%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP055^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:11 AM UTC 2026
% Result : Theorem 2.87s 1.64s
% Output : Refutation 2.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP055^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n004.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:24:41 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : ITP055^2 : TPTP v9.2.1. Released v7.5.0.
% 0.29/0.46 % Domain : Interactive Theorem Proving
% 0.29/0.46 % Problem : Sledgehammer FLPTheorem problem prob_1231__3305662_1
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.29/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.29/0.46 % Source : [Des21]
% 0.29/0.46 % Names : FLPTheorem/prob_1231__3305662_1 [Des21]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.00 v7.5.0
% 0.29/0.46 % Syntax : Number of formulae : 356 ( 128 unt; 62 typ; 0 def)
% 0.29/0.46 % Number of atoms : 674 ( 300 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 6 ( 2 avg)
% 0.29/0.46 % Number of connectives : 4532 ( 120 ~; 7 |; 28 &;4008 @)
% 0.29/0.46 % ( 0 <=>; 369 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 28 ( 7 avg)
% 0.29/0.46 % Number of types : 7 ( 6 usr)
% 0.29/0.46 % Number of type conns : 445 ( 445 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 57 ( 56 usr; 4 con; 0-8 aty)
% 0.29/0.46 % Number of variables : 937 ( 8 ^; 845 !; 31 ?; 937 :)
% 0.29/0.46 % ( 53 !>; 0 ?*; 0 @-; 0 @+)
% 0.29/0.46 % SPC : TH1_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:17:36.018
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % Could-be-implicit typings (11)
% 0.29/0.46 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext,type,
% 0.29/0.46 configuration_ext: $tType > $tType > $tType > $tType > $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_AsynchronousSystem_OmessageValue,type,
% 0.29/0.46 messageValue: $tType > $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_AsynchronousSystem_Omessage,type,
% 0.29/0.46 message: $tType > $tType > $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_Product__Type_Ounit,type,
% 0.29/0.46 product_unit: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_List_Olist,type,
% 0.29/0.46 list: $tType > $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_Set_Oset,type,
% 0.29/0.46 set: $tType > $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_Nat_Onat,type,
% 0.29/0.46 nat: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_t_Int_Oint,type,
% 0.29/0.46 int: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_tf_v,type,
% 0.29/0.46 v: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_tf_s,type,
% 0.29/0.46 s: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_tf_p,type,
% 0.29/0.46 p: $tType ).
% 0.29/0.46
% 0.29/0.46 % Explicit typings (51)
% 0.29/0.46 thf(sy_cl_HOL_Otype,type,
% 0.29/0.46 type:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Nat_Osize,type,
% 0.29/0.46 size:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Oone,type,
% 0.29/0.46 one:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ozero,type,
% 0.29/0.46 zero:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Rings_Oring__1,type,
% 0.29/0.46 ring_1:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.29/0.46 ord:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Nat_Oring__char__0,type,
% 0.29/0.46 ring_char_0:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.29/0.46 order:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ogroup__add,type,
% 0.29/0.46 group_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Rings_Osemiring__1,type,
% 0.29/0.46 semiring_1:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.29/0.46 linorder:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Nat_Osemiring__char__0,type,
% 0.29/0.46 semiring_char_0:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Orderings_Owellorder,type,
% 0.29/0.46 wellorder:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.29/0.46 linordered_idom:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 0.29/0.46 boolean_algebra:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.29/0.46 ordered_ab_group_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.29/0.46 linord219039673up_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.29/0.46 linord1659791738miring:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.29/0.46 canoni770627133id_add:
% 0.29/0.46 !>[A: $tType] : $o ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_BNF__Greatest__Fixpoint_Oshift,type,
% 0.29/0.46 bNF_Greatest_shift:
% 0.29/0.46 !>[A: $tType,B: $tType] : ( ( ( list @ A ) > B ) > A > ( list @ A ) > B ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus,type,
% 0.29/0.46 fLPThe1922692578sensus:
% 0.29/0.46 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus_OinfiniteExecutionCfg,type,
% 0.29/0.46 fLPThe137922386ionCfg:
% 0.29/0.46 !>[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 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus_OinfiniteExecutionMsg,type,
% 0.29/0.46 fLPThe221390223ionMsg:
% 0.29/0.46 !>[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 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpSystem_OterminationFLP,type,
% 0.29/0.46 fLPThe2031355932ionFLP:
% 0.29/0.46 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > ( nat > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) ) > ( nat > ( list @ ( message @ P @ V ) ) ) > $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.29/0.46 one_one:
% 0.29/0.46 !>[A: $tType] : A ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.29/0.46 uminus_uminus:
% 0.29/0.46 !>[A: $tType] : ( A > A ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.29/0.46 zero_zero:
% 0.29/0.46 !>[A: $tType] : A ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Int_Onat,type,
% 0.29/0.46 nat2: int > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Int_Oring__1__class_Oof__int,type,
% 0.29/0.46 ring_1_of_int:
% 0.29/0.46 !>[A: $tType] : ( int > A ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_ListUtilities_OprefixList,type,
% 0.29/0.46 prefixList:
% 0.29/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_List_Ogen__length,type,
% 0.29/0.46 gen_length:
% 0.29/0.46 !>[A: $tType] : ( nat > ( list @ A ) > nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_List_Oinsert,type,
% 0.29/0.46 insert:
% 0.29/0.46 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_List_Olist_OCons,type,
% 0.29/0.46 cons:
% 0.29/0.46 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_List_Olist_ONil,type,
% 0.29/0.46 nil:
% 0.29/0.46 !>[A: $tType] : ( list @ A ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_List_Olist__ex1,type,
% 0.29/0.46 list_ex1:
% 0.29/0.46 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_List_On__lists,type,
% 0.29/0.46 n_lists:
% 0.29/0.46 !>[A: $tType] : ( nat > ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_List_Onths,type,
% 0.29/0.46 nths:
% 0.29/0.46 !>[A: $tType] : ( ( list @ A ) > ( set @ nat ) > ( list @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_List_Oproduct__lists,type,
% 0.29/0.46 product_lists:
% 0.29/0.46 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_List_Osubseqs,type,
% 0.29/0.46 subseqs:
% 0.29/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Nat_OSuc,type,
% 0.29/0.46 suc: nat > nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Nat_Osemiring__1__class_Oof__nat,type,
% 0.29/0.46 semiring_1_of_nat:
% 0.29/0.46 !>[A: $tType] : ( nat > A ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.29/0.46 size_size:
% 0.29/0.46 !>[A: $tType] : ( A > nat ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.29/0.46 ord_less:
% 0.29/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.29/0.46 ord_less_eq:
% 0.29/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_Set_OCollect,type,
% 0.29/0.46 collect:
% 0.29/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_c_member,type,
% 0.29/0.46 member:
% 0.29/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_cfg____,type,
% 0.29/0.46 cfg: configuration_ext @ p @ v @ s @ product_unit ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_fe____,type,
% 0.29/0.46 fe: nat > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_m____,type,
% 0.29/0.46 m: nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_n____,type,
% 0.29/0.46 n: nat ).
% 0.29/0.46
% 0.29/0.46 thf(sy_v_na____,type,
% 0.29/0.46 na: nat ).
% 0.29/0.46
% 0.29/0.46 % Relevant facts (251)
% 0.29/0.46 thf(fact_0__092_060open_062m_A_060_An_092_060close_062,axiom,
% 0.29/0.46 ord_less @ nat @ m @ na ).
% 0.29/0.46
% 0.29/0.46 % \<open>m < n\<close>
% 0.29/0.46 thf(fact_1_MLessN,axiom,
% 0.29/0.46 ord_less @ nat @ m @ n ).
% 0.29/0.46
% 0.29/0.46 % MLessN
% 0.29/0.46 thf(fact_2_IA_I1_J,axiom,
% 0.29/0.46 ( ( ord_less @ nat @ m @ na )
% 0.29/0.46 => ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ m ) @ ( fe @ na ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % IA(1)
% 0.29/0.46 thf(fact_3__092_060open_062m_A_061_An_A_092_060or_062_Am_A_060_An_092_060close_062,axiom,
% 0.29/0.46 ( ( m = na )
% 0.29/0.46 | ( ord_less @ nat @ m @ na ) ) ).
% 0.29/0.46
% 0.29/0.46 % \<open>m = n \<or> m < n\<close>
% 0.29/0.46 thf(fact_4_IA_I2_J,axiom,
% 0.29/0.46 ord_less @ nat @ m @ ( suc @ na ) ).
% 0.29/0.46
% 0.29/0.46 % IA(2)
% 0.29/0.46 thf(fact_5_PrefixListTransitive,axiom,
% 0.29/0.46 ! [A: $tType,L1: list @ A,L2: list @ A,L3: list @ A] :
% 0.29/0.46 ( ( prefixList @ A @ L1 @ L2 )
% 0.29/0.46 => ( ( prefixList @ A @ L2 @ L3 )
% 0.29/0.46 => ( prefixList @ A @ L1 @ L3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % PrefixListTransitive
% 0.29/0.46 thf(fact_6_flpSystem_OterminationFLP_Ocong,axiom,
% 0.29/0.46 ! [V: $tType,S: $tType,P: $tType] :
% 0.29/0.46 ( ( fLPThe2031355932ionFLP @ P @ S @ V )
% 0.29/0.46 = ( fLPThe2031355932ionFLP @ P @ S @ V ) ) ).
% 0.29/0.46
% 0.29/0.46 % flpSystem.terminationFLP.cong
% 0.29/0.46 thf(fact_7_FE_I1_J,axiom,
% 0.29/0.46 ( ( fe @ ( zero_zero @ nat ) )
% 0.29/0.46 = ( cons @ ( configuration_ext @ p @ v @ s @ product_unit ) @ cfg @ ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % FE(1)
% 0.29/0.46 thf(fact_8_prefixList_Ointros_I2_J,axiom,
% 0.29/0.46 ! [A: $tType,Xa: list @ A,Xb: list @ A,X: A] :
% 0.29/0.46 ( ( prefixList @ A @ Xa @ Xb )
% 0.29/0.46 => ( prefixList @ A @ ( cons @ A @ X @ Xa ) @ ( cons @ A @ X @ Xb ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % prefixList.intros(2)
% 0.29/0.46 thf(fact_9_PrefixListMonotonicity,axiom,
% 0.29/0.46 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 0.29/0.46 ( ( prefixList @ A @ L1 @ L2 )
% 0.29/0.46 => ( ord_less @ nat @ ( size_size @ ( list @ A ) @ L1 ) @ ( size_size @ ( list @ A ) @ L2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % PrefixListMonotonicity
% 0.29/0.46 thf(fact_10_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 0.29/0.46 ! [P2: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,Q: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,A4: configuration_ext @ p @ v @ s @ product_unit,A5: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),A6: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),A7: nat] :
% 0.29/0.46 ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 0.29/0.46 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N: nat] :
% 0.29/0.46 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/0.46 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/0.46 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.29/0.46 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 0.29/0.46 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N: nat] :
% 0.29/0.46 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/0.46 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/0.46 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.29/0.46 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % infiniteExecutionCfg_infiniteExecutionMsg.induct(2)
% 0.29/0.46 thf(fact_11_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 0.29/0.46 ! [P2: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,Q: ( configuration_ext @ p @ v @ s @ product_unit ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ) ) > nat > $o,A0: configuration_ext @ p @ v @ s @ product_unit,A1: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),A2: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),A3: nat] :
% 0.29/0.46 ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 0.29/0.46 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N: nat] :
% 0.29/0.46 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/0.46 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/0.46 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.29/0.46 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) )] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 0.29/0.46 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N: nat] :
% 0.29/0.46 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/0.46 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/0.46 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.29/0.46 => ( P2 @ A0 @ A1 @ A2 @ A3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % infiniteExecutionCfg_infiniteExecutionMsg.induct(1)
% 0.29/0.46 thf(fact_12_prefixList_Ointros_I1_J,axiom,
% 0.29/0.46 ! [A: $tType,X: A,Xs: list @ A] : ( prefixList @ A @ ( nil @ A ) @ ( cons @ A @ X @ Xs ) ) ).
% 0.29/0.46
% 0.29/0.46 % prefixList.intros(1)
% 0.29/0.46 thf(fact_13_prefixList_Ocases,axiom,
% 0.29/0.46 ! [A: $tType,A1: list @ A,A2: list @ A] :
% 0.29/0.46 ( ( prefixList @ A @ A1 @ A2 )
% 0.29/0.46 => ( ( ( A1
% 0.29/0.46 = ( nil @ A ) )
% 0.29/0.46 => ! [X2: A,Xs2: list @ A] :
% 0.29/0.46 ( A2
% 0.29/0.46 != ( cons @ A @ X2 @ Xs2 ) ) )
% 0.29/0.46 => ~ ! [Xa2: list @ A,Xb2: list @ A,X2: A] :
% 0.29/0.46 ( ( A1
% 0.29/0.46 = ( cons @ A @ X2 @ Xa2 ) )
% 0.29/0.46 => ( ( A2
% 0.29/0.46 = ( cons @ A @ X2 @ Xb2 ) )
% 0.29/0.46 => ~ ( prefixList @ A @ Xa2 @ Xb2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % prefixList.cases
% 0.29/0.46 thf(fact_14_prefixList_Osimps,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( prefixList @ A )
% 0.29/0.46 = ( ^ [A12: list @ A,A22: list @ A] :
% 0.29/0.46 ( ? [X3: A,Xs3: list @ A] :
% 0.29/0.46 ( ( A12
% 0.29/0.46 = ( nil @ A ) )
% 0.29/0.46 & ( A22
% 0.29/0.46 = ( cons @ A @ X3 @ Xs3 ) ) )
% 0.29/0.46 | ? [Xa3: list @ A,Xb3: list @ A,X3: A] :
% 0.29/0.46 ( ( A12
% 0.29/0.46 = ( cons @ A @ X3 @ Xa3 ) )
% 0.29/0.46 & ( A22
% 0.29/0.46 = ( cons @ A @ X3 @ Xb3 ) )
% 0.29/0.46 & ( prefixList @ A @ Xa3 @ Xb3 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % prefixList.simps
% 0.29/0.46 thf(fact_15_prefixList_Oinducts,axiom,
% 0.29/0.46 ! [A: $tType,X1: list @ A,X22: list @ A,P2: ( list @ A ) > ( list @ A ) > $o] :
% 0.29/0.46 ( ( prefixList @ A @ X1 @ X22 )
% 0.29/0.46 => ( ! [X2: A,Xs2: list @ A] : ( P2 @ ( nil @ A ) @ ( cons @ A @ X2 @ Xs2 ) )
% 0.29/0.46 => ( ! [Xa2: list @ A,Xb2: list @ A,X2: A] :
% 0.29/0.46 ( ( prefixList @ A @ Xa2 @ Xb2 )
% 0.29/0.46 => ( ( P2 @ Xa2 @ Xb2 )
% 0.29/0.46 => ( P2 @ ( cons @ A @ X2 @ Xa2 ) @ ( cons @ A @ X2 @ Xb2 ) ) ) )
% 0.29/0.46 => ( P2 @ X1 @ X22 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % prefixList.inducts
% 0.29/0.46 thf(fact_16_NatPredicateTippingPoint,axiom,
% 0.29/0.46 ! [N2: nat,Pr: nat > $o] :
% 0.29/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 0.29/0.46 => ( ( Pr @ ( zero_zero @ nat ) )
% 0.29/0.46 => ( ~ ( Pr @ N2 )
% 0.29/0.46 => ? [N: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ N @ N2 )
% 0.29/0.46 & ( Pr @ N )
% 0.29/0.46 & ~ ( Pr @ ( suc @ N ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % NatPredicateTippingPoint
% 0.29/0.46 thf(fact_17_infiniteExecutionCfg_Osimps_I1_J,axiom,
% 0.29/0.46 ! [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 ) )] :
% 0.29/0.46 ( ( fLPThe137922386ionCfg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( zero_zero @ nat ) )
% 0.29/0.46 = ( cons @ ( configuration_ext @ p @ v @ s @ product_unit ) @ Cfg2 @ ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % infiniteExecutionCfg.simps(1)
% 0.29/0.46 thf(fact_18_length__greater__0__conv,axiom,
% 0.29/0.46 ! [A: $tType,Xs: list @ A] :
% 0.29/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.29/0.46 = ( Xs
% 0.29/0.46 != ( nil @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % length_greater_0_conv
% 0.29/0.46 thf(fact_19_length__0__conv,axiom,
% 0.29/0.46 ! [A: $tType,Xs: list @ A] :
% 0.29/0.46 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.29/0.46 = ( zero_zero @ nat ) )
% 0.29/0.46 = ( Xs
% 0.29/0.46 = ( nil @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % length_0_conv
% 0.29/0.46 thf(fact_20_less__Suc0,axiom,
% 0.29/0.46 ! [N3: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ N3 @ ( suc @ ( zero_zero @ nat ) ) )
% 0.29/0.46 = ( N3
% 0.29/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_Suc0
% 0.29/0.46 thf(fact_21_zero__less__Suc,axiom,
% 0.29/0.46 ! [N3: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ N3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_less_Suc
% 0.29/0.46 thf(fact_22_lessI,axiom,
% 0.29/0.46 ! [N3: nat] : ( ord_less @ nat @ N3 @ ( suc @ N3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % lessI
% 0.29/0.46 thf(fact_23_Suc__mono,axiom,
% 0.29/0.46 ! [M: nat,N3: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ M @ N3 )
% 0.29/0.46 => ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Suc_mono
% 0.29/0.46 thf(fact_24_Suc__less__eq,axiom,
% 0.29/0.46 ! [M: nat,N3: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N3 ) )
% 0.29/0.46 = ( ord_less @ nat @ M @ N3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % Suc_less_eq
% 0.29/0.46 thf(fact_25_neq0__conv,axiom,
% 0.29/0.46 ! [N3: nat] :
% 0.29/0.46 ( ( N3
% 0.29/0.46 != ( zero_zero @ nat ) )
% 0.29/0.46 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % neq0_conv
% 0.29/0.46 thf(fact_26_less__nat__zero__code,axiom,
% 0.29/0.46 ! [N3: nat] :
% 0.29/0.46 ~ ( ord_less @ nat @ N3 @ ( zero_zero @ nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_nat_zero_code
% 0.29/0.46 thf(fact_27_bot__nat__0_Onot__eq__extremum,axiom,
% 0.29/0.46 ! [A8: nat] :
% 0.29/0.46 ( ( A8
% 0.29/0.46 != ( zero_zero @ nat ) )
% 0.29/0.46 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A8 ) ) ).
% 0.29/0.46
% 0.29/0.46 % bot_nat_0.not_eq_extremum
% 0.29/0.46 thf(fact_28_list_Oinject,axiom,
% 0.29/0.46 ! [A: $tType,X21: A,X222: list @ A,Y21: A,Y22: list @ A] :
% 0.29/0.46 ( ( ( cons @ A @ X21 @ X222 )
% 0.29/0.46 = ( cons @ A @ Y21 @ Y22 ) )
% 0.29/0.46 = ( ( X21 = Y21 )
% 0.29/0.46 & ( X222 = Y22 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % list.inject
% 0.29/0.46 thf(fact_29_old_Onat_Oinject,axiom,
% 0.29/0.46 ! [Nat: nat,Nat2: nat] :
% 0.29/0.46 ( ( ( suc @ Nat )
% 0.29/0.46 = ( suc @ Nat2 ) )
% 0.29/0.46 = ( Nat = Nat2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % old.nat.inject
% 0.29/0.46 thf(fact_30_nat_Oinject,axiom,
% 0.29/0.46 ! [X22: nat,Y2: nat] :
% 0.29/0.46 ( ( ( suc @ X22 )
% 0.29/0.46 = ( suc @ Y2 ) )
% 0.29/0.46 = ( X22 = Y2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % nat.inject
% 0.29/0.46 thf(fact_31_measure__induct__rule,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( wellorder @ B )
% 0.29/0.46 => ! [F: A > B,P2: A > $o,A8: A] :
% 0.29/0.46 ( ! [X2: A] :
% 0.29/0.46 ( ! [Y: A] :
% 0.29/0.46 ( ( ord_less @ B @ ( F @ Y ) @ ( F @ X2 ) )
% 0.29/0.46 => ( P2 @ Y ) )
% 0.29/0.46 => ( P2 @ X2 ) )
% 0.29/0.46 => ( P2 @ A8 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measure_induct_rule
% 0.29/0.46 thf(fact_32_measure__induct,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( wellorder @ B )
% 0.29/0.46 => ! [F: A > B,P2: A > $o,A8: A] :
% 0.29/0.46 ( ! [X2: A] :
% 0.29/0.46 ( ! [Y: A] :
% 0.29/0.46 ( ( ord_less @ B @ ( F @ Y ) @ ( F @ X2 ) )
% 0.29/0.46 => ( P2 @ Y ) )
% 0.29/0.46 => ( P2 @ X2 ) )
% 0.29/0.46 => ( P2 @ A8 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % measure_induct
% 0.29/0.46 thf(fact_33_not__Cons__self2,axiom,
% 0.29/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.29/0.46 ( ( cons @ A @ X @ Xs )
% 0.29/0.46 != Xs ) ).
% 0.29/0.46
% 0.29/0.46 % not_Cons_self2
% 0.29/0.46 thf(fact_34_n__not__Suc__n,axiom,
% 0.29/0.46 ! [N3: nat] :
% 0.29/0.46 ( N3
% 0.29/0.46 != ( suc @ N3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % n_not_Suc_n
% 0.29/0.46 thf(fact_35_Suc__inject,axiom,
% 0.29/0.46 ! [X: nat,Y3: nat] :
% 0.29/0.46 ( ( ( suc @ X )
% 0.29/0.46 = ( suc @ Y3 ) )
% 0.29/0.46 => ( X = Y3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % Suc_inject
% 0.29/0.46 thf(fact_36_infinite__descent__measure,axiom,
% 0.29/0.46 ! [A: $tType,P2: A > $o,V2: A > nat,X: A] :
% 0.29/0.46 ( ! [X2: A] :
% 0.29/0.46 ( ~ ( P2 @ X2 )
% 0.29/0.46 => ? [Y: A] :
% 0.29/0.46 ( ( ord_less @ nat @ ( V2 @ Y ) @ ( V2 @ X2 ) )
% 0.29/0.46 & ~ ( P2 @ Y ) ) )
% 0.29/0.46 => ( P2 @ X ) ) ).
% 0.29/0.46
% 0.29/0.46 % infinite_descent_measure
% 0.29/0.46 thf(fact_37_linorder__neqE__nat,axiom,
% 0.29/0.46 ! [X: nat,Y3: nat] :
% 0.29/0.46 ( ( X != Y3 )
% 0.29/0.46 => ( ~ ( ord_less @ nat @ X @ Y3 )
% 0.29/0.46 => ( ord_less @ nat @ Y3 @ X ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % linorder_neqE_nat
% 0.29/0.46 thf(fact_38_infinite__descent,axiom,
% 0.29/0.46 ! [P2: nat > $o,N3: nat] :
% 0.29/0.46 ( ! [N: nat] :
% 0.29/0.46 ( ~ ( P2 @ N )
% 0.29/0.46 => ? [M2: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ M2 @ N )
% 0.29/0.46 & ~ ( P2 @ M2 ) ) )
% 0.29/0.46 => ( P2 @ N3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % infinite_descent
% 0.29/0.46 thf(fact_39_nat__less__induct,axiom,
% 0.29/0.46 ! [P2: nat > $o,N3: nat] :
% 0.29/0.46 ( ! [N: nat] :
% 0.29/0.46 ( ! [M2: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ M2 @ N )
% 0.29/0.46 => ( P2 @ M2 ) )
% 0.29/0.46 => ( P2 @ N ) )
% 0.29/0.46 => ( P2 @ N3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % nat_less_induct
% 0.29/0.46 thf(fact_40_less__irrefl__nat,axiom,
% 0.29/0.46 ! [N3: nat] :
% 0.29/0.46 ~ ( ord_less @ nat @ N3 @ N3 ) ).
% 0.29/0.46
% 0.29/0.46 % less_irrefl_nat
% 0.29/0.46 thf(fact_41_less__not__refl3,axiom,
% 0.29/0.46 ! [S2: nat,T: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ S2 @ T )
% 0.29/0.46 => ( S2 != T ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_not_refl3
% 0.29/0.46 thf(fact_42_less__not__refl2,axiom,
% 0.29/0.46 ! [N3: nat,M: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ N3 @ M )
% 0.29/0.46 => ( M != N3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_not_refl2
% 0.29/0.46 thf(fact_43_mem__Collect__eq,axiom,
% 0.29/0.46 ! [A: $tType,A8: A,P2: A > $o] :
% 0.29/0.46 ( ( member @ A @ A8 @ ( collect @ A @ P2 ) )
% 0.29/0.46 = ( P2 @ A8 ) ) ).
% 0.29/0.46
% 0.29/0.46 % mem_Collect_eq
% 0.29/0.46 thf(fact_44_Collect__mem__eq,axiom,
% 0.29/0.46 ! [A: $tType,A9: set @ A] :
% 0.29/0.46 ( ( collect @ A
% 0.29/0.46 @ ^ [X3: A] : ( member @ A @ X3 @ A9 ) )
% 0.29/0.46 = A9 ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_mem_eq
% 0.29/0.46 thf(fact_45_Collect__cong,axiom,
% 0.29/0.46 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.29/0.46 ( ! [X2: A] :
% 0.29/0.46 ( ( P2 @ X2 )
% 0.29/0.46 = ( Q @ X2 ) )
% 0.29/0.46 => ( ( collect @ A @ P2 )
% 0.29/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Collect_cong
% 0.29/0.46 thf(fact_46_ext,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.29/0.46 ( ! [X2: A] :
% 0.29/0.46 ( ( F @ X2 )
% 0.29/0.46 = ( G @ X2 ) )
% 0.29/0.46 => ( F = G ) ) ).
% 0.29/0.46
% 0.29/0.46 % ext
% 0.29/0.46 thf(fact_47_less__not__refl,axiom,
% 0.29/0.46 ! [N3: nat] :
% 0.29/0.46 ~ ( ord_less @ nat @ N3 @ N3 ) ).
% 0.29/0.46
% 0.29/0.46 % less_not_refl
% 0.29/0.46 thf(fact_48_nat__neq__iff,axiom,
% 0.29/0.46 ! [M: nat,N3: nat] :
% 0.29/0.46 ( ( M != N3 )
% 0.29/0.46 = ( ( ord_less @ nat @ M @ N3 )
% 0.29/0.46 | ( ord_less @ nat @ N3 @ M ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % nat_neq_iff
% 0.29/0.46 thf(fact_49_size__neq__size__imp__neq,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( size @ A )
% 0.29/0.46 => ! [X: A,Y3: A] :
% 0.29/0.46 ( ( ( size_size @ A @ X )
% 0.29/0.46 != ( size_size @ A @ Y3 ) )
% 0.29/0.46 => ( X != Y3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % size_neq_size_imp_neq
% 0.29/0.46 thf(fact_50_neq__if__length__neq,axiom,
% 0.29/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.29/0.46 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.29/0.46 != ( size_size @ ( list @ A ) @ Ys ) )
% 0.29/0.46 => ( Xs != Ys ) ) ).
% 0.29/0.46
% 0.29/0.46 % neq_if_length_neq
% 0.29/0.46 thf(fact_51_Ex__list__of__length,axiom,
% 0.29/0.46 ! [A: $tType,N3: nat] :
% 0.29/0.46 ? [Xs2: list @ A] :
% 0.29/0.46 ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.29/0.46 = N3 ) ).
% 0.29/0.46
% 0.29/0.46 % Ex_list_of_length
% 0.29/0.46 thf(fact_52_not0__implies__Suc,axiom,
% 0.29/0.46 ! [N3: nat] :
% 0.29/0.46 ( ( N3
% 0.29/0.46 != ( zero_zero @ nat ) )
% 0.29/0.46 => ? [M3: nat] :
% 0.29/0.46 ( N3
% 0.29/0.46 = ( suc @ M3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % not0_implies_Suc
% 0.29/0.46 thf(fact_53_old_Onat_Oinducts,axiom,
% 0.29/0.46 ! [P2: nat > $o,Nat: nat] :
% 0.29/0.46 ( ( P2 @ ( zero_zero @ nat ) )
% 0.29/0.46 => ( ! [Nat3: nat] :
% 0.29/0.46 ( ( P2 @ Nat3 )
% 0.29/0.46 => ( P2 @ ( suc @ Nat3 ) ) )
% 0.29/0.46 => ( P2 @ Nat ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % old.nat.inducts
% 0.29/0.46 thf(fact_54_old_Onat_Oexhaust,axiom,
% 0.29/0.46 ! [Y3: nat] :
% 0.29/0.46 ( ( Y3
% 0.29/0.46 != ( zero_zero @ nat ) )
% 0.29/0.46 => ~ ! [Nat3: nat] :
% 0.29/0.46 ( Y3
% 0.29/0.46 != ( suc @ Nat3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % old.nat.exhaust
% 0.29/0.46 thf(fact_55_Zero__not__Suc,axiom,
% 0.29/0.46 ! [M: nat] :
% 0.29/0.46 ( ( zero_zero @ nat )
% 0.29/0.46 != ( suc @ M ) ) ).
% 0.29/0.46
% 0.29/0.46 % Zero_not_Suc
% 0.29/0.46 thf(fact_56_Zero__neq__Suc,axiom,
% 0.29/0.46 ! [M: nat] :
% 0.29/0.46 ( ( zero_zero @ nat )
% 0.29/0.46 != ( suc @ M ) ) ).
% 0.29/0.46
% 0.29/0.46 % Zero_neq_Suc
% 0.29/0.46 thf(fact_57_Suc__neq__Zero,axiom,
% 0.29/0.46 ! [M: nat] :
% 0.29/0.46 ( ( suc @ M )
% 0.29/0.46 != ( zero_zero @ nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % Suc_neq_Zero
% 0.29/0.46 thf(fact_58_zero__induct,axiom,
% 0.29/0.46 ! [P2: nat > $o,K: nat] :
% 0.29/0.46 ( ( P2 @ K )
% 0.29/0.46 => ( ! [N: nat] :
% 0.29/0.46 ( ( P2 @ ( suc @ N ) )
% 0.29/0.46 => ( P2 @ N ) )
% 0.29/0.46 => ( P2 @ ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % zero_induct
% 0.29/0.46 thf(fact_59_diff__induct,axiom,
% 0.29/0.46 ! [P2: nat > nat > $o,M: nat,N3: nat] :
% 0.29/0.46 ( ! [X2: nat] : ( P2 @ X2 @ ( zero_zero @ nat ) )
% 0.29/0.46 => ( ! [Y4: nat] : ( P2 @ ( zero_zero @ nat ) @ ( suc @ Y4 ) )
% 0.29/0.46 => ( ! [X2: nat,Y4: nat] :
% 0.29/0.46 ( ( P2 @ X2 @ Y4 )
% 0.29/0.46 => ( P2 @ ( suc @ X2 ) @ ( suc @ Y4 ) ) )
% 0.29/0.46 => ( P2 @ M @ N3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % diff_induct
% 0.29/0.46 thf(fact_60_nat__induct,axiom,
% 0.29/0.46 ! [P2: nat > $o,N3: nat] :
% 0.29/0.46 ( ( P2 @ ( zero_zero @ nat ) )
% 0.29/0.46 => ( ! [N: nat] :
% 0.29/0.46 ( ( P2 @ N )
% 0.29/0.46 => ( P2 @ ( suc @ N ) ) )
% 0.29/0.46 => ( P2 @ N3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % nat_induct
% 0.29/0.46 thf(fact_61_nat_OdiscI,axiom,
% 0.29/0.46 ! [Nat: nat,X22: nat] :
% 0.29/0.46 ( ( Nat
% 0.29/0.46 = ( suc @ X22 ) )
% 0.29/0.46 => ( Nat
% 0.29/0.46 != ( zero_zero @ nat ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % nat.discI
% 0.29/0.46 thf(fact_62_old_Onat_Odistinct_I1_J,axiom,
% 0.29/0.46 ! [Nat2: nat] :
% 0.29/0.46 ( ( zero_zero @ nat )
% 0.29/0.46 != ( suc @ Nat2 ) ) ).
% 0.29/0.46
% 0.29/0.46 % old.nat.distinct(1)
% 0.29/0.46 thf(fact_63_old_Onat_Odistinct_I2_J,axiom,
% 0.29/0.46 ! [Nat4: nat] :
% 0.29/0.46 ( ( suc @ Nat4 )
% 0.29/0.46 != ( zero_zero @ nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % old.nat.distinct(2)
% 0.29/0.46 thf(fact_64_nat_Odistinct_I1_J,axiom,
% 0.29/0.46 ! [X22: nat] :
% 0.29/0.46 ( ( zero_zero @ nat )
% 0.29/0.46 != ( suc @ X22 ) ) ).
% 0.29/0.46
% 0.29/0.46 % nat.distinct(1)
% 0.29/0.46 thf(fact_65_infinite__descent0__measure,axiom,
% 0.29/0.46 ! [A: $tType,V2: A > nat,P2: A > $o,X: A] :
% 0.29/0.46 ( ! [X2: A] :
% 0.29/0.46 ( ( ( V2 @ X2 )
% 0.29/0.46 = ( zero_zero @ nat ) )
% 0.29/0.46 => ( P2 @ X2 ) )
% 0.29/0.46 => ( ! [X2: A] :
% 0.29/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V2 @ X2 ) )
% 0.29/0.46 => ( ~ ( P2 @ X2 )
% 0.29/0.46 => ? [Y: A] :
% 0.29/0.46 ( ( ord_less @ nat @ ( V2 @ Y ) @ ( V2 @ X2 ) )
% 0.29/0.46 & ~ ( P2 @ Y ) ) ) )
% 0.29/0.46 => ( P2 @ X ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % infinite_descent0_measure
% 0.29/0.46 thf(fact_66_bot__nat__0_Oextremum__strict,axiom,
% 0.29/0.46 ! [A8: nat] :
% 0.29/0.46 ~ ( ord_less @ nat @ A8 @ ( zero_zero @ nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % bot_nat_0.extremum_strict
% 0.29/0.46 thf(fact_67_infinite__descent0,axiom,
% 0.29/0.46 ! [P2: nat > $o,N3: nat] :
% 0.29/0.46 ( ( P2 @ ( zero_zero @ nat ) )
% 0.29/0.46 => ( ! [N: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.29/0.46 => ( ~ ( P2 @ N )
% 0.29/0.46 => ? [M2: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ M2 @ N )
% 0.29/0.46 & ~ ( P2 @ M2 ) ) ) )
% 0.29/0.46 => ( P2 @ N3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % infinite_descent0
% 0.29/0.46 thf(fact_68_gr__implies__not0,axiom,
% 0.29/0.46 ! [M: nat,N3: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ M @ N3 )
% 0.29/0.46 => ( N3
% 0.29/0.46 != ( zero_zero @ nat ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % gr_implies_not0
% 0.29/0.46 thf(fact_69_less__zeroE,axiom,
% 0.29/0.46 ! [N3: nat] :
% 0.29/0.46 ~ ( ord_less @ nat @ N3 @ ( zero_zero @ nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_zeroE
% 0.29/0.46 thf(fact_70_not__less0,axiom,
% 0.29/0.46 ! [N3: nat] :
% 0.29/0.46 ~ ( ord_less @ nat @ N3 @ ( zero_zero @ nat ) ) ).
% 0.29/0.46
% 0.29/0.46 % not_less0
% 0.29/0.46 thf(fact_71_not__gr0,axiom,
% 0.29/0.46 ! [N3: nat] :
% 0.29/0.46 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N3 ) )
% 0.29/0.46 = ( N3
% 0.29/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % not_gr0
% 0.29/0.46 thf(fact_72_gr0I,axiom,
% 0.29/0.46 ! [N3: nat] :
% 0.29/0.46 ( ( N3
% 0.29/0.46 != ( zero_zero @ nat ) )
% 0.29/0.46 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % gr0I
% 0.29/0.46 thf(fact_73_not__less__less__Suc__eq,axiom,
% 0.29/0.46 ! [N3: nat,M: nat] :
% 0.29/0.46 ( ~ ( ord_less @ nat @ N3 @ M )
% 0.29/0.46 => ( ( ord_less @ nat @ N3 @ ( suc @ M ) )
% 0.29/0.46 = ( N3 = M ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % not_less_less_Suc_eq
% 0.29/0.46 thf(fact_74_strict__inc__induct,axiom,
% 0.29/0.46 ! [I: nat,J: nat,P2: nat > $o] :
% 0.29/0.46 ( ( ord_less @ nat @ I @ J )
% 0.29/0.46 => ( ! [I2: nat] :
% 0.29/0.46 ( ( J
% 0.29/0.46 = ( suc @ I2 ) )
% 0.29/0.46 => ( P2 @ I2 ) )
% 0.29/0.46 => ( ! [I2: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ I2 @ J )
% 0.29/0.46 => ( ( P2 @ ( suc @ I2 ) )
% 0.29/0.46 => ( P2 @ I2 ) ) )
% 0.29/0.46 => ( P2 @ I ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % strict_inc_induct
% 0.29/0.46 thf(fact_75_less__Suc__induct,axiom,
% 0.29/0.46 ! [I: nat,J: nat,P2: nat > nat > $o] :
% 0.29/0.46 ( ( ord_less @ nat @ I @ J )
% 0.29/0.46 => ( ! [I2: nat] : ( P2 @ I2 @ ( suc @ I2 ) )
% 0.29/0.46 => ( ! [I2: nat,J2: nat,K2: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ I2 @ J2 )
% 0.29/0.46 => ( ( ord_less @ nat @ J2 @ K2 )
% 0.29/0.46 => ( ( P2 @ I2 @ J2 )
% 0.29/0.46 => ( ( P2 @ J2 @ K2 )
% 0.29/0.46 => ( P2 @ I2 @ K2 ) ) ) ) )
% 0.29/0.46 => ( P2 @ I @ J ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_Suc_induct
% 0.29/0.46 thf(fact_76_less__trans__Suc,axiom,
% 0.29/0.46 ! [I: nat,J: nat,K: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ I @ J )
% 0.29/0.46 => ( ( ord_less @ nat @ J @ K )
% 0.29/0.46 => ( ord_less @ nat @ ( suc @ I ) @ K ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_trans_Suc
% 0.29/0.46 thf(fact_77_Suc__less__SucD,axiom,
% 0.29/0.46 ! [M: nat,N3: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N3 ) )
% 0.29/0.46 => ( ord_less @ nat @ M @ N3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % Suc_less_SucD
% 0.29/0.46 thf(fact_78_less__antisym,axiom,
% 0.29/0.46 ! [N3: nat,M: nat] :
% 0.29/0.46 ( ~ ( ord_less @ nat @ N3 @ M )
% 0.29/0.46 => ( ( ord_less @ nat @ N3 @ ( suc @ M ) )
% 0.29/0.46 => ( M = N3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_antisym
% 0.29/0.46 thf(fact_79_Suc__less__eq2,axiom,
% 0.29/0.46 ! [N3: nat,M: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ ( suc @ N3 ) @ M )
% 0.29/0.46 = ( ? [M4: nat] :
% 0.29/0.46 ( ( M
% 0.29/0.46 = ( suc @ M4 ) )
% 0.29/0.46 & ( ord_less @ nat @ N3 @ M4 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Suc_less_eq2
% 0.29/0.46 thf(fact_80_All__less__Suc,axiom,
% 0.29/0.46 ! [N3: nat,P2: nat > $o] :
% 0.29/0.46 ( ( ! [I3: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ I3 @ ( suc @ N3 ) )
% 0.29/0.46 => ( P2 @ I3 ) ) )
% 0.29/0.46 = ( ( P2 @ N3 )
% 0.29/0.46 & ! [I3: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ I3 @ N3 )
% 0.29/0.46 => ( P2 @ I3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % All_less_Suc
% 0.29/0.46 thf(fact_81_not__less__eq,axiom,
% 0.29/0.46 ! [M: nat,N3: nat] :
% 0.29/0.46 ( ( ~ ( ord_less @ nat @ M @ N3 ) )
% 0.29/0.46 = ( ord_less @ nat @ N3 @ ( suc @ M ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % not_less_eq
% 0.29/0.46 thf(fact_82_less__Suc__eq,axiom,
% 0.29/0.46 ! [M: nat,N3: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ M @ ( suc @ N3 ) )
% 0.29/0.46 = ( ( ord_less @ nat @ M @ N3 )
% 0.29/0.46 | ( M = N3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_Suc_eq
% 0.29/0.46 thf(fact_83_Ex__less__Suc,axiom,
% 0.29/0.46 ! [N3: nat,P2: nat > $o] :
% 0.29/0.46 ( ( ? [I3: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ I3 @ ( suc @ N3 ) )
% 0.29/0.46 & ( P2 @ I3 ) ) )
% 0.29/0.46 = ( ( P2 @ N3 )
% 0.29/0.46 | ? [I3: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ I3 @ N3 )
% 0.29/0.46 & ( P2 @ I3 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Ex_less_Suc
% 0.29/0.46 thf(fact_84_less__SucI,axiom,
% 0.29/0.46 ! [M: nat,N3: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ M @ N3 )
% 0.29/0.46 => ( ord_less @ nat @ M @ ( suc @ N3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_SucI
% 0.29/0.46 thf(fact_85_less__SucE,axiom,
% 0.29/0.46 ! [M: nat,N3: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ M @ ( suc @ N3 ) )
% 0.29/0.46 => ( ~ ( ord_less @ nat @ M @ N3 )
% 0.29/0.46 => ( M = N3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % less_SucE
% 0.29/0.46 thf(fact_86_Suc__lessI,axiom,
% 0.29/0.46 ! [M: nat,N3: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ M @ N3 )
% 0.29/0.46 => ( ( ( suc @ M )
% 0.29/0.46 != N3 )
% 0.29/0.46 => ( ord_less @ nat @ ( suc @ M ) @ N3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Suc_lessI
% 0.29/0.46 thf(fact_87_Suc__lessE,axiom,
% 0.29/0.46 ! [I: nat,K: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ ( suc @ I ) @ K )
% 0.29/0.46 => ~ ! [J2: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ I @ J2 )
% 0.29/0.46 => ( K
% 0.29/0.46 != ( suc @ J2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Suc_lessE
% 0.29/0.46 thf(fact_88_Suc__lessD,axiom,
% 0.29/0.46 ! [M: nat,N3: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ ( suc @ M ) @ N3 )
% 0.29/0.46 => ( ord_less @ nat @ M @ N3 ) ) ).
% 0.29/0.46
% 0.29/0.46 % Suc_lessD
% 0.29/0.46 thf(fact_89_Nat_OlessE,axiom,
% 0.29/0.46 ! [I: nat,K: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ I @ K )
% 0.29/0.46 => ( ( K
% 0.29/0.46 != ( suc @ I ) )
% 0.29/0.46 => ~ ! [J2: nat] :
% 0.29/0.46 ( ( ord_less @ nat @ I @ J2 )
% 0.29/0.46 => ( K
% 0.29/0.46 != ( suc @ J2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % Nat.lessE
% 0.29/0.46 thf(fact_90_strict__sorted_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ! [P2: ( list @ A ) > $o,A0: list @ A] :
% 0.29/0.46 ( ( P2 @ ( nil @ A ) )
% 0.29/0.46 => ( ! [X2: A,Ys2: list @ A] :
% 0.29/0.46 ( ( P2 @ Ys2 )
% 0.29/0.46 => ( P2 @ ( cons @ A @ X2 @ Ys2 ) ) )
% 0.29/0.46 => ( P2 @ A0 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % strict_sorted.induct
% 0.29/0.46 thf(fact_91_strict__sorted_Ocases,axiom,
% 0.29/0.46 ! [A: $tType] :
% 0.29/0.46 ( ( linorder @ A )
% 0.29/0.46 => ! [X: list @ A] :
% 0.29/0.46 ( ( X
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ~ ! [X2: A,Ys2: list @ A] :
% 0.29/0.46 ( X
% 0.29/0.46 != ( cons @ A @ X2 @ Ys2 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % strict_sorted.cases
% 0.29/0.46 thf(fact_92_map__tailrec__rev_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,P2: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A2: list @ B] :
% 0.29/0.46 ( ! [F2: A > B,X_1: list @ B] : ( P2 @ F2 @ ( nil @ A ) @ X_1 )
% 0.29/0.46 => ( ! [F2: A > B,A10: A,As: list @ A,Bs: list @ B] :
% 0.29/0.46 ( ( P2 @ F2 @ As @ ( cons @ B @ ( F2 @ A10 ) @ Bs ) )
% 0.29/0.46 => ( P2 @ F2 @ ( cons @ A @ A10 @ As ) @ Bs ) )
% 0.29/0.46 => ( P2 @ A0 @ A1 @ A2 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % map_tailrec_rev.induct
% 0.29/0.46 thf(fact_93_list__nonempty__induct,axiom,
% 0.29/0.46 ! [A: $tType,Xs: list @ A,P2: ( list @ A ) > $o] :
% 0.29/0.46 ( ( Xs
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ( ! [X2: A] : ( P2 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.29/0.46 => ( ! [X2: A,Xs2: list @ A] :
% 0.29/0.46 ( ( Xs2
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ( ( P2 @ Xs2 )
% 0.29/0.46 => ( P2 @ ( cons @ A @ X2 @ Xs2 ) ) ) )
% 0.29/0.46 => ( P2 @ Xs ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % list_nonempty_induct
% 0.29/0.46 thf(fact_94_successively_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType,P2: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.29/0.46 ( ! [P3: A > A > $o] : ( P2 @ P3 @ ( nil @ A ) )
% 0.29/0.46 => ( ! [P3: A > A > $o,X2: A] : ( P2 @ P3 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.29/0.46 => ( ! [P3: A > A > $o,X2: A,Y4: A,Xs2: list @ A] :
% 0.29/0.46 ( ( P2 @ P3 @ ( cons @ A @ Y4 @ Xs2 ) )
% 0.29/0.46 => ( P2 @ P3 @ ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Xs2 ) ) ) )
% 0.29/0.46 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % successively.induct
% 0.29/0.46 thf(fact_95_arg__min__list_Oinduct,axiom,
% 0.29/0.46 ! [B: $tType,A: $tType] :
% 0.29/0.46 ( ( linorder @ B )
% 0.29/0.46 => ! [P2: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 0.29/0.46 ( ! [F2: A > B,X2: A] : ( P2 @ F2 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.29/0.46 => ( ! [F2: A > B,X2: A,Y4: A,Zs: list @ A] :
% 0.29/0.46 ( ( P2 @ F2 @ ( cons @ A @ Y4 @ Zs ) )
% 0.29/0.46 => ( P2 @ F2 @ ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Zs ) ) ) )
% 0.29/0.46 => ( ! [A10: A > B] : ( P2 @ A10 @ ( nil @ A ) )
% 0.29/0.46 => ( P2 @ A0 @ A1 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % arg_min_list.induct
% 0.29/0.46 thf(fact_96_remdups__adj_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType,P2: ( list @ A ) > $o,A0: list @ A] :
% 0.29/0.46 ( ( P2 @ ( nil @ A ) )
% 0.29/0.46 => ( ! [X2: A] : ( P2 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.29/0.46 => ( ! [X2: A,Y4: A,Xs2: list @ A] :
% 0.29/0.46 ( ( ( X2 = Y4 )
% 0.29/0.46 => ( P2 @ ( cons @ A @ X2 @ Xs2 ) ) )
% 0.29/0.46 => ( ( ( X2 != Y4 )
% 0.29/0.46 => ( P2 @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 0.29/0.46 => ( P2 @ ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) )
% 0.29/0.46 => ( P2 @ A0 ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % remdups_adj.induct
% 0.29/0.46 thf(fact_97_sorted__wrt_Oinduct,axiom,
% 0.29/0.46 ! [A: $tType,P2: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.29/0.46 ( ! [P3: A > A > $o] : ( P2 @ P3 @ ( nil @ A ) )
% 0.29/0.46 => ( ! [P3: A > A > $o,X2: A,Ys2: list @ A] :
% 0.29/0.46 ( ( P2 @ P3 @ Ys2 )
% 0.29/0.46 => ( P2 @ P3 @ ( cons @ A @ X2 @ Ys2 ) ) )
% 0.29/0.46 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % sorted_wrt.induct
% 0.29/0.46 thf(fact_98_remdups__adj_Ocases,axiom,
% 0.29/0.46 ! [A: $tType,X: list @ A] :
% 0.29/0.46 ( ( X
% 0.29/0.46 != ( nil @ A ) )
% 0.29/0.46 => ( ! [X2: A] :
% 0.29/0.46 ( X
% 0.29/0.46 != ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.29/0.46 => ~ ! [X2: A,Y4: A,Xs2: list @ A] :
% 0.29/0.46 ( X
% 0.29/0.46 != ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 % remdups_adj.cases
% 0.29/0.46 thf(fact_99_transpose_Ocases,axiom,
% 0.29/0.46 ! [A: $tType,X: list @ ( list @ A )] :
% 0.29/0.47 ( ( X
% 0.29/0.47 != ( nil @ ( list @ A ) ) )
% 0.29/0.47 => ( ! [Xss: list @ ( list @ A )] :
% 0.29/0.47 ( X
% 0.29/0.47 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.29/0.47 => ~ ! [X2: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.29/0.47 ( X
% 0.29/0.47 != ( cons @ ( list @ A ) @ ( cons @ A @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % transpose.cases
% 0.29/0.47 thf(fact_100_shuffles_Oinduct,axiom,
% 0.29/0.47 ! [A: $tType,P2: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.29/0.47 ( ! [X_1: list @ A] : ( P2 @ ( nil @ A ) @ X_1 )
% 0.29/0.47 => ( ! [Xs2: list @ A] : ( P2 @ Xs2 @ ( nil @ A ) )
% 0.29/0.47 => ( ! [X2: A,Xs2: list @ A,Y4: A,Ys2: list @ A] :
% 0.29/0.47 ( ( P2 @ Xs2 @ ( cons @ A @ Y4 @ Ys2 ) )
% 0.29/0.47 => ( ( P2 @ ( cons @ A @ X2 @ Xs2 ) @ Ys2 )
% 0.29/0.47 => ( P2 @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys2 ) ) ) )
% 0.29/0.47 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % shuffles.induct
% 0.29/0.47 thf(fact_101_min__list_Oinduct,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( ord @ A )
% 0.29/0.47 => ! [P2: ( list @ A ) > $o,A0: list @ A] :
% 0.29/0.47 ( ! [X2: A,Xs2: list @ A] :
% 0.29/0.47 ( ! [X212: A,X223: list @ A] :
% 0.29/0.47 ( ( Xs2
% 0.29/0.47 = ( cons @ A @ X212 @ X223 ) )
% 0.29/0.47 => ( P2 @ Xs2 ) )
% 0.29/0.47 => ( P2 @ ( cons @ A @ X2 @ Xs2 ) ) )
% 0.29/0.47 => ( ( P2 @ ( nil @ A ) )
% 0.29/0.47 => ( P2 @ A0 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % min_list.induct
% 0.29/0.47 thf(fact_102_min__list_Ocases,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( ord @ A )
% 0.29/0.47 => ! [X: list @ A] :
% 0.29/0.47 ( ! [X2: A,Xs2: list @ A] :
% 0.29/0.47 ( X
% 0.29/0.47 != ( cons @ A @ X2 @ Xs2 ) )
% 0.29/0.47 => ( X
% 0.29/0.47 = ( nil @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % min_list.cases
% 0.29/0.47 thf(fact_103_induct__list012,axiom,
% 0.29/0.47 ! [A: $tType,P2: ( list @ A ) > $o,Xs: list @ A] :
% 0.29/0.47 ( ( P2 @ ( nil @ A ) )
% 0.29/0.47 => ( ! [X2: A] : ( P2 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.29/0.47 => ( ! [X2: A,Y4: A,Zs: list @ A] :
% 0.29/0.47 ( ( P2 @ Zs )
% 0.29/0.47 => ( ( P2 @ ( cons @ A @ Y4 @ Zs ) )
% 0.29/0.47 => ( P2 @ ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Zs ) ) ) ) )
% 0.29/0.47 => ( P2 @ Xs ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % induct_list012
% 0.29/0.47 thf(fact_104_splice_Oinduct,axiom,
% 0.29/0.47 ! [A: $tType,P2: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.29/0.47 ( ! [X_1: list @ A] : ( P2 @ ( nil @ A ) @ X_1 )
% 0.29/0.47 => ( ! [X2: A,Xs2: list @ A,Ys2: list @ A] :
% 0.29/0.47 ( ( P2 @ Ys2 @ Xs2 )
% 0.29/0.47 => ( P2 @ ( cons @ A @ X2 @ Xs2 ) @ Ys2 ) )
% 0.29/0.47 => ( P2 @ A0 @ A1 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % splice.induct
% 0.29/0.47 thf(fact_105_list__induct2_H,axiom,
% 0.29/0.47 ! [A: $tType,B: $tType,P2: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 0.29/0.47 ( ( P2 @ ( nil @ A ) @ ( nil @ B ) )
% 0.29/0.47 => ( ! [X2: A,Xs2: list @ A] : ( P2 @ ( cons @ A @ X2 @ Xs2 ) @ ( nil @ B ) )
% 0.29/0.47 => ( ! [Y4: B,Ys2: list @ B] : ( P2 @ ( nil @ A ) @ ( cons @ B @ Y4 @ Ys2 ) )
% 0.29/0.47 => ( ! [X2: A,Xs2: list @ A,Y4: B,Ys2: list @ B] :
% 0.29/0.47 ( ( P2 @ Xs2 @ Ys2 )
% 0.29/0.47 => ( P2 @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B @ Y4 @ Ys2 ) ) )
% 0.29/0.47 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list_induct2'
% 0.29/0.47 thf(fact_106_neq__Nil__conv,axiom,
% 0.29/0.47 ! [A: $tType,Xs: list @ A] :
% 0.29/0.47 ( ( Xs
% 0.29/0.47 != ( nil @ A ) )
% 0.29/0.47 = ( ? [Y5: A,Ys3: list @ A] :
% 0.29/0.47 ( Xs
% 0.29/0.47 = ( cons @ A @ Y5 @ Ys3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % neq_Nil_conv
% 0.29/0.47 thf(fact_107_list_Oinducts,axiom,
% 0.29/0.47 ! [A: $tType,P2: ( list @ A ) > $o,List: list @ A] :
% 0.29/0.47 ( ( P2 @ ( nil @ A ) )
% 0.29/0.47 => ( ! [X12: A,X23: list @ A] :
% 0.29/0.47 ( ( P2 @ X23 )
% 0.29/0.47 => ( P2 @ ( cons @ A @ X12 @ X23 ) ) )
% 0.29/0.47 => ( P2 @ List ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list.inducts
% 0.29/0.47 thf(fact_108_list_Oexhaust,axiom,
% 0.29/0.47 ! [A: $tType,Y3: list @ A] :
% 0.29/0.47 ( ( Y3
% 0.29/0.47 != ( nil @ A ) )
% 0.29/0.47 => ~ ! [X213: A,X224: list @ A] :
% 0.29/0.47 ( Y3
% 0.29/0.47 != ( cons @ A @ X213 @ X224 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list.exhaust
% 0.29/0.47 thf(fact_109_list_OdiscI,axiom,
% 0.29/0.47 ! [A: $tType,List: list @ A,X21: A,X222: list @ A] :
% 0.29/0.47 ( ( List
% 0.29/0.47 = ( cons @ A @ X21 @ X222 ) )
% 0.29/0.47 => ( List
% 0.29/0.47 != ( nil @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list.discI
% 0.29/0.47 thf(fact_110_list_Odistinct_I1_J,axiom,
% 0.29/0.47 ! [A: $tType,X21: A,X222: list @ A] :
% 0.29/0.47 ( ( nil @ A )
% 0.29/0.47 != ( cons @ A @ X21 @ X222 ) ) ).
% 0.29/0.47
% 0.29/0.47 % list.distinct(1)
% 0.29/0.47 thf(fact_111_length__induct,axiom,
% 0.29/0.47 ! [A: $tType,P2: ( list @ A ) > $o,Xs: list @ A] :
% 0.29/0.47 ( ! [Xs2: list @ A] :
% 0.29/0.47 ( ! [Ys4: list @ A] :
% 0.29/0.47 ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ys4 ) @ ( size_size @ ( list @ A ) @ Xs2 ) )
% 0.29/0.47 => ( P2 @ Ys4 ) )
% 0.29/0.47 => ( P2 @ Xs2 ) )
% 0.29/0.47 => ( P2 @ Xs ) ) ).
% 0.29/0.47
% 0.29/0.47 % length_induct
% 0.29/0.47 thf(fact_112_lift__Suc__mono__less__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( order @ A )
% 0.29/0.47 => ! [F: nat > A,N3: nat,M: nat] :
% 0.29/0.47 ( ! [N: nat] : ( ord_less @ A @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.29/0.47 => ( ( ord_less @ A @ ( F @ N3 ) @ ( F @ M ) )
% 0.29/0.47 = ( ord_less @ nat @ N3 @ M ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lift_Suc_mono_less_iff
% 0.29/0.47 thf(fact_113_lift__Suc__mono__less,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( order @ A )
% 0.29/0.47 => ! [F: nat > A,N3: nat,N4: nat] :
% 0.29/0.47 ( ! [N: nat] : ( ord_less @ A @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.29/0.47 => ( ( ord_less @ nat @ N3 @ N4 )
% 0.29/0.47 => ( ord_less @ A @ ( F @ N3 ) @ ( F @ N4 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lift_Suc_mono_less
% 0.29/0.47 thf(fact_114_less__Suc__eq__0__disj,axiom,
% 0.29/0.47 ! [M: nat,N3: nat] :
% 0.29/0.47 ( ( ord_less @ nat @ M @ ( suc @ N3 ) )
% 0.29/0.47 = ( ( M
% 0.29/0.47 = ( zero_zero @ nat ) )
% 0.29/0.47 | ? [J3: nat] :
% 0.29/0.47 ( ( M
% 0.29/0.47 = ( suc @ J3 ) )
% 0.29/0.47 & ( ord_less @ nat @ J3 @ N3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_Suc_eq_0_disj
% 0.29/0.47 thf(fact_115_gr0__implies__Suc,axiom,
% 0.29/0.47 ! [N3: nat] :
% 0.29/0.47 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N3 )
% 0.29/0.47 => ? [M3: nat] :
% 0.29/0.47 ( N3
% 0.29/0.47 = ( suc @ M3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % gr0_implies_Suc
% 0.29/0.47 thf(fact_116_All__less__Suc2,axiom,
% 0.29/0.47 ! [N3: nat,P2: nat > $o] :
% 0.29/0.47 ( ( ! [I3: nat] :
% 0.29/0.47 ( ( ord_less @ nat @ I3 @ ( suc @ N3 ) )
% 0.29/0.47 => ( P2 @ I3 ) ) )
% 0.29/0.47 = ( ( P2 @ ( zero_zero @ nat ) )
% 0.29/0.47 & ! [I3: nat] :
% 0.29/0.47 ( ( ord_less @ nat @ I3 @ N3 )
% 0.29/0.47 => ( P2 @ ( suc @ I3 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % All_less_Suc2
% 0.29/0.47 thf(fact_117_gr0__conv__Suc,axiom,
% 0.29/0.47 ! [N3: nat] :
% 0.29/0.47 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N3 )
% 0.29/0.47 = ( ? [M5: nat] :
% 0.29/0.47 ( N3
% 0.29/0.47 = ( suc @ M5 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % gr0_conv_Suc
% 0.29/0.47 thf(fact_118_Ex__less__Suc2,axiom,
% 0.29/0.47 ! [N3: nat,P2: nat > $o] :
% 0.29/0.47 ( ( ? [I3: nat] :
% 0.29/0.47 ( ( ord_less @ nat @ I3 @ ( suc @ N3 ) )
% 0.29/0.47 & ( P2 @ I3 ) ) )
% 0.29/0.47 = ( ( P2 @ ( zero_zero @ nat ) )
% 0.29/0.47 | ? [I3: nat] :
% 0.29/0.47 ( ( ord_less @ nat @ I3 @ N3 )
% 0.29/0.47 & ( P2 @ ( suc @ I3 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Ex_less_Suc2
% 0.29/0.47 thf(fact_119_length__Suc__conv,axiom,
% 0.29/0.47 ! [A: $tType,Xs: list @ A,N3: nat] :
% 0.29/0.47 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.29/0.47 = ( suc @ N3 ) )
% 0.29/0.47 = ( ? [Y5: A,Ys3: list @ A] :
% 0.29/0.47 ( ( Xs
% 0.29/0.47 = ( cons @ A @ Y5 @ Ys3 ) )
% 0.29/0.47 & ( ( size_size @ ( list @ A ) @ Ys3 )
% 0.29/0.47 = N3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % length_Suc_conv
% 0.29/0.47 thf(fact_120_Suc__length__conv,axiom,
% 0.29/0.47 ! [A: $tType,N3: nat,Xs: list @ A] :
% 0.29/0.47 ( ( ( suc @ N3 )
% 0.29/0.47 = ( size_size @ ( list @ A ) @ Xs ) )
% 0.29/0.47 = ( ? [Y5: A,Ys3: list @ A] :
% 0.29/0.47 ( ( Xs
% 0.29/0.47 = ( cons @ A @ Y5 @ Ys3 ) )
% 0.29/0.47 & ( ( size_size @ ( list @ A ) @ Ys3 )
% 0.29/0.47 = N3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % Suc_length_conv
% 0.29/0.47 thf(fact_121_list_Osize_I3_J,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( size_size @ ( list @ A ) @ ( nil @ A ) )
% 0.29/0.47 = ( zero_zero @ nat ) ) ).
% 0.29/0.47
% 0.29/0.47 % list.size(3)
% 0.29/0.47 thf(fact_122_list__induct3,axiom,
% 0.29/0.47 ! [B: $tType,A: $tType,C: $tType,Xs: list @ A,Ys: list @ B,Zs2: list @ C,P2: ( list @ A ) > ( list @ B ) > ( list @ C ) > $o] :
% 0.29/0.47 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.29/0.47 = ( size_size @ ( list @ B ) @ Ys ) )
% 0.29/0.47 => ( ( ( size_size @ ( list @ B ) @ Ys )
% 0.29/0.47 = ( size_size @ ( list @ C ) @ Zs2 ) )
% 0.29/0.47 => ( ( P2 @ ( nil @ A ) @ ( nil @ B ) @ ( nil @ C ) )
% 0.29/0.47 => ( ! [X2: A,Xs2: list @ A,Y4: B,Ys2: list @ B,Z: C,Zs: list @ C] :
% 0.29/0.47 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.29/0.47 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 0.29/0.47 => ( ( ( size_size @ ( list @ B ) @ Ys2 )
% 0.29/0.47 = ( size_size @ ( list @ C ) @ Zs ) )
% 0.29/0.47 => ( ( P2 @ Xs2 @ Ys2 @ Zs )
% 0.29/0.47 => ( P2 @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B @ Y4 @ Ys2 ) @ ( cons @ C @ Z @ Zs ) ) ) ) )
% 0.29/0.47 => ( P2 @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list_induct3
% 0.29/0.47 thf(fact_123_list__induct2,axiom,
% 0.29/0.47 ! [A: $tType,B: $tType,Xs: list @ A,Ys: list @ B,P2: ( list @ A ) > ( list @ B ) > $o] :
% 0.29/0.47 ( ( ( size_size @ ( list @ A ) @ Xs )
% 0.29/0.47 = ( size_size @ ( list @ B ) @ Ys ) )
% 0.29/0.47 => ( ( P2 @ ( nil @ A ) @ ( nil @ B ) )
% 0.29/0.47 => ( ! [X2: A,Xs2: list @ A,Y4: B,Ys2: list @ B] :
% 0.29/0.47 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.29/0.47 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 0.29/0.47 => ( ( P2 @ Xs2 @ Ys2 )
% 0.29/0.47 => ( P2 @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B @ Y4 @ Ys2 ) ) ) )
% 0.29/0.47 => ( P2 @ Xs @ Ys ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % list_induct2
% 0.29/0.47 thf(fact_124_infiniteExecutionCfg_Oelims,axiom,
% 0.29/0.47 ! [X: 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 @ ( configuration_ext @ p @ v @ s @ product_unit )] :
% 0.29/0.47 ( ( ( fLPThe137922386ionCfg @ p @ v @ s @ X @ Xa @ Xb @ Xc )
% 0.29/0.47 = Y3 )
% 0.29/0.47 => ( ( ( Xc
% 0.29/0.47 = ( zero_zero @ nat ) )
% 0.29/0.47 => ( Y3
% 0.29/0.47 != ( cons @ ( configuration_ext @ p @ v @ s @ product_unit ) @ X @ ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ) )
% 0.29/0.47 => ~ ! [N: nat] :
% 0.29/0.47 ( ( Xc
% 0.29/0.47 = ( suc @ N ) )
% 0.29/0.47 => ( Y3
% 0.29/0.47 != ( Xa @ ( fLPThe137922386ionCfg @ p @ v @ s @ X @ Xa @ Xb @ N ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % infiniteExecutionCfg.elims
% 0.29/0.47 thf(fact_125_infiniteExecutionMsg_Oelims,axiom,
% 0.29/0.47 ! [X: 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 )] :
% 0.29/0.47 ( ( ( fLPThe221390223ionMsg @ p @ v @ s @ X @ Xa @ Xb @ Xc )
% 0.29/0.47 = Y3 )
% 0.29/0.47 => ( ( ( Xc
% 0.29/0.47 = ( zero_zero @ nat ) )
% 0.29/0.47 => ( Y3
% 0.29/0.47 != ( nil @ ( message @ p @ v ) ) ) )
% 0.29/0.47 => ~ ! [N: nat] :
% 0.29/0.47 ( ( Xc
% 0.29/0.47 = ( suc @ N ) )
% 0.29/0.47 => ( Y3
% 0.29/0.47 != ( Xb @ ( fLPThe137922386ionCfg @ p @ v @ s @ X @ Xa @ Xb @ N ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % infiniteExecutionMsg.elims
% 0.29/0.47 thf(fact_126_infiniteExecutionMsg_Osimps_I2_J,axiom,
% 0.29/0.47 ! [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 ) ),N3: nat] :
% 0.29/0.47 ( ( fLPThe221390223ionMsg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 0.29/0.47 = ( FStepMsg2 @ ( fLPThe137922386ionCfg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % infiniteExecutionMsg.simps(2)
% 0.29/0.47 thf(fact_127_infiniteExecutionCfg_Osimps_I2_J,axiom,
% 0.29/0.47 ! [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 ) ),N3: nat] :
% 0.29/0.47 ( ( fLPThe137922386ionCfg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 0.29/0.47 = ( FStepCfg2 @ ( fLPThe137922386ionCfg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % infiniteExecutionCfg.simps(2)
% 0.29/0.47 thf(fact_128_infiniteExecutionMsg_Osimps_I1_J,axiom,
% 0.29/0.47 ! [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 ) )] :
% 0.29/0.47 ( ( fLPThe221390223ionMsg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( zero_zero @ nat ) )
% 0.29/0.47 = ( nil @ ( message @ p @ v ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % infiniteExecutionMsg.simps(1)
% 0.29/0.47 thf(fact_129_not__gr__zero,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( canoni770627133id_add @ A )
% 0.29/0.47 => ! [N3: A] :
% 0.29/0.47 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N3 ) )
% 0.29/0.47 = ( N3
% 0.29/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % not_gr_zero
% 0.29/0.47 thf(fact_130_length__Cons,axiom,
% 0.29/0.47 ! [A: $tType,X: A,Xs: list @ A] :
% 0.29/0.47 ( ( size_size @ ( list @ A ) @ ( cons @ A @ X @ Xs ) )
% 0.29/0.47 = ( suc @ ( size_size @ ( list @ A ) @ Xs ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % length_Cons
% 0.29/0.47 thf(fact_131_dependent__nat__choice,axiom,
% 0.29/0.47 ! [A: $tType,P2: nat > A > $o,Q: nat > A > A > $o] :
% 0.29/0.47 ( ? [X_12: A] : ( P2 @ ( zero_zero @ nat ) @ X_12 )
% 0.29/0.47 => ( ! [X2: A,N: nat] :
% 0.29/0.47 ( ( P2 @ N @ X2 )
% 0.29/0.47 => ? [Y: A] :
% 0.29/0.47 ( ( P2 @ ( suc @ N ) @ Y )
% 0.29/0.47 & ( Q @ N @ X2 @ Y ) ) )
% 0.29/0.47 => ? [F2: nat > A] :
% 0.29/0.47 ! [N5: nat] :
% 0.29/0.47 ( ( P2 @ N5 @ ( F2 @ N5 ) )
% 0.29/0.47 & ( Q @ N5 @ ( F2 @ N5 ) @ ( F2 @ ( suc @ N5 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % dependent_nat_choice
% 0.29/0.47 thf(fact_132_zero__reorient,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( zero @ A )
% 0.29/0.47 => ! [X: A] :
% 0.29/0.47 ( ( ( zero_zero @ A )
% 0.29/0.47 = X )
% 0.29/0.47 = ( X
% 0.29/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zero_reorient
% 0.29/0.47 thf(fact_133_gr__zeroI,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( canoni770627133id_add @ A )
% 0.29/0.47 => ! [N3: A] :
% 0.29/0.47 ( ( N3
% 0.29/0.47 != ( zero_zero @ A ) )
% 0.29/0.47 => ( ord_less @ A @ ( zero_zero @ A ) @ N3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % gr_zeroI
% 0.29/0.47 thf(fact_134_not__less__zero,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( canoni770627133id_add @ A )
% 0.29/0.47 => ! [N3: A] :
% 0.29/0.47 ~ ( ord_less @ A @ N3 @ ( zero_zero @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % not_less_zero
% 0.29/0.47 thf(fact_135_gr__implies__not__zero,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( canoni770627133id_add @ A )
% 0.29/0.47 => ! [M: A,N3: A] :
% 0.29/0.47 ( ( ord_less @ A @ M @ N3 )
% 0.29/0.47 => ( N3
% 0.29/0.47 != ( zero_zero @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % gr_implies_not_zero
% 0.29/0.47 thf(fact_136_zero__less__iff__neq__zero,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( canoni770627133id_add @ A )
% 0.29/0.47 => ! [N3: A] :
% 0.29/0.47 ( ( ord_less @ A @ ( zero_zero @ A ) @ N3 )
% 0.29/0.47 = ( N3
% 0.29/0.47 != ( zero_zero @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zero_less_iff_neq_zero
% 0.29/0.47 thf(fact_137_n__lists__Nil,axiom,
% 0.29/0.47 ! [A: $tType,N3: nat] :
% 0.29/0.47 ( ( ( N3
% 0.29/0.47 = ( zero_zero @ nat ) )
% 0.29/0.47 => ( ( n_lists @ A @ N3 @ ( nil @ A ) )
% 0.29/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) )
% 0.29/0.47 & ( ( N3
% 0.29/0.47 != ( zero_zero @ nat ) )
% 0.29/0.47 => ( ( n_lists @ A @ N3 @ ( nil @ A ) )
% 0.29/0.47 = ( nil @ ( list @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % n_lists_Nil
% 0.29/0.47 thf(fact_138_flpPseudoConsensus_OinfiniteExecutionCfg_Oelims,axiom,
% 0.29/0.47 ! [P: $tType,V: $tType,S: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,X: 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 @ ( configuration_ext @ P @ V @ S @ product_unit )] :
% 0.29/0.47 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 0.29/0.47 => ( ( ( fLPThe137922386ionCfg @ P @ V @ S @ X @ Xa @ Xb @ Xc )
% 0.29/0.47 = Y3 )
% 0.29/0.47 => ( ( ( Xc
% 0.29/0.47 = ( zero_zero @ nat ) )
% 0.29/0.47 => ( Y3
% 0.29/0.47 != ( cons @ ( configuration_ext @ P @ V @ S @ product_unit ) @ X @ ( nil @ ( configuration_ext @ P @ V @ S @ product_unit ) ) ) ) )
% 0.29/0.47 => ~ ! [N: nat] :
% 0.29/0.47 ( ( Xc
% 0.29/0.47 = ( suc @ N ) )
% 0.29/0.47 => ( Y3
% 0.29/0.47 != ( Xa @ ( fLPThe137922386ionCfg @ P @ V @ S @ X @ Xa @ Xb @ N ) @ ( fLPThe221390223ionMsg @ P @ V @ S @ X @ Xa @ Xb @ N ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpPseudoConsensus.infiniteExecutionCfg.elims
% 0.29/0.47 thf(fact_139_n__lists_Osimps_I1_J,axiom,
% 0.29/0.47 ! [A: $tType,Xs: list @ A] :
% 0.29/0.47 ( ( n_lists @ A @ ( zero_zero @ nat ) @ Xs )
% 0.29/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % n_lists.simps(1)
% 0.29/0.47 thf(fact_140_flpPseudoConsensus_OinfiniteExecutionMsg_Oelims,axiom,
% 0.29/0.47 ! [P: $tType,V: $tType,S: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,X: 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 )] :
% 0.29/0.47 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 0.29/0.47 => ( ( ( fLPThe221390223ionMsg @ P @ V @ S @ X @ Xa @ Xb @ Xc )
% 0.29/0.47 = Y3 )
% 0.29/0.47 => ( ( ( Xc
% 0.29/0.47 = ( zero_zero @ nat ) )
% 0.29/0.47 => ( Y3
% 0.29/0.47 != ( nil @ ( message @ P @ V ) ) ) )
% 0.29/0.47 => ~ ! [N: nat] :
% 0.29/0.47 ( ( Xc
% 0.29/0.47 = ( suc @ N ) )
% 0.29/0.47 => ( Y3
% 0.29/0.47 != ( Xb @ ( fLPThe137922386ionCfg @ P @ V @ S @ X @ Xa @ Xb @ N ) @ ( fLPThe221390223ionMsg @ P @ V @ S @ X @ Xa @ Xb @ N ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpPseudoConsensus.infiniteExecutionMsg.elims
% 0.29/0.47 thf(fact_141_flpPseudoConsensus_OinfiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 0.29/0.47 ! [P: $tType,V: $tType,S: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,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] :
% 0.29/0.47 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 0.29/0.47 => ( ! [Cfg: configuration_ext @ P @ V @ S @ product_unit,FStepCfg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( message @ P @ V ) )] : ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 0.29/0.47 => ( ! [Cfg: configuration_ext @ P @ V @ S @ product_unit,FStepCfg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( message @ P @ V ) ),N: nat] :
% 0.29/0.47 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/0.47 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/0.47 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.29/0.47 => ( ! [Cfg: configuration_ext @ P @ V @ S @ product_unit,FStepCfg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( message @ P @ V ) )] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 0.29/0.47 => ( ! [Cfg: configuration_ext @ P @ V @ S @ product_unit,FStepCfg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( message @ P @ V ) ),N: nat] :
% 0.29/0.47 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/0.47 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/0.47 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.29/0.47 => ( P2 @ A0 @ A1 @ A2 @ A3 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpPseudoConsensus.infiniteExecutionCfg_infiniteExecutionMsg.induct(1)
% 0.29/0.47 thf(fact_142_flpPseudoConsensus_OinfiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 0.29/0.47 ! [P: $tType,V: $tType,S: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,P2: ( configuration_ext @ P @ V @ S @ product_unit ) > ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( message @ P @ V ) ) ) > nat > $o,Q: ( configuration_ext @ P @ V @ S @ product_unit ) > ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) ) > ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( message @ P @ V ) ) ) > nat > $o,A4: configuration_ext @ P @ V @ S @ product_unit,A5: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ),A6: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( message @ P @ V ) ),A7: nat] :
% 0.29/0.47 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 0.29/0.47 => ( ! [Cfg: configuration_ext @ P @ V @ S @ product_unit,FStepCfg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( message @ P @ V ) )] : ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 0.29/0.47 => ( ! [Cfg: configuration_ext @ P @ V @ S @ product_unit,FStepCfg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( message @ P @ V ) ),N: nat] :
% 0.29/0.47 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/0.47 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/0.47 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.29/0.47 => ( ! [Cfg: configuration_ext @ P @ V @ S @ product_unit,FStepCfg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( message @ P @ V ) )] : ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( zero_zero @ nat ) )
% 0.29/0.47 => ( ! [Cfg: configuration_ext @ P @ V @ S @ product_unit,FStepCfg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( message @ P @ V ) ),N: nat] :
% 0.29/0.47 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/0.47 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 0.29/0.47 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 0.29/0.47 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpPseudoConsensus.infiniteExecutionCfg_infiniteExecutionMsg.induct(2)
% 0.29/0.47 thf(fact_143_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I2_J,axiom,
% 0.29/0.47 ! [P: $tType,V: $tType,S: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,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 ) ),N3: nat] :
% 0.29/0.47 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 0.29/0.47 => ( ( fLPThe221390223ionMsg @ P @ V @ S @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 0.29/0.47 = ( FStepMsg2 @ ( fLPThe137922386ionCfg @ P @ V @ S @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe221390223ionMsg @ P @ V @ S @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpPseudoConsensus.infiniteExecutionMsg.simps(2)
% 0.29/0.47 thf(fact_144_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I2_J,axiom,
% 0.29/0.47 ! [P: $tType,V: $tType,S: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,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 ) ),N3: nat] :
% 0.29/0.47 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 0.29/0.47 => ( ( fLPThe137922386ionCfg @ P @ V @ S @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 0.29/0.47 = ( FStepCfg2 @ ( fLPThe137922386ionCfg @ P @ V @ S @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe221390223ionMsg @ P @ V @ S @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpPseudoConsensus.infiniteExecutionCfg.simps(2)
% 0.29/0.47 thf(fact_145_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I1_J,axiom,
% 0.29/0.47 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,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 ) )] :
% 0.29/0.47 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 0.29/0.47 => ( ( fLPThe221390223ionMsg @ P @ V @ S @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( zero_zero @ nat ) )
% 0.29/0.47 = ( nil @ ( message @ P @ V ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpPseudoConsensus.infiniteExecutionMsg.simps(1)
% 0.29/0.47 thf(fact_146_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I1_J,axiom,
% 0.29/0.47 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,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 ) )] :
% 0.29/0.47 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 0.29/0.47 => ( ( fLPThe137922386ionCfg @ P @ V @ S @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( zero_zero @ nat ) )
% 0.29/0.47 = ( cons @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Cfg2 @ ( nil @ ( configuration_ext @ P @ V @ S @ product_unit ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % flpPseudoConsensus.infiniteExecutionCfg.simps(1)
% 0.29/0.47 thf(fact_147_shift__def,axiom,
% 0.29/0.47 ! [B: $tType,A: $tType] :
% 0.29/0.47 ( ( bNF_Greatest_shift @ A @ B )
% 0.29/0.47 = ( ^ [Lab: ( list @ A ) > B,K3: A,Kl: list @ A] : ( Lab @ ( cons @ A @ K3 @ Kl ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % shift_def
% 0.29/0.47 thf(fact_148_less__numeral__extra_I3_J,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord1659791738miring @ A )
% 0.29/0.47 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_numeral_extra(3)
% 0.29/0.47 thf(fact_149_product__lists_Osimps_I1_J,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.29/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % product_lists.simps(1)
% 0.29/0.47 thf(fact_150_subseqs_Osimps_I1_J,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( subseqs @ A @ ( nil @ A ) )
% 0.29/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % subseqs.simps(1)
% 0.29/0.47 thf(fact_151_length__code,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( size_size @ ( list @ A ) )
% 0.29/0.47 = ( gen_length @ A @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % length_code
% 0.29/0.47 thf(fact_152_gen__length__code_I2_J,axiom,
% 0.29/0.47 ! [B: $tType,N3: nat,X: B,Xs: list @ B] :
% 0.29/0.47 ( ( gen_length @ B @ N3 @ ( cons @ B @ X @ Xs ) )
% 0.29/0.47 = ( gen_length @ B @ ( suc @ N3 ) @ Xs ) ) ).
% 0.29/0.47
% 0.29/0.47 % gen_length_code(2)
% 0.29/0.47 thf(fact_153_gen__length__code_I1_J,axiom,
% 0.29/0.47 ! [A: $tType,N3: nat] :
% 0.29/0.47 ( ( gen_length @ A @ N3 @ ( nil @ A ) )
% 0.29/0.47 = N3 ) ).
% 0.29/0.47
% 0.29/0.47 % gen_length_code(1)
% 0.29/0.47 thf(fact_154_insert__Nil,axiom,
% 0.29/0.47 ! [A: $tType,X: A] :
% 0.29/0.47 ( ( insert @ A @ X @ ( nil @ A ) )
% 0.29/0.47 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % insert_Nil
% 0.29/0.47 thf(fact_155_nths__singleton,axiom,
% 0.29/0.47 ! [A: $tType,A9: set @ nat,X: A] :
% 0.29/0.47 ( ( ( member @ nat @ ( zero_zero @ nat ) @ A9 )
% 0.29/0.47 => ( ( nths @ A @ ( cons @ A @ X @ ( nil @ A ) ) @ A9 )
% 0.29/0.47 = ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.29/0.47 & ( ~ ( member @ nat @ ( zero_zero @ nat ) @ A9 )
% 0.29/0.47 => ( ( nths @ A @ ( cons @ A @ X @ ( nil @ A ) ) @ A9 )
% 0.29/0.47 = ( nil @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nths_singleton
% 0.29/0.47 thf(fact_156_of__nat__0__less__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord1659791738miring @ A )
% 0.29/0.47 => ! [N3: nat] :
% 0.29/0.47 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( semiring_1_of_nat @ A @ N3 ) )
% 0.29/0.47 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_nat_0_less_iff
% 0.29/0.47 thf(fact_157_of__nat__eq__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( semiring_char_0 @ A )
% 0.29/0.47 => ! [M: nat,N3: nat] :
% 0.29/0.47 ( ( ( semiring_1_of_nat @ A @ M )
% 0.29/0.47 = ( semiring_1_of_nat @ A @ N3 ) )
% 0.29/0.47 = ( M = N3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_nat_eq_iff
% 0.29/0.47 thf(fact_158_nths__nil,axiom,
% 0.29/0.47 ! [A: $tType,A9: set @ nat] :
% 0.29/0.47 ( ( nths @ A @ ( nil @ A ) @ A9 )
% 0.29/0.47 = ( nil @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % nths_nil
% 0.29/0.47 thf(fact_159_of__nat__0,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( semiring_1 @ A )
% 0.29/0.47 => ( ( semiring_1_of_nat @ A @ ( zero_zero @ nat ) )
% 0.29/0.47 = ( zero_zero @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_nat_0
% 0.29/0.47 thf(fact_160_of__nat__0__eq__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( semiring_char_0 @ A )
% 0.29/0.47 => ! [N3: nat] :
% 0.29/0.47 ( ( ( zero_zero @ A )
% 0.29/0.47 = ( semiring_1_of_nat @ A @ N3 ) )
% 0.29/0.47 = ( ( zero_zero @ nat )
% 0.29/0.47 = N3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_nat_0_eq_iff
% 0.29/0.47 thf(fact_161_of__nat__eq__0__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( semiring_char_0 @ A )
% 0.29/0.47 => ! [M: nat] :
% 0.29/0.47 ( ( ( semiring_1_of_nat @ A @ M )
% 0.29/0.47 = ( zero_zero @ A ) )
% 0.29/0.47 = ( M
% 0.29/0.47 = ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_nat_eq_0_iff
% 0.29/0.47 thf(fact_162_of__nat__less__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord1659791738miring @ A )
% 0.29/0.47 => ! [M: nat,N3: nat] :
% 0.29/0.47 ( ( ord_less @ A @ ( semiring_1_of_nat @ A @ M ) @ ( semiring_1_of_nat @ A @ N3 ) )
% 0.29/0.47 = ( ord_less @ nat @ M @ N3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_nat_less_iff
% 0.29/0.47 thf(fact_163_of__nat__less__0__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord1659791738miring @ A )
% 0.29/0.47 => ! [M: nat] :
% 0.29/0.47 ~ ( ord_less @ A @ ( semiring_1_of_nat @ A @ M ) @ ( zero_zero @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_nat_less_0_iff
% 0.29/0.47 thf(fact_164_of__nat__neq__0,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( semiring_char_0 @ A )
% 0.29/0.47 => ! [N3: nat] :
% 0.29/0.47 ( ( semiring_1_of_nat @ A @ ( suc @ N3 ) )
% 0.29/0.47 != ( zero_zero @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_nat_neq_0
% 0.29/0.47 thf(fact_165_less__imp__of__nat__less,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord1659791738miring @ A )
% 0.29/0.47 => ! [M: nat,N3: nat] :
% 0.29/0.47 ( ( ord_less @ nat @ M @ N3 )
% 0.29/0.47 => ( ord_less @ A @ ( semiring_1_of_nat @ A @ M ) @ ( semiring_1_of_nat @ A @ N3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_imp_of_nat_less
% 0.29/0.47 thf(fact_166_of__nat__less__imp__less,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord1659791738miring @ A )
% 0.29/0.47 => ! [M: nat,N3: nat] :
% 0.29/0.47 ( ( ord_less @ A @ ( semiring_1_of_nat @ A @ M ) @ ( semiring_1_of_nat @ A @ N3 ) )
% 0.29/0.47 => ( ord_less @ nat @ M @ N3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_nat_less_imp_less
% 0.29/0.47 thf(fact_167_nths__all,axiom,
% 0.29/0.47 ! [A: $tType,Xs: list @ A,I4: set @ nat] :
% 0.29/0.47 ( ! [I2: nat] :
% 0.29/0.47 ( ( ord_less @ nat @ I2 @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.29/0.47 => ( member @ nat @ I2 @ I4 ) )
% 0.29/0.47 => ( ( nths @ A @ Xs @ I4 )
% 0.29/0.47 = Xs ) ) ).
% 0.29/0.47
% 0.29/0.47 % nths_all
% 0.29/0.47 thf(fact_168_pos__int__cases,axiom,
% 0.29/0.47 ! [K: int] :
% 0.29/0.47 ( ( ord_less @ int @ ( zero_zero @ int ) @ K )
% 0.29/0.47 => ~ ! [N: nat] :
% 0.29/0.47 ( ( K
% 0.29/0.47 = ( semiring_1_of_nat @ int @ N ) )
% 0.29/0.47 => ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % pos_int_cases
% 0.29/0.47 thf(fact_169_zero__less__imp__eq__int,axiom,
% 0.29/0.47 ! [K: int] :
% 0.29/0.47 ( ( ord_less @ int @ ( zero_zero @ int ) @ K )
% 0.29/0.47 => ? [N: nat] :
% 0.29/0.47 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.29/0.47 & ( K
% 0.29/0.47 = ( semiring_1_of_nat @ int @ N ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zero_less_imp_eq_int
% 0.29/0.47 thf(fact_170_list__ex1__simps_I1_J,axiom,
% 0.29/0.47 ! [A: $tType,P2: A > $o] :
% 0.29/0.47 ~ ( list_ex1 @ A @ P2 @ ( nil @ A ) ) ).
% 0.29/0.47
% 0.29/0.47 % list_ex1_simps(1)
% 0.29/0.47 thf(fact_171_nat__int__comparison_I2_J,axiom,
% 0.29/0.47 ( ( ord_less @ nat )
% 0.29/0.47 = ( ^ [A11: nat,B2: nat] : ( ord_less @ int @ ( semiring_1_of_nat @ int @ A11 ) @ ( semiring_1_of_nat @ int @ B2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_int_comparison(2)
% 0.29/0.47 thf(fact_172_int__ops_I1_J,axiom,
% 0.29/0.47 ( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
% 0.29/0.47 = ( zero_zero @ int ) ) ).
% 0.29/0.47
% 0.29/0.47 % int_ops(1)
% 0.29/0.47 thf(fact_173_neg__int__cases,axiom,
% 0.29/0.47 ! [K: int] :
% 0.29/0.47 ( ( ord_less @ int @ K @ ( zero_zero @ int ) )
% 0.29/0.47 => ~ ! [N: nat] :
% 0.29/0.47 ( ( K
% 0.29/0.47 = ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ N ) ) )
% 0.29/0.47 => ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % neg_int_cases
% 0.29/0.47 thf(fact_174_neg__equal__iff__equal,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( group_add @ A )
% 0.29/0.47 => ! [A8: A,B3: A] :
% 0.29/0.47 ( ( ( uminus_uminus @ A @ A8 )
% 0.29/0.47 = ( uminus_uminus @ A @ B3 ) )
% 0.29/0.47 = ( A8 = B3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % neg_equal_iff_equal
% 0.29/0.47 thf(fact_175_add_Oinverse__inverse,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( group_add @ A )
% 0.29/0.47 => ! [A8: A] :
% 0.29/0.47 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A8 ) )
% 0.29/0.47 = A8 ) ) ).
% 0.29/0.47
% 0.29/0.47 % add.inverse_inverse
% 0.29/0.47 thf(fact_176_add_Oinverse__neutral,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( group_add @ A )
% 0.29/0.47 => ( ( uminus_uminus @ A @ ( zero_zero @ A ) )
% 0.29/0.47 = ( zero_zero @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % add.inverse_neutral
% 0.29/0.47 thf(fact_177_neg__0__equal__iff__equal,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( group_add @ A )
% 0.29/0.47 => ! [A8: A] :
% 0.29/0.47 ( ( ( zero_zero @ A )
% 0.29/0.47 = ( uminus_uminus @ A @ A8 ) )
% 0.29/0.47 = ( ( zero_zero @ A )
% 0.29/0.47 = A8 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % neg_0_equal_iff_equal
% 0.29/0.47 thf(fact_178_neg__equal__0__iff__equal,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( group_add @ A )
% 0.29/0.47 => ! [A8: A] :
% 0.29/0.47 ( ( ( uminus_uminus @ A @ A8 )
% 0.29/0.47 = ( zero_zero @ A ) )
% 0.29/0.47 = ( A8
% 0.29/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % neg_equal_0_iff_equal
% 0.29/0.47 thf(fact_179_equal__neg__zero,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord219039673up_add @ A )
% 0.29/0.47 => ! [A8: A] :
% 0.29/0.47 ( ( A8
% 0.29/0.47 = ( uminus_uminus @ A @ A8 ) )
% 0.29/0.47 = ( A8
% 0.29/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % equal_neg_zero
% 0.29/0.47 thf(fact_180_neg__equal__zero,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord219039673up_add @ A )
% 0.29/0.47 => ! [A8: A] :
% 0.29/0.47 ( ( ( uminus_uminus @ A @ A8 )
% 0.29/0.47 = A8 )
% 0.29/0.47 = ( A8
% 0.29/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % neg_equal_zero
% 0.29/0.47 thf(fact_181_neg__less__iff__less,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( ordered_ab_group_add @ A )
% 0.29/0.47 => ! [B3: A,A8: A] :
% 0.29/0.47 ( ( ord_less @ A @ ( uminus_uminus @ A @ B3 ) @ ( uminus_uminus @ A @ A8 ) )
% 0.29/0.47 = ( ord_less @ A @ A8 @ B3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % neg_less_iff_less
% 0.29/0.47 thf(fact_182_less__neg__neg,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord219039673up_add @ A )
% 0.29/0.47 => ! [A8: A] :
% 0.29/0.47 ( ( ord_less @ A @ A8 @ ( uminus_uminus @ A @ A8 ) )
% 0.29/0.47 = ( ord_less @ A @ A8 @ ( zero_zero @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_neg_neg
% 0.29/0.47 thf(fact_183_neg__less__pos,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord219039673up_add @ A )
% 0.29/0.47 => ! [A8: A] :
% 0.29/0.47 ( ( ord_less @ A @ ( uminus_uminus @ A @ A8 ) @ A8 )
% 0.29/0.47 = ( ord_less @ A @ ( zero_zero @ A ) @ A8 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % neg_less_pos
% 0.29/0.47 thf(fact_184_neg__0__less__iff__less,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( ordered_ab_group_add @ A )
% 0.29/0.47 => ! [A8: A] :
% 0.29/0.47 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( uminus_uminus @ A @ A8 ) )
% 0.29/0.47 = ( ord_less @ A @ A8 @ ( zero_zero @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % neg_0_less_iff_less
% 0.29/0.47 thf(fact_185_neg__less__0__iff__less,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( ordered_ab_group_add @ A )
% 0.29/0.47 => ! [A8: A] :
% 0.29/0.47 ( ( ord_less @ A @ ( uminus_uminus @ A @ A8 ) @ ( zero_zero @ A ) )
% 0.29/0.47 = ( ord_less @ A @ ( zero_zero @ A ) @ A8 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % neg_less_0_iff_less
% 0.29/0.47 thf(fact_186_negative__eq__positive,axiom,
% 0.29/0.47 ! [N3: nat,M: nat] :
% 0.29/0.47 ( ( ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ N3 ) )
% 0.29/0.47 = ( semiring_1_of_nat @ int @ M ) )
% 0.29/0.47 = ( ( N3
% 0.29/0.47 = ( zero_zero @ nat ) )
% 0.29/0.47 & ( M
% 0.29/0.47 = ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % negative_eq_positive
% 0.29/0.47 thf(fact_187_negative__zless,axiom,
% 0.29/0.47 ! [N3: nat,M: nat] : ( ord_less @ int @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ N3 ) ) ) @ ( semiring_1_of_nat @ int @ M ) ) ).
% 0.29/0.47
% 0.29/0.47 % negative_zless
% 0.29/0.47 thf(fact_188_minus__less__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( ordered_ab_group_add @ A )
% 0.29/0.47 => ! [A8: A,B3: A] :
% 0.29/0.47 ( ( ord_less @ A @ ( uminus_uminus @ A @ A8 ) @ B3 )
% 0.29/0.47 = ( ord_less @ A @ ( uminus_uminus @ A @ B3 ) @ A8 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % minus_less_iff
% 0.29/0.47 thf(fact_189_less__minus__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( ordered_ab_group_add @ A )
% 0.29/0.47 => ! [A8: A,B3: A] :
% 0.29/0.47 ( ( ord_less @ A @ A8 @ ( uminus_uminus @ A @ B3 ) )
% 0.29/0.47 = ( ord_less @ A @ B3 @ ( uminus_uminus @ A @ A8 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_minus_iff
% 0.29/0.47 thf(fact_190_verit__negate__coefficient_I2_J,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( ordered_ab_group_add @ A )
% 0.29/0.47 => ! [A8: A,B3: A] :
% 0.29/0.47 ( ( ord_less @ A @ A8 @ B3 )
% 0.29/0.47 => ( ord_less @ A @ ( uminus_uminus @ A @ B3 ) @ ( uminus_uminus @ A @ A8 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % verit_negate_coefficient(2)
% 0.29/0.47 thf(fact_191_minus__equation__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( group_add @ A )
% 0.29/0.47 => ! [A8: A,B3: A] :
% 0.29/0.47 ( ( ( uminus_uminus @ A @ A8 )
% 0.29/0.47 = B3 )
% 0.29/0.47 = ( ( uminus_uminus @ A @ B3 )
% 0.29/0.47 = A8 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % minus_equation_iff
% 0.29/0.47 thf(fact_192_equation__minus__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( group_add @ A )
% 0.29/0.47 => ! [A8: A,B3: A] :
% 0.29/0.47 ( ( A8
% 0.29/0.47 = ( uminus_uminus @ A @ B3 ) )
% 0.29/0.47 = ( B3
% 0.29/0.47 = ( uminus_uminus @ A @ A8 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % equation_minus_iff
% 0.29/0.47 thf(fact_193_int__cases,axiom,
% 0.29/0.47 ! [Z2: int] :
% 0.29/0.47 ( ! [N: nat] :
% 0.29/0.47 ( Z2
% 0.29/0.47 != ( semiring_1_of_nat @ int @ N ) )
% 0.29/0.47 => ~ ! [N: nat] :
% 0.29/0.47 ( Z2
% 0.29/0.47 != ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ N ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % int_cases
% 0.29/0.47 thf(fact_194_int__of__nat__induct,axiom,
% 0.29/0.47 ! [P2: int > $o,Z2: int] :
% 0.29/0.47 ( ! [N: nat] : ( P2 @ ( semiring_1_of_nat @ int @ N ) )
% 0.29/0.47 => ( ! [N: nat] : ( P2 @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ N ) ) ) )
% 0.29/0.47 => ( P2 @ Z2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % int_of_nat_induct
% 0.29/0.47 thf(fact_195_int__cases4,axiom,
% 0.29/0.47 ! [M: int] :
% 0.29/0.47 ( ! [N: nat] :
% 0.29/0.47 ( M
% 0.29/0.47 != ( semiring_1_of_nat @ int @ N ) )
% 0.29/0.47 => ~ ! [N: nat] :
% 0.29/0.47 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 0.29/0.47 => ( M
% 0.29/0.47 != ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ N ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % int_cases4
% 0.29/0.47 thf(fact_196_verit__comp__simplify1_I1_J,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( order @ A )
% 0.29/0.47 => ! [A8: A] :
% 0.29/0.47 ~ ( ord_less @ A @ A8 @ A8 ) ) ).
% 0.29/0.47
% 0.29/0.47 % verit_comp_simplify1(1)
% 0.29/0.47 thf(fact_197_int__cases3,axiom,
% 0.29/0.47 ! [K: int] :
% 0.29/0.47 ( ( K
% 0.29/0.47 != ( zero_zero @ int ) )
% 0.29/0.47 => ( ! [N: nat] :
% 0.29/0.47 ( ( K
% 0.29/0.47 = ( semiring_1_of_nat @ int @ N ) )
% 0.29/0.47 => ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) )
% 0.29/0.47 => ~ ! [N: nat] :
% 0.29/0.47 ( ( K
% 0.29/0.47 = ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ N ) ) )
% 0.29/0.47 => ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % int_cases3
% 0.29/0.47 thf(fact_198_negative__zless__0,axiom,
% 0.29/0.47 ! [N3: nat] : ( ord_less @ int @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ N3 ) ) ) @ ( zero_zero @ int ) ) ).
% 0.29/0.47
% 0.29/0.47 % negative_zless_0
% 0.29/0.47 thf(fact_199_negD,axiom,
% 0.29/0.47 ! [X: int] :
% 0.29/0.47 ( ( ord_less @ int @ X @ ( zero_zero @ int ) )
% 0.29/0.47 => ? [N: nat] :
% 0.29/0.47 ( X
% 0.29/0.47 = ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ N ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % negD
% 0.29/0.47 thf(fact_200_compl__less__compl__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( boolean_algebra @ A )
% 0.29/0.47 => ! [X: A,Y3: A] :
% 0.29/0.47 ( ( ord_less @ A @ ( uminus_uminus @ A @ X ) @ ( uminus_uminus @ A @ Y3 ) )
% 0.29/0.47 = ( ord_less @ A @ Y3 @ X ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % compl_less_compl_iff
% 0.29/0.47 thf(fact_201_compl__less__swap2,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( boolean_algebra @ A )
% 0.29/0.47 => ! [Y3: A,X: A] :
% 0.29/0.47 ( ( ord_less @ A @ ( uminus_uminus @ A @ Y3 ) @ X )
% 0.29/0.47 => ( ord_less @ A @ ( uminus_uminus @ A @ X ) @ Y3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % compl_less_swap2
% 0.29/0.47 thf(fact_202_compl__less__swap1,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( boolean_algebra @ A )
% 0.29/0.47 => ! [Y3: A,X: A] :
% 0.29/0.47 ( ( ord_less @ A @ Y3 @ ( uminus_uminus @ A @ X ) )
% 0.29/0.47 => ( ord_less @ A @ X @ ( uminus_uminus @ A @ Y3 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % compl_less_swap1
% 0.29/0.47 thf(fact_203_zero__less__nat__eq,axiom,
% 0.29/0.47 ! [Z2: int] :
% 0.29/0.47 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( nat2 @ Z2 ) )
% 0.29/0.47 = ( ord_less @ int @ ( zero_zero @ int ) @ Z2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % zero_less_nat_eq
% 0.29/0.47 thf(fact_204_of__int__0__less__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linordered_idom @ A )
% 0.29/0.47 => ! [Z2: int] :
% 0.29/0.47 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( ring_1_of_int @ A @ Z2 ) )
% 0.29/0.47 = ( ord_less @ int @ ( zero_zero @ int ) @ Z2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_int_0_less_iff
% 0.29/0.47 thf(fact_205_of__int__0,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( ring_1 @ A )
% 0.29/0.47 => ( ( ring_1_of_int @ A @ ( zero_zero @ int ) )
% 0.29/0.47 = ( zero_zero @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_int_0
% 0.29/0.47 thf(fact_206_of__int__0__eq__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( ring_char_0 @ A )
% 0.29/0.47 => ! [Z2: int] :
% 0.29/0.47 ( ( ( zero_zero @ A )
% 0.29/0.47 = ( ring_1_of_int @ A @ Z2 ) )
% 0.29/0.47 = ( Z2
% 0.29/0.47 = ( zero_zero @ int ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_int_0_eq_iff
% 0.29/0.47 thf(fact_207_of__int__eq__0__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( ring_char_0 @ A )
% 0.29/0.47 => ! [Z2: int] :
% 0.29/0.47 ( ( ( ring_1_of_int @ A @ Z2 )
% 0.29/0.47 = ( zero_zero @ A ) )
% 0.29/0.47 = ( Z2
% 0.29/0.47 = ( zero_zero @ int ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_int_eq_0_iff
% 0.29/0.47 thf(fact_208_of__int__less__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linordered_idom @ A )
% 0.29/0.47 => ! [W: int,Z2: int] :
% 0.29/0.47 ( ( ord_less @ A @ ( ring_1_of_int @ A @ W ) @ ( ring_1_of_int @ A @ Z2 ) )
% 0.29/0.47 = ( ord_less @ int @ W @ Z2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_int_less_iff
% 0.29/0.47 thf(fact_209_zless__nat__conj,axiom,
% 0.29/0.47 ! [W: int,Z2: int] :
% 0.29/0.47 ( ( ord_less @ nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
% 0.29/0.47 = ( ( ord_less @ int @ ( zero_zero @ int ) @ Z2 )
% 0.29/0.47 & ( ord_less @ int @ W @ Z2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zless_nat_conj
% 0.29/0.47 thf(fact_210_nat__zminus__int,axiom,
% 0.29/0.47 ! [N3: nat] :
% 0.29/0.47 ( ( nat2 @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ N3 ) ) )
% 0.29/0.47 = ( zero_zero @ nat ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_zminus_int
% 0.29/0.47 thf(fact_211_of__int__less__0__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linordered_idom @ A )
% 0.29/0.47 => ! [Z2: int] :
% 0.29/0.47 ( ( ord_less @ A @ ( ring_1_of_int @ A @ Z2 ) @ ( zero_zero @ A ) )
% 0.29/0.47 = ( ord_less @ int @ Z2 @ ( zero_zero @ int ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_int_less_0_iff
% 0.29/0.47 thf(fact_212_nat__zero__as__int,axiom,
% 0.29/0.47 ( ( zero_zero @ nat )
% 0.29/0.47 = ( nat2 @ ( zero_zero @ int ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_zero_as_int
% 0.29/0.47 thf(fact_213_nat__mono__iff,axiom,
% 0.29/0.47 ! [Z2: int,W: int] :
% 0.29/0.47 ( ( ord_less @ int @ ( zero_zero @ int ) @ Z2 )
% 0.29/0.47 => ( ( ord_less @ nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
% 0.29/0.47 = ( ord_less @ int @ W @ Z2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_mono_iff
% 0.29/0.47 thf(fact_214_zless__nat__eq__int__zless,axiom,
% 0.29/0.47 ! [M: nat,Z2: int] :
% 0.29/0.47 ( ( ord_less @ nat @ M @ ( nat2 @ Z2 ) )
% 0.29/0.47 = ( ord_less @ int @ ( semiring_1_of_nat @ int @ M ) @ Z2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % zless_nat_eq_int_zless
% 0.29/0.47 thf(fact_215_of__int__pos,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linordered_idom @ A )
% 0.29/0.47 => ! [Z2: int] :
% 0.29/0.47 ( ( ord_less @ int @ ( zero_zero @ int ) @ Z2 )
% 0.29/0.47 => ( ord_less @ A @ ( zero_zero @ A ) @ ( ring_1_of_int @ A @ Z2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_int_pos
% 0.29/0.47 thf(fact_216_of__nat__less__of__int__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linordered_idom @ A )
% 0.29/0.47 => ! [N3: nat,X: int] :
% 0.29/0.47 ( ( ord_less @ A @ ( semiring_1_of_nat @ A @ N3 ) @ ( ring_1_of_int @ A @ X ) )
% 0.29/0.47 = ( ord_less @ int @ ( semiring_1_of_nat @ int @ N3 ) @ X ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_nat_less_of_int_iff
% 0.29/0.47 thf(fact_217_split__nat,axiom,
% 0.29/0.47 ! [P2: nat > $o,I: int] :
% 0.29/0.47 ( ( P2 @ ( nat2 @ I ) )
% 0.29/0.47 = ( ! [N6: nat] :
% 0.29/0.47 ( ( I
% 0.29/0.47 = ( semiring_1_of_nat @ int @ N6 ) )
% 0.29/0.47 => ( P2 @ N6 ) )
% 0.29/0.47 & ( ( ord_less @ int @ I @ ( zero_zero @ int ) )
% 0.29/0.47 => ( P2 @ ( zero_zero @ nat ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % split_nat
% 0.29/0.47 thf(fact_218_one__less__nat__eq,axiom,
% 0.29/0.47 ! [Z2: int] :
% 0.29/0.47 ( ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ ( nat2 @ Z2 ) )
% 0.29/0.47 = ( ord_less @ int @ ( one_one @ int ) @ Z2 ) ) ).
% 0.29/0.47
% 0.29/0.47 % one_less_nat_eq
% 0.29/0.47 thf(fact_219_nat__less__iff,axiom,
% 0.29/0.47 ! [W: int,M: nat] :
% 0.29/0.47 ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ W )
% 0.29/0.47 => ( ( ord_less @ nat @ ( nat2 @ W ) @ M )
% 0.29/0.47 = ( ord_less @ int @ W @ ( semiring_1_of_nat @ int @ M ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_less_iff
% 0.29/0.47 thf(fact_220_le__zero__eq,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( canoni770627133id_add @ A )
% 0.29/0.47 => ! [N3: A] :
% 0.29/0.47 ( ( ord_less_eq @ A @ N3 @ ( zero_zero @ A ) )
% 0.29/0.47 = ( N3
% 0.29/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_zero_eq
% 0.29/0.47 thf(fact_221_neg__le__iff__le,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( ordered_ab_group_add @ A )
% 0.29/0.47 => ! [B3: A,A8: A] :
% 0.29/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ B3 ) @ ( uminus_uminus @ A @ A8 ) )
% 0.29/0.47 = ( ord_less_eq @ A @ A8 @ B3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % neg_le_iff_le
% 0.29/0.47 thf(fact_222_of__nat__le__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord1659791738miring @ A )
% 0.29/0.47 => ! [M: nat,N3: nat] :
% 0.29/0.47 ( ( ord_less_eq @ A @ ( semiring_1_of_nat @ A @ M ) @ ( semiring_1_of_nat @ A @ N3 ) )
% 0.29/0.47 = ( ord_less_eq @ nat @ M @ N3 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_nat_le_iff
% 0.29/0.47 thf(fact_223_of__nat__1,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( semiring_1 @ A )
% 0.29/0.47 => ( ( semiring_1_of_nat @ A @ ( one_one @ nat ) )
% 0.29/0.47 = ( one_one @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_nat_1
% 0.29/0.47 thf(fact_224_of__nat__1__eq__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( semiring_char_0 @ A )
% 0.29/0.47 => ! [N3: nat] :
% 0.29/0.47 ( ( ( one_one @ A )
% 0.29/0.47 = ( semiring_1_of_nat @ A @ N3 ) )
% 0.29/0.47 = ( N3
% 0.29/0.47 = ( one_one @ nat ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_nat_1_eq_iff
% 0.29/0.47 thf(fact_225_of__nat__eq__1__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( semiring_char_0 @ A )
% 0.29/0.47 => ! [N3: nat] :
% 0.29/0.47 ( ( ( semiring_1_of_nat @ A @ N3 )
% 0.29/0.47 = ( one_one @ A ) )
% 0.29/0.47 = ( N3
% 0.29/0.47 = ( one_one @ nat ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_nat_eq_1_iff
% 0.29/0.47 thf(fact_226_neg__0__le__iff__le,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( ordered_ab_group_add @ A )
% 0.29/0.47 => ! [A8: A] :
% 0.29/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( uminus_uminus @ A @ A8 ) )
% 0.29/0.47 = ( ord_less_eq @ A @ A8 @ ( zero_zero @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % neg_0_le_iff_le
% 0.29/0.47 thf(fact_227_neg__le__0__iff__le,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( ordered_ab_group_add @ A )
% 0.29/0.47 => ! [A8: A] :
% 0.29/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ A8 ) @ ( zero_zero @ A ) )
% 0.29/0.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A8 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % neg_le_0_iff_le
% 0.29/0.47 thf(fact_228_less__eq__neg__nonpos,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord219039673up_add @ A )
% 0.29/0.47 => ! [A8: A] :
% 0.29/0.47 ( ( ord_less_eq @ A @ A8 @ ( uminus_uminus @ A @ A8 ) )
% 0.29/0.47 = ( ord_less_eq @ A @ A8 @ ( zero_zero @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_eq_neg_nonpos
% 0.29/0.47 thf(fact_229_neg__less__eq__nonneg,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord219039673up_add @ A )
% 0.29/0.47 => ! [A8: A] :
% 0.29/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ A8 ) @ A8 )
% 0.29/0.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A8 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % neg_less_eq_nonneg
% 0.29/0.47 thf(fact_230_of__nat__le__0__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord1659791738miring @ A )
% 0.29/0.47 => ! [M: nat] :
% 0.29/0.47 ( ( ord_less_eq @ A @ ( semiring_1_of_nat @ A @ M ) @ ( zero_zero @ A ) )
% 0.29/0.47 = ( M
% 0.29/0.47 = ( zero_zero @ nat ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_nat_le_0_iff
% 0.29/0.47 thf(fact_231_nat__1,axiom,
% 0.29/0.47 ( ( nat2 @ ( one_one @ int ) )
% 0.29/0.47 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_1
% 0.29/0.47 thf(fact_232_nat__le__0,axiom,
% 0.29/0.47 ! [Z2: int] :
% 0.29/0.47 ( ( ord_less_eq @ int @ Z2 @ ( zero_zero @ int ) )
% 0.29/0.47 => ( ( nat2 @ Z2 )
% 0.29/0.47 = ( zero_zero @ nat ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_le_0
% 0.29/0.47 thf(fact_233_nat__0__iff,axiom,
% 0.29/0.47 ! [I: int] :
% 0.29/0.47 ( ( ( nat2 @ I )
% 0.29/0.47 = ( zero_zero @ nat ) )
% 0.29/0.47 = ( ord_less_eq @ int @ I @ ( zero_zero @ int ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % nat_0_iff
% 0.29/0.47 thf(fact_234_of__int__le__0__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linordered_idom @ A )
% 0.29/0.47 => ! [Z2: int] :
% 0.29/0.47 ( ( ord_less_eq @ A @ ( ring_1_of_int @ A @ Z2 ) @ ( zero_zero @ A ) )
% 0.29/0.47 = ( ord_less_eq @ int @ Z2 @ ( zero_zero @ int ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_int_le_0_iff
% 0.29/0.47 thf(fact_235_of__int__0__le__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linordered_idom @ A )
% 0.29/0.47 => ! [Z2: int] :
% 0.29/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( ring_1_of_int @ A @ Z2 ) )
% 0.29/0.47 = ( ord_less_eq @ int @ ( zero_zero @ int ) @ Z2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_int_0_le_iff
% 0.29/0.47 thf(fact_236_of__int__less__1__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linordered_idom @ A )
% 0.29/0.47 => ! [Z2: int] :
% 0.29/0.47 ( ( ord_less @ A @ ( ring_1_of_int @ A @ Z2 ) @ ( one_one @ A ) )
% 0.29/0.47 = ( ord_less @ int @ Z2 @ ( one_one @ int ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_int_less_1_iff
% 0.29/0.47 thf(fact_237_of__int__1__less__iff,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linordered_idom @ A )
% 0.29/0.47 => ! [Z2: int] :
% 0.29/0.47 ( ( ord_less @ A @ ( one_one @ A ) @ ( ring_1_of_int @ A @ Z2 ) )
% 0.29/0.47 = ( ord_less @ int @ ( one_one @ int ) @ Z2 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_int_1_less_iff
% 0.29/0.47 thf(fact_238_of__int__nonneg,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linordered_idom @ A )
% 0.29/0.47 => ! [Z2: int] :
% 0.29/0.47 ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ Z2 )
% 0.29/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( ring_1_of_int @ A @ Z2 ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_int_nonneg
% 0.29/0.47 thf(fact_239_verit__comp__simplify1_I3_J,axiom,
% 0.29/0.47 ! [B: $tType] :
% 0.29/0.47 ( ( linorder @ B )
% 0.29/0.47 => ! [B4: B,A13: B] :
% 0.29/0.47 ( ( ~ ( ord_less_eq @ B @ B4 @ A13 ) )
% 0.29/0.47 = ( ord_less @ B @ A13 @ B4 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % verit_comp_simplify1(3)
% 0.29/0.47 thf(fact_240_le__numeral__extra_I4_J,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord1659791738miring @ A )
% 0.29/0.47 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_numeral_extra(4)
% 0.29/0.47 thf(fact_241_one__reorient,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( one @ A )
% 0.29/0.47 => ! [X: A] :
% 0.29/0.47 ( ( ( one_one @ A )
% 0.29/0.47 = X )
% 0.29/0.47 = ( X
% 0.29/0.47 = ( one_one @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % one_reorient
% 0.29/0.47 thf(fact_242_lift__Suc__antimono__le,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( order @ A )
% 0.29/0.47 => ! [F: nat > A,N3: nat,N4: nat] :
% 0.29/0.47 ( ! [N: nat] : ( ord_less_eq @ A @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 0.29/0.47 => ( ( ord_less_eq @ nat @ N3 @ N4 )
% 0.29/0.47 => ( ord_less_eq @ A @ ( F @ N4 ) @ ( F @ N3 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lift_Suc_antimono_le
% 0.29/0.47 thf(fact_243_lift__Suc__mono__le,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( order @ A )
% 0.29/0.47 => ! [F: nat > A,N3: nat,N4: nat] :
% 0.29/0.47 ( ! [N: nat] : ( ord_less_eq @ A @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 0.29/0.47 => ( ( ord_less_eq @ nat @ N3 @ N4 )
% 0.29/0.47 => ( ord_less_eq @ A @ ( F @ N3 ) @ ( F @ N4 ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % lift_Suc_mono_le
% 0.29/0.47 thf(fact_244_zero__le,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( canoni770627133id_add @ A )
% 0.29/0.47 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 0.29/0.47
% 0.29/0.47 % zero_le
% 0.29/0.47 thf(fact_245_le__numeral__extra_I3_J,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord1659791738miring @ A )
% 0.29/0.47 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % le_numeral_extra(3)
% 0.29/0.47 thf(fact_246_less__numeral__extra_I4_J,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord1659791738miring @ A )
% 0.29/0.47 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_numeral_extra(4)
% 0.29/0.47 thf(fact_247_of__nat__mono,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linord1659791738miring @ A )
% 0.29/0.47 => ! [I: nat,J: nat] :
% 0.29/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.29/0.47 => ( ord_less_eq @ A @ ( semiring_1_of_nat @ A @ I ) @ ( semiring_1_of_nat @ A @ J ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % of_nat_mono
% 0.29/0.47 thf(fact_248_less__minus__one__simps_I4_J,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linordered_idom @ A )
% 0.29/0.47 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_minus_one_simps(4)
% 0.29/0.47 thf(fact_249_less__minus__one__simps_I2_J,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( linordered_idom @ A )
% 0.29/0.47 => ( ord_less @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( one_one @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % less_minus_one_simps(2)
% 0.29/0.47 thf(fact_250_zero__neq__neg__one,axiom,
% 0.29/0.47 ! [A: $tType] :
% 0.29/0.47 ( ( ring_char_0 @ A )
% 0.29/0.47 => ( ( zero_zero @ A )
% 0.29/0.47 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 % zero_neq_neg_one
% 0.29/0.47
% 0.29/0.47 % Type constructors (42)
% 0.29/0.47 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 0.29/0.47 ! [A14: $tType,A15: $tType] :
% 0.29/0.47 ( ( boolean_algebra @ A15 )
% 0.29/0.47 => ( boolean_algebra @ ( A14 > A15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.29/0.47 ! [A14: $tType,A15: $tType] :
% 0.29/0.47 ( ( order @ A15 )
% 0.29/0.47 => ( order @ ( A14 > A15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.29/0.47 ! [A14: $tType,A15: $tType] :
% 0.29/0.47 ( ( ord @ A15 )
% 0.29/0.47 => ( ord @ ( A14 > A15 ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Rings_Olinordered__nonzero__semiring,axiom,
% 0.29/0.47 linord1659791738miring @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Groups_Olinordered__ab__group__add,axiom,
% 0.29/0.47 linord219039673up_add @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Groups_Oordered__ab__group__add,axiom,
% 0.29/0.47 ordered_ab_group_add @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Rings_Olinordered__idom,axiom,
% 0.29/0.47 linordered_idom @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Nat_Osemiring__char__0,axiom,
% 0.29/0.47 semiring_char_0 @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Orderings_Olinorder,axiom,
% 0.29/0.47 linorder @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Rings_Osemiring__1,axiom,
% 0.29/0.47 semiring_1 @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Groups_Ogroup__add,axiom,
% 0.29/0.47 group_add @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Orderings_Oorder_1,axiom,
% 0.29/0.47 order @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Nat_Oring__char__0,axiom,
% 0.29/0.47 ring_char_0 @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Orderings_Oord_2,axiom,
% 0.29/0.47 ord @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Rings_Oring__1,axiom,
% 0.29/0.47 ring_1 @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Groups_Ozero,axiom,
% 0.29/0.47 zero @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Int_Oint___Groups_Oone,axiom,
% 0.29/0.47 one @ int ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.29/0.47 canoni770627133id_add @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_3,axiom,
% 0.29/0.47 linord1659791738miring @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.29/0.47 wellorder @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Nat_Osemiring__char__0_4,axiom,
% 0.29/0.47 semiring_char_0 @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Orderings_Olinorder_5,axiom,
% 0.29/0.47 linorder @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Rings_Osemiring__1_6,axiom,
% 0.29/0.47 semiring_1 @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Orderings_Oorder_7,axiom,
% 0.29/0.47 order @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Orderings_Oord_8,axiom,
% 0.29/0.47 ord @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Ozero_9,axiom,
% 0.29/0.47 zero @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Groups_Oone_10,axiom,
% 0.29/0.47 one @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 0.29/0.47 size @ nat ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_11,axiom,
% 0.29/0.47 ! [A14: $tType] : ( boolean_algebra @ ( set @ A14 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Set_Oset___Orderings_Oorder_12,axiom,
% 0.29/0.47 ! [A14: $tType] : ( order @ ( set @ A14 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Set_Oset___Orderings_Oord_13,axiom,
% 0.29/0.47 ! [A14: $tType] : ( ord @ ( set @ A14 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_14,axiom,
% 0.29/0.47 boolean_algebra @ $o ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder_15,axiom,
% 0.29/0.47 linorder @ $o ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_16,axiom,
% 0.29/0.47 order @ $o ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_HOL_Obool___Orderings_Oord_17,axiom,
% 0.29/0.47 ord @ $o ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_List_Olist___Nat_Osize_18,axiom,
% 0.29/0.47 ! [A14: $tType] : ( size @ ( list @ A14 ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Product__Type_Ounit___Lattices_Oboolean__algebra_19,axiom,
% 0.29/0.47 boolean_algebra @ product_unit ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_20,axiom,
% 0.29/0.47 wellorder @ product_unit ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_21,axiom,
% 0.29/0.47 linorder @ product_unit ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Product__Type_Ounit___Orderings_Oorder_22,axiom,
% 0.29/0.47 order @ product_unit ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_Product__Type_Ounit___Orderings_Oord_23,axiom,
% 0.29/0.47 ord @ product_unit ).
% 0.29/0.47
% 0.29/0.47 thf(tcon_AsynchronousSystem_Omessage___Nat_Osize_24,axiom,
% 0.29/0.47 ! [A14: $tType,A15: $tType] : ( size @ ( message @ A14 @ A15 ) ) ).
% 0.29/0.47
% 0.29/0.47 % Conjectures (1)
% 0.29/0.47 thf(conj_0,conjecture,
% 0.29/0.47 prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ m ) @ ( fe @ na ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 2.80/1.51 ---- Embedded in THF ---
% 2.80/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.80/1.51 %%% Generated on Tue Feb 24 08:24:42 EST 2026
% 2.80/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 2.80/1.51 %%% Logic specification used:
% 2.80/1.51 %%% thf(spec, logic, $$dhol).
% 2.80/1.51
% 2.80/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.W0i8NEZydw/DTF2DTF29027.p
% 2.80/1.51 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext, type, configuration_ext: ($tType > ($tType > ($tType > ($tType > $tType))))).
% 2.80/1.51 thf(ty_t_AsynchronousSystem_OmessageValue, type, messageValue: ($tType > $tType)).
% 2.80/1.51 thf(ty_t_AsynchronousSystem_Omessage, type, message: ($tType > ($tType > $tType))).
% 2.80/1.51 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 2.80/1.51 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.80/1.51 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.80/1.51 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.80/1.51 thf(ty_t_Int_Oint, type, int: $tType).
% 2.80/1.51 thf(ty_tf_v, type, v: $tType).
% 2.80/1.51 thf(ty_tf_s, type, s: $tType).
% 2.80/1.51 thf(ty_tf_p, type, p: $tType).
% 2.80/1.51 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Nat_Osize, type, size: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Rings_Oring__1, type, ring_1: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Nat_Oring__char__0, type, ring_char_0: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Rings_Osemiring__1, type, semiring_1: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Nat_Osemiring__char__0, type, semiring_char_0: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Lattices_Oboolean__algebra, type, boolean_algebra: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Groups_Olinordered__ab__group__add, type, linord219039673up_add: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 2.80/1.51 thf(sy_c_BNF__Greatest__Fixpoint_Oshift, type, bNF_Greatest_shift: (!> [A:$tType,B:$tType]: ((((list @ A) > B) > (A > ((list @ A) > B)))))).
% 2.80/1.51 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus, type, fLPThe1922692578sensus: (!> [P:$tType,S:$tType,V:$tType]: (((P > (S > ((messageValue @ V) > S))) > ((P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))) > ((P > S) > $o)))))).
% 2.80/1.51 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus_OinfiniteExecutionCfg, type, fLPThe137922386ionCfg: (!> [P:$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))))))))).
% 2.80/1.51 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus_OinfiniteExecutionMsg, type, fLPThe221390223ionMsg: (!> [P:$tType,V:$tType,S:$tType]: ((((((configuration_ext @ P) @ V) @ S) @ product_unit) > (((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)))) > (((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((message @ P) @ V)))) > (nat > (list @ ((message @ P) @ V))))))))).
% 2.80/1.51 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpSystem_OterminationFLP, type, fLPThe2031355932ionFLP: (!> [P:$tType,S:$tType,V:$tType]: (((P > (S > ((messageValue @ V) > S))) > ((P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))) > ((P > S) > ((nat > (list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit))) > ((nat > (list @ ((message @ P) @ V))) > $o)))))))).
% 2.80/1.51 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 2.80/1.51 thf(sy_c_Groups_Ouminus__class_Ouminus, type, uminus_uminus: (!> [A:$tType]: ((A > A)))).
% 2.80/1.51 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.80/1.51 thf(sy_c_Int_Onat, type, nat2: (int > nat)).
% 2.80/1.51 thf(sy_c_Int_Oring__1__class_Oof__int, type, ring_1_of_int: (!> [A:$tType]: ((int > A)))).
% 2.80/1.51 thf(sy_c_ListUtilities_OprefixList, type, prefixList: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.80/1.51 thf(sy_c_List_Ogen__length, type, gen_length: (!> [A:$tType]: ((nat > ((list @ A) > nat))))).
% 2.80/1.51 thf(sy_c_List_Oinsert, type, insert: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.80/1.51 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.80/1.51 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.80/1.51 thf(sy_c_List_Olist__ex1, type, list_ex1: (!> [A:$tType]: (((A > $o) > ((list @ A) > $o))))).
% 2.80/1.51 thf(sy_c_List_On__lists, type, n_lists: (!> [A:$tType]: ((nat > ((list @ A) > (list @ (list @ A))))))).
% 2.80/1.51 thf(sy_c_List_Onths, type, nths: (!> [A:$tType]: (((list @ A) > ((set @ nat) > (list @ A)))))).
% 2.80/1.51 thf(sy_c_List_Oproduct__lists, type, product_lists: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 2.80/1.51 thf(sy_c_List_Osubseqs, type, subseqs: (!> [A:$tType]: (((list @ A) > (list @ (list @ A)))))).
% 2.80/1.51 thf(sy_c_Nat_OSuc, type, suc: (nat > nat)).
% 2.80/1.51 thf(sy_c_Nat_Osemiring__1__class_Oof__nat, type, semiring_1_of_nat: (!> [A:$tType]: ((nat > A)))).
% 2.80/1.51 thf(sy_c_Nat_Osize__class_Osize, type, size_size: (!> [A:$tType]: ((A > nat)))).
% 2.80/1.51 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.80/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.80/1.51 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.80/1.51 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.80/1.51 thf(sy_v_cfg____, type, cfg: ((((configuration_ext @ p) @ v) @ s) @ product_unit)).
% 2.80/1.51 thf(sy_v_fe____, type, fe: (nat > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))).
% 2.80/1.51 thf(sy_v_m____, type, m: nat).
% 2.80/1.51 thf(sy_v_n____, type, n: nat).
% 2.80/1.51 thf(sy_v_na____, type, na: nat).
% 2.80/1.51 thf(fact_0__092_060open_062m_A_060_An_092_060close_062, axiom, (((ord_less @ nat) @ m) @ na)).
% 2.80/1.51 thf(fact_1_MLessN, axiom, (((ord_less @ nat) @ m) @ n)).
% 2.80/1.51 thf(fact_2_IA_I1_J, axiom, ((((ord_less @ nat) @ m) @ na) => (((prefixList @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ m)) @ (fe @ na)))).
% 2.80/1.51 thf(fact_3__092_060open_062m_A_061_An_A_092_060or_062_Am_A_060_An_092_060close_062, axiom, ((m = na) | (((ord_less @ nat) @ m) @ na))).
% 2.80/1.51 thf(fact_4_IA_I2_J, axiom, (((ord_less @ nat) @ m) @ (suc @ na))).
% 2.80/1.51 thf(fact_5_PrefixListTransitive, axiom, (! [A:$tType,L1:(list @ A),L2:(list @ A),L3:(list @ A)]: (((((prefixList @ A) @ L1) @ L2) => ((((prefixList @ A) @ L2) @ L3) => (((prefixList @ A) @ L1) @ L3)))))).
% 2.80/1.51 thf(fact_6_flpSystem_OterminationFLP_Ocong, axiom, (! [V:$tType,S:$tType,P:$tType]: (((((fLPThe2031355932ionFLP @ P) @ S) @ V) = (((fLPThe2031355932ionFLP @ P) @ S) @ V))))).
% 2.80/1.51 thf(fact_7_FE_I1_J, axiom, ((fe @ (zero_zero @ nat)) = (((cons @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ cfg) @ (nil @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))))).
% 2.80/1.51 thf(fact_8_prefixList_Ointros_I2_J, axiom, (! [A:$tType,Xa:(list @ A),Xb:(list @ A),X:A]: (((((prefixList @ A) @ Xa) @ Xb) => (((prefixList @ A) @ (((cons @ A) @ X) @ Xa)) @ (((cons @ A) @ X) @ Xb)))))).
% 2.80/1.51 thf(fact_9_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)))))).
% 2.80/1.51 thf(fact_10_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J, axiom, (! [P2:(((((configuration_ext @ p) @ v) @ s) @ product_unit) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))) > (nat > $o)))),Q:(((((configuration_ext @ p) @ v) @ s) @ product_unit) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))) > (nat > $o)))),A4:((((configuration_ext @ p) @ v) @ s) @ product_unit),A5:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),A6:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),A7:nat]: (((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v))))]: (((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ (zero_zero @ nat)))) => ((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),N:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => ((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N)))))) => ((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v))))]: (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (zero_zero @ nat)))) => ((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),N:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => ((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N)))))) => ((((Q @ A4) @ A5) @ A6) @ A7)))))))).
% 2.80/1.51 thf(fact_11_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J, axiom, (! [P2:(((((configuration_ext @ p) @ v) @ s) @ product_unit) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))) > (nat > $o)))),Q:(((((configuration_ext @ p) @ v) @ s) @ product_unit) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))) > (((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))) > (nat > $o)))),A0:((((configuration_ext @ p) @ v) @ s) @ product_unit),A1:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),A2:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),A3:nat]: (((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v))))]: (((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ (zero_zero @ nat)))) => ((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),N:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => ((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N)))))) => ((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v))))]: (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (zero_zero @ nat)))) => ((! [Cfg:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v)))),N:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => ((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N)))))) => ((((P2 @ A0) @ A1) @ A2) @ A3)))))))).
% 2.80/1.51 thf(fact_12_prefixList_Ointros_I1_J, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((prefixList @ A) @ (nil @ A)) @ (((cons @ A) @ X) @ Xs))))).
% 2.80/1.51 thf(fact_13_prefixList_Ocases, axiom, (! [A:$tType,A1:(list @ A),A2:(list @ A)]: (((((prefixList @ A) @ A1) @ A2) => (((A1 = (nil @ A)) => (! [X2:A,Xs2:(list @ A)]: ((A2 != (((cons @ A) @ X2) @ Xs2))))) => (~ ((! [Xa2:(list @ A),Xb2:(list @ A),X2:A]: (((A1 = (((cons @ A) @ X2) @ Xa2)) => ((A2 = (((cons @ A) @ X2) @ Xb2)) => (~ ((((prefixList @ A) @ Xa2) @ Xb2)))))))))))))).
% 2.80/1.51 thf(fact_14_prefixList_Osimps, axiom, (! [A:$tType]: (((prefixList @ A) = (^ [A12:(list @ A),A22:(list @ A)]: (((? [X3:A,Xs3:(list @ A)]: (((A12 = (nil @ A)) & (A22 = (((cons @ A) @ X3) @ Xs3))))) | (? [Xa3:(list @ A),Xb3:(list @ A),X3:A]: (((A12 = (((cons @ A) @ X3) @ Xa3)) & ((A22 = (((cons @ A) @ X3) @ Xb3)) & (((prefixList @ A) @ Xa3) @ Xb3)))))))))))).
% 2.80/1.51 thf(fact_15_prefixList_Oinducts, axiom, (! [A:$tType,X1:(list @ A),X22:(list @ A),P2:((list @ A) > ((list @ A) > $o))]: (((((prefixList @ A) @ X1) @ X22) => ((! [X2:A,Xs2:(list @ A)]: (((P2 @ (nil @ A)) @ (((cons @ A) @ X2) @ Xs2)))) => ((! [Xa2:(list @ A),Xb2:(list @ A),X2:A]: (((((prefixList @ A) @ Xa2) @ Xb2) => (((P2 @ Xa2) @ Xb2) => ((P2 @ (((cons @ A) @ X2) @ Xa2)) @ (((cons @ A) @ X2) @ Xb2)))))) => ((P2 @ X1) @ X22))))))).
% 2.80/1.51 thf(fact_16_NatPredicateTippingPoint, axiom, (! [N2:nat,Pr:(nat > $o)]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N2) => ((Pr @ (zero_zero @ nat)) => ((~ ((Pr @ N2))) => (? [N:nat]: (((((ord_less @ nat) @ N) @ N2) & ((Pr @ N) & (~ ((Pr @ (suc @ N)))))))))))))).
% 2.80/1.51 thf(fact_17_infiniteExecutionCfg_Osimps_I1_J, axiom, (! [Cfg2:((((configuration_ext @ p) @ v) @ s) @ product_unit),FStepCfg2:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))),FStepMsg2:((list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) > ((list @ ((message @ p) @ v)) > (list @ ((message @ p) @ v))))]: (((((((((fLPThe137922386ionCfg @ p) @ v) @ s) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ (zero_zero @ nat)) = (((cons @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ Cfg2) @ (nil @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))))))).
% 2.80/1.51 thf(fact_18_length__greater__0__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ ((size_size @ (list @ A)) @ Xs)) = (Xs != (nil @ A)))))).
% 2.80/1.51 thf(fact_19_length__0__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((size_size @ (list @ A)) @ Xs) = (zero_zero @ nat)) = (Xs = (nil @ A)))))).
% 2.80/1.51 thf(fact_20_less__Suc0, axiom, (! [N3:nat]: (((((ord_less @ nat) @ N3) @ (suc @ (zero_zero @ nat))) = (N3 = (zero_zero @ nat)))))).
% 2.80/1.51 thf(fact_21_zero__less__Suc, axiom, (! [N3:nat]: ((((ord_less @ nat) @ (zero_zero @ nat)) @ (suc @ N3))))).
% 2.80/1.51 thf(fact_22_lessI, axiom, (! [N3:nat]: ((((ord_less @ nat) @ N3) @ (suc @ N3))))).
% 2.80/1.51 thf(fact_23_Suc__mono, axiom, (! [M:nat,N3:nat]: (((((ord_less @ nat) @ M) @ N3) => (((ord_less @ nat) @ (suc @ M)) @ (suc @ N3)))))).
% 2.80/1.51 thf(fact_24_Suc__less__eq, axiom, (! [M:nat,N3:nat]: (((((ord_less @ nat) @ (suc @ M)) @ (suc @ N3)) = (((ord_less @ nat) @ M) @ N3))))).
% 2.80/1.51 thf(fact_25_neq0__conv, axiom, (! [N3:nat]: (((N3 != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ N3))))).
% 2.80/1.51 thf(fact_26_less__nat__zero__code, axiom, (! [N3:nat]: ((~ ((((ord_less @ nat) @ N3) @ (zero_zero @ nat))))))).
% 2.80/1.51 thf(fact_27_bot__nat__0_Onot__eq__extremum, axiom, (! [A8:nat]: (((A8 != (zero_zero @ nat)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ A8))))).
% 2.80/1.51 thf(fact_28_list_Oinject, axiom, (! [A:$tType,X21:A,X222:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X222) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X222 = Y22)))))).
% 2.80/1.51 thf(fact_29_old_Onat_Oinject, axiom, (! [Nat:nat,Nat2:nat]: ((((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))).
% 2.80/1.51 thf(fact_30_nat_Oinject, axiom, (! [X22:nat,Y2:nat]: ((((suc @ X22) = (suc @ Y2)) = (X22 = Y2))))).
% 2.80/1.51 thf(fact_31_measure__induct__rule, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F:(A > B),P2:(A > $o),A8:A]: (((! [X2:A]: (((! [Y:A]: (((((ord_less @ B) @ (F @ Y)) @ (F @ X2)) => (P2 @ Y)))) => (P2 @ X2)))) => (P2 @ A8)))))))).
% 2.80/1.51 thf(fact_32_measure__induct, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F:(A > B),P2:(A > $o),A8:A]: (((! [X2:A]: (((! [Y:A]: (((((ord_less @ B) @ (F @ Y)) @ (F @ X2)) => (P2 @ Y)))) => (P2 @ X2)))) => (P2 @ A8)))))))).
% 2.80/1.51 thf(fact_33_not__Cons__self2, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((cons @ A) @ X) @ Xs) != Xs)))).
% 2.80/1.51 thf(fact_34_n__not__Suc__n, axiom, (! [N3:nat]: ((N3 != (suc @ N3))))).
% 2.80/1.51 thf(fact_35_Suc__inject, axiom, (! [X:nat,Y3:nat]: ((((suc @ X) = (suc @ Y3)) => (X = Y3))))).
% 2.80/1.51 thf(fact_36_infinite__descent__measure, axiom, (! [A:$tType,P2:(A > $o),V2:(A > nat),X:A]: (((! [X2:A]: (((~ ((P2 @ X2))) => (? [Y:A]: (((((ord_less @ nat) @ (V2 @ Y)) @ (V2 @ X2)) & (~ ((P2 @ Y))))))))) => (P2 @ X))))).
% 2.80/1.51 thf(fact_37_linorder__neqE__nat, axiom, (! [X:nat,Y3:nat]: (((X != Y3) => ((~ ((((ord_less @ nat) @ X) @ Y3))) => (((ord_less @ nat) @ Y3) @ X)))))).
% 2.80/1.51 thf(fact_38_infinite__descent, axiom, (! [P2:(nat > $o),N3:nat]: (((! [N:nat]: (((~ ((P2 @ N))) => (? [M2:nat]: (((((ord_less @ nat) @ M2) @ N) & (~ ((P2 @ M2))))))))) => (P2 @ N3))))).
% 2.80/1.51 thf(fact_39_nat__less__induct, axiom, (! [P2:(nat > $o),N3:nat]: (((! [N:nat]: (((! [M2:nat]: (((((ord_less @ nat) @ M2) @ N) => (P2 @ M2)))) => (P2 @ N)))) => (P2 @ N3))))).
% 2.80/1.51 thf(fact_40_less__irrefl__nat, axiom, (! [N3:nat]: ((~ ((((ord_less @ nat) @ N3) @ N3)))))).
% 2.80/1.51 thf(fact_41_less__not__refl3, axiom, (! [S2:nat,T:nat]: (((((ord_less @ nat) @ S2) @ T) => (S2 != T))))).
% 2.80/1.51 thf(fact_42_less__not__refl2, axiom, (! [N3:nat,M:nat]: (((((ord_less @ nat) @ N3) @ M) => (M != N3))))).
% 2.80/1.51 thf(fact_43_mem__Collect__eq, axiom, (! [A:$tType,A8:A,P2:(A > $o)]: (((((member @ A) @ A8) @ ((collect @ A) @ P2)) = (P2 @ A8))))).
% 2.80/1.51 thf(fact_44_Collect__mem__eq, axiom, (! [A:$tType,A9:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A9)))) = A9)))).
% 2.80/1.51 thf(fact_45_Collect__cong, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P2 @ X2) = (Q @ X2)))) => (((collect @ A) @ P2) = ((collect @ A) @ Q)))))).
% 2.80/1.51 thf(fact_46_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X2:A]: (((F @ X2) = (G @ X2)))) => (F = G))))).
% 2.80/1.51 thf(fact_47_less__not__refl, axiom, (! [N3:nat]: ((~ ((((ord_less @ nat) @ N3) @ N3)))))).
% 2.80/1.51 thf(fact_48_nat__neq__iff, axiom, (! [M:nat,N3:nat]: (((M != N3) = ((((ord_less @ nat) @ M) @ N3) | (((ord_less @ nat) @ N3) @ M)))))).
% 2.80/1.51 thf(fact_49_size__neq__size__imp__neq, axiom, (! [A:$tType]: (((size @ A) => (! [X:A,Y3:A]: (((((size_size @ A) @ X) != ((size_size @ A) @ Y3)) => (X != Y3)))))))).
% 2.80/1.51 thf(fact_50_neq__if__length__neq, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((size_size @ (list @ A)) @ Xs) != ((size_size @ (list @ A)) @ Ys)) => (Xs != Ys))))).
% 2.80/1.51 thf(fact_51_Ex__list__of__length, axiom, (! [A:$tType,N3:nat]: ((? [Xs2:(list @ A)]: ((((size_size @ (list @ A)) @ Xs2) = N3)))))).
% 2.80/1.51 thf(fact_52_not0__implies__Suc, axiom, (! [N3:nat]: (((N3 != (zero_zero @ nat)) => (? [M3:nat]: ((N3 = (suc @ M3)))))))).
% 2.80/1.51 thf(fact_53_old_Onat_Oinducts, axiom, (! [P2:(nat > $o),Nat:nat]: (((P2 @ (zero_zero @ nat)) => ((! [Nat3:nat]: (((P2 @ Nat3) => (P2 @ (suc @ Nat3))))) => (P2 @ Nat)))))).
% 2.80/1.51 thf(fact_54_old_Onat_Oexhaust, axiom, (! [Y3:nat]: (((Y3 != (zero_zero @ nat)) => (~ ((! [Nat3:nat]: ((Y3 != (suc @ Nat3)))))))))).
% 2.80/1.51 thf(fact_55_Zero__not__Suc, axiom, (! [M:nat]: (((zero_zero @ nat) != (suc @ M))))).
% 2.80/1.51 thf(fact_56_Zero__neq__Suc, axiom, (! [M:nat]: (((zero_zero @ nat) != (suc @ M))))).
% 2.80/1.51 thf(fact_57_Suc__neq__Zero, axiom, (! [M:nat]: (((suc @ M) != (zero_zero @ nat))))).
% 2.80/1.51 thf(fact_58_zero__induct, axiom, (! [P2:(nat > $o),K:nat]: (((P2 @ K) => ((! [N:nat]: (((P2 @ (suc @ N)) => (P2 @ N)))) => (P2 @ (zero_zero @ nat))))))).
% 2.80/1.51 thf(fact_59_diff__induct, axiom, (! [P2:(nat > (nat > $o)),M:nat,N3:nat]: (((! [X2:nat]: (((P2 @ X2) @ (zero_zero @ nat)))) => ((! [Y4:nat]: (((P2 @ (zero_zero @ nat)) @ (suc @ Y4)))) => ((! [X2:nat,Y4:nat]: ((((P2 @ X2) @ Y4) => ((P2 @ (suc @ X2)) @ (suc @ Y4))))) => ((P2 @ M) @ N3))))))).
% 2.80/1.51 thf(fact_60_nat__induct, axiom, (! [P2:(nat > $o),N3:nat]: (((P2 @ (zero_zero @ nat)) => ((! [N:nat]: (((P2 @ N) => (P2 @ (suc @ N))))) => (P2 @ N3)))))).
% 2.80/1.51 thf(fact_61_nat_OdiscI, axiom, (! [Nat:nat,X22:nat]: (((Nat = (suc @ X22)) => (Nat != (zero_zero @ nat)))))).
% 2.80/1.51 thf(fact_62_old_Onat_Odistinct_I1_J, axiom, (! [Nat2:nat]: (((zero_zero @ nat) != (suc @ Nat2))))).
% 2.80/1.51 thf(fact_63_old_Onat_Odistinct_I2_J, axiom, (! [Nat4:nat]: (((suc @ Nat4) != (zero_zero @ nat))))).
% 2.80/1.51 thf(fact_64_nat_Odistinct_I1_J, axiom, (! [X22:nat]: (((zero_zero @ nat) != (suc @ X22))))).
% 2.80/1.51 thf(fact_65_infinite__descent0__measure, axiom, (! [A:$tType,V2:(A > nat),P2:(A > $o),X:A]: (((! [X2:A]: ((((V2 @ X2) = (zero_zero @ nat)) => (P2 @ X2)))) => ((! [X2:A]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (V2 @ X2)) => ((~ ((P2 @ X2))) => (? [Y:A]: (((((ord_less @ nat) @ (V2 @ Y)) @ (V2 @ X2)) & (~ ((P2 @ Y)))))))))) => (P2 @ X)))))).
% 2.80/1.51 thf(fact_66_bot__nat__0_Oextremum__strict, axiom, (! [A8:nat]: ((~ ((((ord_less @ nat) @ A8) @ (zero_zero @ nat))))))).
% 2.80/1.51 thf(fact_67_infinite__descent0, axiom, (! [P2:(nat > $o),N3:nat]: (((P2 @ (zero_zero @ nat)) => ((! [N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => ((~ ((P2 @ N))) => (? [M2:nat]: (((((ord_less @ nat) @ M2) @ N) & (~ ((P2 @ M2)))))))))) => (P2 @ N3)))))).
% 2.80/1.51 thf(fact_68_gr__implies__not0, axiom, (! [M:nat,N3:nat]: (((((ord_less @ nat) @ M) @ N3) => (N3 != (zero_zero @ nat)))))).
% 2.80/1.51 thf(fact_69_less__zeroE, axiom, (! [N3:nat]: ((~ ((((ord_less @ nat) @ N3) @ (zero_zero @ nat))))))).
% 2.80/1.51 thf(fact_70_not__less0, axiom, (! [N3:nat]: ((~ ((((ord_less @ nat) @ N3) @ (zero_zero @ nat))))))).
% 2.80/1.51 thf(fact_71_not__gr0, axiom, (! [N3:nat]: (((~ ((((ord_less @ nat) @ (zero_zero @ nat)) @ N3))) = (N3 = (zero_zero @ nat)))))).
% 2.80/1.51 thf(fact_72_gr0I, axiom, (! [N3:nat]: (((N3 != (zero_zero @ nat)) => (((ord_less @ nat) @ (zero_zero @ nat)) @ N3))))).
% 2.80/1.51 thf(fact_73_not__less__less__Suc__eq, axiom, (! [N3:nat,M:nat]: (((~ ((((ord_less @ nat) @ N3) @ M))) => ((((ord_less @ nat) @ N3) @ (suc @ M)) = (N3 = M)))))).
% 2.80/1.51 thf(fact_74_strict__inc__induct, axiom, (! [I:nat,J:nat,P2:(nat > $o)]: (((((ord_less @ nat) @ I) @ J) => ((! [I2:nat]: (((J = (suc @ I2)) => (P2 @ I2)))) => ((! [I2:nat]: (((((ord_less @ nat) @ I2) @ J) => ((P2 @ (suc @ I2)) => (P2 @ I2))))) => (P2 @ I))))))).
% 2.80/1.51 thf(fact_75_less__Suc__induct, axiom, (! [I:nat,J:nat,P2:(nat > (nat > $o))]: (((((ord_less @ nat) @ I) @ J) => ((! [I2:nat]: (((P2 @ I2) @ (suc @ I2)))) => ((! [I2:nat,J2:nat,K2:nat]: (((((ord_less @ nat) @ I2) @ J2) => ((((ord_less @ nat) @ J2) @ K2) => (((P2 @ I2) @ J2) => (((P2 @ J2) @ K2) => ((P2 @ I2) @ K2))))))) => ((P2 @ I) @ J))))))).
% 2.80/1.51 thf(fact_76_less__trans__Suc, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ I) @ J) => ((((ord_less @ nat) @ J) @ K) => (((ord_less @ nat) @ (suc @ I)) @ K)))))).
% 2.80/1.51 thf(fact_77_Suc__less__SucD, axiom, (! [M:nat,N3:nat]: (((((ord_less @ nat) @ (suc @ M)) @ (suc @ N3)) => (((ord_less @ nat) @ M) @ N3))))).
% 2.80/1.51 thf(fact_78_less__antisym, axiom, (! [N3:nat,M:nat]: (((~ ((((ord_less @ nat) @ N3) @ M))) => ((((ord_less @ nat) @ N3) @ (suc @ M)) => (M = N3)))))).
% 2.80/1.51 thf(fact_79_Suc__less__eq2, axiom, (! [N3:nat,M:nat]: (((((ord_less @ nat) @ (suc @ N3)) @ M) = (? [M4:nat]: (((M = (suc @ M4)) & (((ord_less @ nat) @ N3) @ M4)))))))).
% 2.80/1.51 thf(fact_80_All__less__Suc, axiom, (! [N3:nat,P2:(nat > $o)]: (((! [I3:nat]: (((((ord_less @ nat) @ I3) @ (suc @ N3)) => (P2 @ I3)))) = ((P2 @ N3) & (! [I3:nat]: (((((ord_less @ nat) @ I3) @ N3) => (P2 @ I3))))))))).
% 2.80/1.51 thf(fact_81_not__less__eq, axiom, (! [M:nat,N3:nat]: (((~ ((((ord_less @ nat) @ M) @ N3))) = (((ord_less @ nat) @ N3) @ (suc @ M)))))).
% 2.80/1.51 thf(fact_82_less__Suc__eq, axiom, (! [M:nat,N3:nat]: (((((ord_less @ nat) @ M) @ (suc @ N3)) = ((((ord_less @ nat) @ M) @ N3) | (M = N3)))))).
% 2.80/1.51 thf(fact_83_Ex__less__Suc, axiom, (! [N3:nat,P2:(nat > $o)]: (((? [I3:nat]: (((((ord_less @ nat) @ I3) @ (suc @ N3)) & (P2 @ I3)))) = ((P2 @ N3) | (? [I3:nat]: (((((ord_less @ nat) @ I3) @ N3) & (P2 @ I3))))))))).
% 2.80/1.51 thf(fact_84_less__SucI, axiom, (! [M:nat,N3:nat]: (((((ord_less @ nat) @ M) @ N3) => (((ord_less @ nat) @ M) @ (suc @ N3)))))).
% 2.80/1.51 thf(fact_85_less__SucE, axiom, (! [M:nat,N3:nat]: (((((ord_less @ nat) @ M) @ (suc @ N3)) => ((~ ((((ord_less @ nat) @ M) @ N3))) => (M = N3)))))).
% 2.80/1.51 thf(fact_86_Suc__lessI, axiom, (! [M:nat,N3:nat]: (((((ord_less @ nat) @ M) @ N3) => (((suc @ M) != N3) => (((ord_less @ nat) @ (suc @ M)) @ N3)))))).
% 2.80/1.51 thf(fact_87_Suc__lessE, axiom, (! [I:nat,K:nat]: (((((ord_less @ nat) @ (suc @ I)) @ K) => (~ ((! [J2:nat]: (((((ord_less @ nat) @ I) @ J2) => (K != (suc @ J2))))))))))).
% 2.80/1.51 thf(fact_88_Suc__lessD, axiom, (! [M:nat,N3:nat]: (((((ord_less @ nat) @ (suc @ M)) @ N3) => (((ord_less @ nat) @ M) @ N3))))).
% 2.80/1.51 thf(fact_89_Nat_OlessE, axiom, (! [I:nat,K:nat]: (((((ord_less @ nat) @ I) @ K) => ((K != (suc @ I)) => (~ ((! [J2:nat]: (((((ord_less @ nat) @ I) @ J2) => (K != (suc @ J2)))))))))))).
% 2.80/1.51 thf(fact_90_strict__sorted_Oinduct, axiom, (! [A:$tType]: (((linorder @ A) => (! [P2:((list @ A) > $o),A0:(list @ A)]: (((P2 @ (nil @ A)) => ((! [X2:A,Ys2:(list @ A)]: (((P2 @ Ys2) => (P2 @ (((cons @ A) @ X2) @ Ys2))))) => (P2 @ A0))))))))).
% 2.80/1.51 thf(fact_91_strict__sorted_Ocases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:(list @ A)]: (((X != (nil @ A)) => (~ ((! [X2:A,Ys2:(list @ A)]: ((X != (((cons @ A) @ X2) @ Ys2))))))))))))).
% 2.80/1.51 thf(fact_92_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P2:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A2:(list @ B)]: (((! [F2:(A > B),X_1:(list @ B)]: ((((P2 @ F2) @ (nil @ A)) @ X_1))) => ((! [F2:(A > B),A10:A,As:(list @ A),Bs:(list @ B)]: (((((P2 @ F2) @ As) @ (((cons @ B) @ (F2 @ A10)) @ Bs)) => (((P2 @ F2) @ (((cons @ A) @ A10) @ As)) @ Bs)))) => (((P2 @ A0) @ A1) @ A2)))))).
% 2.80/1.51 thf(fact_93_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P2:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X2:A]: ((P2 @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X2:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P2 @ Xs2) => (P2 @ (((cons @ A) @ X2) @ Xs2)))))) => (P2 @ Xs))))))).
% 2.80/1.51 thf(fact_94_successively_Oinduct, axiom, (! [A:$tType,P2:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P3:(A > (A > $o))]: (((P2 @ P3) @ (nil @ A)))) => ((! [P3:(A > (A > $o)),X2:A]: (((P2 @ P3) @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [P3:(A > (A > $o)),X2:A,Y4:A,Xs2:(list @ A)]: ((((P2 @ P3) @ (((cons @ A) @ Y4) @ Xs2)) => ((P2 @ P3) @ (((cons @ A) @ X2) @ (((cons @ A) @ Y4) @ Xs2)))))) => ((P2 @ A0) @ A1))))))).
% 2.80/1.51 thf(fact_95_arg__min__list_Oinduct, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [P2:((A > B) > ((list @ A) > $o)),A0:(A > B),A1:(list @ A)]: (((! [F2:(A > B),X2:A]: (((P2 @ F2) @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [F2:(A > B),X2:A,Y4:A,Zs:(list @ A)]: ((((P2 @ F2) @ (((cons @ A) @ Y4) @ Zs)) => ((P2 @ F2) @ (((cons @ A) @ X2) @ (((cons @ A) @ Y4) @ Zs)))))) => ((! [A10:(A > B)]: (((P2 @ A10) @ (nil @ A)))) => ((P2 @ A0) @ A1)))))))))).
% 2.80/1.51 thf(fact_96_remdups__adj_Oinduct, axiom, (! [A:$tType,P2:((list @ A) > $o),A0:(list @ A)]: (((P2 @ (nil @ A)) => ((! [X2:A]: ((P2 @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X2:A,Y4:A,Xs2:(list @ A)]: ((((X2 = Y4) => (P2 @ (((cons @ A) @ X2) @ Xs2))) => (((X2 != Y4) => (P2 @ (((cons @ A) @ Y4) @ Xs2))) => (P2 @ (((cons @ A) @ X2) @ (((cons @ A) @ Y4) @ Xs2))))))) => (P2 @ A0))))))).
% 2.80/1.52 thf(fact_97_sorted__wrt_Oinduct, axiom, (! [A:$tType,P2:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P3:(A > (A > $o))]: (((P2 @ P3) @ (nil @ A)))) => ((! [P3:(A > (A > $o)),X2:A,Ys2:(list @ A)]: ((((P2 @ P3) @ Ys2) => ((P2 @ P3) @ (((cons @ A) @ X2) @ Ys2))))) => ((P2 @ A0) @ A1)))))).
% 2.80/1.52 thf(fact_98_remdups__adj_Ocases, axiom, (! [A:$tType,X:(list @ A)]: (((X != (nil @ A)) => ((! [X2:A]: ((X != (((cons @ A) @ X2) @ (nil @ A))))) => (~ ((! [X2:A,Y4:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X2) @ (((cons @ A) @ Y4) @ Xs2)))))))))))).
% 2.80/1.52 thf(fact_99_transpose_Ocases, axiom, (! [A:$tType,X:(list @ (list @ A))]: (((X != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X2:A,Xs2:(list @ A),Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (((cons @ A) @ X2) @ Xs2)) @ Xss))))))))))).
% 2.80/1.52 thf(fact_100_shuffles_Oinduct, axiom, (! [A:$tType,P2:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P2 @ (nil @ A)) @ X_1))) => ((! [Xs2:(list @ A)]: (((P2 @ Xs2) @ (nil @ A)))) => ((! [X2:A,Xs2:(list @ A),Y4:A,Ys2:(list @ A)]: ((((P2 @ Xs2) @ (((cons @ A) @ Y4) @ Ys2)) => (((P2 @ (((cons @ A) @ X2) @ Xs2)) @ Ys2) => ((P2 @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys2)))))) => ((P2 @ A0) @ A1))))))).
% 2.80/1.52 thf(fact_101_min__list_Oinduct, axiom, (! [A:$tType]: (((ord @ A) => (! [P2:((list @ A) > $o),A0:(list @ A)]: (((! [X2:A,Xs2:(list @ A)]: (((! [X212:A,X223:(list @ A)]: (((Xs2 = (((cons @ A) @ X212) @ X223)) => (P2 @ Xs2)))) => (P2 @ (((cons @ A) @ X2) @ Xs2))))) => ((P2 @ (nil @ A)) => (P2 @ A0))))))))).
% 2.80/1.52 thf(fact_102_min__list_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [X:(list @ A)]: (((! [X2:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X2) @ Xs2)))) => (X = (nil @ A))))))))).
% 2.80/1.52 thf(fact_103_induct__list012, axiom, (! [A:$tType,P2:((list @ A) > $o),Xs:(list @ A)]: (((P2 @ (nil @ A)) => ((! [X2:A]: ((P2 @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X2:A,Y4:A,Zs:(list @ A)]: (((P2 @ Zs) => ((P2 @ (((cons @ A) @ Y4) @ Zs)) => (P2 @ (((cons @ A) @ X2) @ (((cons @ A) @ Y4) @ Zs))))))) => (P2 @ Xs))))))).
% 2.80/1.52 thf(fact_104_splice_Oinduct, axiom, (! [A:$tType,P2:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P2 @ (nil @ A)) @ X_1))) => ((! [X2:A,Xs2:(list @ A),Ys2:(list @ A)]: ((((P2 @ Ys2) @ Xs2) => ((P2 @ (((cons @ A) @ X2) @ Xs2)) @ Ys2)))) => ((P2 @ A0) @ A1)))))).
% 2.80/1.52 thf(fact_105_list__induct2_H, axiom, (! [A:$tType,B:$tType,P2:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys:(list @ B)]: ((((P2 @ (nil @ A)) @ (nil @ B)) => ((! [X2:A,Xs2:(list @ A)]: (((P2 @ (((cons @ A) @ X2) @ Xs2)) @ (nil @ B)))) => ((! [Y4:B,Ys2:(list @ B)]: (((P2 @ (nil @ A)) @ (((cons @ B) @ Y4) @ Ys2)))) => ((! [X2:A,Xs2:(list @ A),Y4:B,Ys2:(list @ B)]: ((((P2 @ Xs2) @ Ys2) => ((P2 @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ B) @ Y4) @ Ys2))))) => ((P2 @ Xs) @ Ys)))))))).
% 2.80/1.52 thf(fact_106_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y5:A,Ys3:(list @ A)]: ((Xs = (((cons @ A) @ Y5) @ Ys3)))))))).
% 2.80/1.52 thf(fact_107_list_Oinducts, axiom, (! [A:$tType,P2:((list @ A) > $o),List:(list @ A)]: (((P2 @ (nil @ A)) => ((! [X12:A,X23:(list @ A)]: (((P2 @ X23) => (P2 @ (((cons @ A) @ X12) @ X23))))) => (P2 @ List)))))).
% 2.80/1.52 thf(fact_108_list_Oexhaust, axiom, (! [A:$tType,Y3:(list @ A)]: (((Y3 != (nil @ A)) => (~ ((! [X213:A,X224:(list @ A)]: ((Y3 != (((cons @ A) @ X213) @ X224)))))))))).
% 2.80/1.52 thf(fact_109_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X222:(list @ A)]: (((List = (((cons @ A) @ X21) @ X222)) => (List != (nil @ A)))))).
% 2.80/1.52 thf(fact_110_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X222:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X222))))).
% 2.80/1.52 thf(fact_111_length__induct, axiom, (! [A:$tType,P2:((list @ A) > $o),Xs:(list @ A)]: (((! [Xs2:(list @ A)]: (((! [Ys4:(list @ A)]: (((((ord_less @ nat) @ ((size_size @ (list @ A)) @ Ys4)) @ ((size_size @ (list @ A)) @ Xs2)) => (P2 @ Ys4)))) => (P2 @ Xs2)))) => (P2 @ Xs))))).
% 2.80/1.52 thf(fact_112_lift__Suc__mono__less__iff, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N3:nat,M:nat]: (((! [N:nat]: ((((ord_less @ A) @ (F @ N)) @ (F @ (suc @ N))))) => ((((ord_less @ A) @ (F @ N3)) @ (F @ M)) = (((ord_less @ nat) @ N3) @ M))))))))).
% 2.80/1.52 thf(fact_113_lift__Suc__mono__less, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N3:nat,N4:nat]: (((! [N:nat]: ((((ord_less @ A) @ (F @ N)) @ (F @ (suc @ N))))) => ((((ord_less @ nat) @ N3) @ N4) => (((ord_less @ A) @ (F @ N3)) @ (F @ N4)))))))))).
% 2.80/1.52 thf(fact_114_less__Suc__eq__0__disj, axiom, (! [M:nat,N3:nat]: (((((ord_less @ nat) @ M) @ (suc @ N3)) = ((M = (zero_zero @ nat)) | (? [J3:nat]: (((M = (suc @ J3)) & (((ord_less @ nat) @ J3) @ N3))))))))).
% 2.80/1.52 thf(fact_115_gr0__implies__Suc, axiom, (! [N3:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N3) => (? [M3:nat]: ((N3 = (suc @ M3)))))))).
% 2.80/1.52 thf(fact_116_All__less__Suc2, axiom, (! [N3:nat,P2:(nat > $o)]: (((! [I3:nat]: (((((ord_less @ nat) @ I3) @ (suc @ N3)) => (P2 @ I3)))) = ((P2 @ (zero_zero @ nat)) & (! [I3:nat]: (((((ord_less @ nat) @ I3) @ N3) => (P2 @ (suc @ I3)))))))))).
% 2.80/1.52 thf(fact_117_gr0__conv__Suc, axiom, (! [N3:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N3) = (? [M5:nat]: ((N3 = (suc @ M5)))))))).
% 2.80/1.52 thf(fact_118_Ex__less__Suc2, axiom, (! [N3:nat,P2:(nat > $o)]: (((? [I3:nat]: (((((ord_less @ nat) @ I3) @ (suc @ N3)) & (P2 @ I3)))) = ((P2 @ (zero_zero @ nat)) | (? [I3:nat]: (((((ord_less @ nat) @ I3) @ N3) & (P2 @ (suc @ I3)))))))))).
% 2.80/1.52 thf(fact_119_length__Suc__conv, axiom, (! [A:$tType,Xs:(list @ A),N3:nat]: (((((size_size @ (list @ A)) @ Xs) = (suc @ N3)) = (? [Y5:A,Ys3:(list @ A)]: (((Xs = (((cons @ A) @ Y5) @ Ys3)) & (((size_size @ (list @ A)) @ Ys3) = N3)))))))).
% 2.80/1.52 thf(fact_120_Suc__length__conv, axiom, (! [A:$tType,N3:nat,Xs:(list @ A)]: ((((suc @ N3) = ((size_size @ (list @ A)) @ Xs)) = (? [Y5:A,Ys3:(list @ A)]: (((Xs = (((cons @ A) @ Y5) @ Ys3)) & (((size_size @ (list @ A)) @ Ys3) = N3)))))))).
% 2.80/1.52 thf(fact_121_list_Osize_I3_J, axiom, (! [A:$tType]: ((((size_size @ (list @ A)) @ (nil @ A)) = (zero_zero @ nat))))).
% 2.80/1.52 thf(fact_122_list__induct3, axiom, (! [B:$tType,A:$tType,C:$tType,Xs:(list @ A),Ys:(list @ B),Zs2:(list @ C),P2:((list @ A) > ((list @ B) > ((list @ C) > $o)))]: (((((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ B)) @ Ys)) => ((((size_size @ (list @ B)) @ Ys) = ((size_size @ (list @ C)) @ Zs2)) => ((((P2 @ (nil @ A)) @ (nil @ B)) @ (nil @ C)) => ((! [X2:A,Xs2:(list @ A),Y4:B,Ys2:(list @ B),Z:C,Zs:(list @ C)]: (((((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ B)) @ Ys2)) => ((((size_size @ (list @ B)) @ Ys2) = ((size_size @ (list @ C)) @ Zs)) => ((((P2 @ Xs2) @ Ys2) @ Zs) => (((P2 @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ B) @ Y4) @ Ys2)) @ (((cons @ C) @ Z) @ Zs))))))) => (((P2 @ Xs) @ Ys) @ Zs2)))))))).
% 2.80/1.52 thf(fact_123_list__induct2, axiom, (! [A:$tType,B:$tType,Xs:(list @ A),Ys:(list @ B),P2:((list @ A) > ((list @ B) > $o))]: (((((size_size @ (list @ A)) @ Xs) = ((size_size @ (list @ B)) @ Ys)) => (((P2 @ (nil @ A)) @ (nil @ B)) => ((! [X2:A,Xs2:(list @ A),Y4:B,Ys2:(list @ B)]: (((((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ B)) @ Ys2)) => (((P2 @ Xs2) @ Ys2) => ((P2 @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ B) @ Y4) @ Ys2)))))) => ((P2 @ Xs) @ Ys))))))).
% 2.80/1.52 thf(fact_124_infiniteExecutionCfg_Oelims, axiom, (! [X:((((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 @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))]: ((((((((((fLPThe137922386ionCfg @ p) @ v) @ s) @ X) @ Xa) @ Xb) @ Xc) = Y3) => (((Xc = (zero_zero @ nat)) => (Y3 != (((cons @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ X) @ (nil @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))))) => (~ ((! [N:nat]: (((Xc = (suc @ N)) => (Y3 != ((Xa @ (((((((fLPThe137922386ionCfg @ p) @ v) @ s) @ X) @ Xa) @ Xb) @ N)) @ (((((((fLPThe221390223ionMsg @ p) @ v) @ s) @ X) @ Xa) @ Xb) @ N))))))))))))).
% 2.80/1.52 thf(fact_125_infiniteExecutionMsg_Oelims, axiom, (! [X:((((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) @ X) @ Xa) @ Xb) @ Xc) = Y3) => (((Xc = (zero_zero @ nat)) => (Y3 != (nil @ ((message @ p) @ v)))) => (~ ((! [N:nat]: (((Xc = (suc @ N)) => (Y3 != ((Xb @ (((((((fLPThe137922386ionCfg @ p) @ v) @ s) @ X) @ Xa) @ Xb) @ N)) @ (((((((fLPThe221390223ionMsg @ p) @ v) @ s) @ X) @ Xa) @ Xb) @ N))))))))))))).
% 2.80/1.52 thf(fact_126_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)))),N3:nat]: (((((((((fLPThe221390223ionMsg @ p) @ v) @ s) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ (suc @ N3)) = ((FStepMsg2 @ (((((((fLPThe137922386ionCfg @ p) @ v) @ s) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ N3)) @ (((((((fLPThe221390223ionMsg @ p) @ v) @ s) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ N3)))))).
% 2.80/1.52 thf(fact_127_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)))),N3:nat]: (((((((((fLPThe137922386ionCfg @ p) @ v) @ s) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ (suc @ N3)) = ((FStepCfg2 @ (((((((fLPThe137922386ionCfg @ p) @ v) @ s) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ N3)) @ (((((((fLPThe221390223ionMsg @ p) @ v) @ s) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ N3)))))).
% 2.80/1.52 thf(fact_128_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)))))).
% 2.80/1.52 thf(fact_129_not__gr__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N3:A]: (((~ ((((ord_less @ A) @ (zero_zero @ A)) @ N3))) = (N3 = (zero_zero @ A))))))))).
% 2.80/1.52 thf(fact_130_length__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((size_size @ (list @ A)) @ (((cons @ A) @ X) @ Xs)) = (suc @ ((size_size @ (list @ A)) @ Xs)))))).
% 2.80/1.52 thf(fact_131_dependent__nat__choice, axiom, (! [A:$tType,P2:(nat > (A > $o)),Q:(nat > (A > (A > $o)))]: (((? [X_12:A]: (((P2 @ (zero_zero @ nat)) @ X_12))) => ((! [X2:A,N:nat]: ((((P2 @ N) @ X2) => (? [Y:A]: ((((P2 @ (suc @ N)) @ Y) & (((Q @ N) @ X2) @ Y))))))) => (? [F2:(nat > A)]: ((! [N5:nat]: ((((P2 @ N5) @ (F2 @ N5)) & (((Q @ N5) @ (F2 @ N5)) @ (F2 @ (suc @ N5))))))))))))).
% 2.80/1.52 thf(fact_132_zero__reorient, axiom, (! [A:$tType]: (((zero @ A) => (! [X:A]: ((((zero_zero @ A) = X) = (X = (zero_zero @ A))))))))).
% 2.80/1.52 thf(fact_133_gr__zeroI, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N3:A]: (((N3 != (zero_zero @ A)) => (((ord_less @ A) @ (zero_zero @ A)) @ N3)))))))).
% 2.80/1.52 thf(fact_134_not__less__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N3:A]: ((~ ((((ord_less @ A) @ N3) @ (zero_zero @ A)))))))))).
% 2.80/1.52 thf(fact_135_gr__implies__not__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [M:A,N3:A]: (((((ord_less @ A) @ M) @ N3) => (N3 != (zero_zero @ A))))))))).
% 2.80/1.52 thf(fact_136_zero__less__iff__neq__zero, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N3:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ N3) = (N3 != (zero_zero @ A))))))))).
% 2.80/1.52 thf(fact_137_n__lists__Nil, axiom, (! [A:$tType,N3:nat]: ((((N3 = (zero_zero @ nat)) => ((((n_lists @ A) @ N3) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))) & ((N3 != (zero_zero @ nat)) => ((((n_lists @ A) @ N3) @ (nil @ A)) = (nil @ (list @ A)))))))).
% 2.80/1.52 thf(fact_138_flpPseudoConsensus_OinfiniteExecutionCfg_Oelims, axiom, (! [P:$tType,V:$tType,S:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Start:(P > S),X:((((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 @ ((((configuration_ext @ P) @ V) @ S) @ product_unit))]: ((((((((fLPThe1922692578sensus @ P) @ S) @ V) @ Trans) @ Sends) @ Start) => (((((((((fLPThe137922386ionCfg @ P) @ V) @ S) @ X) @ Xa) @ Xb) @ Xc) = Y3) => (((Xc = (zero_zero @ nat)) => (Y3 != (((cons @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) @ X) @ (nil @ ((((configuration_ext @ P) @ V) @ S) @ product_unit))))) => (~ ((! [N:nat]: (((Xc = (suc @ N)) => (Y3 != ((Xa @ (((((((fLPThe137922386ionCfg @ P) @ V) @ S) @ X) @ Xa) @ Xb) @ N)) @ (((((((fLPThe221390223ionMsg @ P) @ V) @ S) @ X) @ Xa) @ Xb) @ N)))))))))))))).
% 2.80/1.52 thf(fact_139_n__lists_Osimps_I1_J, axiom, (! [A:$tType,Xs:(list @ A)]: (((((n_lists @ A) @ (zero_zero @ nat)) @ Xs) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.80/1.52 thf(fact_140_flpPseudoConsensus_OinfiniteExecutionMsg_Oelims, axiom, (! [P:$tType,V:$tType,S:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Start:(P > S),X:((((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))]: ((((((((fLPThe1922692578sensus @ P) @ S) @ V) @ Trans) @ Sends) @ Start) => (((((((((fLPThe221390223ionMsg @ P) @ V) @ S) @ X) @ Xa) @ Xb) @ Xc) = Y3) => (((Xc = (zero_zero @ nat)) => (Y3 != (nil @ ((message @ P) @ V)))) => (~ ((! [N:nat]: (((Xc = (suc @ N)) => (Y3 != ((Xb @ (((((((fLPThe137922386ionCfg @ P) @ V) @ S) @ X) @ Xa) @ Xb) @ N)) @ (((((((fLPThe221390223ionMsg @ P) @ V) @ S) @ X) @ Xa) @ Xb) @ N)))))))))))))).
% 2.80/1.52 thf(fact_141_flpPseudoConsensus_OinfiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J, axiom, (! [P:$tType,V:$tType,S:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Start:(P > S),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]: ((((((((fLPThe1922692578sensus @ P) @ S) @ V) @ Trans) @ Sends) @ Start) => ((! [Cfg:((((configuration_ext @ P) @ V) @ S) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((message @ P) @ V))))]: (((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ (zero_zero @ nat)))) => ((! [Cfg:((((configuration_ext @ P) @ V) @ S) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((message @ P) @ V)))),N:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => ((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N)))))) => ((! [Cfg:((((configuration_ext @ P) @ V) @ S) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((message @ P) @ V))))]: (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (zero_zero @ nat)))) => ((! [Cfg:((((configuration_ext @ P) @ V) @ S) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((message @ P) @ V)))),N:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => ((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N)))))) => ((((P2 @ A0) @ A1) @ A2) @ A3))))))))).
% 2.80/1.52 thf(fact_142_flpPseudoConsensus_OinfiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J, axiom, (! [P:$tType,V:$tType,S:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Start:(P > S),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]: ((((((((fLPThe1922692578sensus @ P) @ S) @ V) @ Trans) @ Sends) @ Start) => ((! [Cfg:((((configuration_ext @ P) @ V) @ S) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((message @ P) @ V))))]: (((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ (zero_zero @ nat)))) => ((! [Cfg:((((configuration_ext @ P) @ V) @ S) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((message @ P) @ V)))),N:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => ((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N)))))) => ((! [Cfg:((((configuration_ext @ P) @ V) @ S) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((message @ P) @ V))))]: (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (zero_zero @ nat)))) => ((! [Cfg:((((configuration_ext @ P) @ V) @ S) @ product_unit),FStepCfg:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)))),FStepMsg:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((message @ P) @ V)))),N:nat]: ((((((P2 @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => (((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ N) => ((((Q @ Cfg) @ FStepCfg) @ FStepMsg) @ (suc @ N)))))) => ((((Q @ A4) @ A5) @ A6) @ A7))))))))).
% 2.80/1.52 thf(fact_143_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I2_J, axiom, (! [P:$tType,V:$tType,S:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Start:(P > S),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)))),N3:nat]: ((((((((fLPThe1922692578sensus @ P) @ S) @ V) @ Trans) @ Sends) @ Start) => ((((((((fLPThe221390223ionMsg @ P) @ V) @ S) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ (suc @ N3)) = ((FStepMsg2 @ (((((((fLPThe137922386ionCfg @ P) @ V) @ S) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ N3)) @ (((((((fLPThe221390223ionMsg @ P) @ V) @ S) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ N3))))))).
% 2.80/1.52 thf(fact_144_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I2_J, axiom, (! [P:$tType,V:$tType,S:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Start:(P > S),Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit),FStepCfg2:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)))),FStepMsg2:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((message @ P) @ V)))),N3:nat]: ((((((((fLPThe1922692578sensus @ P) @ S) @ V) @ Trans) @ Sends) @ Start) => ((((((((fLPThe137922386ionCfg @ P) @ V) @ S) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ (suc @ N3)) = ((FStepCfg2 @ (((((((fLPThe137922386ionCfg @ P) @ V) @ S) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ N3)) @ (((((((fLPThe221390223ionMsg @ P) @ V) @ S) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ N3))))))).
% 2.80/1.52 thf(fact_145_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I1_J, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Start:(P > S),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))))]: ((((((((fLPThe1922692578sensus @ P) @ S) @ V) @ Trans) @ Sends) @ Start) => ((((((((fLPThe221390223ionMsg @ P) @ V) @ S) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ (zero_zero @ nat)) = (nil @ ((message @ P) @ V))))))).
% 2.80/1.52 thf(fact_146_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I1_J, axiom, (! [S:$tType,V:$tType,P:$tType,Trans:(P > (S > ((messageValue @ V) > S))),Sends:(P > (S > ((messageValue @ V) > (((message @ P) @ V) > nat)))),Start:(P > S),Cfg2:((((configuration_ext @ P) @ V) @ S) @ product_unit),FStepCfg2:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)))),FStepMsg2:((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (list @ ((message @ P) @ V))))]: ((((((((fLPThe1922692578sensus @ P) @ S) @ V) @ Trans) @ Sends) @ Start) => ((((((((fLPThe137922386ionCfg @ P) @ V) @ S) @ Cfg2) @ FStepCfg2) @ FStepMsg2) @ (zero_zero @ nat)) = (((cons @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) @ Cfg2) @ (nil @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)))))))).
% 2.80/1.52 thf(fact_147_shift__def, axiom, (! [B:$tType,A:$tType]: ((((bNF_Greatest_shift @ A) @ B) = (^ [Lab:((list @ A) > B),K3:A,Kl:(list @ A)]: ((Lab @ (((cons @ A) @ K3) @ Kl)))))))).
% 2.80/1.52 thf(fact_148_less__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))))).
% 2.80/1.52 thf(fact_149_product__lists_Osimps_I1_J, axiom, (! [A:$tType]: ((((product_lists @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.80/1.52 thf(fact_150_subseqs_Osimps_I1_J, axiom, (! [A:$tType]: ((((subseqs @ A) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.80/1.52 thf(fact_151_length__code, axiom, (! [A:$tType]: (((size_size @ (list @ A)) = ((gen_length @ A) @ (zero_zero @ nat)))))).
% 2.80/1.52 thf(fact_152_gen__length__code_I2_J, axiom, (! [B:$tType,N3:nat,X:B,Xs:(list @ B)]: (((((gen_length @ B) @ N3) @ (((cons @ B) @ X) @ Xs)) = (((gen_length @ B) @ (suc @ N3)) @ Xs))))).
% 2.80/1.52 thf(fact_153_gen__length__code_I1_J, axiom, (! [A:$tType,N3:nat]: (((((gen_length @ A) @ N3) @ (nil @ A)) = N3)))).
% 2.80/1.52 thf(fact_154_insert__Nil, axiom, (! [A:$tType,X:A]: (((((insert @ A) @ X) @ (nil @ A)) = (((cons @ A) @ X) @ (nil @ A)))))).
% 2.80/1.52 thf(fact_155_nths__singleton, axiom, (! [A:$tType,A9:(set @ nat),X:A]: ((((((member @ nat) @ (zero_zero @ nat)) @ A9) => ((((nths @ A) @ (((cons @ A) @ X) @ (nil @ A))) @ A9) = (((cons @ A) @ X) @ (nil @ A)))) & ((~ ((((member @ nat) @ (zero_zero @ nat)) @ A9))) => ((((nths @ A) @ (((cons @ A) @ X) @ (nil @ A))) @ A9) = (nil @ A))))))).
% 2.80/1.52 thf(fact_156_of__nat__0__less__iff, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (! [N3:nat]: (((((ord_less @ A) @ (zero_zero @ A)) @ ((semiring_1_of_nat @ A) @ N3)) = (((ord_less @ nat) @ (zero_zero @ nat)) @ N3)))))))).
% 2.80/1.52 thf(fact_157_of__nat__eq__iff, axiom, (! [A:$tType]: (((semiring_char_0 @ A) => (! [M:nat,N3:nat]: (((((semiring_1_of_nat @ A) @ M) = ((semiring_1_of_nat @ A) @ N3)) = (M = N3)))))))).
% 2.80/1.52 thf(fact_158_nths__nil, axiom, (! [A:$tType,A9:(set @ nat)]: (((((nths @ A) @ (nil @ A)) @ A9) = (nil @ A))))).
% 2.80/1.52 thf(fact_159_of__nat__0, axiom, (! [A:$tType]: (((semiring_1 @ A) => (((semiring_1_of_nat @ A) @ (zero_zero @ nat)) = (zero_zero @ A)))))).
% 2.80/1.52 thf(fact_160_of__nat__0__eq__iff, axiom, (! [A:$tType]: (((semiring_char_0 @ A) => (! [N3:nat]: ((((zero_zero @ A) = ((semiring_1_of_nat @ A) @ N3)) = ((zero_zero @ nat) = N3)))))))).
% 2.80/1.52 thf(fact_161_of__nat__eq__0__iff, axiom, (! [A:$tType]: (((semiring_char_0 @ A) => (! [M:nat]: (((((semiring_1_of_nat @ A) @ M) = (zero_zero @ A)) = (M = (zero_zero @ nat))))))))).
% 2.80/1.52 thf(fact_162_of__nat__less__iff, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (! [M:nat,N3:nat]: (((((ord_less @ A) @ ((semiring_1_of_nat @ A) @ M)) @ ((semiring_1_of_nat @ A) @ N3)) = (((ord_less @ nat) @ M) @ N3)))))))).
% 2.80/1.52 thf(fact_163_of__nat__less__0__iff, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (! [M:nat]: ((~ ((((ord_less @ A) @ ((semiring_1_of_nat @ A) @ M)) @ (zero_zero @ A)))))))))).
% 2.80/1.52 thf(fact_164_of__nat__neq__0, axiom, (! [A:$tType]: (((semiring_char_0 @ A) => (! [N3:nat]: ((((semiring_1_of_nat @ A) @ (suc @ N3)) != (zero_zero @ A)))))))).
% 2.80/1.52 thf(fact_165_less__imp__of__nat__less, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (! [M:nat,N3:nat]: (((((ord_less @ nat) @ M) @ N3) => (((ord_less @ A) @ ((semiring_1_of_nat @ A) @ M)) @ ((semiring_1_of_nat @ A) @ N3))))))))).
% 2.80/1.52 thf(fact_166_of__nat__less__imp__less, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (! [M:nat,N3:nat]: (((((ord_less @ A) @ ((semiring_1_of_nat @ A) @ M)) @ ((semiring_1_of_nat @ A) @ N3)) => (((ord_less @ nat) @ M) @ N3)))))))).
% 2.80/1.52 thf(fact_167_nths__all, axiom, (! [A:$tType,Xs:(list @ A),I4:(set @ nat)]: (((! [I2:nat]: (((((ord_less @ nat) @ I2) @ ((size_size @ (list @ A)) @ Xs)) => (((member @ nat) @ I2) @ I4)))) => ((((nths @ A) @ Xs) @ I4) = Xs))))).
% 2.80/1.52 thf(fact_168_pos__int__cases, axiom, (! [K:int]: (((((ord_less @ int) @ (zero_zero @ int)) @ K) => (~ ((! [N:nat]: (((K = ((semiring_1_of_nat @ int) @ N)) => (~ ((((ord_less @ nat) @ (zero_zero @ nat)) @ N)))))))))))).
% 2.80/1.52 thf(fact_169_zero__less__imp__eq__int, axiom, (! [K:int]: (((((ord_less @ int) @ (zero_zero @ int)) @ K) => (? [N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) & (K = ((semiring_1_of_nat @ int) @ N))))))))).
% 2.80/1.52 thf(fact_170_list__ex1__simps_I1_J, axiom, (! [A:$tType,P2:(A > $o)]: ((~ ((((list_ex1 @ A) @ P2) @ (nil @ A))))))).
% 2.80/1.52 thf(fact_171_nat__int__comparison_I2_J, axiom, ((ord_less @ nat) = (^ [A11:nat,B2:nat]: ((((ord_less @ int) @ ((semiring_1_of_nat @ int) @ A11)) @ ((semiring_1_of_nat @ int) @ B2)))))).
% 2.80/1.52 thf(fact_172_int__ops_I1_J, axiom, (((semiring_1_of_nat @ int) @ (zero_zero @ nat)) = (zero_zero @ int))).
% 2.80/1.52 thf(fact_173_neg__int__cases, axiom, (! [K:int]: (((((ord_less @ int) @ K) @ (zero_zero @ int)) => (~ ((! [N:nat]: (((K = ((uminus_uminus @ int) @ ((semiring_1_of_nat @ int) @ N))) => (~ ((((ord_less @ nat) @ (zero_zero @ nat)) @ N)))))))))))).
% 2.80/1.52 thf(fact_174_neg__equal__iff__equal, axiom, (! [A:$tType]: (((group_add @ A) => (! [A8:A,B3:A]: (((((uminus_uminus @ A) @ A8) = ((uminus_uminus @ A) @ B3)) = (A8 = B3)))))))).
% 2.80/1.52 thf(fact_175_add_Oinverse__inverse, axiom, (! [A:$tType]: (((group_add @ A) => (! [A8:A]: ((((uminus_uminus @ A) @ ((uminus_uminus @ A) @ A8)) = A8))))))).
% 2.80/1.52 thf(fact_176_add_Oinverse__neutral, axiom, (! [A:$tType]: (((group_add @ A) => (((uminus_uminus @ A) @ (zero_zero @ A)) = (zero_zero @ A)))))).
% 2.80/1.52 thf(fact_177_neg__0__equal__iff__equal, axiom, (! [A:$tType]: (((group_add @ A) => (! [A8:A]: ((((zero_zero @ A) = ((uminus_uminus @ A) @ A8)) = ((zero_zero @ A) = A8)))))))).
% 2.80/1.52 thf(fact_178_neg__equal__0__iff__equal, axiom, (! [A:$tType]: (((group_add @ A) => (! [A8:A]: (((((uminus_uminus @ A) @ A8) = (zero_zero @ A)) = (A8 = (zero_zero @ A))))))))).
% 2.80/1.52 thf(fact_179_equal__neg__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A8:A]: (((A8 = ((uminus_uminus @ A) @ A8)) = (A8 = (zero_zero @ A))))))))).
% 2.80/1.52 thf(fact_180_neg__equal__zero, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A8:A]: (((((uminus_uminus @ A) @ A8) = A8) = (A8 = (zero_zero @ A))))))))).
% 2.80/1.52 thf(fact_181_neg__less__iff__less, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B3:A,A8:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ B3)) @ ((uminus_uminus @ A) @ A8)) = (((ord_less @ A) @ A8) @ B3)))))))).
% 2.80/1.52 thf(fact_182_less__neg__neg, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A8:A]: (((((ord_less @ A) @ A8) @ ((uminus_uminus @ A) @ A8)) = (((ord_less @ A) @ A8) @ (zero_zero @ A))))))))).
% 2.80/1.52 thf(fact_183_neg__less__pos, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A8:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ A8)) @ A8) = (((ord_less @ A) @ (zero_zero @ A)) @ A8)))))))).
% 2.80/1.52 thf(fact_184_neg__0__less__iff__less, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A]: (((((ord_less @ A) @ (zero_zero @ A)) @ ((uminus_uminus @ A) @ A8)) = (((ord_less @ A) @ A8) @ (zero_zero @ A))))))))).
% 2.80/1.52 thf(fact_185_neg__less__0__iff__less, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ A8)) @ (zero_zero @ A)) = (((ord_less @ A) @ (zero_zero @ A)) @ A8)))))))).
% 2.80/1.52 thf(fact_186_negative__eq__positive, axiom, (! [N3:nat,M:nat]: (((((uminus_uminus @ int) @ ((semiring_1_of_nat @ int) @ N3)) = ((semiring_1_of_nat @ int) @ M)) = ((N3 = (zero_zero @ nat)) & (M = (zero_zero @ nat))))))).
% 2.80/1.52 thf(fact_187_negative__zless, axiom, (! [N3:nat,M:nat]: ((((ord_less @ int) @ ((uminus_uminus @ int) @ ((semiring_1_of_nat @ int) @ (suc @ N3)))) @ ((semiring_1_of_nat @ int) @ M))))).
% 2.80/1.52 thf(fact_188_minus__less__iff, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B3:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ A8)) @ B3) = (((ord_less @ A) @ ((uminus_uminus @ A) @ B3)) @ A8)))))))).
% 2.80/1.52 thf(fact_189_less__minus__iff, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B3:A]: (((((ord_less @ A) @ A8) @ ((uminus_uminus @ A) @ B3)) = (((ord_less @ A) @ B3) @ ((uminus_uminus @ A) @ A8))))))))).
% 2.80/1.52 thf(fact_190_verit__negate__coefficient_I2_J, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A,B3:A]: (((((ord_less @ A) @ A8) @ B3) => (((ord_less @ A) @ ((uminus_uminus @ A) @ B3)) @ ((uminus_uminus @ A) @ A8))))))))).
% 2.80/1.52 thf(fact_191_minus__equation__iff, axiom, (! [A:$tType]: (((group_add @ A) => (! [A8:A,B3:A]: (((((uminus_uminus @ A) @ A8) = B3) = (((uminus_uminus @ A) @ B3) = A8)))))))).
% 2.80/1.52 thf(fact_192_equation__minus__iff, axiom, (! [A:$tType]: (((group_add @ A) => (! [A8:A,B3:A]: (((A8 = ((uminus_uminus @ A) @ B3)) = (B3 = ((uminus_uminus @ A) @ A8))))))))).
% 2.80/1.52 thf(fact_193_int__cases, axiom, (! [Z2:int]: (((! [N:nat]: ((Z2 != ((semiring_1_of_nat @ int) @ N)))) => (~ ((! [N:nat]: ((Z2 != ((uminus_uminus @ int) @ ((semiring_1_of_nat @ int) @ (suc @ N)))))))))))).
% 2.80/1.52 thf(fact_194_int__of__nat__induct, axiom, (! [P2:(int > $o),Z2:int]: (((! [N:nat]: ((P2 @ ((semiring_1_of_nat @ int) @ N)))) => ((! [N:nat]: ((P2 @ ((uminus_uminus @ int) @ ((semiring_1_of_nat @ int) @ (suc @ N)))))) => (P2 @ Z2)))))).
% 2.80/1.52 thf(fact_195_int__cases4, axiom, (! [M:int]: (((! [N:nat]: ((M != ((semiring_1_of_nat @ int) @ N)))) => (~ ((! [N:nat]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ N) => (M != ((uminus_uminus @ int) @ ((semiring_1_of_nat @ int) @ N)))))))))))).
% 2.80/1.52 thf(fact_196_verit__comp__simplify1_I1_J, axiom, (! [A:$tType]: (((order @ A) => (! [A8:A]: ((~ ((((ord_less @ A) @ A8) @ A8))))))))).
% 2.80/1.52 thf(fact_197_int__cases3, axiom, (! [K:int]: (((K != (zero_zero @ int)) => ((! [N:nat]: (((K = ((semiring_1_of_nat @ int) @ N)) => (~ ((((ord_less @ nat) @ (zero_zero @ nat)) @ N)))))) => (~ ((! [N:nat]: (((K = ((uminus_uminus @ int) @ ((semiring_1_of_nat @ int) @ N))) => (~ ((((ord_less @ nat) @ (zero_zero @ nat)) @ N))))))))))))).
% 2.80/1.52 thf(fact_198_negative__zless__0, axiom, (! [N3:nat]: ((((ord_less @ int) @ ((uminus_uminus @ int) @ ((semiring_1_of_nat @ int) @ (suc @ N3)))) @ (zero_zero @ int))))).
% 2.80/1.52 thf(fact_199_negD, axiom, (! [X:int]: (((((ord_less @ int) @ X) @ (zero_zero @ int)) => (? [N:nat]: ((X = ((uminus_uminus @ int) @ ((semiring_1_of_nat @ int) @ (suc @ N)))))))))).
% 2.80/1.52 thf(fact_200_compl__less__compl__iff, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [X:A,Y3:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ X)) @ ((uminus_uminus @ A) @ Y3)) = (((ord_less @ A) @ Y3) @ X)))))))).
% 2.80/1.52 thf(fact_201_compl__less__swap2, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [Y3:A,X:A]: (((((ord_less @ A) @ ((uminus_uminus @ A) @ Y3)) @ X) => (((ord_less @ A) @ ((uminus_uminus @ A) @ X)) @ Y3)))))))).
% 2.80/1.52 thf(fact_202_compl__less__swap1, axiom, (! [A:$tType]: (((boolean_algebra @ A) => (! [Y3:A,X:A]: (((((ord_less @ A) @ Y3) @ ((uminus_uminus @ A) @ X)) => (((ord_less @ A) @ X) @ ((uminus_uminus @ A) @ Y3))))))))).
% 2.80/1.52 thf(fact_203_zero__less__nat__eq, axiom, (! [Z2:int]: (((((ord_less @ nat) @ (zero_zero @ nat)) @ (nat2 @ Z2)) = (((ord_less @ int) @ (zero_zero @ int)) @ Z2))))).
% 2.80/1.52 thf(fact_204_of__int__0__less__iff, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [Z2:int]: (((((ord_less @ A) @ (zero_zero @ A)) @ ((ring_1_of_int @ A) @ Z2)) = (((ord_less @ int) @ (zero_zero @ int)) @ Z2)))))))).
% 2.80/1.52 thf(fact_205_of__int__0, axiom, (! [A:$tType]: (((ring_1 @ A) => (((ring_1_of_int @ A) @ (zero_zero @ int)) = (zero_zero @ A)))))).
% 2.80/1.52 thf(fact_206_of__int__0__eq__iff, axiom, (! [A:$tType]: (((ring_char_0 @ A) => (! [Z2:int]: ((((zero_zero @ A) = ((ring_1_of_int @ A) @ Z2)) = (Z2 = (zero_zero @ int))))))))).
% 2.80/1.52 thf(fact_207_of__int__eq__0__iff, axiom, (! [A:$tType]: (((ring_char_0 @ A) => (! [Z2:int]: (((((ring_1_of_int @ A) @ Z2) = (zero_zero @ A)) = (Z2 = (zero_zero @ int))))))))).
% 2.80/1.52 thf(fact_208_of__int__less__iff, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [W:int,Z2:int]: (((((ord_less @ A) @ ((ring_1_of_int @ A) @ W)) @ ((ring_1_of_int @ A) @ Z2)) = (((ord_less @ int) @ W) @ Z2)))))))).
% 2.80/1.52 thf(fact_209_zless__nat__conj, axiom, (! [W:int,Z2:int]: (((((ord_less @ nat) @ (nat2 @ W)) @ (nat2 @ Z2)) = ((((ord_less @ int) @ (zero_zero @ int)) @ Z2) & (((ord_less @ int) @ W) @ Z2)))))).
% 2.80/1.52 thf(fact_210_nat__zminus__int, axiom, (! [N3:nat]: (((nat2 @ ((uminus_uminus @ int) @ ((semiring_1_of_nat @ int) @ N3))) = (zero_zero @ nat))))).
% 2.80/1.52 thf(fact_211_of__int__less__0__iff, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [Z2:int]: (((((ord_less @ A) @ ((ring_1_of_int @ A) @ Z2)) @ (zero_zero @ A)) = (((ord_less @ int) @ Z2) @ (zero_zero @ int))))))))).
% 2.80/1.52 thf(fact_212_nat__zero__as__int, axiom, ((zero_zero @ nat) = (nat2 @ (zero_zero @ int)))).
% 2.80/1.52 thf(fact_213_nat__mono__iff, axiom, (! [Z2:int,W:int]: (((((ord_less @ int) @ (zero_zero @ int)) @ Z2) => ((((ord_less @ nat) @ (nat2 @ W)) @ (nat2 @ Z2)) = (((ord_less @ int) @ W) @ Z2)))))).
% 2.80/1.52 thf(fact_214_zless__nat__eq__int__zless, axiom, (! [M:nat,Z2:int]: (((((ord_less @ nat) @ M) @ (nat2 @ Z2)) = (((ord_less @ int) @ ((semiring_1_of_nat @ int) @ M)) @ Z2))))).
% 2.80/1.52 thf(fact_215_of__int__pos, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [Z2:int]: (((((ord_less @ int) @ (zero_zero @ int)) @ Z2) => (((ord_less @ A) @ (zero_zero @ A)) @ ((ring_1_of_int @ A) @ Z2))))))))).
% 2.80/1.52 thf(fact_216_of__nat__less__of__int__iff, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [N3:nat,X:int]: (((((ord_less @ A) @ ((semiring_1_of_nat @ A) @ N3)) @ ((ring_1_of_int @ A) @ X)) = (((ord_less @ int) @ ((semiring_1_of_nat @ int) @ N3)) @ X)))))))).
% 2.80/1.52 thf(fact_217_split__nat, axiom, (! [P2:(nat > $o),I:int]: (((P2 @ (nat2 @ I)) = ((! [N6:nat]: (((I = ((semiring_1_of_nat @ int) @ N6)) => (P2 @ N6)))) & ((((ord_less @ int) @ I) @ (zero_zero @ int)) => (P2 @ (zero_zero @ nat)))))))).
% 2.80/1.52 thf(fact_218_one__less__nat__eq, axiom, (! [Z2:int]: (((((ord_less @ nat) @ (suc @ (zero_zero @ nat))) @ (nat2 @ Z2)) = (((ord_less @ int) @ (one_one @ int)) @ Z2))))).
% 2.80/1.52 thf(fact_219_nat__less__iff, axiom, (! [W:int,M:nat]: (((((ord_less_eq @ int) @ (zero_zero @ int)) @ W) => ((((ord_less @ nat) @ (nat2 @ W)) @ M) = (((ord_less @ int) @ W) @ ((semiring_1_of_nat @ int) @ M))))))).
% 2.80/1.52 thf(fact_220_le__zero__eq, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [N3:A]: (((((ord_less_eq @ A) @ N3) @ (zero_zero @ A)) = (N3 = (zero_zero @ A))))))))).
% 2.80/1.52 thf(fact_221_neg__le__iff__le, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B3:A,A8:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ B3)) @ ((uminus_uminus @ A) @ A8)) = (((ord_less_eq @ A) @ A8) @ B3)))))))).
% 2.80/1.52 thf(fact_222_of__nat__le__iff, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (! [M:nat,N3:nat]: (((((ord_less_eq @ A) @ ((semiring_1_of_nat @ A) @ M)) @ ((semiring_1_of_nat @ A) @ N3)) = (((ord_less_eq @ nat) @ M) @ N3)))))))).
% 2.80/1.52 thf(fact_223_of__nat__1, axiom, (! [A:$tType]: (((semiring_1 @ A) => (((semiring_1_of_nat @ A) @ (one_one @ nat)) = (one_one @ A)))))).
% 2.80/1.52 thf(fact_224_of__nat__1__eq__iff, axiom, (! [A:$tType]: (((semiring_char_0 @ A) => (! [N3:nat]: ((((one_one @ A) = ((semiring_1_of_nat @ A) @ N3)) = (N3 = (one_one @ nat))))))))).
% 2.80/1.52 thf(fact_225_of__nat__eq__1__iff, axiom, (! [A:$tType]: (((semiring_char_0 @ A) => (! [N3:nat]: (((((semiring_1_of_nat @ A) @ N3) = (one_one @ A)) = (N3 = (one_one @ nat))))))))).
% 2.80/1.52 thf(fact_226_neg__0__le__iff__le, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ ((uminus_uminus @ A) @ A8)) = (((ord_less_eq @ A) @ A8) @ (zero_zero @ A))))))))).
% 2.80/1.52 thf(fact_227_neg__le__0__iff__le, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A8:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ A8)) @ (zero_zero @ A)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ A8)))))))).
% 2.80/1.52 thf(fact_228_less__eq__neg__nonpos, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A8:A]: (((((ord_less_eq @ A) @ A8) @ ((uminus_uminus @ A) @ A8)) = (((ord_less_eq @ A) @ A8) @ (zero_zero @ A))))))))).
% 2.80/1.52 thf(fact_229_neg__less__eq__nonneg, axiom, (! [A:$tType]: (((linord219039673up_add @ A) => (! [A8:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ A8)) @ A8) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ A8)))))))).
% 2.80/1.52 thf(fact_230_of__nat__le__0__iff, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (! [M:nat]: (((((ord_less_eq @ A) @ ((semiring_1_of_nat @ A) @ M)) @ (zero_zero @ A)) = (M = (zero_zero @ nat))))))))).
% 2.80/1.52 thf(fact_231_nat__1, axiom, ((nat2 @ (one_one @ int)) = (suc @ (zero_zero @ nat)))).
% 2.80/1.52 thf(fact_232_nat__le__0, axiom, (! [Z2:int]: (((((ord_less_eq @ int) @ Z2) @ (zero_zero @ int)) => ((nat2 @ Z2) = (zero_zero @ nat)))))).
% 2.80/1.52 thf(fact_233_nat__0__iff, axiom, (! [I:int]: ((((nat2 @ I) = (zero_zero @ nat)) = (((ord_less_eq @ int) @ I) @ (zero_zero @ int)))))).
% 2.80/1.52 thf(fact_234_of__int__le__0__iff, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [Z2:int]: (((((ord_less_eq @ A) @ ((ring_1_of_int @ A) @ Z2)) @ (zero_zero @ A)) = (((ord_less_eq @ int) @ Z2) @ (zero_zero @ int))))))))).
% 2.80/1.52 thf(fact_235_of__int__0__le__iff, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [Z2:int]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ ((ring_1_of_int @ A) @ Z2)) = (((ord_less_eq @ int) @ (zero_zero @ int)) @ Z2)))))))).
% 2.80/1.52 thf(fact_236_of__int__less__1__iff, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [Z2:int]: (((((ord_less @ A) @ ((ring_1_of_int @ A) @ Z2)) @ (one_one @ A)) = (((ord_less @ int) @ Z2) @ (one_one @ int))))))))).
% 2.80/1.52 thf(fact_237_of__int__1__less__iff, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [Z2:int]: (((((ord_less @ A) @ (one_one @ A)) @ ((ring_1_of_int @ A) @ Z2)) = (((ord_less @ int) @ (one_one @ int)) @ Z2)))))))).
% 2.80/1.52 thf(fact_238_of__int__nonneg, axiom, (! [A:$tType]: (((linordered_idom @ A) => (! [Z2:int]: (((((ord_less_eq @ int) @ (zero_zero @ int)) @ Z2) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ ((ring_1_of_int @ A) @ Z2))))))))).
% 2.80/1.52 thf(fact_239_verit__comp__simplify1_I3_J, axiom, (! [B:$tType]: (((linorder @ B) => (! [B4:B,A13:B]: (((~ ((((ord_less_eq @ B) @ B4) @ A13))) = (((ord_less @ B) @ A13) @ B4)))))))).
% 2.80/1.52 thf(fact_240_le__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (one_one @ A)) @ (one_one @ A)))))).
% 2.80/1.52 thf(fact_241_one__reorient, axiom, (! [A:$tType]: (((one @ A) => (! [X:A]: ((((one_one @ A) = X) = (X = (one_one @ A))))))))).
% 2.80/1.52 thf(fact_242_lift__Suc__antimono__le, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N3:nat,N4:nat]: (((! [N:nat]: ((((ord_less_eq @ A) @ (F @ (suc @ N))) @ (F @ N)))) => ((((ord_less_eq @ nat) @ N3) @ N4) => (((ord_less_eq @ A) @ (F @ N4)) @ (F @ N3)))))))))).
% 2.80/1.52 thf(fact_243_lift__Suc__mono__le, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N3:nat,N4:nat]: (((! [N:nat]: ((((ord_less_eq @ A) @ (F @ N)) @ (F @ (suc @ N))))) => ((((ord_less_eq @ nat) @ N3) @ N4) => (((ord_less_eq @ A) @ (F @ N3)) @ (F @ N4)))))))))).
% 2.80/1.52 thf(fact_244_zero__le, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [X:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X))))))).
% 2.80/1.52 thf(fact_245_le__numeral__extra_I3_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))).
% 2.80/1.52 thf(fact_246_less__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (one_one @ A)))))))).
% 2.80/1.52 thf(fact_247_of__nat__mono, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (! [I:nat,J:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ A) @ ((semiring_1_of_nat @ A) @ I)) @ ((semiring_1_of_nat @ A) @ J))))))))).
% 2.80/1.52 thf(fact_248_less__minus__one__simps_I4_J, axiom, (! [A:$tType]: (((linordered_idom @ A) => (~ ((((ord_less @ A) @ (one_one @ A)) @ ((uminus_uminus @ A) @ (one_one @ A))))))))).
% 2.80/1.52 thf(fact_249_less__minus__one__simps_I2_J, axiom, (! [A:$tType]: (((linordered_idom @ A) => (((ord_less @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) @ (one_one @ A)))))).
% 2.80/1.52 thf(fact_250_zero__neq__neg__one, axiom, (! [A:$tType]: (((ring_char_0 @ A) => ((zero_zero @ A) != ((uminus_uminus @ A) @ (one_one @ A))))))).
% 2.80/1.52 thf(tcon_fun___Lattices_Oboolean__algebra, axiom, (! [A14:$tType,A15:$tType]: (((boolean_algebra @ A15) => (boolean_algebra @ (A14 > A15)))))).
% 2.80/1.52 thf(tcon_fun___Orderings_Oorder, axiom, (! [A14:$tType,A15:$tType]: (((order @ A15) => (order @ (A14 > A15)))))).
% 2.80/1.52 thf(tcon_fun___Orderings_Oord, axiom, (! [A14:$tType,A15:$tType]: (((ord @ A15) => (ord @ (A14 > A15)))))).
% 2.80/1.52 thf(tcon_Int_Oint___Rings_Olinordered__nonzero__semiring, axiom, (linord1659791738miring @ int)).
% 2.80/1.52 thf(tcon_Int_Oint___Groups_Olinordered__ab__group__add, axiom, (linord219039673up_add @ int)).
% 2.80/1.52 thf(tcon_Int_Oint___Groups_Oordered__ab__group__add, axiom, (ordered_ab_group_add @ int)).
% 2.80/1.52 thf(tcon_Int_Oint___Rings_Olinordered__idom, axiom, (linordered_idom @ int)).
% 2.80/1.52 thf(tcon_Int_Oint___Nat_Osemiring__char__0, axiom, (semiring_char_0 @ int)).
% 2.80/1.52 thf(tcon_Int_Oint___Orderings_Olinorder, axiom, (linorder @ int)).
% 2.80/1.52 thf(tcon_Int_Oint___Rings_Osemiring__1, axiom, (semiring_1 @ int)).
% 2.80/1.52 thf(tcon_Int_Oint___Groups_Ogroup__add, axiom, (group_add @ int)).
% 2.80/1.52 thf(tcon_Int_Oint___Orderings_Oorder_1, axiom, (order @ int)).
% 2.80/1.52 thf(tcon_Int_Oint___Nat_Oring__char__0, axiom, (ring_char_0 @ int)).
% 2.80/1.52 thf(tcon_Int_Oint___Orderings_Oord_2, axiom, (ord @ int)).
% 2.80/1.52 thf(tcon_Int_Oint___Rings_Oring__1, axiom, (ring_1 @ int)).
% 2.80/1.52 thf(tcon_Int_Oint___Groups_Ozero, axiom, (zero @ int)).
% 2.80/1.52 thf(tcon_Int_Oint___Groups_Oone, axiom, (one @ int)).
% 2.80/1.52 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 2.80/1.52 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_3, axiom, (linord1659791738miring @ nat)).
% 2.80/1.52 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, (wellorder @ nat)).
% 2.80/1.52 thf(tcon_Nat_Onat___Nat_Osemiring__char__0_4, axiom, (semiring_char_0 @ nat)).
% 2.80/1.52 thf(tcon_Nat_Onat___Orderings_Olinorder_5, axiom, (linorder @ nat)).
% 2.80/1.52 thf(tcon_Nat_Onat___Rings_Osemiring__1_6, axiom, (semiring_1 @ nat)).
% 2.80/1.52 thf(tcon_Nat_Onat___Orderings_Oorder_7, axiom, (order @ nat)).
% 2.80/1.52 thf(tcon_Nat_Onat___Orderings_Oord_8, axiom, (ord @ nat)).
% 2.80/1.52 thf(tcon_Nat_Onat___Groups_Ozero_9, axiom, (zero @ nat)).
% 2.80/1.52 thf(tcon_Nat_Onat___Groups_Oone_10, axiom, (one @ nat)).
% 2.80/1.52 thf(tcon_Nat_Onat___Nat_Osize, axiom, (size @ nat)).
% 2.80/1.52 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_11, axiom, (! [A14:$tType]: ((boolean_algebra @ (set @ A14))))).
% 2.80/1.52 thf(tcon_Set_Oset___Orderings_Oorder_12, axiom, (! [A14:$tType]: ((order @ (set @ A14))))).
% 2.80/1.52 thf(tcon_Set_Oset___Orderings_Oord_13, axiom, (! [A14:$tType]: ((ord @ (set @ A14))))).
% 2.80/1.52 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_14, axiom, (boolean_algebra @ $o)).
% 2.80/1.52 thf(tcon_HOL_Obool___Orderings_Olinorder_15, axiom, (linorder @ $o)).
% 2.80/1.52 thf(tcon_HOL_Obool___Orderings_Oorder_16, axiom, (order @ $o)).
% 2.80/1.52 thf(tcon_HOL_Obool___Orderings_Oord_17, axiom, (ord @ $o)).
% 2.80/1.52 thf(tcon_List_Olist___Nat_Osize_18, axiom, (! [A14:$tType]: ((size @ (list @ A14))))).
% 2.80/1.52 thf(tcon_Product__Type_Ounit___Lattices_Oboolean__algebra_19, axiom, (boolean_algebra @ product_unit)).
% 2.80/1.52 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_20, axiom, (wellorder @ product_unit)).
% 2.80/1.52 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_21, axiom, (linorder @ product_unit)).
% 2.80/1.52 thf(tcon_Product__Type_Ounit___Orderings_Oorder_22, axiom, (order @ product_unit)).
% 2.80/1.52 thf(tcon_Product__Type_Ounit___Orderings_Oord_23, axiom, (ord @ product_unit)).
% 2.80/1.52 thf(tcon_AsynchronousSystem_Omessage___Nat_Osize_24, axiom, (! [A14:$tType,A15:$tType]: ((size @ ((message @ A14) @ A15))))).
% 2.80/1.52 thf(conj_0, conjecture, (((prefixList @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ m)) @ (fe @ na))).
% 2.80/1.52 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.W0i8NEZydw/DTF2DTF29027.p
% 2.80/1.52 ------------------------
% 2.80/1.55 ---- Cleaned THF ---
% 2.80/1.55 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext,type,
% 2.80/1.55 configuration_ext: $tType > $tType > $tType > $tType > $tType ).
% 2.80/1.55
% 2.80/1.55 thf(ty_t_AsynchronousSystem_OmessageValue,type,
% 2.80/1.55 messageValue: $tType > $tType ).
% 2.80/1.55
% 2.80/1.55 thf(ty_t_AsynchronousSystem_Omessage,type,
% 2.80/1.55 message: $tType > $tType > $tType ).
% 2.80/1.55
% 2.80/1.55 thf(ty_t_Product__Type_Ounit,type,
% 2.80/1.55 product_unit: $tType ).
% 2.80/1.55
% 2.80/1.55 thf(ty_t_List_Olist,type,
% 2.80/1.55 list: $tType > $tType ).
% 2.80/1.55
% 2.80/1.55 thf(ty_t_Set_Oset,type,
% 2.80/1.55 set: $tType > $tType ).
% 2.80/1.55
% 2.80/1.55 thf(ty_t_Nat_Onat,type,
% 2.80/1.55 nat: $tType ).
% 2.80/1.55
% 2.80/1.55 thf(ty_t_Int_Oint,type,
% 2.80/1.55 int: $tType ).
% 2.80/1.55
% 2.80/1.55 thf(ty_tf_v,type,
% 2.80/1.55 v: $tType ).
% 2.80/1.55
% 2.80/1.55 thf(ty_tf_s,type,
% 2.80/1.55 s: $tType ).
% 2.80/1.55
% 2.80/1.55 thf(ty_tf_p,type,
% 2.80/1.55 p: $tType ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_HOL_Otype,type,
% 2.80/1.55 type:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Nat_Osize,type,
% 2.80/1.55 size:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Groups_Oone,type,
% 2.80/1.55 one:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Groups_Ozero,type,
% 2.80/1.55 zero:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Rings_Oring__1,type,
% 2.80/1.55 ring_1:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Orderings_Oord,type,
% 2.80/1.55 ord:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Nat_Oring__char__0,type,
% 2.80/1.55 ring_char_0:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Orderings_Oorder,type,
% 2.80/1.55 order:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Groups_Ogroup__add,type,
% 2.80/1.55 group_add:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Rings_Osemiring__1,type,
% 2.80/1.55 semiring_1:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Orderings_Olinorder,type,
% 2.80/1.55 linorder:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Nat_Osemiring__char__0,type,
% 2.80/1.55 semiring_char_0:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Orderings_Owellorder,type,
% 2.80/1.55 wellorder:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Rings_Olinordered__idom,type,
% 2.80/1.55 linordered_idom:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 2.80/1.55 boolean_algebra:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 2.80/1.55 ordered_ab_group_add:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 2.80/1.55 linord219039673up_add:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 2.80/1.55 linord1659791738miring:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.80/1.55 canoni770627133id_add:
% 2.80/1.55 !>[A: $tType] : $o ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_BNF__Greatest__Fixpoint_Oshift,type,
% 2.80/1.55 bNF_Greatest_shift:
% 2.80/1.55 !>[A: $tType,B: $tType] : ( ( ( list @ A ) > B ) > A > ( list @ A ) > B ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus,type,
% 2.80/1.55 fLPThe1922692578sensus:
% 2.80/1.55 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > $o ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus_OinfiniteExecutionCfg,type,
% 2.80/1.55 fLPThe137922386ionCfg:
% 2.80/1.55 !>[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 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpPseudoConsensus_OinfiniteExecutionMsg,type,
% 2.80/1.55 fLPThe221390223ionMsg:
% 2.80/1.55 !>[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 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_FLPTheorem__Mirabelle__yavhmxymmt_OflpSystem_OterminationFLP,type,
% 2.80/1.55 fLPThe2031355932ionFLP:
% 2.80/1.55 !>[P: $tType,S: $tType,V: $tType] : ( ( P > S > ( messageValue @ V ) > S ) > ( P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat ) > ( P > S ) > ( nat > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) ) > ( nat > ( list @ ( message @ P @ V ) ) ) > $o ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_Groups_Oone__class_Oone,type,
% 2.80/1.55 one_one:
% 2.80/1.55 !>[A: $tType] : A ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 2.80/1.55 uminus_uminus:
% 2.80/1.55 !>[A: $tType] : ( A > A ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.80/1.55 zero_zero:
% 2.80/1.55 !>[A: $tType] : A ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_Int_Onat,type,
% 2.80/1.55 nat2: int > nat ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_Int_Oring__1__class_Oof__int,type,
% 2.80/1.55 ring_1_of_int:
% 2.80/1.55 !>[A: $tType] : ( int > A ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_ListUtilities_OprefixList,type,
% 2.80/1.55 prefixList:
% 2.80/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_List_Ogen__length,type,
% 2.80/1.55 gen_length:
% 2.80/1.55 !>[A: $tType] : ( nat > ( list @ A ) > nat ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_List_Oinsert,type,
% 2.80/1.55 insert:
% 2.80/1.55 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_List_Olist_OCons,type,
% 2.80/1.55 cons:
% 2.80/1.55 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_List_Olist_ONil,type,
% 2.80/1.55 nil:
% 2.80/1.55 !>[A: $tType] : ( list @ A ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_List_Olist__ex1,type,
% 2.80/1.55 list_ex1:
% 2.80/1.55 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_List_On__lists,type,
% 2.80/1.55 n_lists:
% 2.80/1.55 !>[A: $tType] : ( nat > ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_List_Onths,type,
% 2.80/1.55 nths:
% 2.80/1.55 !>[A: $tType] : ( ( list @ A ) > ( set @ nat ) > ( list @ A ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_List_Oproduct__lists,type,
% 2.80/1.55 product_lists:
% 2.80/1.55 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_List_Osubseqs,type,
% 2.80/1.55 subseqs:
% 2.80/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_Nat_OSuc,type,
% 2.80/1.55 suc: nat > nat ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_Nat_Osemiring__1__class_Oof__nat,type,
% 2.80/1.55 semiring_1_of_nat:
% 2.80/1.55 !>[A: $tType] : ( nat > A ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_Nat_Osize__class_Osize,type,
% 2.80/1.55 size_size:
% 2.80/1.55 !>[A: $tType] : ( A > nat ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.80/1.55 ord_less:
% 2.80/1.55 !>[A: $tType] : ( A > A > $o ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.80/1.55 ord_less_eq:
% 2.80/1.55 !>[A: $tType] : ( A > A > $o ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_Set_OCollect,type,
% 2.80/1.55 collect:
% 2.80/1.55 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_c_member,type,
% 2.80/1.55 member:
% 2.80/1.55 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_v_cfg____,type,
% 2.80/1.55 cfg: configuration_ext @ p @ v @ s @ product_unit ).
% 2.80/1.55
% 2.80/1.55 thf(sy_v_fe____,type,
% 2.80/1.55 fe: nat > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(sy_v_m____,type,
% 2.80/1.55 m: nat ).
% 2.80/1.55
% 2.80/1.55 thf(sy_v_n____,type,
% 2.80/1.55 n: nat ).
% 2.80/1.55
% 2.80/1.55 thf(sy_v_na____,type,
% 2.80/1.55 na: nat ).
% 2.80/1.55
% 2.80/1.55 thf(fact_0__092_060open_062m_A_060_An_092_060close_062,axiom,
% 2.80/1.55 ord_less @ nat @ m @ na ).
% 2.80/1.55
% 2.80/1.55 thf(fact_1_MLessN,axiom,
% 2.80/1.55 ord_less @ nat @ m @ n ).
% 2.80/1.55
% 2.80/1.55 thf(fact_2_IA_I1_J,axiom,
% 2.80/1.55 ( ( ord_less @ nat @ m @ na )
% 2.80/1.55 => ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ m ) @ ( fe @ na ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_3__092_060open_062m_A_061_An_A_092_060or_062_Am_A_060_An_092_060close_062,axiom,
% 2.80/1.55 ( ( m = na )
% 2.80/1.55 | ( ord_less @ nat @ m @ na ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_4_IA_I2_J,axiom,
% 2.80/1.55 ord_less @ nat @ m @ ( suc @ na ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_5_PrefixListTransitive,axiom,
% 2.80/1.55 ! [A: $tType,L1: list @ A,L2: list @ A,L3: list @ A] :
% 2.80/1.55 ( ( prefixList @ A @ L1 @ L2 )
% 2.80/1.55 => ( ( prefixList @ A @ L2 @ L3 )
% 2.80/1.55 => ( prefixList @ A @ L1 @ L3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_6_flpSystem_OterminationFLP_Ocong,axiom,
% 2.80/1.55 ! [V: $tType,S: $tType,P: $tType] :
% 2.80/1.55 ( ( fLPThe2031355932ionFLP @ P @ S @ V )
% 2.80/1.55 = ( fLPThe2031355932ionFLP @ P @ S @ V ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_7_FE_I1_J,axiom,
% 2.80/1.55 ( ( fe @ ( zero_zero @ nat ) )
% 2.80/1.55 = ( cons @ ( configuration_ext @ p @ v @ s @ product_unit ) @ cfg @ ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_8_prefixList_Ointros_I2_J,axiom,
% 2.80/1.55 ! [A: $tType,Xa: list @ A,Xb: list @ A,X: A] :
% 2.80/1.55 ( ( prefixList @ A @ Xa @ Xb )
% 2.80/1.55 => ( prefixList @ A @ ( cons @ A @ X @ Xa ) @ ( cons @ A @ X @ Xb ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_9_PrefixListMonotonicity,axiom,
% 2.80/1.55 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 2.80/1.55 ( ( prefixList @ A @ L1 @ L2 )
% 2.80/1.55 => ( ord_less @ nat @ ( size_size @ ( list @ A ) @ L1 ) @ ( size_size @ ( list @ A ) @ L2 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_10_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 2.80/1.55 ! [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] :
% 2.80/1.55 ( ! [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 ) )
% 2.80/1.55 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N: nat] :
% 2.80/1.55 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.80/1.55 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.80/1.55 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 2.80/1.55 => ( ! [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 ) )
% 2.80/1.55 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N: nat] :
% 2.80/1.55 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.80/1.55 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.80/1.55 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 2.80/1.55 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_11_infiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 2.80/1.55 ! [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] :
% 2.80/1.55 ( ! [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 ) )
% 2.80/1.55 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N: nat] :
% 2.80/1.55 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.80/1.55 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.80/1.55 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 2.80/1.55 => ( ! [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 ) )
% 2.80/1.55 => ( ! [Cfg: configuration_ext @ p @ v @ s @ product_unit,FStepCfg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) > ( list @ ( message @ p @ v ) ) > ( list @ ( message @ p @ v ) ),N: nat] :
% 2.80/1.55 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.80/1.55 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.80/1.55 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 2.80/1.55 => ( P2 @ A0 @ A1 @ A2 @ A3 ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_12_prefixList_Ointros_I1_J,axiom,
% 2.80/1.55 ! [A: $tType,X: A,Xs: list @ A] : ( prefixList @ A @ ( nil @ A ) @ ( cons @ A @ X @ Xs ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_13_prefixList_Ocases,axiom,
% 2.80/1.55 ! [A: $tType,A1: list @ A,A2: list @ A] :
% 2.80/1.55 ( ( prefixList @ A @ A1 @ A2 )
% 2.80/1.55 => ( ( ( A1
% 2.80/1.55 = ( nil @ A ) )
% 2.80/1.55 => ! [X2: A,Xs2: list @ A] :
% 2.80/1.55 ( A2
% 2.80/1.55 != ( cons @ A @ X2 @ Xs2 ) ) )
% 2.80/1.55 => ~ ! [Xa2: list @ A,Xb2: list @ A,X2: A] :
% 2.80/1.55 ( ( A1
% 2.80/1.55 = ( cons @ A @ X2 @ Xa2 ) )
% 2.80/1.55 => ( ( A2
% 2.80/1.55 = ( cons @ A @ X2 @ Xb2 ) )
% 2.80/1.55 => ~ ( prefixList @ A @ Xa2 @ Xb2 ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_14_prefixList_Osimps,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( prefixList @ A )
% 2.80/1.55 = ( ^ [A12: list @ A,A22: list @ A] :
% 2.80/1.55 ( ? [X3: A,Xs3: list @ A] :
% 2.80/1.55 ( ( A12
% 2.80/1.55 = ( nil @ A ) )
% 2.80/1.55 & ( A22
% 2.80/1.55 = ( cons @ A @ X3 @ Xs3 ) ) )
% 2.80/1.55 | ? [Xa3: list @ A,Xb3: list @ A,X3: A] :
% 2.80/1.55 ( ( A12
% 2.80/1.55 = ( cons @ A @ X3 @ Xa3 ) )
% 2.80/1.55 & ( A22
% 2.80/1.55 = ( cons @ A @ X3 @ Xb3 ) )
% 2.80/1.55 & ( prefixList @ A @ Xa3 @ Xb3 ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_15_prefixList_Oinducts,axiom,
% 2.80/1.55 ! [A: $tType,X1: list @ A,X22: list @ A,P2: ( list @ A ) > ( list @ A ) > $o] :
% 2.80/1.55 ( ( prefixList @ A @ X1 @ X22 )
% 2.80/1.55 => ( ! [X2: A,Xs2: list @ A] : ( P2 @ ( nil @ A ) @ ( cons @ A @ X2 @ Xs2 ) )
% 2.80/1.55 => ( ! [Xa2: list @ A,Xb2: list @ A,X2: A] :
% 2.80/1.55 ( ( prefixList @ A @ Xa2 @ Xb2 )
% 2.80/1.55 => ( ( P2 @ Xa2 @ Xb2 )
% 2.80/1.55 => ( P2 @ ( cons @ A @ X2 @ Xa2 ) @ ( cons @ A @ X2 @ Xb2 ) ) ) )
% 2.80/1.55 => ( P2 @ X1 @ X22 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_16_NatPredicateTippingPoint,axiom,
% 2.80/1.55 ! [N2: nat,Pr: nat > $o] :
% 2.80/1.55 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N2 )
% 2.80/1.55 => ( ( Pr @ ( zero_zero @ nat ) )
% 2.80/1.55 => ( ~ ( Pr @ N2 )
% 2.80/1.55 => ? [N: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ N @ N2 )
% 2.80/1.55 & ( Pr @ N )
% 2.80/1.55 & ~ ( Pr @ ( suc @ N ) ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_17_infiniteExecutionCfg_Osimps_I1_J,axiom,
% 2.80/1.55 ! [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 ) )] :
% 2.80/1.55 ( ( fLPThe137922386ionCfg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( zero_zero @ nat ) )
% 2.80/1.55 = ( cons @ ( configuration_ext @ p @ v @ s @ product_unit ) @ Cfg2 @ ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_18_length__greater__0__conv,axiom,
% 2.80/1.55 ! [A: $tType,Xs: list @ A] :
% 2.80/1.55 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( size_size @ ( list @ A ) @ Xs ) )
% 2.80/1.55 = ( Xs
% 2.80/1.55 != ( nil @ A ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_19_length__0__conv,axiom,
% 2.80/1.55 ! [A: $tType,Xs: list @ A] :
% 2.80/1.55 ( ( ( size_size @ ( list @ A ) @ Xs )
% 2.80/1.55 = ( zero_zero @ nat ) )
% 2.80/1.55 = ( Xs
% 2.80/1.55 = ( nil @ A ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_20_less__Suc0,axiom,
% 2.80/1.55 ! [N3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ N3 @ ( suc @ ( zero_zero @ nat ) ) )
% 2.80/1.55 = ( N3
% 2.80/1.55 = ( zero_zero @ nat ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_21_zero__less__Suc,axiom,
% 2.80/1.55 ! [N3: nat] : ( ord_less @ nat @ ( zero_zero @ nat ) @ ( suc @ N3 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_22_lessI,axiom,
% 2.80/1.55 ! [N3: nat] : ( ord_less @ nat @ N3 @ ( suc @ N3 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_23_Suc__mono,axiom,
% 2.80/1.55 ! [M: nat,N3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ M @ N3 )
% 2.80/1.55 => ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_24_Suc__less__eq,axiom,
% 2.80/1.55 ! [M: nat,N3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N3 ) )
% 2.80/1.55 = ( ord_less @ nat @ M @ N3 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_25_neq0__conv,axiom,
% 2.80/1.55 ! [N3: nat] :
% 2.80/1.55 ( ( N3
% 2.80/1.55 != ( zero_zero @ nat ) )
% 2.80/1.55 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N3 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_26_less__nat__zero__code,axiom,
% 2.80/1.55 ! [N3: nat] :
% 2.80/1.55 ~ ( ord_less @ nat @ N3 @ ( zero_zero @ nat ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_27_bot__nat__0_Onot__eq__extremum,axiom,
% 2.80/1.55 ! [A8: nat] :
% 2.80/1.55 ( ( A8
% 2.80/1.55 != ( zero_zero @ nat ) )
% 2.80/1.55 = ( ord_less @ nat @ ( zero_zero @ nat ) @ A8 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_28_list_Oinject,axiom,
% 2.80/1.55 ! [A: $tType,X21: A,X222: list @ A,Y21: A,Y22: list @ A] :
% 2.80/1.55 ( ( ( cons @ A @ X21 @ X222 )
% 2.80/1.55 = ( cons @ A @ Y21 @ Y22 ) )
% 2.80/1.55 = ( ( X21 = Y21 )
% 2.80/1.55 & ( X222 = Y22 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_29_old_Onat_Oinject,axiom,
% 2.80/1.55 ! [Nat: nat,Nat2: nat] :
% 2.80/1.55 ( ( ( suc @ Nat )
% 2.80/1.55 = ( suc @ Nat2 ) )
% 2.80/1.55 = ( Nat = Nat2 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_30_nat_Oinject,axiom,
% 2.80/1.55 ! [X22: nat,Y2: nat] :
% 2.80/1.55 ( ( ( suc @ X22 )
% 2.80/1.55 = ( suc @ Y2 ) )
% 2.80/1.55 = ( X22 = Y2 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_31_measure__induct__rule,axiom,
% 2.80/1.55 ! [B: $tType,A: $tType] :
% 2.80/1.55 ( ( wellorder @ B )
% 2.80/1.55 => ! [F: A > B,P2: A > $o,A8: A] :
% 2.80/1.55 ( ! [X2: A] :
% 2.80/1.55 ( ! [Y: A] :
% 2.80/1.55 ( ( ord_less @ B @ ( F @ Y ) @ ( F @ X2 ) )
% 2.80/1.55 => ( P2 @ Y ) )
% 2.80/1.55 => ( P2 @ X2 ) )
% 2.80/1.55 => ( P2 @ A8 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_32_measure__induct,axiom,
% 2.80/1.55 ! [B: $tType,A: $tType] :
% 2.80/1.55 ( ( wellorder @ B )
% 2.80/1.55 => ! [F: A > B,P2: A > $o,A8: A] :
% 2.80/1.55 ( ! [X2: A] :
% 2.80/1.55 ( ! [Y: A] :
% 2.80/1.55 ( ( ord_less @ B @ ( F @ Y ) @ ( F @ X2 ) )
% 2.80/1.55 => ( P2 @ Y ) )
% 2.80/1.55 => ( P2 @ X2 ) )
% 2.80/1.55 => ( P2 @ A8 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_33_not__Cons__self2,axiom,
% 2.80/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.80/1.55 ( ( cons @ A @ X @ Xs )
% 2.80/1.55 != Xs ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_34_n__not__Suc__n,axiom,
% 2.80/1.55 ! [N3: nat] :
% 2.80/1.55 ( N3
% 2.80/1.55 != ( suc @ N3 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_35_Suc__inject,axiom,
% 2.80/1.55 ! [X: nat,Y3: nat] :
% 2.80/1.55 ( ( ( suc @ X )
% 2.80/1.55 = ( suc @ Y3 ) )
% 2.80/1.55 => ( X = Y3 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_36_infinite__descent__measure,axiom,
% 2.80/1.55 ! [A: $tType,P2: A > $o,V2: A > nat,X: A] :
% 2.80/1.55 ( ! [X2: A] :
% 2.80/1.55 ( ~ ( P2 @ X2 )
% 2.80/1.55 => ? [Y: A] :
% 2.80/1.55 ( ( ord_less @ nat @ ( V2 @ Y ) @ ( V2 @ X2 ) )
% 2.80/1.55 & ~ ( P2 @ Y ) ) )
% 2.80/1.55 => ( P2 @ X ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_37_linorder__neqE__nat,axiom,
% 2.80/1.55 ! [X: nat,Y3: nat] :
% 2.80/1.55 ( ( X != Y3 )
% 2.80/1.55 => ( ~ ( ord_less @ nat @ X @ Y3 )
% 2.80/1.55 => ( ord_less @ nat @ Y3 @ X ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_38_infinite__descent,axiom,
% 2.80/1.55 ! [P2: nat > $o,N3: nat] :
% 2.80/1.55 ( ! [N: nat] :
% 2.80/1.55 ( ~ ( P2 @ N )
% 2.80/1.55 => ? [M2: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ M2 @ N )
% 2.80/1.55 & ~ ( P2 @ M2 ) ) )
% 2.80/1.55 => ( P2 @ N3 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_39_nat__less__induct,axiom,
% 2.80/1.55 ! [P2: nat > $o,N3: nat] :
% 2.80/1.55 ( ! [N: nat] :
% 2.80/1.55 ( ! [M2: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ M2 @ N )
% 2.80/1.55 => ( P2 @ M2 ) )
% 2.80/1.55 => ( P2 @ N ) )
% 2.80/1.55 => ( P2 @ N3 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_40_less__irrefl__nat,axiom,
% 2.80/1.55 ! [N3: nat] :
% 2.80/1.55 ~ ( ord_less @ nat @ N3 @ N3 ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_41_less__not__refl3,axiom,
% 2.80/1.55 ! [S2: nat,T: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ S2 @ T )
% 2.80/1.55 => ( S2 != T ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_42_less__not__refl2,axiom,
% 2.80/1.55 ! [N3: nat,M: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ N3 @ M )
% 2.80/1.55 => ( M != N3 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_43_mem__Collect__eq,axiom,
% 2.80/1.55 ! [A: $tType,A8: A,P2: A > $o] :
% 2.80/1.55 ( ( member @ A @ A8 @ ( collect @ A @ P2 ) )
% 2.80/1.55 = ( P2 @ A8 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_44_Collect__mem__eq,axiom,
% 2.80/1.55 ! [A: $tType,A9: set @ A] :
% 2.80/1.55 ( ( collect @ A
% 2.80/1.55 @ ^ [X3: A] : ( member @ A @ X3 @ A9 ) )
% 2.80/1.55 = A9 ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_45_Collect__cong,axiom,
% 2.80/1.55 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 2.80/1.55 ( ! [X2: A] :
% 2.80/1.55 ( ( P2 @ X2 )
% 2.80/1.55 = ( Q @ X2 ) )
% 2.80/1.55 => ( ( collect @ A @ P2 )
% 2.80/1.55 = ( collect @ A @ Q ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_46_ext,axiom,
% 2.80/1.55 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.80/1.55 ( ! [X2: A] :
% 2.80/1.55 ( ( F @ X2 )
% 2.80/1.55 = ( G @ X2 ) )
% 2.80/1.55 => ( F = G ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_47_less__not__refl,axiom,
% 2.80/1.55 ! [N3: nat] :
% 2.80/1.55 ~ ( ord_less @ nat @ N3 @ N3 ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_48_nat__neq__iff,axiom,
% 2.80/1.55 ! [M: nat,N3: nat] :
% 2.80/1.55 ( ( M != N3 )
% 2.80/1.55 = ( ( ord_less @ nat @ M @ N3 )
% 2.80/1.55 | ( ord_less @ nat @ N3 @ M ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_49_size__neq__size__imp__neq,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( size @ A )
% 2.80/1.55 => ! [X: A,Y3: A] :
% 2.80/1.55 ( ( ( size_size @ A @ X )
% 2.80/1.55 != ( size_size @ A @ Y3 ) )
% 2.80/1.55 => ( X != Y3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_50_neq__if__length__neq,axiom,
% 2.80/1.55 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.80/1.55 ( ( ( size_size @ ( list @ A ) @ Xs )
% 2.80/1.55 != ( size_size @ ( list @ A ) @ Ys ) )
% 2.80/1.55 => ( Xs != Ys ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_51_Ex__list__of__length,axiom,
% 2.80/1.55 ! [A: $tType,N3: nat] :
% 2.80/1.55 ? [Xs2: list @ A] :
% 2.80/1.55 ( ( size_size @ ( list @ A ) @ Xs2 )
% 2.80/1.55 = N3 ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_52_not0__implies__Suc,axiom,
% 2.80/1.55 ! [N3: nat] :
% 2.80/1.55 ( ( N3
% 2.80/1.55 != ( zero_zero @ nat ) )
% 2.80/1.55 => ? [M3: nat] :
% 2.80/1.55 ( N3
% 2.80/1.55 = ( suc @ M3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_53_old_Onat_Oinducts,axiom,
% 2.80/1.55 ! [P2: nat > $o,Nat: nat] :
% 2.80/1.55 ( ( P2 @ ( zero_zero @ nat ) )
% 2.80/1.55 => ( ! [Nat3: nat] :
% 2.80/1.55 ( ( P2 @ Nat3 )
% 2.80/1.55 => ( P2 @ ( suc @ Nat3 ) ) )
% 2.80/1.55 => ( P2 @ Nat ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_54_old_Onat_Oexhaust,axiom,
% 2.80/1.55 ! [Y3: nat] :
% 2.80/1.55 ( ( Y3
% 2.80/1.55 != ( zero_zero @ nat ) )
% 2.80/1.55 => ~ ! [Nat3: nat] :
% 2.80/1.55 ( Y3
% 2.80/1.55 != ( suc @ Nat3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_55_Zero__not__Suc,axiom,
% 2.80/1.55 ! [M: nat] :
% 2.80/1.55 ( ( zero_zero @ nat )
% 2.80/1.55 != ( suc @ M ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_56_Zero__neq__Suc,axiom,
% 2.80/1.55 ! [M: nat] :
% 2.80/1.55 ( ( zero_zero @ nat )
% 2.80/1.55 != ( suc @ M ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_57_Suc__neq__Zero,axiom,
% 2.80/1.55 ! [M: nat] :
% 2.80/1.55 ( ( suc @ M )
% 2.80/1.55 != ( zero_zero @ nat ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_58_zero__induct,axiom,
% 2.80/1.55 ! [P2: nat > $o,K: nat] :
% 2.80/1.55 ( ( P2 @ K )
% 2.80/1.55 => ( ! [N: nat] :
% 2.80/1.55 ( ( P2 @ ( suc @ N ) )
% 2.80/1.55 => ( P2 @ N ) )
% 2.80/1.55 => ( P2 @ ( zero_zero @ nat ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_59_diff__induct,axiom,
% 2.80/1.55 ! [P2: nat > nat > $o,M: nat,N3: nat] :
% 2.80/1.55 ( ! [X2: nat] : ( P2 @ X2 @ ( zero_zero @ nat ) )
% 2.80/1.55 => ( ! [Y4: nat] : ( P2 @ ( zero_zero @ nat ) @ ( suc @ Y4 ) )
% 2.80/1.55 => ( ! [X2: nat,Y4: nat] :
% 2.80/1.55 ( ( P2 @ X2 @ Y4 )
% 2.80/1.55 => ( P2 @ ( suc @ X2 ) @ ( suc @ Y4 ) ) )
% 2.80/1.55 => ( P2 @ M @ N3 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_60_nat__induct,axiom,
% 2.80/1.55 ! [P2: nat > $o,N3: nat] :
% 2.80/1.55 ( ( P2 @ ( zero_zero @ nat ) )
% 2.80/1.55 => ( ! [N: nat] :
% 2.80/1.55 ( ( P2 @ N )
% 2.80/1.55 => ( P2 @ ( suc @ N ) ) )
% 2.80/1.55 => ( P2 @ N3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_61_nat_OdiscI,axiom,
% 2.80/1.55 ! [Nat: nat,X22: nat] :
% 2.80/1.55 ( ( Nat
% 2.80/1.55 = ( suc @ X22 ) )
% 2.80/1.55 => ( Nat
% 2.80/1.55 != ( zero_zero @ nat ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_62_old_Onat_Odistinct_I1_J,axiom,
% 2.80/1.55 ! [Nat2: nat] :
% 2.80/1.55 ( ( zero_zero @ nat )
% 2.80/1.55 != ( suc @ Nat2 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_63_old_Onat_Odistinct_I2_J,axiom,
% 2.80/1.55 ! [Nat4: nat] :
% 2.80/1.55 ( ( suc @ Nat4 )
% 2.80/1.55 != ( zero_zero @ nat ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_64_nat_Odistinct_I1_J,axiom,
% 2.80/1.55 ! [X22: nat] :
% 2.80/1.55 ( ( zero_zero @ nat )
% 2.80/1.55 != ( suc @ X22 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_65_infinite__descent0__measure,axiom,
% 2.80/1.55 ! [A: $tType,V2: A > nat,P2: A > $o,X: A] :
% 2.80/1.55 ( ! [X2: A] :
% 2.80/1.55 ( ( ( V2 @ X2 )
% 2.80/1.55 = ( zero_zero @ nat ) )
% 2.80/1.55 => ( P2 @ X2 ) )
% 2.80/1.55 => ( ! [X2: A] :
% 2.80/1.55 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( V2 @ X2 ) )
% 2.80/1.55 => ( ~ ( P2 @ X2 )
% 2.80/1.55 => ? [Y: A] :
% 2.80/1.55 ( ( ord_less @ nat @ ( V2 @ Y ) @ ( V2 @ X2 ) )
% 2.80/1.55 & ~ ( P2 @ Y ) ) ) )
% 2.80/1.55 => ( P2 @ X ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_66_bot__nat__0_Oextremum__strict,axiom,
% 2.80/1.55 ! [A8: nat] :
% 2.80/1.55 ~ ( ord_less @ nat @ A8 @ ( zero_zero @ nat ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_67_infinite__descent0,axiom,
% 2.80/1.55 ! [P2: nat > $o,N3: nat] :
% 2.80/1.55 ( ( P2 @ ( zero_zero @ nat ) )
% 2.80/1.55 => ( ! [N: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.80/1.55 => ( ~ ( P2 @ N )
% 2.80/1.55 => ? [M2: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ M2 @ N )
% 2.80/1.55 & ~ ( P2 @ M2 ) ) ) )
% 2.80/1.55 => ( P2 @ N3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_68_gr__implies__not0,axiom,
% 2.80/1.55 ! [M: nat,N3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ M @ N3 )
% 2.80/1.55 => ( N3
% 2.80/1.55 != ( zero_zero @ nat ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_69_less__zeroE,axiom,
% 2.80/1.55 ! [N3: nat] :
% 2.80/1.55 ~ ( ord_less @ nat @ N3 @ ( zero_zero @ nat ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_70_not__less0,axiom,
% 2.80/1.55 ! [N3: nat] :
% 2.80/1.55 ~ ( ord_less @ nat @ N3 @ ( zero_zero @ nat ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_71_not__gr0,axiom,
% 2.80/1.55 ! [N3: nat] :
% 2.80/1.55 ( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N3 ) )
% 2.80/1.55 = ( N3
% 2.80/1.55 = ( zero_zero @ nat ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_72_gr0I,axiom,
% 2.80/1.55 ! [N3: nat] :
% 2.80/1.55 ( ( N3
% 2.80/1.55 != ( zero_zero @ nat ) )
% 2.80/1.55 => ( ord_less @ nat @ ( zero_zero @ nat ) @ N3 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_73_not__less__less__Suc__eq,axiom,
% 2.80/1.55 ! [N3: nat,M: nat] :
% 2.80/1.55 ( ~ ( ord_less @ nat @ N3 @ M )
% 2.80/1.55 => ( ( ord_less @ nat @ N3 @ ( suc @ M ) )
% 2.80/1.55 = ( N3 = M ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_74_strict__inc__induct,axiom,
% 2.80/1.55 ! [I: nat,J: nat,P2: nat > $o] :
% 2.80/1.55 ( ( ord_less @ nat @ I @ J )
% 2.80/1.55 => ( ! [I2: nat] :
% 2.80/1.55 ( ( J
% 2.80/1.55 = ( suc @ I2 ) )
% 2.80/1.55 => ( P2 @ I2 ) )
% 2.80/1.55 => ( ! [I2: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ I2 @ J )
% 2.80/1.55 => ( ( P2 @ ( suc @ I2 ) )
% 2.80/1.55 => ( P2 @ I2 ) ) )
% 2.80/1.55 => ( P2 @ I ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_75_less__Suc__induct,axiom,
% 2.80/1.55 ! [I: nat,J: nat,P2: nat > nat > $o] :
% 2.80/1.55 ( ( ord_less @ nat @ I @ J )
% 2.80/1.55 => ( ! [I2: nat] : ( P2 @ I2 @ ( suc @ I2 ) )
% 2.80/1.55 => ( ! [I2: nat,J2: nat,K2: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ I2 @ J2 )
% 2.80/1.55 => ( ( ord_less @ nat @ J2 @ K2 )
% 2.80/1.55 => ( ( P2 @ I2 @ J2 )
% 2.80/1.55 => ( ( P2 @ J2 @ K2 )
% 2.80/1.55 => ( P2 @ I2 @ K2 ) ) ) ) )
% 2.80/1.55 => ( P2 @ I @ J ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_76_less__trans__Suc,axiom,
% 2.80/1.55 ! [I: nat,J: nat,K: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ I @ J )
% 2.80/1.55 => ( ( ord_less @ nat @ J @ K )
% 2.80/1.55 => ( ord_less @ nat @ ( suc @ I ) @ K ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_77_Suc__less__SucD,axiom,
% 2.80/1.55 ! [M: nat,N3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N3 ) )
% 2.80/1.55 => ( ord_less @ nat @ M @ N3 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_78_less__antisym,axiom,
% 2.80/1.55 ! [N3: nat,M: nat] :
% 2.80/1.55 ( ~ ( ord_less @ nat @ N3 @ M )
% 2.80/1.55 => ( ( ord_less @ nat @ N3 @ ( suc @ M ) )
% 2.80/1.55 => ( M = N3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_79_Suc__less__eq2,axiom,
% 2.80/1.55 ! [N3: nat,M: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ ( suc @ N3 ) @ M )
% 2.80/1.55 = ( ? [M4: nat] :
% 2.80/1.55 ( ( M
% 2.80/1.55 = ( suc @ M4 ) )
% 2.80/1.55 & ( ord_less @ nat @ N3 @ M4 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_80_All__less__Suc,axiom,
% 2.80/1.55 ! [N3: nat,P2: nat > $o] :
% 2.80/1.55 ( ( ! [I3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ I3 @ ( suc @ N3 ) )
% 2.80/1.55 => ( P2 @ I3 ) ) )
% 2.80/1.55 = ( ( P2 @ N3 )
% 2.80/1.55 & ! [I3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ I3 @ N3 )
% 2.80/1.55 => ( P2 @ I3 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_81_not__less__eq,axiom,
% 2.80/1.55 ! [M: nat,N3: nat] :
% 2.80/1.55 ( ( ~ ( ord_less @ nat @ M @ N3 ) )
% 2.80/1.55 = ( ord_less @ nat @ N3 @ ( suc @ M ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_82_less__Suc__eq,axiom,
% 2.80/1.55 ! [M: nat,N3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ M @ ( suc @ N3 ) )
% 2.80/1.55 = ( ( ord_less @ nat @ M @ N3 )
% 2.80/1.55 | ( M = N3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_83_Ex__less__Suc,axiom,
% 2.80/1.55 ! [N3: nat,P2: nat > $o] :
% 2.80/1.55 ( ( ? [I3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ I3 @ ( suc @ N3 ) )
% 2.80/1.55 & ( P2 @ I3 ) ) )
% 2.80/1.55 = ( ( P2 @ N3 )
% 2.80/1.55 | ? [I3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ I3 @ N3 )
% 2.80/1.55 & ( P2 @ I3 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_84_less__SucI,axiom,
% 2.80/1.55 ! [M: nat,N3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ M @ N3 )
% 2.80/1.55 => ( ord_less @ nat @ M @ ( suc @ N3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_85_less__SucE,axiom,
% 2.80/1.55 ! [M: nat,N3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ M @ ( suc @ N3 ) )
% 2.80/1.55 => ( ~ ( ord_less @ nat @ M @ N3 )
% 2.80/1.55 => ( M = N3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_86_Suc__lessI,axiom,
% 2.80/1.55 ! [M: nat,N3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ M @ N3 )
% 2.80/1.55 => ( ( ( suc @ M )
% 2.80/1.55 != N3 )
% 2.80/1.55 => ( ord_less @ nat @ ( suc @ M ) @ N3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_87_Suc__lessE,axiom,
% 2.80/1.55 ! [I: nat,K: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ ( suc @ I ) @ K )
% 2.80/1.55 => ~ ! [J2: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ I @ J2 )
% 2.80/1.55 => ( K
% 2.80/1.55 != ( suc @ J2 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_88_Suc__lessD,axiom,
% 2.80/1.55 ! [M: nat,N3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ ( suc @ M ) @ N3 )
% 2.80/1.55 => ( ord_less @ nat @ M @ N3 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_89_Nat_OlessE,axiom,
% 2.80/1.55 ! [I: nat,K: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ I @ K )
% 2.80/1.55 => ( ( K
% 2.80/1.55 != ( suc @ I ) )
% 2.80/1.55 => ~ ! [J2: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ I @ J2 )
% 2.80/1.55 => ( K
% 2.80/1.55 != ( suc @ J2 ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_90_strict__sorted_Oinduct,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( linorder @ A )
% 2.80/1.55 => ! [P2: ( list @ A ) > $o,A0: list @ A] :
% 2.80/1.55 ( ( P2 @ ( nil @ A ) )
% 2.80/1.55 => ( ! [X2: A,Ys2: list @ A] :
% 2.80/1.55 ( ( P2 @ Ys2 )
% 2.80/1.55 => ( P2 @ ( cons @ A @ X2 @ Ys2 ) ) )
% 2.80/1.55 => ( P2 @ A0 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_91_strict__sorted_Ocases,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( linorder @ A )
% 2.80/1.55 => ! [X: list @ A] :
% 2.80/1.55 ( ( X
% 2.80/1.55 != ( nil @ A ) )
% 2.80/1.55 => ~ ! [X2: A,Ys2: list @ A] :
% 2.80/1.55 ( X
% 2.80/1.55 != ( cons @ A @ X2 @ Ys2 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_92_map__tailrec__rev_Oinduct,axiom,
% 2.80/1.55 ! [A: $tType,B: $tType,P2: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A2: list @ B] :
% 2.80/1.55 ( ! [F2: A > B,X_1: list @ B] : ( P2 @ F2 @ ( nil @ A ) @ X_1 )
% 2.80/1.55 => ( ! [F2: A > B,A10: A,As: list @ A,Bs: list @ B] :
% 2.80/1.55 ( ( P2 @ F2 @ As @ ( cons @ B @ ( F2 @ A10 ) @ Bs ) )
% 2.80/1.55 => ( P2 @ F2 @ ( cons @ A @ A10 @ As ) @ Bs ) )
% 2.80/1.55 => ( P2 @ A0 @ A1 @ A2 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_93_list__nonempty__induct,axiom,
% 2.80/1.55 ! [A: $tType,Xs: list @ A,P2: ( list @ A ) > $o] :
% 2.80/1.55 ( ( Xs
% 2.80/1.55 != ( nil @ A ) )
% 2.80/1.55 => ( ! [X2: A] : ( P2 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.80/1.55 => ( ! [X2: A,Xs2: list @ A] :
% 2.80/1.55 ( ( Xs2
% 2.80/1.55 != ( nil @ A ) )
% 2.80/1.55 => ( ( P2 @ Xs2 )
% 2.80/1.55 => ( P2 @ ( cons @ A @ X2 @ Xs2 ) ) ) )
% 2.80/1.55 => ( P2 @ Xs ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_94_successively_Oinduct,axiom,
% 2.80/1.55 ! [A: $tType,P2: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 2.80/1.55 ( ! [P3: A > A > $o] : ( P2 @ P3 @ ( nil @ A ) )
% 2.80/1.55 => ( ! [P3: A > A > $o,X2: A] : ( P2 @ P3 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.80/1.55 => ( ! [P3: A > A > $o,X2: A,Y4: A,Xs2: list @ A] :
% 2.80/1.55 ( ( P2 @ P3 @ ( cons @ A @ Y4 @ Xs2 ) )
% 2.80/1.55 => ( P2 @ P3 @ ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Xs2 ) ) ) )
% 2.80/1.55 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_95_arg__min__list_Oinduct,axiom,
% 2.80/1.55 ! [B: $tType,A: $tType] :
% 2.80/1.55 ( ( linorder @ B )
% 2.80/1.55 => ! [P2: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 2.80/1.55 ( ! [F2: A > B,X2: A] : ( P2 @ F2 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.80/1.55 => ( ! [F2: A > B,X2: A,Y4: A,Zs: list @ A] :
% 2.80/1.55 ( ( P2 @ F2 @ ( cons @ A @ Y4 @ Zs ) )
% 2.80/1.55 => ( P2 @ F2 @ ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Zs ) ) ) )
% 2.80/1.55 => ( ! [A10: A > B] : ( P2 @ A10 @ ( nil @ A ) )
% 2.80/1.55 => ( P2 @ A0 @ A1 ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_96_remdups__adj_Oinduct,axiom,
% 2.80/1.55 ! [A: $tType,P2: ( list @ A ) > $o,A0: list @ A] :
% 2.80/1.55 ( ( P2 @ ( nil @ A ) )
% 2.80/1.55 => ( ! [X2: A] : ( P2 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.80/1.55 => ( ! [X2: A,Y4: A,Xs2: list @ A] :
% 2.80/1.55 ( ( ( X2 = Y4 )
% 2.80/1.55 => ( P2 @ ( cons @ A @ X2 @ Xs2 ) ) )
% 2.80/1.55 => ( ( ( X2 != Y4 )
% 2.80/1.55 => ( P2 @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 2.80/1.55 => ( P2 @ ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) )
% 2.80/1.55 => ( P2 @ A0 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_97_sorted__wrt_Oinduct,axiom,
% 2.80/1.55 ! [A: $tType,P2: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 2.80/1.55 ( ! [P3: A > A > $o] : ( P2 @ P3 @ ( nil @ A ) )
% 2.80/1.55 => ( ! [P3: A > A > $o,X2: A,Ys2: list @ A] :
% 2.80/1.55 ( ( P2 @ P3 @ Ys2 )
% 2.80/1.55 => ( P2 @ P3 @ ( cons @ A @ X2 @ Ys2 ) ) )
% 2.80/1.55 => ( P2 @ A0 @ A1 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_98_remdups__adj_Ocases,axiom,
% 2.80/1.55 ! [A: $tType,X: list @ A] :
% 2.80/1.55 ( ( X
% 2.80/1.55 != ( nil @ A ) )
% 2.80/1.55 => ( ! [X2: A] :
% 2.80/1.55 ( X
% 2.80/1.55 != ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.80/1.55 => ~ ! [X2: A,Y4: A,Xs2: list @ A] :
% 2.80/1.55 ( X
% 2.80/1.55 != ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_99_transpose_Ocases,axiom,
% 2.80/1.55 ! [A: $tType,X: list @ ( list @ A )] :
% 2.80/1.55 ( ( X
% 2.80/1.55 != ( nil @ ( list @ A ) ) )
% 2.80/1.55 => ( ! [Xss: list @ ( list @ A )] :
% 2.80/1.55 ( X
% 2.80/1.55 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 2.80/1.55 => ~ ! [X2: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 2.80/1.55 ( X
% 2.80/1.55 != ( cons @ ( list @ A ) @ ( cons @ A @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_100_shuffles_Oinduct,axiom,
% 2.80/1.55 ! [A: $tType,P2: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.80/1.55 ( ! [X_1: list @ A] : ( P2 @ ( nil @ A ) @ X_1 )
% 2.80/1.55 => ( ! [Xs2: list @ A] : ( P2 @ Xs2 @ ( nil @ A ) )
% 2.80/1.55 => ( ! [X2: A,Xs2: list @ A,Y4: A,Ys2: list @ A] :
% 2.80/1.55 ( ( P2 @ Xs2 @ ( cons @ A @ Y4 @ Ys2 ) )
% 2.80/1.55 => ( ( P2 @ ( cons @ A @ X2 @ Xs2 ) @ Ys2 )
% 2.80/1.55 => ( P2 @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys2 ) ) ) )
% 2.80/1.55 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_101_min__list_Oinduct,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( ord @ A )
% 2.80/1.55 => ! [P2: ( list @ A ) > $o,A0: list @ A] :
% 2.80/1.55 ( ! [X2: A,Xs2: list @ A] :
% 2.80/1.55 ( ! [X212: A,X223: list @ A] :
% 2.80/1.55 ( ( Xs2
% 2.80/1.55 = ( cons @ A @ X212 @ X223 ) )
% 2.80/1.55 => ( P2 @ Xs2 ) )
% 2.80/1.55 => ( P2 @ ( cons @ A @ X2 @ Xs2 ) ) )
% 2.80/1.55 => ( ( P2 @ ( nil @ A ) )
% 2.80/1.55 => ( P2 @ A0 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_102_min__list_Ocases,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( ord @ A )
% 2.80/1.55 => ! [X: list @ A] :
% 2.80/1.55 ( ! [X2: A,Xs2: list @ A] :
% 2.80/1.55 ( X
% 2.80/1.55 != ( cons @ A @ X2 @ Xs2 ) )
% 2.80/1.55 => ( X
% 2.80/1.55 = ( nil @ A ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_103_induct__list012,axiom,
% 2.80/1.55 ! [A: $tType,P2: ( list @ A ) > $o,Xs: list @ A] :
% 2.80/1.55 ( ( P2 @ ( nil @ A ) )
% 2.80/1.55 => ( ! [X2: A] : ( P2 @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.80/1.55 => ( ! [X2: A,Y4: A,Zs: list @ A] :
% 2.80/1.55 ( ( P2 @ Zs )
% 2.80/1.55 => ( ( P2 @ ( cons @ A @ Y4 @ Zs ) )
% 2.80/1.55 => ( P2 @ ( cons @ A @ X2 @ ( cons @ A @ Y4 @ Zs ) ) ) ) )
% 2.80/1.55 => ( P2 @ Xs ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_104_splice_Oinduct,axiom,
% 2.80/1.55 ! [A: $tType,P2: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.80/1.55 ( ! [X_1: list @ A] : ( P2 @ ( nil @ A ) @ X_1 )
% 2.80/1.55 => ( ! [X2: A,Xs2: list @ A,Ys2: list @ A] :
% 2.80/1.55 ( ( P2 @ Ys2 @ Xs2 )
% 2.80/1.55 => ( P2 @ ( cons @ A @ X2 @ Xs2 ) @ Ys2 ) )
% 2.80/1.55 => ( P2 @ A0 @ A1 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_105_list__induct2_H,axiom,
% 2.80/1.55 ! [A: $tType,B: $tType,P2: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 2.80/1.55 ( ( P2 @ ( nil @ A ) @ ( nil @ B ) )
% 2.80/1.55 => ( ! [X2: A,Xs2: list @ A] : ( P2 @ ( cons @ A @ X2 @ Xs2 ) @ ( nil @ B ) )
% 2.80/1.55 => ( ! [Y4: B,Ys2: list @ B] : ( P2 @ ( nil @ A ) @ ( cons @ B @ Y4 @ Ys2 ) )
% 2.80/1.55 => ( ! [X2: A,Xs2: list @ A,Y4: B,Ys2: list @ B] :
% 2.80/1.55 ( ( P2 @ Xs2 @ Ys2 )
% 2.80/1.55 => ( P2 @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B @ Y4 @ Ys2 ) ) )
% 2.80/1.55 => ( P2 @ Xs @ Ys ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_106_neq__Nil__conv,axiom,
% 2.80/1.55 ! [A: $tType,Xs: list @ A] :
% 2.80/1.55 ( ( Xs
% 2.80/1.55 != ( nil @ A ) )
% 2.80/1.55 = ( ? [Y5: A,Ys3: list @ A] :
% 2.80/1.55 ( Xs
% 2.80/1.55 = ( cons @ A @ Y5 @ Ys3 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_107_list_Oinducts,axiom,
% 2.80/1.55 ! [A: $tType,P2: ( list @ A ) > $o,List: list @ A] :
% 2.80/1.55 ( ( P2 @ ( nil @ A ) )
% 2.80/1.55 => ( ! [X12: A,X23: list @ A] :
% 2.80/1.55 ( ( P2 @ X23 )
% 2.80/1.55 => ( P2 @ ( cons @ A @ X12 @ X23 ) ) )
% 2.80/1.55 => ( P2 @ List ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_108_list_Oexhaust,axiom,
% 2.80/1.55 ! [A: $tType,Y3: list @ A] :
% 2.80/1.55 ( ( Y3
% 2.80/1.55 != ( nil @ A ) )
% 2.80/1.55 => ~ ! [X213: A,X224: list @ A] :
% 2.80/1.55 ( Y3
% 2.80/1.55 != ( cons @ A @ X213 @ X224 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_109_list_OdiscI,axiom,
% 2.80/1.55 ! [A: $tType,List: list @ A,X21: A,X222: list @ A] :
% 2.80/1.55 ( ( List
% 2.80/1.55 = ( cons @ A @ X21 @ X222 ) )
% 2.80/1.55 => ( List
% 2.80/1.55 != ( nil @ A ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_110_list_Odistinct_I1_J,axiom,
% 2.80/1.55 ! [A: $tType,X21: A,X222: list @ A] :
% 2.80/1.55 ( ( nil @ A )
% 2.80/1.55 != ( cons @ A @ X21 @ X222 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_111_length__induct,axiom,
% 2.80/1.55 ! [A: $tType,P2: ( list @ A ) > $o,Xs: list @ A] :
% 2.80/1.55 ( ! [Xs2: list @ A] :
% 2.80/1.55 ( ! [Ys4: list @ A] :
% 2.80/1.55 ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ys4 ) @ ( size_size @ ( list @ A ) @ Xs2 ) )
% 2.80/1.55 => ( P2 @ Ys4 ) )
% 2.80/1.55 => ( P2 @ Xs2 ) )
% 2.80/1.55 => ( P2 @ Xs ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_112_lift__Suc__mono__less__iff,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( order @ A )
% 2.80/1.55 => ! [F: nat > A,N3: nat,M: nat] :
% 2.80/1.55 ( ! [N: nat] : ( ord_less @ A @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 2.80/1.55 => ( ( ord_less @ A @ ( F @ N3 ) @ ( F @ M ) )
% 2.80/1.55 = ( ord_less @ nat @ N3 @ M ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_113_lift__Suc__mono__less,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( order @ A )
% 2.80/1.55 => ! [F: nat > A,N3: nat,N4: nat] :
% 2.80/1.55 ( ! [N: nat] : ( ord_less @ A @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 2.80/1.55 => ( ( ord_less @ nat @ N3 @ N4 )
% 2.80/1.55 => ( ord_less @ A @ ( F @ N3 ) @ ( F @ N4 ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_114_less__Suc__eq__0__disj,axiom,
% 2.80/1.55 ! [M: nat,N3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ M @ ( suc @ N3 ) )
% 2.80/1.55 = ( ( M
% 2.80/1.55 = ( zero_zero @ nat ) )
% 2.80/1.55 | ? [J3: nat] :
% 2.80/1.55 ( ( M
% 2.80/1.55 = ( suc @ J3 ) )
% 2.80/1.55 & ( ord_less @ nat @ J3 @ N3 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_115_gr0__implies__Suc,axiom,
% 2.80/1.55 ! [N3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N3 )
% 2.80/1.55 => ? [M3: nat] :
% 2.80/1.55 ( N3
% 2.80/1.55 = ( suc @ M3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_116_All__less__Suc2,axiom,
% 2.80/1.55 ! [N3: nat,P2: nat > $o] :
% 2.80/1.55 ( ( ! [I3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ I3 @ ( suc @ N3 ) )
% 2.80/1.55 => ( P2 @ I3 ) ) )
% 2.80/1.55 = ( ( P2 @ ( zero_zero @ nat ) )
% 2.80/1.55 & ! [I3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ I3 @ N3 )
% 2.80/1.55 => ( P2 @ ( suc @ I3 ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_117_gr0__conv__Suc,axiom,
% 2.80/1.55 ! [N3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N3 )
% 2.80/1.55 = ( ? [M5: nat] :
% 2.80/1.55 ( N3
% 2.80/1.55 = ( suc @ M5 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_118_Ex__less__Suc2,axiom,
% 2.80/1.55 ! [N3: nat,P2: nat > $o] :
% 2.80/1.55 ( ( ? [I3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ I3 @ ( suc @ N3 ) )
% 2.80/1.55 & ( P2 @ I3 ) ) )
% 2.80/1.55 = ( ( P2 @ ( zero_zero @ nat ) )
% 2.80/1.55 | ? [I3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ I3 @ N3 )
% 2.80/1.55 & ( P2 @ ( suc @ I3 ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_119_length__Suc__conv,axiom,
% 2.80/1.55 ! [A: $tType,Xs: list @ A,N3: nat] :
% 2.80/1.55 ( ( ( size_size @ ( list @ A ) @ Xs )
% 2.80/1.55 = ( suc @ N3 ) )
% 2.80/1.55 = ( ? [Y5: A,Ys3: list @ A] :
% 2.80/1.55 ( ( Xs
% 2.80/1.55 = ( cons @ A @ Y5 @ Ys3 ) )
% 2.80/1.55 & ( ( size_size @ ( list @ A ) @ Ys3 )
% 2.80/1.55 = N3 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_120_Suc__length__conv,axiom,
% 2.80/1.55 ! [A: $tType,N3: nat,Xs: list @ A] :
% 2.80/1.55 ( ( ( suc @ N3 )
% 2.80/1.55 = ( size_size @ ( list @ A ) @ Xs ) )
% 2.80/1.55 = ( ? [Y5: A,Ys3: list @ A] :
% 2.80/1.55 ( ( Xs
% 2.80/1.55 = ( cons @ A @ Y5 @ Ys3 ) )
% 2.80/1.55 & ( ( size_size @ ( list @ A ) @ Ys3 )
% 2.80/1.55 = N3 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_121_list_Osize_I3_J,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( size_size @ ( list @ A ) @ ( nil @ A ) )
% 2.80/1.55 = ( zero_zero @ nat ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_122_list__induct3,axiom,
% 2.80/1.55 ! [B: $tType,A: $tType,C: $tType,Xs: list @ A,Ys: list @ B,Zs2: list @ C,P2: ( list @ A ) > ( list @ B ) > ( list @ C ) > $o] :
% 2.80/1.55 ( ( ( size_size @ ( list @ A ) @ Xs )
% 2.80/1.55 = ( size_size @ ( list @ B ) @ Ys ) )
% 2.80/1.55 => ( ( ( size_size @ ( list @ B ) @ Ys )
% 2.80/1.55 = ( size_size @ ( list @ C ) @ Zs2 ) )
% 2.80/1.55 => ( ( P2 @ ( nil @ A ) @ ( nil @ B ) @ ( nil @ C ) )
% 2.80/1.55 => ( ! [X2: A,Xs2: list @ A,Y4: B,Ys2: list @ B,Z: C,Zs: list @ C] :
% 2.80/1.55 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 2.80/1.55 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 2.80/1.55 => ( ( ( size_size @ ( list @ B ) @ Ys2 )
% 2.80/1.55 = ( size_size @ ( list @ C ) @ Zs ) )
% 2.80/1.55 => ( ( P2 @ Xs2 @ Ys2 @ Zs )
% 2.80/1.55 => ( P2 @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B @ Y4 @ Ys2 ) @ ( cons @ C @ Z @ Zs ) ) ) ) )
% 2.80/1.55 => ( P2 @ Xs @ Ys @ Zs2 ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_123_list__induct2,axiom,
% 2.80/1.55 ! [A: $tType,B: $tType,Xs: list @ A,Ys: list @ B,P2: ( list @ A ) > ( list @ B ) > $o] :
% 2.80/1.55 ( ( ( size_size @ ( list @ A ) @ Xs )
% 2.80/1.55 = ( size_size @ ( list @ B ) @ Ys ) )
% 2.80/1.55 => ( ( P2 @ ( nil @ A ) @ ( nil @ B ) )
% 2.80/1.55 => ( ! [X2: A,Xs2: list @ A,Y4: B,Ys2: list @ B] :
% 2.80/1.55 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 2.80/1.55 = ( size_size @ ( list @ B ) @ Ys2 ) )
% 2.80/1.55 => ( ( P2 @ Xs2 @ Ys2 )
% 2.80/1.55 => ( P2 @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B @ Y4 @ Ys2 ) ) ) )
% 2.80/1.55 => ( P2 @ Xs @ Ys ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_124_infiniteExecutionCfg_Oelims,axiom,
% 2.80/1.55 ! [X: 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 @ ( configuration_ext @ p @ v @ s @ product_unit )] :
% 2.80/1.55 ( ( ( fLPThe137922386ionCfg @ p @ v @ s @ X @ Xa @ Xb @ Xc )
% 2.80/1.55 = Y3 )
% 2.80/1.55 => ( ( ( Xc
% 2.80/1.55 = ( zero_zero @ nat ) )
% 2.80/1.55 => ( Y3
% 2.80/1.55 != ( cons @ ( configuration_ext @ p @ v @ s @ product_unit ) @ X @ ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ) )
% 2.80/1.55 => ~ ! [N: nat] :
% 2.80/1.55 ( ( Xc
% 2.80/1.55 = ( suc @ N ) )
% 2.80/1.55 => ( Y3
% 2.80/1.55 != ( Xa @ ( fLPThe137922386ionCfg @ p @ v @ s @ X @ Xa @ Xb @ N ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_125_infiniteExecutionMsg_Oelims,axiom,
% 2.80/1.55 ! [X: 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 )] :
% 2.80/1.55 ( ( ( fLPThe221390223ionMsg @ p @ v @ s @ X @ Xa @ Xb @ Xc )
% 2.80/1.55 = Y3 )
% 2.80/1.55 => ( ( ( Xc
% 2.80/1.55 = ( zero_zero @ nat ) )
% 2.80/1.55 => ( Y3
% 2.80/1.55 != ( nil @ ( message @ p @ v ) ) ) )
% 2.80/1.55 => ~ ! [N: nat] :
% 2.80/1.55 ( ( Xc
% 2.80/1.55 = ( suc @ N ) )
% 2.80/1.55 => ( Y3
% 2.80/1.55 != ( Xb @ ( fLPThe137922386ionCfg @ p @ v @ s @ X @ Xa @ Xb @ N ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ X @ Xa @ Xb @ N ) ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_126_infiniteExecutionMsg_Osimps_I2_J,axiom,
% 2.80/1.55 ! [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 ) ),N3: nat] :
% 2.80/1.55 ( ( fLPThe221390223ionMsg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 2.80/1.55 = ( FStepMsg2 @ ( fLPThe137922386ionCfg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_127_infiniteExecutionCfg_Osimps_I2_J,axiom,
% 2.80/1.55 ! [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 ) ),N3: nat] :
% 2.80/1.55 ( ( fLPThe137922386ionCfg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 2.80/1.55 = ( FStepCfg2 @ ( fLPThe137922386ionCfg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe221390223ionMsg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_128_infiniteExecutionMsg_Osimps_I1_J,axiom,
% 2.80/1.55 ! [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 ) )] :
% 2.80/1.55 ( ( fLPThe221390223ionMsg @ p @ v @ s @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( zero_zero @ nat ) )
% 2.80/1.55 = ( nil @ ( message @ p @ v ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_129_not__gr__zero,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( canoni770627133id_add @ A )
% 2.80/1.55 => ! [N3: A] :
% 2.80/1.55 ( ( ~ ( ord_less @ A @ ( zero_zero @ A ) @ N3 ) )
% 2.80/1.55 = ( N3
% 2.80/1.55 = ( zero_zero @ A ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_130_length__Cons,axiom,
% 2.80/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.80/1.55 ( ( size_size @ ( list @ A ) @ ( cons @ A @ X @ Xs ) )
% 2.80/1.55 = ( suc @ ( size_size @ ( list @ A ) @ Xs ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_131_dependent__nat__choice,axiom,
% 2.80/1.55 ! [A: $tType,P2: nat > A > $o,Q: nat > A > A > $o] :
% 2.80/1.55 ( ? [X_12: A] : ( P2 @ ( zero_zero @ nat ) @ X_12 )
% 2.80/1.55 => ( ! [X2: A,N: nat] :
% 2.80/1.55 ( ( P2 @ N @ X2 )
% 2.80/1.55 => ? [Y: A] :
% 2.80/1.55 ( ( P2 @ ( suc @ N ) @ Y )
% 2.80/1.55 & ( Q @ N @ X2 @ Y ) ) )
% 2.80/1.55 => ? [F2: nat > A] :
% 2.80/1.55 ! [N5: nat] :
% 2.80/1.55 ( ( P2 @ N5 @ ( F2 @ N5 ) )
% 2.80/1.55 & ( Q @ N5 @ ( F2 @ N5 ) @ ( F2 @ ( suc @ N5 ) ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_132_zero__reorient,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( zero @ A )
% 2.80/1.55 => ! [X: A] :
% 2.80/1.55 ( ( ( zero_zero @ A )
% 2.80/1.55 = X )
% 2.80/1.55 = ( X
% 2.80/1.55 = ( zero_zero @ A ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_133_gr__zeroI,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( canoni770627133id_add @ A )
% 2.80/1.55 => ! [N3: A] :
% 2.80/1.55 ( ( N3
% 2.80/1.55 != ( zero_zero @ A ) )
% 2.80/1.55 => ( ord_less @ A @ ( zero_zero @ A ) @ N3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_134_not__less__zero,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( canoni770627133id_add @ A )
% 2.80/1.55 => ! [N3: A] :
% 2.80/1.55 ~ ( ord_less @ A @ N3 @ ( zero_zero @ A ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_135_gr__implies__not__zero,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( canoni770627133id_add @ A )
% 2.80/1.55 => ! [M: A,N3: A] :
% 2.80/1.55 ( ( ord_less @ A @ M @ N3 )
% 2.80/1.55 => ( N3
% 2.80/1.55 != ( zero_zero @ A ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_136_zero__less__iff__neq__zero,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( canoni770627133id_add @ A )
% 2.80/1.55 => ! [N3: A] :
% 2.80/1.55 ( ( ord_less @ A @ ( zero_zero @ A ) @ N3 )
% 2.80/1.55 = ( N3
% 2.80/1.55 != ( zero_zero @ A ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_137_n__lists__Nil,axiom,
% 2.80/1.55 ! [A: $tType,N3: nat] :
% 2.80/1.55 ( ( ( N3
% 2.80/1.55 = ( zero_zero @ nat ) )
% 2.80/1.55 => ( ( n_lists @ A @ N3 @ ( nil @ A ) )
% 2.80/1.55 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) )
% 2.80/1.55 & ( ( N3
% 2.80/1.55 != ( zero_zero @ nat ) )
% 2.80/1.55 => ( ( n_lists @ A @ N3 @ ( nil @ A ) )
% 2.80/1.55 = ( nil @ ( list @ A ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_138_flpPseudoConsensus_OinfiniteExecutionCfg_Oelims,axiom,
% 2.80/1.55 ! [P: $tType,V: $tType,S: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,X: 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 @ ( configuration_ext @ P @ V @ S @ product_unit )] :
% 2.80/1.55 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 2.80/1.55 => ( ( ( fLPThe137922386ionCfg @ P @ V @ S @ X @ Xa @ Xb @ Xc )
% 2.80/1.55 = Y3 )
% 2.80/1.55 => ( ( ( Xc
% 2.80/1.55 = ( zero_zero @ nat ) )
% 2.80/1.55 => ( Y3
% 2.80/1.55 != ( cons @ ( configuration_ext @ P @ V @ S @ product_unit ) @ X @ ( nil @ ( configuration_ext @ P @ V @ S @ product_unit ) ) ) ) )
% 2.80/1.55 => ~ ! [N: nat] :
% 2.80/1.55 ( ( Xc
% 2.80/1.55 = ( suc @ N ) )
% 2.80/1.55 => ( Y3
% 2.80/1.55 != ( Xa @ ( fLPThe137922386ionCfg @ P @ V @ S @ X @ Xa @ Xb @ N ) @ ( fLPThe221390223ionMsg @ P @ V @ S @ X @ Xa @ Xb @ N ) ) ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_139_n__lists_Osimps_I1_J,axiom,
% 2.80/1.55 ! [A: $tType,Xs: list @ A] :
% 2.80/1.55 ( ( n_lists @ A @ ( zero_zero @ nat ) @ Xs )
% 2.80/1.55 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_140_flpPseudoConsensus_OinfiniteExecutionMsg_Oelims,axiom,
% 2.80/1.55 ! [P: $tType,V: $tType,S: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,X: 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 )] :
% 2.80/1.55 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 2.80/1.55 => ( ( ( fLPThe221390223ionMsg @ P @ V @ S @ X @ Xa @ Xb @ Xc )
% 2.80/1.55 = Y3 )
% 2.80/1.55 => ( ( ( Xc
% 2.80/1.55 = ( zero_zero @ nat ) )
% 2.80/1.55 => ( Y3
% 2.80/1.55 != ( nil @ ( message @ P @ V ) ) ) )
% 2.80/1.55 => ~ ! [N: nat] :
% 2.80/1.55 ( ( Xc
% 2.80/1.55 = ( suc @ N ) )
% 2.80/1.55 => ( Y3
% 2.80/1.55 != ( Xb @ ( fLPThe137922386ionCfg @ P @ V @ S @ X @ Xa @ Xb @ N ) @ ( fLPThe221390223ionMsg @ P @ V @ S @ X @ Xa @ Xb @ N ) ) ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_141_flpPseudoConsensus_OinfiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I1_J,axiom,
% 2.80/1.55 ! [P: $tType,V: $tType,S: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,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] :
% 2.80/1.55 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 2.80/1.55 => ( ! [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 ) )
% 2.80/1.55 => ( ! [Cfg: configuration_ext @ P @ V @ S @ product_unit,FStepCfg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( message @ P @ V ) ),N: nat] :
% 2.80/1.55 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.80/1.55 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.80/1.55 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 2.80/1.55 => ( ! [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 ) )
% 2.80/1.55 => ( ! [Cfg: configuration_ext @ P @ V @ S @ product_unit,FStepCfg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( message @ P @ V ) ),N: nat] :
% 2.80/1.55 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.80/1.55 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.80/1.55 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 2.80/1.55 => ( P2 @ A0 @ A1 @ A2 @ A3 ) ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_142_flpPseudoConsensus_OinfiniteExecutionCfg__infiniteExecutionMsg_Oinduct_I2_J,axiom,
% 2.80/1.55 ! [P: $tType,V: $tType,S: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,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] :
% 2.80/1.55 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 2.80/1.55 => ( ! [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 ) )
% 2.80/1.55 => ( ! [Cfg: configuration_ext @ P @ V @ S @ product_unit,FStepCfg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( message @ P @ V ) ),N: nat] :
% 2.80/1.55 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.80/1.55 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.80/1.55 => ( P2 @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 2.80/1.55 => ( ! [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 ) )
% 2.80/1.55 => ( ! [Cfg: configuration_ext @ P @ V @ S @ product_unit,FStepCfg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ),FStepMsg: ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( list @ ( message @ P @ V ) ),N: nat] :
% 2.80/1.55 ( ( P2 @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.80/1.55 => ( ( Q @ Cfg @ FStepCfg @ FStepMsg @ N )
% 2.80/1.55 => ( Q @ Cfg @ FStepCfg @ FStepMsg @ ( suc @ N ) ) ) )
% 2.80/1.55 => ( Q @ A4 @ A5 @ A6 @ A7 ) ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_143_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I2_J,axiom,
% 2.80/1.55 ! [P: $tType,V: $tType,S: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,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 ) ),N3: nat] :
% 2.80/1.55 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 2.80/1.55 => ( ( fLPThe221390223ionMsg @ P @ V @ S @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 2.80/1.55 = ( FStepMsg2 @ ( fLPThe137922386ionCfg @ P @ V @ S @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe221390223ionMsg @ P @ V @ S @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_144_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I2_J,axiom,
% 2.80/1.55 ! [P: $tType,V: $tType,S: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,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 ) ),N3: nat] :
% 2.80/1.55 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 2.80/1.55 => ( ( fLPThe137922386ionCfg @ P @ V @ S @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( suc @ N3 ) )
% 2.80/1.55 = ( FStepCfg2 @ ( fLPThe137922386ionCfg @ P @ V @ S @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) @ ( fLPThe221390223ionMsg @ P @ V @ S @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ N3 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_145_flpPseudoConsensus_OinfiniteExecutionMsg_Osimps_I1_J,axiom,
% 2.80/1.55 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,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 ) )] :
% 2.80/1.55 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 2.80/1.55 => ( ( fLPThe221390223ionMsg @ P @ V @ S @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( zero_zero @ nat ) )
% 2.80/1.55 = ( nil @ ( message @ P @ V ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_146_flpPseudoConsensus_OinfiniteExecutionCfg_Osimps_I1_J,axiom,
% 2.80/1.55 ! [S: $tType,V: $tType,P: $tType,Trans: P > S > ( messageValue @ V ) > S,Sends: P > S > ( messageValue @ V ) > ( message @ P @ V ) > nat,Start: P > S,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 ) )] :
% 2.80/1.55 ( ( fLPThe1922692578sensus @ P @ S @ V @ Trans @ Sends @ Start )
% 2.80/1.55 => ( ( fLPThe137922386ionCfg @ P @ V @ S @ Cfg2 @ FStepCfg2 @ FStepMsg2 @ ( zero_zero @ nat ) )
% 2.80/1.55 = ( cons @ ( configuration_ext @ P @ V @ S @ product_unit ) @ Cfg2 @ ( nil @ ( configuration_ext @ P @ V @ S @ product_unit ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_147_shift__def,axiom,
% 2.80/1.55 ! [B: $tType,A: $tType] :
% 2.80/1.55 ( ( bNF_Greatest_shift @ A @ B )
% 2.80/1.55 = ( ^ [Lab: ( list @ A ) > B,K3: A,Kl: list @ A] : ( Lab @ ( cons @ A @ K3 @ Kl ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_148_less__numeral__extra_I3_J,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( linord1659791738miring @ A )
% 2.80/1.55 => ~ ( ord_less @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_149_product__lists_Osimps_I1_J,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 2.80/1.55 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_150_subseqs_Osimps_I1_J,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( subseqs @ A @ ( nil @ A ) )
% 2.80/1.55 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_151_length__code,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( size_size @ ( list @ A ) )
% 2.80/1.55 = ( gen_length @ A @ ( zero_zero @ nat ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_152_gen__length__code_I2_J,axiom,
% 2.80/1.55 ! [B: $tType,N3: nat,X: B,Xs: list @ B] :
% 2.80/1.55 ( ( gen_length @ B @ N3 @ ( cons @ B @ X @ Xs ) )
% 2.80/1.55 = ( gen_length @ B @ ( suc @ N3 ) @ Xs ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_153_gen__length__code_I1_J,axiom,
% 2.80/1.55 ! [A: $tType,N3: nat] :
% 2.80/1.55 ( ( gen_length @ A @ N3 @ ( nil @ A ) )
% 2.80/1.55 = N3 ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_154_insert__Nil,axiom,
% 2.80/1.55 ! [A: $tType,X: A] :
% 2.80/1.55 ( ( insert @ A @ X @ ( nil @ A ) )
% 2.80/1.55 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_155_nths__singleton,axiom,
% 2.80/1.55 ! [A: $tType,A9: set @ nat,X: A] :
% 2.80/1.55 ( ( ( member @ nat @ ( zero_zero @ nat ) @ A9 )
% 2.80/1.55 => ( ( nths @ A @ ( cons @ A @ X @ ( nil @ A ) ) @ A9 )
% 2.80/1.55 = ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.80/1.55 & ( ~ ( member @ nat @ ( zero_zero @ nat ) @ A9 )
% 2.80/1.55 => ( ( nths @ A @ ( cons @ A @ X @ ( nil @ A ) ) @ A9 )
% 2.80/1.55 = ( nil @ A ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_156_of__nat__0__less__iff,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( linord1659791738miring @ A )
% 2.80/1.55 => ! [N3: nat] :
% 2.80/1.55 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( semiring_1_of_nat @ A @ N3 ) )
% 2.80/1.55 = ( ord_less @ nat @ ( zero_zero @ nat ) @ N3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_157_of__nat__eq__iff,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( semiring_char_0 @ A )
% 2.80/1.55 => ! [M: nat,N3: nat] :
% 2.80/1.55 ( ( ( semiring_1_of_nat @ A @ M )
% 2.80/1.55 = ( semiring_1_of_nat @ A @ N3 ) )
% 2.80/1.55 = ( M = N3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_158_nths__nil,axiom,
% 2.80/1.55 ! [A: $tType,A9: set @ nat] :
% 2.80/1.55 ( ( nths @ A @ ( nil @ A ) @ A9 )
% 2.80/1.55 = ( nil @ A ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_159_of__nat__0,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( semiring_1 @ A )
% 2.80/1.55 => ( ( semiring_1_of_nat @ A @ ( zero_zero @ nat ) )
% 2.80/1.55 = ( zero_zero @ A ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_160_of__nat__0__eq__iff,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( semiring_char_0 @ A )
% 2.80/1.55 => ! [N3: nat] :
% 2.80/1.55 ( ( ( zero_zero @ A )
% 2.80/1.55 = ( semiring_1_of_nat @ A @ N3 ) )
% 2.80/1.55 = ( ( zero_zero @ nat )
% 2.80/1.55 = N3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_161_of__nat__eq__0__iff,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( semiring_char_0 @ A )
% 2.80/1.55 => ! [M: nat] :
% 2.80/1.55 ( ( ( semiring_1_of_nat @ A @ M )
% 2.80/1.55 = ( zero_zero @ A ) )
% 2.80/1.55 = ( M
% 2.80/1.55 = ( zero_zero @ nat ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_162_of__nat__less__iff,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( linord1659791738miring @ A )
% 2.80/1.55 => ! [M: nat,N3: nat] :
% 2.80/1.55 ( ( ord_less @ A @ ( semiring_1_of_nat @ A @ M ) @ ( semiring_1_of_nat @ A @ N3 ) )
% 2.80/1.55 = ( ord_less @ nat @ M @ N3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_163_of__nat__less__0__iff,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( linord1659791738miring @ A )
% 2.80/1.55 => ! [M: nat] :
% 2.80/1.55 ~ ( ord_less @ A @ ( semiring_1_of_nat @ A @ M ) @ ( zero_zero @ A ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_164_of__nat__neq__0,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( semiring_char_0 @ A )
% 2.80/1.55 => ! [N3: nat] :
% 2.80/1.55 ( ( semiring_1_of_nat @ A @ ( suc @ N3 ) )
% 2.80/1.55 != ( zero_zero @ A ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_165_less__imp__of__nat__less,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( linord1659791738miring @ A )
% 2.80/1.55 => ! [M: nat,N3: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ M @ N3 )
% 2.80/1.55 => ( ord_less @ A @ ( semiring_1_of_nat @ A @ M ) @ ( semiring_1_of_nat @ A @ N3 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_166_of__nat__less__imp__less,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( linord1659791738miring @ A )
% 2.80/1.55 => ! [M: nat,N3: nat] :
% 2.80/1.55 ( ( ord_less @ A @ ( semiring_1_of_nat @ A @ M ) @ ( semiring_1_of_nat @ A @ N3 ) )
% 2.80/1.55 => ( ord_less @ nat @ M @ N3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_167_nths__all,axiom,
% 2.80/1.55 ! [A: $tType,Xs: list @ A,I4: set @ nat] :
% 2.80/1.55 ( ! [I2: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ I2 @ ( size_size @ ( list @ A ) @ Xs ) )
% 2.80/1.55 => ( member @ nat @ I2 @ I4 ) )
% 2.80/1.55 => ( ( nths @ A @ Xs @ I4 )
% 2.80/1.55 = Xs ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_168_pos__int__cases,axiom,
% 2.80/1.55 ! [K: int] :
% 2.80/1.55 ( ( ord_less @ int @ ( zero_zero @ int ) @ K )
% 2.80/1.55 => ~ ! [N: nat] :
% 2.80/1.55 ( ( K
% 2.80/1.55 = ( semiring_1_of_nat @ int @ N ) )
% 2.80/1.55 => ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_169_zero__less__imp__eq__int,axiom,
% 2.80/1.55 ! [K: int] :
% 2.80/1.55 ( ( ord_less @ int @ ( zero_zero @ int ) @ K )
% 2.80/1.55 => ? [N: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.80/1.55 & ( K
% 2.80/1.55 = ( semiring_1_of_nat @ int @ N ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_170_list__ex1__simps_I1_J,axiom,
% 2.80/1.55 ! [A: $tType,P2: A > $o] :
% 2.80/1.55 ~ ( list_ex1 @ A @ P2 @ ( nil @ A ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_171_nat__int__comparison_I2_J,axiom,
% 2.80/1.55 ( ( ord_less @ nat )
% 2.80/1.55 = ( ^ [A11: nat,B2: nat] : ( ord_less @ int @ ( semiring_1_of_nat @ int @ A11 ) @ ( semiring_1_of_nat @ int @ B2 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_172_int__ops_I1_J,axiom,
% 2.80/1.55 ( ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) )
% 2.80/1.55 = ( zero_zero @ int ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_173_neg__int__cases,axiom,
% 2.80/1.55 ! [K: int] :
% 2.80/1.55 ( ( ord_less @ int @ K @ ( zero_zero @ int ) )
% 2.80/1.55 => ~ ! [N: nat] :
% 2.80/1.55 ( ( K
% 2.80/1.55 = ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ N ) ) )
% 2.80/1.55 => ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_174_neg__equal__iff__equal,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( group_add @ A )
% 2.80/1.55 => ! [A8: A,B3: A] :
% 2.80/1.55 ( ( ( uminus_uminus @ A @ A8 )
% 2.80/1.55 = ( uminus_uminus @ A @ B3 ) )
% 2.80/1.55 = ( A8 = B3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_175_add_Oinverse__inverse,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( group_add @ A )
% 2.80/1.55 => ! [A8: A] :
% 2.80/1.55 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A8 ) )
% 2.80/1.55 = A8 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_176_add_Oinverse__neutral,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( group_add @ A )
% 2.80/1.55 => ( ( uminus_uminus @ A @ ( zero_zero @ A ) )
% 2.80/1.55 = ( zero_zero @ A ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_177_neg__0__equal__iff__equal,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( group_add @ A )
% 2.80/1.55 => ! [A8: A] :
% 2.80/1.55 ( ( ( zero_zero @ A )
% 2.80/1.55 = ( uminus_uminus @ A @ A8 ) )
% 2.80/1.55 = ( ( zero_zero @ A )
% 2.80/1.55 = A8 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_178_neg__equal__0__iff__equal,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( group_add @ A )
% 2.80/1.55 => ! [A8: A] :
% 2.80/1.55 ( ( ( uminus_uminus @ A @ A8 )
% 2.80/1.55 = ( zero_zero @ A ) )
% 2.80/1.55 = ( A8
% 2.80/1.55 = ( zero_zero @ A ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_179_equal__neg__zero,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( linord219039673up_add @ A )
% 2.80/1.55 => ! [A8: A] :
% 2.80/1.55 ( ( A8
% 2.80/1.55 = ( uminus_uminus @ A @ A8 ) )
% 2.80/1.55 = ( A8
% 2.80/1.55 = ( zero_zero @ A ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_180_neg__equal__zero,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( linord219039673up_add @ A )
% 2.80/1.55 => ! [A8: A] :
% 2.80/1.55 ( ( ( uminus_uminus @ A @ A8 )
% 2.80/1.55 = A8 )
% 2.80/1.55 = ( A8
% 2.80/1.55 = ( zero_zero @ A ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_181_neg__less__iff__less,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( ordered_ab_group_add @ A )
% 2.80/1.55 => ! [B3: A,A8: A] :
% 2.80/1.55 ( ( ord_less @ A @ ( uminus_uminus @ A @ B3 ) @ ( uminus_uminus @ A @ A8 ) )
% 2.80/1.55 = ( ord_less @ A @ A8 @ B3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_182_less__neg__neg,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( linord219039673up_add @ A )
% 2.80/1.55 => ! [A8: A] :
% 2.80/1.55 ( ( ord_less @ A @ A8 @ ( uminus_uminus @ A @ A8 ) )
% 2.80/1.55 = ( ord_less @ A @ A8 @ ( zero_zero @ A ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_183_neg__less__pos,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( linord219039673up_add @ A )
% 2.80/1.55 => ! [A8: A] :
% 2.80/1.55 ( ( ord_less @ A @ ( uminus_uminus @ A @ A8 ) @ A8 )
% 2.80/1.55 = ( ord_less @ A @ ( zero_zero @ A ) @ A8 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_184_neg__0__less__iff__less,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( ordered_ab_group_add @ A )
% 2.80/1.55 => ! [A8: A] :
% 2.80/1.55 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( uminus_uminus @ A @ A8 ) )
% 2.80/1.55 = ( ord_less @ A @ A8 @ ( zero_zero @ A ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_185_neg__less__0__iff__less,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( ordered_ab_group_add @ A )
% 2.80/1.55 => ! [A8: A] :
% 2.80/1.55 ( ( ord_less @ A @ ( uminus_uminus @ A @ A8 ) @ ( zero_zero @ A ) )
% 2.80/1.55 = ( ord_less @ A @ ( zero_zero @ A ) @ A8 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_186_negative__eq__positive,axiom,
% 2.80/1.55 ! [N3: nat,M: nat] :
% 2.80/1.55 ( ( ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ N3 ) )
% 2.80/1.55 = ( semiring_1_of_nat @ int @ M ) )
% 2.80/1.55 = ( ( N3
% 2.80/1.55 = ( zero_zero @ nat ) )
% 2.80/1.55 & ( M
% 2.80/1.55 = ( zero_zero @ nat ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_187_negative__zless,axiom,
% 2.80/1.55 ! [N3: nat,M: nat] : ( ord_less @ int @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ N3 ) ) ) @ ( semiring_1_of_nat @ int @ M ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_188_minus__less__iff,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( ordered_ab_group_add @ A )
% 2.80/1.55 => ! [A8: A,B3: A] :
% 2.80/1.55 ( ( ord_less @ A @ ( uminus_uminus @ A @ A8 ) @ B3 )
% 2.80/1.55 = ( ord_less @ A @ ( uminus_uminus @ A @ B3 ) @ A8 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_189_less__minus__iff,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( ordered_ab_group_add @ A )
% 2.80/1.55 => ! [A8: A,B3: A] :
% 2.80/1.55 ( ( ord_less @ A @ A8 @ ( uminus_uminus @ A @ B3 ) )
% 2.80/1.55 = ( ord_less @ A @ B3 @ ( uminus_uminus @ A @ A8 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_190_verit__negate__coefficient_I2_J,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( ordered_ab_group_add @ A )
% 2.80/1.55 => ! [A8: A,B3: A] :
% 2.80/1.55 ( ( ord_less @ A @ A8 @ B3 )
% 2.80/1.55 => ( ord_less @ A @ ( uminus_uminus @ A @ B3 ) @ ( uminus_uminus @ A @ A8 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_191_minus__equation__iff,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( group_add @ A )
% 2.80/1.55 => ! [A8: A,B3: A] :
% 2.80/1.55 ( ( ( uminus_uminus @ A @ A8 )
% 2.80/1.55 = B3 )
% 2.80/1.55 = ( ( uminus_uminus @ A @ B3 )
% 2.80/1.55 = A8 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_192_equation__minus__iff,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( group_add @ A )
% 2.80/1.55 => ! [A8: A,B3: A] :
% 2.80/1.55 ( ( A8
% 2.80/1.55 = ( uminus_uminus @ A @ B3 ) )
% 2.80/1.55 = ( B3
% 2.80/1.55 = ( uminus_uminus @ A @ A8 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_193_int__cases,axiom,
% 2.80/1.55 ! [Z2: int] :
% 2.80/1.55 ( ! [N: nat] :
% 2.80/1.55 ( Z2
% 2.80/1.55 != ( semiring_1_of_nat @ int @ N ) )
% 2.80/1.55 => ~ ! [N: nat] :
% 2.80/1.55 ( Z2
% 2.80/1.55 != ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ N ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_194_int__of__nat__induct,axiom,
% 2.80/1.55 ! [P2: int > $o,Z2: int] :
% 2.80/1.55 ( ! [N: nat] : ( P2 @ ( semiring_1_of_nat @ int @ N ) )
% 2.80/1.55 => ( ! [N: nat] : ( P2 @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ N ) ) ) )
% 2.80/1.55 => ( P2 @ Z2 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_195_int__cases4,axiom,
% 2.80/1.55 ! [M: int] :
% 2.80/1.55 ( ! [N: nat] :
% 2.80/1.55 ( M
% 2.80/1.55 != ( semiring_1_of_nat @ int @ N ) )
% 2.80/1.55 => ~ ! [N: nat] :
% 2.80/1.55 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ N )
% 2.80/1.55 => ( M
% 2.80/1.55 != ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ N ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_196_verit__comp__simplify1_I1_J,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( order @ A )
% 2.80/1.55 => ! [A8: A] :
% 2.80/1.55 ~ ( ord_less @ A @ A8 @ A8 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_197_int__cases3,axiom,
% 2.80/1.55 ! [K: int] :
% 2.80/1.55 ( ( K
% 2.80/1.55 != ( zero_zero @ int ) )
% 2.80/1.55 => ( ! [N: nat] :
% 2.80/1.55 ( ( K
% 2.80/1.55 = ( semiring_1_of_nat @ int @ N ) )
% 2.80/1.55 => ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) )
% 2.80/1.55 => ~ ! [N: nat] :
% 2.80/1.55 ( ( K
% 2.80/1.55 = ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ N ) ) )
% 2.80/1.55 => ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ N ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_198_negative__zless__0,axiom,
% 2.80/1.55 ! [N3: nat] : ( ord_less @ int @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ N3 ) ) ) @ ( zero_zero @ int ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_199_negD,axiom,
% 2.80/1.55 ! [X: int] :
% 2.80/1.55 ( ( ord_less @ int @ X @ ( zero_zero @ int ) )
% 2.80/1.55 => ? [N: nat] :
% 2.80/1.55 ( X
% 2.80/1.55 = ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ ( suc @ N ) ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_200_compl__less__compl__iff,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( boolean_algebra @ A )
% 2.80/1.55 => ! [X: A,Y3: A] :
% 2.80/1.55 ( ( ord_less @ A @ ( uminus_uminus @ A @ X ) @ ( uminus_uminus @ A @ Y3 ) )
% 2.80/1.55 = ( ord_less @ A @ Y3 @ X ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_201_compl__less__swap2,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( boolean_algebra @ A )
% 2.80/1.55 => ! [Y3: A,X: A] :
% 2.80/1.55 ( ( ord_less @ A @ ( uminus_uminus @ A @ Y3 ) @ X )
% 2.80/1.55 => ( ord_less @ A @ ( uminus_uminus @ A @ X ) @ Y3 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_202_compl__less__swap1,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( boolean_algebra @ A )
% 2.80/1.55 => ! [Y3: A,X: A] :
% 2.80/1.55 ( ( ord_less @ A @ Y3 @ ( uminus_uminus @ A @ X ) )
% 2.80/1.55 => ( ord_less @ A @ X @ ( uminus_uminus @ A @ Y3 ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_203_zero__less__nat__eq,axiom,
% 2.80/1.55 ! [Z2: int] :
% 2.80/1.55 ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( nat2 @ Z2 ) )
% 2.80/1.55 = ( ord_less @ int @ ( zero_zero @ int ) @ Z2 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_204_of__int__0__less__iff,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( linordered_idom @ A )
% 2.80/1.55 => ! [Z2: int] :
% 2.80/1.55 ( ( ord_less @ A @ ( zero_zero @ A ) @ ( ring_1_of_int @ A @ Z2 ) )
% 2.80/1.55 = ( ord_less @ int @ ( zero_zero @ int ) @ Z2 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_205_of__int__0,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( ring_1 @ A )
% 2.80/1.55 => ( ( ring_1_of_int @ A @ ( zero_zero @ int ) )
% 2.80/1.55 = ( zero_zero @ A ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_206_of__int__0__eq__iff,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( ring_char_0 @ A )
% 2.80/1.55 => ! [Z2: int] :
% 2.80/1.55 ( ( ( zero_zero @ A )
% 2.80/1.55 = ( ring_1_of_int @ A @ Z2 ) )
% 2.80/1.55 = ( Z2
% 2.80/1.55 = ( zero_zero @ int ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_207_of__int__eq__0__iff,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( ring_char_0 @ A )
% 2.80/1.55 => ! [Z2: int] :
% 2.80/1.55 ( ( ( ring_1_of_int @ A @ Z2 )
% 2.80/1.55 = ( zero_zero @ A ) )
% 2.80/1.55 = ( Z2
% 2.80/1.55 = ( zero_zero @ int ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_208_of__int__less__iff,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( linordered_idom @ A )
% 2.80/1.55 => ! [W: int,Z2: int] :
% 2.80/1.55 ( ( ord_less @ A @ ( ring_1_of_int @ A @ W ) @ ( ring_1_of_int @ A @ Z2 ) )
% 2.80/1.55 = ( ord_less @ int @ W @ Z2 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_209_zless__nat__conj,axiom,
% 2.80/1.55 ! [W: int,Z2: int] :
% 2.80/1.55 ( ( ord_less @ nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
% 2.80/1.55 = ( ( ord_less @ int @ ( zero_zero @ int ) @ Z2 )
% 2.80/1.55 & ( ord_less @ int @ W @ Z2 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_210_nat__zminus__int,axiom,
% 2.80/1.55 ! [N3: nat] :
% 2.80/1.55 ( ( nat2 @ ( uminus_uminus @ int @ ( semiring_1_of_nat @ int @ N3 ) ) )
% 2.80/1.55 = ( zero_zero @ nat ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_211_of__int__less__0__iff,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( linordered_idom @ A )
% 2.80/1.55 => ! [Z2: int] :
% 2.80/1.55 ( ( ord_less @ A @ ( ring_1_of_int @ A @ Z2 ) @ ( zero_zero @ A ) )
% 2.80/1.55 = ( ord_less @ int @ Z2 @ ( zero_zero @ int ) ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_212_nat__zero__as__int,axiom,
% 2.80/1.55 ( ( zero_zero @ nat )
% 2.80/1.55 = ( nat2 @ ( zero_zero @ int ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_213_nat__mono__iff,axiom,
% 2.80/1.55 ! [Z2: int,W: int] :
% 2.80/1.55 ( ( ord_less @ int @ ( zero_zero @ int ) @ Z2 )
% 2.80/1.55 => ( ( ord_less @ nat @ ( nat2 @ W ) @ ( nat2 @ Z2 ) )
% 2.80/1.55 = ( ord_less @ int @ W @ Z2 ) ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_214_zless__nat__eq__int__zless,axiom,
% 2.80/1.55 ! [M: nat,Z2: int] :
% 2.80/1.55 ( ( ord_less @ nat @ M @ ( nat2 @ Z2 ) )
% 2.80/1.55 = ( ord_less @ int @ ( semiring_1_of_nat @ int @ M ) @ Z2 ) ) ).
% 2.80/1.55
% 2.80/1.55 thf(fact_215_of__int__pos,axiom,
% 2.80/1.55 ! [A: $tType] :
% 2.80/1.55 ( ( linordered_idom @ A )
% 2.80/1.55 => ! [Z2: int] :
% 2.80/1.55 ( ( ord_less @ int @ ( zero_zero @ int ) @ Z2 )
% 2.80/1.56 => ( ord_less @ A @ ( zero_zero @ A ) @ ( ring_1_of_int @ A @ Z2 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_216_of__nat__less__of__int__iff,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( linordered_idom @ A )
% 2.80/1.56 => ! [N3: nat,X: int] :
% 2.80/1.56 ( ( ord_less @ A @ ( semiring_1_of_nat @ A @ N3 ) @ ( ring_1_of_int @ A @ X ) )
% 2.80/1.56 = ( ord_less @ int @ ( semiring_1_of_nat @ int @ N3 ) @ X ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_217_split__nat,axiom,
% 2.80/1.56 ! [P2: nat > $o,I: int] :
% 2.80/1.56 ( ( P2 @ ( nat2 @ I ) )
% 2.80/1.56 = ( ! [N6: nat] :
% 2.80/1.56 ( ( I
% 2.80/1.56 = ( semiring_1_of_nat @ int @ N6 ) )
% 2.80/1.56 => ( P2 @ N6 ) )
% 2.80/1.56 & ( ( ord_less @ int @ I @ ( zero_zero @ int ) )
% 2.80/1.56 => ( P2 @ ( zero_zero @ nat ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_218_one__less__nat__eq,axiom,
% 2.80/1.56 ! [Z2: int] :
% 2.80/1.56 ( ( ord_less @ nat @ ( suc @ ( zero_zero @ nat ) ) @ ( nat2 @ Z2 ) )
% 2.80/1.56 = ( ord_less @ int @ ( one_one @ int ) @ Z2 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_219_nat__less__iff,axiom,
% 2.80/1.56 ! [W: int,M: nat] :
% 2.80/1.56 ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ W )
% 2.80/1.56 => ( ( ord_less @ nat @ ( nat2 @ W ) @ M )
% 2.80/1.56 = ( ord_less @ int @ W @ ( semiring_1_of_nat @ int @ M ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_220_le__zero__eq,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( canoni770627133id_add @ A )
% 2.80/1.56 => ! [N3: A] :
% 2.80/1.56 ( ( ord_less_eq @ A @ N3 @ ( zero_zero @ A ) )
% 2.80/1.56 = ( N3
% 2.80/1.56 = ( zero_zero @ A ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_221_neg__le__iff__le,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( ordered_ab_group_add @ A )
% 2.80/1.56 => ! [B3: A,A8: A] :
% 2.80/1.56 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ B3 ) @ ( uminus_uminus @ A @ A8 ) )
% 2.80/1.56 = ( ord_less_eq @ A @ A8 @ B3 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_222_of__nat__le__iff,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( linord1659791738miring @ A )
% 2.80/1.56 => ! [M: nat,N3: nat] :
% 2.80/1.56 ( ( ord_less_eq @ A @ ( semiring_1_of_nat @ A @ M ) @ ( semiring_1_of_nat @ A @ N3 ) )
% 2.80/1.56 = ( ord_less_eq @ nat @ M @ N3 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_223_of__nat__1,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( semiring_1 @ A )
% 2.80/1.56 => ( ( semiring_1_of_nat @ A @ ( one_one @ nat ) )
% 2.80/1.56 = ( one_one @ A ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_224_of__nat__1__eq__iff,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( semiring_char_0 @ A )
% 2.80/1.56 => ! [N3: nat] :
% 2.80/1.56 ( ( ( one_one @ A )
% 2.80/1.56 = ( semiring_1_of_nat @ A @ N3 ) )
% 2.80/1.56 = ( N3
% 2.80/1.56 = ( one_one @ nat ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_225_of__nat__eq__1__iff,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( semiring_char_0 @ A )
% 2.80/1.56 => ! [N3: nat] :
% 2.80/1.56 ( ( ( semiring_1_of_nat @ A @ N3 )
% 2.80/1.56 = ( one_one @ A ) )
% 2.80/1.56 = ( N3
% 2.80/1.56 = ( one_one @ nat ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_226_neg__0__le__iff__le,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( ordered_ab_group_add @ A )
% 2.80/1.56 => ! [A8: A] :
% 2.80/1.56 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( uminus_uminus @ A @ A8 ) )
% 2.80/1.56 = ( ord_less_eq @ A @ A8 @ ( zero_zero @ A ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_227_neg__le__0__iff__le,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( ordered_ab_group_add @ A )
% 2.80/1.56 => ! [A8: A] :
% 2.80/1.56 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ A8 ) @ ( zero_zero @ A ) )
% 2.80/1.56 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A8 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_228_less__eq__neg__nonpos,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( linord219039673up_add @ A )
% 2.80/1.56 => ! [A8: A] :
% 2.80/1.56 ( ( ord_less_eq @ A @ A8 @ ( uminus_uminus @ A @ A8 ) )
% 2.80/1.56 = ( ord_less_eq @ A @ A8 @ ( zero_zero @ A ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_229_neg__less__eq__nonneg,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( linord219039673up_add @ A )
% 2.80/1.56 => ! [A8: A] :
% 2.80/1.56 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ A8 ) @ A8 )
% 2.80/1.56 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A8 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_230_of__nat__le__0__iff,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( linord1659791738miring @ A )
% 2.80/1.56 => ! [M: nat] :
% 2.80/1.56 ( ( ord_less_eq @ A @ ( semiring_1_of_nat @ A @ M ) @ ( zero_zero @ A ) )
% 2.80/1.56 = ( M
% 2.80/1.56 = ( zero_zero @ nat ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_231_nat__1,axiom,
% 2.80/1.56 ( ( nat2 @ ( one_one @ int ) )
% 2.80/1.56 = ( suc @ ( zero_zero @ nat ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_232_nat__le__0,axiom,
% 2.80/1.56 ! [Z2: int] :
% 2.80/1.56 ( ( ord_less_eq @ int @ Z2 @ ( zero_zero @ int ) )
% 2.80/1.56 => ( ( nat2 @ Z2 )
% 2.80/1.56 = ( zero_zero @ nat ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_233_nat__0__iff,axiom,
% 2.80/1.56 ! [I: int] :
% 2.80/1.56 ( ( ( nat2 @ I )
% 2.80/1.56 = ( zero_zero @ nat ) )
% 2.80/1.56 = ( ord_less_eq @ int @ I @ ( zero_zero @ int ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_234_of__int__le__0__iff,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( linordered_idom @ A )
% 2.80/1.56 => ! [Z2: int] :
% 2.80/1.56 ( ( ord_less_eq @ A @ ( ring_1_of_int @ A @ Z2 ) @ ( zero_zero @ A ) )
% 2.80/1.56 = ( ord_less_eq @ int @ Z2 @ ( zero_zero @ int ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_235_of__int__0__le__iff,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( linordered_idom @ A )
% 2.80/1.56 => ! [Z2: int] :
% 2.80/1.56 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( ring_1_of_int @ A @ Z2 ) )
% 2.80/1.56 = ( ord_less_eq @ int @ ( zero_zero @ int ) @ Z2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_236_of__int__less__1__iff,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( linordered_idom @ A )
% 2.80/1.56 => ! [Z2: int] :
% 2.80/1.56 ( ( ord_less @ A @ ( ring_1_of_int @ A @ Z2 ) @ ( one_one @ A ) )
% 2.80/1.56 = ( ord_less @ int @ Z2 @ ( one_one @ int ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_237_of__int__1__less__iff,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( linordered_idom @ A )
% 2.80/1.56 => ! [Z2: int] :
% 2.80/1.56 ( ( ord_less @ A @ ( one_one @ A ) @ ( ring_1_of_int @ A @ Z2 ) )
% 2.80/1.56 = ( ord_less @ int @ ( one_one @ int ) @ Z2 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_238_of__int__nonneg,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( linordered_idom @ A )
% 2.80/1.56 => ! [Z2: int] :
% 2.80/1.56 ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ Z2 )
% 2.80/1.56 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( ring_1_of_int @ A @ Z2 ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_239_verit__comp__simplify1_I3_J,axiom,
% 2.80/1.56 ! [B: $tType] :
% 2.80/1.56 ( ( linorder @ B )
% 2.80/1.56 => ! [B4: B,A13: B] :
% 2.80/1.56 ( ( ~ ( ord_less_eq @ B @ B4 @ A13 ) )
% 2.80/1.56 = ( ord_less @ B @ A13 @ B4 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_240_le__numeral__extra_I4_J,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( linord1659791738miring @ A )
% 2.80/1.56 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_241_one__reorient,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( one @ A )
% 2.80/1.56 => ! [X: A] :
% 2.80/1.56 ( ( ( one_one @ A )
% 2.80/1.56 = X )
% 2.80/1.56 = ( X
% 2.80/1.56 = ( one_one @ A ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_242_lift__Suc__antimono__le,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( order @ A )
% 2.80/1.56 => ! [F: nat > A,N3: nat,N4: nat] :
% 2.80/1.56 ( ! [N: nat] : ( ord_less_eq @ A @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 2.80/1.56 => ( ( ord_less_eq @ nat @ N3 @ N4 )
% 2.80/1.56 => ( ord_less_eq @ A @ ( F @ N4 ) @ ( F @ N3 ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_243_lift__Suc__mono__le,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( order @ A )
% 2.80/1.56 => ! [F: nat > A,N3: nat,N4: nat] :
% 2.80/1.56 ( ! [N: nat] : ( ord_less_eq @ A @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 2.80/1.56 => ( ( ord_less_eq @ nat @ N3 @ N4 )
% 2.80/1.56 => ( ord_less_eq @ A @ ( F @ N3 ) @ ( F @ N4 ) ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_244_zero__le,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( canoni770627133id_add @ A )
% 2.80/1.56 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_245_le__numeral__extra_I3_J,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( linord1659791738miring @ A )
% 2.80/1.56 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_246_less__numeral__extra_I4_J,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( linord1659791738miring @ A )
% 2.80/1.56 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_247_of__nat__mono,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( linord1659791738miring @ A )
% 2.80/1.56 => ! [I: nat,J: nat] :
% 2.80/1.56 ( ( ord_less_eq @ nat @ I @ J )
% 2.80/1.56 => ( ord_less_eq @ A @ ( semiring_1_of_nat @ A @ I ) @ ( semiring_1_of_nat @ A @ J ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_248_less__minus__one__simps_I4_J,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( linordered_idom @ A )
% 2.80/1.56 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_249_less__minus__one__simps_I2_J,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( linordered_idom @ A )
% 2.80/1.56 => ( ord_less @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( one_one @ A ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(fact_250_zero__neq__neg__one,axiom,
% 2.80/1.56 ! [A: $tType] :
% 2.80/1.56 ( ( ring_char_0 @ A )
% 2.80/1.56 => ( ( zero_zero @ A )
% 2.80/1.56 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 2.80/1.56 ! [A14: $tType,A15: $tType] :
% 2.80/1.56 ( ( boolean_algebra @ A15 )
% 2.80/1.56 => ( boolean_algebra @ ( A14 > A15 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.80/1.56 ! [A14: $tType,A15: $tType] :
% 2.80/1.56 ( ( order @ A15 )
% 2.80/1.56 => ( order @ ( A14 > A15 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_fun___Orderings_Oord,axiom,
% 2.80/1.56 ! [A14: $tType,A15: $tType] :
% 2.80/1.56 ( ( ord @ A15 )
% 2.80/1.56 => ( ord @ ( A14 > A15 ) ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Int_Oint___Rings_Olinordered__nonzero__semiring,axiom,
% 2.80/1.56 linord1659791738miring @ int ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Int_Oint___Groups_Olinordered__ab__group__add,axiom,
% 2.80/1.56 linord219039673up_add @ int ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Int_Oint___Groups_Oordered__ab__group__add,axiom,
% 2.80/1.56 ordered_ab_group_add @ int ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Int_Oint___Rings_Olinordered__idom,axiom,
% 2.80/1.56 linordered_idom @ int ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Int_Oint___Nat_Osemiring__char__0,axiom,
% 2.80/1.56 semiring_char_0 @ int ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Int_Oint___Orderings_Olinorder,axiom,
% 2.80/1.56 linorder @ int ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Int_Oint___Rings_Osemiring__1,axiom,
% 2.80/1.56 semiring_1 @ int ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Int_Oint___Groups_Ogroup__add,axiom,
% 2.80/1.56 group_add @ int ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Int_Oint___Orderings_Oorder_1,axiom,
% 2.80/1.56 order @ int ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Int_Oint___Nat_Oring__char__0,axiom,
% 2.80/1.56 ring_char_0 @ int ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Int_Oint___Orderings_Oord_2,axiom,
% 2.80/1.56 ord @ int ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Int_Oint___Rings_Oring__1,axiom,
% 2.80/1.56 ring_1 @ int ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Int_Oint___Groups_Ozero,axiom,
% 2.80/1.56 zero @ int ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Int_Oint___Groups_Oone,axiom,
% 2.80/1.56 one @ int ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 2.80/1.56 canoni770627133id_add @ nat ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_3,axiom,
% 2.80/1.56 linord1659791738miring @ nat ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 2.80/1.56 wellorder @ nat ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Nat_Onat___Nat_Osemiring__char__0_4,axiom,
% 2.80/1.56 semiring_char_0 @ nat ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Nat_Onat___Orderings_Olinorder_5,axiom,
% 2.80/1.56 linorder @ nat ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Nat_Onat___Rings_Osemiring__1_6,axiom,
% 2.80/1.56 semiring_1 @ nat ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Nat_Onat___Orderings_Oorder_7,axiom,
% 2.80/1.56 order @ nat ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Nat_Onat___Orderings_Oord_8,axiom,
% 2.80/1.56 ord @ nat ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Nat_Onat___Groups_Ozero_9,axiom,
% 2.80/1.56 zero @ nat ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Nat_Onat___Groups_Oone_10,axiom,
% 2.80/1.56 one @ nat ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 2.80/1.56 size @ nat ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_11,axiom,
% 2.80/1.56 ! [A14: $tType] : ( boolean_algebra @ ( set @ A14 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Set_Oset___Orderings_Oorder_12,axiom,
% 2.80/1.56 ! [A14: $tType] : ( order @ ( set @ A14 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Set_Oset___Orderings_Oord_13,axiom,
% 2.80/1.56 ! [A14: $tType] : ( ord @ ( set @ A14 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_14,axiom,
% 2.80/1.56 boolean_algebra @ $o ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_HOL_Obool___Orderings_Olinorder_15,axiom,
% 2.80/1.56 linorder @ $o ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_HOL_Obool___Orderings_Oorder_16,axiom,
% 2.80/1.56 order @ $o ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_HOL_Obool___Orderings_Oord_17,axiom,
% 2.80/1.56 ord @ $o ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_List_Olist___Nat_Osize_18,axiom,
% 2.80/1.56 ! [A14: $tType] : ( size @ ( list @ A14 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Product__Type_Ounit___Lattices_Oboolean__algebra_19,axiom,
% 2.80/1.56 boolean_algebra @ product_unit ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_20,axiom,
% 2.80/1.56 wellorder @ product_unit ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_21,axiom,
% 2.80/1.56 linorder @ product_unit ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Product__Type_Ounit___Orderings_Oorder_22,axiom,
% 2.80/1.56 order @ product_unit ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_Product__Type_Ounit___Orderings_Oord_23,axiom,
% 2.80/1.56 ord @ product_unit ).
% 2.80/1.56
% 2.80/1.56 thf(tcon_AsynchronousSystem_Omessage___Nat_Osize_24,axiom,
% 2.80/1.56 ! [A14: $tType,A15: $tType] : ( size @ ( message @ A14 @ A15 ) ) ).
% 2.80/1.56
% 2.80/1.56 thf(conj_0,conjecture,
% 2.80/1.56 prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ m ) @ ( fe @ na ) ).
% 2.80/1.56 ------------------------
% 2.80/1.57 % (29310)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_29027 for (2999ds/4Mi)
% 2.80/1.57 % (29310)Instruction limit reached!
% 2.80/1.57 % (29310)------------------------------
% 2.80/1.57 % (29310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.57 % (29310)Termination reason: Unknown
% 2.80/1.57 % (29310)Termination phase: shuffling
% 2.80/1.57
% 2.80/1.57 % (29310)Memory used [KB]: 1407
% 2.80/1.57 % (29310)Time elapsed: 0.003 s
% 2.80/1.57 % (29310)Instructions burned: 6 (million)
% 2.80/1.57 % (29310)------------------------------
% 2.80/1.57 % (29310)------------------------------
% 2.80/1.57 % (29311)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_29027 for (2999ds/27Mi)
% 2.80/1.58 % (29309)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29027 for (2999ds/183Mi)
% 2.80/1.58 % (29312)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29027 for (2999ds/2Mi)
% 2.80/1.58 % (29313)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_29027 for (2999ds/2Mi)
% 2.80/1.58 % (29314)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_29027 for (2999ds/275Mi)
% 2.80/1.58 % (29315)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29027 for (2999ds/18Mi)
% 2.80/1.58 % (29312)Instruction limit reached!
% 2.80/1.58 % (29312)------------------------------
% 2.80/1.58 % (29312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.58 % (29312)Termination reason: Unknown
% 2.80/1.58 % (29312)Termination phase: shuffling
% 2.80/1.58
% 2.80/1.58 % (29312)Memory used [KB]: 1407
% 2.80/1.58 % (29312)Time elapsed: 0.004 s
% 2.80/1.58 % (29312)Instructions burned: 3 (million)
% 2.80/1.58 % (29312)------------------------------
% 2.80/1.58 % (29312)------------------------------
% 2.80/1.58 % (29313)Instruction limit reached!
% 2.80/1.58 % (29313)------------------------------
% 2.80/1.58 % (29313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.58 % (29313)Termination reason: Unknown
% 2.80/1.58 % (29313)Termination phase: shuffling
% 2.80/1.58
% 2.80/1.58 % (29313)Memory used [KB]: 1407
% 2.80/1.58 % (29313)Time elapsed: 0.004 s
% 2.80/1.58 % (29313)Instructions burned: 3 (million)
% 2.80/1.58 % (29313)------------------------------
% 2.80/1.58 % (29313)------------------------------
% 2.80/1.58 % (29316)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29027 for (2999ds/3Mi)
% 2.80/1.58 % (29316)Instruction limit reached!
% 2.80/1.58 % (29316)------------------------------
% 2.80/1.58 % (29316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.58 % (29316)Termination reason: Unknown
% 2.80/1.58 % (29316)Termination phase: shuffling
% 2.80/1.58
% 2.80/1.59 % (29316)Memory used [KB]: 1407
% 2.80/1.59 % (29316)Time elapsed: 0.002 s
% 2.80/1.59 % (29316)Instructions burned: 3 (million)
% 2.80/1.59 % (29316)------------------------------
% 2.80/1.59 % (29316)------------------------------
% 2.80/1.59 % (29311)Instruction limit reached!
% 2.80/1.59 % (29311)------------------------------
% 2.80/1.59 % (29311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.59 % (29311)Termination reason: Unknown
% 2.80/1.59 % (29311)Termination phase: Property scanning
% 2.80/1.59
% 2.80/1.59 % (29311)Memory used [KB]: 1791
% 2.80/1.59 % (29311)Time elapsed: 0.014 s
% 2.80/1.59 % (29311)Instructions burned: 29 (million)
% 2.80/1.59 % (29311)------------------------------
% 2.80/1.59 % (29311)------------------------------
% 2.80/1.59 % (29315)Instruction limit reached!
% 2.80/1.59 % (29315)------------------------------
% 2.80/1.59 % (29315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.59 % (29315)Termination reason: Unknown
% 2.80/1.59 % (29315)Termination phase: shuffling
% 2.80/1.59
% 2.80/1.59 % (29315)Memory used [KB]: 1663
% 2.80/1.59 % (29315)Time elapsed: 0.014 s
% 2.80/1.59 % (29315)Instructions burned: 19 (million)
% 2.80/1.59 % (29315)------------------------------
% 2.80/1.59 % (29315)------------------------------
% 2.80/1.59 % (29319)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_29027 for (2999ds/3Mi)
% 2.80/1.60 % (29319)Instruction limit reached!
% 2.80/1.60 % (29319)------------------------------
% 2.80/1.60 % (29319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.80/1.60 % (29319)Termination reason: Unknown
% 2.80/1.60 % (29319)Termination phase: shuffling
% 2.80/1.60
% 2.80/1.60 % (29319)Memory used [KB]: 1407
% 2.80/1.60 % (29319)Time elapsed: 0.002 s
% 2.80/1.60 % (29319)Instructions burned: 3 (million)
% 2.80/1.60 % (29319)------------------------------
% 2.80/1.60 % (29319)------------------------------
% 2.87/1.60 % (29320)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_29027 for (2999ds/1041Mi)
% 2.87/1.60 % (29317)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_29027 for (2999ds/37Mi)
% 2.87/1.60 % (29318)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_29027 for (2999ds/15Mi)
% 2.87/1.60 % (29322)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29027 for (2999ds/16Mi)
% 2.87/1.61 % (29318)Instruction limit reached!
% 2.87/1.61 % (29318)------------------------------
% 2.87/1.61 % (29318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.61 % (29318)Termination reason: Unknown
% 2.87/1.61 % (29318)Termination phase: shuffling
% 2.87/1.61
% 2.87/1.61 % (29318)Memory used [KB]: 1663
% 2.87/1.61 % (29318)Time elapsed: 0.011 s
% 2.87/1.61 % (29318)Instructions burned: 16 (million)
% 2.87/1.61 % (29318)------------------------------
% 2.87/1.61 % (29318)------------------------------
% 2.87/1.61 % (29321)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29027 for (2999ds/7Mi)
% 2.87/1.61 % (29322)Instruction limit reached!
% 2.87/1.61 % (29322)------------------------------
% 2.87/1.61 % (29322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.61 % (29322)Termination reason: Unknown
% 2.87/1.61 % (29322)Termination phase: shuffling
% 2.87/1.61
% 2.87/1.61 % (29322)Memory used [KB]: 1663
% 2.87/1.61 % (29322)Time elapsed: 0.007 s
% 2.87/1.61 % (29322)Instructions burned: 17 (million)
% 2.87/1.61 % (29322)------------------------------
% 2.87/1.61 % (29322)------------------------------
% 2.87/1.61 % (29321)Instruction limit reached!
% 2.87/1.61 % (29321)------------------------------
% 2.87/1.61 % (29321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.61 % (29321)Termination reason: Unknown
% 2.87/1.61 % (29321)Termination phase: shuffling
% 2.87/1.61
% 2.87/1.61 % (29321)Memory used [KB]: 1535
% 2.87/1.61 % (29321)Time elapsed: 0.007 s
% 2.87/1.61 % (29321)Instructions burned: 8 (million)
% 2.87/1.61 % (29321)------------------------------
% 2.87/1.61 % (29321)------------------------------
% 2.87/1.62 % (29317)Instruction limit reached!
% 2.87/1.62 % (29317)------------------------------
% 2.87/1.62 % (29317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.62 % (29317)Termination reason: Unknown
% 2.87/1.62 % (29317)Termination phase: shuffling
% 2.87/1.62
% 2.87/1.62 % (29317)Memory used [KB]: 2174
% 2.87/1.62 % (29317)Time elapsed: 0.022 s
% 2.87/1.62 % (29317)Instructions burned: 38 (million)
% 2.87/1.62 % (29317)------------------------------
% 2.87/1.62 % (29317)------------------------------
% 2.87/1.62 % (29324)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_29027 for (2999ds/3Mi)
% 2.87/1.62 % (29323)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_29027 for (2999ds/3Mi)
% 2.87/1.62 % (29324)Instruction limit reached!
% 2.87/1.62 % (29324)------------------------------
% 2.87/1.62 % (29324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.62 % (29324)Termination reason: Unknown
% 2.87/1.62 % (29324)Termination phase: shuffling
% 2.87/1.62
% 2.87/1.62 % (29324)Memory used [KB]: 1279
% 2.87/1.62 % (29324)Time elapsed: 0.002 s
% 2.87/1.62 % (29324)Instructions burned: 3 (million)
% 2.87/1.62 % (29324)------------------------------
% 2.87/1.62 % (29324)------------------------------
% 2.87/1.62 % (29323)Instruction limit reached!
% 2.87/1.62 % (29323)------------------------------
% 2.87/1.62 % (29323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.62 % (29323)Termination reason: Unknown
% 2.87/1.62 % (29323)Termination phase: shuffling
% 2.87/1.62
% 2.87/1.62 % (29323)Memory used [KB]: 1407
% 2.87/1.62 % (29323)Time elapsed: 0.003 s
% 2.87/1.62 % (29323)Instructions burned: 5 (million)
% 2.87/1.62 % (29323)------------------------------
% 2.87/1.62 % (29323)------------------------------
% 2.87/1.63 % (29327)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_29027 for (2999ds/4Mi)
% 2.87/1.63 % (29328)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_29027 for (2999ds/18Mi)
% 2.87/1.63 % (29325)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_29027 for (2999ds/7Mi)
% 2.87/1.63 % (29327)Instruction limit reached!
% 2.87/1.63 % (29327)------------------------------
% 2.87/1.63 % (29327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.63 % (29327)Termination reason: Unknown
% 2.87/1.63 % (29327)Termination phase: shuffling
% 2.87/1.63
% 2.87/1.63 % (29327)Memory used [KB]: 1407
% 2.87/1.63 % (29327)Time elapsed: 0.003 s
% 2.87/1.63 % (29327)Instructions burned: 7 (million)
% 2.87/1.63 % (29327)------------------------------
% 2.87/1.63 % (29327)------------------------------
% 2.87/1.63 % (29314)First to succeed.
% 2.87/1.64 % (29314)Refutation found. Thanks to Tanya!
% 2.87/1.64 % SZS status Theorem for DTF2THF_29027
% 2.87/1.64 % SZS output start Proof for DTF2THF_29027
% 2.87/1.64 thf(type_def_5, type, list: ($tType) > $tType).
% 2.87/1.64 thf(type_def_7, type, messageValue: ($tType) > $tType).
% 2.87/1.64 thf(type_def_8, type, message: ($tType * $tType) > $tType).
% 2.87/1.64 thf(type_def_9, type, nat: $tType).
% 2.87/1.64 thf(type_def_10, type, product_unit: $tType).
% 2.87/1.64 thf(type_def_11, type, configuration_ext: ($tType * $tType * $tType * $tType) > $tType).
% 2.87/1.64 thf(type_def_12, type, int: $tType).
% 2.87/1.64 thf(type_def_13, type, set: ($tType) > $tType).
% 2.87/1.64 thf(type_def_14, type, p: $tType).
% 2.87/1.64 thf(type_def_15, type, v: $tType).
% 2.87/1.64 thf(type_def_16, type, s: $tType).
% 2.87/1.64 thf(func_def_0, type, configuration_ext: ($tType * $tType * $tType * $tType) > $tType).
% 2.87/1.64 thf(func_def_1, type, messageValue: ($tType) > $tType).
% 2.87/1.64 thf(func_def_2, type, message: ($tType * $tType) > $tType).
% 2.87/1.64 thf(func_def_3, type, product_unit: $tType).
% 2.87/1.64 thf(func_def_4, type, list: ($tType) > $tType).
% 2.87/1.64 thf(func_def_5, type, set: ($tType) > $tType).
% 2.87/1.64 thf(func_def_6, type, nat: $tType).
% 2.87/1.64 thf(func_def_7, type, int: $tType).
% 2.87/1.64 thf(func_def_8, type, v: $tType).
% 2.87/1.64 thf(func_def_9, type, s: $tType).
% 2.87/1.64 thf(func_def_10, type, p: $tType).
% 2.87/1.64 thf(func_def_11, type, type: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_12, type, size: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_13, type, one: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_14, type, zero: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_15, type, ring_1: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_16, type, ord: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_17, type, ring_char_0: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_18, type, order: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_19, type, group_add: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_20, type, semiring_1: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_21, type, linorder: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_22, type, semiring_char_0: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_23, type, wellorder: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_24, type, linordered_idom: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_25, type, boolean_algebra: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_26, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_27, type, linord219039673up_add: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_28, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_29, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 2.87/1.64 thf(func_def_30, type, bNF_Greatest_shift: !>[X0: $tType, X1: $tType]:((list @ X0 > X1) > X0 > list @ X0 > X1)).
% 2.87/1.64 thf(func_def_31, type, fLPThe1922692578sensus: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > messageValue @ X2 > X1) > (X0 > X1 > messageValue @ X2 > message @ X0 @ X2 > nat) > (X0 > X1) > $o)).
% 2.87/1.64 thf(func_def_32, 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)).
% 2.87/1.64 thf(func_def_33, 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)).
% 2.87/1.64 thf(func_def_34, type, fLPThe2031355932ionFLP: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > messageValue @ X2 > X1) > (X0 > X1 > messageValue @ X2 > message @ X0 @ X2 > nat) > (X0 > X1) > (nat > list @ configuration_ext @ X0 @ X2 @ X1 @ product_unit) > (nat > list @ message @ X0 @ X2) > $o)).
% 2.87/1.64 thf(func_def_35, type, one_one: !>[X0: $tType]:(X0)).
% 2.87/1.64 thf(func_def_36, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 2.87/1.64 thf(func_def_37, type, zero_zero: !>[X0: $tType]:(X0)).
% 2.87/1.64 thf(func_def_38, type, nat2: int > nat).
% 2.87/1.64 thf(func_def_39, type, ring_1_of_int: !>[X0: $tType]:(int > X0)).
% 2.87/1.64 thf(func_def_40, type, prefixList: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 2.87/1.64 thf(func_def_41, type, gen_length: !>[X0: $tType]:(nat > list @ X0 > nat)).
% 2.87/1.64 thf(func_def_42, type, insert: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.87/1.64 thf(func_def_43, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 2.87/1.64 thf(func_def_44, type, nil: !>[X0: $tType]:(list @ X0)).
% 2.87/1.64 thf(func_def_45, type, list_ex1: !>[X0: $tType]:((X0 > $o) > list @ X0 > $o)).
% 2.87/1.64 thf(func_def_46, type, n_lists: !>[X0: $tType]:(nat > list @ X0 > list @ list @ X0)).
% 2.87/1.64 thf(func_def_47, type, nths: !>[X0: $tType]:(list @ X0 > set @ nat > list @ X0)).
% 2.87/1.64 thf(func_def_48, type, product_lists: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 2.87/1.64 thf(func_def_49, type, subseqs: !>[X0: $tType]:(list @ X0 > list @ list @ X0)).
% 2.87/1.64 thf(func_def_50, type, suc: nat > nat).
% 2.87/1.64 thf(func_def_51, type, semiring_1_of_nat: !>[X0: $tType]:(nat > X0)).
% 2.87/1.64 thf(func_def_52, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 2.87/1.64 thf(func_def_53, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.87/1.64 thf(func_def_54, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.87/1.64 thf(func_def_55, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.87/1.64 thf(func_def_56, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.87/1.64 thf(func_def_57, type, cfg: configuration_ext @ p @ v @ s @ product_unit).
% 2.87/1.64 thf(func_def_58, type, fe: nat > list @ configuration_ext @ p @ v @ s @ product_unit).
% 2.87/1.64 thf(func_def_59, type, m: nat).
% 2.87/1.64 thf(func_def_60, type, n: nat).
% 2.87/1.64 thf(func_def_61, type, na: nat).
% 2.87/1.64 thf(func_def_75, 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).
% 2.87/1.64 thf(func_def_76, 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).
% 2.87/1.64 thf(func_def_77, type, sK2: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 2.87/1.64 thf(func_def_78, type, sK3: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_79, type, sK4: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_80, type, sK5: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_81, type, sK6: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 2.87/1.64 thf(func_def_82, type, sK7: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 2.87/1.64 thf(func_def_83, type, sK8: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_84, type, sK9: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_85, type, sK10: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_86, type, sK11: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_87, type, sK12: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_88, type, sK13: !>[X0: $tType]:(list @ X0 > X0)).
% 2.87/1.64 thf(func_def_89, type, sK14: !>[X0: $tType]:(list @ X0 > X0)).
% 2.87/1.64 thf(func_def_90, type, sK15: !>[X0: $tType]:(list @ X0 > X0)).
% 2.87/1.64 thf(func_def_91, type, sK16: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.87/1.64 thf(func_def_92, type, sK17: nat > nat).
% 2.87/1.64 thf(func_def_93, type, sK18: (nat > $o) > nat > nat).
% 2.87/1.64 thf(func_def_94, type, sK19: (nat > $o) > nat > nat).
% 2.87/1.64 thf(func_def_95, type, sK20: nat > nat > nat).
% 2.87/1.64 thf(func_def_96, type, sK21: (nat > $o) > nat).
% 2.87/1.64 thf(func_def_97, type, sK22: nat > nat > nat).
% 2.87/1.64 thf(func_def_98, type, sK23: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_99, type, sK24: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_100, type, sK25: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_101, type, sK26: nat > nat).
% 2.87/1.64 thf(func_def_102, type, sK27: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_103, type, sK28: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_104, type, sK29: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 2.87/1.64 thf(func_def_105, type, sK30: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 2.87/1.64 thf(func_def_106, type, sK31: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_107, type, sK32: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_108, type, sK33: (nat > $o) > nat > nat).
% 2.87/1.64 thf(func_def_109, type, sK34: (nat > $o) > nat > nat).
% 2.87/1.64 thf(func_def_110, type, sK35: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 2.87/1.64 thf(func_def_111, type, sK36: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 2.87/1.64 thf(func_def_112, type, sK37: (nat > $o) > nat > nat).
% 2.87/1.64 thf(func_def_113, type, sK38: !>[X0: $tType]:(nat > list @ X0)).
% 2.87/1.64 thf(func_def_114, type, sK39: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_115, type, sK40: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_116, type, sK41: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_117, type, sK42: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_118, type, sK43: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_119, type, sK44: (nat > $o) > nat).
% 2.87/1.64 thf(func_def_120, type, sK45: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.87/1.64 thf(func_def_121, type, sK46: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_122, type, sK47: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.87/1.64 thf(func_def_123, type, sK48: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.87/1.64 thf(func_def_124, type, sK49: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat > X0)).
% 2.87/1.64 thf(func_def_125, type, sK50: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_126, type, sK51: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat)).
% 2.87/1.64 thf(func_def_127, type, sK52: (nat > nat > $o) > nat).
% 2.87/1.64 thf(func_def_128, type, sK53: (nat > nat > $o) > nat).
% 2.87/1.64 thf(func_def_129, type, sK54: (nat > nat > $o) > nat).
% 2.87/1.64 thf(func_def_130, type, sK55: (nat > nat > $o) > nat).
% 2.87/1.64 thf(func_def_131, type, sK56: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.87/1.64 thf(func_def_132, type, sK57: !>[X0: $tType]:(list @ X0 > nat > X0)).
% 2.87/1.64 thf(func_def_133, type, sK58: !>[X0: $tType]:(list @ X0 > nat > list @ X0)).
% 2.87/1.64 thf(func_def_134, type, sK59: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.87/1.64 thf(func_def_135, type, sK60: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_136, type, sK61: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.87/1.64 thf(func_def_137, type, sK62: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.87/1.64 thf(func_def_138, type, sK63: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 2.87/1.64 thf(func_def_139, type, sK64: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_140, type, sK65: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 2.87/1.64 thf(func_def_141, type, sK66: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.87/1.64 thf(func_def_142, type, sK67: !>[X0: $tType]:(list @ X0 > X0)).
% 2.87/1.64 thf(func_def_143, type, sK68: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.87/1.64 thf(func_def_144, type, sK69: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.87/1.64 thf(func_def_145, type, sK70: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 2.87/1.64 thf(func_def_146, type, sK71: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 2.87/1.64 thf(func_def_147, type, sK72: nat > nat > nat).
% 2.87/1.64 thf(func_def_148, type, sK73: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_149, type, sK74: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_150, type, sK75: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_151, type, sK76: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_152, type, sK77: nat > nat > nat).
% 2.87/1.64 thf(func_def_153, type, sK78: (nat > $o) > nat).
% 2.87/1.64 thf(func_def_154, type, sK79: !>[X0: $tType]:(list @ X0 > X0)).
% 2.87/1.64 thf(func_def_155, type, sK80: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.87/1.64 thf(func_def_156, type, sK81: (nat > $o) > nat > nat).
% 2.87/1.64 thf(func_def_157, type, sK82: (nat > $o) > nat > nat).
% 2.87/1.64 thf(func_def_158, type, sK83: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_159, type, sK84: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_160, type, sK85: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_161, type, sK86: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_162, type, sK87: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_163, type, sK88: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_164, type, sK89: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_165, type, sK90: !>[X0: $tType]:(nat > list @ X0 > X0)).
% 2.87/1.64 thf(func_def_166, type, sK91: !>[X0: $tType]:(nat > list @ X0 > list @ X0)).
% 2.87/1.64 thf(func_def_167, type, sK92: (nat > $o) > nat).
% 2.87/1.64 thf(func_def_168, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > X1)).
% 2.87/1.64 thf(func_def_169, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > list @ X1)).
% 2.87/1.64 thf(func_def_170, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > X0)).
% 2.87/1.64 thf(func_def_171, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_172, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > X2)).
% 2.87/1.64 thf(func_def_173, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType]:((list @ X1 > list @ X0 > list @ X2 > $o) > list @ X2)).
% 2.87/1.64 thf(func_def_174, type, sK99: (nat > $o) > nat > nat).
% 2.87/1.64 thf(func_def_175, type, sK100: (nat > $o) > nat > nat).
% 2.87/1.64 thf(func_def_176, type, sK101: (nat > nat > $o) > nat).
% 2.87/1.64 thf(func_def_177, type, sK102: (nat > nat > $o) > nat).
% 2.87/1.64 thf(func_def_178, type, sK103: (nat > nat > $o) > nat).
% 2.87/1.64 thf(func_def_179, type, sK104: (nat > nat > $o) > nat).
% 2.87/1.64 thf(func_def_180, type, sK105: nat > nat).
% 2.87/1.64 thf(func_def_181, type, sK106: (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).
% 2.87/1.64 thf(func_def_182, type, sK107: (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).
% 2.87/1.64 thf(func_def_183, type, sK108: (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).
% 2.87/1.64 thf(func_def_184, type, sK109: (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).
% 2.87/1.64 thf(func_def_185, type, sK110: (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).
% 2.87/1.64 thf(func_def_186, type, sK111: (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).
% 2.87/1.64 thf(func_def_187, type, sK112: (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).
% 2.87/1.64 thf(func_def_188, type, sK113: (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).
% 2.87/1.64 thf(func_def_189, type, sK114: (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).
% 2.87/1.64 thf(func_def_190, type, sK115: (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).
% 2.87/1.64 thf(func_def_191, type, sK116: (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).
% 2.87/1.64 thf(func_def_192, type, sK117: (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).
% 2.87/1.64 thf(func_def_193, type, sK118: (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).
% 2.87/1.64 thf(func_def_194, type, sK119: (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).
% 2.87/1.64 thf(func_def_195, type, sK120: (nat > $o) > nat).
% 2.87/1.64 thf(func_def_196, type, sK121: !>[X0: $tType]:(list @ X0 > X0)).
% 2.87/1.64 thf(func_def_197, type, sK122: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 2.87/1.64 thf(func_def_198, type, sK123: (nat > $o) > nat).
% 2.87/1.64 thf(func_def_199, type, sK124: nat > nat).
% 2.87/1.64 thf(func_def_200, type, sK125: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_201, type, sK126: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_202, type, sK127: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_203, type, sK128: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 2.87/1.64 thf(func_def_204, type, sK129: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_205, type, sK130: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 2.87/1.64 thf(func_def_206, type, sK131: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0)).
% 2.87/1.64 thf(func_def_207, type, sK132: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 2.87/1.64 thf(func_def_208, type, sK133: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.87/1.64 thf(func_def_209, type, sK134: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 2.87/1.64 thf(func_def_210, type, sK135: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 2.87/1.64 thf(func_def_211, type, sK136: (nat > $o) > nat > nat).
% 2.87/1.64 thf(func_def_212, type, sK137: (nat > $o) > nat > nat).
% 2.87/1.64 thf(func_def_213, type, sK138: (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).
% 2.87/1.64 thf(func_def_214, type, sK139: (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).
% 2.87/1.64 thf(func_def_215, type, sK140: (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).
% 2.87/1.64 thf(func_def_216, type, sK141: (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).
% 2.87/1.64 thf(func_def_217, type, sK142: (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).
% 2.87/1.64 thf(func_def_218, type, sK143: (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).
% 2.87/1.64 thf(func_def_219, type, sK144: (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).
% 2.87/1.64 thf(func_def_220, type, sK145: (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).
% 2.87/1.64 thf(func_def_221, type, sK146: (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).
% 2.87/1.64 thf(func_def_222, type, sK147: (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).
% 2.87/1.64 thf(func_def_223, type, sK148: (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).
% 2.87/1.64 thf(func_def_224, type, sK149: (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).
% 2.87/1.64 thf(func_def_225, type, sK150: (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).
% 2.87/1.64 thf(func_def_226, type, sK151: (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).
% 2.87/1.64 thf(func_def_227, type, sK152: !>[X0: $tType]:(list @ list @ X0 > X0)).
% 2.87/1.64 thf(func_def_228, type, sK153: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 2.87/1.64 thf(func_def_229, type, sK154: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 2.87/1.64 thf(func_def_230, type, sK155: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 2.87/1.64 thf(func_def_232, type, ph157: !>[X0: $tType]:(X0)).
% 2.87/1.64 thf(f1375,plain,(
% 2.87/1.64 $false),
% 2.87/1.64 inference(subsumption_resolution,[status(thm)],[f1373,f1292])).
% 2.87/1.64 thf(f1292,plain,(
% 2.87/1.64 ((ord_less @ nat @ m @ na) = $true)),
% 2.87/1.64 inference(cnf_transformation,[status(thm)],[f376])).
% 2.87/1.64 thf(f376,plain,(
% 2.87/1.64 ((ord_less @ nat @ m @ na) = $true)),
% 2.87/1.64 inference(fool_elimination,[status(thm)],[f375])).
% 2.87/1.64 thf(f375,plain,(
% 2.87/1.64 (ord_less @ nat @ m @ na)),
% 2.87/1.64 inference(rectify,[status(thm)],[f1])).
% 2.87/1.64 thf(f1,axiom,(
% 2.87/1.64 (ord_less @ nat @ m @ na)),
% 2.87/1.64 file('/export/starexec/sandbox2/tmp/tmp.W0i8NEZydw/DTF2THF_29027.p',fact_0__092_060open_062m_A_060_An_092_060close_062)).
% 2.87/1.64 thf(f1373,plain,(
% 2.87/1.64 ((ord_less @ nat @ m @ na) != $true)),
% 2.87/1.64 inference(trivial_inequality_removal,[status(thm)],[f1371])).
% 2.87/1.64 thf(f1371,plain,(
% 2.87/1.64 ($true != $true) | ((ord_less @ nat @ m @ na) != $true)),
% 2.87/1.64 inference(superposition,[status(thm)],[f1278,f1304])).
% 2.87/1.64 thf(f1304,plain,(
% 2.87/1.64 ((prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na)) = $true) | ((ord_less @ nat @ m @ na) != $true)),
% 2.87/1.64 inference(cnf_transformation,[status(thm)],[f861])).
% 2.87/1.64 thf(f861,plain,(
% 2.87/1.64 ((prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na)) = $true) | ((ord_less @ nat @ m @ na) != $true)),
% 2.87/1.64 inference(ennf_transformation,[status(thm)],[f704])).
% 2.87/1.64 thf(f704,plain,(
% 2.87/1.64 ((ord_less @ nat @ m @ na) = $true) => ((prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na)) = $true)),
% 2.87/1.64 inference(fool_elimination,[status(thm)],[f703])).
% 2.87/1.64 thf(f703,plain,(
% 2.87/1.64 (ord_less @ nat @ m @ na) => (prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na))),
% 2.87/1.64 inference(rectify,[status(thm)],[f3])).
% 2.87/1.64 thf(f3,axiom,(
% 2.87/1.64 (ord_less @ nat @ m @ na) => (prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na))),
% 2.87/1.64 file('/export/starexec/sandbox2/tmp/tmp.W0i8NEZydw/DTF2THF_29027.p',fact_2_IA_I1_J)).
% 2.87/1.64 thf(f1278,plain,(
% 2.87/1.64 ((prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na)) != $true)),
% 2.87/1.64 inference(cnf_transformation,[status(thm)],[f785])).
% 2.87/1.64 thf(f785,plain,(
% 2.87/1.64 ((prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na)) != $true)),
% 2.87/1.64 inference(flattening,[status(thm)],[f706])).
% 2.87/1.64 thf(f706,plain,(
% 2.87/1.64 ~((prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na)) = $true)),
% 2.87/1.64 inference(fool_elimination,[status(thm)],[f705])).
% 2.87/1.64 thf(f705,plain,(
% 2.87/1.64 ~(prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na))),
% 2.87/1.64 inference(rectify,[status(thm)],[f295])).
% 2.87/1.64 thf(f295,negated_conjecture,(
% 2.87/1.64 ~(prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na))),
% 2.87/1.64 inference(negated_conjecture,[status(cth)],[f294])).
% 2.87/1.64 thf(f294,conjecture,(
% 2.87/1.64 (prefixList @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ m) @ (fe @ na))),
% 2.87/1.64 file('/export/starexec/sandbox2/tmp/tmp.W0i8NEZydw/DTF2THF_29027.p',conj_0)).
% 2.87/1.64 % SZS output end Proof for DTF2THF_29027
% 2.87/1.64 % (29314)------------------------------
% 2.87/1.64 % (29314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.64 % (29314)Termination reason: Refutation
% 2.87/1.64
% 2.87/1.64 % (29314)Memory used [KB]: 7164
% 2.87/1.64 % (29314)Time elapsed: 0.056 s
% 2.87/1.64 % (29314)Instructions burned: 98 (million)
% 2.87/1.64 % (29314)------------------------------
% 2.87/1.64 % (29314)------------------------------
% 2.87/1.64 % (29308)Success in time 0.075 s
%------------------------------------------------------------------------------