2.45 % (4793)Time elapsed: 0.146 s
% 7.72/2.45 % (4793)Instructions burned: 458 (million)
% 7.72/2.45 % (4793)------------------------------
% 7.72/2.45 % (4793)------------------------------
% 7.72/2.45 % (4861)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_4609 for (2991ds/50Mi)
% 7.72/2.46 % (4863)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_4609 for (2991ds/368Mi)
% 7.72/2.47 % (4840)Instruction limit reached!
% 7.72/2.47 % (4840)------------------------------
% 7.72/2.47 % (4840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.47 % (4840)Termination reason: Unknown
% 7.72/2.47 % (4840)Termination phase: Saturation
% 7.72/2.47
% 7.72/2.47 % (4840)Memory used [KB]: 7291
% 7.72/2.47 % (4840)Time elapsed: 0.065 s
% 7.72/2.47 % (4840)Instructions burned: 217 (million)
% 7.72/2.47 % (4840)------------------------------
% 7.72/2.47 % (4840)------------------------------
% 7.72/2.47 % (4861)Instruction limit reached!
% 7.72/2.47 % (4861)------------------------------
% 7.72/2.47 % (4861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.47 % (4861)Termination reason: Unknown
% 7.72/2.47 % (4861)Termination phase: Property scanning
% 7.72/2.47
% 7.72/2.47 % (4861)Memory used [KB]: 2046
% 7.72/2.47 % (4861)Time elapsed: 0.015 s
% 7.72/2.47 % (4861)Instructions burned: 52 (million)
% 7.72/2.47 % (4861)------------------------------
% 7.72/2.47 % (4861)------------------------------
% 7.72/2.47 % (4848)Instruction limit reached!
% 7.72/2.47 % (4848)------------------------------
% 7.72/2.47 % (4848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.47 % (4848)Termination reason: Unknown
% 7.72/2.47 % (4848)Termination phase: Saturation
% 7.72/2.47
% 7.72/2.47 % (4848)Memory used [KB]: 6908
% 7.72/2.47 % (4848)Time elapsed: 0.054 s
% 7.72/2.47 % (4848)Instructions burned: 184 (million)
% 7.72/2.47 % (4848)------------------------------
% 7.72/2.47 % (4848)------------------------------
% 7.72/2.47 % (4854)Instruction limit reached!
% 7.72/2.47 % (4854)------------------------------
% 7.72/2.47 % (4854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.47 % (4854)Termination reason: Unknown
% 7.72/2.47 % (4854)Termination phase: Saturation
% 7.72/2.47
% 7.72/2.47 % (4854)Memory used [KB]: 2302
% 7.72/2.47 % (4854)Time elapsed: 0.049 s
% 7.72/2.47 % (4854)Instructions burned: 166 (million)
% 7.72/2.47 % (4854)------------------------------
% 7.72/2.47 % (4854)------------------------------
% 7.72/2.48 % (4872)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_4609 for (2991ds/1021Mi)
% 7.72/2.48 % (4873)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_4609 for (2991ds/267Mi)
% 7.72/2.48 % (4874)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_4609 for (2991ds/204Mi)
% 7.72/2.48 % (4875)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_4609 for (2991ds/26Mi)
% 7.72/2.49 % (4875)Instruction limit reached!
% 7.72/2.49 % (4875)------------------------------
% 7.72/2.49 % (4875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.49 % (4875)Termination reason: Unknown
% 7.72/2.49 % (4875)Termination phase: shuffling
% 7.72/2.49
% 7.72/2.49 % (4875)Memory used [KB]: 1791
% 7.72/2.49 % (4875)Time elapsed: 0.008 s
% 7.72/2.49 % (4875)Instructions burned: 27 (million)
% 7.72/2.49 % (4875)------------------------------
% 7.72/2.49 % (4875)------------------------------
% 8.40/2.50 % (4888)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_4609 for (2991ds/53Mi)
% 8.40/2.51 % (4888)Instruction limit reached!
% 8.40/2.51 % (4888)------------------------------
% 8.40/2.51 % (4888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.40/2.51 % (4888)Termination reason: Unknown
% 8.40/2.51 % (4888)Termination phase: Property scanning
% 8.40/2.51
% 8.40/2.51 % (4888)Memory used [KB]: 2046
% 8.40/2.51 % (4888)Time elapsed: 0.015 s
% 8.40/2.51 % (4888)Instructions burned: 53 (million)
% 8.40/2.51 % (4888)------------------------------
% 8.40/2.51 % (4888)------------------------------
% 8.40/2.52 % (4897)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_4609 for (2990ds/4436Mi)
% 8.40/2.54 % (4874)Instruction limit reached!
% 8.40/2.54 % (4874)------------------------------
% 8.40/2.54 % (4874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.40/2.54 % (4874)Termination reason: Unknown
% 8.40/2.54 % (4874)Termination phase: Saturation
% 8.40/2.54
% 8.40/2.54 % (4874)Memory used [KB]: 6908
% 8.40/2.54 % (4874)Time elapsed: 0.064 s
% 8.40/2.54 % (4874)Instructions burned: 205 (million)
% 8.40/2.54 % (4874)------------------------------
% 8.40/2.54 % (4874)------------------------------
% 8.40/2.55 % (4914)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_4609 for (2990ds/1539Mi)
% 8.40/2.56 % (4873)Instruction limit reached!
% 8.40/2.56 % (4873)------------------------------
% 8.40/2.56 % (4873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.40/2.56 % (4873)Termination reason: Unknown
% 8.40/2.56 % (4873)Termination phase: Saturation
% 8.40/2.56
% 8.40/2.56 % (4873)Memory used [KB]: 7291
% 8.40/2.56 % (4873)Time elapsed: 0.085 s
% 8.40/2.56 % (4873)Instructions burned: 269 (million)
% 8.40/2.56 % (4873)------------------------------
% 8.40/2.56 % (4873)------------------------------
% 8.40/2.56 % (4863)Instruction limit reached!
% 8.40/2.56 % (4863)------------------------------
% 8.40/2.56 % (4863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.40/2.56 % (4863)Termination reason: Unknown
% 8.40/2.56 % (4863)Termination phase: Saturation
% 8.40/2.56
% 8.40/2.56 % (4863)Memory used [KB]: 7675
% 8.40/2.56 % (4863)Time elapsed: 0.108 s
% 8.40/2.56 % (4863)Instructions burned: 369 (million)
% 8.40/2.56 % (4863)------------------------------
% 8.40/2.56 % (4863)------------------------------
% 8.40/2.57 % (4923)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_4609 for (2990ds/408Mi)
% 8.40/2.57 % (4924)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_4609 for (2990ds/5205Mi)
% 8.72/2.63 % (4806)Instruction limit reached!
% 8.72/2.63 % (4806)------------------------------
% 8.72/2.63 % (4806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.72/2.63 % (4806)Termination reason: Unknown
% 8.72/2.63 % (4806)Termination phase: Saturation
% 8.72/2.63
% 8.72/2.63 % (4806)Memory used [KB]: 8187
% 8.72/2.63 % (4806)Time elapsed: 0.305 s
% 8.72/2.63 % (4806)Instructions burned: 987 (million)
% 8.72/2.63 % (4806)------------------------------
% 8.72/2.63 % (4806)------------------------------
% 8.72/2.64 % (4955)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_4609 for (2989ds/1913Mi)
% 8.72/2.69 % (4923)Instruction limit reached!
% 8.72/2.69 % (4923)------------------------------
% 8.72/2.69 % (4923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.72/2.69 % (4923)Termination reason: Unknown
% 8.72/2.69 % (4923)Termination phase: Saturation
% 8.72/2.69
% 8.72/2.69 % (4923)Memory used [KB]: 7803
% 8.72/2.69 % (4923)Time elapsed: 0.121 s
% 8.72/2.69 % (4923)Instructions burned: 408 (million)
% 8.72/2.69 % (4923)------------------------------
% 8.72/2.69 % (4923)------------------------------
% 9.16/2.70 % (4975)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_4609 for (2989ds/4350Mi)
% 9.16/2.71 % (4845)Instruction limit reached!
% 9.16/2.71 % (4845)------------------------------
% 9.16/2.71 % (4845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.16/2.71 % (4845)Termination reason: Unknown
% 9.16/2.71 % (4845)Termination phase: Saturation
% 9.16/2.71
% 9.16/2.71 % (4845)Memory used [KB]: 8315
% 9.16/2.71 % (4845)Time elapsed: 0.298 s
% 9.16/2.71 % (4845)Instructions burned: 922 (million)
% 9.16/2.71 % (4845)------------------------------
% 9.16/2.71 % (4845)------------------------------
% 9.16/2.72 % (4983)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_4609 for (2989ds/68Mi)
% 9.16/2.74 % (4983)Instruction limit reached!
% 9.16/2.74 % (4983)------------------------------
% 9.16/2.74 % (4983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.16/2.74 % (4983)Termination reason: Unknown
% 9.16/2.74 % (4983)Termination phase: Function definition elimination
% 9.16/2.74
% 9.16/2.74 % (4983)Memory used [KB]: 2046
% 9.16/2.74 % (4983)Time elapsed: 0.021 s
% 9.16/2.74 % (4983)Instructions burned: 68 (million)
% 9.16/2.74 % (4983)------------------------------
% 9.16/2.74 % (4983)------------------------------
% 9.16/2.75 % (4991)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_4609 for (2988ds/358Mi)
% 9.16/2.77 % (4872)Instruction limit reached!
% 9.16/2.77 % (4872)------------------------------
% 9.16/2.77 % (4872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.16/2.77 % (4872)Termination reason: Unknown
% 9.16/2.77 % (4872)Termination phase: Saturation
% 9.16/2.77
% 9.16/2.77 % (4872)Memory used [KB]: 8955
% 9.16/2.77 % (4872)Time elapsed: 0.293 s
% 9.16/2.77 % (4872)Instructions burned: 1021 (million)
% 9.16/2.77 % (4872)------------------------------
% 9.16/2.77 % (4872)------------------------------
% 9.16/2.78 % (5000)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_4609 for (2988ds/31Mi)
% 9.16/2.79 % (5000)Instruction limit reached!
% 9.16/2.79 % (5000)------------------------------
% 9.16/2.79 % (5000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.16/2.79 % (5000)Termination reason: Unknown
% 9.16/2.79 % (5000)Termination phase: Preprocessing 1
% 9.16/2.79
% 9.16/2.79 % (5000)Memory used [KB]: 1663
% 9.16/2.79 % (5000)Time elapsed: 0.011 s
% 9.16/2.79 % (5000)Instructions burned: 33 (million)
% 9.16/2.79 % (5000)------------------------------
% 9.16/2.79 % (5000)------------------------------
% 9.82/2.80 % (5001)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_4609 for (2988ds/279Mi)
% 9.82/2.82 % (5001)Refutation not found, incomplete strategy
% 9.82/2.82 % (5001)------------------------------
% 9.82/2.82 % (5001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.82/2.82 % (5001)Termination reason: Refutation not found, incomplete strategy
% 9.82/2.82
% 9.82/2.82
% 9.82/2.82 % (5001)Memory used [KB]: 6908
% 9.82/2.82 % (5001)Time elapsed: 0.029 s
% 9.82/2.82 % (5001)Instructions burned: 101 (million)
% 9.82/2.82 % (5001)------------------------------
% 9.82/2.82 % (5001)------------------------------
% 9.82/2.83 % (5010)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_4609 for (2987ds/258Mi)
% 9.82/2.86 % (4991)Instruction limit reached!
% 9.82/2.86 % (4991)------------------------------
% 9.82/2.86 % (4991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.82/2.86 % (4991)Termination reason: Unknown
% 9.82/2.86 % (4991)Termination phase: Saturation
% 9.82/2.86
% 9.82/2.86 % (4991)Memory used [KB]: 7291
% 9.82/2.86 % (4991)Time elapsed: 0.113 s
% 9.82/2.86 % (4991)Instructions burned: 358 (million)
% 9.82/2.86 % (4991)------------------------------
% 9.82/2.86 % (4991)------------------------------
% 9.82/2.87 % (5026)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_4609 for (2987ds/26Mi)
% 9.82/2.88 % (5026)Instruction limit reached!
% 9.82/2.88 % (5026)------------------------------
% 9.82/2.88 % (5026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.82/2.88 % (5026)Termination reason: Unknown
% 9.82/2.88 % (5026)Termination phase: shuffling
% 9.82/2.88
% 9.82/2.88 % (5026)Memory used [KB]: 1791
% 9.82/2.88 % (5026)Time elapsed: 0.008 s
% 9.82/2.88 % (5026)Instructions burned: 26 (million)
% 9.82/2.88 % (5026)------------------------------
% 9.82/2.88 % (5026)------------------------------
% 9.82/2.88 % (5039)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_4609 for (2987ds/995Mi)
% 10.00/2.91 % (5010)Instruction limit reached!
% 10.00/2.91 % (5010)------------------------------
% 10.00/2.91 % (5010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.91 % (5010)Termination reason: Unknown
% 10.00/2.91 % (5010)Termination phase: Saturation
% 10.00/2.91
% 10.00/2.91 % (5010)Memory used [KB]: 7291
% 10.00/2.91 % (5010)Time elapsed: 0.081 s
% 10.00/2.91 % (5010)Instructions burned: 260 (million)
% 10.00/2.91 % (5010)------------------------------
% 10.00/2.91 % (5010)------------------------------
% 10.00/2.92 % (5054)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_4609 for (2986ds/373Mi)
% 10.00/2.98 % (4914)Instruction limit reached!
% 10.00/2.98 % (4914)------------------------------
% 10.00/2.98 % (4914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.00/2.98 % (4914)Termination reason: Unknown
% 10.00/2.98 % (4914)Termination phase: Saturation
% 10.00/2.98
% 10.00/2.98 % (4914)Memory used [KB]: 9466
% 10.00/2.98 % (4914)Time elapsed: 0.428 s
% 10.00/2.98 % (4914)Instructions burned: 1540 (million)
% 10.00/2.98 % (4914)------------------------------
% 10.00/2.98 % (4914)------------------------------
% 10.00/2.99 % (5055)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_4609 for (2986ds/253Mi)
% 12.44/3.04 % (5054)Instruction limit reached!
% 12.44/3.04 % (5054)------------------------------
% 12.44/3.04 % (5054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.44/3.04 % (5054)Termination reason: Unknown
% 12.44/3.04 % (5054)Termination phase: Saturation
% 12.44/3.04
% 12.44/3.04 % (5054)Memory used [KB]: 7291
% 12.44/3.04 % (5054)Time elapsed: 0.121 s
% 12.44/3.04 % (5054)Instructions burned: 375 (million)
% 12.44/3.04 % (5054)------------------------------
% 12.44/3.04 % (5054)------------------------------
% 12.44/3.05 % (5056)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_4609 for (2985ds/832Mi)
% 12.44/3.06 % (5055)Instruction limit reached!
% 12.44/3.06 % (5055)------------------------------
% 12.44/3.06 % (5055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.44/3.06 % (5055)Termination reason: Unknown
% 12.44/3.06 % (5055)Termination phase: Saturation
% 12.44/3.06
% 12.44/3.06 % (5055)Memory used [KB]: 7419
% 12.44/3.06 % (5055)Time elapsed: 0.073 s
% 12.44/3.06 % (5055)Instructions burned: 253 (million)
% 12.44/3.06 % (5055)------------------------------
% 12.44/3.06 % (5055)------------------------------
% 12.44/3.07 % (5057)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_4609 for (2985ds/668Mi)
% 13.02/3.19 % (5039)Instruction limit reached!
% 13.02/3.19 % (5039)------------------------------
% 13.02/3.19 % (5039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.02/3.19 % (5039)Termination reason: Unknown
% 13.02/3.19 % (5039)Termination phase: Saturation
% 13.02/3.19
% 13.02/3.19 % (5039)Memory used [KB]: 9083
% 13.02/3.19 % (5039)Time elapsed: 0.304 s
% 13.02/3.19 % (5039)Instructions burned: 995 (million)
% 13.02/3.19 % (5039)------------------------------
% 13.02/3.19 % (5039)------------------------------
% 13.40/3.20 % (5058)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_4609 for (2984ds/40Mi)
% 13.40/3.21 % (5058)Instruction limit reached!
% 13.40/3.21 % (5058)------------------------------
% 13.40/3.21 % (5058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.40/3.21 % (5058)Termination reason: Unknown
% 13.40/3.21 % (5058)Termination phase: Property scanning
% 13.40/3.21
% 13.40/3.21 % (5058)Memory used [KB]: 2046
% 13.40/3.21 % (5058)Time elapsed: 0.013 s
% 13.40/3.21 % (5058)Instructions burned: 43 (million)
% 13.40/3.21 % (5058)------------------------------
% 13.40/3.21 % (5058)------------------------------
% 13.40/3.22 % (5059)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_4609 for (2983ds/294Mi)
% 13.40/3.23 % (4955)Instruction limit reached!
% 13.40/3.23 % (4955)------------------------------
% 13.40/3.23 % (4955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.40/3.23 % (4955)Termination reason: Unknown
% 13.40/3.23 % (4955)Termination phase: Saturation
% 13.40/3.23
% 13.40/3.23 % (4955)Memory used [KB]: 3326
% 13.40/3.23 % (4955)Time elapsed: 0.593 s
% 13.40/3.23 % (4955)Instructions burned: 1915 (million)
% 13.40/3.23 % (4955)------------------------------
% 13.40/3.23 % (4955)------------------------------
% 13.40/3.24 % (5059)Refutation not found, incomplete strategy
% 13.40/3.24 % (5059)------------------------------
% 13.40/3.24 % (5059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.40/3.24 % (5059)Termination reason: Refutation not found, incomplete strategy
% 13.40/3.24
% 13.40/3.24
% 13.40/3.24 % (5059)Memory used [KB]: 6652
% 13.40/3.24 % (5059)Time elapsed: 0.022 s
% 13.40/3.24 % (5059)Instructions burned: 79 (million)
% 13.40/3.24 % (5059)------------------------------
% 13.40/3.24 % (5059)------------------------------
% 13.40/3.24 % (5060)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_4609 for (2983ds/187Mi)
% 13.40/3.25 % (5061)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_4609 for (2983ds/371Mi)
% 13.40/3.27 % (5057)Instruction limit reached!
% 13.40/3.27 % (5057)------------------------------
% 13.40/3.27 % (5057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.40/3.27 % (5057)Termination reason: Unknown
% 13.40/3.27 % (5057)Termination phase: Saturation
% 13.40/3.27
% 13.40/3.27 % (5057)Memory used [KB]: 14072
% 13.40/3.27 % (5057)Time elapsed: 0.201 s
% 13.40/3.27 % (5057)Instructions burned: 668 (million)
% 13.40/3.27 % (5057)------------------------------
% 13.40/3.27 % (5057)------------------------------
% 13.40/3.28 % (5062)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_4609 for (2983ds/1827Mi)
% 14.01/3.30 % (5060)Instruction limit reached!
% 14.01/3.30 % (5060)------------------------------
% 14.01/3.30 % (5060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.01/3.30 % (5060)Termination reason: Unknown
% 14.01/3.30 % (5060)Termination phase: Saturation
% 14.01/3.30
% 14.01/3.30 % (5060)Memory used [KB]: 7164
% 14.01/3.30 % (5060)Time elapsed: 0.055 s
% 14.01/3.30 % (5060)Instructions burned: 190 (million)
% 14.01/3.30 % (5060)------------------------------
% 14.01/3.30 % (5060)------------------------------
% 14.01/3.31 % (5063)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_4609 for (2983ds/70Mi)
% 14.01/3.31 % (5056)Instruction limit reached!
% 14.01/3.31 % (5056)------------------------------
% 14.01/3.31 % (5056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.01/3.31 % (5056)Termination reason: Unknown
% 14.01/3.31 % (5056)Termination phase: Saturation
% 14.01/3.31
% 14.01/3.31 % (5056)Memory used [KB]: 7931
% 14.01/3.31 % (5056)Time elapsed: 0.283 s
% 14.01/3.31 % (5056)Instructions burned: 834 (million)
% 14.01/3.31 % (5056)------------------------------
% 14.01/3.31 % (5056)------------------------------
% 14.01/3.32 % (5064)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_4609 for (2982ds/316Mi)
% 14.01/3.33 % (5063)Instruction limit reached!
% 14.01/3.33 % (5063)------------------------------
% 14.01/3.33 % (5063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.01/3.33 % (5063)Termination reason: Unknown
% 14.01/3.33 % (5063)Termination phase: Property scanning
% 14.01/3.33
% 14.01/3.33 % (5063)Memory used [KB]: 2046
% 14.01/3.33 % (5063)Time elapsed: 0.021 s
% 14.01/3.33 % (5063)Instructions burned: 73 (million)
% 14.01/3.33 % (5063)------------------------------
% 14.01/3.33 % (5063)------------------------------
% 14.01/3.34 % (5065)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_4609 for (2982ds/932Mi)
% 14.01/3.36 % (5064)Refutation not found, incomplete strategy
% 14.01/3.36 % (5064)------------------------------
% 14.01/3.36 % (5064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.01/3.36 % (5064)Termination reason: Refutation not found, incomplete strategy
% 14.01/3.36
% 14.01/3.36
% 14.01/3.36 % (5064)Memory used [KB]: 6908
% 14.01/3.36 % (5064)Time elapsed: 0.039 s
% 14.01/3.36 % (5064)Instructions burned: 141 (million)
% 14.01/3.36 % (5064)------------------------------
% 14.01/3.36 % (5064)------------------------------
% 14.01/3.37 % (5061)Instruction limit reached!
% 14.01/3.37 % (5061)------------------------------
% 14.01/3.37 % (5061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.01/3.37 % (5061)Termination reason: Unknown
% 14.01/3.37 % (5061)Termination phase: Saturation
% 14.01/3.37
% 14.01/3.37 % (5061)Memory used [KB]: 7291
% 14.01/3.37 % (5061)Time elapsed: 0.119 s
% 14.01/3.37 % (5061)Instructions burned: 373 (million)
% 14.01/3.37 % (5061)------------------------------
% 14.01/3.37 % (5061)------------------------------
% 14.01/3.37 % (5066)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_4609 for (2982ds/4714Mi)
% 14.01/3.38 % (5067)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_4609 for (2982ds/8250Mi)
% 14.85/3.41 % (5066)Refutation not found, incomplete strategy
% 14.85/3.41 % (5066)------------------------------
% 14.85/3.41 % (5066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.85/3.41 % (5066)Termination reason: Refutation not found, incomplete strategy
% 14.85/3.41
% 14.85/3.41
% 14.85/3.41 % (5066)Memory used [KB]: 7164
% 14.85/3.41 % (5066)Time elapsed: 0.037 s
% 14.85/3.41 % (5066)Instructions burned: 128 (million)
% 14.85/3.41 % (5066)------------------------------
% 14.85/3.41 % (5066)------------------------------
% 14.85/3.42 % (5068)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_4609 for (2981ds/770Mi)
% 14.85/3.43 % (5068)Refutation not found, incomplete strategy
% 14.85/3.43 % (5068)------------------------------
% 14.85/3.43 % (5068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.85/3.43 % (5068)Termination reason: Refutation not found, incomplete strategy
% 14.85/3.43
% 14.85/3.43
% 14.85/3.43 % (5068)Memory used [KB]: 6524
% 14.85/3.43 % (5068)Time elapsed: 0.019 s
% 14.85/3.43 % (5068)Instructions burned: 61 (million)
% 14.85/3.43 % (5068)------------------------------
% 14.85/3.43 % (5068)------------------------------
% 14.85/3.44 % (5069)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_4609 for (2981ds/794Mi)
% 15.54/3.63 % (5065)Instruction limit reached!
% 15.54/3.63 % (5065)------------------------------
% 15.54/3.63 % (5065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/3.63 % (5065)Termination reason: Unknown
% 15.54/3.63 % (5065)Termination phase: Saturation
% 15.54/3.63
% 15.54/3.63 % (5065)Memory used [KB]: 9850
% 15.54/3.63 % (5065)Time elapsed: 0.291 s
% 15.54/3.63 % (5065)Instructions burned: 934 (million)
% 15.54/3.63 % (5065)------------------------------
% 15.54/3.63 % (5065)------------------------------
% 15.54/3.64 % (5070)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_4609 for (2979ds/464Mi)
% 15.54/3.69 % (5069)Instruction limit reached!
% 15.54/3.69 % (5069)------------------------------
% 15.54/3.69 % (5069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/3.69 % (5069)Termination reason: Unknown
% 15.54/3.69 % (5069)Termination phase: Saturation
% 15.54/3.69
% 15.54/3.69 % (5069)Memory used [KB]: 6140
% 15.54/3.69 % (5069)Time elapsed: 0.248 s
% 15.54/3.69 % (5069)Instructions burned: 795 (million)
% 15.54/3.69 % (5069)------------------------------
% 15.54/3.69 % (5069)------------------------------
% 16.39/3.70 % (5071)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_4609 for (2979ds/1376Mi)
% 16.39/3.79 % (5070)Instruction limit reached!
% 16.39/3.79 % (5070)------------------------------
% 16.39/3.79 % (5070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.39/3.79 % (5070)Termination reason: Unknown
% 16.39/3.79 % (5070)Termination phase: Saturation
% 16.39/3.79
% 16.39/3.79 % (5070)Memory used [KB]: 7547
% 16.39/3.79 % (5070)Time elapsed: 0.149 s
% 16.39/3.79 % (5070)Instructions burned: 465 (million)
% 16.39/3.79 % (5070)------------------------------
% 16.39/3.79 % (5070)------------------------------
% 16.39/3.79 % (5072)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_4609 for (2978ds/906Mi)
% 16.84/3.87 % (5062)Instruction limit reached!
% 16.84/3.87 % (5062)------------------------------
% 16.84/3.87 % (5062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.84/3.87 % (5062)Termination reason: Unknown
% 16.84/3.87 % (5062)Termination phase: Saturation
% 16.84/3.87
% 16.84/3.87 % (5062)Memory used [KB]: 9210
% 16.84/3.87 % (5062)Time elapsed: 0.593 s
% 16.84/3.87 % (5062)Instructions burned: 1828 (million)
% 16.84/3.87 % (5062)------------------------------
% 16.84/3.87 % (5062)------------------------------
% 16.84/3.88 % (5073)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_4609 for (2977ds/434Mi)
% 16.84/3.88 % (4975)Instruction limit reached!
% 16.84/3.88 % (4975)------------------------------
% 16.84/3.88 % (4975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.84/3.88 % (4975)Termination reason: Unknown
% 16.84/3.88 % (4975)Termination phase: Saturation
% 16.84/3.88
% 16.84/3.88 % (4975)Memory used [KB]: 11129
% 16.84/3.88 % (4975)Time elapsed: 1.184 s
% 16.84/3.88 % (4975)Instructions burned: 4350 (million)
% 16.84/3.88 % (4975)------------------------------
% 16.84/3.88 % (4975)------------------------------
% 16.84/3.89 % (5074)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_4609 for (2977ds/865Mi)
% 17.75/3.91 % (4897)Instruction limit reached!
% 17.75/3.91 % (4897)------------------------------
% 17.75/3.91 % (4897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.75/3.91 % (4897)Termination reason: Unknown
% 17.75/3.91 % (4897)Termination phase: Saturation
% 17.75/3.91
% 17.75/3.91 % (4897)Memory used [KB]: 14839
% 17.75/3.91 % (4897)Time elapsed: 1.391 s
% 17.75/3.91 % (4897)Instructions burned: 4437 (million)
% 17.75/3.91 % (4897)------------------------------
% 17.75/3.91 % (4897)------------------------------
% 17.75/3.92 % (5075)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_4609 for (2976ds/593Mi)
% 17.75/4.01 % (5073)Instruction limit reached!
% 17.75/4.01 % (5073)------------------------------
% 17.75/4.01 % (5073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.75/4.01 % (5073)Termination reason: Unknown
% 17.75/4.01 % (5073)Termination phase: Saturation
% 17.75/4.01
% 17.75/4.01 % (5073)Memory used [KB]: 7675
% 17.75/4.01 % (5073)Time elapsed: 0.128 s
% 17.75/4.01 % (5073)Instructions burned: 437 (million)
% 17.75/4.01 % (5073)------------------------------
% 17.75/4.01 % (5073)------------------------------
% 17.75/4.02 % (5076)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_4609 for (2975ds/443Mi)
% 19.45/4.10 % (5072)Instruction limit reached!
% 19.45/4.10 % (5072)------------------------------
% 19.45/4.10 % (5072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.45/4.10 % (5072)Termination reason: Unknown
% 19.45/4.10 % (5072)Termination phase: Saturation
% 19.45/4.10
% 19.45/4.10 % (5072)Memory used [KB]: 11001
% 19.45/4.10 % (5072)Time elapsed: 0.306 s
% 19.45/4.10 % (5072)Instructions burned: 907 (million)
% 19.45/4.10 % (5072)------------------------------
% 19.45/4.10 % (5072)------------------------------
% 19.45/4.11 % (5075)Instruction limit reached!
% 19.45/4.11 % (5075)------------------------------
% 19.45/4.11 % (5075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.45/4.11 % (5075)Termination reason: Unknown
% 19.45/4.11 % (5075)Termination phase: Saturation
% 19.45/4.11
% 19.45/4.11 % (5075)Memory used [KB]: 8315
% 19.45/4.11 % (5075)Time elapsed: 0.183 s
% 19.45/4.11 % (5075)Instructions burned: 594 (million)
% 19.45/4.11 % (5075)------------------------------
% 19.45/4.11 % (5075)------------------------------
% 19.45/4.11 % (5077)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_4609 for (2974ds/594Mi)
% 19.45/4.12 % (5078)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_4609 for (2974ds/327Mi)
% 19.45/4.12 % (5071)Instruction limit reached!
% 19.45/4.12 % (5071)------------------------------
% 19.45/4.12 % (5071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.45/4.12 % (5071)Termination reason: Unknown
% 19.45/4.12 % (5071)Termination phase: Saturation
% 19.45/4.12
% 19.45/4.12 % (5071)Memory used [KB]: 12537
% 19.45/4.12 % (5071)Time elapsed: 0.422 s
% 19.45/4.12 % (5071)Instructions burned: 1378 (million)
% 19.45/4.12 % (5071)------------------------------
% 19.45/4.12 % (5071)------------------------------
% 20.06/4.13 % (5079)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_4609 for (2974ds/5411Mi)
% 20.06/4.14 % (4924)Instruction limit reached!
% 20.06/4.14 % (4924)------------------------------
% 20.06/4.14 % (4924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.06/4.14 % (4924)Termination reason: Unknown
% 20.06/4.14 % (4924)Termination phase: Saturation
% 20.06/4.14
% 20.06/4.14 % (4924)Memory used [KB]: 15223
% 20.06/4.14 % (4924)Time elapsed: 1.572 s
% 20.06/4.14 % (4924)Instructions burned: 5205 (million)
% 20.06/4.14 % (4924)------------------------------
% 20.06/4.14 % (4924)------------------------------
% 20.06/4.15 % (5080)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_4609 for (2974ds/1762Mi)
% 20.06/4.15 % (5079)Refutation not found, incomplete strategy
% 20.06/4.15 % (5079)------------------------------
% 20.06/4.15 % (5079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.06/4.15 % (5079)Termination reason: Refutation not found, incomplete strategy
% 20.06/4.15
% 20.06/4.15
% 20.06/4.15 % (5079)Memory used [KB]: 6524
% 20.06/4.15 % (5079)Time elapsed: 0.023 s
% 20.06/4.15 % (5079)Instructions burned: 73 (million)
% 20.06/4.15 % (5079)------------------------------
% 20.06/4.15 % (5079)------------------------------
% 20.06/4.16 % (5076)Instruction limit reached!
% 20.06/4.16 % (5076)------------------------------
% 20.06/4.16 % (5076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.06/4.16 % (5076)Termination reason: Unknown
% 20.06/4.16 % (5076)Termination phase: Saturation
% 20.06/4.16
% 20.06/4.16 % (5076)Memory used [KB]: 7419
% 20.06/4.16 % (5076)Time elapsed: 0.141 s
% 20.06/4.16 % (5076)Instructions burned: 444 (million)
% 20.06/4.16 % (5076)------------------------------
% 20.06/4.16 % (5076)------------------------------
% 20.06/4.16 % (5074)Instruction limit reached!
% 20.06/4.16 % (5074)------------------------------
% 20.06/4.16 % (5074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.06/4.16 % (5074)Termination reason: Unknown
% 20.06/4.16 % (5074)Termination phase: Saturation
% 20.06/4.16
% 20.06/4.16 % (5074)Memory used [KB]: 8699
% 20.06/4.16 % (5074)Time elapsed: 0.273 s
% 20.06/4.16 % (5074)Instructions burned: 866 (million)
% 20.06/4.16 % (5074)------------------------------
% 20.06/4.16 % (5074)------------------------------
% 20.06/4.16 % (5081)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_4609 for (2974ds/96Mi)
% 20.06/4.17 % (5082)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_4609 for (2974ds/503Mi)
% 20.06/4.17 % (5083)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_4609 for (2974ds/90Mi)
% 20.06/4.19 % (5081)Instruction limit reached!
% 20.06/4.19 % (5081)------------------------------
% 20.06/4.19 % (5081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.06/4.19 % (5081)Termination reason: Unknown
% 20.06/4.19 % (5081)Termination phase: Saturation
% 20.06/4.19
% 20.06/4.19 % (5081)Memory used [KB]: 6652
% 20.06/4.19 % (5081)Time elapsed: 0.027 s
% 20.06/4.19 % (5081)Instructions burned: 96 (million)
% 20.06/4.19 % (5081)------------------------------
% 20.06/4.19 % (5081)------------------------------
% 20.43/4.20 % (5084)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_4609 for (2974ds/593Mi)
% 20.43/4.20 % (5083)Instruction limit reached!
% 20.43/4.20 % (5083)------------------------------
% 20.43/4.20 % (5083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.43/4.20 % (5083)Termination reason: Unknown
% 20.43/4.20 % (5083)Termination phase: Saturation
% 20.43/4.20
% 20.43/4.20 % (5083)Memory used [KB]: 6652
% 20.43/4.20 % (5083)Time elapsed: 0.028 s
% 20.43/4.20 % (5083)Instructions burned: 92 (million)
% 20.43/4.20 % (5083)------------------------------
% 20.43/4.20 % (5083)------------------------------
% 20.43/4.21 % (5085)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_4609 for (2974ds/1512Mi)
% 20.43/4.22 % (5078)Instruction limit reached!
% 20.43/4.22 % (5078)------------------------------
% 20.43/4.22 % (5078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.43/4.22 % (5078)Termination reason: Unknown
% 20.43/4.22 % (5078)Termination phase: Saturation
% 20.43/4.22
% 20.43/4.22 % (5078)Memory used [KB]: 7675
% 20.43/4.22 % (5078)Time elapsed: 0.105 s
% 20.43/4.22 % (5078)Instructions burned: 329 (million)
% 20.43/4.22 % (5078)------------------------------
% 20.43/4.22 % (5078)------------------------------
% 20.43/4.23 % (5086)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_4609 for (2973ds/569Mi)
% 20.43/4.29 % (5085)First to succeed.
% 20.43/4.29 % (5085)Refutation found. Thanks to Tanya!
% 20.43/4.29 % SZS status Theorem for DTF2THF_4609
% 20.43/4.29 % SZS output start Proof for DTF2THF_4609
% 20.43/4.29 thf(type_def_5, type, configuration_ext: ($tType * $tType * $tType * $tType) > $tType).
% 20.43/4.29 thf(type_def_6, type, message: ($tType * $tType) > $tType).
% 20.43/4.29 thf(type_def_7, type, nat: $tType).
% 20.43/4.29 thf(type_def_9, type, product_unit: $tType).
% 20.43/4.29 thf(type_def_10, type, list: ($tType) > $tType).
% 20.43/4.29 thf(type_def_11, type, set: ($tType) > $tType).
% 20.43/4.29 thf(type_def_12, type, p: $tType).
% 20.43/4.29 thf(type_def_13, type, v: $tType).
% 20.43/4.29 thf(type_def_14, type, s: $tType).
% 20.43/4.29 thf(func_def_0, type, configuration_ext: ($tType * $tType * $tType * $tType) > $tType).
% 20.43/4.29 thf(func_def_1, type, message: ($tType * $tType) > $tType).
% 20.43/4.29 thf(func_def_2, type, product_unit: $tType).
% 20.43/4.29 thf(func_def_3, type, list: ($tType) > $tType).
% 20.43/4.29 thf(func_def_4, type, set: ($tType) > $tType).
% 20.43/4.29 thf(func_def_5, type, nat: $tType).
% 20.43/4.29 thf(func_def_6, type, v: $tType).
% 20.43/4.29 thf(func_def_7, type, s: $tType).
% 20.43/4.29 thf(func_def_8, type, p: $tType).
% 20.43/4.29 thf(func_def_9, type, type: !>[X0: $tType]:($o)).
% 20.43/4.29 thf(func_def_10, type, size: !>[X0: $tType]:($o)).
% 20.43/4.29 thf(func_def_11, type, one: !>[X0: $tType]:($o)).
% 20.43/4.29 thf(func_def_12, type, zero: !>[X0: $tType]:($o)).
% 20.43/4.29 thf(func_def_13, type, neg_numeral: !>[X0: $tType]:($o)).
% 20.43/4.29 thf(func_def_14, type, order: !>[X0: $tType]:($o)).
% 20.43/4.29 thf(func_def_15, type, group_add: !>[X0: $tType]:($o)).
% 20.43/4.29 thf(func_def_16, type, wellorder: !>[X0: $tType]:($o)).
% 20.43/4.29 thf(func_def_17, type, comm_monoid_diff: !>[X0: $tType]:($o)).
% 20.43/4.29 thf(func_def_18, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 20.43/4.29 thf(func_def_19, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 20.43/4.29 thf(func_def_20, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 20.43/4.29 thf(func_def_21, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 20.43/4.29 thf(func_def_22, type, msgs: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(configuration_ext @ X0 @ X1 @ X2 @ X3 > message @ X0 @ X1 > nat)).
% 20.43/4.29 thf(func_def_23, type, enabled: !>[X0: $tType, X1: $tType, X2: $tType]:(configuration_ext @ X0 @ X1 @ X2 @ product_unit > message @ X0 @ X1 > $o)).
% 20.43/4.29 thf(func_def_24, type, firstOccurrence: !>[X0: $tType, X1: $tType, X2: $tType]:(list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit > list @ message @ X0 @ X1 > message @ X0 @ X1 > nat > $o)).
% 20.43/4.29 thf(func_def_25, type, minimalEnabled: !>[X0: $tType, X1: $tType, X2: $tType]:(list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit > list @ message @ X0 @ X1 > message @ X0 @ X1 > $o)).
% 20.43/4.29 thf(func_def_26, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 20.43/4.29 thf(func_def_27, type, one_one: !>[X0: $tType]:(X0)).
% 20.43/4.29 thf(func_def_28, type, zero_zero: !>[X0: $tType]:(X0)).
% 20.43/4.29 thf(func_def_29, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 20.43/4.29 thf(func_def_30, type, prefixList: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 20.43/4.29 thf(func_def_31, type, last: !>[X0: $tType]:(list @ X0 > X0)).
% 20.43/4.29 thf(func_def_32, type, nil: !>[X0: $tType]:(list @ X0)).
% 20.43/4.29 thf(func_def_33, type, tl: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 20.43/4.29 thf(func_def_34, type, list_ex: !>[X0: $tType]:((X0 > $o) > list @ X0 > $o)).
% 20.43/4.29 thf(func_def_35, type, list_ex1: !>[X0: $tType]:((X0 > $o) > list @ X0 > $o)).
% 20.43/4.29 thf(func_def_36, type, nth: !>[X0: $tType]:(list @ X0 > nat > X0)).
% 20.43/4.29 thf(func_def_37, type, remdups_adj: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 20.43/4.29 thf(func_def_38, type, suc: nat > nat).
% 20.43/4.29 thf(func_def_39, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 20.43/4.29 thf(func_def_40, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 20.43/4.29 thf(func_def_41, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 20.43/4.29 thf(func_def_42, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 20.43/4.29 thf(func_def_43, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 20.43/4.29 thf(func_def_44, type, consumedMsg: message @ p @ v).
% 20.43/4.29 thf(func_def_45, type, fe: nat > list @ configuration_ext @ p @ v @ s @ product_unit).
% 20.43/4.29 thf(func_def_46, type, firstOccSet: nat > set @ message @ p @ v).
% 20.43/4.29 thf(func_def_47, type, ft: nat > list @ message @ p @ v).
% 20.43/4.29 thf(func_def_48, type, index: nat).
% 20.43/4.29 thf(func_def_49, type, msg: message @ p @ v).
% 20.43/4.29 thf(func_def_50, type, n0: nat).
% 20.43/4.29 thf(func_def_51, type, n1: nat).
% 20.43/4.29 thf(func_def_52, type, nMsg: nat).
% 20.43/4.29 thf(func_def_53, type, n: nat).
% 20.43/4.29 thf(func_def_68, type, sK0: !>[X0: $tType]:((X0 > $o) > X0)).
% 20.43/4.29 thf(func_def_69, type, sK1: !>[X0: $tType]:((X0 > $o) > X0)).
% 20.43/4.29 thf(func_def_70, type, sP2: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > $o).
% 20.43/4.29 thf(func_def_71, type, sP3: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > $o).
% 20.43/4.29 thf(func_def_72, type, sK4: (nat > $o) > nat).
% 20.43/4.29 thf(func_def_73, type, sK5: nat > nat > nat).
% 20.43/4.29 thf(func_def_74, type, sK6: message @ p @ v > nat).
% 20.43/4.29 thf(func_def_75, type, sK7: nat > nat > nat).
% 20.43/4.29 thf(func_def_76, type, sK8: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 20.43/4.29 thf(func_def_77, type, sK9: nat).
% 20.43/4.29 thf(func_def_78, type, sK10: nat).
% 20.43/4.29 thf(func_def_79, type, sK11: nat > nat).
% 20.43/4.29 thf(func_def_80, type, sK12: nat > nat).
% 20.43/4.29 thf(func_def_81, type, sK13: (nat > $o) > nat).
% 20.43/4.29 thf(func_def_82, type, sK14: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 20.43/4.29 thf(func_def_83, type, sK15: (nat > $o) > nat > nat).
% 20.43/4.29 thf(func_def_84, type, sK16: (nat > $o) > nat > nat).
% 20.43/4.29 thf(func_def_85, type, sK17: nat > nat).
% 20.43/4.29 thf(func_def_86, type, sK18: (nat > $o) > nat > nat > nat).
% 20.43/4.29 thf(func_def_87, type, sK19: !>[X0: $tType]:(list @ X0 > list @ X0 > nat)).
% 20.43/4.29 thf(func_def_88, type, sK20: (nat > nat > $o) > nat).
% 20.43/4.29 thf(func_def_89, type, sK21: (nat > nat > $o) > nat).
% 20.43/4.29 thf(func_def_90, type, sK22: (nat > nat > $o) > nat).
% 20.43/4.29 thf(func_def_91, type, sK23: (nat > nat > $o) > nat).
% 20.43/4.29 thf(func_def_92, type, sK24: (nat > $o) > nat).
% 20.43/4.29 thf(func_def_93, type, sK25: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X0) > X1)).
% 20.43/4.29 thf(func_def_94, type, sK26: nat > (nat > $o) > nat).
% 20.43/4.29 thf(func_def_95, type, sK27: (nat > $o) > nat).
% 20.43/4.29 thf(func_def_96, type, sK28: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 20.43/4.29 thf(func_def_97, type, sK29: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 20.43/4.29 thf(func_def_98, type, sK30: !>[X0: $tType]:((nat > X0) > nat)).
% 20.43/4.29 thf(func_def_99, type, sK31: message @ p @ v > nat > nat > nat).
% 20.43/4.29 thf(func_def_100, type, sK32: (nat > $o) > nat).
% 20.43/4.29 thf(func_def_101, type, sK33: nat > nat).
% 20.43/4.29 thf(func_def_102, type, sK34: (nat > $o) > nat > nat).
% 20.43/4.29 thf(func_def_103, type, sK35: (nat > $o) > nat > nat).
% 20.43/4.29 thf(func_def_104, type, sK36: (nat > $o) > nat > nat).
% 20.43/4.29 thf(func_def_105, type, sK37: (nat > $o) > nat > nat).
% 20.43/4.29 thf(func_def_106, type, sK38: (nat > $o) > nat > nat).
% 20.43/4.29 thf(func_def_107, type, sK39: (nat > $o) > nat > nat).
% 20.43/4.29 thf(func_def_108, type, sK40: !>[X0: $tType]:(nat > list @ X0)).
% 20.43/4.29 thf(func_def_109, type, sK41: (nat > nat > $o) > nat).
% 20.43/4.29 thf(func_def_110, type, sK42: (nat > nat > $o) > nat).
% 20.43/4.29 thf(func_def_111, type, sK43: (nat > nat > $o) > nat).
% 20.43/4.29 thf(func_def_112, type, sK44: (nat > nat > $o) > nat).
% 20.43/4.29 thf(func_def_113, type, sK45: (nat > nat > $o) > nat).
% 20.43/4.29 thf(func_def_114, type, sK46: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit).
% 20.43/4.29 thf(func_def_115, type, sK47: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit).
% 20.43/4.29 thf(func_def_116, type, sK48: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v).
% 20.43/4.29 thf(func_def_117, type, sK49: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > nat).
% 20.43/4.29 thf(func_def_118, type, sK50: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit).
% 20.43/4.29 thf(func_def_119, type, sK51: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit).
% 20.43/4.29 thf(func_def_120, type, sK52: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v).
% 20.43/4.29 thf(func_def_121, type, sK53: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > nat).
% 20.43/4.29 thf(func_def_122, type, sK54: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit).
% 20.43/4.29 thf(func_def_123, type, sK55: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit).
% 20.43/4.29 thf(func_def_124, type, sK56: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v).
% 20.43/4.29 thf(func_def_125, type, sK57: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit).
% 20.43/4.29 thf(func_def_126, type, sK58: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit).
% 20.43/4.29 thf(func_def_127, type, sK59: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v).
% 20.43/4.29 thf(func_def_128, type, sK60: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit).
% 20.43/4.29 thf(func_def_129, type, sK61: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit).
% 20.43/4.29 thf(func_def_130, type, sK62: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v).
% 20.43/4.29 thf(func_def_131, type, sK63: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > nat).
% 20.43/4.29 thf(func_def_132, type, sK64: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit).
% 20.43/4.29 thf(func_def_133, type, sK65: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit).
% 20.43/4.29 thf(func_def_134, type, sK66: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v).
% 20.43/4.29 thf(func_def_135, type, sK67: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > nat).
% 20.43/4.29 thf(func_def_136, type, sK68: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit).
% 20.43/4.29 thf(func_def_137, type, sK69: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit).
% 20.43/4.29 thf(func_def_138, type, sK70: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v).
% 20.43/4.29 thf(func_def_139, type, sK71: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit).
% 20.43/4.29 thf(func_def_140, type, sK72: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit).
% 20.43/4.29 thf(func_def_141, type, sK73: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v).
% 20.43/4.29 thf(func_def_142, type, sK74: (nat > $o) > nat).
% 20.43/4.29 thf(func_def_143, type, sK75: nat > nat).
% 20.43/4.29 thf(func_def_144, type, sK76: (nat > $o) > nat).
% 20.43/4.29 thf(func_def_145, type, sK77: (nat > $o) > nat).
% 20.43/4.29 thf(func_def_146, type, sK78: nat > nat > nat).
% 20.43/4.29 thf(func_def_147, type, sK79: (nat > nat > $o) > nat).
% 20.43/4.29 thf(func_def_148, type, sK80: (nat > nat > $o) > nat).
% 20.43/4.29 thf(func_def_149, type, sK81: (nat > nat > $o) > nat).
% 20.43/4.29 thf(func_def_150, type, sK82: (nat > nat > $o) > nat).
% 20.43/4.29 thf(func_def_151, type, sK83: (nat > $o) > nat).
% 20.43/4.29 thf(func_def_152, type, sK84: nat > nat > nat).
% 20.43/4.29 thf(func_def_153, type, sK85: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 20.43/4.29 thf(func_def_154, type, sK86: !>[X0: $tType]:((nat > X0) > nat)).
% 20.43/4.29 thf(func_def_155, type, sK87: !>[X0: $tType]:((nat > X0) > nat)).
% 20.43/4.29 thf(func_def_156, type, sK88: nat > (nat > $o) > nat).
% 20.43/4.29 thf(func_def_157, type, sK89: (nat > $o) > nat > nat > nat).
% 20.43/4.29 thf(func_def_158, type, sK90: (nat > $o) > nat).
% 20.43/4.29 thf(func_def_159, type, sK91: !>[X0: $tType]:((nat > X0) > nat)).
% 20.43/4.29 thf(func_def_160, type, sK92: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X0) > X1)).
% 20.43/4.29 thf(func_def_161, type, sK93: (nat > $o) > (nat > $o) > nat > nat).
% 20.43/4.29 thf(func_def_162, type, sK94: (nat > $o) > nat > nat).
% 20.43/4.29 thf(func_def_163, type, sK95: (nat > $o) > nat > nat).
% 20.43/4.29 thf(func_def_164, type, sK96: (nat > $o) > nat).
% 20.43/4.29 thf(func_def_165, type, sK97: !>[X0: $tType]:((nat > X0 > $o) > nat > list @ X0)).
% 20.43/4.29 thf(func_def_166, type, sK98: !>[X0: $tType]:((nat > X0 > $o) > nat > nat)).
% 20.43/4.29 thf(func_def_167, type, sK99: !>[X0: $tType]:(nat > (nat > X0 > $o) > X0)).
% 20.43/4.29 thf(func_def_168, type, sK100: !>[X0: $tType]:(list @ X0 > (nat > X0 > $o) > nat > nat)).
% 20.43/4.29 thf(func_def_169, type, sK101: (nat > $o) > nat > nat).
% 20.43/4.29 thf(func_def_170, type, sK102: (nat > $o) > nat > nat).
% 20.43/4.29 thf(func_def_171, type, sK103: nat).
% 20.43/4.29 thf(func_def_172, type, sK104: nat).
% 20.43/4.29 thf(func_def_173, type, sK105: (nat > nat) > nat).
% 20.43/4.29 thf(func_def_174, type, sK106: (nat > nat) > nat).
% 20.43/4.29 thf(func_def_175, type, sK107: (nat > $o) > nat).
% 20.43/4.29 thf(func_def_176, type, sK108: nat > (nat > $o) > nat).
% 20.43/4.29 thf(func_def_178, type, ph110: !>[X0: $tType]:(X0)).
% 20.43/4.29 thf(f2107,plain,(
% 20.43/4.29 $false),
% 20.43/4.29 inference(avatar_sat_refutation,[status(thm)],[f1757,f1779,f2106])).
% 20.43/4.29 thf(f2106,plain,(
% 20.43/4.29 spl109_5),
% 20.43/4.29 inference(avatar_contradiction_clause,[status(thm)],[f2105])).
% 20.43/4.29 thf(f2105,plain,(
% 20.43/4.29 $false | spl109_5),
% 20.43/4.29 inference(subsumption_resolution,[status(thm)],[f2099,f1709])).
% 20.43/4.29 thf(f1709,plain,(
% 20.43/4.29 ( ! [X1 : nat] : (((ord_less_eq @ nat @ X1 @ X1) = $true)) )),
% 20.43/4.29 inference(equality_resolution,[status(thm)],[f1528])).
% 20.43/4.29 thf(f1528,plain,(
% 20.43/4.29 ( ! [X0 : nat,X1 : nat] : ((X0 != X1) | ($true = (ord_less_eq @ nat @ X0 @ X1))) )),
% 20.43/4.29 inference(cnf_transformation,[status(thm)],[f1053])).
% 20.43/4.29 thf(f1053,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : ((X0 != X1) | ($true = (ord_less_eq @ nat @ X0 @ X1)))),
% 20.43/4.29 inference(ennf_transformation,[status(thm)],[f277])).
% 20.43/4.29 thf(f277,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : ((X0 = X1) => ($true = (ord_less_eq @ nat @ X0 @ X1)))),
% 20.43/4.29 inference(fool_elimination,[status(thm)],[f276])).
% 20.43/4.29 thf(f276,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : ((X0 = X1) => (ord_less_eq @ nat @ X0 @ X1))),
% 20.43/4.29 inference(rectify,[status(thm)],[f132])).
% 20.43/4.29 thf(f132,axiom,(
% 20.43/4.29 ! [X14 : nat,X10 : nat] : ((X10 = X14) => (ord_less_eq @ nat @ X14 @ X10))),
% 20.43/4.29 file('/export/starexec/sandbox/tmp/tmp.6wC2JEysVn/DTF2THF_4609.p',fact_131_eq__imp__le)).
% 20.43/4.29 thf(f2099,plain,(
% 20.43/4.29 ($true != (ord_less_eq @ nat @ n1 @ n1)) | spl109_5),
% 20.43/4.29 inference(superposition,[status(thm)],[f1936,f1979])).
% 20.43/4.29 thf(f1979,plain,(
% 20.43/4.29 (nMsg = n1) | spl109_5),
% 20.43/4.29 inference(subsumption_resolution,[status(thm)],[f1978,f1523])).
% 20.43/4.29 thf(f1523,plain,(
% 20.43/4.29 ((ord_less @ nat @ nMsg @ n1) != $true)),
% 20.43/4.29 inference(cnf_transformation,[status(thm)],[f847])).
% 20.43/4.29 thf(f847,plain,(
% 20.43/4.29 ((ord_less @ nat @ nMsg @ n1) != $true)),
% 20.43/4.29 inference(flattening,[status(thm)],[f672])).
% 20.43/4.29 thf(f672,plain,(
% 20.43/4.29 ~((ord_less @ nat @ nMsg @ n1) = $true)),
% 20.43/4.29 inference(fool_elimination,[status(thm)],[f671])).
% 20.43/4.29 thf(f671,plain,(
% 20.43/4.29 ~(ord_less @ nat @ nMsg @ n1)),
% 20.43/4.29 inference(rectify,[status(thm)],[f1])).
% 20.43/4.29 thf(f1,axiom,(
% 20.43/4.29 ~(ord_less @ nat @ nMsg @ n1)),
% 20.43/4.29 file('/export/starexec/sandbox/tmp/tmp.6wC2JEysVn/DTF2THF_4609.p',fact_0_AssumpGreaterOccurrence_I1_J)).
% 20.43/4.29 thf(f1978,plain,(
% 20.43/4.29 ((ord_less @ nat @ nMsg @ n1) = $true) | (nMsg = n1) | spl109_5),
% 20.43/4.29 inference(trivial_inequality_removal,[status(thm)],[f1972])).
% 20.43/4.29 thf(f1972,plain,(
% 20.43/4.29 (nMsg = n1) | ((ord_less @ nat @ nMsg @ n1) = $true) | ($true != $true) | spl109_5),
% 20.43/4.29 inference(superposition,[status(thm)],[f1967,f1520])).
% 20.43/4.29 thf(f1520,plain,(
% 20.43/4.29 ( ! [X0 : nat,X1 : nat] : (((ord_less @ nat @ X1 @ X0) = $true) | (X0 = X1) | ((ord_less @ nat @ X0 @ X1) = $true)) )),
% 20.43/4.29 inference(cnf_transformation,[status(thm)],[f938])).
% 20.43/4.29 thf(f938,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : ((X0 = X1) | ((ord_less @ nat @ X1 @ X0) = $true) | ((ord_less @ nat @ X0 @ X1) = $true))),
% 20.43/4.29 inference(flattening,[status(thm)],[f937])).
% 20.43/4.29 thf(f937,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ X1 @ X0) = $true) | ((ord_less @ nat @ X0 @ X1) = $true)) | (X0 = X1))),
% 20.43/4.29 inference(ennf_transformation,[status(thm)],[f837])).
% 20.43/4.29 thf(f837,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (((ord_less @ nat @ X0 @ X1) != $true) => ((ord_less @ nat @ X1 @ X0) = $true)))),
% 20.43/4.29 inference(flattening,[status(thm)],[f550])).
% 20.43/4.29 thf(f550,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~((ord_less @ nat @ X0 @ X1) = $true) => ((ord_less @ nat @ X1 @ X0) = $true)))),
% 20.43/4.29 inference(fool_elimination,[status(thm)],[f549])).
% 20.43/4.29 thf(f549,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : ((X0 != X1) => (~(ord_less @ nat @ X0 @ X1) => (ord_less @ nat @ X1 @ X0)))),
% 20.43/4.29 inference(rectify,[status(thm)],[f51])).
% 20.43/4.29 thf(f51,axiom,(
% 20.43/4.29 ! [X12 : nat,X13 : nat] : ((X12 != X13) => (~(ord_less @ nat @ X12 @ X13) => (ord_less @ nat @ X13 @ X12)))),
% 20.43/4.29 file('/export/starexec/sandbox/tmp/tmp.6wC2JEysVn/DTF2THF_4609.p',fact_50_linorder__neqE__nat)).
% 20.43/4.29 thf(f1967,plain,(
% 20.43/4.29 ((ord_less @ nat @ n1 @ nMsg) != $true) | spl109_5),
% 20.43/4.29 inference(trivial_inequality_removal,[status(thm)],[f1962])).
% 20.43/4.29 thf(f1962,plain,(
% 20.43/4.29 ($true != $true) | ((ord_less @ nat @ n1 @ nMsg) != $true) | spl109_5),
% 20.43/4.29 inference(superposition,[status(thm)],[f1936,f1321])).
% 20.43/4.29 thf(f1321,plain,(
% 20.43/4.29 ( ! [X0 : nat,X1 : nat] : (($true = (ord_less_eq @ nat @ X0 @ X1)) | ((ord_less @ nat @ X0 @ X1) != $true)) )),
% 20.43/4.29 inference(cnf_transformation,[status(thm)],[f861])).
% 20.43/4.29 thf(f861,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : (($true = (ord_less_eq @ nat @ X0 @ X1)) | ((ord_less @ nat @ X0 @ X1) != $true))),
% 20.43/4.29 inference(ennf_transformation,[status(thm)],[f688])).
% 20.43/4.29 thf(f688,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : (((ord_less @ nat @ X0 @ X1) = $true) => ($true = (ord_less_eq @ nat @ X0 @ X1)))),
% 20.43/4.29 inference(fool_elimination,[status(thm)],[f687])).
% 20.43/4.29 thf(f687,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ X0 @ X1) => (ord_less_eq @ nat @ X0 @ X1))),
% 20.43/4.29 inference(rectify,[status(thm)],[f153])).
% 20.43/4.29 thf(f153,axiom,(
% 20.43/4.29 ! [X14 : nat,X10 : nat] : ((ord_less @ nat @ X14 @ X10) => (ord_less_eq @ nat @ X14 @ X10))),
% 20.43/4.29 file('/export/starexec/sandbox/tmp/tmp.6wC2JEysVn/DTF2THF_4609.p',fact_152_less__imp__le__nat)).
% 20.43/4.29 thf(f1936,plain,(
% 20.43/4.29 ((ord_less_eq @ nat @ n1 @ nMsg) != $true) | spl109_5),
% 20.43/4.29 inference(trivial_inequality_removal,[status(thm)],[f1887])).
% 20.43/4.29 thf(f1887,plain,(
% 20.43/4.29 ((ord_less_eq @ nat @ n1 @ nMsg) != $true) | ($true != $true) | spl109_5),
% 20.43/4.29 inference(superposition,[status(thm)],[f1815,f1632])).
% 20.43/4.29 thf(f1632,plain,(
% 20.43/4.29 ((ord_less @ nat @ nMsg @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) = $true)),
% 20.43/4.29 inference(cnf_transformation,[status(thm)],[f332])).
% 20.43/4.29 thf(f332,plain,(
% 20.43/4.29 ((ord_less @ nat @ nMsg @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) = $true)),
% 20.43/4.29 inference(fool_elimination,[status(thm)],[f331])).
% 20.43/4.29 thf(f331,plain,(
% 20.43/4.29 (ord_less @ nat @ nMsg @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))),
% 20.43/4.29 inference(rectify,[status(thm)],[f2])).
% 20.43/4.29 thf(f2,axiom,(
% 20.43/4.29 (ord_less @ nat @ nMsg @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))),
% 20.43/4.29 file('/export/starexec/sandbox/tmp/tmp.6wC2JEysVn/DTF2THF_4609.p',fact_1__092_060open_062nMsg_A_060_Alength_A_Ife_Aindex_J_092_060close_062)).
% 20.43/4.29 thf(f1815,plain,(
% 20.43/4.29 ( ! [X0 : nat] : (($true != (ord_less @ nat @ X0 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))) | ((ord_less_eq @ nat @ n1 @ X0) != $true)) ) | spl109_5),
% 20.43/4.29 inference(trivial_inequality_removal,[status(thm)],[f1811])).
% 20.43/4.29 thf(f1811,plain,(
% 20.43/4.29 ( ! [X0 : nat] : (((ord_less_eq @ nat @ n1 @ X0) != $true) | ($true != (ord_less @ nat @ X0 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))) | ($true != $true)) ) | spl109_5),
% 20.43/4.29 inference(superposition,[status(thm)],[f1794,f1661])).
% 20.43/4.29 thf(f1661,plain,(
% 20.43/4.29 ( ! [X0 : nat,X1 : nat] : (($true = (ord_less_eq @ nat @ X0 @ X1)) | ((ord_less @ nat @ X0 @ X1) != $true)) )),
% 20.43/4.29 inference(cnf_transformation,[status(thm)],[f1038])).
% 20.43/4.29 thf(f1038,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : (($true = (ord_less_eq @ nat @ X0 @ X1)) | (((ord_less @ nat @ X0 @ X1) != $true) & (X0 != X1)))),
% 20.43/4.29 inference(ennf_transformation,[status(thm)],[f618])).
% 20.43/4.29 thf(f618,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ X0 @ X1) = $true) | (X0 = X1)) => ($true = (ord_less_eq @ nat @ X0 @ X1)))),
% 20.43/4.29 inference(fool_elimination,[status(thm)],[f617])).
% 20.43/4.29 thf(f617,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : (((X0 = X1) | (ord_less @ nat @ X0 @ X1)) => (ord_less_eq @ nat @ X0 @ X1))),
% 20.43/4.29 inference(rectify,[status(thm)],[f151])).
% 20.43/4.29 thf(f151,axiom,(
% 20.43/4.29 ! [X14 : nat,X10 : nat] : (((X10 = X14) | (ord_less @ nat @ X14 @ X10)) => (ord_less_eq @ nat @ X14 @ X10))),
% 20.43/4.29 file('/export/starexec/sandbox/tmp/tmp.6wC2JEysVn/DTF2THF_4609.p',fact_150_less__or__eq__imp__le)).
% 20.43/4.29 thf(f1794,plain,(
% 20.43/4.29 ( ! [X0 : nat] : (($true != (ord_less_eq @ nat @ X0 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))) | ((ord_less_eq @ nat @ n1 @ X0) != $true)) ) | spl109_5),
% 20.43/4.29 inference(trivial_inequality_removal,[status(thm)],[f1785])).
% 20.43/4.29 thf(f1785,plain,(
% 20.43/4.29 ( ! [X0 : nat] : (($true != $true) | ($true != (ord_less_eq @ nat @ X0 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))) | ((ord_less_eq @ nat @ n1 @ X0) != $true)) ) | spl109_5),
% 20.43/4.29 inference(superposition,[status(thm)],[f1756,f1279])).
% 20.43/4.29 thf(f1279,plain,(
% 20.43/4.29 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((ord_less_eq @ nat @ X0 @ X2) = $true) | ($true != (ord_less_eq @ nat @ X1 @ X2)) | ($true != (ord_less_eq @ nat @ X0 @ X1))) )),
% 20.43/4.29 inference(cnf_transformation,[status(thm)],[f957])).
% 20.43/4.29 thf(f957,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat,X2 : nat] : (($true != (ord_less_eq @ nat @ X0 @ X1)) | ($true != (ord_less_eq @ nat @ X1 @ X2)) | ((ord_less_eq @ nat @ X0 @ X2) = $true))),
% 20.43/4.29 inference(flattening,[status(thm)],[f956])).
% 20.43/4.29 thf(f956,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat,X2 : nat] : ((((ord_less_eq @ nat @ X0 @ X2) = $true) | ($true != (ord_less_eq @ nat @ X1 @ X2))) | ($true != (ord_less_eq @ nat @ X0 @ X1)))),
% 20.43/4.29 inference(ennf_transformation,[status(thm)],[f480])).
% 20.43/4.29 thf(f480,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = (ord_less_eq @ nat @ X0 @ X1)) => (($true = (ord_less_eq @ nat @ X1 @ X2)) => ((ord_less_eq @ nat @ X0 @ X2) = $true)))),
% 20.43/4.29 inference(fool_elimination,[status(thm)],[f479])).
% 20.43/4.29 thf(f479,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat,X2 : nat] : ((ord_less_eq @ nat @ X0 @ X1) => ((ord_less_eq @ nat @ X1 @ X2) => (ord_less_eq @ nat @ X0 @ X2)))),
% 20.43/4.29 inference(rectify,[status(thm)],[f133])).
% 20.43/4.29 thf(f133,axiom,(
% 20.43/4.29 ! [X21 : nat,X22 : nat,X26 : nat] : ((ord_less_eq @ nat @ X21 @ X22) => ((ord_less_eq @ nat @ X22 @ X26) => (ord_less_eq @ nat @ X21 @ X26)))),
% 20.43/4.29 file('/export/starexec/sandbox/tmp/tmp.6wC2JEysVn/DTF2THF_4609.p',fact_132_le__trans)).
% 20.43/4.29 thf(f1756,plain,(
% 20.43/4.29 ((ord_less_eq @ nat @ n1 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) != $true) | spl109_5),
% 20.43/4.29 inference(avatar_component_clause,[status(thm)],[f1754])).
% 20.43/4.29 thf(f1754,definition,(
% 20.43/4.29 spl109_5 <=> ((ord_less_eq @ nat @ n1 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) = $true)),
% 20.43/4.29 introduced(definition,[new_symbols(naming,[spl109_5])],[avatar_definition])).
% 20.43/4.29 thf(f1779,plain,(
% 20.43/4.29 ~spl109_2),
% 20.43/4.29 inference(avatar_contradiction_clause,[status(thm)],[f1778])).
% 20.43/4.29 thf(f1778,plain,(
% 20.43/4.29 $false | ~spl109_2),
% 20.43/4.29 inference(subsumption_resolution,[status(thm)],[f1761,f1523])).
% 20.43/4.29 thf(f1761,plain,(
% 20.43/4.29 ((ord_less @ nat @ nMsg @ n1) = $true) | ~spl109_2),
% 20.43/4.29 inference(superposition,[status(thm)],[f1632,f1741])).
% 20.43/4.29 thf(f1741,plain,(
% 20.43/4.29 (n1 = (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) | ~spl109_2),
% 20.43/4.29 inference(avatar_component_clause,[status(thm)],[f1739])).
% 20.43/4.29 thf(f1739,definition,(
% 20.43/4.29 spl109_2 <=> (n1 = (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))),
% 20.43/4.29 introduced(definition,[new_symbols(naming,[spl109_2])],[avatar_definition])).
% 20.43/4.29 thf(f1757,plain,(
% 20.43/4.29 spl109_2 | ~spl109_5),
% 20.43/4.29 inference(avatar_split_clause,[status(thm)],[f1731,f1754,f1739])).
% 20.43/4.29 thf(f1731,plain,(
% 20.43/4.29 ((ord_less_eq @ nat @ n1 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) != $true) | (n1 = (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))),
% 20.43/4.29 inference(trivial_inequality_removal,[status(thm)],[f1728])).
% 20.43/4.29 thf(f1728,plain,(
% 20.43/4.29 ((ord_less_eq @ nat @ n1 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) != $true) | ($true != $true) | (n1 = (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))),
% 20.43/4.29 inference(superposition,[status(thm)],[f1533,f1669])).
% 20.43/4.29 thf(f1669,plain,(
% 20.43/4.29 ( ! [X0 : nat,X1 : nat] : (((ord_less @ nat @ X0 @ X1) = $true) | ($true != (ord_less_eq @ nat @ X0 @ X1)) | (X0 = X1)) )),
% 20.43/4.29 inference(cnf_transformation,[status(thm)],[f949])).
% 20.43/4.29 thf(f949,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : (((ord_less @ nat @ X0 @ X1) = $true) | (X0 = X1) | ($true != (ord_less_eq @ nat @ X0 @ X1)))),
% 20.43/4.29 inference(flattening,[status(thm)],[f948])).
% 20.43/4.29 thf(f948,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : ((((ord_less @ nat @ X0 @ X1) = $true) | (X0 = X1)) | ($true != (ord_less_eq @ nat @ X0 @ X1)))),
% 20.43/4.29 inference(ennf_transformation,[status(thm)],[f662])).
% 20.43/4.29 thf(f662,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : (($true = (ord_less_eq @ nat @ X0 @ X1)) => ((X0 != X1) => ((ord_less @ nat @ X0 @ X1) = $true)))),
% 20.43/4.29 inference(fool_elimination,[status(thm)],[f661])).
% 20.43/4.29 thf(f661,plain,(
% 20.43/4.29 ! [X0 : nat,X1 : nat] : ((ord_less_eq @ nat @ X0 @ X1) => ((X0 != X1) => (ord_less @ nat @ X0 @ X1)))),
% 20.43/4.29 inference(rectify,[status(thm)],[f150])).
% 20.43/4.29 thf(f150,axiom,(
% 20.43/4.29 ! [X14 : nat,X10 : nat] : ((ord_less_eq @ nat @ X14 @ X10) => ((X10 != X14) => (ord_less @ nat @ X14 @ X10)))),
% 20.43/4.29 file('/export/starexec/sandbox/tmp/tmp.6wC2JEysVn/DTF2THF_4609.p',fact_149_le__neq__implies__less)).
% 20.43/4.29 thf(f1533,plain,(
% 20.43/4.29 ((ord_less @ nat @ n1 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) != $true)),
% 20.43/4.29 inference(cnf_transformation,[status(thm)],[f834])).
% 20.43/4.29 thf(f834,plain,(
% 20.43/4.29 ((ord_less @ nat @ n1 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) != $true)),
% 20.43/4.29 inference(flattening,[status(thm)],[f524])).
% 20.43/4.29 thf(f524,plain,(
% 20.43/4.29 ~((ord_less @ nat @ n1 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) = $true)),
% 20.43/4.29 inference(fool_elimination,[status(thm)],[f523])).
% 20.43/4.29 thf(f523,plain,(
% 20.43/4.29 ~(ord_less @ nat @ n1 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))),
% 20.43/4.29 inference(rectify,[status(thm)],[f272])).
% 20.43/4.29 thf(f272,negated_conjecture,(
% 20.43/4.29 ~(ord_less @ nat @ n1 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))),
% 20.43/4.29 inference(negated_conjecture,[status(cth)],[f271])).
% 20.43/4.29 thf(f271,conjecture,(
% 20.43/4.29 (ord_less @ nat @ n1 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))),
% 20.43/4.29 file('/export/starexec/sandbox/tmp/tmp.6wC2JEysVn/DTF2THF_4609.p',conj_0)).
% 20.43/4.29 % SZS output end Proof for DTF2THF_4609
% 20.43/4.29 % (5085)------------------------------
% 20.43/4.29 % (5085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.43/4.29 % (5085)Termination reason: Refutation
% 20.43/4.29
% 20.43/4.29 % (5085)Memory used [KB]: 7419
% 20.43/4.29 % (5085)Time elapsed: 0.083 s
% 20.43/4.29 % (5085)Instructions burned: 261 (million)
% 20.43/4.29 % (5085)------------------------------
% 20.43/4.29 % (5085)------------------------------
% 20.43/4.29 % (4715)Success in time 2.691 s
%------------------------------------------------------------------------------