%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP125^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 08:55:45 AM UTC 2026
% Result : Theorem 20.84s 4.23s
% Output : Refutation 20.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP125^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n020.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 08:27:12 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : ITP125^2 : TPTP v9.2.1. Released v7.5.0.
% 0.30/0.46 % Domain : Interactive Theorem Proving
% 0.30/0.46 % Problem : Sledgehammer Monitor problem prob_453__6453916_1
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Des21]
% 0.30/0.46 % Names : Monitor/prob_453__6453916_1 [Des21]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.33 v8.1.0, 0.50 v7.5.0
% 0.30/0.46 % Syntax : Number of formulae : 351 ( 66 unt; 58 typ; 0 def)
% 0.30/0.46 % Number of atoms : 917 ( 157 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 13 ( 3 avg)
% 0.30/0.46 % Number of connectives : 3757 ( 85 ~; 22 |; 62 &;3057 @)
% 0.30/0.46 % ( 0 <=>; 531 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 21 ( 9 avg)
% 0.30/0.46 % Number of types : 5 ( 4 usr)
% 0.30/0.46 % Number of type conns : 130 ( 130 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 55 ( 54 usr; 13 con; 0-5 aty)
% 0.30/0.46 % Number of variables : 1061 ( 47 ^; 929 !; 47 ?;1061 :)
% 0.30/0.46 % ( 38 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.46 % SPC : TH1_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:17:27.271
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % Could-be-implicit typings (9)
% 0.30/0.46 thf(ty_t_Interval_O_092_060I_062,type,
% 0.30/0.46 i: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Product__Type_Oprod,type,
% 0.30/0.46 product_prod: $tType > $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_MFOTL_Oformula,type,
% 0.30/0.46 formula: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Trace_Oprefix,type,
% 0.30/0.46 prefix: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Trace_Otrace,type,
% 0.30/0.46 trace: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_String_Ochar,type,
% 0.30/0.46 char: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_List_Olist,type,
% 0.30/0.46 list: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Nat_Onat,type,
% 0.30/0.46 nat: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_tf_a,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 % Explicit typings (49)
% 0.30/0.46 thf(sy_cl_HOL_Otype,type,
% 0.30/0.46 type:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Oone,type,
% 0.30/0.46 one:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.30/0.46 ord:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.30/0.46 order:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Ogroup__add,type,
% 0.30/0.46 group_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Ono__bot,type,
% 0.30/0.46 no_bot:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Ono__top,type,
% 0.30/0.46 no_top:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.30/0.46 linorder:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.30/0.46 preorder:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Owellorder,type,
% 0.30/0.46 wellorder:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.30/0.46 semigroup_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Odense__order,type,
% 0.30/0.46 dense_order:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.30/0.46 comm_monoid_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.30/0.46 ab_semigroup_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.30/0.46 dense_linorder:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.30/0.46 cancel_semigroup_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.30/0.46 ordere779506340up_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.30/0.46 canoni770627133id_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.30/0.46 ordere236663937imp_le:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 0.30/0.46 ordere223160158up_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 0.30/0.46 strict2144017051up_add:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Divides_Ounique__euclidean__semiring__numeral,type,
% 0.30/0.46 unique1598680935umeral:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 0.30/0.46 condit1656338222tinuum:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 0.30/0.46 condit1037483654norder:
% 0.30/0.46 !>[A: $tType] : $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Abstract__Monitor_Oprogress__axioms,type,
% 0.30/0.46 abstra417776764axioms:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( ( trace @ A ) > ( list @ B ) > nat > $o ) > ( ( prefix @ A ) > nat ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.30/0.46 one_one:
% 0.30/0.46 !>[A: $tType] : A ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.30/0.46 plus_plus:
% 0.30/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Lattices__Big_Oord__class_Oarg__max,type,
% 0.30/0.46 lattices_ord_arg_max:
% 0.30/0.46 !>[B: $tType,A: $tType] : ( ( B > A ) > ( B > $o ) > B ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_MFOTL_Oformula_OUntil,type,
% 0.30/0.46 until:
% 0.30/0.46 !>[A: $tType] : ( ( formula @ A ) > i > ( formula @ A ) > ( formula @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_MFOTL_Osat,type,
% 0.30/0.46 sat:
% 0.30/0.46 !>[A: $tType] : ( ( trace @ ( product_prod @ ( list @ char ) @ ( list @ A ) ) ) > ( list @ A ) > nat > ( formula @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Monitor__Mirabelle__pzlrlsievl_Oprogress,type,
% 0.30/0.46 monito2027355080ogress:
% 0.30/0.46 !>[A: $tType] : ( ( trace @ ( product_prod @ ( list @ char ) @ ( list @ A ) ) ) > ( formula @ A ) > nat > nat ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.30/0.46 ord_less:
% 0.30/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.30/0.46 ord_less_eq:
% 0.30/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Trace_O_092_060tau_062,type,
% 0.30/0.46 tau:
% 0.30/0.46 !>[A: $tType] : ( ( trace @ A ) > nat > nat ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Trace_Oplen,type,
% 0.30/0.46 plen:
% 0.30/0.46 !>[A: $tType] : ( ( prefix @ A ) > nat ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Trace_Oprefix__of,type,
% 0.30/0.46 prefix_of:
% 0.30/0.46 !>[A: $tType] : ( ( prefix @ A ) > ( trace @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_I____,type,
% 0.30/0.46 i2: i ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v__092_060phi_062,type,
% 0.30/0.46 phi: formula @ a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v__092_060phi_0621____,type,
% 0.30/0.46 phi_1: formula @ a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v__092_060phi_0622____,type,
% 0.30/0.46 phi_2: formula @ a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v__092_060pi_062,type,
% 0.30/0.46 pi: prefix @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v__092_060sigma_062,type,
% 0.30/0.46 sigma: trace @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v__092_060sigma_062_H,type,
% 0.30/0.46 sigma2: trace @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_b____,type,
% 0.30/0.46 b: nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_i,type,
% 0.30/0.46 i3: nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_ia____,type,
% 0.30/0.46 ia: nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_j____,type,
% 0.30/0.46 j: nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_ja____,type,
% 0.30/0.46 ja: nat ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_k____,type,
% 0.30/0.46 k: nat ).
% 0.30/0.46
% 0.30/0.46 % Relevant facts (255)
% 0.30/0.46 thf(fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.30/0.46 ord_less @ nat @ k @ ( monito2027355080ogress @ a @ sigma @ phi_1 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>k < Monitor_Mirabelle_pzlrlsievl.progress \<sigma> \<phi>1 (plen \<pi>)\<close>
% 0.30/0.46 thf(fact_1_assms_I3_J,axiom,
% 0.30/0.46 ord_less @ nat @ i3 @ ( monito2027355080ogress @ a @ sigma @ phi @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ).
% 0.30/0.46
% 0.30/0.46 % assms(3)
% 0.30/0.46 thf(fact_2_assms_I1_J,axiom,
% 0.30/0.46 prefix_of @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi @ sigma ).
% 0.30/0.46
% 0.30/0.46 % assms(1)
% 0.30/0.46 thf(fact_3_nat__neq__iff,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( M != N )
% 0.30/0.46 = ( ( ord_less @ nat @ M @ N )
% 0.30/0.46 | ( ord_less @ nat @ N @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_neq_iff
% 0.30/0.46 thf(fact_4_less__not__refl,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ~ ( ord_less @ nat @ N @ N ) ).
% 0.30/0.46
% 0.30/0.46 % less_not_refl
% 0.30/0.46 thf(fact_5_less__not__refl2,axiom,
% 0.30/0.46 ! [N: nat,M: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ N @ M )
% 0.30/0.46 => ( M != N ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_not_refl2
% 0.30/0.46 thf(fact_6_less__not__refl3,axiom,
% 0.30/0.46 ! [S: nat,T: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ S @ T )
% 0.30/0.46 => ( S != T ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_not_refl3
% 0.30/0.46 thf(fact_7_less__irrefl__nat,axiom,
% 0.30/0.46 ! [N: nat] :
% 0.30/0.46 ~ ( ord_less @ nat @ N @ N ) ).
% 0.30/0.46
% 0.30/0.46 % less_irrefl_nat
% 0.30/0.46 thf(fact_8_nat__less__induct,axiom,
% 0.30/0.46 ! [P: nat > $o,N: nat] :
% 0.30/0.46 ( ! [N2: nat] :
% 0.30/0.46 ( ! [M2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M2 @ N2 )
% 0.30/0.46 => ( P @ M2 ) )
% 0.30/0.46 => ( P @ N2 ) )
% 0.30/0.46 => ( P @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_less_induct
% 0.30/0.46 thf(fact_9_infinite__descent,axiom,
% 0.30/0.46 ! [P: nat > $o,N: nat] :
% 0.30/0.46 ( ! [N2: nat] :
% 0.30/0.46 ( ~ ( P @ N2 )
% 0.30/0.46 => ? [M2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M2 @ N2 )
% 0.30/0.46 & ~ ( P @ M2 ) ) )
% 0.30/0.46 => ( P @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % infinite_descent
% 0.30/0.46 thf(fact_10_linorder__neqE__nat,axiom,
% 0.30/0.46 ! [X: nat,Y: nat] :
% 0.30/0.46 ( ( X != Y )
% 0.30/0.46 => ( ~ ( ord_less @ nat @ X @ Y )
% 0.30/0.46 => ( ord_less @ nat @ Y @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linorder_neqE_nat
% 0.30/0.46 thf(fact_11_infinite__descent__measure,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,V: A > nat,X: A] :
% 0.30/0.46 ( ! [X2: A] :
% 0.30/0.46 ( ~ ( P @ X2 )
% 0.30/0.46 => ? [Y2: A] :
% 0.30/0.46 ( ( ord_less @ nat @ ( V @ Y2 ) @ ( V @ X2 ) )
% 0.30/0.46 & ~ ( P @ Y2 ) ) )
% 0.30/0.46 => ( P @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % infinite_descent_measure
% 0.30/0.46 thf(fact_12__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.30/0.46 ord_less_eq @ nat @ j @ ( monito2027355080ogress @ a @ sigma @ phi_1 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>j__ \<le> Monitor_Mirabelle_pzlrlsievl.progress \<sigma> \<phi>1 (plen \<pi>)\<close>
% 0.30/0.46 thf(fact_13_minf_I11_J,axiom,
% 0.30/0.46 ! [C: $tType,D: $tType] :
% 0.30/0.46 ( ( ord @ C )
% 0.30/0.46 => ! [F: D] :
% 0.30/0.46 ? [Z: C] :
% 0.30/0.46 ! [X3: C] :
% 0.30/0.46 ( ( ord_less @ C @ X3 @ Z )
% 0.30/0.46 => ( F = F ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % minf(11)
% 0.30/0.46 thf(fact_14_assms_I2_J,axiom,
% 0.30/0.46 prefix_of @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi @ sigma2 ).
% 0.30/0.46
% 0.30/0.46 % assms(2)
% 0.30/0.46 thf(fact_15__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.30/0.46 ord_less_eq @ nat @ j @ ( monito2027355080ogress @ a @ sigma @ phi_2 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>j__ \<le> Monitor_Mirabelle_pzlrlsievl.progress \<sigma> \<phi>2 (plen \<pi>)\<close>
% 0.30/0.46 thf(fact_16_le__refl,axiom,
% 0.30/0.46 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 0.30/0.46
% 0.30/0.46 % le_refl
% 0.30/0.46 thf(fact_17_le__trans,axiom,
% 0.30/0.46 ! [I: nat,J: nat,K: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ I @ J )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ J @ K )
% 0.30/0.46 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_trans
% 0.30/0.46 thf(fact_18_eq__imp__le,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( M = N )
% 0.30/0.46 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_imp_le
% 0.30/0.46 thf(fact_19_le__antisym,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ N )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ N @ M )
% 0.30/0.46 => ( M = N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_antisym
% 0.30/0.46 thf(fact_20_nat__le__linear,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ N )
% 0.30/0.46 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_le_linear
% 0.30/0.46 thf(fact_21_Nat_Oex__has__greatest__nat,axiom,
% 0.30/0.46 ! [P: nat > $o,K: nat,B2: nat] :
% 0.30/0.46 ( ( P @ K )
% 0.30/0.46 => ( ! [Y3: nat] :
% 0.30/0.46 ( ( P @ Y3 )
% 0.30/0.46 => ( ord_less_eq @ nat @ Y3 @ B2 ) )
% 0.30/0.46 => ? [X2: nat] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 & ! [Y2: nat] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 => ( ord_less_eq @ nat @ Y2 @ X2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Nat.ex_has_greatest_nat
% 0.30/0.46 thf(fact_22_progress__le,axiom,
% 0.30/0.46 ! [A: $tType,Sigma: trace @ ( product_prod @ ( list @ char ) @ ( list @ A ) ),Phi: formula @ A,J: nat] : ( ord_less_eq @ nat @ ( monito2027355080ogress @ A @ Sigma @ Phi @ J ) @ J ) ).
% 0.30/0.46
% 0.30/0.46 % progress_le
% 0.30/0.46 thf(fact_23_progress__mono,axiom,
% 0.30/0.46 ! [A: $tType,J: nat,J2: nat,Sigma: trace @ ( product_prod @ ( list @ char ) @ ( list @ A ) ),Phi: formula @ A] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ J @ J2 )
% 0.30/0.46 => ( ord_less_eq @ nat @ ( monito2027355080ogress @ A @ Sigma @ Phi @ J ) @ ( monito2027355080ogress @ A @ Sigma @ Phi @ J2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % progress_mono
% 0.30/0.46 thf(fact_24_pinf_I6_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [T: A] :
% 0.30/0.46 ? [Z: A] :
% 0.30/0.46 ! [X3: A] :
% 0.30/0.46 ( ( ord_less @ A @ Z @ X3 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ X3 @ T ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pinf(6)
% 0.30/0.46 thf(fact_25_pinf_I8_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [T: A] :
% 0.30/0.46 ? [Z: A] :
% 0.30/0.46 ! [X3: A] :
% 0.30/0.46 ( ( ord_less @ A @ Z @ X3 )
% 0.30/0.46 => ( ord_less_eq @ A @ T @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pinf(8)
% 0.30/0.46 thf(fact_26_minf_I6_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [T: A] :
% 0.30/0.46 ? [Z: A] :
% 0.30/0.46 ! [X3: A] :
% 0.30/0.46 ( ( ord_less @ A @ X3 @ Z )
% 0.30/0.46 => ( ord_less_eq @ A @ X3 @ T ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % minf(6)
% 0.30/0.46 thf(fact_27_minf_I8_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [T: A] :
% 0.30/0.46 ? [Z: A] :
% 0.30/0.46 ! [X3: A] :
% 0.30/0.46 ( ( ord_less @ A @ X3 @ Z )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ T @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % minf(8)
% 0.30/0.46 thf(fact_28_less__mono__imp__le__mono,axiom,
% 0.30/0.46 ! [F2: nat > nat,I: nat,J: nat] :
% 0.30/0.46 ( ! [I2: nat,J3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I2 @ J3 )
% 0.30/0.46 => ( ord_less @ nat @ ( F2 @ I2 ) @ ( F2 @ J3 ) ) )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ I @ J )
% 0.30/0.46 => ( ord_less_eq @ nat @ ( F2 @ I ) @ ( F2 @ J ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_mono_imp_le_mono
% 0.30/0.46 thf(fact_29_le__neq__implies__less,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M @ N )
% 0.30/0.46 => ( ( M != N )
% 0.30/0.46 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_neq_implies_less
% 0.30/0.46 thf(fact_30_less__or__eq__imp__le,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ( ord_less @ nat @ M @ N )
% 0.30/0.46 | ( M = N ) )
% 0.30/0.46 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_or_eq_imp_le
% 0.30/0.46 thf(fact_31_le__eq__less__or__eq,axiom,
% 0.30/0.46 ( ( ord_less_eq @ nat )
% 0.30/0.46 = ( ^ [M3: nat,N3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M3 @ N3 )
% 0.30/0.46 | ( M3 = N3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_eq_less_or_eq
% 0.30/0.46 thf(fact_32_less__imp__le__nat,axiom,
% 0.30/0.46 ! [M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M @ N )
% 0.30/0.46 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_imp_le_nat
% 0.30/0.46 thf(fact_33_nat__less__le,axiom,
% 0.30/0.46 ( ( ord_less @ nat )
% 0.30/0.46 = ( ^ [M3: nat,N3: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ M3 @ N3 )
% 0.30/0.46 & ( M3 != N3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_less_le
% 0.30/0.46 thf(fact_34_progress__prefix__conv,axiom,
% 0.30/0.46 ! [A: $tType,Pi: prefix @ ( product_prod @ ( list @ char ) @ ( list @ A ) ),Sigma: trace @ ( product_prod @ ( list @ char ) @ ( list @ A ) ),Sigma2: trace @ ( product_prod @ ( list @ char ) @ ( list @ A ) ),Phi: formula @ A] :
% 0.30/0.46 ( ( prefix_of @ ( product_prod @ ( list @ char ) @ ( list @ A ) ) @ Pi @ Sigma )
% 0.30/0.46 => ( ( prefix_of @ ( product_prod @ ( list @ char ) @ ( list @ A ) ) @ Pi @ Sigma2 )
% 0.30/0.46 => ( ( monito2027355080ogress @ A @ Sigma @ Phi @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ A ) ) @ Pi ) )
% 0.30/0.46 = ( monito2027355080ogress @ A @ Sigma2 @ Phi @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ A ) ) @ Pi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % progress_prefix_conv
% 0.30/0.46 thf(fact_35_measure__induct__rule,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( wellorder @ B )
% 0.30/0.46 => ! [F2: A > B,P: A > $o,A2: A] :
% 0.30/0.46 ( ! [X2: A] :
% 0.30/0.46 ( ! [Y2: A] :
% 0.30/0.46 ( ( ord_less @ B @ ( F2 @ Y2 ) @ ( F2 @ X2 ) )
% 0.30/0.46 => ( P @ Y2 ) )
% 0.30/0.46 => ( P @ X2 ) )
% 0.30/0.46 => ( P @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % measure_induct_rule
% 0.30/0.46 thf(fact_36_measure__induct,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( wellorder @ B )
% 0.30/0.46 => ! [F2: A > B,P: A > $o,A2: A] :
% 0.30/0.46 ( ! [X2: A] :
% 0.30/0.46 ( ! [Y2: A] :
% 0.30/0.46 ( ( ord_less @ B @ ( F2 @ Y2 ) @ ( F2 @ X2 ) )
% 0.30/0.46 => ( P @ Y2 ) )
% 0.30/0.46 => ( P @ X2 ) )
% 0.30/0.46 => ( P @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % measure_induct
% 0.30/0.46 thf(fact_37_pinf_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.30/0.46 ( ? [Z2: A] :
% 0.30/0.46 ! [X2: A] :
% 0.30/0.46 ( ( ord_less @ A @ Z2 @ X2 )
% 0.30/0.46 => ( ( P @ X2 )
% 0.30/0.46 = ( P2 @ X2 ) ) )
% 0.30/0.46 => ( ? [Z2: A] :
% 0.30/0.46 ! [X2: A] :
% 0.30/0.46 ( ( ord_less @ A @ Z2 @ X2 )
% 0.30/0.46 => ( ( Q @ X2 )
% 0.30/0.46 = ( Q2 @ X2 ) ) )
% 0.30/0.46 => ? [Z: A] :
% 0.30/0.46 ! [X3: A] :
% 0.30/0.46 ( ( ord_less @ A @ Z @ X3 )
% 0.30/0.46 => ( ( ( P @ X3 )
% 0.30/0.46 & ( Q @ X3 ) )
% 0.30/0.46 = ( ( P2 @ X3 )
% 0.30/0.46 & ( Q2 @ X3 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pinf(1)
% 0.30/0.46 thf(fact_38_pinf_I2_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.30/0.46 ( ? [Z2: A] :
% 0.30/0.46 ! [X2: A] :
% 0.30/0.46 ( ( ord_less @ A @ Z2 @ X2 )
% 0.30/0.46 => ( ( P @ X2 )
% 0.30/0.46 = ( P2 @ X2 ) ) )
% 0.30/0.46 => ( ? [Z2: A] :
% 0.30/0.46 ! [X2: A] :
% 0.30/0.46 ( ( ord_less @ A @ Z2 @ X2 )
% 0.30/0.46 => ( ( Q @ X2 )
% 0.30/0.46 = ( Q2 @ X2 ) ) )
% 0.30/0.46 => ? [Z: A] :
% 0.30/0.46 ! [X3: A] :
% 0.30/0.46 ( ( ord_less @ A @ Z @ X3 )
% 0.30/0.46 => ( ( ( P @ X3 )
% 0.30/0.46 | ( Q @ X3 ) )
% 0.30/0.46 = ( ( P2 @ X3 )
% 0.30/0.46 | ( Q2 @ X3 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pinf(2)
% 0.30/0.46 thf(fact_39_pinf_I3_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [T: A] :
% 0.30/0.46 ? [Z: A] :
% 0.30/0.46 ! [X3: A] :
% 0.30/0.46 ( ( ord_less @ A @ Z @ X3 )
% 0.30/0.46 => ( X3 != T ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pinf(3)
% 0.30/0.46 thf(fact_40_pinf_I4_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [T: A] :
% 0.30/0.46 ? [Z: A] :
% 0.30/0.46 ! [X3: A] :
% 0.30/0.46 ( ( ord_less @ A @ Z @ X3 )
% 0.30/0.46 => ( X3 != T ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pinf(4)
% 0.30/0.46 thf(fact_41_pinf_I5_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [T: A] :
% 0.30/0.46 ? [Z: A] :
% 0.30/0.46 ! [X3: A] :
% 0.30/0.46 ( ( ord_less @ A @ Z @ X3 )
% 0.30/0.46 => ~ ( ord_less @ A @ X3 @ T ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pinf(5)
% 0.30/0.46 thf(fact_42_pinf_I7_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [T: A] :
% 0.30/0.46 ? [Z: A] :
% 0.30/0.46 ! [X3: A] :
% 0.30/0.46 ( ( ord_less @ A @ Z @ X3 )
% 0.30/0.46 => ( ord_less @ A @ T @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pinf(7)
% 0.30/0.46 thf(fact_43_pinf_I11_J,axiom,
% 0.30/0.46 ! [C: $tType,D: $tType] :
% 0.30/0.46 ( ( ord @ C )
% 0.30/0.46 => ! [F: D] :
% 0.30/0.46 ? [Z: C] :
% 0.30/0.46 ! [X3: C] :
% 0.30/0.46 ( ( ord_less @ C @ Z @ X3 )
% 0.30/0.46 => ( F = F ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % pinf(11)
% 0.30/0.46 thf(fact_44_minf_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.30/0.46 ( ? [Z2: A] :
% 0.30/0.46 ! [X2: A] :
% 0.30/0.46 ( ( ord_less @ A @ X2 @ Z2 )
% 0.30/0.46 => ( ( P @ X2 )
% 0.30/0.46 = ( P2 @ X2 ) ) )
% 0.30/0.46 => ( ? [Z2: A] :
% 0.30/0.46 ! [X2: A] :
% 0.30/0.46 ( ( ord_less @ A @ X2 @ Z2 )
% 0.30/0.46 => ( ( Q @ X2 )
% 0.30/0.46 = ( Q2 @ X2 ) ) )
% 0.30/0.46 => ? [Z: A] :
% 0.30/0.46 ! [X3: A] :
% 0.30/0.46 ( ( ord_less @ A @ X3 @ Z )
% 0.30/0.46 => ( ( ( P @ X3 )
% 0.30/0.46 & ( Q @ X3 ) )
% 0.30/0.46 = ( ( P2 @ X3 )
% 0.30/0.46 & ( Q2 @ X3 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % minf(1)
% 0.30/0.46 thf(fact_45_minf_I2_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.30/0.46 ( ? [Z2: A] :
% 0.30/0.46 ! [X2: A] :
% 0.30/0.46 ( ( ord_less @ A @ X2 @ Z2 )
% 0.30/0.46 => ( ( P @ X2 )
% 0.30/0.46 = ( P2 @ X2 ) ) )
% 0.30/0.46 => ( ? [Z2: A] :
% 0.30/0.46 ! [X2: A] :
% 0.30/0.46 ( ( ord_less @ A @ X2 @ Z2 )
% 0.30/0.46 => ( ( Q @ X2 )
% 0.30/0.46 = ( Q2 @ X2 ) ) )
% 0.30/0.46 => ? [Z: A] :
% 0.30/0.46 ! [X3: A] :
% 0.30/0.46 ( ( ord_less @ A @ X3 @ Z )
% 0.30/0.46 => ( ( ( P @ X3 )
% 0.30/0.46 | ( Q @ X3 ) )
% 0.30/0.46 = ( ( P2 @ X3 )
% 0.30/0.46 | ( Q2 @ X3 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % minf(2)
% 0.30/0.46 thf(fact_46_minf_I3_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [T: A] :
% 0.30/0.46 ? [Z: A] :
% 0.30/0.46 ! [X3: A] :
% 0.30/0.46 ( ( ord_less @ A @ X3 @ Z )
% 0.30/0.46 => ( X3 != T ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % minf(3)
% 0.30/0.46 thf(fact_47_minf_I4_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [T: A] :
% 0.30/0.46 ? [Z: A] :
% 0.30/0.46 ! [X3: A] :
% 0.30/0.46 ( ( ord_less @ A @ X3 @ Z )
% 0.30/0.46 => ( X3 != T ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % minf(4)
% 0.30/0.46 thf(fact_48_minf_I5_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [T: A] :
% 0.30/0.46 ? [Z: A] :
% 0.30/0.46 ! [X3: A] :
% 0.30/0.46 ( ( ord_less @ A @ X3 @ Z )
% 0.30/0.46 => ( ord_less @ A @ X3 @ T ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % minf(5)
% 0.30/0.46 thf(fact_49_minf_I7_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [T: A] :
% 0.30/0.46 ? [Z: A] :
% 0.30/0.46 ! [X3: A] :
% 0.30/0.46 ( ( ord_less @ A @ X3 @ Z )
% 0.30/0.46 => ~ ( ord_less @ A @ T @ X3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % minf(7)
% 0.30/0.46 thf(fact_50__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.30/0.46 ord_less_eq @ nat @ ja @ ( monito2027355080ogress @ a @ sigma2 @ phi_1 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>j \<le> Monitor_Mirabelle_pzlrlsievl.progress \<sigma>' \<phi>1 (plen \<pi>)\<close>
% 0.30/0.46 thf(fact_51_order__refl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_refl
% 0.30/0.46 thf(fact_52_Until_OIH_I1_J,axiom,
% 0.30/0.46 ! [I: nat,V2: list @ a] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ ( monito2027355080ogress @ a @ sigma @ phi_1 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) )
% 0.30/0.46 => ( ( sat @ a @ sigma @ V2 @ I @ phi_1 )
% 0.30/0.46 = ( sat @ a @ sigma2 @ V2 @ I @ phi_1 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Until.IH(1)
% 0.30/0.46 thf(fact_53_Lattices__Big_Oex__has__greatest__nat,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,K: A,F2: A > nat,B2: nat] :
% 0.30/0.46 ( ( P @ K )
% 0.30/0.46 => ( ! [Y3: A] :
% 0.30/0.46 ( ( P @ Y3 )
% 0.30/0.46 => ( ord_less @ nat @ ( F2 @ Y3 ) @ B2 ) )
% 0.30/0.46 => ? [X2: A] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 & ! [Y2: A] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 => ( ord_less_eq @ nat @ ( F2 @ Y2 ) @ ( F2 @ X2 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Lattices_Big.ex_has_greatest_nat
% 0.30/0.46 thf(fact_54_nat__descend__induct,axiom,
% 0.30/0.46 ! [N: nat,P: nat > $o,M: nat] :
% 0.30/0.46 ( ! [K2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ N @ K2 )
% 0.30/0.46 => ( P @ K2 ) )
% 0.30/0.46 => ( ! [K2: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ K2 @ N )
% 0.30/0.46 => ( ! [I3: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ K2 @ I3 )
% 0.30/0.46 => ( P @ I3 ) )
% 0.30/0.46 => ( P @ K2 ) ) )
% 0.30/0.46 => ( P @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_descend_induct
% 0.30/0.46 thf(fact_55_complete__interval,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( condit1037483654norder @ A )
% 0.30/0.46 => ! [A2: A,B2: A,P: A > $o] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( P @ A2 )
% 0.30/0.46 => ( ~ ( P @ B2 )
% 0.30/0.46 => ? [C2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ C2 )
% 0.30/0.46 & ( ord_less_eq @ A @ C2 @ B2 )
% 0.30/0.46 & ! [X3: A] :
% 0.30/0.46 ( ( ( ord_less_eq @ A @ A2 @ X3 )
% 0.30/0.46 & ( ord_less @ A @ X3 @ C2 ) )
% 0.30/0.46 => ( P @ X3 ) )
% 0.30/0.46 & ! [D2: A] :
% 0.30/0.46 ( ! [X2: A] :
% 0.30/0.46 ( ( ( ord_less_eq @ A @ A2 @ X2 )
% 0.30/0.46 & ( ord_less @ A @ X2 @ D2 ) )
% 0.30/0.46 => ( P @ X2 ) )
% 0.30/0.46 => ( ord_less_eq @ A @ D2 @ C2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % complete_interval
% 0.30/0.46 thf(fact_56_order_Onot__eq__order__implies__strict,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( A2 != B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.not_eq_order_implies_strict
% 0.30/0.46 thf(fact_57_dual__order_Ostrict__implies__order,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B2: A,A2: A] :
% 0.30/0.46 ( ( ord_less @ A @ B2 @ A2 )
% 0.30/0.46 => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.strict_implies_order
% 0.30/0.46 thf(fact_58_dual__order_Ostrict__iff__order,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ord_less @ A )
% 0.30/0.46 = ( ^ [B3: A,A3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.30/0.46 & ( A3 != B3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.strict_iff_order
% 0.30/0.46 thf(fact_59_dual__order_Oorder__iff__strict,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [B3: A,A3: A] :
% 0.30/0.46 ( ( ord_less @ A @ B3 @ A3 )
% 0.30/0.46 | ( A3 = B3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.order_iff_strict
% 0.30/0.46 thf(fact_60_order_Ostrict__implies__order,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.strict_implies_order
% 0.30/0.46 thf(fact_61__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.30/0.46 ord_less_eq @ nat @ ja @ ( monito2027355080ogress @ a @ sigma2 @ phi_2 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>j \<le> Monitor_Mirabelle_pzlrlsievl.progress \<sigma>' \<phi>2 (plen \<pi>)\<close>
% 0.30/0.46 thf(fact_62_Until_OIH_I2_J,axiom,
% 0.30/0.46 ! [I: nat,V2: list @ a] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ ( monito2027355080ogress @ a @ sigma @ phi_2 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) )
% 0.30/0.46 => ( ( sat @ a @ sigma @ V2 @ I @ phi_2 )
% 0.30/0.46 = ( sat @ a @ sigma2 @ V2 @ I @ phi_2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Until.IH(2)
% 0.30/0.46 thf(fact_63_dual__order_Oantisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B2: A,A2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( A2 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.antisym
% 0.30/0.46 thf(fact_64_dual__order_Oeq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.30/0.46 = ( ^ [A3: A,B3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.30/0.46 & ( ord_less_eq @ A @ A3 @ B3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.eq_iff
% 0.30/0.46 thf(fact_65_dual__order_Otrans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ C3 @ B2 )
% 0.30/0.46 => ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.trans
% 0.30/0.46 thf(fact_66_linorder__wlog,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.30/0.46 ( ! [A4: A,B4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.30/0.46 => ( P @ A4 @ B4 ) )
% 0.30/0.46 => ( ! [A4: A,B4: A] :
% 0.30/0.46 ( ( P @ B4 @ A4 )
% 0.30/0.46 => ( P @ A4 @ B4 ) )
% 0.30/0.46 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linorder_wlog
% 0.30/0.46 thf(fact_67_dual__order_Orefl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.refl
% 0.30/0.46 thf(fact_68_order__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A,Y: A,Z4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Y @ Z4 )
% 0.30/0.46 => ( ord_less_eq @ A @ X @ Z4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_trans
% 0.30/0.46 thf(fact_69_order__class_Oorder_Oantisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( A2 = B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.antisym
% 0.30/0.46 thf(fact_70_ord__le__eq__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( B2 = C3 )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_trans
% 0.30/0.46 thf(fact_71_ord__eq__le__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( A2 = B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ C3 )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_trans
% 0.30/0.46 thf(fact_72_order__class_Oorder_Oeq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.30/0.46 = ( ^ [A3: A,B3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.30/0.46 & ( ord_less_eq @ A @ B3 @ A3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_class.order.eq_iff
% 0.30/0.46 thf(fact_73_antisym__conv,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [Y: A,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ Y @ X )
% 0.30/0.46 => ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 = ( X = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym_conv
% 0.30/0.46 thf(fact_74_le__cases3,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A,Z4: A] :
% 0.30/0.46 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Y @ Z4 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ X @ Z4 ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ X @ Z4 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Z4 @ Y ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Z4 @ Y )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.30/0.46 => ( ( ( ord_less_eq @ A @ Y @ Z4 )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ Z4 @ X ) )
% 0.30/0.46 => ~ ( ( ord_less_eq @ A @ Z4 @ X )
% 0.30/0.46 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_cases3
% 0.30/0.46 thf(fact_75_order_Otrans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ C3 )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.trans
% 0.30/0.46 thf(fact_76_le__cases,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_cases
% 0.30/0.46 thf(fact_77_eq__refl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( X = Y )
% 0.30/0.46 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_refl
% 0.30/0.46 thf(fact_78_linear,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linear
% 0.30/0.46 thf(fact_79_antisym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Y @ X )
% 0.30/0.46 => ( X = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym
% 0.30/0.46 thf(fact_80_eq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.30/0.46 = ( ^ [X4: A,Y5: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.30/0.46 & ( ord_less_eq @ A @ Y5 @ X4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_iff
% 0.30/0.46 thf(fact_81_ord__le__eq__subst,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( ord @ B )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A,F2: A > B,C3: B] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ( F2 @ B2 )
% 0.30/0.46 = C3 )
% 0.30/0.46 => ( ! [X2: A,Y3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_le_eq_subst
% 0.30/0.46 thf(fact_82_ord__eq__le__subst,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( ord @ B )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [A2: A,F2: B > A,B2: B,C3: B] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( F2 @ B2 ) )
% 0.30/0.46 => ( ( ord_less_eq @ B @ B2 @ C3 )
% 0.30/0.46 => ( ! [X2: B,Y3: B] :
% 0.30/0.46 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_le_subst
% 0.30/0.46 thf(fact_83_order__subst2,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType] :
% 0.30/0.46 ( ( ( order @ C )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A,F2: A > C,C3: C] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ C @ ( F2 @ B2 ) @ C3 )
% 0.30/0.46 => ( ! [X2: A,Y3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.30/0.46 => ( ord_less_eq @ C @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.46 => ( ord_less_eq @ C @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst2
% 0.30/0.46 thf(fact_84_order__subst1,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( order @ B )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,F2: B > A,B2: B,C3: B] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( F2 @ B2 ) )
% 0.30/0.46 => ( ( ord_less_eq @ B @ B2 @ C3 )
% 0.30/0.46 => ( ! [X2: B,Y3: B] :
% 0.30/0.46 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_subst1
% 0.30/0.46 thf(fact_85_le__fun__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ( ( ord_less_eq @ ( A > B ) )
% 0.30/0.46 = ( ^ [F3: A > B,G: A > B] :
% 0.30/0.46 ! [X4: A] : ( ord_less_eq @ B @ ( F3 @ X4 ) @ ( G @ X4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_fun_def
% 0.30/0.46 thf(fact_86_le__funI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F2: A > B,G2: A > B] :
% 0.30/0.46 ( ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
% 0.30/0.46 => ( ord_less_eq @ ( A > B ) @ F2 @ G2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funI
% 0.30/0.46 thf(fact_87_le__funE,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F2: A > B,G2: A > B,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funE
% 0.30/0.46 thf(fact_88_le__funD,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [F2: A > B,G2: A > B,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.30/0.46 => ( ord_less_eq @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_funD
% 0.30/0.46 thf(fact_89_ord__eq__less__subst,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( ord @ B )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [A2: A,F2: B > A,B2: B,C3: B] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( F2 @ B2 ) )
% 0.30/0.46 => ( ( ord_less @ B @ B2 @ C3 )
% 0.30/0.46 => ( ! [X2: B,Y3: B] :
% 0.30/0.46 ( ( ord_less @ B @ X2 @ Y3 )
% 0.30/0.46 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.46 => ( ord_less @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_less_subst
% 0.30/0.46 thf(fact_90_ord__less__eq__subst,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( ord @ B )
% 0.30/0.46 & ( ord @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A,F2: A > B,C3: B] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ( F2 @ B2 )
% 0.30/0.46 = C3 )
% 0.30/0.46 => ( ! [X2: A,Y3: A] :
% 0.30/0.46 ( ( ord_less @ A @ X2 @ Y3 )
% 0.30/0.46 => ( ord_less @ B @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.46 => ( ord_less @ B @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_less_eq_subst
% 0.30/0.46 thf(fact_91_order__less__subst1,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( order @ B )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,F2: B > A,B2: B,C3: B] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ ( F2 @ B2 ) )
% 0.30/0.46 => ( ( ord_less @ B @ B2 @ C3 )
% 0.30/0.46 => ( ! [X2: B,Y3: B] :
% 0.30/0.46 ( ( ord_less @ B @ X2 @ Y3 )
% 0.30/0.46 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.46 => ( ord_less @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_less_subst1
% 0.30/0.46 thf(fact_92_order__less__subst2,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType] :
% 0.30/0.46 ( ( ( order @ C )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A,F2: A > C,C3: C] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less @ C @ ( F2 @ B2 ) @ C3 )
% 0.30/0.46 => ( ! [X2: A,Y3: A] :
% 0.30/0.46 ( ( ord_less @ A @ X2 @ Y3 )
% 0.30/0.46 => ( ord_less @ C @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.46 => ( ord_less @ C @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_less_subst2
% 0.30/0.46 thf(fact_93_lt__ex,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( no_bot @ A )
% 0.30/0.46 => ! [X: A] :
% 0.30/0.46 ? [Y3: A] : ( ord_less @ A @ Y3 @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % lt_ex
% 0.30/0.46 thf(fact_94_gt__ex,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( no_top @ A )
% 0.30/0.46 => ! [X: A] :
% 0.30/0.46 ? [X_1: A] : ( ord_less @ A @ X @ X_1 ) ) ).
% 0.30/0.46
% 0.30/0.46 % gt_ex
% 0.30/0.46 thf(fact_95_neqE,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( X != Y )
% 0.30/0.46 => ( ~ ( ord_less @ A @ X @ Y )
% 0.30/0.46 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % neqE
% 0.30/0.46 thf(fact_96_neq__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( X != Y )
% 0.30/0.46 = ( ( ord_less @ A @ X @ Y )
% 0.30/0.46 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % neq_iff
% 0.30/0.46 thf(fact_97_order_Oasym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.asym
% 0.30/0.46 thf(fact_98_dense,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( dense_order @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less @ A @ X @ Y )
% 0.30/0.46 => ? [Z: A] :
% 0.30/0.46 ( ( ord_less @ A @ X @ Z )
% 0.30/0.46 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dense
% 0.30/0.46 thf(fact_99_less__imp__neq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less @ A @ X @ Y )
% 0.30/0.46 => ( X != Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_imp_neq
% 0.30/0.46 thf(fact_100_less__asym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less @ A @ X @ Y )
% 0.30/0.46 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_asym
% 0.30/0.46 thf(fact_101_less__asym_H,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_asym'
% 0.30/0.46 thf(fact_102_less__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A,Y: A,Z4: A] :
% 0.30/0.46 ( ( ord_less @ A @ X @ Y )
% 0.30/0.46 => ( ( ord_less @ A @ Y @ Z4 )
% 0.30/0.46 => ( ord_less @ A @ X @ Z4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_trans
% 0.30/0.46 thf(fact_103_less__linear,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less @ A @ X @ Y )
% 0.30/0.46 | ( X = Y )
% 0.30/0.46 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_linear
% 0.30/0.46 thf(fact_104_less__irrefl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A] :
% 0.30/0.46 ~ ( ord_less @ A @ X @ X ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_irrefl
% 0.30/0.46 thf(fact_105_ord__eq__less__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( A2 = B2 )
% 0.30/0.46 => ( ( ord_less @ A @ B2 @ C3 )
% 0.30/0.46 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_eq_less_trans
% 0.30/0.46 thf(fact_106_ord__less__eq__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( B2 = C3 )
% 0.30/0.46 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ord_less_eq_trans
% 0.30/0.46 thf(fact_107_dual__order_Oasym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B2: A,A2: A] :
% 0.30/0.46 ( ( ord_less @ A @ B2 @ A2 )
% 0.30/0.46 => ~ ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.asym
% 0.30/0.46 thf(fact_108_less__imp__not__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less @ A @ X @ Y )
% 0.30/0.46 => ( X != Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_imp_not_eq
% 0.30/0.46 thf(fact_109_less__not__sym,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less @ A @ X @ Y )
% 0.30/0.46 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_not_sym
% 0.30/0.46 thf(fact_110_less__induct,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( wellorder @ A )
% 0.30/0.46 => ! [P: A > $o,A2: A] :
% 0.30/0.46 ( ! [X2: A] :
% 0.30/0.46 ( ! [Y2: A] :
% 0.30/0.46 ( ( ord_less @ A @ Y2 @ X2 )
% 0.30/0.46 => ( P @ Y2 ) )
% 0.30/0.46 => ( P @ X2 ) )
% 0.30/0.46 => ( P @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_induct
% 0.30/0.46 thf(fact_111_antisym__conv3,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [Y: A,X: A] :
% 0.30/0.46 ( ~ ( ord_less @ A @ Y @ X )
% 0.30/0.46 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.30/0.46 = ( X = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym_conv3
% 0.30/0.46 thf(fact_112_less__imp__not__eq2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less @ A @ X @ Y )
% 0.30/0.46 => ( Y != X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_imp_not_eq2
% 0.30/0.46 thf(fact_113_less__imp__triv,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A,Y: A,P: $o] :
% 0.30/0.46 ( ( ord_less @ A @ X @ Y )
% 0.30/0.46 => ( ( ord_less @ A @ Y @ X )
% 0.30/0.46 => P ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_imp_triv
% 0.30/0.46 thf(fact_114_linorder__cases,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ~ ( ord_less @ A @ X @ Y )
% 0.30/0.46 => ( ( X != Y )
% 0.30/0.46 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linorder_cases
% 0.30/0.46 thf(fact_115_dual__order_Oirrefl,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.irrefl
% 0.30/0.46 thf(fact_116_order_Ostrict__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less @ A @ B2 @ C3 )
% 0.30/0.46 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.strict_trans
% 0.30/0.46 thf(fact_117_less__imp__not__less,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less @ A @ X @ Y )
% 0.30/0.46 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_imp_not_less
% 0.30/0.46 thf(fact_118_exists__least__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( wellorder @ A )
% 0.30/0.46 => ( ( ^ [P3: A > $o] :
% 0.30/0.46 ? [X5: A] : ( P3 @ X5 ) )
% 0.30/0.46 = ( ^ [P4: A > $o] :
% 0.30/0.46 ? [N3: A] :
% 0.30/0.46 ( ( P4 @ N3 )
% 0.30/0.46 & ! [M3: A] :
% 0.30/0.46 ( ( ord_less @ A @ M3 @ N3 )
% 0.30/0.46 => ~ ( P4 @ M3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % exists_least_iff
% 0.30/0.46 thf(fact_119_linorder__less__wlog,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.30/0.46 ( ! [A4: A,B4: A] :
% 0.30/0.46 ( ( ord_less @ A @ A4 @ B4 )
% 0.30/0.46 => ( P @ A4 @ B4 ) )
% 0.30/0.46 => ( ! [A4: A] : ( P @ A4 @ A4 )
% 0.30/0.46 => ( ! [A4: A,B4: A] :
% 0.30/0.46 ( ( P @ B4 @ A4 )
% 0.30/0.46 => ( P @ A4 @ B4 ) )
% 0.30/0.46 => ( P @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % linorder_less_wlog
% 0.30/0.46 thf(fact_120_dual__order_Ostrict__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less @ A @ C3 @ B2 )
% 0.30/0.46 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.strict_trans
% 0.30/0.46 thf(fact_121_not__less__iff__gr__or__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.30/0.46 = ( ( ord_less @ A @ Y @ X )
% 0.30/0.46 | ( X = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_less_iff_gr_or_eq
% 0.30/0.46 thf(fact_122_order_Ostrict__implies__not__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( A2 != B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.strict_implies_not_eq
% 0.30/0.46 thf(fact_123_dual__order_Ostrict__implies__not__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B2: A,A2: A] :
% 0.30/0.46 ( ( ord_less @ A @ B2 @ A2 )
% 0.30/0.46 => ( A2 != B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.strict_implies_not_eq
% 0.30/0.46 thf(fact_124_ex__gt__or__lt,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( condit1656338222tinuum @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ? [B4: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B4 )
% 0.30/0.46 | ( ord_less @ A @ B4 @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ex_gt_or_lt
% 0.30/0.46 thf(fact_125_ex__has__least__nat,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,K: A,M: A > nat] :
% 0.30/0.46 ( ( P @ K )
% 0.30/0.46 => ? [X2: A] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 & ! [Y2: A] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 => ( ord_less_eq @ nat @ ( M @ X2 ) @ ( M @ Y2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ex_has_least_nat
% 0.30/0.46 thf(fact_126_leD,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [Y: A,X: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ Y @ X )
% 0.30/0.46 => ~ ( ord_less @ A @ X @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % leD
% 0.30/0.46 thf(fact_127_leI,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ~ ( ord_less @ A @ X @ Y )
% 0.30/0.46 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % leI
% 0.30/0.46 thf(fact_128_le__less,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [X4: A,Y5: A] :
% 0.30/0.46 ( ( ord_less @ A @ X4 @ Y5 )
% 0.30/0.46 | ( X4 = Y5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_less
% 0.30/0.46 thf(fact_129_less__le,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ord_less @ A )
% 0.30/0.46 = ( ^ [X4: A,Y5: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.30/0.46 & ( X4 != Y5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_le
% 0.30/0.46 thf(fact_130_order__le__less__subst1,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( order @ B )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,F2: B > A,B2: B,C3: B] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ ( F2 @ B2 ) )
% 0.30/0.46 => ( ( ord_less @ B @ B2 @ C3 )
% 0.30/0.46 => ( ! [X2: B,Y3: B] :
% 0.30/0.46 ( ( ord_less @ B @ X2 @ Y3 )
% 0.30/0.46 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.46 => ( ord_less @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_le_less_subst1
% 0.30/0.46 thf(fact_131_order__le__less__subst2,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType] :
% 0.30/0.46 ( ( ( order @ C )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A,F2: A > C,C3: C] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less @ C @ ( F2 @ B2 ) @ C3 )
% 0.30/0.46 => ( ! [X2: A,Y3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.30/0.46 => ( ord_less_eq @ C @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.46 => ( ord_less @ C @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_le_less_subst2
% 0.30/0.46 thf(fact_132_order__less__le__subst1,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( ( order @ B )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,F2: B > A,B2: B,C3: B] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ ( F2 @ B2 ) )
% 0.30/0.46 => ( ( ord_less_eq @ B @ B2 @ C3 )
% 0.30/0.46 => ( ! [X2: B,Y3: B] :
% 0.30/0.46 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.46 => ( ord_less @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_less_le_subst1
% 0.30/0.46 thf(fact_133_order__less__le__subst2,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType] :
% 0.30/0.46 ( ( ( order @ C )
% 0.30/0.46 & ( order @ A ) )
% 0.30/0.46 => ! [A2: A,B2: A,F2: A > C,C3: C] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ C @ ( F2 @ B2 ) @ C3 )
% 0.30/0.46 => ( ! [X2: A,Y3: A] :
% 0.30/0.46 ( ( ord_less @ A @ X2 @ Y3 )
% 0.30/0.46 => ( ord_less @ C @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.46 => ( ord_less @ C @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order_less_le_subst2
% 0.30/0.46 thf(fact_134_not__le,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ~ ( ord_less_eq @ A @ X @ Y ) )
% 0.30/0.46 = ( ord_less @ A @ Y @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_le
% 0.30/0.46 thf(fact_135_not__less,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.30/0.46 = ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_less
% 0.30/0.46 thf(fact_136_le__neq__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( A2 != B2 )
% 0.30/0.46 => ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_neq_trans
% 0.30/0.46 thf(fact_137_antisym__conv1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ~ ( ord_less @ A @ X @ Y )
% 0.30/0.46 => ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 = ( X = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym_conv1
% 0.30/0.46 thf(fact_138_antisym__conv2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.30/0.46 = ( X = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % antisym_conv2
% 0.30/0.46 thf(fact_139_less__imp__le,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less @ A @ X @ Y )
% 0.30/0.46 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_imp_le
% 0.30/0.46 thf(fact_140_le__less__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A,Y: A,Z4: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 => ( ( ord_less @ A @ Y @ Z4 )
% 0.30/0.46 => ( ord_less @ A @ X @ Z4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_less_trans
% 0.30/0.46 thf(fact_141_less__le__trans,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ! [X: A,Y: A,Z4: A] :
% 0.30/0.46 ( ( ord_less @ A @ X @ Y )
% 0.30/0.46 => ( ( ord_less_eq @ A @ Y @ Z4 )
% 0.30/0.46 => ( ord_less @ A @ X @ Z4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_le_trans
% 0.30/0.46 thf(fact_142_dense__ge,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( dense_linorder @ A )
% 0.30/0.46 => ! [Z4: A,Y: A] :
% 0.30/0.46 ( ! [X2: A] :
% 0.30/0.46 ( ( ord_less @ A @ Z4 @ X2 )
% 0.30/0.46 => ( ord_less_eq @ A @ Y @ X2 ) )
% 0.30/0.46 => ( ord_less_eq @ A @ Y @ Z4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dense_ge
% 0.30/0.46 thf(fact_143_dense__le,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( dense_linorder @ A )
% 0.30/0.46 => ! [Y: A,Z4: A] :
% 0.30/0.46 ( ! [X2: A] :
% 0.30/0.46 ( ( ord_less @ A @ X2 @ Y )
% 0.30/0.46 => ( ord_less_eq @ A @ X2 @ Z4 ) )
% 0.30/0.46 => ( ord_less_eq @ A @ Y @ Z4 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dense_le
% 0.30/0.46 thf(fact_144_le__less__linear,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_less_linear
% 0.30/0.46 thf(fact_145_le__imp__less__or__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [X: A,Y: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.30/0.46 => ( ( ord_less @ A @ X @ Y )
% 0.30/0.46 | ( X = Y ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_imp_less_or_eq
% 0.30/0.46 thf(fact_146_less__le__not__le,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( preorder @ A )
% 0.30/0.46 => ( ( ord_less @ A )
% 0.30/0.46 = ( ^ [X4: A,Y5: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.30/0.46 & ~ ( ord_less_eq @ A @ Y5 @ X4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_le_not_le
% 0.30/0.46 thf(fact_147_not__le__imp__less,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [Y: A,X: A] :
% 0.30/0.46 ( ~ ( ord_less_eq @ A @ Y @ X )
% 0.30/0.46 => ( ord_less @ A @ X @ Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_le_imp_less
% 0.30/0.46 thf(fact_148_order_Ostrict__trans1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less @ A @ B2 @ C3 )
% 0.30/0.46 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.strict_trans1
% 0.30/0.46 thf(fact_149_order_Ostrict__trans2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ B2 @ C3 )
% 0.30/0.46 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.strict_trans2
% 0.30/0.46 thf(fact_150_order_Oorder__iff__strict,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [A3: A,B3: A] :
% 0.30/0.46 ( ( ord_less @ A @ A3 @ B3 )
% 0.30/0.46 | ( A3 = B3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.order_iff_strict
% 0.30/0.46 thf(fact_151_order_Ostrict__iff__order,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ( ( ord_less @ A )
% 0.30/0.46 = ( ^ [A3: A,B3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.30/0.46 & ( A3 != B3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % order.strict_iff_order
% 0.30/0.46 thf(fact_152_dual__order_Ostrict__trans1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less @ A @ C3 @ B2 )
% 0.30/0.46 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.strict_trans1
% 0.30/0.46 thf(fact_153_dual__order_Ostrict__trans2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ B2 @ A2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ C3 @ B2 )
% 0.30/0.46 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dual_order.strict_trans2
% 0.30/0.46 thf(fact_154_dense__ge__bounded,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( dense_linorder @ A )
% 0.30/0.46 => ! [Z4: A,X: A,Y: A] :
% 0.30/0.46 ( ( ord_less @ A @ Z4 @ X )
% 0.30/0.46 => ( ! [W: A] :
% 0.30/0.46 ( ( ord_less @ A @ Z4 @ W )
% 0.30/0.46 => ( ( ord_less @ A @ W @ X )
% 0.30/0.46 => ( ord_less_eq @ A @ Y @ W ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ Y @ Z4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dense_ge_bounded
% 0.30/0.46 thf(fact_155_dense__le__bounded,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( dense_linorder @ A )
% 0.30/0.46 => ! [X: A,Y: A,Z4: A] :
% 0.30/0.46 ( ( ord_less @ A @ X @ Y )
% 0.30/0.46 => ( ! [W: A] :
% 0.30/0.46 ( ( ord_less @ A @ X @ W )
% 0.30/0.46 => ( ( ord_less @ A @ W @ Y )
% 0.30/0.46 => ( ord_less_eq @ A @ W @ Z4 ) ) )
% 0.30/0.46 => ( ord_less_eq @ A @ Y @ Z4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % dense_le_bounded
% 0.30/0.46 thf(fact_156_Until_Oprems,axiom,
% 0.30/0.46 ord_less @ nat @ ia @ ( monito2027355080ogress @ a @ sigma @ ( until @ a @ phi_1 @ i2 @ phi_2 ) @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ).
% 0.30/0.46
% 0.30/0.46 % Until.prems
% 0.30/0.46 thf(fact_157_plen__mono,axiom,
% 0.30/0.46 ! [A: $tType,Pi: prefix @ A,Pi2: prefix @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( prefix @ A ) @ Pi @ Pi2 )
% 0.30/0.46 => ( ord_less_eq @ nat @ ( plen @ A @ Pi ) @ ( plen @ A @ Pi2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % plen_mono
% 0.30/0.46 thf(fact_158_verit__comp__simplify1_I3_J,axiom,
% 0.30/0.46 ! [B: $tType] :
% 0.30/0.46 ( ( linorder @ B )
% 0.30/0.46 => ! [B5: B,A5: B] :
% 0.30/0.46 ( ( ~ ( ord_less_eq @ B @ B5 @ A5 ) )
% 0.30/0.46 = ( ord_less @ B @ A5 @ B5 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % verit_comp_simplify1(3)
% 0.30/0.46 thf(fact_159__092_060open_062i_A_060_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_H_A_Iformula_OUntil_A_092_060phi_0621_AI_A_092_060phi_0622_J_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.30/0.46 ord_less @ nat @ ia @ ( monito2027355080ogress @ a @ sigma2 @ ( until @ a @ phi_1 @ i2 @ phi_2 ) @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>i < Monitor_Mirabelle_pzlrlsievl.progress \<sigma>' (formula.Until \<phi>1 I \<phi>2) (plen \<pi>)\<close>
% 0.30/0.46 thf(fact_160_arg__max__nat__lemma,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,K: A,F2: A > nat,B2: nat] :
% 0.30/0.46 ( ( P @ K )
% 0.30/0.46 => ( ! [Y3: A] :
% 0.30/0.46 ( ( P @ Y3 )
% 0.30/0.46 => ( ord_less @ nat @ ( F2 @ Y3 ) @ B2 ) )
% 0.30/0.46 => ( ( P @ ( lattices_ord_arg_max @ A @ nat @ F2 @ P ) )
% 0.30/0.46 & ! [Y2: A] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 => ( ord_less_eq @ nat @ ( F2 @ Y2 ) @ ( F2 @ ( lattices_ord_arg_max @ A @ nat @ F2 @ P ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % arg_max_nat_lemma
% 0.30/0.46 thf(fact_161_arg__max__nat__le,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,X: A,F2: A > nat,B2: nat] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y3: A] :
% 0.30/0.46 ( ( P @ Y3 )
% 0.30/0.46 => ( ord_less @ nat @ ( F2 @ Y3 ) @ B2 ) )
% 0.30/0.46 => ( ord_less_eq @ nat @ ( F2 @ X ) @ ( F2 @ ( lattices_ord_arg_max @ A @ nat @ F2 @ P ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % arg_max_nat_le
% 0.30/0.46 thf(fact_162_progress__axioms_Ointro,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,Progress: ( prefix @ A ) > nat,Sat: ( trace @ A ) > ( list @ B ) > nat > $o] :
% 0.30/0.46 ( ! [Pi3: prefix @ A,Pi4: prefix @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( prefix @ A ) @ Pi3 @ Pi4 )
% 0.30/0.46 => ( ord_less_eq @ nat @ ( Progress @ Pi3 ) @ ( Progress @ Pi4 ) ) )
% 0.30/0.46 => ( ! [Sigma3: trace @ A,X2: nat] :
% 0.30/0.46 ? [Pi5: prefix @ A] :
% 0.30/0.46 ( ( prefix_of @ A @ Pi5 @ Sigma3 )
% 0.30/0.46 & ( ord_less_eq @ nat @ X2 @ ( Progress @ Pi5 ) ) )
% 0.30/0.46 => ( ! [Pi3: prefix @ A,Sigma3: trace @ A,Sigma4: trace @ A,I2: nat,V3: list @ B] :
% 0.30/0.46 ( ( prefix_of @ A @ Pi3 @ Sigma3 )
% 0.30/0.46 => ( ( prefix_of @ A @ Pi3 @ Sigma4 )
% 0.30/0.46 => ( ( ord_less @ nat @ I2 @ ( Progress @ Pi3 ) )
% 0.30/0.46 => ( ( Sat @ Sigma3 @ V3 @ I2 )
% 0.30/0.46 = ( Sat @ Sigma4 @ V3 @ I2 ) ) ) ) )
% 0.30/0.46 => ( abstra417776764axioms @ A @ B @ Sat @ Progress ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % progress_axioms.intro
% 0.30/0.46 thf(fact_163_less__prefix__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ord_less @ ( prefix @ A ) )
% 0.30/0.46 = ( ^ [X4: prefix @ A,Y5: prefix @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( prefix @ A ) @ X4 @ Y5 )
% 0.30/0.46 & ~ ( ord_less_eq @ ( prefix @ A ) @ Y5 @ X4 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_prefix_def
% 0.30/0.46 thf(fact_164_less__fun__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ( ( ord_less @ ( A > B ) )
% 0.30/0.46 = ( ^ [F3: A > B,G: A > B] :
% 0.30/0.46 ( ( ord_less_eq @ ( A > B ) @ F3 @ G )
% 0.30/0.46 & ~ ( ord_less_eq @ ( A > B ) @ G @ F3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_fun_def
% 0.30/0.46 thf(fact_165_arg__max__natI,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,K: A,F2: A > nat,B2: nat] :
% 0.30/0.46 ( ( P @ K )
% 0.30/0.46 => ( ! [Y3: A] :
% 0.30/0.46 ( ( P @ Y3 )
% 0.30/0.46 => ( ord_less @ nat @ ( F2 @ Y3 ) @ B2 ) )
% 0.30/0.46 => ( P @ ( lattices_ord_arg_max @ A @ nat @ F2 @ P ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % arg_max_natI
% 0.30/0.46 thf(fact_166_arg__max__equality,axiom,
% 0.30/0.46 ! [A: $tType,C: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [P: C > $o,K: C,F2: C > A] :
% 0.30/0.46 ( ( P @ K )
% 0.30/0.46 => ( ! [X2: C] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ K ) ) )
% 0.30/0.46 => ( ( F2 @ ( lattices_ord_arg_max @ C @ A @ F2 @ P ) )
% 0.30/0.46 = ( F2 @ K ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % arg_max_equality
% 0.30/0.46 thf(fact_167_arg__maxI,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( ord @ B )
% 0.30/0.46 => ! [P: A > $o,X: A,F2: A > B,Q: A > $o] :
% 0.30/0.46 ( ( P @ X )
% 0.30/0.46 => ( ! [Y3: A] :
% 0.30/0.46 ( ( P @ Y3 )
% 0.30/0.46 => ~ ( ord_less @ B @ ( F2 @ X ) @ ( F2 @ Y3 ) ) )
% 0.30/0.46 => ( ! [X2: A] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 => ( ! [Y2: A] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 => ~ ( ord_less @ B @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.30/0.46 => ( Q @ X2 ) ) )
% 0.30/0.46 => ( Q @ ( lattices_ord_arg_max @ A @ B @ F2 @ P ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % arg_maxI
% 0.30/0.46 thf(fact_168_verit__la__disequality,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( linorder @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( A2 = B2 )
% 0.30/0.46 | ~ ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 | ~ ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % verit_la_disequality
% 0.30/0.46 thf(fact_169_verit__comp__simplify1_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( order @ A )
% 0.30/0.46 => ! [A2: A] :
% 0.30/0.46 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % verit_comp_simplify1(1)
% 0.30/0.46 thf(fact_170_ex__prefix__of,axiom,
% 0.30/0.46 ! [A: $tType,P5: prefix @ A] :
% 0.30/0.46 ? [X_1: trace @ A] : ( prefix_of @ A @ P5 @ X_1 ) ).
% 0.30/0.46
% 0.30/0.46 % ex_prefix_of
% 0.30/0.46 thf(fact_171_prefix__of__antimono,axiom,
% 0.30/0.46 ! [A: $tType,Pi: prefix @ A,Pi2: prefix @ A,S: trace @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( prefix @ A ) @ Pi @ Pi2 )
% 0.30/0.46 => ( ( prefix_of @ A @ Pi2 @ S )
% 0.30/0.46 => ( prefix_of @ A @ Pi @ S ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prefix_of_antimono
% 0.30/0.46 thf(fact_172_prefix__of__imp__linear,axiom,
% 0.30/0.46 ! [A: $tType,Pi: prefix @ A,Sigma: trace @ A,Pi2: prefix @ A] :
% 0.30/0.46 ( ( prefix_of @ A @ Pi @ Sigma )
% 0.30/0.46 => ( ( prefix_of @ A @ Pi2 @ Sigma )
% 0.30/0.46 => ( ( ord_less_eq @ ( prefix @ A ) @ Pi @ Pi2 )
% 0.30/0.46 | ( ord_less_eq @ ( prefix @ A ) @ Pi2 @ Pi ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prefix_of_imp_linear
% 0.30/0.46 thf(fact_173_progress__axioms__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( abstra417776764axioms @ A @ B )
% 0.30/0.46 = ( ^ [Sat2: ( trace @ A ) > ( list @ B ) > nat > $o,Progress2: ( prefix @ A ) > nat] :
% 0.30/0.46 ( ! [Pi6: prefix @ A,Pi7: prefix @ A] :
% 0.30/0.46 ( ( ord_less_eq @ ( prefix @ A ) @ Pi6 @ Pi7 )
% 0.30/0.46 => ( ord_less_eq @ nat @ ( Progress2 @ Pi6 ) @ ( Progress2 @ Pi7 ) ) )
% 0.30/0.46 & ! [Sigma5: trace @ A,X4: nat] :
% 0.30/0.46 ? [Pi6: prefix @ A] :
% 0.30/0.46 ( ( prefix_of @ A @ Pi6 @ Sigma5 )
% 0.30/0.46 & ( ord_less_eq @ nat @ X4 @ ( Progress2 @ Pi6 ) ) )
% 0.30/0.46 & ! [Pi6: prefix @ A,Sigma5: trace @ A,Sigma6: trace @ A,I4: nat,V4: list @ B] :
% 0.30/0.46 ( ( prefix_of @ A @ Pi6 @ Sigma5 )
% 0.30/0.46 => ( ( prefix_of @ A @ Pi6 @ Sigma6 )
% 0.30/0.46 => ( ( ord_less @ nat @ I4 @ ( Progress2 @ Pi6 ) )
% 0.30/0.46 => ( ( Sat2 @ Sigma5 @ V4 @ I4 )
% 0.30/0.46 = ( Sat2 @ Sigma6 @ V4 @ I4 ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % progress_axioms_def
% 0.30/0.46 thf(fact_174_formula_Oinject_I9_J,axiom,
% 0.30/0.46 ! [A: $tType,X91: formula @ A,X92: i,X93: formula @ A,Y91: formula @ A,Y92: i,Y93: formula @ A] :
% 0.30/0.46 ( ( ( until @ A @ X91 @ X92 @ X93 )
% 0.30/0.46 = ( until @ A @ Y91 @ Y92 @ Y93 ) )
% 0.30/0.46 = ( ( X91 = Y91 )
% 0.30/0.46 & ( X92 = Y92 )
% 0.30/0.46 & ( X93 = Y93 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % formula.inject(9)
% 0.30/0.46 thf(fact_175__C21_C,axiom,
% 0.30/0.46 ! [K: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ K ) @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ ia ) @ b ) )
% 0.30/0.46 => ( ord_less @ nat @ K @ ( monito2027355080ogress @ a @ sigma @ phi_2 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % "21"
% 0.30/0.46 thf(fact_176__C11_C,axiom,
% 0.30/0.46 ! [K: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ K ) @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ ia ) @ b ) )
% 0.30/0.46 => ( ord_less @ nat @ K @ ( monito2027355080ogress @ a @ sigma @ phi_1 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % "11"
% 0.30/0.46 thf(fact_177_that,axiom,
% 0.30/0.46 ord_less_eq @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ k ) @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ ia ) @ b ) ).
% 0.30/0.46
% 0.30/0.46 % that
% 0.30/0.46 thf(fact_178_nat__add__left__cancel__less,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 0.30/0.46 = ( ord_less @ nat @ M @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_add_left_cancel_less
% 0.30/0.46 thf(fact_179_nat__add__left__cancel__le,axiom,
% 0.30/0.46 ! [K: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 0.30/0.46 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_add_left_cancel_le
% 0.30/0.46 thf(fact_180__C3_C,axiom,
% 0.30/0.46 ! [K: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ K ) @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ ia ) @ b ) )
% 0.30/0.46 => ( ord_less @ nat @ K @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % "3"
% 0.30/0.46 thf(fact_181__C1_C,axiom,
% 0.30/0.46 ! [K: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ K ) @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ ia ) @ b ) )
% 0.30/0.46 => ( ord_less @ nat @ K @ ( monito2027355080ogress @ a @ sigma @ phi_1 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % "1"
% 0.30/0.46 thf(fact_182__C2_C,axiom,
% 0.30/0.46 ! [K: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ K ) @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ ia ) @ b ) )
% 0.30/0.46 => ( ord_less @ nat @ K @ ( monito2027355080ogress @ a @ sigma @ phi_2 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % "2"
% 0.30/0.46 thf(fact_183__092_060open_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_____092_060close_062,axiom,
% 0.30/0.46 ord_less_eq @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ ia ) @ b ) @ ( one_one @ nat ) ) @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ j ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>\<tau> \<sigma> i + b + 1 \<le> \<tau> \<sigma> j__\<close>
% 0.30/0.46 thf(fact_184__092_060open_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_092_060close_062,axiom,
% 0.30/0.46 ord_less_eq @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ ia ) @ b ) @ ( one_one @ nat ) ) @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ ja ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>\<tau> \<sigma>' i + b + 1 \<le> \<tau> \<sigma>' j\<close>
% 0.30/0.46 thf(fact_185_less___092_060tau_062D,axiom,
% 0.30/0.46 ! [A: $tType,Sigma: trace @ A,I: nat,J: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( tau @ A @ Sigma @ I ) @ ( tau @ A @ Sigma @ J ) )
% 0.30/0.46 => ( ord_less @ nat @ I @ J ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_\<tau>D
% 0.30/0.46 thf(fact_186_ex__le___092_060tau_062,axiom,
% 0.30/0.46 ! [A: $tType,I: nat,X: nat,S: trace @ A] :
% 0.30/0.46 ? [J3: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ I @ J3 )
% 0.30/0.46 & ( ord_less_eq @ nat @ X @ ( tau @ A @ S @ J3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ex_le_\<tau>
% 0.30/0.46 thf(fact_187__092_060tau_062__mono,axiom,
% 0.30/0.46 ! [A: $tType,I: nat,J: nat,S: trace @ A] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ I @ J )
% 0.30/0.46 => ( ord_less_eq @ nat @ ( tau @ A @ S @ I ) @ ( tau @ A @ S @ J ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<tau>_mono
% 0.30/0.46 thf(fact_188_less__add__eq__less,axiom,
% 0.30/0.46 ! [K: nat,L: nat,M: nat,N: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ K @ L )
% 0.30/0.46 => ( ( ( plus_plus @ nat @ M @ L )
% 0.30/0.46 = ( plus_plus @ nat @ K @ N ) )
% 0.30/0.46 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_add_eq_less
% 0.30/0.46 thf(fact_189_trans__less__add2,axiom,
% 0.30/0.46 ! [I: nat,J: nat,M: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ J )
% 0.30/0.46 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trans_less_add2
% 0.30/0.46 thf(fact_190_trans__less__add1,axiom,
% 0.30/0.46 ! [I: nat,J: nat,M: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ J )
% 0.30/0.46 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trans_less_add1
% 0.30/0.46 thf(fact_191_add__less__mono1,axiom,
% 0.30/0.46 ! [I: nat,J: nat,K: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ J )
% 0.30/0.46 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_less_mono1
% 0.30/0.46 thf(fact_192_not__add__less2,axiom,
% 0.30/0.46 ! [J: nat,I: nat] :
% 0.30/0.46 ~ ( ord_less @ nat @ ( plus_plus @ nat @ J @ I ) @ I ) ).
% 0.30/0.46
% 0.30/0.46 % not_add_less2
% 0.30/0.46 thf(fact_193_not__add__less1,axiom,
% 0.30/0.46 ! [I: nat,J: nat] :
% 0.30/0.46 ~ ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ I ) ).
% 0.30/0.46
% 0.30/0.46 % not_add_less1
% 0.30/0.46 thf(fact_194_add__less__mono,axiom,
% 0.30/0.46 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I @ J )
% 0.30/0.46 => ( ( ord_less @ nat @ K @ L )
% 0.30/0.46 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_less_mono
% 0.30/0.46 thf(fact_195_add__lessD1,axiom,
% 0.30/0.46 ! [I: nat,J: nat,K: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ K )
% 0.30/0.46 => ( ord_less @ nat @ I @ K ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_lessD1
% 0.30/0.46 thf(fact_196_add__leE,axiom,
% 0.30/0.46 ! [M: nat,K: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 0.30/0.46 => ~ ( ( ord_less_eq @ nat @ M @ N )
% 0.30/0.46 => ~ ( ord_less_eq @ nat @ K @ N ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_leE
% 0.30/0.46 thf(fact_197_le__add1,axiom,
% 0.30/0.46 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ N @ M ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_add1
% 0.30/0.46 thf(fact_198_le__add2,axiom,
% 0.30/0.46 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ M @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_add2
% 0.30/0.46 thf(fact_199_add__leD1,axiom,
% 0.30/0.46 ! [M: nat,K: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 0.30/0.46 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_leD1
% 0.30/0.46 thf(fact_200_add__leD2,axiom,
% 0.30/0.46 ! [M: nat,K: nat,N: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 0.30/0.46 => ( ord_less_eq @ nat @ K @ N ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_leD2
% 0.30/0.46 thf(fact_201_le__Suc__ex,axiom,
% 0.30/0.46 ! [K: nat,L: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ K @ L )
% 0.30/0.46 => ? [N2: nat] :
% 0.30/0.46 ( L
% 0.30/0.46 = ( plus_plus @ nat @ K @ N2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_Suc_ex
% 0.30/0.46 thf(fact_202_add__le__mono,axiom,
% 0.30/0.46 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ I @ J )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ K @ L )
% 0.30/0.46 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_le_mono
% 0.30/0.46 thf(fact_203_add__le__mono1,axiom,
% 0.30/0.46 ! [I: nat,J: nat,K: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ I @ J )
% 0.30/0.46 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_le_mono1
% 0.30/0.46 thf(fact_204_trans__le__add1,axiom,
% 0.30/0.46 ! [I: nat,J: nat,M: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ I @ J )
% 0.30/0.46 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trans_le_add1
% 0.30/0.46 thf(fact_205_trans__le__add2,axiom,
% 0.30/0.46 ! [I: nat,J: nat,M: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ I @ J )
% 0.30/0.46 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % trans_le_add2
% 0.30/0.46 thf(fact_206_nat__le__iff__add,axiom,
% 0.30/0.46 ( ( ord_less_eq @ nat )
% 0.30/0.46 = ( ^ [M3: nat,N3: nat] :
% 0.30/0.46 ? [K3: nat] :
% 0.30/0.46 ( N3
% 0.30/0.46 = ( plus_plus @ nat @ M3 @ K3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % nat_le_iff_add
% 0.30/0.46 thf(fact_207_ex__has__greatest__nat__lemma,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,K: A,F2: A > nat,N: nat] :
% 0.30/0.46 ( ( P @ K )
% 0.30/0.46 => ( ! [X2: A] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 => ? [Y2: A] :
% 0.30/0.46 ( ( P @ Y2 )
% 0.30/0.46 & ~ ( ord_less_eq @ nat @ ( F2 @ Y2 ) @ ( F2 @ X2 ) ) ) )
% 0.30/0.46 => ? [Y3: A] :
% 0.30/0.46 ( ( P @ Y3 )
% 0.30/0.46 & ~ ( ord_less @ nat @ ( F2 @ Y3 ) @ ( plus_plus @ nat @ ( F2 @ K ) @ N ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ex_has_greatest_nat_lemma
% 0.30/0.46 thf(fact_208_mono__nat__linear__lb,axiom,
% 0.30/0.46 ! [F2: nat > nat,M: nat,K: nat] :
% 0.30/0.46 ( ! [M4: nat,N2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ M4 @ N2 )
% 0.30/0.46 => ( ord_less @ nat @ ( F2 @ M4 ) @ ( F2 @ N2 ) ) )
% 0.30/0.46 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( F2 @ M ) @ K ) @ ( F2 @ ( plus_plus @ nat @ M @ K ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % mono_nat_linear_lb
% 0.30/0.46 thf(fact_209_progress__time__conv,axiom,
% 0.30/0.46 ! [A: $tType,J: nat,Sigma: trace @ ( product_prod @ ( list @ char ) @ ( list @ A ) ),Sigma2: trace @ ( product_prod @ ( list @ char ) @ ( list @ A ) ),Phi: formula @ A] :
% 0.30/0.46 ( ! [I2: nat] :
% 0.30/0.46 ( ( ord_less @ nat @ I2 @ J )
% 0.30/0.46 => ( ( tau @ ( product_prod @ ( list @ char ) @ ( list @ A ) ) @ Sigma @ I2 )
% 0.30/0.46 = ( tau @ ( product_prod @ ( list @ char ) @ ( list @ A ) ) @ Sigma2 @ I2 ) ) )
% 0.30/0.46 => ( ( monito2027355080ogress @ A @ Sigma @ Phi @ J )
% 0.30/0.46 = ( monito2027355080ogress @ A @ Sigma2 @ Phi @ J ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % progress_time_conv
% 0.30/0.46 thf(fact_210_le___092_060tau_062__less,axiom,
% 0.30/0.46 ! [A: $tType,Sigma: trace @ A,I: nat,J: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( tau @ A @ Sigma @ I ) @ ( tau @ A @ Sigma @ J ) )
% 0.30/0.46 => ( ( ord_less @ nat @ J @ I )
% 0.30/0.46 => ( ( tau @ A @ Sigma @ I )
% 0.30/0.46 = ( tau @ A @ Sigma @ J ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_\<tau>_less
% 0.30/0.46 thf(fact_211__092_060tau_062__prefix__conv,axiom,
% 0.30/0.46 ! [A: $tType,P5: prefix @ A,S: trace @ A,S2: trace @ A,I: nat] :
% 0.30/0.46 ( ( prefix_of @ A @ P5 @ S )
% 0.30/0.46 => ( ( prefix_of @ A @ P5 @ S2 )
% 0.30/0.46 => ( ( ord_less @ nat @ I @ ( plen @ A @ P5 ) )
% 0.30/0.46 => ( ( tau @ A @ S @ I )
% 0.30/0.46 = ( tau @ A @ S2 @ I ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<tau>_prefix_conv
% 0.30/0.46 thf(fact_212__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.30/0.46 ~ ! [J3: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ ia ) @ b ) @ ( one_one @ nat ) ) @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ J3 ) )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ J3 @ ( monito2027355080ogress @ a @ sigma2 @ phi_1 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) )
% 0.30/0.46 => ~ ( ord_less_eq @ nat @ J3 @ ( monito2027355080ogress @ a @ sigma2 @ phi_2 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>\<And>thesis. (\<And>j. \<lbrakk>\<tau> \<sigma>' i + b + 1 \<le> \<tau> \<sigma>' j; j \<le> Monitor_Mirabelle_pzlrlsievl.progress \<sigma>' \<phi>1 (plen \<pi>); j \<le> Monitor_Mirabelle_pzlrlsievl.progress \<sigma>' \<phi>2 (plen \<pi>)\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.30/0.46 thf(fact_213__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.30/0.46 ~ ! [J3: nat] :
% 0.30/0.46 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ ia ) @ b ) @ ( one_one @ nat ) ) @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ J3 ) )
% 0.30/0.46 => ( ( ord_less_eq @ nat @ J3 @ ( monito2027355080ogress @ a @ sigma @ phi_1 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) )
% 0.30/0.46 => ~ ( ord_less_eq @ nat @ J3 @ ( monito2027355080ogress @ a @ sigma @ phi_2 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>\<And>thesis. (\<And>j. \<lbrakk>\<tau> \<sigma> i + b + 1 \<le> \<tau> \<sigma> j; j \<le> Monitor_Mirabelle_pzlrlsievl.progress \<sigma> \<phi>1 (plen \<pi>); j \<le> Monitor_Mirabelle_pzlrlsievl.progress \<sigma> \<phi>2 (plen \<pi>)\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.30/0.46 thf(fact_214_add__less__cancel__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere236663937imp_le @ A )
% 0.30/0.46 => ! [A2: A,C3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) )
% 0.30/0.46 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_less_cancel_right
% 0.30/0.46 thf(fact_215_add__left__cancel,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( cancel_semigroup_add @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.30/0.46 = ( plus_plus @ A @ A2 @ C3 ) )
% 0.30/0.46 = ( B2 = C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_left_cancel
% 0.30/0.46 thf(fact_216_add__right__cancel,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( cancel_semigroup_add @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C3: A] :
% 0.30/0.46 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.30/0.46 = ( plus_plus @ A @ C3 @ A2 ) )
% 0.30/0.46 = ( B2 = C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_right_cancel
% 0.30/0.46 thf(fact_217_add__le__cancel__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere236663937imp_le @ A )
% 0.30/0.46 => ! [C3: A,A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) )
% 0.30/0.46 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_le_cancel_left
% 0.30/0.46 thf(fact_218_add__le__cancel__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere236663937imp_le @ A )
% 0.30/0.46 => ! [A2: A,C3: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) )
% 0.30/0.46 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_le_cancel_right
% 0.30/0.46 thf(fact_219_add__less__cancel__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere236663937imp_le @ A )
% 0.30/0.46 => ! [C3: A,A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) )
% 0.30/0.46 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_less_cancel_left
% 0.30/0.46 thf(fact_220_one__reorient,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( one @ A )
% 0.30/0.46 => ! [X: A] :
% 0.30/0.46 ( ( ( one_one @ A )
% 0.30/0.46 = X )
% 0.30/0.46 = ( X
% 0.30/0.46 = ( one_one @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % one_reorient
% 0.30/0.46 thf(fact_221_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ab_semigroup_add @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C3 )
% 0.30/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ab_semigroup_add_class.add_ac(1)
% 0.30/0.46 thf(fact_222_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere779506340up_add @ A )
% 0.30/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.30/0.46 ( ( ( I = J )
% 0.30/0.46 & ( K = L ) )
% 0.30/0.46 => ( ( plus_plus @ A @ I @ K )
% 0.30/0.46 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mono_thms_linordered_semiring(4)
% 0.30/0.46 thf(fact_223_group__cancel_Oadd1,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( comm_monoid_add @ A )
% 0.30/0.46 => ! [A6: A,K: A,A2: A,B2: A] :
% 0.30/0.46 ( ( A6
% 0.30/0.46 = ( plus_plus @ A @ K @ A2 ) )
% 0.30/0.46 => ( ( plus_plus @ A @ A6 @ B2 )
% 0.30/0.46 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % group_cancel.add1
% 0.30/0.46 thf(fact_224_group__cancel_Oadd2,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( comm_monoid_add @ A )
% 0.30/0.46 => ! [B6: A,K: A,B2: A,A2: A] :
% 0.30/0.46 ( ( B6
% 0.30/0.46 = ( plus_plus @ A @ K @ B2 ) )
% 0.30/0.46 => ( ( plus_plus @ A @ A2 @ B6 )
% 0.30/0.46 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % group_cancel.add2
% 0.30/0.46 thf(fact_225_add_Oassoc,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( semigroup_add @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C3 )
% 0.30/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add.assoc
% 0.30/0.46 thf(fact_226_add_Oleft__cancel,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( group_add @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.30/0.46 = ( plus_plus @ A @ A2 @ C3 ) )
% 0.30/0.46 = ( B2 = C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add.left_cancel
% 0.30/0.46 thf(fact_227_add_Oright__cancel,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( group_add @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C3: A] :
% 0.30/0.46 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.30/0.46 = ( plus_plus @ A @ C3 @ A2 ) )
% 0.30/0.46 = ( B2 = C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add.right_cancel
% 0.30/0.46 thf(fact_228_add_Ocommute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ab_semigroup_add @ A )
% 0.30/0.46 => ( ( plus_plus @ A )
% 0.30/0.46 = ( ^ [A3: A,B3: A] : ( plus_plus @ A @ B3 @ A3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add.commute
% 0.30/0.46 thf(fact_229_add_Oleft__commute,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ab_semigroup_add @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C3: A] :
% 0.30/0.46 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C3 ) )
% 0.30/0.46 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add.left_commute
% 0.30/0.46 thf(fact_230_add__left__imp__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( cancel_semigroup_add @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.30/0.46 = ( plus_plus @ A @ A2 @ C3 ) )
% 0.30/0.46 => ( B2 = C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_left_imp_eq
% 0.30/0.46 thf(fact_231_add__right__imp__eq,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( cancel_semigroup_add @ A )
% 0.30/0.46 => ! [B2: A,A2: A,C3: A] :
% 0.30/0.46 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.30/0.46 = ( plus_plus @ A @ C3 @ A2 ) )
% 0.30/0.46 => ( B2 = C3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_right_imp_eq
% 0.30/0.46 thf(fact_232_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere779506340up_add @ A )
% 0.30/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.30/0.46 ( ( ( ord_less_eq @ A @ I @ J )
% 0.30/0.46 & ( K = L ) )
% 0.30/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mono_thms_linordered_semiring(3)
% 0.30/0.46 thf(fact_233_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere779506340up_add @ A )
% 0.30/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.30/0.46 ( ( ( I = J )
% 0.30/0.46 & ( ord_less_eq @ A @ K @ L ) )
% 0.30/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mono_thms_linordered_semiring(2)
% 0.30/0.46 thf(fact_234_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere779506340up_add @ A )
% 0.30/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.30/0.46 ( ( ( ord_less_eq @ A @ I @ J )
% 0.30/0.46 & ( ord_less_eq @ A @ K @ L ) )
% 0.30/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mono_thms_linordered_semiring(1)
% 0.30/0.46 thf(fact_235_add__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere779506340up_add @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A,D3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ C3 @ D3 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ D3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mono
% 0.30/0.46 thf(fact_236_add__left__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere779506340up_add @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_left_mono
% 0.30/0.46 thf(fact_237_less__eqE,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ! [A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ~ ! [C2: A] :
% 0.30/0.46 ( B2
% 0.30/0.46 != ( plus_plus @ A @ A2 @ C2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % less_eqE
% 0.30/0.46 thf(fact_238_add__right__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere779506340up_add @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_right_mono
% 0.30/0.46 thf(fact_239_le__iff__add,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( canoni770627133id_add @ A )
% 0.30/0.46 => ( ( ord_less_eq @ A )
% 0.30/0.46 = ( ^ [A3: A,B3: A] :
% 0.30/0.46 ? [C4: A] :
% 0.30/0.46 ( B3
% 0.30/0.46 = ( plus_plus @ A @ A3 @ C4 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % le_iff_add
% 0.30/0.46 thf(fact_240_add__le__imp__le__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere236663937imp_le @ A )
% 0.30/0.46 => ! [C3: A,A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_le_imp_le_left
% 0.30/0.46 thf(fact_241_add__le__imp__le__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere236663937imp_le @ A )
% 0.30/0.46 => ! [A2: A,C3: A,B2: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) )
% 0.30/0.46 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_le_imp_le_right
% 0.30/0.46 thf(fact_242_add__mono__thms__linordered__field_I5_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere223160158up_add @ A )
% 0.30/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.30/0.46 ( ( ( ord_less @ A @ I @ J )
% 0.30/0.46 & ( ord_less @ A @ K @ L ) )
% 0.30/0.46 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mono_thms_linordered_field(5)
% 0.30/0.46 thf(fact_243_add__mono__thms__linordered__field_I2_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere223160158up_add @ A )
% 0.30/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.30/0.46 ( ( ( I = J )
% 0.30/0.46 & ( ord_less @ A @ K @ L ) )
% 0.30/0.46 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mono_thms_linordered_field(2)
% 0.30/0.46 thf(fact_244_add__mono__thms__linordered__field_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere223160158up_add @ A )
% 0.30/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.30/0.46 ( ( ( ord_less @ A @ I @ J )
% 0.30/0.46 & ( K = L ) )
% 0.30/0.46 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mono_thms_linordered_field(1)
% 0.30/0.46 thf(fact_245_add__strict__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( strict2144017051up_add @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A,D3: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less @ A @ C3 @ D3 )
% 0.30/0.46 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ D3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_strict_mono
% 0.30/0.46 thf(fact_246_add__strict__left__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere223160158up_add @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_strict_left_mono
% 0.30/0.46 thf(fact_247_add__strict__right__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere223160158up_add @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_strict_right_mono
% 0.30/0.46 thf(fact_248_add__less__imp__less__left,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere236663937imp_le @ A )
% 0.30/0.46 => ! [C3: A,A2: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) )
% 0.30/0.46 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_less_imp_less_left
% 0.30/0.46 thf(fact_249_add__less__imp__less__right,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere236663937imp_le @ A )
% 0.30/0.46 => ! [A2: A,C3: A,B2: A] :
% 0.30/0.46 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) )
% 0.30/0.46 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_less_imp_less_right
% 0.30/0.46 thf(fact_250_add__less__le__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere223160158up_add @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A,D3: A] :
% 0.30/0.46 ( ( ord_less @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less_eq @ A @ C3 @ D3 )
% 0.30/0.46 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ D3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_less_le_mono
% 0.30/0.46 thf(fact_251_add__le__less__mono,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere223160158up_add @ A )
% 0.30/0.46 => ! [A2: A,B2: A,C3: A,D3: A] :
% 0.30/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.30/0.46 => ( ( ord_less @ A @ C3 @ D3 )
% 0.30/0.46 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ D3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_le_less_mono
% 0.30/0.46 thf(fact_252_add__mono__thms__linordered__field_I3_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere223160158up_add @ A )
% 0.30/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.30/0.46 ( ( ( ord_less @ A @ I @ J )
% 0.30/0.46 & ( ord_less_eq @ A @ K @ L ) )
% 0.30/0.46 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mono_thms_linordered_field(3)
% 0.30/0.46 thf(fact_253_add__mono__thms__linordered__field_I4_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( ordere223160158up_add @ A )
% 0.30/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.30/0.46 ( ( ( ord_less_eq @ A @ I @ J )
% 0.30/0.46 & ( ord_less @ A @ K @ L ) )
% 0.30/0.46 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % add_mono_thms_linordered_field(4)
% 0.30/0.46 thf(fact_254_discrete,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( unique1598680935umeral @ A )
% 0.30/0.46 => ( ( ord_less @ A )
% 0.30/0.46 = ( ^ [A3: A] : ( ord_less_eq @ A @ ( plus_plus @ A @ A3 @ ( one_one @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % discrete
% 0.30/0.46
% 0.30/0.46 % Type constructors (37)
% 0.30/0.46 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( preorder @ A8 )
% 0.30/0.46 => ( preorder @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( order @ A8 )
% 0.30/0.46 => ( order @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_fun___Orderings_Oord,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( ord @ A8 )
% 0.30/0.46 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 0.30/0.46 condit1037483654norder @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Divides_Ounique__euclidean__semiring__numeral,axiom,
% 0.30/0.46 unique1598680935umeral @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 0.30/0.46 strict2144017051up_add @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 0.30/0.46 ordere223160158up_add @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.30/0.46 ordere236663937imp_le @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.30/0.46 canoni770627133id_add @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 0.30/0.46 ordere779506340up_add @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 0.30/0.46 cancel_semigroup_add @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 0.30/0.46 ab_semigroup_add @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 0.30/0.46 comm_monoid_add @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 0.30/0.46 semigroup_add @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.30/0.46 wellorder @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.30/0.46 preorder @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.30/0.46 linorder @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.30/0.46 no_top @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.30/0.46 order @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.30/0.46 ord @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.30/0.46 one @ nat ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Opreorder_4,axiom,
% 0.30/0.46 preorder @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Olinorder_5,axiom,
% 0.30/0.46 linorder @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oorder_6,axiom,
% 0.30/0.46 order @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_HOL_Obool___Orderings_Oord_7,axiom,
% 0.30/0.46 ord @ $o ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Trace_Oprefix___Orderings_Opreorder_8,axiom,
% 0.30/0.46 ! [A7: $tType] : ( preorder @ ( prefix @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Trace_Oprefix___Orderings_Oorder_9,axiom,
% 0.30/0.46 ! [A7: $tType] : ( order @ ( prefix @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Trace_Oprefix___Orderings_Oord_10,axiom,
% 0.30/0.46 ! [A7: $tType] : ( ord @ ( prefix @ A7 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Interval_O_092_060I_062___Orderings_Opreorder_11,axiom,
% 0.30/0.46 preorder @ i ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Interval_O_092_060I_062___Orderings_Olinorder_12,axiom,
% 0.30/0.46 linorder @ i ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Interval_O_092_060I_062___Orderings_Oorder_13,axiom,
% 0.30/0.46 order @ i ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Interval_O_092_060I_062___Orderings_Oord_14,axiom,
% 0.30/0.46 ord @ i ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Oprod___Orderings_Owellorder_15,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( ( wellorder @ A7 )
% 0.30/0.46 & ( wellorder @ A8 ) )
% 0.30/0.46 => ( wellorder @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Oprod___Orderings_Opreorder_16,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( ( preorder @ A7 )
% 0.30/0.46 & ( preorder @ A8 ) )
% 0.30/0.46 => ( preorder @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Oprod___Orderings_Olinorder_17,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( ( linorder @ A7 )
% 0.30/0.46 & ( linorder @ A8 ) )
% 0.30/0.46 => ( linorder @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Oprod___Orderings_Oorder_18,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( ( order @ A7 )
% 0.30/0.46 & ( order @ A8 ) )
% 0.30/0.46 => ( order @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(tcon_Product__Type_Oprod___Orderings_Oord_19,axiom,
% 0.30/0.46 ! [A7: $tType,A8: $tType] :
% 0.30/0.46 ( ( ( ord @ A7 )
% 0.30/0.46 & ( ord @ A8 ) )
% 0.30/0.46 => ( ord @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Conjectures (1)
% 0.30/0.46 thf(conj_0,conjecture,
% 0.30/0.46 ord_less @ nat @ k @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 0.31/1.50 ---- Embedded in THF ---
% 0.31/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.50 %%% Generated on Tue Feb 24 08:27:13 EST 2026
% 0.31/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.50 %%% Logic specification used:
% 0.31/1.50 %%% thf(spec, logic, $$dhol).
% 0.31/1.50
% 0.31/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.8TCNWeCSne/DTF2DTF8323.p
% 0.31/1.50 thf(ty_t_Interval_O_092_060I_062, type, i: $tType).
% 0.31/1.50 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 0.31/1.50 thf(ty_t_MFOTL_Oformula, type, formula: ($tType > $tType)).
% 0.31/1.50 thf(ty_t_Trace_Oprefix, type, prefix: ($tType > $tType)).
% 0.31/1.50 thf(ty_t_Trace_Otrace, type, trace: ($tType > $tType)).
% 0.31/1.50 thf(ty_t_String_Ochar, type, char: $tType).
% 0.31/1.50 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 0.31/1.50 thf(ty_t_Nat_Onat, type, nat: $tType).
% 0.31/1.50 thf(ty_tf_a, type, a: $tType).
% 0.31/1.50 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Osemigroup__add, type, semigroup_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ocomm__monoid__add, type, comm_monoid_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Oab__semigroup__add, type, ab_semigroup_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Orderings_Odense__linorder, type, dense_linorder: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le, type, ordere236663937imp_le: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add, type, ordere223160158up_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add, type, strict2144017051up_add: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Divides_Ounique__euclidean__semiring__numeral, type, unique1598680935umeral: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum, type, condit1656338222tinuum: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder, type, condit1037483654norder: (!> [A:$tType]: ($o))).
% 0.31/1.50 thf(sy_c_Abstract__Monitor_Oprogress__axioms, type, abstra417776764axioms: (!> [A:$tType,B:$tType]: ((((trace @ A) > ((list @ B) > (nat > $o))) > (((prefix @ A) > nat) > $o))))).
% 0.31/1.50 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 0.31/1.50 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 0.31/1.50 thf(sy_c_Lattices__Big_Oord__class_Oarg__max, type, lattices_ord_arg_max: (!> [B:$tType,A:$tType]: (((B > A) > ((B > $o) > B))))).
% 0.31/1.50 thf(sy_c_MFOTL_Oformula_OUntil, type, until: (!> [A:$tType]: (((formula @ A) > (i > ((formula @ A) > (formula @ A))))))).
% 0.31/1.50 thf(sy_c_MFOTL_Osat, type, sat: (!> [A:$tType]: (((trace @ ((product_prod @ (list @ char)) @ (list @ A))) > ((list @ A) > (nat > ((formula @ A) > $o))))))).
% 0.31/1.50 thf(sy_c_Monitor__Mirabelle__pzlrlsievl_Oprogress, type, monito2027355080ogress: (!> [A:$tType]: (((trace @ ((product_prod @ (list @ char)) @ (list @ A))) > ((formula @ A) > (nat > nat)))))).
% 0.31/1.50 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 0.31/1.50 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 0.31/1.50 thf(sy_c_Trace_O_092_060tau_062, type, tau: (!> [A:$tType]: (((trace @ A) > (nat > nat))))).
% 0.31/1.50 thf(sy_c_Trace_Oplen, type, plen: (!> [A:$tType]: (((prefix @ A) > nat)))).
% 0.31/1.50 thf(sy_c_Trace_Oprefix__of, type, prefix_of: (!> [A:$tType]: (((prefix @ A) > ((trace @ A) > $o))))).
% 0.31/1.50 thf(sy_v_I____, type, i2: i).
% 0.31/1.50 thf(sy_v__092_060phi_062, type, phi: (formula @ a)).
% 0.31/1.50 thf(sy_v__092_060phi_0621____, type, phi_1: (formula @ a)).
% 0.31/1.50 thf(sy_v__092_060phi_0622____, type, phi_2: (formula @ a)).
% 0.31/1.50 thf(sy_v__092_060pi_062, type, pi: (prefix @ ((product_prod @ (list @ char)) @ (list @ a)))).
% 0.31/1.50 thf(sy_v__092_060sigma_062, type, sigma: (trace @ ((product_prod @ (list @ char)) @ (list @ a)))).
% 0.31/1.50 thf(sy_v__092_060sigma_062_H, type, sigma2: (trace @ ((product_prod @ (list @ char)) @ (list @ a)))).
% 0.31/1.50 thf(sy_v_b____, type, b: nat).
% 0.31/1.50 thf(sy_v_i, type, i3: nat).
% 0.31/1.50 thf(sy_v_ia____, type, ia: nat).
% 0.31/1.50 thf(sy_v_j____, type, j: nat).
% 0.31/1.50 thf(sy_v_ja____, type, ja: nat).
% 0.31/1.50 thf(sy_v_k____, type, k: nat).
% 0.31/1.50 thf(fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062, axiom, (((ord_less @ nat) @ k) @ ((((monito2027355080ogress @ a) @ sigma) @ phi_1) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi)))).
% 0.31/1.50 thf(fact_1_assms_I3_J, axiom, (((ord_less @ nat) @ i3) @ ((((monito2027355080ogress @ a) @ sigma) @ phi) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi)))).
% 0.31/1.50 thf(fact_2_assms_I1_J, axiom, (((prefix_of @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi) @ sigma)).
% 0.31/1.50 thf(fact_3_nat__neq__iff, axiom, (! [M:nat,N:nat]: (((M != N) = ((((ord_less @ nat) @ M) @ N) | (((ord_less @ nat) @ N) @ M)))))).
% 0.31/1.50 thf(fact_4_less__not__refl, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 0.31/1.50 thf(fact_5_less__not__refl2, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ N) @ M) => (M != N))))).
% 0.31/1.50 thf(fact_6_less__not__refl3, axiom, (! [S:nat,T:nat]: (((((ord_less @ nat) @ S) @ T) => (S != T))))).
% 0.31/1.50 thf(fact_7_less__irrefl__nat, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 0.31/1.50 thf(fact_8_nat__less__induct, axiom, (! [P:(nat > $o),N:nat]: (((! [N2:nat]: (((! [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) => (P @ M2)))) => (P @ N2)))) => (P @ N))))).
% 0.31/1.50 thf(fact_9_infinite__descent, axiom, (! [P:(nat > $o),N:nat]: (((! [N2:nat]: (((~ ((P @ N2))) => (? [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) & (~ ((P @ M2))))))))) => (P @ N))))).
% 0.31/1.50 thf(fact_10_linorder__neqE__nat, axiom, (! [X:nat,Y:nat]: (((X != Y) => ((~ ((((ord_less @ nat) @ X) @ Y))) => (((ord_less @ nat) @ Y) @ X)))))).
% 0.31/1.50 thf(fact_11_infinite__descent__measure, axiom, (! [A:$tType,P:(A > $o),V:(A > nat),X:A]: (((! [X2:A]: (((~ ((P @ X2))) => (? [Y2:A]: (((((ord_less @ nat) @ (V @ Y2)) @ (V @ X2)) & (~ ((P @ Y2))))))))) => (P @ X))))).
% 0.31/1.50 thf(fact_12__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062, axiom, (((ord_less_eq @ nat) @ j) @ ((((monito2027355080ogress @ a) @ sigma) @ phi_1) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi)))).
% 0.31/1.50 thf(fact_13_minf_I11_J, axiom, (! [C:$tType,D:$tType]: (((ord @ C) => (! [F:D]: ((? [Z:C]: ((! [X3:C]: (((((ord_less @ C) @ X3) @ Z) => (F = F)))))))))))).
% 0.31/1.50 thf(fact_14_assms_I2_J, axiom, (((prefix_of @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi) @ sigma2)).
% 0.31/1.50 thf(fact_15__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062, axiom, (((ord_less_eq @ nat) @ j) @ ((((monito2027355080ogress @ a) @ sigma) @ phi_2) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi)))).
% 0.31/1.50 thf(fact_16_le__refl, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ N) @ N)))).
% 0.31/1.50 thf(fact_17_le__trans, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((ord_less_eq @ nat) @ J) @ K) => (((ord_less_eq @ nat) @ I) @ K)))))).
% 0.31/1.50 thf(fact_18_eq__imp__le, axiom, (! [M:nat,N:nat]: (((M = N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 0.31/1.50 thf(fact_19_le__antisym, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((ord_less_eq @ nat) @ N) @ M) => (M = N)))))).
% 0.31/1.50 thf(fact_20_nat__le__linear, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) | (((ord_less_eq @ nat) @ N) @ M))))).
% 0.31/1.50 thf(fact_21_Nat_Oex__has__greatest__nat, axiom, (! [P:(nat > $o),K:nat,B2:nat]: (((P @ K) => ((! [Y3:nat]: (((P @ Y3) => (((ord_less_eq @ nat) @ Y3) @ B2)))) => (? [X2:nat]: (((P @ X2) & (! [Y2:nat]: (((P @ Y2) => (((ord_less_eq @ nat) @ Y2) @ X2)))))))))))).
% 0.31/1.50 thf(fact_22_progress__le, axiom, (! [A:$tType,Sigma:(trace @ ((product_prod @ (list @ char)) @ (list @ A))),Phi:(formula @ A),J:nat]: ((((ord_less_eq @ nat) @ ((((monito2027355080ogress @ A) @ Sigma) @ Phi) @ J)) @ J)))).
% 0.31/1.50 thf(fact_23_progress__mono, axiom, (! [A:$tType,J:nat,J2:nat,Sigma:(trace @ ((product_prod @ (list @ char)) @ (list @ A))),Phi:(formula @ A)]: (((((ord_less_eq @ nat) @ J) @ J2) => (((ord_less_eq @ nat) @ ((((monito2027355080ogress @ A) @ Sigma) @ Phi) @ J)) @ ((((monito2027355080ogress @ A) @ Sigma) @ Phi) @ J2)))))).
% 0.31/1.50 thf(fact_24_pinf_I6_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ Z) @ X3) => (~ ((((ord_less_eq @ A) @ X3) @ T)))))))))))))).
% 0.31/1.50 thf(fact_25_pinf_I8_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ Z) @ X3) => (((ord_less_eq @ A) @ T) @ X3)))))))))))).
% 0.31/1.50 thf(fact_26_minf_I6_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z) => (((ord_less_eq @ A) @ X3) @ T)))))))))))).
% 0.31/1.50 thf(fact_27_minf_I8_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z) => (~ ((((ord_less_eq @ A) @ T) @ X3)))))))))))))).
% 0.31/1.50 thf(fact_28_less__mono__imp__le__mono, axiom, (! [F2:(nat > nat),I:nat,J:nat]: (((! [I2:nat,J3:nat]: (((((ord_less @ nat) @ I2) @ J3) => (((ord_less @ nat) @ (F2 @ I2)) @ (F2 @ J3))))) => ((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (F2 @ I)) @ (F2 @ J))))))).
% 0.31/1.50 thf(fact_29_le__neq__implies__less, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((M != N) => (((ord_less @ nat) @ M) @ N)))))).
% 0.31/1.50 thf(fact_30_less__or__eq__imp__le, axiom, (! [M:nat,N:nat]: ((((((ord_less @ nat) @ M) @ N) | (M = N)) => (((ord_less_eq @ nat) @ M) @ N))))).
% 0.31/1.50 thf(fact_31_le__eq__less__or__eq, axiom, ((ord_less_eq @ nat) = (^ [M3:nat,N3:nat]: (((((ord_less @ nat) @ M3) @ N3) | (M3 = N3)))))).
% 0.31/1.50 thf(fact_32_less__imp__le__nat, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 0.31/1.50 thf(fact_33_nat__less__le, axiom, ((ord_less @ nat) = (^ [M3:nat,N3:nat]: (((((ord_less_eq @ nat) @ M3) @ N3) & (M3 != N3)))))).
% 0.31/1.50 thf(fact_34_progress__prefix__conv, axiom, (! [A:$tType,Pi:(prefix @ ((product_prod @ (list @ char)) @ (list @ A))),Sigma:(trace @ ((product_prod @ (list @ char)) @ (list @ A))),Sigma2:(trace @ ((product_prod @ (list @ char)) @ (list @ A))),Phi:(formula @ A)]: (((((prefix_of @ ((product_prod @ (list @ char)) @ (list @ A))) @ Pi) @ Sigma) => ((((prefix_of @ ((product_prod @ (list @ char)) @ (list @ A))) @ Pi) @ Sigma2) => (((((monito2027355080ogress @ A) @ Sigma) @ Phi) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ A))) @ Pi)) = ((((monito2027355080ogress @ A) @ Sigma2) @ Phi) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ A))) @ Pi)))))))).
% 0.31/1.50 thf(fact_35_measure__induct__rule, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F2:(A > B),P:(A > $o),A2:A]: (((! [X2:A]: (((! [Y2:A]: (((((ord_less @ B) @ (F2 @ Y2)) @ (F2 @ X2)) => (P @ Y2)))) => (P @ X2)))) => (P @ A2)))))))).
% 0.31/1.50 thf(fact_36_measure__induct, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F2:(A > B),P:(A > $o),A2:A]: (((! [X2:A]: (((! [Y2:A]: (((((ord_less @ B) @ (F2 @ Y2)) @ (F2 @ X2)) => (P @ Y2)))) => (P @ X2)))) => (P @ A2)))))))).
% 0.31/1.50 thf(fact_37_pinf_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => ((P @ X2) = (P2 @ X2))))))) => ((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => ((Q @ X2) = (Q2 @ X2))))))) => (? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ Z) @ X3) => (((P @ X3) & (Q @ X3)) = ((P2 @ X3) & (Q2 @ X3)))))))))))))))).
% 0.31/1.50 thf(fact_38_pinf_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => ((P @ X2) = (P2 @ X2))))))) => ((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ Z2) @ X2) => ((Q @ X2) = (Q2 @ X2))))))) => (? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ Z) @ X3) => (((P @ X3) | (Q @ X3)) = ((P2 @ X3) | (Q2 @ X3)))))))))))))))).
% 0.31/1.50 thf(fact_39_pinf_I3_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ Z) @ X3) => (X3 != T)))))))))))).
% 0.31/1.50 thf(fact_40_pinf_I4_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ Z) @ X3) => (X3 != T)))))))))))).
% 0.31/1.50 thf(fact_41_pinf_I5_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ Z) @ X3) => (~ ((((ord_less @ A) @ X3) @ T)))))))))))))).
% 0.31/1.50 thf(fact_42_pinf_I7_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ Z) @ X3) => (((ord_less @ A) @ T) @ X3)))))))))))).
% 0.31/1.50 thf(fact_43_pinf_I11_J, axiom, (! [C:$tType,D:$tType]: (((ord @ C) => (! [F:D]: ((? [Z:C]: ((! [X3:C]: (((((ord_less @ C) @ Z) @ X3) => (F = F)))))))))))).
% 0.31/1.50 thf(fact_44_minf_I1_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ X2) @ Z2) => ((P @ X2) = (P2 @ X2))))))) => ((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ X2) @ Z2) => ((Q @ X2) = (Q2 @ X2))))))) => (? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z) => (((P @ X3) & (Q @ X3)) = ((P2 @ X3) & (Q2 @ X3)))))))))))))))).
% 0.31/1.50 thf(fact_45_minf_I2_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ X2) @ Z2) => ((P @ X2) = (P2 @ X2))))))) => ((? [Z2:A]: ((! [X2:A]: (((((ord_less @ A) @ X2) @ Z2) => ((Q @ X2) = (Q2 @ X2))))))) => (? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z) => (((P @ X3) | (Q @ X3)) = ((P2 @ X3) | (Q2 @ X3)))))))))))))))).
% 0.31/1.50 thf(fact_46_minf_I3_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z) => (X3 != T)))))))))))).
% 0.31/1.50 thf(fact_47_minf_I4_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z) => (X3 != T)))))))))))).
% 0.31/1.50 thf(fact_48_minf_I5_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z) => (((ord_less @ A) @ X3) @ T)))))))))))).
% 0.31/1.50 thf(fact_49_minf_I7_J, axiom, (! [A:$tType]: (((linorder @ A) => (! [T:A]: ((? [Z:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z) => (~ ((((ord_less @ A) @ T) @ X3)))))))))))))).
% 0.31/1.50 thf(fact_50__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062, axiom, (((ord_less_eq @ nat) @ ja) @ ((((monito2027355080ogress @ a) @ sigma2) @ phi_1) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi)))).
% 0.31/1.50 thf(fact_51_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 0.31/1.50 thf(fact_52_Until_OIH_I1_J, axiom, (! [I:nat,V2:(list @ a)]: (((((ord_less @ nat) @ I) @ ((((monito2027355080ogress @ a) @ sigma) @ phi_1) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi))) => ((((((sat @ a) @ sigma) @ V2) @ I) @ phi_1) = (((((sat @ a) @ sigma2) @ V2) @ I) @ phi_1)))))).
% 0.31/1.50 thf(fact_53_Lattices__Big_Oex__has__greatest__nat, axiom, (! [A:$tType,P:(A > $o),K:A,F2:(A > nat),B2:nat]: (((P @ K) => ((! [Y3:A]: (((P @ Y3) => (((ord_less @ nat) @ (F2 @ Y3)) @ B2)))) => (? [X2:A]: (((P @ X2) & (! [Y2:A]: (((P @ Y2) => (((ord_less_eq @ nat) @ (F2 @ Y2)) @ (F2 @ X2))))))))))))).
% 0.31/1.50 thf(fact_54_nat__descend__induct, axiom, (! [N:nat,P:(nat > $o),M:nat]: (((! [K2:nat]: (((((ord_less @ nat) @ N) @ K2) => (P @ K2)))) => ((! [K2:nat]: (((((ord_less_eq @ nat) @ K2) @ N) => ((! [I3:nat]: (((((ord_less @ nat) @ K2) @ I3) => (P @ I3)))) => (P @ K2))))) => (P @ M)))))).
% 0.31/1.50 thf(fact_55_complete__interval, axiom, (! [A:$tType]: (((condit1037483654norder @ A) => (! [A2:A,B2:A,P:(A > $o)]: (((((ord_less @ A) @ A2) @ B2) => ((P @ A2) => ((~ ((P @ B2))) => (? [C2:A]: (((((ord_less_eq @ A) @ A2) @ C2) & ((((ord_less_eq @ A) @ C2) @ B2) & ((! [X3:A]: ((((((ord_less_eq @ A) @ A2) @ X3) & (((ord_less @ A) @ X3) @ C2)) => (P @ X3)))) & (! [D2:A]: (((! [X2:A]: ((((((ord_less_eq @ A) @ A2) @ X2) & (((ord_less @ A) @ X2) @ D2)) => (P @ X2)))) => (((ord_less_eq @ A) @ D2) @ C2)))))))))))))))))).
% 0.31/1.50 thf(fact_56_order_Onot__eq__order__implies__strict, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((A2 != B2) => ((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less @ A) @ A2) @ B2))))))))).
% 0.31/1.50 thf(fact_57_dual__order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less @ A) @ B2) @ A2) => (((ord_less_eq @ A) @ B2) @ A2)))))))).
% 0.31/1.50 thf(fact_58_dual__order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [B3:A,A3:A]: (((((ord_less_eq @ A) @ B3) @ A3) & (A3 != B3))))))))).
% 0.31/1.50 thf(fact_59_dual__order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [B3:A,A3:A]: (((((ord_less @ A) @ B3) @ A3) | (A3 = B3))))))))).
% 0.31/1.50 thf(fact_60_order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 0.31/1.50 thf(fact_61__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062, axiom, (((ord_less_eq @ nat) @ ja) @ ((((monito2027355080ogress @ a) @ sigma2) @ phi_2) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi)))).
% 0.31/1.50 thf(fact_62_Until_OIH_I2_J, axiom, (! [I:nat,V2:(list @ a)]: (((((ord_less @ nat) @ I) @ ((((monito2027355080ogress @ a) @ sigma) @ phi_2) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi))) => ((((((sat @ a) @ sigma) @ V2) @ I) @ phi_2) = (((((sat @ a) @ sigma2) @ V2) @ I) @ phi_2)))))).
% 0.31/1.50 thf(fact_63_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 0.31/1.50 thf(fact_64_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z3:A]: ((Y4 = Z3))) = (^ [A3:A,B3:A]: (((((ord_less_eq @ A) @ B3) @ A3) & (((ord_less_eq @ A) @ A3) @ B3))))))))).
% 0.31/1.50 thf(fact_65_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C3:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C3) @ B2) => (((ord_less_eq @ A) @ C3) @ A2))))))))).
% 0.31/1.50 thf(fact_66_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A4:A,B4:A]: (((((ord_less_eq @ A) @ A4) @ B4) => ((P @ A4) @ B4)))) => ((! [A4:A,B4:A]: ((((P @ B4) @ A4) => ((P @ A4) @ B4)))) => ((P @ A2) @ B2))))))))).
% 0.31/1.50 thf(fact_67_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 0.31/1.50 thf(fact_68_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,Z4:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z4) => (((ord_less_eq @ A) @ X) @ Z4))))))))).
% 0.31/1.50 thf(fact_69_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 0.31/1.50 thf(fact_70_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 0.31/1.50 thf(fact_71_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C3:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 0.31/1.50 thf(fact_72_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z3:A]: ((Y4 = Z3))) = (^ [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) & (((ord_less_eq @ A) @ B3) @ A3))))))))).
% 0.31/1.50 thf(fact_73_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 0.31/1.50 thf(fact_74_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A,Z4:A]: ((((((ord_less_eq @ A) @ X) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z4)))) => (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z4)))) => (((((ord_less_eq @ A) @ X) @ Z4) => (~ ((((ord_less_eq @ A) @ Z4) @ Y)))) => (((((ord_less_eq @ A) @ Z4) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X)))) => (((((ord_less_eq @ A) @ Y) @ Z4) => (~ ((((ord_less_eq @ A) @ Z4) @ X)))) => (~ (((((ord_less_eq @ A) @ Z4) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y))))))))))))))))).
% 0.31/1.50 thf(fact_75_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C3) => (((ord_less_eq @ A) @ A2) @ C3))))))))).
% 0.31/1.50 thf(fact_76_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.31/1.50 thf(fact_77_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((X = Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 0.31/1.50 thf(fact_78_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.31/1.50 thf(fact_79_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 0.31/1.50 thf(fact_80_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z3:A]: ((Y4 = Z3))) = (^ [X4:A,Y5:A]: (((((ord_less_eq @ A) @ X4) @ Y5) & (((ord_less_eq @ A) @ Y5) @ X4))))))))).
% 0.31/1.50 thf(fact_81_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F2:(A > B),C3:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F2 @ B2) = C3) => ((! [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) => (((ord_less_eq @ B) @ (F2 @ X2)) @ (F2 @ Y3))))) => (((ord_less_eq @ B) @ (F2 @ A2)) @ C3)))))))))).
% 0.31/1.50 thf(fact_82_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F2:(B > A),B2:B,C3:B]: (((A2 = (F2 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C3) => ((! [X2:B,Y3:B]: (((((ord_less_eq @ B) @ X2) @ Y3) => (((ord_less_eq @ A) @ (F2 @ X2)) @ (F2 @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F2 @ C3))))))))))).
% 0.31/1.50 thf(fact_83_order__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A2:A,B2:A,F2:(A > C),C3:C]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C) @ (F2 @ B2)) @ C3) => ((! [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) => (((ord_less_eq @ C) @ (F2 @ X2)) @ (F2 @ Y3))))) => (((ord_less_eq @ C) @ (F2 @ A2)) @ C3)))))))))).
% 0.31/1.50 thf(fact_84_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F2:(B > A),B2:B,C3:B]: (((((ord_less_eq @ A) @ A2) @ (F2 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C3) => ((! [X2:B,Y3:B]: (((((ord_less_eq @ B) @ X2) @ Y3) => (((ord_less_eq @ A) @ (F2 @ X2)) @ (F2 @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F2 @ C3))))))))))).
% 0.31/1.50 thf(fact_85_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F3:(A > B),G:(A > B)]: ((! [X4:A]: ((((ord_less_eq @ B) @ (F3 @ X4)) @ (G @ X4))))))))))).
% 0.31/1.50 thf(fact_86_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F2:(A > B),G2:(A > B)]: (((! [X2:A]: ((((ord_less_eq @ B) @ (F2 @ X2)) @ (G2 @ X2)))) => (((ord_less_eq @ (A > B)) @ F2) @ G2)))))))).
% 0.31/1.50 thf(fact_87_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F2:(A > B),G2:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F2) @ G2) => (((ord_less_eq @ B) @ (F2 @ X)) @ (G2 @ X))))))))).
% 0.31/1.50 thf(fact_88_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F2:(A > B),G2:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F2) @ G2) => (((ord_less_eq @ B) @ (F2 @ X)) @ (G2 @ X))))))))).
% 0.31/1.50 thf(fact_89_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,F2:(B > A),B2:B,C3:B]: (((A2 = (F2 @ B2)) => ((((ord_less @ B) @ B2) @ C3) => ((! [X2:B,Y3:B]: (((((ord_less @ B) @ X2) @ Y3) => (((ord_less @ A) @ (F2 @ X2)) @ (F2 @ Y3))))) => (((ord_less @ A) @ A2) @ (F2 @ C3))))))))))).
% 0.31/1.50 thf(fact_90_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A2:A,B2:A,F2:(A > B),C3:B]: (((((ord_less @ A) @ A2) @ B2) => (((F2 @ B2) = C3) => ((! [X2:A,Y3:A]: (((((ord_less @ A) @ X2) @ Y3) => (((ord_less @ B) @ (F2 @ X2)) @ (F2 @ Y3))))) => (((ord_less @ B) @ (F2 @ A2)) @ C3)))))))))).
% 0.31/1.50 thf(fact_91_order__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F2:(B > A),B2:B,C3:B]: (((((ord_less @ A) @ A2) @ (F2 @ B2)) => ((((ord_less @ B) @ B2) @ C3) => ((! [X2:B,Y3:B]: (((((ord_less @ B) @ X2) @ Y3) => (((ord_less @ A) @ (F2 @ X2)) @ (F2 @ Y3))))) => (((ord_less @ A) @ A2) @ (F2 @ C3))))))))))).
% 0.31/1.50 thf(fact_92_order__less__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A2:A,B2:A,F2:(A > C),C3:C]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ C) @ (F2 @ B2)) @ C3) => ((! [X2:A,Y3:A]: (((((ord_less @ A) @ X2) @ Y3) => (((ord_less @ C) @ (F2 @ X2)) @ (F2 @ Y3))))) => (((ord_less @ C) @ (F2 @ A2)) @ C3)))))))))).
% 0.31/1.50 thf(fact_93_lt__ex, axiom, (! [A:$tType]: (((no_bot @ A) => (! [X:A]: ((? [Y3:A]: ((((ord_less @ A) @ Y3) @ X))))))))).
% 0.31/1.50 thf(fact_94_gt__ex, axiom, (! [A:$tType]: (((no_top @ A) => (! [X:A]: ((? [X_1:A]: ((((ord_less @ A) @ X) @ X_1))))))))).
% 0.31/1.50 thf(fact_95_neqE, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((X != Y) => ((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less @ A) @ Y) @ X))))))))).
% 0.31/1.50 thf(fact_96_neq__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((X != Y) = ((((ord_less @ A) @ X) @ Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 0.31/1.50 thf(fact_97_order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (~ ((((ord_less @ A) @ B2) @ A2)))))))))).
% 0.31/1.50 thf(fact_98_dense, axiom, (! [A:$tType]: (((dense_order @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (? [Z:A]: (((((ord_less @ A) @ X) @ Z) & (((ord_less @ A) @ Z) @ Y))))))))))).
% 0.31/1.50 thf(fact_99_less__imp__neq, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 0.31/1.50 thf(fact_100_less__asym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 0.31/1.50 thf(fact_101_less__asym_H, axiom, (! [A:$tType]: (((preorder @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (~ ((((ord_less @ A) @ B2) @ A2)))))))))).
% 0.31/1.50 thf(fact_102_less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,Z4:A]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ Z4) => (((ord_less @ A) @ X) @ Z4))))))))).
% 0.31/1.50 thf(fact_103_less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) | ((X = Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 0.31/1.50 thf(fact_104_less__irrefl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((~ ((((ord_less @ A) @ X) @ X))))))))).
% 0.31/1.50 thf(fact_105_ord__eq__less__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C3:A]: (((A2 = B2) => ((((ord_less @ A) @ B2) @ C3) => (((ord_less @ A) @ A2) @ C3))))))))).
% 0.31/1.50 thf(fact_106_ord__less__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A2:A,B2:A,C3:A]: (((((ord_less @ A) @ A2) @ B2) => ((B2 = C3) => (((ord_less @ A) @ A2) @ C3))))))))).
% 0.31/1.50 thf(fact_107_dual__order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less @ A) @ B2) @ A2) => (~ ((((ord_less @ A) @ A2) @ B2)))))))))).
% 0.31/1.50 thf(fact_108_less__imp__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 0.31/1.50 thf(fact_109_less__not__sym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 0.31/1.50 thf(fact_110_less__induct, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P:(A > $o),A2:A]: (((! [X2:A]: (((! [Y2:A]: (((((ord_less @ A) @ Y2) @ X2) => (P @ Y2)))) => (P @ X2)))) => (P @ A2)))))))).
% 0.31/1.50 thf(fact_111_antisym__conv3, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y:A,X:A]: (((~ ((((ord_less @ A) @ Y) @ X))) => ((~ ((((ord_less @ A) @ X) @ Y))) = (X = Y))))))))).
% 0.31/1.50 thf(fact_112_less__imp__not__eq2, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (Y != X)))))))).
% 0.31/1.50 thf(fact_113_less__imp__triv, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,P:$o]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ X) => P)))))))).
% 0.31/1.50 thf(fact_114_linorder__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) => ((X != Y) => (((ord_less @ A) @ Y) @ X))))))))).
% 0.31/1.50 thf(fact_115_dual__order_Oirrefl, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((~ ((((ord_less @ A) @ A2) @ A2))))))))).
% 0.31/1.50 thf(fact_116_order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C3:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ B2) @ C3) => (((ord_less @ A) @ A2) @ C3))))))))).
% 0.31/1.50 thf(fact_117_less__imp__not__less, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 0.31/1.50 thf(fact_118_exists__least__iff, axiom, (! [A:$tType]: (((wellorder @ A) => ((^ [P3:(A > $o)]: ((? [X5:A]: ((P3 @ X5))))) = (^ [P4:(A > $o)]: ((? [N3:A]: (((P4 @ N3) & (! [M3:A]: (((((ord_less @ A) @ M3) @ N3) => (~ ((P4 @ M3)))))))))))))))).
% 0.31/1.50 thf(fact_119_linorder__less__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A4:A,B4:A]: (((((ord_less @ A) @ A4) @ B4) => ((P @ A4) @ B4)))) => ((! [A4:A]: (((P @ A4) @ A4))) => ((! [A4:A,B4:A]: ((((P @ B4) @ A4) => ((P @ A4) @ B4)))) => ((P @ A2) @ B2)))))))))).
% 0.31/1.50 thf(fact_120_dual__order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C3:A]: (((((ord_less @ A) @ B2) @ A2) => ((((ord_less @ A) @ C3) @ B2) => (((ord_less @ A) @ C3) @ A2))))))))).
% 0.31/1.50 thf(fact_121_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) = ((((ord_less @ A) @ Y) @ X) | (X = Y))))))))).
% 0.31/1.50 thf(fact_122_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (A2 != B2)))))))).
% 0.31/1.50 thf(fact_123_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A]: (((((ord_less @ A) @ B2) @ A2) => (A2 != B2)))))))).
% 0.31/1.50 thf(fact_124_ex__gt__or__lt, axiom, (! [A:$tType]: (((condit1656338222tinuum @ A) => (! [A2:A]: ((? [B4:A]: (((((ord_less @ A) @ A2) @ B4) | (((ord_less @ A) @ B4) @ A2)))))))))).
% 0.31/1.50 thf(fact_125_ex__has__least__nat, axiom, (! [A:$tType,P:(A > $o),K:A,M:(A > nat)]: (((P @ K) => (? [X2:A]: (((P @ X2) & (! [Y2:A]: (((P @ Y2) => (((ord_less_eq @ nat) @ (M @ X2)) @ (M @ Y2)))))))))))).
% 0.31/1.50 thf(fact_126_leD, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less @ A) @ X) @ Y)))))))))).
% 0.31/1.50 thf(fact_127_leI, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.31/1.50 thf(fact_128_le__less, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [X4:A,Y5:A]: (((((ord_less @ A) @ X4) @ Y5) | (X4 = Y5))))))))).
% 0.31/1.50 thf(fact_129_less__le, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [X4:A,Y5:A]: (((((ord_less_eq @ A) @ X4) @ Y5) & (X4 != Y5))))))))).
% 0.31/1.50 thf(fact_130_order__le__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F2:(B > A),B2:B,C3:B]: (((((ord_less_eq @ A) @ A2) @ (F2 @ B2)) => ((((ord_less @ B) @ B2) @ C3) => ((! [X2:B,Y3:B]: (((((ord_less @ B) @ X2) @ Y3) => (((ord_less @ A) @ (F2 @ X2)) @ (F2 @ Y3))))) => (((ord_less @ A) @ A2) @ (F2 @ C3))))))))))).
% 0.31/1.50 thf(fact_131_order__le__less__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A2:A,B2:A,F2:(A > C),C3:C]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less @ C) @ (F2 @ B2)) @ C3) => ((! [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) => (((ord_less_eq @ C) @ (F2 @ X2)) @ (F2 @ Y3))))) => (((ord_less @ C) @ (F2 @ A2)) @ C3)))))))))).
% 0.31/1.50 thf(fact_132_order__less__le__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A2:A,F2:(B > A),B2:B,C3:B]: (((((ord_less @ A) @ A2) @ (F2 @ B2)) => ((((ord_less_eq @ B) @ B2) @ C3) => ((! [X2:B,Y3:B]: (((((ord_less_eq @ B) @ X2) @ Y3) => (((ord_less_eq @ A) @ (F2 @ X2)) @ (F2 @ Y3))))) => (((ord_less @ A) @ A2) @ (F2 @ C3))))))))))).
% 0.31/1.50 thf(fact_133_order__less__le__subst2, axiom, (! [A:$tType,C:$tType]: ((((order @ C) & (order @ A)) => (! [A2:A,B2:A,F2:(A > C),C3:C]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less_eq @ C) @ (F2 @ B2)) @ C3) => ((! [X2:A,Y3:A]: (((((ord_less @ A) @ X2) @ Y3) => (((ord_less @ C) @ (F2 @ X2)) @ (F2 @ Y3))))) => (((ord_less @ C) @ (F2 @ A2)) @ C3)))))))))).
% 0.31/1.50 thf(fact_134_not__le, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) = (((ord_less @ A) @ Y) @ X)))))))).
% 0.31/1.50 thf(fact_135_not__less, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) = (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.31/1.50 thf(fact_136_le__neq__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((A2 != B2) => (((ord_less @ A) @ A2) @ B2))))))))).
% 0.31/1.50 thf(fact_137_antisym__conv1, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 0.31/1.50 thf(fact_138_antisym__conv2, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((~ ((((ord_less @ A) @ X) @ Y))) = (X = Y))))))))).
% 0.31/1.50 thf(fact_139_less__imp__le, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 0.31/1.50 thf(fact_140_le__less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,Z4:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ Z4) => (((ord_less @ A) @ X) @ Z4))))))))).
% 0.31/1.50 thf(fact_141_less__le__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,Z4:A]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z4) => (((ord_less @ A) @ X) @ Z4))))))))).
% 0.31/1.50 thf(fact_142_dense__ge, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Z4:A,Y:A]: (((! [X2:A]: (((((ord_less @ A) @ Z4) @ X2) => (((ord_less_eq @ A) @ Y) @ X2)))) => (((ord_less_eq @ A) @ Y) @ Z4)))))))).
% 0.31/1.50 thf(fact_143_dense__le, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Y:A,Z4:A]: (((! [X2:A]: (((((ord_less @ A) @ X2) @ Y) => (((ord_less_eq @ A) @ X2) @ Z4)))) => (((ord_less_eq @ A) @ Y) @ Z4)))))))).
% 0.31/1.50 thf(fact_144_le__less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less @ A) @ Y) @ X)))))))).
% 0.31/1.50 thf(fact_145_le__imp__less__or__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less @ A) @ X) @ Y) | (X = Y))))))))).
% 0.31/1.50 thf(fact_146_less__le__not__le, axiom, (! [A:$tType]: (((preorder @ A) => ((ord_less @ A) = (^ [X4:A,Y5:A]: (((((ord_less_eq @ A) @ X4) @ Y5) & (~ ((((ord_less_eq @ A) @ Y5) @ X4))))))))))).
% 0.31/1.50 thf(fact_147_not__le__imp__less, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y:A,X:A]: (((~ ((((ord_less_eq @ A) @ Y) @ X))) => (((ord_less @ A) @ X) @ Y)))))))).
% 0.31/1.50 thf(fact_148_order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less @ A) @ B2) @ C3) => (((ord_less @ A) @ A2) @ C3))))))))).
% 0.31/1.50 thf(fact_149_order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A,B2:A,C3:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C3) => (((ord_less @ A) @ A2) @ C3))))))))).
% 0.31/1.50 thf(fact_150_order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [A3:A,B3:A]: (((((ord_less @ A) @ A3) @ B3) | (A3 = B3))))))))).
% 0.31/1.50 thf(fact_151_order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) & (A3 != B3))))))))).
% 0.31/1.50 thf(fact_152_dual__order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C3:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less @ A) @ C3) @ B2) => (((ord_less @ A) @ C3) @ A2))))))))).
% 0.31/1.50 thf(fact_153_dual__order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A2:A,C3:A]: (((((ord_less @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C3) @ B2) => (((ord_less @ A) @ C3) @ A2))))))))).
% 0.31/1.50 thf(fact_154_dense__ge__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Z4:A,X:A,Y:A]: (((((ord_less @ A) @ Z4) @ X) => ((! [W:A]: (((((ord_less @ A) @ Z4) @ W) => ((((ord_less @ A) @ W) @ X) => (((ord_less_eq @ A) @ Y) @ W))))) => (((ord_less_eq @ A) @ Y) @ Z4))))))))).
% 0.31/1.50 thf(fact_155_dense__le__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [X:A,Y:A,Z4:A]: (((((ord_less @ A) @ X) @ Y) => ((! [W:A]: (((((ord_less @ A) @ X) @ W) => ((((ord_less @ A) @ W) @ Y) => (((ord_less_eq @ A) @ W) @ Z4))))) => (((ord_less_eq @ A) @ Y) @ Z4))))))))).
% 0.31/1.50 thf(fact_156_Until_Oprems, axiom, (((ord_less @ nat) @ ia) @ ((((monito2027355080ogress @ a) @ sigma) @ ((((until @ a) @ phi_1) @ i2) @ phi_2)) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi)))).
% 0.31/1.50 thf(fact_157_plen__mono, axiom, (! [A:$tType,Pi:(prefix @ A),Pi2:(prefix @ A)]: (((((ord_less_eq @ (prefix @ A)) @ Pi) @ Pi2) => (((ord_less_eq @ nat) @ ((plen @ A) @ Pi)) @ ((plen @ A) @ Pi2)))))).
% 0.31/1.50 thf(fact_158_verit__comp__simplify1_I3_J, axiom, (! [B:$tType]: (((linorder @ B) => (! [B5:B,A5:B]: (((~ ((((ord_less_eq @ B) @ B5) @ A5))) = (((ord_less @ B) @ A5) @ B5)))))))).
% 0.31/1.50 thf(fact_159__092_060open_062i_A_060_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_H_A_Iformula_OUntil_A_092_060phi_0621_AI_A_092_060phi_0622_J_A_Iplen_A_092_060pi_062_J_092_060close_062, axiom, (((ord_less @ nat) @ ia) @ ((((monito2027355080ogress @ a) @ sigma2) @ ((((until @ a) @ phi_1) @ i2) @ phi_2)) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi)))).
% 0.31/1.50 thf(fact_160_arg__max__nat__lemma, axiom, (! [A:$tType,P:(A > $o),K:A,F2:(A > nat),B2:nat]: (((P @ K) => ((! [Y3:A]: (((P @ Y3) => (((ord_less @ nat) @ (F2 @ Y3)) @ B2)))) => ((P @ ((((lattices_ord_arg_max @ A) @ nat) @ F2) @ P)) & (! [Y2:A]: (((P @ Y2) => (((ord_less_eq @ nat) @ (F2 @ Y2)) @ (F2 @ ((((lattices_ord_arg_max @ A) @ nat) @ F2) @ P)))))))))))).
% 0.31/1.50 thf(fact_161_arg__max__nat__le, axiom, (! [A:$tType,P:(A > $o),X:A,F2:(A > nat),B2:nat]: (((P @ X) => ((! [Y3:A]: (((P @ Y3) => (((ord_less @ nat) @ (F2 @ Y3)) @ B2)))) => (((ord_less_eq @ nat) @ (F2 @ X)) @ (F2 @ ((((lattices_ord_arg_max @ A) @ nat) @ F2) @ P)))))))).
% 0.31/1.50 thf(fact_162_progress__axioms_Ointro, axiom, (! [B:$tType,A:$tType,Progress:((prefix @ A) > nat),Sat:((trace @ A) > ((list @ B) > (nat > $o)))]: (((! [Pi3:(prefix @ A),Pi4:(prefix @ A)]: (((((ord_less_eq @ (prefix @ A)) @ Pi3) @ Pi4) => (((ord_less_eq @ nat) @ (Progress @ Pi3)) @ (Progress @ Pi4))))) => ((! [Sigma3:(trace @ A),X2:nat]: ((? [Pi5:(prefix @ A)]: (((((prefix_of @ A) @ Pi5) @ Sigma3) & (((ord_less_eq @ nat) @ X2) @ (Progress @ Pi5))))))) => ((! [Pi3:(prefix @ A),Sigma3:(trace @ A),Sigma4:(trace @ A),I2:nat,V3:(list @ B)]: (((((prefix_of @ A) @ Pi3) @ Sigma3) => ((((prefix_of @ A) @ Pi3) @ Sigma4) => ((((ord_less @ nat) @ I2) @ (Progress @ Pi3)) => ((((Sat @ Sigma3) @ V3) @ I2) = (((Sat @ Sigma4) @ V3) @ I2))))))) => ((((abstra417776764axioms @ A) @ B) @ Sat) @ Progress))))))).
% 0.31/1.50 thf(fact_163_less__prefix__def, axiom, (! [A:$tType]: (((ord_less @ (prefix @ A)) = (^ [X4:(prefix @ A),Y5:(prefix @ A)]: (((((ord_less_eq @ (prefix @ A)) @ X4) @ Y5) & (~ ((((ord_less_eq @ (prefix @ A)) @ Y5) @ X4)))))))))).
% 0.31/1.50 thf(fact_164_less__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less @ (A > B)) = (^ [F3:(A > B),G:(A > B)]: (((((ord_less_eq @ (A > B)) @ F3) @ G) & (~ ((((ord_less_eq @ (A > B)) @ G) @ F3))))))))))).
% 0.31/1.50 thf(fact_165_arg__max__natI, axiom, (! [A:$tType,P:(A > $o),K:A,F2:(A > nat),B2:nat]: (((P @ K) => ((! [Y3:A]: (((P @ Y3) => (((ord_less @ nat) @ (F2 @ Y3)) @ B2)))) => (P @ ((((lattices_ord_arg_max @ A) @ nat) @ F2) @ P))))))).
% 0.31/1.50 thf(fact_166_arg__max__equality, axiom, (! [A:$tType,C:$tType]: (((order @ A) => (! [P:(C > $o),K:C,F2:(C > A)]: (((P @ K) => ((! [X2:C]: (((P @ X2) => (((ord_less_eq @ A) @ (F2 @ X2)) @ (F2 @ K))))) => ((F2 @ ((((lattices_ord_arg_max @ C) @ A) @ F2) @ P)) = (F2 @ K)))))))))).
% 0.31/1.50 thf(fact_167_arg__maxI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [P:(A > $o),X:A,F2:(A > B),Q:(A > $o)]: (((P @ X) => ((! [Y3:A]: (((P @ Y3) => (~ ((((ord_less @ B) @ (F2 @ X)) @ (F2 @ Y3))))))) => ((! [X2:A]: (((P @ X2) => ((! [Y2:A]: (((P @ Y2) => (~ ((((ord_less @ B) @ (F2 @ X2)) @ (F2 @ Y2))))))) => (Q @ X2))))) => (Q @ ((((lattices_ord_arg_max @ A) @ B) @ F2) @ P))))))))))).
% 0.31/1.50 thf(fact_168_verit__la__disequality, axiom, (! [A:$tType]: (((linorder @ A) => (! [A2:A,B2:A]: (((A2 = B2) | ((~ ((((ord_less_eq @ A) @ A2) @ B2))) | (~ ((((ord_less_eq @ A) @ B2) @ A2))))))))))).
% 0.31/1.50 thf(fact_169_verit__comp__simplify1_I1_J, axiom, (! [A:$tType]: (((order @ A) => (! [A2:A]: ((~ ((((ord_less @ A) @ A2) @ A2))))))))).
% 0.31/1.50 thf(fact_170_ex__prefix__of, axiom, (! [A:$tType,P5:(prefix @ A)]: ((? [X_1:(trace @ A)]: ((((prefix_of @ A) @ P5) @ X_1)))))).
% 0.31/1.50 thf(fact_171_prefix__of__antimono, axiom, (! [A:$tType,Pi:(prefix @ A),Pi2:(prefix @ A),S:(trace @ A)]: (((((ord_less_eq @ (prefix @ A)) @ Pi) @ Pi2) => ((((prefix_of @ A) @ Pi2) @ S) => (((prefix_of @ A) @ Pi) @ S)))))).
% 0.31/1.50 thf(fact_172_prefix__of__imp__linear, axiom, (! [A:$tType,Pi:(prefix @ A),Sigma:(trace @ A),Pi2:(prefix @ A)]: (((((prefix_of @ A) @ Pi) @ Sigma) => ((((prefix_of @ A) @ Pi2) @ Sigma) => ((((ord_less_eq @ (prefix @ A)) @ Pi) @ Pi2) | (((ord_less_eq @ (prefix @ A)) @ Pi2) @ Pi))))))).
% 0.31/1.50 thf(fact_173_progress__axioms__def, axiom, (! [B:$tType,A:$tType]: ((((abstra417776764axioms @ A) @ B) = (^ [Sat2:((trace @ A) > ((list @ B) > (nat > $o))),Progress2:((prefix @ A) > nat)]: (((! [Pi6:(prefix @ A),Pi7:(prefix @ A)]: (((((ord_less_eq @ (prefix @ A)) @ Pi6) @ Pi7) => (((ord_less_eq @ nat) @ (Progress2 @ Pi6)) @ (Progress2 @ Pi7))))) & ((! [Sigma5:(trace @ A),X4:nat]: ((? [Pi6:(prefix @ A)]: (((((prefix_of @ A) @ Pi6) @ Sigma5) & (((ord_less_eq @ nat) @ X4) @ (Progress2 @ Pi6))))))) & (! [Pi6:(prefix @ A),Sigma5:(trace @ A),Sigma6:(trace @ A),I4:nat,V4:(list @ B)]: (((((prefix_of @ A) @ Pi6) @ Sigma5) => ((((prefix_of @ A) @ Pi6) @ Sigma6) => ((((ord_less @ nat) @ I4) @ (Progress2 @ Pi6)) => ((((Sat2 @ Sigma5) @ V4) @ I4) = (((Sat2 @ Sigma6) @ V4) @ I4))))))))))))))).
% 0.31/1.50 thf(fact_174_formula_Oinject_I9_J, axiom, (! [A:$tType,X91:(formula @ A),X92:i,X93:(formula @ A),Y91:(formula @ A),Y92:i,Y93:(formula @ A)]: (((((((until @ A) @ X91) @ X92) @ X93) = ((((until @ A) @ Y91) @ Y92) @ Y93)) = ((X91 = Y91) & ((X92 = Y92) & (X93 = Y93))))))).
% 0.31/1.50 thf(fact_175__C21_C, axiom, (! [K:nat]: (((((ord_less_eq @ nat) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma2) @ K)) @ (((plus_plus @ nat) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma2) @ ia)) @ b)) => (((ord_less @ nat) @ K) @ ((((monito2027355080ogress @ a) @ sigma) @ phi_2) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi))))))).
% 0.31/1.50 thf(fact_176__C11_C, axiom, (! [K:nat]: (((((ord_less_eq @ nat) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma2) @ K)) @ (((plus_plus @ nat) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma2) @ ia)) @ b)) => (((ord_less @ nat) @ K) @ ((((monito2027355080ogress @ a) @ sigma) @ phi_1) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi))))))).
% 0.31/1.50 thf(fact_177_that, axiom, (((ord_less_eq @ nat) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma2) @ k)) @ (((plus_plus @ nat) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma2) @ ia)) @ b))).
% 0.31/1.50 thf(fact_178_nat__add__left__cancel__less, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less @ nat) @ (((plus_plus @ nat) @ K) @ M)) @ (((plus_plus @ nat) @ K) @ N)) = (((ord_less @ nat) @ M) @ N))))).
% 0.31/1.50 thf(fact_179_nat__add__left__cancel__le, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ K) @ M)) @ (((plus_plus @ nat) @ K) @ N)) = (((ord_less_eq @ nat) @ M) @ N))))).
% 0.31/1.50 thf(fact_180__C3_C, axiom, (! [K:nat]: (((((ord_less_eq @ nat) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma) @ K)) @ (((plus_plus @ nat) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma) @ ia)) @ b)) => (((ord_less @ nat) @ K) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi)))))).
% 0.31/1.50 thf(fact_181__C1_C, axiom, (! [K:nat]: (((((ord_less_eq @ nat) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma) @ K)) @ (((plus_plus @ nat) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma) @ ia)) @ b)) => (((ord_less @ nat) @ K) @ ((((monito2027355080ogress @ a) @ sigma) @ phi_1) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi))))))).
% 0.31/1.50 thf(fact_182__C2_C, axiom, (! [K:nat]: (((((ord_less_eq @ nat) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma) @ K)) @ (((plus_plus @ nat) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma) @ ia)) @ b)) => (((ord_less @ nat) @ K) @ ((((monito2027355080ogress @ a) @ sigma) @ phi_2) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi))))))).
% 0.31/1.50 thf(fact_183__092_060open_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_____092_060close_062, axiom, (((ord_less_eq @ nat) @ (((plus_plus @ nat) @ (((plus_plus @ nat) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma) @ ia)) @ b)) @ (one_one @ nat))) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma) @ j))).
% 0.31/1.50 thf(fact_184__092_060open_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_092_060close_062, axiom, (((ord_less_eq @ nat) @ (((plus_plus @ nat) @ (((plus_plus @ nat) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma2) @ ia)) @ b)) @ (one_one @ nat))) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma2) @ ja))).
% 0.31/1.50 thf(fact_185_less___092_060tau_062D, axiom, (! [A:$tType,Sigma:(trace @ A),I:nat,J:nat]: (((((ord_less @ nat) @ (((tau @ A) @ Sigma) @ I)) @ (((tau @ A) @ Sigma) @ J)) => (((ord_less @ nat) @ I) @ J))))).
% 0.31/1.50 thf(fact_186_ex__le___092_060tau_062, axiom, (! [A:$tType,I:nat,X:nat,S:(trace @ A)]: ((? [J3:nat]: (((((ord_less_eq @ nat) @ I) @ J3) & (((ord_less_eq @ nat) @ X) @ (((tau @ A) @ S) @ J3)))))))).
% 0.31/1.50 thf(fact_187__092_060tau_062__mono, axiom, (! [A:$tType,I:nat,J:nat,S:(trace @ A)]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (((tau @ A) @ S) @ I)) @ (((tau @ A) @ S) @ J)))))).
% 0.31/1.50 thf(fact_188_less__add__eq__less, axiom, (! [K:nat,L:nat,M:nat,N:nat]: (((((ord_less @ nat) @ K) @ L) => (((((plus_plus @ nat) @ M) @ L) = (((plus_plus @ nat) @ K) @ N)) => (((ord_less @ nat) @ M) @ N)))))).
% 0.31/1.50 thf(fact_189_trans__less__add2, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ I) @ (((plus_plus @ nat) @ M) @ J)))))).
% 0.31/1.50 thf(fact_190_trans__less__add1, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ I) @ (((plus_plus @ nat) @ J) @ M)))))).
% 0.31/1.50 thf(fact_191_add__less__mono1, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ (((plus_plus @ nat) @ J) @ K)))))).
% 0.31/1.50 thf(fact_192_not__add__less2, axiom, (! [J:nat,I:nat]: ((~ ((((ord_less @ nat) @ (((plus_plus @ nat) @ J) @ I)) @ I)))))).
% 0.31/1.50 thf(fact_193_not__add__less1, axiom, (! [I:nat,J:nat]: ((~ ((((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ J)) @ I)))))).
% 0.31/1.50 thf(fact_194_add__less__mono, axiom, (! [I:nat,J:nat,K:nat,L:nat]: (((((ord_less @ nat) @ I) @ J) => ((((ord_less @ nat) @ K) @ L) => (((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ (((plus_plus @ nat) @ J) @ L))))))).
% 0.31/1.50 thf(fact_195_add__lessD1, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ J)) @ K) => (((ord_less @ nat) @ I) @ K))))).
% 0.31/1.50 thf(fact_196_add__leE, axiom, (! [M:nat,K:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ M) @ K)) @ N) => (~ (((((ord_less_eq @ nat) @ M) @ N) => (~ ((((ord_less_eq @ nat) @ K) @ N)))))))))).
% 0.31/1.50 thf(fact_197_le__add1, axiom, (! [N:nat,M:nat]: ((((ord_less_eq @ nat) @ N) @ (((plus_plus @ nat) @ N) @ M))))).
% 0.31/1.50 thf(fact_198_le__add2, axiom, (! [N:nat,M:nat]: ((((ord_less_eq @ nat) @ N) @ (((plus_plus @ nat) @ M) @ N))))).
% 0.31/1.50 thf(fact_199_add__leD1, axiom, (! [M:nat,K:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ M) @ K)) @ N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 0.31/1.50 thf(fact_200_add__leD2, axiom, (! [M:nat,K:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ M) @ K)) @ N) => (((ord_less_eq @ nat) @ K) @ N))))).
% 0.31/1.50 thf(fact_201_le__Suc__ex, axiom, (! [K:nat,L:nat]: (((((ord_less_eq @ nat) @ K) @ L) => (? [N2:nat]: ((L = (((plus_plus @ nat) @ K) @ N2)))))))).
% 0.31/1.50 thf(fact_202_add__le__mono, axiom, (! [I:nat,J:nat,K:nat,L:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((ord_less_eq @ nat) @ K) @ L) => (((ord_less_eq @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ (((plus_plus @ nat) @ J) @ L))))))).
% 0.31/1.50 thf(fact_203_add__le__mono1, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ (((plus_plus @ nat) @ J) @ K)))))).
% 0.31/1.50 thf(fact_204_trans__le__add1, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ I) @ (((plus_plus @ nat) @ J) @ M)))))).
% 0.31/1.50 thf(fact_205_trans__le__add2, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ I) @ (((plus_plus @ nat) @ M) @ J)))))).
% 0.31/1.50 thf(fact_206_nat__le__iff__add, axiom, ((ord_less_eq @ nat) = (^ [M3:nat,N3:nat]: ((? [K3:nat]: ((N3 = (((plus_plus @ nat) @ M3) @ K3)))))))).
% 0.31/1.50 thf(fact_207_ex__has__greatest__nat__lemma, axiom, (! [A:$tType,P:(A > $o),K:A,F2:(A > nat),N:nat]: (((P @ K) => ((! [X2:A]: (((P @ X2) => (? [Y2:A]: (((P @ Y2) & (~ ((((ord_less_eq @ nat) @ (F2 @ Y2)) @ (F2 @ X2)))))))))) => (? [Y3:A]: (((P @ Y3) & (~ ((((ord_less @ nat) @ (F2 @ Y3)) @ (((plus_plus @ nat) @ (F2 @ K)) @ N)))))))))))).
% 0.31/1.50 thf(fact_208_mono__nat__linear__lb, axiom, (! [F2:(nat > nat),M:nat,K:nat]: (((! [M4:nat,N2:nat]: (((((ord_less @ nat) @ M4) @ N2) => (((ord_less @ nat) @ (F2 @ M4)) @ (F2 @ N2))))) => (((ord_less_eq @ nat) @ (((plus_plus @ nat) @ (F2 @ M)) @ K)) @ (F2 @ (((plus_plus @ nat) @ M) @ K))))))).
% 0.31/1.50 thf(fact_209_progress__time__conv, axiom, (! [A:$tType,J:nat,Sigma:(trace @ ((product_prod @ (list @ char)) @ (list @ A))),Sigma2:(trace @ ((product_prod @ (list @ char)) @ (list @ A))),Phi:(formula @ A)]: (((! [I2:nat]: (((((ord_less @ nat) @ I2) @ J) => ((((tau @ ((product_prod @ (list @ char)) @ (list @ A))) @ Sigma) @ I2) = (((tau @ ((product_prod @ (list @ char)) @ (list @ A))) @ Sigma2) @ I2))))) => (((((monito2027355080ogress @ A) @ Sigma) @ Phi) @ J) = ((((monito2027355080ogress @ A) @ Sigma2) @ Phi) @ J)))))).
% 0.31/1.50 thf(fact_210_le___092_060tau_062__less, axiom, (! [A:$tType,Sigma:(trace @ A),I:nat,J:nat]: (((((ord_less_eq @ nat) @ (((tau @ A) @ Sigma) @ I)) @ (((tau @ A) @ Sigma) @ J)) => ((((ord_less @ nat) @ J) @ I) => ((((tau @ A) @ Sigma) @ I) = (((tau @ A) @ Sigma) @ J))))))).
% 0.31/1.50 thf(fact_211__092_060tau_062__prefix__conv, axiom, (! [A:$tType,P5:(prefix @ A),S:(trace @ A),S2:(trace @ A),I:nat]: (((((prefix_of @ A) @ P5) @ S) => ((((prefix_of @ A) @ P5) @ S2) => ((((ord_less @ nat) @ I) @ ((plen @ A) @ P5)) => ((((tau @ A) @ S) @ I) = (((tau @ A) @ S2) @ I)))))))).
% 0.31/1.50 thf(fact_212__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [J3:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ (((plus_plus @ nat) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma2) @ ia)) @ b)) @ (one_one @ nat))) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma2) @ J3)) => ((((ord_less_eq @ nat) @ J3) @ ((((monito2027355080ogress @ a) @ sigma2) @ phi_1) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi))) => (~ ((((ord_less_eq @ nat) @ J3) @ ((((monito2027355080ogress @ a) @ sigma2) @ phi_2) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi)))))))))))).
% 0.31/1.50 thf(fact_213__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [J3:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ (((plus_plus @ nat) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma) @ ia)) @ b)) @ (one_one @ nat))) @ (((tau @ ((product_prod @ (list @ char)) @ (list @ a))) @ sigma) @ J3)) => ((((ord_less_eq @ nat) @ J3) @ ((((monito2027355080ogress @ a) @ sigma) @ phi_1) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi))) => (~ ((((ord_less_eq @ nat) @ J3) @ ((((monito2027355080ogress @ a) @ sigma) @ phi_2) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi)))))))))))).
% 0.31/1.50 thf(fact_214_add__less__cancel__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C3:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ C3)) = (((ord_less @ A) @ A2) @ B2)))))))).
% 0.31/1.50 thf(fact_215_add__left__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [A2:A,B2:A,C3:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C3)) = (B2 = C3)))))))).
% 0.31/1.50 thf(fact_216_add__right__cancel, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [B2:A,A2:A,C3:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C3) @ A2)) = (B2 = C3)))))))).
% 0.31/1.50 thf(fact_217_add__le__cancel__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C3:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B2)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 0.31/1.50 thf(fact_218_add__le__cancel__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C3:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ C3)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 0.31/1.50 thf(fact_219_add__less__cancel__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C3:A,A2:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B2)) = (((ord_less @ A) @ A2) @ B2)))))))).
% 0.31/1.50 thf(fact_220_one__reorient, axiom, (! [A:$tType]: (((one @ A) => (! [X:A]: ((((one_one @ A) = X) = (X = (one_one @ A))))))))).
% 0.31/1.50 thf(fact_221_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => (! [A2:A,B2:A,C3:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C3) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C3))))))))).
% 0.31/1.50 thf(fact_222_add__mono__thms__linordered__semiring_I4_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (K = L)) => ((((plus_plus @ A) @ I) @ K) = (((plus_plus @ A) @ J) @ L))))))))).
% 0.31/1.50 thf(fact_223_group__cancel_Oadd1, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [A6:A,K:A,A2:A,B2:A]: (((A6 = (((plus_plus @ A) @ K) @ A2)) => ((((plus_plus @ A) @ A6) @ B2) = (((plus_plus @ A) @ K) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 0.31/1.50 thf(fact_224_group__cancel_Oadd2, axiom, (! [A:$tType]: (((comm_monoid_add @ A) => (! [B6:A,K:A,B2:A,A2:A]: (((B6 = (((plus_plus @ A) @ K) @ B2)) => ((((plus_plus @ A) @ A2) @ B6) = (((plus_plus @ A) @ K) @ (((plus_plus @ A) @ A2) @ B2)))))))))).
% 0.31/1.50 thf(fact_225_add_Oassoc, axiom, (! [A:$tType]: (((semigroup_add @ A) => (! [A2:A,B2:A,C3:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C3) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C3))))))))).
% 0.31/1.50 thf(fact_226_add_Oleft__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [A2:A,B2:A,C3:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C3)) = (B2 = C3)))))))).
% 0.31/1.50 thf(fact_227_add_Oright__cancel, axiom, (! [A:$tType]: (((group_add @ A) => (! [B2:A,A2:A,C3:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C3) @ A2)) = (B2 = C3)))))))).
% 0.31/1.50 thf(fact_228_add_Ocommute, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => ((plus_plus @ A) = (^ [A3:A,B3:A]: ((((plus_plus @ A) @ B3) @ A3)))))))).
% 0.31/1.50 thf(fact_229_add_Oleft__commute, axiom, (! [A:$tType]: (((ab_semigroup_add @ A) => (! [B2:A,A2:A,C3:A]: (((((plus_plus @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C3)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C3))))))))).
% 0.31/1.50 thf(fact_230_add__left__imp__eq, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [A2:A,B2:A,C3:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C3)) => (B2 = C3)))))))).
% 0.31/1.50 thf(fact_231_add__right__imp__eq, axiom, (! [A:$tType]: (((cancel_semigroup_add @ A) => (! [B2:A,A2:A,C3:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C3) @ A2)) => (B2 = C3)))))))).
% 0.31/1.50 thf(fact_232_add__mono__thms__linordered__semiring_I3_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (K = L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.31/1.50 thf(fact_233_add__mono__thms__linordered__semiring_I2_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.31/1.50 thf(fact_234_add__mono__thms__linordered__semiring_I1_J, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.31/1.50 thf(fact_235_add__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C3:A,D3:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C3) @ D3) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ D3)))))))))).
% 0.31/1.50 thf(fact_236_add__left__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B2))))))))).
% 0.31/1.50 thf(fact_237_less__eqE, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (~ ((! [C2:A]: ((B2 != (((plus_plus @ A) @ A2) @ C2))))))))))))).
% 0.31/1.50 thf(fact_238_add__right__mono, axiom, (! [A:$tType]: (((ordere779506340up_add @ A) => (! [A2:A,B2:A,C3:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ C3))))))))).
% 0.31/1.50 thf(fact_239_le__iff__add, axiom, (! [A:$tType]: (((canoni770627133id_add @ A) => ((ord_less_eq @ A) = (^ [A3:A,B3:A]: ((? [C4:A]: ((B3 = (((plus_plus @ A) @ A3) @ C4))))))))))).
% 0.31/1.50 thf(fact_240_add__le__imp__le__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C3:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B2)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 0.31/1.50 thf(fact_241_add__le__imp__le__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C3:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ C3)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 0.31/1.50 thf(fact_242_add__mono__thms__linordered__field_I5_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.31/1.50 thf(fact_243_add__mono__thms__linordered__field_I2_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.31/1.50 thf(fact_244_add__mono__thms__linordered__field_I1_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (K = L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.31/1.50 thf(fact_245_add__strict__mono, axiom, (! [A:$tType]: (((strict2144017051up_add @ A) => (! [A2:A,B2:A,C3:A,D3:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ C3) @ D3) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ D3)))))))))).
% 0.31/1.50 thf(fact_246_add__strict__left__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B2:A,C3:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B2))))))))).
% 0.31/1.50 thf(fact_247_add__strict__right__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B2:A,C3:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ C3))))))))).
% 0.31/1.50 thf(fact_248_add__less__imp__less__left, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [C3:A,A2:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C3) @ A2)) @ (((plus_plus @ A) @ C3) @ B2)) => (((ord_less @ A) @ A2) @ B2)))))))).
% 0.31/1.50 thf(fact_249_add__less__imp__less__right, axiom, (! [A:$tType]: (((ordere236663937imp_le @ A) => (! [A2:A,C3:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ C3)) => (((ord_less @ A) @ A2) @ B2)))))))).
% 0.31/1.50 thf(fact_250_add__less__le__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B2:A,C3:A,D3:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C3) @ D3) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ D3)))))))))).
% 0.31/1.50 thf(fact_251_add__le__less__mono, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [A2:A,B2:A,C3:A,D3:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less @ A) @ C3) @ D3) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C3)) @ (((plus_plus @ A) @ B2) @ D3)))))))))).
% 0.31/1.50 thf(fact_252_add__mono__thms__linordered__field_I3_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (((ord_less_eq @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.31/1.50 thf(fact_253_add__mono__thms__linordered__field_I4_J, axiom, (! [A:$tType]: (((ordere223160158up_add @ A) => (! [I:A,J:A,K:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (((ord_less @ A) @ K) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 0.31/1.50 thf(fact_254_discrete, axiom, (! [A:$tType]: (((unique1598680935umeral @ A) => ((ord_less @ A) = (^ [A3:A]: (((ord_less_eq @ A) @ (((plus_plus @ A) @ A3) @ (one_one @ A)))))))))).
% 0.31/1.50 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: (((preorder @ A8) => (preorder @ (A7 > A8)))))).
% 0.31/1.50 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: (((order @ A8) => (order @ (A7 > A8)))))).
% 0.31/1.50 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: (((ord @ A8) => (ord @ (A7 > A8)))))).
% 0.31/1.50 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder, axiom, (condit1037483654norder @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Divides_Ounique__euclidean__semiring__numeral, axiom, (unique1598680935umeral @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add, axiom, (strict2144017051up_add @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, axiom, (ordere223160158up_add @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, axiom, (ordere236663937imp_le @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, (canoni770627133id_add @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, axiom, (ordere779506340up_add @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add, axiom, (cancel_semigroup_add @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add, axiom, (ab_semigroup_add @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add, axiom, (comm_monoid_add @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Groups_Osemigroup__add, axiom, (semigroup_add @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, (wellorder @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Orderings_Opreorder_1, axiom, (preorder @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Orderings_Ono__top, axiom, (no_top @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Orderings_Oorder_2, axiom, (order @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Orderings_Oord_3, axiom, (ord @ nat)).
% 0.31/1.50 thf(tcon_Nat_Onat___Groups_Oone, axiom, (one @ nat)).
% 0.31/1.50 thf(tcon_HOL_Obool___Orderings_Opreorder_4, axiom, (preorder @ $o)).
% 0.31/1.50 thf(tcon_HOL_Obool___Orderings_Olinorder_5, axiom, (linorder @ $o)).
% 0.31/1.50 thf(tcon_HOL_Obool___Orderings_Oorder_6, axiom, (order @ $o)).
% 0.31/1.50 thf(tcon_HOL_Obool___Orderings_Oord_7, axiom, (ord @ $o)).
% 0.31/1.50 thf(tcon_Trace_Oprefix___Orderings_Opreorder_8, axiom, (! [A7:$tType]: ((preorder @ (prefix @ A7))))).
% 0.31/1.50 thf(tcon_Trace_Oprefix___Orderings_Oorder_9, axiom, (! [A7:$tType]: ((order @ (prefix @ A7))))).
% 0.31/1.50 thf(tcon_Trace_Oprefix___Orderings_Oord_10, axiom, (! [A7:$tType]: ((ord @ (prefix @ A7))))).
% 0.31/1.50 thf(tcon_Interval_O_092_060I_062___Orderings_Opreorder_11, axiom, (preorder @ i)).
% 0.31/1.50 thf(tcon_Interval_O_092_060I_062___Orderings_Olinorder_12, axiom, (linorder @ i)).
% 0.31/1.50 thf(tcon_Interval_O_092_060I_062___Orderings_Oorder_13, axiom, (order @ i)).
% 0.31/1.50 thf(tcon_Interval_O_092_060I_062___Orderings_Oord_14, axiom, (ord @ i)).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Orderings_Owellorder_15, axiom, (! [A7:$tType,A8:$tType]: ((((wellorder @ A7) & (wellorder @ A8)) => (wellorder @ ((product_prod @ A7) @ A8)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Orderings_Opreorder_16, axiom, (! [A7:$tType,A8:$tType]: ((((preorder @ A7) & (preorder @ A8)) => (preorder @ ((product_prod @ A7) @ A8)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Orderings_Olinorder_17, axiom, (! [A7:$tType,A8:$tType]: ((((linorder @ A7) & (linorder @ A8)) => (linorder @ ((product_prod @ A7) @ A8)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Orderings_Oorder_18, axiom, (! [A7:$tType,A8:$tType]: ((((order @ A7) & (order @ A8)) => (order @ ((product_prod @ A7) @ A8)))))).
% 0.31/1.50 thf(tcon_Product__Type_Oprod___Orderings_Oord_19, axiom, (! [A7:$tType,A8:$tType]: ((((ord @ A7) & (ord @ A8)) => (ord @ ((product_prod @ A7) @ A8)))))).
% 0.31/1.50 thf(conj_0, conjecture, (((ord_less @ nat) @ k) @ ((plen @ ((product_prod @ (list @ char)) @ (list @ a))) @ pi))).
% 0.31/1.50 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.8TCNWeCSne/DTF2DTF8323.p
% 0.31/1.50 ------------------------
% 0.31/1.55 ---- Cleaned THF ---
% 0.31/1.55 thf(ty_t_Interval_O_092_060I_062,type,
% 0.31/1.55 i: $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_t_Product__Type_Oprod,type,
% 0.31/1.55 product_prod: $tType > $tType > $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_t_MFOTL_Oformula,type,
% 0.31/1.55 formula: $tType > $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_t_Trace_Oprefix,type,
% 0.31/1.55 prefix: $tType > $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_t_Trace_Otrace,type,
% 0.31/1.55 trace: $tType > $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_t_String_Ochar,type,
% 0.31/1.55 char: $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_t_List_Olist,type,
% 0.31/1.55 list: $tType > $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_t_Nat_Onat,type,
% 0.31/1.55 nat: $tType ).
% 0.31/1.55
% 0.31/1.55 thf(ty_tf_a,type,
% 0.31/1.55 a: $tType ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_HOL_Otype,type,
% 0.31/1.55 type:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Oone,type,
% 0.31/1.55 one:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Orderings_Oord,type,
% 0.31/1.55 ord:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Orderings_Oorder,type,
% 0.31/1.55 order:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Ogroup__add,type,
% 0.31/1.55 group_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Orderings_Ono__bot,type,
% 0.31/1.55 no_bot:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Orderings_Ono__top,type,
% 0.31/1.55 no_top:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Orderings_Olinorder,type,
% 0.31/1.55 linorder:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Orderings_Opreorder,type,
% 0.31/1.55 preorder:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Orderings_Owellorder,type,
% 0.31/1.55 wellorder:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.31/1.55 semigroup_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Orderings_Odense__order,type,
% 0.31/1.55 dense_order:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.31/1.55 comm_monoid_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.31/1.55 ab_semigroup_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.31/1.55 dense_linorder:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.31/1.55 cancel_semigroup_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.31/1.55 ordere779506340up_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.31/1.55 canoni770627133id_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.31/1.55 ordere236663937imp_le:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 0.31/1.55 ordere223160158up_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 0.31/1.55 strict2144017051up_add:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Divides_Ounique__euclidean__semiring__numeral,type,
% 0.31/1.55 unique1598680935umeral:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 0.31/1.55 condit1656338222tinuum:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 0.31/1.55 condit1037483654norder:
% 0.31/1.55 !>[A: $tType] : $o ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Abstract__Monitor_Oprogress__axioms,type,
% 0.31/1.55 abstra417776764axioms:
% 0.31/1.55 !>[A: $tType,B: $tType] : ( ( ( trace @ A ) > ( list @ B ) > nat > $o ) > ( ( prefix @ A ) > nat ) > $o ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.31/1.55 one_one:
% 0.31/1.55 !>[A: $tType] : A ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.31/1.55 plus_plus:
% 0.31/1.55 !>[A: $tType] : ( A > A > A ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Lattices__Big_Oord__class_Oarg__max,type,
% 0.31/1.55 lattices_ord_arg_max:
% 0.31/1.55 !>[B: $tType,A: $tType] : ( ( B > A ) > ( B > $o ) > B ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_MFOTL_Oformula_OUntil,type,
% 0.31/1.55 until:
% 0.31/1.55 !>[A: $tType] : ( ( formula @ A ) > i > ( formula @ A ) > ( formula @ A ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_MFOTL_Osat,type,
% 0.31/1.55 sat:
% 0.31/1.55 !>[A: $tType] : ( ( trace @ ( product_prod @ ( list @ char ) @ ( list @ A ) ) ) > ( list @ A ) > nat > ( formula @ A ) > $o ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Monitor__Mirabelle__pzlrlsievl_Oprogress,type,
% 0.31/1.55 monito2027355080ogress:
% 0.31/1.55 !>[A: $tType] : ( ( trace @ ( product_prod @ ( list @ char ) @ ( list @ A ) ) ) > ( formula @ A ) > nat > nat ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.31/1.55 ord_less:
% 0.31/1.55 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.31/1.55 ord_less_eq:
% 0.31/1.55 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Trace_O_092_060tau_062,type,
% 0.31/1.55 tau:
% 0.31/1.55 !>[A: $tType] : ( ( trace @ A ) > nat > nat ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Trace_Oplen,type,
% 0.31/1.55 plen:
% 0.31/1.55 !>[A: $tType] : ( ( prefix @ A ) > nat ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_c_Trace_Oprefix__of,type,
% 0.31/1.55 prefix_of:
% 0.31/1.55 !>[A: $tType] : ( ( prefix @ A ) > ( trace @ A ) > $o ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_I____,type,
% 0.31/1.55 i2: i ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v__092_060phi_062,type,
% 0.31/1.55 phi: formula @ a ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v__092_060phi_0621____,type,
% 0.31/1.55 phi_1: formula @ a ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v__092_060phi_0622____,type,
% 0.31/1.55 phi_2: formula @ a ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v__092_060pi_062,type,
% 0.31/1.55 pi: prefix @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v__092_060sigma_062,type,
% 0.31/1.55 sigma: trace @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v__092_060sigma_062_H,type,
% 0.31/1.55 sigma2: trace @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_b____,type,
% 0.31/1.55 b: nat ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_i,type,
% 0.31/1.55 i3: nat ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_ia____,type,
% 0.31/1.55 ia: nat ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_j____,type,
% 0.31/1.55 j: nat ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_ja____,type,
% 0.31/1.55 ja: nat ).
% 0.31/1.55
% 0.31/1.55 thf(sy_v_k____,type,
% 0.31/1.55 k: nat ).
% 0.31/1.55
% 0.31/1.55 thf(fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.31/1.55 ord_less @ nat @ k @ ( monito2027355080ogress @ a @ sigma @ phi_1 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_1_assms_I3_J,axiom,
% 0.31/1.55 ord_less @ nat @ i3 @ ( monito2027355080ogress @ a @ sigma @ phi @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_2_assms_I1_J,axiom,
% 0.31/1.55 prefix_of @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi @ sigma ).
% 0.31/1.55
% 0.31/1.55 thf(fact_3_nat__neq__iff,axiom,
% 0.31/1.55 ! [M: nat,N: nat] :
% 0.31/1.55 ( ( M != N )
% 0.31/1.55 = ( ( ord_less @ nat @ M @ N )
% 0.31/1.55 | ( ord_less @ nat @ N @ M ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_4_less__not__refl,axiom,
% 0.31/1.55 ! [N: nat] :
% 0.31/1.55 ~ ( ord_less @ nat @ N @ N ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_5_less__not__refl2,axiom,
% 0.31/1.55 ! [N: nat,M: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ N @ M )
% 0.31/1.55 => ( M != N ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_6_less__not__refl3,axiom,
% 0.31/1.55 ! [S: nat,T: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ S @ T )
% 0.31/1.55 => ( S != T ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_7_less__irrefl__nat,axiom,
% 0.31/1.55 ! [N: nat] :
% 0.31/1.55 ~ ( ord_less @ nat @ N @ N ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_8_nat__less__induct,axiom,
% 0.31/1.55 ! [P: nat > $o,N: nat] :
% 0.31/1.55 ( ! [N2: nat] :
% 0.31/1.55 ( ! [M2: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ M2 @ N2 )
% 0.31/1.55 => ( P @ M2 ) )
% 0.31/1.55 => ( P @ N2 ) )
% 0.31/1.55 => ( P @ N ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_9_infinite__descent,axiom,
% 0.31/1.55 ! [P: nat > $o,N: nat] :
% 0.31/1.55 ( ! [N2: nat] :
% 0.31/1.55 ( ~ ( P @ N2 )
% 0.31/1.55 => ? [M2: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ M2 @ N2 )
% 0.31/1.55 & ~ ( P @ M2 ) ) )
% 0.31/1.55 => ( P @ N ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_10_linorder__neqE__nat,axiom,
% 0.31/1.55 ! [X: nat,Y: nat] :
% 0.31/1.55 ( ( X != Y )
% 0.31/1.55 => ( ~ ( ord_less @ nat @ X @ Y )
% 0.31/1.55 => ( ord_less @ nat @ Y @ X ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_11_infinite__descent__measure,axiom,
% 0.31/1.55 ! [A: $tType,P: A > $o,V: A > nat,X: A] :
% 0.31/1.55 ( ! [X2: A] :
% 0.31/1.55 ( ~ ( P @ X2 )
% 0.31/1.55 => ? [Y2: A] :
% 0.31/1.55 ( ( ord_less @ nat @ ( V @ Y2 ) @ ( V @ X2 ) )
% 0.31/1.55 & ~ ( P @ Y2 ) ) )
% 0.31/1.55 => ( P @ X ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_12__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.31/1.55 ord_less_eq @ nat @ j @ ( monito2027355080ogress @ a @ sigma @ phi_1 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_13_minf_I11_J,axiom,
% 0.31/1.55 ! [C: $tType,D: $tType] :
% 0.31/1.55 ( ( ord @ C )
% 0.31/1.55 => ! [F: D] :
% 0.31/1.55 ? [Z: C] :
% 0.31/1.55 ! [X3: C] :
% 0.31/1.55 ( ( ord_less @ C @ X3 @ Z )
% 0.31/1.55 => ( F = F ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_14_assms_I2_J,axiom,
% 0.31/1.55 prefix_of @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi @ sigma2 ).
% 0.31/1.55
% 0.31/1.55 thf(fact_15__092_060open_062j_____A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.31/1.55 ord_less_eq @ nat @ j @ ( monito2027355080ogress @ a @ sigma @ phi_2 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_16_le__refl,axiom,
% 0.31/1.55 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_17_le__trans,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/1.55 => ( ( ord_less_eq @ nat @ J @ K )
% 0.31/1.55 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_18_eq__imp__le,axiom,
% 0.31/1.55 ! [M: nat,N: nat] :
% 0.31/1.55 ( ( M = N )
% 0.31/1.55 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_19_le__antisym,axiom,
% 0.31/1.55 ! [M: nat,N: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ M @ N )
% 0.31/1.55 => ( ( ord_less_eq @ nat @ N @ M )
% 0.31/1.55 => ( M = N ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_20_nat__le__linear,axiom,
% 0.31/1.55 ! [M: nat,N: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ M @ N )
% 0.31/1.55 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_21_Nat_Oex__has__greatest__nat,axiom,
% 0.31/1.55 ! [P: nat > $o,K: nat,B2: nat] :
% 0.31/1.55 ( ( P @ K )
% 0.31/1.55 => ( ! [Y3: nat] :
% 0.31/1.55 ( ( P @ Y3 )
% 0.31/1.55 => ( ord_less_eq @ nat @ Y3 @ B2 ) )
% 0.31/1.55 => ? [X2: nat] :
% 0.31/1.55 ( ( P @ X2 )
% 0.31/1.55 & ! [Y2: nat] :
% 0.31/1.55 ( ( P @ Y2 )
% 0.31/1.55 => ( ord_less_eq @ nat @ Y2 @ X2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_22_progress__le,axiom,
% 0.31/1.55 ! [A: $tType,Sigma: trace @ ( product_prod @ ( list @ char ) @ ( list @ A ) ),Phi: formula @ A,J: nat] : ( ord_less_eq @ nat @ ( monito2027355080ogress @ A @ Sigma @ Phi @ J ) @ J ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_23_progress__mono,axiom,
% 0.31/1.55 ! [A: $tType,J: nat,J2: nat,Sigma: trace @ ( product_prod @ ( list @ char ) @ ( list @ A ) ),Phi: formula @ A] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ J @ J2 )
% 0.31/1.55 => ( ord_less_eq @ nat @ ( monito2027355080ogress @ A @ Sigma @ Phi @ J ) @ ( monito2027355080ogress @ A @ Sigma @ Phi @ J2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_24_pinf_I6_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [T: A] :
% 0.31/1.55 ? [Z: A] :
% 0.31/1.55 ! [X3: A] :
% 0.31/1.55 ( ( ord_less @ A @ Z @ X3 )
% 0.31/1.55 => ~ ( ord_less_eq @ A @ X3 @ T ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_25_pinf_I8_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [T: A] :
% 0.31/1.55 ? [Z: A] :
% 0.31/1.55 ! [X3: A] :
% 0.31/1.55 ( ( ord_less @ A @ Z @ X3 )
% 0.31/1.55 => ( ord_less_eq @ A @ T @ X3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_26_minf_I6_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [T: A] :
% 0.31/1.55 ? [Z: A] :
% 0.31/1.55 ! [X3: A] :
% 0.31/1.55 ( ( ord_less @ A @ X3 @ Z )
% 0.31/1.55 => ( ord_less_eq @ A @ X3 @ T ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_27_minf_I8_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [T: A] :
% 0.31/1.55 ? [Z: A] :
% 0.31/1.55 ! [X3: A] :
% 0.31/1.55 ( ( ord_less @ A @ X3 @ Z )
% 0.31/1.55 => ~ ( ord_less_eq @ A @ T @ X3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_28_less__mono__imp__le__mono,axiom,
% 0.31/1.55 ! [F2: nat > nat,I: nat,J: nat] :
% 0.31/1.55 ( ! [I2: nat,J3: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ I2 @ J3 )
% 0.31/1.55 => ( ord_less @ nat @ ( F2 @ I2 ) @ ( F2 @ J3 ) ) )
% 0.31/1.55 => ( ( ord_less_eq @ nat @ I @ J )
% 0.31/1.55 => ( ord_less_eq @ nat @ ( F2 @ I ) @ ( F2 @ J ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_29_le__neq__implies__less,axiom,
% 0.31/1.55 ! [M: nat,N: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ M @ N )
% 0.31/1.55 => ( ( M != N )
% 0.31/1.55 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_30_less__or__eq__imp__le,axiom,
% 0.31/1.55 ! [M: nat,N: nat] :
% 0.31/1.55 ( ( ( ord_less @ nat @ M @ N )
% 0.31/1.55 | ( M = N ) )
% 0.31/1.55 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_31_le__eq__less__or__eq,axiom,
% 0.31/1.55 ( ( ord_less_eq @ nat )
% 0.31/1.55 = ( ^ [M3: nat,N3: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ M3 @ N3 )
% 0.31/1.55 | ( M3 = N3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_32_less__imp__le__nat,axiom,
% 0.31/1.55 ! [M: nat,N: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ M @ N )
% 0.31/1.55 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_33_nat__less__le,axiom,
% 0.31/1.55 ( ( ord_less @ nat )
% 0.31/1.55 = ( ^ [M3: nat,N3: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ M3 @ N3 )
% 0.31/1.55 & ( M3 != N3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_34_progress__prefix__conv,axiom,
% 0.31/1.55 ! [A: $tType,Pi: prefix @ ( product_prod @ ( list @ char ) @ ( list @ A ) ),Sigma: trace @ ( product_prod @ ( list @ char ) @ ( list @ A ) ),Sigma2: trace @ ( product_prod @ ( list @ char ) @ ( list @ A ) ),Phi: formula @ A] :
% 0.31/1.55 ( ( prefix_of @ ( product_prod @ ( list @ char ) @ ( list @ A ) ) @ Pi @ Sigma )
% 0.31/1.55 => ( ( prefix_of @ ( product_prod @ ( list @ char ) @ ( list @ A ) ) @ Pi @ Sigma2 )
% 0.31/1.55 => ( ( monito2027355080ogress @ A @ Sigma @ Phi @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ A ) ) @ Pi ) )
% 0.31/1.55 = ( monito2027355080ogress @ A @ Sigma2 @ Phi @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ A ) ) @ Pi ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_35_measure__induct__rule,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType] :
% 0.31/1.55 ( ( wellorder @ B )
% 0.31/1.55 => ! [F2: A > B,P: A > $o,A2: A] :
% 0.31/1.55 ( ! [X2: A] :
% 0.31/1.55 ( ! [Y2: A] :
% 0.31/1.55 ( ( ord_less @ B @ ( F2 @ Y2 ) @ ( F2 @ X2 ) )
% 0.31/1.55 => ( P @ Y2 ) )
% 0.31/1.55 => ( P @ X2 ) )
% 0.31/1.55 => ( P @ A2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_36_measure__induct,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType] :
% 0.31/1.55 ( ( wellorder @ B )
% 0.31/1.55 => ! [F2: A > B,P: A > $o,A2: A] :
% 0.31/1.55 ( ! [X2: A] :
% 0.31/1.55 ( ! [Y2: A] :
% 0.31/1.55 ( ( ord_less @ B @ ( F2 @ Y2 ) @ ( F2 @ X2 ) )
% 0.31/1.55 => ( P @ Y2 ) )
% 0.31/1.55 => ( P @ X2 ) )
% 0.31/1.55 => ( P @ A2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_37_pinf_I1_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.31/1.55 ( ? [Z2: A] :
% 0.31/1.55 ! [X2: A] :
% 0.31/1.55 ( ( ord_less @ A @ Z2 @ X2 )
% 0.31/1.55 => ( ( P @ X2 )
% 0.31/1.55 = ( P2 @ X2 ) ) )
% 0.31/1.55 => ( ? [Z2: A] :
% 0.31/1.55 ! [X2: A] :
% 0.31/1.55 ( ( ord_less @ A @ Z2 @ X2 )
% 0.31/1.55 => ( ( Q @ X2 )
% 0.31/1.55 = ( Q2 @ X2 ) ) )
% 0.31/1.55 => ? [Z: A] :
% 0.31/1.55 ! [X3: A] :
% 0.31/1.55 ( ( ord_less @ A @ Z @ X3 )
% 0.31/1.55 => ( ( ( P @ X3 )
% 0.31/1.55 & ( Q @ X3 ) )
% 0.31/1.55 = ( ( P2 @ X3 )
% 0.31/1.55 & ( Q2 @ X3 ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_38_pinf_I2_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.31/1.55 ( ? [Z2: A] :
% 0.31/1.55 ! [X2: A] :
% 0.31/1.55 ( ( ord_less @ A @ Z2 @ X2 )
% 0.31/1.55 => ( ( P @ X2 )
% 0.31/1.55 = ( P2 @ X2 ) ) )
% 0.31/1.55 => ( ? [Z2: A] :
% 0.31/1.55 ! [X2: A] :
% 0.31/1.55 ( ( ord_less @ A @ Z2 @ X2 )
% 0.31/1.55 => ( ( Q @ X2 )
% 0.31/1.55 = ( Q2 @ X2 ) ) )
% 0.31/1.55 => ? [Z: A] :
% 0.31/1.55 ! [X3: A] :
% 0.31/1.55 ( ( ord_less @ A @ Z @ X3 )
% 0.31/1.55 => ( ( ( P @ X3 )
% 0.31/1.55 | ( Q @ X3 ) )
% 0.31/1.55 = ( ( P2 @ X3 )
% 0.31/1.55 | ( Q2 @ X3 ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_39_pinf_I3_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [T: A] :
% 0.31/1.55 ? [Z: A] :
% 0.31/1.55 ! [X3: A] :
% 0.31/1.55 ( ( ord_less @ A @ Z @ X3 )
% 0.31/1.55 => ( X3 != T ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_40_pinf_I4_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [T: A] :
% 0.31/1.55 ? [Z: A] :
% 0.31/1.55 ! [X3: A] :
% 0.31/1.55 ( ( ord_less @ A @ Z @ X3 )
% 0.31/1.55 => ( X3 != T ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_41_pinf_I5_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [T: A] :
% 0.31/1.55 ? [Z: A] :
% 0.31/1.55 ! [X3: A] :
% 0.31/1.55 ( ( ord_less @ A @ Z @ X3 )
% 0.31/1.55 => ~ ( ord_less @ A @ X3 @ T ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_42_pinf_I7_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [T: A] :
% 0.31/1.55 ? [Z: A] :
% 0.31/1.55 ! [X3: A] :
% 0.31/1.55 ( ( ord_less @ A @ Z @ X3 )
% 0.31/1.55 => ( ord_less @ A @ T @ X3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_43_pinf_I11_J,axiom,
% 0.31/1.55 ! [C: $tType,D: $tType] :
% 0.31/1.55 ( ( ord @ C )
% 0.31/1.55 => ! [F: D] :
% 0.31/1.55 ? [Z: C] :
% 0.31/1.55 ! [X3: C] :
% 0.31/1.55 ( ( ord_less @ C @ Z @ X3 )
% 0.31/1.55 => ( F = F ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_44_minf_I1_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.31/1.55 ( ? [Z2: A] :
% 0.31/1.55 ! [X2: A] :
% 0.31/1.55 ( ( ord_less @ A @ X2 @ Z2 )
% 0.31/1.55 => ( ( P @ X2 )
% 0.31/1.55 = ( P2 @ X2 ) ) )
% 0.31/1.55 => ( ? [Z2: A] :
% 0.31/1.55 ! [X2: A] :
% 0.31/1.55 ( ( ord_less @ A @ X2 @ Z2 )
% 0.31/1.55 => ( ( Q @ X2 )
% 0.31/1.55 = ( Q2 @ X2 ) ) )
% 0.31/1.55 => ? [Z: A] :
% 0.31/1.55 ! [X3: A] :
% 0.31/1.55 ( ( ord_less @ A @ X3 @ Z )
% 0.31/1.55 => ( ( ( P @ X3 )
% 0.31/1.55 & ( Q @ X3 ) )
% 0.31/1.55 = ( ( P2 @ X3 )
% 0.31/1.55 & ( Q2 @ X3 ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_45_minf_I2_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.31/1.55 ( ? [Z2: A] :
% 0.31/1.55 ! [X2: A] :
% 0.31/1.55 ( ( ord_less @ A @ X2 @ Z2 )
% 0.31/1.55 => ( ( P @ X2 )
% 0.31/1.55 = ( P2 @ X2 ) ) )
% 0.31/1.55 => ( ? [Z2: A] :
% 0.31/1.55 ! [X2: A] :
% 0.31/1.55 ( ( ord_less @ A @ X2 @ Z2 )
% 0.31/1.55 => ( ( Q @ X2 )
% 0.31/1.55 = ( Q2 @ X2 ) ) )
% 0.31/1.55 => ? [Z: A] :
% 0.31/1.55 ! [X3: A] :
% 0.31/1.55 ( ( ord_less @ A @ X3 @ Z )
% 0.31/1.55 => ( ( ( P @ X3 )
% 0.31/1.55 | ( Q @ X3 ) )
% 0.31/1.55 = ( ( P2 @ X3 )
% 0.31/1.55 | ( Q2 @ X3 ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_46_minf_I3_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [T: A] :
% 0.31/1.55 ? [Z: A] :
% 0.31/1.55 ! [X3: A] :
% 0.31/1.55 ( ( ord_less @ A @ X3 @ Z )
% 0.31/1.55 => ( X3 != T ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_47_minf_I4_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [T: A] :
% 0.31/1.55 ? [Z: A] :
% 0.31/1.55 ! [X3: A] :
% 0.31/1.55 ( ( ord_less @ A @ X3 @ Z )
% 0.31/1.55 => ( X3 != T ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_48_minf_I5_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [T: A] :
% 0.31/1.55 ? [Z: A] :
% 0.31/1.55 ! [X3: A] :
% 0.31/1.55 ( ( ord_less @ A @ X3 @ Z )
% 0.31/1.55 => ( ord_less @ A @ X3 @ T ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_49_minf_I7_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [T: A] :
% 0.31/1.55 ? [Z: A] :
% 0.31/1.55 ! [X3: A] :
% 0.31/1.55 ( ( ord_less @ A @ X3 @ Z )
% 0.31/1.55 => ~ ( ord_less @ A @ T @ X3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_50__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.31/1.55 ord_less_eq @ nat @ ja @ ( monito2027355080ogress @ a @ sigma2 @ phi_1 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_51_order__refl,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( preorder @ A )
% 0.31/1.55 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_52_Until_OIH_I1_J,axiom,
% 0.31/1.55 ! [I: nat,V2: list @ a] :
% 0.31/1.55 ( ( ord_less @ nat @ I @ ( monito2027355080ogress @ a @ sigma @ phi_1 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) )
% 0.31/1.55 => ( ( sat @ a @ sigma @ V2 @ I @ phi_1 )
% 0.31/1.55 = ( sat @ a @ sigma2 @ V2 @ I @ phi_1 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_53_Lattices__Big_Oex__has__greatest__nat,axiom,
% 0.31/1.55 ! [A: $tType,P: A > $o,K: A,F2: A > nat,B2: nat] :
% 0.31/1.55 ( ( P @ K )
% 0.31/1.55 => ( ! [Y3: A] :
% 0.31/1.55 ( ( P @ Y3 )
% 0.31/1.55 => ( ord_less @ nat @ ( F2 @ Y3 ) @ B2 ) )
% 0.31/1.55 => ? [X2: A] :
% 0.31/1.55 ( ( P @ X2 )
% 0.31/1.55 & ! [Y2: A] :
% 0.31/1.55 ( ( P @ Y2 )
% 0.31/1.55 => ( ord_less_eq @ nat @ ( F2 @ Y2 ) @ ( F2 @ X2 ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_54_nat__descend__induct,axiom,
% 0.31/1.55 ! [N: nat,P: nat > $o,M: nat] :
% 0.31/1.55 ( ! [K2: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ N @ K2 )
% 0.31/1.55 => ( P @ K2 ) )
% 0.31/1.55 => ( ! [K2: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ K2 @ N )
% 0.31/1.55 => ( ! [I3: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ K2 @ I3 )
% 0.31/1.55 => ( P @ I3 ) )
% 0.31/1.55 => ( P @ K2 ) ) )
% 0.31/1.55 => ( P @ M ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_55_complete__interval,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( condit1037483654norder @ A )
% 0.31/1.55 => ! [A2: A,B2: A,P: A > $o] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( P @ A2 )
% 0.31/1.55 => ( ~ ( P @ B2 )
% 0.31/1.55 => ? [C2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ C2 )
% 0.31/1.55 & ( ord_less_eq @ A @ C2 @ B2 )
% 0.31/1.55 & ! [X3: A] :
% 0.31/1.55 ( ( ( ord_less_eq @ A @ A2 @ X3 )
% 0.31/1.55 & ( ord_less @ A @ X3 @ C2 ) )
% 0.31/1.55 => ( P @ X3 ) )
% 0.31/1.55 & ! [D2: A] :
% 0.31/1.55 ( ! [X2: A] :
% 0.31/1.55 ( ( ( ord_less_eq @ A @ A2 @ X2 )
% 0.31/1.55 & ( ord_less @ A @ X2 @ D2 ) )
% 0.31/1.55 => ( P @ X2 ) )
% 0.31/1.55 => ( ord_less_eq @ A @ D2 @ C2 ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_56_order_Onot__eq__order__implies__strict,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( A2 != B2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_57_dual__order_Ostrict__implies__order,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [B2: A,A2: A] :
% 0.31/1.55 ( ( ord_less @ A @ B2 @ A2 )
% 0.31/1.55 => ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_58_dual__order_Ostrict__iff__order,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ( ( ord_less @ A )
% 0.31/1.55 = ( ^ [B3: A,A3: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.31/1.55 & ( A3 != B3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_59_dual__order_Oorder__iff__strict,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ( ( ord_less_eq @ A )
% 0.31/1.55 = ( ^ [B3: A,A3: A] :
% 0.31/1.55 ( ( ord_less @ A @ B3 @ A3 )
% 0.31/1.55 | ( A3 = B3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_60_order_Ostrict__implies__order,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.55 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_61__092_060open_062j_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.31/1.55 ord_less_eq @ nat @ ja @ ( monito2027355080ogress @ a @ sigma2 @ phi_2 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_62_Until_OIH_I2_J,axiom,
% 0.31/1.55 ! [I: nat,V2: list @ a] :
% 0.31/1.55 ( ( ord_less @ nat @ I @ ( monito2027355080ogress @ a @ sigma @ phi_2 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) )
% 0.31/1.55 => ( ( sat @ a @ sigma @ V2 @ I @ phi_2 )
% 0.31/1.55 = ( sat @ a @ sigma2 @ V2 @ I @ phi_2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_63_dual__order_Oantisym,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [B2: A,A2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( A2 = B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_64_dual__order_Oeq__iff,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.31/1.55 = ( ^ [A3: A,B3: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.31/1.55 & ( ord_less_eq @ A @ A3 @ B3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_65_dual__order_Otrans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [B2: A,A2: A,C3: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ C3 @ B2 )
% 0.31/1.55 => ( ord_less_eq @ A @ C3 @ A2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_66_linorder__wlog,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.31/1.55 ( ! [A4: A,B4: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A4 @ B4 )
% 0.31/1.55 => ( P @ A4 @ B4 ) )
% 0.31/1.55 => ( ! [A4: A,B4: A] :
% 0.31/1.55 ( ( P @ B4 @ A4 )
% 0.31/1.55 => ( P @ A4 @ B4 ) )
% 0.31/1.55 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_67_dual__order_Orefl,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_68_order__trans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( preorder @ A )
% 0.31/1.55 => ! [X: A,Y: A,Z4: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/1.55 => ( ( ord_less_eq @ A @ Y @ Z4 )
% 0.31/1.55 => ( ord_less_eq @ A @ X @ Z4 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_69_order__class_Oorder_Oantisym,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.31/1.55 => ( A2 = B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_70_ord__le__eq__trans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ord @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( B2 = C3 )
% 0.31/1.55 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_71_ord__eq__le__trans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ord @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A] :
% 0.31/1.55 ( ( A2 = B2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ B2 @ C3 )
% 0.31/1.55 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_72_order__class_Oorder_Oeq__iff,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.31/1.55 = ( ^ [A3: A,B3: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.31/1.55 & ( ord_less_eq @ A @ B3 @ A3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_73_antisym__conv,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [Y: A,X: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ Y @ X )
% 0.31/1.55 => ( ( ord_less_eq @ A @ X @ Y )
% 0.31/1.55 = ( X = Y ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_74_le__cases3,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [X: A,Y: A,Z4: A] :
% 0.31/1.55 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.31/1.55 => ~ ( ord_less_eq @ A @ Y @ Z4 ) )
% 0.31/1.55 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.31/1.55 => ~ ( ord_less_eq @ A @ X @ Z4 ) )
% 0.31/1.55 => ( ( ( ord_less_eq @ A @ X @ Z4 )
% 0.31/1.55 => ~ ( ord_less_eq @ A @ Z4 @ Y ) )
% 0.31/1.55 => ( ( ( ord_less_eq @ A @ Z4 @ Y )
% 0.31/1.55 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.31/1.55 => ( ( ( ord_less_eq @ A @ Y @ Z4 )
% 0.31/1.55 => ~ ( ord_less_eq @ A @ Z4 @ X ) )
% 0.31/1.55 => ~ ( ( ord_less_eq @ A @ Z4 @ X )
% 0.31/1.55 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_75_order_Otrans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ B2 @ C3 )
% 0.31/1.55 => ( ord_less_eq @ A @ A2 @ C3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_76_le__cases,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.31/1.55 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_77_eq__refl,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( preorder @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( X = Y )
% 0.31/1.55 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_78_linear,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/1.55 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_79_antisym,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/1.55 => ( ( ord_less_eq @ A @ Y @ X )
% 0.31/1.55 => ( X = Y ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_80_eq__iff,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ( ( ^ [Y4: A,Z3: A] : ( Y4 = Z3 ) )
% 0.31/1.55 = ( ^ [X4: A,Y5: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.31/1.55 & ( ord_less_eq @ A @ Y5 @ X4 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_81_ord__le__eq__subst,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType] :
% 0.31/1.55 ( ( ( ord @ B )
% 0.31/1.55 & ( ord @ A ) )
% 0.31/1.55 => ! [A2: A,B2: A,F2: A > B,C3: B] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ( F2 @ B2 )
% 0.31/1.55 = C3 )
% 0.31/1.55 => ( ! [X2: A,Y3: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.31/1.55 => ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.31/1.55 => ( ord_less_eq @ B @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_82_ord__eq__le__subst,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType] :
% 0.31/1.55 ( ( ( ord @ B )
% 0.31/1.55 & ( ord @ A ) )
% 0.31/1.55 => ! [A2: A,F2: B > A,B2: B,C3: B] :
% 0.31/1.55 ( ( A2
% 0.31/1.55 = ( F2 @ B2 ) )
% 0.31/1.55 => ( ( ord_less_eq @ B @ B2 @ C3 )
% 0.31/1.55 => ( ! [X2: B,Y3: B] :
% 0.31/1.55 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 0.31/1.55 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.31/1.55 => ( ord_less_eq @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_83_order__subst2,axiom,
% 0.31/1.55 ! [A: $tType,C: $tType] :
% 0.31/1.55 ( ( ( order @ C )
% 0.31/1.55 & ( order @ A ) )
% 0.31/1.55 => ! [A2: A,B2: A,F2: A > C,C3: C] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ord_less_eq @ C @ ( F2 @ B2 ) @ C3 )
% 0.31/1.55 => ( ! [X2: A,Y3: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.31/1.55 => ( ord_less_eq @ C @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.31/1.55 => ( ord_less_eq @ C @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_84_order__subst1,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType] :
% 0.31/1.55 ( ( ( order @ B )
% 0.31/1.55 & ( order @ A ) )
% 0.31/1.55 => ! [A2: A,F2: B > A,B2: B,C3: B] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ ( F2 @ B2 ) )
% 0.31/1.55 => ( ( ord_less_eq @ B @ B2 @ C3 )
% 0.31/1.55 => ( ! [X2: B,Y3: B] :
% 0.31/1.55 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 0.31/1.55 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.31/1.55 => ( ord_less_eq @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_85_le__fun__def,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType] :
% 0.31/1.55 ( ( ord @ B )
% 0.31/1.55 => ( ( ord_less_eq @ ( A > B ) )
% 0.31/1.55 = ( ^ [F3: A > B,G: A > B] :
% 0.31/1.55 ! [X4: A] : ( ord_less_eq @ B @ ( F3 @ X4 ) @ ( G @ X4 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_86_le__funI,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType] :
% 0.31/1.55 ( ( ord @ B )
% 0.31/1.55 => ! [F2: A > B,G2: A > B] :
% 0.31/1.55 ( ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) )
% 0.31/1.55 => ( ord_less_eq @ ( A > B ) @ F2 @ G2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_87_le__funE,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType] :
% 0.31/1.55 ( ( ord @ B )
% 0.31/1.55 => ! [F2: A > B,G2: A > B,X: A] :
% 0.31/1.55 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.31/1.55 => ( ord_less_eq @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_88_le__funD,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType] :
% 0.31/1.55 ( ( ord @ B )
% 0.31/1.55 => ! [F2: A > B,G2: A > B,X: A] :
% 0.31/1.55 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.31/1.55 => ( ord_less_eq @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_89_ord__eq__less__subst,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType] :
% 0.31/1.55 ( ( ( ord @ B )
% 0.31/1.55 & ( ord @ A ) )
% 0.31/1.55 => ! [A2: A,F2: B > A,B2: B,C3: B] :
% 0.31/1.55 ( ( A2
% 0.31/1.55 = ( F2 @ B2 ) )
% 0.31/1.55 => ( ( ord_less @ B @ B2 @ C3 )
% 0.31/1.55 => ( ! [X2: B,Y3: B] :
% 0.31/1.55 ( ( ord_less @ B @ X2 @ Y3 )
% 0.31/1.55 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.31/1.55 => ( ord_less @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_90_ord__less__eq__subst,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType] :
% 0.31/1.55 ( ( ( ord @ B )
% 0.31/1.55 & ( ord @ A ) )
% 0.31/1.55 => ! [A2: A,B2: A,F2: A > B,C3: B] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ( F2 @ B2 )
% 0.31/1.55 = C3 )
% 0.31/1.55 => ( ! [X2: A,Y3: A] :
% 0.31/1.55 ( ( ord_less @ A @ X2 @ Y3 )
% 0.31/1.55 => ( ord_less @ B @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.31/1.55 => ( ord_less @ B @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_91_order__less__subst1,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType] :
% 0.31/1.55 ( ( ( order @ B )
% 0.31/1.55 & ( order @ A ) )
% 0.31/1.55 => ! [A2: A,F2: B > A,B2: B,C3: B] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ ( F2 @ B2 ) )
% 0.31/1.55 => ( ( ord_less @ B @ B2 @ C3 )
% 0.31/1.55 => ( ! [X2: B,Y3: B] :
% 0.31/1.55 ( ( ord_less @ B @ X2 @ Y3 )
% 0.31/1.55 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.31/1.55 => ( ord_less @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_92_order__less__subst2,axiom,
% 0.31/1.55 ! [A: $tType,C: $tType] :
% 0.31/1.55 ( ( ( order @ C )
% 0.31/1.55 & ( order @ A ) )
% 0.31/1.55 => ! [A2: A,B2: A,F2: A > C,C3: C] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ord_less @ C @ ( F2 @ B2 ) @ C3 )
% 0.31/1.55 => ( ! [X2: A,Y3: A] :
% 0.31/1.55 ( ( ord_less @ A @ X2 @ Y3 )
% 0.31/1.55 => ( ord_less @ C @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.31/1.55 => ( ord_less @ C @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_93_lt__ex,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( no_bot @ A )
% 0.31/1.55 => ! [X: A] :
% 0.31/1.55 ? [Y3: A] : ( ord_less @ A @ Y3 @ X ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_94_gt__ex,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( no_top @ A )
% 0.31/1.55 => ! [X: A] :
% 0.31/1.55 ? [X_1: A] : ( ord_less @ A @ X @ X_1 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_95_neqE,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( X != Y )
% 0.31/1.55 => ( ~ ( ord_less @ A @ X @ Y )
% 0.31/1.55 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_96_neq__iff,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( X != Y )
% 0.31/1.55 = ( ( ord_less @ A @ X @ Y )
% 0.31/1.55 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_97_order_Oasym,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.55 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_98_dense,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( dense_order @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ord_less @ A @ X @ Y )
% 0.31/1.55 => ? [Z: A] :
% 0.31/1.55 ( ( ord_less @ A @ X @ Z )
% 0.31/1.55 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_99_less__imp__neq,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ord_less @ A @ X @ Y )
% 0.31/1.55 => ( X != Y ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_100_less__asym,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( preorder @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ord_less @ A @ X @ Y )
% 0.31/1.55 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_101_less__asym_H,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( preorder @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.55 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_102_less__trans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( preorder @ A )
% 0.31/1.55 => ! [X: A,Y: A,Z4: A] :
% 0.31/1.55 ( ( ord_less @ A @ X @ Y )
% 0.31/1.55 => ( ( ord_less @ A @ Y @ Z4 )
% 0.31/1.55 => ( ord_less @ A @ X @ Z4 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_103_less__linear,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ord_less @ A @ X @ Y )
% 0.31/1.55 | ( X = Y )
% 0.31/1.55 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_104_less__irrefl,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( preorder @ A )
% 0.31/1.55 => ! [X: A] :
% 0.31/1.55 ~ ( ord_less @ A @ X @ X ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_105_ord__eq__less__trans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ord @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A] :
% 0.31/1.55 ( ( A2 = B2 )
% 0.31/1.55 => ( ( ord_less @ A @ B2 @ C3 )
% 0.31/1.55 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_106_ord__less__eq__trans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ord @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( B2 = C3 )
% 0.31/1.55 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_107_dual__order_Oasym,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [B2: A,A2: A] :
% 0.31/1.55 ( ( ord_less @ A @ B2 @ A2 )
% 0.31/1.55 => ~ ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_108_less__imp__not__eq,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ord_less @ A @ X @ Y )
% 0.31/1.55 => ( X != Y ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_109_less__not__sym,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( preorder @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ord_less @ A @ X @ Y )
% 0.31/1.55 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_110_less__induct,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( wellorder @ A )
% 0.31/1.55 => ! [P: A > $o,A2: A] :
% 0.31/1.55 ( ! [X2: A] :
% 0.31/1.55 ( ! [Y2: A] :
% 0.31/1.55 ( ( ord_less @ A @ Y2 @ X2 )
% 0.31/1.55 => ( P @ Y2 ) )
% 0.31/1.55 => ( P @ X2 ) )
% 0.31/1.55 => ( P @ A2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_111_antisym__conv3,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [Y: A,X: A] :
% 0.31/1.55 ( ~ ( ord_less @ A @ Y @ X )
% 0.31/1.55 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.31/1.55 = ( X = Y ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_112_less__imp__not__eq2,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ord_less @ A @ X @ Y )
% 0.31/1.55 => ( Y != X ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_113_less__imp__triv,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( preorder @ A )
% 0.31/1.55 => ! [X: A,Y: A,P: $o] :
% 0.31/1.55 ( ( ord_less @ A @ X @ Y )
% 0.31/1.55 => ( ( ord_less @ A @ Y @ X )
% 0.31/1.55 => P ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_114_linorder__cases,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ~ ( ord_less @ A @ X @ Y )
% 0.31/1.55 => ( ( X != Y )
% 0.31/1.55 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_115_dual__order_Oirrefl,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [A2: A] :
% 0.31/1.55 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_116_order_Ostrict__trans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ord_less @ A @ B2 @ C3 )
% 0.31/1.55 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_117_less__imp__not__less,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( preorder @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ord_less @ A @ X @ Y )
% 0.31/1.55 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_118_exists__least__iff,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( wellorder @ A )
% 0.31/1.55 => ( ( ^ [P3: A > $o] :
% 0.31/1.55 ? [X5: A] : ( P3 @ X5 ) )
% 0.31/1.55 = ( ^ [P4: A > $o] :
% 0.31/1.55 ? [N3: A] :
% 0.31/1.55 ( ( P4 @ N3 )
% 0.31/1.55 & ! [M3: A] :
% 0.31/1.55 ( ( ord_less @ A @ M3 @ N3 )
% 0.31/1.55 => ~ ( P4 @ M3 ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_119_linorder__less__wlog,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.31/1.55 ( ! [A4: A,B4: A] :
% 0.31/1.55 ( ( ord_less @ A @ A4 @ B4 )
% 0.31/1.55 => ( P @ A4 @ B4 ) )
% 0.31/1.55 => ( ! [A4: A] : ( P @ A4 @ A4 )
% 0.31/1.55 => ( ! [A4: A,B4: A] :
% 0.31/1.55 ( ( P @ B4 @ A4 )
% 0.31/1.55 => ( P @ A4 @ B4 ) )
% 0.31/1.55 => ( P @ A2 @ B2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_120_dual__order_Ostrict__trans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [B2: A,A2: A,C3: A] :
% 0.31/1.55 ( ( ord_less @ A @ B2 @ A2 )
% 0.31/1.55 => ( ( ord_less @ A @ C3 @ B2 )
% 0.31/1.55 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_121_not__less__iff__gr__or__eq,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.31/1.55 = ( ( ord_less @ A @ Y @ X )
% 0.31/1.55 | ( X = Y ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_122_order_Ostrict__implies__not__eq,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.55 => ( A2 != B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_123_dual__order_Ostrict__implies__not__eq,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [B2: A,A2: A] :
% 0.31/1.55 ( ( ord_less @ A @ B2 @ A2 )
% 0.31/1.55 => ( A2 != B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_124_ex__gt__or__lt,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( condit1656338222tinuum @ A )
% 0.31/1.55 => ! [A2: A] :
% 0.31/1.55 ? [B4: A] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ B4 )
% 0.31/1.55 | ( ord_less @ A @ B4 @ A2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_125_ex__has__least__nat,axiom,
% 0.31/1.55 ! [A: $tType,P: A > $o,K: A,M: A > nat] :
% 0.31/1.55 ( ( P @ K )
% 0.31/1.55 => ? [X2: A] :
% 0.31/1.55 ( ( P @ X2 )
% 0.31/1.55 & ! [Y2: A] :
% 0.31/1.55 ( ( P @ Y2 )
% 0.31/1.55 => ( ord_less_eq @ nat @ ( M @ X2 ) @ ( M @ Y2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_126_leD,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [Y: A,X: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ Y @ X )
% 0.31/1.55 => ~ ( ord_less @ A @ X @ Y ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_127_leI,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ~ ( ord_less @ A @ X @ Y )
% 0.31/1.55 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_128_le__less,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ( ( ord_less_eq @ A )
% 0.31/1.55 = ( ^ [X4: A,Y5: A] :
% 0.31/1.55 ( ( ord_less @ A @ X4 @ Y5 )
% 0.31/1.55 | ( X4 = Y5 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_129_less__le,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ( ( ord_less @ A )
% 0.31/1.55 = ( ^ [X4: A,Y5: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.31/1.55 & ( X4 != Y5 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_130_order__le__less__subst1,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType] :
% 0.31/1.55 ( ( ( order @ B )
% 0.31/1.55 & ( order @ A ) )
% 0.31/1.55 => ! [A2: A,F2: B > A,B2: B,C3: B] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ ( F2 @ B2 ) )
% 0.31/1.55 => ( ( ord_less @ B @ B2 @ C3 )
% 0.31/1.55 => ( ! [X2: B,Y3: B] :
% 0.31/1.55 ( ( ord_less @ B @ X2 @ Y3 )
% 0.31/1.55 => ( ord_less @ A @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.31/1.55 => ( ord_less @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_131_order__le__less__subst2,axiom,
% 0.31/1.55 ! [A: $tType,C: $tType] :
% 0.31/1.55 ( ( ( order @ C )
% 0.31/1.55 & ( order @ A ) )
% 0.31/1.55 => ! [A2: A,B2: A,F2: A > C,C3: C] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ord_less @ C @ ( F2 @ B2 ) @ C3 )
% 0.31/1.55 => ( ! [X2: A,Y3: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.31/1.55 => ( ord_less_eq @ C @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.31/1.55 => ( ord_less @ C @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_132_order__less__le__subst1,axiom,
% 0.31/1.55 ! [A: $tType,B: $tType] :
% 0.31/1.55 ( ( ( order @ B )
% 0.31/1.55 & ( order @ A ) )
% 0.31/1.55 => ! [A2: A,F2: B > A,B2: B,C3: B] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ ( F2 @ B2 ) )
% 0.31/1.55 => ( ( ord_less_eq @ B @ B2 @ C3 )
% 0.31/1.55 => ( ! [X2: B,Y3: B] :
% 0.31/1.55 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 0.31/1.55 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.31/1.55 => ( ord_less @ A @ A2 @ ( F2 @ C3 ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_133_order__less__le__subst2,axiom,
% 0.31/1.55 ! [A: $tType,C: $tType] :
% 0.31/1.55 ( ( ( order @ C )
% 0.31/1.55 & ( order @ A ) )
% 0.31/1.55 => ! [A2: A,B2: A,F2: A > C,C3: C] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ord_less_eq @ C @ ( F2 @ B2 ) @ C3 )
% 0.31/1.55 => ( ! [X2: A,Y3: A] :
% 0.31/1.55 ( ( ord_less @ A @ X2 @ Y3 )
% 0.31/1.55 => ( ord_less @ C @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) )
% 0.31/1.55 => ( ord_less @ C @ ( F2 @ A2 ) @ C3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_134_not__le,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ~ ( ord_less_eq @ A @ X @ Y ) )
% 0.31/1.55 = ( ord_less @ A @ Y @ X ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_135_not__less,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.31/1.55 = ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_136_le__neq__trans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( A2 != B2 )
% 0.31/1.55 => ( ord_less @ A @ A2 @ B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_137_antisym__conv1,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ~ ( ord_less @ A @ X @ Y )
% 0.31/1.55 => ( ( ord_less_eq @ A @ X @ Y )
% 0.31/1.55 = ( X = Y ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_138_antisym__conv2,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/1.55 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.31/1.55 = ( X = Y ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_139_less__imp__le,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( preorder @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ord_less @ A @ X @ Y )
% 0.31/1.55 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_140_le__less__trans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( preorder @ A )
% 0.31/1.55 => ! [X: A,Y: A,Z4: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/1.55 => ( ( ord_less @ A @ Y @ Z4 )
% 0.31/1.55 => ( ord_less @ A @ X @ Z4 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_141_less__le__trans,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( preorder @ A )
% 0.31/1.55 => ! [X: A,Y: A,Z4: A] :
% 0.31/1.55 ( ( ord_less @ A @ X @ Y )
% 0.31/1.55 => ( ( ord_less_eq @ A @ Y @ Z4 )
% 0.31/1.55 => ( ord_less @ A @ X @ Z4 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_142_dense__ge,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( dense_linorder @ A )
% 0.31/1.55 => ! [Z4: A,Y: A] :
% 0.31/1.55 ( ! [X2: A] :
% 0.31/1.55 ( ( ord_less @ A @ Z4 @ X2 )
% 0.31/1.55 => ( ord_less_eq @ A @ Y @ X2 ) )
% 0.31/1.55 => ( ord_less_eq @ A @ Y @ Z4 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_143_dense__le,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( dense_linorder @ A )
% 0.31/1.55 => ! [Y: A,Z4: A] :
% 0.31/1.55 ( ! [X2: A] :
% 0.31/1.55 ( ( ord_less @ A @ X2 @ Y )
% 0.31/1.55 => ( ord_less_eq @ A @ X2 @ Z4 ) )
% 0.31/1.55 => ( ord_less_eq @ A @ Y @ Z4 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_144_le__less__linear,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/1.55 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_145_le__imp__less__or__eq,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [X: A,Y: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/1.55 => ( ( ord_less @ A @ X @ Y )
% 0.31/1.55 | ( X = Y ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_146_less__le__not__le,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( preorder @ A )
% 0.31/1.55 => ( ( ord_less @ A )
% 0.31/1.55 = ( ^ [X4: A,Y5: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ X4 @ Y5 )
% 0.31/1.55 & ~ ( ord_less_eq @ A @ Y5 @ X4 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_147_not__le__imp__less,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [Y: A,X: A] :
% 0.31/1.55 ( ~ ( ord_less_eq @ A @ Y @ X )
% 0.31/1.55 => ( ord_less @ A @ X @ Y ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_148_order_Ostrict__trans1,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ord_less @ A @ B2 @ C3 )
% 0.31/1.55 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_149_order_Ostrict__trans2,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ B2 @ C3 )
% 0.31/1.55 => ( ord_less @ A @ A2 @ C3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_150_order_Oorder__iff__strict,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ( ( ord_less_eq @ A )
% 0.31/1.55 = ( ^ [A3: A,B3: A] :
% 0.31/1.55 ( ( ord_less @ A @ A3 @ B3 )
% 0.31/1.55 | ( A3 = B3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_151_order_Ostrict__iff__order,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ( ( ord_less @ A )
% 0.31/1.55 = ( ^ [A3: A,B3: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.31/1.55 & ( A3 != B3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_152_dual__order_Ostrict__trans1,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [B2: A,A2: A,C3: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.31/1.55 => ( ( ord_less @ A @ C3 @ B2 )
% 0.31/1.55 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_153_dual__order_Ostrict__trans2,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [B2: A,A2: A,C3: A] :
% 0.31/1.55 ( ( ord_less @ A @ B2 @ A2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ C3 @ B2 )
% 0.31/1.55 => ( ord_less @ A @ C3 @ A2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_154_dense__ge__bounded,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( dense_linorder @ A )
% 0.31/1.55 => ! [Z4: A,X: A,Y: A] :
% 0.31/1.55 ( ( ord_less @ A @ Z4 @ X )
% 0.31/1.55 => ( ! [W: A] :
% 0.31/1.55 ( ( ord_less @ A @ Z4 @ W )
% 0.31/1.55 => ( ( ord_less @ A @ W @ X )
% 0.31/1.55 => ( ord_less_eq @ A @ Y @ W ) ) )
% 0.31/1.55 => ( ord_less_eq @ A @ Y @ Z4 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_155_dense__le__bounded,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( dense_linorder @ A )
% 0.31/1.55 => ! [X: A,Y: A,Z4: A] :
% 0.31/1.55 ( ( ord_less @ A @ X @ Y )
% 0.31/1.55 => ( ! [W: A] :
% 0.31/1.55 ( ( ord_less @ A @ X @ W )
% 0.31/1.55 => ( ( ord_less @ A @ W @ Y )
% 0.31/1.55 => ( ord_less_eq @ A @ W @ Z4 ) ) )
% 0.31/1.55 => ( ord_less_eq @ A @ Y @ Z4 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_156_Until_Oprems,axiom,
% 0.31/1.55 ord_less @ nat @ ia @ ( monito2027355080ogress @ a @ sigma @ ( until @ a @ phi_1 @ i2 @ phi_2 ) @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_157_plen__mono,axiom,
% 0.31/1.55 ! [A: $tType,Pi: prefix @ A,Pi2: prefix @ A] :
% 0.31/1.55 ( ( ord_less_eq @ ( prefix @ A ) @ Pi @ Pi2 )
% 0.31/1.55 => ( ord_less_eq @ nat @ ( plen @ A @ Pi ) @ ( plen @ A @ Pi2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_158_verit__comp__simplify1_I3_J,axiom,
% 0.31/1.55 ! [B: $tType] :
% 0.31/1.55 ( ( linorder @ B )
% 0.31/1.55 => ! [B5: B,A5: B] :
% 0.31/1.55 ( ( ~ ( ord_less_eq @ B @ B5 @ A5 ) )
% 0.31/1.55 = ( ord_less @ B @ A5 @ B5 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_159__092_060open_062i_A_060_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_H_A_Iformula_OUntil_A_092_060phi_0621_AI_A_092_060phi_0622_J_A_Iplen_A_092_060pi_062_J_092_060close_062,axiom,
% 0.31/1.55 ord_less @ nat @ ia @ ( monito2027355080ogress @ a @ sigma2 @ ( until @ a @ phi_1 @ i2 @ phi_2 ) @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_160_arg__max__nat__lemma,axiom,
% 0.31/1.55 ! [A: $tType,P: A > $o,K: A,F2: A > nat,B2: nat] :
% 0.31/1.55 ( ( P @ K )
% 0.31/1.55 => ( ! [Y3: A] :
% 0.31/1.55 ( ( P @ Y3 )
% 0.31/1.55 => ( ord_less @ nat @ ( F2 @ Y3 ) @ B2 ) )
% 0.31/1.55 => ( ( P @ ( lattices_ord_arg_max @ A @ nat @ F2 @ P ) )
% 0.31/1.55 & ! [Y2: A] :
% 0.31/1.55 ( ( P @ Y2 )
% 0.31/1.55 => ( ord_less_eq @ nat @ ( F2 @ Y2 ) @ ( F2 @ ( lattices_ord_arg_max @ A @ nat @ F2 @ P ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_161_arg__max__nat__le,axiom,
% 0.31/1.55 ! [A: $tType,P: A > $o,X: A,F2: A > nat,B2: nat] :
% 0.31/1.55 ( ( P @ X )
% 0.31/1.55 => ( ! [Y3: A] :
% 0.31/1.55 ( ( P @ Y3 )
% 0.31/1.55 => ( ord_less @ nat @ ( F2 @ Y3 ) @ B2 ) )
% 0.31/1.55 => ( ord_less_eq @ nat @ ( F2 @ X ) @ ( F2 @ ( lattices_ord_arg_max @ A @ nat @ F2 @ P ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_162_progress__axioms_Ointro,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType,Progress: ( prefix @ A ) > nat,Sat: ( trace @ A ) > ( list @ B ) > nat > $o] :
% 0.31/1.55 ( ! [Pi3: prefix @ A,Pi4: prefix @ A] :
% 0.31/1.55 ( ( ord_less_eq @ ( prefix @ A ) @ Pi3 @ Pi4 )
% 0.31/1.55 => ( ord_less_eq @ nat @ ( Progress @ Pi3 ) @ ( Progress @ Pi4 ) ) )
% 0.31/1.55 => ( ! [Sigma3: trace @ A,X2: nat] :
% 0.31/1.55 ? [Pi5: prefix @ A] :
% 0.31/1.55 ( ( prefix_of @ A @ Pi5 @ Sigma3 )
% 0.31/1.55 & ( ord_less_eq @ nat @ X2 @ ( Progress @ Pi5 ) ) )
% 0.31/1.55 => ( ! [Pi3: prefix @ A,Sigma3: trace @ A,Sigma4: trace @ A,I2: nat,V3: list @ B] :
% 0.31/1.55 ( ( prefix_of @ A @ Pi3 @ Sigma3 )
% 0.31/1.55 => ( ( prefix_of @ A @ Pi3 @ Sigma4 )
% 0.31/1.55 => ( ( ord_less @ nat @ I2 @ ( Progress @ Pi3 ) )
% 0.31/1.55 => ( ( Sat @ Sigma3 @ V3 @ I2 )
% 0.31/1.55 = ( Sat @ Sigma4 @ V3 @ I2 ) ) ) ) )
% 0.31/1.55 => ( abstra417776764axioms @ A @ B @ Sat @ Progress ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_163_less__prefix__def,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ord_less @ ( prefix @ A ) )
% 0.31/1.55 = ( ^ [X4: prefix @ A,Y5: prefix @ A] :
% 0.31/1.55 ( ( ord_less_eq @ ( prefix @ A ) @ X4 @ Y5 )
% 0.31/1.55 & ~ ( ord_less_eq @ ( prefix @ A ) @ Y5 @ X4 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_164_less__fun__def,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType] :
% 0.31/1.55 ( ( ord @ B )
% 0.31/1.55 => ( ( ord_less @ ( A > B ) )
% 0.31/1.55 = ( ^ [F3: A > B,G: A > B] :
% 0.31/1.55 ( ( ord_less_eq @ ( A > B ) @ F3 @ G )
% 0.31/1.55 & ~ ( ord_less_eq @ ( A > B ) @ G @ F3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_165_arg__max__natI,axiom,
% 0.31/1.55 ! [A: $tType,P: A > $o,K: A,F2: A > nat,B2: nat] :
% 0.31/1.55 ( ( P @ K )
% 0.31/1.55 => ( ! [Y3: A] :
% 0.31/1.55 ( ( P @ Y3 )
% 0.31/1.55 => ( ord_less @ nat @ ( F2 @ Y3 ) @ B2 ) )
% 0.31/1.55 => ( P @ ( lattices_ord_arg_max @ A @ nat @ F2 @ P ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_166_arg__max__equality,axiom,
% 0.31/1.55 ! [A: $tType,C: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [P: C > $o,K: C,F2: C > A] :
% 0.31/1.55 ( ( P @ K )
% 0.31/1.55 => ( ! [X2: C] :
% 0.31/1.55 ( ( P @ X2 )
% 0.31/1.55 => ( ord_less_eq @ A @ ( F2 @ X2 ) @ ( F2 @ K ) ) )
% 0.31/1.55 => ( ( F2 @ ( lattices_ord_arg_max @ C @ A @ F2 @ P ) )
% 0.31/1.55 = ( F2 @ K ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_167_arg__maxI,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType] :
% 0.31/1.55 ( ( ord @ B )
% 0.31/1.55 => ! [P: A > $o,X: A,F2: A > B,Q: A > $o] :
% 0.31/1.55 ( ( P @ X )
% 0.31/1.55 => ( ! [Y3: A] :
% 0.31/1.55 ( ( P @ Y3 )
% 0.31/1.55 => ~ ( ord_less @ B @ ( F2 @ X ) @ ( F2 @ Y3 ) ) )
% 0.31/1.55 => ( ! [X2: A] :
% 0.31/1.55 ( ( P @ X2 )
% 0.31/1.55 => ( ! [Y2: A] :
% 0.31/1.55 ( ( P @ Y2 )
% 0.31/1.55 => ~ ( ord_less @ B @ ( F2 @ X2 ) @ ( F2 @ Y2 ) ) )
% 0.31/1.55 => ( Q @ X2 ) ) )
% 0.31/1.55 => ( Q @ ( lattices_ord_arg_max @ A @ B @ F2 @ P ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_168_verit__la__disequality,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( linorder @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( A2 = B2 )
% 0.31/1.55 | ~ ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 | ~ ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_169_verit__comp__simplify1_I1_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( order @ A )
% 0.31/1.55 => ! [A2: A] :
% 0.31/1.55 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_170_ex__prefix__of,axiom,
% 0.31/1.55 ! [A: $tType,P5: prefix @ A] :
% 0.31/1.55 ? [X_1: trace @ A] : ( prefix_of @ A @ P5 @ X_1 ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_171_prefix__of__antimono,axiom,
% 0.31/1.55 ! [A: $tType,Pi: prefix @ A,Pi2: prefix @ A,S: trace @ A] :
% 0.31/1.55 ( ( ord_less_eq @ ( prefix @ A ) @ Pi @ Pi2 )
% 0.31/1.55 => ( ( prefix_of @ A @ Pi2 @ S )
% 0.31/1.55 => ( prefix_of @ A @ Pi @ S ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_172_prefix__of__imp__linear,axiom,
% 0.31/1.55 ! [A: $tType,Pi: prefix @ A,Sigma: trace @ A,Pi2: prefix @ A] :
% 0.31/1.55 ( ( prefix_of @ A @ Pi @ Sigma )
% 0.31/1.55 => ( ( prefix_of @ A @ Pi2 @ Sigma )
% 0.31/1.55 => ( ( ord_less_eq @ ( prefix @ A ) @ Pi @ Pi2 )
% 0.31/1.55 | ( ord_less_eq @ ( prefix @ A ) @ Pi2 @ Pi ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_173_progress__axioms__def,axiom,
% 0.31/1.55 ! [B: $tType,A: $tType] :
% 0.31/1.55 ( ( abstra417776764axioms @ A @ B )
% 0.31/1.55 = ( ^ [Sat2: ( trace @ A ) > ( list @ B ) > nat > $o,Progress2: ( prefix @ A ) > nat] :
% 0.31/1.55 ( ! [Pi6: prefix @ A,Pi7: prefix @ A] :
% 0.31/1.55 ( ( ord_less_eq @ ( prefix @ A ) @ Pi6 @ Pi7 )
% 0.31/1.55 => ( ord_less_eq @ nat @ ( Progress2 @ Pi6 ) @ ( Progress2 @ Pi7 ) ) )
% 0.31/1.55 & ! [Sigma5: trace @ A,X4: nat] :
% 0.31/1.55 ? [Pi6: prefix @ A] :
% 0.31/1.55 ( ( prefix_of @ A @ Pi6 @ Sigma5 )
% 0.31/1.55 & ( ord_less_eq @ nat @ X4 @ ( Progress2 @ Pi6 ) ) )
% 0.31/1.55 & ! [Pi6: prefix @ A,Sigma5: trace @ A,Sigma6: trace @ A,I4: nat,V4: list @ B] :
% 0.31/1.55 ( ( prefix_of @ A @ Pi6 @ Sigma5 )
% 0.31/1.55 => ( ( prefix_of @ A @ Pi6 @ Sigma6 )
% 0.31/1.55 => ( ( ord_less @ nat @ I4 @ ( Progress2 @ Pi6 ) )
% 0.31/1.55 => ( ( Sat2 @ Sigma5 @ V4 @ I4 )
% 0.31/1.55 = ( Sat2 @ Sigma6 @ V4 @ I4 ) ) ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_174_formula_Oinject_I9_J,axiom,
% 0.31/1.55 ! [A: $tType,X91: formula @ A,X92: i,X93: formula @ A,Y91: formula @ A,Y92: i,Y93: formula @ A] :
% 0.31/1.55 ( ( ( until @ A @ X91 @ X92 @ X93 )
% 0.31/1.55 = ( until @ A @ Y91 @ Y92 @ Y93 ) )
% 0.31/1.55 = ( ( X91 = Y91 )
% 0.31/1.55 & ( X92 = Y92 )
% 0.31/1.55 & ( X93 = Y93 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_175__C21_C,axiom,
% 0.31/1.55 ! [K: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ K ) @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ ia ) @ b ) )
% 0.31/1.55 => ( ord_less @ nat @ K @ ( monito2027355080ogress @ a @ sigma @ phi_2 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_176__C11_C,axiom,
% 0.31/1.55 ! [K: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ K ) @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ ia ) @ b ) )
% 0.31/1.55 => ( ord_less @ nat @ K @ ( monito2027355080ogress @ a @ sigma @ phi_1 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_177_that,axiom,
% 0.31/1.55 ord_less_eq @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ k ) @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ ia ) @ b ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_178_nat__add__left__cancel__less,axiom,
% 0.31/1.55 ! [K: nat,M: nat,N: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 0.31/1.55 = ( ord_less @ nat @ M @ N ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_179_nat__add__left__cancel__le,axiom,
% 0.31/1.55 ! [K: nat,M: nat,N: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 0.31/1.55 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_180__C3_C,axiom,
% 0.31/1.55 ! [K: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ K ) @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ ia ) @ b ) )
% 0.31/1.55 => ( ord_less @ nat @ K @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_181__C1_C,axiom,
% 0.31/1.55 ! [K: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ K ) @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ ia ) @ b ) )
% 0.31/1.55 => ( ord_less @ nat @ K @ ( monito2027355080ogress @ a @ sigma @ phi_1 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_182__C2_C,axiom,
% 0.31/1.55 ! [K: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ K ) @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ ia ) @ b ) )
% 0.31/1.55 => ( ord_less @ nat @ K @ ( monito2027355080ogress @ a @ sigma @ phi_2 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_183__092_060open_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_____092_060close_062,axiom,
% 0.31/1.55 ord_less_eq @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ ia ) @ b ) @ ( one_one @ nat ) ) @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ j ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_184__092_060open_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_092_060close_062,axiom,
% 0.31/1.55 ord_less_eq @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ ia ) @ b ) @ ( one_one @ nat ) ) @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ ja ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_185_less___092_060tau_062D,axiom,
% 0.31/1.55 ! [A: $tType,Sigma: trace @ A,I: nat,J: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ ( tau @ A @ Sigma @ I ) @ ( tau @ A @ Sigma @ J ) )
% 0.31/1.55 => ( ord_less @ nat @ I @ J ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_186_ex__le___092_060tau_062,axiom,
% 0.31/1.55 ! [A: $tType,I: nat,X: nat,S: trace @ A] :
% 0.31/1.55 ? [J3: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ I @ J3 )
% 0.31/1.55 & ( ord_less_eq @ nat @ X @ ( tau @ A @ S @ J3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_187__092_060tau_062__mono,axiom,
% 0.31/1.55 ! [A: $tType,I: nat,J: nat,S: trace @ A] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/1.55 => ( ord_less_eq @ nat @ ( tau @ A @ S @ I ) @ ( tau @ A @ S @ J ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_188_less__add__eq__less,axiom,
% 0.31/1.55 ! [K: nat,L: nat,M: nat,N: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ K @ L )
% 0.31/1.55 => ( ( ( plus_plus @ nat @ M @ L )
% 0.31/1.55 = ( plus_plus @ nat @ K @ N ) )
% 0.31/1.55 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_189_trans__less__add2,axiom,
% 0.31/1.55 ! [I: nat,J: nat,M: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ I @ J )
% 0.31/1.55 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_190_trans__less__add1,axiom,
% 0.31/1.55 ! [I: nat,J: nat,M: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ I @ J )
% 0.31/1.55 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_191_add__less__mono1,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ I @ J )
% 0.31/1.55 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_192_not__add__less2,axiom,
% 0.31/1.55 ! [J: nat,I: nat] :
% 0.31/1.55 ~ ( ord_less @ nat @ ( plus_plus @ nat @ J @ I ) @ I ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_193_not__add__less1,axiom,
% 0.31/1.55 ! [I: nat,J: nat] :
% 0.31/1.55 ~ ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ I ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_194_add__less__mono,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ I @ J )
% 0.31/1.55 => ( ( ord_less @ nat @ K @ L )
% 0.31/1.55 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_195_add__lessD1,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ K )
% 0.31/1.55 => ( ord_less @ nat @ I @ K ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_196_add__leE,axiom,
% 0.31/1.55 ! [M: nat,K: nat,N: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 0.31/1.55 => ~ ( ( ord_less_eq @ nat @ M @ N )
% 0.31/1.55 => ~ ( ord_less_eq @ nat @ K @ N ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_197_le__add1,axiom,
% 0.31/1.55 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ N @ M ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_198_le__add2,axiom,
% 0.31/1.55 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ M @ N ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_199_add__leD1,axiom,
% 0.31/1.55 ! [M: nat,K: nat,N: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 0.31/1.55 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_200_add__leD2,axiom,
% 0.31/1.55 ! [M: nat,K: nat,N: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K ) @ N )
% 0.31/1.55 => ( ord_less_eq @ nat @ K @ N ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_201_le__Suc__ex,axiom,
% 0.31/1.55 ! [K: nat,L: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ K @ L )
% 0.31/1.55 => ? [N2: nat] :
% 0.31/1.55 ( L
% 0.31/1.55 = ( plus_plus @ nat @ K @ N2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_202_add__le__mono,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat,L: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/1.55 => ( ( ord_less_eq @ nat @ K @ L )
% 0.31/1.55 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_203_add__le__mono1,axiom,
% 0.31/1.55 ! [I: nat,J: nat,K: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/1.55 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K ) @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_204_trans__le__add1,axiom,
% 0.31/1.55 ! [I: nat,J: nat,M: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/1.55 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_205_trans__le__add2,axiom,
% 0.31/1.55 ! [I: nat,J: nat,M: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ I @ J )
% 0.31/1.55 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_206_nat__le__iff__add,axiom,
% 0.31/1.55 ( ( ord_less_eq @ nat )
% 0.31/1.55 = ( ^ [M3: nat,N3: nat] :
% 0.31/1.55 ? [K3: nat] :
% 0.31/1.55 ( N3
% 0.31/1.55 = ( plus_plus @ nat @ M3 @ K3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_207_ex__has__greatest__nat__lemma,axiom,
% 0.31/1.55 ! [A: $tType,P: A > $o,K: A,F2: A > nat,N: nat] :
% 0.31/1.55 ( ( P @ K )
% 0.31/1.55 => ( ! [X2: A] :
% 0.31/1.55 ( ( P @ X2 )
% 0.31/1.55 => ? [Y2: A] :
% 0.31/1.55 ( ( P @ Y2 )
% 0.31/1.55 & ~ ( ord_less_eq @ nat @ ( F2 @ Y2 ) @ ( F2 @ X2 ) ) ) )
% 0.31/1.55 => ? [Y3: A] :
% 0.31/1.55 ( ( P @ Y3 )
% 0.31/1.55 & ~ ( ord_less @ nat @ ( F2 @ Y3 ) @ ( plus_plus @ nat @ ( F2 @ K ) @ N ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_208_mono__nat__linear__lb,axiom,
% 0.31/1.55 ! [F2: nat > nat,M: nat,K: nat] :
% 0.31/1.55 ( ! [M4: nat,N2: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ M4 @ N2 )
% 0.31/1.55 => ( ord_less @ nat @ ( F2 @ M4 ) @ ( F2 @ N2 ) ) )
% 0.31/1.55 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( F2 @ M ) @ K ) @ ( F2 @ ( plus_plus @ nat @ M @ K ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_209_progress__time__conv,axiom,
% 0.31/1.55 ! [A: $tType,J: nat,Sigma: trace @ ( product_prod @ ( list @ char ) @ ( list @ A ) ),Sigma2: trace @ ( product_prod @ ( list @ char ) @ ( list @ A ) ),Phi: formula @ A] :
% 0.31/1.55 ( ! [I2: nat] :
% 0.31/1.55 ( ( ord_less @ nat @ I2 @ J )
% 0.31/1.55 => ( ( tau @ ( product_prod @ ( list @ char ) @ ( list @ A ) ) @ Sigma @ I2 )
% 0.31/1.55 = ( tau @ ( product_prod @ ( list @ char ) @ ( list @ A ) ) @ Sigma2 @ I2 ) ) )
% 0.31/1.55 => ( ( monito2027355080ogress @ A @ Sigma @ Phi @ J )
% 0.31/1.55 = ( monito2027355080ogress @ A @ Sigma2 @ Phi @ J ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_210_le___092_060tau_062__less,axiom,
% 0.31/1.55 ! [A: $tType,Sigma: trace @ A,I: nat,J: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ ( tau @ A @ Sigma @ I ) @ ( tau @ A @ Sigma @ J ) )
% 0.31/1.55 => ( ( ord_less @ nat @ J @ I )
% 0.31/1.55 => ( ( tau @ A @ Sigma @ I )
% 0.31/1.55 = ( tau @ A @ Sigma @ J ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_211__092_060tau_062__prefix__conv,axiom,
% 0.31/1.55 ! [A: $tType,P5: prefix @ A,S: trace @ A,S2: trace @ A,I: nat] :
% 0.31/1.55 ( ( prefix_of @ A @ P5 @ S )
% 0.31/1.55 => ( ( prefix_of @ A @ P5 @ S2 )
% 0.31/1.55 => ( ( ord_less @ nat @ I @ ( plen @ A @ P5 ) )
% 0.31/1.55 => ( ( tau @ A @ S @ I )
% 0.31/1.55 = ( tau @ A @ S2 @ I ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_212__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_H_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_H_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_H_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_H_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.31/1.55 ~ ! [J3: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ ia ) @ b ) @ ( one_one @ nat ) ) @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma2 @ J3 ) )
% 0.31/1.55 => ( ( ord_less_eq @ nat @ J3 @ ( monito2027355080ogress @ a @ sigma2 @ phi_1 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) )
% 0.31/1.55 => ~ ( ord_less_eq @ nat @ J3 @ ( monito2027355080ogress @ a @ sigma2 @ phi_2 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_213__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062j_O_A_092_060lbrakk_062_092_060tau_062_A_092_060sigma_062_Ai_A_L_Ab_A_L_A1_A_092_060le_062_A_092_060tau_062_A_092_060sigma_062_Aj_059_Aj_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_059_Aj_A_092_060le_062_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_A_092_060phi_0622_A_Iplen_A_092_060pi_062_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.31/1.55 ~ ! [J3: nat] :
% 0.31/1.55 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( plus_plus @ nat @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ ia ) @ b ) @ ( one_one @ nat ) ) @ ( tau @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ sigma @ J3 ) )
% 0.31/1.55 => ( ( ord_less_eq @ nat @ J3 @ ( monito2027355080ogress @ a @ sigma @ phi_1 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) )
% 0.31/1.55 => ~ ( ord_less_eq @ nat @ J3 @ ( monito2027355080ogress @ a @ sigma @ phi_2 @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_214_add__less__cancel__right,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere236663937imp_le @ A )
% 0.31/1.55 => ! [A2: A,C3: A,B2: A] :
% 0.31/1.55 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) )
% 0.31/1.55 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_215_add__left__cancel,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( cancel_semigroup_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A] :
% 0.31/1.55 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.31/1.55 = ( plus_plus @ A @ A2 @ C3 ) )
% 0.31/1.55 = ( B2 = C3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_216_add__right__cancel,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( cancel_semigroup_add @ A )
% 0.31/1.55 => ! [B2: A,A2: A,C3: A] :
% 0.31/1.55 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.31/1.55 = ( plus_plus @ A @ C3 @ A2 ) )
% 0.31/1.55 = ( B2 = C3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_217_add__le__cancel__left,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere236663937imp_le @ A )
% 0.31/1.55 => ! [C3: A,A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) )
% 0.31/1.55 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_218_add__le__cancel__right,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere236663937imp_le @ A )
% 0.31/1.55 => ! [A2: A,C3: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) )
% 0.31/1.55 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_219_add__less__cancel__left,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere236663937imp_le @ A )
% 0.31/1.55 => ! [C3: A,A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) )
% 0.31/1.55 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_220_one__reorient,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( one @ A )
% 0.31/1.55 => ! [X: A] :
% 0.31/1.55 ( ( ( one_one @ A )
% 0.31/1.55 = X )
% 0.31/1.55 = ( X
% 0.31/1.55 = ( one_one @ A ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_221_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ab_semigroup_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A] :
% 0.31/1.55 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C3 )
% 0.31/1.55 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_222_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere779506340up_add @ A )
% 0.31/1.55 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.55 ( ( ( I = J )
% 0.31/1.55 & ( K = L ) )
% 0.31/1.55 => ( ( plus_plus @ A @ I @ K )
% 0.31/1.55 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_223_group__cancel_Oadd1,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( comm_monoid_add @ A )
% 0.31/1.55 => ! [A6: A,K: A,A2: A,B2: A] :
% 0.31/1.55 ( ( A6
% 0.31/1.55 = ( plus_plus @ A @ K @ A2 ) )
% 0.31/1.55 => ( ( plus_plus @ A @ A6 @ B2 )
% 0.31/1.55 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_224_group__cancel_Oadd2,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( comm_monoid_add @ A )
% 0.31/1.55 => ! [B6: A,K: A,B2: A,A2: A] :
% 0.31/1.55 ( ( B6
% 0.31/1.55 = ( plus_plus @ A @ K @ B2 ) )
% 0.31/1.55 => ( ( plus_plus @ A @ A2 @ B6 )
% 0.31/1.55 = ( plus_plus @ A @ K @ ( plus_plus @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_225_add_Oassoc,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( semigroup_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A] :
% 0.31/1.55 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C3 )
% 0.31/1.55 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_226_add_Oleft__cancel,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( group_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A] :
% 0.31/1.55 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.31/1.55 = ( plus_plus @ A @ A2 @ C3 ) )
% 0.31/1.55 = ( B2 = C3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_227_add_Oright__cancel,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( group_add @ A )
% 0.31/1.55 => ! [B2: A,A2: A,C3: A] :
% 0.31/1.55 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.31/1.55 = ( plus_plus @ A @ C3 @ A2 ) )
% 0.31/1.55 = ( B2 = C3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_228_add_Ocommute,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ab_semigroup_add @ A )
% 0.31/1.55 => ( ( plus_plus @ A )
% 0.31/1.55 = ( ^ [A3: A,B3: A] : ( plus_plus @ A @ B3 @ A3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_229_add_Oleft__commute,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ab_semigroup_add @ A )
% 0.31/1.55 => ! [B2: A,A2: A,C3: A] :
% 0.31/1.55 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C3 ) )
% 0.31/1.55 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_230_add__left__imp__eq,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( cancel_semigroup_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A] :
% 0.31/1.55 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.31/1.55 = ( plus_plus @ A @ A2 @ C3 ) )
% 0.31/1.55 => ( B2 = C3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_231_add__right__imp__eq,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( cancel_semigroup_add @ A )
% 0.31/1.55 => ! [B2: A,A2: A,C3: A] :
% 0.31/1.55 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.31/1.55 = ( plus_plus @ A @ C3 @ A2 ) )
% 0.31/1.55 => ( B2 = C3 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_232_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere779506340up_add @ A )
% 0.31/1.55 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.55 ( ( ( ord_less_eq @ A @ I @ J )
% 0.31/1.55 & ( K = L ) )
% 0.31/1.55 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_233_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere779506340up_add @ A )
% 0.31/1.55 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.55 ( ( ( I = J )
% 0.31/1.55 & ( ord_less_eq @ A @ K @ L ) )
% 0.31/1.55 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_234_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere779506340up_add @ A )
% 0.31/1.55 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.55 ( ( ( ord_less_eq @ A @ I @ J )
% 0.31/1.55 & ( ord_less_eq @ A @ K @ L ) )
% 0.31/1.55 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_235_add__mono,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere779506340up_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A,D3: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ C3 @ D3 )
% 0.31/1.55 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ D3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_236_add__left__mono,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere779506340up_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_237_less__eqE,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( canoni770627133id_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ~ ! [C2: A] :
% 0.31/1.55 ( B2
% 0.31/1.55 != ( plus_plus @ A @ A2 @ C2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_238_add__right__mono,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere779506340up_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_239_le__iff__add,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( canoni770627133id_add @ A )
% 0.31/1.55 => ( ( ord_less_eq @ A )
% 0.31/1.55 = ( ^ [A3: A,B3: A] :
% 0.31/1.55 ? [C4: A] :
% 0.31/1.55 ( B3
% 0.31/1.55 = ( plus_plus @ A @ A3 @ C4 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_240_add__le__imp__le__left,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere236663937imp_le @ A )
% 0.31/1.55 => ! [C3: A,A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) )
% 0.31/1.55 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_241_add__le__imp__le__right,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere236663937imp_le @ A )
% 0.31/1.55 => ! [A2: A,C3: A,B2: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) )
% 0.31/1.55 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_242_add__mono__thms__linordered__field_I5_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere223160158up_add @ A )
% 0.31/1.55 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.55 ( ( ( ord_less @ A @ I @ J )
% 0.31/1.55 & ( ord_less @ A @ K @ L ) )
% 0.31/1.55 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_243_add__mono__thms__linordered__field_I2_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere223160158up_add @ A )
% 0.31/1.55 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.55 ( ( ( I = J )
% 0.31/1.55 & ( ord_less @ A @ K @ L ) )
% 0.31/1.55 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_244_add__mono__thms__linordered__field_I1_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere223160158up_add @ A )
% 0.31/1.55 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.55 ( ( ( ord_less @ A @ I @ J )
% 0.31/1.55 & ( K = L ) )
% 0.31/1.55 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_245_add__strict__mono,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( strict2144017051up_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A,D3: A] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ord_less @ A @ C3 @ D3 )
% 0.31/1.55 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ D3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_246_add__strict__left__mono,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere223160158up_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.55 => ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_247_add__strict__right__mono,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere223160158up_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.55 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_248_add__less__imp__less__left,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere236663937imp_le @ A )
% 0.31/1.55 => ! [C3: A,A2: A,B2: A] :
% 0.31/1.55 ( ( ord_less @ A @ ( plus_plus @ A @ C3 @ A2 ) @ ( plus_plus @ A @ C3 @ B2 ) )
% 0.31/1.55 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_249_add__less__imp__less__right,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere236663937imp_le @ A )
% 0.31/1.55 => ! [A2: A,C3: A,B2: A] :
% 0.31/1.55 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ C3 ) )
% 0.31/1.55 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_250_add__less__le__mono,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere223160158up_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A,D3: A] :
% 0.31/1.55 ( ( ord_less @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ord_less_eq @ A @ C3 @ D3 )
% 0.31/1.55 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ D3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_251_add__le__less__mono,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere223160158up_add @ A )
% 0.31/1.55 => ! [A2: A,B2: A,C3: A,D3: A] :
% 0.31/1.55 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.31/1.55 => ( ( ord_less @ A @ C3 @ D3 )
% 0.31/1.55 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C3 ) @ ( plus_plus @ A @ B2 @ D3 ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_252_add__mono__thms__linordered__field_I3_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere223160158up_add @ A )
% 0.31/1.55 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.55 ( ( ( ord_less @ A @ I @ J )
% 0.31/1.55 & ( ord_less_eq @ A @ K @ L ) )
% 0.31/1.55 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_253_add__mono__thms__linordered__field_I4_J,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( ordere223160158up_add @ A )
% 0.31/1.55 => ! [I: A,J: A,K: A,L: A] :
% 0.31/1.55 ( ( ( ord_less_eq @ A @ I @ J )
% 0.31/1.55 & ( ord_less @ A @ K @ L ) )
% 0.31/1.55 => ( ord_less @ A @ ( plus_plus @ A @ I @ K ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(fact_254_discrete,axiom,
% 0.31/1.55 ! [A: $tType] :
% 0.31/1.55 ( ( unique1598680935umeral @ A )
% 0.31/1.55 => ( ( ord_less @ A )
% 0.31/1.55 = ( ^ [A3: A] : ( ord_less_eq @ A @ ( plus_plus @ A @ A3 @ ( one_one @ A ) ) ) ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.31/1.55 ! [A7: $tType,A8: $tType] :
% 0.31/1.55 ( ( preorder @ A8 )
% 0.31/1.55 => ( preorder @ ( A7 > A8 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.31/1.55 ! [A7: $tType,A8: $tType] :
% 0.31/1.55 ( ( order @ A8 )
% 0.31/1.55 => ( order @ ( A7 > A8 ) ) ) ).
% 0.31/1.55
% 0.31/1.55 thf(tcon_fun___Orderings_Oord,axiom,
% 0.31/1.56 ! [A7: $tType,A8: $tType] :
% 0.31/1.56 ( ( ord @ A8 )
% 0.31/1.56 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 0.31/1.56 condit1037483654norder @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Divides_Ounique__euclidean__semiring__numeral,axiom,
% 0.31/1.56 unique1598680935umeral @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 0.31/1.56 strict2144017051up_add @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 0.31/1.56 ordere223160158up_add @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.31/1.56 ordere236663937imp_le @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.31/1.56 canoni770627133id_add @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 0.31/1.56 ordere779506340up_add @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 0.31/1.56 cancel_semigroup_add @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 0.31/1.56 ab_semigroup_add @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 0.31/1.56 comm_monoid_add @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 0.31/1.56 semigroup_add @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.31/1.56 wellorder @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.31/1.56 preorder @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.31/1.56 linorder @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.31/1.56 no_top @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.31/1.56 order @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.31/1.56 ord @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.31/1.56 one @ nat ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_HOL_Obool___Orderings_Opreorder_4,axiom,
% 0.31/1.56 preorder @ $o ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_HOL_Obool___Orderings_Olinorder_5,axiom,
% 0.31/1.56 linorder @ $o ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_HOL_Obool___Orderings_Oorder_6,axiom,
% 0.31/1.56 order @ $o ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_HOL_Obool___Orderings_Oord_7,axiom,
% 0.31/1.56 ord @ $o ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Trace_Oprefix___Orderings_Opreorder_8,axiom,
% 0.31/1.56 ! [A7: $tType] : ( preorder @ ( prefix @ A7 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Trace_Oprefix___Orderings_Oorder_9,axiom,
% 0.31/1.56 ! [A7: $tType] : ( order @ ( prefix @ A7 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Trace_Oprefix___Orderings_Oord_10,axiom,
% 0.31/1.56 ! [A7: $tType] : ( ord @ ( prefix @ A7 ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Interval_O_092_060I_062___Orderings_Opreorder_11,axiom,
% 0.31/1.56 preorder @ i ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Interval_O_092_060I_062___Orderings_Olinorder_12,axiom,
% 0.31/1.56 linorder @ i ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Interval_O_092_060I_062___Orderings_Oorder_13,axiom,
% 0.31/1.56 order @ i ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Interval_O_092_060I_062___Orderings_Oord_14,axiom,
% 0.31/1.56 ord @ i ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Orderings_Owellorder_15,axiom,
% 0.31/1.56 ! [A7: $tType,A8: $tType] :
% 0.31/1.56 ( ( ( wellorder @ A7 )
% 0.31/1.56 & ( wellorder @ A8 ) )
% 0.31/1.56 => ( wellorder @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Orderings_Opreorder_16,axiom,
% 0.31/1.56 ! [A7: $tType,A8: $tType] :
% 0.31/1.56 ( ( ( preorder @ A7 )
% 0.31/1.56 & ( preorder @ A8 ) )
% 0.31/1.56 => ( preorder @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Orderings_Olinorder_17,axiom,
% 0.31/1.56 ! [A7: $tType,A8: $tType] :
% 0.31/1.56 ( ( ( linorder @ A7 )
% 0.31/1.56 & ( linorder @ A8 ) )
% 0.31/1.56 => ( linorder @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Orderings_Oorder_18,axiom,
% 0.31/1.56 ! [A7: $tType,A8: $tType] :
% 0.31/1.56 ( ( ( order @ A7 )
% 0.31/1.56 & ( order @ A8 ) )
% 0.31/1.56 => ( order @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(tcon_Product__Type_Oprod___Orderings_Oord_19,axiom,
% 0.31/1.56 ! [A7: $tType,A8: $tType] :
% 0.31/1.56 ( ( ( ord @ A7 )
% 0.31/1.56 & ( ord @ A8 ) )
% 0.31/1.56 => ( ord @ ( product_prod @ A7 @ A8 ) ) ) ).
% 0.31/1.56
% 0.31/1.56 thf(conj_0,conjecture,
% 0.31/1.56 ord_less @ nat @ k @ ( plen @ ( product_prod @ ( list @ char ) @ ( list @ a ) ) @ pi ) ).
% 0.31/1.56 ------------------------
% 0.31/1.58 % (8425)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8323 for (2999ds/2Mi)
% 0.31/1.58 % (8425)Instruction limit reached!
% 0.31/1.58 % (8425)------------------------------
% 0.31/1.58 % (8425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.58 % (8425)Termination reason: Unknown
% 0.31/1.58 % (8425)Termination phase: shuffling
% 0.31/1.58
% 0.31/1.58 % (8425)Memory used [KB]: 1279
% 0.31/1.58 % (8425)Time elapsed: 0.002 s
% 0.31/1.58 % (8425)Instructions burned: 2 (million)
% 0.31/1.58 % (8425)------------------------------
% 0.31/1.58 % (8425)------------------------------
% 0.31/1.58 % (8427)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_8323 for (2999ds/275Mi)
% 0.31/1.58 % (8424)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_8323 for (2999ds/27Mi)
% 0.31/1.59 % (8428)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8323 for (2999ds/18Mi)
% 0.31/1.59 % (8422)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8323 for (2999ds/183Mi)
% 0.31/1.59 % (8423)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_8323 for (2999ds/4Mi)
% 0.31/1.59 % (8426)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_8323 for (2999ds/2Mi)
% 0.31/1.59 % (8426)Instruction limit reached!
% 0.31/1.59 % (8426)------------------------------
% 0.31/1.59 % (8426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.59 % (8426)Termination reason: Unknown
% 0.31/1.59 % (8426)Termination phase: shuffling
% 0.31/1.59
% 0.31/1.59 % (8426)Memory used [KB]: 1407
% 0.31/1.59 % (8426)Time elapsed: 0.004 s
% 0.31/1.59 % (8426)Instructions burned: 3 (million)
% 0.31/1.59 % (8426)------------------------------
% 0.31/1.59 % (8426)------------------------------
% 0.31/1.59 % (8429)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8323 for (2999ds/3Mi)
% 0.31/1.59 % (8423)Instruction limit reached!
% 0.31/1.59 % (8423)------------------------------
% 0.31/1.59 % (8423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.59 % (8423)Termination reason: Unknown
% 0.31/1.59 % (8423)Termination phase: shuffling
% 0.31/1.59
% 0.31/1.59 % (8423)Memory used [KB]: 1407
% 0.31/1.59 % (8423)Time elapsed: 0.005 s
% 0.31/1.59 % (8423)Instructions burned: 5 (million)
% 0.31/1.59 % (8423)------------------------------
% 0.31/1.59 % (8423)------------------------------
% 0.31/1.59 % (8429)Instruction limit reached!
% 0.31/1.59 % (8429)------------------------------
% 0.31/1.59 % (8429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.59 % (8429)Termination reason: Unknown
% 0.31/1.59 % (8429)Termination phase: shuffling
% 0.31/1.59
% 0.31/1.59 % (8429)Memory used [KB]: 1407
% 0.31/1.59 % (8429)Time elapsed: 0.002 s
% 0.31/1.59 % (8429)Instructions burned: 3 (million)
% 0.31/1.59 % (8429)------------------------------
% 0.31/1.59 % (8429)------------------------------
% 0.31/1.59 % (8428)Instruction limit reached!
% 0.31/1.59 % (8428)------------------------------
% 0.31/1.59 % (8428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.59 % (8428)Termination reason: Unknown
% 0.31/1.59 % (8428)Termination phase: shuffling
% 0.31/1.59
% 0.31/1.59 % (8428)Memory used [KB]: 1663
% 0.31/1.59 % (8428)Time elapsed: 0.011 s
% 0.31/1.59 % (8428)Instructions burned: 18 (million)
% 0.31/1.59 % (8428)------------------------------
% 0.31/1.59 % (8428)------------------------------
% 2.87/1.60 % (8424)Instruction limit reached!
% 2.87/1.60 % (8424)------------------------------
% 2.87/1.60 % (8424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.60 % (8424)Termination reason: Unknown
% 2.87/1.60 % (8424)Termination phase: Property scanning
% 2.87/1.60
% 2.87/1.60 % (8424)Memory used [KB]: 1791
% 2.87/1.60 % (8424)Time elapsed: 0.016 s
% 2.87/1.60 % (8424)Instructions burned: 28 (million)
% 2.87/1.60 % (8424)------------------------------
% 2.87/1.60 % (8424)------------------------------
% 2.87/1.60 % (8433)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_8323 for (2999ds/3Mi)
% 2.87/1.60 % (8433)Instruction limit reached!
% 2.87/1.60 % (8433)------------------------------
% 2.87/1.60 % (8433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.60 % (8433)Termination reason: Unknown
% 2.87/1.60 % (8433)Termination phase: shuffling
% 2.87/1.60
% 2.87/1.60 % (8433)Memory used [KB]: 1407
% 2.87/1.60 % (8433)Time elapsed: 0.002 s
% 2.87/1.60 % (8433)Instructions burned: 3 (million)
% 2.87/1.60 % (8433)------------------------------
% 2.87/1.60 % (8433)------------------------------
% 2.87/1.60 % (8434)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_8323 for (2999ds/1041Mi)
% 2.87/1.61 % (8431)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_8323 for (2999ds/37Mi)
% 2.87/1.61 % (8432)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_8323 for (2999ds/15Mi)
% 2.87/1.61 % (8436)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_8323 for (2999ds/16Mi)
% 2.87/1.61 % (8435)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_8323 for (2999ds/7Mi)
% 2.87/1.61 % (8435)Instruction limit reached!
% 2.87/1.61 % (8435)------------------------------
% 2.87/1.61 % (8435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.61 % (8435)Termination reason: Unknown
% 2.87/1.61 % (8435)Termination phase: shuffling
% 2.87/1.61
% 2.87/1.61 % (8435)Memory used [KB]: 1535
% 2.87/1.61 % (8435)Time elapsed: 0.005 s
% 2.87/1.61 % (8435)Instructions burned: 8 (million)
% 2.87/1.61 % (8435)------------------------------
% 2.87/1.61 % (8435)------------------------------
% 2.87/1.62 % (8436)Instruction limit reached!
% 2.87/1.62 % (8436)------------------------------
% 2.87/1.62 % (8436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.62 % (8436)Termination reason: Unknown
% 2.87/1.62 % (8436)Termination phase: shuffling
% 2.87/1.62
% 2.87/1.62 % (8436)Memory used [KB]: 1663
% 2.87/1.62 % (8436)Time elapsed: 0.007 s
% 2.87/1.62 % (8436)Instructions burned: 18 (million)
% 2.87/1.62 % (8436)------------------------------
% 2.87/1.62 % (8436)------------------------------
% 2.87/1.62 % (8432)Instruction limit reached!
% 2.87/1.62 % (8432)------------------------------
% 2.87/1.62 % (8432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.62 % (8432)Termination reason: Unknown
% 2.87/1.62 % (8432)Termination phase: shuffling
% 2.87/1.62
% 2.87/1.62 % (8432)Memory used [KB]: 1663
% 2.87/1.62 % (8432)Time elapsed: 0.011 s
% 2.87/1.62 % (8432)Instructions burned: 15 (million)
% 2.87/1.62 % (8432)------------------------------
% 2.87/1.62 % (8432)------------------------------
% 2.87/1.62 % (8437)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_8323 for (2999ds/3Mi)
% 2.87/1.63 % (8438)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_8323 for (2999ds/3Mi)
% 2.87/1.63 % (8431)Instruction limit reached!
% 2.87/1.63 % (8431)------------------------------
% 2.87/1.63 % (8431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.63 % (8431)Termination reason: Unknown
% 2.87/1.63 % (8431)Termination phase: shuffling
% 2.87/1.63
% 2.87/1.63 % (8431)Memory used [KB]: 2174
% 2.87/1.63 % (8431)Time elapsed: 0.021 s
% 2.87/1.63 % (8431)Instructions burned: 37 (million)
% 2.87/1.63 % (8431)------------------------------
% 2.87/1.63 % (8431)------------------------------
% 2.87/1.63 % (8437)Instruction limit reached!
% 2.87/1.63 % (8437)------------------------------
% 2.87/1.63 % (8437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.63 % (8437)Termination reason: Unknown
% 2.87/1.63 % (8437)Termination phase: shuffling
% 2.87/1.63
% 2.87/1.63 % (8437)Memory used [KB]: 1407
% 2.87/1.63 % (8437)Time elapsed: 0.002 s
% 2.87/1.63 % (8437)Instructions burned: 3 (million)
% 2.87/1.63 % (8437)------------------------------
% 2.87/1.63 % (8437)------------------------------
% 2.87/1.63 % (8438)Instruction limit reached!
% 2.87/1.63 % (8438)------------------------------
% 2.87/1.63 % (8438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.63 % (8438)Termination reason: Unknown
% 2.87/1.63 % (8438)Termination phase: shuffling
% 2.87/1.63
% 2.87/1.63 % (8438)Memory used [KB]: 1407
% 2.87/1.63 % (8438)Time elapsed: 0.002 s
% 2.87/1.63 % (8438)Instructions burned: 3 (million)
% 2.87/1.63 % (8438)------------------------------
% 2.87/1.63 % (8438)------------------------------
% 2.87/1.63 % (8439)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_8323 for (2999ds/7Mi)
% 2.87/1.64 % (8442)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_8323 for (2999ds/18Mi)
% 2.87/1.64 % (8440)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_8323 for (2999ds/3Mi)
% 2.87/1.64 % (8439)Instruction limit reached!
% 2.87/1.64 % (8439)------------------------------
% 2.87/1.64 % (8439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.64 % (8439)Termination reason: Unknown
% 2.87/1.64 % (8439)Termination phase: shuffling
% 2.87/1.64
% 2.87/1.64 % (8439)Memory used [KB]: 1407
% 2.87/1.64 % (8439)Time elapsed: 0.005 s
% 2.87/1.64 % (8439)Instructions burned: 7 (million)
% 2.87/1.64 % (8439)------------------------------
% 2.87/1.64 % (8439)------------------------------
% 2.87/1.64 % (8440)Instruction limit reached!
% 2.87/1.64 % (8440)------------------------------
% 2.87/1.64 % (8440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.64 % (8440)Termination reason: Unknown
% 2.87/1.64 % (8440)Termination phase: shuffling
% 2.87/1.64
% 2.87/1.64 % (8440)Memory used [KB]: 1407
% 2.87/1.64 % (8440)Time elapsed: 0.003 s
% 2.87/1.64 % (8440)Instructions burned: 4 (million)
% 2.87/1.64 % (8440)------------------------------
% 2.87/1.64 % (8440)------------------------------
% 2.87/1.64 % (8442)Instruction limit reached!
% 2.87/1.64 % (8442)------------------------------
% 2.87/1.64 % (8442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.64 % (8442)Termination reason: Unknown
% 2.87/1.64 % (8442)Termination phase: shuffling
% 2.87/1.64
% 2.87/1.64 % (8442)Memory used [KB]: 1791
% 2.87/1.64 % (8442)Time elapsed: 0.007 s
% 2.87/1.64 % (8442)Instructions burned: 18 (million)
% 2.87/1.64 % (8442)------------------------------
% 2.87/1.64 % (8442)------------------------------
% 2.87/1.64 % (8441)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_8323 for (2999ds/4Mi)
% 2.87/1.65 % (8441)Instruction limit reached!
% 2.87/1.65 % (8441)------------------------------
% 2.87/1.65 % (8441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.65 % (8441)Termination reason: Unknown
% 2.87/1.65 % (8441)Termination phase: shuffling
% 2.87/1.65
% 2.87/1.65 % (8441)Memory used [KB]: 1407
% 2.87/1.65 % (8441)Time elapsed: 0.005 s
% 2.87/1.65 % (8441)Instructions burned: 5 (million)
% 2.87/1.65 % (8441)------------------------------
% 2.87/1.65 % (8441)------------------------------
% 2.87/1.65 % (8443)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_8323 for (2999ds/710Mi)
% 2.87/1.65 % (8444)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_8323 for (2999ds/6Mi)
% 2.87/1.65 % (8444)Instruction limit reached!
% 2.87/1.65 % (8444)------------------------------
% 2.87/1.65 % (8444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.65 % (8444)Termination reason: Unknown
% 2.87/1.65 % (8444)Termination phase: shuffling
% 2.87/1.65
% 2.87/1.65 % (8444)Memory used [KB]: 1407
% 2.87/1.65 % (8444)Time elapsed: 0.004 s
% 2.87/1.65 % (8444)Instructions burned: 6 (million)
% 2.87/1.65 % (8444)------------------------------
% 2.87/1.65 % (8444)------------------------------
% 2.87/1.65 % (8445)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_8323 for (2999ds/902Mi)
% 2.87/1.66 % (8447)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_8323 for (2998ds/5Mi)
% 2.87/1.66 % (8446)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_8323 for (2999ds/21Mi)
% 2.87/1.66 % (8447)Instruction limit reached!
% 2.87/1.66 % (8447)------------------------------
% 2.87/1.66 % (8447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.66 % (8447)Termination reason: Unknown
% 2.87/1.66 % (8447)Termination phase: shuffling
% 2.87/1.66
% 2.87/1.66 % (8447)Memory used [KB]: 1407
% 2.87/1.66 % (8447)Time elapsed: 0.004 s
% 2.87/1.66 % (8447)Instructions burned: 7 (million)
% 2.87/1.66 % (8447)------------------------------
% 2.87/1.66 % (8447)------------------------------
% 2.87/1.67 % (8446)Instruction limit reached!
% 2.87/1.67 % (8446)------------------------------
% 2.87/1.67 % (8446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.67 % (8446)Termination reason: Unknown
% 2.87/1.67 % (8446)Termination phase: shuffling
% 2.87/1.67
% 2.87/1.67 % (8446)Memory used [KB]: 1791
% 2.87/1.67 % (8446)Time elapsed: 0.010 s
% 2.87/1.67 % (8446)Instructions burned: 21 (million)
% 2.87/1.67 % (8446)------------------------------
% 2.87/1.67 % (8446)------------------------------
% 2.87/1.67 % (8422)Instruction limit reached!
% 2.87/1.67 % (8422)------------------------------
% 2.87/1.67 % (8422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.67 % (8422)Termination reason: Unknown
% 2.87/1.67 % (8422)Termination phase: Saturation
% 2.87/1.67
% 2.87/1.67 % (8422)Memory used [KB]: 7164
% 2.87/1.67 % (8422)Time elapsed: 0.087 s
% 2.87/1.67 % (8422)Instructions burned: 185 (million)
% 2.87/1.67 % (8422)------------------------------
% 2.87/1.67 % (8422)------------------------------
% 2.87/1.67 % (8448)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_8323 for (2998ds/6Mi)
% 2.87/1.67 % (8448)Instruction limit reached!
% 2.87/1.67 % (8448)------------------------------
% 2.87/1.67 % (8448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.67 % (8448)Termination reason: Unknown
% 2.87/1.67 % (8448)Termination phase: shuffling
% 2.87/1.67
% 2.87/1.67 % (8448)Memory used [KB]: 1407
% 2.87/1.67 % (8448)Time elapsed: 0.003 s
% 2.87/1.67 % (8448)Instructions burned: 7 (million)
% 2.87/1.67 % (8448)------------------------------
% 2.87/1.67 % (8448)------------------------------
% 2.87/1.68 % (8427)Instruction limit reached!
% 2.87/1.68 % (8427)------------------------------
% 2.87/1.68 % (8427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.68 % (8427)Termination reason: Unknown
% 2.87/1.68 % (8427)Termination phase: Saturation
% 2.87/1.68
% 2.87/1.68 % (8427)Memory used [KB]: 7164
% 2.87/1.68 % (8427)Time elapsed: 0.098 s
% 2.87/1.68 % (8427)Instructions burned: 276 (million)
% 2.87/1.68 % (8427)------------------------------
% 2.87/1.68 % (8427)------------------------------
% 2.87/1.68 % (8449)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_8323 for (2998ds/377Mi)
% 2.87/1.68 % (8450)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_8323 for (2998ds/779Mi)
% 2.87/1.68 % (8451)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_8323 for (2998ds/19Mi)
% 2.87/1.69 % (8452)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_8323 for (2998ds/879Mi)
% 2.87/1.69 % (8451)Instruction limit reached!
% 2.87/1.69 % (8451)------------------------------
% 2.87/1.69 % (8451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.69 % (8451)Termination reason: Unknown
% 2.87/1.69 % (8451)Termination phase: shuffling
% 2.87/1.69
% 2.87/1.69 % (8451)Memory used [KB]: 1663
% 2.87/1.69 % (8451)Time elapsed: 0.008 s
% 2.87/1.69 % (8451)Instructions burned: 21 (million)
% 2.87/1.69 % (8451)------------------------------
% 2.87/1.69 % (8451)------------------------------
% 2.87/1.70 % (8453)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_8323 for (2998ds/17Mi)
% 2.87/1.71 % (8453)Instruction limit reached!
% 2.87/1.71 % (8453)------------------------------
% 2.87/1.71 % (8453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.71 % (8453)Termination reason: Unknown
% 2.87/1.71 % (8453)Termination phase: shuffling
% 2.87/1.71
% 2.87/1.71 % (8453)Memory used [KB]: 1663
% 2.87/1.71 % (8453)Time elapsed: 0.008 s
% 2.87/1.71 % (8453)Instructions burned: 17 (million)
% 2.87/1.71 % (8453)------------------------------
% 2.87/1.71 % (8453)------------------------------
% 2.87/1.72 % (8454)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_8323 for (2998ds/3Mi)
% 2.87/1.72 % (8454)Instruction limit reached!
% 2.87/1.72 % (8454)------------------------------
% 2.87/1.72 % (8454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.72 % (8454)Termination reason: Unknown
% 2.87/1.72 % (8454)Termination phase: shuffling
% 2.87/1.72
% 2.87/1.72 % (8454)Memory used [KB]: 1407
% 2.87/1.72 % (8454)Time elapsed: 0.002 s
% 2.87/1.72 % (8454)Instructions burned: 3 (million)
% 2.87/1.72 % (8454)------------------------------
% 2.87/1.72 % (8454)------------------------------
% 2.87/1.73 % (8455)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_8323 for (2998ds/30Mi)
% 2.87/1.74 % (8455)Instruction limit reached!
% 2.87/1.74 % (8455)------------------------------
% 2.87/1.74 % (8455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.74 % (8455)Termination reason: Unknown
% 2.87/1.74 % (8455)Termination phase: Property scanning
% 2.87/1.74
% 2.87/1.74 % (8455)Memory used [KB]: 1791
% 2.87/1.74 % (8455)Time elapsed: 0.011 s
% 2.87/1.74 % (8455)Instructions burned: 32 (million)
% 2.87/1.74 % (8455)------------------------------
% 2.87/1.74 % (8455)------------------------------
% 2.87/1.75 % (8456)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_8323 for (2998ds/127Mi)
% 2.87/1.78 % (8456)Instruction limit reached!
% 2.87/1.78 % (8456)------------------------------
% 2.87/1.78 % (8456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.78 % (8456)Termination reason: Unknown
% 2.87/1.78 % (8456)Termination phase: Saturation
% 2.87/1.78
% 2.87/1.78 % (8456)Memory used [KB]: 6908
% 2.87/1.78 % (8456)Time elapsed: 0.038 s
% 2.87/1.78 % (8456)Instructions burned: 129 (million)
% 2.87/1.78 % (8456)------------------------------
% 2.87/1.78 % (8456)------------------------------
% 2.87/1.79 % (8457)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_8323 for (2997ds/100Mi)
% 2.87/1.80 % (8449)Instruction limit reached!
% 2.87/1.80 % (8449)------------------------------
% 2.87/1.80 % (8449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.80 % (8449)Termination reason: Unknown
% 2.87/1.80 % (8449)Termination phase: Saturation
% 2.87/1.80
% 2.87/1.80 % (8449)Memory used [KB]: 7675
% 2.87/1.80 % (8449)Time elapsed: 0.124 s
% 2.87/1.80 % (8449)Instructions burned: 378 (million)
% 2.87/1.80 % (8449)------------------------------
% 2.87/1.80 % (8449)------------------------------
% 2.87/1.81 % (8458)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_8323 for (2997ds/3Mi)
% 2.87/1.81 % (8458)Instruction limit reached!
% 2.87/1.81 % (8458)------------------------------
% 2.87/1.81 % (8458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.81 % (8458)Termination reason: Unknown
% 2.87/1.81 % (8458)Termination phase: shuffling
% 2.87/1.81
% 2.87/1.81 % (8458)Memory used [KB]: 1407
% 2.87/1.81 % (8458)Time elapsed: 0.002 s
% 2.87/1.81 % (8458)Instructions burned: 3 (million)
% 2.87/1.81 % (8458)------------------------------
% 2.87/1.81 % (8458)------------------------------
% 2.87/1.82 % (8457)Instruction limit reached!
% 2.87/1.82 % (8457)------------------------------
% 2.87/1.82 % (8457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.82 % (8457)Termination reason: Unknown
% 2.87/1.82 % (8457)Termination phase: Property scanning
% 2.87/1.82
% 2.87/1.82 % (8457)Memory used [KB]: 2302
% 2.87/1.82 % (8457)Time elapsed: 0.028 s
% 2.87/1.82 % (8457)Instructions burned: 101 (million)
% 2.87/1.82 % (8457)------------------------------
% 2.87/1.82 % (8457)------------------------------
% 2.87/1.82 % (8459)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_8323 for (2997ds/20Mi)
% 2.87/1.83 % (8460)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_8323 for (2997ds/86Mi)
% 2.87/1.83 % (8459)Instruction limit reached!
% 2.87/1.83 % (8459)------------------------------
% 2.87/1.83 % (8459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.83 % (8459)Termination reason: Unknown
% 2.87/1.83 % (8459)Termination phase: shuffling
% 2.87/1.83
% 2.87/1.83 % (8459)Memory used [KB]: 1791
% 2.87/1.83 % (8459)Time elapsed: 0.008 s
% 2.87/1.83 % (8459)Instructions burned: 20 (million)
% 2.87/1.83 % (8459)------------------------------
% 2.87/1.83 % (8459)------------------------------
% 2.87/1.84 % (8461)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_8323 for (2997ds/107Mi)
% 2.87/1.85 % (8460)Instruction limit reached!
% 2.87/1.85 % (8460)------------------------------
% 2.87/1.85 % (8460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.85 % (8460)Termination reason: Unknown
% 2.87/1.85 % (8460)Termination phase: Property scanning
% 2.87/1.85
% 2.87/1.85 % (8460)Memory used [KB]: 2302
% 2.87/1.85 % (8460)Time elapsed: 0.026 s
% 2.87/1.85 % (8460)Instructions burned: 87 (million)
% 2.87/1.85 % (8460)------------------------------
% 2.87/1.85 % (8460)------------------------------
% 2.87/1.86 % (8462)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_8323 for (2997ds/39Mi)
% 2.87/1.87 % (8462)Instruction limit reached!
% 2.87/1.87 % (8462)------------------------------
% 2.87/1.87 % (8462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.87 % (8462)Termination reason: Unknown
% 2.87/1.87 % (8462)Termination phase: Property scanning
% 2.87/1.87
% 2.87/1.87 % (8462)Memory used [KB]: 2174
% 2.87/1.87 % (8462)Time elapsed: 0.012 s
% 2.87/1.87 % (8462)Instructions burned: 40 (million)
% 2.87/1.87 % (8462)------------------------------
% 2.87/1.87 % (8462)------------------------------
% 2.87/1.88 % (8461)Instruction limit reached!
% 2.87/1.88 % (8461)------------------------------
% 2.87/1.88 % (8461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.88 % (8461)Termination reason: Unknown
% 2.87/1.88 % (8461)Termination phase: Saturation
% 2.87/1.88
% 2.87/1.88 % (8461)Memory used [KB]: 6908
% 2.87/1.88 % (8461)Time elapsed: 0.036 s
% 2.87/1.88 % (8461)Instructions burned: 107 (million)
% 2.87/1.88 % (8461)------------------------------
% 2.87/1.88 % (8461)------------------------------
% 2.87/1.88 % (8463)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_8323 for (2996ds/448Mi)
% 2.87/1.88 % (8443)Instruction limit reached!
% 2.87/1.88 % (8443)------------------------------
% 2.87/1.88 % (8443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.88 % (8443)Termination reason: Unknown
% 2.87/1.88 % (8443)Termination phase: Saturation
% 2.87/1.88
% 2.87/1.88 % (8443)Memory used [KB]: 8187
% 2.87/1.88 % (8443)Time elapsed: 0.239 s
% 2.87/1.88 % (8443)Instructions burned: 710 (million)
% 2.87/1.88 % (8443)------------------------------
% 2.87/1.88 % (8443)------------------------------
% 2.87/1.89 % (8464)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_8323 for (2996ds/46Mi)
% 2.87/1.89 % (8465)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_8323 for (2996ds/98Mi)
% 2.87/1.90 % (8452)Refutation not found, non-redundant clauses discarded% (8452)------------------------------
% 2.87/1.90 % (8452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.90 % (8452)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.87/1.90
% 2.87/1.90 % (8452)Memory used [KB]: 7931
% 2.87/1.90 % (8452)Time elapsed: 0.213 s
% 2.87/1.90 % (8452)Instructions burned: 655 (million)
% 2.87/1.90 % (8452)------------------------------
% 2.87/1.90 % (8452)------------------------------
% 2.87/1.90 % (8464)Instruction limit reached!
% 2.87/1.90 % (8464)------------------------------
% 2.87/1.90 % (8464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.90 % (8464)Termination reason: Unknown
% 2.87/1.90 % (8464)Termination phase: Preprocessing 3
% 2.87/1.90
% 2.87/1.90 % (8464)Memory used [KB]: 2046
% 2.87/1.90 % (8464)Time elapsed: 0.017 s
% 2.87/1.90 % (8464)Instructions burned: 48 (million)
% 2.87/1.90 % (8464)------------------------------
% 2.87/1.90 % (8464)------------------------------
% 2.87/1.91 % (8434)Instruction limit reached!
% 2.87/1.91 % (8434)------------------------------
% 2.87/1.91 % (8434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.91 % (8434)Termination reason: Unknown
% 2.87/1.91 % (8434)Termination phase: Saturation
% 2.87/1.91
% 2.87/1.91 % (8434)Memory used [KB]: 9722
% 2.87/1.91 % (8434)Time elapsed: 0.302 s
% 2.87/1.91 % (8434)Instructions burned: 1043 (million)
% 2.87/1.91 % (8434)------------------------------
% 2.87/1.91 % (8434)------------------------------
% 2.87/1.91 % (8467)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_8323 for (2996ds/149Mi)
% 2.87/1.91 % (8466)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_8323 for (2996ds/507Mi)
% 2.87/1.91 % (8445)Instruction limit reached!
% 2.87/1.91 % (8445)------------------------------
% 2.87/1.91 % (8445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.91 % (8445)Termination reason: Unknown
% 2.87/1.91 % (8445)Termination phase: Saturation
% 2.87/1.91
% 2.87/1.91 % (8445)Memory used [KB]: 8955
% 2.87/1.91 % (8445)Time elapsed: 0.263 s
% 2.87/1.91 % (8445)Instructions burned: 902 (million)
% 2.87/1.91 % (8445)------------------------------
% 2.87/1.91 % (8445)------------------------------
% 2.87/1.92 % (8468)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_8323 for (2996ds/39Mi)
% 2.87/1.92 % (8469)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_8323 for (2996ds/6Mi)
% 2.87/1.92 % (8465)Instruction limit reached!
% 2.87/1.92 % (8465)------------------------------
% 2.87/1.92 % (8465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.92 % (8465)Termination reason: Unknown
% 2.87/1.92 % (8465)Termination phase: Property scanning
% 2.87/1.92
% 2.87/1.92 % (8465)Memory used [KB]: 2302
% 2.87/1.92 % (8465)Time elapsed: 0.030 s
% 2.87/1.92 % (8465)Instructions burned: 99 (million)
% 2.87/1.92 % (8465)------------------------------
% 2.87/1.92 % (8465)------------------------------
% 2.87/1.92 % (8469)Instruction limit reached!
% 2.87/1.92 % (8469)------------------------------
% 2.87/1.92 % (8469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.92 % (8469)Termination reason: Unknown
% 2.87/1.92 % (8469)Termination phase: shuffling
% 2.87/1.92
% 2.87/1.92 % (8469)Memory used [KB]: 1407
% 2.87/1.92 % (8469)Time elapsed: 0.003 s
% 2.87/1.92 % (8469)Instructions burned: 7 (million)
% 2.87/1.92 % (8469)------------------------------
% 2.87/1.92 % (8469)------------------------------
% 2.87/1.93 % (8468)Instruction limit reached!
% 2.87/1.93 % (8468)------------------------------
% 2.87/1.93 % (8468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.93 % (8468)Termination reason: Unknown
% 2.87/1.93 % (8468)Termination phase: Naming
% 2.87/1.93
% 2.87/1.93 % (8468)Memory used [KB]: 2046
% 2.87/1.93 % (8468)Time elapsed: 0.013 s
% 2.87/1.93 % (8468)Instructions burned: 39 (million)
% 2.87/1.93 % (8468)------------------------------
% 2.87/1.93 % (8468)------------------------------
% 2.87/1.93 % (8471)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_8323 for (2996ds/47Mi)
% 2.87/1.93 % (8470)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_8323 for (2996ds/1087Mi)
% 2.87/1.94 % (8472)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_8323 for (2996ds/44Mi)
% 2.87/1.94 % (8450)Instruction limit reached!
% 2.87/1.94 % (8450)------------------------------
% 2.87/1.94 % (8450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.94 % (8450)Termination reason: Unknown
% 2.87/1.94 % (8450)Termination phase: Saturation
% 2.87/1.94
% 2.87/1.94 % (8450)Memory used [KB]: 8443
% 2.87/1.94 % (8450)Time elapsed: 0.257 s
% 2.87/1.94 % (8450)Instructions burned: 779 (million)
% 2.87/1.94 % (8450)------------------------------
% 2.87/1.94 % (8450)------------------------------
% 2.87/1.95 % (8472)Instruction limit reached!
% 2.87/1.95 % (8472)------------------------------
% 2.87/1.95 % (8472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.95 % (8472)Termination reason: Unknown
% 2.87/1.95 % (8472)Termination phase: Property scanning
% 2.87/1.95
% 2.87/1.95 % (8472)Memory used [KB]: 2174
% 2.87/1.95 % (8472)Time elapsed: 0.013 s
% 2.87/1.95 % (8472)Instructions burned: 44 (million)
% 2.87/1.95 % (8472)------------------------------
% 2.87/1.95 % (8472)------------------------------
% 2.87/1.95 % (8473)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_8323 for (2996ds/432Mi)
% 2.87/1.95 % (8471)Instruction limit reached!
% 2.87/1.95 % (8471)------------------------------
% 2.87/1.95 % (8471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.95 % (8471)Termination reason: Unknown
% 2.87/1.95 % (8471)Termination phase: Preprocessing 3
% 2.87/1.95
% 2.87/1.95 % (8471)Memory used [KB]: 2174
% 2.87/1.95 % (8471)Time elapsed: 0.016 s
% 2.87/1.95 % (8471)Instructions burned: 50 (million)
% 2.87/1.95 % (8471)------------------------------
% 2.87/1.95 % (8471)------------------------------
% 2.87/1.95 % (8467)Instruction limit reached!
% 2.87/1.95 % (8467)------------------------------
% 2.87/1.95 % (8467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.95 % (8467)Termination reason: Unknown
% 2.87/1.95 % (8467)Termination phase: Saturation
% 2.87/1.95
% 2.87/1.95 % (8467)Memory used [KB]: 6908
% 2.87/1.95 % (8467)Time elapsed: 0.043 s
% 2.87/1.95 % (8467)Instructions burned: 150 (million)
% 2.87/1.95 % (8467)------------------------------
% 2.87/1.95 % (8467)------------------------------
% 2.87/1.96 % (8474)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_8323 for (2996ds/62Mi)
% 2.87/1.96 % (8475)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_8323 for (2996ds/31Mi)
% 2.87/1.96 % (8476)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_8323 for (2996ds/96Mi)
% 2.87/1.97 % (8475)Instruction limit reached!
% 2.87/1.97 % (8475)------------------------------
% 2.87/1.97 % (8475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.97 % (8475)Termination reason: Unknown
% 2.87/1.97 % (8475)Termination phase: Property scanning
% 2.87/1.97
% 2.87/1.97 % (8475)Memory used [KB]: 1791
% 2.87/1.97 % (8475)Time elapsed: 0.011 s
% 2.87/1.97 % (8475)Instructions burned: 34 (million)
% 2.87/1.97 % (8475)------------------------------
% 2.87/1.97 % (8475)------------------------------
% 2.87/1.97 % (8474)Instruction limit reached!
% 2.87/1.97 % (8474)------------------------------
% 2.87/1.97 % (8474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.97 % (8474)Termination reason: Unknown
% 2.87/1.97 % (8474)Termination phase: Property scanning
% 2.87/1.97
% 2.87/1.97 % (8474)Memory used [KB]: 2174
% 2.87/1.97 % (8474)Time elapsed: 0.017 s
% 2.87/1.97 % (8474)Instructions burned: 62 (million)
% 2.87/1.97 % (8474)------------------------------
% 2.87/1.97 % (8474)------------------------------
% 2.87/1.98 % (8477)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_8323 for (2995ds/453Mi)
% 2.87/1.98 % (8478)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_8323 for (2995ds/71Mi)
% 2.87/1.99 % (8476)Instruction limit reached!
% 2.87/1.99 % (8476)------------------------------
% 2.87/1.99 % (8476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/1.99 % (8476)Termination reason: Unknown
% 2.87/1.99 % (8476)Termination phase: Saturation
% 2.87/1.99
% 2.87/1.99 % (8476)Memory used [KB]: 2430
% 2.87/1.99 % (8476)Time elapsed: 0.028 s
% 2.87/1.99 % (8476)Instructions burned: 96 (million)
% 2.87/1.99 % (8476)------------------------------
% 2.87/1.99 % (8476)------------------------------
% 2.87/2.00 % (8478)Instruction limit reached!
% 2.87/2.00 % (8478)------------------------------
% 2.87/2.00 % (8478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.87/2.00 % (8478)Termination reason: Unknown
% 2.87/2.00 % (8478)Termination phase: Function definition elimination
% 2.87/2.00
% 2.87/2.00 % (8478)Memory used [KB]: 2302
% 2.87/2.00 % (8478)Time elapsed: 0.022 s
% 2.87/2.00 % (8478)Instructions burned: 72 (million)
% 2.87/2.00 % (8478)------------------------------
% 2.87/2.00 % (8478)------------------------------
% 2.87/2.01 % (8479)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_8323 for (2995ds/83Mi)
% 5.88/2.02 % (8463)Instruction limit reached!
% 5.88/2.02 % (8463)------------------------------
% 5.88/2.02 % (8463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.02 % (8463)Termination reason: Unknown
% 5.88/2.02 % (8463)Termination phase: Saturation
% 5.88/2.02
% 5.88/2.02 % (8463)Memory used [KB]: 7931
% 5.88/2.02 % (8463)Time elapsed: 0.133 s
% 5.88/2.02 % (8463)Instructions burned: 449 (million)
% 5.88/2.02 % (8463)------------------------------
% 5.88/2.02 % (8463)------------------------------
% 5.88/2.02 % (8480)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_8323 for (2995ds/11Mi)
% 5.88/2.02 % (8480)Instruction limit reached!
% 5.88/2.02 % (8480)------------------------------
% 5.88/2.02 % (8480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.02 % (8480)Termination reason: Unknown
% 5.88/2.02 % (8480)Termination phase: shuffling
% 5.88/2.02
% 5.88/2.02 % (8480)Memory used [KB]: 1535
% 5.88/2.02 % (8480)Time elapsed: 0.005 s
% 5.88/2.02 % (8480)Instructions burned: 11 (million)
% 5.88/2.02 % (8480)------------------------------
% 5.88/2.02 % (8480)------------------------------
% 5.88/2.03 % (8481)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_8323 for (2995ds/41Mi)
% 5.88/2.03 % (8482)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_8323 for (2995ds/6Mi)
% 5.88/2.03 % (8482)Instruction limit reached!
% 5.88/2.03 % (8482)------------------------------
% 5.88/2.03 % (8482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.03 % (8482)Termination reason: Unknown
% 5.88/2.03 % (8482)Termination phase: shuffling
% 5.88/2.03
% 5.88/2.03 % (8482)Memory used [KB]: 1407
% 5.88/2.03 % (8482)Time elapsed: 0.003 s
% 5.88/2.03 % (8482)Instructions burned: 6 (million)
% 5.88/2.03 % (8482)------------------------------
% 5.88/2.03 % (8482)------------------------------
% 5.88/2.04 % (8479)Instruction limit reached!
% 5.88/2.04 % (8479)------------------------------
% 5.88/2.04 % (8479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.04 % (8479)Termination reason: Unknown
% 5.88/2.04 % (8479)Termination phase: Saturation
% 5.88/2.04
% 5.88/2.04 % (8479)Memory used [KB]: 6652
% 5.88/2.04 % (8479)Time elapsed: 0.050 s
% 5.88/2.04 % (8479)Instructions burned: 83 (million)
% 5.88/2.04 % (8479)------------------------------
% 5.88/2.04 % (8479)------------------------------
% 5.88/2.04 % (8481)Instruction limit reached!
% 5.88/2.04 % (8481)------------------------------
% 5.88/2.04 % (8481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.04 % (8481)Termination reason: Unknown
% 5.88/2.04 % (8481)Termination phase: Property scanning
% 5.88/2.04
% 5.88/2.04 % (8481)Memory used [KB]: 2174
% 5.88/2.04 % (8481)Time elapsed: 0.013 s
% 5.88/2.04 % (8481)Instructions burned: 44 (million)
% 5.88/2.04 % (8481)------------------------------
% 5.88/2.04 % (8481)------------------------------
% 5.88/2.04 % (8483)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_8323 for (2995ds/150Mi)
% 5.88/2.05 % (8484)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_8323 for (2995ds/343Mi)
% 5.88/2.05 % (8485)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_8323 for (2995ds/109Mi)
% 5.88/2.08 % (8466)Instruction limit reached!
% 5.88/2.08 % (8466)------------------------------
% 5.88/2.08 % (8466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.08 % (8466)Termination reason: Unknown
% 5.88/2.08 % (8466)Termination phase: Saturation
% 5.88/2.08
% 5.88/2.08 % (8466)Memory used [KB]: 7803
% 5.88/2.08 % (8466)Time elapsed: 0.167 s
% 5.88/2.08 % (8466)Instructions burned: 508 (million)
% 5.88/2.08 % (8466)------------------------------
% 5.88/2.08 % (8466)------------------------------
% 5.88/2.08 % (8485)Instruction limit reached!
% 5.88/2.08 % (8485)------------------------------
% 5.88/2.08 % (8485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.08 % (8485)Termination reason: Unknown
% 5.88/2.08 % (8485)Termination phase: Saturation
% 5.88/2.08
% 5.88/2.08 % (8485)Memory used [KB]: 6780
% 5.88/2.08 % (8485)Time elapsed: 0.033 s
% 5.88/2.08 % (8485)Instructions burned: 111 (million)
% 5.88/2.08 % (8485)------------------------------
% 5.88/2.08 % (8485)------------------------------
% 5.88/2.08 % (8473)Instruction limit reached!
% 5.88/2.08 % (8473)------------------------------
% 5.88/2.08 % (8473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.08 % (8473)Termination reason: Unknown
% 5.88/2.08 % (8473)Termination phase: Saturation
% 5.88/2.08
% 5.88/2.08 % (8473)Memory used [KB]: 3837
% 5.88/2.08 % (8473)Time elapsed: 0.135 s
% 5.88/2.08 % (8473)Instructions burned: 433 (million)
% 5.88/2.08 % (8473)------------------------------
% 5.88/2.08 % (8473)------------------------------
% 5.88/2.08 % (8483)Instruction limit reached!
% 5.88/2.08 % (8483)------------------------------
% 5.88/2.08 % (8483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.88/2.08 % (8483)Termination reason: Unknown
% 5.88/2.08 % (8483)Termination phase: Saturation
% 5.88/2.08
% 5.88/2.08 % (8483)Memory used [KB]: 7036
% 5.88/2.08 % (8483)Time elapsed: 0.044 s
% 5.88/2.08 % (8483)Instructions burned: 150 (million)
% 5.88/2.08 % (8483)------------------------------
% 5.88/2.08 % (8483)------------------------------
% 5.88/2.09 % (8486)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_8323 for (2994ds/253Mi)
% 5.88/2.09 % (8487)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_8323 for (2994ds/140Mi)
% 5.88/2.09 % (8488)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_8323 for (2994ds/614Mi)
% 5.88/2.09 % (8489)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_8323 for (2994ds/202Mi)
% 6.42/2.11 % (8477)Instruction limit reached!
% 6.42/2.11 % (8477)------------------------------
% 6.42/2.11 % (8477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.11 % (8477)Termination reason: Unknown
% 6.42/2.11 % (8477)Termination phase: Saturation
% 6.42/2.11
% 6.42/2.11 % (8477)Memory used [KB]: 7803
% 6.42/2.11 % (8477)Time elapsed: 0.136 s
% 6.42/2.11 % (8477)Instructions burned: 455 (million)
% 6.42/2.11 % (8477)------------------------------
% 6.42/2.11 % (8477)------------------------------
% 6.42/2.12 % (8490)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_8323 for (2994ds/339Mi)
% 6.42/2.13 % (8487)Instruction limit reached!
% 6.42/2.13 % (8487)------------------------------
% 6.42/2.13 % (8487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.13 % (8487)Termination reason: Unknown
% 6.42/2.13 % (8487)Termination phase: Saturation
% 6.42/2.13
% 6.42/2.13 % (8487)Memory used [KB]: 6908
% 6.42/2.13 % (8487)Time elapsed: 0.046 s
% 6.42/2.13 % (8487)Instructions burned: 141 (million)
% 6.42/2.13 % (8487)------------------------------
% 6.42/2.13 % (8487)------------------------------
% 6.42/2.14 % (8491)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_8323 for (2994ds/283Mi)
% 6.42/2.15 % (8484)Instruction limit reached!
% 6.42/2.15 % (8484)------------------------------
% 6.42/2.15 % (8484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.15 % (8484)Termination reason: Unknown
% 6.42/2.15 % (8484)Termination phase: Saturation
% 6.42/2.15
% 6.42/2.15 % (8484)Memory used [KB]: 7291
% 6.42/2.15 % (8484)Time elapsed: 0.105 s
% 6.42/2.15 % (8484)Instructions burned: 343 (million)
% 6.42/2.15 % (8484)------------------------------
% 6.42/2.15 % (8484)------------------------------
% 6.42/2.16 % (8489)Instruction limit reached!
% 6.42/2.16 % (8489)------------------------------
% 6.42/2.16 % (8489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.16 % (8489)Termination reason: Unknown
% 6.42/2.16 % (8489)Termination phase: Saturation
% 6.42/2.16
% 6.42/2.16 % (8489)Memory used [KB]: 7164
% 6.42/2.16 % (8489)Time elapsed: 0.063 s
% 6.42/2.16 % (8489)Instructions burned: 203 (million)
% 6.42/2.16 % (8489)------------------------------
% 6.42/2.16 % (8489)------------------------------
% 6.42/2.16 % (8492)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_8323 for (2994ds/134Mi)
% 6.42/2.16 % (8486)Instruction limit reached!
% 6.42/2.16 % (8486)------------------------------
% 6.42/2.16 % (8486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.42/2.16 % (8486)Termination reason: Unknown
% 6.42/2.16 % (8486)Termination phase: Saturation
% 6.42/2.16
% 6.42/2.16 % (8486)Memory used [KB]: 7675
% 6.42/2.16 % (8486)Time elapsed: 0.077 s
% 6.42/2.16 % (8486)Instructions burned: 253 (million)
% 6.42/2.16 % (8486)------------------------------
% 6.42/2.16 % (8486)------------------------------
% 6.42/2.17 % (8493)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_8323 for (2993ds/298Mi)
% 6.42/2.17 % (8494)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_8323 for (2993ds/192Mi)
% 6.83/2.20 % (8492)Instruction limit reached!
% 6.83/2.20 % (8492)------------------------------
% 6.83/2.20 % (8492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.20 % (8492)Termination reason: Unknown
% 6.83/2.20 % (8492)Termination phase: Saturation
% 6.83/2.20
% 6.83/2.20 % (8492)Memory used [KB]: 6908
% 6.83/2.20 % (8492)Time elapsed: 0.039 s
% 6.83/2.20 % (8492)Instructions burned: 134 (million)
% 6.83/2.20 % (8492)------------------------------
% 6.83/2.20 % (8492)------------------------------
% 6.83/2.21 % (8495)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_8323 for (2993ds/258Mi)
% 6.83/2.22 % (8490)Instruction limit reached!
% 6.83/2.22 % (8490)------------------------------
% 6.83/2.22 % (8490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.22 % (8490)Termination reason: Unknown
% 6.83/2.22 % (8490)Termination phase: Saturation
% 6.83/2.22
% 6.83/2.22 % (8490)Memory used [KB]: 7291
% 6.83/2.22 % (8490)Time elapsed: 0.099 s
% 6.83/2.22 % (8490)Instructions burned: 341 (million)
% 6.83/2.22 % (8490)------------------------------
% 6.83/2.22 % (8490)------------------------------
% 6.83/2.23 % (8491)Instruction limit reached!
% 6.83/2.23 % (8491)------------------------------
% 6.83/2.23 % (8491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.23 % (8491)Termination reason: Unknown
% 6.83/2.23 % (8491)Termination phase: Saturation
% 6.83/2.23
% 6.83/2.23 % (8491)Memory used [KB]: 7675
% 6.83/2.23 % (8491)Time elapsed: 0.085 s
% 6.83/2.23 % (8491)Instructions burned: 283 (million)
% 6.83/2.23 % (8491)------------------------------
% 6.83/2.23 % (8491)------------------------------
% 6.83/2.23 % (8494)Instruction limit reached!
% 6.83/2.23 % (8494)------------------------------
% 6.83/2.23 % (8494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.23 % (8494)Termination reason: Unknown
% 6.83/2.23 % (8494)Termination phase: Saturation
% 6.83/2.23
% 6.83/2.23 % (8494)Memory used [KB]: 7803
% 6.83/2.23 % (8494)Time elapsed: 0.059 s
% 6.83/2.23 % (8494)Instructions burned: 194 (million)
% 6.83/2.23 % (8494)------------------------------
% 6.83/2.23 % (8494)------------------------------
% 6.83/2.23 % (8496)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_8323 for (2993ds/90Mi)
% 6.83/2.24 % (8497)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_8323 for (2993ds/231Mi)
% 6.83/2.24 % (8498)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_8323 for (2993ds/458Mi)
% 6.83/2.25 % (8493)Instruction limit reached!
% 6.83/2.25 % (8493)------------------------------
% 6.83/2.25 % (8493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.25 % (8493)Termination reason: Unknown
% 6.83/2.25 % (8493)Termination phase: Saturation
% 6.83/2.25
% 6.83/2.25 % (8493)Memory used [KB]: 7803
% 6.83/2.25 % (8493)Time elapsed: 0.085 s
% 6.83/2.25 % (8493)Instructions burned: 300 (million)
% 6.83/2.25 % (8493)------------------------------
% 6.83/2.25 % (8493)------------------------------
% 6.83/2.26 % (8496)Instruction limit reached!
% 6.83/2.26 % (8496)------------------------------
% 6.83/2.26 % (8496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.26 % (8496)Termination reason: Unknown
% 6.83/2.26 % (8496)Termination phase: Property scanning
% 6.83/2.26
% 6.83/2.26 % (8496)Memory used [KB]: 2302
% 6.83/2.26 % (8496)Time elapsed: 0.027 s
% 6.83/2.26 % (8496)Instructions burned: 91 (million)
% 6.83/2.26 % (8496)------------------------------
% 6.83/2.26 % (8496)------------------------------
% 6.83/2.26 % (8499)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_8323 for (2993ds/31Mi)
% 6.83/2.27 % (8500)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_8323 for (2993ds/297Mi)
% 6.83/2.27 % (8499)Instruction limit reached!
% 6.83/2.27 % (8499)------------------------------
% 6.83/2.27 % (8499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.27 % (8499)Termination reason: Unknown
% 6.83/2.27 % (8499)Termination phase: Property scanning
% 6.83/2.27
% 6.83/2.27 % (8499)Memory used [KB]: 1791
% 6.83/2.27 % (8499)Time elapsed: 0.011 s
% 6.83/2.27 % (8499)Instructions burned: 33 (million)
% 6.83/2.27 % (8499)------------------------------
% 6.83/2.27 % (8499)------------------------------
% 6.83/2.28 % (8470)Instruction limit reached!
% 6.83/2.28 % (8470)------------------------------
% 6.83/2.28 % (8470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.28 % (8470)Termination reason: Unknown
% 6.83/2.28 % (8470)Termination phase: Saturation
% 6.83/2.28
% 6.83/2.28 % (8470)Memory used [KB]: 8187
% 6.83/2.28 % (8470)Time elapsed: 0.344 s
% 6.83/2.28 % (8470)Instructions burned: 1088 (million)
% 6.83/2.28 % (8470)------------------------------
% 6.83/2.28 % (8470)------------------------------
% 6.83/2.28 % (8488)Instruction limit reached!
% 6.83/2.28 % (8488)------------------------------
% 6.83/2.28 % (8488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.28 % (8488)Termination reason: Unknown
% 6.83/2.28 % (8488)Termination phase: Saturation
% 6.83/2.28
% 6.83/2.28 % (8488)Memory used [KB]: 8699
% 6.83/2.28 % (8488)Time elapsed: 0.186 s
% 6.83/2.28 % (8488)Instructions burned: 614 (million)
% 6.83/2.28 % (8488)------------------------------
% 6.83/2.28 % (8488)------------------------------
% 6.83/2.28 % (8501)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_8323 for (2992ds/987Mi)
% 6.83/2.28 % (8495)Instruction limit reached!
% 6.83/2.28 % (8495)------------------------------
% 6.83/2.28 % (8495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.28 % (8495)Termination reason: Unknown
% 6.83/2.28 % (8495)Termination phase: Saturation
% 6.83/2.28
% 6.83/2.28 % (8495)Memory used [KB]: 7547
% 6.83/2.28 % (8495)Time elapsed: 0.078 s
% 6.83/2.28 % (8495)Instructions burned: 258 (million)
% 6.83/2.28 % (8495)------------------------------
% 6.83/2.28 % (8495)------------------------------
% 6.83/2.29 % (8502)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_8323 for (2992ds/182Mi)
% 6.83/2.29 % (8503)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_8323 for (2992ds/182Mi)
% 6.83/2.29 % (8504)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_8323 for (2992ds/154Mi)
% 7.68/2.30 % (8497)Instruction limit reached!
% 7.68/2.30 % (8497)------------------------------
% 7.68/2.30 % (8497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.68/2.30 % (8497)Termination reason: Unknown
% 7.68/2.30 % (8497)Termination phase: Saturation
% 7.68/2.30
% 7.68/2.30 % (8497)Memory used [KB]: 6908
% 7.68/2.30 % (8497)Time elapsed: 0.061 s
% 7.68/2.30 % (8497)Instructions burned: 234 (million)
% 7.68/2.30 % (8497)------------------------------
% 7.68/2.30 % (8497)------------------------------
% 7.68/2.31 % (8505)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_8323 for (2992ds/79Mi)
% 7.68/2.33 % (8505)Instruction limit reached!
% 7.68/2.33 % (8505)------------------------------
% 7.68/2.33 % (8505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.68/2.33 % (8505)Termination reason: Unknown
% 7.68/2.33 % (8505)Termination phase: Property scanning
% 7.68/2.33
% 7.68/2.33 % (8505)Memory used [KB]: 2302
% 7.68/2.33 % (8505)Time elapsed: 0.025 s
% 7.68/2.33 % (8505)Instructions burned: 82 (million)
% 7.68/2.33 % (8505)------------------------------
% 7.68/2.33 % (8505)------------------------------
% 7.68/2.34 % (8504)Instruction limit reached!
% 7.68/2.34 % (8504)------------------------------
% 7.68/2.34 % (8504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.68/2.34 % (8504)Termination reason: Unknown
% 7.68/2.34 % (8504)Termination phase: Saturation
% 7.68/2.34
% 7.68/2.34 % (8504)Memory used [KB]: 2686
% 7.68/2.34 % (8504)Time elapsed: 0.043 s
% 7.68/2.34 % (8504)Instructions burned: 156 (million)
% 7.68/2.34 % (8504)------------------------------
% 7.68/2.34 % (8504)------------------------------
% 7.68/2.34 % (8502)Instruction limit reached!
% 7.68/2.34 % (8502)------------------------------
% 7.68/2.34 % (8502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.68/2.34 % (8502)Termination reason: Unknown
% 7.68/2.34 % (8502)Termination phase: Saturation
% 7.68/2.34
% 7.68/2.34 % (8502)Memory used [KB]: 7036
% 7.68/2.34 % (8502)Time elapsed: 0.052 s
% 7.68/2.34 % (8502)Instructions burned: 182 (million)
% 7.68/2.34 % (8502)------------------------------
% 7.68/2.34 % (8502)------------------------------
% 7.68/2.34 % (8506)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_8323 for (2992ds/216Mi)
% 7.68/2.34 % (8503)Instruction limit reached!
% 7.68/2.34 % (8503)------------------------------
% 7.68/2.34 % (8503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.68/2.34 % (8503)Termination reason: Unknown
% 7.68/2.34 % (8503)Termination phase: Saturation
% 7.68/2.34
% 7.68/2.34 % (8503)Memory used [KB]: 7164
% 7.68/2.34 % (8503)Time elapsed: 0.056 s
% 7.68/2.34 % (8503)Instructions burned: 183 (million)
% 7.68/2.34 % (8503)------------------------------
% 7.68/2.34 % (8503)------------------------------
% 7.68/2.34 % (8507)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_8323 for (2992ds/114Mi)
% 7.68/2.35 % (8508)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_8323 for (2992ds/922Mi)
% 7.68/2.35 % (8509)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_8323 for (2992ds/182Mi)
% 7.68/2.36 % (8500)Instruction limit reached!
% 7.68/2.36 % (8500)------------------------------
% 7.68/2.36 % (8500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.68/2.36 % (8500)Termination reason: Unknown
% 7.68/2.36 % (8500)Termination phase: Saturation
% 7.68/2.36
% 7.68/2.36 % (8500)Memory used [KB]: 7675
% 7.68/2.36 % (8500)Time elapsed: 0.090 s
% 7.68/2.36 % (8500)Instructions burned: 298 (million)
% 7.68/2.36 % (8500)------------------------------
% 7.68/2.36 % (8500)------------------------------
% 7.68/2.37 % (8510)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_8323 for (2992ds/164Mi)
% 7.68/2.38 % (8507)Instruction limit reached!
% 7.68/2.38 % (8507)------------------------------
% 7.68/2.38 % (8507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.68/2.38 % (8507)Termination reason: Unknown
% 7.68/2.38 % (8507)Termination phase: Saturation
% 7.68/2.38
% 7.68/2.38 % (8507)Memory used [KB]: 6908
% 7.68/2.38 % (8507)Time elapsed: 0.034 s
% 7.68/2.38 % (8507)Instructions burned: 115 (million)
% 7.68/2.38 % (8507)------------------------------
% 7.68/2.38 % (8507)------------------------------
% 7.68/2.38 % (8498)Instruction limit reached!
% 7.68/2.38 % (8498)------------------------------
% 7.68/2.38 % (8498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.68/2.38 % (8498)Termination reason: Unknown
% 7.68/2.38 % (8498)Termination phase: Saturation
% 7.68/2.38
% 7.68/2.38 % (8498)Memory used [KB]: 7675
% 7.68/2.38 % (8498)Time elapsed: 0.139 s
% 7.68/2.38 % (8498)Instructions burned: 459 (million)
% 7.68/2.38 % (8498)------------------------------
% 7.68/2.38 % (8498)------------------------------
% 7.68/2.39 % (8511)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_8323 for (2991ds/50Mi)
% 7.68/2.39 % (8512)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_8323 for (2991ds/368Mi)
% 8.26/2.40 % (8506)Instruction limit reached!
% 8.26/2.40 % (8506)------------------------------
% 8.26/2.40 % (8506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.26/2.40 % (8506)Termination reason: Unknown
% 8.26/2.40 % (8506)Termination phase: Saturation
% 8.26/2.40
% 8.26/2.40 % (8506)Memory used [KB]: 7419
% 8.26/2.40 % (8506)Time elapsed: 0.061 s
% 8.26/2.40 % (8506)Instructions burned: 216 (million)
% 8.26/2.40 % (8506)------------------------------
% 8.26/2.40 % (8506)------------------------------
% 8.26/2.40 % (8511)Instruction limit reached!
% 8.26/2.40 % (8511)------------------------------
% 8.26/2.40 % (8511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.26/2.40 % (8511)Termination reason: Unknown
% 8.26/2.40 % (8511)Termination phase: Property scanning
% 8.26/2.40
% 8.26/2.40 % (8511)Memory used [KB]: 2174
% 8.26/2.40 % (8511)Time elapsed: 0.015 s
% 8.26/2.40 % (8511)Instructions burned: 52 (million)
% 8.26/2.40 % (8511)------------------------------
% 8.26/2.40 % (8511)------------------------------
% 8.26/2.40 % (8509)Instruction limit reached!
% 8.26/2.40 % (8509)------------------------------
% 8.26/2.40 % (8509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.26/2.40 % (8509)Termination reason: Unknown
% 8.26/2.40 % (8509)Termination phase: Saturation
% 8.26/2.40
% 8.26/2.40 % (8509)Memory used [KB]: 7291
% 8.26/2.40 % (8509)Time elapsed: 0.051 s
% 8.26/2.40 % (8509)Instructions burned: 183 (million)
% 8.26/2.40 % (8509)------------------------------
% 8.26/2.40 % (8509)------------------------------
% 8.26/2.41 % (8513)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_8323 for (2991ds/1021Mi)
% 8.26/2.41 % (8514)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_8323 for (2991ds/267Mi)
% 8.26/2.41 % (8515)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_8323 for (2991ds/204Mi)
% 8.26/2.41 % (8510)Instruction limit reached!
% 8.26/2.41 % (8510)------------------------------
% 8.26/2.41 % (8510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.26/2.41 % (8510)Termination reason: Unknown
% 8.26/2.41 % (8510)Termination phase: Saturation
% 8.26/2.41
% 8.26/2.41 % (8510)Memory used [KB]: 2430
% 8.26/2.41 % (8510)Time elapsed: 0.048 s
% 8.26/2.41 % (8510)Instructions burned: 167 (million)
% 8.26/2.41 % (8510)------------------------------
% 8.26/2.41 % (8510)------------------------------
% 8.26/2.42 % (8516)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_8323 for (2991ds/26Mi)
% 8.26/2.43 % (8516)Instruction limit reached!
% 8.26/2.43 % (8516)------------------------------
% 8.26/2.43 % (8516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.26/2.43 % (8516)Termination reason: Unknown
% 8.26/2.43 % (8516)Termination phase: shuffling
% 8.26/2.43
% 8.26/2.43 % (8516)Memory used [KB]: 1918
% 8.26/2.43 % (8516)Time elapsed: 0.009 s
% 8.26/2.43 % (8516)Instructions burned: 29 (million)
% 8.26/2.43 % (8516)------------------------------
% 8.26/2.43 % (8516)------------------------------
% 8.26/2.44 % (8517)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_8323 for (2991ds/53Mi)
% 8.26/2.45 % (8517)Instruction limit reached!
% 8.26/2.45 % (8517)------------------------------
% 8.26/2.45 % (8517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.26/2.45 % (8517)Termination reason: Unknown
% 8.26/2.45 % (8517)Termination phase: Property scanning
% 8.26/2.45
% 8.26/2.45 % (8517)Memory used [KB]: 2174
% 8.26/2.45 % (8517)Time elapsed: 0.016 s
% 8.26/2.45 % (8517)Instructions burned: 56 (million)
% 8.26/2.45 % (8517)------------------------------
% 8.26/2.45 % (8517)------------------------------
% 8.26/2.46 % (8518)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_8323 for (2991ds/4436Mi)
% 8.26/2.47 % (8515)Instruction limit reached!
% 8.26/2.47 % (8515)------------------------------
% 8.26/2.47 % (8515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.26/2.47 % (8515)Termination reason: Unknown
% 8.26/2.47 % (8515)Termination phase: Saturation
% 8.26/2.47
% 8.26/2.47 % (8515)Memory used [KB]: 7036
% 8.26/2.47 % (8515)Time elapsed: 0.061 s
% 8.26/2.47 % (8515)Instructions burned: 206 (million)
% 8.26/2.47 % (8515)------------------------------
% 8.26/2.47 % (8515)------------------------------
% 8.26/2.48 % (8519)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_8323 for (2990ds/1539Mi)
% 8.26/2.49 % (8514)Instruction limit reached!
% 8.26/2.49 % (8514)------------------------------
% 8.26/2.49 % (8514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.26/2.49 % (8514)Termination reason: Unknown
% 8.26/2.49 % (8514)Termination phase: Saturation
% 8.26/2.49
% 8.26/2.49 % (8514)Memory used [KB]: 7547
% 8.26/2.49 % (8514)Time elapsed: 0.080 s
% 8.26/2.49 % (8514)Instructions burned: 267 (million)
% 8.26/2.49 % (8514)------------------------------
% 8.26/2.49 % (8514)------------------------------
% 8.67/2.50 % (8520)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_8323 for (2990ds/408Mi)
% 8.67/2.50 % (8512)Instruction limit reached!
% 8.67/2.50 % (8512)------------------------------
% 8.67/2.50 % (8512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.67/2.50 % (8512)Termination reason: Unknown
% 8.67/2.50 % (8512)Termination phase: Saturation
% 8.67/2.50
% 8.67/2.50 % (8512)Memory used [KB]: 8315
% 8.67/2.50 % (8512)Time elapsed: 0.114 s
% 8.67/2.50 % (8512)Instructions burned: 370 (million)
% 8.67/2.50 % (8512)------------------------------
% 8.67/2.50 % (8512)------------------------------
% 8.67/2.51 % (8521)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_8323 for (2990ds/5205Mi)
% 8.67/2.58 % (8501)Instruction limit reached!
% 8.67/2.58 % (8501)------------------------------
% 8.67/2.58 % (8501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.67/2.58 % (8501)Termination reason: Unknown
% 8.67/2.58 % (8501)Termination phase: Saturation
% 8.67/2.58
% 8.67/2.58 % (8501)Memory used [KB]: 10618
% 8.67/2.58 % (8501)Time elapsed: 0.307 s
% 8.67/2.58 % (8501)Instructions burned: 989 (million)
% 8.67/2.58 % (8501)------------------------------
% 8.67/2.58 % (8501)------------------------------
% 8.67/2.60 % (8522)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_8323 for (2989ds/1913Mi)
% 9.11/2.62 % (8520)Instruction limit reached!
% 9.11/2.62 % (8520)------------------------------
% 9.11/2.62 % (8520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.62 % (8520)Termination reason: Unknown
% 9.11/2.62 % (8520)Termination phase: Saturation
% 9.11/2.62
% 9.11/2.62 % (8520)Memory used [KB]: 7931
% 9.11/2.62 % (8520)Time elapsed: 0.147 s
% 9.11/2.62 % (8520)Instructions burned: 410 (million)
% 9.11/2.62 % (8520)------------------------------
% 9.11/2.62 % (8520)------------------------------
% 9.11/2.63 % (8508)Instruction limit reached!
% 9.11/2.63 % (8508)------------------------------
% 9.11/2.63 % (8508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.63 % (8508)Termination reason: Unknown
% 9.11/2.63 % (8508)Termination phase: Saturation
% 9.11/2.63
% 9.11/2.63 % (8508)Memory used [KB]: 7803
% 9.11/2.63 % (8508)Time elapsed: 0.288 s
% 9.11/2.63 % (8508)Instructions burned: 922 (million)
% 9.11/2.63 % (8508)------------------------------
% 9.11/2.63 % (8508)------------------------------
% 9.11/2.63 % (8523)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_8323 for (2989ds/4350Mi)
% 9.11/2.64 % (8524)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_8323 for (2989ds/68Mi)
% 9.11/2.66 % (8524)Instruction limit reached!
% 9.11/2.66 % (8524)------------------------------
% 9.11/2.66 % (8524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.66 % (8524)Termination reason: Unknown
% 9.11/2.66 % (8524)Termination phase: Property scanning
% 9.11/2.66
% 9.11/2.66 % (8524)Memory used [KB]: 2302
% 9.11/2.66 % (8524)Time elapsed: 0.021 s
% 9.11/2.66 % (8524)Instructions burned: 68 (million)
% 9.11/2.66 % (8524)------------------------------
% 9.11/2.66 % (8524)------------------------------
% 9.11/2.67 % (8525)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_8323 for (2989ds/358Mi)
% 9.56/2.73 % (8513)Instruction limit reached!
% 9.56/2.73 % (8513)------------------------------
% 9.56/2.73 % (8513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.56/2.73 % (8513)Termination reason: Unknown
% 9.56/2.73 % (8513)Termination phase: Saturation
% 9.56/2.73
% 9.56/2.73 % (8513)Memory used [KB]: 9083
% 9.56/2.73 % (8513)Time elapsed: 0.318 s
% 9.56/2.73 % (8513)Instructions burned: 1023 (million)
% 9.56/2.73 % (8513)------------------------------
% 9.56/2.73 % (8513)------------------------------
% 9.56/2.74 % (8526)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_8323 for (2988ds/31Mi)
% 9.56/2.75 % (8526)Instruction limit reached!
% 9.56/2.75 % (8526)------------------------------
% 9.56/2.75 % (8526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.56/2.75 % (8526)Termination reason: Unknown
% 9.56/2.75 % (8526)Termination phase: Property scanning
% 9.56/2.75
% 9.56/2.75 % (8526)Memory used [KB]: 1791
% 9.56/2.75 % (8526)Time elapsed: 0.012 s
% 9.56/2.75 % (8526)Instructions burned: 34 (million)
% 9.56/2.75 % (8526)------------------------------
% 9.56/2.75 % (8526)------------------------------
% 9.56/2.76 % (8527)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_8323 for (2988ds/279Mi)
% 9.56/2.78 % (8525)Instruction limit reached!
% 9.56/2.78 % (8525)------------------------------
% 9.56/2.78 % (8525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.56/2.78 % (8525)Termination reason: Unknown
% 9.56/2.78 % (8525)Termination phase: Saturation
% 9.56/2.78
% 9.56/2.78 % (8525)Memory used [KB]: 7419
% 9.56/2.78 % (8525)Time elapsed: 0.134 s
% 9.56/2.78 % (8525)Instructions burned: 359 (million)
% 9.56/2.78 % (8525)------------------------------
% 9.56/2.78 % (8525)------------------------------
% 9.56/2.79 % (8527)Refutation not found, incomplete strategy
% 9.56/2.79 % (8527)------------------------------
% 9.56/2.79 % (8527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.56/2.79 % (8527)Termination reason: Refutation not found, incomplete strategy
% 9.56/2.79
% 9.56/2.79
% 9.56/2.79 % (8527)Memory used [KB]: 6908
% 9.56/2.79 % (8527)Time elapsed: 0.034 s
% 9.56/2.79 % (8527)Instructions burned: 121 (million)
% 9.56/2.79 % (8527)------------------------------
% 9.56/2.79 % (8527)------------------------------
% 9.56/2.79 % (8528)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_8323 for (2987ds/258Mi)
% 10.07/2.80 % (8529)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_8323 for (2987ds/26Mi)
% 10.07/2.81 % (8529)Instruction limit reached!
% 10.07/2.81 % (8529)------------------------------
% 10.07/2.81 % (8529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.07/2.81 % (8529)Termination reason: Unknown
% 10.07/2.81 % (8529)Termination phase: shuffling
% 10.07/2.81
% 10.07/2.81 % (8529)Memory used [KB]: 1918
% 10.07/2.81 % (8529)Time elapsed: 0.009 s
% 10.07/2.81 % (8529)Instructions burned: 28 (million)
% 10.07/2.81 % (8529)------------------------------
% 10.07/2.81 % (8529)------------------------------
% 10.07/2.82 % (8530)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_8323 for (2987ds/995Mi)
% 10.07/2.87 % (8528)Instruction limit reached!
% 10.07/2.87 % (8528)------------------------------
% 10.07/2.87 % (8528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.07/2.87 % (8528)Termination reason: Unknown
% 10.07/2.87 % (8528)Termination phase: Saturation
% 10.07/2.87
% 10.07/2.87 % (8528)Memory used [KB]: 7164
% 10.07/2.87 % (8528)Time elapsed: 0.077 s
% 10.07/2.87 % (8528)Instructions burned: 258 (million)
% 10.07/2.87 % (8528)------------------------------
% 10.07/2.87 % (8528)------------------------------
% 10.07/2.88 % (8531)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_8323 for (2986ds/373Mi)
% 10.18/2.95 % (8519)Instruction limit reached!
% 10.18/2.95 % (8519)------------------------------
% 10.18/2.95 % (8519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.18/2.95 % (8519)Termination reason: Unknown
% 10.18/2.95 % (8519)Termination phase: Saturation
% 10.18/2.95
% 10.18/2.95 % (8519)Memory used [KB]: 11513
% 10.18/2.95 % (8519)Time elapsed: 0.492 s
% 10.18/2.95 % (8519)Instructions burned: 1540 (million)
% 10.18/2.95 % (8519)------------------------------
% 10.18/2.95 % (8519)------------------------------
% 10.18/2.96 % (8532)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_8323 for (2985ds/253Mi)
% 10.18/3.00 % (8531)Instruction limit reached!
% 10.18/3.00 % (8531)------------------------------
% 10.18/3.00 % (8531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.18/3.00 % (8531)Termination reason: Unknown
% 10.18/3.00 % (8531)Termination phase: Saturation
% 10.18/3.00
% 10.18/3.00 % (8531)Memory used [KB]: 8571
% 10.18/3.00 % (8531)Time elapsed: 0.119 s
% 10.18/3.00 % (8531)Instructions burned: 374 (million)
% 10.18/3.00 % (8531)------------------------------
% 10.18/3.00 % (8531)------------------------------
% 10.18/3.01 % (8533)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_8323 for (2985ds/832Mi)
% 12.85/3.04 % (8532)Instruction limit reached!
% 12.85/3.04 % (8532)------------------------------
% 12.85/3.04 % (8532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.85/3.04 % (8532)Termination reason: Unknown
% 12.85/3.04 % (8532)Termination phase: Saturation
% 12.85/3.04
% 12.85/3.04 % (8532)Memory used [KB]: 7547
% 12.85/3.04 % (8532)Time elapsed: 0.074 s
% 12.85/3.04 % (8532)Instructions burned: 253 (million)
% 12.85/3.04 % (8532)------------------------------
% 12.85/3.04 % (8532)------------------------------
% 12.85/3.05 % (8534)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_8323 for (2985ds/668Mi)
% 13.40/3.11 % (8530)Instruction limit reached!
% 13.40/3.11 % (8530)------------------------------
% 13.40/3.11 % (8530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.40/3.11 % (8530)Termination reason: Unknown
% 13.40/3.11 % (8530)Termination phase: Saturation
% 13.40/3.11
% 13.40/3.11 % (8530)Memory used [KB]: 9338
% 13.40/3.11 % (8530)Time elapsed: 0.297 s
% 13.40/3.11 % (8530)Instructions burned: 995 (million)
% 13.40/3.11 % (8530)------------------------------
% 13.40/3.11 % (8530)------------------------------
% 13.40/3.12 % (8535)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_8323 for (2984ds/40Mi)
% 13.40/3.14 % (8535)Instruction limit reached!
% 13.40/3.14 % (8535)------------------------------
% 13.40/3.14 % (8535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.40/3.14 % (8535)Termination reason: Unknown
% 13.40/3.14 % (8535)Termination phase: Property scanning
% 13.40/3.14
% 13.40/3.14 % (8535)Memory used [KB]: 2174
% 13.40/3.14 % (8535)Time elapsed: 0.013 s
% 13.40/3.14 % (8535)Instructions burned: 42 (million)
% 13.40/3.14 % (8535)------------------------------
% 13.40/3.14 % (8535)------------------------------
% 13.40/3.14 % (8536)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_8323 for (2984ds/294Mi)
% 13.40/3.17 % (8536)Refutation not found, incomplete strategy
% 13.40/3.17 % (8536)------------------------------
% 13.40/3.17 % (8536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.40/3.17 % (8536)Termination reason: Refutation not found, incomplete strategy
% 13.40/3.17
% 13.40/3.17
% 13.40/3.17 % (8536)Memory used [KB]: 6780
% 13.40/3.17 % (8536)Time elapsed: 0.026 s
% 13.40/3.17 % (8536)Instructions burned: 91 (million)
% 13.40/3.17 % (8536)------------------------------
% 13.40/3.17 % (8536)------------------------------
% 13.40/3.18 % (8537)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_8323 for (2983ds/187Mi)
% 13.40/3.19 % (8522)Instruction limit reached!
% 13.40/3.19 % (8522)------------------------------
% 13.40/3.19 % (8522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.40/3.19 % (8522)Termination reason: Unknown
% 13.40/3.19 % (8522)Termination phase: Saturation
% 13.40/3.19
% 13.40/3.19 % (8522)Memory used [KB]: 5117
% 13.40/3.19 % (8522)Time elapsed: 0.611 s
% 13.40/3.19 % (8522)Instructions burned: 1913 (million)
% 13.40/3.19 % (8522)------------------------------
% 13.40/3.19 % (8522)------------------------------
% 13.80/3.20 % (8538)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_8323 for (2983ds/371Mi)
% 13.80/3.23 % (8537)Instruction limit reached!
% 13.80/3.23 % (8537)------------------------------
% 13.80/3.23 % (8537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.80/3.23 % (8537)Termination reason: Unknown
% 13.80/3.23 % (8537)Termination phase: Saturation
% 13.80/3.23
% 13.80/3.23 % (8537)Memory used [KB]: 7164
% 13.80/3.23 % (8537)Time elapsed: 0.055 s
% 13.80/3.23 % (8537)Instructions burned: 188 (million)
% 13.80/3.23 % (8537)------------------------------
% 13.80/3.23 % (8537)------------------------------
% 13.80/3.24 % (8539)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_8323 for (2983ds/1827Mi)
% 13.80/3.25 % (8534)Instruction limit reached!
% 13.80/3.25 % (8534)------------------------------
% 13.80/3.25 % (8534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.80/3.25 % (8534)Termination reason: Unknown
% 13.80/3.25 % (8534)Termination phase: Saturation
% 13.80/3.25
% 13.80/3.25 % (8534)Memory used [KB]: 13560
% 13.80/3.25 % (8534)Time elapsed: 0.201 s
% 13.80/3.25 % (8534)Instructions burned: 671 (million)
% 13.80/3.25 % (8534)------------------------------
% 13.80/3.25 % (8534)------------------------------
% 13.80/3.26 % (8540)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_8323 for (2983ds/70Mi)
% 13.80/3.26 % (8533)Instruction limit reached!
% 13.80/3.26 % (8533)------------------------------
% 13.80/3.26 % (8533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.80/3.26 % (8533)Termination reason: Unknown
% 13.80/3.26 % (8533)Termination phase: Saturation
% 13.80/3.26
% 13.80/3.26 % (8533)Memory used [KB]: 7931
% 13.80/3.26 % (8533)Time elapsed: 0.258 s
% 13.80/3.26 % (8533)Instructions burned: 835 (million)
% 13.80/3.26 % (8533)------------------------------
% 13.80/3.26 % (8533)------------------------------
% 13.80/3.27 % (8541)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_8323 for (2982ds/316Mi)
% 13.80/3.28 % (8540)Instruction limit reached!
% 13.80/3.28 % (8540)------------------------------
% 13.80/3.28 % (8540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.80/3.28 % (8540)Termination reason: Unknown
% 13.80/3.28 % (8540)Termination phase: Preprocessing 3
% 13.80/3.28
% 13.80/3.28 % (8540)Memory used [KB]: 2174
% 13.80/3.28 % (8540)Time elapsed: 0.020 s
% 13.80/3.28 % (8540)Instructions burned: 71 (million)
% 13.80/3.28 % (8540)------------------------------
% 13.80/3.28 % (8540)------------------------------
% 13.80/3.29 % (8542)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_8323 for (2982ds/932Mi)
% 14.67/3.32 % (8538)Instruction limit reached!
% 14.67/3.32 % (8538)------------------------------
% 14.67/3.32 % (8538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.67/3.32 % (8538)Termination reason: Unknown
% 14.67/3.32 % (8538)Termination phase: Saturation
% 14.67/3.32
% 14.67/3.32 % (8538)Memory used [KB]: 7675
% 14.67/3.32 % (8538)Time elapsed: 0.117 s
% 14.67/3.32 % (8538)Instructions burned: 374 (million)
% 14.67/3.32 % (8538)------------------------------
% 14.67/3.32 % (8538)------------------------------
% 14.67/3.33 % (8543)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_8323 for (2982ds/4714Mi)
% 14.67/3.33 % (8541)Refutation not found, incomplete strategy
% 14.67/3.33 % (8541)------------------------------
% 14.67/3.33 % (8541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.67/3.33 % (8541)Termination reason: Refutation not found, incomplete strategy
% 14.67/3.33
% 14.67/3.33
% 14.67/3.33 % (8541)Memory used [KB]: 7419
% 14.67/3.33 % (8541)Time elapsed: 0.054 s
% 14.67/3.33 % (8541)Instructions burned: 197 (million)
% 14.67/3.33 % (8541)------------------------------
% 14.67/3.33 % (8541)------------------------------
% 14.67/3.34 % (8544)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_8323 for (2982ds/8250Mi)
% 14.67/3.38 % (8543)Refutation not found, incomplete strategy
% 14.67/3.38 % (8543)------------------------------
% 14.67/3.38 % (8543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.67/3.38 % (8543)Termination reason: Refutation not found, incomplete strategy
% 14.67/3.38
% 14.67/3.38
% 14.67/3.38 % (8543)Memory used [KB]: 7547
% 14.67/3.38 % (8543)Time elapsed: 0.054 s
% 14.67/3.38 % (8543)Instructions burned: 192 (million)
% 14.67/3.38 % (8543)------------------------------
% 14.67/3.38 % (8543)------------------------------
% 14.67/3.39 % (8545)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_8323 for (2981ds/770Mi)
% 15.21/3.41 % (8545)Refutation not found, incomplete strategy
% 15.21/3.41 % (8545)------------------------------
% 15.21/3.41 % (8545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.21/3.41 % (8545)Termination reason: Refutation not found, incomplete strategy
% 15.21/3.41
% 15.21/3.41
% 15.21/3.41 % (8545)Memory used [KB]: 6524
% 15.21/3.41 % (8545)Time elapsed: 0.018 s
% 15.21/3.41 % (8545)Instructions burned: 53 (million)
% 15.21/3.41 % (8545)------------------------------
% 15.21/3.41 % (8545)------------------------------
% 15.21/3.42 % (8546)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_8323 for (2981ds/794Mi)
% 15.54/3.58 % (8542)Instruction limit reached!
% 15.54/3.58 % (8542)------------------------------
% 15.54/3.58 % (8542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/3.58 % (8542)Termination reason: Unknown
% 15.54/3.58 % (8542)Termination phase: Saturation
% 15.54/3.58
% 15.54/3.58 % (8542)Memory used [KB]: 10746
% 15.54/3.58 % (8542)Time elapsed: 0.293 s
% 15.54/3.58 % (8542)Instructions burned: 934 (million)
% 15.54/3.58 % (8542)------------------------------
% 15.54/3.58 % (8542)------------------------------
% 15.54/3.59 % (8547)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_8323 for (2979ds/464Mi)
% 16.16/3.66 % (8546)Instruction limit reached!
% 16.16/3.66 % (8546)------------------------------
% 16.16/3.66 % (8546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.16/3.66 % (8546)Termination reason: Unknown
% 16.16/3.66 % (8546)Termination phase: Saturation
% 16.16/3.66
% 16.16/3.66 % (8546)Memory used [KB]: 5373
% 16.16/3.66 % (8546)Time elapsed: 0.243 s
% 16.16/3.66 % (8546)Instructions burned: 794 (million)
% 16.16/3.66 % (8546)------------------------------
% 16.16/3.66 % (8546)------------------------------
% 16.16/3.67 % (8548)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_8323 for (2979ds/1376Mi)
% 16.70/3.73 % (8547)Instruction limit reached!
% 16.70/3.73 % (8547)------------------------------
% 16.70/3.73 % (8547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.70/3.73 % (8547)Termination reason: Unknown
% 16.70/3.73 % (8547)Termination phase: Saturation
% 16.70/3.73
% 16.70/3.73 % (8547)Memory used [KB]: 7675
% 16.70/3.73 % (8547)Time elapsed: 0.140 s
% 16.70/3.73 % (8547)Instructions burned: 467 (million)
% 16.70/3.73 % (8547)------------------------------
% 16.70/3.73 % (8547)------------------------------
% 16.70/3.74 % (8549)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_8323 for (2978ds/906Mi)
% 17.14/3.83 % (8539)Instruction limit reached!
% 17.14/3.83 % (8539)------------------------------
% 17.14/3.83 % (8539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.14/3.83 % (8539)Termination reason: Unknown
% 17.14/3.83 % (8539)Termination phase: Saturation
% 17.14/3.83
% 17.14/3.83 % (8539)Memory used [KB]: 11129
% 17.14/3.83 % (8539)Time elapsed: 0.584 s
% 17.14/3.83 % (8539)Instructions burned: 1829 (million)
% 17.14/3.83 % (8539)------------------------------
% 17.14/3.83 % (8539)------------------------------
% 17.14/3.84 % (8550)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_8323 for (2977ds/434Mi)
% 17.14/3.84 % (8518)Instruction limit reached!
% 17.14/3.84 % (8518)------------------------------
% 17.14/3.84 % (8518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.14/3.84 % (8518)Termination reason: Unknown
% 17.14/3.84 % (8518)Termination phase: Saturation
% 17.14/3.84
% 17.14/3.84 % (8518)Memory used [KB]: 11385
% 17.14/3.84 % (8518)Time elapsed: 1.401 s
% 17.14/3.84 % (8518)Instructions burned: 4437 (million)
% 17.14/3.84 % (8518)------------------------------
% 17.14/3.84 % (8518)------------------------------
% 17.14/3.85 % (8551)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_8323 for (2977ds/865Mi)
% 18.00/3.95 % (8523)Instruction limit reached!
% 18.00/3.95 % (8523)------------------------------
% 18.00/3.95 % (8523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.00/3.95 % (8523)Termination reason: Unknown
% 18.00/3.95 % (8523)Termination phase: Saturation
% 18.00/3.95
% 18.00/3.95 % (8523)Memory used [KB]: 12792
% 18.00/3.95 % (8523)Time elapsed: 1.336 s
% 18.00/3.95 % (8523)Instructions burned: 4351 (million)
% 18.00/3.95 % (8523)------------------------------
% 18.00/3.95 % (8523)------------------------------
% 18.00/3.96 % (8552)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_8323 for (2976ds/593Mi)
% 18.00/3.97 % (8550)Instruction limit reached!
% 18.00/3.97 % (8550)------------------------------
% 18.00/3.97 % (8550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.00/3.97 % (8550)Termination reason: Unknown
% 18.00/3.97 % (8550)Termination phase: Saturation
% 18.00/3.97
% 18.00/3.97 % (8550)Memory used [KB]: 7675
% 18.00/3.97 % (8550)Time elapsed: 0.130 s
% 18.00/3.97 % (8550)Instructions burned: 434 (million)
% 18.00/3.97 % (8550)------------------------------
% 18.00/3.97 % (8550)------------------------------
% 18.00/3.98 % (8553)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_8323 for (2975ds/443Mi)
% 18.00/3.98 % (8521)Instruction limit reached!
% 18.00/3.98 % (8521)------------------------------
% 18.00/3.98 % (8521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.00/3.98 % (8521)Termination reason: Unknown
% 18.00/3.98 % (8521)Termination phase: Saturation
% 18.00/3.98
% 18.00/3.98 % (8521)Memory used [KB]: 16375
% 18.00/3.98 % (8521)Time elapsed: 1.492 s
% 18.00/3.98 % (8521)Instructions burned: 5206 (million)
% 18.00/3.98 % (8521)------------------------------
% 18.00/3.98 % (8521)------------------------------
% 18.00/3.99 % (8554)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_8323 for (2975ds/594Mi)
% 19.83/4.06 % (8549)Instruction limit reached!
% 19.83/4.06 % (8549)------------------------------
% 19.83/4.06 % (8549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.83/4.06 % (8549)Termination reason: Unknown
% 19.83/4.06 % (8549)Termination phase: Saturation
% 19.83/4.06
% 19.83/4.06 % (8549)Memory used [KB]: 11001
% 19.83/4.06 % (8549)Time elapsed: 0.330 s
% 19.83/4.06 % (8549)Instructions burned: 906 (million)
% 19.83/4.06 % (8549)------------------------------
% 19.83/4.06 % (8549)------------------------------
% 19.83/4.07 % (8555)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_8323 for (2975ds/327Mi)
% 19.83/4.07 % (8548)Instruction limit reached!
% 19.83/4.07 % (8548)------------------------------
% 19.83/4.07 % (8548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.83/4.07 % (8548)Termination reason: Unknown
% 19.83/4.07 % (8548)Termination phase: Saturation
% 19.83/4.07
% 19.83/4.07 % (8548)Memory used [KB]: 13304
% 19.83/4.07 % (8548)Time elapsed: 0.407 s
% 19.83/4.07 % (8548)Instructions burned: 1379 (million)
% 19.83/4.07 % (8548)------------------------------
% 19.83/4.07 % (8548)------------------------------
% 19.83/4.08 % (8556)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_8323 for (2974ds/5411Mi)
% 19.83/4.11 % (8551)Instruction limit reached!
% 19.83/4.11 % (8551)------------------------------
% 19.83/4.11 % (8551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.83/4.11 % (8551)Termination reason: Unknown
% 19.83/4.11 % (8551)Termination phase: Saturation
% 19.83/4.11
% 19.83/4.11 % (8551)Memory used [KB]: 8955
% 19.83/4.11 % (8551)Time elapsed: 0.256 s
% 19.83/4.11 % (8551)Instructions burned: 866 (million)
% 19.83/4.11 % (8551)------------------------------
% 19.83/4.11 % (8551)------------------------------
% 19.83/4.11 % (8553)Instruction limit reached!
% 19.83/4.11 % (8553)------------------------------
% 19.83/4.11 % (8553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.83/4.11 % (8553)Termination reason: Unknown
% 19.83/4.11 % (8553)Termination phase: Saturation
% 19.83/4.11
% 19.83/4.11 % (8553)Memory used [KB]: 8187
% 19.83/4.11 % (8553)Time elapsed: 0.137 s
% 19.83/4.11 % (8553)Instructions burned: 445 (million)
% 19.83/4.11 % (8553)------------------------------
% 19.83/4.11 % (8553)------------------------------
% 20.48/4.12 % (8557)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_8323 for (2974ds/1762Mi)
% 20.48/4.12 % (8558)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_8323 for (2974ds/96Mi)
% 20.48/4.13 % (8552)Instruction limit reached!
% 20.48/4.13 % (8552)------------------------------
% 20.48/4.13 % (8552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.48/4.13 % (8552)Termination reason: Unknown
% 20.48/4.13 % (8552)Termination phase: Saturation
% 20.48/4.13
% 20.48/4.13 % (8552)Memory used [KB]: 9210
% 20.48/4.13 % (8552)Time elapsed: 0.175 s
% 20.48/4.13 % (8552)Instructions burned: 594 (million)
% 20.48/4.13 % (8552)------------------------------
% 20.48/4.13 % (8552)------------------------------
% 20.48/4.14 % (8559)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_8323 for (2974ds/503Mi)
% 20.48/4.15 % (8558)Instruction limit reached!
% 20.48/4.15 % (8558)------------------------------
% 20.48/4.15 % (8558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.48/4.15 % (8558)Termination reason: Unknown
% 20.48/4.15 % (8558)Termination phase: Property scanning
% 20.48/4.15
% 20.48/4.15 % (8558)Memory used [KB]: 2302
% 20.48/4.15 % (8558)Time elapsed: 0.027 s
% 20.48/4.15 % (8558)Instructions burned: 98 (million)
% 20.48/4.15 % (8558)------------------------------
% 20.48/4.15 % (8558)------------------------------
% 20.48/4.16 % (8560)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_8323 for (2974ds/90Mi)
% 20.48/4.17 % (8555)Instruction limit reached!
% 20.48/4.17 % (8555)------------------------------
% 20.48/4.17 % (8555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.48/4.17 % (8555)Termination reason: Unknown
% 20.48/4.17 % (8555)Termination phase: Saturation
% 20.48/4.17
% 20.48/4.17 % (8555)Memory used [KB]: 7803
% 20.48/4.17 % (8555)Time elapsed: 0.104 s
% 20.48/4.17 % (8555)Instructions burned: 330 (million)
% 20.48/4.17 % (8555)------------------------------
% 20.48/4.17 % (8555)------------------------------
% 20.48/4.18 % (8554)Instruction limit reached!
% 20.48/4.18 % (8554)------------------------------
% 20.48/4.18 % (8554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.48/4.18 % (8554)Termination reason: Unknown
% 20.48/4.18 % (8554)Termination phase: Saturation
% 20.48/4.18
% 20.48/4.18 % (8554)Memory used [KB]: 8443
% 20.48/4.18 % (8554)Time elapsed: 0.190 s
% 20.48/4.18 % (8554)Instructions burned: 596 (million)
% 20.48/4.18 % (8554)------------------------------
% 20.48/4.18 % (8554)------------------------------
% 20.48/4.18 % (8561)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_8323 for (2973ds/593Mi)
% 20.48/4.18 % (8560)Instruction limit reached!
% 20.48/4.18 % (8560)------------------------------
% 20.48/4.18 % (8560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.48/4.18 % (8560)Termination reason: Unknown
% 20.48/4.18 % (8560)Termination phase: Property scanning
% 20.48/4.18
% 20.48/4.18 % (8560)Memory used [KB]: 2302
% 20.48/4.18 % (8560)Time elapsed: 0.027 s
% 20.48/4.18 % (8560)Instructions burned: 91 (million)
% 20.48/4.18 % (8560)------------------------------
% 20.48/4.18 % (8560)------------------------------
% 20.48/4.19 % (8562)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_8323 for (2973ds/1512Mi)
% 20.48/4.19 % (8563)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_8323 for (2973ds/569Mi)
% 20.84/4.22 % (8556)First to succeed.
% 20.84/4.23 % (8556)Refutation found. Thanks to Tanya!
% 20.84/4.23 % SZS status Theorem for DTF2THF_8323
% 20.84/4.23 % SZS output start Proof for DTF2THF_8323
% 20.84/4.23 thf(type_def_5, type, trace: ($tType) > $tType).
% 20.84/4.23 thf(type_def_6, type, list: ($tType) > $tType).
% 20.84/4.23 thf(type_def_7, type, nat: $tType).
% 20.84/4.23 thf(type_def_9, type, prefix: ($tType) > $tType).
% 20.84/4.23 thf(type_def_10, type, formula: ($tType) > $tType).
% 20.84/4.23 thf(type_def_11, type, i: $tType).
% 20.84/4.23 thf(type_def_12, type, char: $tType).
% 20.84/4.23 thf(type_def_13, type, product_prod: ($tType * $tType) > $tType).
% 20.84/4.23 thf(type_def_14, type, a: $tType).
% 20.84/4.23 thf(func_def_0, type, i: $tType).
% 20.84/4.23 thf(func_def_1, type, product_prod: ($tType * $tType) > $tType).
% 20.84/4.23 thf(func_def_2, type, formula: ($tType) > $tType).
% 20.84/4.23 thf(func_def_3, type, prefix: ($tType) > $tType).
% 20.84/4.23 thf(func_def_4, type, trace: ($tType) > $tType).
% 20.84/4.23 thf(func_def_5, type, char: $tType).
% 20.84/4.23 thf(func_def_6, type, list: ($tType) > $tType).
% 20.84/4.23 thf(func_def_7, type, nat: $tType).
% 20.84/4.23 thf(func_def_8, type, a: $tType).
% 20.84/4.23 thf(func_def_9, type, type: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_10, type, one: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_11, type, ord: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_12, type, order: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_13, type, group_add: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_14, type, no_bot: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_15, type, no_top: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_16, type, linorder: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_17, type, preorder: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_18, type, wellorder: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_19, type, semigroup_add: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_20, type, dense_order: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_21, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_22, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_23, type, dense_linorder: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_24, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_25, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_26, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_27, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_28, type, ordere223160158up_add: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_29, type, strict2144017051up_add: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_30, type, unique1598680935umeral: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_31, type, condit1656338222tinuum: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_32, type, condit1037483654norder: !>[X0: $tType]:($o)).
% 20.84/4.23 thf(func_def_33, type, abstra417776764axioms: !>[X0: $tType, X1: $tType]:((trace @ X0 > list @ X1 > nat > $o) > (prefix @ X0 > nat) > $o)).
% 20.84/4.23 thf(func_def_34, type, one_one: !>[X0: $tType]:(X0)).
% 20.84/4.23 thf(func_def_35, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 20.84/4.23 thf(func_def_36, type, lattices_ord_arg_max: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_37, type, until: !>[X0: $tType]:(formula @ X0 > i > formula @ X0 > formula @ X0)).
% 20.84/4.23 thf(func_def_38, type, sat: !>[X0: $tType]:(trace @ product_prod @ list @ char @ list @ X0 > list @ X0 > nat > formula @ X0 > $o)).
% 20.84/4.23 thf(func_def_39, type, monito2027355080ogress: !>[X0: $tType]:(trace @ product_prod @ list @ char @ list @ X0 > formula @ X0 > nat > nat)).
% 20.84/4.23 thf(func_def_40, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 20.84/4.23 thf(func_def_41, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 20.84/4.23 thf(func_def_42, type, tau: !>[X0: $tType]:(trace @ X0 > nat > nat)).
% 20.84/4.23 thf(func_def_43, type, plen: !>[X0: $tType]:(prefix @ X0 > nat)).
% 20.84/4.23 thf(func_def_44, type, prefix_of: !>[X0: $tType]:(prefix @ X0 > trace @ X0 > $o)).
% 20.84/4.23 thf(func_def_45, type, i2: i).
% 20.84/4.23 thf(func_def_46, type, phi: formula @ a).
% 20.84/4.23 thf(func_def_47, type, phi_1: formula @ a).
% 20.84/4.23 thf(func_def_48, type, phi_2: formula @ a).
% 20.84/4.23 thf(func_def_49, type, pi: prefix @ product_prod @ list @ char @ list @ a).
% 20.84/4.23 thf(func_def_50, type, sigma: trace @ product_prod @ list @ char @ list @ a).
% 20.84/4.23 thf(func_def_51, type, sigma2: trace @ product_prod @ list @ char @ list @ a).
% 20.84/4.23 thf(func_def_52, type, b: nat).
% 20.84/4.23 thf(func_def_53, type, i3: nat).
% 20.84/4.23 thf(func_def_54, type, ia: nat).
% 20.84/4.23 thf(func_def_55, type, j: nat).
% 20.84/4.23 thf(func_def_56, type, ja: nat).
% 20.84/4.23 thf(func_def_57, type, k: nat).
% 20.84/4.23 thf(func_def_76, type, sP0: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > $o)).
% 20.84/4.23 thf(func_def_77, type, sP1: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > $o)).
% 20.84/4.23 thf(func_def_78, type, sP2: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 20.84/4.23 thf(func_def_79, type, sP3: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 20.84/4.23 thf(func_def_80, type, sP4: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 20.84/4.23 thf(func_def_81, type, sP5: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > $o)).
% 20.84/4.23 thf(func_def_82, type, sP6: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > $o)).
% 20.84/4.23 thf(func_def_83, type, sK7: (nat > $o) > nat).
% 20.84/4.23 thf(func_def_84, type, sK8: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_85, type, sK9: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_86, type, sK10: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_87, type, sK11: !>[X0: $tType]:(nat > (X0 > nat) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_88, type, sK12: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_89, type, sK13: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_90, type, sK14: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_91, type, sK15: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_92, type, sK16: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_93, type, sK17: !>[X0: $tType]:(X0 > X0)).
% 20.84/4.23 thf(func_def_94, type, sK18: !>[X0: $tType]:(X0 > X0)).
% 20.84/4.23 thf(func_def_95, type, sK19: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_96, type, sK20: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_97, type, sK21: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_98, type, sK22: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_99, type, sK23: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 20.84/4.23 thf(func_def_100, type, sK24: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 20.84/4.23 thf(func_def_101, type, sK25: !>[X0: $tType]:(X0 > X0)).
% 20.84/4.23 thf(func_def_102, type, sK26: !>[X0: $tType]:(X0 > X0)).
% 20.84/4.23 thf(func_def_103, type, sK27: (nat > nat) > nat).
% 20.84/4.23 thf(func_def_104, type, sK28: (nat > nat) > nat).
% 20.84/4.23 thf(func_def_105, type, sK29: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 20.84/4.23 thf(func_def_106, type, sK30: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 20.84/4.23 thf(func_def_107, type, sK31: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_108, type, sK32: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_109, type, sK33: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_110, type, sK34: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_111, type, sK35: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_112, type, sK36: nat > nat > nat).
% 20.84/4.23 thf(func_def_113, type, sK37: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 20.84/4.23 thf(func_def_114, type, sK38: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 20.84/4.23 thf(func_def_115, type, sK39: !>[X0: $tType]:(X0 > X0)).
% 20.84/4.23 thf(func_def_116, type, sK40: !>[X0: $tType]:(X0 > X0)).
% 20.84/4.23 thf(func_def_117, type, sK41: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_118, type, sK42: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_119, type, sK43: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_120, type, sK44: !>[X0: $tType]:(trace @ X0 > nat > nat > nat)).
% 20.84/4.23 thf(func_def_121, type, sK45: !>[X0: $tType]:(X0 > X0)).
% 20.84/4.23 thf(func_def_122, type, sK46: (nat > $o) > nat > nat).
% 20.84/4.23 thf(func_def_123, type, sK47: (nat > $o) > nat > nat).
% 20.84/4.23 thf(func_def_124, type, sK48: !>[X0: $tType]:(X0 > X0)).
% 20.84/4.23 thf(func_def_125, type, sK49: !>[X0: $tType]:(X0 > X0)).
% 20.84/4.23 thf(func_def_126, type, sK50: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_127, type, sK51: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_128, type, sK52: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_129, type, sK53: !>[X0: $tType]:(nat > (X0 > nat) > X0 > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_130, type, sK54: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_131, type, sK55: !>[X0: $tType]:(X0 > X0)).
% 20.84/4.23 thf(func_def_132, type, sK56: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 20.84/4.23 thf(func_def_133, type, sK57: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 20.84/4.23 thf(func_def_134, type, sK58: (nat > $o) > nat).
% 20.84/4.23 thf(func_def_135, type, sK59: nat > (nat > $o) > nat).
% 20.84/4.23 thf(func_def_136, type, sK60: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 20.84/4.23 thf(func_def_137, type, sK61: (nat > nat) > nat).
% 20.84/4.23 thf(func_def_138, type, sK62: (nat > nat) > nat).
% 20.84/4.23 thf(func_def_139, type, sK63: !>[X0: $tType]:(X0 > X0)).
% 20.84/4.23 thf(func_def_140, type, sK64: (nat > $o) > nat).
% 20.84/4.23 thf(func_def_141, type, sK65: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 20.84/4.23 thf(func_def_142, type, sK66: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 20.84/4.23 thf(func_def_143, type, sK67: !>[X0: $tType]:(X0 > X0)).
% 20.84/4.23 thf(func_def_144, type, sK68: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 20.84/4.23 thf(func_def_145, type, sK69: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 20.84/4.23 thf(func_def_146, type, sK70: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 20.84/4.23 thf(func_def_147, type, sK71: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 20.84/4.23 thf(func_def_148, type, sK72: !>[X0: $tType]:(trace @ product_prod @ list @ char @ list @ X0 > trace @ product_prod @ list @ char @ list @ X0 > nat > nat)).
% 20.84/4.23 thf(func_def_149, type, sK73: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 20.84/4.23 thf(func_def_150, type, sK74: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 20.84/4.23 thf(func_def_152, type, ph76: !>[X0: $tType]:(X0)).
% 20.84/4.23 thf(f2602,plain,(
% 20.84/4.23 $false),
% 20.84/4.23 inference(trivial_inequality_removal,[status(thm)],[f2570])).
% 20.84/4.23 thf(f2570,plain,(
% 20.84/4.23 ($true != $true)),
% 20.84/4.23 inference(superposition,[status(thm)],[f1825,f1277])).
% 20.84/4.23 thf(f1277,plain,(
% 20.84/4.23 ((ord_less @ nat @ k @ (monito2027355080ogress @ a @ sigma @ phi_1 @ (plen @ product_prod @ list @ char @ list @ a @ pi))) = $true)),
% 20.84/4.23 inference(cnf_transformation,[status(thm)],[f355])).
% 20.84/4.23 thf(f355,plain,(
% 20.84/4.23 ((ord_less @ nat @ k @ (monito2027355080ogress @ a @ sigma @ phi_1 @ (plen @ product_prod @ list @ char @ list @ a @ pi))) = $true)),
% 20.84/4.23 inference(fool_elimination,[status(thm)],[f354])).
% 20.84/4.23 thf(f354,plain,(
% 20.84/4.23 (ord_less @ nat @ k @ (monito2027355080ogress @ a @ sigma @ phi_1 @ (plen @ product_prod @ list @ char @ list @ a @ pi)))),
% 20.84/4.23 inference(rectify,[status(thm)],[f1])).
% 20.84/4.23 thf(f1,axiom,(
% 20.84/4.23 (ord_less @ nat @ k @ (monito2027355080ogress @ a @ sigma @ phi_1 @ (plen @ product_prod @ list @ char @ list @ a @ pi)))),
% 20.84/4.23 file('/export/starexec/sandbox/tmp/tmp.8TCNWeCSne/DTF2THF_8323.p',fact_0__092_060open_062k_A_060_AMonitor__Mirabelle__pzlrlsievl_Oprogress_A_092_060sigma_062_A_092_060phi_0621_A_Iplen_A_092_060pi_062_J_092_060close_062)).
% 20.84/4.23 thf(f1825,plain,(
% 20.84/4.23 ( ! [X0 : $tType,X2 : formula @ X0,X1 : trace @ product_prod @ list @ char @ list @ X0] : (((ord_less @ nat @ k @ (monito2027355080ogress @ X0 @ X1 @ X2 @ (plen @ product_prod @ list @ char @ list @ a @ pi))) != $true)) )),
% 20.84/4.23 inference(trivial_inequality_removal,[status(thm)],[f1794])).
% 20.84/4.23 thf(f1794,plain,(
% 20.84/4.23 ( ! [X0 : $tType,X2 : formula @ X0,X1 : trace @ product_prod @ list @ char @ list @ X0] : (($true != $true) | ((ord_less @ nat @ k @ (monito2027355080ogress @ X0 @ X1 @ X2 @ (plen @ product_prod @ list @ char @ list @ a @ pi))) != $true)) )),
% 20.84/4.23 inference(superposition,[status(thm)],[f1531,f1341])).
% 20.84/4.23 thf(f1341,plain,(
% 20.84/4.23 ( ! [X0 : $tType,X2 : formula @ X0,X3 : nat,X1 : trace @ product_prod @ list @ char @ list @ X0] : (($true = (ord_less_eq @ nat @ (monito2027355080ogress @ X0 @ X1 @ X2 @ X3) @ X3))) )),
% 20.84/4.23 inference(cnf_transformation,[status(thm)],[f861])).
% 20.84/4.23 thf(f861,plain,(
% 20.84/4.23 ! [X0 : $tType,X1 : trace @ product_prod @ list @ char @ list @ X0,X2 : formula @ X0,X3 : nat] : ($true = (ord_less_eq @ nat @ (monito2027355080ogress @ X0 @ X1 @ X2 @ X3) @ X3))),
% 20.84/4.23 inference(fool_elimination,[status(thm)],[f860])).
% 20.84/4.23 thf(f860,plain,(
% 20.84/4.23 ! [X0 : $tType,X1 : trace @ product_prod @ list @ char @ list @ X0,X2 : formula @ X0,X3 : nat] : (ord_less_eq @ nat @ (monito2027355080ogress @ X0 @ X1 @ X2 @ X3) @ X3)),
% 20.84/4.23 inference(rectify,[status(thm)],[f23])).
% 20.84/4.23 thf(f23,axiom,(
% 20.84/4.23 ! [X0 : $tType,X24 : trace @ product_prod @ list @ char @ list @ X0,X25 : formula @ X0,X20 : nat] : (ord_less_eq @ nat @ (monito2027355080ogress @ X0 @ X24 @ X25 @ X20) @ X20)),
% 20.84/4.23 file('/export/starexec/sandbox/tmp/tmp.8TCNWeCSne/DTF2THF_8323.p',fact_22_progress__le)).
% 20.84/4.23 thf(f1531,plain,(
% 20.84/4.23 ( ! [X0 : nat] : (((ord_less_eq @ nat @ X0 @ (plen @ product_prod @ list @ char @ list @ a @ pi)) != $true) | ($true != (ord_less @ nat @ k @ X0))) )),
% 20.84/4.23 inference(subsumption_resolution,[status(thm)],[f1511,f1278])).
% 20.84/4.23 thf(f1278,plain,(
% 20.84/4.23 (order @ nat = $true)),
% 20.84/4.23 inference(cnf_transformation,[status(thm)],[f775])).
% 20.84/4.23 thf(f775,plain,(
% 20.84/4.23 (order @ nat = $true)),
% 20.84/4.23 inference(fool_elimination,[status(thm)],[f774])).
% 20.84/4.23 thf(f774,plain,(
% 20.84/4.23 order @ nat),
% 20.84/4.23 inference(rectify,[status(thm)],[f274])).
% 20.84/4.23 thf(f274,axiom,(
% 20.84/4.23 order @ nat),
% 20.84/4.23 file('/export/starexec/sandbox/tmp/tmp.8TCNWeCSne/DTF2THF_8323.p',tcon_Nat_Onat___Orderings_Oorder_2)).
% 20.84/4.23 thf(f1511,plain,(
% 20.84/4.23 ( ! [X0 : nat] : (((ord_less_eq @ nat @ X0 @ (plen @ product_prod @ list @ char @ list @ a @ pi)) != $true) | ($true != (ord_less @ nat @ k @ X0)) | (order @ nat != $true)) )),
% 20.84/4.23 inference(trivial_inequality_removal,[status(thm)],[f1480])).
% 20.84/4.23 thf(f1480,plain,(
% 20.84/4.23 ( ! [X0 : nat] : (($true != $true) | ((ord_less_eq @ nat @ X0 @ (plen @ product_prod @ list @ char @ list @ a @ pi)) != $true) | (order @ nat != $true) | ($true != (ord_less @ nat @ k @ X0))) )),
% 20.84/4.23 inference(superposition,[status(thm)],[f1243,f1259])).
% 20.84/4.23 thf(f1259,plain,(
% 20.84/4.23 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (((ord_less @ X0 @ X1 @ X3) = $true) | ($true != (ord_less_eq @ X0 @ X2 @ X3)) | ((ord_less @ X0 @ X1 @ X2) != $true) | (order @ X0 != $true)) )),
% 20.84/4.23 inference(cnf_transformation,[status(thm)],[f1057])).
% 20.84/4.23 thf(f1057,plain,(
% 20.84/4.23 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (((ord_less @ X0 @ X1 @ X2) != $true) | ($true != (ord_less_eq @ X0 @ X2 @ X3)) | ((ord_less @ X0 @ X1 @ X3) = $true)) | (order @ X0 != $true))),
% 20.84/4.23 inference(flattening,[status(thm)],[f1056])).
% 20.84/4.23 thf(f1056,plain,(
% 20.84/4.23 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((((ord_less @ X0 @ X1 @ X3) = $true) | ($true != (ord_less_eq @ X0 @ X2 @ X3))) | ((ord_less @ X0 @ X1 @ X2) != $true)) | (order @ X0 != $true))),
% 20.84/4.23 inference(ennf_transformation,[status(thm)],[f395])).
% 20.84/4.23 thf(f395,plain,(
% 20.84/4.23 ! [X0 : $tType] : ((order @ X0 = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (((ord_less @ X0 @ X1 @ X2) = $true) => (($true = (ord_less_eq @ X0 @ X2 @ X3)) => ((ord_less @ X0 @ X1 @ X3) = $true))))),
% 20.84/4.23 inference(fool_elimination,[status(thm)],[f394])).
% 20.84/4.23 thf(f394,plain,(
% 20.84/4.23 ! [X0 : $tType] : (order @ X0 => ! [X1 : X0,X2 : X0,X3 : X0] : ((ord_less @ X0 @ X1 @ X2) => ((ord_less_eq @ X0 @ X2 @ X3) => (ord_less @ X0 @ X1 @ X3))))),
% 20.84/4.23 inference(rectify,[status(thm)],[f150])).
% 20.84/4.23 thf(f150,axiom,(
% 20.84/4.23 ! [X0 : $tType] : (order @ X0 => ! [X34 : X0,X22 : X0,X48 : X0] : ((ord_less @ X0 @ X34 @ X22) => ((ord_less_eq @ X0 @ X22 @ X48) => (ord_less @ X0 @ X34 @ X48))))),
% 20.84/4.23 file('/export/starexec/sandbox/tmp/tmp.8TCNWeCSne/DTF2THF_8323.p',fact_149_order_Ostrict__trans2)).
% 20.84/4.23 thf(f1243,plain,(
% 20.84/4.23 ((ord_less @ nat @ k @ (plen @ product_prod @ list @ char @ list @ a @ pi)) != $true)),
% 20.84/4.23 inference(cnf_transformation,[status(thm)],[f878])).
% 20.84/4.23 thf(f878,plain,(
% 20.84/4.23 ((ord_less @ nat @ k @ (plen @ product_prod @ list @ char @ list @ a @ pi)) != $true)),
% 20.84/4.23 inference(flattening,[status(thm)],[f627])).
% 20.84/4.23 thf(f627,plain,(
% 20.84/4.23 ~((ord_less @ nat @ k @ (plen @ product_prod @ list @ char @ list @ a @ pi)) = $true)),
% 20.84/4.23 inference(fool_elimination,[status(thm)],[f626])).
% 20.84/4.23 thf(f626,plain,(
% 20.84/4.23 ~(ord_less @ nat @ k @ (plen @ product_prod @ list @ char @ list @ a @ pi))),
% 20.84/4.23 inference(rectify,[status(thm)],[f294])).
% 20.84/4.23 thf(f294,negated_conjecture,(
% 20.84/4.23 ~(ord_less @ nat @ k @ (plen @ product_prod @ list @ char @ list @ a @ pi))),
% 20.84/4.23 inference(negated_conjecture,[status(cth)],[f293])).
% 20.84/4.23 thf(f293,conjecture,(
% 20.84/4.23 (ord_less @ nat @ k @ (plen @ product_prod @ list @ char @ list @ a @ pi))),
% 20.84/4.23 file('/export/starexec/sandbox/tmp/tmp.8TCNWeCSne/DTF2THF_8323.p',conj_0)).
% 20.84/4.23 % SZS output end Proof for DTF2THF_8323
% 20.84/4.23 % (8556)------------------------------
% 20.84/4.23 % (8556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.84/4.23 % (8556)Termination reason: Refutation
% 20.84/4.23
% 20.84/4.23 % (8556)Memory used [KB]: 7547
% 20.84/4.23 % (8556)Time elapsed: 0.141 s
% 20.84/4.23 % (8556)Instructions burned: 452 (million)
% 20.84/4.23 % (8556)------------------------------
% 20.84/4.23 % (8556)------------------------------
% 20.84/4.23 % (8421)Success in time 2.657 s
%------------------------------------------------------------------------------