%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP060^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:13 AM UTC 2026
% Result : Theorem 2.56s 1.80s
% Output : Refutation 2.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ITP060^2 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n021.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:25:08 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : ITP060^2 : TPTP v9.2.1. Released v7.5.0.
% 0.19/0.45 % Domain : Interactive Theorem Proving
% 0.19/0.45 % Problem : Sledgehammer FLPTheorem problem prob_828__3301664_1
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.19/0.45 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Des21]
% 0.19/0.45 % Names : FLPTheorem/prob_828__3301664_1 [Des21]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.00 v7.5.0
% 0.19/0.45 % Syntax : Number of formulae : 314 ( 127 unt; 46 typ; 0 def)
% 0.19/0.45 % Number of atoms : 590 ( 205 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 7 ( 2 avg)
% 0.19/0.45 % Number of connectives : 3704 ( 83 ~; 11 |; 36 &;3267 @)
% 0.19/0.45 % ( 0 <=>; 307 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 21 ( 7 avg)
% 0.19/0.45 % Number of types : 6 ( 5 usr)
% 0.19/0.45 % Number of type conns : 180 ( 180 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 42 ( 41 usr; 7 con; 0-7 aty)
% 0.19/0.45 % Number of variables : 643 ( 17 ^; 560 !; 30 ?; 643 :)
% 0.19/0.45 % ( 36 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.45 % SPC : TH1_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This file was generated by Sledgehammer 2021-02-23 16:16:57.179
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % Could-be-implicit typings (8)
% 0.19/0.45 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext,type,
% 0.19/0.45 configuration_ext: $tType > $tType > $tType > $tType > $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_AsynchronousSystem_Omessage,type,
% 0.19/0.45 message: $tType > $tType > $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_Product__Type_Ounit,type,
% 0.19/0.45 product_unit: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_List_Olist,type,
% 0.19/0.45 list: $tType > $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_Nat_Onat,type,
% 0.19/0.45 nat: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_tf_v,type,
% 0.19/0.45 v: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_tf_s,type,
% 0.19/0.45 s: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_tf_p,type,
% 0.19/0.45 p: $tType ).
% 0.19/0.45
% 0.19/0.45 % Explicit typings (38)
% 0.19/0.45 thf(sy_cl_HOL_Otype,type,
% 0.19/0.45 type:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Nat_Osize,type,
% 0.19/0.45 size:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Groups_Oone,type,
% 0.19/0.45 one:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Groups_Ozero,type,
% 0.19/0.45 zero:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Num_Oneg__numeral,type,
% 0.19/0.45 neg_numeral:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Oorder,type,
% 0.19/0.45 order:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Groups_Ogroup__add,type,
% 0.19/0.45 group_add:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Owellorder,type,
% 0.19/0.45 wellorder:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Groups_Ocomm__monoid__diff,type,
% 0.19/0.45 comm_monoid_diff:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.19/0.45 ordered_ab_group_add:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.19/0.45 cancel1352612707id_add:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.19/0.45 cancel146912293up_add:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.19/0.45 linord1659791738miring:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.19/0.45 canoni770627133id_add:
% 0.19/0.45 !>[A: $tType] : $o ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_AsynchronousSystem_Oenabled,type,
% 0.19/0.45 enabled:
% 0.19/0.45 !>[P: $tType,V: $tType,S: $tType] : ( ( configuration_ext @ P @ V @ S @ product_unit ) > ( message @ P @ V ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Execution_Oexecution_OfirstOccurrence,type,
% 0.19/0.45 firstOccurrence:
% 0.19/0.45 !>[P: $tType,V: $tType,S: $tType] : ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( message @ P @ V ) > nat > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus_OinfiniteExecutionCfg,type,
% 0.19/0.45 fLPThe137922386ionCfg:
% 0.19/0.45 !>[P: $tType,V: $tType,S: $tType] : ( ( 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 > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus_OinfiniteExecutionMsg,type,
% 0.19/0.45 fLPThe221390223ionMsg:
% 0.19/0.45 !>[P: $tType,V: $tType,S: $tType] : ( ( 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 > ( list @ ( message @ P @ V ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.19/0.45 minus_minus:
% 0.19/0.45 !>[A: $tType] : ( A > A > A ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.19/0.45 one_one:
% 0.19/0.45 !>[A: $tType] : A ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.19/0.45 zero_zero:
% 0.19/0.45 !>[A: $tType] : A ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_ListUtilities_OprefixList,type,
% 0.19/0.45 prefixList:
% 0.19/0.45 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_List_Olast,type,
% 0.19/0.45 last:
% 0.19/0.45 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_List_Olist_ONil,type,
% 0.19/0.45 nil:
% 0.19/0.45 !>[A: $tType] : ( list @ A ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_List_Onth,type,
% 0.19/0.45 nth:
% 0.19/0.45 !>[A: $tType] : ( ( list @ A ) > nat > A ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Nat_OSuc,type,
% 0.19/0.45 suc: nat > nat ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.19/0.45 size_size:
% 0.19/0.45 !>[A: $tType] : ( A > nat ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.19/0.45 ord_less:
% 0.19/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.19/0.45 ord_less_eq:
% 0.19/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_fe____,type,
% 0.19/0.45 fe: nat > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_ft____,type,
% 0.19/0.45 ft: nat > ( list @ ( message @ p @ v ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_index____,type,
% 0.19/0.45 index: nat ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_msgInSet____,type,
% 0.19/0.45 msgInSet: message @ p @ v ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_msg____,type,
% 0.19/0.45 msg: message @ p @ v ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_n0____,type,
% 0.19/0.45 n0: nat ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_n1____,type,
% 0.19/0.45 n1: nat ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_nMsg____,type,
% 0.19/0.45 nMsg: nat ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_n____,type,
% 0.19/0.45 n: nat ).
% 0.19/0.45
% 0.19/0.45 % Relevant facts (251)
% 0.19/0.45 thf(fact_0_Occ3_H,axiom,
% 0.19/0.45 ord_less @ nat @ n1 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ).
% 0.19/0.45
% 0.19/0.45 % Occ3'
% 0.19/0.45 thf(fact_1_SameCfgOnLow,axiom,
% 0.19/0.45 ! [I: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) )
% 0.19/0.45 => ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ I )
% 0.19/0.45 = ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ I ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % SameCfgOnLow
% 0.19/0.45 thf(fact_2__092_060open_062fe_Aindex_A_B_An1_A_061_Afe_A_ISuc_Aindex_J_A_B_An1_092_060close_062,axiom,
% 0.19/0.45 ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ n1 )
% 0.19/0.45 = ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ n1 ) ) ).
% 0.19/0.45
% 0.19/0.45 % \<open>fe index ! n1 = fe (Suc index) ! n1\<close>
% 0.19/0.45 thf(fact_3__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_060_Alength_A_Ife_Aindex_J_092_060close_062,axiom,
% 0.19/0.45 ord_less @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ).
% 0.19/0.45
% 0.19/0.45 % \<open>length (fe index) - 1 < length (fe index)\<close>
% 0.19/0.45 thf(fact_4_AssumptionSubset2_I3_J,axiom,
% 0.19/0.45 ord_less @ nat @ n1 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % AssumptionSubset2(3)
% 0.19/0.45 thf(fact_5_AssumpOcc6_H_I1_J,axiom,
% 0.19/0.45 ord_less @ nat @ ( zero_zero @ nat ) @ n1 ).
% 0.19/0.45
% 0.19/0.45 % AssumpOcc6'(1)
% 0.19/0.45 thf(fact_6_diff__Suc__1,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ( ( minus_minus @ nat @ ( suc @ N ) @ ( one_one @ nat ) )
% 0.19/0.45 = N ) ).
% 0.19/0.45
% 0.19/0.45 % diff_Suc_1
% 0.19/0.45 thf(fact_7_diff__Suc__Suc,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( minus_minus @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.19/0.45 = ( minus_minus @ nat @ M @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % diff_Suc_Suc
% 0.19/0.45 thf(fact_8_Suc__diff__diff,axiom,
% 0.19/0.45 ! [M: nat,N: nat,K: nat] :
% 0.19/0.45 ( ( minus_minus @ nat @ ( minus_minus @ nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 0.19/0.45 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ N ) @ K ) ) ).
% 0.19/0.45
% 0.19/0.45 % Suc_diff_diff
% 0.19/0.45 thf(fact_9_NotEmpty_I1_J,axiom,
% 0.19/0.45 ( ( fe @ ( suc @ index ) )
% 0.19/0.45 != ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % NotEmpty(1)
% 0.19/0.45 thf(fact_10_IPrefixListEx,axiom,
% 0.19/0.45 ! [I: nat] : ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ I ) @ ( fe @ ( suc @ I ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % IPrefixListEx
% 0.19/0.45 thf(fact_11_diff__Suc__eq__diff__pred,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( minus_minus @ nat @ M @ ( suc @ N ) )
% 0.19/0.45 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ ( one_one @ nat ) ) @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % diff_Suc_eq_diff_pred
% 0.19/0.45 thf(fact_12_AssumpOcc6_H_I3_J,axiom,
% 0.19/0.45 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) ) @ msgInSet ).
% 0.19/0.45
% 0.19/0.45 % AssumpOcc6'(3)
% 0.19/0.45 thf(fact_13__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,
% 0.19/0.45 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 ) ) ).
% 0.19/0.45
% 0.19/0.45 % \<open>length (fe index) - 1 \<le> length (fe (Suc index)) - 1\<close>
% 0.19/0.45 thf(fact_14_NotEmpty_I2_J,axiom,
% 0.19/0.45 ( ( fe @ index )
% 0.19/0.45 != ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % NotEmpty(2)
% 0.19/0.45 thf(fact_15__092_060open_062n1_A_N_ASuc_A0_A_060_Alength_A_Ife_Aindex_J_A_N_ASuc_A0_092_060close_062,axiom,
% 0.19/0.45 ord_less @ nat @ ( minus_minus @ nat @ n1 @ ( suc @ ( zero_zero @ nat ) ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % \<open>n1 - Suc 0 < length (fe index) - Suc 0\<close>
% 0.19/0.45 thf(fact_16_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 0.19/0.45 ! [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] :
% 0.19/0.45 ( ! [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 ) )
% 0.19/0.45 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N2: nat] :
% 0.19/0.45 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.19/0.45 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.19/0.45 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 0.19/0.45 => ( ! [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 ) )
% 0.19/0.45 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N2: nat] :
% 0.19/0.45 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.19/0.45 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.19/0.45 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 0.19/0.45 => ( P2 @ A0 @ A1 @ A2 @ A3 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % infiniteExecutionCfg_infiniteExecutionMsg.induct(1)
% 0.19/0.45 thf(fact_17_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 0.19/0.45 ! [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] :
% 0.19/0.45 ( ! [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 ) )
% 0.19/0.45 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N2: nat] :
% 0.19/0.45 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.19/0.45 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.19/0.45 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 0.19/0.45 => ( ! [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 ) )
% 0.19/0.45 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N2: nat] :
% 0.19/0.45 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.19/0.45 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 0.19/0.45 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 0.19/0.45 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % infiniteExecutionCfg_infiniteExecutionMsg.induct(2)
% 0.19/0.45 thf(fact_18_old_Onat_Oinject,axiom,
% 0.19/0.45 ! [Nat: nat,Nat2: nat] :
% 0.19/0.45 ( ( ( suc @ Nat )
% 0.19/0.45 = ( suc @ Nat2 ) )
% 0.19/0.45 = ( Nat = Nat2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % old.nat.inject
% 0.19/0.45 thf(fact_19_nat_Oinject,axiom,
% 0.19/0.45 ! [X2: nat,Y2: nat] :
% 0.19/0.45 ( ( ( suc @ X2 )
% 0.19/0.45 = ( suc @ Y2 ) )
% 0.19/0.45 = ( X2 = Y2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % nat.inject
% 0.19/0.45 thf(fact_20_AssumptionSubset_I1_J,axiom,
% 0.19/0.45 ord_less_eq @ nat @ n1 @ nMsg ).
% 0.19/0.45
% 0.19/0.45 % AssumptionSubset(1)
% 0.19/0.45 thf(fact_21__092_060open_062fe_Aindex_A_092_060in_062_D_Alength_092_060close_062,axiom,
% 0.19/0.45 ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ).
% 0.19/0.45
% 0.19/0.45 % \<open>fe index \<in># length\<close>
% 0.19/0.45 thf(fact_22_Suc__less__eq,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.19/0.45 = ( ord_less @ nat @ M @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % Suc_less_eq
% 0.19/0.45 thf(fact_23_Suc__mono,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ M @ N )
% 0.19/0.45 => ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Suc_mono
% 0.19/0.45 thf(fact_24_lessI,axiom,
% 0.19/0.45 ! [N: nat] : ( ord_less @ nat @ N @ ( suc @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % lessI
% 0.19/0.45 thf(fact_25_neq0__conv,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ( ( N
% 0.19/0.45 != ( zero_zero @ nat ) )
% 0.19/0.45 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % neq0_conv
% 0.19/0.45 thf(fact_26_less__nat__zero__code,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_nat_zero_code
% 0.19/0.45 thf(fact_27_bot__nat__0_Onot__eq__extremum,axiom,
% 0.19/0.45 ! [A8: nat] :
% 0.19/0.45 ( ( A8
% 0.19/0.45 != ( zero_zero @ nat ) )
% 0.19/0.45 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A8 ) ) ).
% 0.19/0.45
% 0.19/0.45 % bot_nat_0.not_eq_extremum
% 0.19/0.45 thf(fact_28_Suc__le__mono,axiom,
% 0.19/0.45 ! [N: nat,M: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.19/0.45 = ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.19/0.45
% 0.19/0.45 % Suc_le_mono
% 0.19/0.45 thf(fact_29_le0,axiom,
% 0.19/0.45 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 0.19/0.45
% 0.19/0.45 % le0
% 0.19/0.45 thf(fact_30_bot__nat__0_Oextremum,axiom,
% 0.19/0.45 ! [A8: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A8 ) ).
% 0.19/0.45
% 0.19/0.45 % bot_nat_0.extremum
% 0.19/0.45 thf(fact_31_diff__self__eq__0,axiom,
% 0.19/0.45 ! [M: nat] :
% 0.19/0.45 ( ( minus_minus @ nat @ M @ M )
% 0.19/0.45 = ( zero_zero @ nat ) ) ).
% 0.19/0.45
% 0.19/0.45 % diff_self_eq_0
% 0.19/0.45 thf(fact_32_diff__0__eq__0,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ( ( minus_minus @ nat @ ( zero_zero @ nat ) @ N )
% 0.19/0.45 = ( zero_zero @ nat ) ) ).
% 0.19/0.45
% 0.19/0.45 % diff_0_eq_0
% 0.19/0.45 thf(fact_33_diff__diff__cancel,axiom,
% 0.19/0.45 ! [I2: nat,N: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ I2 @ N )
% 0.19/0.45 => ( ( minus_minus @ nat @ N @ ( minus_minus @ nat @ N @ I2 ) )
% 0.19/0.45 = I2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % diff_diff_cancel
% 0.19/0.45 thf(fact_34_Occ4_H,axiom,
% 0.19/0.45 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ n1 ) @ msgInSet ).
% 0.19/0.45
% 0.19/0.45 % Occ4'
% 0.19/0.45 thf(fact_35_AssumptionSubset2_I4_J,axiom,
% 0.19/0.45 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ n1 ) @ msgInSet ).
% 0.19/0.45
% 0.19/0.45 % AssumptionSubset2(4)
% 0.19/0.45 thf(fact_36__092_060open_062enabled_A_Ife_Aindex_A_B_A_Ilength_A_Ife_Aindex_J_A_N_A1_J_J_AmsgInSet_092_060close_062,axiom,
% 0.19/0.45 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) ) @ msgInSet ).
% 0.19/0.45
% 0.19/0.45 % \<open>enabled (fe index ! (length (fe index) - 1)) msgInSet\<close>
% 0.19/0.45 thf(fact_37_zero__less__Suc,axiom,
% 0.19/0.45 ! [N: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % zero_less_Suc
% 0.19/0.45 thf(fact_38_less__Suc0,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ N @ ( suc @ ( zero_zero @ nat ) ) )
% 0.19/0.45 = ( N
% 0.19/0.45 = ( zero_zero @ nat ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_Suc0
% 0.19/0.45 thf(fact_39_zero__less__diff,axiom,
% 0.19/0.45 ! [N: nat,M: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( minus_minus @ nat @ N @ M ) )
% 0.19/0.45 = ( ord_less @ nat @ M @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % zero_less_diff
% 0.19/0.45 thf(fact_40_diff__is__0__eq,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ( minus_minus @ nat @ M @ N )
% 0.19/0.45 = ( zero_zero @ nat ) )
% 0.19/0.45 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % diff_is_0_eq
% 0.19/0.45 thf(fact_41_diff__is__0__eq_H,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ M @ N )
% 0.19/0.45 => ( ( minus_minus @ nat @ M @ N )
% 0.19/0.45 = ( zero_zero @ nat ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % diff_is_0_eq'
% 0.19/0.45 thf(fact_42_less__one,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ N @ ( one_one @ nat ) )
% 0.19/0.45 = ( N
% 0.19/0.45 = ( zero_zero @ nat ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_one
% 0.19/0.45 thf(fact_43_Suc__pred,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.19/0.45 => ( ( suc @ ( minus_minus @ nat @ N @ ( suc @ ( zero_zero @ nat ) ) ) )
% 0.19/0.45 = N ) ) ).
% 0.19/0.45
% 0.19/0.45 % Suc_pred
% 0.19/0.45 thf(fact_44_Suc__diff__1,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.19/0.45 => ( ( suc @ ( minus_minus @ nat @ N @ ( one_one @ nat ) ) )
% 0.19/0.45 = N ) ) ).
% 0.19/0.45
% 0.19/0.45 % Suc_diff_1
% 0.19/0.45 thf(fact_45_less__eq__nat_Osimps_I1_J,axiom,
% 0.19/0.45 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 0.19/0.45
% 0.19/0.45 % less_eq_nat.simps(1)
% 0.19/0.45 thf(fact_46_gr0I,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ( ( N
% 0.19/0.45 != ( zero_zero @ nat ) )
% 0.19/0.45 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % gr0I
% 0.19/0.45 thf(fact_47_le__0__eq,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ N @ ( zero_zero @ nat ) )
% 0.19/0.45 = ( N
% 0.19/0.45 = ( zero_zero @ nat ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_0_eq
% 0.19/0.45 thf(fact_48_le__refl,axiom,
% 0.19/0.45 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 0.19/0.45
% 0.19/0.45 % le_refl
% 0.19/0.45 thf(fact_49_not__gr0,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) )
% 0.19/0.45 = ( N
% 0.19/0.45 = ( zero_zero @ nat ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % not_gr0
% 0.19/0.45 thf(fact_50_le__trans,axiom,
% 0.19/0.45 ! [I2: nat,J: nat,K: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ I2 @ J )
% 0.19/0.45 => ( ( ord_less_eq @ nat @ J @ K )
% 0.19/0.45 => ( ord_less_eq @ nat @ I2 @ K ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_trans
% 0.19/0.45 thf(fact_51_eq__imp__le,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( M = N )
% 0.19/0.45 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % eq_imp_le
% 0.19/0.45 thf(fact_52_not__less0,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.19/0.45
% 0.19/0.45 % not_less0
% 0.19/0.45 thf(fact_53_le__antisym,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ M @ N )
% 0.19/0.45 => ( ( ord_less_eq @ nat @ N @ M )
% 0.19/0.45 => ( M = N ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_antisym
% 0.19/0.45 thf(fact_54_less__zeroE,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_zeroE
% 0.19/0.45 thf(fact_55_nat__less__le,axiom,
% 0.19/0.45 ( ( ord_less @ nat )
% 0.19/0.45 = ( ^ [M2: nat,N3: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ M2 @ N3 )
% 0.19/0.45 & ( M2 != N3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % nat_less_le
% 0.19/0.45 thf(fact_56_nat__neq__iff,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( M != N )
% 0.19/0.45 = ( ( ord_less @ nat @ M @ N )
% 0.19/0.45 | ( ord_less @ nat @ N @ M ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % nat_neq_iff
% 0.19/0.45 thf(fact_57_less__not__refl,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ~ ( ord_less @ nat @ N @ N ) ).
% 0.19/0.45
% 0.19/0.45 % less_not_refl
% 0.19/0.45 thf(fact_58_nat__le__linear,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ M @ N )
% 0.19/0.45 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.19/0.45
% 0.19/0.45 % nat_le_linear
% 0.19/0.45 thf(fact_59_less__not__refl2,axiom,
% 0.19/0.45 ! [N: nat,M: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ N @ M )
% 0.19/0.45 => ( M != N ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_not_refl2
% 0.19/0.45 thf(fact_60_less__not__refl3,axiom,
% 0.19/0.45 ! [S2: nat,T: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ S2 @ T )
% 0.19/0.45 => ( S2 != T ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_not_refl3
% 0.19/0.45 thf(fact_61_measure__induct,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType] :
% 0.19/0.45 ( ( wellorder @ B )
% 0.19/0.45 => ! [F: A > B,P2: A > $o,A8: A] :
% 0.19/0.45 ( ! [X: A] :
% 0.19/0.45 ( ! [Y: A] :
% 0.19/0.45 ( ( ord_less @ B @ ( F @ Y ) @ ( F @ X ) )
% 0.19/0.45 => ( P2 @ Y ) )
% 0.19/0.45 => ( P2 @ X ) )
% 0.19/0.45 => ( P2 @ A8 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % measure_induct
% 0.19/0.45 thf(fact_62_ex__least__nat__le,axiom,
% 0.19/0.45 ! [P2: nat > $o,N: nat] :
% 0.19/0.45 ( ( P2 @ N )
% 0.19/0.45 => ( ~ ( P2 @ ( zero_zero @ nat ) )
% 0.19/0.45 => ? [K2: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ K2 @ N )
% 0.19/0.45 & ! [I: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ I @ K2 )
% 0.19/0.45 => ~ ( P2 @ I ) )
% 0.19/0.45 & ( P2 @ K2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ex_least_nat_le
% 0.19/0.45 thf(fact_63_gr__implies__not0,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ M @ N )
% 0.19/0.45 => ( N
% 0.19/0.45 != ( zero_zero @ nat ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % gr_implies_not0
% 0.19/0.45 thf(fact_64_less__imp__le__nat,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ M @ N )
% 0.19/0.45 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_imp_le_nat
% 0.19/0.45 thf(fact_65_less__irrefl__nat,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ~ ( ord_less @ nat @ N @ N ) ).
% 0.19/0.45
% 0.19/0.45 % less_irrefl_nat
% 0.19/0.45 thf(fact_66_nat__less__induct,axiom,
% 0.19/0.45 ! [P2: nat > $o,N: nat] :
% 0.19/0.45 ( ! [N2: nat] :
% 0.19/0.45 ( ! [M3: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ M3 @ N2 )
% 0.19/0.45 => ( P2 @ M3 ) )
% 0.19/0.45 => ( P2 @ N2 ) )
% 0.19/0.45 => ( P2 @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % nat_less_induct
% 0.19/0.45 thf(fact_67_infinite__descent,axiom,
% 0.19/0.45 ! [P2: nat > $o,N: nat] :
% 0.19/0.45 ( ! [N2: nat] :
% 0.19/0.45 ( ~ ( P2 @ N2 )
% 0.19/0.45 => ? [M3: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ M3 @ N2 )
% 0.19/0.45 & ~ ( P2 @ M3 ) ) )
% 0.19/0.45 => ( P2 @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % infinite_descent
% 0.19/0.45 thf(fact_68_le__eq__less__or__eq,axiom,
% 0.19/0.45 ( ( ord_less_eq @ nat )
% 0.19/0.45 = ( ^ [M2: nat,N3: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ M2 @ N3 )
% 0.19/0.45 | ( M2 = N3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_eq_less_or_eq
% 0.19/0.45 thf(fact_69_ex__least__nat__less,axiom,
% 0.19/0.45 ! [P2: nat > $o,N: nat] :
% 0.19/0.45 ( ( P2 @ N )
% 0.19/0.45 => ( ~ ( P2 @ ( zero_zero @ nat ) )
% 0.19/0.45 => ? [K2: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ K2 @ N )
% 0.19/0.45 & ! [I: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ I @ K2 )
% 0.19/0.45 => ~ ( P2 @ I ) )
% 0.19/0.45 & ( P2 @ ( suc @ K2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ex_least_nat_less
% 0.19/0.45 thf(fact_70_infinite__descent0,axiom,
% 0.19/0.45 ! [P2: nat > $o,N: nat] :
% 0.19/0.45 ( ( P2 @ ( zero_zero @ nat ) )
% 0.19/0.45 => ( ! [N2: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.19/0.45 => ( ~ ( P2 @ N2 )
% 0.19/0.45 => ? [M3: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ M3 @ N2 )
% 0.19/0.45 & ~ ( P2 @ M3 ) ) ) )
% 0.19/0.45 => ( P2 @ N ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % infinite_descent0
% 0.19/0.45 thf(fact_71_less__or__eq__imp__le,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ( ord_less @ nat @ M @ N )
% 0.19/0.45 | ( M = N ) )
% 0.19/0.45 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_or_eq_imp_le
% 0.19/0.45 thf(fact_72_linorder__neqE__nat,axiom,
% 0.19/0.45 ! [X3: nat,Y3: nat] :
% 0.19/0.45 ( ( X3 != Y3 )
% 0.19/0.45 => ( ~ ( ord_less @ nat @ X3 @ Y3 )
% 0.19/0.45 => ( ord_less @ nat @ Y3 @ X3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % linorder_neqE_nat
% 0.19/0.45 thf(fact_73_Nat_Oex__has__greatest__nat,axiom,
% 0.19/0.45 ! [P2: nat > $o,K: nat,B2: nat] :
% 0.19/0.45 ( ( P2 @ K )
% 0.19/0.45 => ( ! [Y4: nat] :
% 0.19/0.45 ( ( P2 @ Y4 )
% 0.19/0.45 => ( ord_less_eq @ nat @ Y4 @ B2 ) )
% 0.19/0.45 => ? [X: nat] :
% 0.19/0.45 ( ( P2 @ X )
% 0.19/0.45 & ! [Y: nat] :
% 0.19/0.45 ( ( P2 @ Y )
% 0.19/0.45 => ( ord_less_eq @ nat @ Y @ X ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Nat.ex_has_greatest_nat
% 0.19/0.45 thf(fact_74_le__neq__implies__less,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ M @ N )
% 0.19/0.45 => ( ( M != N )
% 0.19/0.45 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_neq_implies_less
% 0.19/0.45 thf(fact_75_measure__induct__rule,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType] :
% 0.19/0.45 ( ( wellorder @ B )
% 0.19/0.45 => ! [F: A > B,P2: A > $o,A8: A] :
% 0.19/0.45 ( ! [X: A] :
% 0.19/0.45 ( ! [Y: A] :
% 0.19/0.45 ( ( ord_less @ B @ ( F @ Y ) @ ( F @ X ) )
% 0.19/0.45 => ( P2 @ Y ) )
% 0.19/0.45 => ( P2 @ X ) )
% 0.19/0.45 => ( P2 @ A8 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % measure_induct_rule
% 0.19/0.45 thf(fact_76_less__mono__imp__le__mono,axiom,
% 0.19/0.45 ! [F: nat > nat,I2: nat,J: nat] :
% 0.19/0.45 ( ! [I3: nat,J2: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ I3 @ J2 )
% 0.19/0.45 => ( ord_less @ nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 0.19/0.45 => ( ( ord_less_eq @ nat @ I2 @ J )
% 0.19/0.45 => ( ord_less_eq @ nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_mono_imp_le_mono
% 0.19/0.45 thf(fact_77_size__neq__size__imp__neq,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( size @ A )
% 0.19/0.45 => ! [X3: A,Y3: A] :
% 0.19/0.45 ( ( ( size_size @ A @ X3 )
% 0.19/0.45 != ( size_size @ A @ Y3 ) )
% 0.19/0.45 => ( X3 != Y3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % size_neq_size_imp_neq
% 0.19/0.45 thf(fact_78_infinite__descent__measure,axiom,
% 0.19/0.45 ! [A: $tType,P2: A > $o,V2: A > nat,X3: A] :
% 0.19/0.45 ( ! [X: A] :
% 0.19/0.45 ( ~ ( P2 @ X )
% 0.19/0.45 => ? [Y: A] :
% 0.19/0.45 ( ( ord_less @ nat @ ( V2 @ Y ) @ ( V2 @ X ) )
% 0.19/0.45 & ~ ( P2 @ Y ) ) )
% 0.19/0.45 => ( P2 @ X3 ) ) ).
% 0.19/0.45
% 0.19/0.45 % infinite_descent_measure
% 0.19/0.45 thf(fact_79_bot__nat__0_Oextremum__strict,axiom,
% 0.19/0.45 ! [A8: nat] :
% 0.19/0.45 ~ ( ord_less @ nat @ A8 @ ( zero_zero @ nat ) ) ).
% 0.19/0.45
% 0.19/0.45 % bot_nat_0.extremum_strict
% 0.19/0.45 thf(fact_80_bot__nat__0_Oextremum__unique,axiom,
% 0.19/0.45 ! [A8: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ A8 @ ( zero_zero @ nat ) )
% 0.19/0.45 = ( A8
% 0.19/0.45 = ( zero_zero @ nat ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % bot_nat_0.extremum_unique
% 0.19/0.45 thf(fact_81_infinite__descent0__measure,axiom,
% 0.19/0.45 ! [A: $tType,V2: A > nat,P2: A > $o,X3: A] :
% 0.19/0.45 ( ! [X: A] :
% 0.19/0.45 ( ( ( V2 @ X )
% 0.19/0.45 = ( zero_zero @ nat ) )
% 0.19/0.45 => ( P2 @ X ) )
% 0.19/0.45 => ( ! [X: A] :
% 0.19/0.45 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V2 @ X ) )
% 0.19/0.45 => ( ~ ( P2 @ X )
% 0.19/0.45 => ? [Y: A] :
% 0.19/0.45 ( ( ord_less @ nat @ ( V2 @ Y ) @ ( V2 @ X ) )
% 0.19/0.45 & ~ ( P2 @ Y ) ) ) )
% 0.19/0.45 => ( P2 @ X3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % infinite_descent0_measure
% 0.19/0.45 thf(fact_82_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.19/0.45 ! [A8: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ A8 @ ( zero_zero @ nat ) )
% 0.19/0.45 => ( A8
% 0.19/0.45 = ( zero_zero @ nat ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % bot_nat_0.extremum_uniqueI
% 0.19/0.45 thf(fact_83_lift__Suc__mono__le,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A )
% 0.19/0.45 => ! [F: nat > A,N: nat,N4: nat] :
% 0.19/0.45 ( ! [N2: nat] : ( ord_less_eq @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.19/0.45 => ( ( ord_less_eq @ nat @ N @ N4 )
% 0.19/0.45 => ( ord_less_eq @ A @ ( F @ N ) @ ( F @ N4 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lift_Suc_mono_le
% 0.19/0.45 thf(fact_84_lift__Suc__antimono__le,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A )
% 0.19/0.45 => ! [F: nat > A,N: nat,N4: nat] :
% 0.19/0.45 ( ! [N2: nat] : ( ord_less_eq @ A @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.19/0.45 => ( ( ord_less_eq @ nat @ N @ N4 )
% 0.19/0.45 => ( ord_less_eq @ A @ ( F @ N4 ) @ ( F @ N ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lift_Suc_antimono_le
% 0.19/0.45 thf(fact_85_le__imp__less__Suc,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ M @ N )
% 0.19/0.45 => ( ord_less @ nat @ M @ ( suc @ N ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_imp_less_Suc
% 0.19/0.45 thf(fact_86_less__eq__Suc__le,axiom,
% 0.19/0.45 ( ( ord_less @ nat )
% 0.19/0.45 = ( ^ [N3: nat] : ( ord_less_eq @ nat @ ( suc @ N3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_eq_Suc_le
% 0.19/0.45 thf(fact_87_less__Suc__eq__le,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.19/0.45 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_Suc_eq_le
% 0.19/0.45 thf(fact_88_le__less__Suc__eq,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ M @ N )
% 0.19/0.45 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 0.19/0.45 = ( N = M ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_less_Suc_eq
% 0.19/0.45 thf(fact_89_Suc__le__lessD,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 0.19/0.45 => ( ord_less @ nat @ M @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % Suc_le_lessD
% 0.19/0.45 thf(fact_90_inc__induct,axiom,
% 0.19/0.45 ! [I2: nat,J: nat,P2: nat > $o] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ I2 @ J )
% 0.19/0.45 => ( ( P2 @ J )
% 0.19/0.45 => ( ! [N2: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ I2 @ N2 )
% 0.19/0.45 => ( ( ord_less @ nat @ N2 @ J )
% 0.19/0.45 => ( ( P2 @ ( suc @ N2 ) )
% 0.19/0.45 => ( P2 @ N2 ) ) ) )
% 0.19/0.45 => ( P2 @ I2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % inc_induct
% 0.19/0.45 thf(fact_91_dec__induct,axiom,
% 0.19/0.45 ! [I2: nat,J: nat,P2: nat > $o] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ I2 @ J )
% 0.19/0.45 => ( ( P2 @ I2 )
% 0.19/0.45 => ( ! [N2: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ I2 @ N2 )
% 0.19/0.45 => ( ( ord_less @ nat @ N2 @ J )
% 0.19/0.45 => ( ( P2 @ N2 )
% 0.19/0.45 => ( P2 @ ( suc @ N2 ) ) ) ) )
% 0.19/0.45 => ( P2 @ J ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dec_induct
% 0.19/0.45 thf(fact_92_Suc__le__eq,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 0.19/0.45 = ( ord_less @ nat @ M @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % Suc_le_eq
% 0.19/0.45 thf(fact_93_Suc__leI,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ M @ N )
% 0.19/0.45 => ( ord_less_eq @ nat @ ( suc @ M ) @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % Suc_leI
% 0.19/0.45 thf(fact_94_diff__less__mono,axiom,
% 0.19/0.45 ! [A8: nat,B2: nat,C: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ A8 @ B2 )
% 0.19/0.45 => ( ( ord_less_eq @ nat @ C @ A8 )
% 0.19/0.45 => ( ord_less @ nat @ ( minus_minus @ nat @ A8 @ C ) @ ( minus_minus @ nat @ B2 @ C ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % diff_less_mono
% 0.19/0.45 thf(fact_95_less__diff__iff,axiom,
% 0.19/0.45 ! [K: nat,M: nat,N: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ K @ M )
% 0.19/0.45 => ( ( ord_less_eq @ nat @ K @ N )
% 0.19/0.45 => ( ( ord_less @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 0.19/0.45 = ( ord_less @ nat @ M @ N ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_diff_iff
% 0.19/0.45 thf(fact_96_less__Suc__eq__0__disj,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.19/0.45 = ( ( M
% 0.19/0.45 = ( zero_zero @ nat ) )
% 0.19/0.45 | ? [J3: nat] :
% 0.19/0.45 ( ( M
% 0.19/0.45 = ( suc @ J3 ) )
% 0.19/0.45 & ( ord_less @ nat @ J3 @ N ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_Suc_eq_0_disj
% 0.19/0.45 thf(fact_97_gr0__implies__Suc,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.19/0.45 => ? [M4: nat] :
% 0.19/0.45 ( N
% 0.19/0.45 = ( suc @ M4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % gr0_implies_Suc
% 0.19/0.45 thf(fact_98_All__less__Suc2,axiom,
% 0.19/0.45 ! [N: nat,P2: nat > $o] :
% 0.19/0.45 ( ( ! [I4: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ I4 @ ( suc @ N ) )
% 0.19/0.45 => ( P2 @ I4 ) ) )
% 0.19/0.45 = ( ( P2 @ ( zero_zero @ nat ) )
% 0.19/0.45 & ! [I4: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ I4 @ N )
% 0.19/0.45 => ( P2 @ ( suc @ I4 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % All_less_Suc2
% 0.19/0.45 thf(fact_99_gr0__conv__Suc,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.19/0.45 = ( ? [M2: nat] :
% 0.19/0.45 ( N
% 0.19/0.45 = ( suc @ M2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % gr0_conv_Suc
% 0.19/0.45 thf(fact_100_Ex__less__Suc2,axiom,
% 0.19/0.45 ! [N: nat,P2: nat > $o] :
% 0.19/0.45 ( ( ? [I4: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ I4 @ ( suc @ N ) )
% 0.19/0.45 & ( P2 @ I4 ) ) )
% 0.19/0.45 = ( ( P2 @ ( zero_zero @ nat ) )
% 0.19/0.45 | ? [I4: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ I4 @ N )
% 0.19/0.45 & ( P2 @ ( suc @ I4 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Ex_less_Suc2
% 0.19/0.45 thf(fact_101_diff__less,axiom,
% 0.19/0.45 ! [N: nat,M: nat] :
% 0.19/0.45 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.19/0.45 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 0.19/0.45 => ( ord_less @ nat @ ( minus_minus @ nat @ M @ N ) @ M ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % diff_less
% 0.19/0.45 thf(fact_102_transitive__stepwise__le,axiom,
% 0.19/0.45 ! [M: nat,N: nat,R: nat > nat > $o] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ M @ N )
% 0.19/0.45 => ( ! [X: nat] : ( R @ X @ X )
% 0.19/0.45 => ( ! [X: nat,Y4: nat,Z: nat] :
% 0.19/0.45 ( ( R @ X @ Y4 )
% 0.19/0.45 => ( ( R @ Y4 @ Z )
% 0.19/0.45 => ( R @ X @ Z ) ) )
% 0.19/0.45 => ( ! [N2: nat] : ( R @ N2 @ ( suc @ N2 ) )
% 0.19/0.45 => ( R @ M @ N ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % transitive_stepwise_le
% 0.19/0.45 thf(fact_103_nat__induct__at__least,axiom,
% 0.19/0.45 ! [M: nat,N: nat,P2: nat > $o] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ M @ N )
% 0.19/0.45 => ( ( P2 @ M )
% 0.19/0.45 => ( ! [N2: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.19/0.45 => ( ( P2 @ N2 )
% 0.19/0.45 => ( P2 @ ( suc @ N2 ) ) ) )
% 0.19/0.45 => ( P2 @ N ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % nat_induct_at_least
% 0.19/0.45 thf(fact_104_full__nat__induct,axiom,
% 0.19/0.45 ! [P2: nat > $o,N: nat] :
% 0.19/0.45 ( ! [N2: nat] :
% 0.19/0.45 ( ! [M3: nat] :
% 0.19/0.45 ( ( ord_less_eq @ nat @ ( suc @ M3 ) @ N2 )
% 0.19/0.45 => ( P2 @ M3 ) )
% 0.19/0.45 => ( P2 @ N2 ) )
% 0.19/0.45 => ( P2 @ N ) ) ).
% 0.19/0.45
% 0.19/0.45 % full_nat_induct
% 0.19/0.45 thf(fact_105_not__less__eq__eq,axiom,
% 0.19/0.45 ! [M: nat,N: nat] :
% 0.19/0.45 ( ( ~ ( ord_less_eq @ nat @ M @ N ) )
% 0.19/0.45 = ( ord_less_eq @ nat @ ( suc @ N ) @ M ) ) ).
% 0.19/0.45
% 0.19/0.45 % not_less_eq_eq
% 0.19/0.45 thf(fact_106_Suc__n__not__le__n,axiom,
% 0.19/0.45 ! [N: nat] :
% 0.19/0.45 ~ ( ord_less_eq @ nat @ ( suc @ N ) @ N ) ).
% 0.19/0.46
% 0.19/0.46 % Suc_n_not_le_n
% 0.19/0.46 thf(fact_107_le__Suc__eq,axiom,
% 0.19/0.46 ! [M: nat,N: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ M @ ( suc @ N ) )
% 0.19/0.46 = ( ( ord_less_eq @ nat @ M @ N )
% 0.19/0.46 | ( M
% 0.19/0.46 = ( suc @ N ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % le_Suc_eq
% 0.19/0.46 thf(fact_108_Suc__le__D,axiom,
% 0.19/0.46 ! [N: nat,M5: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ ( suc @ N ) @ M5 )
% 0.19/0.46 => ? [M4: nat] :
% 0.19/0.46 ( M5
% 0.19/0.46 = ( suc @ M4 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Suc_le_D
% 0.19/0.46 thf(fact_109_le__SucI,axiom,
% 0.19/0.46 ! [M: nat,N: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ M @ N )
% 0.19/0.46 => ( ord_less_eq @ nat @ M @ ( suc @ N ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % le_SucI
% 0.19/0.46 thf(fact_110_le__SucE,axiom,
% 0.19/0.46 ! [M: nat,N: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ M @ ( suc @ N ) )
% 0.19/0.46 => ( ~ ( ord_less_eq @ nat @ M @ N )
% 0.19/0.46 => ( M
% 0.19/0.46 = ( suc @ N ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % le_SucE
% 0.19/0.46 thf(fact_111_Suc__leD,axiom,
% 0.19/0.46 ! [M: nat,N: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 0.19/0.46 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.19/0.46
% 0.19/0.46 % Suc_leD
% 0.19/0.46 thf(fact_112_diff__le__mono2,axiom,
% 0.19/0.46 ! [M: nat,N: nat,L: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ M @ N )
% 0.19/0.46 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ L @ N ) @ ( minus_minus @ nat @ L @ M ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_le_mono2
% 0.19/0.46 thf(fact_113_le__diff__iff_H,axiom,
% 0.19/0.46 ! [A8: nat,C: nat,B2: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ A8 @ C )
% 0.19/0.46 => ( ( ord_less_eq @ nat @ B2 @ C )
% 0.19/0.46 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ A8 ) @ ( minus_minus @ nat @ C @ B2 ) )
% 0.19/0.46 = ( ord_less_eq @ nat @ B2 @ A8 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % le_diff_iff'
% 0.19/0.46 thf(fact_114_diff__le__self,axiom,
% 0.19/0.46 ! [M: nat,N: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ N ) @ M ) ).
% 0.19/0.46
% 0.19/0.46 % diff_le_self
% 0.19/0.46 thf(fact_115_diff__le__mono,axiom,
% 0.19/0.46 ! [M: nat,N: nat,L: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ M @ N )
% 0.19/0.46 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ L ) @ ( minus_minus @ nat @ N @ L ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_le_mono
% 0.19/0.46 thf(fact_116_Nat_Odiff__diff__eq,axiom,
% 0.19/0.46 ! [K: nat,M: nat,N: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ K @ M )
% 0.19/0.46 => ( ( ord_less_eq @ nat @ K @ N )
% 0.19/0.46 => ( ( minus_minus @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 0.19/0.46 = ( minus_minus @ nat @ M @ N ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Nat.diff_diff_eq
% 0.19/0.46 thf(fact_117_le__diff__iff,axiom,
% 0.19/0.46 ! [K: nat,M: nat,N: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ K @ M )
% 0.19/0.46 => ( ( ord_less_eq @ nat @ K @ N )
% 0.19/0.46 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 0.19/0.46 = ( ord_less_eq @ nat @ M @ N ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % le_diff_iff
% 0.19/0.46 thf(fact_118_eq__diff__iff,axiom,
% 0.19/0.46 ! [K: nat,M: nat,N: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ K @ M )
% 0.19/0.46 => ( ( ord_less_eq @ nat @ K @ N )
% 0.19/0.46 => ( ( ( minus_minus @ nat @ M @ K )
% 0.19/0.46 = ( minus_minus @ nat @ N @ K ) )
% 0.19/0.46 = ( M = N ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % eq_diff_iff
% 0.19/0.46 thf(fact_119_not0__implies__Suc,axiom,
% 0.19/0.46 ! [N: nat] :
% 0.19/0.46 ( ( N
% 0.19/0.46 != ( zero_zero @ nat ) )
% 0.19/0.46 => ? [M4: nat] :
% 0.19/0.46 ( N
% 0.19/0.46 = ( suc @ M4 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % not0_implies_Suc
% 0.19/0.46 thf(fact_120_old_Onat_Oinducts,axiom,
% 0.19/0.46 ! [P2: nat > $o,Nat: nat] :
% 0.19/0.46 ( ( P2 @ ( zero_zero @ nat ) )
% 0.19/0.46 => ( ! [Nat3: nat] :
% 0.19/0.46 ( ( P2 @ Nat3 )
% 0.19/0.46 => ( P2 @ ( suc @ Nat3 ) ) )
% 0.19/0.46 => ( P2 @ Nat ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.nat.inducts
% 0.19/0.46 thf(fact_121_old_Onat_Oexhaust,axiom,
% 0.19/0.46 ! [Y3: nat] :
% 0.19/0.46 ( ( Y3
% 0.19/0.46 != ( zero_zero @ nat ) )
% 0.19/0.46 => ~ ! [Nat3: nat] :
% 0.19/0.46 ( Y3
% 0.19/0.46 != ( suc @ Nat3 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.nat.exhaust
% 0.19/0.46 thf(fact_122_Zero__not__Suc,axiom,
% 0.19/0.46 ! [M: nat] :
% 0.19/0.46 ( ( zero_zero @ nat )
% 0.19/0.46 != ( suc @ M ) ) ).
% 0.19/0.46
% 0.19/0.46 % Zero_not_Suc
% 0.19/0.46 thf(fact_123_Zero__neq__Suc,axiom,
% 0.19/0.46 ! [M: nat] :
% 0.19/0.46 ( ( zero_zero @ nat )
% 0.19/0.46 != ( suc @ M ) ) ).
% 0.19/0.46
% 0.19/0.46 % Zero_neq_Suc
% 0.19/0.46 thf(fact_124_Suc__neq__Zero,axiom,
% 0.19/0.46 ! [M: nat] :
% 0.19/0.46 ( ( suc @ M )
% 0.19/0.46 != ( zero_zero @ nat ) ) ).
% 0.19/0.46
% 0.19/0.46 % Suc_neq_Zero
% 0.19/0.46 thf(fact_125_zero__induct,axiom,
% 0.19/0.46 ! [P2: nat > $o,K: nat] :
% 0.19/0.46 ( ( P2 @ K )
% 0.19/0.46 => ( ! [N2: nat] :
% 0.19/0.46 ( ( P2 @ ( suc @ N2 ) )
% 0.19/0.46 => ( P2 @ N2 ) )
% 0.19/0.46 => ( P2 @ ( zero_zero @ nat ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % zero_induct
% 0.19/0.46 thf(fact_126_diff__induct,axiom,
% 0.19/0.46 ! [P2: nat > nat > $o,M: nat,N: nat] :
% 0.19/0.46 ( ! [X: nat] : ( P2 @ X @ ( zero_zero @ nat ) )
% 0.19/0.46 => ( ! [Y4: nat] : ( P2 @ ( zero_zero @ nat ) @ ( suc @ Y4 ) )
% 0.19/0.46 => ( ! [X: nat,Y4: nat] :
% 0.19/0.46 ( ( P2 @ X @ Y4 )
% 0.19/0.46 => ( P2 @ ( suc @ X ) @ ( suc @ Y4 ) ) )
% 0.19/0.46 => ( P2 @ M @ N ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_induct
% 0.19/0.46 thf(fact_127_nat__induct,axiom,
% 0.19/0.46 ! [P2: nat > $o,N: nat] :
% 0.19/0.46 ( ( P2 @ ( zero_zero @ nat ) )
% 0.19/0.46 => ( ! [N2: nat] :
% 0.19/0.46 ( ( P2 @ N2 )
% 0.19/0.46 => ( P2 @ ( suc @ N2 ) ) )
% 0.19/0.46 => ( P2 @ N ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % nat_induct
% 0.19/0.46 thf(fact_128_nat_OdiscI,axiom,
% 0.19/0.46 ! [Nat: nat,X2: nat] :
% 0.19/0.46 ( ( Nat
% 0.19/0.46 = ( suc @ X2 ) )
% 0.19/0.46 => ( Nat
% 0.19/0.46 != ( zero_zero @ nat ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % nat.discI
% 0.19/0.46 thf(fact_129_old_Onat_Odistinct_I1_J,axiom,
% 0.19/0.46 ! [Nat2: nat] :
% 0.19/0.46 ( ( zero_zero @ nat )
% 0.19/0.46 != ( suc @ Nat2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.nat.distinct(1)
% 0.19/0.46 thf(fact_130_old_Onat_Odistinct_I2_J,axiom,
% 0.19/0.46 ! [Nat4: nat] :
% 0.19/0.46 ( ( suc @ Nat4 )
% 0.19/0.46 != ( zero_zero @ nat ) ) ).
% 0.19/0.46
% 0.19/0.46 % old.nat.distinct(2)
% 0.19/0.46 thf(fact_131_nat_Odistinct_I1_J,axiom,
% 0.19/0.46 ! [X2: nat] :
% 0.19/0.46 ( ( zero_zero @ nat )
% 0.19/0.46 != ( suc @ X2 ) ) ).
% 0.19/0.46
% 0.19/0.46 % nat.distinct(1)
% 0.19/0.46 thf(fact_132_minus__nat_Odiff__0,axiom,
% 0.19/0.46 ! [M: nat] :
% 0.19/0.46 ( ( minus_minus @ nat @ M @ ( zero_zero @ nat ) )
% 0.19/0.46 = M ) ).
% 0.19/0.46
% 0.19/0.46 % minus_nat.diff_0
% 0.19/0.46 thf(fact_133_diffs0__imp__equal,axiom,
% 0.19/0.46 ! [M: nat,N: nat] :
% 0.19/0.46 ( ( ( minus_minus @ nat @ M @ N )
% 0.19/0.46 = ( zero_zero @ nat ) )
% 0.19/0.46 => ( ( ( minus_minus @ nat @ N @ M )
% 0.19/0.46 = ( zero_zero @ nat ) )
% 0.19/0.46 => ( M = N ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diffs0_imp_equal
% 0.19/0.46 thf(fact_134_lift__Suc__mono__less__iff,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( order @ A )
% 0.19/0.46 => ! [F: nat > A,N: nat,M: nat] :
% 0.19/0.46 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.19/0.46 => ( ( ord_less @ A @ ( F @ N ) @ ( F @ M ) )
% 0.19/0.46 = ( ord_less @ nat @ N @ M ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lift_Suc_mono_less_iff
% 0.19/0.46 thf(fact_135_lift__Suc__mono__less,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( order @ A )
% 0.19/0.46 => ! [F: nat > A,N: nat,N4: nat] :
% 0.19/0.46 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.19/0.46 => ( ( ord_less @ nat @ N @ N4 )
% 0.19/0.46 => ( ord_less @ A @ ( F @ N ) @ ( F @ N4 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % lift_Suc_mono_less
% 0.19/0.46 thf(fact_136_diff__Suc__less,axiom,
% 0.19/0.46 ! [N: nat,I2: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.19/0.46 => ( ord_less @ nat @ ( minus_minus @ nat @ N @ ( suc @ I2 ) ) @ N ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_Suc_less
% 0.19/0.46 thf(fact_137_nat__induct__non__zero,axiom,
% 0.19/0.46 ! [N: nat,P2: nat > $o] :
% 0.19/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.19/0.46 => ( ( P2 @ ( one_one @ nat ) )
% 0.19/0.46 => ( ! [N2: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.19/0.46 => ( ( P2 @ N2 )
% 0.19/0.46 => ( P2 @ ( suc @ N2 ) ) ) )
% 0.19/0.46 => ( P2 @ N ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % nat_induct_non_zero
% 0.19/0.46 thf(fact_138_Suc__diff__le,axiom,
% 0.19/0.46 ! [N: nat,M: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ N @ M )
% 0.19/0.46 => ( ( minus_minus @ nat @ ( suc @ M ) @ N )
% 0.19/0.46 = ( suc @ ( minus_minus @ nat @ M @ N ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Suc_diff_le
% 0.19/0.46 thf(fact_139_One__nat__def,axiom,
% 0.19/0.46 ( ( one_one @ nat )
% 0.19/0.46 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % One_nat_def
% 0.19/0.46 thf(fact_140_not__less__less__Suc__eq,axiom,
% 0.19/0.46 ! [N: nat,M: nat] :
% 0.19/0.46 ( ~ ( ord_less @ nat @ N @ M )
% 0.19/0.46 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 0.19/0.46 = ( N = M ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % not_less_less_Suc_eq
% 0.19/0.46 thf(fact_141_strict__inc__induct,axiom,
% 0.19/0.46 ! [I2: nat,J: nat,P2: nat > $o] :
% 0.19/0.46 ( ( ord_less @ nat @ I2 @ J )
% 0.19/0.46 => ( ! [I3: nat] :
% 0.19/0.46 ( ( J
% 0.19/0.46 = ( suc @ I3 ) )
% 0.19/0.46 => ( P2 @ I3 ) )
% 0.19/0.46 => ( ! [I3: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I3 @ J )
% 0.19/0.46 => ( ( P2 @ ( suc @ I3 ) )
% 0.19/0.46 => ( P2 @ I3 ) ) )
% 0.19/0.46 => ( P2 @ I2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % strict_inc_induct
% 0.19/0.46 thf(fact_142_less__Suc__induct,axiom,
% 0.19/0.46 ! [I2: nat,J: nat,P2: nat > nat > $o] :
% 0.19/0.46 ( ( ord_less @ nat @ I2 @ J )
% 0.19/0.46 => ( ! [I3: nat] : ( P2 @ I3 @ ( suc @ I3 ) )
% 0.19/0.46 => ( ! [I3: nat,J2: nat,K2: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I3 @ J2 )
% 0.19/0.46 => ( ( ord_less @ nat @ J2 @ K2 )
% 0.19/0.46 => ( ( P2 @ I3 @ J2 )
% 0.19/0.46 => ( ( P2 @ J2 @ K2 )
% 0.19/0.46 => ( P2 @ I3 @ K2 ) ) ) ) )
% 0.19/0.46 => ( P2 @ I2 @ J ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % less_Suc_induct
% 0.19/0.46 thf(fact_143_less__trans__Suc,axiom,
% 0.19/0.46 ! [I2: nat,J: nat,K: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I2 @ J )
% 0.19/0.46 => ( ( ord_less @ nat @ J @ K )
% 0.19/0.46 => ( ord_less @ nat @ ( suc @ I2 ) @ K ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % less_trans_Suc
% 0.19/0.46 thf(fact_144_Suc__less__SucD,axiom,
% 0.19/0.46 ! [M: nat,N: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.19/0.46 => ( ord_less @ nat @ M @ N ) ) ).
% 0.19/0.46
% 0.19/0.46 % Suc_less_SucD
% 0.19/0.46 thf(fact_145_less__antisym,axiom,
% 0.19/0.46 ! [N: nat,M: nat] :
% 0.19/0.46 ( ~ ( ord_less @ nat @ N @ M )
% 0.19/0.46 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 0.19/0.46 => ( M = N ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % less_antisym
% 0.19/0.46 thf(fact_146_Suc__less__eq2,axiom,
% 0.19/0.46 ! [N: nat,M: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ ( suc @ N ) @ M )
% 0.19/0.46 = ( ? [M6: nat] :
% 0.19/0.46 ( ( M
% 0.19/0.46 = ( suc @ M6 ) )
% 0.19/0.46 & ( ord_less @ nat @ N @ M6 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Suc_less_eq2
% 0.19/0.46 thf(fact_147_All__less__Suc,axiom,
% 0.19/0.46 ! [N: nat,P2: nat > $o] :
% 0.19/0.46 ( ( ! [I4: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I4 @ ( suc @ N ) )
% 0.19/0.46 => ( P2 @ I4 ) ) )
% 0.19/0.46 = ( ( P2 @ N )
% 0.19/0.46 & ! [I4: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I4 @ N )
% 0.19/0.46 => ( P2 @ I4 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % All_less_Suc
% 0.19/0.46 thf(fact_148_not__less__eq,axiom,
% 0.19/0.46 ! [M: nat,N: nat] :
% 0.19/0.46 ( ( ~ ( ord_less @ nat @ M @ N ) )
% 0.19/0.46 = ( ord_less @ nat @ N @ ( suc @ M ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % not_less_eq
% 0.19/0.46 thf(fact_149_less__Suc__eq,axiom,
% 0.19/0.46 ! [M: nat,N: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.19/0.46 = ( ( ord_less @ nat @ M @ N )
% 0.19/0.46 | ( M = N ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % less_Suc_eq
% 0.19/0.46 thf(fact_150_Ex__less__Suc,axiom,
% 0.19/0.46 ! [N: nat,P2: nat > $o] :
% 0.19/0.46 ( ( ? [I4: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I4 @ ( suc @ N ) )
% 0.19/0.46 & ( P2 @ I4 ) ) )
% 0.19/0.46 = ( ( P2 @ N )
% 0.19/0.46 | ? [I4: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I4 @ N )
% 0.19/0.46 & ( P2 @ I4 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Ex_less_Suc
% 0.19/0.46 thf(fact_151_less__SucI,axiom,
% 0.19/0.46 ! [M: nat,N: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ M @ N )
% 0.19/0.46 => ( ord_less @ nat @ M @ ( suc @ N ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % less_SucI
% 0.19/0.46 thf(fact_152_less__SucE,axiom,
% 0.19/0.46 ! [M: nat,N: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.19/0.46 => ( ~ ( ord_less @ nat @ M @ N )
% 0.19/0.46 => ( M = N ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % less_SucE
% 0.19/0.46 thf(fact_153_Suc__lessI,axiom,
% 0.19/0.46 ! [M: nat,N: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ M @ N )
% 0.19/0.46 => ( ( ( suc @ M )
% 0.19/0.46 != N )
% 0.19/0.46 => ( ord_less @ nat @ ( suc @ M ) @ N ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Suc_lessI
% 0.19/0.46 thf(fact_154_Suc__lessE,axiom,
% 0.19/0.46 ! [I2: nat,K: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ ( suc @ I2 ) @ K )
% 0.19/0.46 => ~ ! [J2: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I2 @ J2 )
% 0.19/0.46 => ( K
% 0.19/0.46 != ( suc @ J2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Suc_lessE
% 0.19/0.46 thf(fact_155_Suc__lessD,axiom,
% 0.19/0.46 ! [M: nat,N: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ ( suc @ M ) @ N )
% 0.19/0.46 => ( ord_less @ nat @ M @ N ) ) ).
% 0.19/0.46
% 0.19/0.46 % Suc_lessD
% 0.19/0.46 thf(fact_156_Nat_OlessE,axiom,
% 0.19/0.46 ! [I2: nat,K: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I2 @ K )
% 0.19/0.46 => ( ( K
% 0.19/0.46 != ( suc @ I2 ) )
% 0.19/0.46 => ~ ! [J2: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I2 @ J2 )
% 0.19/0.46 => ( K
% 0.19/0.46 != ( suc @ J2 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Nat.lessE
% 0.19/0.46 thf(fact_157_less__imp__diff__less,axiom,
% 0.19/0.46 ! [J: nat,K: nat,N: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ J @ K )
% 0.19/0.46 => ( ord_less @ nat @ ( minus_minus @ nat @ J @ N ) @ K ) ) ).
% 0.19/0.46
% 0.19/0.46 % less_imp_diff_less
% 0.19/0.46 thf(fact_158_diff__less__mono2,axiom,
% 0.19/0.46 ! [M: nat,N: nat,L: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ M @ N )
% 0.19/0.46 => ( ( ord_less @ nat @ M @ L )
% 0.19/0.46 => ( ord_less @ nat @ ( minus_minus @ nat @ L @ N ) @ ( minus_minus @ nat @ L @ M ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_less_mono2
% 0.19/0.46 thf(fact_159_Suc__diff__eq__diff__pred,axiom,
% 0.19/0.46 ! [N: nat,M: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.19/0.46 => ( ( minus_minus @ nat @ ( suc @ M ) @ N )
% 0.19/0.46 = ( minus_minus @ nat @ M @ ( minus_minus @ nat @ N @ ( one_one @ nat ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Suc_diff_eq_diff_pred
% 0.19/0.46 thf(fact_160_Suc__pred_H,axiom,
% 0.19/0.46 ! [N: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.19/0.46 => ( N
% 0.19/0.46 = ( suc @ ( minus_minus @ nat @ N @ ( one_one @ nat ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Suc_pred'
% 0.19/0.46 thf(fact_161_n__not__Suc__n,axiom,
% 0.19/0.46 ! [N: nat] :
% 0.19/0.46 ( N
% 0.19/0.46 != ( suc @ N ) ) ).
% 0.19/0.46
% 0.19/0.46 % n_not_Suc_n
% 0.19/0.46 thf(fact_162_Suc__inject,axiom,
% 0.19/0.46 ! [X3: nat,Y3: nat] :
% 0.19/0.46 ( ( ( suc @ X3 )
% 0.19/0.46 = ( suc @ Y3 ) )
% 0.19/0.46 => ( X3 = Y3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % Suc_inject
% 0.19/0.46 thf(fact_163_diff__commute,axiom,
% 0.19/0.46 ! [I2: nat,J: nat,K: nat] :
% 0.19/0.46 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I2 @ J ) @ K )
% 0.19/0.46 = ( minus_minus @ nat @ ( minus_minus @ nat @ I2 @ K ) @ J ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_commute
% 0.19/0.46 thf(fact_164_diff__less__Suc,axiom,
% 0.19/0.46 ! [M: nat,N: nat] : ( ord_less @ nat @ ( minus_minus @ nat @ M @ N ) @ ( suc @ M ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_less_Suc
% 0.19/0.46 thf(fact_165_Suc__diff__Suc,axiom,
% 0.19/0.46 ! [N: nat,M: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ N @ M )
% 0.19/0.46 => ( ( suc @ ( minus_minus @ nat @ M @ ( suc @ N ) ) )
% 0.19/0.46 = ( minus_minus @ nat @ M @ N ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Suc_diff_Suc
% 0.19/0.46 thf(fact_166_zero__induct__lemma,axiom,
% 0.19/0.46 ! [P2: nat > $o,K: nat,I2: nat] :
% 0.19/0.46 ( ( P2 @ K )
% 0.19/0.46 => ( ! [N2: nat] :
% 0.19/0.46 ( ( P2 @ ( suc @ N2 ) )
% 0.19/0.46 => ( P2 @ N2 ) )
% 0.19/0.46 => ( P2 @ ( minus_minus @ nat @ K @ I2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % zero_induct_lemma
% 0.19/0.46 thf(fact_167_AssumptionSubset3_I3_J,axiom,
% 0.19/0.46 ord_less @ nat @ nMsg @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % AssumptionSubset3(3)
% 0.19/0.46 thf(fact_168_length__greater__0__conv,axiom,
% 0.19/0.46 ! [A: $tType,Xs: list @ A] :
% 0.19/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.19/0.46 = ( Xs
% 0.19/0.46 != ( nil @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % length_greater_0_conv
% 0.19/0.46 thf(fact_169_length__0__conv,axiom,
% 0.19/0.46 ! [A: $tType,Xs: list @ A] :
% 0.19/0.46 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.19/0.46 = ( zero_zero @ nat ) )
% 0.19/0.46 = ( Xs
% 0.19/0.46 = ( nil @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % length_0_conv
% 0.19/0.46 thf(fact_170_diff__numeral__special_I9_J,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( neg_numeral @ A )
% 0.19/0.46 => ( ( minus_minus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
% 0.19/0.46 = ( zero_zero @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_numeral_special(9)
% 0.19/0.46 thf(fact_171_diff__gt__0__iff__gt,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ordered_ab_group_add @ A )
% 0.19/0.46 => ! [A8: A,B2: A] :
% 0.19/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A8 @ B2 ) )
% 0.19/0.46 = ( ord_less @ A @ B2 @ A8 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_gt_0_iff_gt
% 0.19/0.46 thf(fact_172_diff__ge__0__iff__ge,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ordered_ab_group_add @ A )
% 0.19/0.46 => ! [A8: A,B2: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A8 @ B2 ) )
% 0.19/0.46 = ( ord_less_eq @ A @ B2 @ A8 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_ge_0_iff_ge
% 0.19/0.46 thf(fact_173_EnabledIntermediate,axiom,
% 0.19/0.46 ! [I: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) )
% 0.19/0.46 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ I )
% 0.19/0.46 => ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ I ) @ msg ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % EnabledIntermediate
% 0.19/0.46 thf(fact_174__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,
% 0.19/0.46 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 ).
% 0.19/0.46
% 0.19/0.46 % \<open>enabled (fe (Suc index) ! (length (fe (Suc index)) - 1)) msg\<close>
% 0.19/0.46 thf(fact_175_LastOfIndex,axiom,
% 0.19/0.46 ( ( 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 ) ) ) )
% 0.19/0.46 = ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % LastOfIndex
% 0.19/0.46 thf(fact_176_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( cancel1352612707id_add @ A )
% 0.19/0.46 => ! [A8: A] :
% 0.19/0.46 ( ( minus_minus @ A @ A8 @ A8 )
% 0.19/0.46 = ( zero_zero @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % cancel_comm_monoid_add_class.diff_cancel
% 0.19/0.46 thf(fact_177_AssumptionFirstOccSetDecrOrConsumed_I1_J,axiom,
% 0.19/0.46 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) @ msg ).
% 0.19/0.46
% 0.19/0.46 % AssumptionFirstOccSetDecrOrConsumed(1)
% 0.19/0.46 thf(fact_178_Occ2_H,axiom,
% 0.19/0.46 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) @ msgInSet ).
% 0.19/0.46
% 0.19/0.46 % Occ2'
% 0.19/0.46 thf(fact_179_le__zero__eq,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( canoni770627133id_add @ A )
% 0.19/0.46 => ! [N: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 0.19/0.46 = ( N
% 0.19/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % le_zero_eq
% 0.19/0.46 thf(fact_180_not__gr__zero,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( canoni770627133id_add @ A )
% 0.19/0.46 => ! [N: A] :
% 0.19/0.46 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 0.19/0.46 = ( N
% 0.19/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % not_gr_zero
% 0.19/0.46 thf(fact_181_diff__self,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( group_add @ A )
% 0.19/0.46 => ! [A8: A] :
% 0.19/0.46 ( ( minus_minus @ A @ A8 @ A8 )
% 0.19/0.46 = ( zero_zero @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_self
% 0.19/0.46 thf(fact_182_diff__0__right,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( group_add @ A )
% 0.19/0.46 => ! [A8: A] :
% 0.19/0.46 ( ( minus_minus @ A @ A8 @ ( zero_zero @ A ) )
% 0.19/0.46 = A8 ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_0_right
% 0.19/0.46 thf(fact_183_zero__diff,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( comm_monoid_diff @ A )
% 0.19/0.46 => ! [A8: A] :
% 0.19/0.46 ( ( minus_minus @ A @ ( zero_zero @ A ) @ A8 )
% 0.19/0.46 = ( zero_zero @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % zero_diff
% 0.19/0.46 thf(fact_184_diff__zero,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( cancel1352612707id_add @ A )
% 0.19/0.46 => ! [A8: A] :
% 0.19/0.46 ( ( minus_minus @ A @ A8 @ ( zero_zero @ A ) )
% 0.19/0.46 = A8 ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_zero
% 0.19/0.46 thf(fact_185_EnabledInSuc,axiom,
% 0.19/0.46 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) ) @ msg ).
% 0.19/0.46
% 0.19/0.46 % EnabledInSuc
% 0.19/0.46 thf(fact_186_AssumptionSubset2_I2_J,axiom,
% 0.19/0.46 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) ) @ msgInSet ).
% 0.19/0.46
% 0.19/0.46 % AssumptionSubset2(2)
% 0.19/0.46 thf(fact_187_AssumptionSubset3_I4_J,axiom,
% 0.19/0.46 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ nMsg ) @ msg ).
% 0.19/0.46
% 0.19/0.46 % AssumptionSubset3(4)
% 0.19/0.46 thf(fact_188_AssumptionCase1ImplThesis_H,axiom,
% 0.19/0.46 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg ).
% 0.19/0.46
% 0.19/0.46 % AssumptionCase1ImplThesis'
% 0.19/0.46 thf(fact_189_zero__reorient,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( zero @ A )
% 0.19/0.46 => ! [X3: A] :
% 0.19/0.46 ( ( ( zero_zero @ A )
% 0.19/0.46 = X3 )
% 0.19/0.46 = ( X3
% 0.19/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % zero_reorient
% 0.19/0.46 thf(fact_190_one__reorient,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( one @ A )
% 0.19/0.46 => ! [X3: A] :
% 0.19/0.46 ( ( ( one_one @ A )
% 0.19/0.46 = X3 )
% 0.19/0.46 = ( X3
% 0.19/0.46 = ( one_one @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % one_reorient
% 0.19/0.46 thf(fact_191_diff__eq__diff__eq,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( group_add @ A )
% 0.19/0.46 => ! [A8: A,B2: A,C: A,D: A] :
% 0.19/0.46 ( ( ( minus_minus @ A @ A8 @ B2 )
% 0.19/0.46 = ( minus_minus @ A @ C @ D ) )
% 0.19/0.46 => ( ( A8 = B2 )
% 0.19/0.46 = ( C = D ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_eq_diff_eq
% 0.19/0.46 thf(fact_192_diff__right__commute,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( cancel146912293up_add @ A )
% 0.19/0.46 => ! [A8: A,C: A,B2: A] :
% 0.19/0.46 ( ( minus_minus @ A @ ( minus_minus @ A @ A8 @ C ) @ B2 )
% 0.19/0.46 = ( minus_minus @ A @ ( minus_minus @ A @ A8 @ B2 ) @ C ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_right_commute
% 0.19/0.46 thf(fact_193_neq__if__length__neq,axiom,
% 0.19/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.19/0.46 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.19/0.46 != ( size_size @ ( list @ A ) @ Ys ) )
% 0.19/0.46 => ( Xs != Ys ) ) ).
% 0.19/0.46
% 0.19/0.46 % neq_if_length_neq
% 0.19/0.46 thf(fact_194_Ex__list__of__length,axiom,
% 0.19/0.46 ! [A: $tType,N: nat] :
% 0.19/0.46 ? [Xs2: list @ A] :
% 0.19/0.46 ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.19/0.46 = N ) ).
% 0.19/0.46
% 0.19/0.46 % Ex_list_of_length
% 0.19/0.46 thf(fact_195_last__conv__nth,axiom,
% 0.19/0.46 ! [A: $tType,Xs: list @ A] :
% 0.19/0.46 ( ( Xs
% 0.19/0.46 != ( nil @ A ) )
% 0.19/0.46 => ( ( last @ A @ Xs )
% 0.19/0.46 = ( nth @ A @ Xs @ ( minus_minus @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( one_one @ nat ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % last_conv_nth
% 0.19/0.46 thf(fact_196_zero__le,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( canoni770627133id_add @ A )
% 0.19/0.46 => ! [X3: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X3 ) ) ).
% 0.19/0.46
% 0.19/0.46 % zero_le
% 0.19/0.46 thf(fact_197_le__numeral__extra_I3_J,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( linord1659791738miring @ A )
% 0.19/0.46 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % le_numeral_extra(3)
% 0.19/0.46 thf(fact_198_zero__less__iff__neq__zero,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( canoni770627133id_add @ A )
% 0.19/0.46 => ! [N: A] :
% 0.19/0.46 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 0.19/0.46 = ( N
% 0.19/0.46 != ( zero_zero @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % zero_less_iff_neq_zero
% 0.19/0.46 thf(fact_199_gr__implies__not__zero,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( canoni770627133id_add @ A )
% 0.19/0.46 => ! [M: A,N: A] :
% 0.19/0.46 ( ( ord_less @ A @ M @ N )
% 0.19/0.46 => ( N
% 0.19/0.46 != ( zero_zero @ A ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % gr_implies_not_zero
% 0.19/0.46 thf(fact_200_not__less__zero,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( canoni770627133id_add @ A )
% 0.19/0.46 => ! [N: A] :
% 0.19/0.46 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % not_less_zero
% 0.19/0.46 thf(fact_201_gr__zeroI,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( canoni770627133id_add @ A )
% 0.19/0.46 => ! [N: A] :
% 0.19/0.46 ( ( N
% 0.19/0.46 != ( zero_zero @ A ) )
% 0.19/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % gr_zeroI
% 0.19/0.46 thf(fact_202_less__numeral__extra_I3_J,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( linord1659791738miring @ A )
% 0.19/0.46 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % less_numeral_extra(3)
% 0.19/0.46 thf(fact_203_le__numeral__extra_I4_J,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( linord1659791738miring @ A )
% 0.19/0.46 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % le_numeral_extra(4)
% 0.19/0.46 thf(fact_204_diff__mono,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ordered_ab_group_add @ A )
% 0.19/0.46 => ! [A8: A,B2: A,D: A,C: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ A8 @ B2 )
% 0.19/0.46 => ( ( ord_less_eq @ A @ D @ C )
% 0.19/0.46 => ( ord_less_eq @ A @ ( minus_minus @ A @ A8 @ C ) @ ( minus_minus @ A @ B2 @ D ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_mono
% 0.19/0.46 thf(fact_205_diff__left__mono,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ordered_ab_group_add @ A )
% 0.19/0.46 => ! [B2: A,A8: A,C: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ B2 @ A8 )
% 0.19/0.46 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A8 ) @ ( minus_minus @ A @ C @ B2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_left_mono
% 0.19/0.46 thf(fact_206_diff__right__mono,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ordered_ab_group_add @ A )
% 0.19/0.46 => ! [A8: A,B2: A,C: A] :
% 0.19/0.46 ( ( ord_less_eq @ A @ A8 @ B2 )
% 0.19/0.46 => ( ord_less_eq @ A @ ( minus_minus @ A @ A8 @ C ) @ ( minus_minus @ A @ B2 @ C ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_right_mono
% 0.19/0.46 thf(fact_207_diff__eq__diff__less__eq,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ordered_ab_group_add @ A )
% 0.19/0.46 => ! [A8: A,B2: A,C: A,D: A] :
% 0.19/0.46 ( ( ( minus_minus @ A @ A8 @ B2 )
% 0.19/0.46 = ( minus_minus @ A @ C @ D ) )
% 0.19/0.46 => ( ( ord_less_eq @ A @ A8 @ B2 )
% 0.19/0.46 = ( ord_less_eq @ A @ C @ D ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_eq_diff_less_eq
% 0.19/0.46 thf(fact_208_eq__iff__diff__eq__0,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( group_add @ A )
% 0.19/0.46 => ( ( ^ [Y5: A,Z2: A] : ( Y5 = Z2 ) )
% 0.19/0.46 = ( ^ [A9: A,B3: A] :
% 0.19/0.46 ( ( minus_minus @ A @ A9 @ B3 )
% 0.19/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % eq_iff_diff_eq_0
% 0.19/0.46 thf(fact_209_less__numeral__extra_I4_J,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( linord1659791738miring @ A )
% 0.19/0.46 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % less_numeral_extra(4)
% 0.19/0.46 thf(fact_210_diff__strict__mono,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ordered_ab_group_add @ A )
% 0.19/0.46 => ! [A8: A,B2: A,D: A,C: A] :
% 0.19/0.46 ( ( ord_less @ A @ A8 @ B2 )
% 0.19/0.46 => ( ( ord_less @ A @ D @ C )
% 0.19/0.46 => ( ord_less @ A @ ( minus_minus @ A @ A8 @ C ) @ ( minus_minus @ A @ B2 @ D ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_strict_mono
% 0.19/0.46 thf(fact_211_diff__eq__diff__less,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ordered_ab_group_add @ A )
% 0.19/0.46 => ! [A8: A,B2: A,C: A,D: A] :
% 0.19/0.46 ( ( ( minus_minus @ A @ A8 @ B2 )
% 0.19/0.46 = ( minus_minus @ A @ C @ D ) )
% 0.19/0.46 => ( ( ord_less @ A @ A8 @ B2 )
% 0.19/0.46 = ( ord_less @ A @ C @ D ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_eq_diff_less
% 0.19/0.46 thf(fact_212_diff__strict__left__mono,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ordered_ab_group_add @ A )
% 0.19/0.46 => ! [B2: A,A8: A,C: A] :
% 0.19/0.46 ( ( ord_less @ A @ B2 @ A8 )
% 0.19/0.46 => ( ord_less @ A @ ( minus_minus @ A @ C @ A8 ) @ ( minus_minus @ A @ C @ B2 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_strict_left_mono
% 0.19/0.46 thf(fact_213_diff__strict__right__mono,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ordered_ab_group_add @ A )
% 0.19/0.46 => ! [A8: A,B2: A,C: A] :
% 0.19/0.46 ( ( ord_less @ A @ A8 @ B2 )
% 0.19/0.46 => ( ord_less @ A @ ( minus_minus @ A @ A8 @ C ) @ ( minus_minus @ A @ B2 @ C ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % diff_strict_right_mono
% 0.19/0.46 thf(fact_214_length__induct,axiom,
% 0.19/0.46 ! [A: $tType,P2: ( list @ A ) > $o,Xs: list @ A] :
% 0.19/0.46 ( ! [Xs2: list @ A] :
% 0.19/0.46 ( ! [Ys2: list @ A] :
% 0.19/0.46 ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ys2 ) @ ( size_size @ ( list @ A ) @ Xs2 ) )
% 0.19/0.46 => ( P2 @ Ys2 ) )
% 0.19/0.46 => ( P2 @ Xs2 ) )
% 0.19/0.46 => ( P2 @ Xs ) ) ).
% 0.19/0.46
% 0.19/0.46 % length_induct
% 0.19/0.46 thf(fact_215_le__iff__diff__le__0,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ordered_ab_group_add @ A )
% 0.19/0.46 => ( ( ord_less_eq @ A )
% 0.19/0.46 = ( ^ [A9: A,B3: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ A9 @ B3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % le_iff_diff_le_0
% 0.19/0.46 thf(fact_216_less__numeral__extra_I1_J,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( linord1659791738miring @ A )
% 0.19/0.46 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % less_numeral_extra(1)
% 0.19/0.46 thf(fact_217_less__iff__diff__less__0,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ordered_ab_group_add @ A )
% 0.19/0.46 => ( ( ord_less @ A )
% 0.19/0.46 = ( ^ [A9: A,B3: A] : ( ord_less @ A @ ( minus_minus @ A @ A9 @ B3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % less_iff_diff_less_0
% 0.19/0.46 thf(fact_218_list_Osize_I3_J,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( size_size @ ( list @ A ) @ ( nil @ A ) )
% 0.19/0.46 = ( zero_zero @ nat ) ) ).
% 0.19/0.46
% 0.19/0.46 % list.size(3)
% 0.19/0.46 thf(fact_219_nth__equalityI,axiom,
% 0.19/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.19/0.46 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.19/0.46 = ( size_size @ ( list @ A ) @ Ys ) )
% 0.19/0.46 => ( ! [I3: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I3 @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.19/0.46 => ( ( nth @ A @ Xs @ I3 )
% 0.19/0.46 = ( nth @ A @ Ys @ I3 ) ) )
% 0.19/0.46 => ( Xs = Ys ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % nth_equalityI
% 0.19/0.46 thf(fact_220_Skolem__list__nth,axiom,
% 0.19/0.46 ! [A: $tType,K: nat,P2: nat > A > $o] :
% 0.19/0.46 ( ( ! [I4: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I4 @ K )
% 0.19/0.46 => ? [X4: A] : ( P2 @ I4 @ X4 ) ) )
% 0.19/0.46 = ( ? [Xs3: list @ A] :
% 0.19/0.46 ( ( ( size_size @ ( list @ A ) @ Xs3 )
% 0.19/0.46 = K )
% 0.19/0.46 & ! [I4: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I4 @ K )
% 0.19/0.46 => ( P2 @ I4 @ ( nth @ A @ Xs3 @ I4 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Skolem_list_nth
% 0.19/0.46 thf(fact_221_list__eq__iff__nth__eq,axiom,
% 0.19/0.46 ! [A: $tType] :
% 0.19/0.46 ( ( ^ [Y5: list @ A,Z2: list @ A] : ( Y5 = Z2 ) )
% 0.19/0.46 = ( ^ [Xs3: list @ A,Ys3: list @ A] :
% 0.19/0.46 ( ( ( size_size @ ( list @ A ) @ Xs3 )
% 0.19/0.46 = ( size_size @ ( list @ A ) @ Ys3 ) )
% 0.19/0.46 & ! [I4: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ A ) @ Xs3 ) )
% 0.19/0.46 => ( ( nth @ A @ Xs3 @ I4 )
% 0.19/0.46 = ( nth @ A @ Ys3 @ I4 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % list_eq_iff_nth_eq
% 0.19/0.46 thf(fact_222_PrefixSameOnLow,axiom,
% 0.19/0.46 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 0.19/0.46 ( ( prefixList @ A @ L1 @ L2 )
% 0.19/0.46 => ! [Index: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ Index @ ( size_size @ ( list @ A ) @ L1 ) )
% 0.19/0.46 => ( ( nth @ A @ L1 @ Index )
% 0.19/0.46 = ( nth @ A @ L2 @ Index ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % PrefixSameOnLow
% 0.19/0.46 thf(fact_223_infiniteExecutionMsg_Osimps_I1_J,axiom,
% 0.19/0.46 ! [Cfg2: configuration_ext @ p @ v @ s @ product_unit,FStepCfg2: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg2: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] :
% 0.19/0.46 ( ( fLPThe221390223ionMsg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( zero_zero @ nat ) )
% 0.19/0.46 = ( nil @ ( message @ p @ v ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % infiniteExecutionMsg.simps(1)
% 0.19/0.46 thf(fact_224_AssumptionFair_I3_J,axiom,
% 0.19/0.46 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ n0 ) @ msg ).
% 0.19/0.46
% 0.19/0.46 % AssumptionFair(3)
% 0.19/0.46 thf(fact_225_AssumptionFair_I2_J,axiom,
% 0.19/0.46 ord_less @ nat @ n0 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ) ).
% 0.19/0.46
% 0.19/0.46 % AssumptionFair(2)
% 0.19/0.46 thf(fact_226_MinPredicate,axiom,
% 0.19/0.46 ! [P2: nat > $o] :
% 0.19/0.46 ( ? [X_1: nat] : ( P2 @ X_1 )
% 0.19/0.46 => ? [N0: nat] :
% 0.19/0.46 ( ( P2 @ N0 )
% 0.19/0.46 & ! [N5: nat] :
% 0.19/0.46 ( ( P2 @ N5 )
% 0.19/0.46 => ( ord_less_eq @ nat @ N0 @ N5 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % MinPredicate
% 0.19/0.46 thf(fact_227_PrefixListTransitive,axiom,
% 0.19/0.46 ! [A: $tType,L1: list @ A,L2: list @ A,L3: list @ A] :
% 0.19/0.46 ( ( prefixList @ A @ L1 @ L2 )
% 0.19/0.46 => ( ( prefixList @ A @ L2 @ L3 )
% 0.19/0.46 => ( prefixList @ A @ L1 @ L3 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % PrefixListTransitive
% 0.19/0.46 thf(fact_228_KeepProperty,axiom,
% 0.19/0.46 ! [Low: nat,P2: nat > $o,Q: nat > $o] :
% 0.19/0.46 ( ! [I3: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ Low @ I3 )
% 0.19/0.46 => ( ( P2 @ I3 )
% 0.19/0.46 => ( ( P2 @ ( suc @ I3 ) )
% 0.19/0.46 & ( Q @ I3 ) ) ) )
% 0.19/0.46 => ( ( P2 @ Low )
% 0.19/0.46 => ! [I: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ Low @ I )
% 0.19/0.46 => ( Q @ I ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % KeepProperty
% 0.19/0.46 thf(fact_229_NatPredicateTippingPoint,axiom,
% 0.19/0.46 ! [N22: nat,Pr: nat > $o] :
% 0.19/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N22 )
% 0.19/0.46 => ( ( Pr @ ( zero_zero @ nat ) )
% 0.19/0.46 => ( ~ ( Pr @ N22 )
% 0.19/0.46 => ? [N2: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ N2 @ N22 )
% 0.19/0.46 & ( Pr @ N2 )
% 0.19/0.46 & ~ ( Pr @ ( suc @ N2 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % NatPredicateTippingPoint
% 0.19/0.46 thf(fact_230_MinPredicate2,axiom,
% 0.19/0.46 ! [P2: nat > $o] :
% 0.19/0.46 ( ? [X_1: nat] : ( P2 @ X_1 )
% 0.19/0.46 => ? [N0: nat] :
% 0.19/0.46 ( ( P2 @ N0 )
% 0.19/0.46 & ( ( N0
% 0.19/0.46 = ( zero_zero @ nat ) )
% 0.19/0.46 | ~ ( P2 @ ( minus_minus @ nat @ N0 @ ( one_one @ nat ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % MinPredicate2
% 0.19/0.46 thf(fact_231_PrefixListMonotonicity,axiom,
% 0.19/0.46 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 0.19/0.46 ( ( prefixList @ A @ L1 @ L2 )
% 0.19/0.46 => ( ord_less @ nat @ ( size_size @ ( list @ A ) @ L1 ) @ ( size_size @ ( list @ A ) @ L2 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % PrefixListMonotonicity
% 0.19/0.46 thf(fact_232_infiniteExecutionMsg_Oelims,axiom,
% 0.19/0.46 ! [X3: configuration_ext @ p @ v @ s @ product_unit,Xa: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),Xb: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),Xc: nat,Y3: list @ ( message @ p @ v )] :
% 0.19/0.46 ( ( ( fLPThe221390223ionMsg @ p @ v @ s @ X3 @ Xa @ Xb @ Xc )
% 0.19/0.46 = Y3 )
% 0.19/0.46 => ( ( ( Xc
% 0.19/0.46 = ( zero_zero @ nat ) )
% 0.19/0.46 => ( Y3
% 0.19/0.46 != ( nil @ ( message @ p @ v ) ) ) )
% 0.19/0.46 => ~ ! [N2: nat] :
% 0.19/0.46 ( ( Xc
% 0.19/0.46 = ( suc @ N2 ) )
% 0.19/0.46 => ( Y3
% 0.19/0.46 != ( Xb @ ( fLPThe137922386ionCfg @ p @ v @ s @ X3 @ Xa @ Xb @ N2 ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ X3 @ Xa @ Xb @ N2 ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % infiniteExecutionMsg.elims
% 0.19/0.46 thf(fact_233_infiniteExecutionCfg_Osimps_I2_J,axiom,
% 0.19/0.46 ! [Cfg2: configuration_ext @ p @ v @ s @ product_unit,FStepCfg2: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg2: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N: nat] :
% 0.19/0.46 ( ( fLPThe137922386ionCfg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N ) )
% 0.19/0.46 = ( FStepCfg2 @ ( fLPThe137922386ionCfg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % infiniteExecutionCfg.simps(2)
% 0.19/0.46 thf(fact_234_infiniteExecutionMsg_Osimps_I2_J,axiom,
% 0.19/0.46 ! [Cfg2: configuration_ext @ p @ v @ s @ product_unit,FStepCfg2: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg2: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N: nat] :
% 0.19/0.46 ( ( fLPThe221390223ionMsg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N ) )
% 0.19/0.46 = ( FStepMsg2 @ ( fLPThe137922386ionCfg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % infiniteExecutionMsg.simps(2)
% 0.19/0.46 thf(fact_235_AssumpOcc6_H_I2_J,axiom,
% 0.19/0.46 ( msgInSet
% 0.19/0.46 != ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % AssumpOcc6'(2)
% 0.19/0.46 thf(fact_236_AssumptionFairContr,axiom,
% 0.19/0.46 ! [N5: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ n @ N5 )
% 0.19/0.46 => ! [N02: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ N02 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N5 ) ) )
% 0.19/0.46 => ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) @ N02 )
% 0.19/0.46 => ( msg
% 0.19/0.46 != ( nth @ ( message @ p @ v ) @ ( ft @ N5 ) @ N02 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % AssumptionFairContr
% 0.19/0.46 thf(fact_237_IPrefixList,axiom,
% 0.19/0.46 ! [I: nat] : ( prefixList @ ( message @ p @ v ) @ ( ft @ I ) @ ( ft @ ( suc @ I ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % IPrefixList
% 0.19/0.46 thf(fact_238_ShorterTrace,axiom,
% 0.19/0.46 ord_less @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % ShorterTrace
% 0.19/0.46 thf(fact_239_SameMsgOnLow,axiom,
% 0.19/0.46 ! [I: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 0.19/0.46 => ( ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ I )
% 0.19/0.46 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % SameMsgOnLow
% 0.19/0.46 thf(fact_240_SmallIndexTrace_H,axiom,
% 0.19/0.46 ord_less @ nat @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) ).
% 0.19/0.46
% 0.19/0.46 % SmallIndexTrace'
% 0.19/0.46 thf(fact_241_NotConsumedIntermediate,axiom,
% 0.19/0.46 ! [I: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 0.19/0.46 => ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ I )
% 0.19/0.46 => ( ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I )
% 0.19/0.46 != msg ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % NotConsumedIntermediate
% 0.19/0.46 thf(fact_242__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,
% 0.19/0.46 ~ ? [I: nat] :
% 0.19/0.46 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 0.19/0.46 & ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ I )
% 0.19/0.46 & ( msg
% 0.19/0.46 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % \<open>\<not> (\<exists>i<length (ft (Suc index)). length (ft index) \<le> i \<and> msg = ft (Suc index) ! i)\<close>
% 0.19/0.46 thf(fact_243_OccSameMsg_H,axiom,
% 0.19/0.46 ! [N5: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ n1 @ N5 )
% 0.19/0.46 => ( ( ord_less @ nat @ N5 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 0.19/0.46 => ( ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ N5 )
% 0.19/0.46 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ N5 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % OccSameMsg'
% 0.19/0.46 thf(fact_244_AssumptionSubset_I2_J,axiom,
% 0.19/0.46 firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msgInSet @ n1 ).
% 0.19/0.46
% 0.19/0.46 % AssumptionSubset(2)
% 0.19/0.46 thf(fact_245_MessageStaysOrConsumed,axiom,
% 0.19/0.46 ! [N1: nat,N22: nat,N: nat,Msg: message @ p @ v] :
% 0.19/0.46 ( ( ( ord_less_eq @ nat @ N1 @ N22 )
% 0.19/0.46 & ( ord_less @ nat @ N22 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ N ) ) )
% 0.19/0.46 & ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N ) @ N1 ) @ Msg ) )
% 0.19/0.46 => ( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N ) @ N22 ) @ Msg )
% 0.19/0.46 | ? [N03: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ N1 @ N03 )
% 0.19/0.46 & ( ord_less @ nat @ N03 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N ) ) )
% 0.19/0.46 & ( ( nth @ ( message @ p @ v ) @ ( ft @ N ) @ N03 )
% 0.19/0.46 = Msg ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % MessageStaysOrConsumed
% 0.19/0.46 thf(fact_246_AssumptionSubset_I3_J,axiom,
% 0.19/0.46 firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg ).
% 0.19/0.46
% 0.19/0.46 % AssumptionSubset(3)
% 0.19/0.46 thf(fact_247_Occ5_H,axiom,
% 0.19/0.46 ! [N5: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ n1 @ N5 )
% 0.19/0.46 => ( ( ord_less @ nat @ N5 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 0.19/0.46 => ( msgInSet
% 0.19/0.46 != ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ N5 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Occ5'
% 0.19/0.46 thf(fact_248_Case2ImplThesis,axiom,
% 0.19/0.46 ( ? [N02: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ n0 @ N02 )
% 0.19/0.46 & ( ord_less @ nat @ N02 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
% 0.19/0.46 & ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ N02 )
% 0.19/0.46 = msg ) )
% 0.19/0.46 => ? [N6: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ n @ N6 )
% 0.19/0.46 & ? [N03: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ n0 @ N03 )
% 0.19/0.46 & ( ord_less @ nat @ N03 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N6 ) ) )
% 0.19/0.46 & ( msg
% 0.19/0.46 = ( nth @ ( message @ p @ v ) @ ( ft @ N6 ) @ N03 ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % Case2ImplThesis
% 0.19/0.46 thf(fact_249_AssumptionSubset2_I5_J,axiom,
% 0.19/0.46 ! [N5: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ n1 @ N5 )
% 0.19/0.46 => ( ( ord_less @ nat @ N5 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 0.19/0.46 => ( msgInSet
% 0.19/0.46 != ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ N5 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % AssumptionSubset2(5)
% 0.19/0.46 thf(fact_250_AssumptionSubset3_I5_J,axiom,
% 0.19/0.46 ! [N5: nat] :
% 0.19/0.46 ( ( ord_less_eq @ nat @ nMsg @ N5 )
% 0.19/0.46 => ( ( ord_less @ nat @ N5 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 0.19/0.46 => ( msg
% 0.19/0.46 != ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ N5 ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 % AssumptionSubset3(5)
% 0.19/0.46
% 0.19/0.46 % Type constructors (16)
% 0.19/0.46 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.19/0.46 ! [A10: $tType,A11: $tType] :
% 0.19/0.46 ( ( order @ A11 )
% 0.19/0.46 => ( order @ ( A10 > A11 ) ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.19/0.46 canoni770627133id_add @ nat ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 0.19/0.46 linord1659791738miring @ nat ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 0.19/0.46 cancel146912293up_add @ nat ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 0.19/0.46 cancel1352612707id_add @ nat ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff,axiom,
% 0.19/0.46 comm_monoid_diff @ nat ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.19/0.46 wellorder @ nat ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Nat_Onat___Orderings_Oorder_1,axiom,
% 0.19/0.46 order @ nat ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.19/0.46 zero @ nat ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.19/0.46 one @ nat ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 0.19/0.46 size @ nat ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_HOL_Obool___Orderings_Oorder_2,axiom,
% 0.19/0.46 order @ $o ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_List_Olist___Nat_Osize_3,axiom,
% 0.19/0.46 ! [A10: $tType] : ( size @ ( list @ A10 ) ) ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_4,axiom,
% 0.19/0.46 wellorder @ product_unit ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_Product__Type_Ounit___Orderings_Oorder_5,axiom,
% 0.19/0.46 order @ product_unit ).
% 0.19/0.46
% 0.19/0.46 thf(tcon_AsynchronousSystem_Omessage___Nat_Osize_6,axiom,
% 0.19/0.46 ! [A10: $tType,A11: $tType] : ( size @ ( message @ A10 @ A11 ) ) ).
% 0.19/0.46
% 0.19/0.46 % Conjectures (1)
% 0.19/0.46 thf(conj_0,conjecture,
% 0.19/0.46 ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) )
% 0.19/0.46 = ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 2.36/1.68 ---- Embedded in THF ---
% 2.36/1.68 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.36/1.68 %%% Generated on Tue Feb 24 08:25:10 EST 2026
% 2.36/1.68 %%% using '$$dhol' embedding, version 1.3.0.
% 2.36/1.68 %%% Logic specification used:
% 2.36/1.68 %%% thf(spec, logic, $$dhol).
% 2.36/1.68
% 2.36/1.68 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.kfyzaKl7u5/DTF2DTF14431.p
% 2.36/1.68 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext, type, configuration_ext: ($tType > ($tType > ($tType > ($tType > $tType))))).
% 2.36/1.68 thf(ty_t_AsynchronousSystem_Omessage, type, message: ($tType > ($tType > $tType))).
% 2.36/1.68 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 2.36/1.68 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.36/1.68 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.36/1.68 thf(ty_tf_v, type, v: $tType).
% 2.36/1.68 thf(ty_tf_s, type, s: $tType).
% 2.36/1.68 thf(ty_tf_p, type, p: $tType).
% 2.36/1.68 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.36/1.68 thf(sy_cl_Nat_Osize, type, size: (!> [A:$tType]: ($o))).
% 2.36/1.68 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: ($o))).
% 2.36/1.68 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 2.36/1.68 thf(sy_cl_Num_Oneg__numeral, type, neg_numeral: (!> [A:$tType]: ($o))).
% 2.36/1.68 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.36/1.68 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 2.36/1.68 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 2.36/1.68 thf(sy_cl_Groups_Ocomm__monoid__diff, type, comm_monoid_diff: (!> [A:$tType]: ($o))).
% 2.36/1.68 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: ($o))).
% 2.36/1.68 thf(sy_cl_Groups_Ocancel__comm__monoid__add, type, cancel1352612707id_add: (!> [A:$tType]: ($o))).
% 2.36/1.68 thf(sy_cl_Groups_Ocancel__ab__semigroup__add, type, cancel146912293up_add: (!> [A:$tType]: ($o))).
% 2.36/1.68 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: ($o))).
% 2.36/1.68 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 2.36/1.68 thf(sy_c_AsynchronousSystem_Oenabled, type, enabled: (!> [P:$tType,V:$tType,S:$tType]: ((((((configuration_ext @ P) @ V) @ S) @ product_unit) > (((message @ P) @ V) > $o))))).
% 2.36/1.68 thf(sy_c_Execution_Oexecution_OfirstOccurrence, type, firstOccurrence: (!> [P:$tType,V:$tType,S:$tType]: (((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (((message @ P) @ V) > (nat > $o))))))).
% 2.36/1.68 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus_OinfiniteExecutionCfg, type, fLPThe137922386ionCfg: (!> [P:$tType,V:$tType,S:$tType]: ((((((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 > (list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit))))))))).
% 2.36/1.68 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus_OinfiniteExecutionMsg, type, fLPThe221390223ionMsg: (!> [P:$tType,V:$tType,S:$tType]: ((((((configuration_ext @ P) @ V) @ S) @ product_unit) > (((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)))) > (((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((message @ P) @ V)))) > (nat > (list @ ((message @ P) @ V))))))))).
% 2.36/1.68 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 2.36/1.68 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 2.36/1.68 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.36/1.68 thf(sy_c_ListUtilities_OprefixList, type, prefixList: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.36/1.68 thf(sy_c_List_Olast, type, last: (!> [A:$tType]: (((list @ A) > A)))).
% 2.36/1.68 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.36/1.68 thf(sy_c_List_Onth, type, nth: (!> [A:$tType]: (((list @ A) > (nat > A))))).
% 2.36/1.68 thf(sy_c_Nat_OSuc, type, suc: (nat > nat)).
% 2.36/1.68 thf(sy_c_Nat_Osize__class_Osize, type, size_size: (!> [A:$tType]: ((A > nat)))).
% 2.36/1.68 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.36/1.68 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.36/1.68 thf(sy_v_fe____, type, fe: (nat > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))).
% 2.36/1.68 thf(sy_v_ft____, type, ft: (nat > (list @ ((message @ p) @ v)))).
% 2.36/1.68 thf(sy_v_index____, type, index: nat).
% 2.36/1.68 thf(sy_v_msgInSet____, type, msgInSet: ((message @ p) @ v)).
% 2.36/1.68 thf(sy_v_msg____, type, msg: ((message @ p) @ v)).
% 2.36/1.68 thf(sy_v_n0____, type, n0: nat).
% 2.36/1.68 thf(sy_v_n1____, type, n1: nat).
% 2.36/1.68 thf(sy_v_nMsg____, type, nMsg: nat).
% 2.36/1.68 thf(sy_v_n____, type, n: nat).
% 2.36/1.68 thf(fact_0_Occ3_H, axiom, (((ord_less @ nat) @ n1) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index)))).
% 2.36/1.68 thf(fact_1_SameCfgOnLow, axiom, (! [I:nat]: (((((ord_less @ nat) @ I) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) => ((((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index)) @ I) = (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ I)))))).
% 2.36/1.68 thf(fact_2__092_060open_062fe_Aindex_A_B_An1_A_061_Afe_A_ISuc_Aindex_J_A_B_An1_092_060close_062, axiom, ((((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index)) @ n1) = (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ n1))).
% 2.36/1.68 thf(fact_3__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_060_Alength_A_Ife_Aindex_J_092_060close_062, axiom, (((ord_less @ nat) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) @ (one_one @ nat))) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index)))).
% 2.36/1.68 thf(fact_4_AssumptionSubset2_I3_J, axiom, (((ord_less @ nat) @ n1) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ (suc @ index))))).
% 2.36/1.68 thf(fact_5_AssumpOcc6_H_I1_J, axiom, (((ord_less @ nat) @ (zero_zero @ nat)) @ n1)).
% 2.36/1.68 thf(fact_6_diff__Suc__1, axiom, (! [N:nat]: (((((minus_minus @ nat) @ (suc @ N)) @ (one_one @ nat)) = N)))).
% 2.36/1.68 thf(fact_7_diff__Suc__Suc, axiom, (! [M:nat,N:nat]: (((((minus_minus @ nat) @ (suc @ M)) @ (suc @ N)) = (((minus_minus @ nat) @ M) @ N))))).
% 2.36/1.68 thf(fact_8_Suc__diff__diff, axiom, (! [M:nat,N:nat,K:nat]: (((((minus_minus @ nat) @ (((minus_minus @ nat) @ (suc @ M)) @ N)) @ (suc @ K)) = (((minus_minus @ nat) @ (((minus_minus @ nat) @ M) @ N)) @ K))))).
% 2.36/1.68 thf(fact_9_NotEmpty_I1_J, axiom, ((fe @ (suc @ index)) != (nil @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))).
% 2.36/1.68 thf(fact_10_IPrefixListEx, axiom, (! [I:nat]: ((((prefixList @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ I)) @ (fe @ (suc @ I)))))).
% 2.36/1.68 thf(fact_11_diff__Suc__eq__diff__pred, axiom, (! [M:nat,N:nat]: (((((minus_minus @ nat) @ M) @ (suc @ N)) = (((minus_minus @ nat) @ (((minus_minus @ nat) @ M) @ (one_one @ nat))) @ N))))).
% 2.36/1.68 thf(fact_12_AssumpOcc6_H_I3_J, axiom, (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index)) @ (((minus_minus @ nat) @ n1) @ (one_one @ nat)))) @ msgInSet)).
% 2.36/1.68 thf(fact_13__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Alength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_092_060close_062, axiom, (((ord_less_eq @ nat) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) @ (one_one @ nat))) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ (suc @ index)))) @ (one_one @ nat)))).
% 2.36/1.68 thf(fact_14_NotEmpty_I2_J, axiom, ((fe @ index) != (nil @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))).
% 2.36/1.68 thf(fact_15__092_060open_062n1_A_N_ASuc_A0_A_060_Alength_A_Ife_Aindex_J_A_N_ASuc_A0_092_060close_062, axiom, (((ord_less @ nat) @ (((minus_minus @ nat) @ n1) @ (suc @ (zero_zero @ nat)))) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) @ (suc @ (zero_zero @ nat))))).
% 2.36/1.68 thf(fact_16_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)))),N2:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N2) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N2) => ((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N2)))))) => ((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v))))]: (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (zero_zero @ nat)))) => ((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),N2:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N2) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N2) => ((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N2)))))) => ((((P2 @ A0) @ A1) @ A2) @ A3)))))))).
% 2.36/1.68 thf(fact_17_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J, axiom, (! [P2:(((((configuration_ext @ p) @ v) @ s) @ product_unit) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))) > (nat > $o)))),Q:(((((configuration_ext @ p) @ v) @ s) @ product_unit) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))) > (nat > $o)))),A4:((((configuration_ext @ p) @ v) @ s) @ product_unit),A5:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),A6:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),A7:nat]: (((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v))))]: (((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ (zero_zero @ nat)))) => ((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),N2:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N2) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N2) => ((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N2)))))) => ((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v))))]: (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (zero_zero @ nat)))) => ((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),N2:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N2) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N2) => ((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N2)))))) => ((((Q @ A4) @ A5) @ A6) @ A7)))))))).
% 2.36/1.68 thf(fact_18_old_Onat_Oinject, axiom, (! [Nat:nat,Nat2:nat]: ((((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))).
% 2.36/1.68 thf(fact_19_nat_Oinject, axiom, (! [X2:nat,Y2:nat]: ((((suc @ X2) = (suc @ Y2)) = (X2 = Y2))))).
% 2.36/1.68 thf(fact_20_AssumptionSubset_I1_J, axiom, (((ord_less_eq @ nat) @ n1) @ nMsg)).
% 2.36/1.68 thf(fact_21__092_060open_062fe_Aindex_A_092_060in_062_D_Alength_092_060close_062, axiom, (((ord_less @ nat) @ (zero_zero @ nat)) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index)))).
% 2.36/1.68 thf(fact_22_Suc__less__eq, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (suc @ M)) @ (suc @ N)) = (((ord_less @ nat) @ M) @ N))))).
% 2.36/1.68 thf(fact_23_Suc__mono, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less @ nat) @ (suc @ M)) @ (suc @ N)))))).
% 2.36/1.68 thf(fact_24_lessI, axiom, (! [N:nat]: ((((ord_less @ nat) @ N) @ (suc @ N))))).
% 2.36/1.68 thf(fact_25_neq0__conv, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ N))))).
% 2.36/1.68 thf(fact_26_less__nat__zero__code, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.36/1.68 thf(fact_27_bot__nat__0_Onot__eq__extremum, axiom, (! [A8:nat]: (((A8 != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ A8))))).
% 2.36/1.68 thf(fact_28_Suc__le__mono, axiom, (! [N:nat,M:nat]: (((((ord_less_eq @ nat) @ (suc @ N)) @ (suc @ M)) = (((ord_less_eq @ nat) @ N) @ M))))).
% 2.36/1.68 thf(fact_29_le0, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N)))).
% 2.36/1.68 thf(fact_30_bot__nat__0_Oextremum, axiom, (! [A8:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ A8)))).
% 2.36/1.68 thf(fact_31_diff__self__eq__0, axiom, (! [M:nat]: (((((minus_minus @ nat) @ M) @ M) = (zero_zero @ nat))))).
% 2.36/1.68 thf(fact_32_diff__0__eq__0, axiom, (! [N:nat]: (((((minus_minus @ nat) @ (zero_zero @ nat)) @ N) = (zero_zero @ nat))))).
% 2.36/1.68 thf(fact_33_diff__diff__cancel, axiom, (! [I2:nat,N:nat]: (((((ord_less_eq @ nat) @ I2) @ N) => ((((minus_minus @ nat) @ N) @ (((minus_minus @ nat) @ N) @ I2)) = I2))))).
% 2.36/1.68 thf(fact_34_Occ4_H, axiom, (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index)) @ n1)) @ msgInSet)).
% 2.36/1.68 thf(fact_35_AssumptionSubset2_I4_J, axiom, (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ n1)) @ msgInSet)).
% 2.36/1.68 thf(fact_36__092_060open_062enabled_A_Ife_Aindex_A_B_A_Ilength_A_Ife_Aindex_J_A_N_A1_J_J_AmsgInSet_092_060close_062, axiom, (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index)) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) @ (one_one @ nat)))) @ msgInSet)).
% 2.36/1.68 thf(fact_37_zero__less__Suc, axiom, (! [N:nat]: ((((ord_less @ nat) @ (zero_zero @ nat)) @ (suc @ N))))).
% 2.36/1.68 thf(fact_38_less__Suc0, axiom, (! [N:nat]: (((((ord_less @ nat) @ N) @ (suc @ (zero_zero @ nat))) = (N = (zero_zero @ nat)))))).
% 2.36/1.68 thf(fact_39_zero__less__diff, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (((minus_minus @ nat) @ N) @ M)) = (((ord_less @ nat) @ M) @ N))))).
% 2.36/1.68 thf(fact_40_diff__is__0__eq, axiom, (! [M:nat,N:nat]: ((((((minus_minus @ nat) @ M) @ N) = (zero_zero @ nat)) = (((ord_less_eq @ nat) @ M) @ N))))).
% 2.36/1.68 thf(fact_41_diff__is__0__eq_H, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((minus_minus @ nat) @ M) @ N) = (zero_zero @ nat)))))).
% 2.36/1.68 thf(fact_42_less__one, axiom, (! [N:nat]: (((((ord_less @ nat) @ N) @ (one_one @ nat)) = (N = (zero_zero @ nat)))))).
% 2.36/1.68 thf(fact_43_Suc__pred, axiom, (! [N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => ((suc @ (((minus_minus @ nat) @ N) @ (suc @ (zero_zero @ nat)))) = N))))).
% 2.36/1.68 thf(fact_44_Suc__diff__1, axiom, (! [N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => ((suc @ (((minus_minus @ nat) @ N) @ (one_one @ nat))) = N))))).
% 2.36/1.68 thf(fact_45_less__eq__nat_Osimps_I1_J, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N)))).
% 2.36/1.68 thf(fact_46_gr0I, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) => (((ord_less @ nat) @ (zero_zero @ nat)) @ N))))).
% 2.36/1.68 thf(fact_47_le__0__eq, axiom, (! [N:nat]: (((((ord_less_eq @ nat) @ N) @ (zero_zero @ nat)) = (N = (zero_zero @ nat)))))).
% 2.36/1.68 thf(fact_48_le__refl, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ N) @ N)))).
% 2.36/1.68 thf(fact_49_not__gr0, axiom, (! [N:nat]: (((~ ((((ord_less @ nat) @ (zero_zero @ nat)) @ N))) = (N = (zero_zero @ nat)))))).
% 2.36/1.68 thf(fact_50_le__trans, axiom, (! [I2:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I2) @ J) => ((((ord_less_eq @ nat) @ J) @ K) => (((ord_less_eq @ nat) @ I2) @ K)))))).
% 2.36/1.68 thf(fact_51_eq__imp__le, axiom, (! [M:nat,N:nat]: (((M = N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.36/1.68 thf(fact_52_not__less0, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.36/1.68 thf(fact_53_le__antisym, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((ord_less_eq @ nat) @ N) @ M) => (M = N)))))).
% 2.36/1.68 thf(fact_54_less__zeroE, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ (zero_zero @ nat))))))).
% 2.36/1.68 thf(fact_55_nat__less__le, axiom, ((ord_less @ nat) = (^ [M2:nat,N3:nat]: (((((ord_less_eq @ nat) @ M2) @ N3) & (M2 != N3)))))).
% 2.36/1.68 thf(fact_56_nat__neq__iff, axiom, (! [M:nat,N:nat]: (((M != N) = ((((ord_less @ nat) @ M) @ N) | (((ord_less @ nat) @ N) @ M)))))).
% 2.36/1.68 thf(fact_57_less__not__refl, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.36/1.68 thf(fact_58_nat__le__linear, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) | (((ord_less_eq @ nat) @ N) @ M))))).
% 2.36/1.68 thf(fact_59_less__not__refl2, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ N) @ M) => (M != N))))).
% 2.36/1.68 thf(fact_60_less__not__refl3, axiom, (! [S2:nat,T:nat]: (((((ord_less @ nat) @ S2) @ T) => (S2 != T))))).
% 2.36/1.68 thf(fact_61_measure__induct, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F:(A > B),P2:(A > $o),A8:A]: (((! [X:A]: (((! [Y:A]: (((((ord_less @ B) @ (F @ Y)) @ (F @ X)) => (P2 @ Y)))) => (P2 @ X)))) => (P2 @ A8)))))))).
% 2.36/1.68 thf(fact_62_ex__least__nat__le, axiom, (! [P2:(nat > $o),N:nat]: (((P2 @ N) => ((~ ((P2 @ (zero_zero @ nat)))) => (? [K2:nat]: (((((ord_less_eq @ nat) @ K2) @ N) & ((! [I:nat]: (((((ord_less @ nat) @ I) @ K2) => (~ ((P2 @ I)))))) & (P2 @ K2)))))))))).
% 2.36/1.68 thf(fact_63_gr__implies__not0, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (N != (zero_zero @ nat)))))).
% 2.36/1.68 thf(fact_64_less__imp__le__nat, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.36/1.68 thf(fact_65_less__irrefl__nat, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.36/1.68 thf(fact_66_nat__less__induct, axiom, (! [P2:(nat > $o),N:nat]: (((! [N2:nat]: (((! [M3:nat]: (((((ord_less @ nat) @ M3) @ N2) => (P2 @ M3)))) => (P2 @ N2)))) => (P2 @ N))))).
% 2.36/1.68 thf(fact_67_infinite__descent, axiom, (! [P2:(nat > $o),N:nat]: (((! [N2:nat]: (((~ ((P2 @ N2))) => (? [M3:nat]: (((((ord_less @ nat) @ M3) @ N2) & (~ ((P2 @ M3))))))))) => (P2 @ N))))).
% 2.36/1.68 thf(fact_68_le__eq__less__or__eq, axiom, ((ord_less_eq @ nat) = (^ [M2:nat,N3:nat]: (((((ord_less @ nat) @ M2) @ N3) | (M2 = N3)))))).
% 2.36/1.68 thf(fact_69_ex__least__nat__less, axiom, (! [P2:(nat > $o),N:nat]: (((P2 @ N) => ((~ ((P2 @ (zero_zero @ nat)))) => (? [K2:nat]: (((((ord_less @ nat) @ K2) @ N) & ((! [I:nat]: (((((ord_less_eq @ nat) @ I) @ K2) => (~ ((P2 @ I)))))) & (P2 @ (suc @ K2))))))))))).
% 2.36/1.68 thf(fact_70_infinite__descent0, axiom, (! [P2:(nat > $o),N:nat]: (((P2 @ (zero_zero @ nat)) => ((! [N2:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) => ((~ ((P2 @ N2))) => (? [M3:nat]: (((((ord_less @ nat) @ M3) @ N2) & (~ ((P2 @ M3)))))))))) => (P2 @ N)))))).
% 2.36/1.68 thf(fact_71_less__or__eq__imp__le, axiom, (! [M:nat,N:nat]: ((((((ord_less @ nat) @ M) @ N) | (M = N)) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.36/1.68 thf(fact_72_linorder__neqE__nat, axiom, (! [X3:nat,Y3:nat]: (((X3 != Y3) => ((~ ((((ord_less @ nat) @ X3) @ Y3))) => (((ord_less @ nat) @ Y3) @ X3)))))).
% 2.36/1.68 thf(fact_73_Nat_Oex__has__greatest__nat, axiom, (! [P2:(nat > $o),K:nat,B2:nat]: (((P2 @ K) => ((! [Y4:nat]: (((P2 @ Y4) => (((ord_less_eq @ nat) @ Y4) @ B2)))) => (? [X:nat]: (((P2 @ X) & (! [Y:nat]: (((P2 @ Y) => (((ord_less_eq @ nat) @ Y) @ X)))))))))))).
% 2.36/1.68 thf(fact_74_le__neq__implies__less, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((M != N) => (((ord_less @ nat) @ M) @ N)))))).
% 2.36/1.68 thf(fact_75_measure__induct__rule, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F:(A > B),P2:(A > $o),A8:A]: (((! [X:A]: (((! [Y:A]: (((((ord_less @ B) @ (F @ Y)) @ (F @ X)) => (P2 @ Y)))) => (P2 @ X)))) => (P2 @ A8)))))))).
% 2.36/1.68 thf(fact_76_less__mono__imp__le__mono, axiom, (! [F:(nat > nat),I2:nat,J:nat]: (((! [I3:nat,J2:nat]: (((((ord_less @ nat) @ I3) @ J2) => (((ord_less @ nat) @ (F @ I3)) @ (F @ J2))))) => ((((ord_less_eq @ nat) @ I2) @ J) => (((ord_less_eq @ nat) @ (F @ I2)) @ (F @ J))))))).
% 2.36/1.68 thf(fact_77_size__neq__size__imp__neq, axiom, (! [A:$tType]: (((size @ A) => (! [X3:A,Y3:A]: (((((size_size @ A) @ X3) != ((size_size @ A) @ Y3)) => (X3 != Y3)))))))).
% 2.36/1.68 thf(fact_78_infinite__descent__measure, axiom, (! [A:$tType,P2:(A > $o),V2:(A > nat),X3:A]: (((! [X:A]: (((~ ((P2 @ X))) => (? [Y:A]: (((((ord_less @ nat) @ (V2 @ Y)) @ (V2 @ X)) & (~ ((P2 @ Y))))))))) => (P2 @ X3))))).
% 2.36/1.68 thf(fact_79_bot__nat__0_Oextremum__strict, axiom, (! [A8:nat]: ((~ ((((ord_less @ nat) @ A8) @ (zero_zero @ nat))))))).
% 2.36/1.68 thf(fact_80_bot__nat__0_Oextremum__unique, axiom, (! [A8:nat]: (((((ord_less_eq @ nat) @ A8) @ (zero_zero @ nat)) = (A8 = (zero_zero @ nat)))))).
% 2.36/1.68 thf(fact_81_infinite__descent0__measure, axiom, (! [A:$tType,V2:(A > nat),P2:(A > $o),X3:A]: (((! [X:A]: ((((V2 @ X) = (zero_zero @ nat)) => (P2 @ X)))) => ((! [X:A]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (V2 @ X)) => ((~ ((P2 @ X))) => (? [Y:A]: (((((ord_less @ nat) @ (V2 @ Y)) @ (V2 @ X)) & (~ ((P2 @ Y)))))))))) => (P2 @ X3)))))).
% 2.36/1.68 thf(fact_82_bot__nat__0_Oextremum__uniqueI, axiom, (! [A8:nat]: (((((ord_less_eq @ nat) @ A8) @ (zero_zero @ nat)) => (A8 = (zero_zero @ nat)))))).
% 2.36/1.68 thf(fact_83_lift__Suc__mono__le, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N:nat,N4:nat]: (((! [N2:nat]: ((((ord_less_eq @ A) @ (F @ N2)) @ (F @ (suc @ N2))))) => ((((ord_less_eq @ nat) @ N) @ N4) => (((ord_less_eq @ A) @ (F @ N)) @ (F @ N4)))))))))).
% 2.36/1.68 thf(fact_84_lift__Suc__antimono__le, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N:nat,N4:nat]: (((! [N2:nat]: ((((ord_less_eq @ A) @ (F @ (suc @ N2))) @ (F @ N2)))) => ((((ord_less_eq @ nat) @ N) @ N4) => (((ord_less_eq @ A) @ (F @ N4)) @ (F @ N)))))))))).
% 2.36/1.68 thf(fact_85_le__imp__less__Suc, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => (((ord_less @ nat) @ M) @ (suc @ N)))))).
% 2.36/1.68 thf(fact_86_less__eq__Suc__le, axiom, ((ord_less @ nat) = (^ [N3:nat]: (((ord_less_eq @ nat) @ (suc @ N3)))))).
% 2.36/1.68 thf(fact_87_less__Suc__eq__le, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ (suc @ N)) = (((ord_less_eq @ nat) @ M) @ N))))).
% 2.36/1.68 thf(fact_88_le__less__Suc__eq, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((ord_less @ nat) @ N) @ (suc @ M)) = (N = M)))))).
% 2.36/1.68 thf(fact_89_Suc__le__lessD, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ (suc @ M)) @ N) => (((ord_less @ nat) @ M) @ N))))).
% 2.36/1.68 thf(fact_90_inc__induct, axiom, (! [I2:nat,J:nat,P2:(nat > $o)]: (((((ord_less_eq @ nat) @ I2) @ J) => ((P2 @ J) => ((! [N2:nat]: (((((ord_less_eq @ nat) @ I2) @ N2) => ((((ord_less @ nat) @ N2) @ J) => ((P2 @ (suc @ N2)) => (P2 @ N2)))))) => (P2 @ I2))))))).
% 2.36/1.68 thf(fact_91_dec__induct, axiom, (! [I2:nat,J:nat,P2:(nat > $o)]: (((((ord_less_eq @ nat) @ I2) @ J) => ((P2 @ I2) => ((! [N2:nat]: (((((ord_less_eq @ nat) @ I2) @ N2) => ((((ord_less @ nat) @ N2) @ J) => ((P2 @ N2) => (P2 @ (suc @ N2))))))) => (P2 @ J))))))).
% 2.36/1.68 thf(fact_92_Suc__le__eq, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ (suc @ M)) @ N) = (((ord_less @ nat) @ M) @ N))))).
% 2.36/1.68 thf(fact_93_Suc__leI, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ (suc @ M)) @ N))))).
% 2.36/1.68 thf(fact_94_diff__less__mono, axiom, (! [A8:nat,B2:nat,C:nat]: (((((ord_less @ nat) @ A8) @ B2) => ((((ord_less_eq @ nat) @ C) @ A8) => (((ord_less @ nat) @ (((minus_minus @ nat) @ A8) @ C)) @ (((minus_minus @ nat) @ B2) @ C))))))).
% 2.36/1.68 thf(fact_95_less__diff__iff, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ K) @ M) => ((((ord_less_eq @ nat) @ K) @ N) => ((((ord_less @ nat) @ (((minus_minus @ nat) @ M) @ K)) @ (((minus_minus @ nat) @ N) @ K)) = (((ord_less @ nat) @ M) @ N))))))).
% 2.36/1.68 thf(fact_96_less__Suc__eq__0__disj, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ (suc @ N)) = ((M = (zero_zero @ nat)) | (? [J3:nat]: (((M = (suc @ J3)) & (((ord_less @ nat) @ J3) @ N))))))))).
% 2.36/1.68 thf(fact_97_gr0__implies__Suc, axiom, (! [N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => (? [M4:nat]: ((N = (suc @ M4)))))))).
% 2.36/1.68 thf(fact_98_All__less__Suc2, axiom, (! [N:nat,P2:(nat > $o)]: (((! [I4:nat]: (((((ord_less @ nat) @ I4) @ (suc @ N)) => (P2 @ I4)))) = ((P2 @ (zero_zero @ nat)) & (! [I4:nat]: (((((ord_less @ nat) @ I4) @ N) => (P2 @ (suc @ I4)))))))))).
% 2.36/1.68 thf(fact_99_gr0__conv__Suc, axiom, (! [N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) = (? [M2:nat]: ((N = (suc @ M2)))))))).
% 2.36/1.68 thf(fact_100_Ex__less__Suc2, axiom, (! [N:nat,P2:(nat > $o)]: (((? [I4:nat]: (((((ord_less @ nat) @ I4) @ (suc @ N)) & (P2 @ I4)))) = ((P2 @ (zero_zero @ nat)) | (? [I4:nat]: (((((ord_less @ nat) @ I4) @ N) & (P2 @ (suc @ I4)))))))))).
% 2.36/1.68 thf(fact_101_diff__less, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => ((((ord_less @ nat) @ (zero_zero @ nat)) @ M) => (((ord_less @ nat) @ (((minus_minus @ nat) @ M) @ N)) @ M)))))).
% 2.36/1.68 thf(fact_102_transitive__stepwise__le, axiom, (! [M:nat,N:nat,R:(nat > (nat > $o))]: (((((ord_less_eq @ nat) @ M) @ N) => ((! [X:nat]: (((R @ X) @ X))) => ((! [X:nat,Y4:nat,Z:nat]: ((((R @ X) @ Y4) => (((R @ Y4) @ Z) => ((R @ X) @ Z))))) => ((! [N2:nat]: (((R @ N2) @ (suc @ N2)))) => ((R @ M) @ N)))))))).
% 2.36/1.68 thf(fact_103_nat__induct__at__least, axiom, (! [M:nat,N:nat,P2:(nat > $o)]: (((((ord_less_eq @ nat) @ M) @ N) => ((P2 @ M) => ((! [N2:nat]: (((((ord_less_eq @ nat) @ M) @ N2) => ((P2 @ N2) => (P2 @ (suc @ N2)))))) => (P2 @ N))))))).
% 2.36/1.68 thf(fact_104_full__nat__induct, axiom, (! [P2:(nat > $o),N:nat]: (((! [N2:nat]: (((! [M3:nat]: (((((ord_less_eq @ nat) @ (suc @ M3)) @ N2) => (P2 @ M3)))) => (P2 @ N2)))) => (P2 @ N))))).
% 2.36/1.68 thf(fact_105_not__less__eq__eq, axiom, (! [M:nat,N:nat]: (((~ ((((ord_less_eq @ nat) @ M) @ N))) = (((ord_less_eq @ nat) @ (suc @ N)) @ M))))).
% 2.36/1.68 thf(fact_106_Suc__n__not__le__n, axiom, (! [N:nat]: ((~ ((((ord_less_eq @ nat) @ (suc @ N)) @ N)))))).
% 2.36/1.68 thf(fact_107_le__Suc__eq, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ (suc @ N)) = ((((ord_less_eq @ nat) @ M) @ N) | (M = (suc @ N))))))).
% 2.36/1.68 thf(fact_108_Suc__le__D, axiom, (! [N:nat,M5:nat]: (((((ord_less_eq @ nat) @ (suc @ N)) @ M5) => (? [M4:nat]: ((M5 = (suc @ M4)))))))).
% 2.36/1.68 thf(fact_109_le__SucI, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ M) @ (suc @ N)))))).
% 2.36/1.68 thf(fact_110_le__SucE, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ (suc @ N)) => ((~ ((((ord_less_eq @ nat) @ M) @ N))) => (M = (suc @ N))))))).
% 2.36/1.68 thf(fact_111_Suc__leD, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ (suc @ M)) @ N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.36/1.68 thf(fact_112_diff__le__mono2, axiom, (! [M:nat,N:nat,L:nat]: (((((ord_less_eq @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ (((minus_minus @ nat) @ L) @ N)) @ (((minus_minus @ nat) @ L) @ M)))))).
% 2.36/1.68 thf(fact_113_le__diff__iff_H, axiom, (! [A8:nat,C:nat,B2:nat]: (((((ord_less_eq @ nat) @ A8) @ C) => ((((ord_less_eq @ nat) @ B2) @ C) => ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ C) @ A8)) @ (((minus_minus @ nat) @ C) @ B2)) = (((ord_less_eq @ nat) @ B2) @ A8))))))).
% 2.36/1.68 thf(fact_114_diff__le__self, axiom, (! [M:nat,N:nat]: ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ M) @ N)) @ M)))).
% 2.36/1.68 thf(fact_115_diff__le__mono, axiom, (! [M:nat,N:nat,L:nat]: (((((ord_less_eq @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ (((minus_minus @ nat) @ M) @ L)) @ (((minus_minus @ nat) @ N) @ L)))))).
% 2.36/1.68 thf(fact_116_Nat_Odiff__diff__eq, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ K) @ M) => ((((ord_less_eq @ nat) @ K) @ N) => ((((minus_minus @ nat) @ (((minus_minus @ nat) @ M) @ K)) @ (((minus_minus @ nat) @ N) @ K)) = (((minus_minus @ nat) @ M) @ N))))))).
% 2.36/1.68 thf(fact_117_le__diff__iff, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ K) @ M) => ((((ord_less_eq @ nat) @ K) @ N) => ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ M) @ K)) @ (((minus_minus @ nat) @ N) @ K)) = (((ord_less_eq @ nat) @ M) @ N))))))).
% 2.36/1.68 thf(fact_118_eq__diff__iff, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ K) @ M) => ((((ord_less_eq @ nat) @ K) @ N) => (((((minus_minus @ nat) @ M) @ K) = (((minus_minus @ nat) @ N) @ K)) = (M = N))))))).
% 2.36/1.68 thf(fact_119_not0__implies__Suc, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) => (? [M4:nat]: ((N = (suc @ M4)))))))).
% 2.36/1.68 thf(fact_120_old_Onat_Oinducts, axiom, (! [P2:(nat > $o),Nat:nat]: (((P2 @ (zero_zero @ nat)) => ((! [Nat3:nat]: (((P2 @ Nat3) => (P2 @ (suc @ Nat3))))) => (P2 @ Nat)))))).
% 2.36/1.68 thf(fact_121_old_Onat_Oexhaust, axiom, (! [Y3:nat]: (((Y3 != (zero_zero @ nat)) => (~ ((! [Nat3:nat]: ((Y3 != (suc @ Nat3)))))))))).
% 2.36/1.68 thf(fact_122_Zero__not__Suc, axiom, (! [M:nat]: (((zero_zero @ nat) != (suc @ M))))).
% 2.36/1.68 thf(fact_123_Zero__neq__Suc, axiom, (! [M:nat]: (((zero_zero @ nat) != (suc @ M))))).
% 2.36/1.68 thf(fact_124_Suc__neq__Zero, axiom, (! [M:nat]: (((suc @ M) != (zero_zero @ nat))))).
% 2.36/1.68 thf(fact_125_zero__induct, axiom, (! [P2:(nat > $o),K:nat]: (((P2 @ K) => ((! [N2:nat]: (((P2 @ (suc @ N2)) => (P2 @ N2)))) => (P2 @ (zero_zero @ nat))))))).
% 2.36/1.68 thf(fact_126_diff__induct, axiom, (! [P2:(nat > (nat > $o)),M:nat,N:nat]: (((! [X:nat]: (((P2 @ X) @ (zero_zero @ nat)))) => ((! [Y4:nat]: (((P2 @ (zero_zero @ nat)) @ (suc @ Y4)))) => ((! [X:nat,Y4:nat]: ((((P2 @ X) @ Y4) => ((P2 @ (suc @ X)) @ (suc @ Y4))))) => ((P2 @ M) @ N))))))).
% 2.36/1.68 thf(fact_127_nat__induct, axiom, (! [P2:(nat > $o),N:nat]: (((P2 @ (zero_zero @ nat)) => ((! [N2:nat]: (((P2 @ N2) => (P2 @ (suc @ N2))))) => (P2 @ N)))))).
% 2.36/1.68 thf(fact_128_nat_OdiscI, axiom, (! [Nat:nat,X2:nat]: (((Nat = (suc @ X2)) => (Nat != (zero_zero @ nat)))))).
% 2.36/1.68 thf(fact_129_old_Onat_Odistinct_I1_J, axiom, (! [Nat2:nat]: (((zero_zero @ nat) != (suc @ Nat2))))).
% 2.36/1.68 thf(fact_130_old_Onat_Odistinct_I2_J, axiom, (! [Nat4:nat]: (((suc @ Nat4) != (zero_zero @ nat))))).
% 2.36/1.68 thf(fact_131_nat_Odistinct_I1_J, axiom, (! [X2:nat]: (((zero_zero @ nat) != (suc @ X2))))).
% 2.36/1.68 thf(fact_132_minus__nat_Odiff__0, axiom, (! [M:nat]: (((((minus_minus @ nat) @ M) @ (zero_zero @ nat)) = M)))).
% 2.36/1.68 thf(fact_133_diffs0__imp__equal, axiom, (! [M:nat,N:nat]: ((((((minus_minus @ nat) @ M) @ N) = (zero_zero @ nat)) => (((((minus_minus @ nat) @ N) @ M) = (zero_zero @ nat)) => (M = N)))))).
% 2.36/1.68 thf(fact_134_lift__Suc__mono__less__iff, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N:nat,M:nat]: (((! [N2:nat]: ((((ord_less @ A) @ (F @ N2)) @ (F @ (suc @ N2))))) => ((((ord_less @ A) @ (F @ N)) @ (F @ M)) = (((ord_less @ nat) @ N) @ M))))))))).
% 2.36/1.68 thf(fact_135_lift__Suc__mono__less, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N:nat,N4:nat]: (((! [N2:nat]: ((((ord_less @ A) @ (F @ N2)) @ (F @ (suc @ N2))))) => ((((ord_less @ nat) @ N) @ N4) => (((ord_less @ A) @ (F @ N)) @ (F @ N4)))))))))).
% 2.36/1.68 thf(fact_136_diff__Suc__less, axiom, (! [N:nat,I2:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => (((ord_less @ nat) @ (((minus_minus @ nat) @ N) @ (suc @ I2))) @ N))))).
% 2.36/1.68 thf(fact_137_nat__induct__non__zero, axiom, (! [N:nat,P2:(nat > $o)]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => ((P2 @ (one_one @ nat)) => ((! [N2:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) => ((P2 @ N2) => (P2 @ (suc @ N2)))))) => (P2 @ N))))))).
% 2.36/1.68 thf(fact_138_Suc__diff__le, axiom, (! [N:nat,M:nat]: (((((ord_less_eq @ nat) @ N) @ M) => ((((minus_minus @ nat) @ (suc @ M)) @ N) = (suc @ (((minus_minus @ nat) @ M) @ N))))))).
% 2.36/1.68 thf(fact_139_One__nat__def, axiom, ((one_one @ nat) = (suc @ (zero_zero @ nat)))).
% 2.36/1.68 thf(fact_140_not__less__less__Suc__eq, axiom, (! [N:nat,M:nat]: (((~ ((((ord_less @ nat) @ N) @ M))) => ((((ord_less @ nat) @ N) @ (suc @ M)) = (N = M)))))).
% 2.36/1.68 thf(fact_141_strict__inc__induct, axiom, (! [I2:nat,J:nat,P2:(nat > $o)]: (((((ord_less @ nat) @ I2) @ J) => ((! [I3:nat]: (((J = (suc @ I3)) => (P2 @ I3)))) => ((! [I3:nat]: (((((ord_less @ nat) @ I3) @ J) => ((P2 @ (suc @ I3)) => (P2 @ I3))))) => (P2 @ I2))))))).
% 2.36/1.68 thf(fact_142_less__Suc__induct, axiom, (! [I2:nat,J:nat,P2:(nat > (nat > $o))]: (((((ord_less @ nat) @ I2) @ J) => ((! [I3:nat]: (((P2 @ I3) @ (suc @ I3)))) => ((! [I3:nat,J2:nat,K2:nat]: (((((ord_less @ nat) @ I3) @ J2) => ((((ord_less @ nat) @ J2) @ K2) => (((P2 @ I3) @ J2) => (((P2 @ J2) @ K2) => ((P2 @ I3) @ K2))))))) => ((P2 @ I2) @ J))))))).
% 2.36/1.68 thf(fact_143_less__trans__Suc, axiom, (! [I2:nat,J:nat,K:nat]: (((((ord_less @ nat) @ I2) @ J) => ((((ord_less @ nat) @ J) @ K) => (((ord_less @ nat) @ (suc @ I2)) @ K)))))).
% 2.36/1.68 thf(fact_144_Suc__less__SucD, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (suc @ M)) @ (suc @ N)) => (((ord_less @ nat) @ M) @ N))))).
% 2.36/1.68 thf(fact_145_less__antisym, axiom, (! [N:nat,M:nat]: (((~ ((((ord_less @ nat) @ N) @ M))) => ((((ord_less @ nat) @ N) @ (suc @ M)) => (M = N)))))).
% 2.36/1.68 thf(fact_146_Suc__less__eq2, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ (suc @ N)) @ M) = (? [M6:nat]: (((M = (suc @ M6)) & (((ord_less @ nat) @ N) @ M6)))))))).
% 2.36/1.68 thf(fact_147_All__less__Suc, axiom, (! [N:nat,P2:(nat > $o)]: (((! [I4:nat]: (((((ord_less @ nat) @ I4) @ (suc @ N)) => (P2 @ I4)))) = ((P2 @ N) & (! [I4:nat]: (((((ord_less @ nat) @ I4) @ N) => (P2 @ I4))))))))).
% 2.36/1.68 thf(fact_148_not__less__eq, axiom, (! [M:nat,N:nat]: (((~ ((((ord_less @ nat) @ M) @ N))) = (((ord_less @ nat) @ N) @ (suc @ M)))))).
% 2.36/1.68 thf(fact_149_less__Suc__eq, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ (suc @ N)) = ((((ord_less @ nat) @ M) @ N) | (M = N)))))).
% 2.36/1.68 thf(fact_150_Ex__less__Suc, axiom, (! [N:nat,P2:(nat > $o)]: (((? [I4:nat]: (((((ord_less @ nat) @ I4) @ (suc @ N)) & (P2 @ I4)))) = ((P2 @ N) | (? [I4:nat]: (((((ord_less @ nat) @ I4) @ N) & (P2 @ I4))))))))).
% 2.36/1.68 thf(fact_151_less__SucI, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less @ nat) @ M) @ (suc @ N)))))).
% 2.36/1.68 thf(fact_152_less__SucE, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ (suc @ N)) => ((~ ((((ord_less @ nat) @ M) @ N))) => (M = N)))))).
% 2.36/1.68 thf(fact_153_Suc__lessI, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((suc @ M) != N) => (((ord_less @ nat) @ (suc @ M)) @ N)))))).
% 2.36/1.68 thf(fact_154_Suc__lessE, axiom, (! [I2:nat,K:nat]: (((((ord_less @ nat) @ (suc @ I2)) @ K) => (~ ((! [J2:nat]: (((((ord_less @ nat) @ I2) @ J2) => (K != (suc @ J2))))))))))).
% 2.36/1.68 thf(fact_155_Suc__lessD, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (suc @ M)) @ N) => (((ord_less @ nat) @ M) @ N))))).
% 2.36/1.68 thf(fact_156_Nat_OlessE, axiom, (! [I2:nat,K:nat]: (((((ord_less @ nat) @ I2) @ K) => ((K != (suc @ I2)) => (~ ((! [J2:nat]: (((((ord_less @ nat) @ I2) @ J2) => (K != (suc @ J2)))))))))))).
% 2.36/1.68 thf(fact_157_less__imp__diff__less, axiom, (! [J:nat,K:nat,N:nat]: (((((ord_less @ nat) @ J) @ K) => (((ord_less @ nat) @ (((minus_minus @ nat) @ J) @ N)) @ K))))).
% 2.36/1.68 thf(fact_158_diff__less__mono2, axiom, (! [M:nat,N:nat,L:nat]: (((((ord_less @ nat) @ M) @ N) => ((((ord_less @ nat) @ M) @ L) => (((ord_less @ nat) @ (((minus_minus @ nat) @ L) @ N)) @ (((minus_minus @ nat) @ L) @ M))))))).
% 2.36/1.68 thf(fact_159_Suc__diff__eq__diff__pred, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => ((((minus_minus @ nat) @ (suc @ M)) @ N) = (((minus_minus @ nat) @ M) @ (((minus_minus @ nat) @ N) @ (one_one @ nat)))))))).
% 2.36/1.68 thf(fact_160_Suc__pred_H, axiom, (! [N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => (N = (suc @ (((minus_minus @ nat) @ N) @ (one_one @ nat)))))))).
% 2.36/1.68 thf(fact_161_n__not__Suc__n, axiom, (! [N:nat]: ((N != (suc @ N))))).
% 2.36/1.68 thf(fact_162_Suc__inject, axiom, (! [X3:nat,Y3:nat]: ((((suc @ X3) = (suc @ Y3)) => (X3 = Y3))))).
% 2.36/1.68 thf(fact_163_diff__commute, axiom, (! [I2:nat,J:nat,K:nat]: (((((minus_minus @ nat) @ (((minus_minus @ nat) @ I2) @ J)) @ K) = (((minus_minus @ nat) @ (((minus_minus @ nat) @ I2) @ K)) @ J))))).
% 2.36/1.68 thf(fact_164_diff__less__Suc, axiom, (! [M:nat,N:nat]: ((((ord_less @ nat) @ (((minus_minus @ nat) @ M) @ N)) @ (suc @ M))))).
% 2.36/1.68 thf(fact_165_Suc__diff__Suc, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ N) @ M) => ((suc @ (((minus_minus @ nat) @ M) @ (suc @ N))) = (((minus_minus @ nat) @ M) @ N)))))).
% 2.36/1.68 thf(fact_166_zero__induct__lemma, axiom, (! [P2:(nat > $o),K:nat,I2:nat]: (((P2 @ K) => ((! [N2:nat]: (((P2 @ (suc @ N2)) => (P2 @ N2)))) => (P2 @ (((minus_minus @ nat) @ K) @ I2))))))).
% 2.36/1.68 thf(fact_167_AssumptionSubset3_I3_J, axiom, (((ord_less @ nat) @ nMsg) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ (suc @ index))))).
% 2.36/1.68 thf(fact_168_length__greater__0__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ ((size_size @ (list @ A)) @ Xs)) = (Xs != (nil @ A)))))).
% 2.36/1.68 thf(fact_169_length__0__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((size_size @ (list @ A)) @ Xs) = (zero_zero @ nat)) = (Xs = (nil @ A)))))).
% 2.36/1.68 thf(fact_170_diff__numeral__special_I9_J, axiom, (! [A:$tType]: (((neg_numeral @ A) => ((((minus_minus @ A) @ (one_one @ A)) @ (one_one @ A)) = (zero_zero @ A)))))).
% 2.36/1.68 thf(fact_171_diff__gt__0__iff__gt, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B2:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ (((minus_minus @ A) @ A8) @ B2)) = (((ord_less @ A) @ B2) @ A8)))))))).
% 2.36/1.68 thf(fact_172_diff__ge__0__iff__ge, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((minus_minus @ A) @ A8) @ B2)) = (((ord_less_eq @ A) @ B2) @ A8)))))))).
% 2.36/1.68 thf(fact_173_EnabledIntermediate, axiom, (! [I:nat]: (((((ord_less @ nat) @ I) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ (suc @ index)))) => ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) @ (one_one @ nat))) @ I) => (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ I)) @ msg)))))).
% 2.36/1.68 thf(fact_174__092_060open_062enabled_A_Ife_A_ISuc_Aindex_J_A_B_A_Ilength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_J_J_Amsg_092_060close_062, axiom, (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ (suc @ index)))) @ (one_one @ nat)))) @ msg)).
% 2.36/1.68 thf(fact_175_LastOfIndex, axiom, ((((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) @ (suc @ (zero_zero @ nat)))) = ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index)))).
% 2.36/1.68 thf(fact_176_cancel__comm__monoid__add__class_Odiff__cancel, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A8:A]: (((((minus_minus @ A) @ A8) @ A8) = (zero_zero @ A)))))))).
% 2.36/1.68 thf(fact_177_AssumptionFirstOccSetDecrOrConsumed_I1_J, axiom, (((((enabled @ p) @ v) @ s) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index))) @ msg)).
% 2.36/1.68 thf(fact_178_Occ2_H, axiom, (((((enabled @ p) @ v) @ s) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index))) @ msgInSet)).
% 2.36/1.68 thf(fact_179_le__zero__eq, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less_eq @ A) @ N) @ (zero_zero @ A)) = (N = (zero_zero @ A))))))))).
% 2.36/1.68 thf(fact_180_not__gr__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((~ ((((ord_less @ A) @ (zero_zero @ A)) @ N))) = (N = (zero_zero @ A))))))))).
% 2.36/1.68 thf(fact_181_diff__self, axiom, (! [A:$tType]: (((group_add @ A) => (! [A8:A]: (((((minus_minus @ A) @ A8) @ A8) = (zero_zero @ A)))))))).
% 2.36/1.68 thf(fact_182_diff__0__right, axiom, (! [A:$tType]: (((group_add @ A) => (! [A8:A]: (((((minus_minus @ A) @ A8) @ (zero_zero @ A)) = A8))))))).
% 2.36/1.68 thf(fact_183_zero__diff, axiom, (! [A:$tType]: (((comm_monoid_diff @ A) => (! [A8:A]: (((((minus_minus @ A) @ (zero_zero @ A)) @ A8) = (zero_zero @ A)))))))).
% 2.36/1.68 thf(fact_184_diff__zero, axiom, (! [A:$tType]: (((cancel1352612707id_add @ A) => (! [A8:A]: (((((minus_minus @ A) @ A8) @ (zero_zero @ A)) = A8))))))).
% 2.36/1.68 thf(fact_185_EnabledInSuc, axiom, (((((enabled @ p) @ v) @ s) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index)))) @ msg)).
% 2.36/1.68 thf(fact_186_AssumptionSubset2_I2_J, axiom, (((((enabled @ p) @ v) @ s) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index)))) @ msgInSet)).
% 2.36/1.68 thf(fact_187_AssumptionSubset3_I4_J, axiom, (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ nMsg)) @ msg)).
% 2.36/1.68 thf(fact_188_AssumptionCase1ImplThesis_H, axiom, (((((enabled @ p) @ v) @ s) @ ((last @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ n))) @ msg)).
% 2.36/1.68 thf(fact_189_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X3:A]: ((((zero_zero @ A) = X3) = (X3 = (zero_zero @ A))))))))).
% 2.36/1.68 thf(fact_190_one__reorient, axiom, (! [A:$tType]: (((one @ A) => (! [X3:A]: ((((one_one @ A) = X3) = (X3 = (one_one @ A))))))))).
% 2.36/1.68 thf(fact_191_diff__eq__diff__eq, axiom, (! [A:$tType]: (((group_add @ A) => (! [A8:A,B2:A,C:A,D:A]: ((((((minus_minus @ A) @ A8) @ B2) = (((minus_minus @ A) @ C) @ D)) => ((A8 = B2) = (C = D))))))))).
% 2.36/1.68 thf(fact_192_diff__right__commute, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [A8:A,C:A,B2:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A8) @ C)) @ B2) = (((minus_minus @ A) @ (((minus_minus @ A) @ A8) @ B2)) @ C)))))))).
% 2.36/1.68 thf(fact_193_neq__if__length__neq, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((size_size @ (list @ A)) @ Xs) != ((size_size @ (list @ A)) @ Ys)) => (Xs != Ys))))).
% 2.36/1.68 thf(fact_194_Ex__list__of__length, axiom, (! [A:$tType,N:nat]: ((? [Xs2:(list @ A)]: ((((size_size @ (list @ A)) @ Xs2) = N)))))).
% 2.36/1.68 thf(fact_195_last__conv__nth, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((last @ A) @ Xs) = (((nth @ A) @ Xs) @ (((minus_minus @ nat) @ ((size_size @ (list @ A)) @ Xs)) @ (one_one @ nat)))))))).
% 2.36/1.68 thf(fact_196_zero__le, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X3:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X3))))))).
% 2.36/1.68 thf(fact_197_le__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))).
% 2.36/1.68 thf(fact_198_zero__less__iff__neq__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ N) = (N != (zero_zero @ A))))))))).
% 2.36/1.68 thf(fact_199_gr__implies__not__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [M:A,N:A]: (((((ord_less @ A) @ M) @ N) => (N != (zero_zero @ A))))))))).
% 2.36/1.68 thf(fact_200_not__less__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: ((~ ((((ord_less @ A) @ N) @ (zero_zero @ A)))))))))).
% 2.36/1.68 thf(fact_201_gr__zeroI, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N:A]: (((N != (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ N)))))))).
% 2.36/1.68 thf(fact_202_less__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))))).
% 2.36/1.68 thf(fact_203_le__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (one_one @ A)) @ (one_one @ A)))))).
% 2.36/1.68 thf(fact_204_diff__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B2:A,D:A,C:A]: (((((ord_less_eq @ A) @ A8) @ B2) => ((((ord_less_eq @ A) @ D) @ C) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A8) @ C)) @ (((minus_minus @ A) @ B2) @ D)))))))))).
% 2.36/1.68 thf(fact_205_diff__left__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B2:A,A8:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A8) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ C) @ A8)) @ (((minus_minus @ A) @ C) @ B2))))))))).
% 2.36/1.68 thf(fact_206_diff__right__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A8) @ B2) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A8) @ C)) @ (((minus_minus @ A) @ B2) @ C))))))))).
% 2.36/1.68 thf(fact_207_diff__eq__diff__less__eq, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B2:A,C:A,D:A]: ((((((minus_minus @ A) @ A8) @ B2) = (((minus_minus @ A) @ C) @ D)) => ((((ord_less_eq @ A) @ A8) @ B2) = (((ord_less_eq @ A) @ C) @ D))))))))).
% 2.36/1.68 thf(fact_208_eq__iff__diff__eq__0, axiom, (! [A:$tType]: (((group_add @ A) => ((^ [Y5:A,Z2:A]: ((Y5 = Z2))) = (^ [A9:A,B3:A]: (((((minus_minus @ A) @ A9) @ B3) = (zero_zero @ A))))))))).
% 2.36/1.68 thf(fact_209_less__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (one_one @ A)))))))).
% 2.36/1.68 thf(fact_210_diff__strict__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B2:A,D:A,C:A]: (((((ord_less @ A) @ A8) @ B2) => ((((ord_less @ A) @ D) @ C) => (((ord_less @ A) @ (((minus_minus @ A) @ A8) @ C)) @ (((minus_minus @ A) @ B2) @ D)))))))))).
% 2.36/1.68 thf(fact_211_diff__eq__diff__less, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B2:A,C:A,D:A]: ((((((minus_minus @ A) @ A8) @ B2) = (((minus_minus @ A) @ C) @ D)) => ((((ord_less @ A) @ A8) @ B2) = (((ord_less @ A) @ C) @ D))))))))).
% 2.36/1.68 thf(fact_212_diff__strict__left__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B2:A,A8:A,C:A]: (((((ord_less @ A) @ B2) @ A8) => (((ord_less @ A) @ (((minus_minus @ A) @ C) @ A8)) @ (((minus_minus @ A) @ C) @ B2))))))))).
% 2.36/1.68 thf(fact_213_diff__strict__right__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B2:A,C:A]: (((((ord_less @ A) @ A8) @ B2) => (((ord_less @ A) @ (((minus_minus @ A) @ A8) @ C)) @ (((minus_minus @ A) @ B2) @ C))))))))).
% 2.36/1.68 thf(fact_214_length__induct, axiom, (! [A:$tType,P2:((list @ A) > $o),Xs:(list @ A)]: (((! [Xs2:(list @ A)]: (((! [Ys2:(list @ A)]: (((((ord_less @ nat) @ ((size_size @ (list @ A)) @ Ys2)) @ ((size_size @ (list @ A)) @ Xs2)) => (P2 @ Ys2)))) => (P2 @ Xs2)))) => (P2 @ Xs))))).
% 2.36/1.68 thf(fact_215_le__iff__diff__le__0, axiom, (! [A:$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))))))))).
% 2.36/1.68 thf(fact_216_less__numeral__extra_I1_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less @ A) @ (zero_zero @ A)) @ (one_one @ A)))))).
% 2.36/1.68 thf(fact_217_less__iff__diff__less__0, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => ((ord_less @ A) = (^ [A9:A,B3:A]: ((((ord_less @ A) @ (((minus_minus @ A) @ A9) @ B3)) @ (zero_zero @ A))))))))).
% 2.36/1.68 thf(fact_218_list_Osize_I3_J, axiom, (! [A:$tType]: ((((size_size @ (list @ A)) @ (nil @ A)) = (zero_zero @ nat))))).
% 2.36/1.68 thf(fact_219_nth__equalityI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ A)) @ Ys)) => ((! [I3:nat]: (((((ord_less @ nat) @ I3) @ ((size_size @ (list @ A)) @ Xs)) => ((((nth @ A) @ Xs) @ I3) = (((nth @ A) @ Ys) @ I3))))) => (Xs = Ys)))))).
% 2.36/1.68 thf(fact_220_Skolem__list__nth, axiom, (! [A:$tType,K:nat,P2:(nat > (A > $o))]: (((! [I4:nat]: (((((ord_less @ nat) @ I4) @ K) => (? [X4:A]: (((P2 @ I4) @ X4)))))) = (? [Xs3:(list @ A)]: (((((size_size @ (list @ A)) @ Xs3) = K) & (! [I4:nat]: (((((ord_less @ nat) @ I4) @ K) => ((P2 @ I4) @ (((nth @ A) @ Xs3) @ I4)))))))))))).
% 2.36/1.68 thf(fact_221_list__eq__iff__nth__eq, axiom, (! [A:$tType]: (((^ [Y5:(list @ A),Z2:(list @ A)]: ((Y5 = Z2))) = (^ [Xs3:(list @ A),Ys3:(list @ A)]: (((((size_size @ (list @ A)) @ Xs3) = ((size_size @ (list @ A)) @ Ys3)) & (! [I4:nat]: (((((ord_less @ nat) @ I4) @ ((size_size @ (list @ A)) @ Xs3)) => ((((nth @ A) @ Xs3) @ I4) = (((nth @ A) @ Ys3) @ I4)))))))))))).
% 2.36/1.68 thf(fact_222_PrefixSameOnLow, axiom, (! [A:$tType,L1:(list @ A),L2:(list @ A)]: (((((prefixList @ A) @ L1) @ L2) => (! [Index:nat]: (((((ord_less @ nat) @ Index) @ ((size_size @ (list @ A)) @ L1)) => ((((nth @ A) @ L1) @ Index) = (((nth @ A) @ L2) @ Index))))))))).
% 2.36/1.68 thf(fact_223_infiniteExecutionMsg_Osimps_I1_J, axiom, (! [Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg2:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg2:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v))))]: (((((((((fLPThe221390223ionMsg @ p) @ v) @ s) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ (zero_zero @ nat)) = (nil @ ((message @ p) @ v)))))).
% 2.36/1.68 thf(fact_224_AssumptionFair_I3_J, axiom, (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ n)) @ n0)) @ msg)).
% 2.36/1.68 thf(fact_225_AssumptionFair_I2_J, axiom, (((ord_less @ nat) @ n0) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ n)))).
% 2.36/1.68 thf(fact_226_MinPredicate, axiom, (! [P2:(nat > $o)]: (((? [X_1:nat]: ((P2 @ X_1))) => (? [N0:nat]: (((P2 @ N0) & (! [N5:nat]: (((P2 @ N5) => (((ord_less_eq @ nat) @ N0) @ N5))))))))))).
% 2.36/1.68 thf(fact_227_PrefixListTransitive, axiom, (! [A:$tType,L1:(list @ A),L2:(list @ A),L3:(list @ A)]: (((((prefixList @ A) @ L1) @ L2) => ((((prefixList @ A) @ L2) @ L3) => (((prefixList @ A) @ L1) @ L3)))))).
% 2.36/1.68 thf(fact_228_KeepProperty, axiom, (! [Low:nat,P2:(nat > $o),Q:(nat > $o)]: (((! [I3:nat]: (((((ord_less_eq @ nat) @ Low) @ I3) => ((P2 @ I3) => ((P2 @ (suc @ I3)) & (Q @ I3)))))) => ((P2 @ Low) => (! [I:nat]: (((((ord_less_eq @ nat) @ Low) @ I) => (Q @ I))))))))).
% 2.36/1.68 thf(fact_229_NatPredicateTippingPoint, axiom, (! [N22:nat,Pr:(nat > $o)]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N22) => ((Pr @ (zero_zero @ nat)) => ((~ ((Pr @ N22))) => (? [N2:nat]: (((((ord_less @ nat) @ N2) @ N22) & ((Pr @ N2) & (~ ((Pr @ (suc @ N2)))))))))))))).
% 2.36/1.68 thf(fact_230_MinPredicate2, axiom, (! [P2:(nat > $o)]: (((? [X_1:nat]: ((P2 @ X_1))) => (? [N0:nat]: (((P2 @ N0) & ((N0 = (zero_zero @ nat)) | (~ ((P2 @ (((minus_minus @ nat) @ N0) @ (one_one @ nat))))))))))))).
% 2.36/1.68 thf(fact_231_PrefixListMonotonicity, axiom, (! [A:$tType,L1:(list @ A),L2:(list @ A)]: (((((prefixList @ A) @ L1) @ L2) => (((ord_less @ nat) @ ((size_size @ (list @ A)) @ L1)) @ ((size_size @ (list @ A)) @ L2)))))).
% 2.36/1.68 thf(fact_232_infiniteExecutionMsg_Oelims, axiom, (! [X3:((((configuration_ext @ p) @ v) @ s) @ product_unit),Xa:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),Xb:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),Xc:nat,Y3:(list @ ((message @ p) @ v))]: ((((((((((fLPThe221390223ionMsg @ p) @ v) @ s) @ X3) @ Xa) @ Xb) @ Xc) = Y3) => (((Xc = (zero_zero @ nat)) => (Y3 != (nil @ ((message @ p) @ v)))) => (~ ((! [N2:nat]: (((Xc = (suc @ N2)) => (Y3 != ((Xb @ (((((((fLPThe137922386ionCfg @ p) @ v) @ s) @ X3) @ Xa) @ Xb) @ N2)) @ (((((((fLPThe221390223ionMsg @ p) @ v) @ s) @ X3) @ Xa) @ Xb) @ N2))))))))))))).
% 2.36/1.68 thf(fact_233_infiniteExecutionCfg_Osimps_I2_J, axiom, (! [Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg2:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg2:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),N:nat]: (((((((((fLPThe137922386ionCfg @ p) @ v) @ s) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ (suc @ N)) = ((FStepCfg2 @ (((((((fLPThe137922386ionCfg @ p) @ v) @ s) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ N)) @ (((((((fLPThe221390223ionMsg @ p) @ v) @ s) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ N)))))).
% 2.36/1.68 thf(fact_234_infiniteExecutionMsg_Osimps_I2_J, axiom, (! [Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg2:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg2:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),N:nat]: (((((((((fLPThe221390223ionMsg @ p) @ v) @ s) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ (suc @ N)) = ((FStepMsg2 @ (((((((fLPThe137922386ionCfg @ p) @ v) @ s) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ N)) @ (((((((fLPThe221390223ionMsg @ p) @ v) @ s) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ N)))))).
% 2.36/1.68 thf(fact_235_AssumpOcc6_H_I2_J, axiom, (msgInSet != (((nth @ ((message @ p) @ v)) @ (ft @ index)) @ (((minus_minus @ nat) @ n1) @ (one_one @ nat))))).
% 2.36/1.68 thf(fact_236_AssumptionFairContr, axiom, (! [N5:nat]: (((((ord_less_eq @ nat) @ n) @ N5) => (! [N02:nat]: (((((ord_less @ nat) @ N02) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ N5))) => ((((ord_less_eq @ nat) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ n))) @ N02) => (msg != (((nth @ ((message @ p) @ v)) @ (ft @ N5)) @ N02)))))))))).
% 2.36/1.68 thf(fact_237_IPrefixList, axiom, (! [I:nat]: ((((prefixList @ ((message @ p) @ v)) @ (ft @ I)) @ (ft @ (suc @ I)))))).
% 2.36/1.68 thf(fact_238_ShorterTrace, axiom, (((ord_less @ nat) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ (suc @ index))))).
% 2.36/1.68 thf(fact_239_SameMsgOnLow, axiom, (! [I:nat]: (((((ord_less @ nat) @ I) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) => ((((nth @ ((message @ p) @ v)) @ (ft @ index)) @ I) = (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ I)))))).
% 2.36/1.68 thf(fact_240_SmallIndexTrace_H, axiom, (((ord_less @ nat) @ (((minus_minus @ nat) @ n1) @ (one_one @ nat))) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index)))).
% 2.36/1.68 thf(fact_241_NotConsumedIntermediate, axiom, (! [I:nat]: (((((ord_less @ nat) @ I) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ (suc @ index)))) => ((((ord_less_eq @ nat) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) @ I) => ((((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ I) != msg)))))).
% 2.36/1.68 thf(fact_242__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ift_A_ISuc_Aindex_J_J_O_Alength_A_Ift_Aindex_J_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062, axiom, (~ ((? [I:nat]: (((((ord_less @ nat) @ I) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ (suc @ index)))) & ((((ord_less_eq @ nat) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) @ I) & (msg = (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ I))))))))).
% 2.36/1.68 thf(fact_243_OccSameMsg_H, axiom, (! [N5:nat]: (((((ord_less_eq @ nat) @ n1) @ N5) => ((((ord_less @ nat) @ N5) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) => ((((nth @ ((message @ p) @ v)) @ (ft @ index)) @ N5) = (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ N5))))))).
% 2.36/1.68 thf(fact_244_AssumptionSubset_I2_J, axiom, (((((((firstOccurrence @ p) @ v) @ s) @ (fe @ (suc @ index))) @ (ft @ (suc @ index))) @ msgInSet) @ n1)).
% 2.36/1.68 thf(fact_245_MessageStaysOrConsumed, axiom, (! [N1:nat,N22:nat,N: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 @ N))) & (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ N)) @ N1)) @ Msg))) => ((((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ N)) @ N22)) @ Msg) | (? [N03:nat]: (((((ord_less_eq @ nat) @ N1) @ N03) & ((((ord_less @ nat) @ N03) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ N))) & ((((nth @ ((message @ p) @ v)) @ (ft @ N)) @ N03) = Msg)))))))))).
% 2.36/1.68 thf(fact_246_AssumptionSubset_I3_J, axiom, (((((((firstOccurrence @ p) @ v) @ s) @ (fe @ (suc @ index))) @ (ft @ (suc @ index))) @ msg) @ nMsg)).
% 2.36/1.68 thf(fact_247_Occ5_H, axiom, (! [N5:nat]: (((((ord_less_eq @ nat) @ n1) @ N5) => ((((ord_less @ nat) @ N5) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) => (msgInSet != (((nth @ ((message @ p) @ v)) @ (ft @ index)) @ N5))))))).
% 2.36/1.68 thf(fact_248_Case2ImplThesis, axiom, ((? [N02:nat]: (((((ord_less_eq @ nat) @ n0) @ N02) & ((((ord_less @ nat) @ N02) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ n))) & ((((nth @ ((message @ p) @ v)) @ (ft @ n)) @ N02) = msg))))) => (? [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))))))))))).
% 2.36/1.68 thf(fact_249_AssumptionSubset2_I5_J, axiom, (! [N5:nat]: (((((ord_less_eq @ nat) @ n1) @ N5) => ((((ord_less @ nat) @ N5) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ (suc @ index)))) => (msgInSet != (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ N5))))))).
% 2.36/1.68 thf(fact_250_AssumptionSubset3_I5_J, axiom, (! [N5:nat]: (((((ord_less_eq @ nat) @ nMsg) @ N5) => ((((ord_less @ nat) @ N5) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ (suc @ index)))) => (msg != (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ N5))))))).
% 2.36/1.68 thf(tcon_fun___Orderings_Oorder, axiom, (! [A10:$tType,A11:$tType]: (((order @ A11) => (order @ (A10 > A11)))))).
% 2.36/1.68 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 2.36/1.68 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, axiom, (linord1659791738miring @ nat)).
% 2.36/1.68 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add, axiom, (cancel146912293up_add @ nat)).
% 2.36/1.68 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add, axiom, (cancel1352612707id_add @ nat)).
% 2.36/1.68 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff, axiom, (comm_monoid_diff @ nat)).
% 2.36/1.68 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, (wellorder @ nat)).
% 2.36/1.68 thf(tcon_Nat_Onat___Orderings_Oorder_1, axiom, (order @ nat)).
% 2.36/1.68 thf(tcon_Nat_Onat___Groups_Ozero, axiom, (zero @ nat)).
% 2.36/1.68 thf(tcon_Nat_Onat___Groups_Oone, axiom, (one @ nat)).
% 2.36/1.68 thf(tcon_Nat_Onat___Nat_Osize, axiom, (size @ nat)).
% 2.36/1.68 thf(tcon_HOL_Obool___Orderings_Oorder_2, axiom, (order @ $o)).
% 2.36/1.68 thf(tcon_List_Olist___Nat_Osize_3, axiom, (! [A10:$tType]: ((size @ (list @ A10))))).
% 2.36/1.68 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_4, axiom, (wellorder @ product_unit)).
% 2.36/1.68 thf(tcon_Product__Type_Ounit___Orderings_Oorder_5, axiom, (order @ product_unit)).
% 2.36/1.68 thf(tcon_AsynchronousSystem_Omessage___Nat_Osize_6, axiom, (! [A10:$tType,A11:$tType]: ((size @ ((message @ A10) @ A11))))).
% 2.36/1.68 thf(conj_0, conjecture, ((((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ (((minus_minus @ nat) @ n1) @ (one_one @ nat))) = (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index)) @ (((minus_minus @ nat) @ n1) @ (one_one @ nat))))).
% 2.36/1.68 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.kfyzaKl7u5/DTF2DTF14431.p
% 2.36/1.68 ------------------------
% 2.54/1.71 ---- Cleaned THF ---
% 2.54/1.71 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext,type,
% 2.54/1.71 configuration_ext: $tType > $tType > $tType > $tType > $tType ).
% 2.54/1.71
% 2.54/1.71 thf(ty_t_AsynchronousSystem_Omessage,type,
% 2.54/1.71 message: $tType > $tType > $tType ).
% 2.54/1.71
% 2.54/1.71 thf(ty_t_Product__Type_Ounit,type,
% 2.54/1.71 product_unit: $tType ).
% 2.54/1.71
% 2.54/1.71 thf(ty_t_List_Olist,type,
% 2.54/1.71 list: $tType > $tType ).
% 2.54/1.71
% 2.54/1.71 thf(ty_t_Nat_Onat,type,
% 2.54/1.71 nat: $tType ).
% 2.54/1.71
% 2.54/1.71 thf(ty_tf_v,type,
% 2.54/1.71 v: $tType ).
% 2.54/1.71
% 2.54/1.71 thf(ty_tf_s,type,
% 2.54/1.71 s: $tType ).
% 2.54/1.71
% 2.54/1.71 thf(ty_tf_p,type,
% 2.54/1.71 p: $tType ).
% 2.54/1.71
% 2.54/1.71 thf(sy_cl_HOL_Otype,type,
% 2.54/1.71 type:
% 2.54/1.71 !>[A: $tType] : $o ).
% 2.54/1.71
% 2.54/1.71 thf(sy_cl_Nat_Osize,type,
% 2.54/1.71 size:
% 2.54/1.71 !>[A: $tType] : $o ).
% 2.54/1.71
% 2.54/1.71 thf(sy_cl_Groups_Oone,type,
% 2.54/1.71 one:
% 2.54/1.71 !>[A: $tType] : $o ).
% 2.54/1.71
% 2.54/1.71 thf(sy_cl_Groups_Ozero,type,
% 2.54/1.71 zero:
% 2.54/1.71 !>[A: $tType] : $o ).
% 2.54/1.71
% 2.54/1.71 thf(sy_cl_Num_Oneg__numeral,type,
% 2.54/1.71 neg_numeral:
% 2.54/1.71 !>[A: $tType] : $o ).
% 2.54/1.71
% 2.54/1.71 thf(sy_cl_Orderings_Oorder,type,
% 2.54/1.71 order:
% 2.54/1.71 !>[A: $tType] : $o ).
% 2.54/1.71
% 2.54/1.71 thf(sy_cl_Groups_Ogroup__add,type,
% 2.54/1.71 group_add:
% 2.54/1.71 !>[A: $tType] : $o ).
% 2.54/1.71
% 2.54/1.71 thf(sy_cl_Orderings_Owellorder,type,
% 2.54/1.71 wellorder:
% 2.54/1.71 !>[A: $tType] : $o ).
% 2.54/1.71
% 2.54/1.71 thf(sy_cl_Groups_Ocomm__monoid__diff,type,
% 2.54/1.71 comm_monoid_diff:
% 2.54/1.71 !>[A: $tType] : $o ).
% 2.54/1.71
% 2.54/1.71 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 2.54/1.71 ordered_ab_group_add:
% 2.54/1.71 !>[A: $tType] : $o ).
% 2.54/1.71
% 2.54/1.71 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 2.54/1.71 cancel1352612707id_add:
% 2.54/1.71 !>[A: $tType] : $o ).
% 2.54/1.71
% 2.54/1.71 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 2.54/1.71 cancel146912293up_add:
% 2.54/1.71 !>[A: $tType] : $o ).
% 2.54/1.71
% 2.54/1.71 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 2.54/1.71 linord1659791738miring:
% 2.54/1.71 !>[A: $tType] : $o ).
% 2.54/1.71
% 2.54/1.71 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.54/1.71 canoni770627133id_add:
% 2.54/1.71 !>[A: $tType] : $o ).
% 2.54/1.71
% 2.54/1.71 thf(sy_c_AsynchronousSystem_Oenabled,type,
% 2.54/1.71 enabled:
% 2.54/1.71 !>[P: $tType,V: $tType,S: $tType] : ( ( configuration_ext @ P @ V @ S @ product_unit ) > ( message @ P @ V ) > $o ) ).
% 2.54/1.71
% 2.54/1.71 thf(sy_c_Execution_Oexecution_OfirstOccurrence,type,
% 2.54/1.71 firstOccurrence:
% 2.54/1.71 !>[P: $tType,V: $tType,S: $tType] : ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( message @ P @ V ) > nat > $o ) ).
% 2.54/1.71
% 2.54/1.71 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus_OinfiniteExecutionCfg,type,
% 2.54/1.71 fLPThe137922386ionCfg:
% 2.54/1.71 !>[P: $tType,V: $tType,S: $tType] : ( ( 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 > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus_OinfiniteExecutionMsg,type,
% 2.54/1.71 fLPThe221390223ionMsg:
% 2.54/1.71 !>[P: $tType,V: $tType,S: $tType] : ( ( 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 > ( list @ ( message @ P @ V ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 2.54/1.71 minus_minus:
% 2.54/1.71 !>[A: $tType] : ( A > A > A ) ).
% 2.54/1.71
% 2.54/1.71 thf(sy_c_Groups_Oone__class_Oone,type,
% 2.54/1.71 one_one:
% 2.54/1.71 !>[A: $tType] : A ).
% 2.54/1.71
% 2.54/1.71 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.54/1.71 zero_zero:
% 2.54/1.71 !>[A: $tType] : A ).
% 2.54/1.71
% 2.54/1.71 thf(sy_c_ListUtilities_OprefixList,type,
% 2.54/1.71 prefixList:
% 2.54/1.71 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.54/1.71
% 2.54/1.71 thf(sy_c_List_Olast,type,
% 2.54/1.71 last:
% 2.54/1.71 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 2.54/1.71
% 2.54/1.71 thf(sy_c_List_Olist_ONil,type,
% 2.54/1.71 nil:
% 2.54/1.71 !>[A: $tType] : ( list @ A ) ).
% 2.54/1.71
% 2.54/1.71 thf(sy_c_List_Onth,type,
% 2.54/1.71 nth:
% 2.54/1.71 !>[A: $tType] : ( ( list @ A ) > nat > A ) ).
% 2.54/1.71
% 2.54/1.71 thf(sy_c_Nat_OSuc,type,
% 2.54/1.71 suc: nat > nat ).
% 2.54/1.71
% 2.54/1.71 thf(sy_c_Nat_Osize__class_Osize,type,
% 2.54/1.71 size_size:
% 2.54/1.71 !>[A: $tType] : ( A > nat ) ).
% 2.54/1.71
% 2.54/1.71 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.54/1.71 ord_less:
% 2.54/1.71 !>[A: $tType] : ( A > A > $o ) ).
% 2.54/1.71
% 2.54/1.71 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.54/1.71 ord_less_eq:
% 2.54/1.71 !>[A: $tType] : ( A > A > $o ) ).
% 2.54/1.71
% 2.54/1.71 thf(sy_v_fe____,type,
% 2.54/1.71 fe: nat > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(sy_v_ft____,type,
% 2.54/1.71 ft: nat > ( list @ ( message @ p @ v ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(sy_v_index____,type,
% 2.54/1.71 index: nat ).
% 2.54/1.71
% 2.54/1.71 thf(sy_v_msgInSet____,type,
% 2.54/1.71 msgInSet: message @ p @ v ).
% 2.54/1.71
% 2.54/1.71 thf(sy_v_msg____,type,
% 2.54/1.71 msg: message @ p @ v ).
% 2.54/1.71
% 2.54/1.71 thf(sy_v_n0____,type,
% 2.54/1.71 n0: nat ).
% 2.54/1.71
% 2.54/1.71 thf(sy_v_n1____,type,
% 2.54/1.71 n1: nat ).
% 2.54/1.71
% 2.54/1.71 thf(sy_v_nMsg____,type,
% 2.54/1.71 nMsg: nat ).
% 2.54/1.71
% 2.54/1.71 thf(sy_v_n____,type,
% 2.54/1.71 n: nat ).
% 2.54/1.71
% 2.54/1.71 thf(fact_0_Occ3_H,axiom,
% 2.54/1.71 ord_less @ nat @ n1 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_1_SameCfgOnLow,axiom,
% 2.54/1.71 ! [I: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) )
% 2.54/1.71 => ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ I )
% 2.54/1.71 = ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ I ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_2__092_060open_062fe_Aindex_A_B_An1_A_061_Afe_A_ISuc_Aindex_J_A_B_An1_092_060close_062,axiom,
% 2.54/1.71 ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ n1 )
% 2.54/1.71 = ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ n1 ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_3__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_060_Alength_A_Ife_Aindex_J_092_060close_062,axiom,
% 2.54/1.71 ord_less @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_4_AssumptionSubset2_I3_J,axiom,
% 2.54/1.71 ord_less @ nat @ n1 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_5_AssumpOcc6_H_I1_J,axiom,
% 2.54/1.71 ord_less @ nat @ ( zero_zero @ nat ) @ n1 ).
% 2.54/1.71
% 2.54/1.71 thf(fact_6_diff__Suc__1,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ( ( minus_minus @ nat @ ( suc @ N ) @ ( one_one @ nat ) )
% 2.54/1.71 = N ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_7_diff__Suc__Suc,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( minus_minus @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 2.54/1.71 = ( minus_minus @ nat @ M @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_8_Suc__diff__diff,axiom,
% 2.54/1.71 ! [M: nat,N: nat,K: nat] :
% 2.54/1.71 ( ( minus_minus @ nat @ ( minus_minus @ nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 2.54/1.71 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ N ) @ K ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_9_NotEmpty_I1_J,axiom,
% 2.54/1.71 ( ( fe @ ( suc @ index ) )
% 2.54/1.71 != ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_10_IPrefixListEx,axiom,
% 2.54/1.71 ! [I: nat] : ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ I ) @ ( fe @ ( suc @ I ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_11_diff__Suc__eq__diff__pred,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( minus_minus @ nat @ M @ ( suc @ N ) )
% 2.54/1.71 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ ( one_one @ nat ) ) @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_12_AssumpOcc6_H_I3_J,axiom,
% 2.54/1.71 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) ) @ msgInSet ).
% 2.54/1.71
% 2.54/1.71 thf(fact_13__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Alength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_092_060close_062,axiom,
% 2.54/1.71 ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_14_NotEmpty_I2_J,axiom,
% 2.54/1.71 ( ( fe @ index )
% 2.54/1.71 != ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_15__092_060open_062n1_A_N_ASuc_A0_A_060_Alength_A_Ife_Aindex_J_A_N_ASuc_A0_092_060close_062,axiom,
% 2.54/1.71 ord_less @ nat @ ( minus_minus @ nat @ n1 @ ( suc @ ( zero_zero @ nat ) ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( suc @ ( zero_zero @ nat ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_16_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 2.54/1.71 ! [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] :
% 2.54/1.71 ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 2.54/1.71 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N2: nat] :
% 2.54/1.71 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 2.54/1.71 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 2.54/1.71 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 2.54/1.71 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 2.54/1.71 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N2: nat] :
% 2.54/1.71 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 2.54/1.71 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 2.54/1.71 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 2.54/1.71 => ( P2 @ A0 @ A1 @ A2 @ A3 ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_17_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 2.54/1.71 ! [P2: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,Q: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,A4: configuration_ext @ p @ v @ s @ product_unit,A5: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),A6: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),A7: nat] :
% 2.54/1.71 ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 2.54/1.71 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N2: nat] :
% 2.54/1.71 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 2.54/1.71 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 2.54/1.71 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 2.54/1.71 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 2.54/1.71 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N2: nat] :
% 2.54/1.71 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 2.54/1.71 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N2 )
% 2.54/1.71 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N2 ) ) ) )
% 2.54/1.71 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_18_old_Onat_Oinject,axiom,
% 2.54/1.71 ! [Nat: nat,Nat2: nat] :
% 2.54/1.71 ( ( ( suc @ Nat )
% 2.54/1.71 = ( suc @ Nat2 ) )
% 2.54/1.71 = ( Nat = Nat2 ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_19_nat_Oinject,axiom,
% 2.54/1.71 ! [X2: nat,Y2: nat] :
% 2.54/1.71 ( ( ( suc @ X2 )
% 2.54/1.71 = ( suc @ Y2 ) )
% 2.54/1.71 = ( X2 = Y2 ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_20_AssumptionSubset_I1_J,axiom,
% 2.54/1.71 ord_less_eq @ nat @ n1 @ nMsg ).
% 2.54/1.71
% 2.54/1.71 thf(fact_21__092_060open_062fe_Aindex_A_092_060in_062_D_Alength_092_060close_062,axiom,
% 2.54/1.71 ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_22_Suc__less__eq,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 2.54/1.71 = ( ord_less @ nat @ M @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_23_Suc__mono,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ M @ N )
% 2.54/1.71 => ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_24_lessI,axiom,
% 2.54/1.71 ! [N: nat] : ( ord_less @ nat @ N @ ( suc @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_25_neq0__conv,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ( ( N
% 2.54/1.71 != ( zero_zero @ nat ) )
% 2.54/1.71 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_26_less__nat__zero__code,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_27_bot__nat__0_Onot__eq__extremum,axiom,
% 2.54/1.71 ! [A8: nat] :
% 2.54/1.71 ( ( A8
% 2.54/1.71 != ( zero_zero @ nat ) )
% 2.54/1.71 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A8 ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_28_Suc__le__mono,axiom,
% 2.54/1.71 ! [N: nat,M: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ ( suc @ N ) @ ( suc @ M ) )
% 2.54/1.71 = ( ord_less_eq @ nat @ N @ M ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_29_le0,axiom,
% 2.54/1.71 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_30_bot__nat__0_Oextremum,axiom,
% 2.54/1.71 ! [A8: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A8 ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_31_diff__self__eq__0,axiom,
% 2.54/1.71 ! [M: nat] :
% 2.54/1.71 ( ( minus_minus @ nat @ M @ M )
% 2.54/1.71 = ( zero_zero @ nat ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_32_diff__0__eq__0,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ( ( minus_minus @ nat @ ( zero_zero @ nat ) @ N )
% 2.54/1.71 = ( zero_zero @ nat ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_33_diff__diff__cancel,axiom,
% 2.54/1.71 ! [I2: nat,N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ I2 @ N )
% 2.54/1.71 => ( ( minus_minus @ nat @ N @ ( minus_minus @ nat @ N @ I2 ) )
% 2.54/1.71 = I2 ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_34_Occ4_H,axiom,
% 2.54/1.71 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ n1 ) @ msgInSet ).
% 2.54/1.71
% 2.54/1.71 thf(fact_35_AssumptionSubset2_I4_J,axiom,
% 2.54/1.71 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ n1 ) @ msgInSet ).
% 2.54/1.71
% 2.54/1.71 thf(fact_36__092_060open_062enabled_A_Ife_Aindex_A_B_A_Ilength_A_Ife_Aindex_J_A_N_A1_J_J_AmsgInSet_092_060close_062,axiom,
% 2.54/1.71 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) ) @ msgInSet ).
% 2.54/1.71
% 2.54/1.71 thf(fact_37_zero__less__Suc,axiom,
% 2.54/1.71 ! [N: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_38_less__Suc0,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ N @ ( suc @ ( zero_zero @ nat ) ) )
% 2.54/1.71 = ( N
% 2.54/1.71 = ( zero_zero @ nat ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_39_zero__less__diff,axiom,
% 2.54/1.71 ! [N: nat,M: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( minus_minus @ nat @ N @ M ) )
% 2.54/1.71 = ( ord_less @ nat @ M @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_40_diff__is__0__eq,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ( minus_minus @ nat @ M @ N )
% 2.54/1.71 = ( zero_zero @ nat ) )
% 2.54/1.71 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_41_diff__is__0__eq_H,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ M @ N )
% 2.54/1.71 => ( ( minus_minus @ nat @ M @ N )
% 2.54/1.71 = ( zero_zero @ nat ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_42_less__one,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ N @ ( one_one @ nat ) )
% 2.54/1.71 = ( N
% 2.54/1.71 = ( zero_zero @ nat ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_43_Suc__pred,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.54/1.71 => ( ( suc @ ( minus_minus @ nat @ N @ ( suc @ ( zero_zero @ nat ) ) ) )
% 2.54/1.71 = N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_44_Suc__diff__1,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.54/1.71 => ( ( suc @ ( minus_minus @ nat @ N @ ( one_one @ nat ) ) )
% 2.54/1.71 = N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_45_less__eq__nat_Osimps_I1_J,axiom,
% 2.54/1.71 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_46_gr0I,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ( ( N
% 2.54/1.71 != ( zero_zero @ nat ) )
% 2.54/1.71 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_47_le__0__eq,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ N @ ( zero_zero @ nat ) )
% 2.54/1.71 = ( N
% 2.54/1.71 = ( zero_zero @ nat ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_48_le__refl,axiom,
% 2.54/1.71 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_49_not__gr0,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) )
% 2.54/1.71 = ( N
% 2.54/1.71 = ( zero_zero @ nat ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_50_le__trans,axiom,
% 2.54/1.71 ! [I2: nat,J: nat,K: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ I2 @ J )
% 2.54/1.71 => ( ( ord_less_eq @ nat @ J @ K )
% 2.54/1.71 => ( ord_less_eq @ nat @ I2 @ K ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_51_eq__imp__le,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( M = N )
% 2.54/1.71 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_52_not__less0,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_53_le__antisym,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ M @ N )
% 2.54/1.71 => ( ( ord_less_eq @ nat @ N @ M )
% 2.54/1.71 => ( M = N ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_54_less__zeroE,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ~ ( ord_less @ nat @ N @ ( zero_zero @ nat ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_55_nat__less__le,axiom,
% 2.54/1.71 ( ( ord_less @ nat )
% 2.54/1.71 = ( ^ [M2: nat,N3: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ M2 @ N3 )
% 2.54/1.71 & ( M2 != N3 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_56_nat__neq__iff,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( M != N )
% 2.54/1.71 = ( ( ord_less @ nat @ M @ N )
% 2.54/1.71 | ( ord_less @ nat @ N @ M ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_57_less__not__refl,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ~ ( ord_less @ nat @ N @ N ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_58_nat__le__linear,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ M @ N )
% 2.54/1.71 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_59_less__not__refl2,axiom,
% 2.54/1.71 ! [N: nat,M: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ N @ M )
% 2.54/1.71 => ( M != N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_60_less__not__refl3,axiom,
% 2.54/1.71 ! [S2: nat,T: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ S2 @ T )
% 2.54/1.71 => ( S2 != T ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_61_measure__induct,axiom,
% 2.54/1.71 ! [B: $tType,A: $tType] :
% 2.54/1.71 ( ( wellorder @ B )
% 2.54/1.71 => ! [F: A > B,P2: A > $o,A8: A] :
% 2.54/1.71 ( ! [X: A] :
% 2.54/1.71 ( ! [Y: A] :
% 2.54/1.71 ( ( ord_less @ B @ ( F @ Y ) @ ( F @ X ) )
% 2.54/1.71 => ( P2 @ Y ) )
% 2.54/1.71 => ( P2 @ X ) )
% 2.54/1.71 => ( P2 @ A8 ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_62_ex__least__nat__le,axiom,
% 2.54/1.71 ! [P2: nat > $o,N: nat] :
% 2.54/1.71 ( ( P2 @ N )
% 2.54/1.71 => ( ~ ( P2 @ ( zero_zero @ nat ) )
% 2.54/1.71 => ? [K2: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ K2 @ N )
% 2.54/1.71 & ! [I: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I @ K2 )
% 2.54/1.71 => ~ ( P2 @ I ) )
% 2.54/1.71 & ( P2 @ K2 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_63_gr__implies__not0,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ M @ N )
% 2.54/1.71 => ( N
% 2.54/1.71 != ( zero_zero @ nat ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_64_less__imp__le__nat,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ M @ N )
% 2.54/1.71 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_65_less__irrefl__nat,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ~ ( ord_less @ nat @ N @ N ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_66_nat__less__induct,axiom,
% 2.54/1.71 ! [P2: nat > $o,N: nat] :
% 2.54/1.71 ( ! [N2: nat] :
% 2.54/1.71 ( ! [M3: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ M3 @ N2 )
% 2.54/1.71 => ( P2 @ M3 ) )
% 2.54/1.71 => ( P2 @ N2 ) )
% 2.54/1.71 => ( P2 @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_67_infinite__descent,axiom,
% 2.54/1.71 ! [P2: nat > $o,N: nat] :
% 2.54/1.71 ( ! [N2: nat] :
% 2.54/1.71 ( ~ ( P2 @ N2 )
% 2.54/1.71 => ? [M3: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ M3 @ N2 )
% 2.54/1.71 & ~ ( P2 @ M3 ) ) )
% 2.54/1.71 => ( P2 @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_68_le__eq__less__or__eq,axiom,
% 2.54/1.71 ( ( ord_less_eq @ nat )
% 2.54/1.71 = ( ^ [M2: nat,N3: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ M2 @ N3 )
% 2.54/1.71 | ( M2 = N3 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_69_ex__least__nat__less,axiom,
% 2.54/1.71 ! [P2: nat > $o,N: nat] :
% 2.54/1.71 ( ( P2 @ N )
% 2.54/1.71 => ( ~ ( P2 @ ( zero_zero @ nat ) )
% 2.54/1.71 => ? [K2: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ K2 @ N )
% 2.54/1.71 & ! [I: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ I @ K2 )
% 2.54/1.71 => ~ ( P2 @ I ) )
% 2.54/1.71 & ( P2 @ ( suc @ K2 ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_70_infinite__descent0,axiom,
% 2.54/1.71 ! [P2: nat > $o,N: nat] :
% 2.54/1.71 ( ( P2 @ ( zero_zero @ nat ) )
% 2.54/1.71 => ( ! [N2: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 2.54/1.71 => ( ~ ( P2 @ N2 )
% 2.54/1.71 => ? [M3: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ M3 @ N2 )
% 2.54/1.71 & ~ ( P2 @ M3 ) ) ) )
% 2.54/1.71 => ( P2 @ N ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_71_less__or__eq__imp__le,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ( ord_less @ nat @ M @ N )
% 2.54/1.71 | ( M = N ) )
% 2.54/1.71 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_72_linorder__neqE__nat,axiom,
% 2.54/1.71 ! [X3: nat,Y3: nat] :
% 2.54/1.71 ( ( X3 != Y3 )
% 2.54/1.71 => ( ~ ( ord_less @ nat @ X3 @ Y3 )
% 2.54/1.71 => ( ord_less @ nat @ Y3 @ X3 ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_73_Nat_Oex__has__greatest__nat,axiom,
% 2.54/1.71 ! [P2: nat > $o,K: nat,B2: nat] :
% 2.54/1.71 ( ( P2 @ K )
% 2.54/1.71 => ( ! [Y4: nat] :
% 2.54/1.71 ( ( P2 @ Y4 )
% 2.54/1.71 => ( ord_less_eq @ nat @ Y4 @ B2 ) )
% 2.54/1.71 => ? [X: nat] :
% 2.54/1.71 ( ( P2 @ X )
% 2.54/1.71 & ! [Y: nat] :
% 2.54/1.71 ( ( P2 @ Y )
% 2.54/1.71 => ( ord_less_eq @ nat @ Y @ X ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_74_le__neq__implies__less,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ M @ N )
% 2.54/1.71 => ( ( M != N )
% 2.54/1.71 => ( ord_less @ nat @ M @ N ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_75_measure__induct__rule,axiom,
% 2.54/1.71 ! [B: $tType,A: $tType] :
% 2.54/1.71 ( ( wellorder @ B )
% 2.54/1.71 => ! [F: A > B,P2: A > $o,A8: A] :
% 2.54/1.71 ( ! [X: A] :
% 2.54/1.71 ( ! [Y: A] :
% 2.54/1.71 ( ( ord_less @ B @ ( F @ Y ) @ ( F @ X ) )
% 2.54/1.71 => ( P2 @ Y ) )
% 2.54/1.71 => ( P2 @ X ) )
% 2.54/1.71 => ( P2 @ A8 ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_76_less__mono__imp__le__mono,axiom,
% 2.54/1.71 ! [F: nat > nat,I2: nat,J: nat] :
% 2.54/1.71 ( ! [I3: nat,J2: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I3 @ J2 )
% 2.54/1.71 => ( ord_less @ nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 2.54/1.71 => ( ( ord_less_eq @ nat @ I2 @ J )
% 2.54/1.71 => ( ord_less_eq @ nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_77_size__neq__size__imp__neq,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( size @ A )
% 2.54/1.71 => ! [X3: A,Y3: A] :
% 2.54/1.71 ( ( ( size_size @ A @ X3 )
% 2.54/1.71 != ( size_size @ A @ Y3 ) )
% 2.54/1.71 => ( X3 != Y3 ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_78_infinite__descent__measure,axiom,
% 2.54/1.71 ! [A: $tType,P2: A > $o,V2: A > nat,X3: A] :
% 2.54/1.71 ( ! [X: A] :
% 2.54/1.71 ( ~ ( P2 @ X )
% 2.54/1.71 => ? [Y: A] :
% 2.54/1.71 ( ( ord_less @ nat @ ( V2 @ Y ) @ ( V2 @ X ) )
% 2.54/1.71 & ~ ( P2 @ Y ) ) )
% 2.54/1.71 => ( P2 @ X3 ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_79_bot__nat__0_Oextremum__strict,axiom,
% 2.54/1.71 ! [A8: nat] :
% 2.54/1.71 ~ ( ord_less @ nat @ A8 @ ( zero_zero @ nat ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_80_bot__nat__0_Oextremum__unique,axiom,
% 2.54/1.71 ! [A8: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ A8 @ ( zero_zero @ nat ) )
% 2.54/1.71 = ( A8
% 2.54/1.71 = ( zero_zero @ nat ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_81_infinite__descent0__measure,axiom,
% 2.54/1.71 ! [A: $tType,V2: A > nat,P2: A > $o,X3: A] :
% 2.54/1.71 ( ! [X: A] :
% 2.54/1.71 ( ( ( V2 @ X )
% 2.54/1.71 = ( zero_zero @ nat ) )
% 2.54/1.71 => ( P2 @ X ) )
% 2.54/1.71 => ( ! [X: A] :
% 2.54/1.71 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V2 @ X ) )
% 2.54/1.71 => ( ~ ( P2 @ X )
% 2.54/1.71 => ? [Y: A] :
% 2.54/1.71 ( ( ord_less @ nat @ ( V2 @ Y ) @ ( V2 @ X ) )
% 2.54/1.71 & ~ ( P2 @ Y ) ) ) )
% 2.54/1.71 => ( P2 @ X3 ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_82_bot__nat__0_Oextremum__uniqueI,axiom,
% 2.54/1.71 ! [A8: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ A8 @ ( zero_zero @ nat ) )
% 2.54/1.71 => ( A8
% 2.54/1.71 = ( zero_zero @ nat ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_83_lift__Suc__mono__le,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( order @ A )
% 2.54/1.71 => ! [F: nat > A,N: nat,N4: nat] :
% 2.54/1.71 ( ! [N2: nat] : ( ord_less_eq @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 2.54/1.71 => ( ( ord_less_eq @ nat @ N @ N4 )
% 2.54/1.71 => ( ord_less_eq @ A @ ( F @ N ) @ ( F @ N4 ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_84_lift__Suc__antimono__le,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( order @ A )
% 2.54/1.71 => ! [F: nat > A,N: nat,N4: nat] :
% 2.54/1.71 ( ! [N2: nat] : ( ord_less_eq @ A @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 2.54/1.71 => ( ( ord_less_eq @ nat @ N @ N4 )
% 2.54/1.71 => ( ord_less_eq @ A @ ( F @ N4 ) @ ( F @ N ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_85_le__imp__less__Suc,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ M @ N )
% 2.54/1.71 => ( ord_less @ nat @ M @ ( suc @ N ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_86_less__eq__Suc__le,axiom,
% 2.54/1.71 ( ( ord_less @ nat )
% 2.54/1.71 = ( ^ [N3: nat] : ( ord_less_eq @ nat @ ( suc @ N3 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_87_less__Suc__eq__le,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 2.54/1.71 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_88_le__less__Suc__eq,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ M @ N )
% 2.54/1.71 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 2.54/1.71 = ( N = M ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_89_Suc__le__lessD,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 2.54/1.71 => ( ord_less @ nat @ M @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_90_inc__induct,axiom,
% 2.54/1.71 ! [I2: nat,J: nat,P2: nat > $o] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ I2 @ J )
% 2.54/1.71 => ( ( P2 @ J )
% 2.54/1.71 => ( ! [N2: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ I2 @ N2 )
% 2.54/1.71 => ( ( ord_less @ nat @ N2 @ J )
% 2.54/1.71 => ( ( P2 @ ( suc @ N2 ) )
% 2.54/1.71 => ( P2 @ N2 ) ) ) )
% 2.54/1.71 => ( P2 @ I2 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_91_dec__induct,axiom,
% 2.54/1.71 ! [I2: nat,J: nat,P2: nat > $o] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ I2 @ J )
% 2.54/1.71 => ( ( P2 @ I2 )
% 2.54/1.71 => ( ! [N2: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ I2 @ N2 )
% 2.54/1.71 => ( ( ord_less @ nat @ N2 @ J )
% 2.54/1.71 => ( ( P2 @ N2 )
% 2.54/1.71 => ( P2 @ ( suc @ N2 ) ) ) ) )
% 2.54/1.71 => ( P2 @ J ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_92_Suc__le__eq,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 2.54/1.71 = ( ord_less @ nat @ M @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_93_Suc__leI,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ M @ N )
% 2.54/1.71 => ( ord_less_eq @ nat @ ( suc @ M ) @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_94_diff__less__mono,axiom,
% 2.54/1.71 ! [A8: nat,B2: nat,C: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ A8 @ B2 )
% 2.54/1.71 => ( ( ord_less_eq @ nat @ C @ A8 )
% 2.54/1.71 => ( ord_less @ nat @ ( minus_minus @ nat @ A8 @ C ) @ ( minus_minus @ nat @ B2 @ C ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_95_less__diff__iff,axiom,
% 2.54/1.71 ! [K: nat,M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ K @ M )
% 2.54/1.71 => ( ( ord_less_eq @ nat @ K @ N )
% 2.54/1.71 => ( ( ord_less @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 2.54/1.71 = ( ord_less @ nat @ M @ N ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_96_less__Suc__eq__0__disj,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 2.54/1.71 = ( ( M
% 2.54/1.71 = ( zero_zero @ nat ) )
% 2.54/1.71 | ? [J3: nat] :
% 2.54/1.71 ( ( M
% 2.54/1.71 = ( suc @ J3 ) )
% 2.54/1.71 & ( ord_less @ nat @ J3 @ N ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_97_gr0__implies__Suc,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.54/1.71 => ? [M4: nat] :
% 2.54/1.71 ( N
% 2.54/1.71 = ( suc @ M4 ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_98_All__less__Suc2,axiom,
% 2.54/1.71 ! [N: nat,P2: nat > $o] :
% 2.54/1.71 ( ( ! [I4: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I4 @ ( suc @ N ) )
% 2.54/1.71 => ( P2 @ I4 ) ) )
% 2.54/1.71 = ( ( P2 @ ( zero_zero @ nat ) )
% 2.54/1.71 & ! [I4: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I4 @ N )
% 2.54/1.71 => ( P2 @ ( suc @ I4 ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_99_gr0__conv__Suc,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.54/1.71 = ( ? [M2: nat] :
% 2.54/1.71 ( N
% 2.54/1.71 = ( suc @ M2 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_100_Ex__less__Suc2,axiom,
% 2.54/1.71 ! [N: nat,P2: nat > $o] :
% 2.54/1.71 ( ( ? [I4: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I4 @ ( suc @ N ) )
% 2.54/1.71 & ( P2 @ I4 ) ) )
% 2.54/1.71 = ( ( P2 @ ( zero_zero @ nat ) )
% 2.54/1.71 | ? [I4: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I4 @ N )
% 2.54/1.71 & ( P2 @ ( suc @ I4 ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_101_diff__less,axiom,
% 2.54/1.71 ! [N: nat,M: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.54/1.71 => ( ( ord_less @ nat @ ( zero_zero @ nat ) @ M )
% 2.54/1.71 => ( ord_less @ nat @ ( minus_minus @ nat @ M @ N ) @ M ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_102_transitive__stepwise__le,axiom,
% 2.54/1.71 ! [M: nat,N: nat,R: nat > nat > $o] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ M @ N )
% 2.54/1.71 => ( ! [X: nat] : ( R @ X @ X )
% 2.54/1.71 => ( ! [X: nat,Y4: nat,Z: nat] :
% 2.54/1.71 ( ( R @ X @ Y4 )
% 2.54/1.71 => ( ( R @ Y4 @ Z )
% 2.54/1.71 => ( R @ X @ Z ) ) )
% 2.54/1.71 => ( ! [N2: nat] : ( R @ N2 @ ( suc @ N2 ) )
% 2.54/1.71 => ( R @ M @ N ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_103_nat__induct__at__least,axiom,
% 2.54/1.71 ! [M: nat,N: nat,P2: nat > $o] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ M @ N )
% 2.54/1.71 => ( ( P2 @ M )
% 2.54/1.71 => ( ! [N2: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ M @ N2 )
% 2.54/1.71 => ( ( P2 @ N2 )
% 2.54/1.71 => ( P2 @ ( suc @ N2 ) ) ) )
% 2.54/1.71 => ( P2 @ N ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_104_full__nat__induct,axiom,
% 2.54/1.71 ! [P2: nat > $o,N: nat] :
% 2.54/1.71 ( ! [N2: nat] :
% 2.54/1.71 ( ! [M3: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ ( suc @ M3 ) @ N2 )
% 2.54/1.71 => ( P2 @ M3 ) )
% 2.54/1.71 => ( P2 @ N2 ) )
% 2.54/1.71 => ( P2 @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_105_not__less__eq__eq,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ~ ( ord_less_eq @ nat @ M @ N ) )
% 2.54/1.71 = ( ord_less_eq @ nat @ ( suc @ N ) @ M ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_106_Suc__n__not__le__n,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ~ ( ord_less_eq @ nat @ ( suc @ N ) @ N ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_107_le__Suc__eq,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ M @ ( suc @ N ) )
% 2.54/1.71 = ( ( ord_less_eq @ nat @ M @ N )
% 2.54/1.71 | ( M
% 2.54/1.71 = ( suc @ N ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_108_Suc__le__D,axiom,
% 2.54/1.71 ! [N: nat,M5: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ ( suc @ N ) @ M5 )
% 2.54/1.71 => ? [M4: nat] :
% 2.54/1.71 ( M5
% 2.54/1.71 = ( suc @ M4 ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_109_le__SucI,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ M @ N )
% 2.54/1.71 => ( ord_less_eq @ nat @ M @ ( suc @ N ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_110_le__SucE,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ M @ ( suc @ N ) )
% 2.54/1.71 => ( ~ ( ord_less_eq @ nat @ M @ N )
% 2.54/1.71 => ( M
% 2.54/1.71 = ( suc @ N ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_111_Suc__leD,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 2.54/1.71 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_112_diff__le__mono2,axiom,
% 2.54/1.71 ! [M: nat,N: nat,L: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ M @ N )
% 2.54/1.71 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ L @ N ) @ ( minus_minus @ nat @ L @ M ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_113_le__diff__iff_H,axiom,
% 2.54/1.71 ! [A8: nat,C: nat,B2: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ A8 @ C )
% 2.54/1.71 => ( ( ord_less_eq @ nat @ B2 @ C )
% 2.54/1.71 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ A8 ) @ ( minus_minus @ nat @ C @ B2 ) )
% 2.54/1.71 = ( ord_less_eq @ nat @ B2 @ A8 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_114_diff__le__self,axiom,
% 2.54/1.71 ! [M: nat,N: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ N ) @ M ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_115_diff__le__mono,axiom,
% 2.54/1.71 ! [M: nat,N: nat,L: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ M @ N )
% 2.54/1.71 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ L ) @ ( minus_minus @ nat @ N @ L ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_116_Nat_Odiff__diff__eq,axiom,
% 2.54/1.71 ! [K: nat,M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ K @ M )
% 2.54/1.71 => ( ( ord_less_eq @ nat @ K @ N )
% 2.54/1.71 => ( ( minus_minus @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 2.54/1.71 = ( minus_minus @ nat @ M @ N ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_117_le__diff__iff,axiom,
% 2.54/1.71 ! [K: nat,M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ K @ M )
% 2.54/1.71 => ( ( ord_less_eq @ nat @ K @ N )
% 2.54/1.71 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 2.54/1.71 = ( ord_less_eq @ nat @ M @ N ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_118_eq__diff__iff,axiom,
% 2.54/1.71 ! [K: nat,M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ K @ M )
% 2.54/1.71 => ( ( ord_less_eq @ nat @ K @ N )
% 2.54/1.71 => ( ( ( minus_minus @ nat @ M @ K )
% 2.54/1.71 = ( minus_minus @ nat @ N @ K ) )
% 2.54/1.71 = ( M = N ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_119_not0__implies__Suc,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ( ( N
% 2.54/1.71 != ( zero_zero @ nat ) )
% 2.54/1.71 => ? [M4: nat] :
% 2.54/1.71 ( N
% 2.54/1.71 = ( suc @ M4 ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_120_old_Onat_Oinducts,axiom,
% 2.54/1.71 ! [P2: nat > $o,Nat: nat] :
% 2.54/1.71 ( ( P2 @ ( zero_zero @ nat ) )
% 2.54/1.71 => ( ! [Nat3: nat] :
% 2.54/1.71 ( ( P2 @ Nat3 )
% 2.54/1.71 => ( P2 @ ( suc @ Nat3 ) ) )
% 2.54/1.71 => ( P2 @ Nat ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_121_old_Onat_Oexhaust,axiom,
% 2.54/1.71 ! [Y3: nat] :
% 2.54/1.71 ( ( Y3
% 2.54/1.71 != ( zero_zero @ nat ) )
% 2.54/1.71 => ~ ! [Nat3: nat] :
% 2.54/1.71 ( Y3
% 2.54/1.71 != ( suc @ Nat3 ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_122_Zero__not__Suc,axiom,
% 2.54/1.71 ! [M: nat] :
% 2.54/1.71 ( ( zero_zero @ nat )
% 2.54/1.71 != ( suc @ M ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_123_Zero__neq__Suc,axiom,
% 2.54/1.71 ! [M: nat] :
% 2.54/1.71 ( ( zero_zero @ nat )
% 2.54/1.71 != ( suc @ M ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_124_Suc__neq__Zero,axiom,
% 2.54/1.71 ! [M: nat] :
% 2.54/1.71 ( ( suc @ M )
% 2.54/1.71 != ( zero_zero @ nat ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_125_zero__induct,axiom,
% 2.54/1.71 ! [P2: nat > $o,K: nat] :
% 2.54/1.71 ( ( P2 @ K )
% 2.54/1.71 => ( ! [N2: nat] :
% 2.54/1.71 ( ( P2 @ ( suc @ N2 ) )
% 2.54/1.71 => ( P2 @ N2 ) )
% 2.54/1.71 => ( P2 @ ( zero_zero @ nat ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_126_diff__induct,axiom,
% 2.54/1.71 ! [P2: nat > nat > $o,M: nat,N: nat] :
% 2.54/1.71 ( ! [X: nat] : ( P2 @ X @ ( zero_zero @ nat ) )
% 2.54/1.71 => ( ! [Y4: nat] : ( P2 @ ( zero_zero @ nat ) @ ( suc @ Y4 ) )
% 2.54/1.71 => ( ! [X: nat,Y4: nat] :
% 2.54/1.71 ( ( P2 @ X @ Y4 )
% 2.54/1.71 => ( P2 @ ( suc @ X ) @ ( suc @ Y4 ) ) )
% 2.54/1.71 => ( P2 @ M @ N ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_127_nat__induct,axiom,
% 2.54/1.71 ! [P2: nat > $o,N: nat] :
% 2.54/1.71 ( ( P2 @ ( zero_zero @ nat ) )
% 2.54/1.71 => ( ! [N2: nat] :
% 2.54/1.71 ( ( P2 @ N2 )
% 2.54/1.71 => ( P2 @ ( suc @ N2 ) ) )
% 2.54/1.71 => ( P2 @ N ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_128_nat_OdiscI,axiom,
% 2.54/1.71 ! [Nat: nat,X2: nat] :
% 2.54/1.71 ( ( Nat
% 2.54/1.71 = ( suc @ X2 ) )
% 2.54/1.71 => ( Nat
% 2.54/1.71 != ( zero_zero @ nat ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_129_old_Onat_Odistinct_I1_J,axiom,
% 2.54/1.71 ! [Nat2: nat] :
% 2.54/1.71 ( ( zero_zero @ nat )
% 2.54/1.71 != ( suc @ Nat2 ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_130_old_Onat_Odistinct_I2_J,axiom,
% 2.54/1.71 ! [Nat4: nat] :
% 2.54/1.71 ( ( suc @ Nat4 )
% 2.54/1.71 != ( zero_zero @ nat ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_131_nat_Odistinct_I1_J,axiom,
% 2.54/1.71 ! [X2: nat] :
% 2.54/1.71 ( ( zero_zero @ nat )
% 2.54/1.71 != ( suc @ X2 ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_132_minus__nat_Odiff__0,axiom,
% 2.54/1.71 ! [M: nat] :
% 2.54/1.71 ( ( minus_minus @ nat @ M @ ( zero_zero @ nat ) )
% 2.54/1.71 = M ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_133_diffs0__imp__equal,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ( minus_minus @ nat @ M @ N )
% 2.54/1.71 = ( zero_zero @ nat ) )
% 2.54/1.71 => ( ( ( minus_minus @ nat @ N @ M )
% 2.54/1.71 = ( zero_zero @ nat ) )
% 2.54/1.71 => ( M = N ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_134_lift__Suc__mono__less__iff,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( order @ A )
% 2.54/1.71 => ! [F: nat > A,N: nat,M: nat] :
% 2.54/1.71 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 2.54/1.71 => ( ( ord_less @ A @ ( F @ N ) @ ( F @ M ) )
% 2.54/1.71 = ( ord_less @ nat @ N @ M ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_135_lift__Suc__mono__less,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( order @ A )
% 2.54/1.71 => ! [F: nat > A,N: nat,N4: nat] :
% 2.54/1.71 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 2.54/1.71 => ( ( ord_less @ nat @ N @ N4 )
% 2.54/1.71 => ( ord_less @ A @ ( F @ N ) @ ( F @ N4 ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_136_diff__Suc__less,axiom,
% 2.54/1.71 ! [N: nat,I2: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.54/1.71 => ( ord_less @ nat @ ( minus_minus @ nat @ N @ ( suc @ I2 ) ) @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_137_nat__induct__non__zero,axiom,
% 2.54/1.71 ! [N: nat,P2: nat > $o] :
% 2.54/1.71 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.54/1.71 => ( ( P2 @ ( one_one @ nat ) )
% 2.54/1.71 => ( ! [N2: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 2.54/1.71 => ( ( P2 @ N2 )
% 2.54/1.71 => ( P2 @ ( suc @ N2 ) ) ) )
% 2.54/1.71 => ( P2 @ N ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_138_Suc__diff__le,axiom,
% 2.54/1.71 ! [N: nat,M: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ N @ M )
% 2.54/1.71 => ( ( minus_minus @ nat @ ( suc @ M ) @ N )
% 2.54/1.71 = ( suc @ ( minus_minus @ nat @ M @ N ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_139_One__nat__def,axiom,
% 2.54/1.71 ( ( one_one @ nat )
% 2.54/1.71 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_140_not__less__less__Suc__eq,axiom,
% 2.54/1.71 ! [N: nat,M: nat] :
% 2.54/1.71 ( ~ ( ord_less @ nat @ N @ M )
% 2.54/1.71 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 2.54/1.71 = ( N = M ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_141_strict__inc__induct,axiom,
% 2.54/1.71 ! [I2: nat,J: nat,P2: nat > $o] :
% 2.54/1.71 ( ( ord_less @ nat @ I2 @ J )
% 2.54/1.71 => ( ! [I3: nat] :
% 2.54/1.71 ( ( J
% 2.54/1.71 = ( suc @ I3 ) )
% 2.54/1.71 => ( P2 @ I3 ) )
% 2.54/1.71 => ( ! [I3: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I3 @ J )
% 2.54/1.71 => ( ( P2 @ ( suc @ I3 ) )
% 2.54/1.71 => ( P2 @ I3 ) ) )
% 2.54/1.71 => ( P2 @ I2 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_142_less__Suc__induct,axiom,
% 2.54/1.71 ! [I2: nat,J: nat,P2: nat > nat > $o] :
% 2.54/1.71 ( ( ord_less @ nat @ I2 @ J )
% 2.54/1.71 => ( ! [I3: nat] : ( P2 @ I3 @ ( suc @ I3 ) )
% 2.54/1.71 => ( ! [I3: nat,J2: nat,K2: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I3 @ J2 )
% 2.54/1.71 => ( ( ord_less @ nat @ J2 @ K2 )
% 2.54/1.71 => ( ( P2 @ I3 @ J2 )
% 2.54/1.71 => ( ( P2 @ J2 @ K2 )
% 2.54/1.71 => ( P2 @ I3 @ K2 ) ) ) ) )
% 2.54/1.71 => ( P2 @ I2 @ J ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_143_less__trans__Suc,axiom,
% 2.54/1.71 ! [I2: nat,J: nat,K: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I2 @ J )
% 2.54/1.71 => ( ( ord_less @ nat @ J @ K )
% 2.54/1.71 => ( ord_less @ nat @ ( suc @ I2 ) @ K ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_144_Suc__less__SucD,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 2.54/1.71 => ( ord_less @ nat @ M @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_145_less__antisym,axiom,
% 2.54/1.71 ! [N: nat,M: nat] :
% 2.54/1.71 ( ~ ( ord_less @ nat @ N @ M )
% 2.54/1.71 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 2.54/1.71 => ( M = N ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_146_Suc__less__eq2,axiom,
% 2.54/1.71 ! [N: nat,M: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ ( suc @ N ) @ M )
% 2.54/1.71 = ( ? [M6: nat] :
% 2.54/1.71 ( ( M
% 2.54/1.71 = ( suc @ M6 ) )
% 2.54/1.71 & ( ord_less @ nat @ N @ M6 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_147_All__less__Suc,axiom,
% 2.54/1.71 ! [N: nat,P2: nat > $o] :
% 2.54/1.71 ( ( ! [I4: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I4 @ ( suc @ N ) )
% 2.54/1.71 => ( P2 @ I4 ) ) )
% 2.54/1.71 = ( ( P2 @ N )
% 2.54/1.71 & ! [I4: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I4 @ N )
% 2.54/1.71 => ( P2 @ I4 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_148_not__less__eq,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ~ ( ord_less @ nat @ M @ N ) )
% 2.54/1.71 = ( ord_less @ nat @ N @ ( suc @ M ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_149_less__Suc__eq,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 2.54/1.71 = ( ( ord_less @ nat @ M @ N )
% 2.54/1.71 | ( M = N ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_150_Ex__less__Suc,axiom,
% 2.54/1.71 ! [N: nat,P2: nat > $o] :
% 2.54/1.71 ( ( ? [I4: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I4 @ ( suc @ N ) )
% 2.54/1.71 & ( P2 @ I4 ) ) )
% 2.54/1.71 = ( ( P2 @ N )
% 2.54/1.71 | ? [I4: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I4 @ N )
% 2.54/1.71 & ( P2 @ I4 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_151_less__SucI,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ M @ N )
% 2.54/1.71 => ( ord_less @ nat @ M @ ( suc @ N ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_152_less__SucE,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 2.54/1.71 => ( ~ ( ord_less @ nat @ M @ N )
% 2.54/1.71 => ( M = N ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_153_Suc__lessI,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ M @ N )
% 2.54/1.71 => ( ( ( suc @ M )
% 2.54/1.71 != N )
% 2.54/1.71 => ( ord_less @ nat @ ( suc @ M ) @ N ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_154_Suc__lessE,axiom,
% 2.54/1.71 ! [I2: nat,K: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ ( suc @ I2 ) @ K )
% 2.54/1.71 => ~ ! [J2: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I2 @ J2 )
% 2.54/1.71 => ( K
% 2.54/1.71 != ( suc @ J2 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_155_Suc__lessD,axiom,
% 2.54/1.71 ! [M: nat,N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ ( suc @ M ) @ N )
% 2.54/1.71 => ( ord_less @ nat @ M @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_156_Nat_OlessE,axiom,
% 2.54/1.71 ! [I2: nat,K: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I2 @ K )
% 2.54/1.71 => ( ( K
% 2.54/1.71 != ( suc @ I2 ) )
% 2.54/1.71 => ~ ! [J2: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I2 @ J2 )
% 2.54/1.71 => ( K
% 2.54/1.71 != ( suc @ J2 ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_157_less__imp__diff__less,axiom,
% 2.54/1.71 ! [J: nat,K: nat,N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ J @ K )
% 2.54/1.71 => ( ord_less @ nat @ ( minus_minus @ nat @ J @ N ) @ K ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_158_diff__less__mono2,axiom,
% 2.54/1.71 ! [M: nat,N: nat,L: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ M @ N )
% 2.54/1.71 => ( ( ord_less @ nat @ M @ L )
% 2.54/1.71 => ( ord_less @ nat @ ( minus_minus @ nat @ L @ N ) @ ( minus_minus @ nat @ L @ M ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_159_Suc__diff__eq__diff__pred,axiom,
% 2.54/1.71 ! [N: nat,M: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.54/1.71 => ( ( minus_minus @ nat @ ( suc @ M ) @ N )
% 2.54/1.71 = ( minus_minus @ nat @ M @ ( minus_minus @ nat @ N @ ( one_one @ nat ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_160_Suc__pred_H,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.54/1.71 => ( N
% 2.54/1.71 = ( suc @ ( minus_minus @ nat @ N @ ( one_one @ nat ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_161_n__not__Suc__n,axiom,
% 2.54/1.71 ! [N: nat] :
% 2.54/1.71 ( N
% 2.54/1.71 != ( suc @ N ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_162_Suc__inject,axiom,
% 2.54/1.71 ! [X3: nat,Y3: nat] :
% 2.54/1.71 ( ( ( suc @ X3 )
% 2.54/1.71 = ( suc @ Y3 ) )
% 2.54/1.71 => ( X3 = Y3 ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_163_diff__commute,axiom,
% 2.54/1.71 ! [I2: nat,J: nat,K: nat] :
% 2.54/1.71 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I2 @ J ) @ K )
% 2.54/1.71 = ( minus_minus @ nat @ ( minus_minus @ nat @ I2 @ K ) @ J ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_164_diff__less__Suc,axiom,
% 2.54/1.71 ! [M: nat,N: nat] : ( ord_less @ nat @ ( minus_minus @ nat @ M @ N ) @ ( suc @ M ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_165_Suc__diff__Suc,axiom,
% 2.54/1.71 ! [N: nat,M: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ N @ M )
% 2.54/1.71 => ( ( suc @ ( minus_minus @ nat @ M @ ( suc @ N ) ) )
% 2.54/1.71 = ( minus_minus @ nat @ M @ N ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_166_zero__induct__lemma,axiom,
% 2.54/1.71 ! [P2: nat > $o,K: nat,I2: nat] :
% 2.54/1.71 ( ( P2 @ K )
% 2.54/1.71 => ( ! [N2: nat] :
% 2.54/1.71 ( ( P2 @ ( suc @ N2 ) )
% 2.54/1.71 => ( P2 @ N2 ) )
% 2.54/1.71 => ( P2 @ ( minus_minus @ nat @ K @ I2 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_167_AssumptionSubset3_I3_J,axiom,
% 2.54/1.71 ord_less @ nat @ nMsg @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_168_length__greater__0__conv,axiom,
% 2.54/1.71 ! [A: $tType,Xs: list @ A] :
% 2.54/1.71 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ A ) @ Xs ) )
% 2.54/1.71 = ( Xs
% 2.54/1.71 != ( nil @ A ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_169_length__0__conv,axiom,
% 2.54/1.71 ! [A: $tType,Xs: list @ A] :
% 2.54/1.71 ( ( ( size_size @ ( list @ A ) @ Xs )
% 2.54/1.71 = ( zero_zero @ nat ) )
% 2.54/1.71 = ( Xs
% 2.54/1.71 = ( nil @ A ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_170_diff__numeral__special_I9_J,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( neg_numeral @ A )
% 2.54/1.71 => ( ( minus_minus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
% 2.54/1.71 = ( zero_zero @ A ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_171_diff__gt__0__iff__gt,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( ordered_ab_group_add @ A )
% 2.54/1.71 => ! [A8: A,B2: A] :
% 2.54/1.71 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A8 @ B2 ) )
% 2.54/1.71 = ( ord_less @ A @ B2 @ A8 ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_172_diff__ge__0__iff__ge,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( ordered_ab_group_add @ A )
% 2.54/1.71 => ! [A8: A,B2: A] :
% 2.54/1.71 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A8 @ B2 ) )
% 2.54/1.71 = ( ord_less_eq @ A @ B2 @ A8 ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_173_EnabledIntermediate,axiom,
% 2.54/1.71 ! [I: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) )
% 2.54/1.71 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ I )
% 2.54/1.71 => ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ I ) @ msg ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_174__092_060open_062enabled_A_Ife_A_ISuc_Aindex_J_A_B_A_Ilength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_J_J_Amsg_092_060close_062,axiom,
% 2.54/1.71 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) ) @ msg ).
% 2.54/1.71
% 2.54/1.71 thf(fact_175_LastOfIndex,axiom,
% 2.54/1.71 ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( suc @ ( zero_zero @ nat ) ) ) )
% 2.54/1.71 = ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_176_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( cancel1352612707id_add @ A )
% 2.54/1.71 => ! [A8: A] :
% 2.54/1.71 ( ( minus_minus @ A @ A8 @ A8 )
% 2.54/1.71 = ( zero_zero @ A ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_177_AssumptionFirstOccSetDecrOrConsumed_I1_J,axiom,
% 2.54/1.71 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) @ msg ).
% 2.54/1.71
% 2.54/1.71 thf(fact_178_Occ2_H,axiom,
% 2.54/1.71 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) ) @ msgInSet ).
% 2.54/1.71
% 2.54/1.71 thf(fact_179_le__zero__eq,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( canoni770627133id_add @ A )
% 2.54/1.71 => ! [N: A] :
% 2.54/1.71 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 2.54/1.71 = ( N
% 2.54/1.71 = ( zero_zero @ A ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_180_not__gr__zero,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( canoni770627133id_add @ A )
% 2.54/1.71 => ! [N: A] :
% 2.54/1.71 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N ) )
% 2.54/1.71 = ( N
% 2.54/1.71 = ( zero_zero @ A ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_181_diff__self,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( group_add @ A )
% 2.54/1.71 => ! [A8: A] :
% 2.54/1.71 ( ( minus_minus @ A @ A8 @ A8 )
% 2.54/1.71 = ( zero_zero @ A ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_182_diff__0__right,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( group_add @ A )
% 2.54/1.71 => ! [A8: A] :
% 2.54/1.71 ( ( minus_minus @ A @ A8 @ ( zero_zero @ A ) )
% 2.54/1.71 = A8 ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_183_zero__diff,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( comm_monoid_diff @ A )
% 2.54/1.71 => ! [A8: A] :
% 2.54/1.71 ( ( minus_minus @ A @ ( zero_zero @ A ) @ A8 )
% 2.54/1.71 = ( zero_zero @ A ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_184_diff__zero,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( cancel1352612707id_add @ A )
% 2.54/1.71 => ! [A8: A] :
% 2.54/1.71 ( ( minus_minus @ A @ A8 @ ( zero_zero @ A ) )
% 2.54/1.71 = A8 ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_185_EnabledInSuc,axiom,
% 2.54/1.71 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) ) @ msg ).
% 2.54/1.71
% 2.54/1.71 thf(fact_186_AssumptionSubset2_I2_J,axiom,
% 2.54/1.71 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) ) @ msgInSet ).
% 2.54/1.71
% 2.54/1.71 thf(fact_187_AssumptionSubset3_I4_J,axiom,
% 2.54/1.71 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ nMsg ) @ msg ).
% 2.54/1.71
% 2.54/1.71 thf(fact_188_AssumptionCase1ImplThesis_H,axiom,
% 2.54/1.71 enabled @ p @ v @ s @ ( last @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) ) @ msg ).
% 2.54/1.71
% 2.54/1.71 thf(fact_189_zero__reorient,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( zero @ A )
% 2.54/1.71 => ! [X3: A] :
% 2.54/1.71 ( ( ( zero_zero @ A )
% 2.54/1.71 = X3 )
% 2.54/1.71 = ( X3
% 2.54/1.71 = ( zero_zero @ A ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_190_one__reorient,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( one @ A )
% 2.54/1.71 => ! [X3: A] :
% 2.54/1.71 ( ( ( one_one @ A )
% 2.54/1.71 = X3 )
% 2.54/1.71 = ( X3
% 2.54/1.71 = ( one_one @ A ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_191_diff__eq__diff__eq,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( group_add @ A )
% 2.54/1.71 => ! [A8: A,B2: A,C: A,D: A] :
% 2.54/1.71 ( ( ( minus_minus @ A @ A8 @ B2 )
% 2.54/1.71 = ( minus_minus @ A @ C @ D ) )
% 2.54/1.71 => ( ( A8 = B2 )
% 2.54/1.71 = ( C = D ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_192_diff__right__commute,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( cancel146912293up_add @ A )
% 2.54/1.71 => ! [A8: A,C: A,B2: A] :
% 2.54/1.71 ( ( minus_minus @ A @ ( minus_minus @ A @ A8 @ C ) @ B2 )
% 2.54/1.71 = ( minus_minus @ A @ ( minus_minus @ A @ A8 @ B2 ) @ C ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_193_neq__if__length__neq,axiom,
% 2.54/1.71 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.54/1.71 ( ( ( size_size @ ( list @ A ) @ Xs )
% 2.54/1.71 != ( size_size @ ( list @ A ) @ Ys ) )
% 2.54/1.71 => ( Xs != Ys ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_194_Ex__list__of__length,axiom,
% 2.54/1.71 ! [A: $tType,N: nat] :
% 2.54/1.71 ? [Xs2: list @ A] :
% 2.54/1.71 ( ( size_size @ ( list @ A ) @ Xs2 )
% 2.54/1.71 = N ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_195_last__conv__nth,axiom,
% 2.54/1.71 ! [A: $tType,Xs: list @ A] :
% 2.54/1.71 ( ( Xs
% 2.54/1.71 != ( nil @ A ) )
% 2.54/1.71 => ( ( last @ A @ Xs )
% 2.54/1.71 = ( nth @ A @ Xs @ ( minus_minus @ nat @ ( size_size @ ( list @ A ) @ Xs ) @ ( one_one @ nat ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_196_zero__le,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( canoni770627133id_add @ A )
% 2.54/1.71 => ! [X3: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X3 ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_197_le__numeral__extra_I3_J,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( linord1659791738miring @ A )
% 2.54/1.71 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_198_zero__less__iff__neq__zero,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( canoni770627133id_add @ A )
% 2.54/1.71 => ! [N: A] :
% 2.54/1.71 ( ( ord_less @ A @ ( zero_zero @ A ) @ N )
% 2.54/1.71 = ( N
% 2.54/1.71 != ( zero_zero @ A ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_199_gr__implies__not__zero,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( canoni770627133id_add @ A )
% 2.54/1.71 => ! [M: A,N: A] :
% 2.54/1.71 ( ( ord_less @ A @ M @ N )
% 2.54/1.71 => ( N
% 2.54/1.71 != ( zero_zero @ A ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_200_not__less__zero,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( canoni770627133id_add @ A )
% 2.54/1.71 => ! [N: A] :
% 2.54/1.71 ~ ( ord_less @ A @ N @ ( zero_zero @ A ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_201_gr__zeroI,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( canoni770627133id_add @ A )
% 2.54/1.71 => ! [N: A] :
% 2.54/1.71 ( ( N
% 2.54/1.71 != ( zero_zero @ A ) )
% 2.54/1.71 => ( ord_less @ A @ ( zero_zero @ A ) @ N ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_202_less__numeral__extra_I3_J,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( linord1659791738miring @ A )
% 2.54/1.71 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_203_le__numeral__extra_I4_J,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( linord1659791738miring @ A )
% 2.54/1.71 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_204_diff__mono,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( ordered_ab_group_add @ A )
% 2.54/1.71 => ! [A8: A,B2: A,D: A,C: A] :
% 2.54/1.71 ( ( ord_less_eq @ A @ A8 @ B2 )
% 2.54/1.71 => ( ( ord_less_eq @ A @ D @ C )
% 2.54/1.71 => ( ord_less_eq @ A @ ( minus_minus @ A @ A8 @ C ) @ ( minus_minus @ A @ B2 @ D ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_205_diff__left__mono,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( ordered_ab_group_add @ A )
% 2.54/1.71 => ! [B2: A,A8: A,C: A] :
% 2.54/1.71 ( ( ord_less_eq @ A @ B2 @ A8 )
% 2.54/1.71 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A8 ) @ ( minus_minus @ A @ C @ B2 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_206_diff__right__mono,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( ordered_ab_group_add @ A )
% 2.54/1.71 => ! [A8: A,B2: A,C: A] :
% 2.54/1.71 ( ( ord_less_eq @ A @ A8 @ B2 )
% 2.54/1.71 => ( ord_less_eq @ A @ ( minus_minus @ A @ A8 @ C ) @ ( minus_minus @ A @ B2 @ C ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_207_diff__eq__diff__less__eq,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( ordered_ab_group_add @ A )
% 2.54/1.71 => ! [A8: A,B2: A,C: A,D: A] :
% 2.54/1.71 ( ( ( minus_minus @ A @ A8 @ B2 )
% 2.54/1.71 = ( minus_minus @ A @ C @ D ) )
% 2.54/1.71 => ( ( ord_less_eq @ A @ A8 @ B2 )
% 2.54/1.71 = ( ord_less_eq @ A @ C @ D ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_208_eq__iff__diff__eq__0,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( group_add @ A )
% 2.54/1.71 => ( ( ^ [Y5: A,Z2: A] : ( Y5 = Z2 ) )
% 2.54/1.71 = ( ^ [A9: A,B3: A] :
% 2.54/1.71 ( ( minus_minus @ A @ A9 @ B3 )
% 2.54/1.71 = ( zero_zero @ A ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_209_less__numeral__extra_I4_J,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( linord1659791738miring @ A )
% 2.54/1.71 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_210_diff__strict__mono,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( ordered_ab_group_add @ A )
% 2.54/1.71 => ! [A8: A,B2: A,D: A,C: A] :
% 2.54/1.71 ( ( ord_less @ A @ A8 @ B2 )
% 2.54/1.71 => ( ( ord_less @ A @ D @ C )
% 2.54/1.71 => ( ord_less @ A @ ( minus_minus @ A @ A8 @ C ) @ ( minus_minus @ A @ B2 @ D ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_211_diff__eq__diff__less,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( ordered_ab_group_add @ A )
% 2.54/1.71 => ! [A8: A,B2: A,C: A,D: A] :
% 2.54/1.71 ( ( ( minus_minus @ A @ A8 @ B2 )
% 2.54/1.71 = ( minus_minus @ A @ C @ D ) )
% 2.54/1.71 => ( ( ord_less @ A @ A8 @ B2 )
% 2.54/1.71 = ( ord_less @ A @ C @ D ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_212_diff__strict__left__mono,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( ordered_ab_group_add @ A )
% 2.54/1.71 => ! [B2: A,A8: A,C: A] :
% 2.54/1.71 ( ( ord_less @ A @ B2 @ A8 )
% 2.54/1.71 => ( ord_less @ A @ ( minus_minus @ A @ C @ A8 ) @ ( minus_minus @ A @ C @ B2 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_213_diff__strict__right__mono,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( ordered_ab_group_add @ A )
% 2.54/1.71 => ! [A8: A,B2: A,C: A] :
% 2.54/1.71 ( ( ord_less @ A @ A8 @ B2 )
% 2.54/1.71 => ( ord_less @ A @ ( minus_minus @ A @ A8 @ C ) @ ( minus_minus @ A @ B2 @ C ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_214_length__induct,axiom,
% 2.54/1.71 ! [A: $tType,P2: ( list @ A ) > $o,Xs: list @ A] :
% 2.54/1.71 ( ! [Xs2: list @ A] :
% 2.54/1.71 ( ! [Ys2: list @ A] :
% 2.54/1.71 ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ys2 ) @ ( size_size @ ( list @ A ) @ Xs2 ) )
% 2.54/1.71 => ( P2 @ Ys2 ) )
% 2.54/1.71 => ( P2 @ Xs2 ) )
% 2.54/1.71 => ( P2 @ Xs ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_215_le__iff__diff__le__0,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( ordered_ab_group_add @ A )
% 2.54/1.71 => ( ( ord_less_eq @ A )
% 2.54/1.71 = ( ^ [A9: A,B3: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ A9 @ B3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_216_less__numeral__extra_I1_J,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( linord1659791738miring @ A )
% 2.54/1.71 => ( ord_less @ A @ ( zero_zero @ A ) @ ( one_one @ A ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_217_less__iff__diff__less__0,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( ordered_ab_group_add @ A )
% 2.54/1.71 => ( ( ord_less @ A )
% 2.54/1.71 = ( ^ [A9: A,B3: A] : ( ord_less @ A @ ( minus_minus @ A @ A9 @ B3 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_218_list_Osize_I3_J,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( size_size @ ( list @ A ) @ ( nil @ A ) )
% 2.54/1.71 = ( zero_zero @ nat ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_219_nth__equalityI,axiom,
% 2.54/1.71 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.54/1.71 ( ( ( size_size @ ( list @ A ) @ Xs )
% 2.54/1.71 = ( size_size @ ( list @ A ) @ Ys ) )
% 2.54/1.71 => ( ! [I3: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I3 @ ( size_size @ ( list @ A ) @ Xs ) )
% 2.54/1.71 => ( ( nth @ A @ Xs @ I3 )
% 2.54/1.71 = ( nth @ A @ Ys @ I3 ) ) )
% 2.54/1.71 => ( Xs = Ys ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_220_Skolem__list__nth,axiom,
% 2.54/1.71 ! [A: $tType,K: nat,P2: nat > A > $o] :
% 2.54/1.71 ( ( ! [I4: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I4 @ K )
% 2.54/1.71 => ? [X4: A] : ( P2 @ I4 @ X4 ) ) )
% 2.54/1.71 = ( ? [Xs3: list @ A] :
% 2.54/1.71 ( ( ( size_size @ ( list @ A ) @ Xs3 )
% 2.54/1.71 = K )
% 2.54/1.71 & ! [I4: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I4 @ K )
% 2.54/1.71 => ( P2 @ I4 @ ( nth @ A @ Xs3 @ I4 ) ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_221_list__eq__iff__nth__eq,axiom,
% 2.54/1.71 ! [A: $tType] :
% 2.54/1.71 ( ( ^ [Y5: list @ A,Z2: list @ A] : ( Y5 = Z2 ) )
% 2.54/1.71 = ( ^ [Xs3: list @ A,Ys3: list @ A] :
% 2.54/1.71 ( ( ( size_size @ ( list @ A ) @ Xs3 )
% 2.54/1.71 = ( size_size @ ( list @ A ) @ Ys3 ) )
% 2.54/1.71 & ! [I4: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ A ) @ Xs3 ) )
% 2.54/1.71 => ( ( nth @ A @ Xs3 @ I4 )
% 2.54/1.71 = ( nth @ A @ Ys3 @ I4 ) ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_222_PrefixSameOnLow,axiom,
% 2.54/1.71 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 2.54/1.71 ( ( prefixList @ A @ L1 @ L2 )
% 2.54/1.71 => ! [Index: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ Index @ ( size_size @ ( list @ A ) @ L1 ) )
% 2.54/1.71 => ( ( nth @ A @ L1 @ Index )
% 2.54/1.71 = ( nth @ A @ L2 @ Index ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_223_infiniteExecutionMsg_Osimps_I1_J,axiom,
% 2.54/1.71 ! [Cfg2: configuration_ext @ p @ v @ s @ product_unit,FStepCfg2: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg2: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] :
% 2.54/1.71 ( ( fLPThe221390223ionMsg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( zero_zero @ nat ) )
% 2.54/1.71 = ( nil @ ( message @ p @ v ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_224_AssumptionFair_I3_J,axiom,
% 2.54/1.71 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ n0 ) @ msg ).
% 2.54/1.71
% 2.54/1.71 thf(fact_225_AssumptionFair_I2_J,axiom,
% 2.54/1.71 ord_less @ nat @ n0 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_226_MinPredicate,axiom,
% 2.54/1.71 ! [P2: nat > $o] :
% 2.54/1.71 ( ? [X_1: nat] : ( P2 @ X_1 )
% 2.54/1.71 => ? [N0: nat] :
% 2.54/1.71 ( ( P2 @ N0 )
% 2.54/1.71 & ! [N5: nat] :
% 2.54/1.71 ( ( P2 @ N5 )
% 2.54/1.71 => ( ord_less_eq @ nat @ N0 @ N5 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_227_PrefixListTransitive,axiom,
% 2.54/1.71 ! [A: $tType,L1: list @ A,L2: list @ A,L3: list @ A] :
% 2.54/1.71 ( ( prefixList @ A @ L1 @ L2 )
% 2.54/1.71 => ( ( prefixList @ A @ L2 @ L3 )
% 2.54/1.71 => ( prefixList @ A @ L1 @ L3 ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_228_KeepProperty,axiom,
% 2.54/1.71 ! [Low: nat,P2: nat > $o,Q: nat > $o] :
% 2.54/1.71 ( ! [I3: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ Low @ I3 )
% 2.54/1.71 => ( ( P2 @ I3 )
% 2.54/1.71 => ( ( P2 @ ( suc @ I3 ) )
% 2.54/1.71 & ( Q @ I3 ) ) ) )
% 2.54/1.71 => ( ( P2 @ Low )
% 2.54/1.71 => ! [I: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ Low @ I )
% 2.54/1.71 => ( Q @ I ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_229_NatPredicateTippingPoint,axiom,
% 2.54/1.71 ! [N22: nat,Pr: nat > $o] :
% 2.54/1.71 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N22 )
% 2.54/1.71 => ( ( Pr @ ( zero_zero @ nat ) )
% 2.54/1.71 => ( ~ ( Pr @ N22 )
% 2.54/1.71 => ? [N2: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ N2 @ N22 )
% 2.54/1.71 & ( Pr @ N2 )
% 2.54/1.71 & ~ ( Pr @ ( suc @ N2 ) ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_230_MinPredicate2,axiom,
% 2.54/1.71 ! [P2: nat > $o] :
% 2.54/1.71 ( ? [X_1: nat] : ( P2 @ X_1 )
% 2.54/1.71 => ? [N0: nat] :
% 2.54/1.71 ( ( P2 @ N0 )
% 2.54/1.71 & ( ( N0
% 2.54/1.71 = ( zero_zero @ nat ) )
% 2.54/1.71 | ~ ( P2 @ ( minus_minus @ nat @ N0 @ ( one_one @ nat ) ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_231_PrefixListMonotonicity,axiom,
% 2.54/1.71 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 2.54/1.71 ( ( prefixList @ A @ L1 @ L2 )
% 2.54/1.71 => ( ord_less @ nat @ ( size_size @ ( list @ A ) @ L1 ) @ ( size_size @ ( list @ A ) @ L2 ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_232_infiniteExecutionMsg_Oelims,axiom,
% 2.54/1.71 ! [X3: configuration_ext @ p @ v @ s @ product_unit,Xa: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),Xb: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),Xc: nat,Y3: list @ ( message @ p @ v )] :
% 2.54/1.71 ( ( ( fLPThe221390223ionMsg @ p @ v @ s @ X3 @ Xa @ Xb @ Xc )
% 2.54/1.71 = Y3 )
% 2.54/1.71 => ( ( ( Xc
% 2.54/1.71 = ( zero_zero @ nat ) )
% 2.54/1.71 => ( Y3
% 2.54/1.71 != ( nil @ ( message @ p @ v ) ) ) )
% 2.54/1.71 => ~ ! [N2: nat] :
% 2.54/1.71 ( ( Xc
% 2.54/1.71 = ( suc @ N2 ) )
% 2.54/1.71 => ( Y3
% 2.54/1.71 != ( Xb @ ( fLPThe137922386ionCfg @ p @ v @ s @ X3 @ Xa @ Xb @ N2 ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ X3 @ Xa @ Xb @ N2 ) ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_233_infiniteExecutionCfg_Osimps_I2_J,axiom,
% 2.54/1.71 ! [Cfg2: configuration_ext @ p @ v @ s @ product_unit,FStepCfg2: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg2: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N: nat] :
% 2.54/1.71 ( ( fLPThe137922386ionCfg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N ) )
% 2.54/1.71 = ( FStepCfg2 @ ( fLPThe137922386ionCfg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_234_infiniteExecutionMsg_Osimps_I2_J,axiom,
% 2.54/1.71 ! [Cfg2: configuration_ext @ p @ v @ s @ product_unit,FStepCfg2: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg2: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N: nat] :
% 2.54/1.71 ( ( fLPThe221390223ionMsg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N ) )
% 2.54/1.71 = ( FStepMsg2 @ ( fLPThe137922386ionCfg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_235_AssumpOcc6_H_I2_J,axiom,
% 2.54/1.71 ( msgInSet
% 2.54/1.71 != ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_236_AssumptionFairContr,axiom,
% 2.54/1.71 ! [N5: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ n @ N5 )
% 2.54/1.71 => ! [N02: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ N02 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N5 ) ) )
% 2.54/1.71 => ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) @ N02 )
% 2.54/1.71 => ( msg
% 2.54/1.71 != ( nth @ ( message @ p @ v ) @ ( ft @ N5 ) @ N02 ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_237_IPrefixList,axiom,
% 2.54/1.71 ! [I: nat] : ( prefixList @ ( message @ p @ v ) @ ( ft @ I ) @ ( ft @ ( suc @ I ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_238_ShorterTrace,axiom,
% 2.54/1.71 ord_less @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_239_SameMsgOnLow,axiom,
% 2.54/1.71 ! [I: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 2.54/1.71 => ( ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ I )
% 2.54/1.71 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_240_SmallIndexTrace_H,axiom,
% 2.54/1.71 ord_less @ nat @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_241_NotConsumedIntermediate,axiom,
% 2.54/1.71 ! [I: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 2.54/1.71 => ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ I )
% 2.54/1.71 => ( ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I )
% 2.54/1.71 != msg ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_242__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ift_A_ISuc_Aindex_J_J_O_Alength_A_Ift_Aindex_J_A_092_060le_062_Ai_A_092_060and_062_Amsg_A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062,axiom,
% 2.54/1.71 ~ ? [I: nat] :
% 2.54/1.71 ( ( ord_less @ nat @ I @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 2.54/1.71 & ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ I )
% 2.54/1.71 & ( msg
% 2.54/1.71 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_243_OccSameMsg_H,axiom,
% 2.54/1.71 ! [N5: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ n1 @ N5 )
% 2.54/1.71 => ( ( ord_less @ nat @ N5 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 2.54/1.71 => ( ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ N5 )
% 2.54/1.71 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ N5 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_244_AssumptionSubset_I2_J,axiom,
% 2.54/1.71 firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msgInSet @ n1 ).
% 2.54/1.71
% 2.54/1.71 thf(fact_245_MessageStaysOrConsumed,axiom,
% 2.54/1.71 ! [N1: nat,N22: nat,N: nat,Msg: message @ p @ v] :
% 2.54/1.71 ( ( ( ord_less_eq @ nat @ N1 @ N22 )
% 2.54/1.71 & ( ord_less @ nat @ N22 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ N ) ) )
% 2.54/1.71 & ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N ) @ N1 ) @ Msg ) )
% 2.54/1.71 => ( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N ) @ N22 ) @ Msg )
% 2.54/1.71 | ? [N03: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ N1 @ N03 )
% 2.54/1.71 & ( ord_less @ nat @ N03 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N ) ) )
% 2.54/1.71 & ( ( nth @ ( message @ p @ v ) @ ( ft @ N ) @ N03 )
% 2.54/1.71 = Msg ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_246_AssumptionSubset_I3_J,axiom,
% 2.54/1.71 firstOccurrence @ p @ v @ s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg ).
% 2.54/1.71
% 2.54/1.71 thf(fact_247_Occ5_H,axiom,
% 2.54/1.71 ! [N5: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ n1 @ N5 )
% 2.54/1.71 => ( ( ord_less @ nat @ N5 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 2.54/1.71 => ( msgInSet
% 2.54/1.71 != ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ N5 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_248_Case2ImplThesis,axiom,
% 2.54/1.71 ( ? [N02: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ n0 @ N02 )
% 2.54/1.71 & ( ord_less @ nat @ N02 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) )
% 2.54/1.71 & ( ( nth @ ( message @ p @ v ) @ ( ft @ n ) @ N02 )
% 2.54/1.71 = msg ) )
% 2.54/1.71 => ? [N6: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ n @ N6 )
% 2.54/1.71 & ? [N03: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ n0 @ N03 )
% 2.54/1.71 & ( ord_less @ nat @ N03 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N6 ) ) )
% 2.54/1.71 & ( msg
% 2.54/1.71 = ( nth @ ( message @ p @ v ) @ ( ft @ N6 ) @ N03 ) ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_249_AssumptionSubset2_I5_J,axiom,
% 2.54/1.71 ! [N5: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ n1 @ N5 )
% 2.54/1.71 => ( ( ord_less @ nat @ N5 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 2.54/1.71 => ( msgInSet
% 2.54/1.71 != ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ N5 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(fact_250_AssumptionSubset3_I5_J,axiom,
% 2.54/1.71 ! [N5: nat] :
% 2.54/1.71 ( ( ord_less_eq @ nat @ nMsg @ N5 )
% 2.54/1.71 => ( ( ord_less @ nat @ N5 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) )
% 2.54/1.71 => ( msg
% 2.54/1.71 != ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ N5 ) ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.54/1.71 ! [A10: $tType,A11: $tType] :
% 2.54/1.71 ( ( order @ A11 )
% 2.54/1.71 => ( order @ ( A10 > A11 ) ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 2.54/1.71 canoni770627133id_add @ nat ).
% 2.54/1.71
% 2.54/1.71 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 2.54/1.71 linord1659791738miring @ nat ).
% 2.54/1.71
% 2.54/1.71 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 2.54/1.71 cancel146912293up_add @ nat ).
% 2.54/1.71
% 2.54/1.71 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 2.54/1.71 cancel1352612707id_add @ nat ).
% 2.54/1.71
% 2.54/1.71 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff,axiom,
% 2.54/1.71 comm_monoid_diff @ nat ).
% 2.54/1.71
% 2.54/1.71 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 2.54/1.71 wellorder @ nat ).
% 2.54/1.71
% 2.54/1.71 thf(tcon_Nat_Onat___Orderings_Oorder_1,axiom,
% 2.54/1.71 order @ nat ).
% 2.54/1.71
% 2.54/1.71 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 2.54/1.71 zero @ nat ).
% 2.54/1.71
% 2.54/1.71 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 2.54/1.71 one @ nat ).
% 2.54/1.71
% 2.54/1.71 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 2.54/1.71 size @ nat ).
% 2.54/1.71
% 2.54/1.71 thf(tcon_HOL_Obool___Orderings_Oorder_2,axiom,
% 2.54/1.71 order @ $o ).
% 2.54/1.71
% 2.54/1.71 thf(tcon_List_Olist___Nat_Osize_3,axiom,
% 2.54/1.71 ! [A10: $tType] : ( size @ ( list @ A10 ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_4,axiom,
% 2.54/1.71 wellorder @ product_unit ).
% 2.54/1.71
% 2.54/1.71 thf(tcon_Product__Type_Ounit___Orderings_Oorder_5,axiom,
% 2.54/1.71 order @ product_unit ).
% 2.54/1.71
% 2.54/1.71 thf(tcon_AsynchronousSystem_Omessage___Nat_Osize_6,axiom,
% 2.54/1.71 ! [A10: $tType,A11: $tType] : ( size @ ( message @ A10 @ A11 ) ) ).
% 2.54/1.71
% 2.54/1.71 thf(conj_0,conjecture,
% 2.54/1.71 ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) )
% 2.54/1.71 = ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ ( minus_minus @ nat @ n1 @ ( one_one @ nat ) ) ) ) ).
% 2.54/1.71 ------------------------
% 2.54/1.74 % (14647)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14431 for (2999ds/183Mi)
% 2.54/1.74 % (14649)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_14431 for (2999ds/27Mi)
% 2.54/1.74 % (14653)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14431 for (2999ds/18Mi)
% 2.54/1.74 % (14653)Instruction limit reached!
% 2.54/1.74 % (14653)------------------------------
% 2.54/1.74 % (14653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.74 % (14653)Termination reason: Unknown
% 2.54/1.74 % (14653)Termination phase: shuffling
% 2.54/1.74
% 2.54/1.74 % (14653)Memory used [KB]: 1535
% 2.54/1.74 % (14653)Time elapsed: 0.007 s
% 2.54/1.74 % (14653)Instructions burned: 18 (million)
% 2.54/1.74 % (14653)------------------------------
% 2.54/1.74 % (14653)------------------------------
% 2.54/1.75 % (14648)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_14431 for (2999ds/4Mi)
% 2.54/1.75 % (14650)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14431 for (2999ds/2Mi)
% 2.54/1.75 % (14651)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_14431 for (2999ds/2Mi)
% 2.54/1.75 % (14652)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_14431 for (2999ds/275Mi)
% 2.54/1.75 % (14649)Instruction limit reached!
% 2.54/1.75 % (14649)------------------------------
% 2.54/1.75 % (14649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.75 % (14649)Termination reason: Unknown
% 2.54/1.75 % (14649)Termination phase: Property scanning
% 2.54/1.75
% 2.54/1.75 % (14649)Memory used [KB]: 1535
% 2.54/1.75 % (14649)Time elapsed: 0.010 s
% 2.54/1.75 % (14649)Instructions burned: 29 (million)
% 2.54/1.75 % (14649)------------------------------
% 2.54/1.75 % (14649)------------------------------
% 2.54/1.75 % (14648)Instruction limit reached!
% 2.54/1.75 % (14648)------------------------------
% 2.54/1.75 % (14648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.75 % (14648)Termination reason: Unknown
% 2.54/1.75 % (14648)Termination phase: shuffling
% 2.54/1.75
% 2.54/1.75 % (14648)Memory used [KB]: 1279
% 2.54/1.75 % (14648)Time elapsed: 0.004 s
% 2.54/1.75 % (14648)Instructions burned: 5 (million)
% 2.54/1.75 % (14648)------------------------------
% 2.54/1.75 % (14648)------------------------------
% 2.54/1.75 % (14650)Instruction limit reached!
% 2.54/1.75 % (14650)------------------------------
% 2.54/1.75 % (14650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.75 % (14650)Termination reason: Unknown
% 2.54/1.75 % (14650)Termination phase: shuffling
% 2.54/1.75
% 2.54/1.75 % (14650)Memory used [KB]: 1279
% 2.54/1.75 % (14650)Time elapsed: 0.004 s
% 2.54/1.75 % (14650)Instructions burned: 3 (million)
% 2.54/1.75 % (14650)------------------------------
% 2.54/1.75 % (14650)------------------------------
% 2.54/1.75 % (14651)Instruction limit reached!
% 2.54/1.75 % (14651)------------------------------
% 2.54/1.75 % (14651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.75 % (14651)Termination reason: Unknown
% 2.54/1.75 % (14651)Termination phase: shuffling
% 2.54/1.75
% 2.54/1.75 % (14651)Memory used [KB]: 1279
% 2.54/1.75 % (14651)Time elapsed: 0.004 s
% 2.54/1.75 % (14651)Instructions burned: 3 (million)
% 2.54/1.75 % (14651)------------------------------
% 2.54/1.75 % (14651)------------------------------
% 2.54/1.75 % (14666)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14431 for (2999ds/3Mi)
% 2.54/1.75 % (14666)Instruction limit reached!
% 2.54/1.75 % (14666)------------------------------
% 2.54/1.75 % (14666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.75 % (14666)Termination reason: Unknown
% 2.54/1.75 % (14666)Termination phase: shuffling
% 2.54/1.75
% 2.54/1.75 % (14666)Memory used [KB]: 1279
% 2.54/1.75 % (14666)Time elapsed: 0.002 s
% 2.54/1.75 % (14666)Instructions burned: 3 (million)
% 2.54/1.75 % (14666)------------------------------
% 2.54/1.75 % (14666)------------------------------
% 2.54/1.76 % (14670)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_14431 for (2999ds/37Mi)
% 2.54/1.76 % (14671)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_14431 for (2999ds/15Mi)
% 2.54/1.76 % (14674)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14431 for (2999ds/7Mi)
% 2.54/1.77 % (14672)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_14431 for (2999ds/3Mi)
% 2.54/1.77 % (14673)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_14431 for (2999ds/1041Mi)
% 2.54/1.77 % (14670)Instruction limit reached!
% 2.54/1.77 % (14670)------------------------------
% 2.54/1.77 % (14670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.77 % (14670)Termination reason: Unknown
% 2.54/1.77 % (14670)Termination phase: Property scanning
% 2.54/1.77
% 2.54/1.77 % (14670)Memory used [KB]: 2046
% 2.54/1.77 % (14670)Time elapsed: 0.011 s
% 2.54/1.77 % (14670)Instructions burned: 37 (million)
% 2.54/1.77 % (14670)------------------------------
% 2.54/1.77 % (14670)------------------------------
% 2.54/1.77 % (14674)Instruction limit reached!
% 2.54/1.77 % (14674)------------------------------
% 2.54/1.77 % (14674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.77 % (14674)Termination reason: Unknown
% 2.54/1.77 % (14674)Termination phase: shuffling
% 2.54/1.77
% 2.54/1.77 % (14674)Memory used [KB]: 1407
% 2.54/1.77 % (14674)Time elapsed: 0.004 s
% 2.54/1.77 % (14674)Instructions burned: 9 (million)
% 2.54/1.77 % (14674)------------------------------
% 2.54/1.77 % (14674)------------------------------
% 2.54/1.77 % (14672)Instruction limit reached!
% 2.54/1.77 % (14672)------------------------------
% 2.54/1.77 % (14672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.77 % (14672)Termination reason: Unknown
% 2.54/1.77 % (14672)Termination phase: shuffling
% 2.54/1.77
% 2.54/1.77 % (14672)Memory used [KB]: 1279
% 2.54/1.77 % (14672)Time elapsed: 0.004 s
% 2.54/1.77 % (14672)Instructions burned: 3 (million)
% 2.54/1.77 % (14672)------------------------------
% 2.54/1.77 % (14672)------------------------------
% 2.54/1.77 % (14671)Instruction limit reached!
% 2.54/1.77 % (14671)------------------------------
% 2.54/1.77 % (14671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.77 % (14671)Termination reason: Unknown
% 2.54/1.77 % (14671)Termination phase: shuffling
% 2.54/1.77
% 2.54/1.77 % (14671)Memory used [KB]: 1535
% 2.54/1.77 % (14671)Time elapsed: 0.009 s
% 2.54/1.77 % (14671)Instructions burned: 16 (million)
% 2.54/1.77 % (14671)------------------------------
% 2.54/1.77 % (14671)------------------------------
% 2.54/1.78 % (14679)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14431 for (2999ds/16Mi)
% 2.54/1.78 % (14681)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_14431 for (2999ds/3Mi)
% 2.54/1.78 % (14681)Instruction limit reached!
% 2.54/1.78 % (14681)------------------------------
% 2.54/1.78 % (14681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.78 % (14681)Termination reason: Unknown
% 2.54/1.78 % (14681)Termination phase: shuffling
% 2.54/1.78
% 2.54/1.78 % (14681)Memory used [KB]: 1279
% 2.54/1.78 % (14681)Time elapsed: 0.002 s
% 2.54/1.78 % (14681)Instructions burned: 3 (million)
% 2.54/1.78 % (14681)------------------------------
% 2.54/1.78 % (14681)------------------------------
% 2.54/1.78 % (14685)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_14431 for (2999ds/7Mi)
% 2.54/1.78 % (14679)Instruction limit reached!
% 2.54/1.78 % (14679)------------------------------
% 2.54/1.78 % (14679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.78 % (14679)Termination reason: Unknown
% 2.54/1.78 % (14679)Termination phase: shuffling
% 2.54/1.78
% 2.54/1.78 % (14679)Memory used [KB]: 1535
% 2.54/1.78 % (14679)Time elapsed: 0.007 s
% 2.54/1.78 % (14679)Instructions burned: 18 (million)
% 2.54/1.78 % (14679)------------------------------
% 2.54/1.78 % (14679)------------------------------
% 2.54/1.78 % (14685)Instruction limit reached!
% 2.54/1.78 % (14685)------------------------------
% 2.54/1.78 % (14685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.78 % (14685)Termination reason: Unknown
% 2.54/1.78 % (14685)Termination phase: shuffling
% 2.54/1.78
% 2.54/1.78 % (14685)Memory used [KB]: 1407
% 2.54/1.78 % (14685)Time elapsed: 0.004 s
% 2.54/1.78 % (14685)Instructions burned: 9 (million)
% 2.54/1.78 % (14685)------------------------------
% 2.54/1.78 % (14685)------------------------------
% 2.54/1.79 % (14682)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_14431 for (2999ds/3Mi)
% 2.54/1.79 % (14690)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_14431 for (2999ds/3Mi)
% 2.54/1.79 % (14682)Instruction limit reached!
% 2.54/1.79 % (14682)------------------------------
% 2.54/1.79 % (14682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.79 % (14682)Termination reason: Unknown
% 2.54/1.79 % (14682)Termination phase: shuffling
% 2.54/1.79
% 2.54/1.79 % (14682)Memory used [KB]: 1279
% 2.54/1.79 % (14682)Time elapsed: 0.004 s
% 2.54/1.79 % (14682)Instructions burned: 4 (million)
% 2.54/1.79 % (14682)------------------------------
% 2.54/1.79 % (14682)------------------------------
% 2.54/1.79 % (14690)Instruction limit reached!
% 2.54/1.79 % (14690)------------------------------
% 2.54/1.79 % (14690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.79 % (14690)Termination reason: Unknown
% 2.54/1.79 % (14690)Termination phase: shuffling
% 2.54/1.79
% 2.54/1.79 % (14690)Memory used [KB]: 1279
% 2.54/1.79 % (14690)Time elapsed: 0.002 s
% 2.54/1.79 % (14690)Instructions burned: 4 (million)
% 2.54/1.79 % (14690)------------------------------
% 2.54/1.79 % (14690)------------------------------
% 2.54/1.79 % (14693)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_14431 for (2999ds/4Mi)
% 2.54/1.79 % (14693)Instruction limit reached!
% 2.54/1.79 % (14693)------------------------------
% 2.54/1.79 % (14693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.79 % (14693)Termination reason: Unknown
% 2.54/1.79 % (14693)Termination phase: shuffling
% 2.54/1.79
% 2.54/1.79 % (14693)Memory used [KB]: 1407
% 2.54/1.79 % (14693)Time elapsed: 0.003 s
% 2.54/1.79 % (14693)Instructions burned: 7 (million)
% 2.54/1.79 % (14694)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_14431 for (2999ds/18Mi)
% 2.54/1.79 % (14693)------------------------------
% 2.54/1.79 % (14693)------------------------------
% 2.54/1.79 % (14647)Instruction limit reached!
% 2.54/1.79 % (14647)------------------------------
% 2.54/1.79 % (14647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.79 % (14647)Termination reason: Unknown
% 2.54/1.79 % (14647)Termination phase: Saturation
% 2.54/1.79
% 2.54/1.79 % (14647)Memory used [KB]: 6908
% 2.54/1.79 % (14647)Time elapsed: 0.057 s
% 2.54/1.79 % (14647)Instructions burned: 183 (million)
% 2.54/1.79 % (14647)------------------------------
% 2.54/1.79 % (14647)------------------------------
% 2.56/1.80 % (14697)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14431 for (2999ds/6Mi)
% 2.56/1.80 % (14697)Instruction limit reached!
% 2.56/1.80 % (14697)------------------------------
% 2.56/1.80 % (14697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.80 % (14697)Termination reason: Unknown
% 2.56/1.80 % (14697)Termination phase: shuffling
% 2.56/1.80
% 2.56/1.80 % (14697)Memory used [KB]: 1279
% 2.56/1.80 % (14697)Time elapsed: 0.003 s
% 2.56/1.80 % (14697)Instructions burned: 6 (million)
% 2.56/1.80 % (14697)------------------------------
% 2.56/1.80 % (14697)------------------------------
% 2.56/1.80 % (14694)Instruction limit reached!
% 2.56/1.80 % (14694)------------------------------
% 2.56/1.80 % (14694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.80 % (14694)Termination reason: Unknown
% 2.56/1.80 % (14694)Termination phase: shuffling
% 2.56/1.80
% 2.56/1.80 % (14694)Memory used [KB]: 1535
% 2.56/1.80 % (14694)Time elapsed: 0.007 s
% 2.56/1.80 % (14694)Instructions burned: 18 (million)
% 2.56/1.80 % (14694)------------------------------
% 2.56/1.80 % (14694)------------------------------
% 2.56/1.80 % (14652)First to succeed.
% 2.56/1.80 % (14699)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_14431 for (2999ds/902Mi)
% 2.56/1.80 % (14700)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_14431 for (2999ds/21Mi)
% 2.56/1.80 % (14652)Refutation found. Thanks to Tanya!
% 2.56/1.80 % SZS status Theorem for DTF2THF_14431
% 2.56/1.80 % SZS output start Proof for DTF2THF_14431
% 2.56/1.80 thf(type_def_5, type, product_unit: $tType).
% 2.56/1.80 thf(type_def_6, type, configuration_ext: ($tType * $tType * $tType * $tType) > $tType).
% 2.56/1.80 thf(type_def_7, type, message: ($tType * $tType) > $tType).
% 2.56/1.80 thf(type_def_9, type, list: ($tType) > $tType).
% 2.56/1.80 thf(type_def_10, type, nat: $tType).
% 2.56/1.80 thf(type_def_11, type, p: $tType).
% 2.56/1.80 thf(type_def_12, type, v: $tType).
% 2.56/1.80 thf(type_def_13, type, s: $tType).
% 2.56/1.80 thf(func_def_0, type, configuration_ext: ($tType * $tType * $tType * $tType) > $tType).
% 2.56/1.80 thf(func_def_1, type, message: ($tType * $tType) > $tType).
% 2.56/1.80 thf(func_def_2, type, product_unit: $tType).
% 2.56/1.80 thf(func_def_3, type, list: ($tType) > $tType).
% 2.56/1.80 thf(func_def_4, type, nat: $tType).
% 2.56/1.80 thf(func_def_5, type, v: $tType).
% 2.56/1.80 thf(func_def_6, type, s: $tType).
% 2.56/1.80 thf(func_def_7, type, p: $tType).
% 2.56/1.80 thf(func_def_8, type, type: !>[X0: $tType]:($o)).
% 2.56/1.80 thf(func_def_9, type, size: !>[X0: $tType]:($o)).
% 2.56/1.80 thf(func_def_10, type, one: !>[X0: $tType]:($o)).
% 2.56/1.80 thf(func_def_11, type, zero: !>[X0: $tType]:($o)).
% 2.56/1.80 thf(func_def_12, type, neg_numeral: !>[X0: $tType]:($o)).
% 2.56/1.80 thf(func_def_13, type, order: !>[X0: $tType]:($o)).
% 2.56/1.80 thf(func_def_14, type, group_add: !>[X0: $tType]:($o)).
% 2.56/1.80 thf(func_def_15, type, wellorder: !>[X0: $tType]:($o)).
% 2.56/1.80 thf(func_def_16, type, comm_monoid_diff: !>[X0: $tType]:($o)).
% 2.56/1.80 thf(func_def_17, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 2.56/1.80 thf(func_def_18, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 2.56/1.80 thf(func_def_19, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 2.56/1.80 thf(func_def_20, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 2.56/1.80 thf(func_def_21, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 2.56/1.80 thf(func_def_22, type, enabled: !>[X0: $tType, X1: $tType, X2: $tType]:(configuration_ext @ X0 @ X1 @ X2 @ product_unit > message @ X0 @ X1 > $o)).
% 2.56/1.80 thf(func_def_23, 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)).
% 2.56/1.80 thf(func_def_24, type, fLPThe137922386ionCfg: !>[X0: $tType, X1: $tType, X2: $tType]:(configuration_ext @ X0 @ X1 @ X2 @ product_unit > (list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit > list @ message @ X0 @ X1 > list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit) > (list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit > list @ message @ X0 @ X1 > list @ message @ X0 @ X1) > nat > list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit)).
% 2.56/1.80 thf(func_def_25, type, fLPThe221390223ionMsg: !>[X0: $tType, X1: $tType, X2: $tType]:(configuration_ext @ X0 @ X1 @ X2 @ product_unit > (list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit > list @ message @ X0 @ X1 > list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit) > (list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit > list @ message @ X0 @ X1 > list @ message @ X0 @ X1) > nat > list @ message @ X0 @ X1)).
% 2.56/1.80 thf(func_def_26, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.56/1.80 thf(func_def_27, type, one_one: !>[X0: $tType]:(X0)).
% 2.56/1.80 thf(func_def_28, type, zero_zero: !>[X0: $tType]:(X0)).
% 2.56/1.80 thf(func_def_29, type, prefixList: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 2.56/1.80 thf(func_def_30, type, last: !>[X0: $tType]:(list @ X0 > X0)).
% 2.56/1.80 thf(func_def_31, type, nil: !>[X0: $tType]:(list @ X0)).
% 2.56/1.80 thf(func_def_32, type, nth: !>[X0: $tType]:(list @ X0 > nat > X0)).
% 2.56/1.80 thf(func_def_33, type, suc: nat > nat).
% 2.56/1.80 thf(func_def_34, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 2.56/1.80 thf(func_def_35, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.56/1.80 thf(func_def_36, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.56/1.80 thf(func_def_37, type, fe: nat > list @ configuration_ext @ p @ v @ s @ product_unit).
% 2.56/1.80 thf(func_def_38, type, ft: nat > list @ message @ p @ v).
% 2.56/1.80 thf(func_def_39, type, index: nat).
% 2.56/1.80 thf(func_def_40, type, msgInSet: message @ p @ v).
% 2.56/1.80 thf(func_def_41, type, msg: message @ p @ v).
% 2.56/1.80 thf(func_def_42, type, n0: nat).
% 2.56/1.80 thf(func_def_43, type, n1: nat).
% 2.56/1.80 thf(func_def_44, type, nMsg: nat).
% 2.56/1.80 thf(func_def_45, type, n: nat).
% 2.56/1.80 thf(func_def_59, 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).
% 2.56/1.80 thf(func_def_60, 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).
% 2.56/1.80 thf(func_def_61, type, sK2: (nat > $o) > nat).
% 2.56/1.80 thf(func_def_62, type, sK3: (nat > nat) > nat).
% 2.56/1.80 thf(func_def_63, type, sK4: (nat > nat) > nat).
% 2.56/1.80 thf(func_def_64, type, sK5: nat > nat > nat).
% 2.56/1.80 thf(func_def_65, type, sK6: !>[X0: $tType]:(nat > list @ X0)).
% 2.56/1.80 thf(func_def_66, type, sK7: (nat > $o) > nat > nat > nat).
% 2.56/1.80 thf(func_def_67, type, sK8: (nat > $o) > nat).
% 2.56/1.80 thf(func_def_68, type, sK9: nat > nat).
% 2.56/1.80 thf(func_def_69, type, sK10: (nat > nat > $o) > nat).
% 2.56/1.80 thf(func_def_70, type, sK11: (nat > nat > $o) > nat).
% 2.56/1.80 thf(func_def_71, type, sK12: (nat > nat > $o) > nat).
% 2.56/1.80 thf(func_def_72, type, sK13: (nat > nat > $o) > nat).
% 2.56/1.80 thf(func_def_73, type, sK14: (nat > $o) > nat).
% 2.56/1.80 thf(func_def_74, type, sK15: nat > (nat > $o) > nat).
% 2.56/1.80 thf(func_def_75, type, sK16: nat > nat).
% 2.56/1.80 thf(func_def_76, type, sK17: (nat > $o) > nat).
% 2.56/1.80 thf(func_def_77, type, sK18: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 2.56/1.80 thf(func_def_78, type, sK19: (nat > $o) > nat > nat).
% 2.56/1.80 thf(func_def_79, type, sK20: (nat > $o) > nat).
% 2.56/1.80 thf(func_def_80, type, sK21: nat > nat).
% 2.56/1.80 thf(func_def_81, type, sK22: (nat > $o) > nat).
% 2.56/1.80 thf(func_def_82, type, sK23: (nat > $o) > nat > nat).
% 2.56/1.80 thf(func_def_83, type, sK24: (nat > $o) > nat > nat).
% 2.56/1.80 thf(func_def_84, type, sK25: (nat > $o) > nat).
% 2.56/1.80 thf(func_def_85, type, sK26: nat > nat).
% 2.56/1.80 thf(func_def_86, type, sK27: (nat > $o) > nat).
% 2.56/1.80 thf(func_def_87, type, sK28: (nat > $o) > nat > nat).
% 2.56/1.80 thf(func_def_88, type, sK29: (nat > $o) > nat > nat).
% 2.56/1.80 thf(func_def_89, type, sK30: (nat > $o) > nat > nat).
% 2.56/1.80 thf(func_def_90, type, sK31: (nat > $o) > nat > nat).
% 2.56/1.80 thf(func_def_91, type, sK32: (nat > $o) > nat > nat > nat).
% 2.56/1.80 thf(func_def_92, type, sK33: nat > nat).
% 2.56/1.80 thf(func_def_93, type, sK34: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 2.56/1.80 thf(func_def_94, type, sK35: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 2.56/1.80 thf(func_def_95, type, sK36: (nat > $o) > nat).
% 2.56/1.80 thf(func_def_96, type, sK37: (nat > $o) > (nat > $o) > nat > nat).
% 2.56/1.80 thf(func_def_97, type, sK38: (nat > $o) > nat).
% 2.56/1.80 thf(func_def_98, type, sK39: nat > nat > nat).
% 2.56/1.80 thf(func_def_99, type, sK40: (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).
% 2.56/1.80 thf(func_def_100, type, sK41: (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).
% 2.56/1.80 thf(func_def_101, type, sK42: (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).
% 2.56/1.80 thf(func_def_102, type, sK43: (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).
% 2.56/1.80 thf(func_def_103, type, sK44: (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).
% 2.56/1.80 thf(func_def_104, type, sK45: (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).
% 2.56/1.80 thf(func_def_105, type, sK46: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v).
% 2.56/1.80 thf(func_def_106, type, sK47: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit).
% 2.56/1.80 thf(func_def_107, type, sK48: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit).
% 2.56/1.80 thf(func_def_108, type, sK49: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v).
% 2.56/1.80 thf(func_def_109, type, sK50: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > configuration_ext @ p @ v @ s @ product_unit).
% 2.56/1.80 thf(func_def_110, type, sK51: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit).
% 2.56/1.80 thf(func_def_111, type, sK52: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v).
% 2.56/1.80 thf(func_def_112, type, sK53: (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > (configuration_ext @ p @ v @ s @ product_unit > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ configuration_ext @ p @ v @ s @ product_unit) > (list @ configuration_ext @ p @ v @ s @ product_unit > list @ message @ p @ v > list @ message @ p @ v) > nat > $o) > nat).
% 2.56/1.80 thf(func_def_113, type, sK54: (nat > $o) > nat).
% 2.56/1.80 thf(func_def_114, type, sK55: !>[X0: $tType]:(list @ X0 > list @ X0 > nat)).
% 2.56/1.80 thf(func_def_115, type, sK56: !>[X0: $tType]:((nat > X0 > $o) > nat > list @ X0)).
% 2.56/1.80 thf(func_def_116, type, sK57: !>[X0: $tType]:((nat > X0 > $o) > nat > nat)).
% 2.56/1.80 thf(func_def_117, type, sK58: !>[X0: $tType]:(nat > (nat > X0 > $o) > X0)).
% 2.56/1.80 thf(func_def_118, type, sK59: !>[X0: $tType]:(list @ X0 > (nat > X0 > $o) > nat > nat)).
% 2.56/1.80 thf(func_def_119, type, sK60: nat > (nat > $o) > nat).
% 2.56/1.80 thf(func_def_120, type, sK61: nat > nat > nat).
% 2.56/1.80 thf(func_def_121, type, sK62: nat > nat > nat).
% 2.56/1.80 thf(func_def_122, type, sK63: nat > (nat > $o) > nat).
% 2.56/1.80 thf(func_def_123, type, sK64: (nat > $o) > nat > nat).
% 2.56/1.80 thf(func_def_124, type, sK65: (nat > $o) > nat > nat).
% 2.56/1.80 thf(func_def_125, type, sK66: (nat > $o) > nat).
% 2.56/1.80 thf(func_def_126, type, sK67: (nat > $o) > nat > nat).
% 2.56/1.80 thf(func_def_127, type, sK68: (nat > $o) > nat > nat).
% 2.56/1.80 thf(func_def_128, type, sK69: (nat > nat > $o) > nat).
% 2.56/1.80 thf(func_def_129, type, sK70: (nat > nat > $o) > nat).
% 2.56/1.80 thf(func_def_130, type, sK71: (nat > nat > $o) > nat).
% 2.56/1.80 thf(func_def_131, type, sK72: (nat > nat > $o) > nat).
% 2.56/1.80 thf(func_def_132, type, sK73: (nat > nat > $o) > nat).
% 2.56/1.80 thf(func_def_133, type, sK74: (nat > nat > $o) > nat).
% 2.56/1.80 thf(func_def_134, type, sK75: (nat > nat > $o) > nat).
% 2.56/1.80 thf(func_def_135, type, sK76: (nat > nat > $o) > nat).
% 2.56/1.80 thf(func_def_136, type, sK77: (nat > nat > $o) > nat).
% 2.56/1.80 thf(func_def_137, type, sK78: (nat > $o) > nat > nat).
% 2.56/1.80 thf(func_def_138, type, sK79: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.56/1.80 thf(func_def_139, type, sK80: (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).
% 2.56/1.80 thf(func_def_140, type, sK81: (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).
% 2.56/1.80 thf(func_def_141, type, sK82: (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).
% 2.56/1.80 thf(func_def_142, type, sK83: (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).
% 2.56/1.80 thf(func_def_143, type, sK84: (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).
% 2.56/1.80 thf(func_def_144, type, sK85: (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).
% 2.56/1.80 thf(func_def_145, type, sK86: (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).
% 2.56/1.80 thf(func_def_146, type, sK87: (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).
% 2.56/1.80 thf(func_def_147, type, sK88: (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).
% 2.56/1.80 thf(func_def_148, type, sK89: (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).
% 2.56/1.80 thf(func_def_149, type, sK90: (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).
% 2.56/1.80 thf(func_def_150, type, sK91: (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).
% 2.56/1.80 thf(func_def_151, type, sK92: (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).
% 2.56/1.80 thf(func_def_152, type, sK93: (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).
% 2.56/1.80 thf(func_def_154, type, ph95: !>[X0: $tType]:(X0)).
% 2.56/1.80 thf(f1440,plain,(
% 2.56/1.80 $false),
% 2.56/1.80 inference(subsumption_resolution,[status(thm)],[f1417,f1304])).
% 2.56/1.80 thf(f1304,plain,(
% 2.56/1.80 ((ord_less @ nat @ n1 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) = $true)),
% 2.56/1.80 inference(cnf_transformation,[status(thm)],[f546])).
% 2.56/1.80 thf(f546,plain,(
% 2.56/1.80 ((ord_less @ nat @ n1 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) = $true)),
% 2.56/1.80 inference(fool_elimination,[status(thm)],[f545])).
% 2.56/1.80 thf(f545,plain,(
% 2.56/1.80 (ord_less @ nat @ n1 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))),
% 2.56/1.80 inference(rectify,[status(thm)],[f1])).
% 2.56/1.80 thf(f1,axiom,(
% 2.56/1.80 (ord_less @ nat @ n1 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))),
% 2.56/1.80 file('/export/starexec/sandbox/tmp/tmp.kfyzaKl7u5/DTF2THF_14431.p',fact_0_Occ3_H)).
% 2.56/1.80 thf(f1417,plain,(
% 2.56/1.80 ((ord_less @ nat @ n1 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) != $true)),
% 2.56/1.80 inference(trivial_inequality_removal,[status(thm)],[f1413])).
% 2.56/1.80 thf(f1413,plain,(
% 2.56/1.80 ($true != $true) | ((ord_less @ nat @ n1 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) != $true)),
% 2.56/1.80 inference(superposition,[status(thm)],[f1400,f1217])).
% 2.56/1.80 thf(f1217,plain,(
% 2.56/1.80 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = (ord_less @ nat @ (minus_minus @ nat @ X0 @ X2) @ X1)) | ($true != (ord_less @ nat @ X0 @ X1))) )),
% 2.56/1.80 inference(cnf_transformation,[status(thm)],[f890])).
% 2.56/1.80 thf(f890,plain,(
% 2.56/1.80 ! [X0 : nat,X1 : nat,X2 : nat] : (($true != (ord_less @ nat @ X0 @ X1)) | ($true = (ord_less @ nat @ (minus_minus @ nat @ X0 @ X2) @ X1)))),
% 2.56/1.80 inference(ennf_transformation,[status(thm)],[f528])).
% 2.56/1.80 thf(f528,plain,(
% 2.56/1.80 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = (ord_less @ nat @ X0 @ X1)) => ($true = (ord_less @ nat @ (minus_minus @ nat @ X0 @ X2) @ X1)))),
% 2.56/1.80 inference(fool_elimination,[status(thm)],[f527])).
% 2.56/1.80 thf(f527,plain,(
% 2.56/1.80 ! [X0 : nat,X1 : nat,X2 : nat] : ((ord_less @ nat @ X0 @ X1) => (ord_less @ nat @ (minus_minus @ nat @ X0 @ X2) @ X1))),
% 2.56/1.80 inference(rectify,[status(thm)],[f158])).
% 2.56/1.80 thf(f158,axiom,(
% 2.56/1.80 ! [X28 : nat,X7 : nat,X5 : nat] : ((ord_less @ nat @ X28 @ X7) => (ord_less @ nat @ (minus_minus @ nat @ X28 @ X5) @ X7))),
% 2.56/1.80 file('/export/starexec/sandbox/tmp/tmp.kfyzaKl7u5/DTF2THF_14431.p',fact_157_less__imp__diff__less)).
% 2.56/1.80 thf(f1400,plain,(
% 2.56/1.80 ($true != (ord_less @ nat @ (minus_minus @ nat @ n1 @ one_one @ nat) @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))))),
% 2.56/1.80 inference(trivial_inequality_removal,[status(thm)],[f1399])).
% 2.56/1.80 thf(f1399,plain,(
% 2.56/1.80 ($true != (ord_less @ nat @ (minus_minus @ nat @ n1 @ one_one @ nat) @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))) | ((nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index) @ (minus_minus @ nat @ n1 @ one_one @ nat)) != (nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index) @ (minus_minus @ nat @ n1 @ one_one @ nat)))),
% 2.56/1.80 inference(superposition,[status(thm)],[f1161,f1087])).
% 2.56/1.80 thf(f1087,plain,(
% 2.56/1.80 ( ! [X0 : nat] : (((nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ (suc @ index)) @ X0) = (nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index) @ X0)) | ($true != (ord_less @ nat @ X0 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))))) )),
% 2.56/1.80 inference(cnf_transformation,[status(thm)],[f887])).
% 2.56/1.80 thf(f887,plain,(
% 2.56/1.80 ! [X0 : nat] : (($true != (ord_less @ nat @ X0 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))) | ((nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ (suc @ index)) @ X0) = (nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index) @ X0)))),
% 2.56/1.80 inference(ennf_transformation,[status(thm)],[f690])).
% 2.56/1.80 thf(f690,plain,(
% 2.56/1.80 ! [X0 : nat] : (($true = (ord_less @ nat @ X0 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))) => ((nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ (suc @ index)) @ X0) = (nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index) @ X0)))),
% 2.56/1.80 inference(fool_elimination,[status(thm)],[f689])).
% 2.56/1.80 thf(f689,plain,(
% 2.56/1.80 ! [X0 : nat] : ((ord_less @ nat @ X0 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) => ((nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ (suc @ index)) @ X0) = (nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index) @ X0)))),
% 2.56/1.80 inference(rectify,[status(thm)],[f2])).
% 2.56/1.80 thf(f2,axiom,(
% 2.56/1.80 ! [X4 : nat] : ((ord_less @ nat @ X4 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) => ((nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index) @ X4) = (nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ (suc @ index)) @ X4)))),
% 2.56/1.80 file('/export/starexec/sandbox/tmp/tmp.kfyzaKl7u5/DTF2THF_14431.p',fact_1_SameCfgOnLow)).
% 2.56/1.80 thf(f1161,plain,(
% 2.56/1.80 ((nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index) @ (minus_minus @ nat @ n1 @ one_one @ nat)) != (nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ (suc @ index)) @ (minus_minus @ nat @ n1 @ one_one @ nat)))),
% 2.56/1.80 inference(cnf_transformation,[status(thm)],[f727])).
% 2.56/1.80 thf(f727,plain,(
% 2.56/1.80 ((nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index) @ (minus_minus @ nat @ n1 @ one_one @ nat)) != (nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ (suc @ index)) @ (minus_minus @ nat @ n1 @ one_one @ nat)))),
% 2.56/1.80 inference(flattening,[status(thm)],[f269])).
% 2.56/1.80 thf(f269,negated_conjecture,(
% 2.56/1.80 ~((nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index) @ (minus_minus @ nat @ n1 @ one_one @ nat)) = (nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ (suc @ index)) @ (minus_minus @ nat @ n1 @ one_one @ nat)))),
% 2.56/1.80 inference(negated_conjecture,[status(cth)],[f268])).
% 2.56/1.80 thf(f268,conjecture,(
% 2.56/1.80 ((nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index) @ (minus_minus @ nat @ n1 @ one_one @ nat)) = (nth @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ (suc @ index)) @ (minus_minus @ nat @ n1 @ one_one @ nat)))),
% 2.56/1.80 file('/export/starexec/sandbox/tmp/tmp.kfyzaKl7u5/DTF2THF_14431.p',conj_0)).
% 2.56/1.80 % SZS output end Proof for DTF2THF_14431
% 2.56/1.80 % (14652)------------------------------
% 2.56/1.80 % (14652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.56/1.80 % (14652)Termination reason: Refutation
% 2.56/1.80
% 2.56/1.80 % (14652)Memory used [KB]: 6780
% 2.56/1.80 % (14652)Time elapsed: 0.058 s
% 2.56/1.80 % (14652)Instructions burned: 95 (million)
% 2.56/1.80 % (14652)------------------------------
% 2.56/1.80 % (14652)------------------------------
% 2.56/1.80 % (14640)Success in time 0.081 s
%------------------------------------------------------------------------------