%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP059^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 08:55:13 AM UTC 2026
% Result : Theorem 36.19s 6.45s
% Output : Refutation 36.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP059^2 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n026.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:25:10 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : ITP059^2 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.46 % Domain : Interactive Theorem Proving
% 0.30/0.46 % Problem : Sledgehammer FLPTheorem problem prob_747__3300826_1
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Des21]
% 0.30/0.46 % Names : FLPTheorem/prob_747__3300826_1 [Des21]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.00 v8.1.0, 0.25 v7.5.0
% 0.30/0.46 % Syntax : Number of formulae : 318 ( 120 unt; 50 typ; 0 def)
% 0.30/0.46 % Number of atoms : 601 ( 203 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 7 ( 2 avg)
% 0.30/0.46 % Number of connectives : 3600 ( 85 ~; 15 |; 42 &;3150 @)
% 0.30/0.46 % ( 0 <=>; 308 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 21 ( 7 avg)
% 0.30/0.46 % Number of types : 6 ( 5 usr)
% 0.30/0.46 % Number of type conns : 156 ( 156 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 46 ( 45 usr; 8 con; 0-7 aty)
% 0.30/0.46 % Number of variables : 638 ( 17 ^; 549 !; 35 ?; 638 :)
% 0.30/0.46 % ( 37 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.46 % SPC : TH1_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:16:46.464
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % Could-be-implicit typings (9)
% 0.30/0.46 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext,type,
% 0.30/0.46 configuration_ext: $tType > $tType > $tType > $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_AsynchronousSystem_Omessage,type,
% 0.30/0.46 message: $tType > $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Product__Type_Ounit,type,
% 0.30/0.46 product_unit: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_List_Olist,type,
% 0.30/0.46 list: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Set_Oset,type,
% 0.30/0.46 set: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Nat_Onat,type,
% 0.30/0.46 nat: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_tf_v,type,
% 0.30/0.46 v: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_tf_s,type,
% 0.30/0.46 s: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_tf_p,type,
% 0.30/0.46 p: $tType ).
% 0.30/0.46
% 0.30/0.46 % Explicit typings (41)
% 0.30/0.46 thf(sy_cl_HOL_Otype,type,
% 0.30/0.46 type:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Nat_Osize,type,
% 0.30/0.46 size:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Oone,type,
% 0.30/0.46 one:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Ozero,type,
% 0.30/0.46 zero:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Num_Oneg__numeral,type,
% 0.30/0.46 neg_numeral:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.30/0.46 order:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Ogroup__add,type,
% 0.30/0.46 group_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Owellorder,type,
% 0.30/0.46 wellorder:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Ocomm__monoid__diff,type,
% 0.30/0.46 comm_monoid_diff:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.30/0.46 ordered_ab_group_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.30/0.46 cancel1352612707id_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.30/0.46 cancel146912293up_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.30/0.46 linord1659791738miring:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.30/0.46 canoni770627133id_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_AsynchronousSystem_Oconfiguration_Omsgs,type,
% 0.30/0.46 msgs:
% 0.30/0.46 !>[P: $tType,V: $tType,S: $tType,Z: $tType] : ( ( configuration_ext @ P @ V @ S @ Z ) > ( message @ P @ V ) > nat ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_AsynchronousSystem_Oenabled,type,
% 0.30/0.46 enabled:
% 0.30/0.46 !>[P: $tType,V: $tType,S: $tType] : ( ( configuration_ext @ P @ V @ S @ product_unit ) > ( message @ P @ V ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_AsynchronousSystem_OisReceiverOf,type,
% 0.30/0.46 isReceiverOf:
% 0.30/0.46 !>[P: $tType,V: $tType] : ( P > ( message @ P @ V ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Execution_Oexecution_OfirstOccurrence,type,
% 0.30/0.46 firstOccurrence:
% 0.30/0.46 !>[P: $tType,V: $tType,S: $tType] : ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( message @ P @ V ) > nat > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.30/0.46 minus_minus:
% 0.30/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.30/0.46 one_one:
% 0.30/0.46 !>[A: $tType] : A ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.30/0.46 zero_zero:
% 0.30/0.46 !>[A: $tType] : A ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_ListUtilities_OprefixList,type,
% 0.30/0.46 prefixList:
% 0.30/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olast,type,
% 0.30/0.46 last:
% 0.30/0.46 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist_ONil,type,
% 0.30/0.46 nil:
% 0.30/0.46 !>[A: $tType] : ( list @ A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Onth,type,
% 0.30/0.46 nth:
% 0.30/0.46 !>[A: $tType] : ( ( list @ A ) > nat > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nat_OSuc,type,
% 0.30/0.46 suc: nat > nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.30/0.46 size_size:
% 0.30/0.46 !>[A: $tType] : ( A > nat ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.30/0.46 ord_less:
% 0.30/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.30/0.46 ord_less_eq:
% 0.30/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member,type,
% 0.30/0.46 member:
% 0.30/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_fe____,type,
% 0.30/0.46 fe: nat > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_firstOccSet____,type,
% 0.30/0.46 firstOccSet: nat > ( set @ ( message @ p @ v ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_ft____,type,
% 0.30/0.46 ft: nat > ( list @ ( message @ p @ v ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_index____,type,
% 0.30/0.46 index: nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_msgInSet____,type,
% 0.30/0.46 msgInSet: message @ p @ v ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_msg____,type,
% 0.30/0.46 msg: message @ p @ v ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_n0____,type,
% 0.30/0.46 n0: nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_n1____,type,
% 0.30/0.46 n1: nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_nMsg____,type,
% 0.30/0.46 nMsg: nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_n____,type,
% 0.30/0.46 n: nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_p____,type,
% 0.30/0.46 p2: p ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (251)
% 0.30/0.46 thf(fact_0_AssumpOcc6_I1_J,axiom,
% 0.30/0.46 ord_less @ nat @ ( zero_zero @ nat ) @ nMsg ).
% 0.30/0.46
% 0.30/0.46 % AssumpOcc6(1)
% 0.30/0.46 thf(fact_1_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 0.30/0.46 ! [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] :
% 0.30/0.46 ( ! [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 ) )
% 0.30/0.46 => ( ! [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 ) ),N: nat] :
% 0.30/0.46 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.30/0.46 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.30/0.46 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.30/0.46 => ( ! [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 ) )
% 0.30/0.46 => ( ! [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 ) ),N: nat] :
% 0.30/0.46 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.30/0.46 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.30/0.46 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.30/0.46 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % infiniteExecutionCfg_infiniteExecutionMsg.induct(2)
% 0.30/0.46 thf(fact_2_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 0.30/0.46 ! [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 ) ),A2: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),A3: nat] :
% 0.30/0.46 ( ! [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 ) )
% 0.30/0.46 => ( ! [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 ) ),N: nat] :
% 0.30/0.46 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.30/0.46 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.30/0.46 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.30/0.46 => ( ! [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 ) )
% 0.30/0.46 => ( ! [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 ) ),N: nat] :
% 0.30/0.46 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.30/0.46 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.30/0.46 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.30/0.46 => ( P2 @ A0 @ A1 @ A2 @ A3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % infiniteExecutionCfg_infiniteExecutionMsg.induct(1)
% 0.30/0.46 thf(fact_3_AssumptionSubset_I3_J,axiom,
% 0.30/0.46 firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg ).
% 0.30/0.46
% 0.30/0.46 % AssumptionSubset(3)
% 0.30/0.46 thf(fact_4_SmallIndex,axiom,
% 0.30/0.46 ! [NMsg: nat] :
% 0.30/0.46 ( ( firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ NMsg )
% 0.30/0.46 => ( ord_less @ nat @ NMsg @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % SmallIndex
% 0.30/0.46 thf(fact_5_AssumptionSubset3_I3_J,axiom,
% 0.30/0.46 ord_less @ nat @ nMsg @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % AssumptionSubset3(3)
% 0.30/0.46 thf(fact_6_AssumptionSubset2_I3_J,axiom,
% 0.30/0.46 ord_less @ nat @ n1 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % AssumptionSubset2(3)
% 0.30/0.46 thf(fact_7_Suc__pred,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.30/0.46 => ( ( suc @ ( minus_minus @ nat @ N2 @ ( suc @ ( zero_zero @ nat ) ) ) )
% 0.30/0.46 = N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_pred
% 0.30/0.46 thf(fact_8_zero__less__diff,axiom,
% 0.30/0.46 ! [N2: nat,M: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( minus_minus @ nat @ N2 @ M ) )
% 0.30/0.46 = ( ord_less @ nat @ M @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_diff
% 0.30/0.46 thf(fact_9_less__Suc0,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ N2 @ ( suc @ ( zero_zero @ nat ) ) )
% 0.30/0.46 = ( N2
% 0.30/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_Suc0
% 0.30/0.46 thf(fact_10_zero__less__Suc,axiom,
% 0.30/0.46 ! [N2: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_Suc
% 0.30/0.46 thf(fact_11_diff__gt__0__iff__gt,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_ab_group_add @ A )
% 0.30/0.46 => ! [A8: A,B: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A8 @ B ) )
% 0.30/0.46 = ( ord_less @ A @ B @ A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_gt_0_iff_gt
% 0.30/0.46 thf(fact_12_diff__0__eq__0,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ( ( minus_minus @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.30/0.46 = ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_0_eq_0
% 0.30/0.46 thf(fact_13_diff__self__eq__0,axiom,
% 0.30/0.46 ! [M: nat] :
% 0.30/0.46 ( ( minus_minus @ nat @ M @ M )
% 0.30/0.46 = ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_self_eq_0
% 0.30/0.46 thf(fact_14_diff__Suc__Suc,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( minus_minus @ nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.30/0.46 = ( minus_minus @ nat @ M @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_Suc_Suc
% 0.30/0.46 thf(fact_15_Suc__diff__diff,axiom,
% 0.30/0.46 ! [M: nat,N2: nat,K: nat] :
% 0.30/0.46 ( ( minus_minus @ nat @ ( minus_minus @ nat @ ( suc @ M ) @ N2 ) @ ( suc @ K ) )
% 0.30/0.46 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ N2 ) @ K ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_diff_diff
% 0.30/0.46 thf(fact_16_neq0__conv,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ( ( N2
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % neq0_conv
% 0.30/0.46 thf(fact_17_less__nat__zero__code,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ~ ( ord_less @ nat @ N2 @ ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_nat_zero_code
% 0.30/0.46 thf(fact_18_old_Onat_Oinject,axiom,
% 0.30/0.46 ! [Nat: nat,Nat2: nat] :
% 0.30/0.46 ( ( ( suc @ Nat )
% 0.30/0.46 = ( suc @ Nat2 ) )
% 0.30/0.46 = ( Nat = Nat2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.nat.inject
% 0.30/0.46 thf(fact_19_nat_Oinject,axiom,
% 0.30/0.46 ! [X2: nat,Y2: nat] :
% 0.30/0.46 ( ( ( suc @ X2 )
% 0.30/0.46 = ( suc @ Y2 ) )
% 0.30/0.46 = ( X2 = Y2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat.inject
% 0.30/0.46 thf(fact_20_not__gr__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ! [N2: A] :
% 0.30/0.46 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N2 ) )
% 0.30/0.46 = ( N2
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_gr_zero
% 0.30/0.46 thf(fact_21_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( cancel1352612707id_add @ A )
% 0.30/0.46 => ! [A8: A] :
% 0.30/0.46 ( ( minus_minus @ A @ A8 @ A8 )
% 0.30/0.46 = ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % cancel_comm_monoid_add_class.diff_cancel
% 0.30/0.46 thf(fact_22_diff__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( cancel1352612707id_add @ A )
% 0.30/0.46 => ! [A8: A] :
% 0.30/0.46 ( ( minus_minus @ A @ A8 @ ( zero_zero @ A ) )
% 0.30/0.46 = A8 ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_zero
% 0.30/0.46 thf(fact_23_zero__diff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( comm_monoid_diff @ A )
% 0.30/0.46 => ! [A8: A] :
% 0.30/0.46 ( ( minus_minus @ A @ ( zero_zero @ A ) @ A8 )
% 0.30/0.46 = ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_diff
% 0.30/0.46 thf(fact_24_diff__0__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( group_add @ A )
% 0.30/0.46 => ! [A8: A] :
% 0.30/0.46 ( ( minus_minus @ A @ A8 @ ( zero_zero @ A ) )
% 0.30/0.46 = A8 ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_0_right
% 0.30/0.46 thf(fact_25_diff__self,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( group_add @ A )
% 0.30/0.46 => ! [A8: A] :
% 0.30/0.46 ( ( minus_minus @ A @ A8 @ A8 )
% 0.30/0.46 = ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_self
% 0.30/0.46 thf(fact_26_Suc__less__eq,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.30/0.46 = ( ord_less @ nat @ M @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_less_eq
% 0.30/0.46 thf(fact_27_Suc__mono,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ N2 )
% 0.30/0.46 => ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_mono
% 0.30/0.46 thf(fact_28_lessI,axiom,
% 0.30/0.46 ! [N2: nat] : ( ord_less @ nat @ N2 @ ( suc @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % lessI
% 0.30/0.46 thf(fact_29_bot__nat__0_Onot__eq__extremum,axiom,
% 0.30/0.46 ! [A8: nat] :
% 0.30/0.46 ( ( A8
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A8 ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_nat_0.not_eq_extremum
% 0.30/0.46 thf(fact_30_AssumptionSubset_I2_J,axiom,
% 0.30/0.46 firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msgInSet @ n1 ).
% 0.30/0.46
% 0.30/0.46 % AssumptionSubset(2)
% 0.30/0.46 thf(fact_31_AssumptionSubset_I1_J,axiom,
% 0.30/0.46 ord_less_eq @ nat @ n1 @ nMsg ).
% 0.30/0.46
% 0.30/0.46 % AssumptionSubset(1)
% 0.30/0.46 thf(fact_32_zero__reorient,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( zero @ A )
% 0.30/0.46 => ! [X: A] :
% 0.30/0.46 ( ( ( zero_zero @ A )
% 0.30/0.46 = X )
% 0.30/0.46 = ( X
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_reorient
% 0.30/0.46 thf(fact_33_measure__induct__rule,axiom,
% 0.30/0.46 ! [B2: $tType,A: $tType] :
% 0.30/0.46 ( ( wellorder @ B2 )
% 0.30/0.46 => ! [F: A > B2,P2: A > $o,A8: A] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ! [Y: A] :
% 0.30/0.46 ( ( ord_less @ B2 @ ( F @ Y ) @ ( F @ X3 ) )
% 0.30/0.46 => ( P2 @ Y ) )
% 0.30/0.46 => ( P2 @ X3 ) )
% 0.30/0.46 => ( P2 @ A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % measure_induct_rule
% 0.30/0.46 thf(fact_34_measure__induct,axiom,
% 0.30/0.46 ! [B2: $tType,A: $tType] :
% 0.30/0.46 ( ( wellorder @ B2 )
% 0.30/0.46 => ! [F: A > B2,P2: A > $o,A8: A] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ! [Y: A] :
% 0.30/0.46 ( ( ord_less @ B2 @ ( F @ Y ) @ ( F @ X3 ) )
% 0.30/0.46 => ( P2 @ Y ) )
% 0.30/0.46 => ( P2 @ X3 ) )
% 0.30/0.46 => ( P2 @ A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % measure_induct
% 0.30/0.46 thf(fact_35_diff__right__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( cancel146912293up_add @ A )
% 0.30/0.46 => ! [A8: A,C: A,B: A] :
% 0.30/0.46 ( ( minus_minus @ A @ ( minus_minus @ A @ A8 @ C ) @ B )
% 0.30/0.46 = ( minus_minus @ A @ ( minus_minus @ A @ A8 @ B ) @ C ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_right_commute
% 0.30/0.46 thf(fact_36_diff__eq__diff__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( group_add @ A )
% 0.30/0.46 => ! [A8: A,B: A,C: A,D: A] :
% 0.30/0.46 ( ( ( minus_minus @ A @ A8 @ B )
% 0.30/0.46 = ( minus_minus @ A @ C @ D ) )
% 0.30/0.46 => ( ( A8 = B )
% 0.30/0.46 = ( C = D ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_eq_diff_eq
% 0.30/0.46 thf(fact_37_n__not__Suc__n,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ( N2
% 0.30/0.46 != ( suc @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % n_not_Suc_n
% 0.30/0.46 thf(fact_38_Suc__inject,axiom,
% 0.30/0.46 ! [X: nat,Y3: nat] :
% 0.30/0.46 ( ( ( suc @ X )
% 0.30/0.46 = ( suc @ Y3 ) )
% 0.30/0.46 => ( X = Y3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_inject
% 0.30/0.46 thf(fact_39_infinite__descent__measure,axiom,
% 0.30/0.46 ! [A: $tType,P2: A > $o,V2: A > nat,X: A] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ~ ( P2 @ X3 )
% 0.30/0.46 => ? [Y: A] :
% 0.30/0.46 ( ( ord_less @ nat @ ( V2 @ Y ) @ ( V2 @ X3 ) )
% 0.30/0.46 & ~ ( P2 @ Y ) ) )
% 0.30/0.46 => ( P2 @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % infinite_descent_measure
% 0.30/0.46 thf(fact_40_linorder__neqE__nat,axiom,
% 0.30/0.46 ! [X: nat,Y3: nat] :
% 0.30/0.46 ( ( X != Y3 )
% 0.30/0.46 => ( ~ ( ord_less @ nat @ X @ Y3 )
% 0.30/0.46 => ( ord_less @ nat @ Y3 @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linorder_neqE_nat
% 0.30/0.46 thf(fact_41_infinite__descent,axiom,
% 0.30/0.46 ! [P2: nat > $o,N2: nat] :
% 0.30/0.46 ( ! [N: nat] :
% 0.30/0.46 ( ~ ( P2 @ N )
% 0.30/0.46 => ? [M2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M2 @ N )
% 0.30/0.46 & ~ ( P2 @ M2 ) ) )
% 0.30/0.46 => ( P2 @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % infinite_descent
% 0.30/0.46 thf(fact_42_nat__less__induct,axiom,
% 0.30/0.46 ! [P2: nat > $o,N2: nat] :
% 0.30/0.46 ( ! [N: nat] :
% 0.30/0.46 ( ! [M2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M2 @ N )
% 0.30/0.46 => ( P2 @ M2 ) )
% 0.30/0.46 => ( P2 @ N ) )
% 0.30/0.46 => ( P2 @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_less_induct
% 0.30/0.46 thf(fact_43_less__irrefl__nat,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ~ ( ord_less @ nat @ N2 @ N2 ) ).
% 0.30/0.46
% 0.30/0.46 % less_irrefl_nat
% 0.30/0.46 thf(fact_44_less__not__refl3,axiom,
% 0.30/0.46 ! [S2: nat,T: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ S2 @ T )
% 0.30/0.46 => ( S2 != T ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_not_refl3
% 0.30/0.46 thf(fact_45_less__not__refl2,axiom,
% 0.30/0.46 ! [N2: nat,M: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ N2 @ M )
% 0.30/0.46 => ( M != N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_not_refl2
% 0.30/0.46 thf(fact_46_less__not__refl,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ~ ( ord_less @ nat @ N2 @ N2 ) ).
% 0.30/0.46
% 0.30/0.46 % less_not_refl
% 0.30/0.46 thf(fact_47_nat__neq__iff,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( M != N2 )
% 0.30/0.46 = ( ( ord_less @ nat @ M @ N2 )
% 0.30/0.46 | ( ord_less @ nat @ N2 @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_neq_iff
% 0.30/0.46 thf(fact_48_size__neq__size__imp__neq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( size @ A )
% 0.30/0.46 => ! [X: A,Y3: A] :
% 0.30/0.46 ( ( ( size_size @ A @ X )
% 0.30/0.46 != ( size_size @ A @ Y3 ) )
% 0.30/0.46 => ( X != Y3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % size_neq_size_imp_neq
% 0.30/0.46 thf(fact_49_diff__commute,axiom,
% 0.30/0.46 ! [I: nat,J: nat,K: nat] :
% 0.30/0.46 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I @ J ) @ K )
% 0.30/0.46 = ( minus_minus @ nat @ ( minus_minus @ nat @ I @ K ) @ J ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_commute
% 0.30/0.46 thf(fact_50_zero__less__iff__neq__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ! [N2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ N2 )
% 0.30/0.46 = ( N2
% 0.30/0.46 != ( zero_zero @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_less_iff_neq_zero
% 0.30/0.46 thf(fact_51_gr__implies__not__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ! [M: A,N2: A] :
% 0.30/0.46 ( ( ord_less @ A @ M @ N2 )
% 0.30/0.46 => ( N2
% 0.30/0.46 != ( zero_zero @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % gr_implies_not_zero
% 0.30/0.46 thf(fact_52_not__less__zero,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ! [N2: A] :
% 0.30/0.46 ~ ( ord_less @ A @ N2 @ ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_less_zero
% 0.30/0.46 thf(fact_53_gr__zeroI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ! [N2: A] :
% 0.30/0.46 ( ( N2
% 0.30/0.46 != ( zero_zero @ A ) )
% 0.30/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % gr_zeroI
% 0.30/0.46 thf(fact_54_eq__iff__diff__eq__0,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( group_add @ A )
% 0.30/0.46 => ( ( ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 0.30/0.46 = ( ^ [A9: A,B3: A] :
% 0.30/0.46 ( ( minus_minus @ A @ A9 @ B3 )
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_iff_diff_eq_0
% 0.30/0.46 thf(fact_55_diff__strict__right__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_ab_group_add @ A )
% 0.30/0.46 => ! [A8: A,B: A,C: A] :
% 0.30/0.46 ( ( ord_less @ A @ A8 @ B )
% 0.30/0.46 => ( ord_less @ A @ ( minus_minus @ A @ A8 @ C ) @ ( minus_minus @ A @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_strict_right_mono
% 0.30/0.46 thf(fact_56_diff__strict__left__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_ab_group_add @ A )
% 0.30/0.46 => ! [B: A,A8: A,C: A] :
% 0.30/0.46 ( ( ord_less @ A @ B @ A8 )
% 0.30/0.46 => ( ord_less @ A @ ( minus_minus @ A @ C @ A8 ) @ ( minus_minus @ A @ C @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_strict_left_mono
% 0.30/0.46 thf(fact_57_diff__eq__diff__less,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_ab_group_add @ A )
% 0.30/0.46 => ! [A8: A,B: A,C: A,D: A] :
% 0.30/0.46 ( ( ( minus_minus @ A @ A8 @ B )
% 0.30/0.46 = ( minus_minus @ A @ C @ D ) )
% 0.30/0.46 => ( ( ord_less @ A @ A8 @ B )
% 0.30/0.46 = ( ord_less @ A @ C @ D ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_eq_diff_less
% 0.30/0.46 thf(fact_58_diff__strict__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_ab_group_add @ A )
% 0.30/0.46 => ! [A8: A,B: A,D: A,C: A] :
% 0.30/0.46 ( ( ord_less @ A @ A8 @ B )
% 0.30/0.46 => ( ( ord_less @ A @ D @ C )
% 0.30/0.46 => ( ord_less @ A @ ( minus_minus @ A @ A8 @ C ) @ ( minus_minus @ A @ B @ D ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_strict_mono
% 0.30/0.46 thf(fact_59_not0__implies__Suc,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ( ( N2
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 => ? [M3: nat] :
% 0.30/0.46 ( N2
% 0.30/0.46 = ( suc @ M3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not0_implies_Suc
% 0.30/0.46 thf(fact_60_old_Onat_Oinducts,axiom,
% 0.30/0.46 ! [P2: nat > $o,Nat: nat] :
% 0.30/0.46 ( ( P2 @ ( zero_zero @ nat ) )
% 0.30/0.46 => ( ! [Nat3: nat] :
% 0.30/0.46 ( ( P2 @ Nat3 )
% 0.30/0.46 => ( P2 @ ( suc @ Nat3 ) ) )
% 0.30/0.46 => ( P2 @ Nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.nat.inducts
% 0.30/0.46 thf(fact_61_old_Onat_Oexhaust,axiom,
% 0.30/0.46 ! [Y3: nat] :
% 0.30/0.46 ( ( Y3
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 => ~ ! [Nat3: nat] :
% 0.30/0.46 ( Y3
% 0.30/0.46 != ( suc @ Nat3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.nat.exhaust
% 0.30/0.46 thf(fact_62_Zero__not__Suc,axiom,
% 0.30/0.46 ! [M: nat] :
% 0.30/0.46 ( ( zero_zero @ nat )
% 0.30/0.46 != ( suc @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % Zero_not_Suc
% 0.30/0.46 thf(fact_63_Zero__neq__Suc,axiom,
% 0.30/0.46 ! [M: nat] :
% 0.30/0.46 ( ( zero_zero @ nat )
% 0.30/0.46 != ( suc @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % Zero_neq_Suc
% 0.30/0.46 thf(fact_64_Suc__neq__Zero,axiom,
% 0.30/0.46 ! [M: nat] :
% 0.30/0.46 ( ( suc @ M )
% 0.30/0.46 != ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_neq_Zero
% 0.30/0.46 thf(fact_65_zero__induct,axiom,
% 0.30/0.46 ! [P2: nat > $o,K: nat] :
% 0.30/0.46 ( ( P2 @ K )
% 0.30/0.46 => ( ! [N: nat] :
% 0.30/0.46 ( ( P2 @ ( suc @ N ) )
% 0.30/0.46 => ( P2 @ N ) )
% 0.30/0.46 => ( P2 @ ( zero_zero @ nat ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_induct
% 0.30/0.46 thf(fact_66_diff__induct,axiom,
% 0.30/0.46 ! [P2: nat > nat > $o,M: nat,N2: nat] :
% 0.30/0.46 ( ! [X3: nat] : ( P2 @ X3 @ ( zero_zero @ nat ) )
% 0.30/0.46 => ( ! [Y5: nat] : ( P2 @ ( zero_zero @ nat ) @ ( suc @ Y5 ) )
% 0.30/0.46 => ( ! [X3: nat,Y5: nat] :
% 0.30/0.46 ( ( P2 @ X3 @ Y5 )
% 0.30/0.46 => ( P2 @ ( suc @ X3 ) @ ( suc @ Y5 ) ) )
% 0.30/0.46 => ( P2 @ M @ N2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_induct
% 0.30/0.46 thf(fact_67_nat__induct,axiom,
% 0.30/0.46 ! [P2: nat > $o,N2: nat] :
% 0.30/0.46 ( ( P2 @ ( zero_zero @ nat ) )
% 0.30/0.46 => ( ! [N: nat] :
% 0.30/0.46 ( ( P2 @ N )
% 0.30/0.46 => ( P2 @ ( suc @ N ) ) )
% 0.30/0.46 => ( P2 @ N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_induct
% 0.30/0.46 thf(fact_68_nat_OdiscI,axiom,
% 0.30/0.46 ! [Nat: nat,X2: nat] :
% 0.30/0.46 ( ( Nat
% 0.30/0.46 = ( suc @ X2 ) )
% 0.30/0.46 => ( Nat
% 0.30/0.46 != ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat.discI
% 0.30/0.46 thf(fact_69_old_Onat_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [Nat2: nat] :
% 0.30/0.46 ( ( zero_zero @ nat )
% 0.30/0.46 != ( suc @ Nat2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.nat.distinct(1)
% 0.30/0.46 thf(fact_70_old_Onat_Odistinct_I2_J,axiom,
% 0.30/0.46 ! [Nat4: nat] :
% 0.30/0.46 ( ( suc @ Nat4 )
% 0.30/0.46 != ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % old.nat.distinct(2)
% 0.30/0.46 thf(fact_71_nat_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [X2: nat] :
% 0.30/0.46 ( ( zero_zero @ nat )
% 0.30/0.46 != ( suc @ X2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat.distinct(1)
% 0.30/0.46 thf(fact_72_not__less__less__Suc__eq,axiom,
% 0.30/0.46 ! [N2: nat,M: nat] :
% 0.30/0.46 ( ~ ( ord_less @ nat @ N2 @ M )
% 0.30/0.46 => ( ( ord_less @ nat @ N2 @ ( suc @ M ) )
% 0.30/0.46 = ( N2 = M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_less_less_Suc_eq
% 0.30/0.46 thf(fact_73_strict__inc__induct,axiom,
% 0.30/0.46 ! [I: nat,J: nat,P2: nat > $o] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ J )
% 0.30/0.46 => ( ! [I2: nat] :
% 0.30/0.46 ( ( J
% 0.30/0.46 = ( suc @ I2 ) )
% 0.30/0.46 => ( P2 @ I2 ) )
% 0.30/0.46 => ( ! [I2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I2 @ J )
% 0.30/0.46 => ( ( P2 @ ( suc @ I2 ) )
% 0.30/0.46 => ( P2 @ I2 ) ) )
% 0.30/0.46 => ( P2 @ I ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % strict_inc_induct
% 0.30/0.46 thf(fact_74_less__Suc__induct,axiom,
% 0.30/0.46 ! [I: nat,J: nat,P2: nat > nat > $o] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ J )
% 0.30/0.46 => ( ! [I2: nat] : ( P2 @ I2 @ ( suc @ I2 ) )
% 0.30/0.46 => ( ! [I2: nat,J2: nat,K2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I2 @ J2 )
% 0.30/0.46 => ( ( ord_less @ nat @ J2 @ K2 )
% 0.30/0.46 => ( ( P2 @ I2 @ J2 )
% 0.30/0.46 => ( ( P2 @ J2 @ K2 )
% 0.30/0.46 => ( P2 @ I2 @ K2 ) ) ) ) )
% 0.30/0.46 => ( P2 @ I @ J ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_Suc_induct
% 0.30/0.46 thf(fact_75_less__trans__Suc,axiom,
% 0.30/0.46 ! [I: nat,J: nat,K: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ J )
% 0.30/0.46 => ( ( ord_less @ nat @ J @ K )
% 0.30/0.46 => ( ord_less @ nat @ ( suc @ I ) @ K ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_trans_Suc
% 0.30/0.46 thf(fact_76_Suc__less__SucD,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.30/0.46 => ( ord_less @ nat @ M @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_less_SucD
% 0.30/0.46 thf(fact_77_less__antisym,axiom,
% 0.30/0.46 ! [N2: nat,M: nat] :
% 0.30/0.46 ( ~ ( ord_less @ nat @ N2 @ M )
% 0.30/0.46 => ( ( ord_less @ nat @ N2 @ ( suc @ M ) )
% 0.30/0.46 => ( M = N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_antisym
% 0.30/0.46 thf(fact_78_Suc__less__eq2,axiom,
% 0.30/0.46 ! [N2: nat,M: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( suc @ N2 ) @ M )
% 0.30/0.46 = ( ? [M4: nat] :
% 0.30/0.46 ( ( M
% 0.30/0.46 = ( suc @ M4 ) )
% 0.30/0.46 & ( ord_less @ nat @ N2 @ M4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_less_eq2
% 0.30/0.46 thf(fact_79_All__less__Suc,axiom,
% 0.30/0.46 ! [N2: nat,P2: nat > $o] :
% 0.30/0.46 ( ( ! [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ ( suc @ N2 ) )
% 0.30/0.46 => ( P2 @ I3 ) ) )
% 0.30/0.46 = ( ( P2 @ N2 )
% 0.30/0.46 & ! [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ N2 )
% 0.30/0.46 => ( P2 @ I3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % All_less_Suc
% 0.30/0.46 thf(fact_80_not__less__eq,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ~ ( ord_less @ nat @ M @ N2 ) )
% 0.30/0.46 = ( ord_less @ nat @ N2 @ ( suc @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_less_eq
% 0.30/0.46 thf(fact_81_less__Suc__eq,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ ( suc @ N2 ) )
% 0.30/0.46 = ( ( ord_less @ nat @ M @ N2 )
% 0.30/0.46 | ( M = N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_Suc_eq
% 0.30/0.46 thf(fact_82_Ex__less__Suc,axiom,
% 0.30/0.46 ! [N2: nat,P2: nat > $o] :
% 0.30/0.46 ( ( ? [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ ( suc @ N2 ) )
% 0.30/0.46 & ( P2 @ I3 ) ) )
% 0.30/0.46 = ( ( P2 @ N2 )
% 0.30/0.46 | ? [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ N2 )
% 0.30/0.46 & ( P2 @ I3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Ex_less_Suc
% 0.30/0.46 thf(fact_83_less__SucI,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ N2 )
% 0.30/0.46 => ( ord_less @ nat @ M @ ( suc @ N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_SucI
% 0.30/0.46 thf(fact_84_less__SucE,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ ( suc @ N2 ) )
% 0.30/0.46 => ( ~ ( ord_less @ nat @ M @ N2 )
% 0.30/0.46 => ( M = N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_SucE
% 0.30/0.46 thf(fact_85_Suc__lessI,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ N2 )
% 0.30/0.46 => ( ( ( suc @ M )
% 0.30/0.46 != N2 )
% 0.30/0.46 => ( ord_less @ nat @ ( suc @ M ) @ N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_lessI
% 0.30/0.46 thf(fact_86_Suc__lessE,axiom,
% 0.30/0.46 ! [I: nat,K: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( suc @ I ) @ K )
% 0.30/0.46 => ~ ! [J2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ J2 )
% 0.30/0.46 => ( K
% 0.30/0.46 != ( suc @ J2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_lessE
% 0.30/0.46 thf(fact_87_Suc__lessD,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( suc @ M ) @ N2 )
% 0.30/0.46 => ( ord_less @ nat @ M @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_lessD
% 0.30/0.46 thf(fact_88_Nat_OlessE,axiom,
% 0.30/0.46 ! [I: nat,K: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ K )
% 0.30/0.46 => ( ( K
% 0.30/0.46 != ( suc @ I ) )
% 0.30/0.46 => ~ ! [J2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ J2 )
% 0.30/0.46 => ( K
% 0.30/0.46 != ( suc @ J2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Nat.lessE
% 0.30/0.46 thf(fact_89_infinite__descent0__measure,axiom,
% 0.30/0.46 ! [A: $tType,V2: A > nat,P2: A > $o,X: A] :
% 0.30/0.46 ( ! [X3: A] :
% 0.30/0.46 ( ( ( V2 @ X3 )
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 => ( P2 @ X3 ) )
% 0.30/0.46 => ( ! [X3: A] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V2 @ X3 ) )
% 0.30/0.46 => ( ~ ( P2 @ X3 )
% 0.30/0.46 => ? [Y: A] :
% 0.30/0.46 ( ( ord_less @ nat @ ( V2 @ Y ) @ ( V2 @ X3 ) )
% 0.30/0.46 & ~ ( P2 @ Y ) ) ) )
% 0.30/0.46 => ( P2 @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % infinite_descent0_measure
% 0.30/0.46 thf(fact_90_bot__nat__0_Oextremum__strict,axiom,
% 0.30/0.46 ! [A8: nat] :
% 0.30/0.46 ~ ( ord_less @ nat @ A8 @ ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_nat_0.extremum_strict
% 0.30/0.46 thf(fact_91_infinite__descent0,axiom,
% 0.30/0.46 ! [P2: nat > $o,N2: nat] :
% 0.30/0.46 ( ( P2 @ ( zero_zero @ nat ) )
% 0.30/0.46 => ( ! [N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.30/0.46 => ( ~ ( P2 @ N )
% 0.30/0.46 => ? [M2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M2 @ N )
% 0.30/0.46 & ~ ( P2 @ M2 ) ) ) )
% 0.30/0.46 => ( P2 @ N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % infinite_descent0
% 0.30/0.46 thf(fact_92_gr__implies__not0,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ N2 )
% 0.30/0.46 => ( N2
% 0.30/0.46 != ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % gr_implies_not0
% 0.30/0.46 thf(fact_93_less__zeroE,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ~ ( ord_less @ nat @ N2 @ ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_zeroE
% 0.30/0.46 thf(fact_94_not__less0,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ~ ( ord_less @ nat @ N2 @ ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_less0
% 0.30/0.46 thf(fact_95_not__gr0,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 ) )
% 0.30/0.46 = ( N2
% 0.30/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_gr0
% 0.30/0.46 thf(fact_96_gr0I,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ( ( N2
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % gr0I
% 0.30/0.46 thf(fact_97_zero__induct__lemma,axiom,
% 0.30/0.46 ! [P2: nat > $o,K: nat,I: nat] :
% 0.30/0.46 ( ( P2 @ K )
% 0.30/0.46 => ( ! [N: nat] :
% 0.30/0.46 ( ( P2 @ ( suc @ N ) )
% 0.30/0.46 => ( P2 @ N ) )
% 0.30/0.46 => ( P2 @ ( minus_minus @ nat @ K @ I ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_induct_lemma
% 0.30/0.46 thf(fact_98_minus__nat_Odiff__0,axiom,
% 0.30/0.46 ! [M: nat] :
% 0.30/0.46 ( ( minus_minus @ nat @ M @ ( zero_zero @ nat ) )
% 0.30/0.46 = M ) ).
% 0.30/0.46
% 0.30/0.46 % minus_nat.diff_0
% 0.30/0.46 thf(fact_99_diffs0__imp__equal,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ( minus_minus @ nat @ M @ N2 )
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 => ( ( ( minus_minus @ nat @ N2 @ M )
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 => ( M = N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diffs0_imp_equal
% 0.30/0.46 thf(fact_100_less__imp__diff__less,axiom,
% 0.30/0.46 ! [J: nat,K: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ J @ K )
% 0.30/0.46 => ( ord_less @ nat @ ( minus_minus @ nat @ J @ N2 ) @ K ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_imp_diff_less
% 0.30/0.46 thf(fact_101_diff__less__mono2,axiom,
% 0.30/0.46 ! [M: nat,N2: nat,L: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ N2 )
% 0.30/0.46 => ( ( ord_less @ nat @ M @ L )
% 0.30/0.46 => ( ord_less @ nat @ ( minus_minus @ nat @ L @ N2 ) @ ( minus_minus @ nat @ L @ M ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_less_mono2
% 0.30/0.46 thf(fact_102_less__iff__diff__less__0,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_ab_group_add @ A )
% 0.30/0.46 => ( ( ord_less @ A )
% 0.30/0.46 = ( ^ [A9: A,B3: A] : ( ord_less @ A @ ( minus_minus @ A @ A9 @ B3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_iff_diff_less_0
% 0.30/0.46 thf(fact_103_lift__Suc__mono__less__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [F: nat > A,N2: nat,M: nat] :
% 0.30/0.46 ( ! [N: nat] : ( ord_less @ A @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.30/0.46 => ( ( ord_less @ A @ ( F @ N2 ) @ ( F @ M ) )
% 0.30/0.46 = ( ord_less @ nat @ N2 @ M ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lift_Suc_mono_less_iff
% 0.30/0.46 thf(fact_104_lift__Suc__mono__less,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [F: nat > A,N2: nat,N3: nat] :
% 0.30/0.46 ( ! [N: nat] : ( ord_less @ A @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.30/0.46 => ( ( ord_less @ nat @ N2 @ N3 )
% 0.30/0.46 => ( ord_less @ A @ ( F @ N2 ) @ ( F @ N3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lift_Suc_mono_less
% 0.30/0.46 thf(fact_105_less__Suc__eq__0__disj,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ ( suc @ N2 ) )
% 0.30/0.46 = ( ( M
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 | ? [J3: nat] :
% 0.30/0.46 ( ( M
% 0.30/0.46 = ( suc @ J3 ) )
% 0.30/0.46 & ( ord_less @ nat @ J3 @ N2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_Suc_eq_0_disj
% 0.30/0.46 thf(fact_106_gr0__implies__Suc,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.30/0.46 => ? [M3: nat] :
% 0.30/0.46 ( N2
% 0.30/0.46 = ( suc @ M3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % gr0_implies_Suc
% 0.30/0.46 thf(fact_107_All__less__Suc2,axiom,
% 0.30/0.46 ! [N2: nat,P2: nat > $o] :
% 0.30/0.46 ( ( ! [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ ( suc @ N2 ) )
% 0.30/0.46 => ( P2 @ I3 ) ) )
% 0.30/0.46 = ( ( P2 @ ( zero_zero @ nat ) )
% 0.30/0.46 & ! [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ N2 )
% 0.30/0.46 => ( P2 @ ( suc @ I3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % All_less_Suc2
% 0.30/0.46 thf(fact_108_gr0__conv__Suc,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.30/0.46 = ( ? [M5: nat] :
% 0.30/0.46 ( N2
% 0.30/0.46 = ( suc @ M5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % gr0_conv_Suc
% 0.30/0.46 thf(fact_109_Ex__less__Suc2,axiom,
% 0.30/0.46 ! [N2: nat,P2: nat > $o] :
% 0.30/0.46 ( ( ? [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ ( suc @ N2 ) )
% 0.30/0.46 & ( P2 @ I3 ) ) )
% 0.30/0.46 = ( ( P2 @ ( zero_zero @ nat ) )
% 0.30/0.46 | ? [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ N2 )
% 0.30/0.46 & ( P2 @ ( suc @ I3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Ex_less_Suc2
% 0.30/0.46 thf(fact_110_diff__less__Suc,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] : ( ord_less @ nat @ ( minus_minus @ nat @ M @ N2 ) @ ( suc @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_less_Suc
% 0.30/0.46 thf(fact_111_Suc__diff__Suc,axiom,
% 0.30/0.46 ! [N2: nat,M: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ N2 @ M )
% 0.30/0.46 => ( ( suc @ ( minus_minus @ nat @ M @ ( suc @ N2 ) ) )
% 0.30/0.46 = ( minus_minus @ nat @ M @ N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_diff_Suc
% 0.30/0.46 thf(fact_112_diff__less,axiom,
% 0.30/0.46 ! [N2: nat,M: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.30/0.46 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 0.30/0.46 => ( ord_less @ nat @ ( minus_minus @ nat @ M @ N2 ) @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_less
% 0.30/0.46 thf(fact_113_diff__Suc__less,axiom,
% 0.30/0.46 ! [N2: nat,I: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.30/0.46 => ( ord_less @ nat @ ( minus_minus @ nat @ N2 @ ( suc @ I ) ) @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_Suc_less
% 0.30/0.46 thf(fact_114_SameCfgOnLow,axiom,
% 0.30/0.46 ! [I4: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) )
% 0.30/0.46 => ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ I4 )
% 0.30/0.46 = ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % SameCfgOnLow
% 0.30/0.46 thf(fact_115__092_060open_062fe_Aindex_A_B_AnMsg_A_061_Afe_A_ISuc_Aindex_J_A_B_AnMsg_092_060close_062,axiom,
% 0.30/0.46 ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ nMsg )
% 0.30/0.46 = ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ nMsg ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>fe index ! nMsg = fe (Suc index) ! nMsg\<close>
% 0.30/0.46 thf(fact_116_ShorterTrace,axiom,
% 0.30/0.46 ord_less @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ShorterTrace
% 0.30/0.46 thf(fact_117_NotEmpty_I1_J,axiom,
% 0.30/0.46 ( ( fe @ ( suc @ index ) )
% 0.30/0.46 != ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % NotEmpty(1)
% 0.30/0.46 thf(fact_118_IPrefixList,axiom,
% 0.30/0.46 ! [I4: nat] : ( prefixList @ ( message @ p @ v ) @ ( ft @ I4 ) @ ( ft @ ( suc @ I4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % IPrefixList
% 0.30/0.46 thf(fact_119_IPrefixListEx,axiom,
% 0.30/0.46 ! [I4: nat] : ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ I4 ) @ ( fe @ ( suc @ I4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % IPrefixListEx
% 0.30/0.46 thf(fact_120_NatPredicateTippingPoint,axiom,
% 0.30/0.46 ! [N22: nat,Pr: nat > $o] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N22 )
% 0.30/0.46 => ( ( Pr @ ( zero_zero @ nat ) )
% 0.30/0.46 => ( ~ ( Pr @ N22 )
% 0.30/0.46 => ? [N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ N @ N22 )
% 0.30/0.46 & ( Pr @ N )
% 0.30/0.46 & ~ ( Pr @ ( suc @ N ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % NatPredicateTippingPoint
% 0.30/0.46 thf(fact_121_NotEmpty_I2_J,axiom,
% 0.30/0.46 ( ( fe @ index )
% 0.30/0.46 != ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % NotEmpty(2)
% 0.30/0.46 thf(fact_122_AssumptionFair_I4_J,axiom,
% 0.30/0.46 isReceiverOf @ p @ v @ p2 @ msg ).
% 0.30/0.46
% 0.30/0.46 % AssumptionFair(4)
% 0.30/0.46 thf(fact_123_AssumpOcc6_I2_J,axiom,
% 0.30/0.46 ( msg
% 0.30/0.46 != ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % AssumpOcc6(2)
% 0.30/0.46 thf(fact_124_Occ1,axiom,
% 0.30/0.46 ? [P3: p] : ( isReceiverOf @ p @ v @ P3 @ msg ) ).
% 0.30/0.46
% 0.30/0.46 % Occ1
% 0.30/0.46 thf(fact_125_AssumptionSubset2_I1_J,axiom,
% 0.30/0.46 ? [P3: p] : ( isReceiverOf @ p @ v @ P3 @ msgInSet ) ).
% 0.30/0.46
% 0.30/0.46 % AssumptionSubset2(1)
% 0.30/0.46 thf(fact_126_SameMsgOnLow,axiom,
% 0.30/0.46 ! [I4: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 0.30/0.46 => ( ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ I4 )
% 0.30/0.46 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % SameMsgOnLow
% 0.30/0.46 thf(fact_127_le__zero__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ! [N2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ N2 @ ( zero_zero @ A ) )
% 0.30/0.46 = ( N2
% 0.30/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_zero_eq
% 0.30/0.46 thf(fact_128_Suc__le__mono,axiom,
% 0.30/0.46 ! [N2: nat,M: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( suc @ N2 ) @ ( suc @ M ) )
% 0.30/0.46 = ( ord_less_eq @ nat @ N2 @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_le_mono
% 0.30/0.46 thf(fact_129_le0,axiom,
% 0.30/0.46 ! [N2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N2 ) ).
% 0.30/0.46
% 0.30/0.46 % le0
% 0.30/0.46 thf(fact_130_bot__nat__0_Oextremum,axiom,
% 0.30/0.46 ! [A8: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A8 ) ).
% 0.30/0.46
% 0.30/0.46 % bot_nat_0.extremum
% 0.30/0.46 thf(fact_131_diff__diff__cancel,axiom,
% 0.30/0.46 ! [I: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ I @ N2 )
% 0.30/0.46 => ( ( minus_minus @ nat @ N2 @ ( minus_minus @ nat @ N2 @ I ) )
% 0.30/0.46 = I ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_diff_cancel
% 0.30/0.46 thf(fact_132__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,
% 0.30/0.46 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 ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>length (fe index) - 1 \<le> length (fe (Suc index)) - 1\<close>
% 0.30/0.46 thf(fact_133__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,
% 0.30/0.46 ~ ? [I4: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 0.30/0.46 & ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ I4 )
% 0.30/0.46 & ( msg
% 0.30/0.46 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>\<not> (\<exists>i<length (ft (Suc index)). length (ft index) \<le> i \<and> msg = ft (Suc index) ! i)\<close>
% 0.30/0.46 thf(fact_134_NotConsumedIntermediate,axiom,
% 0.30/0.46 ! [I4: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ I4 )
% 0.30/0.46 => ( ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I4 )
% 0.30/0.46 != msg ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % NotConsumedIntermediate
% 0.30/0.46 thf(fact_135_OccSameMsg,axiom,
% 0.30/0.46 ! [N4: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ nMsg @ N4 )
% 0.30/0.46 => ( ( ord_less @ nat @ N4 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 0.30/0.46 => ( ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ N4 )
% 0.30/0.46 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ N4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % OccSameMsg
% 0.30/0.46 thf(fact_136_diff__ge__0__iff__ge,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_ab_group_add @ A )
% 0.30/0.46 => ! [A8: A,B: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A8 @ B ) )
% 0.30/0.46 = ( ord_less_eq @ A @ B @ A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_ge_0_iff_ge
% 0.30/0.46 thf(fact_137_Occ5,axiom,
% 0.30/0.46 ! [N4: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ nMsg @ N4 )
% 0.30/0.46 => ( ( ord_less @ nat @ N4 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 0.30/0.46 => ( msg
% 0.30/0.46 != ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ N4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Occ5
% 0.30/0.46 thf(fact_138_diff__is__0__eq,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ( minus_minus @ nat @ M @ N2 )
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 = ( ord_less_eq @ nat @ M @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_is_0_eq
% 0.30/0.46 thf(fact_139_diff__is__0__eq_H,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.30/0.46 => ( ( minus_minus @ nat @ M @ N2 )
% 0.30/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_is_0_eq'
% 0.30/0.46 thf(fact_140_less__one,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ N2 @ ( one_one @ nat ) )
% 0.30/0.46 = ( N2
% 0.30/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_one
% 0.30/0.46 thf(fact_141_diff__Suc__1,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ( ( minus_minus @ nat @ ( suc @ N2 ) @ ( one_one @ nat ) )
% 0.30/0.46 = N2 ) ).
% 0.30/0.46
% 0.30/0.46 % diff_Suc_1
% 0.30/0.46 thf(fact_142_AssumptionSubset3_I5_J,axiom,
% 0.30/0.46 ! [N4: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ nMsg @ N4 )
% 0.30/0.46 => ( ( ord_less @ nat @ N4 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 0.30/0.46 => ( msg
% 0.30/0.46 != ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ N4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % AssumptionSubset3(5)
% 0.30/0.46 thf(fact_143_AssumptionSubset2_I5_J,axiom,
% 0.30/0.46 ! [N4: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ n1 @ N4 )
% 0.30/0.46 => ( ( ord_less @ nat @ N4 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 0.30/0.46 => ( msgInSet
% 0.30/0.46 != ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ N4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % AssumptionSubset2(5)
% 0.30/0.46 thf(fact_144__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,
% 0.30/0.46 ~ ? [I4: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I4 @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) )
% 0.30/0.46 & ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ I4 )
% 0.30/0.46 & ( msg
% 0.30/0.46 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>\<not> (\<exists>i<length (fe (Suc index)) - 1. length (fe index) - 1 \<le> i \<and> msg = ft (Suc index) ! i)\<close>
% 0.30/0.46 thf(fact_145_Suc__diff__1,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.30/0.46 => ( ( suc @ ( minus_minus @ nat @ N2 @ ( one_one @ nat ) ) )
% 0.30/0.46 = N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_diff_1
% 0.30/0.46 thf(fact_146_AssumptionFairContr,axiom,
% 0.30/0.46 ! [N4: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ n @ N4 )
% 0.30/0.46 => ! [N0: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ N0 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N4 ) ) )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) @ N0 )
% 0.30/0.46 => ( msg
% 0.30/0.46 != ( nth @ ( message @ p @ v ) @ ( ft @ N4 ) @ N0 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % AssumptionFairContr
% 0.30/0.46 thf(fact_147_AssumpOcc6_I3_J,axiom,
% 0.30/0.46 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) @ msg ).
% 0.30/0.46
% 0.30/0.46 % AssumpOcc6(3)
% 0.30/0.46 thf(fact_148_le__refl,axiom,
% 0.30/0.46 ! [N2: nat] : ( ord_less_eq @ nat @ N2 @ N2 ) ).
% 0.30/0.46
% 0.30/0.46 % le_refl
% 0.30/0.46 thf(fact_149_le__trans,axiom,
% 0.30/0.46 ! [I: nat,J: nat,K: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ I @ J )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ J @ K )
% 0.30/0.46 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_trans
% 0.30/0.46 thf(fact_150_eq__imp__le,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( M = N2 )
% 0.30/0.46 => ( ord_less_eq @ nat @ M @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_imp_le
% 0.30/0.46 thf(fact_151_le__antisym,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ N2 @ M )
% 0.30/0.46 => ( M = N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_antisym
% 0.30/0.46 thf(fact_152_nat__le__linear,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.30/0.46 | ( ord_less_eq @ nat @ N2 @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_le_linear
% 0.30/0.46 thf(fact_153_one__reorient,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( one @ A )
% 0.30/0.46 => ! [X: A] :
% 0.30/0.46 ( ( ( one_one @ A )
% 0.30/0.46 = X )
% 0.30/0.46 = ( X
% 0.30/0.46 = ( one_one @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % one_reorient
% 0.30/0.46 thf(fact_154_Nat_Oex__has__greatest__nat,axiom,
% 0.30/0.46 ! [P2: nat > $o,K: nat,B: nat] :
% 0.30/0.46 ( ( P2 @ K )
% 0.30/0.46 => ( ! [Y5: nat] :
% 0.30/0.46 ( ( P2 @ Y5 )
% 0.30/0.46 => ( ord_less_eq @ nat @ Y5 @ B ) )
% 0.30/0.46 => ? [X3: nat] :
% 0.30/0.46 ( ( P2 @ X3 )
% 0.30/0.46 & ! [Y: nat] :
% 0.30/0.46 ( ( P2 @ Y )
% 0.30/0.46 => ( ord_less_eq @ nat @ Y @ X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Nat.ex_has_greatest_nat
% 0.30/0.46 thf(fact_155_PrefixListTransitive,axiom,
% 0.30/0.46 ! [A: $tType,L1: list @ A,L2: list @ A,L3: list @ A] :
% 0.30/0.46 ( ( prefixList @ A @ L1 @ L2 )
% 0.30/0.46 => ( ( prefixList @ A @ L2 @ L3 )
% 0.30/0.46 => ( prefixList @ A @ L1 @ L3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % PrefixListTransitive
% 0.30/0.46 thf(fact_156_MinPredicate,axiom,
% 0.30/0.46 ! [P2: nat > $o] :
% 0.30/0.46 ( ? [X_1: nat] : ( P2 @ X_1 )
% 0.30/0.46 => ? [N02: nat] :
% 0.30/0.46 ( ( P2 @ N02 )
% 0.30/0.46 & ! [N4: nat] :
% 0.30/0.46 ( ( P2 @ N4 )
% 0.30/0.46 => ( ord_less_eq @ nat @ N02 @ N4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % MinPredicate
% 0.30/0.46 thf(fact_157_lift__Suc__antimono__le,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [F: nat > A,N2: nat,N3: nat] :
% 0.30/0.46 ( ! [N: nat] : ( ord_less_eq @ A @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ N2 @ N3 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F @ N3 ) @ ( F @ N2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lift_Suc_antimono_le
% 0.30/0.46 thf(fact_158_lift__Suc__mono__le,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [F: nat > A,N2: nat,N3: nat] :
% 0.30/0.46 ( ! [N: nat] : ( ord_less_eq @ A @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ N2 @ N3 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F @ N2 ) @ ( F @ N3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lift_Suc_mono_le
% 0.30/0.46 thf(fact_159_KeepProperty,axiom,
% 0.30/0.46 ! [Low: nat,P2: nat > $o,Q: nat > $o] :
% 0.30/0.46 ( ! [I2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ Low @ I2 )
% 0.30/0.46 => ( ( P2 @ I2 )
% 0.30/0.46 => ( ( P2 @ ( suc @ I2 ) )
% 0.30/0.46 & ( Q @ I2 ) ) ) )
% 0.30/0.46 => ( ( P2 @ Low )
% 0.30/0.46 => ! [I4: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ Low @ I4 )
% 0.30/0.46 => ( Q @ I4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % KeepProperty
% 0.30/0.46 thf(fact_160_PrefixSameOnLow,axiom,
% 0.30/0.46 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 0.30/0.46 ( ( prefixList @ A @ L1 @ L2 )
% 0.30/0.46 => ! [Index: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ Index @ ( size_size @ ( list @ A ) @ L1 ) )
% 0.30/0.46 => ( ( nth @ A @ L1 @ Index )
% 0.30/0.46 = ( nth @ A @ L2 @ Index ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % PrefixSameOnLow
% 0.30/0.46 thf(fact_161_zero__le,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % zero_le
% 0.30/0.46 thf(fact_162_diff__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_ab_group_add @ A )
% 0.30/0.46 => ! [A8: A,B: A,D: A,C: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A8 @ B )
% 0.30/0.46 => ( ( ord_less_eq @ A @ D @ C )
% 0.30/0.46 => ( ord_less_eq @ A @ ( minus_minus @ A @ A8 @ C ) @ ( minus_minus @ A @ B @ D ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_mono
% 0.30/0.46 thf(fact_163_diff__left__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_ab_group_add @ A )
% 0.30/0.46 => ! [B: A,A8: A,C: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B @ A8 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A8 ) @ ( minus_minus @ A @ C @ B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_left_mono
% 0.30/0.46 thf(fact_164_diff__right__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_ab_group_add @ A )
% 0.30/0.46 => ! [A8: A,B: A,C: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A8 @ B )
% 0.30/0.46 => ( ord_less_eq @ A @ ( minus_minus @ A @ A8 @ C ) @ ( minus_minus @ A @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_right_mono
% 0.30/0.46 thf(fact_165_diff__eq__diff__less__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_ab_group_add @ A )
% 0.30/0.46 => ! [A8: A,B: A,C: A,D: A] :
% 0.30/0.46 ( ( ( minus_minus @ A @ A8 @ B )
% 0.30/0.46 = ( minus_minus @ A @ C @ D ) )
% 0.30/0.46 => ( ( ord_less_eq @ A @ A8 @ B )
% 0.30/0.46 = ( ord_less_eq @ A @ C @ D ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_eq_diff_less_eq
% 0.30/0.46 thf(fact_166_Suc__leD,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N2 )
% 0.30/0.46 => ( ord_less_eq @ nat @ M @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_leD
% 0.30/0.46 thf(fact_167_le__SucE,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ ( suc @ N2 ) )
% 0.30/0.46 => ( ~ ( ord_less_eq @ nat @ M @ N2 )
% 0.30/0.46 => ( M
% 0.30/0.46 = ( suc @ N2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_SucE
% 0.30/0.46 thf(fact_168_le__SucI,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.30/0.46 => ( ord_less_eq @ nat @ M @ ( suc @ N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_SucI
% 0.30/0.46 thf(fact_169_Suc__le__D,axiom,
% 0.30/0.46 ! [N2: nat,M6: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( suc @ N2 ) @ M6 )
% 0.30/0.46 => ? [M3: nat] :
% 0.30/0.46 ( M6
% 0.30/0.46 = ( suc @ M3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_le_D
% 0.30/0.46 thf(fact_170_le__Suc__eq,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ ( suc @ N2 ) )
% 0.30/0.46 = ( ( ord_less_eq @ nat @ M @ N2 )
% 0.30/0.46 | ( M
% 0.30/0.46 = ( suc @ N2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_Suc_eq
% 0.30/0.46 thf(fact_171_Suc__n__not__le__n,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ~ ( ord_less_eq @ nat @ ( suc @ N2 ) @ N2 ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_n_not_le_n
% 0.30/0.46 thf(fact_172_not__less__eq__eq,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ~ ( ord_less_eq @ nat @ M @ N2 ) )
% 0.30/0.46 = ( ord_less_eq @ nat @ ( suc @ N2 ) @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_less_eq_eq
% 0.30/0.46 thf(fact_173_full__nat__induct,axiom,
% 0.30/0.46 ! [P2: nat > $o,N2: nat] :
% 0.30/0.46 ( ! [N: nat] :
% 0.30/0.46 ( ! [M2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( suc @ M2 ) @ N )
% 0.30/0.46 => ( P2 @ M2 ) )
% 0.30/0.46 => ( P2 @ N ) )
% 0.30/0.46 => ( P2 @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % full_nat_induct
% 0.30/0.46 thf(fact_174_nat__induct__at__least,axiom,
% 0.30/0.46 ! [M: nat,N2: nat,P2: nat > $o] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.30/0.46 => ( ( P2 @ M )
% 0.30/0.46 => ( ! [N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ N )
% 0.30/0.46 => ( ( P2 @ N )
% 0.30/0.46 => ( P2 @ ( suc @ N ) ) ) )
% 0.30/0.46 => ( P2 @ N2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_induct_at_least
% 0.30/0.46 thf(fact_175_transitive__stepwise__le,axiom,
% 0.30/0.46 ! [M: nat,N2: nat,R: nat > nat > $o] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.30/0.46 => ( ! [X3: nat] : ( R @ X3 @ X3 )
% 0.30/0.46 => ( ! [X3: nat,Y5: nat,Z3: nat] :
% 0.30/0.46 ( ( R @ X3 @ Y5 )
% 0.30/0.46 => ( ( R @ Y5 @ Z3 )
% 0.30/0.46 => ( R @ X3 @ Z3 ) ) )
% 0.30/0.46 => ( ! [N: nat] : ( R @ N @ ( suc @ N ) )
% 0.30/0.46 => ( R @ M @ N2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % transitive_stepwise_le
% 0.30/0.46 thf(fact_176_less__eq__nat_Osimps_I1_J,axiom,
% 0.30/0.46 ! [N2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N2 ) ).
% 0.30/0.46
% 0.30/0.46 % less_eq_nat.simps(1)
% 0.30/0.46 thf(fact_177_le__0__eq,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ N2 @ ( zero_zero @ nat ) )
% 0.30/0.46 = ( N2
% 0.30/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_0_eq
% 0.30/0.46 thf(fact_178_bot__nat__0_Oextremum__unique,axiom,
% 0.30/0.46 ! [A8: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ A8 @ ( zero_zero @ nat ) )
% 0.30/0.46 = ( A8
% 0.30/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_nat_0.extremum_unique
% 0.30/0.46 thf(fact_179_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.30/0.46 ! [A8: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ A8 @ ( zero_zero @ nat ) )
% 0.30/0.46 => ( A8
% 0.30/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bot_nat_0.extremum_uniqueI
% 0.30/0.46 thf(fact_180_nat__less__le,axiom,
% 0.30/0.46 ( ( ord_less @ nat )
% 0.30/0.46 = ( ^ [M5: nat,N5: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M5 @ N5 )
% 0.30/0.46 & ( M5 != N5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_less_le
% 0.30/0.46 thf(fact_181_less__imp__le__nat,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ N2 )
% 0.30/0.46 => ( ord_less_eq @ nat @ M @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_imp_le_nat
% 0.30/0.46 thf(fact_182_le__eq__less__or__eq,axiom,
% 0.30/0.46 ( ( ord_less_eq @ nat )
% 0.30/0.46 = ( ^ [M5: nat,N5: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M5 @ N5 )
% 0.30/0.46 | ( M5 = N5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_eq_less_or_eq
% 0.30/0.46 thf(fact_183_less__or__eq__imp__le,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ( ord_less @ nat @ M @ N2 )
% 0.30/0.46 | ( M = N2 ) )
% 0.30/0.46 => ( ord_less_eq @ nat @ M @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_or_eq_imp_le
% 0.30/0.46 thf(fact_184_le__neq__implies__less,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.30/0.46 => ( ( M != N2 )
% 0.30/0.46 => ( ord_less @ nat @ M @ N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_neq_implies_less
% 0.30/0.46 thf(fact_185_less__mono__imp__le__mono,axiom,
% 0.30/0.46 ! [F: nat > nat,I: nat,J: nat] :
% 0.30/0.46 ( ! [I2: nat,J2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I2 @ J2 )
% 0.30/0.46 => ( ord_less @ nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ I @ J )
% 0.30/0.46 => ( ord_less_eq @ nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_mono_imp_le_mono
% 0.30/0.46 thf(fact_186_eq__diff__iff,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ K @ M )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ K @ N2 )
% 0.30/0.46 => ( ( ( minus_minus @ nat @ M @ K )
% 0.30/0.46 = ( minus_minus @ nat @ N2 @ K ) )
% 0.30/0.46 = ( M = N2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_diff_iff
% 0.30/0.46 thf(fact_187_le__diff__iff,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ K @ M )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ K @ N2 )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N2 @ K ) )
% 0.30/0.46 = ( ord_less_eq @ nat @ M @ N2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_diff_iff
% 0.30/0.46 thf(fact_188_Nat_Odiff__diff__eq,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ K @ M )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ K @ N2 )
% 0.30/0.46 => ( ( minus_minus @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N2 @ K ) )
% 0.30/0.46 = ( minus_minus @ nat @ M @ N2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Nat.diff_diff_eq
% 0.30/0.46 thf(fact_189_diff__le__mono,axiom,
% 0.30/0.46 ! [M: nat,N2: nat,L: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.30/0.46 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ L ) @ ( minus_minus @ nat @ N2 @ L ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_le_mono
% 0.30/0.46 thf(fact_190_diff__le__self,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ N2 ) @ M ) ).
% 0.30/0.46
% 0.30/0.46 % diff_le_self
% 0.30/0.46 thf(fact_191_le__diff__iff_H,axiom,
% 0.30/0.46 ! [A8: nat,C: nat,B: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ A8 @ C )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ B @ C )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ A8 ) @ ( minus_minus @ nat @ C @ B ) )
% 0.30/0.46 = ( ord_less_eq @ nat @ B @ A8 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_diff_iff'
% 0.30/0.46 thf(fact_192_diff__le__mono2,axiom,
% 0.30/0.46 ! [M: nat,N2: nat,L: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.30/0.46 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ L @ N2 ) @ ( minus_minus @ nat @ L @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_le_mono2
% 0.30/0.46 thf(fact_193_MinPredicate2,axiom,
% 0.30/0.46 ! [P2: nat > $o] :
% 0.30/0.46 ( ? [X_1: nat] : ( P2 @ X_1 )
% 0.30/0.46 => ? [N02: nat] :
% 0.30/0.46 ( ( P2 @ N02 )
% 0.30/0.46 & ( ( N02
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 | ~ ( P2 @ ( minus_minus @ nat @ N02 @ ( one_one @ nat ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % MinPredicate2
% 0.30/0.46 thf(fact_194_PrefixListMonotonicity,axiom,
% 0.30/0.46 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 0.30/0.46 ( ( prefixList @ A @ L1 @ L2 )
% 0.30/0.46 => ( ord_less @ nat @ ( size_size @ ( list @ A ) @ L1 ) @ ( size_size @ ( list @ A ) @ L2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % PrefixListMonotonicity
% 0.30/0.46 thf(fact_195_le__iff__diff__le__0,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordered_ab_group_add @ A )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [A9: A,B3: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ A9 @ B3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_iff_diff_le_0
% 0.30/0.46 thf(fact_196_Suc__leI,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ N2 )
% 0.30/0.46 => ( ord_less_eq @ nat @ ( suc @ M ) @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_leI
% 0.30/0.46 thf(fact_197_Suc__le__eq,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N2 )
% 0.30/0.46 = ( ord_less @ nat @ M @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_le_eq
% 0.30/0.46 thf(fact_198_dec__induct,axiom,
% 0.30/0.46 ! [I: nat,J: nat,P2: nat > $o] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ I @ J )
% 0.30/0.46 => ( ( P2 @ I )
% 0.30/0.46 => ( ! [N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ I @ N )
% 0.30/0.46 => ( ( ord_less @ nat @ N @ J )
% 0.30/0.46 => ( ( P2 @ N )
% 0.30/0.46 => ( P2 @ ( suc @ N ) ) ) ) )
% 0.30/0.46 => ( P2 @ J ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dec_induct
% 0.30/0.46 thf(fact_199_inc__induct,axiom,
% 0.30/0.46 ! [I: nat,J: nat,P2: nat > $o] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ I @ J )
% 0.30/0.46 => ( ( P2 @ J )
% 0.30/0.46 => ( ! [N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ I @ N )
% 0.30/0.46 => ( ( ord_less @ nat @ N @ J )
% 0.30/0.46 => ( ( P2 @ ( suc @ N ) )
% 0.30/0.46 => ( P2 @ N ) ) ) )
% 0.30/0.46 => ( P2 @ I ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % inc_induct
% 0.30/0.46 thf(fact_200_Suc__le__lessD,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N2 )
% 0.30/0.46 => ( ord_less @ nat @ M @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_le_lessD
% 0.30/0.46 thf(fact_201_le__less__Suc__eq,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.30/0.46 => ( ( ord_less @ nat @ N2 @ ( suc @ M ) )
% 0.30/0.46 = ( N2 = M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_less_Suc_eq
% 0.30/0.46 thf(fact_202_less__Suc__eq__le,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ ( suc @ N2 ) )
% 0.30/0.46 = ( ord_less_eq @ nat @ M @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_Suc_eq_le
% 0.30/0.46 thf(fact_203_less__eq__Suc__le,axiom,
% 0.30/0.46 ( ( ord_less @ nat )
% 0.30/0.46 = ( ^ [N5: nat] : ( ord_less_eq @ nat @ ( suc @ N5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_eq_Suc_le
% 0.30/0.46 thf(fact_204_le__imp__less__Suc,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.30/0.46 => ( ord_less @ nat @ M @ ( suc @ N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_imp_less_Suc
% 0.30/0.46 thf(fact_205_ex__least__nat__le,axiom,
% 0.30/0.46 ! [P2: nat > $o,N2: nat] :
% 0.30/0.46 ( ( P2 @ N2 )
% 0.30/0.46 => ( ~ ( P2 @ ( zero_zero @ nat ) )
% 0.30/0.46 => ? [K2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ K2 @ N2 )
% 0.30/0.46 & ! [I4: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I4 @ K2 )
% 0.30/0.46 => ~ ( P2 @ I4 ) )
% 0.30/0.46 & ( P2 @ K2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ex_least_nat_le
% 0.30/0.46 thf(fact_206_Suc__diff__le,axiom,
% 0.30/0.46 ! [N2: nat,M: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ N2 @ M )
% 0.30/0.46 => ( ( minus_minus @ nat @ ( suc @ M ) @ N2 )
% 0.30/0.46 = ( suc @ ( minus_minus @ nat @ M @ N2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_diff_le
% 0.30/0.46 thf(fact_207_less__diff__iff,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ K @ M )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ K @ N2 )
% 0.30/0.46 => ( ( ord_less @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N2 @ K ) )
% 0.30/0.46 = ( ord_less @ nat @ M @ N2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_diff_iff
% 0.30/0.46 thf(fact_208_diff__less__mono,axiom,
% 0.30/0.46 ! [A8: nat,B: nat,C: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ A8 @ B )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ C @ A8 )
% 0.30/0.46 => ( ord_less @ nat @ ( minus_minus @ nat @ A8 @ C ) @ ( minus_minus @ nat @ B @ C ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_less_mono
% 0.30/0.46 thf(fact_209_One__nat__def,axiom,
% 0.30/0.46 ( ( one_one @ nat )
% 0.30/0.46 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % One_nat_def
% 0.30/0.46 thf(fact_210_diff__Suc__eq__diff__pred,axiom,
% 0.30/0.46 ! [M: nat,N2: nat] :
% 0.30/0.46 ( ( minus_minus @ nat @ M @ ( suc @ N2 ) )
% 0.30/0.46 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ ( one_one @ nat ) ) @ N2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_Suc_eq_diff_pred
% 0.30/0.46 thf(fact_211_ex__least__nat__less,axiom,
% 0.30/0.46 ! [P2: nat > $o,N2: nat] :
% 0.30/0.46 ( ( P2 @ N2 )
% 0.30/0.46 => ( ~ ( P2 @ ( zero_zero @ nat ) )
% 0.30/0.46 => ? [K2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ K2 @ N2 )
% 0.30/0.46 & ! [I4: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ I4 @ K2 )
% 0.30/0.46 => ~ ( P2 @ I4 ) )
% 0.30/0.46 & ( P2 @ ( suc @ K2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ex_least_nat_less
% 0.30/0.46 thf(fact_212_nat__induct__non__zero,axiom,
% 0.30/0.46 ! [N2: nat,P2: nat > $o] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.30/0.46 => ( ( P2 @ ( one_one @ nat ) )
% 0.30/0.46 => ( ! [N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.30/0.46 => ( ( P2 @ N )
% 0.30/0.46 => ( P2 @ ( suc @ N ) ) ) )
% 0.30/0.46 => ( P2 @ N2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_induct_non_zero
% 0.30/0.46 thf(fact_213_Suc__pred_H,axiom,
% 0.30/0.46 ! [N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.30/0.46 => ( N2
% 0.30/0.46 = ( suc @ ( minus_minus @ nat @ N2 @ ( one_one @ nat ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_pred'
% 0.30/0.46 thf(fact_214_Suc__diff__eq__diff__pred,axiom,
% 0.30/0.46 ! [N2: nat,M: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.30/0.46 => ( ( minus_minus @ nat @ ( suc @ M ) @ N2 )
% 0.30/0.46 = ( minus_minus @ nat @ M @ ( minus_minus @ nat @ N2 @ ( one_one @ nat ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Suc_diff_eq_diff_pred
% 0.30/0.46 thf(fact_215_AssumptionSubset2_I6_J,axiom,
% 0.30/0.46 ( ( n1
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 => ( ~ ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) ) @ msgInSet )
% 0.30/0.46 | ( msgInSet
% 0.30/0.46 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % AssumptionSubset2(6)
% 0.30/0.46 thf(fact_216_AssumptionSubset3_I6_J,axiom,
% 0.30/0.46 ( ( nMsg
% 0.30/0.46 != ( zero_zero @ nat ) )
% 0.30/0.46 => ( ~ ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) @ msg )
% 0.30/0.46 | ( msg
% 0.30/0.46 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % AssumptionSubset3(6)
% 0.30/0.46 thf(fact_217_EnabledIntermediate,axiom,
% 0.30/0.46 ! [I4: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ I4 )
% 0.30/0.46 => ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ I4 ) @ msg ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % EnabledIntermediate
% 0.30/0.46 thf(fact_218_length__greater__0__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.30/0.46 = ( Xs
% 0.30/0.46 != ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % length_greater_0_conv
% 0.30/0.46 thf(fact_219_AssumptionFair_I2_J,axiom,
% 0.30/0.46 ord_less @ nat @ n0 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ) ).
% 0.30/0.46
% 0.30/0.46 % AssumptionFair(2)
% 0.30/0.46 thf(fact_220_Occ4,axiom,
% 0.30/0.46 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ nMsg ) @ msg ).
% 0.30/0.46
% 0.30/0.46 % Occ4
% 0.30/0.46 thf(fact_221_AssumptionFair_I3_J,axiom,
% 0.30/0.46 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ n0 ) @ msg ).
% 0.30/0.46
% 0.30/0.46 % AssumptionFair(3)
% 0.30/0.46 thf(fact_222_AssumptionSubset3_I4_J,axiom,
% 0.30/0.46 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ nMsg ) @ msg ).
% 0.30/0.46
% 0.30/0.46 % AssumptionSubset3(4)
% 0.30/0.46 thf(fact_223_AssumptionSubset2_I4_J,axiom,
% 0.30/0.46 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ n1 ) @ msgInSet ).
% 0.30/0.46
% 0.30/0.46 % AssumptionSubset2(4)
% 0.30/0.46 thf(fact_224_MessageStaysOrConsumed,axiom,
% 0.30/0.46 ! [N1: nat,N22: nat,N2: nat,Msg: message @ p @ v] :
% 0.30/0.46 ( ( ( ord_less_eq @ nat @ N1 @ N22 )
% 0.30/0.46 & ( ord_less @ nat @ N22 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ N2 ) ) )
% 0.30/0.46 & ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N2 ) @ N1 ) @ Msg ) )
% 0.30/0.46 => ( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N2 ) @ N22 ) @ Msg )
% 0.30/0.46 | ? [N03: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ N1 @ N03 )
% 0.30/0.46 & ( ord_less @ nat @ N03 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N2 ) ) )
% 0.30/0.46 & ( ( nth @ ( message @ p @ v ) @ ( ft @ N2 ) @ N03 )
% 0.30/0.46 = Msg ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % MessageStaysOrConsumed
% 0.30/0.46 thf(fact_225__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,
% 0.30/0.46 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 ).
% 0.30/0.46
% 0.30/0.46 % \<open>enabled (fe (Suc index) ! (length (fe (Suc index)) - 1)) msg\<close>
% 0.30/0.46 thf(fact_226_length__0__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.30/0.46 = ( zero_zero @ nat ) )
% 0.30/0.46 = ( Xs
% 0.30/0.46 = ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % length_0_conv
% 0.30/0.46 thf(fact_227_Occ2,axiom,
% 0.30/0.46 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) @ msg ).
% 0.30/0.46
% 0.30/0.46 % Occ2
% 0.30/0.46 thf(fact_228_AssumptionCase1ImplThesis_H,axiom,
% 0.30/0.46 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg ).
% 0.30/0.46
% 0.30/0.46 % AssumptionCase1ImplThesis'
% 0.30/0.46 thf(fact_229_neq__if__length__neq,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.30/0.46 != ( size_size @ ( list @ A ) @ Ys ) )
% 0.30/0.46 => ( Xs != Ys ) ) ).
% 0.30/0.46
% 0.30/0.46 % neq_if_length_neq
% 0.30/0.46 thf(fact_230_Ex__list__of__length,axiom,
% 0.30/0.46 ! [A: $tType,N2: nat] :
% 0.30/0.46 ? [Xs2: list @ A] :
% 0.30/0.46 ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.30/0.46 = N2 ) ).
% 0.30/0.46
% 0.30/0.46 % Ex_list_of_length
% 0.30/0.46 thf(fact_231_length__induct,axiom,
% 0.30/0.46 ! [A: $tType,P2: ( list @ A ) > $o,Xs: list @ A] :
% 0.30/0.46 ( ! [Xs2: list @ A] :
% 0.30/0.46 ( ! [Ys2: list @ A] :
% 0.30/0.46 ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ys2 ) @ ( size_size @ ( list @ A ) @ Xs2 ) )
% 0.30/0.46 => ( P2 @ Ys2 ) )
% 0.30/0.46 => ( P2 @ Xs2 ) )
% 0.30/0.46 => ( P2 @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % length_induct
% 0.30/0.46 thf(fact_232_list_Osize_I3_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( size_size @ ( list @ A ) @ ( nil @ A ) )
% 0.30/0.46 = ( zero_zero @ nat ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.size(3)
% 0.30/0.46 thf(fact_233_list__eq__iff__nth__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ^ [Y4: list @ A,Z2: list @ A] : ( Y4 = Z2 ) )
% 0.30/0.46 = ( ^ [Xs3: list @ A,Ys3: list @ A] :
% 0.30/0.46 ( ( ( size_size @ ( list @ A ) @ Xs3 )
% 0.30/0.46 = ( size_size @ ( list @ A ) @ Ys3 ) )
% 0.30/0.46 & ! [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ ( size_size @ ( list @ A ) @ Xs3 ) )
% 0.30/0.46 => ( ( nth @ A @ Xs3 @ I3 )
% 0.30/0.46 = ( nth @ A @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_eq_iff_nth_eq
% 0.30/0.46 thf(fact_234_Skolem__list__nth,axiom,
% 0.30/0.46 ! [A: $tType,K: nat,P2: nat > A > $o] :
% 0.30/0.46 ( ( ! [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ K )
% 0.30/0.46 => ? [X4: A] : ( P2 @ I3 @ X4 ) ) )
% 0.30/0.46 = ( ? [Xs3: list @ A] :
% 0.30/0.46 ( ( ( size_size @ ( list @ A ) @ Xs3 )
% 0.30/0.46 = K )
% 0.30/0.46 & ! [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I3 @ K )
% 0.30/0.46 => ( P2 @ I3 @ ( nth @ A @ Xs3 @ I3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Skolem_list_nth
% 0.30/0.46 thf(fact_235_nth__equalityI,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.30/0.46 = ( size_size @ ( list @ A ) @ Ys ) )
% 0.30/0.46 => ( ! [I2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I2 @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.30/0.46 => ( ( nth @ A @ Xs @ I2 )
% 0.30/0.46 = ( nth @ A @ Ys @ I2 ) ) )
% 0.30/0.46 => ( Xs = Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nth_equalityI
% 0.30/0.46 thf(fact_236_EnabledOrConsumed,axiom,
% 0.30/0.46 ( ( 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 )
% 0.30/0.46 | ? [N03: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ n0 @ N03 )
% 0.30/0.46 & ( ord_less @ nat @ N03 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
% 0.30/0.46 & ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ N03 )
% 0.30/0.46 = msg ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % EnabledOrConsumed
% 0.30/0.46 thf(fact_237_Case2ImplThesis,axiom,
% 0.30/0.46 ( ? [N0: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ n0 @ N0 )
% 0.30/0.46 & ( ord_less @ nat @ N0 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
% 0.30/0.46 & ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ N0 )
% 0.30/0.46 = msg ) )
% 0.30/0.46 => ? [N6: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ n @ N6 )
% 0.30/0.46 & ? [N03: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ n0 @ N03 )
% 0.30/0.46 & ( ord_less @ nat @ N03 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N6 ) ) )
% 0.30/0.46 & ( msg
% 0.30/0.46 = ( nth @ ( message @ p @ v ) @ ( ft @ N6 ) @ N03 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Case2ImplThesis
% 0.30/0.46 thf(fact_238_EnabledInSuc,axiom,
% 0.30/0.46 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) ) @ msg ).
% 0.30/0.46
% 0.30/0.46 % EnabledInSuc
% 0.30/0.46 thf(fact_239_AssumptionSubset2_I2_J,axiom,
% 0.30/0.46 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) ) @ msgInSet ).
% 0.30/0.46
% 0.30/0.46 % AssumptionSubset2(2)
% 0.30/0.46 thf(fact_240_LastOfIndex,axiom,
% 0.30/0.46 ( ( 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 ) ) ) )
% 0.30/0.46 = ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LastOfIndex
% 0.30/0.46 thf(fact_241_EnabledOrConsumedAtLast,axiom,
% 0.30/0.46 ( ( enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg )
% 0.30/0.46 | ? [N03: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ n0 @ N03 )
% 0.30/0.46 & ( ord_less @ nat @ N03 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
% 0.30/0.46 & ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ N03 )
% 0.30/0.46 = msg ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % EnabledOrConsumedAtLast
% 0.30/0.46 thf(fact_242_last__conv__nth,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ( last @ A @ Xs )
% 0.30/0.46 = ( nth @ A @ Xs @ ( minus_minus @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( one_one @ nat ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % last_conv_nth
% 0.30/0.46 thf(fact_243_diff__numeral__special_I9_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( neg_numeral @ A )
% 0.30/0.46 => ( ( minus_minus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
% 0.30/0.46 = ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % diff_numeral_special(9)
% 0.30/0.46 thf(fact_244__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,
% 0.30/0.46 ! [Msg: message @ p @ v,N04: nat,N7: nat] :
% 0.30/0.46 ( ( firstOccurrence @ p @ v @ s @ ( fe @ N7 ) @ ( ft @ N7 ) @ Msg @ N04 )
% 0.30/0.46 => ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N7 ) ) @ Msg ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>\<And>n0 msg. \<forall>n. execution.firstOccurrence (fe n) (ft n) msg n0 \<longrightarrow> msg \<in># msgs (last (fe n))\<close>
% 0.30/0.46 thf(fact_245_le__numeral__extra_I3_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord1659791738miring @ A )
% 0.30/0.46 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_numeral_extra(3)
% 0.30/0.46 thf(fact_246_less__numeral__extra_I3_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord1659791738miring @ A )
% 0.30/0.46 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_numeral_extra(3)
% 0.30/0.46 thf(fact_247_le__numeral__extra_I4_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord1659791738miring @ A )
% 0.30/0.46 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_numeral_extra(4)
% 0.30/0.46 thf(fact_248_less__numeral__extra_I4_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord1659791738miring @ A )
% 0.30/0.46 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_numeral_extra(4)
% 0.30/0.46 thf(fact_249_less__numeral__extra_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linord1659791738miring @ A )
% 0.30/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_numeral_extra(1)
% 0.30/0.46 thf(fact_250__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,
% 0.30/0.46 ! [N7: nat,X5: message @ p @ v] :
% 0.30/0.46 ( ( member @ ( message @ p @ v ) @ X5 @ ( firstOccSet @ N7 ) )
% 0.30/0.46 => ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N7 ) ) @ X5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>\<forall>n. \<forall>msg'\<in>firstOccSet n. msg' \<in># msgs (last (fe n))\<close>
% 0.30/0.46
% 0.30/0.46 % Type constructors (16)
% 0.30/0.46 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.30/0.46 ! [A10: $tType,A11: $tType] :
% 0.30/0.46 ( ( order @ A11 )
% 0.30/0.46 => ( order @ ( A10 > A11 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.30/0.46 canoni770627133id_add @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 0.30/0.46 linord1659791738miring @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 0.30/0.46 cancel146912293up_add @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 0.30/0.46 cancel1352612707id_add @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff,axiom,
% 0.30/0.46 comm_monoid_diff @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.30/0.46 wellorder @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Oorder_1,axiom,
% 0.30/0.46 order @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.30/0.46 zero @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.30/0.46 one @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 0.30/0.46 size @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oorder_2,axiom,
% 0.30/0.46 order @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_List_Olist___Nat_Osize_3,axiom,
% 0.30/0.46 ! [A10: $tType] : ( size @ ( list @ A10 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_4,axiom,
% 0.30/0.46 wellorder @ product_unit ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Ounit___Orderings_Oorder_5,axiom,
% 0.30/0.46 order @ product_unit ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_AsynchronousSystem_Omessage___Nat_Osize_6,axiom,
% 0.30/0.46 ! [A10: $tType,A11: $tType] : ( size @ ( message @ A10 @ A11 ) ) ).
% 0.30/0.46
% 0.30/0.46 % Conjectures (1)
% 0.30/0.46 thf(conj_0,conjecture,
% 0.30/0.46 ord_less @ nat @ ( minus_minus @ nat @ nMsg @ ( suc @ ( zero_zero @ nat ) ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 0.31/1.50 ---- Embedded in THF ---
% 0.31/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.50 %%% Generated on Tue Feb 24 08:25:11 EST 2026
% 0.31/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.50 %%% Logic specification used:
% 0.31/1.50 %%% thf(spec, logic, $$dhol).
% 0.31/1.50
% 0.31/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.YNdYCGZgEX/DTF2DTF24154.p
% 0.31/1.50 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext, type, configuration_ext: ($tType > ($tType > ($tType > ($tType > $tType))))).
% 0.31/1.50 thf(ty_t_AsynchronousSystem_Omessage, type, message: ($tType > ($tType > $tType))).
% 0.31/1.50 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 0.31/1.50 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 0.31/1.50 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.31/1.50 thf(ty_t_Nat_Onat, type, nat: $tType).
% 0.31/1.50 thf(ty_tf_v, type, v: $tType).
% 0.31/1.50 thf(ty_tf_s, type, s: $tType).
% 0.31/1.50 thf(ty_tf_p, type, p: $tType).
% 0.31/1.50 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Nat_Osize, type, size: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Num_Oneg__numeral, type, neg_numeral: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ocomm__monoid__diff, type, comm_monoid_diff: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ocancel__comm__monoid__add, type, cancel1352612707id_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ocancel__ab__semigroup__add, type, cancel146912293up_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_c_AsynchronousSystem_Oconfiguration_Omsgs, type, msgs: (!> [P:$tType,V:$tType,S:$tType,Z:$tType]: ((((((configuration_ext @ P) @ V) @ S) @ Z) > (((message @ P) @ V) > nat))))).
% 0.31/1.50 thf(sy_c_AsynchronousSystem_Oenabled, type, enabled: (!> [P:$tType,V:$tType,S:$tType]: ((((((configuration_ext @ P) @ V) @ S) @ product_unit) > (((message @ P) @ V) > $o))))).
% 0.31/1.50 thf(sy_c_AsynchronousSystem_OisReceiverOf, type, isReceiverOf: (!> [P:$tType,V:$tType]: ((P > (((message @ P) @ V) > $o))))).
% 0.31/1.50 thf(sy_c_Execution_Oexecution_OfirstOccurrence, type, firstOccurrence: (!> [P:$tType,V:$tType,S:$tType]: (((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (((message @ P) @ V) > (nat > $o))))))).
% 0.31/1.50 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 0.31/1.50 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 0.31/1.50 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 0.31/1.50 thf(sy_c_ListUtilities_OprefixList, type, prefixList: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 0.31/1.50 thf(sy_c_List_Olast, type, last: (!> [A:$tType]: (((list @ A) > A)))).
% 0.31/1.50 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 0.31/1.50 thf(sy_c_List_Onth, type, nth: (!> [A:$tType]: (((list @ A) > (nat > A))))).
% 0.31/1.50 thf(sy_c_Nat_OSuc, type, suc: (nat > nat)).
% 0.31/1.50 thf(sy_c_Nat_Osize__class_Osize, type, size_size: (!> [A:$tType]: ((A > nat)))).
% 0.31/1.50 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 0.31/1.50 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 0.31/1.50 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.31/1.50 thf(sy_v_fe____, type, fe: (nat > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))).
% 0.31/1.50 thf(sy_v_firstOccSet____, type, firstOccSet: (nat > (set @ ((message @ p) @ v)))).
% 0.31/1.50 thf(sy_v_ft____, type, ft: (nat > (list @ ((message @ p) @ v)))).
% 0.31/1.50 thf(sy_v_index____, type, index: nat).
% 0.31/1.50 thf(sy_v_msgInSet____, type, msgInSet: ((message @ p) @ v)).
% 0.31/1.50 thf(sy_v_msg____, type, msg: ((message @ p) @ v)).
% 0.31/1.50 thf(sy_v_n0____, type, n0: nat).
% 0.31/1.50 thf(sy_v_n1____, type, n1: nat).
% 0.31/1.50 thf(sy_v_nMsg____, type, nMsg: nat).
% 0.31/1.50 thf(sy_v_n____, type, n: nat).
% 0.31/1.50 thf(sy_v_p____, type, p2: p).
% 0.31/1.50 thf(fact_0_AssumpOcc6_I1_J, axiom, (((ord_less @ nat) @ (zero_zero @ nat)) @ nMsg)).
% 0.31/1.50 thf(fact_1_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)))),N:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => ((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N)))))) => ((! [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)))),N:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => ((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N)))))) => ((((Q @ A4) @ A5) @ A6) @ A7)))))))).
% 0.31/1.50 thf(fact_2_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)))),A2:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),A3: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)))),N:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => ((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N)))))) => ((! [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)))),N:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => ((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N)))))) => ((((P2 @ A0) @ A1) @ A2) @ A3)))))))).
% 0.31/1.50 thf(fact_3_AssumptionSubset_I3_J, axiom, (((((((firstOccurrence @ p) @ v) @ s) @ (fe @ (suc @ index))) @ (ft @ (suc @ index))) @ msg) @ nMsg)).
% 0.31/1.50 thf(fact_4_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))))))).
% 0.31/1.50 thf(fact_5_AssumptionSubset3_I3_J, axiom, (((ord_less @ nat) @ nMsg) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ (suc @ index))))).
% 0.31/1.50 thf(fact_6_AssumptionSubset2_I3_J, axiom, (((ord_less @ nat) @ n1) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ (suc @ index))))).
% 0.31/1.50 thf(fact_7_Suc__pred, axiom, (! [N2:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) => ((suc @ (((minus_minus @ nat) @ N2) @ (suc @ (zero_zero @ nat)))) = N2))))).
% 0.31/1.50 thf(fact_8_zero__less__diff, axiom, (! [N2:nat,M:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (((minus_minus @ nat) @ N2) @ M)) = (((ord_less @ nat) @ M) @ N2))))).
% 0.31/1.50 thf(fact_9_less__Suc0, axiom, (! [N2:nat]: (((((ord_less @ nat) @ N2) @ (suc @ (zero_zero @ nat))) = (N2 = (zero_zero @ nat)))))).
% 0.31/1.50 thf(fact_10_zero__less__Suc, axiom, (! [N2:nat]: ((((ord_less @ nat) @ (zero_zero @ nat)) @ (suc @ N2))))).
% 0.31/1.50 thf(fact_11_diff__gt__0__iff__gt, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((minus_minus @ A) @ A8) @ B)) = (((ord_less @ A) @ B) @ A8)))))))).
% 0.31/1.50 thf(fact_12_diff__0__eq__0, axiom, (! [N2:nat]: (((((minus_minus @ nat) @ (zero_zero @ nat)) @ N2) = (zero_zero @ nat))))).
% 0.31/1.50 thf(fact_13_diff__self__eq__0, axiom, (! [M:nat]: (((((minus_minus @ nat) @ M) @ M) = (zero_zero @ nat))))).
% 0.31/1.50 thf(fact_14_diff__Suc__Suc, axiom, (! [M:nat,N2:nat]: (((((minus_minus @ nat) @ (suc @ M)) @ (suc @ N2)) = (((minus_minus @ nat) @ M) @ N2))))).
% 0.31/1.50 thf(fact_15_Suc__diff__diff, axiom, (! [M:nat,N2:nat,K:nat]: (((((minus_minus @ nat) @ (((minus_minus @ nat) @ (suc @ M)) @ N2)) @ (suc @ K)) = (((minus_minus @ nat) @ (((minus_minus @ nat) @ M) @ N2)) @ K))))).
% 0.31/1.50 thf(fact_16_neq0__conv, axiom, (! [N2:nat]: (((N2 != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ N2))))).
% 0.31/1.50 thf(fact_17_less__nat__zero__code, axiom, (! [N2:nat]: ((~ ((((ord_less @ nat) @ N2) @ (zero_zero @ nat))))))).
% 0.31/1.50 thf(fact_18_old_Onat_Oinject, axiom, (! [Nat:nat,Nat2:nat]: ((((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))).
% 0.31/1.50 thf(fact_19_nat_Oinject, axiom, (! [X2:nat,Y2:nat]: ((((suc @ X2) = (suc @ Y2)) = (X2 = Y2))))).
% 0.31/1.50 thf(fact_20_not__gr__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N2:A]: (((~ ((((ord_less @ A) @ (zero_zero @ A)) @ N2))) = (N2 = (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_21_cancel__comm__monoid__add__class_Odiff__cancel, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A8:A]: (((((minus_minus @ A) @ A8) @ A8) = (zero_zero @ A)))))))).
% 0.31/1.50 thf(fact_22_diff__zero, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A8:A]: (((((minus_minus @ A) @ A8) @ (zero_zero @ A)) = A8))))))).
% 0.31/1.50 thf(fact_23_zero__diff, axiom, (! [A:$tType]: (((comm_monoid_diff @ A) => (! [A8:A]: (((((minus_minus @ A) @ (zero_zero @ A)) @ A8) = (zero_zero @ A)))))))).
% 0.31/1.50 thf(fact_24_diff__0__right, axiom, (! [A:$tType]: (((group_add @ A) => (! [A8:A]: (((((minus_minus @ A) @ A8) @ (zero_zero @ A)) = A8))))))).
% 0.31/1.50 thf(fact_25_diff__self, axiom, (! [A:$tType]: (((group_add @ A) => (! [A8:A]: (((((minus_minus @ A) @ A8) @ A8) = (zero_zero @ A)))))))).
% 0.31/1.50 thf(fact_26_Suc__less__eq, axiom, (! [M:nat,N2:nat]: (((((ord_less @ nat) @ (suc @ M)) @ (suc @ N2)) = (((ord_less @ nat) @ M) @ N2))))).
% 0.31/1.50 thf(fact_27_Suc__mono, axiom, (! [M:nat,N2:nat]: (((((ord_less @ nat) @ M) @ N2) => (((ord_less @ nat) @ (suc @ M)) @ (suc @ N2)))))).
% 0.31/1.50 thf(fact_28_lessI, axiom, (! [N2:nat]: ((((ord_less @ nat) @ N2) @ (suc @ N2))))).
% 0.31/1.50 thf(fact_29_bot__nat__0_Onot__eq__extremum, axiom, (! [A8:nat]: (((A8 != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ A8))))).
% 0.31/1.50 thf(fact_30_AssumptionSubset_I2_J, axiom, (((((((firstOccurrence @ p) @ v) @ s) @ (fe @ (suc @ index))) @ (ft @ (suc @ index))) @ msgInSet) @ n1)).
% 0.31/1.50 thf(fact_31_AssumptionSubset_I1_J, axiom, (((ord_less_eq @ nat) @ n1) @ nMsg)).
% 0.31/1.50 thf(fact_32_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X:A]: ((((zero_zero @ A) = X) = (X = (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_33_measure__induct__rule, axiom, (! [B2:$tType,A:$tType]: (((wellorder @ B2) => (! [F:(A > B2),P2:(A > $o),A8:A]: (((! [X3:A]: (((! [Y:A]: (((((ord_less @ B2) @ (F @ Y)) @ (F @ X3)) => (P2 @ Y)))) => (P2 @ X3)))) => (P2 @ A8)))))))).
% 0.31/1.50 thf(fact_34_measure__induct, axiom, (! [B2:$tType,A:$tType]: (((wellorder @ B2) => (! [F:(A > B2),P2:(A > $o),A8:A]: (((! [X3:A]: (((! [Y:A]: (((((ord_less @ B2) @ (F @ Y)) @ (F @ X3)) => (P2 @ Y)))) => (P2 @ X3)))) => (P2 @ A8)))))))).
% 0.31/1.50 thf(fact_35_diff__right__commute, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [A8:A,C:A,B:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A8) @ C)) @ B) = (((minus_minus @ A) @ (((minus_minus @ A) @ A8) @ B)) @ C)))))))).
% 0.31/1.50 thf(fact_36_diff__eq__diff__eq, axiom, (! [A:$tType]: (((group_add @ A) => (! [A8:A,B:A,C:A,D:A]: ((((((minus_minus @ A) @ A8) @ B) = (((minus_minus @ A) @ C) @ D)) => ((A8 = B) = (C = D))))))))).
% 0.31/1.50 thf(fact_37_n__not__Suc__n, axiom, (! [N2:nat]: ((N2 != (suc @ N2))))).
% 0.31/1.50 thf(fact_38_Suc__inject, axiom, (! [X:nat,Y3:nat]: ((((suc @ X) = (suc @ Y3)) => (X = Y3))))).
% 0.31/1.50 thf(fact_39_infinite__descent__measure, axiom, (! [A:$tType,P2:(A > $o),V2:(A > nat),X:A]: (((! [X3:A]: (((~ ((P2 @ X3))) => (? [Y:A]: (((((ord_less @ nat) @ (V2 @ Y)) @ (V2 @ X3)) & (~ ((P2 @ Y))))))))) => (P2 @ X))))).
% 0.31/1.50 thf(fact_40_linorder__neqE__nat, axiom, (! [X:nat,Y3:nat]: (((X != Y3) => ((~ ((((ord_less @ nat) @ X) @ Y3))) => (((ord_less @ nat) @ Y3) @ X)))))).
% 0.31/1.50 thf(fact_41_infinite__descent, axiom, (! [P2:(nat > $o),N2:nat]: (((! [N:nat]: (((~ ((P2 @ N))) => (? [M2:nat]: (((((ord_less @ nat) @ M2) @ N) & (~ ((P2 @ M2))))))))) => (P2 @ N2))))).
% 0.31/1.50 thf(fact_42_nat__less__induct, axiom, (! [P2:(nat > $o),N2:nat]: (((! [N:nat]: (((! [M2:nat]: (((((ord_less @ nat) @ M2) @ N) => (P2 @ M2)))) => (P2 @ N)))) => (P2 @ N2))))).
% 0.31/1.50 thf(fact_43_less__irrefl__nat, axiom, (! [N2:nat]: ((~ ((((ord_less @ nat) @ N2) @ N2)))))).
% 0.31/1.50 thf(fact_44_less__not__refl3, axiom, (! [S2:nat,T:nat]: (((((ord_less @ nat) @ S2) @ T) => (S2 != T))))).
% 0.31/1.50 thf(fact_45_less__not__refl2, axiom, (! [N2:nat,M:nat]: (((((ord_less @ nat) @ N2) @ M) => (M != N2))))).
% 0.31/1.50 thf(fact_46_less__not__refl, axiom, (! [N2:nat]: ((~ ((((ord_less @ nat) @ N2) @ N2)))))).
% 0.31/1.50 thf(fact_47_nat__neq__iff, axiom, (! [M:nat,N2:nat]: (((M != N2) = ((((ord_less @ nat) @ M) @ N2) | (((ord_less @ nat) @ N2) @ M)))))).
% 0.31/1.50 thf(fact_48_size__neq__size__imp__neq, axiom, (! [A:$tType]: (((size @ A) => (! [X:A,Y3:A]: (((((size_size @ A) @ X) != ((size_size @ A) @ Y3)) => (X != Y3)))))))).
% 0.31/1.50 thf(fact_49_diff__commute, axiom, (! [I:nat,J:nat,K:nat]: (((((minus_minus @ nat) @ (((minus_minus @ nat) @ I) @ J)) @ K) = (((minus_minus @ nat) @ (((minus_minus @ nat) @ I) @ K)) @ J))))).
% 0.31/1.50 thf(fact_50_zero__less__iff__neq__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ N2) = (N2 != (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_51_gr__implies__not__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [M:A,N2:A]: (((((ord_less @ A) @ M) @ N2) => (N2 != (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_52_not__less__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N2:A]: ((~ ((((ord_less @ A) @ N2) @ (zero_zero @ A)))))))))).
% 0.31/1.50 thf(fact_53_gr__zeroI, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N2:A]: (((N2 != (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ N2)))))))).
% 0.31/1.50 thf(fact_54_eq__iff__diff__eq__0, axiom, (! [A:$tType]: (((group_add @ A) => ((^ [Y4:A,Z2:A]: ((Y4 = Z2))) = (^ [A9:A,B3:A]: (((((minus_minus @ A) @ A9) @ B3) = (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_55_diff__strict__right__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B:A,C:A]: (((((ord_less @ A) @ A8) @ B) => (((ord_less @ A) @ (((minus_minus @ A) @ A8) @ C)) @ (((minus_minus @ A) @ B) @ C))))))))).
% 0.31/1.50 thf(fact_56_diff__strict__left__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B:A,A8:A,C:A]: (((((ord_less @ A) @ B) @ A8) => (((ord_less @ A) @ (((minus_minus @ A) @ C) @ A8)) @ (((minus_minus @ A) @ C) @ B))))))))).
% 0.31/1.50 thf(fact_57_diff__eq__diff__less, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B:A,C:A,D:A]: ((((((minus_minus @ A) @ A8) @ B) = (((minus_minus @ A) @ C) @ D)) => ((((ord_less @ A) @ A8) @ B) = (((ord_less @ A) @ C) @ D))))))))).
% 0.31/1.50 thf(fact_58_diff__strict__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B:A,D:A,C:A]: (((((ord_less @ A) @ A8) @ B) => ((((ord_less @ A) @ D) @ C) => (((ord_less @ A) @ (((minus_minus @ A) @ A8) @ C)) @ (((minus_minus @ A) @ B) @ D)))))))))).
% 0.31/1.50 thf(fact_59_not0__implies__Suc, axiom, (! [N2:nat]: (((N2 != (zero_zero @ nat)) => (? [M3:nat]: ((N2 = (suc @ M3)))))))).
% 0.31/1.50 thf(fact_60_old_Onat_Oinducts, axiom, (! [P2:(nat > $o),Nat:nat]: (((P2 @ (zero_zero @ nat)) => ((! [Nat3:nat]: (((P2 @ Nat3) => (P2 @ (suc @ Nat3))))) => (P2 @ Nat)))))).
% 0.31/1.50 thf(fact_61_old_Onat_Oexhaust, axiom, (! [Y3:nat]: (((Y3 != (zero_zero @ nat)) => (~ ((! [Nat3:nat]: ((Y3 != (suc @ Nat3)))))))))).
% 0.31/1.50 thf(fact_62_Zero__not__Suc, axiom, (! [M:nat]: (((zero_zero @ nat) != (suc @ M))))).
% 0.31/1.50 thf(fact_63_Zero__neq__Suc, axiom, (! [M:nat]: (((zero_zero @ nat) != (suc @ M))))).
% 0.31/1.50 thf(fact_64_Suc__neq__Zero, axiom, (! [M:nat]: (((suc @ M) != (zero_zero @ nat))))).
% 0.31/1.50 thf(fact_65_zero__induct, axiom, (! [P2:(nat > $o),K:nat]: (((P2 @ K) => ((! [N:nat]: (((P2 @ (suc @ N)) => (P2 @ N)))) => (P2 @ (zero_zero @ nat))))))).
% 0.31/1.50 thf(fact_66_diff__induct, axiom, (! [P2:(nat > (nat > $o)),M:nat,N2:nat]: (((! [X3:nat]: (((P2 @ X3) @ (zero_zero @ nat)))) => ((! [Y5:nat]: (((P2 @ (zero_zero @ nat)) @ (suc @ Y5)))) => ((! [X3:nat,Y5:nat]: ((((P2 @ X3) @ Y5) => ((P2 @ (suc @ X3)) @ (suc @ Y5))))) => ((P2 @ M) @ N2))))))).
% 0.31/1.50 thf(fact_67_nat__induct, axiom, (! [P2:(nat > $o),N2:nat]: (((P2 @ (zero_zero @ nat)) => ((! [N:nat]: (((P2 @ N) => (P2 @ (suc @ N))))) => (P2 @ N2)))))).
% 0.31/1.50 thf(fact_68_nat_OdiscI, axiom, (! [Nat:nat,X2:nat]: (((Nat = (suc @ X2)) => (Nat != (zero_zero @ nat)))))).
% 0.31/1.50 thf(fact_69_old_Onat_Odistinct_I1_J, axiom, (! [Nat2:nat]: (((zero_zero @ nat) != (suc @ Nat2))))).
% 0.31/1.50 thf(fact_70_old_Onat_Odistinct_I2_J, axiom, (! [Nat4:nat]: (((suc @ Nat4) != (zero_zero @ nat))))).
% 0.31/1.50 thf(fact_71_nat_Odistinct_I1_J, axiom, (! [X2:nat]: (((zero_zero @ nat) != (suc @ X2))))).
% 0.31/1.50 thf(fact_72_not__less__less__Suc__eq, axiom, (! [N2:nat,M:nat]: (((~ ((((ord_less @ nat) @ N2) @ M))) => ((((ord_less @ nat) @ N2) @ (suc @ M)) = (N2 = M)))))).
% 0.31/1.50 thf(fact_73_strict__inc__induct, axiom, (! [I:nat,J:nat,P2:(nat > $o)]: (((((ord_less @ nat) @ I) @ J) => ((! [I2:nat]: (((J = (suc @ I2)) => (P2 @ I2)))) => ((! [I2:nat]: (((((ord_less @ nat) @ I2) @ J) => ((P2 @ (suc @ I2)) => (P2 @ I2))))) => (P2 @ I))))))).
% 0.31/1.50 thf(fact_74_less__Suc__induct, axiom, (! [I:nat,J:nat,P2:(nat > (nat > $o))]: (((((ord_less @ nat) @ I) @ J) => ((! [I2:nat]: (((P2 @ I2) @ (suc @ I2)))) => ((! [I2:nat,J2:nat,K2:nat]: (((((ord_less @ nat) @ I2) @ J2) => ((((ord_less @ nat) @ J2) @ K2) => (((P2 @ I2) @ J2) => (((P2 @ J2) @ K2) => ((P2 @ I2) @ K2))))))) => ((P2 @ I) @ J))))))).
% 0.31/1.50 thf(fact_75_less__trans__Suc, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ I) @ J) => ((((ord_less @ nat) @ J) @ K) => (((ord_less @ nat) @ (suc @ I)) @ K)))))).
% 0.31/1.50 thf(fact_76_Suc__less__SucD, axiom, (! [M:nat,N2:nat]: (((((ord_less @ nat) @ (suc @ M)) @ (suc @ N2)) => (((ord_less @ nat) @ M) @ N2))))).
% 0.31/1.50 thf(fact_77_less__antisym, axiom, (! [N2:nat,M:nat]: (((~ ((((ord_less @ nat) @ N2) @ M))) => ((((ord_less @ nat) @ N2) @ (suc @ M)) => (M = N2)))))).
% 0.31/1.50 thf(fact_78_Suc__less__eq2, axiom, (! [N2:nat,M:nat]: (((((ord_less @ nat) @ (suc @ N2)) @ M) = (? [M4:nat]: (((M = (suc @ M4)) & (((ord_less @ nat) @ N2) @ M4)))))))).
% 0.31/1.50 thf(fact_79_All__less__Suc, axiom, (! [N2:nat,P2:(nat > $o)]: (((! [I3:nat]: (((((ord_less @ nat) @ I3) @ (suc @ N2)) => (P2 @ I3)))) = ((P2 @ N2) & (! [I3:nat]: (((((ord_less @ nat) @ I3) @ N2) => (P2 @ I3))))))))).
% 0.31/1.50 thf(fact_80_not__less__eq, axiom, (! [M:nat,N2:nat]: (((~ ((((ord_less @ nat) @ M) @ N2))) = (((ord_less @ nat) @ N2) @ (suc @ M)))))).
% 0.31/1.50 thf(fact_81_less__Suc__eq, axiom, (! [M:nat,N2:nat]: (((((ord_less @ nat) @ M) @ (suc @ N2)) = ((((ord_less @ nat) @ M) @ N2) | (M = N2)))))).
% 0.31/1.50 thf(fact_82_Ex__less__Suc, axiom, (! [N2:nat,P2:(nat > $o)]: (((? [I3:nat]: (((((ord_less @ nat) @ I3) @ (suc @ N2)) & (P2 @ I3)))) = ((P2 @ N2) | (? [I3:nat]: (((((ord_less @ nat) @ I3) @ N2) & (P2 @ I3))))))))).
% 0.31/1.50 thf(fact_83_less__SucI, axiom, (! [M:nat,N2:nat]: (((((ord_less @ nat) @ M) @ N2) => (((ord_less @ nat) @ M) @ (suc @ N2)))))).
% 0.31/1.50 thf(fact_84_less__SucE, axiom, (! [M:nat,N2:nat]: (((((ord_less @ nat) @ M) @ (suc @ N2)) => ((~ ((((ord_less @ nat) @ M) @ N2))) => (M = N2)))))).
% 0.31/1.50 thf(fact_85_Suc__lessI, axiom, (! [M:nat,N2:nat]: (((((ord_less @ nat) @ M) @ N2) => (((suc @ M) != N2) => (((ord_less @ nat) @ (suc @ M)) @ N2)))))).
% 0.31/1.50 thf(fact_86_Suc__lessE, axiom, (! [I:nat,K:nat]: (((((ord_less @ nat) @ (suc @ I)) @ K) => (~ ((! [J2:nat]: (((((ord_less @ nat) @ I) @ J2) => (K != (suc @ J2))))))))))).
% 0.31/1.50 thf(fact_87_Suc__lessD, axiom, (! [M:nat,N2:nat]: (((((ord_less @ nat) @ (suc @ M)) @ N2) => (((ord_less @ nat) @ M) @ N2))))).
% 0.31/1.50 thf(fact_88_Nat_OlessE, axiom, (! [I:nat,K:nat]: (((((ord_less @ nat) @ I) @ K) => ((K != (suc @ I)) => (~ ((! [J2:nat]: (((((ord_less @ nat) @ I) @ J2) => (K != (suc @ J2)))))))))))).
% 0.31/1.50 thf(fact_89_infinite__descent0__measure, axiom, (! [A:$tType,V2:(A > nat),P2:(A > $o),X:A]: (((! [X3:A]: ((((V2 @ X3) = (zero_zero @ nat)) => (P2 @ X3)))) => ((! [X3:A]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (V2 @ X3)) => ((~ ((P2 @ X3))) => (? [Y:A]: (((((ord_less @ nat) @ (V2 @ Y)) @ (V2 @ X3)) & (~ ((P2 @ Y)))))))))) => (P2 @ X)))))).
% 0.31/1.50 thf(fact_90_bot__nat__0_Oextremum__strict, axiom, (! [A8:nat]: ((~ ((((ord_less @ nat) @ A8) @ (zero_zero @ nat))))))).
% 0.31/1.50 thf(fact_91_infinite__descent0, axiom, (! [P2:(nat > $o),N2:nat]: (((P2 @ (zero_zero @ nat)) => ((! [N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => ((~ ((P2 @ N))) => (? [M2:nat]: (((((ord_less @ nat) @ M2) @ N) & (~ ((P2 @ M2)))))))))) => (P2 @ N2)))))).
% 0.31/1.50 thf(fact_92_gr__implies__not0, axiom, (! [M:nat,N2:nat]: (((((ord_less @ nat) @ M) @ N2) => (N2 != (zero_zero @ nat)))))).
% 0.31/1.50 thf(fact_93_less__zeroE, axiom, (! [N2:nat]: ((~ ((((ord_less @ nat) @ N2) @ (zero_zero @ nat))))))).
% 0.31/1.50 thf(fact_94_not__less0, axiom, (! [N2:nat]: ((~ ((((ord_less @ nat) @ N2) @ (zero_zero @ nat))))))).
% 0.31/1.50 thf(fact_95_not__gr0, axiom, (! [N2:nat]: (((~ ((((ord_less @ nat) @ (zero_zero @ nat)) @ N2))) = (N2 = (zero_zero @ nat)))))).
% 0.31/1.50 thf(fact_96_gr0I, axiom, (! [N2:nat]: (((N2 != (zero_zero @ nat)) => (((ord_less @ nat) @ (zero_zero @ nat)) @ N2))))).
% 0.31/1.50 thf(fact_97_zero__induct__lemma, axiom, (! [P2:(nat > $o),K:nat,I:nat]: (((P2 @ K) => ((! [N:nat]: (((P2 @ (suc @ N)) => (P2 @ N)))) => (P2 @ (((minus_minus @ nat) @ K) @ I))))))).
% 0.31/1.50 thf(fact_98_minus__nat_Odiff__0, axiom, (! [M:nat]: (((((minus_minus @ nat) @ M) @ (zero_zero @ nat)) = M)))).
% 0.31/1.50 thf(fact_99_diffs0__imp__equal, axiom, (! [M:nat,N2:nat]: ((((((minus_minus @ nat) @ M) @ N2) = (zero_zero @ nat)) => (((((minus_minus @ nat) @ N2) @ M) = (zero_zero @ nat)) => (M = N2)))))).
% 0.31/1.50 thf(fact_100_less__imp__diff__less, axiom, (! [J:nat,K:nat,N2:nat]: (((((ord_less @ nat) @ J) @ K) => (((ord_less @ nat) @ (((minus_minus @ nat) @ J) @ N2)) @ K))))).
% 0.31/1.50 thf(fact_101_diff__less__mono2, axiom, (! [M:nat,N2:nat,L:nat]: (((((ord_less @ nat) @ M) @ N2) => ((((ord_less @ nat) @ M) @ L) => (((ord_less @ nat) @ (((minus_minus @ nat) @ L) @ N2)) @ (((minus_minus @ nat) @ L) @ M))))))).
% 0.31/1.50 thf(fact_102_less__iff__diff__less__0, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => ((ord_less @ A) = (^ [A9:A,B3:A]: ((((ord_less @ A) @ (((minus_minus @ A) @ A9) @ B3)) @ (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_103_lift__Suc__mono__less__iff, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N2:nat,M:nat]: (((! [N:nat]: ((((ord_less @ A) @ (F @ N)) @ (F @ (suc @ N))))) => ((((ord_less @ A) @ (F @ N2)) @ (F @ M)) = (((ord_less @ nat) @ N2) @ M))))))))).
% 0.31/1.50 thf(fact_104_lift__Suc__mono__less, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N2:nat,N3:nat]: (((! [N:nat]: ((((ord_less @ A) @ (F @ N)) @ (F @ (suc @ N))))) => ((((ord_less @ nat) @ N2) @ N3) => (((ord_less @ A) @ (F @ N2)) @ (F @ N3)))))))))).
% 0.31/1.50 thf(fact_105_less__Suc__eq__0__disj, axiom, (! [M:nat,N2:nat]: (((((ord_less @ nat) @ M) @ (suc @ N2)) = ((M = (zero_zero @ nat)) | (? [J3:nat]: (((M = (suc @ J3)) & (((ord_less @ nat) @ J3) @ N2))))))))).
% 0.31/1.50 thf(fact_106_gr0__implies__Suc, axiom, (! [N2:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) => (? [M3:nat]: ((N2 = (suc @ M3)))))))).
% 0.31/1.50 thf(fact_107_All__less__Suc2, axiom, (! [N2:nat,P2:(nat > $o)]: (((! [I3:nat]: (((((ord_less @ nat) @ I3) @ (suc @ N2)) => (P2 @ I3)))) = ((P2 @ (zero_zero @ nat)) & (! [I3:nat]: (((((ord_less @ nat) @ I3) @ N2) => (P2 @ (suc @ I3)))))))))).
% 0.31/1.50 thf(fact_108_gr0__conv__Suc, axiom, (! [N2:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) = (? [M5:nat]: ((N2 = (suc @ M5)))))))).
% 0.31/1.50 thf(fact_109_Ex__less__Suc2, axiom, (! [N2:nat,P2:(nat > $o)]: (((? [I3:nat]: (((((ord_less @ nat) @ I3) @ (suc @ N2)) & (P2 @ I3)))) = ((P2 @ (zero_zero @ nat)) | (? [I3:nat]: (((((ord_less @ nat) @ I3) @ N2) & (P2 @ (suc @ I3)))))))))).
% 0.31/1.50 thf(fact_110_diff__less__Suc, axiom, (! [M:nat,N2:nat]: ((((ord_less @ nat) @ (((minus_minus @ nat) @ M) @ N2)) @ (suc @ M))))).
% 0.31/1.50 thf(fact_111_Suc__diff__Suc, axiom, (! [N2:nat,M:nat]: (((((ord_less @ nat) @ N2) @ M) => ((suc @ (((minus_minus @ nat) @ M) @ (suc @ N2))) = (((minus_minus @ nat) @ M) @ N2)))))).
% 0.31/1.50 thf(fact_112_diff__less, axiom, (! [N2:nat,M:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) => ((((ord_less @ nat) @ (zero_zero @ nat)) @ M) => (((ord_less @ nat) @ (((minus_minus @ nat) @ M) @ N2)) @ M)))))).
% 0.31/1.50 thf(fact_113_diff__Suc__less, axiom, (! [N2:nat,I:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) => (((ord_less @ nat) @ (((minus_minus @ nat) @ N2) @ (suc @ I))) @ N2))))).
% 0.31/1.50 thf(fact_114_SameCfgOnLow, axiom, (! [I4:nat]: (((((ord_less @ nat) @ I4) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) => ((((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index)) @ I4) = (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ I4)))))).
% 0.31/1.50 thf(fact_115__092_060open_062fe_Aindex_A_B_AnMsg_A_061_Afe_A_ISuc_Aindex_J_A_B_AnMsg_092_060close_062, axiom, ((((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index)) @ nMsg) = (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ nMsg))).
% 0.31/1.50 thf(fact_116_ShorterTrace, axiom, (((ord_less @ nat) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ (suc @ index))))).
% 0.31/1.50 thf(fact_117_NotEmpty_I1_J, axiom, ((fe @ (suc @ index)) != (nil @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))).
% 0.31/1.50 thf(fact_118_IPrefixList, axiom, (! [I4:nat]: ((((prefixList @ ((message @ p) @ v)) @ (ft @ I4)) @ (ft @ (suc @ I4)))))).
% 0.31/1.50 thf(fact_119_IPrefixListEx, axiom, (! [I4:nat]: ((((prefixList @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ I4)) @ (fe @ (suc @ I4)))))).
% 0.31/1.50 thf(fact_120_NatPredicateTippingPoint, axiom, (! [N22:nat,Pr:(nat > $o)]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N22) => ((Pr @ (zero_zero @ nat)) => ((~ ((Pr @ N22))) => (? [N:nat]: (((((ord_less @ nat) @ N) @ N22) & ((Pr @ N) & (~ ((Pr @ (suc @ N)))))))))))))).
% 0.31/1.50 thf(fact_121_NotEmpty_I2_J, axiom, ((fe @ index) != (nil @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))).
% 0.31/1.50 thf(fact_122_AssumptionFair_I4_J, axiom, ((((isReceiverOf @ p) @ v) @ p2) @ msg)).
% 0.31/1.50 thf(fact_123_AssumpOcc6_I2_J, axiom, (msg != (((nth @ ((message @ p) @ v)) @ (ft @ index)) @ (((minus_minus @ nat) @ nMsg) @ (one_one @ nat))))).
% 0.31/1.50 thf(fact_124_Occ1, axiom, (? [P3:p]: (((((isReceiverOf @ p) @ v) @ P3) @ msg)))).
% 0.31/1.50 thf(fact_125_AssumptionSubset2_I1_J, axiom, (? [P3:p]: (((((isReceiverOf @ p) @ v) @ P3) @ msgInSet)))).
% 0.31/1.50 thf(fact_126_SameMsgOnLow, axiom, (! [I4:nat]: (((((ord_less @ nat) @ I4) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) => ((((nth @ ((message @ p) @ v)) @ (ft @ index)) @ I4) = (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ I4)))))).
% 0.31/1.50 thf(fact_127_le__zero__eq, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N2:A]: (((((ord_less_eq @ A) @ N2) @ (zero_zero @ A)) = (N2 = (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_128_Suc__le__mono, axiom, (! [N2:nat,M:nat]: (((((ord_less_eq @ nat) @ (suc @ N2)) @ (suc @ M)) = (((ord_less_eq @ nat) @ N2) @ M))))).
% 0.31/1.50 thf(fact_129_le0, axiom, (! [N2:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N2)))).
% 0.31/1.50 thf(fact_130_bot__nat__0_Oextremum, axiom, (! [A8:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ A8)))).
% 0.31/1.50 thf(fact_131_diff__diff__cancel, axiom, (! [I:nat,N2:nat]: (((((ord_less_eq @ nat) @ I) @ N2) => ((((minus_minus @ nat) @ N2) @ (((minus_minus @ nat) @ N2) @ I)) = I))))).
% 0.31/1.50 thf(fact_132__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)))).
% 0.31/1.50 thf(fact_133__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, (~ ((? [I4:nat]: (((((ord_less @ nat) @ I4) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ (suc @ index)))) & ((((ord_less_eq @ nat) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) @ I4) & (msg = (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ I4))))))))).
% 0.31/1.50 thf(fact_134_NotConsumedIntermediate, axiom, (! [I4:nat]: (((((ord_less @ nat) @ I4) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ (suc @ index)))) => ((((ord_less_eq @ nat) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) @ I4) => ((((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ I4) != msg)))))).
% 0.31/1.50 thf(fact_135_OccSameMsg, axiom, (! [N4:nat]: (((((ord_less_eq @ nat) @ nMsg) @ N4) => ((((ord_less @ nat) @ N4) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) => ((((nth @ ((message @ p) @ v)) @ (ft @ index)) @ N4) = (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ N4))))))).
% 0.31/1.50 thf(fact_136_diff__ge__0__iff__ge, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((minus_minus @ A) @ A8) @ B)) = (((ord_less_eq @ A) @ B) @ A8)))))))).
% 0.31/1.50 thf(fact_137_Occ5, axiom, (! [N4:nat]: (((((ord_less_eq @ nat) @ nMsg) @ N4) => ((((ord_less @ nat) @ N4) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) => (msg != (((nth @ ((message @ p) @ v)) @ (ft @ index)) @ N4))))))).
% 0.31/1.50 thf(fact_138_diff__is__0__eq, axiom, (! [M:nat,N2:nat]: ((((((minus_minus @ nat) @ M) @ N2) = (zero_zero @ nat)) = (((ord_less_eq @ nat) @ M) @ N2))))).
% 0.31/1.50 thf(fact_139_diff__is__0__eq_H, axiom, (! [M:nat,N2:nat]: (((((ord_less_eq @ nat) @ M) @ N2) => ((((minus_minus @ nat) @ M) @ N2) = (zero_zero @ nat)))))).
% 0.31/1.50 thf(fact_140_less__one, axiom, (! [N2:nat]: (((((ord_less @ nat) @ N2) @ (one_one @ nat)) = (N2 = (zero_zero @ nat)))))).
% 0.31/1.50 thf(fact_141_diff__Suc__1, axiom, (! [N2:nat]: (((((minus_minus @ nat) @ (suc @ N2)) @ (one_one @ nat)) = N2)))).
% 0.31/1.50 thf(fact_142_AssumptionSubset3_I5_J, axiom, (! [N4:nat]: (((((ord_less_eq @ nat) @ nMsg) @ N4) => ((((ord_less @ nat) @ N4) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ (suc @ index)))) => (msg != (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ N4))))))).
% 0.31/1.50 thf(fact_143_AssumptionSubset2_I5_J, axiom, (! [N4:nat]: (((((ord_less_eq @ nat) @ n1) @ N4) => ((((ord_less @ nat) @ N4) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ (suc @ index)))) => (msgInSet != (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ N4))))))).
% 0.31/1.50 thf(fact_144__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, (~ ((? [I4:nat]: (((((ord_less @ nat) @ I4) @ (((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))) @ I4) & (msg = (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ I4))))))))).
% 0.31/1.50 thf(fact_145_Suc__diff__1, axiom, (! [N2:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) => ((suc @ (((minus_minus @ nat) @ N2) @ (one_one @ nat))) = N2))))).
% 0.31/1.50 thf(fact_146_AssumptionFairContr, axiom, (! [N4:nat]: (((((ord_less_eq @ nat) @ n) @ N4) => (! [N0:nat]: (((((ord_less @ nat) @ N0) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ N4))) => ((((ord_less_eq @ nat) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ n))) @ N0) => (msg != (((nth @ ((message @ p) @ v)) @ (ft @ N4)) @ N0)))))))))).
% 0.31/1.50 thf(fact_147_AssumpOcc6_I3_J, axiom, (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index)) @ (((minus_minus @ nat) @ nMsg) @ (one_one @ nat)))) @ msg)).
% 0.31/1.50 thf(fact_148_le__refl, axiom, (! [N2:nat]: ((((ord_less_eq @ nat) @ N2) @ N2)))).
% 0.31/1.50 thf(fact_149_le__trans, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((ord_less_eq @ nat) @ J) @ K) => (((ord_less_eq @ nat) @ I) @ K)))))).
% 0.31/1.50 thf(fact_150_eq__imp__le, axiom, (! [M:nat,N2:nat]: (((M = N2) => (((ord_less_eq @ nat) @ M) @ N2))))).
% 0.31/1.50 thf(fact_151_le__antisym, axiom, (! [M:nat,N2:nat]: (((((ord_less_eq @ nat) @ M) @ N2) => ((((ord_less_eq @ nat) @ N2) @ M) => (M = N2)))))).
% 0.31/1.50 thf(fact_152_nat__le__linear, axiom, (! [M:nat,N2:nat]: (((((ord_less_eq @ nat) @ M) @ N2) | (((ord_less_eq @ nat) @ N2) @ M))))).
% 0.31/1.50 thf(fact_153_one__reorient, axiom, (! [A:$tType]: (((one @ A) => (! [X:A]: ((((one_one @ A) = X) = (X = (one_one @ A))))))))).
% 0.31/1.50 thf(fact_154_Nat_Oex__has__greatest__nat, axiom, (! [P2:(nat > $o),K:nat,B:nat]: (((P2 @ K) => ((! [Y5:nat]: (((P2 @ Y5) => (((ord_less_eq @ nat) @ Y5) @ B)))) => (? [X3:nat]: (((P2 @ X3) & (! [Y:nat]: (((P2 @ Y) => (((ord_less_eq @ nat) @ Y) @ X3)))))))))))).
% 0.31/1.50 thf(fact_155_PrefixListTransitive, axiom, (! [A:$tType,L1:(list @ A),L2:(list @ A),L3:(list @ A)]: (((((prefixList @ A) @ L1) @ L2) => ((((prefixList @ A) @ L2) @ L3) => (((prefixList @ A) @ L1) @ L3)))))).
% 0.31/1.50 thf(fact_156_MinPredicate, axiom, (! [P2:(nat > $o)]: (((? [X_1:nat]: ((P2 @ X_1))) => (? [N02:nat]: (((P2 @ N02) & (! [N4:nat]: (((P2 @ N4) => (((ord_less_eq @ nat) @ N02) @ N4))))))))))).
% 0.31/1.50 thf(fact_157_lift__Suc__antimono__le, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N2:nat,N3:nat]: (((! [N:nat]: ((((ord_less_eq @ A) @ (F @ (suc @ N))) @ (F @ N)))) => ((((ord_less_eq @ nat) @ N2) @ N3) => (((ord_less_eq @ A) @ (F @ N3)) @ (F @ N2)))))))))).
% 0.31/1.50 thf(fact_158_lift__Suc__mono__le, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N2:nat,N3:nat]: (((! [N:nat]: ((((ord_less_eq @ A) @ (F @ N)) @ (F @ (suc @ N))))) => ((((ord_less_eq @ nat) @ N2) @ N3) => (((ord_less_eq @ A) @ (F @ N2)) @ (F @ N3)))))))))).
% 0.31/1.50 thf(fact_159_KeepProperty, axiom, (! [Low:nat,P2:(nat > $o),Q:(nat > $o)]: (((! [I2:nat]: (((((ord_less_eq @ nat) @ Low) @ I2) => ((P2 @ I2) => ((P2 @ (suc @ I2)) & (Q @ I2)))))) => ((P2 @ Low) => (! [I4:nat]: (((((ord_less_eq @ nat) @ Low) @ I4) => (Q @ I4))))))))).
% 0.31/1.50 thf(fact_160_PrefixSameOnLow, axiom, (! [A:$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))))))))).
% 0.31/1.50 thf(fact_161_zero__le, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X))))))).
% 0.31/1.50 thf(fact_162_diff__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B:A,D:A,C:A]: (((((ord_less_eq @ A) @ A8) @ B) => ((((ord_less_eq @ A) @ D) @ C) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A8) @ C)) @ (((minus_minus @ A) @ B) @ D)))))))))).
% 0.31/1.50 thf(fact_163_diff__left__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B:A,A8:A,C:A]: (((((ord_less_eq @ A) @ B) @ A8) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ C) @ A8)) @ (((minus_minus @ A) @ C) @ B))))))))).
% 0.31/1.50 thf(fact_164_diff__right__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B:A,C:A]: (((((ord_less_eq @ A) @ A8) @ B) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A8) @ C)) @ (((minus_minus @ A) @ B) @ C))))))))).
% 0.31/1.50 thf(fact_165_diff__eq__diff__less__eq, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B:A,C:A,D:A]: ((((((minus_minus @ A) @ A8) @ B) = (((minus_minus @ A) @ C) @ D)) => ((((ord_less_eq @ A) @ A8) @ B) = (((ord_less_eq @ A) @ C) @ D))))))))).
% 0.31/1.50 thf(fact_166_Suc__leD, axiom, (! [M:nat,N2:nat]: (((((ord_less_eq @ nat) @ (suc @ M)) @ N2) => (((ord_less_eq @ nat) @ M) @ N2))))).
% 0.31/1.50 thf(fact_167_le__SucE, axiom, (! [M:nat,N2:nat]: (((((ord_less_eq @ nat) @ M) @ (suc @ N2)) => ((~ ((((ord_less_eq @ nat) @ M) @ N2))) => (M = (suc @ N2))))))).
% 0.31/1.50 thf(fact_168_le__SucI, axiom, (! [M:nat,N2:nat]: (((((ord_less_eq @ nat) @ M) @ N2) => (((ord_less_eq @ nat) @ M) @ (suc @ N2)))))).
% 0.31/1.50 thf(fact_169_Suc__le__D, axiom, (! [N2:nat,M6:nat]: (((((ord_less_eq @ nat) @ (suc @ N2)) @ M6) => (? [M3:nat]: ((M6 = (suc @ M3)))))))).
% 0.31/1.50 thf(fact_170_le__Suc__eq, axiom, (! [M:nat,N2:nat]: (((((ord_less_eq @ nat) @ M) @ (suc @ N2)) = ((((ord_less_eq @ nat) @ M) @ N2) | (M = (suc @ N2))))))).
% 0.31/1.50 thf(fact_171_Suc__n__not__le__n, axiom, (! [N2:nat]: ((~ ((((ord_less_eq @ nat) @ (suc @ N2)) @ N2)))))).
% 0.31/1.50 thf(fact_172_not__less__eq__eq, axiom, (! [M:nat,N2:nat]: (((~ ((((ord_less_eq @ nat) @ M) @ N2))) = (((ord_less_eq @ nat) @ (suc @ N2)) @ M))))).
% 0.31/1.50 thf(fact_173_full__nat__induct, axiom, (! [P2:(nat > $o),N2:nat]: (((! [N:nat]: (((! [M2:nat]: (((((ord_less_eq @ nat) @ (suc @ M2)) @ N) => (P2 @ M2)))) => (P2 @ N)))) => (P2 @ N2))))).
% 0.31/1.50 thf(fact_174_nat__induct__at__least, axiom, (! [M:nat,N2:nat,P2:(nat > $o)]: (((((ord_less_eq @ nat) @ M) @ N2) => ((P2 @ M) => ((! [N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((P2 @ N) => (P2 @ (suc @ N)))))) => (P2 @ N2))))))).
% 0.31/1.50 thf(fact_175_transitive__stepwise__le, axiom, (! [M:nat,N2:nat,R:(nat > (nat > $o))]: (((((ord_less_eq @ nat) @ M) @ N2) => ((! [X3:nat]: (((R @ X3) @ X3))) => ((! [X3:nat,Y5:nat,Z3:nat]: ((((R @ X3) @ Y5) => (((R @ Y5) @ Z3) => ((R @ X3) @ Z3))))) => ((! [N:nat]: (((R @ N) @ (suc @ N)))) => ((R @ M) @ N2)))))))).
% 0.31/1.50 thf(fact_176_less__eq__nat_Osimps_I1_J, axiom, (! [N2:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N2)))).
% 0.31/1.50 thf(fact_177_le__0__eq, axiom, (! [N2:nat]: (((((ord_less_eq @ nat) @ N2) @ (zero_zero @ nat)) = (N2 = (zero_zero @ nat)))))).
% 0.31/1.50 thf(fact_178_bot__nat__0_Oextremum__unique, axiom, (! [A8:nat]: (((((ord_less_eq @ nat) @ A8) @ (zero_zero @ nat)) = (A8 = (zero_zero @ nat)))))).
% 0.31/1.50 thf(fact_179_bot__nat__0_Oextremum__uniqueI, axiom, (! [A8:nat]: (((((ord_less_eq @ nat) @ A8) @ (zero_zero @ nat)) => (A8 = (zero_zero @ nat)))))).
% 0.31/1.50 thf(fact_180_nat__less__le, axiom, ((ord_less @ nat) = (^ [M5:nat,N5:nat]: (((((ord_less_eq @ nat) @ M5) @ N5) & (M5 != N5)))))).
% 0.31/1.50 thf(fact_181_less__imp__le__nat, axiom, (! [M:nat,N2:nat]: (((((ord_less @ nat) @ M) @ N2) => (((ord_less_eq @ nat) @ M) @ N2))))).
% 0.31/1.50 thf(fact_182_le__eq__less__or__eq, axiom, ((ord_less_eq @ nat) = (^ [M5:nat,N5:nat]: (((((ord_less @ nat) @ M5) @ N5) | (M5 = N5)))))).
% 0.31/1.50 thf(fact_183_less__or__eq__imp__le, axiom, (! [M:nat,N2:nat]: ((((((ord_less @ nat) @ M) @ N2) | (M = N2)) => (((ord_less_eq @ nat) @ M) @ N2))))).
% 0.31/1.50 thf(fact_184_le__neq__implies__less, axiom, (! [M:nat,N2:nat]: (((((ord_less_eq @ nat) @ M) @ N2) => ((M != N2) => (((ord_less @ nat) @ M) @ N2)))))).
% 0.31/1.50 thf(fact_185_less__mono__imp__le__mono, axiom, (! [F:(nat > nat),I:nat,J:nat]: (((! [I2:nat,J2:nat]: (((((ord_less @ nat) @ I2) @ J2) => (((ord_less @ nat) @ (F @ I2)) @ (F @ J2))))) => ((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (F @ I)) @ (F @ J))))))).
% 0.31/1.50 thf(fact_186_eq__diff__iff, axiom, (! [K:nat,M:nat,N2:nat]: (((((ord_less_eq @ nat) @ K) @ M) => ((((ord_less_eq @ nat) @ K) @ N2) => (((((minus_minus @ nat) @ M) @ K) = (((minus_minus @ nat) @ N2) @ K)) = (M = N2))))))).
% 0.31/1.50 thf(fact_187_le__diff__iff, axiom, (! [K:nat,M:nat,N2:nat]: (((((ord_less_eq @ nat) @ K) @ M) => ((((ord_less_eq @ nat) @ K) @ N2) => ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ M) @ K)) @ (((minus_minus @ nat) @ N2) @ K)) = (((ord_less_eq @ nat) @ M) @ N2))))))).
% 0.31/1.50 thf(fact_188_Nat_Odiff__diff__eq, axiom, (! [K:nat,M:nat,N2:nat]: (((((ord_less_eq @ nat) @ K) @ M) => ((((ord_less_eq @ nat) @ K) @ N2) => ((((minus_minus @ nat) @ (((minus_minus @ nat) @ M) @ K)) @ (((minus_minus @ nat) @ N2) @ K)) = (((minus_minus @ nat) @ M) @ N2))))))).
% 0.31/1.50 thf(fact_189_diff__le__mono, axiom, (! [M:nat,N2:nat,L:nat]: (((((ord_less_eq @ nat) @ M) @ N2) => (((ord_less_eq @ nat) @ (((minus_minus @ nat) @ M) @ L)) @ (((minus_minus @ nat) @ N2) @ L)))))).
% 0.31/1.50 thf(fact_190_diff__le__self, axiom, (! [M:nat,N2:nat]: ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ M) @ N2)) @ M)))).
% 0.31/1.50 thf(fact_191_le__diff__iff_H, axiom, (! [A8:nat,C:nat,B:nat]: (((((ord_less_eq @ nat) @ A8) @ C) => ((((ord_less_eq @ nat) @ B) @ C) => ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ C) @ A8)) @ (((minus_minus @ nat) @ C) @ B)) = (((ord_less_eq @ nat) @ B) @ A8))))))).
% 0.31/1.50 thf(fact_192_diff__le__mono2, axiom, (! [M:nat,N2:nat,L:nat]: (((((ord_less_eq @ nat) @ M) @ N2) => (((ord_less_eq @ nat) @ (((minus_minus @ nat) @ L) @ N2)) @ (((minus_minus @ nat) @ L) @ M)))))).
% 0.31/1.50 thf(fact_193_MinPredicate2, axiom, (! [P2:(nat > $o)]: (((? [X_1:nat]: ((P2 @ X_1))) => (? [N02:nat]: (((P2 @ N02) & ((N02 = (zero_zero @ nat)) | (~ ((P2 @ (((minus_minus @ nat) @ N02) @ (one_one @ nat))))))))))))).
% 0.31/1.50 thf(fact_194_PrefixListMonotonicity, axiom, (! [A:$tType,L1:(list @ A),L2:(list @ A)]: (((((prefixList @ A) @ L1) @ L2) => (((ord_less @ nat) @ ((size_size @ (list @ A)) @ L1)) @ ((size_size @ (list @ A)) @ L2)))))).
% 0.31/1.50 thf(fact_195_le__iff__diff__le__0, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => ((ord_less_eq @ A) = (^ [A9:A,B3:A]: ((((ord_less_eq @ A) @ (((minus_minus @ A) @ A9) @ B3)) @ (zero_zero @ A))))))))).
% 0.31/1.50 thf(fact_196_Suc__leI, axiom, (! [M:nat,N2:nat]: (((((ord_less @ nat) @ M) @ N2) => (((ord_less_eq @ nat) @ (suc @ M)) @ N2))))).
% 0.31/1.50 thf(fact_197_Suc__le__eq, axiom, (! [M:nat,N2:nat]: (((((ord_less_eq @ nat) @ (suc @ M)) @ N2) = (((ord_less @ nat) @ M) @ N2))))).
% 0.31/1.50 thf(fact_198_dec__induct, axiom, (! [I:nat,J:nat,P2:(nat > $o)]: (((((ord_less_eq @ nat) @ I) @ J) => ((P2 @ I) => ((! [N:nat]: (((((ord_less_eq @ nat) @ I) @ N) => ((((ord_less @ nat) @ N) @ J) => ((P2 @ N) => (P2 @ (suc @ N))))))) => (P2 @ J))))))).
% 0.31/1.50 thf(fact_199_inc__induct, axiom, (! [I:nat,J:nat,P2:(nat > $o)]: (((((ord_less_eq @ nat) @ I) @ J) => ((P2 @ J) => ((! [N:nat]: (((((ord_less_eq @ nat) @ I) @ N) => ((((ord_less @ nat) @ N) @ J) => ((P2 @ (suc @ N)) => (P2 @ N)))))) => (P2 @ I))))))).
% 0.31/1.50 thf(fact_200_Suc__le__lessD, axiom, (! [M:nat,N2:nat]: (((((ord_less_eq @ nat) @ (suc @ M)) @ N2) => (((ord_less @ nat) @ M) @ N2))))).
% 0.31/1.50 thf(fact_201_le__less__Suc__eq, axiom, (! [M:nat,N2:nat]: (((((ord_less_eq @ nat) @ M) @ N2) => ((((ord_less @ nat) @ N2) @ (suc @ M)) = (N2 = M)))))).
% 0.31/1.50 thf(fact_202_less__Suc__eq__le, axiom, (! [M:nat,N2:nat]: (((((ord_less @ nat) @ M) @ (suc @ N2)) = (((ord_less_eq @ nat) @ M) @ N2))))).
% 0.31/1.50 thf(fact_203_less__eq__Suc__le, axiom, ((ord_less @ nat) = (^ [N5:nat]: (((ord_less_eq @ nat) @ (suc @ N5)))))).
% 0.31/1.50 thf(fact_204_le__imp__less__Suc, axiom, (! [M:nat,N2:nat]: (((((ord_less_eq @ nat) @ M) @ N2) => (((ord_less @ nat) @ M) @ (suc @ N2)))))).
% 0.31/1.50 thf(fact_205_ex__least__nat__le, axiom, (! [P2:(nat > $o),N2:nat]: (((P2 @ N2) => ((~ ((P2 @ (zero_zero @ nat)))) => (? [K2:nat]: (((((ord_less_eq @ nat) @ K2) @ N2) & ((! [I4:nat]: (((((ord_less @ nat) @ I4) @ K2) => (~ ((P2 @ I4)))))) & (P2 @ K2)))))))))).
% 0.31/1.50 thf(fact_206_Suc__diff__le, axiom, (! [N2:nat,M:nat]: (((((ord_less_eq @ nat) @ N2) @ M) => ((((minus_minus @ nat) @ (suc @ M)) @ N2) = (suc @ (((minus_minus @ nat) @ M) @ N2))))))).
% 0.31/1.50 thf(fact_207_less__diff__iff, axiom, (! [K:nat,M:nat,N2:nat]: (((((ord_less_eq @ nat) @ K) @ M) => ((((ord_less_eq @ nat) @ K) @ N2) => ((((ord_less @ nat) @ (((minus_minus @ nat) @ M) @ K)) @ (((minus_minus @ nat) @ N2) @ K)) = (((ord_less @ nat) @ M) @ N2))))))).
% 0.31/1.50 thf(fact_208_diff__less__mono, axiom, (! [A8:nat,B:nat,C:nat]: (((((ord_less @ nat) @ A8) @ B) => ((((ord_less_eq @ nat) @ C) @ A8) => (((ord_less @ nat) @ (((minus_minus @ nat) @ A8) @ C)) @ (((minus_minus @ nat) @ B) @ C))))))).
% 0.31/1.50 thf(fact_209_One__nat__def, axiom, ((one_one @ nat) = (suc @ (zero_zero @ nat)))).
% 0.31/1.50 thf(fact_210_diff__Suc__eq__diff__pred, axiom, (! [M:nat,N2:nat]: (((((minus_minus @ nat) @ M) @ (suc @ N2)) = (((minus_minus @ nat) @ (((minus_minus @ nat) @ M) @ (one_one @ nat))) @ N2))))).
% 0.31/1.50 thf(fact_211_ex__least__nat__less, axiom, (! [P2:(nat > $o),N2:nat]: (((P2 @ N2) => ((~ ((P2 @ (zero_zero @ nat)))) => (? [K2:nat]: (((((ord_less @ nat) @ K2) @ N2) & ((! [I4:nat]: (((((ord_less_eq @ nat) @ I4) @ K2) => (~ ((P2 @ I4)))))) & (P2 @ (suc @ K2))))))))))).
% 0.31/1.50 thf(fact_212_nat__induct__non__zero, axiom, (! [N2:nat,P2:(nat > $o)]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) => ((P2 @ (one_one @ nat)) => ((! [N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => ((P2 @ N) => (P2 @ (suc @ N)))))) => (P2 @ N2))))))).
% 0.31/1.50 thf(fact_213_Suc__pred_H, axiom, (! [N2:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) => (N2 = (suc @ (((minus_minus @ nat) @ N2) @ (one_one @ nat)))))))).
% 0.31/1.50 thf(fact_214_Suc__diff__eq__diff__pred, axiom, (! [N2:nat,M:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) => ((((minus_minus @ nat) @ (suc @ M)) @ N2) = (((minus_minus @ nat) @ M) @ (((minus_minus @ nat) @ N2) @ (one_one @ nat)))))))).
% 0.31/1.50 thf(fact_215_AssumptionSubset2_I6_J, axiom, ((n1 != (zero_zero @ nat)) => ((~ ((((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ (((minus_minus @ nat) @ n1) @ (one_one @ nat)))) @ msgInSet))) | (msgInSet = (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ (((minus_minus @ nat) @ n1) @ (one_one @ nat))))))).
% 0.31/1.50 thf(fact_216_AssumptionSubset3_I6_J, axiom, ((nMsg != (zero_zero @ nat)) => ((~ ((((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ (((minus_minus @ nat) @ nMsg) @ (one_one @ nat)))) @ msg))) | (msg = (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ (((minus_minus @ nat) @ nMsg) @ (one_one @ nat))))))).
% 0.31/1.50 thf(fact_217_EnabledIntermediate, axiom, (! [I4:nat]: (((((ord_less @ nat) @ I4) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ (suc @ index)))) => ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) @ (one_one @ nat))) @ I4) => (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ I4)) @ msg)))))).
% 0.31/1.50 thf(fact_218_length__greater__0__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ ((size_size @ (list @ A)) @ Xs)) = (Xs != (nil @ A)))))).
% 0.31/1.50 thf(fact_219_AssumptionFair_I2_J, axiom, (((ord_less @ nat) @ n0) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ n)))).
% 0.31/1.50 thf(fact_220_Occ4, axiom, (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index)) @ nMsg)) @ msg)).
% 0.31/1.50 thf(fact_221_AssumptionFair_I3_J, axiom, (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ n)) @ n0)) @ msg)).
% 0.31/1.50 thf(fact_222_AssumptionSubset3_I4_J, axiom, (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ nMsg)) @ msg)).
% 0.31/1.50 thf(fact_223_AssumptionSubset2_I4_J, axiom, (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ n1)) @ msgInSet)).
% 0.31/1.50 thf(fact_224_MessageStaysOrConsumed, axiom, (! [N1:nat,N22:nat,N2:nat,Msg:((message @ p) @ v)]: ((((((ord_less_eq @ nat) @ N1) @ N22) & ((((ord_less @ nat) @ N22) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ N2))) & (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ N2)) @ N1)) @ Msg))) => ((((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ N2)) @ N22)) @ Msg) | (? [N03:nat]: (((((ord_less_eq @ nat) @ N1) @ N03) & ((((ord_less @ nat) @ N03) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ N2))) & ((((nth @ ((message @ p) @ v)) @ (ft @ N2)) @ N03) = Msg)))))))))).
% 0.31/1.50 thf(fact_225__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)).
% 0.31/1.50 thf(fact_226_length__0__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((size_size @ (list @ A)) @ Xs) = (zero_zero @ nat)) = (Xs = (nil @ A)))))).
% 0.31/1.50 thf(fact_227_Occ2, axiom, (((((enabled @ p) @ v) @ s) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index))) @ msg)).
% 0.31/1.50 thf(fact_228_AssumptionCase1ImplThesis_H, axiom, (((((enabled @ p) @ v) @ s) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ n))) @ msg)).
% 0.31/1.50 thf(fact_229_neq__if__length__neq, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((size_size @ (list @ A)) @ Xs) != ((size_size @ (list @ A)) @ Ys)) => (Xs != Ys))))).
% 0.31/1.50 thf(fact_230_Ex__list__of__length, axiom, (! [A:$tType,N2:nat]: ((? [Xs2:(list @ A)]: ((((size_size @ (list @ A)) @ Xs2) = N2)))))).
% 0.31/1.50 thf(fact_231_length__induct, axiom, (! [A:$tType,P2:((list @ A) > $o),Xs:(list @ A)]: (((! [Xs2:(list @ A)]: (((! [Ys2:(list @ A)]: (((((ord_less @ nat) @ ((size_size @ (list @ A)) @ Ys2)) @ ((size_size @ (list @ A)) @ Xs2)) => (P2 @ Ys2)))) => (P2 @ Xs2)))) => (P2 @ Xs))))).
% 0.31/1.50 thf(fact_232_list_Osize_I3_J, axiom, (! [A:$tType]: ((((size_size @ (list @ A)) @ (nil @ A)) = (zero_zero @ nat))))).
% 0.31/1.50 thf(fact_233_list__eq__iff__nth__eq, axiom, (! [A:$tType]: (((^ [Y4:(list @ A),Z2:(list @ A)]: ((Y4 = Z2))) = (^ [Xs3:(list @ A),Ys3:(list @ A)]: (((((size_size @ (list @ A)) @ Xs3) = ((size_size @ (list @ A)) @ Ys3)) & (! [I3:nat]: (((((ord_less @ nat) @ I3) @ ((size_size @ (list @ A)) @ Xs3)) => ((((nth @ A) @ Xs3) @ I3) = (((nth @ A) @ Ys3) @ I3)))))))))))).
% 0.31/1.50 thf(fact_234_Skolem__list__nth, axiom, (! [A:$tType,K:nat,P2:(nat > (A > $o))]: (((! [I3:nat]: (((((ord_less @ nat) @ I3) @ K) => (? [X4:A]: (((P2 @ I3) @ X4)))))) = (? [Xs3:(list @ A)]: (((((size_size @ (list @ A)) @ Xs3) = K) & (! [I3:nat]: (((((ord_less @ nat) @ I3) @ K) => ((P2 @ I3) @ (((nth @ A) @ Xs3) @ I3)))))))))))).
% 0.31/1.50 thf(fact_235_nth__equalityI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ A)) @ Ys)) => ((! [I2:nat]: (((((ord_less @ nat) @ I2) @ ((size_size @ (list @ A)) @ Xs)) => ((((nth @ A) @ Xs) @ I2) = (((nth @ A) @ Ys) @ I2))))) => (Xs = Ys)))))).
% 0.31/1.50 thf(fact_236_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) | (? [N03:nat]: (((((ord_less_eq @ nat) @ n0) @ N03) & ((((ord_less @ nat) @ N03) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ n))) & ((((nth @ ((message @ p) @ v)) @ (ft @ n)) @ N03) = msg))))))).
% 0.31/1.50 thf(fact_237_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) & (? [N03:nat]: (((((ord_less_eq @ nat) @ n0) @ N03) & ((((ord_less @ nat) @ N03) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ N6))) & (msg = (((nth @ ((message @ p) @ v)) @ (ft @ N6)) @ N03))))))))))).
% 0.31/1.50 thf(fact_238_EnabledInSuc, axiom, (((((enabled @ p) @ v) @ s) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index)))) @ msg)).
% 0.31/1.50 thf(fact_239_AssumptionSubset2_I2_J, axiom, (((((enabled @ p) @ v) @ s) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index)))) @ msgInSet)).
% 0.31/1.50 thf(fact_240_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)))).
% 0.31/1.50 thf(fact_241_EnabledOrConsumedAtLast, axiom, ((((((enabled @ p) @ v) @ s) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ n))) @ msg) | (? [N03:nat]: (((((ord_less_eq @ nat) @ n0) @ N03) & ((((ord_less @ nat) @ N03) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ n))) & ((((nth @ ((message @ p) @ v)) @ (ft @ n)) @ N03) = msg))))))).
% 0.31/1.50 thf(fact_242_last__conv__nth, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((last @ A) @ Xs) = (((nth @ A) @ Xs) @ (((minus_minus @ nat) @ ((size_size @ (list @ A)) @ Xs)) @ (one_one @ nat)))))))).
% 0.31/1.50 thf(fact_243_diff__numeral__special_I9_J, axiom, (! [A:$tType]: (((neg_numeral @ A) => ((((minus_minus @ A) @ (one_one @ A)) @ (one_one @ A)) = (zero_zero @ A)))))).
% 0.31/1.50 thf(fact_244__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, (! [Msg:((message @ p) @ v),N04:nat,N7:nat]: (((((((((firstOccurrence @ p) @ v) @ s) @ (fe @ N7)) @ (ft @ N7)) @ Msg) @ N04) => (((ord_less @ nat) @ (zero_zero @ nat)) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ N7))) @ Msg)))))).
% 0.31/1.50 thf(fact_245_le__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))).
% 0.31/1.50 thf(fact_246_less__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))))).
% 0.31/1.50 thf(fact_247_le__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (one_one @ A)) @ (one_one @ A)))))).
% 0.31/1.50 thf(fact_248_less__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (one_one @ A)))))))).
% 0.31/1.50 thf(fact_249_less__numeral__extra_I1_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 0.31/1.50 thf(fact_250__092_060open_062_092_060forall_062n_O_A_092_060forall_062msg_H_092_060in_062firstOccSet_An_O_Amsg_H_A_092_060in_062_D_Amsgs_A_Ilast_A_Ife_An_J_J_092_060close_062, axiom, (! [N7:nat,X5:((message @ p) @ v)]: (((((member @ ((message @ p) @ v)) @ X5) @ (firstOccSet @ N7)) => (((ord_less @ nat) @ (zero_zero @ nat)) @ ((((((msgs @ p) @ v) @ s) @ product_unit) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ N7))) @ X5)))))).
% 0.31/1.50 thf(tcon_fun___Orderings_Oorder, axiom, (! [A10:$tType,A11:$tType]: (((order @ A11) => (order @ (A10 > A11)))))).
% 0.31/1.50 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, axiom, (linord1659791738miring @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add, axiom, (cancel146912293up_add @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add, axiom, (cancel1352612707id_add @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff, axiom, (comm_monoid_diff @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, (wellorder @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Orderings_Oorder_1, axiom, (order @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Groups_Ozero, axiom, (zero @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Groups_Oone, axiom, (one @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Nat_Osize, axiom, (size @ nat)).
% 0.31/1.50 thf(tcon_HOL_Obool___Orderings_Oorder_2, axiom, (order @ $o)).
% 0.31/1.50 thf(tcon_List_Olist___Nat_Osize_3, axiom, (! [A10:$tType]: ((size @ (list @ A10))))).
% 0.31/1.50 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_4, axiom, (wellorder @ product_unit)).
% 0.31/1.50 thf(tcon_Product__Type_Ounit___Orderings_Oorder_5, axiom, (order @ product_unit)).
% 0.31/1.50 thf(tcon_AsynchronousSystem_Omessage___Nat_Osize_6, axiom, (! [A10:$tType,A11:$tType]: ((size @ ((message @ A10) @ A11))))).
% 0.31/1.50 thf(conj_0, conjecture, (((ord_less @ nat) @ (((minus_minus @ nat) @ nMsg) @ (suc @ (zero_zero @ nat)))) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) @ (suc @ (zero_zero @ nat))))).
% 0.31/1.50 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.YNdYCGZgEX/DTF2DTF24154.p
% 0.31/1.50 ------------------------
% 0.31/1.54 ---- Cleaned THF ---
% 0.31/1.54 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext,type,
% 0.31/1.54 configuration_ext: $tType > $tType > $tType > $tType > $tType ).
% 0.31/1.54
% 0.31/1.54 thf(ty_t_AsynchronousSystem_Omessage,type,
% 0.31/1.54 message: $tType > $tType > $tType ).
% 0.31/1.54
% 0.31/1.54 thf(ty_t_Product__Type_Ounit,type,
% 0.31/1.54 product_unit: $tType ).
% 0.31/1.54
% 0.31/1.54 thf(ty_t_List_Olist,type,
% 0.31/1.54 list: $tType > $tType ).
% 0.31/1.54
% 0.31/1.54 thf(ty_t_Set_Oset,type,
% 0.31/1.54 set: $tType > $tType ).
% 0.31/1.54
% 0.31/1.54 thf(ty_t_Nat_Onat,type,
% 0.31/1.54 nat: $tType ).
% 0.31/1.54
% 0.31/1.54 thf(ty_tf_v,type,
% 0.31/1.54 v: $tType ).
% 0.31/1.54
% 0.31/1.54 thf(ty_tf_s,type,
% 0.31/1.54 s: $tType ).
% 0.31/1.54
% 0.31/1.54 thf(ty_tf_p,type,
% 0.31/1.54 p: $tType ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_HOL_Otype,type,
% 0.31/1.54 type:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Nat_Osize,type,
% 0.31/1.54 size:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Groups_Oone,type,
% 0.31/1.54 one:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Groups_Ozero,type,
% 0.31/1.54 zero:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Num_Oneg__numeral,type,
% 0.31/1.54 neg_numeral:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Orderings_Oorder,type,
% 0.31/1.54 order:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Groups_Ogroup__add,type,
% 0.31/1.54 group_add:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Orderings_Owellorder,type,
% 0.31/1.54 wellorder:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Groups_Ocomm__monoid__diff,type,
% 0.31/1.54 comm_monoid_diff:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.31/1.54 ordered_ab_group_add:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.31/1.54 cancel1352612707id_add:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.31/1.54 cancel146912293up_add:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.31/1.54 linord1659791738miring:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.31/1.54 canoni770627133id_add:
% 0.31/1.54 !>[A: $tType] : $o ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_AsynchronousSystem_Oconfiguration_Omsgs,type,
% 0.31/1.54 msgs:
% 0.31/1.54 !>[P: $tType,V: $tType,S: $tType,Z: $tType] : ( ( configuration_ext @ P @ V @ S @ Z ) > ( message @ P @ V ) > nat ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_AsynchronousSystem_Oenabled,type,
% 0.31/1.54 enabled:
% 0.31/1.54 !>[P: $tType,V: $tType,S: $tType] : ( ( configuration_ext @ P @ V @ S @ product_unit ) > ( message @ P @ V ) > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_AsynchronousSystem_OisReceiverOf,type,
% 0.31/1.54 isReceiverOf:
% 0.31/1.54 !>[P: $tType,V: $tType] : ( P > ( message @ P @ V ) > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Execution_Oexecution_OfirstOccurrence,type,
% 0.31/1.54 firstOccurrence:
% 0.31/1.54 !>[P: $tType,V: $tType,S: $tType] : ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( message @ P @ V ) > nat > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.31/1.54 minus_minus:
% 0.31/1.54 !>[A: $tType] : ( A > A > A ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.31/1.54 one_one:
% 0.31/1.54 !>[A: $tType] : A ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.31/1.54 zero_zero:
% 0.31/1.54 !>[A: $tType] : A ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_ListUtilities_OprefixList,type,
% 0.31/1.54 prefixList:
% 0.31/1.54 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_List_Olast,type,
% 0.31/1.54 last:
% 0.31/1.54 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_List_Olist_ONil,type,
% 0.31/1.54 nil:
% 0.31/1.54 !>[A: $tType] : ( list @ A ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_List_Onth,type,
% 0.31/1.54 nth:
% 0.31/1.54 !>[A: $tType] : ( ( list @ A ) > nat > A ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Nat_OSuc,type,
% 0.31/1.54 suc: nat > nat ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.31/1.54 size_size:
% 0.31/1.54 !>[A: $tType] : ( A > nat ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.31/1.54 ord_less:
% 0.31/1.54 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.31/1.54 ord_less_eq:
% 0.31/1.54 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_c_member,type,
% 0.31/1.54 member:
% 0.31/1.54 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_fe____,type,
% 0.31/1.54 fe: nat > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_firstOccSet____,type,
% 0.31/1.54 firstOccSet: nat > ( set @ ( message @ p @ v ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_ft____,type,
% 0.31/1.54 ft: nat > ( list @ ( message @ p @ v ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_index____,type,
% 0.31/1.54 index: nat ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_msgInSet____,type,
% 0.31/1.54 msgInSet: message @ p @ v ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_msg____,type,
% 0.31/1.54 msg: message @ p @ v ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_n0____,type,
% 0.31/1.54 n0: nat ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_n1____,type,
% 0.31/1.54 n1: nat ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_nMsg____,type,
% 0.31/1.54 nMsg: nat ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_n____,type,
% 0.31/1.54 n: nat ).
% 0.31/1.54
% 0.31/1.54 thf(sy_v_p____,type,
% 0.31/1.54 p2: p ).
% 0.31/1.54
% 0.31/1.54 thf(fact_0_AssumpOcc6_I1_J,axiom,
% 0.31/1.54 ord_less @ nat @ ( zero_zero @ nat ) @ nMsg ).
% 0.31/1.54
% 0.31/1.54 thf(fact_1_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 0.31/1.54 ! [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] :
% 0.31/1.54 ( ! [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 ) )
% 0.31/1.54 => ( ! [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 ) ),N: nat] :
% 0.31/1.54 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.31/1.54 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.31/1.54 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.31/1.54 => ( ! [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 ) )
% 0.31/1.54 => ( ! [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 ) ),N: nat] :
% 0.31/1.54 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.31/1.54 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.31/1.54 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.31/1.54 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_2_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 0.31/1.54 ! [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 ) ),A2: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),A3: nat] :
% 0.31/1.54 ( ! [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 ) )
% 0.31/1.54 => ( ! [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 ) ),N: nat] :
% 0.31/1.54 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.31/1.54 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.31/1.54 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.31/1.54 => ( ! [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 ) )
% 0.31/1.54 => ( ! [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 ) ),N: nat] :
% 0.31/1.54 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.31/1.54 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.31/1.54 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.31/1.54 => ( P2 @ A0 @ A1 @ A2 @ A3 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_3_AssumptionSubset_I3_J,axiom,
% 0.31/1.54 firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg ).
% 0.31/1.54
% 0.31/1.54 thf(fact_4_SmallIndex,axiom,
% 0.31/1.54 ! [NMsg: nat] :
% 0.31/1.54 ( ( firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ NMsg )
% 0.31/1.54 => ( ord_less @ nat @ NMsg @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_5_AssumptionSubset3_I3_J,axiom,
% 0.31/1.54 ord_less @ nat @ nMsg @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_6_AssumptionSubset2_I3_J,axiom,
% 0.31/1.54 ord_less @ nat @ n1 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_7_Suc__pred,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.31/1.54 => ( ( suc @ ( minus_minus @ nat @ N2 @ ( suc @ ( zero_zero @ nat ) ) ) )
% 0.31/1.54 = N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_8_zero__less__diff,axiom,
% 0.31/1.54 ! [N2: nat,M: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( minus_minus @ nat @ N2 @ M ) )
% 0.31/1.54 = ( ord_less @ nat @ M @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_9_less__Suc0,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ N2 @ ( suc @ ( zero_zero @ nat ) ) )
% 0.31/1.54 = ( N2
% 0.31/1.54 = ( zero_zero @ nat ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_10_zero__less__Suc,axiom,
% 0.31/1.54 ! [N2: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_11_diff__gt__0__iff__gt,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ! [A8: A,B: A] :
% 0.31/1.54 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A8 @ B ) )
% 0.31/1.54 = ( ord_less @ A @ B @ A8 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_12_diff__0__eq__0,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ( ( minus_minus @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.31/1.54 = ( zero_zero @ nat ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_13_diff__self__eq__0,axiom,
% 0.31/1.54 ! [M: nat] :
% 0.31/1.54 ( ( minus_minus @ nat @ M @ M )
% 0.31/1.54 = ( zero_zero @ nat ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_14_diff__Suc__Suc,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( minus_minus @ nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.31/1.54 = ( minus_minus @ nat @ M @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_15_Suc__diff__diff,axiom,
% 0.31/1.54 ! [M: nat,N2: nat,K: nat] :
% 0.31/1.54 ( ( minus_minus @ nat @ ( minus_minus @ nat @ ( suc @ M ) @ N2 ) @ ( suc @ K ) )
% 0.31/1.54 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ N2 ) @ K ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_16_neq0__conv,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ( ( N2
% 0.31/1.54 != ( zero_zero @ nat ) )
% 0.31/1.54 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_17_less__nat__zero__code,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ~ ( ord_less @ nat @ N2 @ ( zero_zero @ nat ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_18_old_Onat_Oinject,axiom,
% 0.31/1.54 ! [Nat: nat,Nat2: nat] :
% 0.31/1.54 ( ( ( suc @ Nat )
% 0.31/1.54 = ( suc @ Nat2 ) )
% 0.31/1.54 = ( Nat = Nat2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_19_nat_Oinject,axiom,
% 0.31/1.54 ! [X2: nat,Y2: nat] :
% 0.31/1.54 ( ( ( suc @ X2 )
% 0.31/1.54 = ( suc @ Y2 ) )
% 0.31/1.54 = ( X2 = Y2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_20_not__gr__zero,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( canoni770627133id_add @ A )
% 0.31/1.54 => ! [N2: A] :
% 0.31/1.54 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N2 ) )
% 0.31/1.54 = ( N2
% 0.31/1.54 = ( zero_zero @ A ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_21_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( cancel1352612707id_add @ A )
% 0.31/1.54 => ! [A8: A] :
% 0.31/1.54 ( ( minus_minus @ A @ A8 @ A8 )
% 0.31/1.54 = ( zero_zero @ A ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_22_diff__zero,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( cancel1352612707id_add @ A )
% 0.31/1.54 => ! [A8: A] :
% 0.31/1.54 ( ( minus_minus @ A @ A8 @ ( zero_zero @ A ) )
% 0.31/1.54 = A8 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_23_zero__diff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( comm_monoid_diff @ A )
% 0.31/1.54 => ! [A8: A] :
% 0.31/1.54 ( ( minus_minus @ A @ ( zero_zero @ A ) @ A8 )
% 0.31/1.54 = ( zero_zero @ A ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_24_diff__0__right,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( group_add @ A )
% 0.31/1.54 => ! [A8: A] :
% 0.31/1.54 ( ( minus_minus @ A @ A8 @ ( zero_zero @ A ) )
% 0.31/1.54 = A8 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_25_diff__self,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( group_add @ A )
% 0.31/1.54 => ! [A8: A] :
% 0.31/1.54 ( ( minus_minus @ A @ A8 @ A8 )
% 0.31/1.54 = ( zero_zero @ A ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_26_Suc__less__eq,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.31/1.54 = ( ord_less @ nat @ M @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_27_Suc__mono,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ M @ N2 )
% 0.31/1.54 => ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_28_lessI,axiom,
% 0.31/1.54 ! [N2: nat] : ( ord_less @ nat @ N2 @ ( suc @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_29_bot__nat__0_Onot__eq__extremum,axiom,
% 0.31/1.54 ! [A8: nat] :
% 0.31/1.54 ( ( A8
% 0.31/1.54 != ( zero_zero @ nat ) )
% 0.31/1.54 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A8 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_30_AssumptionSubset_I2_J,axiom,
% 0.31/1.54 firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msgInSet @ n1 ).
% 0.31/1.54
% 0.31/1.54 thf(fact_31_AssumptionSubset_I1_J,axiom,
% 0.31/1.54 ord_less_eq @ nat @ n1 @ nMsg ).
% 0.31/1.54
% 0.31/1.54 thf(fact_32_zero__reorient,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( zero @ A )
% 0.31/1.54 => ! [X: A] :
% 0.31/1.54 ( ( ( zero_zero @ A )
% 0.31/1.54 = X )
% 0.31/1.54 = ( X
% 0.31/1.54 = ( zero_zero @ A ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_33_measure__induct__rule,axiom,
% 0.31/1.54 ! [B2: $tType,A: $tType] :
% 0.31/1.54 ( ( wellorder @ B2 )
% 0.31/1.54 => ! [F: A > B2,P2: A > $o,A8: A] :
% 0.31/1.54 ( ! [X3: A] :
% 0.31/1.54 ( ! [Y: A] :
% 0.31/1.54 ( ( ord_less @ B2 @ ( F @ Y ) @ ( F @ X3 ) )
% 0.31/1.54 => ( P2 @ Y ) )
% 0.31/1.54 => ( P2 @ X3 ) )
% 0.31/1.54 => ( P2 @ A8 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_34_measure__induct,axiom,
% 0.31/1.54 ! [B2: $tType,A: $tType] :
% 0.31/1.54 ( ( wellorder @ B2 )
% 0.31/1.54 => ! [F: A > B2,P2: A > $o,A8: A] :
% 0.31/1.54 ( ! [X3: A] :
% 0.31/1.54 ( ! [Y: A] :
% 0.31/1.54 ( ( ord_less @ B2 @ ( F @ Y ) @ ( F @ X3 ) )
% 0.31/1.54 => ( P2 @ Y ) )
% 0.31/1.54 => ( P2 @ X3 ) )
% 0.31/1.54 => ( P2 @ A8 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_35_diff__right__commute,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( cancel146912293up_add @ A )
% 0.31/1.54 => ! [A8: A,C: A,B: A] :
% 0.31/1.54 ( ( minus_minus @ A @ ( minus_minus @ A @ A8 @ C ) @ B )
% 0.31/1.54 = ( minus_minus @ A @ ( minus_minus @ A @ A8 @ B ) @ C ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_36_diff__eq__diff__eq,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( group_add @ A )
% 0.31/1.54 => ! [A8: A,B: A,C: A,D: A] :
% 0.31/1.54 ( ( ( minus_minus @ A @ A8 @ B )
% 0.31/1.54 = ( minus_minus @ A @ C @ D ) )
% 0.31/1.54 => ( ( A8 = B )
% 0.31/1.54 = ( C = D ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_37_n__not__Suc__n,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ( N2
% 0.31/1.54 != ( suc @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_38_Suc__inject,axiom,
% 0.31/1.54 ! [X: nat,Y3: nat] :
% 0.31/1.54 ( ( ( suc @ X )
% 0.31/1.54 = ( suc @ Y3 ) )
% 0.31/1.54 => ( X = Y3 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_39_infinite__descent__measure,axiom,
% 0.31/1.54 ! [A: $tType,P2: A > $o,V2: A > nat,X: A] :
% 0.31/1.54 ( ! [X3: A] :
% 0.31/1.54 ( ~ ( P2 @ X3 )
% 0.31/1.54 => ? [Y: A] :
% 0.31/1.54 ( ( ord_less @ nat @ ( V2 @ Y ) @ ( V2 @ X3 ) )
% 0.31/1.54 & ~ ( P2 @ Y ) ) )
% 0.31/1.54 => ( P2 @ X ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_40_linorder__neqE__nat,axiom,
% 0.31/1.54 ! [X: nat,Y3: nat] :
% 0.31/1.54 ( ( X != Y3 )
% 0.31/1.54 => ( ~ ( ord_less @ nat @ X @ Y3 )
% 0.31/1.54 => ( ord_less @ nat @ Y3 @ X ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_41_infinite__descent,axiom,
% 0.31/1.54 ! [P2: nat > $o,N2: nat] :
% 0.31/1.54 ( ! [N: nat] :
% 0.31/1.54 ( ~ ( P2 @ N )
% 0.31/1.54 => ? [M2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ M2 @ N )
% 0.31/1.54 & ~ ( P2 @ M2 ) ) )
% 0.31/1.54 => ( P2 @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_42_nat__less__induct,axiom,
% 0.31/1.54 ! [P2: nat > $o,N2: nat] :
% 0.31/1.54 ( ! [N: nat] :
% 0.31/1.54 ( ! [M2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ M2 @ N )
% 0.31/1.54 => ( P2 @ M2 ) )
% 0.31/1.54 => ( P2 @ N ) )
% 0.31/1.54 => ( P2 @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_43_less__irrefl__nat,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ~ ( ord_less @ nat @ N2 @ N2 ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_44_less__not__refl3,axiom,
% 0.31/1.54 ! [S2: nat,T: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ S2 @ T )
% 0.31/1.54 => ( S2 != T ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_45_less__not__refl2,axiom,
% 0.31/1.54 ! [N2: nat,M: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ N2 @ M )
% 0.31/1.54 => ( M != N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_46_less__not__refl,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ~ ( ord_less @ nat @ N2 @ N2 ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_47_nat__neq__iff,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( M != N2 )
% 0.31/1.54 = ( ( ord_less @ nat @ M @ N2 )
% 0.31/1.54 | ( ord_less @ nat @ N2 @ M ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_48_size__neq__size__imp__neq,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( size @ A )
% 0.31/1.54 => ! [X: A,Y3: A] :
% 0.31/1.54 ( ( ( size_size @ A @ X )
% 0.31/1.54 != ( size_size @ A @ Y3 ) )
% 0.31/1.54 => ( X != Y3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_49_diff__commute,axiom,
% 0.31/1.54 ! [I: nat,J: nat,K: nat] :
% 0.31/1.54 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I @ J ) @ K )
% 0.31/1.54 = ( minus_minus @ nat @ ( minus_minus @ nat @ I @ K ) @ J ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_50_zero__less__iff__neq__zero,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( canoni770627133id_add @ A )
% 0.31/1.54 => ! [N2: A] :
% 0.31/1.54 ( ( ord_less @ A @ ( zero_zero @ A ) @ N2 )
% 0.31/1.54 = ( N2
% 0.31/1.54 != ( zero_zero @ A ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_51_gr__implies__not__zero,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( canoni770627133id_add @ A )
% 0.31/1.54 => ! [M: A,N2: A] :
% 0.31/1.54 ( ( ord_less @ A @ M @ N2 )
% 0.31/1.54 => ( N2
% 0.31/1.54 != ( zero_zero @ A ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_52_not__less__zero,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( canoni770627133id_add @ A )
% 0.31/1.54 => ! [N2: A] :
% 0.31/1.54 ~ ( ord_less @ A @ N2 @ ( zero_zero @ A ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_53_gr__zeroI,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( canoni770627133id_add @ A )
% 0.31/1.54 => ! [N2: A] :
% 0.31/1.54 ( ( N2
% 0.31/1.54 != ( zero_zero @ A ) )
% 0.31/1.54 => ( ord_less @ A @ ( zero_zero @ A ) @ N2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_54_eq__iff__diff__eq__0,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( group_add @ A )
% 0.31/1.54 => ( ( ^ [Y4: A,Z2: A] : ( Y4 = Z2 ) )
% 0.31/1.54 = ( ^ [A9: A,B3: A] :
% 0.31/1.54 ( ( minus_minus @ A @ A9 @ B3 )
% 0.31/1.54 = ( zero_zero @ A ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_55_diff__strict__right__mono,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ! [A8: A,B: A,C: A] :
% 0.31/1.54 ( ( ord_less @ A @ A8 @ B )
% 0.31/1.54 => ( ord_less @ A @ ( minus_minus @ A @ A8 @ C ) @ ( minus_minus @ A @ B @ C ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_56_diff__strict__left__mono,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ! [B: A,A8: A,C: A] :
% 0.31/1.54 ( ( ord_less @ A @ B @ A8 )
% 0.31/1.54 => ( ord_less @ A @ ( minus_minus @ A @ C @ A8 ) @ ( minus_minus @ A @ C @ B ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_57_diff__eq__diff__less,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ! [A8: A,B: A,C: A,D: A] :
% 0.31/1.54 ( ( ( minus_minus @ A @ A8 @ B )
% 0.31/1.54 = ( minus_minus @ A @ C @ D ) )
% 0.31/1.54 => ( ( ord_less @ A @ A8 @ B )
% 0.31/1.54 = ( ord_less @ A @ C @ D ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_58_diff__strict__mono,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ! [A8: A,B: A,D: A,C: A] :
% 0.31/1.54 ( ( ord_less @ A @ A8 @ B )
% 0.31/1.54 => ( ( ord_less @ A @ D @ C )
% 0.31/1.54 => ( ord_less @ A @ ( minus_minus @ A @ A8 @ C ) @ ( minus_minus @ A @ B @ D ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_59_not0__implies__Suc,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ( ( N2
% 0.31/1.54 != ( zero_zero @ nat ) )
% 0.31/1.54 => ? [M3: nat] :
% 0.31/1.54 ( N2
% 0.31/1.54 = ( suc @ M3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_60_old_Onat_Oinducts,axiom,
% 0.31/1.54 ! [P2: nat > $o,Nat: nat] :
% 0.31/1.54 ( ( P2 @ ( zero_zero @ nat ) )
% 0.31/1.54 => ( ! [Nat3: nat] :
% 0.31/1.54 ( ( P2 @ Nat3 )
% 0.31/1.54 => ( P2 @ ( suc @ Nat3 ) ) )
% 0.31/1.54 => ( P2 @ Nat ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_61_old_Onat_Oexhaust,axiom,
% 0.31/1.54 ! [Y3: nat] :
% 0.31/1.54 ( ( Y3
% 0.31/1.54 != ( zero_zero @ nat ) )
% 0.31/1.54 => ~ ! [Nat3: nat] :
% 0.31/1.54 ( Y3
% 0.31/1.54 != ( suc @ Nat3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_62_Zero__not__Suc,axiom,
% 0.31/1.54 ! [M: nat] :
% 0.31/1.54 ( ( zero_zero @ nat )
% 0.31/1.54 != ( suc @ M ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_63_Zero__neq__Suc,axiom,
% 0.31/1.54 ! [M: nat] :
% 0.31/1.54 ( ( zero_zero @ nat )
% 0.31/1.54 != ( suc @ M ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_64_Suc__neq__Zero,axiom,
% 0.31/1.54 ! [M: nat] :
% 0.31/1.54 ( ( suc @ M )
% 0.31/1.54 != ( zero_zero @ nat ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_65_zero__induct,axiom,
% 0.31/1.54 ! [P2: nat > $o,K: nat] :
% 0.31/1.54 ( ( P2 @ K )
% 0.31/1.54 => ( ! [N: nat] :
% 0.31/1.54 ( ( P2 @ ( suc @ N ) )
% 0.31/1.54 => ( P2 @ N ) )
% 0.31/1.54 => ( P2 @ ( zero_zero @ nat ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_66_diff__induct,axiom,
% 0.31/1.54 ! [P2: nat > nat > $o,M: nat,N2: nat] :
% 0.31/1.54 ( ! [X3: nat] : ( P2 @ X3 @ ( zero_zero @ nat ) )
% 0.31/1.54 => ( ! [Y5: nat] : ( P2 @ ( zero_zero @ nat ) @ ( suc @ Y5 ) )
% 0.31/1.54 => ( ! [X3: nat,Y5: nat] :
% 0.31/1.54 ( ( P2 @ X3 @ Y5 )
% 0.31/1.54 => ( P2 @ ( suc @ X3 ) @ ( suc @ Y5 ) ) )
% 0.31/1.54 => ( P2 @ M @ N2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_67_nat__induct,axiom,
% 0.31/1.54 ! [P2: nat > $o,N2: nat] :
% 0.31/1.54 ( ( P2 @ ( zero_zero @ nat ) )
% 0.31/1.54 => ( ! [N: nat] :
% 0.31/1.54 ( ( P2 @ N )
% 0.31/1.54 => ( P2 @ ( suc @ N ) ) )
% 0.31/1.54 => ( P2 @ N2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_68_nat_OdiscI,axiom,
% 0.31/1.54 ! [Nat: nat,X2: nat] :
% 0.31/1.54 ( ( Nat
% 0.31/1.54 = ( suc @ X2 ) )
% 0.31/1.54 => ( Nat
% 0.31/1.54 != ( zero_zero @ nat ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_69_old_Onat_Odistinct_I1_J,axiom,
% 0.31/1.54 ! [Nat2: nat] :
% 0.31/1.54 ( ( zero_zero @ nat )
% 0.31/1.54 != ( suc @ Nat2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_70_old_Onat_Odistinct_I2_J,axiom,
% 0.31/1.54 ! [Nat4: nat] :
% 0.31/1.54 ( ( suc @ Nat4 )
% 0.31/1.54 != ( zero_zero @ nat ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_71_nat_Odistinct_I1_J,axiom,
% 0.31/1.54 ! [X2: nat] :
% 0.31/1.54 ( ( zero_zero @ nat )
% 0.31/1.54 != ( suc @ X2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_72_not__less__less__Suc__eq,axiom,
% 0.31/1.54 ! [N2: nat,M: nat] :
% 0.31/1.54 ( ~ ( ord_less @ nat @ N2 @ M )
% 0.31/1.54 => ( ( ord_less @ nat @ N2 @ ( suc @ M ) )
% 0.31/1.54 = ( N2 = M ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_73_strict__inc__induct,axiom,
% 0.31/1.54 ! [I: nat,J: nat,P2: nat > $o] :
% 0.31/1.54 ( ( ord_less @ nat @ I @ J )
% 0.31/1.54 => ( ! [I2: nat] :
% 0.31/1.54 ( ( J
% 0.31/1.54 = ( suc @ I2 ) )
% 0.31/1.54 => ( P2 @ I2 ) )
% 0.31/1.54 => ( ! [I2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I2 @ J )
% 0.31/1.54 => ( ( P2 @ ( suc @ I2 ) )
% 0.31/1.54 => ( P2 @ I2 ) ) )
% 0.31/1.54 => ( P2 @ I ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_74_less__Suc__induct,axiom,
% 0.31/1.54 ! [I: nat,J: nat,P2: nat > nat > $o] :
% 0.31/1.54 ( ( ord_less @ nat @ I @ J )
% 0.31/1.54 => ( ! [I2: nat] : ( P2 @ I2 @ ( suc @ I2 ) )
% 0.31/1.54 => ( ! [I2: nat,J2: nat,K2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I2 @ J2 )
% 0.31/1.54 => ( ( ord_less @ nat @ J2 @ K2 )
% 0.31/1.54 => ( ( P2 @ I2 @ J2 )
% 0.31/1.54 => ( ( P2 @ J2 @ K2 )
% 0.31/1.54 => ( P2 @ I2 @ K2 ) ) ) ) )
% 0.31/1.54 => ( P2 @ I @ J ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_75_less__trans__Suc,axiom,
% 0.31/1.54 ! [I: nat,J: nat,K: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I @ J )
% 0.31/1.54 => ( ( ord_less @ nat @ J @ K )
% 0.31/1.54 => ( ord_less @ nat @ ( suc @ I ) @ K ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_76_Suc__less__SucD,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 0.31/1.54 => ( ord_less @ nat @ M @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_77_less__antisym,axiom,
% 0.31/1.54 ! [N2: nat,M: nat] :
% 0.31/1.54 ( ~ ( ord_less @ nat @ N2 @ M )
% 0.31/1.54 => ( ( ord_less @ nat @ N2 @ ( suc @ M ) )
% 0.31/1.54 => ( M = N2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_78_Suc__less__eq2,axiom,
% 0.31/1.54 ! [N2: nat,M: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ ( suc @ N2 ) @ M )
% 0.31/1.54 = ( ? [M4: nat] :
% 0.31/1.54 ( ( M
% 0.31/1.54 = ( suc @ M4 ) )
% 0.31/1.54 & ( ord_less @ nat @ N2 @ M4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_79_All__less__Suc,axiom,
% 0.31/1.54 ! [N2: nat,P2: nat > $o] :
% 0.31/1.54 ( ( ! [I3: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I3 @ ( suc @ N2 ) )
% 0.31/1.54 => ( P2 @ I3 ) ) )
% 0.31/1.54 = ( ( P2 @ N2 )
% 0.31/1.54 & ! [I3: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I3 @ N2 )
% 0.31/1.54 => ( P2 @ I3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_80_not__less__eq,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ~ ( ord_less @ nat @ M @ N2 ) )
% 0.31/1.54 = ( ord_less @ nat @ N2 @ ( suc @ M ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_81_less__Suc__eq,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ M @ ( suc @ N2 ) )
% 0.31/1.54 = ( ( ord_less @ nat @ M @ N2 )
% 0.31/1.54 | ( M = N2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_82_Ex__less__Suc,axiom,
% 0.31/1.54 ! [N2: nat,P2: nat > $o] :
% 0.31/1.54 ( ( ? [I3: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I3 @ ( suc @ N2 ) )
% 0.31/1.54 & ( P2 @ I3 ) ) )
% 0.31/1.54 = ( ( P2 @ N2 )
% 0.31/1.54 | ? [I3: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I3 @ N2 )
% 0.31/1.54 & ( P2 @ I3 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_83_less__SucI,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ M @ N2 )
% 0.31/1.54 => ( ord_less @ nat @ M @ ( suc @ N2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_84_less__SucE,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ M @ ( suc @ N2 ) )
% 0.31/1.54 => ( ~ ( ord_less @ nat @ M @ N2 )
% 0.31/1.54 => ( M = N2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_85_Suc__lessI,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ M @ N2 )
% 0.31/1.54 => ( ( ( suc @ M )
% 0.31/1.54 != N2 )
% 0.31/1.54 => ( ord_less @ nat @ ( suc @ M ) @ N2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_86_Suc__lessE,axiom,
% 0.31/1.54 ! [I: nat,K: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ ( suc @ I ) @ K )
% 0.31/1.54 => ~ ! [J2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I @ J2 )
% 0.31/1.54 => ( K
% 0.31/1.54 != ( suc @ J2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_87_Suc__lessD,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ ( suc @ M ) @ N2 )
% 0.31/1.54 => ( ord_less @ nat @ M @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_88_Nat_OlessE,axiom,
% 0.31/1.54 ! [I: nat,K: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I @ K )
% 0.31/1.54 => ( ( K
% 0.31/1.54 != ( suc @ I ) )
% 0.31/1.54 => ~ ! [J2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I @ J2 )
% 0.31/1.54 => ( K
% 0.31/1.54 != ( suc @ J2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_89_infinite__descent0__measure,axiom,
% 0.31/1.54 ! [A: $tType,V2: A > nat,P2: A > $o,X: A] :
% 0.31/1.54 ( ! [X3: A] :
% 0.31/1.54 ( ( ( V2 @ X3 )
% 0.31/1.54 = ( zero_zero @ nat ) )
% 0.31/1.54 => ( P2 @ X3 ) )
% 0.31/1.54 => ( ! [X3: A] :
% 0.31/1.54 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V2 @ X3 ) )
% 0.31/1.54 => ( ~ ( P2 @ X3 )
% 0.31/1.54 => ? [Y: A] :
% 0.31/1.54 ( ( ord_less @ nat @ ( V2 @ Y ) @ ( V2 @ X3 ) )
% 0.31/1.54 & ~ ( P2 @ Y ) ) ) )
% 0.31/1.54 => ( P2 @ X ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_90_bot__nat__0_Oextremum__strict,axiom,
% 0.31/1.54 ! [A8: nat] :
% 0.31/1.54 ~ ( ord_less @ nat @ A8 @ ( zero_zero @ nat ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_91_infinite__descent0,axiom,
% 0.31/1.54 ! [P2: nat > $o,N2: nat] :
% 0.31/1.54 ( ( P2 @ ( zero_zero @ nat ) )
% 0.31/1.54 => ( ! [N: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.31/1.54 => ( ~ ( P2 @ N )
% 0.31/1.54 => ? [M2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ M2 @ N )
% 0.31/1.54 & ~ ( P2 @ M2 ) ) ) )
% 0.31/1.54 => ( P2 @ N2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_92_gr__implies__not0,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ M @ N2 )
% 0.31/1.54 => ( N2
% 0.31/1.54 != ( zero_zero @ nat ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_93_less__zeroE,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ~ ( ord_less @ nat @ N2 @ ( zero_zero @ nat ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_94_not__less0,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ~ ( ord_less @ nat @ N2 @ ( zero_zero @ nat ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_95_not__gr0,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 ) )
% 0.31/1.54 = ( N2
% 0.31/1.54 = ( zero_zero @ nat ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_96_gr0I,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ( ( N2
% 0.31/1.54 != ( zero_zero @ nat ) )
% 0.31/1.54 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_97_zero__induct__lemma,axiom,
% 0.31/1.54 ! [P2: nat > $o,K: nat,I: nat] :
% 0.31/1.54 ( ( P2 @ K )
% 0.31/1.54 => ( ! [N: nat] :
% 0.31/1.54 ( ( P2 @ ( suc @ N ) )
% 0.31/1.54 => ( P2 @ N ) )
% 0.31/1.54 => ( P2 @ ( minus_minus @ nat @ K @ I ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_98_minus__nat_Odiff__0,axiom,
% 0.31/1.54 ! [M: nat] :
% 0.31/1.54 ( ( minus_minus @ nat @ M @ ( zero_zero @ nat ) )
% 0.31/1.54 = M ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_99_diffs0__imp__equal,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ( minus_minus @ nat @ M @ N2 )
% 0.31/1.54 = ( zero_zero @ nat ) )
% 0.31/1.54 => ( ( ( minus_minus @ nat @ N2 @ M )
% 0.31/1.54 = ( zero_zero @ nat ) )
% 0.31/1.54 => ( M = N2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_100_less__imp__diff__less,axiom,
% 0.31/1.54 ! [J: nat,K: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ J @ K )
% 0.31/1.54 => ( ord_less @ nat @ ( minus_minus @ nat @ J @ N2 ) @ K ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_101_diff__less__mono2,axiom,
% 0.31/1.54 ! [M: nat,N2: nat,L: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ M @ N2 )
% 0.31/1.54 => ( ( ord_less @ nat @ M @ L )
% 0.31/1.54 => ( ord_less @ nat @ ( minus_minus @ nat @ L @ N2 ) @ ( minus_minus @ nat @ L @ M ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_102_less__iff__diff__less__0,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ( ( ord_less @ A )
% 0.31/1.54 = ( ^ [A9: A,B3: A] : ( ord_less @ A @ ( minus_minus @ A @ A9 @ B3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_103_lift__Suc__mono__less__iff,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [F: nat > A,N2: nat,M: nat] :
% 0.31/1.54 ( ! [N: nat] : ( ord_less @ A @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.31/1.54 => ( ( ord_less @ A @ ( F @ N2 ) @ ( F @ M ) )
% 0.31/1.54 = ( ord_less @ nat @ N2 @ M ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_104_lift__Suc__mono__less,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [F: nat > A,N2: nat,N3: nat] :
% 0.31/1.54 ( ! [N: nat] : ( ord_less @ A @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.31/1.54 => ( ( ord_less @ nat @ N2 @ N3 )
% 0.31/1.54 => ( ord_less @ A @ ( F @ N2 ) @ ( F @ N3 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_105_less__Suc__eq__0__disj,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ M @ ( suc @ N2 ) )
% 0.31/1.54 = ( ( M
% 0.31/1.54 = ( zero_zero @ nat ) )
% 0.31/1.54 | ? [J3: nat] :
% 0.31/1.54 ( ( M
% 0.31/1.54 = ( suc @ J3 ) )
% 0.31/1.54 & ( ord_less @ nat @ J3 @ N2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_106_gr0__implies__Suc,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.31/1.54 => ? [M3: nat] :
% 0.31/1.54 ( N2
% 0.31/1.54 = ( suc @ M3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_107_All__less__Suc2,axiom,
% 0.31/1.54 ! [N2: nat,P2: nat > $o] :
% 0.31/1.54 ( ( ! [I3: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I3 @ ( suc @ N2 ) )
% 0.31/1.54 => ( P2 @ I3 ) ) )
% 0.31/1.54 = ( ( P2 @ ( zero_zero @ nat ) )
% 0.31/1.54 & ! [I3: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I3 @ N2 )
% 0.31/1.54 => ( P2 @ ( suc @ I3 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_108_gr0__conv__Suc,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.31/1.54 = ( ? [M5: nat] :
% 0.31/1.54 ( N2
% 0.31/1.54 = ( suc @ M5 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_109_Ex__less__Suc2,axiom,
% 0.31/1.54 ! [N2: nat,P2: nat > $o] :
% 0.31/1.54 ( ( ? [I3: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I3 @ ( suc @ N2 ) )
% 0.31/1.54 & ( P2 @ I3 ) ) )
% 0.31/1.54 = ( ( P2 @ ( zero_zero @ nat ) )
% 0.31/1.54 | ? [I3: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I3 @ N2 )
% 0.31/1.54 & ( P2 @ ( suc @ I3 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_110_diff__less__Suc,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] : ( ord_less @ nat @ ( minus_minus @ nat @ M @ N2 ) @ ( suc @ M ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_111_Suc__diff__Suc,axiom,
% 0.31/1.54 ! [N2: nat,M: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ N2 @ M )
% 0.31/1.54 => ( ( suc @ ( minus_minus @ nat @ M @ ( suc @ N2 ) ) )
% 0.31/1.54 = ( minus_minus @ nat @ M @ N2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_112_diff__less,axiom,
% 0.31/1.54 ! [N2: nat,M: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.31/1.54 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 0.31/1.54 => ( ord_less @ nat @ ( minus_minus @ nat @ M @ N2 ) @ M ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_113_diff__Suc__less,axiom,
% 0.31/1.54 ! [N2: nat,I: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.31/1.54 => ( ord_less @ nat @ ( minus_minus @ nat @ N2 @ ( suc @ I ) ) @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_114_SameCfgOnLow,axiom,
% 0.31/1.54 ! [I4: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) )
% 0.31/1.54 => ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ I4 )
% 0.31/1.54 = ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_115__092_060open_062fe_Aindex_A_B_AnMsg_A_061_Afe_A_ISuc_Aindex_J_A_B_AnMsg_092_060close_062,axiom,
% 0.31/1.54 ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ nMsg )
% 0.31/1.54 = ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ nMsg ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_116_ShorterTrace,axiom,
% 0.31/1.54 ord_less @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_117_NotEmpty_I1_J,axiom,
% 0.31/1.54 ( ( fe @ ( suc @ index ) )
% 0.31/1.54 != ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_118_IPrefixList,axiom,
% 0.31/1.54 ! [I4: nat] : ( prefixList @ ( message @ p @ v ) @ ( ft @ I4 ) @ ( ft @ ( suc @ I4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_119_IPrefixListEx,axiom,
% 0.31/1.54 ! [I4: nat] : ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ I4 ) @ ( fe @ ( suc @ I4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_120_NatPredicateTippingPoint,axiom,
% 0.31/1.54 ! [N22: nat,Pr: nat > $o] :
% 0.31/1.54 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N22 )
% 0.31/1.54 => ( ( Pr @ ( zero_zero @ nat ) )
% 0.31/1.54 => ( ~ ( Pr @ N22 )
% 0.31/1.54 => ? [N: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ N @ N22 )
% 0.31/1.54 & ( Pr @ N )
% 0.31/1.54 & ~ ( Pr @ ( suc @ N ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_121_NotEmpty_I2_J,axiom,
% 0.31/1.54 ( ( fe @ index )
% 0.31/1.54 != ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_122_AssumptionFair_I4_J,axiom,
% 0.31/1.54 isReceiverOf @ p @ v @ p2 @ msg ).
% 0.31/1.54
% 0.31/1.54 thf(fact_123_AssumpOcc6_I2_J,axiom,
% 0.31/1.54 ( msg
% 0.31/1.54 != ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_124_Occ1,axiom,
% 0.31/1.54 ? [P3: p] : ( isReceiverOf @ p @ v @ P3 @ msg ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_125_AssumptionSubset2_I1_J,axiom,
% 0.31/1.54 ? [P3: p] : ( isReceiverOf @ p @ v @ P3 @ msgInSet ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_126_SameMsgOnLow,axiom,
% 0.31/1.54 ! [I4: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 0.31/1.54 => ( ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ I4 )
% 0.31/1.54 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_127_le__zero__eq,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( canoni770627133id_add @ A )
% 0.31/1.54 => ! [N2: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ N2 @ ( zero_zero @ A ) )
% 0.31/1.54 = ( N2
% 0.31/1.54 = ( zero_zero @ A ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_128_Suc__le__mono,axiom,
% 0.31/1.54 ! [N2: nat,M: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ ( suc @ N2 ) @ ( suc @ M ) )
% 0.31/1.54 = ( ord_less_eq @ nat @ N2 @ M ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_129_le0,axiom,
% 0.31/1.54 ! [N2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N2 ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_130_bot__nat__0_Oextremum,axiom,
% 0.31/1.54 ! [A8: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A8 ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_131_diff__diff__cancel,axiom,
% 0.31/1.54 ! [I: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ I @ N2 )
% 0.31/1.54 => ( ( minus_minus @ nat @ N2 @ ( minus_minus @ nat @ N2 @ I ) )
% 0.31/1.54 = I ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_132__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,
% 0.31/1.54 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 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_133__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,
% 0.31/1.54 ~ ? [I4: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 0.31/1.54 & ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ I4 )
% 0.31/1.54 & ( msg
% 0.31/1.54 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_134_NotConsumedIntermediate,axiom,
% 0.31/1.54 ! [I4: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 0.31/1.54 => ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ I4 )
% 0.31/1.54 => ( ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I4 )
% 0.31/1.54 != msg ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_135_OccSameMsg,axiom,
% 0.31/1.54 ! [N4: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ nMsg @ N4 )
% 0.31/1.54 => ( ( ord_less @ nat @ N4 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 0.31/1.54 => ( ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ N4 )
% 0.31/1.54 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ N4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_136_diff__ge__0__iff__ge,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ! [A8: A,B: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A8 @ B ) )
% 0.31/1.54 = ( ord_less_eq @ A @ B @ A8 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_137_Occ5,axiom,
% 0.31/1.54 ! [N4: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ nMsg @ N4 )
% 0.31/1.54 => ( ( ord_less @ nat @ N4 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 0.31/1.54 => ( msg
% 0.31/1.54 != ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ N4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_138_diff__is__0__eq,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ( minus_minus @ nat @ M @ N2 )
% 0.31/1.54 = ( zero_zero @ nat ) )
% 0.31/1.54 = ( ord_less_eq @ nat @ M @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_139_diff__is__0__eq_H,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.31/1.54 => ( ( minus_minus @ nat @ M @ N2 )
% 0.31/1.54 = ( zero_zero @ nat ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_140_less__one,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ N2 @ ( one_one @ nat ) )
% 0.31/1.54 = ( N2
% 0.31/1.54 = ( zero_zero @ nat ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_141_diff__Suc__1,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ( ( minus_minus @ nat @ ( suc @ N2 ) @ ( one_one @ nat ) )
% 0.31/1.54 = N2 ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_142_AssumptionSubset3_I5_J,axiom,
% 0.31/1.54 ! [N4: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ nMsg @ N4 )
% 0.31/1.54 => ( ( ord_less @ nat @ N4 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 0.31/1.54 => ( msg
% 0.31/1.54 != ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ N4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_143_AssumptionSubset2_I5_J,axiom,
% 0.31/1.54 ! [N4: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ n1 @ N4 )
% 0.31/1.54 => ( ( ord_less @ nat @ N4 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 0.31/1.54 => ( msgInSet
% 0.31/1.54 != ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ N4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_144__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,
% 0.31/1.54 ~ ? [I4: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I4 @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) )
% 0.31/1.54 & ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ I4 )
% 0.31/1.54 & ( msg
% 0.31/1.54 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_145_Suc__diff__1,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.31/1.54 => ( ( suc @ ( minus_minus @ nat @ N2 @ ( one_one @ nat ) ) )
% 0.31/1.54 = N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_146_AssumptionFairContr,axiom,
% 0.31/1.54 ! [N4: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ n @ N4 )
% 0.31/1.54 => ! [N0: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ N0 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N4 ) ) )
% 0.31/1.54 => ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) @ N0 )
% 0.31/1.54 => ( msg
% 0.31/1.54 != ( nth @ ( message @ p @ v ) @ ( ft @ N4 ) @ N0 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_147_AssumpOcc6_I3_J,axiom,
% 0.31/1.54 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) @ msg ).
% 0.31/1.54
% 0.31/1.54 thf(fact_148_le__refl,axiom,
% 0.31/1.54 ! [N2: nat] : ( ord_less_eq @ nat @ N2 @ N2 ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_149_le__trans,axiom,
% 0.31/1.54 ! [I: nat,J: nat,K: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/1.54 => ( ( ord_less_eq @ nat @ J @ K )
% 0.31/1.54 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_150_eq__imp__le,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( M = N2 )
% 0.31/1.54 => ( ord_less_eq @ nat @ M @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_151_le__antisym,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.31/1.54 => ( ( ord_less_eq @ nat @ N2 @ M )
% 0.31/1.54 => ( M = N2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_152_nat__le__linear,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.31/1.54 | ( ord_less_eq @ nat @ N2 @ M ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_153_one__reorient,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( one @ A )
% 0.31/1.54 => ! [X: A] :
% 0.31/1.54 ( ( ( one_one @ A )
% 0.31/1.54 = X )
% 0.31/1.54 = ( X
% 0.31/1.54 = ( one_one @ A ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_154_Nat_Oex__has__greatest__nat,axiom,
% 0.31/1.54 ! [P2: nat > $o,K: nat,B: nat] :
% 0.31/1.54 ( ( P2 @ K )
% 0.31/1.54 => ( ! [Y5: nat] :
% 0.31/1.54 ( ( P2 @ Y5 )
% 0.31/1.54 => ( ord_less_eq @ nat @ Y5 @ B ) )
% 0.31/1.54 => ? [X3: nat] :
% 0.31/1.54 ( ( P2 @ X3 )
% 0.31/1.54 & ! [Y: nat] :
% 0.31/1.54 ( ( P2 @ Y )
% 0.31/1.54 => ( ord_less_eq @ nat @ Y @ X3 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_155_PrefixListTransitive,axiom,
% 0.31/1.54 ! [A: $tType,L1: list @ A,L2: list @ A,L3: list @ A] :
% 0.31/1.54 ( ( prefixList @ A @ L1 @ L2 )
% 0.31/1.54 => ( ( prefixList @ A @ L2 @ L3 )
% 0.31/1.54 => ( prefixList @ A @ L1 @ L3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_156_MinPredicate,axiom,
% 0.31/1.54 ! [P2: nat > $o] :
% 0.31/1.54 ( ? [X_1: nat] : ( P2 @ X_1 )
% 0.31/1.54 => ? [N02: nat] :
% 0.31/1.54 ( ( P2 @ N02 )
% 0.31/1.54 & ! [N4: nat] :
% 0.31/1.54 ( ( P2 @ N4 )
% 0.31/1.54 => ( ord_less_eq @ nat @ N02 @ N4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_157_lift__Suc__antimono__le,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [F: nat > A,N2: nat,N3: nat] :
% 0.31/1.54 ( ! [N: nat] : ( ord_less_eq @ A @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 0.31/1.54 => ( ( ord_less_eq @ nat @ N2 @ N3 )
% 0.31/1.54 => ( ord_less_eq @ A @ ( F @ N3 ) @ ( F @ N2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_158_lift__Suc__mono__le,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( order @ A )
% 0.31/1.54 => ! [F: nat > A,N2: nat,N3: nat] :
% 0.31/1.54 ( ! [N: nat] : ( ord_less_eq @ A @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.31/1.54 => ( ( ord_less_eq @ nat @ N2 @ N3 )
% 0.31/1.54 => ( ord_less_eq @ A @ ( F @ N2 ) @ ( F @ N3 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_159_KeepProperty,axiom,
% 0.31/1.54 ! [Low: nat,P2: nat > $o,Q: nat > $o] :
% 0.31/1.54 ( ! [I2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ Low @ I2 )
% 0.31/1.54 => ( ( P2 @ I2 )
% 0.31/1.54 => ( ( P2 @ ( suc @ I2 ) )
% 0.31/1.54 & ( Q @ I2 ) ) ) )
% 0.31/1.54 => ( ( P2 @ Low )
% 0.31/1.54 => ! [I4: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ Low @ I4 )
% 0.31/1.54 => ( Q @ I4 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_160_PrefixSameOnLow,axiom,
% 0.31/1.54 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 0.31/1.54 ( ( prefixList @ A @ L1 @ L2 )
% 0.31/1.54 => ! [Index: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ Index @ ( size_size @ ( list @ A ) @ L1 ) )
% 0.31/1.54 => ( ( nth @ A @ L1 @ Index )
% 0.31/1.54 = ( nth @ A @ L2 @ Index ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_161_zero__le,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( canoni770627133id_add @ A )
% 0.31/1.54 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_162_diff__mono,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ! [A8: A,B: A,D: A,C: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A8 @ B )
% 0.31/1.54 => ( ( ord_less_eq @ A @ D @ C )
% 0.31/1.54 => ( ord_less_eq @ A @ ( minus_minus @ A @ A8 @ C ) @ ( minus_minus @ A @ B @ D ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_163_diff__left__mono,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ! [B: A,A8: A,C: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ B @ A8 )
% 0.31/1.54 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A8 ) @ ( minus_minus @ A @ C @ B ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_164_diff__right__mono,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ! [A8: A,B: A,C: A] :
% 0.31/1.54 ( ( ord_less_eq @ A @ A8 @ B )
% 0.31/1.54 => ( ord_less_eq @ A @ ( minus_minus @ A @ A8 @ C ) @ ( minus_minus @ A @ B @ C ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_165_diff__eq__diff__less__eq,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ! [A8: A,B: A,C: A,D: A] :
% 0.31/1.54 ( ( ( minus_minus @ A @ A8 @ B )
% 0.31/1.54 = ( minus_minus @ A @ C @ D ) )
% 0.31/1.54 => ( ( ord_less_eq @ A @ A8 @ B )
% 0.31/1.54 = ( ord_less_eq @ A @ C @ D ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_166_Suc__leD,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N2 )
% 0.31/1.54 => ( ord_less_eq @ nat @ M @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_167_le__SucE,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ M @ ( suc @ N2 ) )
% 0.31/1.54 => ( ~ ( ord_less_eq @ nat @ M @ N2 )
% 0.31/1.54 => ( M
% 0.31/1.54 = ( suc @ N2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_168_le__SucI,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.31/1.54 => ( ord_less_eq @ nat @ M @ ( suc @ N2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_169_Suc__le__D,axiom,
% 0.31/1.54 ! [N2: nat,M6: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ ( suc @ N2 ) @ M6 )
% 0.31/1.54 => ? [M3: nat] :
% 0.31/1.54 ( M6
% 0.31/1.54 = ( suc @ M3 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_170_le__Suc__eq,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ M @ ( suc @ N2 ) )
% 0.31/1.54 = ( ( ord_less_eq @ nat @ M @ N2 )
% 0.31/1.54 | ( M
% 0.31/1.54 = ( suc @ N2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_171_Suc__n__not__le__n,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ~ ( ord_less_eq @ nat @ ( suc @ N2 ) @ N2 ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_172_not__less__eq__eq,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ~ ( ord_less_eq @ nat @ M @ N2 ) )
% 0.31/1.54 = ( ord_less_eq @ nat @ ( suc @ N2 ) @ M ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_173_full__nat__induct,axiom,
% 0.31/1.54 ! [P2: nat > $o,N2: nat] :
% 0.31/1.54 ( ! [N: nat] :
% 0.31/1.54 ( ! [M2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ ( suc @ M2 ) @ N )
% 0.31/1.54 => ( P2 @ M2 ) )
% 0.31/1.54 => ( P2 @ N ) )
% 0.31/1.54 => ( P2 @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_174_nat__induct__at__least,axiom,
% 0.31/1.54 ! [M: nat,N2: nat,P2: nat > $o] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.31/1.54 => ( ( P2 @ M )
% 0.31/1.54 => ( ! [N: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ M @ N )
% 0.31/1.54 => ( ( P2 @ N )
% 0.31/1.54 => ( P2 @ ( suc @ N ) ) ) )
% 0.31/1.54 => ( P2 @ N2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_175_transitive__stepwise__le,axiom,
% 0.31/1.54 ! [M: nat,N2: nat,R: nat > nat > $o] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.31/1.54 => ( ! [X3: nat] : ( R @ X3 @ X3 )
% 0.31/1.54 => ( ! [X3: nat,Y5: nat,Z3: nat] :
% 0.31/1.54 ( ( R @ X3 @ Y5 )
% 0.31/1.54 => ( ( R @ Y5 @ Z3 )
% 0.31/1.54 => ( R @ X3 @ Z3 ) ) )
% 0.31/1.54 => ( ! [N: nat] : ( R @ N @ ( suc @ N ) )
% 0.31/1.54 => ( R @ M @ N2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_176_less__eq__nat_Osimps_I1_J,axiom,
% 0.31/1.54 ! [N2: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N2 ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_177_le__0__eq,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ N2 @ ( zero_zero @ nat ) )
% 0.31/1.54 = ( N2
% 0.31/1.54 = ( zero_zero @ nat ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_178_bot__nat__0_Oextremum__unique,axiom,
% 0.31/1.54 ! [A8: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ A8 @ ( zero_zero @ nat ) )
% 0.31/1.54 = ( A8
% 0.31/1.54 = ( zero_zero @ nat ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_179_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.31/1.54 ! [A8: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ A8 @ ( zero_zero @ nat ) )
% 0.31/1.54 => ( A8
% 0.31/1.54 = ( zero_zero @ nat ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_180_nat__less__le,axiom,
% 0.31/1.54 ( ( ord_less @ nat )
% 0.31/1.54 = ( ^ [M5: nat,N5: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ M5 @ N5 )
% 0.31/1.54 & ( M5 != N5 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_181_less__imp__le__nat,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ M @ N2 )
% 0.31/1.54 => ( ord_less_eq @ nat @ M @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_182_le__eq__less__or__eq,axiom,
% 0.31/1.54 ( ( ord_less_eq @ nat )
% 0.31/1.54 = ( ^ [M5: nat,N5: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ M5 @ N5 )
% 0.31/1.54 | ( M5 = N5 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_183_less__or__eq__imp__le,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ( ord_less @ nat @ M @ N2 )
% 0.31/1.54 | ( M = N2 ) )
% 0.31/1.54 => ( ord_less_eq @ nat @ M @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_184_le__neq__implies__less,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.31/1.54 => ( ( M != N2 )
% 0.31/1.54 => ( ord_less @ nat @ M @ N2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_185_less__mono__imp__le__mono,axiom,
% 0.31/1.54 ! [F: nat > nat,I: nat,J: nat] :
% 0.31/1.54 ( ! [I2: nat,J2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I2 @ J2 )
% 0.31/1.54 => ( ord_less @ nat @ ( F @ I2 ) @ ( F @ J2 ) ) )
% 0.31/1.54 => ( ( ord_less_eq @ nat @ I @ J )
% 0.31/1.54 => ( ord_less_eq @ nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_186_eq__diff__iff,axiom,
% 0.31/1.54 ! [K: nat,M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ K @ M )
% 0.31/1.54 => ( ( ord_less_eq @ nat @ K @ N2 )
% 0.31/1.54 => ( ( ( minus_minus @ nat @ M @ K )
% 0.31/1.54 = ( minus_minus @ nat @ N2 @ K ) )
% 0.31/1.54 = ( M = N2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_187_le__diff__iff,axiom,
% 0.31/1.54 ! [K: nat,M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ K @ M )
% 0.31/1.54 => ( ( ord_less_eq @ nat @ K @ N2 )
% 0.31/1.54 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N2 @ K ) )
% 0.31/1.54 = ( ord_less_eq @ nat @ M @ N2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_188_Nat_Odiff__diff__eq,axiom,
% 0.31/1.54 ! [K: nat,M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ K @ M )
% 0.31/1.54 => ( ( ord_less_eq @ nat @ K @ N2 )
% 0.31/1.54 => ( ( minus_minus @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N2 @ K ) )
% 0.31/1.54 = ( minus_minus @ nat @ M @ N2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_189_diff__le__mono,axiom,
% 0.31/1.54 ! [M: nat,N2: nat,L: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.31/1.54 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ L ) @ ( minus_minus @ nat @ N2 @ L ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_190_diff__le__self,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ N2 ) @ M ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_191_le__diff__iff_H,axiom,
% 0.31/1.54 ! [A8: nat,C: nat,B: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ A8 @ C )
% 0.31/1.54 => ( ( ord_less_eq @ nat @ B @ C )
% 0.31/1.54 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ A8 ) @ ( minus_minus @ nat @ C @ B ) )
% 0.31/1.54 = ( ord_less_eq @ nat @ B @ A8 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_192_diff__le__mono2,axiom,
% 0.31/1.54 ! [M: nat,N2: nat,L: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.31/1.54 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ L @ N2 ) @ ( minus_minus @ nat @ L @ M ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_193_MinPredicate2,axiom,
% 0.31/1.54 ! [P2: nat > $o] :
% 0.31/1.54 ( ? [X_1: nat] : ( P2 @ X_1 )
% 0.31/1.54 => ? [N02: nat] :
% 0.31/1.54 ( ( P2 @ N02 )
% 0.31/1.54 & ( ( N02
% 0.31/1.54 = ( zero_zero @ nat ) )
% 0.31/1.54 | ~ ( P2 @ ( minus_minus @ nat @ N02 @ ( one_one @ nat ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_194_PrefixListMonotonicity,axiom,
% 0.31/1.54 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 0.31/1.54 ( ( prefixList @ A @ L1 @ L2 )
% 0.31/1.54 => ( ord_less @ nat @ ( size_size @ ( list @ A ) @ L1 ) @ ( size_size @ ( list @ A ) @ L2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_195_le__iff__diff__le__0,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ordered_ab_group_add @ A )
% 0.31/1.54 => ( ( ord_less_eq @ A )
% 0.31/1.54 = ( ^ [A9: A,B3: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ A9 @ B3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_196_Suc__leI,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ M @ N2 )
% 0.31/1.54 => ( ord_less_eq @ nat @ ( suc @ M ) @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_197_Suc__le__eq,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N2 )
% 0.31/1.54 = ( ord_less @ nat @ M @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_198_dec__induct,axiom,
% 0.31/1.54 ! [I: nat,J: nat,P2: nat > $o] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/1.54 => ( ( P2 @ I )
% 0.31/1.54 => ( ! [N: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ I @ N )
% 0.31/1.54 => ( ( ord_less @ nat @ N @ J )
% 0.31/1.54 => ( ( P2 @ N )
% 0.31/1.54 => ( P2 @ ( suc @ N ) ) ) ) )
% 0.31/1.54 => ( P2 @ J ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_199_inc__induct,axiom,
% 0.31/1.54 ! [I: nat,J: nat,P2: nat > $o] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/1.54 => ( ( P2 @ J )
% 0.31/1.54 => ( ! [N: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ I @ N )
% 0.31/1.54 => ( ( ord_less @ nat @ N @ J )
% 0.31/1.54 => ( ( P2 @ ( suc @ N ) )
% 0.31/1.54 => ( P2 @ N ) ) ) )
% 0.31/1.54 => ( P2 @ I ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_200_Suc__le__lessD,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N2 )
% 0.31/1.54 => ( ord_less @ nat @ M @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_201_le__less__Suc__eq,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.31/1.54 => ( ( ord_less @ nat @ N2 @ ( suc @ M ) )
% 0.31/1.54 = ( N2 = M ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_202_less__Suc__eq__le,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ M @ ( suc @ N2 ) )
% 0.31/1.54 = ( ord_less_eq @ nat @ M @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_203_less__eq__Suc__le,axiom,
% 0.31/1.54 ( ( ord_less @ nat )
% 0.31/1.54 = ( ^ [N5: nat] : ( ord_less_eq @ nat @ ( suc @ N5 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_204_le__imp__less__Suc,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.31/1.54 => ( ord_less @ nat @ M @ ( suc @ N2 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_205_ex__least__nat__le,axiom,
% 0.31/1.54 ! [P2: nat > $o,N2: nat] :
% 0.31/1.54 ( ( P2 @ N2 )
% 0.31/1.54 => ( ~ ( P2 @ ( zero_zero @ nat ) )
% 0.31/1.54 => ? [K2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ K2 @ N2 )
% 0.31/1.54 & ! [I4: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I4 @ K2 )
% 0.31/1.54 => ~ ( P2 @ I4 ) )
% 0.31/1.54 & ( P2 @ K2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_206_Suc__diff__le,axiom,
% 0.31/1.54 ! [N2: nat,M: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ N2 @ M )
% 0.31/1.54 => ( ( minus_minus @ nat @ ( suc @ M ) @ N2 )
% 0.31/1.54 = ( suc @ ( minus_minus @ nat @ M @ N2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_207_less__diff__iff,axiom,
% 0.31/1.54 ! [K: nat,M: nat,N2: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ K @ M )
% 0.31/1.54 => ( ( ord_less_eq @ nat @ K @ N2 )
% 0.31/1.54 => ( ( ord_less @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N2 @ K ) )
% 0.31/1.54 = ( ord_less @ nat @ M @ N2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_208_diff__less__mono,axiom,
% 0.31/1.54 ! [A8: nat,B: nat,C: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ A8 @ B )
% 0.31/1.54 => ( ( ord_less_eq @ nat @ C @ A8 )
% 0.31/1.54 => ( ord_less @ nat @ ( minus_minus @ nat @ A8 @ C ) @ ( minus_minus @ nat @ B @ C ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_209_One__nat__def,axiom,
% 0.31/1.54 ( ( one_one @ nat )
% 0.31/1.54 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_210_diff__Suc__eq__diff__pred,axiom,
% 0.31/1.54 ! [M: nat,N2: nat] :
% 0.31/1.54 ( ( minus_minus @ nat @ M @ ( suc @ N2 ) )
% 0.31/1.54 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ ( one_one @ nat ) ) @ N2 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_211_ex__least__nat__less,axiom,
% 0.31/1.54 ! [P2: nat > $o,N2: nat] :
% 0.31/1.54 ( ( P2 @ N2 )
% 0.31/1.54 => ( ~ ( P2 @ ( zero_zero @ nat ) )
% 0.31/1.54 => ? [K2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ K2 @ N2 )
% 0.31/1.54 & ! [I4: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ I4 @ K2 )
% 0.31/1.54 => ~ ( P2 @ I4 ) )
% 0.31/1.54 & ( P2 @ ( suc @ K2 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_212_nat__induct__non__zero,axiom,
% 0.31/1.54 ! [N2: nat,P2: nat > $o] :
% 0.31/1.54 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.31/1.54 => ( ( P2 @ ( one_one @ nat ) )
% 0.31/1.54 => ( ! [N: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.31/1.54 => ( ( P2 @ N )
% 0.31/1.54 => ( P2 @ ( suc @ N ) ) ) )
% 0.31/1.54 => ( P2 @ N2 ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_213_Suc__pred_H,axiom,
% 0.31/1.54 ! [N2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.31/1.54 => ( N2
% 0.31/1.54 = ( suc @ ( minus_minus @ nat @ N2 @ ( one_one @ nat ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_214_Suc__diff__eq__diff__pred,axiom,
% 0.31/1.54 ! [N2: nat,M: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.31/1.54 => ( ( minus_minus @ nat @ ( suc @ M ) @ N2 )
% 0.31/1.54 = ( minus_minus @ nat @ M @ ( minus_minus @ nat @ N2 @ ( one_one @ nat ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_215_AssumptionSubset2_I6_J,axiom,
% 0.31/1.54 ( ( n1
% 0.31/1.54 != ( zero_zero @ nat ) )
% 0.31/1.54 => ( ~ ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) ) @ msgInSet )
% 0.31/1.54 | ( msgInSet
% 0.31/1.54 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_216_AssumptionSubset3_I6_J,axiom,
% 0.31/1.54 ( ( nMsg
% 0.31/1.54 != ( zero_zero @ nat ) )
% 0.31/1.54 => ( ~ ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) @ msg )
% 0.31/1.54 | ( msg
% 0.31/1.54 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ ( minus_minus @ nat @ nMsg @ ( one_one @ nat ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_217_EnabledIntermediate,axiom,
% 0.31/1.54 ! [I4: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) )
% 0.31/1.54 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ I4 )
% 0.31/1.54 => ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ I4 ) @ msg ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_218_length__greater__0__conv,axiom,
% 0.31/1.54 ! [A: $tType,Xs: list @ A] :
% 0.31/1.54 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.31/1.54 = ( Xs
% 0.31/1.54 != ( nil @ A ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_219_AssumptionFair_I2_J,axiom,
% 0.31/1.54 ord_less @ nat @ n0 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_220_Occ4,axiom,
% 0.31/1.54 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ nMsg ) @ msg ).
% 0.31/1.54
% 0.31/1.54 thf(fact_221_AssumptionFair_I3_J,axiom,
% 0.31/1.54 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ n0 ) @ msg ).
% 0.31/1.54
% 0.31/1.54 thf(fact_222_AssumptionSubset3_I4_J,axiom,
% 0.31/1.54 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ nMsg ) @ msg ).
% 0.31/1.54
% 0.31/1.54 thf(fact_223_AssumptionSubset2_I4_J,axiom,
% 0.31/1.54 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ n1 ) @ msgInSet ).
% 0.31/1.54
% 0.31/1.54 thf(fact_224_MessageStaysOrConsumed,axiom,
% 0.31/1.54 ! [N1: nat,N22: nat,N2: nat,Msg: message @ p @ v] :
% 0.31/1.54 ( ( ( ord_less_eq @ nat @ N1 @ N22 )
% 0.31/1.54 & ( ord_less @ nat @ N22 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ N2 ) ) )
% 0.31/1.54 & ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N2 ) @ N1 ) @ Msg ) )
% 0.31/1.54 => ( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N2 ) @ N22 ) @ Msg )
% 0.31/1.54 | ? [N03: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ N1 @ N03 )
% 0.31/1.54 & ( ord_less @ nat @ N03 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N2 ) ) )
% 0.31/1.54 & ( ( nth @ ( message @ p @ v ) @ ( ft @ N2 ) @ N03 )
% 0.31/1.54 = Msg ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_225__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,
% 0.31/1.54 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 ).
% 0.31/1.54
% 0.31/1.54 thf(fact_226_length__0__conv,axiom,
% 0.31/1.54 ! [A: $tType,Xs: list @ A] :
% 0.31/1.54 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.31/1.54 = ( zero_zero @ nat ) )
% 0.31/1.54 = ( Xs
% 0.31/1.54 = ( nil @ A ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_227_Occ2,axiom,
% 0.31/1.54 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) @ msg ).
% 0.31/1.54
% 0.31/1.54 thf(fact_228_AssumptionCase1ImplThesis_H,axiom,
% 0.31/1.54 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg ).
% 0.31/1.54
% 0.31/1.54 thf(fact_229_neq__if__length__neq,axiom,
% 0.31/1.54 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.31/1.54 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.31/1.54 != ( size_size @ ( list @ A ) @ Ys ) )
% 0.31/1.54 => ( Xs != Ys ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_230_Ex__list__of__length,axiom,
% 0.31/1.54 ! [A: $tType,N2: nat] :
% 0.31/1.54 ? [Xs2: list @ A] :
% 0.31/1.54 ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.31/1.54 = N2 ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_231_length__induct,axiom,
% 0.31/1.54 ! [A: $tType,P2: ( list @ A ) > $o,Xs: list @ A] :
% 0.31/1.54 ( ! [Xs2: list @ A] :
% 0.31/1.54 ( ! [Ys2: list @ A] :
% 0.31/1.54 ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ys2 ) @ ( size_size @ ( list @ A ) @ Xs2 ) )
% 0.31/1.54 => ( P2 @ Ys2 ) )
% 0.31/1.54 => ( P2 @ Xs2 ) )
% 0.31/1.54 => ( P2 @ Xs ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_232_list_Osize_I3_J,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( size_size @ ( list @ A ) @ ( nil @ A ) )
% 0.31/1.54 = ( zero_zero @ nat ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_233_list__eq__iff__nth__eq,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( ^ [Y4: list @ A,Z2: list @ A] : ( Y4 = Z2 ) )
% 0.31/1.54 = ( ^ [Xs3: list @ A,Ys3: list @ A] :
% 0.31/1.54 ( ( ( size_size @ ( list @ A ) @ Xs3 )
% 0.31/1.54 = ( size_size @ ( list @ A ) @ Ys3 ) )
% 0.31/1.54 & ! [I3: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I3 @ ( size_size @ ( list @ A ) @ Xs3 ) )
% 0.31/1.54 => ( ( nth @ A @ Xs3 @ I3 )
% 0.31/1.54 = ( nth @ A @ Ys3 @ I3 ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_234_Skolem__list__nth,axiom,
% 0.31/1.54 ! [A: $tType,K: nat,P2: nat > A > $o] :
% 0.31/1.54 ( ( ! [I3: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I3 @ K )
% 0.31/1.54 => ? [X4: A] : ( P2 @ I3 @ X4 ) ) )
% 0.31/1.54 = ( ? [Xs3: list @ A] :
% 0.31/1.54 ( ( ( size_size @ ( list @ A ) @ Xs3 )
% 0.31/1.54 = K )
% 0.31/1.54 & ! [I3: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I3 @ K )
% 0.31/1.54 => ( P2 @ I3 @ ( nth @ A @ Xs3 @ I3 ) ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_235_nth__equalityI,axiom,
% 0.31/1.54 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.31/1.54 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.31/1.54 = ( size_size @ ( list @ A ) @ Ys ) )
% 0.31/1.54 => ( ! [I2: nat] :
% 0.31/1.54 ( ( ord_less @ nat @ I2 @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.31/1.54 => ( ( nth @ A @ Xs @ I2 )
% 0.31/1.54 = ( nth @ A @ Ys @ I2 ) ) )
% 0.31/1.54 => ( Xs = Ys ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_236_EnabledOrConsumed,axiom,
% 0.31/1.54 ( ( 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 )
% 0.31/1.54 | ? [N03: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ n0 @ N03 )
% 0.31/1.54 & ( ord_less @ nat @ N03 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
% 0.31/1.54 & ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ N03 )
% 0.31/1.54 = msg ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_237_Case2ImplThesis,axiom,
% 0.31/1.54 ( ? [N0: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ n0 @ N0 )
% 0.31/1.54 & ( ord_less @ nat @ N0 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
% 0.31/1.54 & ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ N0 )
% 0.31/1.54 = msg ) )
% 0.31/1.54 => ? [N6: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ n @ N6 )
% 0.31/1.54 & ? [N03: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ n0 @ N03 )
% 0.31/1.54 & ( ord_less @ nat @ N03 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N6 ) ) )
% 0.31/1.54 & ( msg
% 0.31/1.54 = ( nth @ ( message @ p @ v ) @ ( ft @ N6 ) @ N03 ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_238_EnabledInSuc,axiom,
% 0.31/1.54 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) ) @ msg ).
% 0.31/1.54
% 0.31/1.54 thf(fact_239_AssumptionSubset2_I2_J,axiom,
% 0.31/1.54 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) ) @ msgInSet ).
% 0.31/1.54
% 0.31/1.54 thf(fact_240_LastOfIndex,axiom,
% 0.31/1.54 ( ( 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 ) ) ) )
% 0.31/1.54 = ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_241_EnabledOrConsumedAtLast,axiom,
% 0.31/1.54 ( ( enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg )
% 0.31/1.54 | ? [N03: nat] :
% 0.31/1.54 ( ( ord_less_eq @ nat @ n0 @ N03 )
% 0.31/1.54 & ( ord_less @ nat @ N03 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
% 0.31/1.54 & ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ N03 )
% 0.31/1.54 = msg ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_242_last__conv__nth,axiom,
% 0.31/1.54 ! [A: $tType,Xs: list @ A] :
% 0.31/1.54 ( ( Xs
% 0.31/1.54 != ( nil @ A ) )
% 0.31/1.54 => ( ( last @ A @ Xs )
% 0.31/1.54 = ( nth @ A @ Xs @ ( minus_minus @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( one_one @ nat ) ) ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_243_diff__numeral__special_I9_J,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( neg_numeral @ A )
% 0.31/1.54 => ( ( minus_minus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
% 0.31/1.54 = ( zero_zero @ A ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_244__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,
% 0.31/1.54 ! [Msg: message @ p @ v,N04: nat,N7: nat] :
% 0.31/1.54 ( ( firstOccurrence @ p @ v @ s @ ( fe @ N7 ) @ ( ft @ N7 ) @ Msg @ N04 )
% 0.31/1.54 => ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N7 ) ) @ Msg ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_245_le__numeral__extra_I3_J,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linord1659791738miring @ A )
% 0.31/1.54 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_246_less__numeral__extra_I3_J,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linord1659791738miring @ A )
% 0.31/1.54 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_247_le__numeral__extra_I4_J,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linord1659791738miring @ A )
% 0.31/1.54 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_248_less__numeral__extra_I4_J,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linord1659791738miring @ A )
% 0.31/1.54 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_249_less__numeral__extra_I1_J,axiom,
% 0.31/1.54 ! [A: $tType] :
% 0.31/1.54 ( ( linord1659791738miring @ A )
% 0.31/1.54 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(fact_250__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,
% 0.31/1.54 ! [N7: nat,X5: message @ p @ v] :
% 0.31/1.54 ( ( member @ ( message @ p @ v ) @ X5 @ ( firstOccSet @ N7 ) )
% 0.31/1.54 => ( ord_less @ nat @ ( zero_zero @ nat ) @ ( msgs @ p @ v @ s @ product_unit @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N7 ) ) @ X5 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.31/1.54 ! [A10: $tType,A11: $tType] :
% 0.31/1.54 ( ( order @ A11 )
% 0.31/1.54 => ( order @ ( A10 > A11 ) ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.31/1.54 canoni770627133id_add @ nat ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 0.31/1.54 linord1659791738miring @ nat ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 0.31/1.54 cancel146912293up_add @ nat ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 0.31/1.54 cancel1352612707id_add @ nat ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff,axiom,
% 0.31/1.54 comm_monoid_diff @ nat ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.31/1.54 wellorder @ nat ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Nat_Onat___Orderings_Oorder_1,axiom,
% 0.31/1.54 order @ nat ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.31/1.54 zero @ nat ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.31/1.54 one @ nat ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 0.31/1.54 size @ nat ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_HOL_Obool___Orderings_Oorder_2,axiom,
% 0.31/1.54 order @ $o ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_List_Olist___Nat_Osize_3,axiom,
% 0.31/1.54 ! [A10: $tType] : ( size @ ( list @ A10 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_4,axiom,
% 0.31/1.54 wellorder @ product_unit ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_Product__Type_Ounit___Orderings_Oorder_5,axiom,
% 0.31/1.54 order @ product_unit ).
% 0.31/1.54
% 0.31/1.54 thf(tcon_AsynchronousSystem_Omessage___Nat_Osize_6,axiom,
% 0.31/1.54 ! [A10: $tType,A11: $tType] : ( size @ ( message @ A10 @ A11 ) ) ).
% 0.31/1.54
% 0.31/1.54 thf(conj_0,conjecture,
% 0.31/1.54 ord_less @ nat @ ( minus_minus @ nat @ nMsg @ ( suc @ ( zero_zero @ nat ) ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.31/1.54 ------------------------
% 0.31/1.56 % (24429)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_24154 for (2999ds/4Mi)
% 0.31/1.56 % (24433)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_24154 for (2999ds/275Mi)
% 0.31/1.56 % (24434)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24154 for (2999ds/18Mi)
% 0.31/1.57 % (24429)Instruction limit reached!
% 0.31/1.57 % (24429)------------------------------
% 0.31/1.57 % (24429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.57 % (24429)Termination reason: Unknown
% 0.31/1.57 % (24429)Termination phase: shuffling
% 0.31/1.57
% 0.31/1.57 % (24429)Memory used [KB]: 1407
% 0.31/1.57 % (24429)Time elapsed: 0.003 s
% 0.31/1.57 % (24429)Instructions burned: 6 (million)
% 0.31/1.57 % (24429)------------------------------
% 0.31/1.57 % (24429)------------------------------
% 0.31/1.57 % (24434)Instruction limit reached!
% 0.31/1.57 % (24434)------------------------------
% 0.31/1.57 % (24434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.57 % (24434)Termination reason: Unknown
% 0.31/1.57 % (24434)Termination phase: shuffling
% 0.31/1.57
% 0.31/1.57 % (24434)Memory used [KB]: 1535
% 0.31/1.57 % (24434)Time elapsed: 0.008 s
% 0.31/1.57 % (24434)Instructions burned: 20 (million)
% 0.31/1.57 % (24434)------------------------------
% 0.31/1.57 % (24434)------------------------------
% 0.31/1.57 % (24428)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24154 for (2999ds/183Mi)
% 0.31/1.57 % (24430)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_24154 for (2999ds/27Mi)
% 0.31/1.57 % (24431)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24154 for (2999ds/2Mi)
% 0.31/1.57 % (24432)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_24154 for (2999ds/2Mi)
% 0.31/1.57 % (24431)Instruction limit reached!
% 0.31/1.57 % (24431)------------------------------
% 0.31/1.57 % (24431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.57 % (24431)Termination reason: Unknown
% 0.31/1.57 % (24431)Termination phase: shuffling
% 0.31/1.57
% 0.31/1.57 % (24431)Memory used [KB]: 1279
% 0.31/1.57 % (24431)Time elapsed: 0.003 s
% 0.31/1.57 % (24431)Instructions burned: 2 (million)
% 0.31/1.57 % (24431)------------------------------
% 0.31/1.57 % (24431)------------------------------
% 0.31/1.57 % (24432)Instruction limit reached!
% 0.31/1.57 % (24432)------------------------------
% 0.31/1.57 % (24432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.57 % (24432)Termination reason: Unknown
% 0.31/1.57 % (24432)Termination phase: shuffling
% 0.31/1.57
% 0.31/1.57 % (24432)Memory used [KB]: 1279
% 0.31/1.57 % (24432)Time elapsed: 0.003 s
% 0.31/1.57 % (24432)Instructions burned: 2 (million)
% 0.31/1.57 % (24432)------------------------------
% 0.31/1.57 % (24432)------------------------------
% 0.31/1.58 % (24435)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_24154 for (2999ds/3Mi)
% 0.31/1.58 % (24435)Instruction limit reached!
% 0.31/1.58 % (24435)------------------------------
% 0.31/1.58 % (24435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.58 % (24435)Termination reason: Unknown
% 0.31/1.58 % (24435)Termination phase: shuffling
% 0.31/1.58
% 0.31/1.58 % (24435)Memory used [KB]: 1279
% 0.31/1.58 % (24435)Time elapsed: 0.003 s
% 0.31/1.58 % (24435)Instructions burned: 4 (million)
% 0.31/1.58 % (24435)------------------------------
% 0.31/1.58 % (24435)------------------------------
% 0.31/1.58 % (24436)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_24154 for (2999ds/37Mi)
% 0.31/1.59 % (24430)Instruction limit reached!
% 0.31/1.59 % (24430)------------------------------
% 0.31/1.59 % (24430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.59 % (24430)Termination reason: Unknown
% 0.31/1.59 % (24430)Termination phase: Property scanning
% 0.31/1.59
% 0.31/1.59 % (24430)Memory used [KB]: 1535
% 0.31/1.59 % (24430)Time elapsed: 0.018 s
% 0.31/1.59 % (24430)Instructions burned: 27 (million)
% 0.31/1.59 % (24430)------------------------------
% 0.31/1.59 % (24430)------------------------------
% 0.31/1.59 % (24439)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_24154 for (2999ds/1041Mi)
% 0.31/1.59 % (24437)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_24154 for (2999ds/15Mi)
% 0.31/1.59 % (24438)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_24154 for (2999ds/3Mi)
% 0.31/1.59 % (24438)Instruction limit reached!
% 0.31/1.59 % (24438)------------------------------
% 0.31/1.59 % (24438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.59 % (24438)Termination reason: Unknown
% 0.31/1.59 % (24438)Termination phase: shuffling
% 0.31/1.59
% 0.31/1.59 % (24438)Memory used [KB]: 1279
% 0.31/1.59 % (24438)Time elapsed: 0.004 s
% 0.31/1.59 % (24438)Instructions burned: 3 (million)
% 0.31/1.59 % (24438)------------------------------
% 0.31/1.59 % (24438)------------------------------
% 0.31/1.59 % (24436)Instruction limit reached!
% 0.31/1.59 % (24436)------------------------------
% 0.31/1.59 % (24436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.59 % (24436)Termination reason: Unknown
% 0.31/1.59 % (24436)Termination phase: Property scanning
% 0.31/1.59
% 0.31/1.59 % (24436)Memory used [KB]: 2046
% 0.31/1.59 % (24436)Time elapsed: 0.013 s
% 0.31/1.59 % (24436)Instructions burned: 39 (million)
% 0.31/1.59 % (24436)------------------------------
% 0.31/1.59 % (24436)------------------------------
% 2.90/1.60 % (24437)Instruction limit reached!
% 2.90/1.60 % (24437)------------------------------
% 2.90/1.60 % (24437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.60 % (24437)Termination reason: Unknown
% 2.90/1.60 % (24437)Termination phase: shuffling
% 2.90/1.60
% 2.90/1.60 % (24437)Memory used [KB]: 1535
% 2.90/1.60 % (24437)Time elapsed: 0.011 s
% 2.90/1.60 % (24437)Instructions burned: 15 (million)
% 2.90/1.60 % (24437)------------------------------
% 2.90/1.60 % (24437)------------------------------
% 2.90/1.60 % (24440)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_24154 for (2999ds/7Mi)
% 2.90/1.60 % (24442)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_24154 for (2999ds/3Mi)
% 2.90/1.60 % (24442)Instruction limit reached!
% 2.90/1.60 % (24442)------------------------------
% 2.90/1.60 % (24442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.60 % (24442)Termination reason: Unknown
% 2.90/1.60 % (24442)Termination phase: shuffling
% 2.90/1.60
% 2.90/1.60 % (24442)Memory used [KB]: 1279
% 2.90/1.60 % (24442)Time elapsed: 0.002 s
% 2.90/1.60 % (24442)Instructions burned: 3 (million)
% 2.90/1.60 % (24442)------------------------------
% 2.90/1.60 % (24442)------------------------------
% 2.90/1.61 % (24440)Instruction limit reached!
% 2.90/1.61 % (24440)------------------------------
% 2.90/1.61 % (24440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.61 % (24440)Termination reason: Unknown
% 2.90/1.61 % (24440)Termination phase: shuffling
% 2.90/1.61
% 2.90/1.61 % (24440)Memory used [KB]: 1407
% 2.90/1.61 % (24440)Time elapsed: 0.006 s
% 2.90/1.61 % (24440)Instructions burned: 7 (million)
% 2.90/1.61 % (24440)------------------------------
% 2.90/1.61 % (24440)------------------------------
% 2.90/1.61 % (24441)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_24154 for (2999ds/16Mi)
% 2.90/1.61 % (24443)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_24154 for (2999ds/3Mi)
% 2.90/1.61 % (24444)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_24154 for (2999ds/7Mi)
% 2.90/1.62 % (24443)Instruction limit reached!
% 2.90/1.62 % (24443)------------------------------
% 2.90/1.62 % (24443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.62 % (24443)Termination reason: Unknown
% 2.90/1.62 % (24443)Termination phase: shuffling
% 2.90/1.62
% 2.90/1.62 % (24443)Memory used [KB]: 1279
% 2.90/1.62 % (24443)Time elapsed: 0.003 s
% 2.90/1.62 % (24443)Instructions burned: 3 (million)
% 2.90/1.62 % (24443)------------------------------
% 2.90/1.62 % (24443)------------------------------
% 2.90/1.62 % (24444)Instruction limit reached!
% 2.90/1.62 % (24444)------------------------------
% 2.90/1.62 % (24444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.62 % (24444)Termination reason: Unknown
% 2.90/1.62 % (24444)Termination phase: shuffling
% 2.90/1.62
% 2.90/1.62 % (24444)Memory used [KB]: 1407
% 2.90/1.62 % (24444)Time elapsed: 0.005 s
% 2.90/1.62 % (24444)Instructions burned: 9 (million)
% 2.90/1.62 % (24444)------------------------------
% 2.90/1.62 % (24444)------------------------------
% 2.90/1.62 % (24441)Instruction limit reached!
% 2.90/1.62 % (24441)------------------------------
% 2.90/1.62 % (24441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.62 % (24441)Termination reason: Unknown
% 2.90/1.62 % (24441)Termination phase: shuffling
% 2.90/1.62
% 2.90/1.62 % (24441)Memory used [KB]: 1535
% 2.90/1.62 % (24441)Time elapsed: 0.012 s
% 2.90/1.62 % (24441)Instructions burned: 17 (million)
% 2.90/1.62 % (24441)------------------------------
% 2.90/1.62 % (24441)------------------------------
% 2.90/1.62 % (24445)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_24154 for (2999ds/3Mi)
% 2.90/1.62 % (24445)Instruction limit reached!
% 2.90/1.62 % (24445)------------------------------
% 2.90/1.62 % (24445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.62 % (24445)Termination reason: Unknown
% 2.90/1.62 % (24445)Termination phase: shuffling
% 2.90/1.62
% 2.90/1.62 % (24445)Memory used [KB]: 1279
% 2.90/1.62 % (24445)Time elapsed: 0.003 s
% 2.90/1.62 % (24445)Instructions burned: 4 (million)
% 2.90/1.62 % (24445)------------------------------
% 2.90/1.62 % (24445)------------------------------
% 2.90/1.63 % (24446)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_24154 for (2999ds/4Mi)
% 2.90/1.63 % (24446)Instruction limit reached!
% 2.90/1.63 % (24446)------------------------------
% 2.90/1.63 % (24446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.63 % (24446)Termination reason: Unknown
% 2.90/1.63 % (24446)Termination phase: shuffling
% 2.90/1.63
% 2.90/1.63 % (24446)Memory used [KB]: 1279
% 2.90/1.63 % (24446)Time elapsed: 0.003 s
% 2.90/1.63 % (24446)Instructions burned: 4 (million)
% 2.90/1.63 % (24446)------------------------------
% 2.90/1.63 % (24446)------------------------------
% 2.90/1.63 % (24447)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_24154 for (2999ds/18Mi)
% 2.90/1.63 % (24449)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_24154 for (2999ds/6Mi)
% 2.90/1.63 % (24449)Instruction limit reached!
% 2.90/1.63 % (24449)------------------------------
% 2.90/1.63 % (24449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.63 % (24449)Termination reason: Unknown
% 2.90/1.63 % (24449)Termination phase: shuffling
% 2.90/1.63
% 2.90/1.63 % (24449)Memory used [KB]: 1407
% 2.90/1.63 % (24449)Time elapsed: 0.004 s
% 2.90/1.63 % (24449)Instructions burned: 8 (million)
% 2.90/1.63 % (24449)------------------------------
% 2.90/1.63 % (24449)------------------------------
% 2.90/1.63 % (24447)Instruction limit reached!
% 2.90/1.63 % (24447)------------------------------
% 2.90/1.63 % (24447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.63 % (24447)Termination reason: Unknown
% 2.90/1.63 % (24447)Termination phase: shuffling
% 2.90/1.63
% 2.90/1.63 % (24447)Memory used [KB]: 1535
% 2.90/1.63 % (24447)Time elapsed: 0.008 s
% 2.90/1.63 % (24447)Instructions burned: 18 (million)
% 2.90/1.63 % (24447)------------------------------
% 2.90/1.63 % (24447)------------------------------
% 2.90/1.64 % (24450)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_24154 for (2999ds/902Mi)
% 2.90/1.64 % (24448)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_24154 for (2999ds/710Mi)
% 2.90/1.64 % (24451)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_24154 for (2999ds/21Mi)
% 2.90/1.64 % (24452)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_24154 for (2999ds/5Mi)
% 2.90/1.65 % (24452)Instruction limit reached!
% 2.90/1.65 % (24452)------------------------------
% 2.90/1.65 % (24452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.65 % (24452)Termination reason: Unknown
% 2.90/1.65 % (24452)Termination phase: shuffling
% 2.90/1.65
% 2.90/1.65 % (24452)Memory used [KB]: 1407
% 2.90/1.65 % (24452)Time elapsed: 0.004 s
% 2.90/1.65 % (24452)Instructions burned: 8 (million)
% 2.90/1.65 % (24452)------------------------------
% 2.90/1.65 % (24452)------------------------------
% 2.90/1.65 % (24428)Instruction limit reached!
% 2.90/1.65 % (24428)------------------------------
% 2.90/1.65 % (24428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.65 % (24428)Termination reason: Unknown
% 2.90/1.65 % (24428)Termination phase: Saturation
% 2.90/1.65
% 2.90/1.65 % (24428)Memory used [KB]: 6908
% 2.90/1.65 % (24428)Time elapsed: 0.079 s
% 2.90/1.65 % (24428)Instructions burned: 183 (million)
% 2.90/1.65 % (24428)------------------------------
% 2.90/1.65 % (24428)------------------------------
% 2.90/1.65 % (24451)Instruction limit reached!
% 2.90/1.65 % (24451)------------------------------
% 2.90/1.65 % (24451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.65 % (24451)Termination reason: Unknown
% 2.90/1.65 % (24451)Termination phase: shuffling
% 2.90/1.65
% 2.90/1.65 % (24451)Memory used [KB]: 1535
% 2.90/1.65 % (24451)Time elapsed: 0.008 s
% 2.90/1.65 % (24451)Instructions burned: 22 (million)
% 2.90/1.65 % (24451)------------------------------
% 2.90/1.65 % (24451)------------------------------
% 2.90/1.65 % (24433)Instruction limit reached!
% 2.90/1.65 % (24433)------------------------------
% 2.90/1.65 % (24433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.65 % (24433)Termination reason: Unknown
% 2.90/1.65 % (24433)Termination phase: Saturation
% 2.90/1.65
% 2.90/1.65 % (24433)Memory used [KB]: 7164
% 2.90/1.65 % (24433)Time elapsed: 0.090 s
% 2.90/1.65 % (24433)Instructions burned: 277 (million)
% 2.90/1.65 % (24433)------------------------------
% 2.90/1.65 % (24433)------------------------------
% 2.90/1.66 % (24453)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_24154 for (2999ds/6Mi)
% 2.90/1.66 % (24454)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_24154 for (2999ds/377Mi)
% 2.90/1.66 % (24453)Instruction limit reached!
% 2.90/1.66 % (24453)------------------------------
% 2.90/1.66 % (24453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.66 % (24453)Termination reason: Unknown
% 2.90/1.66 % (24453)Termination phase: shuffling
% 2.90/1.66
% 2.90/1.66 % (24453)Memory used [KB]: 1407
% 2.90/1.66 % (24453)Time elapsed: 0.004 s
% 2.90/1.66 % (24453)Instructions burned: 8 (million)
% 2.90/1.66 % (24453)------------------------------
% 2.90/1.66 % (24453)------------------------------
% 2.90/1.66 % (24455)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_24154 for (2999ds/779Mi)
% 2.90/1.66 % (24456)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_24154 for (2999ds/19Mi)
% 2.90/1.67 % (24457)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_24154 for (2998ds/879Mi)
% 2.90/1.67 % (24456)Instruction limit reached!
% 2.90/1.67 % (24456)------------------------------
% 2.90/1.67 % (24456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.67 % (24456)Termination reason: Unknown
% 2.90/1.67 % (24456)Termination phase: shuffling
% 2.90/1.67
% 2.90/1.67 % (24456)Memory used [KB]: 1663
% 2.90/1.67 % (24456)Time elapsed: 0.007 s
% 2.90/1.67 % (24456)Instructions burned: 20 (million)
% 2.90/1.67 % (24456)------------------------------
% 2.90/1.67 % (24456)------------------------------
% 2.90/1.68 % (24458)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_24154 for (2998ds/17Mi)
% 2.90/1.68 % (24458)Instruction limit reached!
% 2.90/1.68 % (24458)------------------------------
% 2.90/1.68 % (24458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.68 % (24458)Termination reason: Unknown
% 2.90/1.68 % (24458)Termination phase: shuffling
% 2.90/1.68
% 2.90/1.68 % (24458)Memory used [KB]: 1535
% 2.90/1.68 % (24458)Time elapsed: 0.007 s
% 2.90/1.68 % (24458)Instructions burned: 19 (million)
% 2.90/1.68 % (24458)------------------------------
% 2.90/1.68 % (24458)------------------------------
% 2.90/1.69 % (24459)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_24154 for (2998ds/3Mi)
% 2.90/1.69 % (24459)Instruction limit reached!
% 2.90/1.69 % (24459)------------------------------
% 2.90/1.69 % (24459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.69 % (24459)Termination reason: Unknown
% 2.90/1.69 % (24459)Termination phase: shuffling
% 2.90/1.69
% 2.90/1.69 % (24459)Memory used [KB]: 1279
% 2.90/1.69 % (24459)Time elapsed: 0.002 s
% 2.90/1.69 % (24459)Instructions burned: 3 (million)
% 2.90/1.69 % (24459)------------------------------
% 2.90/1.69 % (24459)------------------------------
% 2.90/1.70 % (24460)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_24154 for (2998ds/30Mi)
% 2.90/1.71 % (24460)Instruction limit reached!
% 2.90/1.71 % (24460)------------------------------
% 2.90/1.71 % (24460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.71 % (24460)Termination reason: Unknown
% 2.90/1.71 % (24460)Termination phase: Property scanning
% 2.90/1.71
% 2.90/1.71 % (24460)Memory used [KB]: 1663
% 2.90/1.71 % (24460)Time elapsed: 0.011 s
% 2.90/1.71 % (24460)Instructions burned: 30 (million)
% 2.90/1.71 % (24460)------------------------------
% 2.90/1.71 % (24460)------------------------------
% 2.90/1.72 % (24461)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_24154 for (2998ds/127Mi)
% 2.90/1.76 % (24461)Instruction limit reached!
% 2.90/1.76 % (24461)------------------------------
% 2.90/1.76 % (24461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.76 % (24461)Termination reason: Unknown
% 2.90/1.76 % (24461)Termination phase: Saturation
% 2.90/1.76
% 2.90/1.76 % (24461)Memory used [KB]: 6780
% 2.90/1.76 % (24461)Time elapsed: 0.060 s
% 2.90/1.76 % (24461)Instructions burned: 127 (million)
% 2.90/1.76 % (24461)------------------------------
% 2.90/1.76 % (24461)------------------------------
% 2.90/1.77 % (24462)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_24154 for (2997ds/100Mi)
% 2.90/1.78 % (24454)Instruction limit reached!
% 2.90/1.78 % (24454)------------------------------
% 2.90/1.78 % (24454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.78 % (24454)Termination reason: Unknown
% 2.90/1.78 % (24454)Termination phase: Saturation
% 2.90/1.78
% 2.90/1.78 % (24454)Memory used [KB]: 7419
% 2.90/1.78 % (24454)Time elapsed: 0.123 s
% 2.90/1.78 % (24454)Instructions burned: 379 (million)
% 2.90/1.78 % (24454)------------------------------
% 2.90/1.78 % (24454)------------------------------
% 2.90/1.79 % (24463)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_24154 for (2997ds/3Mi)
% 2.90/1.79 % (24463)Instruction limit reached!
% 2.90/1.79 % (24463)------------------------------
% 2.90/1.79 % (24463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.79 % (24463)Termination reason: Unknown
% 2.90/1.79 % (24463)Termination phase: shuffling
% 2.90/1.79
% 2.90/1.79 % (24463)Memory used [KB]: 1279
% 2.90/1.79 % (24463)Time elapsed: 0.002 s
% 2.90/1.79 % (24463)Instructions burned: 4 (million)
% 2.90/1.79 % (24463)------------------------------
% 2.90/1.79 % (24463)------------------------------
% 2.90/1.80 % (24462)Instruction limit reached!
% 2.90/1.80 % (24462)------------------------------
% 2.90/1.80 % (24462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.80 % (24462)Termination reason: Unknown
% 2.90/1.80 % (24462)Termination phase: Saturation
% 2.90/1.80
% 2.90/1.80 % (24462)Memory used [KB]: 6652
% 2.90/1.80 % (24462)Time elapsed: 0.028 s
% 2.90/1.80 % (24462)Instructions burned: 102 (million)
% 2.90/1.80 % (24462)------------------------------
% 2.90/1.80 % (24462)------------------------------
% 2.90/1.80 % (24464)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_24154 for (2997ds/20Mi)
% 2.90/1.81 % (24464)Instruction limit reached!
% 2.90/1.81 % (24464)------------------------------
% 2.90/1.81 % (24464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.81 % (24464)Termination reason: Unknown
% 2.90/1.81 % (24464)Termination phase: shuffling
% 2.90/1.81
% 2.90/1.81 % (24464)Memory used [KB]: 1535
% 2.90/1.81 % (24464)Time elapsed: 0.008 s
% 2.90/1.81 % (24464)Instructions burned: 21 (million)
% 2.90/1.81 % (24464)------------------------------
% 2.90/1.81 % (24464)------------------------------
% 2.90/1.81 % (24465)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_24154 for (2997ds/86Mi)
% 2.90/1.82 % (24466)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_24154 for (2997ds/107Mi)
% 2.90/1.83 % (24465)Instruction limit reached!
% 2.90/1.83 % (24465)------------------------------
% 2.90/1.83 % (24465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.83 % (24465)Termination reason: Unknown
% 2.90/1.83 % (24465)Termination phase: Saturation
% 2.90/1.83
% 2.90/1.83 % (24465)Memory used [KB]: 6524
% 2.90/1.83 % (24465)Time elapsed: 0.027 s
% 2.90/1.83 % (24465)Instructions burned: 88 (million)
% 2.90/1.83 % (24465)------------------------------
% 2.90/1.83 % (24465)------------------------------
% 2.90/1.84 % (24467)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_24154 for (2997ds/39Mi)
% 2.90/1.85 % (24466)Instruction limit reached!
% 2.90/1.85 % (24466)------------------------------
% 2.90/1.85 % (24466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.85 % (24466)Termination reason: Unknown
% 2.90/1.85 % (24466)Termination phase: Saturation
% 2.90/1.85
% 2.90/1.85 % (24466)Memory used [KB]: 6652
% 2.90/1.85 % (24466)Time elapsed: 0.034 s
% 2.90/1.85 % (24466)Instructions burned: 109 (million)
% 2.90/1.85 % (24466)------------------------------
% 2.90/1.85 % (24466)------------------------------
% 2.90/1.85 % (24467)Instruction limit reached!
% 2.90/1.85 % (24467)------------------------------
% 2.90/1.85 % (24467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.85 % (24467)Termination reason: Unknown
% 2.90/1.85 % (24467)Termination phase: Property scanning
% 2.90/1.85
% 2.90/1.85 % (24467)Memory used [KB]: 2046
% 2.90/1.85 % (24467)Time elapsed: 0.012 s
% 2.90/1.85 % (24467)Instructions burned: 42 (million)
% 2.90/1.85 % (24467)------------------------------
% 2.90/1.85 % (24467)------------------------------
% 2.90/1.86 % (24468)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_24154 for (2996ds/448Mi)
% 2.90/1.86 % (24469)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_24154 for (2996ds/46Mi)
% 2.90/1.88 % (24469)Instruction limit reached!
% 2.90/1.88 % (24469)------------------------------
% 2.90/1.88 % (24469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.88 % (24469)Termination reason: Unknown
% 2.90/1.88 % (24469)Termination phase: Preprocessing 3
% 2.90/1.88
% 2.90/1.88 % (24469)Memory used [KB]: 1791
% 2.90/1.88 % (24469)Time elapsed: 0.016 s
% 2.90/1.88 % (24469)Instructions burned: 48 (million)
% 2.90/1.88 % (24469)------------------------------
% 2.90/1.88 % (24469)------------------------------
% 2.90/1.89 % (24470)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_24154 for (2996ds/98Mi)
% 2.90/1.90 % (24448)Instruction limit reached!
% 2.90/1.90 % (24448)------------------------------
% 2.90/1.90 % (24448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.90 % (24448)Termination reason: Unknown
% 2.90/1.90 % (24448)Termination phase: Saturation
% 2.90/1.90
% 2.90/1.90 % (24448)Memory used [KB]: 7675
% 2.90/1.90 % (24448)Time elapsed: 0.261 s
% 2.90/1.90 % (24448)Instructions burned: 712 (million)
% 2.90/1.90 % (24448)------------------------------
% 2.90/1.90 % (24448)------------------------------
% 2.90/1.90 % (24455)Instruction limit reached!
% 2.90/1.90 % (24455)------------------------------
% 2.90/1.90 % (24455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.90 % (24455)Termination reason: Unknown
% 2.90/1.90 % (24455)Termination phase: Saturation
% 2.90/1.90
% 2.90/1.90 % (24455)Memory used [KB]: 7675
% 2.90/1.90 % (24455)Time elapsed: 0.246 s
% 2.90/1.90 % (24455)Instructions burned: 779 (million)
% 2.90/1.90 % (24455)------------------------------
% 2.90/1.90 % (24455)------------------------------
% 2.90/1.91 % (24471)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_24154 for (2996ds/507Mi)
% 2.90/1.91 % (24470)Instruction limit reached!
% 2.90/1.91 % (24470)------------------------------
% 2.90/1.91 % (24470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.91 % (24470)Termination reason: Unknown
% 2.90/1.91 % (24470)Termination phase: Saturation
% 2.90/1.91
% 2.90/1.91 % (24470)Memory used [KB]: 2174
% 2.90/1.91 % (24470)Time elapsed: 0.028 s
% 2.90/1.91 % (24470)Instructions burned: 101 (million)
% 2.90/1.91 % (24470)------------------------------
% 2.90/1.91 % (24470)------------------------------
% 2.90/1.91 % (24472)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_24154 for (2996ds/149Mi)
% 2.90/1.92 % (24473)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_24154 for (2996ds/39Mi)
% 2.90/1.93 % (24439)Instruction limit reached!
% 2.90/1.93 % (24439)------------------------------
% 2.90/1.93 % (24439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.93 % (24439)Termination reason: Unknown
% 2.90/1.93 % (24439)Termination phase: Saturation
% 2.90/1.93
% 2.90/1.93 % (24439)Memory used [KB]: 8827
% 2.90/1.93 % (24439)Time elapsed: 0.341 s
% 2.90/1.93 % (24439)Instructions burned: 1044 (million)
% 2.90/1.93 % (24439)------------------------------
% 2.90/1.93 % (24439)------------------------------
% 2.90/1.93 % (24450)Instruction limit reached!
% 2.90/1.93 % (24450)------------------------------
% 2.90/1.93 % (24450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.93 % (24450)Termination reason: Unknown
% 2.90/1.93 % (24450)Termination phase: Saturation
% 2.90/1.93
% 2.90/1.93 % (24450)Memory used [KB]: 9210
% 2.90/1.93 % (24450)Time elapsed: 0.298 s
% 2.90/1.93 % (24450)Instructions burned: 905 (million)
% 2.90/1.93 % (24450)------------------------------
% 2.90/1.93 % (24450)------------------------------
% 2.90/1.94 % (24473)Instruction limit reached!
% 2.90/1.94 % (24473)------------------------------
% 2.90/1.94 % (24473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.94 % (24473)Termination reason: Unknown
% 2.90/1.94 % (24473)Termination phase: Preprocessing 3
% 2.90/1.94
% 2.90/1.94 % (24473)Memory used [KB]: 1791
% 2.90/1.94 % (24473)Time elapsed: 0.013 s
% 2.90/1.94 % (24473)Instructions burned: 40 (million)
% 2.90/1.94 % (24473)------------------------------
% 2.90/1.94 % (24473)------------------------------
% 2.90/1.94 % (24474)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_24154 for (2996ds/6Mi)
% 2.90/1.94 % (24474)Instruction limit reached!
% 2.90/1.94 % (24474)------------------------------
% 2.90/1.94 % (24474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.94 % (24474)Termination reason: Unknown
% 2.90/1.94 % (24474)Termination phase: shuffling
% 2.90/1.94
% 2.90/1.94 % (24474)Memory used [KB]: 1407
% 2.90/1.94 % (24474)Time elapsed: 0.003 s
% 2.90/1.94 % (24474)Instructions burned: 7 (million)
% 2.90/1.94 % (24474)------------------------------
% 2.90/1.94 % (24474)------------------------------
% 2.90/1.94 % (24475)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_24154 for (2996ds/1087Mi)
% 2.90/1.94 % (24476)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_24154 for (2996ds/47Mi)
% 2.90/1.95 % (24477)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_24154 for (2996ds/44Mi)
% 2.90/1.96 % (24457)Instruction limit reached!
% 2.90/1.96 % (24457)------------------------------
% 2.90/1.96 % (24457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.96 % (24457)Termination reason: Unknown
% 2.90/1.96 % (24457)Termination phase: Saturation
% 2.90/1.96
% 2.90/1.96 % (24457)Memory used [KB]: 7931
% 2.90/1.96 % (24457)Time elapsed: 0.291 s
% 2.90/1.96 % (24457)Instructions burned: 881 (million)
% 2.90/1.96 % (24457)------------------------------
% 2.90/1.96 % (24457)------------------------------
% 2.90/1.96 % (24472)Instruction limit reached!
% 2.90/1.96 % (24472)------------------------------
% 2.90/1.96 % (24472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.96 % (24472)Termination reason: Unknown
% 2.90/1.96 % (24472)Termination phase: Saturation
% 2.90/1.96
% 2.90/1.96 % (24472)Memory used [KB]: 6780
% 2.90/1.96 % (24472)Time elapsed: 0.047 s
% 2.90/1.96 % (24472)Instructions burned: 150 (million)
% 2.90/1.96 % (24472)------------------------------
% 2.90/1.96 % (24472)------------------------------
% 2.90/1.96 % (24476)Instruction limit reached!
% 2.90/1.96 % (24476)------------------------------
% 2.90/1.96 % (24476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.96 % (24476)Termination reason: Unknown
% 2.90/1.96 % (24476)Termination phase: Property scanning
% 2.90/1.96
% 2.90/1.96 % (24476)Memory used [KB]: 1918
% 2.90/1.96 % (24476)Time elapsed: 0.016 s
% 2.90/1.96 % (24476)Instructions burned: 48 (million)
% 2.90/1.96 % (24476)------------------------------
% 2.90/1.96 % (24476)------------------------------
% 2.90/1.96 % (24477)Instruction limit reached!
% 2.90/1.96 % (24477)------------------------------
% 2.90/1.96 % (24477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.96 % (24477)Termination reason: Unknown
% 2.90/1.96 % (24477)Termination phase: Property scanning
% 2.90/1.96
% 2.90/1.96 % (24477)Memory used [KB]: 1918
% 2.90/1.96 % (24477)Time elapsed: 0.014 s
% 2.90/1.96 % (24477)Instructions burned: 47 (million)
% 2.90/1.96 % (24477)------------------------------
% 2.90/1.96 % (24477)------------------------------
% 2.90/1.97 % (24478)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_24154 for (2995ds/432Mi)
% 2.90/1.97 % (24479)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_24154 for (2995ds/62Mi)
% 2.90/1.97 % (24480)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_24154 for (2995ds/31Mi)
% 2.90/1.97 % (24481)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_24154 for (2995ds/96Mi)
% 2.90/1.98 % (24480)Instruction limit reached!
% 2.90/1.98 % (24480)------------------------------
% 2.90/1.98 % (24480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.98 % (24480)Termination reason: Unknown
% 2.90/1.98 % (24480)Termination phase: Preprocessing 1
% 2.90/1.98
% 2.90/1.98 % (24480)Memory used [KB]: 1535
% 2.90/1.98 % (24480)Time elapsed: 0.011 s
% 2.90/1.98 % (24480)Instructions burned: 33 (million)
% 2.90/1.98 % (24480)------------------------------
% 2.90/1.98 % (24480)------------------------------
% 2.90/1.99 % (24479)Instruction limit reached!
% 2.90/1.99 % (24479)------------------------------
% 2.90/1.99 % (24479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/1.99 % (24479)Termination reason: Unknown
% 2.90/1.99 % (24479)Termination phase: Property scanning
% 2.90/1.99
% 2.90/1.99 % (24479)Memory used [KB]: 2046
% 2.90/1.99 % (24479)Time elapsed: 0.018 s
% 2.90/1.99 % (24479)Instructions burned: 65 (million)
% 2.90/1.99 % (24479)------------------------------
% 2.90/1.99 % (24479)------------------------------
% 2.90/1.99 % (24482)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_24154 for (2995ds/453Mi)
% 2.90/2.00 % (24483)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_24154 for (2995ds/71Mi)
% 2.90/2.00 % (24468)Instruction limit reached!
% 2.90/2.00 % (24468)------------------------------
% 2.90/2.00 % (24468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/2.00 % (24468)Termination reason: Unknown
% 2.90/2.00 % (24468)Termination phase: Saturation
% 2.90/2.00
% 2.90/2.00 % (24468)Memory used [KB]: 7675
% 2.90/2.00 % (24468)Time elapsed: 0.139 s
% 2.90/2.00 % (24468)Instructions burned: 448 (million)
% 2.90/2.00 % (24468)------------------------------
% 2.90/2.00 % (24468)------------------------------
% 2.90/2.00 % (24481)Instruction limit reached!
% 2.90/2.00 % (24481)------------------------------
% 2.90/2.00 % (24481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.90/2.00 % (24481)Termination reason: Unknown
% 2.90/2.00 % (24481)Termination phase: Saturation
% 2.90/2.00
% 2.90/2.00 % (24481)Memory used [KB]: 6524
% 2.90/2.00 % (24481)Time elapsed: 0.028 s
% 2.90/2.00 % (24481)Instructions burned: 96 (million)
% 2.90/2.00 % (24481)------------------------------
% 2.90/2.00 % (24481)------------------------------
% 2.90/2.01 % (24484)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_24154 for (2995ds/83Mi)
% 6.04/2.01 % (24485)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_24154 for (2995ds/11Mi)
% 6.04/2.02 % (24483)Instruction limit reached!
% 6.04/2.02 % (24483)------------------------------
% 6.04/2.02 % (24483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.02 % (24483)Termination reason: Unknown
% 6.04/2.02 % (24483)Termination phase: Property scanning
% 6.04/2.02
% 6.04/2.02 % (24483)Memory used [KB]: 1918
% 6.04/2.02 % (24483)Time elapsed: 0.021 s
% 6.04/2.02 % (24483)Instructions burned: 72 (million)
% 6.04/2.02 % (24483)------------------------------
% 6.04/2.02 % (24483)------------------------------
% 6.04/2.02 % (24485)Instruction limit reached!
% 6.04/2.02 % (24485)------------------------------
% 6.04/2.02 % (24485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.02 % (24485)Termination reason: Unknown
% 6.04/2.02 % (24485)Termination phase: shuffling
% 6.04/2.02
% 6.04/2.02 % (24485)Memory used [KB]: 1535
% 6.04/2.02 % (24485)Time elapsed: 0.008 s
% 6.04/2.02 % (24485)Instructions burned: 11 (million)
% 6.04/2.02 % (24485)------------------------------
% 6.04/2.02 % (24485)------------------------------
% 6.04/2.02 % (24486)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_24154 for (2995ds/41Mi)
% 6.04/2.03 % (24484)Instruction limit reached!
% 6.04/2.03 % (24484)------------------------------
% 6.04/2.03 % (24484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.03 % (24484)Termination reason: Unknown
% 6.04/2.03 % (24484)Termination phase: Saturation
% 6.04/2.03
% 6.04/2.03 % (24484)Memory used [KB]: 6396
% 6.04/2.03 % (24484)Time elapsed: 0.025 s
% 6.04/2.03 % (24484)Instructions burned: 83 (million)
% 6.04/2.03 % (24484)------------------------------
% 6.04/2.03 % (24484)------------------------------
% 6.04/2.04 % (24486)Instruction limit reached!
% 6.04/2.04 % (24486)------------------------------
% 6.04/2.04 % (24486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.04 % (24486)Termination reason: Unknown
% 6.04/2.04 % (24486)Termination phase: Property scanning
% 6.04/2.04
% 6.04/2.04 % (24486)Memory used [KB]: 2046
% 6.04/2.04 % (24486)Time elapsed: 0.013 s
% 6.04/2.04 % (24486)Instructions burned: 45 (million)
% 6.04/2.04 % (24486)------------------------------
% 6.04/2.04 % (24486)------------------------------
% 6.04/2.04 % (24487)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_24154 for (2995ds/6Mi)
% 6.04/2.04 % (24488)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_24154 for (2995ds/150Mi)
% 6.04/2.04 % (24487)Instruction limit reached!
% 6.04/2.04 % (24487)------------------------------
% 6.04/2.04 % (24487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.04 % (24487)Termination reason: Unknown
% 6.04/2.04 % (24487)Termination phase: shuffling
% 6.04/2.04
% 6.04/2.04 % (24487)Memory used [KB]: 1407
% 6.04/2.04 % (24487)Time elapsed: 0.006 s
% 6.04/2.04 % (24487)Instructions burned: 7 (million)
% 6.04/2.04 % (24487)------------------------------
% 6.04/2.04 % (24487)------------------------------
% 6.04/2.05 % (24489)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_24154 for (2995ds/343Mi)
% 6.04/2.06 % (24490)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_24154 for (2995ds/109Mi)
% 6.04/2.07 % (24471)Instruction limit reached!
% 6.04/2.07 % (24471)------------------------------
% 6.04/2.07 % (24471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.07 % (24471)Termination reason: Unknown
% 6.04/2.07 % (24471)Termination phase: Saturation
% 6.04/2.07
% 6.04/2.07 % (24471)Memory used [KB]: 7803
% 6.04/2.07 % (24471)Time elapsed: 0.168 s
% 6.04/2.07 % (24471)Instructions burned: 509 (million)
% 6.04/2.07 % (24471)------------------------------
% 6.04/2.07 % (24471)------------------------------
% 6.04/2.08 % (24491)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_24154 for (2994ds/253Mi)
% 6.04/2.08 % (24488)Instruction limit reached!
% 6.04/2.08 % (24488)------------------------------
% 6.04/2.08 % (24488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.08 % (24488)Termination reason: Unknown
% 6.04/2.08 % (24488)Termination phase: Saturation
% 6.04/2.08
% 6.04/2.08 % (24488)Memory used [KB]: 6908
% 6.04/2.08 % (24488)Time elapsed: 0.047 s
% 6.04/2.08 % (24488)Instructions burned: 150 (million)
% 6.04/2.08 % (24488)------------------------------
% 6.04/2.08 % (24488)------------------------------
% 6.04/2.09 % (24492)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_24154 for (2994ds/140Mi)
% 6.04/2.10 % (24478)Instruction limit reached!
% 6.04/2.10 % (24478)------------------------------
% 6.04/2.10 % (24478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.10 % (24478)Termination reason: Unknown
% 6.04/2.10 % (24478)Termination phase: Saturation
% 6.04/2.10
% 6.04/2.10 % (24478)Memory used [KB]: 3837
% 6.04/2.10 % (24478)Time elapsed: 0.137 s
% 6.04/2.10 % (24478)Instructions burned: 432 (million)
% 6.04/2.10 % (24478)------------------------------
% 6.04/2.10 % (24478)------------------------------
% 6.57/2.11 % (24493)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_24154 for (2994ds/614Mi)
% 6.57/2.12 % (24490)Instruction limit reached!
% 6.57/2.12 % (24490)------------------------------
% 6.57/2.12 % (24490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.12 % (24490)Termination reason: Unknown
% 6.57/2.12 % (24490)Termination phase: Saturation
% 6.57/2.12
% 6.57/2.12 % (24490)Memory used [KB]: 6652
% 6.57/2.12 % (24490)Time elapsed: 0.061 s
% 6.57/2.12 % (24490)Instructions burned: 109 (million)
% 6.57/2.12 % (24490)------------------------------
% 6.57/2.12 % (24490)------------------------------
% 6.57/2.13 % (24482)Instruction limit reached!
% 6.57/2.13 % (24482)------------------------------
% 6.57/2.13 % (24482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.13 % (24482)Termination reason: Unknown
% 6.57/2.13 % (24482)Termination phase: Saturation
% 6.57/2.13
% 6.57/2.13 % (24482)Memory used [KB]: 7164
% 6.57/2.13 % (24482)Time elapsed: 0.138 s
% 6.57/2.13 % (24482)Instructions burned: 453 (million)
% 6.57/2.13 % (24482)------------------------------
% 6.57/2.13 % (24482)------------------------------
% 6.57/2.13 % (24494)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_24154 for (2994ds/202Mi)
% 6.57/2.14 % (24495)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_24154 for (2994ds/339Mi)
% 6.57/2.14 % (24492)Instruction limit reached!
% 6.57/2.14 % (24492)------------------------------
% 6.57/2.14 % (24492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.14 % (24492)Termination reason: Unknown
% 6.57/2.14 % (24492)Termination phase: Saturation
% 6.57/2.14
% 6.57/2.14 % (24492)Memory used [KB]: 6652
% 6.57/2.14 % (24492)Time elapsed: 0.045 s
% 6.57/2.14 % (24492)Instructions burned: 140 (million)
% 6.57/2.14 % (24492)------------------------------
% 6.57/2.14 % (24492)------------------------------
% 6.57/2.15 % (24496)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_24154 for (2994ds/283Mi)
% 6.57/2.16 % (24489)Instruction limit reached!
% 6.57/2.16 % (24489)------------------------------
% 6.57/2.16 % (24489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.16 % (24489)Termination reason: Unknown
% 6.57/2.16 % (24489)Termination phase: Saturation
% 6.57/2.16
% 6.57/2.16 % (24489)Memory used [KB]: 7164
% 6.57/2.16 % (24489)Time elapsed: 0.110 s
% 6.57/2.16 % (24489)Instructions burned: 344 (million)
% 6.57/2.16 % (24489)------------------------------
% 6.57/2.16 % (24489)------------------------------
% 6.57/2.16 % (24491)Instruction limit reached!
% 6.57/2.16 % (24491)------------------------------
% 6.57/2.16 % (24491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.57/2.16 % (24491)Termination reason: Unknown
% 6.57/2.16 % (24491)Termination phase: Saturation
% 6.57/2.16
% 6.57/2.16 % (24491)Memory used [KB]: 7547
% 6.57/2.16 % (24491)Time elapsed: 0.078 s
% 6.57/2.16 % (24491)Instructions burned: 255 (million)
% 6.57/2.16 % (24491)------------------------------
% 6.57/2.16 % (24491)------------------------------
% 6.57/2.16 % (24497)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_24154 for (2994ds/134Mi)
% 6.57/2.17 % (24498)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_24154 for (2993ds/298Mi)
% 7.02/2.20 % (24494)Instruction limit reached!
% 7.02/2.20 % (24494)------------------------------
% 7.02/2.20 % (24494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.20 % (24494)Termination reason: Unknown
% 7.02/2.20 % (24494)Termination phase: Saturation
% 7.02/2.20
% 7.02/2.20 % (24494)Memory used [KB]: 7291
% 7.02/2.20 % (24494)Time elapsed: 0.068 s
% 7.02/2.20 % (24494)Instructions burned: 203 (million)
% 7.02/2.20 % (24494)------------------------------
% 7.02/2.20 % (24494)------------------------------
% 7.02/2.21 % (24497)Instruction limit reached!
% 7.02/2.21 % (24497)------------------------------
% 7.02/2.21 % (24497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.21 % (24497)Termination reason: Unknown
% 7.02/2.21 % (24497)Termination phase: Saturation
% 7.02/2.21
% 7.02/2.21 % (24497)Memory used [KB]: 6652
% 7.02/2.21 % (24497)Time elapsed: 0.042 s
% 7.02/2.21 % (24497)Instructions burned: 135 (million)
% 7.02/2.21 % (24497)------------------------------
% 7.02/2.21 % (24497)------------------------------
% 7.02/2.21 % (24499)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_24154 for (2993ds/192Mi)
% 7.02/2.22 % (24500)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_24154 for (2993ds/258Mi)
% 7.02/2.24 % (24496)Instruction limit reached!
% 7.02/2.24 % (24496)------------------------------
% 7.02/2.24 % (24496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.24 % (24496)Termination reason: Unknown
% 7.02/2.24 % (24496)Termination phase: Saturation
% 7.02/2.24
% 7.02/2.24 % (24496)Memory used [KB]: 7164
% 7.02/2.24 % (24496)Time elapsed: 0.090 s
% 7.02/2.24 % (24496)Instructions burned: 284 (million)
% 7.02/2.24 % (24496)------------------------------
% 7.02/2.24 % (24496)------------------------------
% 7.02/2.24 % (24495)Instruction limit reached!
% 7.02/2.24 % (24495)------------------------------
% 7.02/2.24 % (24495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.24 % (24495)Termination reason: Unknown
% 7.02/2.24 % (24495)Termination phase: Saturation
% 7.02/2.24
% 7.02/2.24 % (24495)Memory used [KB]: 7547
% 7.02/2.24 % (24495)Time elapsed: 0.107 s
% 7.02/2.24 % (24495)Instructions burned: 339 (million)
% 7.02/2.24 % (24495)------------------------------
% 7.02/2.24 % (24495)------------------------------
% 7.02/2.25 % (24501)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_24154 for (2993ds/90Mi)
% 7.02/2.25 % (24502)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_24154 for (2993ds/231Mi)
% 7.02/2.26 % (24498)Instruction limit reached!
% 7.02/2.26 % (24498)------------------------------
% 7.02/2.26 % (24498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.26 % (24498)Termination reason: Unknown
% 7.02/2.26 % (24498)Termination phase: Saturation
% 7.02/2.26
% 7.02/2.26 % (24498)Memory used [KB]: 7675
% 7.02/2.26 % (24498)Time elapsed: 0.088 s
% 7.02/2.26 % (24498)Instructions burned: 298 (million)
% 7.02/2.26 % (24498)------------------------------
% 7.02/2.26 % (24498)------------------------------
% 7.02/2.26 % (24503)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_24154 for (2993ds/458Mi)
% 7.02/2.27 % (24501)Instruction limit reached!
% 7.02/2.27 % (24501)------------------------------
% 7.02/2.27 % (24501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.27 % (24501)Termination reason: Unknown
% 7.02/2.27 % (24501)Termination phase: Saturation
% 7.02/2.27
% 7.02/2.27 % (24501)Memory used [KB]: 6524
% 7.02/2.27 % (24501)Time elapsed: 0.027 s
% 7.02/2.27 % (24501)Instructions burned: 91 (million)
% 7.02/2.27 % (24501)------------------------------
% 7.02/2.27 % (24501)------------------------------
% 7.02/2.27 % (24499)Instruction limit reached!
% 7.02/2.27 % (24499)------------------------------
% 7.02/2.27 % (24499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.27 % (24499)Termination reason: Unknown
% 7.02/2.27 % (24499)Termination phase: Saturation
% 7.02/2.27
% 7.02/2.27 % (24499)Memory used [KB]: 7547
% 7.02/2.27 % (24499)Time elapsed: 0.064 s
% 7.02/2.27 % (24499)Instructions burned: 194 (million)
% 7.02/2.27 % (24499)------------------------------
% 7.02/2.27 % (24499)------------------------------
% 7.02/2.28 % (24504)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_24154 for (2992ds/31Mi)
% 7.02/2.28 % (24505)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_24154 for (2992ds/297Mi)
% 7.02/2.29 % (24475)Instruction limit reached!
% 7.02/2.29 % (24475)------------------------------
% 7.02/2.29 % (24475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.29 % (24475)Termination reason: Unknown
% 7.02/2.29 % (24475)Termination phase: Saturation
% 7.02/2.29
% 7.02/2.29 % (24475)Memory used [KB]: 8571
% 7.02/2.29 % (24475)Time elapsed: 0.348 s
% 7.02/2.29 % (24475)Instructions burned: 1089 (million)
% 7.02/2.29 % (24475)------------------------------
% 7.02/2.29 % (24475)------------------------------
% 7.02/2.29 % (24500)Instruction limit reached!
% 7.02/2.29 % (24500)------------------------------
% 7.02/2.29 % (24500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.29 % (24500)Termination reason: Unknown
% 7.02/2.29 % (24500)Termination phase: Saturation
% 7.02/2.29
% 7.02/2.29 % (24500)Memory used [KB]: 7164
% 7.02/2.29 % (24500)Time elapsed: 0.077 s
% 7.02/2.29 % (24500)Instructions burned: 259 (million)
% 7.02/2.29 % (24500)------------------------------
% 7.02/2.29 % (24500)------------------------------
% 7.02/2.29 % (24504)Instruction limit reached!
% 7.02/2.29 % (24504)------------------------------
% 7.02/2.29 % (24504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.29 % (24504)Termination reason: Unknown
% 7.02/2.29 % (24504)Termination phase: Preprocessing 1
% 7.02/2.29
% 7.02/2.29 % (24504)Memory used [KB]: 1535
% 7.02/2.29 % (24504)Time elapsed: 0.011 s
% 7.02/2.29 % (24504)Instructions burned: 33 (million)
% 7.02/2.29 % (24504)------------------------------
% 7.02/2.29 % (24504)------------------------------
% 7.77/2.30 % (24506)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_24154 for (2992ds/987Mi)
% 7.77/2.30 % (24507)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_24154 for (2992ds/182Mi)
% 7.77/2.30 % (24508)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_24154 for (2992ds/182Mi)
% 7.77/2.30 % (24493)Instruction limit reached!
% 7.77/2.30 % (24493)------------------------------
% 7.77/2.30 % (24493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.30 % (24493)Termination reason: Unknown
% 7.77/2.30 % (24493)Termination phase: Saturation
% 7.77/2.30
% 7.77/2.30 % (24493)Memory used [KB]: 8187
% 7.77/2.30 % (24493)Time elapsed: 0.192 s
% 7.77/2.30 % (24493)Instructions burned: 615 (million)
% 7.77/2.30 % (24493)------------------------------
% 7.77/2.30 % (24493)------------------------------
% 7.77/2.31 % (24509)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_24154 for (2992ds/154Mi)
% 7.77/2.32 % (24502)Instruction limit reached!
% 7.77/2.32 % (24502)------------------------------
% 7.77/2.32 % (24502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.32 % (24502)Termination reason: Unknown
% 7.77/2.32 % (24502)Termination phase: Saturation
% 7.77/2.32
% 7.77/2.32 % (24502)Memory used [KB]: 7164
% 7.77/2.32 % (24502)Time elapsed: 0.087 s
% 7.77/2.32 % (24502)Instructions burned: 233 (million)
% 7.77/2.32 % (24502)------------------------------
% 7.77/2.32 % (24502)------------------------------
% 7.77/2.32 % (24510)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_24154 for (2992ds/79Mi)
% 7.77/2.35 % (24510)Instruction limit reached!
% 7.77/2.35 % (24510)------------------------------
% 7.77/2.35 % (24510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.35 % (24510)Termination reason: Unknown
% 7.77/2.35 % (24510)Termination phase: Saturation
% 7.77/2.35
% 7.77/2.35 % (24510)Memory used [KB]: 6524
% 7.77/2.35 % (24510)Time elapsed: 0.023 s
% 7.77/2.35 % (24510)Instructions burned: 79 (million)
% 7.77/2.35 % (24510)------------------------------
% 7.77/2.35 % (24510)------------------------------
% 7.77/2.35 % (24509)Refutation not found, incomplete strategy
% 7.77/2.35 % (24509)------------------------------
% 7.77/2.35 % (24509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.35 % (24509)Termination reason: Refutation not found, incomplete strategy
% 7.77/2.35
% 7.77/2.35
% 7.77/2.35 % (24509)Memory used [KB]: 7036
% 7.77/2.35 % (24509)Time elapsed: 0.036 s
% 7.77/2.35 % (24509)Instructions burned: 127 (million)
% 7.77/2.35 % (24509)------------------------------
% 7.77/2.35 % (24509)------------------------------
% 7.77/2.35 % (24507)Instruction limit reached!
% 7.77/2.35 % (24507)------------------------------
% 7.77/2.35 % (24507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.35 % (24507)Termination reason: Unknown
% 7.77/2.35 % (24507)Termination phase: Saturation
% 7.77/2.35
% 7.77/2.35 % (24507)Memory used [KB]: 6780
% 7.77/2.35 % (24507)Time elapsed: 0.055 s
% 7.77/2.35 % (24507)Instructions burned: 182 (million)
% 7.77/2.35 % (24507)------------------------------
% 7.77/2.35 % (24507)------------------------------
% 7.77/2.36 % (24511)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_24154 for (2991ds/216Mi)
% 7.77/2.36 % (24508)Instruction limit reached!
% 7.77/2.36 % (24508)------------------------------
% 7.77/2.36 % (24508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.36 % (24508)Termination reason: Unknown
% 7.77/2.36 % (24508)Termination phase: Saturation
% 7.77/2.36
% 7.77/2.36 % (24508)Memory used [KB]: 6908
% 7.77/2.36 % (24508)Time elapsed: 0.058 s
% 7.77/2.36 % (24508)Instructions burned: 182 (million)
% 7.77/2.36 % (24508)------------------------------
% 7.77/2.36 % (24508)------------------------------
% 7.77/2.36 % (24512)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_24154 for (2991ds/114Mi)
% 7.77/2.36 % (24513)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_24154 for (2991ds/922Mi)
% 7.77/2.37 % (24514)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_24154 for (2991ds/182Mi)
% 7.77/2.38 % (24505)Instruction limit reached!
% 7.77/2.38 % (24505)------------------------------
% 7.77/2.38 % (24505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.38 % (24505)Termination reason: Unknown
% 7.77/2.38 % (24505)Termination phase: Saturation
% 7.77/2.38
% 7.77/2.38 % (24505)Memory used [KB]: 7164
% 7.77/2.38 % (24505)Time elapsed: 0.119 s
% 7.77/2.38 % (24505)Instructions burned: 299 (million)
% 7.77/2.38 % (24505)------------------------------
% 7.77/2.38 % (24505)------------------------------
% 7.77/2.39 % (24515)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_24154 for (2991ds/164Mi)
% 7.77/2.39 % (24512)Instruction limit reached!
% 7.77/2.39 % (24512)------------------------------
% 7.77/2.39 % (24512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.39 % (24512)Termination reason: Unknown
% 7.77/2.39 % (24512)Termination phase: Saturation
% 7.77/2.39
% 7.77/2.39 % (24512)Memory used [KB]: 6652
% 7.77/2.39 % (24512)Time elapsed: 0.035 s
% 7.77/2.39 % (24512)Instructions burned: 116 (million)
% 7.77/2.39 % (24512)------------------------------
% 7.77/2.39 % (24512)------------------------------
% 8.40/2.40 % (24516)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_24154 for (2991ds/50Mi)
% 8.40/2.41 % (24503)Instruction limit reached!
% 8.40/2.41 % (24503)------------------------------
% 8.40/2.41 % (24503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.40/2.41 % (24503)Termination reason: Unknown
% 8.40/2.41 % (24503)Termination phase: Saturation
% 8.40/2.41
% 8.40/2.41 % (24503)Memory used [KB]: 7675
% 8.40/2.41 % (24503)Time elapsed: 0.167 s
% 8.40/2.41 % (24503)Instructions burned: 458 (million)
% 8.40/2.41 % (24503)------------------------------
% 8.40/2.41 % (24503)------------------------------
% 8.40/2.42 % (24516)Instruction limit reached!
% 8.40/2.42 % (24516)------------------------------
% 8.40/2.42 % (24516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.40/2.42 % (24516)Termination reason: Unknown
% 8.40/2.42 % (24516)Termination phase: Property scanning
% 8.40/2.42
% 8.40/2.42 % (24516)Memory used [KB]: 2046
% 8.40/2.42 % (24516)Time elapsed: 0.014 s
% 8.40/2.42 % (24516)Instructions burned: 50 (million)
% 8.40/2.42 % (24516)------------------------------
% 8.40/2.42 % (24516)------------------------------
% 8.40/2.42 % (24514)Instruction limit reached!
% 8.40/2.42 % (24514)------------------------------
% 8.40/2.42 % (24514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.40/2.42 % (24514)Termination reason: Unknown
% 8.40/2.42 % (24514)Termination phase: Saturation
% 8.40/2.42
% 8.40/2.42 % (24514)Memory used [KB]: 6780
% 8.40/2.42 % (24514)Time elapsed: 0.052 s
% 8.40/2.42 % (24514)Instructions burned: 182 (million)
% 8.40/2.42 % (24514)------------------------------
% 8.40/2.42 % (24514)------------------------------
% 8.40/2.42 % (24511)Instruction limit reached!
% 8.40/2.42 % (24511)------------------------------
% 8.40/2.42 % (24511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.40/2.42 % (24511)Termination reason: Unknown
% 8.40/2.42 % (24511)Termination phase: Saturation
% 8.40/2.42
% 8.40/2.42 % (24511)Memory used [KB]: 7291
% 8.40/2.42 % (24511)Time elapsed: 0.064 s
% 8.40/2.42 % (24511)Instructions burned: 218 (million)
% 8.40/2.42 % (24511)------------------------------
% 8.40/2.42 % (24511)------------------------------
% 8.40/2.42 % (24517)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_24154 for (2991ds/368Mi)
% 8.40/2.43 % (24518)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_24154 for (2991ds/1021Mi)
% 8.40/2.43 % (24519)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_24154 for (2991ds/267Mi)
% 8.40/2.43 % (24520)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_24154 for (2991ds/204Mi)
% 8.40/2.44 % (24515)Instruction limit reached!
% 8.40/2.44 % (24515)------------------------------
% 8.40/2.44 % (24515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.40/2.44 % (24515)Termination reason: Unknown
% 8.40/2.44 % (24515)Termination phase: Saturation
% 8.40/2.44
% 8.40/2.44 % (24515)Memory used [KB]: 2302
% 8.40/2.44 % (24515)Time elapsed: 0.052 s
% 8.40/2.44 % (24515)Instructions burned: 164 (million)
% 8.40/2.44 % (24515)------------------------------
% 8.40/2.44 % (24515)------------------------------
% 8.40/2.45 % (24521)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_24154 for (2991ds/26Mi)
% 8.40/2.46 % (24521)Instruction limit reached!
% 8.40/2.46 % (24521)------------------------------
% 8.40/2.46 % (24521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.40/2.46 % (24521)Termination reason: Unknown
% 8.40/2.46 % (24521)Termination phase: shuffling
% 8.40/2.46
% 8.40/2.46 % (24521)Memory used [KB]: 1791
% 8.40/2.46 % (24521)Time elapsed: 0.010 s
% 8.40/2.46 % (24521)Instructions burned: 28 (million)
% 8.40/2.46 % (24521)------------------------------
% 8.40/2.46 % (24521)------------------------------
% 8.40/2.47 % (24522)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_24154 for (2990ds/53Mi)
% 8.40/2.48 % (24522)Instruction limit reached!
% 8.40/2.48 % (24522)------------------------------
% 8.40/2.48 % (24522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.40/2.48 % (24522)Termination reason: Unknown
% 8.40/2.48 % (24522)Termination phase: Property scanning
% 8.40/2.48
% 8.40/2.48 % (24522)Memory used [KB]: 2046
% 8.40/2.48 % (24522)Time elapsed: 0.017 s
% 8.40/2.48 % (24522)Instructions burned: 54 (million)
% 8.40/2.48 % (24522)------------------------------
% 8.40/2.48 % (24522)------------------------------
% 8.40/2.49 % (24520)Instruction limit reached!
% 8.40/2.49 % (24520)------------------------------
% 8.40/2.49 % (24520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.40/2.49 % (24520)Termination reason: Unknown
% 8.40/2.49 % (24520)Termination phase: Saturation
% 8.40/2.49
% 8.40/2.49 % (24520)Memory used [KB]: 6780
% 8.40/2.49 % (24520)Time elapsed: 0.064 s
% 8.40/2.49 % (24520)Instructions burned: 204 (million)
% 8.40/2.49 % (24520)------------------------------
% 8.40/2.49 % (24520)------------------------------
% 8.40/2.49 % (24523)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_24154 for (2990ds/4436Mi)
% 8.90/2.50 % (24524)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_24154 for (2990ds/1539Mi)
% 8.90/2.51 % (24519)Instruction limit reached!
% 8.90/2.51 % (24519)------------------------------
% 8.90/2.51 % (24519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.51 % (24519)Termination reason: Unknown
% 8.90/2.51 % (24519)Termination phase: Saturation
% 8.90/2.51
% 8.90/2.51 % (24519)Memory used [KB]: 7291
% 8.90/2.51 % (24519)Time elapsed: 0.086 s
% 8.90/2.51 % (24519)Instructions burned: 269 (million)
% 8.90/2.51 % (24519)------------------------------
% 8.90/2.51 % (24519)------------------------------
% 8.90/2.52 % (24525)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_24154 for (2990ds/408Mi)
% 8.90/2.52 % (24517)Instruction limit reached!
% 8.90/2.52 % (24517)------------------------------
% 8.90/2.52 % (24517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.52 % (24517)Termination reason: Unknown
% 8.90/2.52 % (24517)Termination phase: Saturation
% 8.90/2.52
% 8.90/2.52 % (24517)Memory used [KB]: 7675
% 8.90/2.52 % (24517)Time elapsed: 0.106 s
% 8.90/2.52 % (24517)Instructions burned: 368 (million)
% 8.90/2.52 % (24517)------------------------------
% 8.90/2.52 % (24517)------------------------------
% 8.90/2.53 % (24526)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_24154 for (2990ds/5205Mi)
% 9.11/2.60 % (24506)Instruction limit reached!
% 9.11/2.60 % (24506)------------------------------
% 9.11/2.60 % (24506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.60 % (24506)Termination reason: Unknown
% 9.11/2.60 % (24506)Termination phase: Saturation
% 9.11/2.60
% 9.11/2.60 % (24506)Memory used [KB]: 8187
% 9.11/2.60 % (24506)Time elapsed: 0.302 s
% 9.11/2.60 % (24506)Instructions burned: 987 (million)
% 9.11/2.60 % (24506)------------------------------
% 9.11/2.60 % (24506)------------------------------
% 9.11/2.61 % (24527)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_24154 for (2989ds/1913Mi)
% 9.11/2.65 % (24525)Instruction limit reached!
% 9.11/2.65 % (24525)------------------------------
% 9.11/2.65 % (24525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.65 % (24525)Termination reason: Unknown
% 9.11/2.65 % (24525)Termination phase: Saturation
% 9.11/2.65
% 9.11/2.65 % (24525)Memory used [KB]: 7675
% 9.11/2.65 % (24525)Time elapsed: 0.125 s
% 9.11/2.65 % (24525)Instructions burned: 408 (million)
% 9.11/2.65 % (24525)------------------------------
% 9.11/2.65 % (24525)------------------------------
% 9.11/2.66 % (24528)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_24154 for (2989ds/4350Mi)
% 9.11/2.66 % (24513)Instruction limit reached!
% 9.11/2.66 % (24513)------------------------------
% 9.11/2.66 % (24513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.66 % (24513)Termination reason: Unknown
% 9.11/2.66 % (24513)Termination phase: Saturation
% 9.11/2.66
% 9.11/2.66 % (24513)Memory used [KB]: 8187
% 9.11/2.66 % (24513)Time elapsed: 0.294 s
% 9.11/2.66 % (24513)Instructions burned: 923 (million)
% 9.11/2.66 % (24513)------------------------------
% 9.11/2.66 % (24513)------------------------------
% 9.11/2.67 % (24529)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_24154 for (2988ds/68Mi)
% 9.11/2.69 % (24529)Instruction limit reached!
% 9.11/2.69 % (24529)------------------------------
% 9.11/2.69 % (24529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.69 % (24529)Termination reason: Unknown
% 9.11/2.69 % (24529)Termination phase: Property scanning
% 9.11/2.69
% 9.11/2.69 % (24529)Memory used [KB]: 1918
% 9.11/2.69 % (24529)Time elapsed: 0.022 s
% 9.11/2.69 % (24529)Instructions burned: 69 (million)
% 9.11/2.69 % (24529)------------------------------
% 9.11/2.69 % (24529)------------------------------
% 9.89/2.70 % (24530)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_24154 for (2988ds/358Mi)
% 9.89/2.75 % (24518)Instruction limit reached!
% 9.89/2.75 % (24518)------------------------------
% 9.89/2.75 % (24518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.89/2.75 % (24518)Termination reason: Unknown
% 9.89/2.75 % (24518)Termination phase: Saturation
% 9.89/2.75
% 9.89/2.75 % (24518)Memory used [KB]: 8571
% 9.89/2.75 % (24518)Time elapsed: 0.322 s
% 9.89/2.75 % (24518)Instructions burned: 1023 (million)
% 9.89/2.75 % (24518)------------------------------
% 9.89/2.75 % (24518)------------------------------
% 9.89/2.76 % (24531)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_24154 for (2988ds/31Mi)
% 9.89/2.77 % (24531)Instruction limit reached!
% 9.89/2.77 % (24531)------------------------------
% 9.89/2.77 % (24531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.89/2.77 % (24531)Termination reason: Unknown
% 9.89/2.77 % (24531)Termination phase: Preprocessing 1
% 9.89/2.77
% 9.89/2.77 % (24531)Memory used [KB]: 1535
% 9.89/2.77 % (24531)Time elapsed: 0.011 s
% 9.89/2.77 % (24531)Instructions burned: 33 (million)
% 9.89/2.77 % (24531)------------------------------
% 9.89/2.77 % (24531)------------------------------
% 9.89/2.78 % (24532)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_24154 for (2987ds/279Mi)
% 10.24/2.80 % (24532)Refutation not found, incomplete strategy
% 10.24/2.80 % (24532)------------------------------
% 10.24/2.80 % (24532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.24/2.80 % (24532)Termination reason: Refutation not found, incomplete strategy
% 10.24/2.80
% 10.24/2.80
% 10.24/2.80 % (24532)Memory used [KB]: 6780
% 10.24/2.80 % (24532)Time elapsed: 0.028 s
% 10.24/2.80 % (24532)Instructions burned: 96 (million)
% 10.24/2.80 % (24532)------------------------------
% 10.24/2.80 % (24532)------------------------------
% 10.24/2.81 % (24530)Instruction limit reached!
% 10.24/2.81 % (24530)------------------------------
% 10.24/2.81 % (24530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.24/2.81 % (24530)Termination reason: Unknown
% 10.24/2.81 % (24530)Termination phase: Saturation
% 10.24/2.81
% 10.24/2.81 % (24530)Memory used [KB]: 7164
% 10.24/2.81 % (24530)Time elapsed: 0.115 s
% 10.24/2.81 % (24530)Instructions burned: 358 (million)
% 10.24/2.81 % (24530)------------------------------
% 10.24/2.81 % (24530)------------------------------
% 10.24/2.81 % (24533)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_24154 for (2987ds/258Mi)
% 10.24/2.82 % (24534)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_24154 for (2987ds/26Mi)
% 10.24/2.83 % (24534)Instruction limit reached!
% 10.24/2.83 % (24534)------------------------------
% 10.24/2.83 % (24534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.24/2.83 % (24534)Termination reason: Unknown
% 10.24/2.83 % (24534)Termination phase: shuffling
% 10.24/2.83
% 10.24/2.83 % (24534)Memory used [KB]: 1791
% 10.24/2.83 % (24534)Time elapsed: 0.008 s
% 10.24/2.83 % (24534)Instructions burned: 26 (million)
% 10.24/2.83 % (24534)------------------------------
% 10.24/2.83 % (24534)------------------------------
% 10.24/2.84 % (24535)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_24154 for (2987ds/995Mi)
% 10.24/2.89 % (24533)Instruction limit reached!
% 10.24/2.89 % (24533)------------------------------
% 10.24/2.89 % (24533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.24/2.89 % (24533)Termination reason: Unknown
% 10.24/2.89 % (24533)Termination phase: Saturation
% 10.24/2.89
% 10.24/2.89 % (24533)Memory used [KB]: 7291
% 10.24/2.89 % (24533)Time elapsed: 0.082 s
% 10.24/2.89 % (24533)Instructions burned: 260 (million)
% 10.24/2.89 % (24533)------------------------------
% 10.24/2.89 % (24533)------------------------------
% 10.51/2.90 % (24536)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_24154 for (2986ds/373Mi)
% 10.51/2.99 % (24524)Instruction limit reached!
% 10.51/2.99 % (24524)------------------------------
% 10.51/2.99 % (24524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.51/2.99 % (24524)Termination reason: Unknown
% 10.51/2.99 % (24524)Termination phase: Saturation
% 10.51/2.99
% 10.51/2.99 % (24524)Memory used [KB]: 9083
% 10.51/2.99 % (24524)Time elapsed: 0.491 s
% 10.51/2.99 % (24524)Instructions burned: 1539 (million)
% 10.51/2.99 % (24524)------------------------------
% 10.51/2.99 % (24524)------------------------------
% 10.51/3.00 % (24537)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_24154 for (2985ds/253Mi)
% 13.13/3.02 % (24536)Instruction limit reached!
% 13.13/3.02 % (24536)------------------------------
% 13.13/3.02 % (24536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.13/3.02 % (24536)Termination reason: Unknown
% 13.13/3.02 % (24536)Termination phase: Saturation
% 13.13/3.02
% 13.13/3.02 % (24536)Memory used [KB]: 7291
% 13.13/3.02 % (24536)Time elapsed: 0.122 s
% 13.13/3.02 % (24536)Instructions burned: 374 (million)
% 13.13/3.02 % (24536)------------------------------
% 13.13/3.02 % (24536)------------------------------
% 13.13/3.03 % (24538)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_24154 for (2985ds/832Mi)
% 13.13/3.07 % (24537)Instruction limit reached!
% 13.13/3.07 % (24537)------------------------------
% 13.13/3.07 % (24537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.13/3.07 % (24537)Termination reason: Unknown
% 13.13/3.07 % (24537)Termination phase: Saturation
% 13.13/3.07
% 13.13/3.07 % (24537)Memory used [KB]: 7291
% 13.13/3.07 % (24537)Time elapsed: 0.073 s
% 13.13/3.07 % (24537)Instructions burned: 255 (million)
% 13.13/3.07 % (24537)------------------------------
% 13.13/3.07 % (24537)------------------------------
% 13.13/3.08 % (24539)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_24154 for (2984ds/668Mi)
% 13.73/3.14 % (24535)Instruction limit reached!
% 13.73/3.14 % (24535)------------------------------
% 13.73/3.14 % (24535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.73/3.14 % (24535)Termination reason: Unknown
% 13.73/3.14 % (24535)Termination phase: Saturation
% 13.73/3.14
% 13.73/3.14 % (24535)Memory used [KB]: 9083
% 13.73/3.14 % (24535)Time elapsed: 0.307 s
% 13.73/3.14 % (24535)Instructions burned: 997 (million)
% 13.73/3.14 % (24535)------------------------------
% 13.73/3.14 % (24535)------------------------------
% 13.73/3.15 % (24540)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_24154 for (2984ds/40Mi)
% 13.73/3.16 % (24540)Instruction limit reached!
% 13.73/3.16 % (24540)------------------------------
% 13.73/3.16 % (24540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.73/3.16 % (24540)Termination reason: Unknown
% 13.73/3.16 % (24540)Termination phase: Property scanning
% 13.73/3.16
% 13.73/3.16 % (24540)Memory used [KB]: 2046
% 13.73/3.16 % (24540)Time elapsed: 0.013 s
% 13.73/3.16 % (24540)Instructions burned: 41 (million)
% 13.73/3.16 % (24540)------------------------------
% 13.73/3.16 % (24540)------------------------------
% 13.73/3.17 % (24541)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_24154 for (2983ds/294Mi)
% 13.73/3.20 % (24541)Refutation not found, incomplete strategy
% 13.73/3.20 % (24541)------------------------------
% 13.73/3.20 % (24541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.73/3.20 % (24541)Termination reason: Refutation not found, incomplete strategy
% 13.73/3.20
% 13.73/3.20
% 13.73/3.20 % (24541)Memory used [KB]: 6652
% 13.73/3.20 % (24541)Time elapsed: 0.022 s
% 13.73/3.20 % (24541)Instructions burned: 79 (million)
% 13.73/3.20 % (24541)------------------------------
% 13.73/3.20 % (24541)------------------------------
% 14.09/3.20 % (24527)Instruction limit reached!
% 14.09/3.20 % (24527)------------------------------
% 14.09/3.20 % (24527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.09/3.20 % (24527)Termination reason: Unknown
% 14.09/3.20 % (24527)Termination phase: Saturation
% 14.09/3.20
% 14.09/3.20 % (24527)Memory used [KB]: 3454
% 14.09/3.20 % (24527)Time elapsed: 0.596 s
% 14.09/3.20 % (24527)Instructions burned: 1913 (million)
% 14.09/3.20 % (24527)------------------------------
% 14.09/3.20 % (24527)------------------------------
% 14.09/3.21 % (24542)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_24154 for (2983ds/187Mi)
% 14.09/3.22 % (24543)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_24154 for (2983ds/371Mi)
% 14.09/3.26 % (24542)Instruction limit reached!
% 14.09/3.26 % (24542)------------------------------
% 14.09/3.26 % (24542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.09/3.26 % (24542)Termination reason: Unknown
% 14.09/3.26 % (24542)Termination phase: Saturation
% 14.09/3.26
% 14.09/3.26 % (24542)Memory used [KB]: 7036
% 14.09/3.26 % (24542)Time elapsed: 0.054 s
% 14.09/3.26 % (24542)Instructions burned: 187 (million)
% 14.09/3.26 % (24542)------------------------------
% 14.09/3.26 % (24542)------------------------------
% 14.09/3.27 % (24544)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_24154 for (2982ds/1827Mi)
% 14.09/3.29 % (24539)Instruction limit reached!
% 14.09/3.29 % (24539)------------------------------
% 14.09/3.29 % (24539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.09/3.29 % (24539)Termination reason: Unknown
% 14.09/3.29 % (24539)Termination phase: Saturation
% 14.09/3.29
% 14.09/3.29 % (24539)Memory used [KB]: 13944
% 14.09/3.29 % (24539)Time elapsed: 0.208 s
% 14.09/3.29 % (24539)Instructions burned: 670 (million)
% 14.09/3.29 % (24539)------------------------------
% 14.09/3.29 % (24539)------------------------------
% 14.69/3.30 % (24538)Instruction limit reached!
% 14.69/3.30 % (24538)------------------------------
% 14.69/3.30 % (24538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.69/3.30 % (24538)Termination reason: Unknown
% 14.69/3.30 % (24538)Termination phase: Saturation
% 14.69/3.30
% 14.69/3.30 % (24538)Memory used [KB]: 8187
% 14.69/3.30 % (24538)Time elapsed: 0.265 s
% 14.69/3.30 % (24538)Instructions burned: 832 (million)
% 14.69/3.30 % (24538)------------------------------
% 14.69/3.30 % (24538)------------------------------
% 14.69/3.30 % (24545)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_24154 for (2982ds/70Mi)
% 14.69/3.31 % (24546)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_24154 for (2982ds/316Mi)
% 14.69/3.32 % (24545)Instruction limit reached!
% 14.69/3.32 % (24545)------------------------------
% 14.69/3.32 % (24545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.69/3.32 % (24545)Termination reason: Unknown
% 14.69/3.32 % (24545)Termination phase: Property scanning
% 14.69/3.32
% 14.69/3.32 % (24545)Memory used [KB]: 2046
% 14.69/3.32 % (24545)Time elapsed: 0.020 s
% 14.69/3.32 % (24545)Instructions burned: 72 (million)
% 14.69/3.32 % (24545)------------------------------
% 14.69/3.32 % (24545)------------------------------
% 14.69/3.33 % (24547)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_24154 for (2982ds/932Mi)
% 14.69/3.35 % (24546)Refutation not found, incomplete strategy
% 14.69/3.35 % (24546)------------------------------
% 14.69/3.35 % (24546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.69/3.35 % (24546)Termination reason: Refutation not found, incomplete strategy
% 14.69/3.35
% 14.69/3.35
% 14.69/3.35 % (24546)Memory used [KB]: 6908
% 14.69/3.35 % (24546)Time elapsed: 0.039 s
% 14.69/3.35 % (24546)Instructions burned: 137 (million)
% 14.69/3.35 % (24546)------------------------------
% 14.69/3.35 % (24546)------------------------------
% 14.69/3.36 % (24548)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_24154 for (2982ds/4714Mi)
% 14.69/3.39 % (24548)Refutation not found, incomplete strategy
% 14.69/3.39 % (24548)------------------------------
% 14.69/3.39 % (24548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.69/3.39 % (24548)Termination reason: Refutation not found, incomplete strategy
% 14.69/3.39
% 14.69/3.39
% 14.69/3.39 % (24548)Memory used [KB]: 7036
% 14.69/3.39 % (24548)Time elapsed: 0.035 s
% 14.69/3.39 % (24548)Instructions burned: 125 (million)
% 14.69/3.39 % (24548)------------------------------
% 14.69/3.39 % (24548)------------------------------
% 14.69/3.39 % (24543)Instruction limit reached!
% 14.69/3.39 % (24543)------------------------------
% 14.69/3.39 % (24543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.69/3.39 % (24543)Termination reason: Unknown
% 14.69/3.39 % (24543)Termination phase: Saturation
% 14.69/3.39
% 14.69/3.39 % (24543)Memory used [KB]: 7164
% 14.69/3.39 % (24543)Time elapsed: 0.172 s
% 14.69/3.39 % (24543)Instructions burned: 373 (million)
% 14.69/3.39 % (24543)------------------------------
% 14.69/3.39 % (24543)------------------------------
% 15.57/3.40 % (24549)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_24154 for (2981ds/8250Mi)
% 15.57/3.40 % (24550)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_24154 for (2981ds/770Mi)
% 16.18/3.61 % (24547)Instruction limit reached!
% 16.18/3.61 % (24547)------------------------------
% 16.18/3.61 % (24547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.18/3.61 % (24547)Termination reason: Unknown
% 16.18/3.61 % (24547)Termination phase: Saturation
% 16.18/3.61
% 16.18/3.61 % (24547)Memory used [KB]: 8699
% 16.18/3.61 % (24547)Time elapsed: 0.285 s
% 16.18/3.61 % (24547)Instructions burned: 933 (million)
% 16.18/3.61 % (24547)------------------------------
% 16.18/3.61 % (24547)------------------------------
% 16.18/3.62 % (24551)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_24154 for (2979ds/794Mi)
% 16.18/3.66 % (24550)Instruction limit reached!
% 16.18/3.66 % (24550)------------------------------
% 16.18/3.66 % (24550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.18/3.66 % (24550)Termination reason: Unknown
% 16.18/3.66 % (24550)Termination phase: Saturation
% 16.18/3.66
% 16.18/3.66 % (24550)Memory used [KB]: 7803
% 16.18/3.66 % (24550)Time elapsed: 0.261 s
% 16.18/3.66 % (24550)Instructions burned: 770 (million)
% 16.18/3.66 % (24550)------------------------------
% 16.18/3.66 % (24550)------------------------------
% 16.18/3.67 % (24552)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_24154 for (2978ds/464Mi)
% 17.34/3.81 % (24552)Instruction limit reached!
% 17.34/3.81 % (24552)------------------------------
% 17.34/3.81 % (24552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.34/3.81 % (24552)Termination reason: Unknown
% 17.34/3.81 % (24552)Termination phase: Saturation
% 17.34/3.81
% 17.34/3.81 % (24552)Memory used [KB]: 6908
% 17.34/3.81 % (24552)Time elapsed: 0.139 s
% 17.34/3.81 % (24552)Instructions burned: 465 (million)
% 17.34/3.81 % (24552)------------------------------
% 17.34/3.81 % (24552)------------------------------
% 17.34/3.82 % (24553)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_24154 for (2977ds/1376Mi)
% 17.34/3.86 % (24544)Instruction limit reached!
% 17.34/3.86 % (24544)------------------------------
% 17.34/3.86 % (24544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.34/3.86 % (24544)Termination reason: Unknown
% 17.34/3.86 % (24544)Termination phase: Saturation
% 17.34/3.86
% 17.34/3.86 % (24544)Memory used [KB]: 10618
% 17.34/3.86 % (24544)Time elapsed: 0.595 s
% 17.34/3.86 % (24544)Instructions burned: 1828 (million)
% 17.34/3.86 % (24544)------------------------------
% 17.34/3.86 % (24544)------------------------------
% 17.34/3.87 % (24551)Instruction limit reached!
% 17.34/3.87 % (24551)------------------------------
% 17.34/3.87 % (24551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.34/3.87 % (24551)Termination reason: Unknown
% 17.34/3.87 % (24551)Termination phase: Saturation
% 17.34/3.87
% 17.34/3.87 % (24551)Memory used [KB]: 5756
% 17.34/3.87 % (24551)Time elapsed: 0.249 s
% 17.34/3.87 % (24551)Instructions burned: 795 (million)
% 17.34/3.87 % (24551)------------------------------
% 17.34/3.87 % (24551)------------------------------
% 17.34/3.87 % (24554)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_24154 for (2976ds/906Mi)
% 17.34/3.88 % (24555)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_24154 for (2976ds/434Mi)
% 18.66/3.92 % (24523)Instruction limit reached!
% 18.66/3.92 % (24523)------------------------------
% 18.66/3.92 % (24523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.66/3.92 % (24523)Termination reason: Unknown
% 18.66/3.92 % (24523)Termination phase: Saturation
% 18.66/3.92
% 18.66/3.92 % (24523)Memory used [KB]: 14711
% 18.66/3.92 % (24523)Time elapsed: 1.426 s
% 18.66/3.92 % (24523)Instructions burned: 4437 (million)
% 18.66/3.92 % (24523)------------------------------
% 18.66/3.92 % (24523)------------------------------
% 18.66/3.92 % (24528)Instruction limit reached!
% 18.66/3.92 % (24528)------------------------------
% 18.66/3.92 % (24528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.66/3.92 % (24528)Termination reason: Unknown
% 18.66/3.92 % (24528)Termination phase: Saturation
% 18.66/3.92
% 18.66/3.92 % (24528)Memory used [KB]: 11769
% 18.66/3.92 % (24528)Time elapsed: 1.266 s
% 18.66/3.92 % (24528)Instructions burned: 4352 (million)
% 18.66/3.92 % (24528)------------------------------
% 18.66/3.92 % (24528)------------------------------
% 18.66/3.93 % (24556)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_24154 for (2976ds/865Mi)
% 18.66/3.93 % (24557)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_24154 for (2976ds/593Mi)
% 18.66/4.00 % (24555)Instruction limit reached!
% 18.66/4.00 % (24555)------------------------------
% 18.66/4.00 % (24555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.66/4.00 % (24555)Termination reason: Unknown
% 18.66/4.00 % (24555)Termination phase: Saturation
% 18.66/4.00
% 18.66/4.00 % (24555)Memory used [KB]: 7675
% 18.66/4.00 % (24555)Time elapsed: 0.124 s
% 18.66/4.00 % (24555)Instructions burned: 435 (million)
% 18.66/4.00 % (24555)------------------------------
% 18.66/4.00 % (24555)------------------------------
% 20.07/4.01 % (24558)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_24154 for (2975ds/443Mi)
% 20.67/4.12 % (24557)Instruction limit reached!
% 20.67/4.12 % (24557)------------------------------
% 20.67/4.12 % (24557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.67/4.12 % (24557)Termination reason: Unknown
% 20.67/4.12 % (24557)Termination phase: Saturation
% 20.67/4.12
% 20.67/4.12 % (24557)Memory used [KB]: 8315
% 20.67/4.12 % (24557)Time elapsed: 0.188 s
% 20.67/4.12 % (24557)Instructions burned: 595 (million)
% 20.67/4.12 % (24557)------------------------------
% 20.67/4.12 % (24557)------------------------------
% 20.67/4.13 % (24559)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_24154 for (2974ds/594Mi)
% 20.67/4.15 % (24558)Instruction limit reached!
% 20.67/4.15 % (24558)------------------------------
% 20.67/4.15 % (24558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.67/4.15 % (24558)Termination reason: Unknown
% 20.67/4.15 % (24558)Termination phase: Saturation
% 20.67/4.15
% 20.67/4.15 % (24558)Memory used [KB]: 7547
% 20.67/4.15 % (24558)Time elapsed: 0.162 s
% 20.67/4.15 % (24558)Instructions burned: 443 (million)
% 20.67/4.15 % (24558)------------------------------
% 20.67/4.15 % (24558)------------------------------
% 20.67/4.16 % (24560)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_24154 for (2973ds/327Mi)
% 20.67/4.16 % (24526)Instruction limit reached!
% 20.67/4.16 % (24526)------------------------------
% 20.67/4.16 % (24526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.67/4.16 % (24526)Termination reason: Unknown
% 20.67/4.16 % (24526)Termination phase: Saturation
% 20.67/4.16
% 20.67/4.16 % (24526)Memory used [KB]: 16758
% 20.67/4.16 % (24526)Time elapsed: 1.632 s
% 20.67/4.16 % (24526)Instructions burned: 5205 (million)
% 20.67/4.16 % (24526)------------------------------
% 20.67/4.16 % (24526)------------------------------
% 20.67/4.18 % (24561)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_24154 for (2973ds/5411Mi)
% 20.67/4.18 % (24554)Instruction limit reached!
% 20.67/4.18 % (24554)------------------------------
% 20.67/4.18 % (24554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.67/4.18 % (24554)Termination reason: Unknown
% 20.67/4.18 % (24554)Termination phase: Saturation
% 20.67/4.18
% 20.67/4.18 % (24554)Memory used [KB]: 11001
% 20.67/4.18 % (24554)Time elapsed: 0.309 s
% 20.67/4.18 % (24554)Instructions burned: 906 (million)
% 20.67/4.18 % (24554)------------------------------
% 20.67/4.18 % (24554)------------------------------
% 20.67/4.19 % (24562)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_24154 for (2973ds/1762Mi)
% 21.23/4.20 % (24556)Instruction limit reached!
% 21.23/4.20 % (24556)------------------------------
% 21.23/4.20 % (24556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.23/4.20 % (24556)Termination reason: Unknown
% 21.23/4.20 % (24556)Termination phase: Saturation
% 21.23/4.20
% 21.23/4.20 % (24556)Memory used [KB]: 8571
% 21.23/4.20 % (24556)Time elapsed: 0.276 s
% 21.23/4.20 % (24556)Instructions burned: 865 (million)
% 21.23/4.20 % (24556)------------------------------
% 21.23/4.20 % (24556)------------------------------
% 21.23/4.21 % (24563)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_24154 for (2973ds/96Mi)
% 21.23/4.24 % (24563)Instruction limit reached!
% 21.23/4.24 % (24563)------------------------------
% 21.23/4.24 % (24563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.23/4.24 % (24563)Termination reason: Unknown
% 21.23/4.24 % (24563)Termination phase: Saturation
% 21.23/4.24
% 21.23/4.24 % (24563)Memory used [KB]: 6652
% 21.23/4.24 % (24563)Time elapsed: 0.028 s
% 21.23/4.24 % (24563)Instructions burned: 97 (million)
% 21.23/4.24 % (24563)------------------------------
% 21.23/4.24 % (24563)------------------------------
% 21.23/4.25 % (24564)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_24154 for (2973ds/503Mi)
% 21.23/4.27 % (24560)Instruction limit reached!
% 21.23/4.27 % (24560)------------------------------
% 21.23/4.27 % (24560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.23/4.27 % (24560)Termination reason: Unknown
% 21.23/4.27 % (24560)Termination phase: Saturation
% 21.23/4.27
% 21.23/4.27 % (24560)Memory used [KB]: 7547
% 21.23/4.27 % (24560)Time elapsed: 0.105 s
% 21.23/4.27 % (24560)Instructions burned: 329 (million)
% 21.23/4.27 % (24560)------------------------------
% 21.23/4.27 % (24560)------------------------------
% 21.23/4.27 % (24565)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_24154 for (2972ds/90Mi)
% 21.61/4.30 % (24553)Instruction limit reached!
% 21.61/4.30 % (24553)------------------------------
% 21.61/4.30 % (24553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.61/4.30 % (24553)Termination reason: Unknown
% 21.61/4.30 % (24553)Termination phase: Saturation
% 21.61/4.30
% 21.61/4.30 % (24553)Memory used [KB]: 12281
% 21.61/4.30 % (24553)Time elapsed: 0.477 s
% 21.61/4.30 % (24553)Instructions burned: 1376 (million)
% 21.61/4.30 % (24553)------------------------------
% 21.61/4.30 % (24553)------------------------------
% 21.61/4.30 % (24565)Instruction limit reached!
% 21.61/4.30 % (24565)------------------------------
% 21.61/4.30 % (24565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.61/4.30 % (24565)Termination reason: Unknown
% 21.61/4.30 % (24565)Termination phase: Saturation
% 21.61/4.30
% 21.61/4.30 % (24565)Memory used [KB]: 6524
% 21.61/4.30 % (24565)Time elapsed: 0.027 s
% 21.61/4.30 % (24565)Instructions burned: 91 (million)
% 21.61/4.30 % (24565)------------------------------
% 21.61/4.30 % (24565)------------------------------
% 21.61/4.31 % (24566)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_24154 for (2972ds/593Mi)
% 21.61/4.31 % (24567)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_24154 for (2972ds/1512Mi)
% 21.61/4.32 % (24559)Instruction limit reached!
% 21.61/4.32 % (24559)------------------------------
% 21.61/4.32 % (24559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.61/4.32 % (24559)Termination reason: Unknown
% 21.61/4.32 % (24559)Termination phase: Saturation
% 21.61/4.32
% 21.61/4.32 % (24559)Memory used [KB]: 7803
% 21.61/4.32 % (24559)Time elapsed: 0.189 s
% 21.61/4.32 % (24559)Instructions burned: 594 (million)
% 21.61/4.32 % (24559)------------------------------
% 21.61/4.32 % (24559)------------------------------
% 21.61/4.33 % (24568)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_24154 for (2972ds/569Mi)
% 21.61/4.39 % (24564)Instruction limit reached!
% 21.61/4.39 % (24564)------------------------------
% 21.61/4.39 % (24564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.61/4.39 % (24564)Termination reason: Unknown
% 21.61/4.39 % (24564)Termination phase: Saturation
% 21.61/4.39
% 21.61/4.39 % (24564)Memory used [KB]: 7675
% 21.61/4.39 % (24564)Time elapsed: 0.142 s
% 21.61/4.39 % (24564)Instructions burned: 503 (million)
% 21.61/4.39 % (24564)------------------------------
% 21.61/4.39 % (24564)------------------------------
% 22.10/4.40 % (24569)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_24154 for (2971ds/501Mi)
% 22.10/4.49 % (24566)Instruction limit reached!
% 22.10/4.49 % (24566)------------------------------
% 22.10/4.49 % (24566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.10/4.49 % (24566)Termination reason: Unknown
% 22.10/4.49 % (24566)Termination phase: Saturation
% 22.10/4.49
% 22.10/4.49 % (24566)Memory used [KB]: 7931
% 22.10/4.49 % (24566)Time elapsed: 0.182 s
% 22.10/4.49 % (24566)Instructions burned: 594 (million)
% 22.10/4.49 % (24566)------------------------------
% 22.10/4.49 % (24566)------------------------------
% 22.40/4.50 % (24568)Instruction limit reached!
% 22.40/4.50 % (24568)------------------------------
% 22.40/4.50 % (24568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.40/4.50 % (24568)Termination reason: Unknown
% 22.40/4.50 % (24568)Termination phase: Saturation
% 22.40/4.50
% 22.40/4.50 % (24568)Memory used [KB]: 7931
% 22.40/4.50 % (24568)Time elapsed: 0.173 s
% 22.40/4.50 % (24568)Instructions burned: 571 (million)
% 22.40/4.50 % (24568)------------------------------
% 22.40/4.50 % (24568)------------------------------
% 22.40/4.50 % (24570)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_24154 for (2970ds/562Mi)
% 22.40/4.51 % (24571)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_24154 for (2970ds/406Mi)
% 22.40/4.55 % (24569)Instruction limit reached!
% 22.40/4.55 % (24569)------------------------------
% 22.40/4.55 % (24569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.40/4.55 % (24569)Termination reason: Unknown
% 22.40/4.55 % (24569)Termination phase: Saturation
% 22.40/4.55
% 22.40/4.55 % (24569)Memory used [KB]: 8059
% 22.40/4.55 % (24569)Time elapsed: 0.154 s
% 22.40/4.55 % (24569)Instructions burned: 504 (million)
% 22.40/4.55 % (24569)------------------------------
% 22.40/4.55 % (24569)------------------------------
% 22.40/4.56 % (24572)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_24154 for (2969ds/582Mi)
% 22.84/4.64 % (24571)Instruction limit reached!
% 22.84/4.64 % (24571)------------------------------
% 22.84/4.64 % (24571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.84/4.64 % (24571)Termination reason: Unknown
% 22.84/4.64 % (24571)Termination phase: Saturation
% 22.84/4.64
% 22.84/4.64 % (24571)Memory used [KB]: 7547
% 22.84/4.64 % (24571)Time elapsed: 0.132 s
% 22.84/4.64 % (24571)Instructions burned: 408 (million)
% 22.84/4.64 % (24571)------------------------------
% 22.84/4.64 % (24571)------------------------------
% 22.84/4.65 % (24573)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_24154 for (2969ds/456Mi)
% 22.84/4.67 % (24570)Instruction limit reached!
% 22.84/4.67 % (24570)------------------------------
% 22.84/4.67 % (24570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.84/4.67 % (24570)Termination reason: Unknown
% 22.84/4.67 % (24570)Termination phase: Saturation
% 22.84/4.67
% 22.84/4.67 % (24570)Memory used [KB]: 7547
% 22.84/4.67 % (24570)Time elapsed: 0.176 s
% 22.84/4.67 % (24570)Instructions burned: 562 (million)
% 22.84/4.67 % (24570)------------------------------
% 22.84/4.67 % (24570)------------------------------
% 22.84/4.68 % (24562)Instruction limit reached!
% 22.84/4.68 % (24562)------------------------------
% 22.84/4.68 % (24562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.84/4.68 % (24562)Termination reason: Unknown
% 22.84/4.68 % (24562)Termination phase: Saturation
% 22.84/4.68
% 22.84/4.68 % (24562)Memory used [KB]: 8827
% 22.84/4.68 % (24562)Time elapsed: 0.492 s
% 22.84/4.68 % (24562)Instructions burned: 1762 (million)
% 22.84/4.68 % (24562)------------------------------
% 22.84/4.68 % (24562)------------------------------
% 22.84/4.68 % (24574)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_24154 for (2968ds/393Mi)
% 22.84/4.69 % (24575)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_24154 for (2968ds/1335Mi)
% 23.78/4.75 % (24572)Instruction limit reached!
% 23.78/4.75 % (24572)------------------------------
% 23.78/4.75 % (24572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.78/4.75 % (24572)Termination reason: Unknown
% 23.78/4.75 % (24572)Termination phase: Saturation
% 23.78/4.75
% 23.78/4.75 % (24572)Memory used [KB]: 7291
% 23.78/4.75 % (24572)Time elapsed: 0.186 s
% 23.78/4.75 % (24572)Instructions burned: 584 (million)
% 23.78/4.75 % (24572)------------------------------
% 23.78/4.75 % (24572)------------------------------
% 23.78/4.76 % (24576)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_24154 for (2968ds/3373Mi)
% 23.78/4.79 % (24573)Instruction limit reached!
% 23.78/4.79 % (24573)------------------------------
% 23.78/4.79 % (24573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.78/4.79 % (24573)Termination reason: Unknown
% 23.78/4.79 % (24573)Termination phase: Saturation
% 23.78/4.79
% 23.78/4.79 % (24573)Memory used [KB]: 7675
% 23.78/4.79 % (24573)Time elapsed: 0.142 s
% 23.78/4.79 % (24573)Instructions burned: 457 (million)
% 23.78/4.79 % (24573)------------------------------
% 23.78/4.79 % (24573)------------------------------
% 23.78/4.79 % (24567)Instruction limit reached!
% 23.78/4.79 % (24567)------------------------------
% 23.78/4.79 % (24567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.78/4.79 % (24567)Termination reason: Unknown
% 23.78/4.79 % (24567)Termination phase: Saturation
% 23.78/4.79
% 23.78/4.79 % (24567)Memory used [KB]: 8571
% 23.78/4.79 % (24567)Time elapsed: 0.482 s
% 23.78/4.79 % (24567)Instructions burned: 1514 (million)
% 23.78/4.79 % (24567)------------------------------
% 23.78/4.79 % (24567)------------------------------
% 23.78/4.80 % (24574)Instruction limit reached!
% 23.78/4.80 % (24574)------------------------------
% 23.78/4.80 % (24574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.78/4.80 % (24574)Termination reason: Unknown
% 23.78/4.80 % (24574)Termination phase: Saturation
% 23.78/4.80
% 23.78/4.80 % (24574)Memory used [KB]: 7419
% 23.78/4.80 % (24574)Time elapsed: 0.113 s
% 23.78/4.80 % (24574)Instructions burned: 394 (million)
% 23.78/4.80 % (24574)------------------------------
% 23.78/4.80 % (24574)------------------------------
% 24.84/4.80 % (24577)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_24154 for (2967ds/474Mi)
% 24.84/4.80 % (24578)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_24154 for (2967ds/157Mi)
% 24.84/4.80 % (24579)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_24154 for (2967ds/590Mi)
% 24.84/4.85 % (24578)Instruction limit reached!
% 24.84/4.85 % (24578)------------------------------
% 24.84/4.85 % (24578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.84/4.85 % (24578)Termination reason: Unknown
% 24.84/4.85 % (24578)Termination phase: Saturation
% 24.84/4.85
% 24.84/4.85 % (24578)Memory used [KB]: 6908
% 24.84/4.85 % (24578)Time elapsed: 0.045 s
% 24.84/4.85 % (24578)Instructions burned: 158 (million)
% 24.84/4.85 % (24578)------------------------------
% 24.84/4.85 % (24578)------------------------------
% 24.84/4.85 % (24580)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_24154 for (2967ds/104Mi)
% 24.84/4.89 % (24580)Instruction limit reached!
% 24.84/4.89 % (24580)------------------------------
% 24.84/4.89 % (24580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.84/4.89 % (24580)Termination reason: Unknown
% 24.84/4.89 % (24580)Termination phase: Saturation
% 24.84/4.89
% 24.84/4.89 % (24580)Memory used [KB]: 2430
% 24.84/4.89 % (24580)Time elapsed: 0.033 s
% 24.84/4.89 % (24580)Instructions burned: 105 (million)
% 24.84/4.89 % (24580)------------------------------
% 24.84/4.89 % (24580)------------------------------
% 24.84/4.90 % (24581)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_24154 for (2966ds/414Mi)
% 25.03/4.95 % (24577)Instruction limit reached!
% 25.03/4.95 % (24577)------------------------------
% 25.03/4.95 % (24577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.03/4.95 % (24577)Termination reason: Unknown
% 25.03/4.95 % (24577)Termination phase: Saturation
% 25.03/4.95
% 25.03/4.95 % (24577)Memory used [KB]: 7803
% 25.03/4.95 % (24577)Time elapsed: 0.150 s
% 25.03/4.95 % (24577)Instructions burned: 475 (million)
% 25.03/4.95 % (24577)------------------------------
% 25.03/4.95 % (24577)------------------------------
% 25.03/4.96 % (24582)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_24154 for (2966ds/715Mi)
% 25.03/4.98 % (24579)Instruction limit reached!
% 25.03/4.98 % (24579)------------------------------
% 25.03/4.98 % (24579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.03/4.98 % (24579)Termination reason: Unknown
% 25.03/4.98 % (24579)Termination phase: Saturation
% 25.03/4.98
% 25.03/4.98 % (24579)Memory used [KB]: 7675
% 25.03/4.98 % (24579)Time elapsed: 0.181 s
% 25.03/4.98 % (24579)Instructions burned: 592 (million)
% 25.03/4.98 % (24579)------------------------------
% 25.03/4.98 % (24579)------------------------------
% 25.03/4.99 % (24583)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_24154 for (2965ds/961Mi)
% 25.03/5.02 % (24581)Instruction limit reached!
% 25.03/5.02 % (24581)------------------------------
% 25.03/5.02 % (24581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.03/5.02 % (24581)Termination reason: Unknown
% 25.03/5.02 % (24581)Termination phase: Saturation
% 25.03/5.02
% 25.03/5.02 % (24581)Memory used [KB]: 7036
% 25.03/5.02 % (24581)Time elapsed: 0.125 s
% 25.03/5.02 % (24581)Instructions burned: 415 (million)
% 25.03/5.02 % (24581)------------------------------
% 25.03/5.02 % (24581)------------------------------
% 27.06/5.03 % (24584)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_24154 for (2965ds/1213Mi)
% 27.06/5.11 % (24575)Instruction limit reached!
% 27.06/5.11 % (24575)------------------------------
% 27.06/5.11 % (24575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.06/5.11 % (24575)Termination reason: Unknown
% 27.06/5.11 % (24575)Termination phase: Saturation
% 27.06/5.11
% 27.06/5.11 % (24575)Memory used [KB]: 8315
% 27.06/5.11 % (24575)Time elapsed: 0.421 s
% 27.06/5.11 % (24575)Instructions burned: 1336 (million)
% 27.06/5.11 % (24575)------------------------------
% 27.06/5.11 % (24575)------------------------------
% 27.06/5.12 % (24585)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_24154 for (2964ds/1979Mi)
% 27.79/5.18 % (24582)Instruction limit reached!
% 27.79/5.18 % (24582)------------------------------
% 27.79/5.18 % (24582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.79/5.18 % (24582)Termination reason: Unknown
% 27.79/5.18 % (24582)Termination phase: Saturation
% 27.79/5.18
% 27.79/5.18 % (24582)Memory used [KB]: 3965
% 27.79/5.18 % (24582)Time elapsed: 0.226 s
% 27.79/5.18 % (24582)Instructions burned: 718 (million)
% 27.79/5.18 % (24582)------------------------------
% 27.79/5.18 % (24582)------------------------------
% 27.79/5.19 % (24586)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_24154 for (2963ds/481Mi)
% 28.55/5.30 % (24583)Instruction limit reached!
% 28.55/5.30 % (24583)------------------------------
% 28.55/5.30 % (24583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.55/5.30 % (24583)Termination reason: Unknown
% 28.55/5.30 % (24583)Termination phase: Saturation
% 28.55/5.30
% 28.55/5.30 % (24583)Memory used [KB]: 7803
% 28.55/5.30 % (24583)Time elapsed: 0.310 s
% 28.55/5.30 % (24583)Instructions burned: 962 (million)
% 28.55/5.30 % (24583)------------------------------
% 28.55/5.30 % (24583)------------------------------
% 28.55/5.31 % (24587)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_24154 for (2962ds/783Mi)
% 28.55/5.34 % (24586)Instruction limit reached!
% 28.55/5.34 % (24586)------------------------------
% 28.55/5.34 % (24586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.55/5.34 % (24586)Termination reason: Unknown
% 28.55/5.34 % (24586)Termination phase: Saturation
% 28.55/5.34
% 28.55/5.34 % (24586)Memory used [KB]: 7419
% 28.55/5.34 % (24586)Time elapsed: 0.154 s
% 28.55/5.34 % (24586)Instructions burned: 484 (million)
% 28.55/5.34 % (24586)------------------------------
% 28.55/5.34 % (24586)------------------------------
% 28.55/5.35 % (24588)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_24154 for (2962ds/432Mi)
% 29.01/5.41 % (24584)Instruction limit reached!
% 29.01/5.41 % (24584)------------------------------
% 29.01/5.41 % (24584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.01/5.41 % (24584)Termination reason: Unknown
% 29.01/5.41 % (24584)Termination phase: Saturation
% 29.01/5.41
% 29.01/5.41 % (24584)Memory used [KB]: 8187
% 29.01/5.41 % (24584)Time elapsed: 0.376 s
% 29.01/5.41 % (24584)Instructions burned: 1214 (million)
% 29.01/5.41 % (24584)------------------------------
% 29.01/5.41 % (24584)------------------------------
% 29.01/5.42 % (24589)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_24154 for (2961ds/1670Mi)
% 29.01/5.49 % (24588)Instruction limit reached!
% 29.01/5.49 % (24588)------------------------------
% 29.01/5.49 % (24588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.01/5.49 % (24588)Termination reason: Unknown
% 29.01/5.49 % (24588)Termination phase: Saturation
% 29.01/5.49
% 29.01/5.49 % (24588)Memory used [KB]: 7291
% 29.01/5.49 % (24588)Time elapsed: 0.137 s
% 29.01/5.49 % (24588)Instructions burned: 434 (million)
% 29.01/5.49 % (24588)------------------------------
% 29.01/5.49 % (24588)------------------------------
% 29.86/5.50 % (24590)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_24154 for (2960ds/90Mi)
% 29.86/5.53 % (24590)Instruction limit reached!
% 29.86/5.53 % (24590)------------------------------
% 29.86/5.53 % (24590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.86/5.53 % (24590)Termination reason: Unknown
% 29.86/5.53 % (24590)Termination phase: Saturation
% 29.86/5.53
% 29.86/5.53 % (24590)Memory used [KB]: 6524
% 29.86/5.53 % (24590)Time elapsed: 0.027 s
% 29.86/5.53 % (24590)Instructions burned: 91 (million)
% 29.86/5.53 % (24590)------------------------------
% 29.86/5.53 % (24590)------------------------------
% 29.86/5.53 % (24591)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_24154 for (2960ds/346Mi)
% 29.86/5.56 % (24587)Instruction limit reached!
% 29.86/5.56 % (24587)------------------------------
% 29.86/5.56 % (24587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.86/5.56 % (24587)Termination reason: Unknown
% 29.86/5.56 % (24587)Termination phase: Saturation
% 29.86/5.56
% 29.86/5.56 % (24587)Memory used [KB]: 8315
% 29.86/5.56 % (24587)Time elapsed: 0.243 s
% 29.86/5.56 % (24587)Instructions burned: 785 (million)
% 29.86/5.56 % (24587)------------------------------
% 29.86/5.56 % (24587)------------------------------
% 29.86/5.57 % (24592)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_24154 for (2959ds/401Mi)
% 30.45/5.65 % (24591)Instruction limit reached!
% 30.45/5.65 % (24591)------------------------------
% 30.45/5.65 % (24591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.45/5.65 % (24591)Termination reason: Unknown
% 30.45/5.65 % (24591)Termination phase: Saturation
% 30.45/5.65
% 30.45/5.65 % (24591)Memory used [KB]: 7419
% 30.45/5.65 % (24591)Time elapsed: 0.112 s
% 30.45/5.65 % (24591)Instructions burned: 348 (million)
% 30.45/5.65 % (24591)------------------------------
% 30.45/5.65 % (24591)------------------------------
% 30.45/5.66 % (24593)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_24154 for (2959ds/6454Mi)
% 30.45/5.69 % (24592)Instruction limit reached!
% 30.45/5.69 % (24592)------------------------------
% 30.45/5.69 % (24592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.45/5.69 % (24592)Termination reason: Unknown
% 30.45/5.69 % (24592)Termination phase: Saturation
% 30.45/5.69
% 30.45/5.69 % (24592)Memory used [KB]: 7803
% 30.45/5.69 % (24592)Time elapsed: 0.124 s
% 30.45/5.69 % (24592)Instructions burned: 404 (million)
% 30.45/5.69 % (24592)------------------------------
% 30.45/5.69 % (24592)------------------------------
% 31.01/5.70 % (24594)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_24154 for (2958ds/283Mi)
% 31.01/5.74 % (24585)Instruction limit reached!
% 31.01/5.74 % (24585)------------------------------
% 31.01/5.74 % (24585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.01/5.74 % (24585)Termination reason: Unknown
% 31.01/5.74 % (24585)Termination phase: Saturation
% 31.01/5.74
% 31.01/5.74 % (24585)Memory used [KB]: 7419
% 31.01/5.74 % (24585)Time elapsed: 0.624 s
% 31.01/5.74 % (24585)Instructions burned: 1979 (million)
% 31.01/5.74 % (24585)------------------------------
% 31.01/5.74 % (24585)------------------------------
% 31.01/5.75 % (24595)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_24154 for (2958ds/865Mi)
% 31.01/5.79 % (24594)Instruction limit reached!
% 31.01/5.79 % (24594)------------------------------
% 31.01/5.79 % (24594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.01/5.79 % (24594)Termination reason: Unknown
% 31.01/5.79 % (24594)Termination phase: Saturation
% 31.01/5.79
% 31.01/5.79 % (24594)Memory used [KB]: 7419
% 31.01/5.79 % (24594)Time elapsed: 0.089 s
% 31.01/5.79 % (24594)Instructions burned: 285 (million)
% 31.01/5.79 % (24594)------------------------------
% 31.01/5.79 % (24594)------------------------------
% 31.01/5.79 % (24596)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_24154 for (2957ds/4528Mi)
% 32.04/5.81 % (24576)Instruction limit reached!
% 32.04/5.81 % (24576)------------------------------
% 32.04/5.81 % (24576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.04/5.81 % (24576)Termination reason: Unknown
% 32.04/5.81 % (24576)Termination phase: Saturation
% 32.04/5.81
% 32.04/5.81 % (24576)Memory used [KB]: 11641
% 32.04/5.81 % (24576)Time elapsed: 1.052 s
% 32.04/5.81 % (24576)Instructions burned: 3376 (million)
% 32.04/5.81 % (24576)------------------------------
% 32.04/5.81 % (24576)------------------------------
% 32.04/5.82 % (24597)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_24154 for (2957ds/1001Mi)
% 32.04/5.89 % (24561)Refutation not found, non-redundant clauses discarded% (24561)------------------------------
% 32.04/5.89 % (24561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.04/5.89 % (24561)Termination reason: Refutation not found, non-redundant clauses discarded
% 32.04/5.89
% 32.04/5.89 % (24561)Memory used [KB]: 12920
% 32.04/5.89 % (24561)Time elapsed: 1.716 s
% 32.04/5.89 % (24561)Instructions burned: 5407 (million)
% 32.04/5.89 % (24561)------------------------------
% 32.04/5.89 % (24561)------------------------------
% 32.26/5.90 % (24598)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_24154 for (2956ds/102Mi)
% 32.26/5.93 % (24598)Instruction limit reached!
% 32.26/5.93 % (24598)------------------------------
% 32.26/5.93 % (24598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.26/5.93 % (24598)Termination reason: Unknown
% 32.26/5.93 % (24598)Termination phase: Saturation
% 32.26/5.93
% 32.26/5.93 % (24598)Memory used [KB]: 6652
% 32.26/5.93 % (24598)Time elapsed: 0.029 s
% 32.26/5.93 % (24598)Instructions burned: 103 (million)
% 32.26/5.93 % (24598)------------------------------
% 32.26/5.93 % (24598)------------------------------
% 32.26/5.94 % (24589)Instruction limit reached!
% 32.26/5.94 % (24589)------------------------------
% 32.26/5.94 % (24589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.26/5.94 % (24589)Termination reason: Unknown
% 32.26/5.94 % (24589)Termination phase: Saturation
% 32.26/5.94
% 32.26/5.94 % (24589)Memory used [KB]: 9594
% 32.26/5.94 % (24589)Time elapsed: 0.521 s
% 32.26/5.94 % (24589)Instructions burned: 1672 (million)
% 32.26/5.94 % (24589)------------------------------
% 32.26/5.94 % (24589)------------------------------
% 32.26/5.94 % (24599)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_24154 for (2956ds/952Mi)
% 32.26/5.95 % (24600)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_24154 for (2956ds/578Mi)
% 34.22/6.03 % (24595)Instruction limit reached!
% 34.22/6.03 % (24595)------------------------------
% 34.22/6.03 % (24595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.22/6.03 % (24595)Termination reason: Unknown
% 34.22/6.03 % (24595)Termination phase: Saturation
% 34.22/6.03
% 34.22/6.03 % (24595)Memory used [KB]: 8571
% 34.22/6.03 % (24595)Time elapsed: 0.281 s
% 34.22/6.03 % (24595)Instructions burned: 866 (million)
% 34.22/6.03 % (24595)------------------------------
% 34.22/6.03 % (24595)------------------------------
% 34.22/6.04 % (24601)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_24154 for (2955ds/643Mi)
% 34.22/6.06 % (24549)Instruction limit reached!
% 34.22/6.06 % (24549)------------------------------
% 34.22/6.06 % (24549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.22/6.06 % (24549)Termination reason: Unknown
% 34.22/6.06 % (24549)Termination phase: Saturation
% 34.22/6.06
% 34.22/6.06 % (24549)Memory used [KB]: 17782
% 34.22/6.06 % (24549)Time elapsed: 2.656 s
% 34.22/6.06 % (24549)Instructions burned: 8252 (million)
% 34.22/6.06 % (24549)------------------------------
% 34.22/6.06 % (24549)------------------------------
% 34.22/6.07 % (24602)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_24154 for (2954ds/865Mi)
% 34.22/6.11 % (24597)Instruction limit reached!
% 34.22/6.11 % (24597)------------------------------
% 34.22/6.11 % (24597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.22/6.11 % (24597)Termination reason: Unknown
% 34.22/6.11 % (24597)Termination phase: Saturation
% 34.22/6.11
% 34.22/6.11 % (24597)Memory used [KB]: 8187
% 34.22/6.11 % (24597)Time elapsed: 0.296 s
% 34.22/6.11 % (24597)Instructions burned: 1001 (million)
% 34.22/6.11 % (24597)------------------------------
% 34.22/6.11 % (24597)------------------------------
% 34.22/6.12 % (24603)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_24154 for (2954ds/1174Mi)
% 34.78/6.12 % (24600)Instruction limit reached!
% 34.78/6.12 % (24600)------------------------------
% 34.78/6.12 % (24600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.78/6.12 % (24600)Termination reason: Unknown
% 34.78/6.12 % (24600)Termination phase: Saturation
% 34.78/6.12
% 34.78/6.12 % (24600)Memory used [KB]: 8059
% 34.78/6.12 % (24600)Time elapsed: 0.179 s
% 34.78/6.12 % (24600)Instructions burned: 578 (million)
% 34.78/6.12 % (24600)------------------------------
% 34.78/6.12 % (24600)------------------------------
% 34.78/6.13 % (24604)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_24154 for (2954ds/644Mi)
% 35.00/6.24 % (24599)Instruction limit reached!
% 35.00/6.24 % (24599)------------------------------
% 35.00/6.24 % (24599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.00/6.24 % (24599)Termination reason: Unknown
% 35.00/6.24 % (24599)Termination phase: Saturation
% 35.00/6.24
% 35.00/6.24 % (24599)Memory used [KB]: 8571
% 35.00/6.24 % (24599)Time elapsed: 0.302 s
% 35.00/6.24 % (24599)Instructions burned: 955 (million)
% 35.00/6.24 % (24599)------------------------------
% 35.00/6.24 % (24599)------------------------------
% 35.00/6.24 % (24601)Instruction limit reached!
% 35.00/6.24 % (24601)------------------------------
% 35.00/6.24 % (24601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.00/6.24 % (24601)Termination reason: Unknown
% 35.00/6.24 % (24601)Termination phase: Saturation
% 35.00/6.24
% 35.00/6.24 % (24601)Memory used [KB]: 8187
% 35.00/6.24 % (24601)Time elapsed: 0.201 s
% 35.00/6.24 % (24601)Instructions burned: 644 (million)
% 35.00/6.24 % (24601)------------------------------
% 35.00/6.24 % (24601)------------------------------
% 35.00/6.25 % (24605)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_24154 for (2953ds/1201Mi)
% 35.00/6.25 % (24606)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_24154 for (2953ds/1046Mi)
% 35.46/6.34 % (24602)Instruction limit reached!
% 35.46/6.34 % (24602)------------------------------
% 35.46/6.34 % (24602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.46/6.34 % (24602)Termination reason: Unknown
% 35.46/6.34 % (24602)Termination phase: Saturation
% 35.46/6.34
% 35.46/6.34 % (24602)Memory used [KB]: 8315
% 35.46/6.34 % (24602)Time elapsed: 0.278 s
% 35.46/6.34 % (24602)Instructions burned: 867 (million)
% 35.46/6.34 % (24602)------------------------------
% 35.46/6.34 % (24602)------------------------------
% 35.46/6.34 % (24604)Instruction limit reached!
% 35.46/6.34 % (24604)------------------------------
% 35.46/6.34 % (24604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.46/6.34 % (24604)Termination reason: Unknown
% 35.46/6.34 % (24604)Termination phase: Saturation
% 35.46/6.34
% 35.46/6.34 % (24604)Memory used [KB]: 9210
% 35.46/6.34 % (24604)Time elapsed: 0.211 s
% 35.46/6.34 % (24604)Instructions burned: 646 (million)
% 35.46/6.34 % (24604)------------------------------
% 35.46/6.34 % (24604)------------------------------
% 35.46/6.35 % (24607)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_24154 for (2952ds/222Mi)
% 35.46/6.35 % (24608)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_24154 for (2952ds/68Mi)
% 35.46/6.37 % (24608)Instruction limit reached!
% 35.46/6.37 % (24608)------------------------------
% 35.46/6.37 % (24608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.46/6.37 % (24608)Termination reason: Unknown
% 35.46/6.37 % (24608)Termination phase: Property scanning
% 35.46/6.37
% 35.46/6.37 % (24608)Memory used [KB]: 1918
% 35.46/6.37 % (24608)Time elapsed: 0.021 s
% 35.46/6.37 % (24608)Instructions burned: 70 (million)
% 35.46/6.37 % (24608)------------------------------
% 35.46/6.37 % (24608)------------------------------
% 35.46/6.38 % (24609)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=454:si=on:rtra=on_0 on DTF2THF_24154 for (2951ds/454Mi)
% 36.19/6.42 % (24607)Instruction limit reached!
% 36.19/6.42 % (24607)------------------------------
% 36.19/6.42 % (24607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.19/6.42 % (24607)Termination reason: Unknown
% 36.19/6.42 % (24607)Termination phase: Saturation
% 36.19/6.42
% 36.19/6.42 % (24607)Memory used [KB]: 7291
% 36.19/6.42 % (24607)Time elapsed: 0.066 s
% 36.19/6.42 % (24607)Instructions burned: 223 (million)
% 36.19/6.42 % (24607)------------------------------
% 36.19/6.42 % (24607)------------------------------
% 36.19/6.43 % (24610)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_24154 for (2951ds/360Mi)
% 36.19/6.45 % (24603)First to succeed.
% 36.19/6.45 % (24603)Refutation found. Thanks to Tanya!
% 36.19/6.45 % SZS status Theorem for DTF2THF_24154
% 36.19/6.45 % SZS output start Proof for DTF2THF_24154
% 36.19/6.45 thf(type_def_5, type, configuration_ext: ($tType * $tType * $tType * $tType) > $tType).
% 36.19/6.45 thf(type_def_6, type, message: ($tType * $tType) > $tType).
% 36.19/6.45 thf(type_def_7, type, nat: $tType).
% 36.19/6.45 thf(type_def_9, type, product_unit: $tType).
% 36.19/6.45 thf(type_def_10, type, list: ($tType) > $tType).
% 36.19/6.45 thf(type_def_11, type, set: ($tType) > $tType).
% 36.19/6.45 thf(type_def_12, type, p: $tType).
% 36.19/6.45 thf(type_def_13, type, v: $tType).
% 36.19/6.45 thf(type_def_14, type, s: $tType).
% 36.19/6.45 thf(func_def_0, type, configuration_ext: ($tType * $tType * $tType * $tType) > $tType).
% 36.19/6.45 thf(func_def_1, type, message: ($tType * $tType) > $tType).
% 36.19/6.45 thf(func_def_2, type, product_unit: $tType).
% 36.19/6.45 thf(func_def_3, type, list: ($tType) > $tType).
% 36.19/6.45 thf(func_def_4, type, set: ($tType) > $tType).
% 36.19/6.45 thf(func_def_5, type, nat: $tType).
% 36.19/6.45 thf(func_def_6, type, v: $tType).
% 36.19/6.45 thf(func_def_7, type, s: $tType).
% 36.19/6.45 thf(func_def_8, type, p: $tType).
% 36.19/6.45 thf(func_def_9, type, type: !>[X0: $tType]:($o)).
% 36.19/6.45 thf(func_def_10, type, size: !>[X0: $tType]:($o)).
% 36.19/6.45 thf(func_def_11, type, one: !>[X0: $tType]:($o)).
% 36.19/6.45 thf(func_def_12, type, zero: !>[X0: $tType]:($o)).
% 36.19/6.45 thf(func_def_13, type, neg_numeral: !>[X0: $tType]:($o)).
% 36.19/6.45 thf(func_def_14, type, order: !>[X0: $tType]:($o)).
% 36.19/6.45 thf(func_def_15, type, group_add: !>[X0: $tType]:($o)).
% 36.19/6.45 thf(func_def_16, type, wellorder: !>[X0: $tType]:($o)).
% 36.19/6.45 thf(func_def_17, type, comm_monoid_diff: !>[X0: $tType]:($o)).
% 36.19/6.45 thf(func_def_18, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 36.19/6.45 thf(func_def_19, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 36.19/6.45 thf(func_def_20, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 36.19/6.45 thf(func_def_21, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 36.19/6.45 thf(func_def_22, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 36.19/6.45 thf(func_def_23, type, msgs: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(configuration_ext @ X0 @ X1 @ X2 @ X3 > message @ X0 @ X1 > nat)).
% 36.19/6.45 thf(func_def_24, type, enabled: !>[X0: $tType, X1: $tType, X2: $tType]:(configuration_ext @ X0 @ X1 @ X2 @ product_unit > message @ X0 @ X1 > $o)).
% 36.19/6.45 thf(func_def_25, type, isReceiverOf: !>[X0: $tType, X1: $tType]:(X0 > message @ X0 @ X1 > $o)).
% 36.19/6.45 thf(func_def_26, 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)).
% 36.19/6.45 thf(func_def_27, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 36.19/6.45 thf(func_def_28, type, one_one: !>[X0: $tType]:(X0)).
% 36.19/6.45 thf(func_def_29, type, zero_zero: !>[X0: $tType]:(X0)).
% 36.19/6.45 thf(func_def_30, type, prefixList: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 36.19/6.45 thf(func_def_31, type, last: !>[X0: $tType]:(list @ X0 > X0)).
% 36.19/6.45 thf(func_def_32, type, nil: !>[X0: $tType]:(list @ X0)).
% 36.19/6.45 thf(func_def_33, type, nth: !>[X0: $tType]:(list @ X0 > nat > X0)).
% 36.19/6.45 thf(func_def_34, type, suc: nat > nat).
% 36.19/6.45 thf(func_def_35, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 36.19/6.45 thf(func_def_36, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 36.19/6.45 thf(func_def_37, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 36.19/6.45 thf(func_def_38, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 36.19/6.45 thf(func_def_39, type, fe: nat > list @ configuration_ext @ p @ v @ s @ product_unit).
% 36.19/6.45 thf(func_def_40, type, firstOccSet: nat > set @ message @ p @ v).
% 36.19/6.45 thf(func_def_41, type, ft: nat > list @ message @ p @ v).
% 36.19/6.45 thf(func_def_42, type, index: nat).
% 36.19/6.45 thf(func_def_43, type, msgInSet: message @ p @ v).
% 36.19/6.45 thf(func_def_44, type, msg: message @ p @ v).
% 36.19/6.45 thf(func_def_45, type, n0: nat).
% 36.19/6.45 thf(func_def_46, type, n1: nat).
% 36.19/6.45 thf(func_def_47, type, nMsg: nat).
% 36.19/6.45 thf(func_def_48, type, n: nat).
% 36.19/6.45 thf(func_def_49, type, p2: p).
% 36.19/6.45 thf(func_def_64, type, sP0: (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).
% 36.19/6.45 thf(func_def_65, type, sP1: (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).
% 36.19/6.45 thf(func_def_66, type, sK2: nat > nat).
% 36.19/6.45 thf(func_def_67, type, sK3: (nat > $o) > (nat > $o) > nat > nat).
% 36.19/6.45 thf(func_def_68, type, sK4: (nat > $o) > nat > nat).
% 36.19/6.45 thf(func_def_69, type, sK5: nat > (nat > $o) > nat).
% 36.19/6.45 thf(func_def_70, type, sK6: (nat > $o) > nat).
% 36.19/6.45 thf(func_def_71, type, sK7: nat > nat).
% 36.19/6.45 thf(func_def_72, type, sK8: (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).
% 36.19/6.45 thf(func_def_73, type, sK9: (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).
% 36.19/6.45 thf(func_def_74, type, sK10: (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).
% 36.19/6.45 thf(func_def_75, type, sK11: (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).
% 36.19/6.45 thf(func_def_76, type, sK12: (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).
% 36.19/6.45 thf(func_def_77, type, sK13: (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).
% 36.19/6.45 thf(func_def_78, type, sK14: (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).
% 36.19/6.45 thf(func_def_79, type, sK15: (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).
% 36.19/6.45 thf(func_def_80, type, sK16: (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).
% 36.19/6.45 thf(func_def_81, type, sK17: (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).
% 36.19/6.45 thf(func_def_82, type, sK18: (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).
% 36.19/6.45 thf(func_def_83, type, sK19: (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).
% 36.19/6.45 thf(func_def_84, type, sK20: (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).
% 36.19/6.45 thf(func_def_85, type, sK21: (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).
% 36.19/6.45 thf(func_def_86, type, sK22: (nat > $o) > nat).
% 36.19/6.45 thf(func_def_87, type, sK23: nat).
% 36.19/6.45 thf(func_def_88, type, sK24: !>[X0: $tType]:(list @ X0 > list @ X0 > nat)).
% 36.19/6.45 thf(func_def_89, type, sK25: !>[X0: $tType]:(nat > list @ X0)).
% 36.19/6.45 thf(func_def_90, type, sK26: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X0) > X1)).
% 36.19/6.45 thf(func_def_91, type, sK27: (nat > $o) > nat).
% 36.19/6.45 thf(func_def_92, type, sK28: p).
% 36.19/6.45 thf(func_def_93, type, sK29: nat > (nat > $o) > nat).
% 36.19/6.45 thf(func_def_94, type, sK30: (nat > $o) > nat).
% 36.19/6.45 thf(func_def_95, type, sK31: (nat > $o) > nat > nat).
% 36.19/6.45 thf(func_def_96, type, sK32: nat > nat).
% 36.19/6.45 thf(func_def_97, type, sK33: (nat > $o) > nat).
% 36.19/6.45 thf(func_def_98, type, sK34: !>[X0: $tType]:((nat > X0) > nat)).
% 36.19/6.45 thf(func_def_99, type, sK35: (nat > nat > $o) > nat).
% 36.19/6.45 thf(func_def_100, type, sK36: (nat > nat > $o) > nat).
% 36.19/6.45 thf(func_def_101, type, sK37: (nat > nat > $o) > nat).
% 36.19/6.45 thf(func_def_102, type, sK38: (nat > nat > $o) > nat).
% 36.19/6.45 thf(func_def_103, type, sK39: (nat > nat > $o) > nat).
% 36.19/6.45 thf(func_def_104, type, sK40: nat).
% 36.19/6.45 thf(func_def_105, type, sK41: nat).
% 36.19/6.45 thf(func_def_106, type, sK42: (nat > $o) > nat).
% 36.19/6.45 thf(func_def_107, type, sK43: (nat > nat > $o) > nat).
% 36.19/6.45 thf(func_def_108, type, sK44: (nat > nat > $o) > nat).
% 36.19/6.45 thf(func_def_109, type, sK45: (nat > nat > $o) > nat).
% 36.19/6.45 thf(func_def_110, type, sK46: (nat > nat > $o) > nat).
% 36.19/6.45 thf(func_def_111, type, sK47: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 36.19/6.45 thf(func_def_112, type, sK48: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 36.19/6.45 thf(func_def_113, type, sK49: !>[X0: $tType]:((nat > X0) > nat)).
% 36.19/6.45 thf(func_def_114, type, sK50: nat > nat > nat).
% 36.19/6.45 thf(func_def_115, type, sK51: p).
% 36.19/6.45 thf(func_def_116, type, sK52: (nat > $o) > nat > nat).
% 36.19/6.45 thf(func_def_117, type, sK53: (nat > $o) > nat > nat).
% 36.19/6.45 thf(func_def_118, type, sK54: (nat > $o) > nat).
% 36.19/6.45 thf(func_def_119, type, sK55: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 36.19/6.45 thf(func_def_120, type, sK56: (nat > $o) > nat).
% 36.19/6.45 thf(func_def_121, type, sK57: (nat > $o) > nat).
% 36.19/6.45 thf(func_def_122, type, sK58: !>[X0: $tType]:((nat > X0) > nat)).
% 36.19/6.45 thf(func_def_123, type, sK59: (nat > $o) > nat).
% 36.19/6.45 thf(func_def_124, type, sK60: (nat > nat > $o) > nat).
% 36.19/6.45 thf(func_def_125, type, sK61: (nat > nat > $o) > nat).
% 36.19/6.45 thf(func_def_126, type, sK62: (nat > nat > $o) > nat).
% 36.19/6.45 thf(func_def_127, type, sK63: (nat > nat > $o) > nat).
% 36.19/6.45 thf(func_def_128, type, sK64: (nat > nat) > nat).
% 36.19/6.45 thf(func_def_129, type, sK65: (nat > nat) > nat).
% 36.19/6.45 thf(func_def_130, 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) > configuration_ext @ p @ v @ s @ product_unit).
% 36.19/6.45 thf(func_def_131, 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) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit).
% 36.19/6.45 thf(func_def_132, 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 > (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).
% 36.19/6.45 thf(func_def_133, 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) > (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).
% 36.19/6.45 thf(func_def_134, 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) > (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).
% 36.19/6.45 thf(func_def_135, 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 > (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).
% 36.19/6.45 thf(func_def_136, 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) > (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).
% 36.19/6.45 thf(func_def_137, 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) > (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).
% 36.19/6.45 thf(func_def_138, type, sK74: (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).
% 36.19/6.45 thf(func_def_139, type, sK75: (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).
% 36.19/6.45 thf(func_def_140, type, sK76: (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).
% 36.19/6.45 thf(func_def_141, type, sK77: (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).
% 36.19/6.45 thf(func_def_142, type, sK78: (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).
% 36.19/6.45 thf(func_def_143, type, sK79: (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).
% 36.19/6.45 thf(func_def_144, type, sK80: nat > nat > nat).
% 36.19/6.45 thf(func_def_145, type, sK81: (nat > $o) > nat).
% 36.19/6.45 thf(func_def_146, type, sK82: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X0) > X1)).
% 36.19/6.45 thf(func_def_147, type, sK83: (nat > $o) > nat > nat > nat).
% 36.19/6.45 thf(func_def_148, type, sK84: nat > (nat > $o) > nat).
% 36.19/6.45 thf(func_def_149, type, sK85: nat).
% 36.19/6.45 thf(func_def_150, type, sK86: !>[X0: $tType]:((nat > X0) > nat)).
% 36.19/6.45 thf(func_def_151, type, sK87: (nat > $o) > nat).
% 36.19/6.45 thf(func_def_152, type, sK88: message @ p @ v > nat > nat > nat).
% 36.19/6.45 thf(func_def_153, type, sK89: nat > nat).
% 36.19/6.45 thf(func_def_154, type, sK90: (nat > $o) > nat > nat > nat).
% 36.19/6.45 thf(func_def_155, type, sK91: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 36.19/6.45 thf(func_def_157, type, ph93: !>[X0: $tType]:(X0)).
% 36.19/6.45 thf(func_def_158, type, sK94: nat).
% 36.19/6.45 thf(func_def_159, type, sK95: nat).
% 36.19/6.45 thf(func_def_160, type, sK96: nat).
% 36.19/6.45 thf(func_def_161, type, sK97: nat).
% 36.19/6.45 thf(func_def_162, type, sK98: nat).
% 36.19/6.45 thf(func_def_163, type, sK99: nat).
% 36.19/6.45 thf(f4016,plain,(
% 36.19/6.45 $false),
% 36.19/6.45 inference(avatar_sat_refutation,[status(thm)],[f1767,f2105,f3945])).
% 36.19/6.45 thf(f3945,plain,(
% 36.19/6.45 spl92_21),
% 36.19/6.45 inference(avatar_contradiction_clause,[status(thm)],[f3944])).
% 36.19/6.45 thf(f3944,plain,(
% 36.19/6.45 $false | spl92_21),
% 36.19/6.45 inference(subsumption_resolution,[status(thm)],[f3943,f1762])).
% 36.19/6.45 thf(f1762,plain,(
% 36.19/6.45 ((ord_less_eq @ nat @ one_one @ nat @ nMsg) != $true) | spl92_21),
% 36.19/6.45 inference(avatar_component_clause,[status(thm)],[f1760])).
% 36.19/6.45 thf(f1760,definition,(
% 36.19/6.45 spl92_21 <=> ((ord_less_eq @ nat @ one_one @ nat @ nMsg) = $true)),
% 36.19/6.45 introduced(definition,[new_symbols(naming,[spl92_21])],[avatar_definition])).
% 36.19/6.45 thf(f3943,plain,(
% 36.19/6.45 ((ord_less_eq @ nat @ one_one @ nat @ nMsg) = $true)),
% 36.19/6.45 inference(forward_demodulation,[status(thm)],[f3892,f1278])).
% 36.19/6.45 thf(f1278,plain,(
% 36.19/6.45 ((suc @ zero_zero @ nat) = one_one @ nat)),
% 36.19/6.45 inference(cnf_transformation,[status(thm)],[f210])).
% 36.19/6.45 thf(f210,axiom,(
% 36.19/6.45 ((suc @ zero_zero @ nat) = one_one @ nat)),
% 36.19/6.45 file('/export/starexec/sandbox2/tmp/tmp.YNdYCGZgEX/DTF2THF_24154.p',fact_209_One__nat__def)).
% 36.19/6.45 thf(f3892,plain,(
% 36.19/6.45 ((ord_less_eq @ nat @ (suc @ zero_zero @ nat) @ nMsg) = $true)),
% 36.19/6.45 inference(trivial_inequality_removal,[status(thm)],[f3777])).
% 36.19/6.45 thf(f3777,plain,(
% 36.19/6.45 ($true != $true) | ((ord_less_eq @ nat @ (suc @ zero_zero @ nat) @ nMsg) = $true)),
% 36.19/6.45 inference(superposition,[status(thm)],[f1388,f1169])).
% 36.19/6.45 thf(f1169,plain,(
% 36.19/6.45 ((ord_less @ nat @ zero_zero @ nat @ nMsg) = $true)),
% 36.19/6.45 inference(cnf_transformation,[status(thm)],[f480])).
% 36.19/6.45 thf(f480,plain,(
% 36.19/6.45 ((ord_less @ nat @ zero_zero @ nat @ nMsg) = $true)),
% 36.19/6.45 inference(fool_elimination,[status(thm)],[f479])).
% 36.19/6.45 thf(f479,plain,(
% 36.19/6.45 (ord_less @ nat @ zero_zero @ nat @ nMsg)),
% 36.19/6.45 inference(rectify,[status(thm)],[f1])).
% 36.19/6.45 thf(f1,axiom,(
% 36.19/6.45 (ord_less @ nat @ zero_zero @ nat @ nMsg)),
% 36.19/6.45 file('/export/starexec/sandbox2/tmp/tmp.YNdYCGZgEX/DTF2THF_24154.p',fact_0_AssumpOcc6_I1_J)).
% 36.19/6.45 thf(f1388,plain,(
% 36.19/6.45 ( ! [X0 : nat,X1 : nat] : (((ord_less_eq @ nat @ (suc @ X0) @ X1) = $true) | ((ord_less @ nat @ X0 @ X1) != $true)) )),
% 36.19/6.45 inference(cnf_transformation,[status(thm)],[f972])).
% 36.19/6.45 thf(f972,plain,(
% 36.19/6.45 ! [X0 : nat,X1 : nat] : (((ord_less_eq @ nat @ (suc @ X0) @ X1) = $true) | ((ord_less @ nat @ X0 @ X1) != $true))),
% 36.19/6.45 inference(ennf_transformation,[status(thm)],[f682])).
% 36.19/6.45 thf(f682,plain,(
% 36.19/6.45 ! [X0 : nat,X1 : nat] : (((ord_less @ nat @ X0 @ X1) = $true) => ((ord_less_eq @ nat @ (suc @ X0) @ X1) = $true))),
% 36.19/6.45 inference(fool_elimination,[status(thm)],[f681])).
% 36.19/6.45 thf(f681,plain,(
% 36.19/6.45 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ X0 @ X1) => (ord_less_eq @ nat @ (suc @ X0) @ X1))),
% 36.19/6.45 inference(rectify,[status(thm)],[f197])).
% 36.19/6.45 thf(f197,axiom,(
% 36.19/6.45 ! [X21 : nat,X20 : nat] : ((ord_less @ nat @ X21 @ X20) => (ord_less_eq @ nat @ (suc @ X21) @ X20))),
% 36.19/6.45 file('/export/starexec/sandbox2/tmp/tmp.YNdYCGZgEX/DTF2THF_24154.p',fact_196_Suc__leI)).
% 36.19/6.45 thf(f2105,plain,(
% 36.19/6.45 spl92_22),
% 36.19/6.45 inference(avatar_contradiction_clause,[status(thm)],[f2104])).
% 36.19/6.45 thf(f2104,plain,(
% 36.19/6.45 $false | spl92_22),
% 36.19/6.45 inference(subsumption_resolution,[status(thm)],[f1953,f1256])).
% 36.19/6.45 thf(f1256,plain,(
% 36.19/6.45 ((firstOccurrence @ p @ v @ s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ nMsg) = $true)),
% 36.19/6.45 inference(cnf_transformation,[status(thm)],[f516])).
% 36.19/6.45 thf(f516,plain,(
% 36.19/6.45 ((firstOccurrence @ p @ v @ s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ nMsg) = $true)),
% 36.19/6.45 inference(fool_elimination,[status(thm)],[f515])).
% 36.19/6.45 thf(f515,plain,(
% 36.19/6.45 (firstOccurrence @ p @ v @ s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ nMsg)),
% 36.19/6.45 inference(rectify,[status(thm)],[f4])).
% 36.19/6.45 thf(f4,axiom,(
% 36.19/6.45 (firstOccurrence @ p @ v @ s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ nMsg)),
% 36.19/6.45 file('/export/starexec/sandbox2/tmp/tmp.YNdYCGZgEX/DTF2THF_24154.p',fact_3_AssumptionSubset_I3_J)).
% 36.19/6.45 thf(f1953,plain,(
% 36.19/6.45 ((firstOccurrence @ p @ v @ s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ nMsg) != $true) | spl92_22),
% 36.19/6.45 inference(trivial_inequality_removal,[status(thm)],[f1848])).
% 36.19/6.45 thf(f1848,plain,(
% 36.19/6.45 ($true != $true) | ((firstOccurrence @ p @ v @ s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ nMsg) != $true) | spl92_22),
% 36.19/6.45 inference(superposition,[status(thm)],[f1766,f1340])).
% 36.19/6.45 thf(f1340,plain,(
% 36.19/6.45 ( ! [X0 : nat] : (((firstOccurrence @ p @ v @ s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ X0) != $true) | ((ord_less @ nat @ X0 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) = $true)) )),
% 36.19/6.45 inference(cnf_transformation,[status(thm)],[f965])).
% 36.19/6.45 thf(f965,plain,(
% 36.19/6.45 ! [X0 : nat] : (((ord_less @ nat @ X0 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) = $true) | ((firstOccurrence @ p @ v @ s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ X0) != $true))),
% 36.19/6.45 inference(ennf_transformation,[status(thm)],[f430])).
% 36.19/6.45 thf(f430,plain,(
% 36.19/6.45 ! [X0 : nat] : (((firstOccurrence @ p @ v @ s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ X0) = $true) => ((ord_less @ nat @ X0 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) = $true))),
% 36.19/6.45 inference(fool_elimination,[status(thm)],[f429])).
% 36.19/6.45 thf(f429,plain,(
% 36.19/6.45 ! [X0 : nat] : ((firstOccurrence @ p @ v @ s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ X0) => (ord_less @ nat @ X0 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))))),
% 36.19/6.45 inference(rectify,[status(thm)],[f5])).
% 36.19/6.45 thf(f5,axiom,(
% 36.19/6.45 ! [X19 : nat] : ((firstOccurrence @ p @ v @ s @ (fe @ (suc @ index)) @ (ft @ (suc @ index)) @ msg @ X19) => (ord_less @ nat @ X19 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))))),
% 36.19/6.45 file('/export/starexec/sandbox2/tmp/tmp.YNdYCGZgEX/DTF2THF_24154.p',fact_4_SmallIndex)).
% 36.19/6.45 thf(f1766,plain,(
% 36.19/6.45 ((ord_less @ nat @ nMsg @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) != $true) | spl92_22),
% 36.19/6.45 inference(avatar_component_clause,[status(thm)],[f1764])).
% 36.19/6.45 thf(f1764,definition,(
% 36.19/6.45 spl92_22 <=> ((ord_less @ nat @ nMsg @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) = $true)),
% 36.19/6.45 introduced(definition,[new_symbols(naming,[spl92_22])],[avatar_definition])).
% 36.19/6.45 thf(f1767,plain,(
% 36.19/6.45 ~spl92_21 | ~spl92_22),
% 36.19/6.45 inference(avatar_split_clause,[status(thm)],[f1600,f1764,f1760])).
% 36.19/6.45 thf(f1600,plain,(
% 36.19/6.45 ((ord_less @ nat @ nMsg @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) != $true) | ((ord_less_eq @ nat @ one_one @ nat @ nMsg) != $true)),
% 36.19/6.45 inference(trivial_inequality_removal,[status(thm)],[f1487])).
% 36.19/6.45 thf(f1487,plain,(
% 36.19/6.45 ($true != $true) | ((ord_less_eq @ nat @ one_one @ nat @ nMsg) != $true) | ((ord_less @ nat @ nMsg @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) != $true)),
% 36.19/6.45 inference(superposition,[status(thm)],[f1479,f1214])).
% 36.19/6.45 thf(f1214,plain,(
% 36.19/6.45 ( ! [X2 : nat,X0 : nat,X1 : nat] : (((ord_less @ nat @ (minus_minus @ nat @ X0 @ X2) @ (minus_minus @ nat @ X1 @ X2)) = $true) | ((ord_less @ nat @ X0 @ X1) != $true) | ((ord_less_eq @ nat @ X2 @ X0) != $true)) )),
% 36.19/6.45 inference(cnf_transformation,[status(thm)],[f947])).
% 36.19/6.45 thf(f947,plain,(
% 36.19/6.45 ! [X0 : nat,X1 : nat,X2 : nat] : (((ord_less @ nat @ (minus_minus @ nat @ X0 @ X2) @ (minus_minus @ nat @ X1 @ X2)) = $true) | ((ord_less @ nat @ X0 @ X1) != $true) | ((ord_less_eq @ nat @ X2 @ X0) != $true))),
% 36.19/6.45 inference(flattening,[status(thm)],[f946])).
% 36.19/6.45 thf(f946,plain,(
% 36.19/6.45 ! [X0 : nat,X1 : nat,X2 : nat] : ((((ord_less @ nat @ (minus_minus @ nat @ X0 @ X2) @ (minus_minus @ nat @ X1 @ X2)) = $true) | ((ord_less_eq @ nat @ X2 @ X0) != $true)) | ((ord_less @ nat @ X0 @ X1) != $true))),
% 36.19/6.45 inference(ennf_transformation,[status(thm)],[f638])).
% 36.19/6.45 thf(f638,plain,(
% 36.19/6.45 ! [X0 : nat,X1 : nat,X2 : nat] : (((ord_less @ nat @ X0 @ X1) = $true) => (((ord_less_eq @ nat @ X2 @ X0) = $true) => ((ord_less @ nat @ (minus_minus @ nat @ X0 @ X2) @ (minus_minus @ nat @ X1 @ X2)) = $true)))),
% 36.19/6.45 inference(fool_elimination,[status(thm)],[f637])).
% 36.19/6.45 thf(f637,plain,(
% 36.19/6.45 ! [X0 : nat,X1 : nat,X2 : nat] : ((ord_less @ nat @ X0 @ X1) => ((ord_less_eq @ nat @ X2 @ X0) => (ord_less @ nat @ (minus_minus @ nat @ X0 @ X2) @ (minus_minus @ nat @ X1 @ X2))))),
% 36.19/6.45 inference(rectify,[status(thm)],[f209])).
% 36.19/6.45 thf(f209,axiom,(
% 36.19/6.45 ! [X22 : nat,X23 : nat,X34 : nat] : ((ord_less @ nat @ X22 @ X23) => ((ord_less_eq @ nat @ X34 @ X22) => (ord_less @ nat @ (minus_minus @ nat @ X22 @ X34) @ (minus_minus @ nat @ X23 @ X34))))),
% 36.19/6.45 file('/export/starexec/sandbox2/tmp/tmp.YNdYCGZgEX/DTF2THF_24154.p',fact_208_diff__less__mono)).
% 36.19/6.45 thf(f1479,plain,(
% 36.19/6.45 ($true != (ord_less @ nat @ (minus_minus @ nat @ nMsg @ one_one @ nat) @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ one_one @ nat)))),
% 36.19/6.45 inference(forward_demodulation,[status(thm)],[f1152,f1278])).
% 36.19/6.45 thf(f1152,plain,(
% 36.19/6.45 ((ord_less @ nat @ (minus_minus @ nat @ nMsg @ (suc @ zero_zero @ nat)) @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ (suc @ zero_zero @ nat))) != $true)),
% 36.19/6.45 inference(cnf_transformation,[status(thm)],[f786])).
% 36.19/6.45 thf(f786,plain,(
% 36.19/6.45 ((ord_less @ nat @ (minus_minus @ nat @ nMsg @ (suc @ zero_zero @ nat)) @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ (suc @ zero_zero @ nat))) != $true)),
% 36.19/6.45 inference(flattening,[status(thm)],[f690])).
% 36.19/6.45 thf(f690,plain,(
% 36.19/6.45 ~((ord_less @ nat @ (minus_minus @ nat @ nMsg @ (suc @ zero_zero @ nat)) @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ (suc @ zero_zero @ nat))) = $true)),
% 36.19/6.45 inference(fool_elimination,[status(thm)],[f689])).
% 36.19/6.45 thf(f689,plain,(
% 36.19/6.45 ~(ord_less @ nat @ (minus_minus @ nat @ nMsg @ (suc @ zero_zero @ nat)) @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ (suc @ zero_zero @ nat)))),
% 36.19/6.45 inference(rectify,[status(thm)],[f269])).
% 36.19/6.45 thf(f269,negated_conjecture,(
% 36.19/6.45 ~(ord_less @ nat @ (minus_minus @ nat @ nMsg @ (suc @ zero_zero @ nat)) @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ (suc @ zero_zero @ nat)))),
% 36.19/6.45 inference(negated_conjecture,[status(cth)],[f268])).
% 36.19/6.45 thf(f268,conjecture,(
% 36.19/6.45 (ord_less @ nat @ (minus_minus @ nat @ nMsg @ (suc @ zero_zero @ nat)) @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ (suc @ zero_zero @ nat)))),
% 36.19/6.45 file('/export/starexec/sandbox2/tmp/tmp.YNdYCGZgEX/DTF2THF_24154.p',conj_0)).
% 36.19/6.45 % SZS output end Proof for DTF2THF_24154
% 36.19/6.45 % (24603)------------------------------
% 36.19/6.45 % (24603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.19/6.45 % (24603)Termination reason: Refutation
% 36.19/6.45
% 36.19/6.45 % (24603)Memory used [KB]: 8827
% 36.19/6.45 % (24603)Time elapsed: 0.325 s
% 36.19/6.45 % (24603)Instructions burned: 986 (million)
% 36.19/6.45 % (24603)------------------------------
% 36.19/6.45 % (24603)------------------------------
% 36.19/6.45 % (24427)Success in time 4.9 s
%------------------------------------------------------------------------------