%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP061^2 : 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 08:55:14 AM UTC 2026
% Result : Theorem 115.99s 17.79s
% Output : Refutation 115.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP061^2 : 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
% 0.18/0.34 % Computer : n020.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 08:25:12 EST 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.47 ---- Original DTF file ---
% 0.21/0.47 thf(spec,logic,$$dhol).
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % File : ITP061^2 : TPTP v9.2.1. Released v7.5.0.
% 0.21/0.47 % Domain : Interactive Theorem Proving
% 0.21/0.47 % Problem : Sledgehammer FLPTheorem problem prob_979__3303242_1
% 0.21/0.47 % Version : Especial.
% 0.21/0.47 % English :
% 0.21/0.47
% 0.21/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.21/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.21/0.47 % Source : [Des21]
% 0.21/0.47 % Names : FLPTheorem/prob_979__3303242_1 [Des21]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % Rating : 0.33 v9.0.0, 0.00 v8.2.0, 0.33 v8.1.0, 0.25 v7.5.0
% 0.21/0.47 % Syntax : Number of formulae : 340 ( 93 unt; 54 typ; 0 def)
% 0.21/0.47 % Number of atoms : 826 ( 171 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 13 ( 2 avg)
% 0.21/0.47 % Number of connectives : 3221 ( 83 ~; 18 |; 42 &;2603 @)
% 0.21/0.47 % ( 0 <=>; 475 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 17 ( 8 avg)
% 0.21/0.47 % Number of types : 6 ( 5 usr)
% 0.21/0.47 % Number of type conns : 126 ( 126 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 50 ( 49 usr; 10 con; 0-7 aty)
% 0.21/0.47 % Number of variables : 880 ( 48 ^; 771 !; 23 ?; 880 :)
% 0.21/0.47 % ( 38 !>; 0 ?*; 0 @-; 0 @+)
% 0.21/0.47 % SPC : TH1_THM_EQU_NAR
% 0.21/0.47
% 0.21/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 16:17:10.250
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % Could-be-implicit typings (9)
% 0.21/0.47 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext,type,
% 0.21/0.47 configuration_ext: $tType > $tType > $tType > $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_AsynchronousSystem_Omessage,type,
% 0.21/0.47 message: $tType > $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Product__Type_Ounit,type,
% 0.21/0.47 product_unit: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_List_Olist,type,
% 0.21/0.47 list: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Set_Oset,type,
% 0.21/0.47 set: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Nat_Onat,type,
% 0.21/0.47 nat: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_v,type,
% 0.21/0.47 v: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_s,type,
% 0.21/0.47 s: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_tf_p,type,
% 0.21/0.47 p: $tType ).
% 0.21/0.47
% 0.21/0.47 % Explicit typings (45)
% 0.21/0.47 thf(sy_cl_HOL_Otype,type,
% 0.21/0.47 type:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Nat_Osize,type,
% 0.21/0.47 size:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Oone,type,
% 0.21/0.47 one:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Ominus,type,
% 0.21/0.47 minus:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Oord,type,
% 0.21/0.47 ord:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Oorder,type,
% 0.21/0.47 order:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Ogroup__add,type,
% 0.21/0.47 group_add:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Ono__bot,type,
% 0.21/0.47 no_bot:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Ono__top,type,
% 0.21/0.47 no_top:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Olinorder,type,
% 0.21/0.47 linorder:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Opreorder,type,
% 0.21/0.47 preorder:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Owellorder,type,
% 0.21/0.47 wellorder:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Odense__order,type,
% 0.21/0.47 dense_order:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.21/0.47 dense_linorder:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.21/0.47 ordered_ab_group_add:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.21/0.47 cancel146912293up_add:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.21/0.47 linord1659791738miring:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_AsynchronousSystem_Oenabled,type,
% 0.21/0.47 enabled:
% 0.21/0.47 !>[P: $tType,V: $tType,S: $tType] : ( ( configuration_ext @ P @ V @ S @ product_unit ) > ( message @ P @ V ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_AsynchronousSystem_OisReceiverOf,type,
% 0.21/0.47 isReceiverOf:
% 0.21/0.47 !>[P: $tType,V: $tType] : ( P > ( message @ P @ V ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Execution_Oexecution_OfirstOccurrence,type,
% 0.21/0.47 firstOccurrence:
% 0.21/0.47 !>[P: $tType,V: $tType,S: $tType] : ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( message @ P @ V ) > nat > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Execution_Oexecution_OminimalEnabled,type,
% 0.21/0.47 minimalEnabled:
% 0.21/0.47 !>[P: $tType,V: $tType,S: $tType] : ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( message @ P @ V ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.21/0.47 minus_minus:
% 0.21/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.21/0.47 one_one:
% 0.21/0.47 !>[A: $tType] : A ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_ListUtilities_OprefixList,type,
% 0.21/0.47 prefixList:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_ONil,type,
% 0.21/0.47 nil:
% 0.21/0.47 !>[A: $tType] : ( list @ A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Onth,type,
% 0.21/0.47 nth:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > nat > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Nat_OSuc,type,
% 0.21/0.47 suc: nat > nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.21/0.47 size_size:
% 0.21/0.47 !>[A: $tType] : ( A > nat ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.21/0.47 ord_less:
% 0.21/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.21/0.47 ord_less_eq:
% 0.21/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Set_OCollect,type,
% 0.21/0.47 collect:
% 0.21/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_member,type,
% 0.21/0.47 member:
% 0.21/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_OccM_H____,type,
% 0.21/0.47 occM: nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_OccM____,type,
% 0.21/0.47 occM2: nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_consumedMsg____,type,
% 0.21/0.47 consumedMsg: message @ p @ v ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_fe____,type,
% 0.21/0.47 fe: nat > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_firstOccSet____,type,
% 0.21/0.47 firstOccSet: nat > ( set @ ( message @ p @ v ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_ft____,type,
% 0.21/0.47 ft: nat > ( list @ ( message @ p @ v ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_index____,type,
% 0.21/0.47 index: nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_msg_H____,type,
% 0.21/0.47 msg: message @ p @ v ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_msg____,type,
% 0.21/0.47 msg2: message @ p @ v ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_msga____,type,
% 0.21/0.47 msga: message @ p @ v ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_n0____,type,
% 0.21/0.47 n0: nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_n____,type,
% 0.21/0.47 n: nat ).
% 0.21/0.47
% 0.21/0.47 thf(sy_v_p____,type,
% 0.21/0.47 p2: p ).
% 0.21/0.47
% 0.21/0.47 % Relevant facts (253)
% 0.21/0.47 thf(fact_0_AssumpOccMFirstOccurrence_I3_J,axiom,
% 0.21/0.47 ord_less @ nat @ occM2 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ).
% 0.21/0.47
% 0.21/0.47 % AssumpOccMFirstOccurrence(3)
% 0.21/0.47 thf(fact_1__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_AOccM_092_060close_062,axiom,
% 0.21/0.47 ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ occM2 ).
% 0.21/0.47
% 0.21/0.47 % \<open>length (fe index) - 1 \<le> OccM\<close>
% 0.21/0.47 thf(fact_2_OccM_H_I3_J,axiom,
% 0.21/0.47 ord_less @ nat @ occM @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ).
% 0.21/0.47
% 0.21/0.47 % OccM'(3)
% 0.21/0.47 thf(fact_3__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Alength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_092_060close_062,axiom,
% 0.21/0.47 ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) ).
% 0.21/0.47
% 0.21/0.47 % \<open>length (fe index) - 1 \<le> length (fe (Suc index)) - 1\<close>
% 0.21/0.47 thf(fact_4_NotEmpty_I2_J,axiom,
% 0.21/0.47 ( ( fe @ index )
% 0.21/0.47 != ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % NotEmpty(2)
% 0.21/0.47 thf(fact_5_minus__apply,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( minus @ B )
% 0.21/0.47 => ( ( minus_minus @ ( A > B ) )
% 0.21/0.47 = ( ^ [A2: A > B,B2: A > B,X: A] : ( minus_minus @ B @ ( A2 @ X ) @ ( B2 @ X ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % minus_apply
% 0.21/0.47 thf(fact_6_AssumptionFair_I2_J,axiom,
% 0.21/0.47 ord_less @ nat @ n0 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ) ).
% 0.21/0.47
% 0.21/0.47 % AssumptionFair(2)
% 0.21/0.47 thf(fact_7_one__natural_Orsp,axiom,
% 0.21/0.47 ( ( one_one @ nat )
% 0.21/0.47 = ( one_one @ nat ) ) ).
% 0.21/0.47
% 0.21/0.47 % one_natural.rsp
% 0.21/0.47 thf(fact_8_diff__commute,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat] :
% 0.21/0.47 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I @ J ) @ K )
% 0.21/0.47 = ( minus_minus @ nat @ ( minus_minus @ nat @ I @ K ) @ J ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_commute
% 0.21/0.47 thf(fact_9_Ex__list__of__length,axiom,
% 0.21/0.47 ! [A: $tType,N: nat] :
% 0.21/0.47 ? [Xs: list @ A] :
% 0.21/0.47 ( ( size_size @ ( list @ A ) @ Xs )
% 0.21/0.47 = N ) ).
% 0.21/0.47
% 0.21/0.47 % Ex_list_of_length
% 0.21/0.47 thf(fact_10_neq__if__length__neq,axiom,
% 0.21/0.47 ! [A: $tType,Xs2: list @ A,Ys: list @ A] :
% 0.21/0.47 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.21/0.47 != ( size_size @ ( list @ A ) @ Ys ) )
% 0.21/0.47 => ( Xs2 != Ys ) ) ).
% 0.21/0.47
% 0.21/0.47 % neq_if_length_neq
% 0.21/0.47 thf(fact_11_size__neq__size__imp__neq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( size @ A )
% 0.21/0.47 => ! [X2: A,Y: A] :
% 0.21/0.47 ( ( ( size_size @ A @ X2 )
% 0.21/0.47 != ( size_size @ A @ Y ) )
% 0.21/0.47 => ( X2 != Y ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % size_neq_size_imp_neq
% 0.21/0.47 thf(fact_12_fun__diff__def,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( minus @ B )
% 0.21/0.47 => ( ( minus_minus @ ( A > B ) )
% 0.21/0.47 = ( ^ [A2: A > B,B2: A > B,X: A] : ( minus_minus @ B @ ( A2 @ X ) @ ( B2 @ X ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % fun_diff_def
% 0.21/0.47 thf(fact_13_diff__eq__diff__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( group_add @ A )
% 0.21/0.47 => ! [A3: A,B3: A,C: A,D: A] :
% 0.21/0.47 ( ( ( minus_minus @ A @ A3 @ B3 )
% 0.21/0.47 = ( minus_minus @ A @ C @ D ) )
% 0.21/0.47 => ( ( A3 = B3 )
% 0.21/0.47 = ( C = D ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_eq_diff_eq
% 0.21/0.47 thf(fact_14_nat_Oinject,axiom,
% 0.21/0.47 ! [X22: nat,Y2: nat] :
% 0.21/0.47 ( ( ( suc @ X22 )
% 0.21/0.47 = ( suc @ Y2 ) )
% 0.21/0.47 = ( X22 = Y2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat.inject
% 0.21/0.47 thf(fact_15_old_Onat_Oinject,axiom,
% 0.21/0.47 ! [Nat: nat,Nat2: nat] :
% 0.21/0.47 ( ( ( suc @ Nat )
% 0.21/0.47 = ( suc @ Nat2 ) )
% 0.21/0.47 = ( Nat = Nat2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % old.nat.inject
% 0.21/0.47 thf(fact_16_NotEmpty_I1_J,axiom,
% 0.21/0.47 ( ( fe @ ( suc @ index ) )
% 0.21/0.47 != ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % NotEmpty(1)
% 0.21/0.47 thf(fact_17_lessI,axiom,
% 0.21/0.47 ! [N: nat] : ( ord_less @ nat @ N @ ( suc @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % lessI
% 0.21/0.47 thf(fact_18_Suc__mono,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ M @ N )
% 0.21/0.47 => ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_mono
% 0.21/0.47 thf(fact_19_Suc__less__eq,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.21/0.47 = ( ord_less @ nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_less_eq
% 0.21/0.47 thf(fact_20_Suc__le__mono,axiom,
% 0.21/0.47 ! [N: nat,M: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.21/0.47 = ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_le_mono
% 0.21/0.47 thf(fact_21_Suc__diff__diff,axiom,
% 0.21/0.47 ! [M: nat,N: nat,K: nat] :
% 0.21/0.47 ( ( minus_minus @ nat @ ( minus_minus @ nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 0.21/0.47 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ N ) @ K ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_diff_diff
% 0.21/0.47 thf(fact_22_diff__Suc__Suc,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( minus_minus @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.21/0.47 = ( minus_minus @ nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_Suc_Suc
% 0.21/0.47 thf(fact_23_diff__diff__cancel,axiom,
% 0.21/0.47 ! [I: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ I @ N )
% 0.21/0.47 => ( ( minus_minus @ nat @ N @ ( minus_minus @ nat @ N @ I ) )
% 0.21/0.47 = I ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_diff_cancel
% 0.21/0.47 thf(fact_24_diff__Suc__1,axiom,
% 0.21/0.47 ! [N: nat] :
% 0.21/0.47 ( ( minus_minus @ nat @ ( suc @ N ) @ ( one_one @ nat ) )
% 0.21/0.47 = N ) ).
% 0.21/0.47
% 0.21/0.47 % diff_Suc_1
% 0.21/0.47 thf(fact_25_Nat_OlessE,axiom,
% 0.21/0.47 ! [I: nat,K: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ I @ K )
% 0.21/0.47 => ( ( K
% 0.21/0.47 != ( suc @ I ) )
% 0.21/0.47 => ~ ! [J2: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ I @ J2 )
% 0.21/0.47 => ( K
% 0.21/0.47 != ( suc @ J2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Nat.lessE
% 0.21/0.47 thf(fact_26_Suc__leD,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 0.21/0.47 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_leD
% 0.21/0.47 thf(fact_27_Suc__leI,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ M @ N )
% 0.21/0.47 => ( ord_less_eq @ nat @ ( suc @ M ) @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_leI
% 0.21/0.47 thf(fact_28_le__SucE,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ M @ ( suc @ N ) )
% 0.21/0.47 => ( ~ ( ord_less_eq @ nat @ M @ N )
% 0.21/0.47 => ( M
% 0.21/0.47 = ( suc @ N ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_SucE
% 0.21/0.47 thf(fact_29_le__SucI,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.21/0.47 => ( ord_less_eq @ nat @ M @ ( suc @ N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_SucI
% 0.21/0.47 thf(fact_30_le__refl,axiom,
% 0.21/0.47 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 0.21/0.47
% 0.21/0.47 % le_refl
% 0.21/0.47 thf(fact_31_Suc__le__D,axiom,
% 0.21/0.47 ! [N: nat,M2: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ ( suc @ N ) @ M2 )
% 0.21/0.47 => ? [M3: nat] :
% 0.21/0.47 ( M2
% 0.21/0.47 = ( suc @ M3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_le_D
% 0.21/0.47 thf(fact_32_le__trans,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.21/0.47 => ( ( ord_less_eq @ nat @ J @ K )
% 0.21/0.47 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_trans
% 0.21/0.47 thf(fact_33_Suc__le__eq,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 0.21/0.47 = ( ord_less @ nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_le_eq
% 0.21/0.47 thf(fact_34_Suc__lessD,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ ( suc @ M ) @ N )
% 0.21/0.47 => ( ord_less @ nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_lessD
% 0.21/0.47 thf(fact_35_Suc__lessE,axiom,
% 0.21/0.47 ! [I: nat,K: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ ( suc @ I ) @ K )
% 0.21/0.47 => ~ ! [J2: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ I @ J2 )
% 0.21/0.47 => ( K
% 0.21/0.47 != ( suc @ J2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_lessE
% 0.21/0.47 thf(fact_36_Suc__lessI,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ M @ N )
% 0.21/0.47 => ( ( ( suc @ M )
% 0.21/0.47 != N )
% 0.21/0.47 => ( ord_less @ nat @ ( suc @ M ) @ N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_lessI
% 0.21/0.47 thf(fact_37_eq__imp__le,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( M = N )
% 0.21/0.47 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % eq_imp_le
% 0.21/0.47 thf(fact_38_le__Suc__eq,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ M @ ( suc @ N ) )
% 0.21/0.47 = ( ( ord_less_eq @ nat @ M @ N )
% 0.21/0.47 | ( M
% 0.21/0.47 = ( suc @ N ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_Suc_eq
% 0.21/0.47 thf(fact_39_less__SucE,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.21/0.47 => ( ~ ( ord_less @ nat @ M @ N )
% 0.21/0.47 => ( M = N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_SucE
% 0.21/0.47 thf(fact_40_less__SucI,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ M @ N )
% 0.21/0.47 => ( ord_less @ nat @ M @ ( suc @ N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_SucI
% 0.21/0.47 thf(fact_41_Suc__inject,axiom,
% 0.21/0.47 ! [X2: nat,Y: nat] :
% 0.21/0.47 ( ( ( suc @ X2 )
% 0.21/0.47 = ( suc @ Y ) )
% 0.21/0.47 => ( X2 = Y ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_inject
% 0.21/0.47 thf(fact_42_dec__induct,axiom,
% 0.21/0.47 ! [I: nat,J: nat,P2: nat > $o] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.21/0.47 => ( ( P2 @ I )
% 0.21/0.47 => ( ! [N2: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ I @ N2 )
% 0.21/0.47 => ( ( ord_less @ nat @ N2 @ J )
% 0.21/0.47 => ( ( P2 @ N2 )
% 0.21/0.47 => ( P2 @ ( suc @ N2 ) ) ) ) )
% 0.21/0.47 => ( P2 @ J ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dec_induct
% 0.21/0.47 thf(fact_43_mem__Collect__eq,axiom,
% 0.21/0.47 ! [A: $tType,A3: A,P2: A > $o] :
% 0.21/0.47 ( ( member @ A @ A3 @ ( collect @ A @ P2 ) )
% 0.21/0.47 = ( P2 @ A3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % mem_Collect_eq
% 0.21/0.47 thf(fact_44_Collect__mem__eq,axiom,
% 0.21/0.47 ! [A: $tType,A4: set @ A] :
% 0.21/0.47 ( ( collect @ A
% 0.21/0.47 @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 0.21/0.47 = A4 ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mem_eq
% 0.21/0.47 thf(fact_45_Collect__cong,axiom,
% 0.21/0.47 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ( P2 @ X3 )
% 0.21/0.47 = ( Q @ X3 ) )
% 0.21/0.47 => ( ( collect @ A @ P2 )
% 0.21/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_cong
% 0.21/0.47 thf(fact_46_ext,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ( F @ X3 )
% 0.21/0.47 = ( G @ X3 ) )
% 0.21/0.47 => ( F = G ) ) ).
% 0.21/0.47
% 0.21/0.47 % ext
% 0.21/0.47 thf(fact_47_inc__induct,axiom,
% 0.21/0.47 ! [I: nat,J: nat,P2: nat > $o] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.21/0.47 => ( ( P2 @ J )
% 0.21/0.47 => ( ! [N2: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ I @ N2 )
% 0.21/0.47 => ( ( ord_less @ nat @ N2 @ J )
% 0.21/0.47 => ( ( P2 @ ( suc @ N2 ) )
% 0.21/0.47 => ( P2 @ N2 ) ) ) )
% 0.21/0.47 => ( P2 @ I ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % inc_induct
% 0.21/0.47 thf(fact_48_le__antisym,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.21/0.47 => ( ( ord_less_eq @ nat @ N @ M )
% 0.21/0.47 => ( M = N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_antisym
% 0.21/0.47 thf(fact_49_Ex__less__Suc,axiom,
% 0.21/0.47 ! [N: nat,P2: nat > $o] :
% 0.21/0.47 ( ( ? [I2: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ I2 @ ( suc @ N ) )
% 0.21/0.47 & ( P2 @ I2 ) ) )
% 0.21/0.47 = ( ( P2 @ N )
% 0.21/0.47 | ? [I2: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ I2 @ N )
% 0.21/0.47 & ( P2 @ I2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Ex_less_Suc
% 0.21/0.47 thf(fact_50_less__Suc__eq,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.21/0.47 = ( ( ord_less @ nat @ M @ N )
% 0.21/0.47 | ( M = N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_Suc_eq
% 0.21/0.47 thf(fact_51_n__not__Suc__n,axiom,
% 0.21/0.47 ! [N: nat] :
% 0.21/0.47 ( N
% 0.21/0.47 != ( suc @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % n_not_Suc_n
% 0.21/0.47 thf(fact_52_nat__less__le,axiom,
% 0.21/0.47 ( ( ord_less @ nat )
% 0.21/0.47 = ( ^ [M4: nat,N3: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ M4 @ N3 )
% 0.21/0.47 & ( M4 != N3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat_less_le
% 0.21/0.47 thf(fact_53_nat__neq__iff,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( M != N )
% 0.21/0.47 = ( ( ord_less @ nat @ M @ N )
% 0.21/0.47 | ( ord_less @ nat @ N @ M ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat_neq_iff
% 0.21/0.47 thf(fact_54_not__less__eq,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ~ ( ord_less @ nat @ M @ N ) )
% 0.21/0.47 = ( ord_less @ nat @ N @ ( suc @ M ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_less_eq
% 0.21/0.47 thf(fact_55_All__less__Suc,axiom,
% 0.21/0.47 ! [N: nat,P2: nat > $o] :
% 0.21/0.47 ( ( ! [I2: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ I2 @ ( suc @ N ) )
% 0.21/0.47 => ( P2 @ I2 ) ) )
% 0.21/0.47 = ( ( P2 @ N )
% 0.21/0.47 & ! [I2: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ I2 @ N )
% 0.21/0.47 => ( P2 @ I2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % All_less_Suc
% 0.21/0.47 thf(fact_56_Suc__le__lessD,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 0.21/0.47 => ( ord_less @ nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_le_lessD
% 0.21/0.47 thf(fact_57_Suc__less__eq2,axiom,
% 0.21/0.47 ! [N: nat,M: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ ( suc @ N ) @ M )
% 0.21/0.47 = ( ? [M5: nat] :
% 0.21/0.47 ( ( M
% 0.21/0.47 = ( suc @ M5 ) )
% 0.21/0.47 & ( ord_less @ nat @ N @ M5 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_less_eq2
% 0.21/0.47 thf(fact_58_less__antisym,axiom,
% 0.21/0.47 ! [N: nat,M: nat] :
% 0.21/0.47 ( ~ ( ord_less @ nat @ N @ M )
% 0.21/0.47 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 0.21/0.47 => ( M = N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_antisym
% 0.21/0.47 thf(fact_59_Suc__less__SucD,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.21/0.47 => ( ord_less @ nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_less_SucD
% 0.21/0.47 thf(fact_60_less__not__refl,axiom,
% 0.21/0.47 ! [N: nat] :
% 0.21/0.47 ~ ( ord_less @ nat @ N @ N ) ).
% 0.21/0.47
% 0.21/0.47 % less_not_refl
% 0.21/0.47 thf(fact_61_nat__le__linear,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.21/0.47 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat_le_linear
% 0.21/0.47 thf(fact_62_Suc__n__not__le__n,axiom,
% 0.21/0.47 ! [N: nat] :
% 0.21/0.47 ~ ( ord_less_eq @ nat @ ( suc @ N ) @ N ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_n_not_le_n
% 0.21/0.47 thf(fact_63_le__less__Suc__eq,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.21/0.47 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 0.21/0.47 = ( N = M ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_less_Suc_eq
% 0.21/0.47 thf(fact_64_less__Suc__eq__le,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.21/0.47 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_Suc_eq_le
% 0.21/0.47 thf(fact_65_less__eq__Suc__le,axiom,
% 0.21/0.47 ( ( ord_less @ nat )
% 0.21/0.47 = ( ^ [N3: nat] : ( ord_less_eq @ nat @ ( suc @ N3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_eq_Suc_le
% 0.21/0.47 thf(fact_66_less__not__refl2,axiom,
% 0.21/0.47 ! [N: nat,M: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ N @ M )
% 0.21/0.47 => ( M != N ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_not_refl2
% 0.21/0.47 thf(fact_67_less__not__refl3,axiom,
% 0.21/0.47 ! [S2: nat,T: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ S2 @ T )
% 0.21/0.47 => ( S2 != T ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_not_refl3
% 0.21/0.47 thf(fact_68_less__trans__Suc,axiom,
% 0.21/0.47 ! [I: nat,J: nat,K: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ I @ J )
% 0.21/0.47 => ( ( ord_less @ nat @ J @ K )
% 0.21/0.47 => ( ord_less @ nat @ ( suc @ I ) @ K ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_trans_Suc
% 0.21/0.47 thf(fact_69_measure__induct,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( wellorder @ B )
% 0.21/0.47 => ! [F: A > B,P2: A > $o,A3: A] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ! [Y3: A] :
% 0.21/0.47 ( ( ord_less @ B @ ( F @ Y3 ) @ ( F @ X3 ) )
% 0.21/0.47 => ( P2 @ Y3 ) )
% 0.21/0.47 => ( P2 @ X3 ) )
% 0.21/0.47 => ( P2 @ A3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % measure_induct
% 0.21/0.47 thf(fact_70_not__less__eq__eq,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ~ ( ord_less_eq @ nat @ M @ N ) )
% 0.21/0.47 = ( ord_less_eq @ nat @ ( suc @ N ) @ M ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_less_eq_eq
% 0.21/0.47 thf(fact_71_full__nat__induct,axiom,
% 0.21/0.47 ! [P2: nat > $o,N: nat] :
% 0.21/0.47 ( ! [N2: nat] :
% 0.21/0.47 ( ! [M6: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ ( suc @ M6 ) @ N2 )
% 0.21/0.47 => ( P2 @ M6 ) )
% 0.21/0.47 => ( P2 @ N2 ) )
% 0.21/0.47 => ( P2 @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % full_nat_induct
% 0.21/0.47 thf(fact_72_le__imp__less__Suc,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.21/0.47 => ( ord_less @ nat @ M @ ( suc @ N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_imp_less_Suc
% 0.21/0.47 thf(fact_73_less__Suc__induct,axiom,
% 0.21/0.47 ! [I: nat,J: nat,P2: nat > nat > $o] :
% 0.21/0.47 ( ( ord_less @ nat @ I @ J )
% 0.21/0.47 => ( ! [I3: nat] : ( P2 @ I3 @ ( suc @ I3 ) )
% 0.21/0.47 => ( ! [I3: nat,J2: nat,K2: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ I3 @ J2 )
% 0.21/0.47 => ( ( ord_less @ nat @ J2 @ K2 )
% 0.21/0.47 => ( ( P2 @ I3 @ J2 )
% 0.21/0.47 => ( ( P2 @ J2 @ K2 )
% 0.21/0.47 => ( P2 @ I3 @ K2 ) ) ) ) )
% 0.21/0.47 => ( P2 @ I @ J ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_Suc_induct
% 0.21/0.47 thf(fact_74_less__imp__le__nat,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ M @ N )
% 0.21/0.47 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_imp_le_nat
% 0.21/0.47 thf(fact_75_less__irrefl__nat,axiom,
% 0.21/0.47 ! [N: nat] :
% 0.21/0.47 ~ ( ord_less @ nat @ N @ N ) ).
% 0.21/0.47
% 0.21/0.47 % less_irrefl_nat
% 0.21/0.47 thf(fact_76_nat__less__induct,axiom,
% 0.21/0.47 ! [P2: nat > $o,N: nat] :
% 0.21/0.47 ( ! [N2: nat] :
% 0.21/0.47 ( ! [M6: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ M6 @ N2 )
% 0.21/0.47 => ( P2 @ M6 ) )
% 0.21/0.47 => ( P2 @ N2 ) )
% 0.21/0.47 => ( P2 @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat_less_induct
% 0.21/0.47 thf(fact_77_infinite__descent,axiom,
% 0.21/0.47 ! [P2: nat > $o,N: nat] :
% 0.21/0.47 ( ! [N2: nat] :
% 0.21/0.47 ( ~ ( P2 @ N2 )
% 0.21/0.47 => ? [M6: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ M6 @ N2 )
% 0.21/0.47 & ~ ( P2 @ M6 ) ) )
% 0.21/0.47 => ( P2 @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % infinite_descent
% 0.21/0.47 thf(fact_78_le__eq__less__or__eq,axiom,
% 0.21/0.47 ( ( ord_less_eq @ nat )
% 0.21/0.47 = ( ^ [M4: nat,N3: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ M4 @ N3 )
% 0.21/0.47 | ( M4 = N3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_eq_less_or_eq
% 0.21/0.47 thf(fact_79_less__or__eq__imp__le,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ( ord_less @ nat @ M @ N )
% 0.21/0.47 | ( M = N ) )
% 0.21/0.47 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_or_eq_imp_le
% 0.21/0.47 thf(fact_80_linorder__neqE__nat,axiom,
% 0.21/0.47 ! [X2: nat,Y: nat] :
% 0.21/0.47 ( ( X2 != Y )
% 0.21/0.47 => ( ~ ( ord_less @ nat @ X2 @ Y )
% 0.21/0.47 => ( ord_less @ nat @ Y @ X2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % linorder_neqE_nat
% 0.21/0.47 thf(fact_81_strict__inc__induct,axiom,
% 0.21/0.47 ! [I: nat,J: nat,P2: nat > $o] :
% 0.21/0.47 ( ( ord_less @ nat @ I @ J )
% 0.21/0.47 => ( ! [I3: nat] :
% 0.21/0.47 ( ( J
% 0.21/0.47 = ( suc @ I3 ) )
% 0.21/0.47 => ( P2 @ I3 ) )
% 0.21/0.47 => ( ! [I3: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ I3 @ J )
% 0.21/0.47 => ( ( P2 @ ( suc @ I3 ) )
% 0.21/0.47 => ( P2 @ I3 ) ) )
% 0.21/0.47 => ( P2 @ I ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % strict_inc_induct
% 0.21/0.47 thf(fact_82_Nat_Oex__has__greatest__nat,axiom,
% 0.21/0.47 ! [P2: nat > $o,K: nat,B3: nat] :
% 0.21/0.47 ( ( P2 @ K )
% 0.21/0.47 => ( ! [Y4: nat] :
% 0.21/0.47 ( ( P2 @ Y4 )
% 0.21/0.47 => ( ord_less_eq @ nat @ Y4 @ B3 ) )
% 0.21/0.47 => ? [X3: nat] :
% 0.21/0.47 ( ( P2 @ X3 )
% 0.21/0.47 & ! [Y3: nat] :
% 0.21/0.47 ( ( P2 @ Y3 )
% 0.21/0.47 => ( ord_less_eq @ nat @ Y3 @ X3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Nat.ex_has_greatest_nat
% 0.21/0.47 thf(fact_83_le__neq__implies__less,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.21/0.47 => ( ( M != N )
% 0.21/0.47 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_neq_implies_less
% 0.21/0.47 thf(fact_84_measure__induct__rule,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( wellorder @ B )
% 0.21/0.47 => ! [F: A > B,P2: A > $o,A3: A] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ! [Y3: A] :
% 0.21/0.47 ( ( ord_less @ B @ ( F @ Y3 ) @ ( F @ X3 ) )
% 0.21/0.47 => ( P2 @ Y3 ) )
% 0.21/0.47 => ( P2 @ X3 ) )
% 0.21/0.47 => ( P2 @ A3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % measure_induct_rule
% 0.21/0.47 thf(fact_85_nat__induct__at__least,axiom,
% 0.21/0.47 ! [M: nat,N: nat,P2: nat > $o] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.21/0.47 => ( ( P2 @ M )
% 0.21/0.47 => ( ! [N2: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.21/0.47 => ( ( P2 @ N2 )
% 0.21/0.47 => ( P2 @ ( suc @ N2 ) ) ) )
% 0.21/0.47 => ( P2 @ N ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat_induct_at_least
% 0.21/0.47 thf(fact_86_not__less__less__Suc__eq,axiom,
% 0.21/0.47 ! [N: nat,M: nat] :
% 0.21/0.47 ( ~ ( ord_less @ nat @ N @ M )
% 0.21/0.47 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 0.21/0.47 = ( N = M ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_less_less_Suc_eq
% 0.21/0.47 thf(fact_87_less__mono__imp__le__mono,axiom,
% 0.21/0.47 ! [F: nat > nat,I: nat,J: nat] :
% 0.21/0.47 ( ! [I3: nat,J2: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ I3 @ J2 )
% 0.21/0.47 => ( ord_less @ nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 0.21/0.47 => ( ( ord_less_eq @ nat @ I @ J )
% 0.21/0.47 => ( ord_less_eq @ nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_mono_imp_le_mono
% 0.21/0.47 thf(fact_88_transitive__stepwise__le,axiom,
% 0.21/0.47 ! [M: nat,N: nat,R: nat > nat > $o] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.21/0.47 => ( ! [X3: nat] : ( R @ X3 @ X3 )
% 0.21/0.47 => ( ! [X3: nat,Y4: nat,Z: nat] :
% 0.21/0.47 ( ( R @ X3 @ Y4 )
% 0.21/0.47 => ( ( R @ Y4 @ Z )
% 0.21/0.47 => ( R @ X3 @ Z ) ) )
% 0.21/0.47 => ( ! [N2: nat] : ( R @ N2 @ ( suc @ N2 ) )
% 0.21/0.47 => ( R @ M @ N ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % transitive_stepwise_le
% 0.21/0.47 thf(fact_89_infinite__descent__measure,axiom,
% 0.21/0.47 ! [A: $tType,P2: A > $o,V2: A > nat,X2: A] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ~ ( P2 @ X3 )
% 0.21/0.47 => ? [Y3: A] :
% 0.21/0.47 ( ( ord_less @ nat @ ( V2 @ Y3 ) @ ( V2 @ X3 ) )
% 0.21/0.47 & ~ ( P2 @ Y3 ) ) )
% 0.21/0.47 => ( P2 @ X2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % infinite_descent_measure
% 0.21/0.47 thf(fact_90_lift__Suc__mono__le,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [F: nat > A,N: nat,N4: nat] :
% 0.21/0.47 ( ! [N2: nat] : ( ord_less_eq @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.21/0.47 => ( ( ord_less_eq @ nat @ N @ N4 )
% 0.21/0.47 => ( ord_less_eq @ A @ ( F @ N ) @ ( F @ N4 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % lift_Suc_mono_le
% 0.21/0.47 thf(fact_91_lift__Suc__mono__less,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [F: nat > A,N: nat,N4: nat] :
% 0.21/0.47 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.21/0.47 => ( ( ord_less @ nat @ N @ N4 )
% 0.21/0.47 => ( ord_less @ A @ ( F @ N ) @ ( F @ N4 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % lift_Suc_mono_less
% 0.21/0.47 thf(fact_92_lift__Suc__antimono__le,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [F: nat > A,N: nat,N4: nat] :
% 0.21/0.47 ( ! [N2: nat] : ( ord_less_eq @ A @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.21/0.47 => ( ( ord_less_eq @ nat @ N @ N4 )
% 0.21/0.47 => ( ord_less_eq @ A @ ( F @ N4 ) @ ( F @ N ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % lift_Suc_antimono_le
% 0.21/0.47 thf(fact_93_lift__Suc__mono__less__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [F: nat > A,N: nat,M: nat] :
% 0.21/0.47 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.21/0.47 => ( ( ord_less @ A @ ( F @ N ) @ ( F @ M ) )
% 0.21/0.47 = ( ord_less @ nat @ N @ M ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % lift_Suc_mono_less_iff
% 0.21/0.47 thf(fact_94_diff__less__Suc,axiom,
% 0.21/0.47 ! [M: nat,N: nat] : ( ord_less @ nat @ ( minus_minus @ nat @ M @ N ) @ ( suc @ M ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_less_Suc
% 0.21/0.47 thf(fact_95_Suc__diff__Suc,axiom,
% 0.21/0.47 ! [N: nat,M: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ N @ M )
% 0.21/0.47 => ( ( suc @ ( minus_minus @ nat @ M @ ( suc @ N ) ) )
% 0.21/0.47 = ( minus_minus @ nat @ M @ N ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_diff_Suc
% 0.21/0.47 thf(fact_96_Suc__diff__le,axiom,
% 0.21/0.47 ! [N: nat,M: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ N @ M )
% 0.21/0.47 => ( ( minus_minus @ nat @ ( suc @ M ) @ N )
% 0.21/0.47 = ( suc @ ( minus_minus @ nat @ M @ N ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Suc_diff_le
% 0.21/0.47 thf(fact_97_zero__induct__lemma,axiom,
% 0.21/0.47 ! [P2: nat > $o,K: nat,I: nat] :
% 0.21/0.47 ( ( P2 @ K )
% 0.21/0.47 => ( ! [N2: nat] :
% 0.21/0.47 ( ( P2 @ ( suc @ N2 ) )
% 0.21/0.47 => ( P2 @ N2 ) )
% 0.21/0.47 => ( P2 @ ( minus_minus @ nat @ K @ I ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % zero_induct_lemma
% 0.21/0.47 thf(fact_98_diff__less__mono,axiom,
% 0.21/0.47 ! [A3: nat,B3: nat,C: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ A3 @ B3 )
% 0.21/0.47 => ( ( ord_less_eq @ nat @ C @ A3 )
% 0.21/0.47 => ( ord_less @ nat @ ( minus_minus @ nat @ A3 @ C ) @ ( minus_minus @ nat @ B3 @ C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_less_mono
% 0.21/0.47 thf(fact_99_less__diff__iff,axiom,
% 0.21/0.47 ! [K: nat,M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ K @ M )
% 0.21/0.47 => ( ( ord_less_eq @ nat @ K @ N )
% 0.21/0.47 => ( ( ord_less @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 0.21/0.47 = ( ord_less @ nat @ M @ N ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_diff_iff
% 0.21/0.47 thf(fact_100_diff__Suc__eq__diff__pred,axiom,
% 0.21/0.47 ! [M: nat,N: nat] :
% 0.21/0.47 ( ( minus_minus @ nat @ M @ ( suc @ N ) )
% 0.21/0.47 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ ( one_one @ nat ) ) @ N ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_Suc_eq_diff_pred
% 0.21/0.47 thf(fact_101_diff__strict__right__mono,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ordered_ab_group_add @ A )
% 0.21/0.47 => ! [A3: A,B3: A,C: A] :
% 0.21/0.47 ( ( ord_less @ A @ A3 @ B3 )
% 0.21/0.47 => ( ord_less @ A @ ( minus_minus @ A @ A3 @ C ) @ ( minus_minus @ A @ B3 @ C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_strict_right_mono
% 0.21/0.47 thf(fact_102_diff__strict__left__mono,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ordered_ab_group_add @ A )
% 0.21/0.47 => ! [B3: A,A3: A,C: A] :
% 0.21/0.47 ( ( ord_less @ A @ B3 @ A3 )
% 0.21/0.47 => ( ord_less @ A @ ( minus_minus @ A @ C @ A3 ) @ ( minus_minus @ A @ C @ B3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_strict_left_mono
% 0.21/0.47 thf(fact_103_diff__eq__diff__less,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ordered_ab_group_add @ A )
% 0.21/0.47 => ! [A3: A,B3: A,C: A,D: A] :
% 0.21/0.47 ( ( ( minus_minus @ A @ A3 @ B3 )
% 0.21/0.47 = ( minus_minus @ A @ C @ D ) )
% 0.21/0.47 => ( ( ord_less @ A @ A3 @ B3 )
% 0.21/0.47 = ( ord_less @ A @ C @ D ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_eq_diff_less
% 0.21/0.47 thf(fact_104_diff__strict__mono,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ordered_ab_group_add @ A )
% 0.21/0.47 => ! [A3: A,B3: A,D: A,C: A] :
% 0.21/0.47 ( ( ord_less @ A @ A3 @ B3 )
% 0.21/0.47 => ( ( ord_less @ A @ D @ C )
% 0.21/0.47 => ( ord_less @ A @ ( minus_minus @ A @ A3 @ C ) @ ( minus_minus @ A @ B3 @ D ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_strict_mono
% 0.21/0.47 thf(fact_105_diff__eq__diff__less__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ordered_ab_group_add @ A )
% 0.21/0.47 => ! [A3: A,B3: A,C: A,D: A] :
% 0.21/0.47 ( ( ( minus_minus @ A @ A3 @ B3 )
% 0.21/0.47 = ( minus_minus @ A @ C @ D ) )
% 0.21/0.47 => ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.21/0.47 = ( ord_less_eq @ A @ C @ D ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_eq_diff_less_eq
% 0.21/0.47 thf(fact_106_diff__right__mono,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ordered_ab_group_add @ A )
% 0.21/0.47 => ! [A3: A,B3: A,C: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.21/0.47 => ( ord_less_eq @ A @ ( minus_minus @ A @ A3 @ C ) @ ( minus_minus @ A @ B3 @ C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_right_mono
% 0.21/0.47 thf(fact_107_diff__left__mono,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ordered_ab_group_add @ A )
% 0.21/0.47 => ! [B3: A,A3: A,C: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.21/0.47 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A3 ) @ ( minus_minus @ A @ C @ B3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_left_mono
% 0.21/0.47 thf(fact_108_diff__mono,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ordered_ab_group_add @ A )
% 0.21/0.47 => ! [A3: A,B3: A,D: A,C: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ D @ C )
% 0.21/0.47 => ( ord_less_eq @ A @ ( minus_minus @ A @ A3 @ C ) @ ( minus_minus @ A @ B3 @ D ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_mono
% 0.21/0.47 thf(fact_109_length__induct,axiom,
% 0.21/0.47 ! [A: $tType,P2: ( list @ A ) > $o,Xs2: list @ A] :
% 0.21/0.47 ( ! [Xs: list @ A] :
% 0.21/0.47 ( ! [Ys2: list @ A] :
% 0.21/0.47 ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ys2 ) @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.21/0.47 => ( P2 @ Ys2 ) )
% 0.21/0.47 => ( P2 @ Xs ) )
% 0.21/0.47 => ( P2 @ Xs2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % length_induct
% 0.21/0.47 thf(fact_110_less__imp__diff__less,axiom,
% 0.21/0.47 ! [J: nat,K: nat,N: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ J @ K )
% 0.21/0.47 => ( ord_less @ nat @ ( minus_minus @ nat @ J @ N ) @ K ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_imp_diff_less
% 0.21/0.47 thf(fact_111_diff__less__mono2,axiom,
% 0.21/0.47 ! [M: nat,N: nat,L: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ M @ N )
% 0.21/0.47 => ( ( ord_less @ nat @ M @ L )
% 0.21/0.47 => ( ord_less @ nat @ ( minus_minus @ nat @ L @ N ) @ ( minus_minus @ nat @ L @ M ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_less_mono2
% 0.21/0.47 thf(fact_112_diff__le__mono2,axiom,
% 0.21/0.47 ! [M: nat,N: nat,L: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.21/0.47 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ L @ N ) @ ( minus_minus @ nat @ L @ M ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_le_mono2
% 0.21/0.47 thf(fact_113_le__diff__iff_H,axiom,
% 0.21/0.47 ! [A3: nat,C: nat,B3: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ A3 @ C )
% 0.21/0.47 => ( ( ord_less_eq @ nat @ B3 @ C )
% 0.21/0.47 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ A3 ) @ ( minus_minus @ nat @ C @ B3 ) )
% 0.21/0.47 = ( ord_less_eq @ nat @ B3 @ A3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_diff_iff'
% 0.21/0.47 thf(fact_114_diff__le__self,axiom,
% 0.21/0.47 ! [M: nat,N: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ N ) @ M ) ).
% 0.21/0.47
% 0.21/0.47 % diff_le_self
% 0.21/0.47 thf(fact_115_diff__le__mono,axiom,
% 0.21/0.47 ! [M: nat,N: nat,L: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.21/0.47 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ L ) @ ( minus_minus @ nat @ N @ L ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_le_mono
% 0.21/0.47 thf(fact_116_Nat_Odiff__diff__eq,axiom,
% 0.21/0.47 ! [K: nat,M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ K @ M )
% 0.21/0.47 => ( ( ord_less_eq @ nat @ K @ N )
% 0.21/0.47 => ( ( minus_minus @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 0.21/0.47 = ( minus_minus @ nat @ M @ N ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Nat.diff_diff_eq
% 0.21/0.47 thf(fact_117_le__diff__iff,axiom,
% 0.21/0.47 ! [K: nat,M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ K @ M )
% 0.21/0.47 => ( ( ord_less_eq @ nat @ K @ N )
% 0.21/0.47 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 0.21/0.47 = ( ord_less_eq @ nat @ M @ N ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_diff_iff
% 0.21/0.47 thf(fact_118_eq__diff__iff,axiom,
% 0.21/0.47 ! [K: nat,M: nat,N: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ K @ M )
% 0.21/0.47 => ( ( ord_less_eq @ nat @ K @ N )
% 0.21/0.47 => ( ( ( minus_minus @ nat @ M @ K )
% 0.21/0.47 = ( minus_minus @ nat @ N @ K ) )
% 0.21/0.47 = ( M = N ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eq_diff_iff
% 0.21/0.47 thf(fact_119_one__reorient,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( one @ A )
% 0.21/0.47 => ! [X2: A] :
% 0.21/0.47 ( ( ( one_one @ A )
% 0.21/0.47 = X2 )
% 0.21/0.47 = ( X2
% 0.21/0.47 = ( one_one @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % one_reorient
% 0.21/0.47 thf(fact_120_diff__right__commute,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( cancel146912293up_add @ A )
% 0.21/0.47 => ! [A3: A,C: A,B3: A] :
% 0.21/0.47 ( ( minus_minus @ A @ ( minus_minus @ A @ A3 @ C ) @ B3 )
% 0.21/0.47 = ( minus_minus @ A @ ( minus_minus @ A @ A3 @ B3 ) @ C ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % diff_right_commute
% 0.21/0.47 thf(fact_121_Subset,axiom,
% 0.21/0.47 ! [MsgInSet: message @ p @ v] :
% 0.21/0.47 ( ( member @ ( message @ p @ v ) @ MsgInSet @ ( firstOccSet @ ( suc @ index ) ) )
% 0.21/0.47 => ( member @ ( message @ p @ v ) @ MsgInSet @ ( firstOccSet @ index ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Subset
% 0.21/0.47 thf(fact_122_SameCfgOnLow,axiom,
% 0.21/0.47 ! [I4: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) )
% 0.21/0.47 => ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ I4 )
% 0.21/0.47 = ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % SameCfgOnLow
% 0.21/0.47 thf(fact_123__092_060open_062_092_060not_062_AOccM_A_060_Alength_A_Ift_Aindex_J_092_060close_062,axiom,
% 0.21/0.47 ~ ( ord_less @ nat @ occM2 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % \<open>\<not> OccM < length (ft index)\<close>
% 0.21/0.47 thf(fact_124_IPrefixListEx,axiom,
% 0.21/0.47 ! [I4: nat] : ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ I4 ) @ ( fe @ ( suc @ I4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % IPrefixListEx
% 0.21/0.47 thf(fact_125_order__refl,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_refl
% 0.21/0.47 thf(fact_126_nat__descend__induct,axiom,
% 0.21/0.47 ! [N: nat,P2: nat > $o,M: nat] :
% 0.21/0.47 ( ! [K2: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ N @ K2 )
% 0.21/0.47 => ( P2 @ K2 ) )
% 0.21/0.47 => ( ! [K2: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ K2 @ N )
% 0.21/0.47 => ( ! [I4: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ K2 @ I4 )
% 0.21/0.47 => ( P2 @ I4 ) )
% 0.21/0.47 => ( P2 @ K2 ) ) )
% 0.21/0.47 => ( P2 @ M ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nat_descend_induct
% 0.21/0.47 thf(fact_127_Lattices__Big_Oex__has__greatest__nat,axiom,
% 0.21/0.47 ! [A: $tType,P2: A > $o,K: A,F: A > nat,B3: nat] :
% 0.21/0.47 ( ( P2 @ K )
% 0.21/0.47 => ( ! [Y4: A] :
% 0.21/0.47 ( ( P2 @ Y4 )
% 0.21/0.47 => ( ord_less @ nat @ ( F @ Y4 ) @ B3 ) )
% 0.21/0.47 => ? [X3: A] :
% 0.21/0.47 ( ( P2 @ X3 )
% 0.21/0.47 & ! [Y3: A] :
% 0.21/0.47 ( ( P2 @ Y3 )
% 0.21/0.47 => ( ord_less_eq @ nat @ ( F @ Y3 ) @ ( F @ X3 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Lattices_Big.ex_has_greatest_nat
% 0.21/0.47 thf(fact_128_KeepProperty,axiom,
% 0.21/0.47 ! [Low: nat,P2: nat > $o,Q: nat > $o] :
% 0.21/0.47 ( ! [I3: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ Low @ I3 )
% 0.21/0.47 => ( ( P2 @ I3 )
% 0.21/0.47 => ( ( P2 @ ( suc @ I3 ) )
% 0.21/0.47 & ( Q @ I3 ) ) ) )
% 0.21/0.47 => ( ( P2 @ Low )
% 0.21/0.47 => ! [I4: nat] :
% 0.21/0.47 ( ( ord_less_eq @ nat @ Low @ I4 )
% 0.21/0.47 => ( Q @ I4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % KeepProperty
% 0.21/0.47 thf(fact_129_less__numeral__extra_I4_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linord1659791738miring @ A )
% 0.21/0.47 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_numeral_extra(4)
% 0.21/0.47 thf(fact_130_le__numeral__extra_I4_J,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linord1659791738miring @ A )
% 0.21/0.47 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_numeral_extra(4)
% 0.21/0.47 thf(fact_131_LengthStep,axiom,
% 0.21/0.47 ord_less @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % LengthStep
% 0.21/0.47 thf(fact_132_ConsumedMsg_I1_J,axiom,
% 0.21/0.47 minimalEnabled @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ consumedMsg ).
% 0.21/0.47
% 0.21/0.47 % ConsumedMsg(1)
% 0.21/0.47 thf(fact_133_PrefixListTransitive,axiom,
% 0.21/0.47 ! [A: $tType,L1: list @ A,L2: list @ A,L3: list @ A] :
% 0.21/0.47 ( ( prefixList @ A @ L1 @ L2 )
% 0.21/0.47 => ( ( prefixList @ A @ L2 @ L3 )
% 0.21/0.47 => ( prefixList @ A @ L1 @ L3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % PrefixListTransitive
% 0.21/0.47 thf(fact_134_PrefixSameOnLow,axiom,
% 0.21/0.47 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 0.21/0.47 ( ( prefixList @ A @ L1 @ L2 )
% 0.21/0.47 => ! [Index: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ Index @ ( size_size @ ( list @ A ) @ L1 ) )
% 0.21/0.47 => ( ( nth @ A @ L1 @ Index )
% 0.21/0.47 = ( nth @ A @ L2 @ Index ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % PrefixSameOnLow
% 0.21/0.47 thf(fact_135_PrefixListMonotonicity,axiom,
% 0.21/0.47 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 0.21/0.47 ( ( prefixList @ A @ L1 @ L2 )
% 0.21/0.47 => ( ord_less @ nat @ ( size_size @ ( list @ A ) @ L1 ) @ ( size_size @ ( list @ A ) @ L2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % PrefixListMonotonicity
% 0.21/0.47 thf(fact_136_nth__equalityI,axiom,
% 0.21/0.47 ! [A: $tType,Xs2: list @ A,Ys: list @ A] :
% 0.21/0.47 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.21/0.47 = ( size_size @ ( list @ A ) @ Ys ) )
% 0.21/0.47 => ( ! [I3: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ I3 @ ( size_size @ ( list @ A ) @ Xs2 ) )
% 0.21/0.47 => ( ( nth @ A @ Xs2 @ I3 )
% 0.21/0.47 = ( nth @ A @ Ys @ I3 ) ) )
% 0.21/0.47 => ( Xs2 = Ys ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % nth_equalityI
% 0.21/0.47 thf(fact_137_Skolem__list__nth,axiom,
% 0.21/0.47 ! [A: $tType,K: nat,P2: nat > A > $o] :
% 0.21/0.47 ( ( ! [I2: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ I2 @ K )
% 0.21/0.47 => ? [X4: A] : ( P2 @ I2 @ X4 ) ) )
% 0.21/0.47 = ( ? [Xs3: list @ A] :
% 0.21/0.47 ( ( ( size_size @ ( list @ A ) @ Xs3 )
% 0.21/0.47 = K )
% 0.21/0.47 & ! [I2: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ I2 @ K )
% 0.21/0.47 => ( P2 @ I2 @ ( nth @ A @ Xs3 @ I2 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Skolem_list_nth
% 0.21/0.47 thf(fact_138_list__eq__iff__nth__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ^ [Y5: list @ A,Z2: list @ A] : ( Y5 = Z2 ) )
% 0.21/0.47 = ( ^ [Xs3: list @ A,Ys3: list @ A] :
% 0.21/0.47 ( ( ( size_size @ ( list @ A ) @ Xs3 )
% 0.21/0.47 = ( size_size @ ( list @ A ) @ Ys3 ) )
% 0.21/0.47 & ! [I2: nat] :
% 0.21/0.47 ( ( ord_less @ nat @ I2 @ ( size_size @ ( list @ A ) @ Xs3 ) )
% 0.21/0.47 => ( ( nth @ A @ Xs3 @ I2 )
% 0.21/0.47 = ( nth @ A @ Ys3 @ I2 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % list_eq_iff_nth_eq
% 0.21/0.47 thf(fact_139_dual__order_Oantisym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [B3: A,A3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.21/0.47 => ( A3 = B3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.antisym
% 0.21/0.47 thf(fact_140_dual__order_Oeq__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ( ( ^ [Y5: A,Z2: A] : ( Y5 = Z2 ) )
% 0.21/0.47 = ( ^ [A5: A,B4: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ B4 @ A5 )
% 0.21/0.47 & ( ord_less_eq @ A @ A5 @ B4 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.eq_iff
% 0.21/0.47 thf(fact_141_dual__order_Otrans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [B3: A,A3: A,C: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ C @ B3 )
% 0.21/0.47 => ( ord_less_eq @ A @ C @ A3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.trans
% 0.21/0.47 thf(fact_142_linorder__wlog,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [P2: A > A > $o,A3: A,B3: A] :
% 0.21/0.47 ( ! [A6: A,B5: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A6 @ B5 )
% 0.21/0.47 => ( P2 @ A6 @ B5 ) )
% 0.21/0.47 => ( ! [A6: A,B5: A] :
% 0.21/0.47 ( ( P2 @ B5 @ A6 )
% 0.21/0.47 => ( P2 @ A6 @ B5 ) )
% 0.21/0.47 => ( P2 @ A3 @ B3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % linorder_wlog
% 0.21/0.47 thf(fact_143_dual__order_Orefl,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.refl
% 0.21/0.47 thf(fact_144_order__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [X2: A,Y: A,Z3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.21/0.47 => ( ( ord_less_eq @ A @ Y @ Z3 )
% 0.21/0.47 => ( ord_less_eq @ A @ X2 @ Z3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_trans
% 0.21/0.47 thf(fact_145_order__class_Oorder_Oantisym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [A3: A,B3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.21/0.47 => ( A3 = B3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_class.order.antisym
% 0.21/0.47 thf(fact_146_ord__le__eq__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord @ A )
% 0.21/0.47 => ! [A3: A,B3: A,C: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.21/0.47 => ( ( B3 = C )
% 0.21/0.47 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_le_eq_trans
% 0.21/0.47 thf(fact_147_ord__eq__le__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord @ A )
% 0.21/0.47 => ! [A3: A,B3: A,C: A] :
% 0.21/0.47 ( ( A3 = B3 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.21/0.47 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_eq_le_trans
% 0.21/0.47 thf(fact_148_order__class_Oorder_Oeq__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ( ( ^ [Y5: A,Z2: A] : ( Y5 = Z2 ) )
% 0.21/0.47 = ( ^ [A5: A,B4: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A5 @ B4 )
% 0.21/0.47 & ( ord_less_eq @ A @ B4 @ A5 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_class.order.eq_iff
% 0.21/0.47 thf(fact_149_antisym__conv,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [Y: A,X2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ Y @ X2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ X2 @ Y )
% 0.21/0.47 = ( X2 = Y ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % antisym_conv
% 0.21/0.47 thf(fact_150_le__cases3,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [X2: A,Y: A,Z3: A] :
% 0.21/0.47 ( ( ( ord_less_eq @ A @ X2 @ Y )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ Y @ Z3 ) )
% 0.21/0.47 => ( ( ( ord_less_eq @ A @ Y @ X2 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ X2 @ Z3 ) )
% 0.21/0.47 => ( ( ( ord_less_eq @ A @ X2 @ Z3 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ Z3 @ Y ) )
% 0.21/0.47 => ( ( ( ord_less_eq @ A @ Z3 @ Y )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ Y @ X2 ) )
% 0.21/0.47 => ( ( ( ord_less_eq @ A @ Y @ Z3 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ Z3 @ X2 ) )
% 0.21/0.47 => ~ ( ( ord_less_eq @ A @ Z3 @ X2 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_cases3
% 0.21/0.47 thf(fact_151_order_Otrans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [A3: A,B3: A,C: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.21/0.47 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.trans
% 0.21/0.47 thf(fact_152_le__cases,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [X2: A,Y: A] :
% 0.21/0.47 ( ~ ( ord_less_eq @ A @ X2 @ Y )
% 0.21/0.47 => ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_cases
% 0.21/0.47 thf(fact_153_eq__refl,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [X2: A,Y: A] :
% 0.21/0.47 ( ( X2 = Y )
% 0.21/0.47 => ( ord_less_eq @ A @ X2 @ Y ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eq_refl
% 0.21/0.47 thf(fact_154_linear,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [X2: A,Y: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.21/0.47 | ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % linear
% 0.21/0.47 thf(fact_155_antisym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [X2: A,Y: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.21/0.47 => ( ( ord_less_eq @ A @ Y @ X2 )
% 0.21/0.47 => ( X2 = Y ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % antisym
% 0.21/0.47 thf(fact_156_eq__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ( ( ^ [Y5: A,Z2: A] : ( Y5 = Z2 ) )
% 0.21/0.47 = ( ^ [X: A,Y6: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X @ Y6 )
% 0.21/0.47 & ( ord_less_eq @ A @ Y6 @ X ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eq_iff
% 0.21/0.47 thf(fact_157_ord__le__eq__subst,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( ord @ B )
% 0.21/0.47 & ( ord @ A ) )
% 0.21/0.47 => ! [A3: A,B3: A,F: A > B,C: B] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.21/0.47 => ( ( ( F @ B3 )
% 0.21/0.47 = C )
% 0.21/0.47 => ( ! [X3: A,Y4: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.21/0.47 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.21/0.47 => ( ord_less_eq @ B @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_le_eq_subst
% 0.21/0.47 thf(fact_158_ord__eq__le__subst,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( ord @ B )
% 0.21/0.47 & ( ord @ A ) )
% 0.21/0.47 => ! [A3: A,F: B > A,B3: B,C: B] :
% 0.21/0.47 ( ( A3
% 0.21/0.47 = ( F @ B3 ) )
% 0.21/0.47 => ( ( ord_less_eq @ B @ B3 @ C )
% 0.21/0.47 => ( ! [X3: B,Y4: B] :
% 0.21/0.47 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 0.21/0.47 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.21/0.47 => ( ord_less_eq @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_eq_le_subst
% 0.21/0.47 thf(fact_159_order__subst2,axiom,
% 0.21/0.47 ! [A: $tType,C2: $tType] :
% 0.21/0.47 ( ( ( order @ C2 )
% 0.21/0.47 & ( order @ A ) )
% 0.21/0.47 => ! [A3: A,B3: A,F: A > C2,C: C2] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.21/0.47 => ( ( ord_less_eq @ C2 @ ( F @ B3 ) @ C )
% 0.21/0.47 => ( ! [X3: A,Y4: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.21/0.47 => ( ord_less_eq @ C2 @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.21/0.47 => ( ord_less_eq @ C2 @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_subst2
% 0.21/0.47 thf(fact_160_order__subst1,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( order @ B )
% 0.21/0.47 & ( order @ A ) )
% 0.21/0.47 => ! [A3: A,F: B > A,B3: B,C: B] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A3 @ ( F @ B3 ) )
% 0.21/0.47 => ( ( ord_less_eq @ B @ B3 @ C )
% 0.21/0.47 => ( ! [X3: B,Y4: B] :
% 0.21/0.47 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 0.21/0.47 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.21/0.47 => ( ord_less_eq @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_subst1
% 0.21/0.47 thf(fact_161_le__fun__def,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( ord @ B )
% 0.21/0.47 => ( ( ord_less_eq @ ( A > B ) )
% 0.21/0.47 = ( ^ [F2: A > B,G2: A > B] :
% 0.21/0.47 ! [X: A] : ( ord_less_eq @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_fun_def
% 0.21/0.47 thf(fact_162_le__funI,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( ord @ B )
% 0.21/0.47 => ! [F: A > B,G: A > B] :
% 0.21/0.47 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.21/0.47 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_funI
% 0.21/0.47 thf(fact_163_le__funE,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( ord @ B )
% 0.21/0.47 => ! [F: A > B,G: A > B,X2: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.21/0.47 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_funE
% 0.21/0.47 thf(fact_164_le__funD,axiom,
% 0.21/0.47 ! [B: $tType,A: $tType] :
% 0.21/0.47 ( ( ord @ B )
% 0.21/0.47 => ! [F: A > B,G: A > B,X2: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.21/0.47 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_funD
% 0.21/0.47 thf(fact_165_dual__order_Ostrict__implies__not__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [B3: A,A3: A] :
% 0.21/0.47 ( ( ord_less @ A @ B3 @ A3 )
% 0.21/0.47 => ( A3 != B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.strict_implies_not_eq
% 0.21/0.47 thf(fact_166_order_Ostrict__implies__not__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [A3: A,B3: A] :
% 0.21/0.47 ( ( ord_less @ A @ A3 @ B3 )
% 0.21/0.47 => ( A3 != B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.strict_implies_not_eq
% 0.21/0.47 thf(fact_167_not__less__iff__gr__or__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [X2: A,Y: A] :
% 0.21/0.47 ( ( ~ ( ord_less @ A @ X2 @ Y ) )
% 0.21/0.47 = ( ( ord_less @ A @ Y @ X2 )
% 0.21/0.47 | ( X2 = Y ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_less_iff_gr_or_eq
% 0.21/0.47 thf(fact_168_dual__order_Ostrict__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [B3: A,A3: A,C: A] :
% 0.21/0.47 ( ( ord_less @ A @ B3 @ A3 )
% 0.21/0.47 => ( ( ord_less @ A @ C @ B3 )
% 0.21/0.47 => ( ord_less @ A @ C @ A3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.strict_trans
% 0.21/0.47 thf(fact_169_linorder__less__wlog,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [P2: A > A > $o,A3: A,B3: A] :
% 0.21/0.47 ( ! [A6: A,B5: A] :
% 0.21/0.47 ( ( ord_less @ A @ A6 @ B5 )
% 0.21/0.47 => ( P2 @ A6 @ B5 ) )
% 0.21/0.47 => ( ! [A6: A] : ( P2 @ A6 @ A6 )
% 0.21/0.47 => ( ! [A6: A,B5: A] :
% 0.21/0.47 ( ( P2 @ B5 @ A6 )
% 0.21/0.47 => ( P2 @ A6 @ B5 ) )
% 0.21/0.47 => ( P2 @ A3 @ B3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % linorder_less_wlog
% 0.21/0.47 thf(fact_170_exists__least__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( wellorder @ A )
% 0.21/0.47 => ( ( ^ [P3: A > $o] :
% 0.21/0.47 ? [X4: A] : ( P3 @ X4 ) )
% 0.21/0.47 = ( ^ [P4: A > $o] :
% 0.21/0.47 ? [N3: A] :
% 0.21/0.47 ( ( P4 @ N3 )
% 0.21/0.47 & ! [M4: A] :
% 0.21/0.47 ( ( ord_less @ A @ M4 @ N3 )
% 0.21/0.47 => ~ ( P4 @ M4 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % exists_least_iff
% 0.21/0.47 thf(fact_171_less__imp__not__less,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [X2: A,Y: A] :
% 0.21/0.47 ( ( ord_less @ A @ X2 @ Y )
% 0.21/0.47 => ~ ( ord_less @ A @ Y @ X2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_imp_not_less
% 0.21/0.47 thf(fact_172_order_Ostrict__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [A3: A,B3: A,C: A] :
% 0.21/0.47 ( ( ord_less @ A @ A3 @ B3 )
% 0.21/0.47 => ( ( ord_less @ A @ B3 @ C )
% 0.21/0.47 => ( ord_less @ A @ A3 @ C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.strict_trans
% 0.21/0.47 thf(fact_173_dual__order_Oirrefl,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [A3: A] :
% 0.21/0.47 ~ ( ord_less @ A @ A3 @ A3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.irrefl
% 0.21/0.47 thf(fact_174_linorder__cases,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [X2: A,Y: A] :
% 0.21/0.47 ( ~ ( ord_less @ A @ X2 @ Y )
% 0.21/0.47 => ( ( X2 != Y )
% 0.21/0.47 => ( ord_less @ A @ Y @ X2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % linorder_cases
% 0.21/0.47 thf(fact_175_less__imp__triv,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [X2: A,Y: A,P2: $o] :
% 0.21/0.47 ( ( ord_less @ A @ X2 @ Y )
% 0.21/0.47 => ( ( ord_less @ A @ Y @ X2 )
% 0.21/0.47 => P2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_imp_triv
% 0.21/0.47 thf(fact_176_less__imp__not__eq2,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [X2: A,Y: A] :
% 0.21/0.47 ( ( ord_less @ A @ X2 @ Y )
% 0.21/0.47 => ( Y != X2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_imp_not_eq2
% 0.21/0.47 thf(fact_177_antisym__conv3,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [Y: A,X2: A] :
% 0.21/0.47 ( ~ ( ord_less @ A @ Y @ X2 )
% 0.21/0.47 => ( ( ~ ( ord_less @ A @ X2 @ Y ) )
% 0.21/0.47 = ( X2 = Y ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % antisym_conv3
% 0.21/0.47 thf(fact_178_less__induct,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( wellorder @ A )
% 0.21/0.47 => ! [P2: A > $o,A3: A] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ! [Y3: A] :
% 0.21/0.47 ( ( ord_less @ A @ Y3 @ X3 )
% 0.21/0.47 => ( P2 @ Y3 ) )
% 0.21/0.47 => ( P2 @ X3 ) )
% 0.21/0.47 => ( P2 @ A3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_induct
% 0.21/0.47 thf(fact_179_less__not__sym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [X2: A,Y: A] :
% 0.21/0.47 ( ( ord_less @ A @ X2 @ Y )
% 0.21/0.47 => ~ ( ord_less @ A @ Y @ X2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_not_sym
% 0.21/0.47 thf(fact_180_less__imp__not__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [X2: A,Y: A] :
% 0.21/0.47 ( ( ord_less @ A @ X2 @ Y )
% 0.21/0.47 => ( X2 != Y ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_imp_not_eq
% 0.21/0.47 thf(fact_181_dual__order_Oasym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [B3: A,A3: A] :
% 0.21/0.47 ( ( ord_less @ A @ B3 @ A3 )
% 0.21/0.47 => ~ ( ord_less @ A @ A3 @ B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.asym
% 0.21/0.47 thf(fact_182_ord__less__eq__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord @ A )
% 0.21/0.47 => ! [A3: A,B3: A,C: A] :
% 0.21/0.47 ( ( ord_less @ A @ A3 @ B3 )
% 0.21/0.47 => ( ( B3 = C )
% 0.21/0.47 => ( ord_less @ A @ A3 @ C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_less_eq_trans
% 0.21/0.47 thf(fact_183_ord__eq__less__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord @ A )
% 0.21/0.47 => ! [A3: A,B3: A,C: A] :
% 0.21/0.47 ( ( A3 = B3 )
% 0.21/0.47 => ( ( ord_less @ A @ B3 @ C )
% 0.21/0.47 => ( ord_less @ A @ A3 @ C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_eq_less_trans
% 0.21/0.47 thf(fact_184_less__irrefl,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [X2: A] :
% 0.21/0.47 ~ ( ord_less @ A @ X2 @ X2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_irrefl
% 0.21/0.47 thf(fact_185_less__linear,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [X2: A,Y: A] :
% 0.21/0.47 ( ( ord_less @ A @ X2 @ Y )
% 0.21/0.47 | ( X2 = Y )
% 0.21/0.47 | ( ord_less @ A @ Y @ X2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_linear
% 0.21/0.47 thf(fact_186_less__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [X2: A,Y: A,Z3: A] :
% 0.21/0.47 ( ( ord_less @ A @ X2 @ Y )
% 0.21/0.47 => ( ( ord_less @ A @ Y @ Z3 )
% 0.21/0.47 => ( ord_less @ A @ X2 @ Z3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_trans
% 0.21/0.47 thf(fact_187_less__asym_H,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [A3: A,B3: A] :
% 0.21/0.47 ( ( ord_less @ A @ A3 @ B3 )
% 0.21/0.47 => ~ ( ord_less @ A @ B3 @ A3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_asym'
% 0.21/0.47 thf(fact_188_less__asym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [X2: A,Y: A] :
% 0.21/0.47 ( ( ord_less @ A @ X2 @ Y )
% 0.21/0.47 => ~ ( ord_less @ A @ Y @ X2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_asym
% 0.21/0.47 thf(fact_189_less__imp__neq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [X2: A,Y: A] :
% 0.21/0.47 ( ( ord_less @ A @ X2 @ Y )
% 0.21/0.47 => ( X2 != Y ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % less_imp_neq
% 0.21/0.47 thf(fact_190_dense,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( dense_order @ A )
% 0.21/0.47 => ! [X2: A,Y: A] :
% 0.21/0.47 ( ( ord_less @ A @ X2 @ Y )
% 0.21/0.47 => ? [Z: A] :
% 0.21/0.47 ( ( ord_less @ A @ X2 @ Z )
% 0.21/0.47 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dense
% 0.21/0.47 thf(fact_191_order_Oasym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [A3: A,B3: A] :
% 0.21/0.47 ( ( ord_less @ A @ A3 @ B3 )
% 0.21/0.47 => ~ ( ord_less @ A @ B3 @ A3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.asym
% 0.21/0.47 thf(fact_192_neq__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [X2: A,Y: A] :
% 0.21/0.47 ( ( X2 != Y )
% 0.21/0.47 = ( ( ord_less @ A @ X2 @ Y )
% 0.21/0.47 | ( ord_less @ A @ Y @ X2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % neq_iff
% 0.21/0.47 thf(fact_193_neqE,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [X2: A,Y: A] :
% 0.21/0.47 ( ( X2 != Y )
% 0.21/0.47 => ( ~ ( ord_less @ A @ X2 @ Y )
% 0.21/0.47 => ( ord_less @ A @ Y @ X2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % neqE
% 0.21/0.47 thf(fact_194_gt__ex,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( no_top @ A )
% 0.21/0.47 => ! [X2: A] :
% 0.21/0.47 ? [X_1: A] : ( ord_less @ A @ X2 @ X_1 ) ) ).
% 0.21/0.47
% 0.21/0.47 % gt_ex
% 0.21/0.47 thf(fact_195_lt__ex,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( no_bot @ A )
% 0.21/0.47 => ! [X2: A] :
% 0.21/0.47 ? [Y4: A] : ( ord_less @ A @ Y4 @ X2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % lt_ex
% 0.21/0.47 thf(fact_196_order__less__subst2,axiom,
% 0.21/0.47 ! [A: $tType,C2: $tType] :
% 0.21/0.47 ( ( ( order @ C2 )
% 0.21/0.47 & ( order @ A ) )
% 0.21/0.47 => ! [A3: A,B3: A,F: A > C2,C: C2] :
% 0.21/0.47 ( ( ord_less @ A @ A3 @ B3 )
% 0.21/0.47 => ( ( ord_less @ C2 @ ( F @ B3 ) @ C )
% 0.21/0.47 => ( ! [X3: A,Y4: A] :
% 0.21/0.47 ( ( ord_less @ A @ X3 @ Y4 )
% 0.21/0.47 => ( ord_less @ C2 @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.21/0.47 => ( ord_less @ C2 @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_less_subst2
% 0.21/0.47 thf(fact_197_order__less__subst1,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( order @ B )
% 0.21/0.47 & ( order @ A ) )
% 0.21/0.47 => ! [A3: A,F: B > A,B3: B,C: B] :
% 0.21/0.47 ( ( ord_less @ A @ A3 @ ( F @ B3 ) )
% 0.21/0.47 => ( ( ord_less @ B @ B3 @ C )
% 0.21/0.47 => ( ! [X3: B,Y4: B] :
% 0.21/0.47 ( ( ord_less @ B @ X3 @ Y4 )
% 0.21/0.47 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.21/0.47 => ( ord_less @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_less_subst1
% 0.21/0.47 thf(fact_198_ord__less__eq__subst,axiom,
% 0.21/0.47 ! [A: $tType,B: $tType] :
% 0.21/0.47 ( ( ( ord @ B )
% 0.21/0.47 & ( ord @ A ) )
% 0.32/0.47 => ! [A3: A,B3: A,F: A > B,C: B] :
% 0.32/0.47 ( ( ord_less @ A @ A3 @ B3 )
% 0.32/0.47 => ( ( ( F @ B3 )
% 0.32/0.47 = C )
% 0.32/0.47 => ( ! [X3: A,Y4: A] :
% 0.32/0.47 ( ( ord_less @ A @ X3 @ Y4 )
% 0.32/0.47 => ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less @ B @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_less_eq_subst
% 0.32/0.47 thf(fact_199_ord__eq__less__subst,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType] :
% 0.32/0.47 ( ( ( ord @ B )
% 0.32/0.47 & ( ord @ A ) )
% 0.32/0.47 => ! [A3: A,F: B > A,B3: B,C: B] :
% 0.32/0.47 ( ( A3
% 0.32/0.47 = ( F @ B3 ) )
% 0.32/0.47 => ( ( ord_less @ B @ B3 @ C )
% 0.32/0.47 => ( ! [X3: B,Y4: B] :
% 0.32/0.47 ( ( ord_less @ B @ X3 @ Y4 )
% 0.32/0.47 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.47 => ( ord_less @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord_eq_less_subst
% 0.32/0.47 thf(fact_200_ex__has__least__nat,axiom,
% 0.32/0.47 ! [A: $tType,P2: A > $o,K: A,M: A > nat] :
% 0.32/0.47 ( ( P2 @ K )
% 0.32/0.47 => ? [X3: A] :
% 0.32/0.47 ( ( P2 @ X3 )
% 0.32/0.47 & ! [Y3: A] :
% 0.32/0.47 ( ( P2 @ Y3 )
% 0.32/0.47 => ( ord_less_eq @ nat @ ( M @ X3 ) @ ( M @ Y3 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ex_has_least_nat
% 0.32/0.47 thf(fact_201_MinPredicate,axiom,
% 0.32/0.47 ! [P2: nat > $o] :
% 0.32/0.47 ( ? [X_12: nat] : ( P2 @ X_12 )
% 0.32/0.47 => ? [N0: nat] :
% 0.32/0.47 ( ( P2 @ N0 )
% 0.32/0.47 & ! [N5: nat] :
% 0.32/0.47 ( ( P2 @ N5 )
% 0.32/0.47 => ( ord_less_eq @ nat @ N0 @ N5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % MinPredicate
% 0.32/0.47 thf(fact_202_order_Onot__eq__order__implies__strict,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( order @ A )
% 0.32/0.47 => ! [A3: A,B3: A] :
% 0.32/0.47 ( ( A3 != B3 )
% 0.32/0.47 => ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/0.47 => ( ord_less @ A @ A3 @ B3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order.not_eq_order_implies_strict
% 0.32/0.47 thf(fact_203_dual__order_Ostrict__implies__order,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( order @ A )
% 0.32/0.47 => ! [B3: A,A3: A] :
% 0.32/0.47 ( ( ord_less @ A @ B3 @ A3 )
% 0.32/0.47 => ( ord_less_eq @ A @ B3 @ A3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.strict_implies_order
% 0.32/0.47 thf(fact_204_dual__order_Ostrict__iff__order,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( order @ A )
% 0.32/0.47 => ( ( ord_less @ A )
% 0.32/0.47 = ( ^ [B4: A,A5: A] :
% 0.32/0.47 ( ( ord_less_eq @ A @ B4 @ A5 )
% 0.32/0.47 & ( A5 != B4 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.strict_iff_order
% 0.32/0.47 thf(fact_205_dual__order_Oorder__iff__strict,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( order @ A )
% 0.32/0.47 => ( ( ord_less_eq @ A )
% 0.32/0.47 = ( ^ [B4: A,A5: A] :
% 0.32/0.47 ( ( ord_less @ A @ B4 @ A5 )
% 0.32/0.47 | ( A5 = B4 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.order_iff_strict
% 0.32/0.47 thf(fact_206_order_Ostrict__implies__order,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( order @ A )
% 0.32/0.47 => ! [A3: A,B3: A] :
% 0.32/0.47 ( ( ord_less @ A @ A3 @ B3 )
% 0.32/0.47 => ( ord_less_eq @ A @ A3 @ B3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order.strict_implies_order
% 0.32/0.47 thf(fact_207_dense__le__bounded,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( dense_linorder @ A )
% 0.32/0.47 => ! [X2: A,Y: A,Z3: A] :
% 0.32/0.47 ( ( ord_less @ A @ X2 @ Y )
% 0.32/0.47 => ( ! [W: A] :
% 0.32/0.47 ( ( ord_less @ A @ X2 @ W )
% 0.32/0.47 => ( ( ord_less @ A @ W @ Y )
% 0.32/0.47 => ( ord_less_eq @ A @ W @ Z3 ) ) )
% 0.32/0.47 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dense_le_bounded
% 0.32/0.47 thf(fact_208_dense__ge__bounded,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( dense_linorder @ A )
% 0.32/0.47 => ! [Z3: A,X2: A,Y: A] :
% 0.32/0.47 ( ( ord_less @ A @ Z3 @ X2 )
% 0.32/0.47 => ( ! [W: A] :
% 0.32/0.47 ( ( ord_less @ A @ Z3 @ W )
% 0.32/0.47 => ( ( ord_less @ A @ W @ X2 )
% 0.32/0.47 => ( ord_less_eq @ A @ Y @ W ) ) )
% 0.32/0.47 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dense_ge_bounded
% 0.32/0.47 thf(fact_209_dual__order_Ostrict__trans2,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( order @ A )
% 0.32/0.47 => ! [B3: A,A3: A,C: A] :
% 0.32/0.47 ( ( ord_less @ A @ B3 @ A3 )
% 0.32/0.47 => ( ( ord_less_eq @ A @ C @ B3 )
% 0.32/0.47 => ( ord_less @ A @ C @ A3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.strict_trans2
% 0.32/0.47 thf(fact_210_dual__order_Ostrict__trans1,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( order @ A )
% 0.32/0.47 => ! [B3: A,A3: A,C: A] :
% 0.32/0.47 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.32/0.47 => ( ( ord_less @ A @ C @ B3 )
% 0.32/0.47 => ( ord_less @ A @ C @ A3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dual_order.strict_trans1
% 0.32/0.47 thf(fact_211_order_Ostrict__iff__order,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( order @ A )
% 0.32/0.47 => ( ( ord_less @ A )
% 0.32/0.47 = ( ^ [A5: A,B4: A] :
% 0.32/0.47 ( ( ord_less_eq @ A @ A5 @ B4 )
% 0.32/0.47 & ( A5 != B4 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order.strict_iff_order
% 0.32/0.47 thf(fact_212_order_Oorder__iff__strict,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( order @ A )
% 0.32/0.47 => ( ( ord_less_eq @ A )
% 0.32/0.47 = ( ^ [A5: A,B4: A] :
% 0.32/0.47 ( ( ord_less @ A @ A5 @ B4 )
% 0.32/0.47 | ( A5 = B4 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order.order_iff_strict
% 0.32/0.47 thf(fact_213_order_Ostrict__trans2,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( order @ A )
% 0.32/0.47 => ! [A3: A,B3: A,C: A] :
% 0.32/0.47 ( ( ord_less @ A @ A3 @ B3 )
% 0.32/0.47 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.32/0.47 => ( ord_less @ A @ A3 @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order.strict_trans2
% 0.32/0.47 thf(fact_214_order_Ostrict__trans1,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( order @ A )
% 0.32/0.47 => ! [A3: A,B3: A,C: A] :
% 0.32/0.47 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/0.47 => ( ( ord_less @ A @ B3 @ C )
% 0.32/0.47 => ( ord_less @ A @ A3 @ C ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % order.strict_trans1
% 0.32/0.47 thf(fact_215_not__le__imp__less,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linorder @ A )
% 0.32/0.47 => ! [Y: A,X2: A] :
% 0.32/0.47 ( ~ ( ord_less_eq @ A @ Y @ X2 )
% 0.32/0.47 => ( ord_less @ A @ X2 @ Y ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % not_le_imp_less
% 0.32/0.47 thf(fact_216_less__le__not__le,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( preorder @ A )
% 0.32/0.47 => ( ( ord_less @ A )
% 0.32/0.47 = ( ^ [X: A,Y6: A] :
% 0.32/0.47 ( ( ord_less_eq @ A @ X @ Y6 )
% 0.32/0.47 & ~ ( ord_less_eq @ A @ Y6 @ X ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_le_not_le
% 0.32/0.47 thf(fact_217_le__imp__less__or__eq,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( order @ A )
% 0.32/0.47 => ! [X2: A,Y: A] :
% 0.32/0.47 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/0.47 => ( ( ord_less @ A @ X2 @ Y )
% 0.32/0.47 | ( X2 = Y ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % le_imp_less_or_eq
% 0.32/0.47 thf(fact_218_le__less__linear,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linorder @ A )
% 0.32/0.47 => ! [X2: A,Y: A] :
% 0.32/0.47 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/0.47 | ( ord_less @ A @ Y @ X2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % le_less_linear
% 0.32/0.47 thf(fact_219_dense__le,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( dense_linorder @ A )
% 0.32/0.47 => ! [Y: A,Z3: A] :
% 0.32/0.47 ( ! [X3: A] :
% 0.32/0.47 ( ( ord_less @ A @ X3 @ Y )
% 0.32/0.47 => ( ord_less_eq @ A @ X3 @ Z3 ) )
% 0.32/0.47 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dense_le
% 0.32/0.47 thf(fact_220_dense__ge,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( dense_linorder @ A )
% 0.32/0.47 => ! [Z3: A,Y: A] :
% 0.32/0.47 ( ! [X3: A] :
% 0.32/0.47 ( ( ord_less @ A @ Z3 @ X3 )
% 0.32/0.47 => ( ord_less_eq @ A @ Y @ X3 ) )
% 0.32/0.47 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % dense_ge
% 0.32/0.47 thf(fact_221_less__le__trans,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( preorder @ A )
% 0.32/0.47 => ! [X2: A,Y: A,Z3: A] :
% 0.32/0.47 ( ( ord_less @ A @ X2 @ Y )
% 0.32/0.47 => ( ( ord_less_eq @ A @ Y @ Z3 )
% 0.32/0.47 => ( ord_less @ A @ X2 @ Z3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % less_le_trans
% 0.32/0.47 thf(fact_222_le__less__trans,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( preorder @ A )
% 0.32/0.47 => ! [X2: A,Y: A,Z3: A] :
% 0.32/0.47 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/0.47 => ( ( ord_less @ A @ Y @ Z3 )
% 0.32/0.47 => ( ord_less @ A @ X2 @ Z3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % le_less_trans
% 0.32/0.47 thf(fact_223_less__imp__le,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.48 ( ( preorder @ A )
% 0.32/0.48 => ! [X2: A,Y: A] :
% 0.32/0.48 ( ( ord_less @ A @ X2 @ Y )
% 0.32/0.48 => ( ord_less_eq @ A @ X2 @ Y ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % less_imp_le
% 0.32/0.48 thf(fact_224_antisym__conv2,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ! [X2: A,Y: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/0.48 => ( ( ~ ( ord_less @ A @ X2 @ Y ) )
% 0.32/0.48 = ( X2 = Y ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % antisym_conv2
% 0.32/0.48 thf(fact_225_antisym__conv1,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ! [X2: A,Y: A] :
% 0.32/0.48 ( ~ ( ord_less @ A @ X2 @ Y )
% 0.32/0.48 => ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/0.48 = ( X2 = Y ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % antisym_conv1
% 0.32/0.48 thf(fact_226_le__neq__trans,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ! [A3: A,B3: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/0.48 => ( ( A3 != B3 )
% 0.32/0.48 => ( ord_less @ A @ A3 @ B3 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_neq_trans
% 0.32/0.48 thf(fact_227_not__less,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( linorder @ A )
% 0.32/0.48 => ! [X2: A,Y: A] :
% 0.32/0.48 ( ( ~ ( ord_less @ A @ X2 @ Y ) )
% 0.32/0.48 = ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % not_less
% 0.32/0.48 thf(fact_228_not__le,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( linorder @ A )
% 0.32/0.48 => ! [X2: A,Y: A] :
% 0.32/0.48 ( ( ~ ( ord_less_eq @ A @ X2 @ Y ) )
% 0.32/0.48 = ( ord_less @ A @ Y @ X2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % not_le
% 0.32/0.48 thf(fact_229_order__less__le__subst2,axiom,
% 0.32/0.48 ! [A: $tType,C2: $tType] :
% 0.32/0.48 ( ( ( order @ C2 )
% 0.32/0.48 & ( order @ A ) )
% 0.32/0.48 => ! [A3: A,B3: A,F: A > C2,C: C2] :
% 0.32/0.48 ( ( ord_less @ A @ A3 @ B3 )
% 0.32/0.48 => ( ( ord_less_eq @ C2 @ ( F @ B3 ) @ C )
% 0.32/0.48 => ( ! [X3: A,Y4: A] :
% 0.32/0.48 ( ( ord_less @ A @ X3 @ Y4 )
% 0.32/0.48 => ( ord_less @ C2 @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.48 => ( ord_less @ C2 @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % order_less_le_subst2
% 0.32/0.48 thf(fact_230_order__less__le__subst1,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType] :
% 0.32/0.48 ( ( ( order @ B )
% 0.32/0.48 & ( order @ A ) )
% 0.32/0.48 => ! [A3: A,F: B > A,B3: B,C: B] :
% 0.32/0.48 ( ( ord_less @ A @ A3 @ ( F @ B3 ) )
% 0.32/0.48 => ( ( ord_less_eq @ B @ B3 @ C )
% 0.32/0.48 => ( ! [X3: B,Y4: B] :
% 0.32/0.48 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 0.32/0.48 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.48 => ( ord_less @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % order_less_le_subst1
% 0.32/0.48 thf(fact_231_order__le__less__subst2,axiom,
% 0.32/0.48 ! [A: $tType,C2: $tType] :
% 0.32/0.48 ( ( ( order @ C2 )
% 0.32/0.48 & ( order @ A ) )
% 0.32/0.48 => ! [A3: A,B3: A,F: A > C2,C: C2] :
% 0.32/0.48 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/0.48 => ( ( ord_less @ C2 @ ( F @ B3 ) @ C )
% 0.32/0.48 => ( ! [X3: A,Y4: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.32/0.48 => ( ord_less_eq @ C2 @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.48 => ( ord_less @ C2 @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % order_le_less_subst2
% 0.32/0.48 thf(fact_232_order__le__less__subst1,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType] :
% 0.32/0.48 ( ( ( order @ B )
% 0.32/0.48 & ( order @ A ) )
% 0.32/0.48 => ! [A3: A,F: B > A,B3: B,C: B] :
% 0.32/0.48 ( ( ord_less_eq @ A @ A3 @ ( F @ B3 ) )
% 0.32/0.48 => ( ( ord_less @ B @ B3 @ C )
% 0.32/0.48 => ( ! [X3: B,Y4: B] :
% 0.32/0.48 ( ( ord_less @ B @ X3 @ Y4 )
% 0.32/0.48 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/0.48 => ( ord_less @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % order_le_less_subst1
% 0.32/0.48 thf(fact_233_less__le,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ( ( ord_less @ A )
% 0.32/0.48 = ( ^ [X: A,Y6: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ X @ Y6 )
% 0.32/0.48 & ( X != Y6 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % less_le
% 0.32/0.48 thf(fact_234_le__less,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ( ( ord_less_eq @ A )
% 0.32/0.48 = ( ^ [X: A,Y6: A] :
% 0.32/0.48 ( ( ord_less @ A @ X @ Y6 )
% 0.32/0.48 | ( X = Y6 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % le_less
% 0.32/0.48 thf(fact_235_leI,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( linorder @ A )
% 0.32/0.48 => ! [X2: A,Y: A] :
% 0.32/0.48 ( ~ ( ord_less @ A @ X2 @ Y )
% 0.32/0.48 => ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % leI
% 0.32/0.48 thf(fact_236_leD,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ! [Y: A,X2: A] :
% 0.32/0.48 ( ( ord_less_eq @ A @ Y @ X2 )
% 0.32/0.48 => ~ ( ord_less @ A @ X2 @ Y ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % leD
% 0.32/0.48 thf(fact_237_AssumpMinImplAllBigger,axiom,
% 0.32/0.48 minimalEnabled @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ msg ).
% 0.32/0.48
% 0.32/0.48 % AssumpMinImplAllBigger
% 0.32/0.48 thf(fact_238__092_060open_062execution_OfirstOccurrence_A_Ife_Aindex_J_A_Ift_Aindex_J_Amsg_AOccM_092_060close_062,axiom,
% 0.32/0.48 firstOccurrence @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ msga @ occM2 ).
% 0.32/0.48
% 0.32/0.48 % \<open>execution.firstOccurrence (fe index) (ft index) msg OccM\<close>
% 0.32/0.48 thf(fact_239_SameMsgOnLow,axiom,
% 0.32/0.48 ! [I4: nat] :
% 0.32/0.48 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 0.32/0.48 => ( ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ I4 )
% 0.32/0.48 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % SameMsgOnLow
% 0.32/0.48 thf(fact_240_OccM_H_I5_J,axiom,
% 0.32/0.48 ! [N5: nat] :
% 0.32/0.48 ( ( ord_less_eq @ nat @ occM @ N5 )
% 0.32/0.48 => ( ( ord_less @ nat @ N5 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 0.32/0.48 => ( msg
% 0.32/0.48 != ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ N5 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % OccM'(5)
% 0.32/0.48 thf(fact_241_IPrefixList,axiom,
% 0.32/0.48 ! [I4: nat] : ( prefixList @ ( message @ p @ v ) @ ( ft @ I4 ) @ ( ft @ ( suc @ I4 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % IPrefixList
% 0.32/0.48 thf(fact_242_OccM_H_I1_J,axiom,
% 0.32/0.48 ? [P5: p] : ( isReceiverOf @ p @ v @ P5 @ msg ) ).
% 0.32/0.48
% 0.32/0.48 % OccM'(1)
% 0.32/0.48 thf(fact_243_FirstOccMsg_H,axiom,
% 0.32/0.48 firstOccurrence @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ msg @ occM ).
% 0.32/0.48
% 0.32/0.48 % FirstOccMsg'
% 0.32/0.48 thf(fact_244_AssumpOccMFirstOccurrence_I5_J,axiom,
% 0.32/0.48 ! [N5: nat] :
% 0.32/0.48 ( ( ord_less_eq @ nat @ occM2 @ N5 )
% 0.32/0.48 => ( ( ord_less @ nat @ N5 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 0.32/0.48 => ( msga
% 0.32/0.48 != ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ N5 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % AssumpOccMFirstOccurrence(5)
% 0.32/0.48 thf(fact_245_OccM_H_I4_J,axiom,
% 0.32/0.48 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ occM ) @ msg ).
% 0.32/0.48
% 0.32/0.48 % OccM'(4)
% 0.32/0.48 thf(fact_246_AssumptionFairContr,axiom,
% 0.32/0.48 ! [N5: nat] :
% 0.32/0.48 ( ( ord_less_eq @ nat @ n @ N5 )
% 0.32/0.48 => ! [N02: nat] :
% 0.32/0.48 ( ( ord_less @ nat @ N02 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N5 ) ) )
% 0.32/0.48 => ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) @ N02 )
% 0.32/0.48 => ( msg2
% 0.32/0.48 != ( nth @ ( message @ p @ v ) @ ( ft @ N5 ) @ N02 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % AssumptionFairContr
% 0.32/0.48 thf(fact_247_less__fun__def,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType] :
% 0.32/0.48 ( ( ord @ B )
% 0.32/0.48 => ( ( ord_less @ ( A > B ) )
% 0.32/0.48 = ( ^ [F2: A > B,G2: A > B] :
% 0.32/0.48 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.32/0.48 & ~ ( ord_less_eq @ ( A > B ) @ G2 @ F2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % less_fun_def
% 0.32/0.48 thf(fact_248_MessageStaysOrConsumed,axiom,
% 0.32/0.48 ! [N1: nat,N22: nat,N: nat,Msg: message @ p @ v] :
% 0.32/0.48 ( ( ( ord_less_eq @ nat @ N1 @ N22 )
% 0.32/0.48 & ( ord_less @ nat @ N22 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ N ) ) )
% 0.32/0.48 & ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N ) @ N1 ) @ Msg ) )
% 0.32/0.48 => ( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N ) @ N22 ) @ Msg )
% 0.32/0.48 | ? [N03: nat] :
% 0.32/0.48 ( ( ord_less_eq @ nat @ N1 @ N03 )
% 0.32/0.48 & ( ord_less @ nat @ N03 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N ) ) )
% 0.32/0.48 & ( ( nth @ ( message @ p @ v ) @ ( ft @ N ) @ N03 )
% 0.32/0.48 = Msg ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % MessageStaysOrConsumed
% 0.32/0.48 thf(fact_249__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_O_Alength_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Ai_A_092_060and_062_Amsg_____A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062,axiom,
% 0.32/0.48 ~ ? [I4: nat] :
% 0.32/0.48 ( ( ord_less @ nat @ I4 @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) )
% 0.32/0.48 & ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ I4 )
% 0.32/0.48 & ( msg2
% 0.32/0.48 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % \<open>\<not> (\<exists>i<length (fe (Suc index)) - 1. length (fe index) - 1 \<le> i \<and> msg__ = ft (Suc index) ! i)\<close>
% 0.32/0.48 thf(fact_250_AssumptionFair_I4_J,axiom,
% 0.32/0.48 isReceiverOf @ p @ v @ p2 @ msg2 ).
% 0.32/0.48
% 0.32/0.48 % AssumptionFair(4)
% 0.32/0.48 thf(fact_251_AssumpOccMFirstOccurrence_I1_J,axiom,
% 0.32/0.48 ? [P5: p] : ( isReceiverOf @ p @ v @ P5 @ msga ) ).
% 0.32/0.48
% 0.32/0.48 % AssumpOccMFirstOccurrence(1)
% 0.32/0.48 thf(fact_252_AssumptionFair_I3_J,axiom,
% 0.32/0.48 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ n0 ) @ msg2 ).
% 0.32/0.48
% 0.32/0.48 % AssumptionFair(3)
% 0.32/0.48
% 0.32/0.48 % Type constructors (32)
% 0.32/0.48 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.32/0.48 ! [A7: $tType,A8: $tType] :
% 0.32/0.48 ( ( preorder @ A8 )
% 0.32/0.48 => ( preorder @ ( A7 > A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.32/0.48 ! [A7: $tType,A8: $tType] :
% 0.32/0.48 ( ( order @ A8 )
% 0.32/0.48 => ( order @ ( A7 > A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Orderings_Oord,axiom,
% 0.32/0.48 ! [A7: $tType,A8: $tType] :
% 0.32/0.48 ( ( ord @ A8 )
% 0.32/0.48 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Groups_Ominus,axiom,
% 0.32/0.48 ! [A7: $tType,A8: $tType] :
% 0.32/0.48 ( ( minus @ A8 )
% 0.32/0.48 => ( minus @ ( A7 > A8 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 0.32/0.48 linord1659791738miring @ nat ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 0.32/0.48 cancel146912293up_add @ nat ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.32/0.48 wellorder @ nat ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.32/0.48 preorder @ nat ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.32/0.48 linorder @ nat ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.32/0.48 no_top @ nat ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.32/0.48 order @ nat ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.32/0.48 ord @ nat ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Nat_Onat___Groups_Ominus_4,axiom,
% 0.32/0.48 minus @ nat ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.32/0.48 one @ nat ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 0.32/0.48 size @ nat ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Orderings_Opreorder_5,axiom,
% 0.32/0.48 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Orderings_Oorder_6,axiom,
% 0.32/0.48 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Orderings_Oord_7,axiom,
% 0.32/0.48 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Groups_Ominus_8,axiom,
% 0.32/0.48 ! [A7: $tType] : ( minus @ ( set @ A7 ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Orderings_Opreorder_9,axiom,
% 0.32/0.48 preorder @ $o ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Orderings_Olinorder_10,axiom,
% 0.32/0.48 linorder @ $o ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Orderings_Oorder_11,axiom,
% 0.32/0.48 order @ $o ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Orderings_Oord_12,axiom,
% 0.32/0.48 ord @ $o ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Groups_Ominus_13,axiom,
% 0.32/0.48 minus @ $o ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_List_Olist___Nat_Osize_14,axiom,
% 0.32/0.48 ! [A7: $tType] : ( size @ ( list @ A7 ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_15,axiom,
% 0.32/0.48 wellorder @ product_unit ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_16,axiom,
% 0.32/0.48 preorder @ product_unit ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_17,axiom,
% 0.32/0.48 linorder @ product_unit ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Product__Type_Ounit___Orderings_Oorder_18,axiom,
% 0.32/0.48 order @ product_unit ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Product__Type_Ounit___Orderings_Oord_19,axiom,
% 0.32/0.48 ord @ product_unit ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Product__Type_Ounit___Groups_Ominus_20,axiom,
% 0.32/0.48 minus @ product_unit ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_AsynchronousSystem_Omessage___Nat_Osize_21,axiom,
% 0.32/0.48 ! [A7: $tType,A8: $tType] : ( size @ ( message @ A7 @ A8 ) ) ).
% 0.32/0.48
% 0.32/0.48 % Conjectures (1)
% 0.32/0.48 thf(conj_0,conjecture,
% 0.32/0.48 ( occM2
% 0.32/0.48 = ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) ) ).
% 0.32/0.48
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 ------------------------
% 0.32/1.50 ---- Embedded in THF ---
% 0.32/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.50 %%% Generated on Tue Feb 24 08:25:13 EST 2026
% 0.32/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.50 %%% Logic specification used:
% 0.32/1.50 %%% thf(spec, logic, $$dhol).
% 0.32/1.50
% 0.32/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.0mkoVbkNSb/DTF2DTF32065.p
% 0.32/1.50 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext, type, configuration_ext: ($tType > ($tType > ($tType > ($tType > $tType))))).
% 0.32/1.50 thf(ty_t_AsynchronousSystem_Omessage, type, message: ($tType > ($tType > $tType))).
% 0.32/1.50 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 0.32/1.50 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 0.32/1.50 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.32/1.50 thf(ty_t_Nat_Onat, type, nat: $tType).
% 0.32/1.50 thf(ty_tf_v, type, v: $tType).
% 0.32/1.50 thf(ty_tf_s, type, s: $tType).
% 0.32/1.50 thf(ty_tf_p, type, p: $tType).
% 0.32/1.50 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 0.32/1.50 thf(sy_cl_Nat_Osize, type, size: (!> [A:$tType]: ($o))).
% 0.32/1.50 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: ($o))).
% 0.32/1.50 thf(sy_cl_Groups_Ominus, type, minus: (!> [A:$tType]: ($o))).
% 0.32/1.50 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 0.32/1.50 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 0.32/1.50 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: ($o))).
% 0.32/1.50 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: ($o))).
% 0.32/1.50 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: ($o))).
% 0.32/1.50 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 0.32/1.50 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 0.32/1.50 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: ($o))).
% 0.32/1.50 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: ($o))).
% 0.32/1.50 thf(sy_cl_Orderings_Odense__linorder, type, dense_linorder: (!> [A:$tType]: ($o))).
% 0.32/1.50 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: ($o))).
% 0.32/1.50 thf(sy_cl_Groups_Ocancel__ab__semigroup__add, type, cancel146912293up_add: (!> [A:$tType]: ($o))).
% 0.32/1.50 thf(sy_cl_Rings_Olinordered__nonzero__semiring, type, linord1659791738miring: (!> [A:$tType]: ($o))).
% 0.32/1.50 thf(sy_c_AsynchronousSystem_Oenabled, type, enabled: (!> [P:$tType,V:$tType,S:$tType]: ((((((configuration_ext @ P) @ V) @ S) @ product_unit) > (((message @ P) @ V) > $o))))).
% 0.32/1.50 thf(sy_c_AsynchronousSystem_OisReceiverOf, type, isReceiverOf: (!> [P:$tType,V:$tType]: ((P > (((message @ P) @ V) > $o))))).
% 0.32/1.50 thf(sy_c_Execution_Oexecution_OfirstOccurrence, type, firstOccurrence: (!> [P:$tType,V:$tType,S:$tType]: (((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (((message @ P) @ V) > (nat > $o))))))).
% 0.32/1.50 thf(sy_c_Execution_Oexecution_OminimalEnabled, type, minimalEnabled: (!> [P:$tType,V:$tType,S:$tType]: (((list @ ((((configuration_ext @ P) @ V) @ S) @ product_unit)) > ((list @ ((message @ P) @ V)) > (((message @ P) @ V) > $o)))))).
% 0.32/1.50 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 0.32/1.50 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 0.32/1.50 thf(sy_c_ListUtilities_OprefixList, type, prefixList: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 0.32/1.50 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 0.32/1.50 thf(sy_c_List_Onth, type, nth: (!> [A:$tType]: (((list @ A) > (nat > A))))).
% 0.32/1.50 thf(sy_c_Nat_OSuc, type, suc: (nat > nat)).
% 0.32/1.50 thf(sy_c_Nat_Osize__class_Osize, type, size_size: (!> [A:$tType]: ((A > nat)))).
% 0.32/1.50 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 0.32/1.50 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 0.32/1.50 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.32/1.50 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.32/1.50 thf(sy_v_OccM_H____, type, occM: nat).
% 0.32/1.50 thf(sy_v_OccM____, type, occM2: nat).
% 0.32/1.50 thf(sy_v_consumedMsg____, type, consumedMsg: ((message @ p) @ v)).
% 0.32/1.50 thf(sy_v_fe____, type, fe: (nat > (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))).
% 0.32/1.50 thf(sy_v_firstOccSet____, type, firstOccSet: (nat > (set @ ((message @ p) @ v)))).
% 0.32/1.50 thf(sy_v_ft____, type, ft: (nat > (list @ ((message @ p) @ v)))).
% 0.32/1.50 thf(sy_v_index____, type, index: nat).
% 0.32/1.50 thf(sy_v_msg_H____, type, msg: ((message @ p) @ v)).
% 0.32/1.50 thf(sy_v_msg____, type, msg2: ((message @ p) @ v)).
% 0.32/1.50 thf(sy_v_msga____, type, msga: ((message @ p) @ v)).
% 0.32/1.50 thf(sy_v_n0____, type, n0: nat).
% 0.32/1.50 thf(sy_v_n____, type, n: nat).
% 0.32/1.50 thf(sy_v_p____, type, p2: p).
% 0.32/1.50 thf(fact_0_AssumpOccMFirstOccurrence_I3_J, axiom, (((ord_less @ nat) @ occM2) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index)))).
% 0.32/1.50 thf(fact_1__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_AOccM_092_060close_062, axiom, (((ord_less_eq @ nat) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) @ (one_one @ nat))) @ occM2)).
% 0.32/1.50 thf(fact_2_OccM_H_I3_J, axiom, (((ord_less @ nat) @ occM) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index)))).
% 0.32/1.50 thf(fact_3__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Alength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_092_060close_062, axiom, (((ord_less_eq @ nat) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) @ (one_one @ nat))) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ (suc @ index)))) @ (one_one @ nat)))).
% 0.32/1.50 thf(fact_4_NotEmpty_I2_J, axiom, ((fe @ index) != (nil @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))).
% 0.32/1.50 thf(fact_5_minus__apply, axiom, (! [B:$tType,A:$tType]: (((minus @ B) => ((minus_minus @ (A > B)) = (^ [A2:(A > B),B2:(A > B),X:A]: ((((minus_minus @ B) @ (A2 @ X)) @ (B2 @ X))))))))).
% 0.32/1.50 thf(fact_6_AssumptionFair_I2_J, axiom, (((ord_less @ nat) @ n0) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ n)))).
% 0.32/1.50 thf(fact_7_one__natural_Orsp, axiom, ((one_one @ nat) = (one_one @ nat))).
% 0.32/1.50 thf(fact_8_diff__commute, axiom, (! [I:nat,J:nat,K:nat]: (((((minus_minus @ nat) @ (((minus_minus @ nat) @ I) @ J)) @ K) = (((minus_minus @ nat) @ (((minus_minus @ nat) @ I) @ K)) @ J))))).
% 0.32/1.50 thf(fact_9_Ex__list__of__length, axiom, (! [A:$tType,N:nat]: ((? [Xs:(list @ A)]: ((((size_size @ (list @ A)) @ Xs) = N)))))).
% 0.32/1.50 thf(fact_10_neq__if__length__neq, axiom, (! [A:$tType,Xs2:(list @ A),Ys:(list @ A)]: (((((size_size @ (list @ A)) @ Xs2) != ((size_size @ (list @ A)) @ Ys)) => (Xs2 != Ys))))).
% 0.32/1.50 thf(fact_11_size__neq__size__imp__neq, axiom, (! [A:$tType]: (((size @ A) => (! [X2:A,Y:A]: (((((size_size @ A) @ X2) != ((size_size @ A) @ Y)) => (X2 != Y)))))))).
% 0.32/1.50 thf(fact_12_fun__diff__def, axiom, (! [B:$tType,A:$tType]: (((minus @ B) => ((minus_minus @ (A > B)) = (^ [A2:(A > B),B2:(A > B),X:A]: ((((minus_minus @ B) @ (A2 @ X)) @ (B2 @ X))))))))).
% 0.32/1.50 thf(fact_13_diff__eq__diff__eq, axiom, (! [A:$tType]: (((group_add @ A) => (! [A3:A,B3:A,C:A,D:A]: ((((((minus_minus @ A) @ A3) @ B3) = (((minus_minus @ A) @ C) @ D)) => ((A3 = B3) = (C = D))))))))).
% 0.32/1.50 thf(fact_14_nat_Oinject, axiom, (! [X22:nat,Y2:nat]: ((((suc @ X22) = (suc @ Y2)) = (X22 = Y2))))).
% 0.32/1.50 thf(fact_15_old_Onat_Oinject, axiom, (! [Nat:nat,Nat2:nat]: ((((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))).
% 0.32/1.50 thf(fact_16_NotEmpty_I1_J, axiom, ((fe @ (suc @ index)) != (nil @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)))).
% 0.32/1.50 thf(fact_17_lessI, axiom, (! [N:nat]: ((((ord_less @ nat) @ N) @ (suc @ N))))).
% 0.32/1.50 thf(fact_18_Suc__mono, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less @ nat) @ (suc @ M)) @ (suc @ N)))))).
% 0.32/1.50 thf(fact_19_Suc__less__eq, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (suc @ M)) @ (suc @ N)) = (((ord_less @ nat) @ M) @ N))))).
% 0.32/1.50 thf(fact_20_Suc__le__mono, axiom, (! [N:nat,M:nat]: (((((ord_less_eq @ nat) @ (suc @ N)) @ (suc @ M)) = (((ord_less_eq @ nat) @ N) @ M))))).
% 0.32/1.50 thf(fact_21_Suc__diff__diff, axiom, (! [M:nat,N:nat,K:nat]: (((((minus_minus @ nat) @ (((minus_minus @ nat) @ (suc @ M)) @ N)) @ (suc @ K)) = (((minus_minus @ nat) @ (((minus_minus @ nat) @ M) @ N)) @ K))))).
% 0.32/1.50 thf(fact_22_diff__Suc__Suc, axiom, (! [M:nat,N:nat]: (((((minus_minus @ nat) @ (suc @ M)) @ (suc @ N)) = (((minus_minus @ nat) @ M) @ N))))).
% 0.32/1.50 thf(fact_23_diff__diff__cancel, axiom, (! [I:nat,N:nat]: (((((ord_less_eq @ nat) @ I) @ N) => ((((minus_minus @ nat) @ N) @ (((minus_minus @ nat) @ N) @ I)) = I))))).
% 0.32/1.50 thf(fact_24_diff__Suc__1, axiom, (! [N:nat]: (((((minus_minus @ nat) @ (suc @ N)) @ (one_one @ nat)) = N)))).
% 0.32/1.50 thf(fact_25_Nat_OlessE, axiom, (! [I:nat,K:nat]: (((((ord_less @ nat) @ I) @ K) => ((K != (suc @ I)) => (~ ((! [J2:nat]: (((((ord_less @ nat) @ I) @ J2) => (K != (suc @ J2)))))))))))).
% 0.32/1.50 thf(fact_26_Suc__leD, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ (suc @ M)) @ N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 0.32/1.50 thf(fact_27_Suc__leI, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ (suc @ M)) @ N))))).
% 0.32/1.50 thf(fact_28_le__SucE, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ (suc @ N)) => ((~ ((((ord_less_eq @ nat) @ M) @ N))) => (M = (suc @ N))))))).
% 0.32/1.50 thf(fact_29_le__SucI, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ M) @ (suc @ N)))))).
% 0.32/1.50 thf(fact_30_le__refl, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ N) @ N)))).
% 0.32/1.50 thf(fact_31_Suc__le__D, axiom, (! [N:nat,M2:nat]: (((((ord_less_eq @ nat) @ (suc @ N)) @ M2) => (? [M3:nat]: ((M2 = (suc @ M3)))))))).
% 0.32/1.50 thf(fact_32_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)))))).
% 0.32/1.50 thf(fact_33_Suc__le__eq, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ (suc @ M)) @ N) = (((ord_less @ nat) @ M) @ N))))).
% 0.32/1.50 thf(fact_34_Suc__lessD, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (suc @ M)) @ N) => (((ord_less @ nat) @ M) @ N))))).
% 0.32/1.50 thf(fact_35_Suc__lessE, axiom, (! [I:nat,K:nat]: (((((ord_less @ nat) @ (suc @ I)) @ K) => (~ ((! [J2:nat]: (((((ord_less @ nat) @ I) @ J2) => (K != (suc @ J2))))))))))).
% 0.32/1.50 thf(fact_36_Suc__lessI, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((suc @ M) != N) => (((ord_less @ nat) @ (suc @ M)) @ N)))))).
% 0.32/1.50 thf(fact_37_eq__imp__le, axiom, (! [M:nat,N:nat]: (((M = N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 0.32/1.50 thf(fact_38_le__Suc__eq, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ (suc @ N)) = ((((ord_less_eq @ nat) @ M) @ N) | (M = (suc @ N))))))).
% 0.32/1.50 thf(fact_39_less__SucE, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ (suc @ N)) => ((~ ((((ord_less @ nat) @ M) @ N))) => (M = N)))))).
% 0.32/1.50 thf(fact_40_less__SucI, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less @ nat) @ M) @ (suc @ N)))))).
% 0.32/1.50 thf(fact_41_Suc__inject, axiom, (! [X2:nat,Y:nat]: ((((suc @ X2) = (suc @ Y)) => (X2 = Y))))).
% 0.32/1.50 thf(fact_42_dec__induct, axiom, (! [I:nat,J:nat,P2:(nat > $o)]: (((((ord_less_eq @ nat) @ I) @ J) => ((P2 @ I) => ((! [N2:nat]: (((((ord_less_eq @ nat) @ I) @ N2) => ((((ord_less @ nat) @ N2) @ J) => ((P2 @ N2) => (P2 @ (suc @ N2))))))) => (P2 @ J))))))).
% 0.32/1.50 thf(fact_43_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P2:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P2)) = (P2 @ A3))))).
% 0.32/1.50 thf(fact_44_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X:A]: ((((member @ A) @ X) @ A4)))) = A4)))).
% 0.32/1.50 thf(fact_45_Collect__cong, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P2 @ X3) = (Q @ X3)))) => (((collect @ A) @ P2) = ((collect @ A) @ Q)))))).
% 0.32/1.50 thf(fact_46_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 0.32/1.50 thf(fact_47_inc__induct, axiom, (! [I:nat,J:nat,P2:(nat > $o)]: (((((ord_less_eq @ nat) @ I) @ J) => ((P2 @ J) => ((! [N2:nat]: (((((ord_less_eq @ nat) @ I) @ N2) => ((((ord_less @ nat) @ N2) @ J) => ((P2 @ (suc @ N2)) => (P2 @ N2)))))) => (P2 @ I))))))).
% 0.32/1.50 thf(fact_48_le__antisym, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((ord_less_eq @ nat) @ N) @ M) => (M = N)))))).
% 0.32/1.50 thf(fact_49_Ex__less__Suc, axiom, (! [N:nat,P2:(nat > $o)]: (((? [I2:nat]: (((((ord_less @ nat) @ I2) @ (suc @ N)) & (P2 @ I2)))) = ((P2 @ N) | (? [I2:nat]: (((((ord_less @ nat) @ I2) @ N) & (P2 @ I2))))))))).
% 0.32/1.50 thf(fact_50_less__Suc__eq, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ (suc @ N)) = ((((ord_less @ nat) @ M) @ N) | (M = N)))))).
% 0.32/1.50 thf(fact_51_n__not__Suc__n, axiom, (! [N:nat]: ((N != (suc @ N))))).
% 0.32/1.50 thf(fact_52_nat__less__le, axiom, ((ord_less @ nat) = (^ [M4:nat,N3:nat]: (((((ord_less_eq @ nat) @ M4) @ N3) & (M4 != N3)))))).
% 0.32/1.50 thf(fact_53_nat__neq__iff, axiom, (! [M:nat,N:nat]: (((M != N) = ((((ord_less @ nat) @ M) @ N) | (((ord_less @ nat) @ N) @ M)))))).
% 0.32/1.50 thf(fact_54_not__less__eq, axiom, (! [M:nat,N:nat]: (((~ ((((ord_less @ nat) @ M) @ N))) = (((ord_less @ nat) @ N) @ (suc @ M)))))).
% 0.32/1.50 thf(fact_55_All__less__Suc, axiom, (! [N:nat,P2:(nat > $o)]: (((! [I2:nat]: (((((ord_less @ nat) @ I2) @ (suc @ N)) => (P2 @ I2)))) = ((P2 @ N) & (! [I2:nat]: (((((ord_less @ nat) @ I2) @ N) => (P2 @ I2))))))))).
% 0.32/1.50 thf(fact_56_Suc__le__lessD, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ (suc @ M)) @ N) => (((ord_less @ nat) @ M) @ N))))).
% 0.32/1.50 thf(fact_57_Suc__less__eq2, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ (suc @ N)) @ M) = (? [M5:nat]: (((M = (suc @ M5)) & (((ord_less @ nat) @ N) @ M5)))))))).
% 0.32/1.50 thf(fact_58_less__antisym, axiom, (! [N:nat,M:nat]: (((~ ((((ord_less @ nat) @ N) @ M))) => ((((ord_less @ nat) @ N) @ (suc @ M)) => (M = N)))))).
% 0.32/1.50 thf(fact_59_Suc__less__SucD, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ (suc @ M)) @ (suc @ N)) => (((ord_less @ nat) @ M) @ N))))).
% 0.32/1.50 thf(fact_60_less__not__refl, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 0.32/1.50 thf(fact_61_nat__le__linear, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) | (((ord_less_eq @ nat) @ N) @ M))))).
% 0.32/1.50 thf(fact_62_Suc__n__not__le__n, axiom, (! [N:nat]: ((~ ((((ord_less_eq @ nat) @ (suc @ N)) @ N)))))).
% 0.32/1.50 thf(fact_63_le__less__Suc__eq, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((ord_less @ nat) @ N) @ (suc @ M)) = (N = M)))))).
% 0.32/1.50 thf(fact_64_less__Suc__eq__le, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ (suc @ N)) = (((ord_less_eq @ nat) @ M) @ N))))).
% 0.32/1.50 thf(fact_65_less__eq__Suc__le, axiom, ((ord_less @ nat) = (^ [N3:nat]: (((ord_less_eq @ nat) @ (suc @ N3)))))).
% 0.32/1.50 thf(fact_66_less__not__refl2, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ N) @ M) => (M != N))))).
% 0.32/1.50 thf(fact_67_less__not__refl3, axiom, (! [S2:nat,T:nat]: (((((ord_less @ nat) @ S2) @ T) => (S2 != T))))).
% 0.32/1.50 thf(fact_68_less__trans__Suc, axiom, (! [I:nat,J:nat,K:nat]: (((((ord_less @ nat) @ I) @ J) => ((((ord_less @ nat) @ J) @ K) => (((ord_less @ nat) @ (suc @ I)) @ K)))))).
% 0.32/1.50 thf(fact_69_measure__induct, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F:(A > B),P2:(A > $o),A3:A]: (((! [X3:A]: (((! [Y3:A]: (((((ord_less @ B) @ (F @ Y3)) @ (F @ X3)) => (P2 @ Y3)))) => (P2 @ X3)))) => (P2 @ A3)))))))).
% 0.32/1.50 thf(fact_70_not__less__eq__eq, axiom, (! [M:nat,N:nat]: (((~ ((((ord_less_eq @ nat) @ M) @ N))) = (((ord_less_eq @ nat) @ (suc @ N)) @ M))))).
% 0.32/1.50 thf(fact_71_full__nat__induct, axiom, (! [P2:(nat > $o),N:nat]: (((! [N2:nat]: (((! [M6:nat]: (((((ord_less_eq @ nat) @ (suc @ M6)) @ N2) => (P2 @ M6)))) => (P2 @ N2)))) => (P2 @ N))))).
% 0.32/1.50 thf(fact_72_le__imp__less__Suc, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => (((ord_less @ nat) @ M) @ (suc @ N)))))).
% 0.32/1.50 thf(fact_73_less__Suc__induct, axiom, (! [I:nat,J:nat,P2:(nat > (nat > $o))]: (((((ord_less @ nat) @ I) @ J) => ((! [I3:nat]: (((P2 @ I3) @ (suc @ I3)))) => ((! [I3:nat,J2:nat,K2:nat]: (((((ord_less @ nat) @ I3) @ J2) => ((((ord_less @ nat) @ J2) @ K2) => (((P2 @ I3) @ J2) => (((P2 @ J2) @ K2) => ((P2 @ I3) @ K2))))))) => ((P2 @ I) @ J))))))).
% 0.32/1.50 thf(fact_74_less__imp__le__nat, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 0.32/1.50 thf(fact_75_less__irrefl__nat, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 0.32/1.50 thf(fact_76_nat__less__induct, axiom, (! [P2:(nat > $o),N:nat]: (((! [N2:nat]: (((! [M6:nat]: (((((ord_less @ nat) @ M6) @ N2) => (P2 @ M6)))) => (P2 @ N2)))) => (P2 @ N))))).
% 0.32/1.50 thf(fact_77_infinite__descent, axiom, (! [P2:(nat > $o),N:nat]: (((! [N2:nat]: (((~ ((P2 @ N2))) => (? [M6:nat]: (((((ord_less @ nat) @ M6) @ N2) & (~ ((P2 @ M6))))))))) => (P2 @ N))))).
% 0.32/1.50 thf(fact_78_le__eq__less__or__eq, axiom, ((ord_less_eq @ nat) = (^ [M4:nat,N3:nat]: (((((ord_less @ nat) @ M4) @ N3) | (M4 = N3)))))).
% 0.32/1.50 thf(fact_79_less__or__eq__imp__le, axiom, (! [M:nat,N:nat]: ((((((ord_less @ nat) @ M) @ N) | (M = N)) => (((ord_less_eq @ nat) @ M) @ N))))).
% 0.32/1.50 thf(fact_80_linorder__neqE__nat, axiom, (! [X2:nat,Y:nat]: (((X2 != Y) => ((~ ((((ord_less @ nat) @ X2) @ Y))) => (((ord_less @ nat) @ Y) @ X2)))))).
% 0.32/1.50 thf(fact_81_strict__inc__induct, axiom, (! [I:nat,J:nat,P2:(nat > $o)]: (((((ord_less @ nat) @ I) @ J) => ((! [I3:nat]: (((J = (suc @ I3)) => (P2 @ I3)))) => ((! [I3:nat]: (((((ord_less @ nat) @ I3) @ J) => ((P2 @ (suc @ I3)) => (P2 @ I3))))) => (P2 @ I))))))).
% 0.32/1.50 thf(fact_82_Nat_Oex__has__greatest__nat, axiom, (! [P2:(nat > $o),K:nat,B3:nat]: (((P2 @ K) => ((! [Y4:nat]: (((P2 @ Y4) => (((ord_less_eq @ nat) @ Y4) @ B3)))) => (? [X3:nat]: (((P2 @ X3) & (! [Y3:nat]: (((P2 @ Y3) => (((ord_less_eq @ nat) @ Y3) @ X3)))))))))))).
% 0.32/1.50 thf(fact_83_le__neq__implies__less, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((M != N) => (((ord_less @ nat) @ M) @ N)))))).
% 0.32/1.50 thf(fact_84_measure__induct__rule, axiom, (! [B:$tType,A:$tType]: (((wellorder @ B) => (! [F:(A > B),P2:(A > $o),A3:A]: (((! [X3:A]: (((! [Y3:A]: (((((ord_less @ B) @ (F @ Y3)) @ (F @ X3)) => (P2 @ Y3)))) => (P2 @ X3)))) => (P2 @ A3)))))))).
% 0.32/1.50 thf(fact_85_nat__induct__at__least, axiom, (! [M:nat,N:nat,P2:(nat > $o)]: (((((ord_less_eq @ nat) @ M) @ N) => ((P2 @ M) => ((! [N2:nat]: (((((ord_less_eq @ nat) @ M) @ N2) => ((P2 @ N2) => (P2 @ (suc @ N2)))))) => (P2 @ N))))))).
% 0.32/1.50 thf(fact_86_not__less__less__Suc__eq, axiom, (! [N:nat,M:nat]: (((~ ((((ord_less @ nat) @ N) @ M))) => ((((ord_less @ nat) @ N) @ (suc @ M)) = (N = M)))))).
% 0.32/1.50 thf(fact_87_less__mono__imp__le__mono, axiom, (! [F:(nat > nat),I:nat,J:nat]: (((! [I3:nat,J2:nat]: (((((ord_less @ nat) @ I3) @ J2) => (((ord_less @ nat) @ (F @ I3)) @ (F @ J2))))) => ((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (F @ I)) @ (F @ J))))))).
% 0.32/1.50 thf(fact_88_transitive__stepwise__le, axiom, (! [M:nat,N:nat,R:(nat > (nat > $o))]: (((((ord_less_eq @ nat) @ M) @ N) => ((! [X3:nat]: (((R @ X3) @ X3))) => ((! [X3:nat,Y4:nat,Z:nat]: ((((R @ X3) @ Y4) => (((R @ Y4) @ Z) => ((R @ X3) @ Z))))) => ((! [N2:nat]: (((R @ N2) @ (suc @ N2)))) => ((R @ M) @ N)))))))).
% 0.32/1.50 thf(fact_89_infinite__descent__measure, axiom, (! [A:$tType,P2:(A > $o),V2:(A > nat),X2:A]: (((! [X3:A]: (((~ ((P2 @ X3))) => (? [Y3:A]: (((((ord_less @ nat) @ (V2 @ Y3)) @ (V2 @ X3)) & (~ ((P2 @ Y3))))))))) => (P2 @ X2))))).
% 0.32/1.50 thf(fact_90_lift__Suc__mono__le, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N:nat,N4:nat]: (((! [N2:nat]: ((((ord_less_eq @ A) @ (F @ N2)) @ (F @ (suc @ N2))))) => ((((ord_less_eq @ nat) @ N) @ N4) => (((ord_less_eq @ A) @ (F @ N)) @ (F @ N4)))))))))).
% 0.32/1.50 thf(fact_91_lift__Suc__mono__less, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N:nat,N4:nat]: (((! [N2:nat]: ((((ord_less @ A) @ (F @ N2)) @ (F @ (suc @ N2))))) => ((((ord_less @ nat) @ N) @ N4) => (((ord_less @ A) @ (F @ N)) @ (F @ N4)))))))))).
% 0.32/1.50 thf(fact_92_lift__Suc__antimono__le, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N:nat,N4:nat]: (((! [N2:nat]: ((((ord_less_eq @ A) @ (F @ (suc @ N2))) @ (F @ N2)))) => ((((ord_less_eq @ nat) @ N) @ N4) => (((ord_less_eq @ A) @ (F @ N4)) @ (F @ N)))))))))).
% 0.32/1.50 thf(fact_93_lift__Suc__mono__less__iff, axiom, (! [A:$tType]: (((order @ A) => (! [F:(nat > A),N:nat,M:nat]: (((! [N2:nat]: ((((ord_less @ A) @ (F @ N2)) @ (F @ (suc @ N2))))) => ((((ord_less @ A) @ (F @ N)) @ (F @ M)) = (((ord_less @ nat) @ N) @ M))))))))).
% 0.32/1.50 thf(fact_94_diff__less__Suc, axiom, (! [M:nat,N:nat]: ((((ord_less @ nat) @ (((minus_minus @ nat) @ M) @ N)) @ (suc @ M))))).
% 0.32/1.50 thf(fact_95_Suc__diff__Suc, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ N) @ M) => ((suc @ (((minus_minus @ nat) @ M) @ (suc @ N))) = (((minus_minus @ nat) @ M) @ N)))))).
% 0.32/1.50 thf(fact_96_Suc__diff__le, axiom, (! [N:nat,M:nat]: (((((ord_less_eq @ nat) @ N) @ M) => ((((minus_minus @ nat) @ (suc @ M)) @ N) = (suc @ (((minus_minus @ nat) @ M) @ N))))))).
% 0.32/1.50 thf(fact_97_zero__induct__lemma, axiom, (! [P2:(nat > $o),K:nat,I:nat]: (((P2 @ K) => ((! [N2:nat]: (((P2 @ (suc @ N2)) => (P2 @ N2)))) => (P2 @ (((minus_minus @ nat) @ K) @ I))))))).
% 0.32/1.50 thf(fact_98_diff__less__mono, axiom, (! [A3:nat,B3:nat,C:nat]: (((((ord_less @ nat) @ A3) @ B3) => ((((ord_less_eq @ nat) @ C) @ A3) => (((ord_less @ nat) @ (((minus_minus @ nat) @ A3) @ C)) @ (((minus_minus @ nat) @ B3) @ C))))))).
% 0.32/1.50 thf(fact_99_less__diff__iff, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ K) @ M) => ((((ord_less_eq @ nat) @ K) @ N) => ((((ord_less @ nat) @ (((minus_minus @ nat) @ M) @ K)) @ (((minus_minus @ nat) @ N) @ K)) = (((ord_less @ nat) @ M) @ N))))))).
% 0.32/1.50 thf(fact_100_diff__Suc__eq__diff__pred, axiom, (! [M:nat,N:nat]: (((((minus_minus @ nat) @ M) @ (suc @ N)) = (((minus_minus @ nat) @ (((minus_minus @ nat) @ M) @ (one_one @ nat))) @ N))))).
% 0.32/1.50 thf(fact_101_diff__strict__right__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A3:A,B3:A,C:A]: (((((ord_less @ A) @ A3) @ B3) => (((ord_less @ A) @ (((minus_minus @ A) @ A3) @ C)) @ (((minus_minus @ A) @ B3) @ C))))))))).
% 0.32/1.50 thf(fact_102_diff__strict__left__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B3:A,A3:A,C:A]: (((((ord_less @ A) @ B3) @ A3) => (((ord_less @ A) @ (((minus_minus @ A) @ C) @ A3)) @ (((minus_minus @ A) @ C) @ B3))))))))).
% 0.32/1.50 thf(fact_103_diff__eq__diff__less, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A3:A,B3:A,C:A,D:A]: ((((((minus_minus @ A) @ A3) @ B3) = (((minus_minus @ A) @ C) @ D)) => ((((ord_less @ A) @ A3) @ B3) = (((ord_less @ A) @ C) @ D))))))))).
% 0.32/1.50 thf(fact_104_diff__strict__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A3:A,B3:A,D:A,C:A]: (((((ord_less @ A) @ A3) @ B3) => ((((ord_less @ A) @ D) @ C) => (((ord_less @ A) @ (((minus_minus @ A) @ A3) @ C)) @ (((minus_minus @ A) @ B3) @ D)))))))))).
% 0.32/1.50 thf(fact_105_diff__eq__diff__less__eq, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A3:A,B3:A,C:A,D:A]: ((((((minus_minus @ A) @ A3) @ B3) = (((minus_minus @ A) @ C) @ D)) => ((((ord_less_eq @ A) @ A3) @ B3) = (((ord_less_eq @ A) @ C) @ D))))))))).
% 0.32/1.50 thf(fact_106_diff__right__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A3:A,B3:A,C:A]: (((((ord_less_eq @ A) @ A3) @ B3) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A3) @ C)) @ (((minus_minus @ A) @ B3) @ C))))))))).
% 0.32/1.50 thf(fact_107_diff__left__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [B3:A,A3:A,C:A]: (((((ord_less_eq @ A) @ B3) @ A3) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ C) @ A3)) @ (((minus_minus @ A) @ C) @ B3))))))))).
% 0.32/1.50 thf(fact_108_diff__mono, axiom, (! [A:$tType]: (((ordered_ab_group_add @ A) => (! [A3:A,B3:A,D:A,C:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less_eq @ A) @ D) @ C) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A3) @ C)) @ (((minus_minus @ A) @ B3) @ D)))))))))).
% 0.32/1.50 thf(fact_109_length__induct, axiom, (! [A:$tType,P2:((list @ A) > $o),Xs2:(list @ A)]: (((! [Xs:(list @ A)]: (((! [Ys2:(list @ A)]: (((((ord_less @ nat) @ ((size_size @ (list @ A)) @ Ys2)) @ ((size_size @ (list @ A)) @ Xs)) => (P2 @ Ys2)))) => (P2 @ Xs)))) => (P2 @ Xs2))))).
% 0.32/1.50 thf(fact_110_less__imp__diff__less, axiom, (! [J:nat,K:nat,N:nat]: (((((ord_less @ nat) @ J) @ K) => (((ord_less @ nat) @ (((minus_minus @ nat) @ J) @ N)) @ K))))).
% 0.32/1.50 thf(fact_111_diff__less__mono2, axiom, (! [M:nat,N:nat,L:nat]: (((((ord_less @ nat) @ M) @ N) => ((((ord_less @ nat) @ M) @ L) => (((ord_less @ nat) @ (((minus_minus @ nat) @ L) @ N)) @ (((minus_minus @ nat) @ L) @ M))))))).
% 0.32/1.50 thf(fact_112_diff__le__mono2, axiom, (! [M:nat,N:nat,L:nat]: (((((ord_less_eq @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ (((minus_minus @ nat) @ L) @ N)) @ (((minus_minus @ nat) @ L) @ M)))))).
% 0.32/1.50 thf(fact_113_le__diff__iff_H, axiom, (! [A3:nat,C:nat,B3:nat]: (((((ord_less_eq @ nat) @ A3) @ C) => ((((ord_less_eq @ nat) @ B3) @ C) => ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ C) @ A3)) @ (((minus_minus @ nat) @ C) @ B3)) = (((ord_less_eq @ nat) @ B3) @ A3))))))).
% 0.32/1.50 thf(fact_114_diff__le__self, axiom, (! [M:nat,N:nat]: ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ M) @ N)) @ M)))).
% 0.32/1.50 thf(fact_115_diff__le__mono, axiom, (! [M:nat,N:nat,L:nat]: (((((ord_less_eq @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ (((minus_minus @ nat) @ M) @ L)) @ (((minus_minus @ nat) @ N) @ L)))))).
% 0.32/1.50 thf(fact_116_Nat_Odiff__diff__eq, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ K) @ M) => ((((ord_less_eq @ nat) @ K) @ N) => ((((minus_minus @ nat) @ (((minus_minus @ nat) @ M) @ K)) @ (((minus_minus @ nat) @ N) @ K)) = (((minus_minus @ nat) @ M) @ N))))))).
% 0.32/1.50 thf(fact_117_le__diff__iff, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ K) @ M) => ((((ord_less_eq @ nat) @ K) @ N) => ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ M) @ K)) @ (((minus_minus @ nat) @ N) @ K)) = (((ord_less_eq @ nat) @ M) @ N))))))).
% 0.32/1.50 thf(fact_118_eq__diff__iff, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ K) @ M) => ((((ord_less_eq @ nat) @ K) @ N) => (((((minus_minus @ nat) @ M) @ K) = (((minus_minus @ nat) @ N) @ K)) = (M = N))))))).
% 0.32/1.50 thf(fact_119_one__reorient, axiom, (! [A:$tType]: (((one @ A) => (! [X2:A]: ((((one_one @ A) = X2) = (X2 = (one_one @ A))))))))).
% 0.32/1.50 thf(fact_120_diff__right__commute, axiom, (! [A:$tType]: (((cancel146912293up_add @ A) => (! [A3:A,C:A,B3:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A3) @ C)) @ B3) = (((minus_minus @ A) @ (((minus_minus @ A) @ A3) @ B3)) @ C)))))))).
% 0.32/1.50 thf(fact_121_Subset, axiom, (! [MsgInSet:((message @ p) @ v)]: (((((member @ ((message @ p) @ v)) @ MsgInSet) @ (firstOccSet @ (suc @ index))) => (((member @ ((message @ p) @ v)) @ MsgInSet) @ (firstOccSet @ index)))))).
% 0.32/1.50 thf(fact_122_SameCfgOnLow, axiom, (! [I4:nat]: (((((ord_less @ nat) @ I4) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) => ((((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index)) @ I4) = (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ (suc @ index))) @ I4)))))).
% 0.32/1.50 thf(fact_123__092_060open_062_092_060not_062_AOccM_A_060_Alength_A_Ift_Aindex_J_092_060close_062, axiom, (~ ((((ord_less @ nat) @ occM2) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index)))))).
% 0.32/1.50 thf(fact_124_IPrefixListEx, axiom, (! [I4:nat]: ((((prefixList @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ I4)) @ (fe @ (suc @ I4)))))).
% 0.32/1.50 thf(fact_125_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A]: ((((ord_less_eq @ A) @ X2) @ X2))))))).
% 0.32/1.50 thf(fact_126_nat__descend__induct, axiom, (! [N:nat,P2:(nat > $o),M:nat]: (((! [K2:nat]: (((((ord_less @ nat) @ N) @ K2) => (P2 @ K2)))) => ((! [K2:nat]: (((((ord_less_eq @ nat) @ K2) @ N) => ((! [I4:nat]: (((((ord_less @ nat) @ K2) @ I4) => (P2 @ I4)))) => (P2 @ K2))))) => (P2 @ M)))))).
% 0.32/1.50 thf(fact_127_Lattices__Big_Oex__has__greatest__nat, axiom, (! [A:$tType,P2:(A > $o),K:A,F:(A > nat),B3:nat]: (((P2 @ K) => ((! [Y4:A]: (((P2 @ Y4) => (((ord_less @ nat) @ (F @ Y4)) @ B3)))) => (? [X3:A]: (((P2 @ X3) & (! [Y3:A]: (((P2 @ Y3) => (((ord_less_eq @ nat) @ (F @ Y3)) @ (F @ X3))))))))))))).
% 0.32/1.50 thf(fact_128_KeepProperty, axiom, (! [Low:nat,P2:(nat > $o),Q:(nat > $o)]: (((! [I3:nat]: (((((ord_less_eq @ nat) @ Low) @ I3) => ((P2 @ I3) => ((P2 @ (suc @ I3)) & (Q @ I3)))))) => ((P2 @ Low) => (! [I4:nat]: (((((ord_less_eq @ nat) @ Low) @ I4) => (Q @ I4))))))))).
% 0.32/1.50 thf(fact_129_less__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (~ ((((ord_less @ A) @ (one_one @ A)) @ (one_one @ A)))))))).
% 0.32/1.50 thf(fact_130_le__numeral__extra_I4_J, axiom, (! [A:$tType]: (((linord1659791738miring @ A) => (((ord_less_eq @ A) @ (one_one @ A)) @ (one_one @ A)))))).
% 0.32/1.50 thf(fact_131_LengthStep, axiom, (((ord_less @ nat) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ (suc @ index))))).
% 0.32/1.50 thf(fact_132_ConsumedMsg_I1_J, axiom, ((((((minimalEnabled @ p) @ v) @ s) @ (fe @ index)) @ (ft @ index)) @ consumedMsg)).
% 0.32/1.50 thf(fact_133_PrefixListTransitive, axiom, (! [A:$tType,L1:(list @ A),L2:(list @ A),L3:(list @ A)]: (((((prefixList @ A) @ L1) @ L2) => ((((prefixList @ A) @ L2) @ L3) => (((prefixList @ A) @ L1) @ L3)))))).
% 0.32/1.50 thf(fact_134_PrefixSameOnLow, axiom, (! [A:$tType,L1:(list @ A),L2:(list @ A)]: (((((prefixList @ A) @ L1) @ L2) => (! [Index:nat]: (((((ord_less @ nat) @ Index) @ ((size_size @ (list @ A)) @ L1)) => ((((nth @ A) @ L1) @ Index) = (((nth @ A) @ L2) @ Index))))))))).
% 0.32/1.50 thf(fact_135_PrefixListMonotonicity, axiom, (! [A:$tType,L1:(list @ A),L2:(list @ A)]: (((((prefixList @ A) @ L1) @ L2) => (((ord_less @ nat) @ ((size_size @ (list @ A)) @ L1)) @ ((size_size @ (list @ A)) @ L2)))))).
% 0.32/1.50 thf(fact_136_nth__equalityI, axiom, (! [A:$tType,Xs2:(list @ A),Ys:(list @ A)]: (((((size_size @ (list @ A)) @ Xs2) = ((size_size @ (list @ A)) @ Ys)) => ((! [I3:nat]: (((((ord_less @ nat) @ I3) @ ((size_size @ (list @ A)) @ Xs2)) => ((((nth @ A) @ Xs2) @ I3) = (((nth @ A) @ Ys) @ I3))))) => (Xs2 = Ys)))))).
% 0.32/1.50 thf(fact_137_Skolem__list__nth, axiom, (! [A:$tType,K:nat,P2:(nat > (A > $o))]: (((! [I2:nat]: (((((ord_less @ nat) @ I2) @ K) => (? [X4:A]: (((P2 @ I2) @ X4)))))) = (? [Xs3:(list @ A)]: (((((size_size @ (list @ A)) @ Xs3) = K) & (! [I2:nat]: (((((ord_less @ nat) @ I2) @ K) => ((P2 @ I2) @ (((nth @ A) @ Xs3) @ I2)))))))))))).
% 0.32/1.50 thf(fact_138_list__eq__iff__nth__eq, axiom, (! [A:$tType]: (((^ [Y5:(list @ A),Z2:(list @ A)]: ((Y5 = Z2))) = (^ [Xs3:(list @ A),Ys3:(list @ A)]: (((((size_size @ (list @ A)) @ Xs3) = ((size_size @ (list @ A)) @ Ys3)) & (! [I2:nat]: (((((ord_less @ nat) @ I2) @ ((size_size @ (list @ A)) @ Xs3)) => ((((nth @ A) @ Xs3) @ I2) = (((nth @ A) @ Ys3) @ I2)))))))))))).
% 0.32/1.50 thf(fact_139_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A3:A]: (((((ord_less_eq @ A) @ B3) @ A3) => ((((ord_less_eq @ A) @ A3) @ B3) => (A3 = B3))))))))).
% 0.32/1.50 thf(fact_140_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y5:A,Z2:A]: ((Y5 = Z2))) = (^ [A5:A,B4:A]: (((((ord_less_eq @ A) @ B4) @ A5) & (((ord_less_eq @ A) @ A5) @ B4))))))))).
% 0.32/1.50 thf(fact_141_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A3:A,C:A]: (((((ord_less_eq @ A) @ B3) @ A3) => ((((ord_less_eq @ A) @ C) @ B3) => (((ord_less_eq @ A) @ C) @ A3))))))))).
% 0.32/1.50 thf(fact_142_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P2:(A > (A > $o)),A3:A,B3:A]: (((! [A6:A,B5:A]: (((((ord_less_eq @ A) @ A6) @ B5) => ((P2 @ A6) @ B5)))) => ((! [A6:A,B5:A]: ((((P2 @ B5) @ A6) => ((P2 @ A6) @ B5)))) => ((P2 @ A3) @ B3))))))))).
% 0.32/1.50 thf(fact_143_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A]: ((((ord_less_eq @ A) @ A3) @ A3))))))).
% 0.32/1.50 thf(fact_144_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A,Z3:A]: (((((ord_less_eq @ A) @ X2) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z3) => (((ord_less_eq @ A) @ X2) @ Z3))))))))).
% 0.32/1.50 thf(fact_145_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less_eq @ A) @ B3) @ A3) => (A3 = B3))))))))).
% 0.32/1.50 thf(fact_146_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B3:A,C:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((B3 = C) => (((ord_less_eq @ A) @ A3) @ C))))))))).
% 0.32/1.50 thf(fact_147_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B3:A,C:A]: (((A3 = B3) => ((((ord_less_eq @ A) @ B3) @ C) => (((ord_less_eq @ A) @ A3) @ C))))))))).
% 0.32/1.50 thf(fact_148_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y5:A,Z2:A]: ((Y5 = Z2))) = (^ [A5:A,B4:A]: (((((ord_less_eq @ A) @ A5) @ B4) & (((ord_less_eq @ A) @ B4) @ A5))))))))).
% 0.32/1.50 thf(fact_149_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X2:A]: (((((ord_less_eq @ A) @ Y) @ X2) => ((((ord_less_eq @ A) @ X2) @ Y) = (X2 = Y))))))))).
% 0.32/1.50 thf(fact_150_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A,Z3:A]: ((((((ord_less_eq @ A) @ X2) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z3)))) => (((((ord_less_eq @ A) @ Y) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Z3)))) => (((((ord_less_eq @ A) @ X2) @ Z3) => (~ ((((ord_less_eq @ A) @ Z3) @ Y)))) => (((((ord_less_eq @ A) @ Z3) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X2)))) => (((((ord_less_eq @ A) @ Y) @ Z3) => (~ ((((ord_less_eq @ A) @ Z3) @ X2)))) => (~ (((((ord_less_eq @ A) @ Z3) @ X2) => (~ ((((ord_less_eq @ A) @ X2) @ Y))))))))))))))))).
% 0.32/1.50 thf(fact_151_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B3:A,C:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less_eq @ A) @ B3) @ C) => (((ord_less_eq @ A) @ A3) @ C))))))))).
% 0.32/1.50 thf(fact_152_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X2) @ Y))) => (((ord_less_eq @ A) @ Y) @ X2)))))))).
% 0.32/1.50 thf(fact_153_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A]: (((X2 = Y) => (((ord_less_eq @ A) @ X2) @ Y)))))))).
% 0.32/1.50 thf(fact_154_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) | (((ord_less_eq @ A) @ Y) @ X2)))))))).
% 0.32/1.50 thf(fact_155_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) => ((((ord_less_eq @ A) @ Y) @ X2) => (X2 = Y))))))))).
% 0.32/1.50 thf(fact_156_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y5:A,Z2:A]: ((Y5 = Z2))) = (^ [X:A,Y6:A]: (((((ord_less_eq @ A) @ X) @ Y6) & (((ord_less_eq @ A) @ Y6) @ X))))))))).
% 0.32/1.50 thf(fact_157_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,B3:A,F:(A > B),C:B]: (((((ord_less_eq @ A) @ A3) @ B3) => (((F @ B3) = C) => ((! [X3:A,Y4:A]: (((((ord_less_eq @ A) @ X3) @ Y4) => (((ord_less_eq @ B) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less_eq @ B) @ (F @ A3)) @ C)))))))))).
% 0.32/1.50 thf(fact_158_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,F:(B > A),B3:B,C:B]: (((A3 = (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C) => ((! [X3:B,Y4:B]: (((((ord_less_eq @ B) @ X3) @ Y4) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A3) @ (F @ C))))))))))).
% 0.32/1.50 thf(fact_159_order__subst2, axiom, (! [A:$tType,C2:$tType]: ((((order @ C2) & (order @ A)) => (! [A3:A,B3:A,F:(A > C2),C:C2]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less_eq @ C2) @ (F @ B3)) @ C) => ((! [X3:A,Y4:A]: (((((ord_less_eq @ A) @ X3) @ Y4) => (((ord_less_eq @ C2) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less_eq @ C2) @ (F @ A3)) @ C)))))))))).
% 0.32/1.50 thf(fact_160_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A3:A,F:(B > A),B3:B,C:B]: (((((ord_less_eq @ A) @ A3) @ (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C) => ((! [X3:B,Y4:B]: (((((ord_less_eq @ B) @ X3) @ Y4) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A3) @ (F @ C))))))))))).
% 0.32/1.50 thf(fact_161_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: ((! [X:A]: ((((ord_less_eq @ B) @ (F2 @ X)) @ (G2 @ X))))))))))).
% 0.32/1.50 thf(fact_162_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B)]: (((! [X3:A]: ((((ord_less_eq @ B) @ (F @ X3)) @ (G @ X3)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 0.32/1.50 thf(fact_163_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X2:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X2)) @ (G @ X2))))))))).
% 0.32/1.50 thf(fact_164_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X2:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X2)) @ (G @ X2))))))))).
% 0.32/1.50 thf(fact_165_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A3:A]: (((((ord_less @ A) @ B3) @ A3) => (A3 != B3)))))))).
% 0.32/1.50 thf(fact_166_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B3:A]: (((((ord_less @ A) @ A3) @ B3) => (A3 != B3)))))))).
% 0.32/1.50 thf(fact_167_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((~ ((((ord_less @ A) @ X2) @ Y))) = ((((ord_less @ A) @ Y) @ X2) | (X2 = Y))))))))).
% 0.32/1.50 thf(fact_168_dual__order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A3:A,C:A]: (((((ord_less @ A) @ B3) @ A3) => ((((ord_less @ A) @ C) @ B3) => (((ord_less @ A) @ C) @ A3))))))))).
% 0.32/1.50 thf(fact_169_linorder__less__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P2:(A > (A > $o)),A3:A,B3:A]: (((! [A6:A,B5:A]: (((((ord_less @ A) @ A6) @ B5) => ((P2 @ A6) @ B5)))) => ((! [A6:A]: (((P2 @ A6) @ A6))) => ((! [A6:A,B5:A]: ((((P2 @ B5) @ A6) => ((P2 @ A6) @ B5)))) => ((P2 @ A3) @ B3)))))))))).
% 0.32/1.50 thf(fact_170_exists__least__iff, axiom, (! [A:$tType]: (((wellorder @ A) => ((^ [P3:(A > $o)]: ((? [X4:A]: ((P3 @ X4))))) = (^ [P4:(A > $o)]: ((? [N3:A]: (((P4 @ N3) & (! [M4:A]: (((((ord_less @ A) @ M4) @ N3) => (~ ((P4 @ M4)))))))))))))))).
% 0.32/1.50 thf(fact_171_less__imp__not__less, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) => (~ ((((ord_less @ A) @ Y) @ X2)))))))))).
% 0.32/1.50 thf(fact_172_order_Ostrict__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B3:A,C:A]: (((((ord_less @ A) @ A3) @ B3) => ((((ord_less @ A) @ B3) @ C) => (((ord_less @ A) @ A3) @ C))))))))).
% 0.32/1.50 thf(fact_173_dual__order_Oirrefl, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A]: ((~ ((((ord_less @ A) @ A3) @ A3))))))))).
% 0.32/1.50 thf(fact_174_linorder__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((~ ((((ord_less @ A) @ X2) @ Y))) => ((X2 != Y) => (((ord_less @ A) @ Y) @ X2))))))))).
% 0.32/1.50 thf(fact_175_less__imp__triv, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A,P2:$o]: (((((ord_less @ A) @ X2) @ Y) => ((((ord_less @ A) @ Y) @ X2) => P2)))))))).
% 0.32/1.50 thf(fact_176_less__imp__not__eq2, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) => (Y != X2)))))))).
% 0.32/1.50 thf(fact_177_antisym__conv3, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y:A,X2:A]: (((~ ((((ord_less @ A) @ Y) @ X2))) => ((~ ((((ord_less @ A) @ X2) @ Y))) = (X2 = Y))))))))).
% 0.32/1.50 thf(fact_178_less__induct, axiom, (! [A:$tType]: (((wellorder @ A) => (! [P2:(A > $o),A3:A]: (((! [X3:A]: (((! [Y3:A]: (((((ord_less @ A) @ Y3) @ X3) => (P2 @ Y3)))) => (P2 @ X3)))) => (P2 @ A3)))))))).
% 0.32/1.50 thf(fact_179_less__not__sym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) => (~ ((((ord_less @ A) @ Y) @ X2)))))))))).
% 0.32/1.50 thf(fact_180_less__imp__not__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) => (X2 != Y)))))))).
% 0.32/1.50 thf(fact_181_dual__order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A3:A]: (((((ord_less @ A) @ B3) @ A3) => (~ ((((ord_less @ A) @ A3) @ B3)))))))))).
% 0.32/1.50 thf(fact_182_ord__less__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B3:A,C:A]: (((((ord_less @ A) @ A3) @ B3) => ((B3 = C) => (((ord_less @ A) @ A3) @ C))))))))).
% 0.32/1.50 thf(fact_183_ord__eq__less__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B3:A,C:A]: (((A3 = B3) => ((((ord_less @ A) @ B3) @ C) => (((ord_less @ A) @ A3) @ C))))))))).
% 0.32/1.50 thf(fact_184_less__irrefl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A]: ((~ ((((ord_less @ A) @ X2) @ X2))))))))).
% 0.32/1.50 thf(fact_185_less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) | ((X2 = Y) | (((ord_less @ A) @ Y) @ X2))))))))).
% 0.32/1.50 thf(fact_186_less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A,Z3:A]: (((((ord_less @ A) @ X2) @ Y) => ((((ord_less @ A) @ Y) @ Z3) => (((ord_less @ A) @ X2) @ Z3))))))))).
% 0.32/1.50 thf(fact_187_less__asym_H, axiom, (! [A:$tType]: (((preorder @ A) => (! [A3:A,B3:A]: (((((ord_less @ A) @ A3) @ B3) => (~ ((((ord_less @ A) @ B3) @ A3)))))))))).
% 0.32/1.50 thf(fact_188_less__asym, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) => (~ ((((ord_less @ A) @ Y) @ X2)))))))))).
% 0.32/1.50 thf(fact_189_less__imp__neq, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) => (X2 != Y)))))))).
% 0.32/1.50 thf(fact_190_dense, axiom, (! [A:$tType]: (((dense_order @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) => (? [Z:A]: (((((ord_less @ A) @ X2) @ Z) & (((ord_less @ A) @ Z) @ Y))))))))))).
% 0.32/1.50 thf(fact_191_order_Oasym, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B3:A]: (((((ord_less @ A) @ A3) @ B3) => (~ ((((ord_less @ A) @ B3) @ A3)))))))))).
% 0.32/1.50 thf(fact_192_neq__iff, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((X2 != Y) = ((((ord_less @ A) @ X2) @ Y) | (((ord_less @ A) @ Y) @ X2))))))))).
% 0.32/1.50 thf(fact_193_neqE, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((X2 != Y) => ((~ ((((ord_less @ A) @ X2) @ Y))) => (((ord_less @ A) @ Y) @ X2))))))))).
% 0.32/1.50 thf(fact_194_gt__ex, axiom, (! [A:$tType]: (((no_top @ A) => (! [X2:A]: ((? [X_1:A]: ((((ord_less @ A) @ X2) @ X_1))))))))).
% 0.32/1.50 thf(fact_195_lt__ex, axiom, (! [A:$tType]: (((no_bot @ A) => (! [X2:A]: ((? [Y4:A]: ((((ord_less @ A) @ Y4) @ X2))))))))).
% 0.32/1.50 thf(fact_196_order__less__subst2, axiom, (! [A:$tType,C2:$tType]: ((((order @ C2) & (order @ A)) => (! [A3:A,B3:A,F:(A > C2),C:C2]: (((((ord_less @ A) @ A3) @ B3) => ((((ord_less @ C2) @ (F @ B3)) @ C) => ((! [X3:A,Y4:A]: (((((ord_less @ A) @ X3) @ Y4) => (((ord_less @ C2) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less @ C2) @ (F @ A3)) @ C)))))))))).
% 0.32/1.50 thf(fact_197_order__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A3:A,F:(B > A),B3:B,C:B]: (((((ord_less @ A) @ A3) @ (F @ B3)) => ((((ord_less @ B) @ B3) @ C) => ((! [X3:B,Y4:B]: (((((ord_less @ B) @ X3) @ Y4) => (((ord_less @ A) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less @ A) @ A3) @ (F @ C))))))))))).
% 0.32/1.50 thf(fact_198_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,B3:A,F:(A > B),C:B]: (((((ord_less @ A) @ A3) @ B3) => (((F @ B3) = C) => ((! [X3:A,Y4:A]: (((((ord_less @ A) @ X3) @ Y4) => (((ord_less @ B) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less @ B) @ (F @ A3)) @ C)))))))))).
% 0.32/1.50 thf(fact_199_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,F:(B > A),B3:B,C:B]: (((A3 = (F @ B3)) => ((((ord_less @ B) @ B3) @ C) => ((! [X3:B,Y4:B]: (((((ord_less @ B) @ X3) @ Y4) => (((ord_less @ A) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less @ A) @ A3) @ (F @ C))))))))))).
% 0.32/1.50 thf(fact_200_ex__has__least__nat, axiom, (! [A:$tType,P2:(A > $o),K:A,M:(A > nat)]: (((P2 @ K) => (? [X3:A]: (((P2 @ X3) & (! [Y3:A]: (((P2 @ Y3) => (((ord_less_eq @ nat) @ (M @ X3)) @ (M @ Y3)))))))))))).
% 0.32/1.50 thf(fact_201_MinPredicate, axiom, (! [P2:(nat > $o)]: (((? [X_12:nat]: ((P2 @ X_12))) => (? [N0:nat]: (((P2 @ N0) & (! [N5:nat]: (((P2 @ N5) => (((ord_less_eq @ nat) @ N0) @ N5))))))))))).
% 0.32/1.50 thf(fact_202_order_Onot__eq__order__implies__strict, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B3:A]: (((A3 != B3) => ((((ord_less_eq @ A) @ A3) @ B3) => (((ord_less @ A) @ A3) @ B3))))))))).
% 0.32/1.50 thf(fact_203_dual__order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A3:A]: (((((ord_less @ A) @ B3) @ A3) => (((ord_less_eq @ A) @ B3) @ A3)))))))).
% 0.32/1.50 thf(fact_204_dual__order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [B4:A,A5:A]: (((((ord_less_eq @ A) @ B4) @ A5) & (A5 != B4))))))))).
% 0.32/1.50 thf(fact_205_dual__order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [B4:A,A5:A]: (((((ord_less @ A) @ B4) @ A5) | (A5 = B4))))))))).
% 0.32/1.50 thf(fact_206_order_Ostrict__implies__order, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B3:A]: (((((ord_less @ A) @ A3) @ B3) => (((ord_less_eq @ A) @ A3) @ B3)))))))).
% 0.32/1.50 thf(fact_207_dense__le__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [X2:A,Y:A,Z3:A]: (((((ord_less @ A) @ X2) @ Y) => ((! [W:A]: (((((ord_less @ A) @ X2) @ W) => ((((ord_less @ A) @ W) @ Y) => (((ord_less_eq @ A) @ W) @ Z3))))) => (((ord_less_eq @ A) @ Y) @ Z3))))))))).
% 0.32/1.50 thf(fact_208_dense__ge__bounded, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Z3:A,X2:A,Y:A]: (((((ord_less @ A) @ Z3) @ X2) => ((! [W:A]: (((((ord_less @ A) @ Z3) @ W) => ((((ord_less @ A) @ W) @ X2) => (((ord_less_eq @ A) @ Y) @ W))))) => (((ord_less_eq @ A) @ Y) @ Z3))))))))).
% 0.32/1.50 thf(fact_209_dual__order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A3:A,C:A]: (((((ord_less @ A) @ B3) @ A3) => ((((ord_less_eq @ A) @ C) @ B3) => (((ord_less @ A) @ C) @ A3))))))))).
% 0.32/1.50 thf(fact_210_dual__order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A3:A,C:A]: (((((ord_less_eq @ A) @ B3) @ A3) => ((((ord_less @ A) @ C) @ B3) => (((ord_less @ A) @ C) @ A3))))))))).
% 0.32/1.50 thf(fact_211_order_Ostrict__iff__order, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [A5:A,B4:A]: (((((ord_less_eq @ A) @ A5) @ B4) & (A5 != B4))))))))).
% 0.32/1.50 thf(fact_212_order_Oorder__iff__strict, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [A5:A,B4:A]: (((((ord_less @ A) @ A5) @ B4) | (A5 = B4))))))))).
% 0.32/1.50 thf(fact_213_order_Ostrict__trans2, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B3:A,C:A]: (((((ord_less @ A) @ A3) @ B3) => ((((ord_less_eq @ A) @ B3) @ C) => (((ord_less @ A) @ A3) @ C))))))))).
% 0.32/1.50 thf(fact_214_order_Ostrict__trans1, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B3:A,C:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less @ A) @ B3) @ C) => (((ord_less @ A) @ A3) @ C))))))))).
% 0.32/1.50 thf(fact_215_not__le__imp__less, axiom, (! [A:$tType]: (((linorder @ A) => (! [Y:A,X2:A]: (((~ ((((ord_less_eq @ A) @ Y) @ X2))) => (((ord_less @ A) @ X2) @ Y)))))))).
% 0.32/1.50 thf(fact_216_less__le__not__le, axiom, (! [A:$tType]: (((preorder @ A) => ((ord_less @ A) = (^ [X:A,Y6:A]: (((((ord_less_eq @ A) @ X) @ Y6) & (~ ((((ord_less_eq @ A) @ Y6) @ X))))))))))).
% 0.32/1.50 thf(fact_217_le__imp__less__or__eq, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) => ((((ord_less @ A) @ X2) @ Y) | (X2 = Y))))))))).
% 0.32/1.50 thf(fact_218_le__less__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) | (((ord_less @ A) @ Y) @ X2)))))))).
% 0.32/1.50 thf(fact_219_dense__le, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Y:A,Z3:A]: (((! [X3:A]: (((((ord_less @ A) @ X3) @ Y) => (((ord_less_eq @ A) @ X3) @ Z3)))) => (((ord_less_eq @ A) @ Y) @ Z3)))))))).
% 0.32/1.50 thf(fact_220_dense__ge, axiom, (! [A:$tType]: (((dense_linorder @ A) => (! [Z3:A,Y:A]: (((! [X3:A]: (((((ord_less @ A) @ Z3) @ X3) => (((ord_less_eq @ A) @ Y) @ X3)))) => (((ord_less_eq @ A) @ Y) @ Z3)))))))).
% 0.32/1.50 thf(fact_221_less__le__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A,Z3:A]: (((((ord_less @ A) @ X2) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z3) => (((ord_less @ A) @ X2) @ Z3))))))))).
% 0.32/1.50 thf(fact_222_le__less__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A,Z3:A]: (((((ord_less_eq @ A) @ X2) @ Y) => ((((ord_less @ A) @ Y) @ Z3) => (((ord_less @ A) @ X2) @ Z3))))))))).
% 0.32/1.50 thf(fact_223_less__imp__le, axiom, (! [A:$tType]: (((preorder @ A) => (! [X2:A,Y:A]: (((((ord_less @ A) @ X2) @ Y) => (((ord_less_eq @ A) @ X2) @ Y)))))))).
% 0.32/1.50 thf(fact_224_antisym__conv2, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y:A]: (((((ord_less_eq @ A) @ X2) @ Y) => ((~ ((((ord_less @ A) @ X2) @ Y))) = (X2 = Y))))))))).
% 0.32/1.50 thf(fact_225_antisym__conv1, axiom, (! [A:$tType]: (((order @ A) => (! [X2:A,Y:A]: (((~ ((((ord_less @ A) @ X2) @ Y))) => ((((ord_less_eq @ A) @ X2) @ Y) = (X2 = Y))))))))).
% 0.32/1.50 thf(fact_226_le__neq__trans, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((A3 != B3) => (((ord_less @ A) @ A3) @ B3))))))))).
% 0.32/1.50 thf(fact_227_not__less, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((~ ((((ord_less @ A) @ X2) @ Y))) = (((ord_less_eq @ A) @ Y) @ X2)))))))).
% 0.32/1.50 thf(fact_228_not__le, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X2) @ Y))) = (((ord_less @ A) @ Y) @ X2)))))))).
% 0.32/1.50 thf(fact_229_order__less__le__subst2, axiom, (! [A:$tType,C2:$tType]: ((((order @ C2) & (order @ A)) => (! [A3:A,B3:A,F:(A > C2),C:C2]: (((((ord_less @ A) @ A3) @ B3) => ((((ord_less_eq @ C2) @ (F @ B3)) @ C) => ((! [X3:A,Y4:A]: (((((ord_less @ A) @ X3) @ Y4) => (((ord_less @ C2) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less @ C2) @ (F @ A3)) @ C)))))))))).
% 0.32/1.50 thf(fact_230_order__less__le__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A3:A,F:(B > A),B3:B,C:B]: (((((ord_less @ A) @ A3) @ (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C) => ((! [X3:B,Y4:B]: (((((ord_less_eq @ B) @ X3) @ Y4) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less @ A) @ A3) @ (F @ C))))))))))).
% 0.32/1.50 thf(fact_231_order__le__less__subst2, axiom, (! [A:$tType,C2:$tType]: ((((order @ C2) & (order @ A)) => (! [A3:A,B3:A,F:(A > C2),C:C2]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less @ C2) @ (F @ B3)) @ C) => ((! [X3:A,Y4:A]: (((((ord_less_eq @ A) @ X3) @ Y4) => (((ord_less_eq @ C2) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less @ C2) @ (F @ A3)) @ C)))))))))).
% 0.32/1.50 thf(fact_232_order__le__less__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A3:A,F:(B > A),B3:B,C:B]: (((((ord_less_eq @ A) @ A3) @ (F @ B3)) => ((((ord_less @ B) @ B3) @ C) => ((! [X3:B,Y4:B]: (((((ord_less @ B) @ X3) @ Y4) => (((ord_less @ A) @ (F @ X3)) @ (F @ Y4))))) => (((ord_less @ A) @ A3) @ (F @ C))))))))))).
% 0.32/1.50 thf(fact_233_less__le, axiom, (! [A:$tType]: (((order @ A) => ((ord_less @ A) = (^ [X:A,Y6:A]: (((((ord_less_eq @ A) @ X) @ Y6) & (X != Y6))))))))).
% 0.32/1.50 thf(fact_234_le__less, axiom, (! [A:$tType]: (((order @ A) => ((ord_less_eq @ A) = (^ [X:A,Y6:A]: (((((ord_less @ A) @ X) @ Y6) | (X = Y6))))))))).
% 0.32/1.50 thf(fact_235_leI, axiom, (! [A:$tType]: (((linorder @ A) => (! [X2:A,Y:A]: (((~ ((((ord_less @ A) @ X2) @ Y))) => (((ord_less_eq @ A) @ Y) @ X2)))))))).
% 0.32/1.50 thf(fact_236_leD, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X2:A]: (((((ord_less_eq @ A) @ Y) @ X2) => (~ ((((ord_less @ A) @ X2) @ Y)))))))))).
% 0.32/1.50 thf(fact_237_AssumpMinImplAllBigger, axiom, ((((((minimalEnabled @ p) @ v) @ s) @ (fe @ index)) @ (ft @ index)) @ msg)).
% 0.32/1.50 thf(fact_238__092_060open_062execution_OfirstOccurrence_A_Ife_Aindex_J_A_Ift_Aindex_J_Amsg_AOccM_092_060close_062, axiom, (((((((firstOccurrence @ p) @ v) @ s) @ (fe @ index)) @ (ft @ index)) @ msga) @ occM2)).
% 0.32/1.50 thf(fact_239_SameMsgOnLow, axiom, (! [I4:nat]: (((((ord_less @ nat) @ I4) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) => ((((nth @ ((message @ p) @ v)) @ (ft @ index)) @ I4) = (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ I4)))))).
% 0.32/1.50 thf(fact_240_OccM_H_I5_J, axiom, (! [N5:nat]: (((((ord_less_eq @ nat) @ occM) @ N5) => ((((ord_less @ nat) @ N5) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) => (msg != (((nth @ ((message @ p) @ v)) @ (ft @ index)) @ N5))))))).
% 0.32/1.50 thf(fact_241_IPrefixList, axiom, (! [I4:nat]: ((((prefixList @ ((message @ p) @ v)) @ (ft @ I4)) @ (ft @ (suc @ I4)))))).
% 0.32/1.50 thf(fact_242_OccM_H_I1_J, axiom, (? [P5:p]: (((((isReceiverOf @ p) @ v) @ P5) @ msg)))).
% 0.32/1.50 thf(fact_243_FirstOccMsg_H, axiom, (((((((firstOccurrence @ p) @ v) @ s) @ (fe @ index)) @ (ft @ index)) @ msg) @ occM)).
% 0.32/1.50 thf(fact_244_AssumpOccMFirstOccurrence_I5_J, axiom, (! [N5:nat]: (((((ord_less_eq @ nat) @ occM2) @ N5) => ((((ord_less @ nat) @ N5) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ index))) => (msga != (((nth @ ((message @ p) @ v)) @ (ft @ index)) @ N5))))))).
% 0.32/1.50 thf(fact_245_OccM_H_I4_J, axiom, (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ index)) @ occM)) @ msg)).
% 0.32/1.50 thf(fact_246_AssumptionFairContr, axiom, (! [N5:nat]: (((((ord_less_eq @ nat) @ n) @ N5) => (! [N02:nat]: (((((ord_less @ nat) @ N02) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ N5))) => ((((ord_less_eq @ nat) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ n))) @ N02) => (msg2 != (((nth @ ((message @ p) @ v)) @ (ft @ N5)) @ N02)))))))))).
% 0.32/1.50 thf(fact_247_less__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: (((((ord_less_eq @ (A > B)) @ F2) @ G2) & (~ ((((ord_less_eq @ (A > B)) @ G2) @ F2))))))))))).
% 0.32/1.50 thf(fact_248_MessageStaysOrConsumed, axiom, (! [N1:nat,N22:nat,N:nat,Msg:((message @ p) @ v)]: ((((((ord_less_eq @ nat) @ N1) @ N22) & ((((ord_less @ nat) @ N22) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ N))) & (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ N)) @ N1)) @ Msg))) => ((((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ N)) @ N22)) @ Msg) | (? [N03:nat]: (((((ord_less_eq @ nat) @ N1) @ N03) & ((((ord_less @ nat) @ N03) @ ((size_size @ (list @ ((message @ p) @ v))) @ (ft @ N))) & ((((nth @ ((message @ p) @ v)) @ (ft @ N)) @ N03) = Msg)))))))))).
% 0.32/1.50 thf(fact_249__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_O_Alength_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Ai_A_092_060and_062_Amsg_____A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062, axiom, (~ ((? [I4:nat]: (((((ord_less @ nat) @ I4) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ (suc @ index)))) @ (one_one @ nat))) & ((((ord_less_eq @ nat) @ (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) @ (one_one @ nat))) @ I4) & (msg2 = (((nth @ ((message @ p) @ v)) @ (ft @ (suc @ index))) @ I4))))))))).
% 0.32/1.50 thf(fact_250_AssumptionFair_I4_J, axiom, ((((isReceiverOf @ p) @ v) @ p2) @ msg2)).
% 0.32/1.50 thf(fact_251_AssumpOccMFirstOccurrence_I1_J, axiom, (? [P5:p]: (((((isReceiverOf @ p) @ v) @ P5) @ msga)))).
% 0.32/1.50 thf(fact_252_AssumptionFair_I3_J, axiom, (((((enabled @ p) @ v) @ s) @ (((nth @ ((((configuration_ext @ p) @ v) @ s) @ product_unit)) @ (fe @ n)) @ n0)) @ msg2)).
% 0.32/1.50 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: (((preorder @ A8) => (preorder @ (A7 > A8)))))).
% 0.32/1.50 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: (((order @ A8) => (order @ (A7 > A8)))))).
% 0.32/1.50 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: (((ord @ A8) => (ord @ (A7 > A8)))))).
% 0.32/1.50 thf(tcon_fun___Groups_Ominus, axiom, (! [A7:$tType,A8:$tType]: (((minus @ A8) => (minus @ (A7 > A8)))))).
% 0.32/1.50 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, axiom, (linord1659791738miring @ nat)).
% 0.32/1.50 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add, axiom, (cancel146912293up_add @ nat)).
% 0.32/1.50 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, (wellorder @ nat)).
% 0.32/1.50 thf(tcon_Nat_Onat___Orderings_Opreorder_1, axiom, (preorder @ nat)).
% 0.32/1.50 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 0.32/1.50 thf(tcon_Nat_Onat___Orderings_Ono__top, axiom, (no_top @ nat)).
% 0.32/1.50 thf(tcon_Nat_Onat___Orderings_Oorder_2, axiom, (order @ nat)).
% 0.32/1.50 thf(tcon_Nat_Onat___Orderings_Oord_3, axiom, (ord @ nat)).
% 0.32/1.50 thf(tcon_Nat_Onat___Groups_Ominus_4, axiom, (minus @ nat)).
% 0.32/1.50 thf(tcon_Nat_Onat___Groups_Oone, axiom, (one @ nat)).
% 0.32/1.50 thf(tcon_Nat_Onat___Nat_Osize, axiom, (size @ nat)).
% 0.32/1.50 thf(tcon_Set_Oset___Orderings_Opreorder_5, axiom, (! [A7:$tType]: ((preorder @ (set @ A7))))).
% 0.32/1.50 thf(tcon_Set_Oset___Orderings_Oorder_6, axiom, (! [A7:$tType]: ((order @ (set @ A7))))).
% 0.32/1.50 thf(tcon_Set_Oset___Orderings_Oord_7, axiom, (! [A7:$tType]: ((ord @ (set @ A7))))).
% 0.32/1.50 thf(tcon_Set_Oset___Groups_Ominus_8, axiom, (! [A7:$tType]: ((minus @ (set @ A7))))).
% 0.32/1.50 thf(tcon_HOL_Obool___Orderings_Opreorder_9, axiom, (preorder @ $o)).
% 0.32/1.50 thf(tcon_HOL_Obool___Orderings_Olinorder_10, axiom, (linorder @ $o)).
% 0.32/1.50 thf(tcon_HOL_Obool___Orderings_Oorder_11, axiom, (order @ $o)).
% 0.32/1.50 thf(tcon_HOL_Obool___Orderings_Oord_12, axiom, (ord @ $o)).
% 0.32/1.50 thf(tcon_HOL_Obool___Groups_Ominus_13, axiom, (minus @ $o)).
% 0.32/1.50 thf(tcon_List_Olist___Nat_Osize_14, axiom, (! [A7:$tType]: ((size @ (list @ A7))))).
% 0.32/1.50 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_15, axiom, (wellorder @ product_unit)).
% 0.32/1.50 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_16, axiom, (preorder @ product_unit)).
% 0.32/1.50 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_17, axiom, (linorder @ product_unit)).
% 0.32/1.50 thf(tcon_Product__Type_Ounit___Orderings_Oorder_18, axiom, (order @ product_unit)).
% 0.32/1.50 thf(tcon_Product__Type_Ounit___Orderings_Oord_19, axiom, (ord @ product_unit)).
% 0.32/1.50 thf(tcon_Product__Type_Ounit___Groups_Ominus_20, axiom, (minus @ product_unit)).
% 0.32/1.50 thf(tcon_AsynchronousSystem_Omessage___Nat_Osize_21, axiom, (! [A7:$tType,A8:$tType]: ((size @ ((message @ A7) @ A8))))).
% 0.32/1.50 thf(conj_0, conjecture, (occM2 = (((minus_minus @ nat) @ ((size_size @ (list @ ((((configuration_ext @ p) @ v) @ s) @ product_unit))) @ (fe @ index))) @ (one_one @ nat)))).
% 0.32/1.50 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.0mkoVbkNSb/DTF2DTF32065.p
% 0.32/1.50 ------------------------
% 0.32/1.53 ---- Cleaned THF ---
% 0.32/1.53 thf(ty_t_AsynchronousSystem_Oconfiguration_Oconfiguration__ext,type,
% 0.32/1.53 configuration_ext: $tType > $tType > $tType > $tType > $tType ).
% 0.32/1.53
% 0.32/1.53 thf(ty_t_AsynchronousSystem_Omessage,type,
% 0.32/1.53 message: $tType > $tType > $tType ).
% 0.32/1.53
% 0.32/1.53 thf(ty_t_Product__Type_Ounit,type,
% 0.32/1.53 product_unit: $tType ).
% 0.32/1.53
% 0.32/1.53 thf(ty_t_List_Olist,type,
% 0.32/1.53 list: $tType > $tType ).
% 0.32/1.53
% 0.32/1.53 thf(ty_t_Set_Oset,type,
% 0.32/1.53 set: $tType > $tType ).
% 0.32/1.53
% 0.32/1.53 thf(ty_t_Nat_Onat,type,
% 0.32/1.53 nat: $tType ).
% 0.32/1.53
% 0.32/1.53 thf(ty_tf_v,type,
% 0.32/1.53 v: $tType ).
% 0.32/1.53
% 0.32/1.53 thf(ty_tf_s,type,
% 0.32/1.53 s: $tType ).
% 0.32/1.53
% 0.32/1.53 thf(ty_tf_p,type,
% 0.32/1.53 p: $tType ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_HOL_Otype,type,
% 0.32/1.53 type:
% 0.32/1.53 !>[A: $tType] : $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Nat_Osize,type,
% 0.32/1.53 size:
% 0.32/1.53 !>[A: $tType] : $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Groups_Oone,type,
% 0.32/1.53 one:
% 0.32/1.53 !>[A: $tType] : $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Groups_Ominus,type,
% 0.32/1.53 minus:
% 0.32/1.53 !>[A: $tType] : $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Orderings_Oord,type,
% 0.32/1.53 ord:
% 0.32/1.53 !>[A: $tType] : $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Orderings_Oorder,type,
% 0.32/1.53 order:
% 0.32/1.53 !>[A: $tType] : $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Groups_Ogroup__add,type,
% 0.32/1.53 group_add:
% 0.32/1.53 !>[A: $tType] : $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Orderings_Ono__bot,type,
% 0.32/1.53 no_bot:
% 0.32/1.53 !>[A: $tType] : $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Orderings_Ono__top,type,
% 0.32/1.53 no_top:
% 0.32/1.53 !>[A: $tType] : $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Orderings_Olinorder,type,
% 0.32/1.53 linorder:
% 0.32/1.53 !>[A: $tType] : $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Orderings_Opreorder,type,
% 0.32/1.53 preorder:
% 0.32/1.53 !>[A: $tType] : $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Orderings_Owellorder,type,
% 0.32/1.53 wellorder:
% 0.32/1.53 !>[A: $tType] : $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Orderings_Odense__order,type,
% 0.32/1.53 dense_order:
% 0.32/1.53 !>[A: $tType] : $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.32/1.53 dense_linorder:
% 0.32/1.53 !>[A: $tType] : $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.32/1.53 ordered_ab_group_add:
% 0.32/1.53 !>[A: $tType] : $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.32/1.53 cancel146912293up_add:
% 0.32/1.53 !>[A: $tType] : $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_cl_Rings_Olinordered__nonzero__semiring,type,
% 0.32/1.53 linord1659791738miring:
% 0.32/1.53 !>[A: $tType] : $o ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_AsynchronousSystem_Oenabled,type,
% 0.32/1.53 enabled:
% 0.32/1.53 !>[P: $tType,V: $tType,S: $tType] : ( ( configuration_ext @ P @ V @ S @ product_unit ) > ( message @ P @ V ) > $o ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_AsynchronousSystem_OisReceiverOf,type,
% 0.32/1.53 isReceiverOf:
% 0.32/1.53 !>[P: $tType,V: $tType] : ( P > ( message @ P @ V ) > $o ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Execution_Oexecution_OfirstOccurrence,type,
% 0.32/1.53 firstOccurrence:
% 0.32/1.53 !>[P: $tType,V: $tType,S: $tType] : ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( message @ P @ V ) > nat > $o ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Execution_Oexecution_OminimalEnabled,type,
% 0.32/1.53 minimalEnabled:
% 0.32/1.53 !>[P: $tType,V: $tType,S: $tType] : ( ( list @ ( configuration_ext @ P @ V @ S @ product_unit ) ) > ( list @ ( message @ P @ V ) ) > ( message @ P @ V ) > $o ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.32/1.53 minus_minus:
% 0.32/1.53 !>[A: $tType] : ( A > A > A ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.32/1.53 one_one:
% 0.32/1.53 !>[A: $tType] : A ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_ListUtilities_OprefixList,type,
% 0.32/1.53 prefixList:
% 0.32/1.53 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_List_Olist_ONil,type,
% 0.32/1.53 nil:
% 0.32/1.53 !>[A: $tType] : ( list @ A ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_List_Onth,type,
% 0.32/1.53 nth:
% 0.32/1.53 !>[A: $tType] : ( ( list @ A ) > nat > A ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Nat_OSuc,type,
% 0.32/1.53 suc: nat > nat ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Nat_Osize__class_Osize,type,
% 0.32/1.53 size_size:
% 0.32/1.53 !>[A: $tType] : ( A > nat ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.32/1.53 ord_less:
% 0.32/1.53 !>[A: $tType] : ( A > A > $o ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.32/1.53 ord_less_eq:
% 0.32/1.53 !>[A: $tType] : ( A > A > $o ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_Set_OCollect,type,
% 0.32/1.53 collect:
% 0.32/1.53 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_c_member,type,
% 0.32/1.53 member:
% 0.32/1.53 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_v_OccM_H____,type,
% 0.32/1.53 occM: nat ).
% 0.32/1.53
% 0.32/1.53 thf(sy_v_OccM____,type,
% 0.32/1.53 occM2: nat ).
% 0.32/1.53
% 0.32/1.53 thf(sy_v_consumedMsg____,type,
% 0.32/1.53 consumedMsg: message @ p @ v ).
% 0.32/1.53
% 0.32/1.53 thf(sy_v_fe____,type,
% 0.32/1.53 fe: nat > ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_v_firstOccSet____,type,
% 0.32/1.53 firstOccSet: nat > ( set @ ( message @ p @ v ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_v_ft____,type,
% 0.32/1.53 ft: nat > ( list @ ( message @ p @ v ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(sy_v_index____,type,
% 0.32/1.53 index: nat ).
% 0.32/1.53
% 0.32/1.53 thf(sy_v_msg_H____,type,
% 0.32/1.53 msg: message @ p @ v ).
% 0.32/1.53
% 0.32/1.53 thf(sy_v_msg____,type,
% 0.32/1.53 msg2: message @ p @ v ).
% 0.32/1.53
% 0.32/1.53 thf(sy_v_msga____,type,
% 0.32/1.53 msga: message @ p @ v ).
% 0.32/1.53
% 0.32/1.53 thf(sy_v_n0____,type,
% 0.32/1.53 n0: nat ).
% 0.32/1.53
% 0.32/1.53 thf(sy_v_n____,type,
% 0.32/1.53 n: nat ).
% 0.32/1.53
% 0.32/1.53 thf(sy_v_p____,type,
% 0.32/1.53 p2: p ).
% 0.32/1.53
% 0.32/1.53 thf(fact_0_AssumpOccMFirstOccurrence_I3_J,axiom,
% 0.32/1.53 ord_less @ nat @ occM2 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_1__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_AOccM_092_060close_062,axiom,
% 0.32/1.53 ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ occM2 ).
% 0.32/1.53
% 0.32/1.53 thf(fact_2_OccM_H_I3_J,axiom,
% 0.32/1.53 ord_less @ nat @ occM @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_3__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Alength_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_092_060close_062,axiom,
% 0.32/1.53 ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_4_NotEmpty_I2_J,axiom,
% 0.32/1.53 ( ( fe @ index )
% 0.32/1.53 != ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_5_minus__apply,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType] :
% 0.32/1.53 ( ( minus @ B )
% 0.32/1.53 => ( ( minus_minus @ ( A > B ) )
% 0.32/1.53 = ( ^ [A2: A > B,B2: A > B,X: A] : ( minus_minus @ B @ ( A2 @ X ) @ ( B2 @ X ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_6_AssumptionFair_I2_J,axiom,
% 0.32/1.53 ord_less @ nat @ n0 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ n ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_7_one__natural_Orsp,axiom,
% 0.32/1.53 ( ( one_one @ nat )
% 0.32/1.53 = ( one_one @ nat ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_8_diff__commute,axiom,
% 0.32/1.53 ! [I: nat,J: nat,K: nat] :
% 0.32/1.53 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I @ J ) @ K )
% 0.32/1.53 = ( minus_minus @ nat @ ( minus_minus @ nat @ I @ K ) @ J ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_9_Ex__list__of__length,axiom,
% 0.32/1.53 ! [A: $tType,N: nat] :
% 0.32/1.53 ? [Xs: list @ A] :
% 0.32/1.53 ( ( size_size @ ( list @ A ) @ Xs )
% 0.32/1.53 = N ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_10_neq__if__length__neq,axiom,
% 0.32/1.53 ! [A: $tType,Xs2: list @ A,Ys: list @ A] :
% 0.32/1.53 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.32/1.53 != ( size_size @ ( list @ A ) @ Ys ) )
% 0.32/1.53 => ( Xs2 != Ys ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_11_size__neq__size__imp__neq,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( size @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ( size_size @ A @ X2 )
% 0.32/1.53 != ( size_size @ A @ Y ) )
% 0.32/1.53 => ( X2 != Y ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_12_fun__diff__def,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType] :
% 0.32/1.53 ( ( minus @ B )
% 0.32/1.53 => ( ( minus_minus @ ( A > B ) )
% 0.32/1.53 = ( ^ [A2: A > B,B2: A > B,X: A] : ( minus_minus @ B @ ( A2 @ X ) @ ( B2 @ X ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_13_diff__eq__diff__eq,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( group_add @ A )
% 0.32/1.53 => ! [A3: A,B3: A,C: A,D: A] :
% 0.32/1.53 ( ( ( minus_minus @ A @ A3 @ B3 )
% 0.32/1.53 = ( minus_minus @ A @ C @ D ) )
% 0.32/1.53 => ( ( A3 = B3 )
% 0.32/1.53 = ( C = D ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_14_nat_Oinject,axiom,
% 0.32/1.53 ! [X22: nat,Y2: nat] :
% 0.32/1.53 ( ( ( suc @ X22 )
% 0.32/1.53 = ( suc @ Y2 ) )
% 0.32/1.53 = ( X22 = Y2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_15_old_Onat_Oinject,axiom,
% 0.32/1.53 ! [Nat: nat,Nat2: nat] :
% 0.32/1.53 ( ( ( suc @ Nat )
% 0.32/1.53 = ( suc @ Nat2 ) )
% 0.32/1.53 = ( Nat = Nat2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_16_NotEmpty_I1_J,axiom,
% 0.32/1.53 ( ( fe @ ( suc @ index ) )
% 0.32/1.53 != ( nil @ ( configuration_ext @ p @ v @ s @ product_unit ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_17_lessI,axiom,
% 0.32/1.53 ! [N: nat] : ( ord_less @ nat @ N @ ( suc @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_18_Suc__mono,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ M @ N )
% 0.32/1.53 => ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_19_Suc__less__eq,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.32/1.53 = ( ord_less @ nat @ M @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_20_Suc__le__mono,axiom,
% 0.32/1.53 ! [N: nat,M: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.32/1.53 = ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_21_Suc__diff__diff,axiom,
% 0.32/1.53 ! [M: nat,N: nat,K: nat] :
% 0.32/1.53 ( ( minus_minus @ nat @ ( minus_minus @ nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 0.32/1.53 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ N ) @ K ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_22_diff__Suc__Suc,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( minus_minus @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.32/1.53 = ( minus_minus @ nat @ M @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_23_diff__diff__cancel,axiom,
% 0.32/1.53 ! [I: nat,N: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ I @ N )
% 0.32/1.53 => ( ( minus_minus @ nat @ N @ ( minus_minus @ nat @ N @ I ) )
% 0.32/1.53 = I ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_24_diff__Suc__1,axiom,
% 0.32/1.53 ! [N: nat] :
% 0.32/1.53 ( ( minus_minus @ nat @ ( suc @ N ) @ ( one_one @ nat ) )
% 0.32/1.53 = N ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_25_Nat_OlessE,axiom,
% 0.32/1.53 ! [I: nat,K: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I @ K )
% 0.32/1.53 => ( ( K
% 0.32/1.53 != ( suc @ I ) )
% 0.32/1.53 => ~ ! [J2: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I @ J2 )
% 0.32/1.53 => ( K
% 0.32/1.53 != ( suc @ J2 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_26_Suc__leD,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 0.32/1.53 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_27_Suc__leI,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ M @ N )
% 0.32/1.53 => ( ord_less_eq @ nat @ ( suc @ M ) @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_28_le__SucE,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ M @ ( suc @ N ) )
% 0.32/1.53 => ( ~ ( ord_less_eq @ nat @ M @ N )
% 0.32/1.53 => ( M
% 0.32/1.53 = ( suc @ N ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_29_le__SucI,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ M @ N )
% 0.32/1.53 => ( ord_less_eq @ nat @ M @ ( suc @ N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_30_le__refl,axiom,
% 0.32/1.53 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_31_Suc__le__D,axiom,
% 0.32/1.53 ! [N: nat,M2: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ ( suc @ N ) @ M2 )
% 0.32/1.53 => ? [M3: nat] :
% 0.32/1.53 ( M2
% 0.32/1.53 = ( suc @ M3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_32_le__trans,axiom,
% 0.32/1.53 ! [I: nat,J: nat,K: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ I @ J )
% 0.32/1.53 => ( ( ord_less_eq @ nat @ J @ K )
% 0.32/1.53 => ( ord_less_eq @ nat @ I @ K ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_33_Suc__le__eq,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 0.32/1.53 = ( ord_less @ nat @ M @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_34_Suc__lessD,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ ( suc @ M ) @ N )
% 0.32/1.53 => ( ord_less @ nat @ M @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_35_Suc__lessE,axiom,
% 0.32/1.53 ! [I: nat,K: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ ( suc @ I ) @ K )
% 0.32/1.53 => ~ ! [J2: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I @ J2 )
% 0.32/1.53 => ( K
% 0.32/1.53 != ( suc @ J2 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_36_Suc__lessI,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ M @ N )
% 0.32/1.53 => ( ( ( suc @ M )
% 0.32/1.53 != N )
% 0.32/1.53 => ( ord_less @ nat @ ( suc @ M ) @ N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_37_eq__imp__le,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( M = N )
% 0.32/1.53 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_38_le__Suc__eq,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ M @ ( suc @ N ) )
% 0.32/1.53 = ( ( ord_less_eq @ nat @ M @ N )
% 0.32/1.53 | ( M
% 0.32/1.53 = ( suc @ N ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_39_less__SucE,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.32/1.53 => ( ~ ( ord_less @ nat @ M @ N )
% 0.32/1.53 => ( M = N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_40_less__SucI,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ M @ N )
% 0.32/1.53 => ( ord_less @ nat @ M @ ( suc @ N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_41_Suc__inject,axiom,
% 0.32/1.53 ! [X2: nat,Y: nat] :
% 0.32/1.53 ( ( ( suc @ X2 )
% 0.32/1.53 = ( suc @ Y ) )
% 0.32/1.53 => ( X2 = Y ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_42_dec__induct,axiom,
% 0.32/1.53 ! [I: nat,J: nat,P2: nat > $o] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ I @ J )
% 0.32/1.53 => ( ( P2 @ I )
% 0.32/1.53 => ( ! [N2: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ I @ N2 )
% 0.32/1.53 => ( ( ord_less @ nat @ N2 @ J )
% 0.32/1.53 => ( ( P2 @ N2 )
% 0.32/1.53 => ( P2 @ ( suc @ N2 ) ) ) ) )
% 0.32/1.53 => ( P2 @ J ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_43_mem__Collect__eq,axiom,
% 0.32/1.53 ! [A: $tType,A3: A,P2: A > $o] :
% 0.32/1.53 ( ( member @ A @ A3 @ ( collect @ A @ P2 ) )
% 0.32/1.53 = ( P2 @ A3 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_44_Collect__mem__eq,axiom,
% 0.32/1.53 ! [A: $tType,A4: set @ A] :
% 0.32/1.53 ( ( collect @ A
% 0.32/1.53 @ ^ [X: A] : ( member @ A @ X @ A4 ) )
% 0.32/1.53 = A4 ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_45_Collect__cong,axiom,
% 0.32/1.53 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.32/1.53 ( ! [X3: A] :
% 0.32/1.53 ( ( P2 @ X3 )
% 0.32/1.53 = ( Q @ X3 ) )
% 0.32/1.53 => ( ( collect @ A @ P2 )
% 0.32/1.53 = ( collect @ A @ Q ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_46_ext,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.32/1.53 ( ! [X3: A] :
% 0.32/1.53 ( ( F @ X3 )
% 0.32/1.53 = ( G @ X3 ) )
% 0.32/1.53 => ( F = G ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_47_inc__induct,axiom,
% 0.32/1.53 ! [I: nat,J: nat,P2: nat > $o] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ I @ J )
% 0.32/1.53 => ( ( P2 @ J )
% 0.32/1.53 => ( ! [N2: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ I @ N2 )
% 0.32/1.53 => ( ( ord_less @ nat @ N2 @ J )
% 0.32/1.53 => ( ( P2 @ ( suc @ N2 ) )
% 0.32/1.53 => ( P2 @ N2 ) ) ) )
% 0.32/1.53 => ( P2 @ I ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_48_le__antisym,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ M @ N )
% 0.32/1.53 => ( ( ord_less_eq @ nat @ N @ M )
% 0.32/1.53 => ( M = N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_49_Ex__less__Suc,axiom,
% 0.32/1.53 ! [N: nat,P2: nat > $o] :
% 0.32/1.53 ( ( ? [I2: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I2 @ ( suc @ N ) )
% 0.32/1.53 & ( P2 @ I2 ) ) )
% 0.32/1.53 = ( ( P2 @ N )
% 0.32/1.53 | ? [I2: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I2 @ N )
% 0.32/1.53 & ( P2 @ I2 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_50_less__Suc__eq,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.32/1.53 = ( ( ord_less @ nat @ M @ N )
% 0.32/1.53 | ( M = N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_51_n__not__Suc__n,axiom,
% 0.32/1.53 ! [N: nat] :
% 0.32/1.53 ( N
% 0.32/1.53 != ( suc @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_52_nat__less__le,axiom,
% 0.32/1.53 ( ( ord_less @ nat )
% 0.32/1.53 = ( ^ [M4: nat,N3: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ M4 @ N3 )
% 0.32/1.53 & ( M4 != N3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_53_nat__neq__iff,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( M != N )
% 0.32/1.53 = ( ( ord_less @ nat @ M @ N )
% 0.32/1.53 | ( ord_less @ nat @ N @ M ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_54_not__less__eq,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ~ ( ord_less @ nat @ M @ N ) )
% 0.32/1.53 = ( ord_less @ nat @ N @ ( suc @ M ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_55_All__less__Suc,axiom,
% 0.32/1.53 ! [N: nat,P2: nat > $o] :
% 0.32/1.53 ( ( ! [I2: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I2 @ ( suc @ N ) )
% 0.32/1.53 => ( P2 @ I2 ) ) )
% 0.32/1.53 = ( ( P2 @ N )
% 0.32/1.53 & ! [I2: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I2 @ N )
% 0.32/1.53 => ( P2 @ I2 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_56_Suc__le__lessD,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ ( suc @ M ) @ N )
% 0.32/1.53 => ( ord_less @ nat @ M @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_57_Suc__less__eq2,axiom,
% 0.32/1.53 ! [N: nat,M: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ ( suc @ N ) @ M )
% 0.32/1.53 = ( ? [M5: nat] :
% 0.32/1.53 ( ( M
% 0.32/1.53 = ( suc @ M5 ) )
% 0.32/1.53 & ( ord_less @ nat @ N @ M5 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_58_less__antisym,axiom,
% 0.32/1.53 ! [N: nat,M: nat] :
% 0.32/1.53 ( ~ ( ord_less @ nat @ N @ M )
% 0.32/1.53 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 0.32/1.53 => ( M = N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_59_Suc__less__SucD,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.32/1.53 => ( ord_less @ nat @ M @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_60_less__not__refl,axiom,
% 0.32/1.53 ! [N: nat] :
% 0.32/1.53 ~ ( ord_less @ nat @ N @ N ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_61_nat__le__linear,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ M @ N )
% 0.32/1.53 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_62_Suc__n__not__le__n,axiom,
% 0.32/1.53 ! [N: nat] :
% 0.32/1.53 ~ ( ord_less_eq @ nat @ ( suc @ N ) @ N ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_63_le__less__Suc__eq,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ M @ N )
% 0.32/1.53 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 0.32/1.53 = ( N = M ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_64_less__Suc__eq__le,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ M @ ( suc @ N ) )
% 0.32/1.53 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_65_less__eq__Suc__le,axiom,
% 0.32/1.53 ( ( ord_less @ nat )
% 0.32/1.53 = ( ^ [N3: nat] : ( ord_less_eq @ nat @ ( suc @ N3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_66_less__not__refl2,axiom,
% 0.32/1.53 ! [N: nat,M: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ N @ M )
% 0.32/1.53 => ( M != N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_67_less__not__refl3,axiom,
% 0.32/1.53 ! [S2: nat,T: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ S2 @ T )
% 0.32/1.53 => ( S2 != T ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_68_less__trans__Suc,axiom,
% 0.32/1.53 ! [I: nat,J: nat,K: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I @ J )
% 0.32/1.53 => ( ( ord_less @ nat @ J @ K )
% 0.32/1.53 => ( ord_less @ nat @ ( suc @ I ) @ K ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_69_measure__induct,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType] :
% 0.32/1.53 ( ( wellorder @ B )
% 0.32/1.53 => ! [F: A > B,P2: A > $o,A3: A] :
% 0.32/1.53 ( ! [X3: A] :
% 0.32/1.53 ( ! [Y3: A] :
% 0.32/1.53 ( ( ord_less @ B @ ( F @ Y3 ) @ ( F @ X3 ) )
% 0.32/1.53 => ( P2 @ Y3 ) )
% 0.32/1.53 => ( P2 @ X3 ) )
% 0.32/1.53 => ( P2 @ A3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_70_not__less__eq__eq,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ~ ( ord_less_eq @ nat @ M @ N ) )
% 0.32/1.53 = ( ord_less_eq @ nat @ ( suc @ N ) @ M ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_71_full__nat__induct,axiom,
% 0.32/1.53 ! [P2: nat > $o,N: nat] :
% 0.32/1.53 ( ! [N2: nat] :
% 0.32/1.53 ( ! [M6: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ ( suc @ M6 ) @ N2 )
% 0.32/1.53 => ( P2 @ M6 ) )
% 0.32/1.53 => ( P2 @ N2 ) )
% 0.32/1.53 => ( P2 @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_72_le__imp__less__Suc,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ M @ N )
% 0.32/1.53 => ( ord_less @ nat @ M @ ( suc @ N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_73_less__Suc__induct,axiom,
% 0.32/1.53 ! [I: nat,J: nat,P2: nat > nat > $o] :
% 0.32/1.53 ( ( ord_less @ nat @ I @ J )
% 0.32/1.53 => ( ! [I3: nat] : ( P2 @ I3 @ ( suc @ I3 ) )
% 0.32/1.53 => ( ! [I3: nat,J2: nat,K2: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I3 @ J2 )
% 0.32/1.53 => ( ( ord_less @ nat @ J2 @ K2 )
% 0.32/1.53 => ( ( P2 @ I3 @ J2 )
% 0.32/1.53 => ( ( P2 @ J2 @ K2 )
% 0.32/1.53 => ( P2 @ I3 @ K2 ) ) ) ) )
% 0.32/1.53 => ( P2 @ I @ J ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_74_less__imp__le__nat,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ M @ N )
% 0.32/1.53 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_75_less__irrefl__nat,axiom,
% 0.32/1.53 ! [N: nat] :
% 0.32/1.53 ~ ( ord_less @ nat @ N @ N ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_76_nat__less__induct,axiom,
% 0.32/1.53 ! [P2: nat > $o,N: nat] :
% 0.32/1.53 ( ! [N2: nat] :
% 0.32/1.53 ( ! [M6: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ M6 @ N2 )
% 0.32/1.53 => ( P2 @ M6 ) )
% 0.32/1.53 => ( P2 @ N2 ) )
% 0.32/1.53 => ( P2 @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_77_infinite__descent,axiom,
% 0.32/1.53 ! [P2: nat > $o,N: nat] :
% 0.32/1.53 ( ! [N2: nat] :
% 0.32/1.53 ( ~ ( P2 @ N2 )
% 0.32/1.53 => ? [M6: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ M6 @ N2 )
% 0.32/1.53 & ~ ( P2 @ M6 ) ) )
% 0.32/1.53 => ( P2 @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_78_le__eq__less__or__eq,axiom,
% 0.32/1.53 ( ( ord_less_eq @ nat )
% 0.32/1.53 = ( ^ [M4: nat,N3: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ M4 @ N3 )
% 0.32/1.53 | ( M4 = N3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_79_less__or__eq__imp__le,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ( ord_less @ nat @ M @ N )
% 0.32/1.53 | ( M = N ) )
% 0.32/1.53 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_80_linorder__neqE__nat,axiom,
% 0.32/1.53 ! [X2: nat,Y: nat] :
% 0.32/1.53 ( ( X2 != Y )
% 0.32/1.53 => ( ~ ( ord_less @ nat @ X2 @ Y )
% 0.32/1.53 => ( ord_less @ nat @ Y @ X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_81_strict__inc__induct,axiom,
% 0.32/1.53 ! [I: nat,J: nat,P2: nat > $o] :
% 0.32/1.53 ( ( ord_less @ nat @ I @ J )
% 0.32/1.53 => ( ! [I3: nat] :
% 0.32/1.53 ( ( J
% 0.32/1.53 = ( suc @ I3 ) )
% 0.32/1.53 => ( P2 @ I3 ) )
% 0.32/1.53 => ( ! [I3: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I3 @ J )
% 0.32/1.53 => ( ( P2 @ ( suc @ I3 ) )
% 0.32/1.53 => ( P2 @ I3 ) ) )
% 0.32/1.53 => ( P2 @ I ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_82_Nat_Oex__has__greatest__nat,axiom,
% 0.32/1.53 ! [P2: nat > $o,K: nat,B3: nat] :
% 0.32/1.53 ( ( P2 @ K )
% 0.32/1.53 => ( ! [Y4: nat] :
% 0.32/1.53 ( ( P2 @ Y4 )
% 0.32/1.53 => ( ord_less_eq @ nat @ Y4 @ B3 ) )
% 0.32/1.53 => ? [X3: nat] :
% 0.32/1.53 ( ( P2 @ X3 )
% 0.32/1.53 & ! [Y3: nat] :
% 0.32/1.53 ( ( P2 @ Y3 )
% 0.32/1.53 => ( ord_less_eq @ nat @ Y3 @ X3 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_83_le__neq__implies__less,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ M @ N )
% 0.32/1.53 => ( ( M != N )
% 0.32/1.53 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_84_measure__induct__rule,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType] :
% 0.32/1.53 ( ( wellorder @ B )
% 0.32/1.53 => ! [F: A > B,P2: A > $o,A3: A] :
% 0.32/1.53 ( ! [X3: A] :
% 0.32/1.53 ( ! [Y3: A] :
% 0.32/1.53 ( ( ord_less @ B @ ( F @ Y3 ) @ ( F @ X3 ) )
% 0.32/1.53 => ( P2 @ Y3 ) )
% 0.32/1.53 => ( P2 @ X3 ) )
% 0.32/1.53 => ( P2 @ A3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_85_nat__induct__at__least,axiom,
% 0.32/1.53 ! [M: nat,N: nat,P2: nat > $o] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ M @ N )
% 0.32/1.53 => ( ( P2 @ M )
% 0.32/1.53 => ( ! [N2: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ M @ N2 )
% 0.32/1.53 => ( ( P2 @ N2 )
% 0.32/1.53 => ( P2 @ ( suc @ N2 ) ) ) )
% 0.32/1.53 => ( P2 @ N ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_86_not__less__less__Suc__eq,axiom,
% 0.32/1.53 ! [N: nat,M: nat] :
% 0.32/1.53 ( ~ ( ord_less @ nat @ N @ M )
% 0.32/1.53 => ( ( ord_less @ nat @ N @ ( suc @ M ) )
% 0.32/1.53 = ( N = M ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_87_less__mono__imp__le__mono,axiom,
% 0.32/1.53 ! [F: nat > nat,I: nat,J: nat] :
% 0.32/1.53 ( ! [I3: nat,J2: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I3 @ J2 )
% 0.32/1.53 => ( ord_less @ nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 0.32/1.53 => ( ( ord_less_eq @ nat @ I @ J )
% 0.32/1.53 => ( ord_less_eq @ nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_88_transitive__stepwise__le,axiom,
% 0.32/1.53 ! [M: nat,N: nat,R: nat > nat > $o] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ M @ N )
% 0.32/1.53 => ( ! [X3: nat] : ( R @ X3 @ X3 )
% 0.32/1.53 => ( ! [X3: nat,Y4: nat,Z: nat] :
% 0.32/1.53 ( ( R @ X3 @ Y4 )
% 0.32/1.53 => ( ( R @ Y4 @ Z )
% 0.32/1.53 => ( R @ X3 @ Z ) ) )
% 0.32/1.53 => ( ! [N2: nat] : ( R @ N2 @ ( suc @ N2 ) )
% 0.32/1.53 => ( R @ M @ N ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_89_infinite__descent__measure,axiom,
% 0.32/1.53 ! [A: $tType,P2: A > $o,V2: A > nat,X2: A] :
% 0.32/1.53 ( ! [X3: A] :
% 0.32/1.53 ( ~ ( P2 @ X3 )
% 0.32/1.53 => ? [Y3: A] :
% 0.32/1.53 ( ( ord_less @ nat @ ( V2 @ Y3 ) @ ( V2 @ X3 ) )
% 0.32/1.53 & ~ ( P2 @ Y3 ) ) )
% 0.32/1.53 => ( P2 @ X2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_90_lift__Suc__mono__le,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [F: nat > A,N: nat,N4: nat] :
% 0.32/1.53 ( ! [N2: nat] : ( ord_less_eq @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/1.53 => ( ( ord_less_eq @ nat @ N @ N4 )
% 0.32/1.53 => ( ord_less_eq @ A @ ( F @ N ) @ ( F @ N4 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_91_lift__Suc__mono__less,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [F: nat > A,N: nat,N4: nat] :
% 0.32/1.53 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/1.53 => ( ( ord_less @ nat @ N @ N4 )
% 0.32/1.53 => ( ord_less @ A @ ( F @ N ) @ ( F @ N4 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_92_lift__Suc__antimono__le,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [F: nat > A,N: nat,N4: nat] :
% 0.32/1.53 ( ! [N2: nat] : ( ord_less_eq @ A @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 0.32/1.53 => ( ( ord_less_eq @ nat @ N @ N4 )
% 0.32/1.53 => ( ord_less_eq @ A @ ( F @ N4 ) @ ( F @ N ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_93_lift__Suc__mono__less__iff,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [F: nat > A,N: nat,M: nat] :
% 0.32/1.53 ( ! [N2: nat] : ( ord_less @ A @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 0.32/1.53 => ( ( ord_less @ A @ ( F @ N ) @ ( F @ M ) )
% 0.32/1.53 = ( ord_less @ nat @ N @ M ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_94_diff__less__Suc,axiom,
% 0.32/1.53 ! [M: nat,N: nat] : ( ord_less @ nat @ ( minus_minus @ nat @ M @ N ) @ ( suc @ M ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_95_Suc__diff__Suc,axiom,
% 0.32/1.53 ! [N: nat,M: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ N @ M )
% 0.32/1.53 => ( ( suc @ ( minus_minus @ nat @ M @ ( suc @ N ) ) )
% 0.32/1.53 = ( minus_minus @ nat @ M @ N ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_96_Suc__diff__le,axiom,
% 0.32/1.53 ! [N: nat,M: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ N @ M )
% 0.32/1.53 => ( ( minus_minus @ nat @ ( suc @ M ) @ N )
% 0.32/1.53 = ( suc @ ( minus_minus @ nat @ M @ N ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_97_zero__induct__lemma,axiom,
% 0.32/1.53 ! [P2: nat > $o,K: nat,I: nat] :
% 0.32/1.53 ( ( P2 @ K )
% 0.32/1.53 => ( ! [N2: nat] :
% 0.32/1.53 ( ( P2 @ ( suc @ N2 ) )
% 0.32/1.53 => ( P2 @ N2 ) )
% 0.32/1.53 => ( P2 @ ( minus_minus @ nat @ K @ I ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_98_diff__less__mono,axiom,
% 0.32/1.53 ! [A3: nat,B3: nat,C: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ A3 @ B3 )
% 0.32/1.53 => ( ( ord_less_eq @ nat @ C @ A3 )
% 0.32/1.53 => ( ord_less @ nat @ ( minus_minus @ nat @ A3 @ C ) @ ( minus_minus @ nat @ B3 @ C ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_99_less__diff__iff,axiom,
% 0.32/1.53 ! [K: nat,M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ K @ M )
% 0.32/1.53 => ( ( ord_less_eq @ nat @ K @ N )
% 0.32/1.53 => ( ( ord_less @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 0.32/1.53 = ( ord_less @ nat @ M @ N ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_100_diff__Suc__eq__diff__pred,axiom,
% 0.32/1.53 ! [M: nat,N: nat] :
% 0.32/1.53 ( ( minus_minus @ nat @ M @ ( suc @ N ) )
% 0.32/1.53 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ ( one_one @ nat ) ) @ N ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_101_diff__strict__right__mono,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( ordered_ab_group_add @ A )
% 0.32/1.53 => ! [A3: A,B3: A,C: A] :
% 0.32/1.53 ( ( ord_less @ A @ A3 @ B3 )
% 0.32/1.53 => ( ord_less @ A @ ( minus_minus @ A @ A3 @ C ) @ ( minus_minus @ A @ B3 @ C ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_102_diff__strict__left__mono,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( ordered_ab_group_add @ A )
% 0.32/1.53 => ! [B3: A,A3: A,C: A] :
% 0.32/1.53 ( ( ord_less @ A @ B3 @ A3 )
% 0.32/1.53 => ( ord_less @ A @ ( minus_minus @ A @ C @ A3 ) @ ( minus_minus @ A @ C @ B3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_103_diff__eq__diff__less,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( ordered_ab_group_add @ A )
% 0.32/1.53 => ! [A3: A,B3: A,C: A,D: A] :
% 0.32/1.53 ( ( ( minus_minus @ A @ A3 @ B3 )
% 0.32/1.53 = ( minus_minus @ A @ C @ D ) )
% 0.32/1.53 => ( ( ord_less @ A @ A3 @ B3 )
% 0.32/1.53 = ( ord_less @ A @ C @ D ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_104_diff__strict__mono,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( ordered_ab_group_add @ A )
% 0.32/1.53 => ! [A3: A,B3: A,D: A,C: A] :
% 0.32/1.53 ( ( ord_less @ A @ A3 @ B3 )
% 0.32/1.53 => ( ( ord_less @ A @ D @ C )
% 0.32/1.53 => ( ord_less @ A @ ( minus_minus @ A @ A3 @ C ) @ ( minus_minus @ A @ B3 @ D ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_105_diff__eq__diff__less__eq,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( ordered_ab_group_add @ A )
% 0.32/1.53 => ! [A3: A,B3: A,C: A,D: A] :
% 0.32/1.53 ( ( ( minus_minus @ A @ A3 @ B3 )
% 0.32/1.53 = ( minus_minus @ A @ C @ D ) )
% 0.32/1.53 => ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/1.53 = ( ord_less_eq @ A @ C @ D ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_106_diff__right__mono,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( ordered_ab_group_add @ A )
% 0.32/1.53 => ! [A3: A,B3: A,C: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/1.53 => ( ord_less_eq @ A @ ( minus_minus @ A @ A3 @ C ) @ ( minus_minus @ A @ B3 @ C ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_107_diff__left__mono,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( ordered_ab_group_add @ A )
% 0.32/1.53 => ! [B3: A,A3: A,C: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.32/1.53 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A3 ) @ ( minus_minus @ A @ C @ B3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_108_diff__mono,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( ordered_ab_group_add @ A )
% 0.32/1.53 => ! [A3: A,B3: A,D: A,C: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/1.53 => ( ( ord_less_eq @ A @ D @ C )
% 0.32/1.53 => ( ord_less_eq @ A @ ( minus_minus @ A @ A3 @ C ) @ ( minus_minus @ A @ B3 @ D ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_109_length__induct,axiom,
% 0.32/1.53 ! [A: $tType,P2: ( list @ A ) > $o,Xs2: list @ A] :
% 0.32/1.53 ( ! [Xs: list @ A] :
% 0.32/1.53 ( ! [Ys2: list @ A] :
% 0.32/1.53 ( ( ord_less @ nat @ ( size_size @ ( list @ A ) @ Ys2 ) @ ( size_size @ ( list @ A ) @ Xs ) )
% 0.32/1.53 => ( P2 @ Ys2 ) )
% 0.32/1.53 => ( P2 @ Xs ) )
% 0.32/1.53 => ( P2 @ Xs2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_110_less__imp__diff__less,axiom,
% 0.32/1.53 ! [J: nat,K: nat,N: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ J @ K )
% 0.32/1.53 => ( ord_less @ nat @ ( minus_minus @ nat @ J @ N ) @ K ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_111_diff__less__mono2,axiom,
% 0.32/1.53 ! [M: nat,N: nat,L: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ M @ N )
% 0.32/1.53 => ( ( ord_less @ nat @ M @ L )
% 0.32/1.53 => ( ord_less @ nat @ ( minus_minus @ nat @ L @ N ) @ ( minus_minus @ nat @ L @ M ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_112_diff__le__mono2,axiom,
% 0.32/1.53 ! [M: nat,N: nat,L: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ M @ N )
% 0.32/1.53 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ L @ N ) @ ( minus_minus @ nat @ L @ M ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_113_le__diff__iff_H,axiom,
% 0.32/1.53 ! [A3: nat,C: nat,B3: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ A3 @ C )
% 0.32/1.53 => ( ( ord_less_eq @ nat @ B3 @ C )
% 0.32/1.53 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ A3 ) @ ( minus_minus @ nat @ C @ B3 ) )
% 0.32/1.53 = ( ord_less_eq @ nat @ B3 @ A3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_114_diff__le__self,axiom,
% 0.32/1.53 ! [M: nat,N: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ N ) @ M ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_115_diff__le__mono,axiom,
% 0.32/1.53 ! [M: nat,N: nat,L: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ M @ N )
% 0.32/1.53 => ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ L ) @ ( minus_minus @ nat @ N @ L ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_116_Nat_Odiff__diff__eq,axiom,
% 0.32/1.53 ! [K: nat,M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ K @ M )
% 0.32/1.53 => ( ( ord_less_eq @ nat @ K @ N )
% 0.32/1.53 => ( ( minus_minus @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 0.32/1.53 = ( minus_minus @ nat @ M @ N ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_117_le__diff__iff,axiom,
% 0.32/1.53 ! [K: nat,M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ K @ M )
% 0.32/1.53 => ( ( ord_less_eq @ nat @ K @ N )
% 0.32/1.53 => ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ M @ K ) @ ( minus_minus @ nat @ N @ K ) )
% 0.32/1.53 = ( ord_less_eq @ nat @ M @ N ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_118_eq__diff__iff,axiom,
% 0.32/1.53 ! [K: nat,M: nat,N: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ K @ M )
% 0.32/1.53 => ( ( ord_less_eq @ nat @ K @ N )
% 0.32/1.53 => ( ( ( minus_minus @ nat @ M @ K )
% 0.32/1.53 = ( minus_minus @ nat @ N @ K ) )
% 0.32/1.53 = ( M = N ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_119_one__reorient,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( one @ A )
% 0.32/1.53 => ! [X2: A] :
% 0.32/1.53 ( ( ( one_one @ A )
% 0.32/1.53 = X2 )
% 0.32/1.53 = ( X2
% 0.32/1.53 = ( one_one @ A ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_120_diff__right__commute,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( cancel146912293up_add @ A )
% 0.32/1.53 => ! [A3: A,C: A,B3: A] :
% 0.32/1.53 ( ( minus_minus @ A @ ( minus_minus @ A @ A3 @ C ) @ B3 )
% 0.32/1.53 = ( minus_minus @ A @ ( minus_minus @ A @ A3 @ B3 ) @ C ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_121_Subset,axiom,
% 0.32/1.53 ! [MsgInSet: message @ p @ v] :
% 0.32/1.53 ( ( member @ ( message @ p @ v ) @ MsgInSet @ ( firstOccSet @ ( suc @ index ) ) )
% 0.32/1.53 => ( member @ ( message @ p @ v ) @ MsgInSet @ ( firstOccSet @ index ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_122_SameCfgOnLow,axiom,
% 0.32/1.53 ! [I4: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) )
% 0.32/1.53 => ( ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ I4 )
% 0.32/1.53 = ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_123__092_060open_062_092_060not_062_AOccM_A_060_Alength_A_Ift_Aindex_J_092_060close_062,axiom,
% 0.32/1.53 ~ ( ord_less @ nat @ occM2 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_124_IPrefixListEx,axiom,
% 0.32/1.53 ! [I4: nat] : ( prefixList @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ I4 ) @ ( fe @ ( suc @ I4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_125_order__refl,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( preorder @ A )
% 0.32/1.53 => ! [X2: A] : ( ord_less_eq @ A @ X2 @ X2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_126_nat__descend__induct,axiom,
% 0.32/1.53 ! [N: nat,P2: nat > $o,M: nat] :
% 0.32/1.53 ( ! [K2: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ N @ K2 )
% 0.32/1.53 => ( P2 @ K2 ) )
% 0.32/1.53 => ( ! [K2: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ K2 @ N )
% 0.32/1.53 => ( ! [I4: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ K2 @ I4 )
% 0.32/1.53 => ( P2 @ I4 ) )
% 0.32/1.53 => ( P2 @ K2 ) ) )
% 0.32/1.53 => ( P2 @ M ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_127_Lattices__Big_Oex__has__greatest__nat,axiom,
% 0.32/1.53 ! [A: $tType,P2: A > $o,K: A,F: A > nat,B3: nat] :
% 0.32/1.53 ( ( P2 @ K )
% 0.32/1.53 => ( ! [Y4: A] :
% 0.32/1.53 ( ( P2 @ Y4 )
% 0.32/1.53 => ( ord_less @ nat @ ( F @ Y4 ) @ B3 ) )
% 0.32/1.53 => ? [X3: A] :
% 0.32/1.53 ( ( P2 @ X3 )
% 0.32/1.53 & ! [Y3: A] :
% 0.32/1.53 ( ( P2 @ Y3 )
% 0.32/1.53 => ( ord_less_eq @ nat @ ( F @ Y3 ) @ ( F @ X3 ) ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_128_KeepProperty,axiom,
% 0.32/1.53 ! [Low: nat,P2: nat > $o,Q: nat > $o] :
% 0.32/1.53 ( ! [I3: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ Low @ I3 )
% 0.32/1.53 => ( ( P2 @ I3 )
% 0.32/1.53 => ( ( P2 @ ( suc @ I3 ) )
% 0.32/1.53 & ( Q @ I3 ) ) ) )
% 0.32/1.53 => ( ( P2 @ Low )
% 0.32/1.53 => ! [I4: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ Low @ I4 )
% 0.32/1.53 => ( Q @ I4 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_129_less__numeral__extra_I4_J,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linord1659791738miring @ A )
% 0.32/1.53 => ~ ( ord_less @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_130_le__numeral__extra_I4_J,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linord1659791738miring @ A )
% 0.32/1.53 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_131_LengthStep,axiom,
% 0.32/1.53 ord_less @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ ( suc @ index ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_132_ConsumedMsg_I1_J,axiom,
% 0.32/1.53 minimalEnabled @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ consumedMsg ).
% 0.32/1.53
% 0.32/1.53 thf(fact_133_PrefixListTransitive,axiom,
% 0.32/1.53 ! [A: $tType,L1: list @ A,L2: list @ A,L3: list @ A] :
% 0.32/1.53 ( ( prefixList @ A @ L1 @ L2 )
% 0.32/1.53 => ( ( prefixList @ A @ L2 @ L3 )
% 0.32/1.53 => ( prefixList @ A @ L1 @ L3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_134_PrefixSameOnLow,axiom,
% 0.32/1.53 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 0.32/1.53 ( ( prefixList @ A @ L1 @ L2 )
% 0.32/1.53 => ! [Index: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ Index @ ( size_size @ ( list @ A ) @ L1 ) )
% 0.32/1.53 => ( ( nth @ A @ L1 @ Index )
% 0.32/1.53 = ( nth @ A @ L2 @ Index ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_135_PrefixListMonotonicity,axiom,
% 0.32/1.53 ! [A: $tType,L1: list @ A,L2: list @ A] :
% 0.32/1.53 ( ( prefixList @ A @ L1 @ L2 )
% 0.32/1.53 => ( ord_less @ nat @ ( size_size @ ( list @ A ) @ L1 ) @ ( size_size @ ( list @ A ) @ L2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_136_nth__equalityI,axiom,
% 0.32/1.53 ! [A: $tType,Xs2: list @ A,Ys: list @ A] :
% 0.32/1.53 ( ( ( size_size @ ( list @ A ) @ Xs2 )
% 0.32/1.53 = ( size_size @ ( list @ A ) @ Ys ) )
% 0.32/1.53 => ( ! [I3: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I3 @ ( size_size @ ( list @ A ) @ Xs2 ) )
% 0.32/1.53 => ( ( nth @ A @ Xs2 @ I3 )
% 0.32/1.53 = ( nth @ A @ Ys @ I3 ) ) )
% 0.32/1.53 => ( Xs2 = Ys ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_137_Skolem__list__nth,axiom,
% 0.32/1.53 ! [A: $tType,K: nat,P2: nat > A > $o] :
% 0.32/1.53 ( ( ! [I2: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I2 @ K )
% 0.32/1.53 => ? [X4: A] : ( P2 @ I2 @ X4 ) ) )
% 0.32/1.53 = ( ? [Xs3: list @ A] :
% 0.32/1.53 ( ( ( size_size @ ( list @ A ) @ Xs3 )
% 0.32/1.53 = K )
% 0.32/1.53 & ! [I2: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I2 @ K )
% 0.32/1.53 => ( P2 @ I2 @ ( nth @ A @ Xs3 @ I2 ) ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_138_list__eq__iff__nth__eq,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( ^ [Y5: list @ A,Z2: list @ A] : ( Y5 = Z2 ) )
% 0.32/1.53 = ( ^ [Xs3: list @ A,Ys3: list @ A] :
% 0.32/1.53 ( ( ( size_size @ ( list @ A ) @ Xs3 )
% 0.32/1.53 = ( size_size @ ( list @ A ) @ Ys3 ) )
% 0.32/1.53 & ! [I2: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I2 @ ( size_size @ ( list @ A ) @ Xs3 ) )
% 0.32/1.53 => ( ( nth @ A @ Xs3 @ I2 )
% 0.32/1.53 = ( nth @ A @ Ys3 @ I2 ) ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_139_dual__order_Oantisym,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [B3: A,A3: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.32/1.53 => ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/1.53 => ( A3 = B3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_140_dual__order_Oeq__iff,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ( ( ^ [Y5: A,Z2: A] : ( Y5 = Z2 ) )
% 0.32/1.53 = ( ^ [A5: A,B4: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ B4 @ A5 )
% 0.32/1.53 & ( ord_less_eq @ A @ A5 @ B4 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_141_dual__order_Otrans,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [B3: A,A3: A,C: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.32/1.53 => ( ( ord_less_eq @ A @ C @ B3 )
% 0.32/1.53 => ( ord_less_eq @ A @ C @ A3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_142_linorder__wlog,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linorder @ A )
% 0.32/1.53 => ! [P2: A > A > $o,A3: A,B3: A] :
% 0.32/1.53 ( ! [A6: A,B5: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ A6 @ B5 )
% 0.32/1.53 => ( P2 @ A6 @ B5 ) )
% 0.32/1.53 => ( ! [A6: A,B5: A] :
% 0.32/1.53 ( ( P2 @ B5 @ A6 )
% 0.32/1.53 => ( P2 @ A6 @ B5 ) )
% 0.32/1.53 => ( P2 @ A3 @ B3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_143_dual__order_Orefl,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_144_order__trans,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( preorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A,Z3: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/1.53 => ( ( ord_less_eq @ A @ Y @ Z3 )
% 0.32/1.53 => ( ord_less_eq @ A @ X2 @ Z3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_145_order__class_Oorder_Oantisym,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [A3: A,B3: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/1.53 => ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.32/1.53 => ( A3 = B3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_146_ord__le__eq__trans,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( ord @ A )
% 0.32/1.53 => ! [A3: A,B3: A,C: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/1.53 => ( ( B3 = C )
% 0.32/1.53 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_147_ord__eq__le__trans,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( ord @ A )
% 0.32/1.53 => ! [A3: A,B3: A,C: A] :
% 0.32/1.53 ( ( A3 = B3 )
% 0.32/1.53 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.32/1.53 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_148_order__class_Oorder_Oeq__iff,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ( ( ^ [Y5: A,Z2: A] : ( Y5 = Z2 ) )
% 0.32/1.53 = ( ^ [A5: A,B4: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ A5 @ B4 )
% 0.32/1.53 & ( ord_less_eq @ A @ B4 @ A5 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_149_antisym__conv,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [Y: A,X2: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ Y @ X2 )
% 0.32/1.53 => ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/1.53 = ( X2 = Y ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_150_le__cases3,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A,Z3: A] :
% 0.32/1.53 ( ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/1.53 => ~ ( ord_less_eq @ A @ Y @ Z3 ) )
% 0.32/1.53 => ( ( ( ord_less_eq @ A @ Y @ X2 )
% 0.32/1.53 => ~ ( ord_less_eq @ A @ X2 @ Z3 ) )
% 0.32/1.53 => ( ( ( ord_less_eq @ A @ X2 @ Z3 )
% 0.32/1.53 => ~ ( ord_less_eq @ A @ Z3 @ Y ) )
% 0.32/1.53 => ( ( ( ord_less_eq @ A @ Z3 @ Y )
% 0.32/1.53 => ~ ( ord_less_eq @ A @ Y @ X2 ) )
% 0.32/1.53 => ( ( ( ord_less_eq @ A @ Y @ Z3 )
% 0.32/1.53 => ~ ( ord_less_eq @ A @ Z3 @ X2 ) )
% 0.32/1.53 => ~ ( ( ord_less_eq @ A @ Z3 @ X2 )
% 0.32/1.53 => ~ ( ord_less_eq @ A @ X2 @ Y ) ) ) ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_151_order_Otrans,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [A3: A,B3: A,C: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/1.53 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.32/1.53 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_152_le__cases,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ~ ( ord_less_eq @ A @ X2 @ Y )
% 0.32/1.53 => ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_153_eq__refl,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( preorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( X2 = Y )
% 0.32/1.53 => ( ord_less_eq @ A @ X2 @ Y ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_154_linear,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/1.53 | ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_155_antisym,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/1.53 => ( ( ord_less_eq @ A @ Y @ X2 )
% 0.32/1.53 => ( X2 = Y ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_156_eq__iff,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ( ( ^ [Y5: A,Z2: A] : ( Y5 = Z2 ) )
% 0.32/1.53 = ( ^ [X: A,Y6: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ X @ Y6 )
% 0.32/1.53 & ( ord_less_eq @ A @ Y6 @ X ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_157_ord__le__eq__subst,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType] :
% 0.32/1.53 ( ( ( ord @ B )
% 0.32/1.53 & ( ord @ A ) )
% 0.32/1.53 => ! [A3: A,B3: A,F: A > B,C: B] :
% 0.32/1.53 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/1.53 => ( ( ( F @ B3 )
% 0.32/1.53 = C )
% 0.32/1.53 => ( ! [X3: A,Y4: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.32/1.53 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/1.53 => ( ord_less_eq @ B @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_158_ord__eq__le__subst,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType] :
% 0.32/1.53 ( ( ( ord @ B )
% 0.32/1.53 & ( ord @ A ) )
% 0.32/1.53 => ! [A3: A,F: B > A,B3: B,C: B] :
% 0.32/1.53 ( ( A3
% 0.32/1.53 = ( F @ B3 ) )
% 0.32/1.53 => ( ( ord_less_eq @ B @ B3 @ C )
% 0.32/1.53 => ( ! [X3: B,Y4: B] :
% 0.32/1.53 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 0.32/1.53 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/1.53 => ( ord_less_eq @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_159_order__subst2,axiom,
% 0.32/1.53 ! [A: $tType,C2: $tType] :
% 0.32/1.53 ( ( ( order @ C2 )
% 0.32/1.53 & ( order @ A ) )
% 0.32/1.53 => ! [A3: A,B3: A,F: A > C2,C: C2] :
% 0.32/1.53 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/1.53 => ( ( ord_less_eq @ C2 @ ( F @ B3 ) @ C )
% 0.32/1.53 => ( ! [X3: A,Y4: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.32/1.53 => ( ord_less_eq @ C2 @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/1.53 => ( ord_less_eq @ C2 @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_160_order__subst1,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType] :
% 0.32/1.53 ( ( ( order @ B )
% 0.32/1.53 & ( order @ A ) )
% 0.32/1.53 => ! [A3: A,F: B > A,B3: B,C: B] :
% 0.32/1.53 ( ( ord_less_eq @ A @ A3 @ ( F @ B3 ) )
% 0.32/1.53 => ( ( ord_less_eq @ B @ B3 @ C )
% 0.32/1.53 => ( ! [X3: B,Y4: B] :
% 0.32/1.53 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 0.32/1.53 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/1.53 => ( ord_less_eq @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_161_le__fun__def,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType] :
% 0.32/1.53 ( ( ord @ B )
% 0.32/1.53 => ( ( ord_less_eq @ ( A > B ) )
% 0.32/1.53 = ( ^ [F2: A > B,G2: A > B] :
% 0.32/1.53 ! [X: A] : ( ord_less_eq @ B @ ( F2 @ X ) @ ( G2 @ X ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_162_le__funI,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType] :
% 0.32/1.53 ( ( ord @ B )
% 0.32/1.53 => ! [F: A > B,G: A > B] :
% 0.32/1.53 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.32/1.53 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_163_le__funE,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType] :
% 0.32/1.53 ( ( ord @ B )
% 0.32/1.53 => ! [F: A > B,G: A > B,X2: A] :
% 0.32/1.53 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.32/1.53 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_164_le__funD,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType] :
% 0.32/1.53 ( ( ord @ B )
% 0.32/1.53 => ! [F: A > B,G: A > B,X2: A] :
% 0.32/1.53 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.32/1.53 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_165_dual__order_Ostrict__implies__not__eq,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [B3: A,A3: A] :
% 0.32/1.53 ( ( ord_less @ A @ B3 @ A3 )
% 0.32/1.53 => ( A3 != B3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_166_order_Ostrict__implies__not__eq,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [A3: A,B3: A] :
% 0.32/1.53 ( ( ord_less @ A @ A3 @ B3 )
% 0.32/1.53 => ( A3 != B3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_167_not__less__iff__gr__or__eq,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ~ ( ord_less @ A @ X2 @ Y ) )
% 0.32/1.53 = ( ( ord_less @ A @ Y @ X2 )
% 0.32/1.53 | ( X2 = Y ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_168_dual__order_Ostrict__trans,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [B3: A,A3: A,C: A] :
% 0.32/1.53 ( ( ord_less @ A @ B3 @ A3 )
% 0.32/1.53 => ( ( ord_less @ A @ C @ B3 )
% 0.32/1.53 => ( ord_less @ A @ C @ A3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_169_linorder__less__wlog,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linorder @ A )
% 0.32/1.53 => ! [P2: A > A > $o,A3: A,B3: A] :
% 0.32/1.53 ( ! [A6: A,B5: A] :
% 0.32/1.53 ( ( ord_less @ A @ A6 @ B5 )
% 0.32/1.53 => ( P2 @ A6 @ B5 ) )
% 0.32/1.53 => ( ! [A6: A] : ( P2 @ A6 @ A6 )
% 0.32/1.53 => ( ! [A6: A,B5: A] :
% 0.32/1.53 ( ( P2 @ B5 @ A6 )
% 0.32/1.53 => ( P2 @ A6 @ B5 ) )
% 0.32/1.53 => ( P2 @ A3 @ B3 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_170_exists__least__iff,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( wellorder @ A )
% 0.32/1.53 => ( ( ^ [P3: A > $o] :
% 0.32/1.53 ? [X4: A] : ( P3 @ X4 ) )
% 0.32/1.53 = ( ^ [P4: A > $o] :
% 0.32/1.53 ? [N3: A] :
% 0.32/1.53 ( ( P4 @ N3 )
% 0.32/1.53 & ! [M4: A] :
% 0.32/1.53 ( ( ord_less @ A @ M4 @ N3 )
% 0.32/1.53 => ~ ( P4 @ M4 ) ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_171_less__imp__not__less,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( preorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 => ~ ( ord_less @ A @ Y @ X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_172_order_Ostrict__trans,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [A3: A,B3: A,C: A] :
% 0.32/1.53 ( ( ord_less @ A @ A3 @ B3 )
% 0.32/1.53 => ( ( ord_less @ A @ B3 @ C )
% 0.32/1.53 => ( ord_less @ A @ A3 @ C ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_173_dual__order_Oirrefl,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [A3: A] :
% 0.32/1.53 ~ ( ord_less @ A @ A3 @ A3 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_174_linorder__cases,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ~ ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 => ( ( X2 != Y )
% 0.32/1.53 => ( ord_less @ A @ Y @ X2 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_175_less__imp__triv,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( preorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A,P2: $o] :
% 0.32/1.53 ( ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 => ( ( ord_less @ A @ Y @ X2 )
% 0.32/1.53 => P2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_176_less__imp__not__eq2,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 => ( Y != X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_177_antisym__conv3,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linorder @ A )
% 0.32/1.53 => ! [Y: A,X2: A] :
% 0.32/1.53 ( ~ ( ord_less @ A @ Y @ X2 )
% 0.32/1.53 => ( ( ~ ( ord_less @ A @ X2 @ Y ) )
% 0.32/1.53 = ( X2 = Y ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_178_less__induct,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( wellorder @ A )
% 0.32/1.53 => ! [P2: A > $o,A3: A] :
% 0.32/1.53 ( ! [X3: A] :
% 0.32/1.53 ( ! [Y3: A] :
% 0.32/1.53 ( ( ord_less @ A @ Y3 @ X3 )
% 0.32/1.53 => ( P2 @ Y3 ) )
% 0.32/1.53 => ( P2 @ X3 ) )
% 0.32/1.53 => ( P2 @ A3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_179_less__not__sym,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( preorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 => ~ ( ord_less @ A @ Y @ X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_180_less__imp__not__eq,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 => ( X2 != Y ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_181_dual__order_Oasym,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [B3: A,A3: A] :
% 0.32/1.53 ( ( ord_less @ A @ B3 @ A3 )
% 0.32/1.53 => ~ ( ord_less @ A @ A3 @ B3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_182_ord__less__eq__trans,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( ord @ A )
% 0.32/1.53 => ! [A3: A,B3: A,C: A] :
% 0.32/1.53 ( ( ord_less @ A @ A3 @ B3 )
% 0.32/1.53 => ( ( B3 = C )
% 0.32/1.53 => ( ord_less @ A @ A3 @ C ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_183_ord__eq__less__trans,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( ord @ A )
% 0.32/1.53 => ! [A3: A,B3: A,C: A] :
% 0.32/1.53 ( ( A3 = B3 )
% 0.32/1.53 => ( ( ord_less @ A @ B3 @ C )
% 0.32/1.53 => ( ord_less @ A @ A3 @ C ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_184_less__irrefl,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( preorder @ A )
% 0.32/1.53 => ! [X2: A] :
% 0.32/1.53 ~ ( ord_less @ A @ X2 @ X2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_185_less__linear,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 | ( X2 = Y )
% 0.32/1.53 | ( ord_less @ A @ Y @ X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_186_less__trans,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( preorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A,Z3: A] :
% 0.32/1.53 ( ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 => ( ( ord_less @ A @ Y @ Z3 )
% 0.32/1.53 => ( ord_less @ A @ X2 @ Z3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_187_less__asym_H,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( preorder @ A )
% 0.32/1.53 => ! [A3: A,B3: A] :
% 0.32/1.53 ( ( ord_less @ A @ A3 @ B3 )
% 0.32/1.53 => ~ ( ord_less @ A @ B3 @ A3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_188_less__asym,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( preorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 => ~ ( ord_less @ A @ Y @ X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_189_less__imp__neq,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 => ( X2 != Y ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_190_dense,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( dense_order @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 => ? [Z: A] :
% 0.32/1.53 ( ( ord_less @ A @ X2 @ Z )
% 0.32/1.53 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_191_order_Oasym,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [A3: A,B3: A] :
% 0.32/1.53 ( ( ord_less @ A @ A3 @ B3 )
% 0.32/1.53 => ~ ( ord_less @ A @ B3 @ A3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_192_neq__iff,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( X2 != Y )
% 0.32/1.53 = ( ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 | ( ord_less @ A @ Y @ X2 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_193_neqE,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( X2 != Y )
% 0.32/1.53 => ( ~ ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 => ( ord_less @ A @ Y @ X2 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_194_gt__ex,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( no_top @ A )
% 0.32/1.53 => ! [X2: A] :
% 0.32/1.53 ? [X_1: A] : ( ord_less @ A @ X2 @ X_1 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_195_lt__ex,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( no_bot @ A )
% 0.32/1.53 => ! [X2: A] :
% 0.32/1.53 ? [Y4: A] : ( ord_less @ A @ Y4 @ X2 ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_196_order__less__subst2,axiom,
% 0.32/1.53 ! [A: $tType,C2: $tType] :
% 0.32/1.53 ( ( ( order @ C2 )
% 0.32/1.53 & ( order @ A ) )
% 0.32/1.53 => ! [A3: A,B3: A,F: A > C2,C: C2] :
% 0.32/1.53 ( ( ord_less @ A @ A3 @ B3 )
% 0.32/1.53 => ( ( ord_less @ C2 @ ( F @ B3 ) @ C )
% 0.32/1.53 => ( ! [X3: A,Y4: A] :
% 0.32/1.53 ( ( ord_less @ A @ X3 @ Y4 )
% 0.32/1.53 => ( ord_less @ C2 @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/1.53 => ( ord_less @ C2 @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_197_order__less__subst1,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType] :
% 0.32/1.53 ( ( ( order @ B )
% 0.32/1.53 & ( order @ A ) )
% 0.32/1.53 => ! [A3: A,F: B > A,B3: B,C: B] :
% 0.32/1.53 ( ( ord_less @ A @ A3 @ ( F @ B3 ) )
% 0.32/1.53 => ( ( ord_less @ B @ B3 @ C )
% 0.32/1.53 => ( ! [X3: B,Y4: B] :
% 0.32/1.53 ( ( ord_less @ B @ X3 @ Y4 )
% 0.32/1.53 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/1.53 => ( ord_less @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_198_ord__less__eq__subst,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType] :
% 0.32/1.53 ( ( ( ord @ B )
% 0.32/1.53 & ( ord @ A ) )
% 0.32/1.53 => ! [A3: A,B3: A,F: A > B,C: B] :
% 0.32/1.53 ( ( ord_less @ A @ A3 @ B3 )
% 0.32/1.53 => ( ( ( F @ B3 )
% 0.32/1.53 = C )
% 0.32/1.53 => ( ! [X3: A,Y4: A] :
% 0.32/1.53 ( ( ord_less @ A @ X3 @ Y4 )
% 0.32/1.53 => ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/1.53 => ( ord_less @ B @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_199_ord__eq__less__subst,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType] :
% 0.32/1.53 ( ( ( ord @ B )
% 0.32/1.53 & ( ord @ A ) )
% 0.32/1.53 => ! [A3: A,F: B > A,B3: B,C: B] :
% 0.32/1.53 ( ( A3
% 0.32/1.53 = ( F @ B3 ) )
% 0.32/1.53 => ( ( ord_less @ B @ B3 @ C )
% 0.32/1.53 => ( ! [X3: B,Y4: B] :
% 0.32/1.53 ( ( ord_less @ B @ X3 @ Y4 )
% 0.32/1.53 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/1.53 => ( ord_less @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_200_ex__has__least__nat,axiom,
% 0.32/1.53 ! [A: $tType,P2: A > $o,K: A,M: A > nat] :
% 0.32/1.53 ( ( P2 @ K )
% 0.32/1.53 => ? [X3: A] :
% 0.32/1.53 ( ( P2 @ X3 )
% 0.32/1.53 & ! [Y3: A] :
% 0.32/1.53 ( ( P2 @ Y3 )
% 0.32/1.53 => ( ord_less_eq @ nat @ ( M @ X3 ) @ ( M @ Y3 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_201_MinPredicate,axiom,
% 0.32/1.53 ! [P2: nat > $o] :
% 0.32/1.53 ( ? [X_12: nat] : ( P2 @ X_12 )
% 0.32/1.53 => ? [N0: nat] :
% 0.32/1.53 ( ( P2 @ N0 )
% 0.32/1.53 & ! [N5: nat] :
% 0.32/1.53 ( ( P2 @ N5 )
% 0.32/1.53 => ( ord_less_eq @ nat @ N0 @ N5 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_202_order_Onot__eq__order__implies__strict,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [A3: A,B3: A] :
% 0.32/1.53 ( ( A3 != B3 )
% 0.32/1.53 => ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/1.53 => ( ord_less @ A @ A3 @ B3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_203_dual__order_Ostrict__implies__order,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [B3: A,A3: A] :
% 0.32/1.53 ( ( ord_less @ A @ B3 @ A3 )
% 0.32/1.53 => ( ord_less_eq @ A @ B3 @ A3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_204_dual__order_Ostrict__iff__order,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ( ( ord_less @ A )
% 0.32/1.53 = ( ^ [B4: A,A5: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ B4 @ A5 )
% 0.32/1.53 & ( A5 != B4 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_205_dual__order_Oorder__iff__strict,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ( ( ord_less_eq @ A )
% 0.32/1.53 = ( ^ [B4: A,A5: A] :
% 0.32/1.53 ( ( ord_less @ A @ B4 @ A5 )
% 0.32/1.53 | ( A5 = B4 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_206_order_Ostrict__implies__order,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [A3: A,B3: A] :
% 0.32/1.53 ( ( ord_less @ A @ A3 @ B3 )
% 0.32/1.53 => ( ord_less_eq @ A @ A3 @ B3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_207_dense__le__bounded,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( dense_linorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A,Z3: A] :
% 0.32/1.53 ( ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 => ( ! [W: A] :
% 0.32/1.53 ( ( ord_less @ A @ X2 @ W )
% 0.32/1.53 => ( ( ord_less @ A @ W @ Y )
% 0.32/1.53 => ( ord_less_eq @ A @ W @ Z3 ) ) )
% 0.32/1.53 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_208_dense__ge__bounded,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( dense_linorder @ A )
% 0.32/1.53 => ! [Z3: A,X2: A,Y: A] :
% 0.32/1.53 ( ( ord_less @ A @ Z3 @ X2 )
% 0.32/1.53 => ( ! [W: A] :
% 0.32/1.53 ( ( ord_less @ A @ Z3 @ W )
% 0.32/1.53 => ( ( ord_less @ A @ W @ X2 )
% 0.32/1.53 => ( ord_less_eq @ A @ Y @ W ) ) )
% 0.32/1.53 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_209_dual__order_Ostrict__trans2,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [B3: A,A3: A,C: A] :
% 0.32/1.53 ( ( ord_less @ A @ B3 @ A3 )
% 0.32/1.53 => ( ( ord_less_eq @ A @ C @ B3 )
% 0.32/1.53 => ( ord_less @ A @ C @ A3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_210_dual__order_Ostrict__trans1,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [B3: A,A3: A,C: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.32/1.53 => ( ( ord_less @ A @ C @ B3 )
% 0.32/1.53 => ( ord_less @ A @ C @ A3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_211_order_Ostrict__iff__order,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ( ( ord_less @ A )
% 0.32/1.53 = ( ^ [A5: A,B4: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ A5 @ B4 )
% 0.32/1.53 & ( A5 != B4 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_212_order_Oorder__iff__strict,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ( ( ord_less_eq @ A )
% 0.32/1.53 = ( ^ [A5: A,B4: A] :
% 0.32/1.53 ( ( ord_less @ A @ A5 @ B4 )
% 0.32/1.53 | ( A5 = B4 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_213_order_Ostrict__trans2,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [A3: A,B3: A,C: A] :
% 0.32/1.53 ( ( ord_less @ A @ A3 @ B3 )
% 0.32/1.53 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.32/1.53 => ( ord_less @ A @ A3 @ C ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_214_order_Ostrict__trans1,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [A3: A,B3: A,C: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/1.53 => ( ( ord_less @ A @ B3 @ C )
% 0.32/1.53 => ( ord_less @ A @ A3 @ C ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_215_not__le__imp__less,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linorder @ A )
% 0.32/1.53 => ! [Y: A,X2: A] :
% 0.32/1.53 ( ~ ( ord_less_eq @ A @ Y @ X2 )
% 0.32/1.53 => ( ord_less @ A @ X2 @ Y ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_216_less__le__not__le,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( preorder @ A )
% 0.32/1.53 => ( ( ord_less @ A )
% 0.32/1.53 = ( ^ [X: A,Y6: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ X @ Y6 )
% 0.32/1.53 & ~ ( ord_less_eq @ A @ Y6 @ X ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_217_le__imp__less__or__eq,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/1.53 => ( ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 | ( X2 = Y ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_218_le__less__linear,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/1.53 | ( ord_less @ A @ Y @ X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_219_dense__le,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( dense_linorder @ A )
% 0.32/1.53 => ! [Y: A,Z3: A] :
% 0.32/1.53 ( ! [X3: A] :
% 0.32/1.53 ( ( ord_less @ A @ X3 @ Y )
% 0.32/1.53 => ( ord_less_eq @ A @ X3 @ Z3 ) )
% 0.32/1.53 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_220_dense__ge,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( dense_linorder @ A )
% 0.32/1.53 => ! [Z3: A,Y: A] :
% 0.32/1.53 ( ! [X3: A] :
% 0.32/1.53 ( ( ord_less @ A @ Z3 @ X3 )
% 0.32/1.53 => ( ord_less_eq @ A @ Y @ X3 ) )
% 0.32/1.53 => ( ord_less_eq @ A @ Y @ Z3 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_221_less__le__trans,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( preorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A,Z3: A] :
% 0.32/1.53 ( ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 => ( ( ord_less_eq @ A @ Y @ Z3 )
% 0.32/1.53 => ( ord_less @ A @ X2 @ Z3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_222_le__less__trans,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( preorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A,Z3: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/1.53 => ( ( ord_less @ A @ Y @ Z3 )
% 0.32/1.53 => ( ord_less @ A @ X2 @ Z3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_223_less__imp__le,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( preorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 => ( ord_less_eq @ A @ X2 @ Y ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_224_antisym__conv2,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/1.53 => ( ( ~ ( ord_less @ A @ X2 @ Y ) )
% 0.32/1.53 = ( X2 = Y ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_225_antisym__conv1,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ~ ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 => ( ( ord_less_eq @ A @ X2 @ Y )
% 0.32/1.53 = ( X2 = Y ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_226_le__neq__trans,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [A3: A,B3: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/1.53 => ( ( A3 != B3 )
% 0.32/1.53 => ( ord_less @ A @ A3 @ B3 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_227_not__less,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ~ ( ord_less @ A @ X2 @ Y ) )
% 0.32/1.53 = ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_228_not__le,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ( ~ ( ord_less_eq @ A @ X2 @ Y ) )
% 0.32/1.53 = ( ord_less @ A @ Y @ X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_229_order__less__le__subst2,axiom,
% 0.32/1.53 ! [A: $tType,C2: $tType] :
% 0.32/1.53 ( ( ( order @ C2 )
% 0.32/1.53 & ( order @ A ) )
% 0.32/1.53 => ! [A3: A,B3: A,F: A > C2,C: C2] :
% 0.32/1.53 ( ( ord_less @ A @ A3 @ B3 )
% 0.32/1.53 => ( ( ord_less_eq @ C2 @ ( F @ B3 ) @ C )
% 0.32/1.53 => ( ! [X3: A,Y4: A] :
% 0.32/1.53 ( ( ord_less @ A @ X3 @ Y4 )
% 0.32/1.53 => ( ord_less @ C2 @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/1.53 => ( ord_less @ C2 @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_230_order__less__le__subst1,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType] :
% 0.32/1.53 ( ( ( order @ B )
% 0.32/1.53 & ( order @ A ) )
% 0.32/1.53 => ! [A3: A,F: B > A,B3: B,C: B] :
% 0.32/1.53 ( ( ord_less @ A @ A3 @ ( F @ B3 ) )
% 0.32/1.53 => ( ( ord_less_eq @ B @ B3 @ C )
% 0.32/1.53 => ( ! [X3: B,Y4: B] :
% 0.32/1.53 ( ( ord_less_eq @ B @ X3 @ Y4 )
% 0.32/1.53 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/1.53 => ( ord_less @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_231_order__le__less__subst2,axiom,
% 0.32/1.53 ! [A: $tType,C2: $tType] :
% 0.32/1.53 ( ( ( order @ C2 )
% 0.32/1.53 & ( order @ A ) )
% 0.32/1.53 => ! [A3: A,B3: A,F: A > C2,C: C2] :
% 0.32/1.53 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/1.53 => ( ( ord_less @ C2 @ ( F @ B3 ) @ C )
% 0.32/1.53 => ( ! [X3: A,Y4: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ X3 @ Y4 )
% 0.32/1.53 => ( ord_less_eq @ C2 @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/1.53 => ( ord_less @ C2 @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_232_order__le__less__subst1,axiom,
% 0.32/1.53 ! [A: $tType,B: $tType] :
% 0.32/1.53 ( ( ( order @ B )
% 0.32/1.53 & ( order @ A ) )
% 0.32/1.53 => ! [A3: A,F: B > A,B3: B,C: B] :
% 0.32/1.53 ( ( ord_less_eq @ A @ A3 @ ( F @ B3 ) )
% 0.32/1.53 => ( ( ord_less @ B @ B3 @ C )
% 0.32/1.53 => ( ! [X3: B,Y4: B] :
% 0.32/1.53 ( ( ord_less @ B @ X3 @ Y4 )
% 0.32/1.53 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y4 ) ) )
% 0.32/1.53 => ( ord_less @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_233_less__le,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ( ( ord_less @ A )
% 0.32/1.53 = ( ^ [X: A,Y6: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ X @ Y6 )
% 0.32/1.53 & ( X != Y6 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_234_le__less,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ( ( ord_less_eq @ A )
% 0.32/1.53 = ( ^ [X: A,Y6: A] :
% 0.32/1.53 ( ( ord_less @ A @ X @ Y6 )
% 0.32/1.53 | ( X = Y6 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_235_leI,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( linorder @ A )
% 0.32/1.53 => ! [X2: A,Y: A] :
% 0.32/1.53 ( ~ ( ord_less @ A @ X2 @ Y )
% 0.32/1.53 => ( ord_less_eq @ A @ Y @ X2 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_236_leD,axiom,
% 0.32/1.53 ! [A: $tType] :
% 0.32/1.53 ( ( order @ A )
% 0.32/1.53 => ! [Y: A,X2: A] :
% 0.32/1.53 ( ( ord_less_eq @ A @ Y @ X2 )
% 0.32/1.53 => ~ ( ord_less @ A @ X2 @ Y ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_237_AssumpMinImplAllBigger,axiom,
% 0.32/1.53 minimalEnabled @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ msg ).
% 0.32/1.53
% 0.32/1.53 thf(fact_238__092_060open_062execution_OfirstOccurrence_A_Ife_Aindex_J_A_Ift_Aindex_J_Amsg_AOccM_092_060close_062,axiom,
% 0.32/1.53 firstOccurrence @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ msga @ occM2 ).
% 0.32/1.53
% 0.32/1.53 thf(fact_239_SameMsgOnLow,axiom,
% 0.32/1.53 ! [I4: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I4 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 0.32/1.53 => ( ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ I4 )
% 0.32/1.53 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_240_OccM_H_I5_J,axiom,
% 0.32/1.53 ! [N5: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ occM @ N5 )
% 0.32/1.53 => ( ( ord_less @ nat @ N5 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 0.32/1.53 => ( msg
% 0.32/1.53 != ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ N5 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_241_IPrefixList,axiom,
% 0.32/1.53 ! [I4: nat] : ( prefixList @ ( message @ p @ v ) @ ( ft @ I4 ) @ ( ft @ ( suc @ I4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_242_OccM_H_I1_J,axiom,
% 0.32/1.53 ? [P5: p] : ( isReceiverOf @ p @ v @ P5 @ msg ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_243_FirstOccMsg_H,axiom,
% 0.32/1.53 firstOccurrence @ p @ v @ s @ ( fe @ index ) @ ( ft @ index ) @ msg @ occM ).
% 0.32/1.53
% 0.32/1.53 thf(fact_244_AssumpOccMFirstOccurrence_I5_J,axiom,
% 0.32/1.53 ! [N5: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ occM2 @ N5 )
% 0.32/1.53 => ( ( ord_less @ nat @ N5 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ index ) ) )
% 0.32/1.53 => ( msga
% 0.32/1.53 != ( nth @ ( message @ p @ v ) @ ( ft @ index ) @ N5 ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_245_OccM_H_I4_J,axiom,
% 0.32/1.53 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ index ) @ occM ) @ msg ).
% 0.32/1.53
% 0.32/1.53 thf(fact_246_AssumptionFairContr,axiom,
% 0.32/1.53 ! [N5: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ n @ N5 )
% 0.32/1.53 => ! [N02: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ N02 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N5 ) ) )
% 0.32/1.53 => ( ( ord_less_eq @ nat @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ n ) ) @ N02 )
% 0.32/1.53 => ( msg2
% 0.32/1.53 != ( nth @ ( message @ p @ v ) @ ( ft @ N5 ) @ N02 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_247_less__fun__def,axiom,
% 0.32/1.53 ! [B: $tType,A: $tType] :
% 0.32/1.53 ( ( ord @ B )
% 0.32/1.53 => ( ( ord_less @ ( A > B ) )
% 0.32/1.53 = ( ^ [F2: A > B,G2: A > B] :
% 0.32/1.53 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.32/1.53 & ~ ( ord_less_eq @ ( A > B ) @ G2 @ F2 ) ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_248_MessageStaysOrConsumed,axiom,
% 0.32/1.53 ! [N1: nat,N22: nat,N: nat,Msg: message @ p @ v] :
% 0.32/1.53 ( ( ( ord_less_eq @ nat @ N1 @ N22 )
% 0.32/1.53 & ( ord_less @ nat @ N22 @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ N ) ) )
% 0.32/1.53 & ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N ) @ N1 ) @ Msg ) )
% 0.32/1.53 => ( ( enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ N ) @ N22 ) @ Msg )
% 0.32/1.53 | ? [N03: nat] :
% 0.32/1.53 ( ( ord_less_eq @ nat @ N1 @ N03 )
% 0.32/1.53 & ( ord_less @ nat @ N03 @ ( size_size @ ( list @ ( message @ p @ v ) ) @ ( ft @ N ) ) )
% 0.32/1.53 & ( ( nth @ ( message @ p @ v ) @ ( ft @ N ) @ N03 )
% 0.32/1.53 = Msg ) ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_249__092_060open_062_092_060not_062_A_I_092_060exists_062i_060length_A_Ife_A_ISuc_Aindex_J_J_A_N_A1_O_Alength_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_Ai_A_092_060and_062_Amsg_____A_061_Aft_A_ISuc_Aindex_J_A_B_Ai_J_092_060close_062,axiom,
% 0.32/1.53 ~ ? [I4: nat] :
% 0.32/1.53 ( ( ord_less @ nat @ I4 @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ ( suc @ index ) ) ) @ ( one_one @ nat ) ) )
% 0.32/1.53 & ( ord_less_eq @ nat @ ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) @ I4 )
% 0.32/1.53 & ( msg2
% 0.32/1.53 = ( nth @ ( message @ p @ v ) @ ( ft @ ( suc @ index ) ) @ I4 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_250_AssumptionFair_I4_J,axiom,
% 0.32/1.53 isReceiverOf @ p @ v @ p2 @ msg2 ).
% 0.32/1.53
% 0.32/1.53 thf(fact_251_AssumpOccMFirstOccurrence_I1_J,axiom,
% 0.32/1.53 ? [P5: p] : ( isReceiverOf @ p @ v @ P5 @ msga ) ).
% 0.32/1.53
% 0.32/1.53 thf(fact_252_AssumptionFair_I3_J,axiom,
% 0.32/1.53 enabled @ p @ v @ s @ ( nth @ ( configuration_ext @ p @ v @ s @ product_unit ) @ ( fe @ n ) @ n0 ) @ msg2 ).
% 0.32/1.53
% 0.32/1.53 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.32/1.53 ! [A7: $tType,A8: $tType] :
% 0.32/1.53 ( ( preorder @ A8 )
% 0.32/1.53 => ( preorder @ ( A7 > A8 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.32/1.53 ! [A7: $tType,A8: $tType] :
% 0.32/1.53 ( ( order @ A8 )
% 0.32/1.53 => ( order @ ( A7 > A8 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(tcon_fun___Orderings_Oord,axiom,
% 0.32/1.53 ! [A7: $tType,A8: $tType] :
% 0.32/1.53 ( ( ord @ A8 )
% 0.32/1.53 => ( ord @ ( A7 > A8 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(tcon_fun___Groups_Ominus,axiom,
% 0.32/1.53 ! [A7: $tType,A8: $tType] :
% 0.32/1.53 ( ( minus @ A8 )
% 0.32/1.53 => ( minus @ ( A7 > A8 ) ) ) ).
% 0.32/1.53
% 0.32/1.53 thf(tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring,axiom,
% 0.32/1.54 linord1659791738miring @ nat ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 0.32/1.54 cancel146912293up_add @ nat ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.32/1.54 wellorder @ nat ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.32/1.54 preorder @ nat ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.32/1.54 linorder @ nat ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.32/1.54 no_top @ nat ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.32/1.54 order @ nat ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.32/1.54 ord @ nat ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Groups_Ominus_4,axiom,
% 0.32/1.54 minus @ nat ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.32/1.54 one @ nat ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Nat_Osize,axiom,
% 0.32/1.54 size @ nat ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Set_Oset___Orderings_Opreorder_5,axiom,
% 0.32/1.54 ! [A7: $tType] : ( preorder @ ( set @ A7 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Set_Oset___Orderings_Oorder_6,axiom,
% 0.32/1.54 ! [A7: $tType] : ( order @ ( set @ A7 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Set_Oset___Orderings_Oord_7,axiom,
% 0.32/1.54 ! [A7: $tType] : ( ord @ ( set @ A7 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Set_Oset___Groups_Ominus_8,axiom,
% 0.32/1.54 ! [A7: $tType] : ( minus @ ( set @ A7 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_HOL_Obool___Orderings_Opreorder_9,axiom,
% 0.32/1.54 preorder @ $o ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_HOL_Obool___Orderings_Olinorder_10,axiom,
% 0.32/1.54 linorder @ $o ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_HOL_Obool___Orderings_Oorder_11,axiom,
% 0.32/1.54 order @ $o ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_HOL_Obool___Orderings_Oord_12,axiom,
% 0.32/1.54 ord @ $o ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_HOL_Obool___Groups_Ominus_13,axiom,
% 0.32/1.54 minus @ $o ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_List_Olist___Nat_Osize_14,axiom,
% 0.32/1.54 ! [A7: $tType] : ( size @ ( list @ A7 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Product__Type_Ounit___Orderings_Owellorder_15,axiom,
% 0.32/1.54 wellorder @ product_unit ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Product__Type_Ounit___Orderings_Opreorder_16,axiom,
% 0.32/1.54 preorder @ product_unit ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Product__Type_Ounit___Orderings_Olinorder_17,axiom,
% 0.32/1.54 linorder @ product_unit ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Product__Type_Ounit___Orderings_Oorder_18,axiom,
% 0.32/1.54 order @ product_unit ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Product__Type_Ounit___Orderings_Oord_19,axiom,
% 0.32/1.54 ord @ product_unit ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Product__Type_Ounit___Groups_Ominus_20,axiom,
% 0.32/1.54 minus @ product_unit ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_AsynchronousSystem_Omessage___Nat_Osize_21,axiom,
% 0.32/1.54 ! [A7: $tType,A8: $tType] : ( size @ ( message @ A7 @ A8 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(conj_0,conjecture,
% 0.32/1.54 ( occM2
% 0.32/1.54 = ( minus_minus @ nat @ ( size_size @ ( list @ ( configuration_ext @ p @ v @ s @ product_unit ) ) @ ( fe @ index ) ) @ ( one_one @ nat ) ) ) ).
% 0.32/1.54 ------------------------
% 0.32/1.56 % (32259)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_32065 for (2999ds/4Mi)
% 0.32/1.56 % (32261)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32065 for (2999ds/2Mi)
% 0.32/1.56 % (32259)Instruction limit reached!
% 0.32/1.56 % (32259)------------------------------
% 0.32/1.56 % (32259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.56 % (32259)Termination reason: Unknown
% 0.32/1.56 % (32259)Termination phase: shuffling
% 0.32/1.56
% 0.32/1.56 % (32259)Memory used [KB]: 1407
% 0.32/1.56 % (32259)Time elapsed: 0.003 s
% 0.32/1.56 % (32259)Instructions burned: 6 (million)
% 0.32/1.56 % (32259)------------------------------
% 0.32/1.56 % (32259)------------------------------
% 0.32/1.56 % (32261)Instruction limit reached!
% 0.32/1.56 % (32261)------------------------------
% 0.32/1.56 % (32261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.56 % (32261)Termination reason: Unknown
% 0.32/1.56 % (32261)Termination phase: shuffling
% 0.32/1.56
% 0.32/1.56 % (32261)Memory used [KB]: 1407
% 0.32/1.56 % (32261)Time elapsed: 0.002 s
% 0.32/1.56 % (32261)Instructions burned: 2 (million)
% 0.32/1.56 % (32261)------------------------------
% 0.32/1.56 % (32261)------------------------------
% 0.32/1.56 % (32262)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_32065 for (2999ds/2Mi)
% 0.32/1.56 % (32262)Instruction limit reached!
% 0.32/1.56 % (32262)------------------------------
% 0.32/1.56 % (32262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.56 % (32262)Termination reason: Unknown
% 0.32/1.56 % (32262)Termination phase: shuffling
% 0.32/1.56
% 0.32/1.56 % (32262)Memory used [KB]: 1407
% 0.32/1.56 % (32262)Time elapsed: 0.003 s
% 0.32/1.56 % (32262)Instructions burned: 4 (million)
% 0.32/1.56 % (32262)------------------------------
% 0.32/1.56 % (32262)------------------------------
% 0.32/1.56 % (32258)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32065 for (2999ds/183Mi)
% 0.32/1.56 % (32263)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_32065 for (2999ds/275Mi)
% 0.32/1.56 % (32260)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_32065 for (2999ds/27Mi)
% 0.32/1.57 % (32265)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32065 for (2999ds/3Mi)
% 0.32/1.57 % (32265)Instruction limit reached!
% 0.32/1.57 % (32265)------------------------------
% 0.32/1.57 % (32265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.57 % (32265)Termination reason: Unknown
% 0.32/1.57 % (32265)Termination phase: shuffling
% 0.32/1.57
% 0.32/1.57 % (32265)Memory used [KB]: 1407
% 0.32/1.57 % (32266)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_32065 for (2999ds/37Mi)
% 0.32/1.57 % (32264)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32065 for (2999ds/18Mi)
% 0.32/1.57 % (32265)Time elapsed: 0.002 s
% 0.32/1.57 % (32265)Instructions burned: 3 (million)
% 0.32/1.57 % (32265)------------------------------
% 0.32/1.57 % (32265)------------------------------
% 0.32/1.57 % (32267)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_32065 for (2999ds/15Mi)
% 0.32/1.57 % (32264)Instruction limit reached!
% 0.32/1.57 % (32264)------------------------------
% 0.32/1.57 % (32264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.57 % (32264)Termination reason: Unknown
% 0.32/1.57 % (32264)Termination phase: shuffling
% 0.32/1.57
% 0.32/1.57 % (32264)Memory used [KB]: 1663
% 0.32/1.57 % (32264)Time elapsed: 0.008 s
% 0.32/1.57 % (32264)Instructions burned: 18 (million)
% 0.32/1.57 % (32264)------------------------------
% 0.32/1.57 % (32264)------------------------------
% 0.32/1.58 % (32268)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_32065 for (2999ds/3Mi)
% 0.32/1.58 % (32267)Instruction limit reached!
% 0.32/1.58 % (32267)------------------------------
% 0.32/1.58 % (32267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.58 % (32267)Termination reason: Unknown
% 0.32/1.58 % (32267)Termination phase: shuffling
% 0.32/1.58
% 0.32/1.58 % (32267)Memory used [KB]: 1663
% 0.32/1.58 % (32267)Time elapsed: 0.008 s
% 0.32/1.58 % (32267)Instructions burned: 17 (million)
% 0.32/1.58 % (32267)------------------------------
% 0.32/1.58 % (32267)------------------------------
% 0.32/1.58 % (32268)Instruction limit reached!
% 0.32/1.58 % (32268)------------------------------
% 0.32/1.58 % (32268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.58 % (32268)Termination reason: Unknown
% 0.32/1.58 % (32268)Termination phase: shuffling
% 0.32/1.58
% 0.32/1.58 % (32268)Memory used [KB]: 1407
% 0.32/1.58 % (32268)Time elapsed: 0.002 s
% 0.32/1.58 % (32268)Instructions burned: 3 (million)
% 0.32/1.58 % (32268)------------------------------
% 0.32/1.58 % (32268)------------------------------
% 0.32/1.58 % (32266)Instruction limit reached!
% 0.32/1.58 % (32266)------------------------------
% 0.32/1.58 % (32266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.58 % (32266)Termination reason: Unknown
% 0.32/1.58 % (32266)Termination phase: Property scanning
% 0.32/1.58
% 0.32/1.58 % (32266)Memory used [KB]: 2046
% 0.32/1.58 % (32266)Time elapsed: 0.012 s
% 0.32/1.58 % (32266)Instructions burned: 37 (million)
% 0.32/1.58 % (32266)------------------------------
% 0.32/1.58 % (32266)------------------------------
% 0.32/1.58 % (32260)Instruction limit reached!
% 0.32/1.58 % (32260)------------------------------
% 0.32/1.58 % (32260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.58 % (32260)Termination reason: Unknown
% 0.32/1.58 % (32260)Termination phase: Property scanning
% 0.32/1.58
% 0.32/1.58 % (32260)Memory used [KB]: 1663
% 0.32/1.58 % (32260)Time elapsed: 0.018 s
% 0.32/1.58 % (32260)Instructions burned: 28 (million)
% 0.32/1.58 % (32260)------------------------------
% 0.32/1.58 % (32260)------------------------------
% 0.32/1.58 % (32269)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_32065 for (2999ds/1041Mi)
% 0.32/1.59 % (32270)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_32065 for (2999ds/7Mi)
% 0.32/1.59 % (32271)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_32065 for (2999ds/16Mi)
% 0.32/1.59 % (32272)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_32065 for (2999ds/3Mi)
% 0.32/1.59 % (32270)Instruction limit reached!
% 0.32/1.59 % (32270)------------------------------
% 0.32/1.59 % (32270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.59 % (32270)Termination reason: Unknown
% 0.32/1.59 % (32270)Termination phase: shuffling
% 0.32/1.59
% 0.32/1.59 % (32270)Memory used [KB]: 1535
% 0.32/1.59 % (32270)Time elapsed: 0.004 s
% 0.32/1.59 % (32270)Instructions burned: 9 (million)
% 0.32/1.59 % (32270)------------------------------
% 0.32/1.59 % (32270)------------------------------
% 0.32/1.59 % (32263)Refutation not found, incomplete strategy
% 0.32/1.59 % (32263)------------------------------
% 0.32/1.59 % (32263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.59 % (32263)Termination reason: Refutation not found, incomplete strategy
% 0.32/1.59
% 0.32/1.59
% 0.32/1.59 % (32263)Memory used [KB]: 6780
% 0.32/1.59 % (32263)Time elapsed: 0.031 s
% 0.32/1.59 % (32263)Instructions burned: 76 (million)
% 0.32/1.59 % (32263)------------------------------
% 0.32/1.59 % (32263)------------------------------
% 0.32/1.59 % (32272)Instruction limit reached!
% 0.32/1.59 % (32272)------------------------------
% 0.32/1.59 % (32272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.59 % (32272)Termination reason: Unknown
% 0.32/1.59 % (32272)Termination phase: shuffling
% 0.32/1.59
% 0.32/1.59 % (32272)Memory used [KB]: 1407
% 0.32/1.59 % (32272)Time elapsed: 0.003 s
% 0.32/1.59 % (32272)Instructions burned: 5 (million)
% 0.32/1.59 % (32272)------------------------------
% 0.32/1.59 % (32272)------------------------------
% 0.32/1.59 % (32271)Instruction limit reached!
% 0.32/1.59 % (32271)------------------------------
% 0.32/1.59 % (32271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.59 % (32271)Termination reason: Unknown
% 0.32/1.59 % (32271)Termination phase: shuffling
% 0.32/1.59
% 0.32/1.59 % (32271)Memory used [KB]: 1663
% 0.32/1.59 % (32271)Time elapsed: 0.007 s
% 0.32/1.59 % (32271)Instructions burned: 18 (million)
% 0.32/1.59 % (32271)------------------------------
% 0.32/1.59 % (32271)------------------------------
% 2.93/1.60 % (32273)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_32065 for (2999ds/3Mi)
% 2.93/1.60 % (32273)Instruction limit reached!
% 2.93/1.60 % (32273)------------------------------
% 2.93/1.60 % (32273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.60 % (32273)Termination reason: Unknown
% 2.93/1.60 % (32273)Termination phase: shuffling
% 2.93/1.60
% 2.93/1.60 % (32273)Memory used [KB]: 1407
% 2.93/1.60 % (32273)Time elapsed: 0.004 s
% 2.93/1.60 % (32273)Instructions burned: 3 (million)
% 2.93/1.60 % (32273)------------------------------
% 2.93/1.60 % (32273)------------------------------
% 2.93/1.60 % (32275)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_32065 for (2999ds/3Mi)
% 2.93/1.60 % (32276)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_32065 for (2999ds/4Mi)
% 2.93/1.60 % (32275)Instruction limit reached!
% 2.93/1.60 % (32275)------------------------------
% 2.93/1.60 % (32275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.60 % (32275)Termination reason: Unknown
% 2.93/1.60 % (32275)Termination phase: shuffling
% 2.93/1.60
% 2.93/1.60 % (32275)Memory used [KB]: 1407
% 2.93/1.60 % (32275)Time elapsed: 0.003 s
% 2.93/1.60 % (32275)Instructions burned: 6 (million)
% 2.93/1.60 % (32275)------------------------------
% 2.93/1.60 % (32275)------------------------------
% 2.93/1.60 % (32277)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_32065 for (2999ds/18Mi)
% 2.93/1.60 % (32276)Instruction limit reached!
% 2.93/1.60 % (32276)------------------------------
% 2.93/1.60 % (32276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.60 % (32276)Termination reason: Unknown
% 2.93/1.60 % (32276)Termination phase: shuffling
% 2.93/1.60
% 2.93/1.60 % (32276)Memory used [KB]: 1407
% 2.93/1.60 % (32276)Time elapsed: 0.003 s
% 2.93/1.60 % (32276)Instructions burned: 5 (million)
% 2.93/1.60 % (32276)------------------------------
% 2.93/1.60 % (32276)------------------------------
% 2.93/1.61 % (32274)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_32065 for (2999ds/7Mi)
% 2.93/1.61 % (32277)Instruction limit reached!
% 2.93/1.61 % (32277)------------------------------
% 2.93/1.61 % (32277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.61 % (32277)Termination reason: Unknown
% 2.93/1.61 % (32277)Termination phase: Property scanning
% 2.93/1.61
% 2.93/1.61 % (32277)Memory used [KB]: 1791
% 2.93/1.61 % (32277)Time elapsed: 0.008 s
% 2.93/1.61 % (32277)Instructions burned: 21 (million)
% 2.93/1.61 % (32277)------------------------------
% 2.93/1.61 % (32277)------------------------------
% 2.93/1.61 % (32274)Instruction limit reached!
% 2.93/1.61 % (32274)------------------------------
% 2.93/1.61 % (32274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.61 % (32274)Termination reason: Unknown
% 2.93/1.61 % (32274)Termination phase: shuffling
% 2.93/1.61
% 2.93/1.61 % (32274)Memory used [KB]: 1407
% 2.93/1.61 % (32274)Time elapsed: 0.004 s
% 2.93/1.61 % (32274)Instructions burned: 7 (million)
% 2.93/1.61 % (32274)------------------------------
% 2.93/1.61 % (32274)------------------------------
% 2.93/1.61 % (32279)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32065 for (2999ds/6Mi)
% 2.93/1.61 % (32279)Instruction limit reached!
% 2.93/1.61 % (32279)------------------------------
% 2.93/1.61 % (32279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.61 % (32279)Termination reason: Unknown
% 2.93/1.61 % (32279)Termination phase: shuffling
% 2.93/1.61
% 2.93/1.61 % (32279)Memory used [KB]: 1407
% 2.93/1.61 % (32279)Time elapsed: 0.003 s
% 2.93/1.61 % (32279)Instructions burned: 6 (million)
% 2.93/1.61 % (32279)------------------------------
% 2.93/1.61 % (32279)------------------------------
% 2.93/1.61 % (32280)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_32065 for (2999ds/902Mi)
% 2.93/1.62 % (32278)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_32065 for (2999ds/710Mi)
% 2.93/1.62 % (32283)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_32065 for (2999ds/21Mi)
% 2.93/1.62 % (32258)Instruction limit reached!
% 2.93/1.62 % (32258)------------------------------
% 2.93/1.62 % (32258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.62 % (32258)Termination reason: Unknown
% 2.93/1.62 % (32258)Termination phase: Saturation
% 2.93/1.62
% 2.93/1.62 % (32258)Memory used [KB]: 7036
% 2.93/1.62 % (32258)Time elapsed: 0.066 s
% 2.93/1.62 % (32258)Instructions burned: 183 (million)
% 2.93/1.62 % (32258)------------------------------
% 2.93/1.62 % (32258)------------------------------
% 2.93/1.62 % (32288)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_32065 for (2999ds/6Mi)
% 2.93/1.62 % (32288)Instruction limit reached!
% 2.93/1.62 % (32288)------------------------------
% 2.93/1.62 % (32288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.62 % (32288)Termination reason: Unknown
% 2.93/1.62 % (32288)Termination phase: shuffling
% 2.93/1.62
% 2.93/1.62 % (32288)Memory used [KB]: 1407
% 2.93/1.62 % (32288)Time elapsed: 0.003 s
% 2.93/1.62 % (32288)Instructions burned: 7 (million)
% 2.93/1.62 % (32288)------------------------------
% 2.93/1.62 % (32288)------------------------------
% 2.93/1.63 % (32283)Instruction limit reached!
% 2.93/1.63 % (32283)------------------------------
% 2.93/1.63 % (32283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.63 % (32283)Termination reason: Unknown
% 2.93/1.63 % (32283)Termination phase: Property scanning
% 2.93/1.63
% 2.93/1.63 % (32283)Memory used [KB]: 1791
% 2.93/1.63 % (32283)Time elapsed: 0.008 s
% 2.93/1.63 % (32283)Instructions burned: 21 (million)
% 2.93/1.63 % (32283)------------------------------
% 2.93/1.63 % (32283)------------------------------
% 2.93/1.63 % (32284)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_32065 for (2999ds/5Mi)
% 2.93/1.63 % (32284)Instruction limit reached!
% 2.93/1.63 % (32284)------------------------------
% 2.93/1.63 % (32284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.63 % (32284)Termination reason: Unknown
% 2.93/1.63 % (32284)Termination phase: shuffling
% 2.93/1.63
% 2.93/1.63 % (32284)Memory used [KB]: 1407
% 2.93/1.63 % (32284)Time elapsed: 0.004 s
% 2.93/1.63 % (32284)Instructions burned: 5 (million)
% 2.93/1.63 % (32284)------------------------------
% 2.93/1.63 % (32284)------------------------------
% 2.93/1.63 % (32289)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_32065 for (2999ds/377Mi)
% 2.93/1.63 % (32290)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_32065 for (2999ds/779Mi)
% 2.93/1.64 % (32291)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_32065 for (2999ds/19Mi)
% 2.93/1.64 % (32292)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_32065 for (2999ds/879Mi)
% 2.93/1.64 % (32291)Instruction limit reached!
% 2.93/1.64 % (32291)------------------------------
% 2.93/1.64 % (32291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.64 % (32291)Termination reason: Unknown
% 2.93/1.64 % (32291)Termination phase: shuffling
% 2.93/1.64
% 2.93/1.64 % (32291)Memory used [KB]: 1791
% 2.93/1.64 % (32291)Time elapsed: 0.007 s
% 2.93/1.64 % (32291)Instructions burned: 22 (million)
% 2.93/1.64 % (32291)------------------------------
% 2.93/1.64 % (32291)------------------------------
% 2.93/1.65 % (32280)Refutation not found, incomplete strategy
% 2.93/1.65 % (32280)------------------------------
% 2.93/1.65 % (32280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.65 % (32280)Termination reason: Refutation not found, incomplete strategy
% 2.93/1.65
% 2.93/1.65
% 2.93/1.65 % (32280)Memory used [KB]: 6908
% 2.93/1.65 % (32280)Time elapsed: 0.034 s
% 2.93/1.65 % (32280)Instructions burned: 98 (million)
% 2.93/1.65 % (32280)------------------------------
% 2.93/1.65 % (32280)------------------------------
% 2.93/1.65 % (32293)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_32065 for (2998ds/17Mi)
% 2.93/1.66 % (32296)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_32065 for (2998ds/3Mi)
% 2.93/1.66 % (32293)Instruction limit reached!
% 2.93/1.66 % (32293)------------------------------
% 2.93/1.66 % (32293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.66 % (32293)Termination reason: Unknown
% 2.93/1.66 % (32293)Termination phase: shuffling
% 2.93/1.66
% 2.93/1.66 % (32293)Memory used [KB]: 1663
% 2.93/1.66 % (32293)Time elapsed: 0.007 s
% 2.93/1.66 % (32293)Instructions burned: 19 (million)
% 2.93/1.66 % (32293)------------------------------
% 2.93/1.66 % (32293)------------------------------
% 2.93/1.66 % (32296)Instruction limit reached!
% 2.93/1.66 % (32296)------------------------------
% 2.93/1.66 % (32296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.66 % (32296)Termination reason: Unknown
% 2.93/1.66 % (32296)Termination phase: shuffling
% 2.93/1.66
% 2.93/1.66 % (32296)Memory used [KB]: 1407
% 2.93/1.66 % (32296)Time elapsed: 0.003 s
% 2.93/1.66 % (32296)Instructions burned: 3 (million)
% 2.93/1.66 % (32296)------------------------------
% 2.93/1.66 % (32296)------------------------------
% 2.93/1.67 % (32298)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_32065 for (2998ds/30Mi)
% 2.93/1.69 % (32305)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_32065 for (2998ds/127Mi)
% 2.93/1.69 % (32298)Instruction limit reached!
% 2.93/1.69 % (32298)------------------------------
% 2.93/1.69 % (32298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.69 % (32298)Termination reason: Unknown
% 2.93/1.69 % (32298)Termination phase: Preprocessing 1
% 2.93/1.69
% 2.93/1.69 % (32298)Memory used [KB]: 1791
% 2.93/1.69 % (32298)Time elapsed: 0.014 s
% 2.93/1.69 % (32298)Instructions burned: 32 (million)
% 2.93/1.69 % (32298)------------------------------
% 2.93/1.69 % (32298)------------------------------
% 2.93/1.70 % (32310)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_32065 for (2998ds/100Mi)
% 2.93/1.74 % (32310)Instruction limit reached!
% 2.93/1.74 % (32310)------------------------------
% 2.93/1.74 % (32310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.74 % (32310)Termination reason: Unknown
% 2.93/1.74 % (32310)Termination phase: Saturation
% 2.93/1.74
% 2.93/1.74 % (32310)Memory used [KB]: 6652
% 2.93/1.74 % (32310)Time elapsed: 0.042 s
% 2.93/1.74 % (32310)Instructions burned: 100 (million)
% 2.93/1.74 % (32310)------------------------------
% 2.93/1.74 % (32310)------------------------------
% 2.93/1.75 % (32305)Instruction limit reached!
% 2.93/1.75 % (32305)------------------------------
% 2.93/1.75 % (32305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.75 % (32305)Termination reason: Unknown
% 2.93/1.75 % (32305)Termination phase: Saturation
% 2.93/1.75
% 2.93/1.75 % (32305)Memory used [KB]: 6908
% 2.93/1.75 % (32305)Time elapsed: 0.090 s
% 2.93/1.75 % (32305)Instructions burned: 128 (million)
% 2.93/1.75 % (32305)------------------------------
% 2.93/1.75 % (32305)------------------------------
% 2.93/1.76 % (32325)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_32065 for (2997ds/3Mi)
% 2.93/1.76 % (32325)Instruction limit reached!
% 2.93/1.76 % (32325)------------------------------
% 2.93/1.76 % (32325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.76 % (32325)Termination reason: Unknown
% 2.93/1.76 % (32325)Termination phase: shuffling
% 2.93/1.76
% 2.93/1.76 % (32325)Memory used [KB]: 1407
% 2.93/1.76 % (32325)Time elapsed: 0.004 s
% 2.93/1.76 % (32325)Instructions burned: 5 (million)
% 2.93/1.76 % (32325)------------------------------
% 2.93/1.76 % (32325)------------------------------
% 2.93/1.77 % (32328)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_32065 for (2997ds/20Mi)
% 2.93/1.77 % (32329)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_32065 for (2997ds/86Mi)
% 2.93/1.77 % (32328)Instruction limit reached!
% 2.93/1.77 % (32328)------------------------------
% 2.93/1.77 % (32328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.77 % (32328)Termination reason: Unknown
% 2.93/1.77 % (32328)Termination phase: Property scanning
% 2.93/1.77
% 2.93/1.77 % (32328)Memory used [KB]: 1663
% 2.93/1.77 % (32328)Time elapsed: 0.009 s
% 2.93/1.77 % (32328)Instructions burned: 21 (million)
% 2.93/1.77 % (32328)------------------------------
% 2.93/1.77 % (32328)------------------------------
% 2.93/1.78 % (32333)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_32065 for (2997ds/107Mi)
% 2.93/1.79 % (32289)Instruction limit reached!
% 2.93/1.79 % (32289)------------------------------
% 2.93/1.79 % (32289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.79 % (32289)Termination reason: Unknown
% 2.93/1.79 % (32289)Termination phase: Saturation
% 2.93/1.79
% 2.93/1.79 % (32289)Memory used [KB]: 7675
% 2.93/1.79 % (32289)Time elapsed: 0.162 s
% 2.93/1.79 % (32289)Instructions burned: 379 (million)
% 2.93/1.79 % (32289)------------------------------
% 2.93/1.79 % (32289)------------------------------
% 2.93/1.79 % (32329)Instruction limit reached!
% 2.93/1.79 % (32329)------------------------------
% 2.93/1.79 % (32329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.79 % (32329)Termination reason: Unknown
% 2.93/1.79 % (32329)Termination phase: Saturation
% 2.93/1.79
% 2.93/1.79 % (32329)Memory used [KB]: 6780
% 2.93/1.79 % (32329)Time elapsed: 0.027 s
% 2.93/1.79 % (32329)Instructions burned: 87 (million)
% 2.93/1.79 % (32329)------------------------------
% 2.93/1.79 % (32329)------------------------------
% 2.93/1.80 % (32334)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_32065 for (2997ds/39Mi)
% 2.93/1.80 % (32335)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_32065 for (2997ds/448Mi)
% 2.93/1.81 % (32334)Instruction limit reached!
% 2.93/1.81 % (32334)------------------------------
% 2.93/1.81 % (32334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.81 % (32334)Termination reason: Unknown
% 2.93/1.81 % (32334)Termination phase: Property scanning
% 2.93/1.81
% 2.93/1.81 % (32334)Memory used [KB]: 2046
% 2.93/1.81 % (32334)Time elapsed: 0.012 s
% 2.93/1.81 % (32334)Instructions burned: 41 (million)
% 2.93/1.81 % (32334)------------------------------
% 2.93/1.81 % (32334)------------------------------
% 2.93/1.82 % (32333)Instruction limit reached!
% 2.93/1.82 % (32333)------------------------------
% 2.93/1.82 % (32333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.82 % (32333)Termination reason: Unknown
% 2.93/1.82 % (32333)Termination phase: Saturation
% 2.93/1.82
% 2.93/1.82 % (32333)Memory used [KB]: 6908
% 2.93/1.82 % (32333)Time elapsed: 0.037 s
% 2.93/1.82 % (32333)Instructions burned: 109 (million)
% 2.93/1.82 % (32333)------------------------------
% 2.93/1.82 % (32333)------------------------------
% 2.93/1.82 % (32336)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_32065 for (2997ds/46Mi)
% 2.93/1.83 % (32337)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_32065 for (2997ds/98Mi)
% 2.93/1.84 % (32336)Instruction limit reached!
% 2.93/1.84 % (32336)------------------------------
% 2.93/1.84 % (32336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.84 % (32336)Termination reason: Unknown
% 2.93/1.84 % (32336)Termination phase: Preprocessing 3
% 2.93/1.84
% 2.93/1.84 % (32336)Memory used [KB]: 2046
% 2.93/1.84 % (32336)Time elapsed: 0.015 s
% 2.93/1.84 % (32336)Instructions burned: 46 (million)
% 2.93/1.84 % (32336)------------------------------
% 2.93/1.84 % (32336)------------------------------
% 2.93/1.85 % (32338)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_32065 for (2997ds/507Mi)
% 2.93/1.86 % (32337)Instruction limit reached!
% 2.93/1.86 % (32337)------------------------------
% 2.93/1.86 % (32337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.86 % (32337)Termination reason: Unknown
% 2.93/1.86 % (32337)Termination phase: Saturation
% 2.93/1.86
% 2.93/1.86 % (32337)Memory used [KB]: 2174
% 2.93/1.86 % (32337)Time elapsed: 0.030 s
% 2.93/1.86 % (32337)Instructions burned: 99 (million)
% 2.93/1.86 % (32337)------------------------------
% 2.93/1.86 % (32337)------------------------------
% 2.93/1.87 % (32341)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_32065 for (2996ds/149Mi)
% 2.93/1.88 % (32338)Refutation not found, incomplete strategy
% 2.93/1.88 % (32338)------------------------------
% 2.93/1.88 % (32338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.88 % (32338)Termination reason: Refutation not found, incomplete strategy
% 2.93/1.88
% 2.93/1.88
% 2.93/1.88 % (32338)Memory used [KB]: 7036
% 2.93/1.88 % (32338)Time elapsed: 0.032 s
% 2.93/1.88 % (32338)Instructions burned: 102 (million)
% 2.93/1.88 % (32338)------------------------------
% 2.93/1.88 % (32338)------------------------------
% 2.93/1.89 % (32350)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_32065 for (2996ds/39Mi)
% 2.93/1.89 % (32278)Instruction limit reached!
% 2.93/1.89 % (32278)------------------------------
% 2.93/1.89 % (32278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.89 % (32278)Termination reason: Unknown
% 2.93/1.89 % (32278)Termination phase: Saturation
% 2.93/1.89
% 2.93/1.89 % (32278)Memory used [KB]: 8059
% 2.93/1.89 % (32278)Time elapsed: 0.276 s
% 2.93/1.89 % (32278)Instructions burned: 710 (million)
% 2.93/1.89 % (32278)------------------------------
% 2.93/1.89 % (32278)------------------------------
% 2.93/1.90 % (32350)Instruction limit reached!
% 2.93/1.90 % (32350)------------------------------
% 2.93/1.90 % (32350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.90 % (32350)Termination reason: Unknown
% 2.93/1.90 % (32350)Termination phase: Preprocessing 3
% 2.93/1.90
% 2.93/1.90 % (32350)Memory used [KB]: 2046
% 2.93/1.90 % (32350)Time elapsed: 0.014 s
% 2.93/1.90 % (32350)Instructions burned: 40 (million)
% 2.93/1.90 % (32350)------------------------------
% 2.93/1.90 % (32350)------------------------------
% 2.93/1.90 % (32357)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_32065 for (2996ds/6Mi)
% 2.93/1.91 % (32290)Instruction limit reached!
% 2.93/1.91 % (32290)------------------------------
% 2.93/1.91 % (32290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.91 % (32290)Termination reason: Unknown
% 2.93/1.91 % (32290)Termination phase: Saturation
% 2.93/1.91
% 2.93/1.91 % (32290)Memory used [KB]: 7931
% 2.93/1.91 % (32290)Time elapsed: 0.272 s
% 2.93/1.91 % (32290)Instructions burned: 780 (million)
% 2.93/1.91 % (32290)------------------------------
% 2.93/1.91 % (32290)------------------------------
% 2.93/1.91 % (32357)Instruction limit reached!
% 2.93/1.91 % (32357)------------------------------
% 2.93/1.91 % (32357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.91 % (32357)Termination reason: Unknown
% 2.93/1.91 % (32357)Termination phase: shuffling
% 2.93/1.91
% 2.93/1.91 % (32357)Memory used [KB]: 1407
% 2.93/1.91 % (32357)Time elapsed: 0.004 s
% 2.93/1.91 % (32357)Instructions burned: 9 (million)
% 2.93/1.91 % (32357)------------------------------
% 2.93/1.91 % (32357)------------------------------
% 2.93/1.91 % (32361)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_32065 for (2996ds/1087Mi)
% 2.93/1.91 % (32363)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_32065 for (2996ds/47Mi)
% 2.93/1.92 % (32365)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_32065 for (2996ds/44Mi)
% 2.93/1.92 % (32341)Instruction limit reached!
% 2.93/1.92 % (32341)------------------------------
% 2.93/1.92 % (32341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.92 % (32341)Termination reason: Unknown
% 2.93/1.92 % (32341)Termination phase: Saturation
% 2.93/1.92
% 2.93/1.92 % (32341)Memory used [KB]: 7036
% 2.93/1.92 % (32341)Time elapsed: 0.051 s
% 2.93/1.92 % (32341)Instructions burned: 149 (million)
% 2.93/1.92 % (32341)------------------------------
% 2.93/1.92 % (32341)------------------------------
% 2.93/1.93 % (32365)Instruction limit reached!
% 2.93/1.93 % (32365)------------------------------
% 2.93/1.93 % (32365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.93 % (32365)Termination reason: Unknown
% 2.93/1.93 % (32365)Termination phase: Property scanning
% 2.93/1.93
% 2.93/1.93 % (32365)Memory used [KB]: 2046
% 2.93/1.93 % (32365)Time elapsed: 0.013 s
% 2.93/1.93 % (32365)Instructions burned: 45 (million)
% 2.93/1.93 % (32365)------------------------------
% 2.93/1.93 % (32365)------------------------------
% 2.93/1.93 % (32370)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_32065 for (2996ds/432Mi)
% 2.93/1.93 % (32363)Instruction limit reached!
% 2.93/1.93 % (32363)------------------------------
% 2.93/1.93 % (32363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.93 % (32363)Termination reason: Unknown
% 2.93/1.93 % (32363)Termination phase: Property scanning
% 2.93/1.93
% 2.93/1.93 % (32363)Memory used [KB]: 2174
% 2.93/1.93 % (32363)Time elapsed: 0.016 s
% 2.93/1.93 % (32363)Instructions burned: 49 (million)
% 2.93/1.93 % (32363)------------------------------
% 2.93/1.93 % (32363)------------------------------
% 2.93/1.93 % (32269)Instruction limit reached!
% 2.93/1.93 % (32269)------------------------------
% 2.93/1.93 % (32269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.93 % (32269)Termination reason: Unknown
% 2.93/1.93 % (32269)Termination phase: Saturation
% 2.93/1.93
% 2.93/1.93 % (32269)Memory used [KB]: 9722
% 2.93/1.93 % (32269)Time elapsed: 0.351 s
% 2.93/1.93 % (32269)Instructions burned: 1042 (million)
% 2.93/1.93 % (32269)------------------------------
% 2.93/1.93 % (32269)------------------------------
% 2.93/1.94 % (32374)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_32065 for (2996ds/62Mi)
% 2.93/1.94 % (32378)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_32065 for (2996ds/31Mi)
% 2.93/1.94 % (32335)Instruction limit reached!
% 2.93/1.94 % (32335)------------------------------
% 2.93/1.94 % (32335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.94 % (32335)Termination reason: Unknown
% 2.93/1.94 % (32335)Termination phase: Saturation
% 2.93/1.94
% 2.93/1.94 % (32335)Memory used [KB]: 7803
% 2.93/1.94 % (32335)Time elapsed: 0.137 s
% 2.93/1.94 % (32335)Instructions burned: 450 (million)
% 2.93/1.94 % (32335)------------------------------
% 2.93/1.94 % (32335)------------------------------
% 2.93/1.94 % (32381)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_32065 for (2995ds/96Mi)
% 2.93/1.95 % (32292)Instruction limit reached!
% 2.93/1.95 % (32292)------------------------------
% 2.93/1.95 % (32292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.95 % (32292)Termination reason: Unknown
% 2.93/1.95 % (32292)Termination phase: Saturation
% 2.93/1.95
% 2.93/1.95 % (32292)Memory used [KB]: 7675
% 2.93/1.95 % (32292)Time elapsed: 0.309 s
% 2.93/1.95 % (32292)Instructions burned: 881 (million)
% 2.93/1.95 % (32292)------------------------------
% 2.93/1.95 % (32292)------------------------------
% 2.93/1.95 % (32378)Instruction limit reached!
% 2.93/1.95 % (32378)------------------------------
% 2.93/1.95 % (32378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.95 % (32378)Termination reason: Unknown
% 2.93/1.95 % (32378)Termination phase: Preprocessing 1
% 2.93/1.95
% 2.93/1.95 % (32378)Memory used [KB]: 1791
% 2.93/1.95 % (32378)Time elapsed: 0.011 s
% 2.93/1.95 % (32378)Instructions burned: 32 (million)
% 2.93/1.95 % (32378)------------------------------
% 2.93/1.95 % (32378)------------------------------
% 2.93/1.95 % (32385)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_32065 for (2995ds/453Mi)
% 2.93/1.95 % (32374)Instruction limit reached!
% 2.93/1.95 % (32374)------------------------------
% 2.93/1.95 % (32374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.95 % (32374)Termination reason: Unknown
% 2.93/1.95 % (32374)Termination phase: Preprocessing 2
% 2.93/1.95
% 2.93/1.95 % (32374)Memory used [KB]: 2174
% 2.93/1.95 % (32374)Time elapsed: 0.019 s
% 2.93/1.95 % (32374)Instructions burned: 62 (million)
% 2.93/1.95 % (32374)------------------------------
% 2.93/1.95 % (32374)------------------------------
% 2.93/1.96 % (32389)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_32065 for (2995ds/71Mi)
% 2.93/1.96 % (32391)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_32065 for (2995ds/83Mi)
% 2.93/1.96 % (32392)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_32065 for (2995ds/11Mi)
% 2.93/1.97 % (32392)Instruction limit reached!
% 2.93/1.97 % (32392)------------------------------
% 2.93/1.97 % (32392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.97 % (32392)Termination reason: Unknown
% 2.93/1.97 % (32392)Termination phase: shuffling
% 2.93/1.97
% 2.93/1.97 % (32392)Memory used [KB]: 1535
% 2.93/1.97 % (32392)Time elapsed: 0.005 s
% 2.93/1.97 % (32392)Instructions burned: 12 (million)
% 2.93/1.97 % (32392)------------------------------
% 2.93/1.97 % (32392)------------------------------
% 2.93/1.97 % (32381)Instruction limit reached!
% 2.93/1.97 % (32381)------------------------------
% 2.93/1.97 % (32381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.97 % (32381)Termination reason: Unknown
% 2.93/1.97 % (32381)Termination phase: Saturation
% 2.93/1.97
% 2.93/1.97 % (32381)Memory used [KB]: 6780
% 2.93/1.97 % (32381)Time elapsed: 0.030 s
% 2.93/1.97 % (32381)Instructions burned: 97 (million)
% 2.93/1.97 % (32381)------------------------------
% 2.93/1.97 % (32381)------------------------------
% 2.93/1.98 % (32389)Instruction limit reached!
% 2.93/1.98 % (32389)------------------------------
% 2.93/1.98 % (32389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.98 % (32389)Termination reason: Unknown
% 2.93/1.98 % (32389)Termination phase: Property scanning
% 2.93/1.98
% 2.93/1.98 % (32389)Memory used [KB]: 2174
% 2.93/1.98 % (32389)Time elapsed: 0.022 s
% 2.93/1.98 % (32389)Instructions burned: 72 (million)
% 2.93/1.98 % (32389)------------------------------
% 2.93/1.98 % (32389)------------------------------
% 2.93/1.98 % (32398)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_32065 for (2995ds/41Mi)
% 2.93/1.98 % (32401)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32065 for (2995ds/6Mi)
% 2.93/1.98 % (32401)Instruction limit reached!
% 2.93/1.98 % (32401)------------------------------
% 2.93/1.98 % (32401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.98 % (32401)Termination reason: Unknown
% 2.93/1.98 % (32401)Termination phase: shuffling
% 2.93/1.98
% 2.93/1.98 % (32401)Memory used [KB]: 1407
% 2.93/1.98 % (32401)Time elapsed: 0.003 s
% 2.93/1.98 % (32401)Instructions burned: 6 (million)
% 2.93/1.98 % (32401)------------------------------
% 2.93/1.98 % (32401)------------------------------
% 2.93/1.98 % (32391)Instruction limit reached!
% 2.93/1.98 % (32391)------------------------------
% 2.93/1.98 % (32391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.98 % (32391)Termination reason: Unknown
% 2.93/1.98 % (32391)Termination phase: Saturation
% 2.93/1.98
% 2.93/1.98 % (32391)Memory used [KB]: 6652
% 2.93/1.98 % (32391)Time elapsed: 0.027 s
% 2.93/1.98 % (32391)Instructions burned: 84 (million)
% 2.93/1.98 % (32391)------------------------------
% 2.93/1.98 % (32391)------------------------------
% 2.93/1.99 % (32404)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_32065 for (2995ds/150Mi)
% 2.93/1.99 % (32398)Instruction limit reached!
% 2.93/1.99 % (32398)------------------------------
% 2.93/1.99 % (32398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.93/1.99 % (32398)Termination reason: Unknown
% 2.93/1.99 % (32398)Termination phase: Property scanning
% 2.93/1.99
% 2.93/1.99 % (32398)Memory used [KB]: 2046
% 2.93/1.99 % (32398)Time elapsed: 0.013 s
% 2.93/1.99 % (32398)Instructions burned: 44 (million)
% 2.93/1.99 % (32398)------------------------------
% 2.93/1.99 % (32398)------------------------------
% 2.93/1.99 % (32408)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_32065 for (2995ds/343Mi)
% 2.93/1.99 % (32409)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_32065 for (2995ds/109Mi)
% 2.93/2.00 % (32412)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_32065 for (2995ds/253Mi)
% 6.11/2.03 % (32409)Instruction limit reached!
% 6.11/2.03 % (32409)------------------------------
% 6.11/2.03 % (32409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.03 % (32409)Termination reason: Unknown
% 6.11/2.03 % (32409)Termination phase: Saturation
% 6.11/2.03
% 6.11/2.03 % (32409)Memory used [KB]: 6908
% 6.11/2.03 % (32409)Time elapsed: 0.033 s
% 6.11/2.03 % (32409)Instructions burned: 109 (million)
% 6.11/2.03 % (32409)------------------------------
% 6.11/2.03 % (32409)------------------------------
% 6.11/2.03 % (32412)Refutation not found, incomplete strategy
% 6.11/2.03 % (32412)------------------------------
% 6.11/2.03 % (32412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.03 % (32412)Termination reason: Refutation not found, incomplete strategy
% 6.11/2.03
% 6.11/2.03
% 6.11/2.03 % (32412)Memory used [KB]: 7036
% 6.11/2.03 % (32412)Time elapsed: 0.031 s
% 6.11/2.03 % (32412)Instructions burned: 99 (million)
% 6.11/2.03 % (32412)------------------------------
% 6.11/2.03 % (32412)------------------------------
% 6.11/2.03 % (32404)Instruction limit reached!
% 6.11/2.03 % (32404)------------------------------
% 6.11/2.03 % (32404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.03 % (32404)Termination reason: Unknown
% 6.11/2.03 % (32404)Termination phase: Saturation
% 6.11/2.03
% 6.11/2.03 % (32404)Memory used [KB]: 7164
% 6.11/2.03 % (32404)Time elapsed: 0.047 s
% 6.11/2.03 % (32404)Instructions burned: 150 (million)
% 6.11/2.03 % (32404)------------------------------
% 6.11/2.03 % (32404)------------------------------
% 6.11/2.04 % (32425)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_32065 for (2995ds/140Mi)
% 6.11/2.04 % (32426)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_32065 for (2995ds/614Mi)
% 6.11/2.04 % (32427)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_32065 for (2994ds/202Mi)
% 6.11/2.06 % (32427)Refutation not found, incomplete strategy
% 6.11/2.06 % (32427)------------------------------
% 6.11/2.06 % (32427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.06 % (32427)Termination reason: Refutation not found, incomplete strategy
% 6.11/2.06
% 6.11/2.06
% 6.11/2.06 % (32427)Memory used [KB]: 6652
% 6.11/2.06 % (32427)Time elapsed: 0.019 s
% 6.11/2.06 % (32427)Instructions burned: 56 (million)
% 6.11/2.06 % (32427)------------------------------
% 6.11/2.06 % (32427)------------------------------
% 6.11/2.07 % (32370)Instruction limit reached!
% 6.11/2.07 % (32370)------------------------------
% 6.11/2.07 % (32370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.07 % (32370)Termination reason: Unknown
% 6.11/2.07 % (32370)Termination phase: Saturation
% 6.11/2.07
% 6.11/2.07 % (32370)Memory used [KB]: 3709
% 6.11/2.07 % (32370)Time elapsed: 0.162 s
% 6.11/2.07 % (32370)Instructions burned: 432 (million)
% 6.11/2.07 % (32370)------------------------------
% 6.11/2.07 % (32370)------------------------------
% 6.11/2.07 % (32443)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_32065 for (2994ds/339Mi)
% 6.11/2.08 % (32449)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_32065 for (2994ds/283Mi)
% 6.11/2.08 % (32425)Instruction limit reached!
% 6.11/2.08 % (32425)------------------------------
% 6.11/2.08 % (32425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.08 % (32425)Termination reason: Unknown
% 6.11/2.08 % (32425)Termination phase: Saturation
% 6.11/2.08
% 6.11/2.08 % (32425)Memory used [KB]: 6780
% 6.11/2.08 % (32425)Time elapsed: 0.048 s
% 6.11/2.08 % (32425)Instructions burned: 141 (million)
% 6.11/2.08 % (32425)------------------------------
% 6.11/2.08 % (32425)------------------------------
% 6.11/2.08 % (32385)Instruction limit reached!
% 6.11/2.08 % (32385)------------------------------
% 6.11/2.08 % (32385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.08 % (32385)Termination reason: Unknown
% 6.11/2.08 % (32385)Termination phase: Saturation
% 6.11/2.08
% 6.11/2.08 % (32385)Memory used [KB]: 7547
% 6.11/2.08 % (32385)Time elapsed: 0.136 s
% 6.11/2.08 % (32385)Instructions burned: 455 (million)
% 6.11/2.08 % (32385)------------------------------
% 6.11/2.08 % (32385)------------------------------
% 6.11/2.09 % (32450)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_32065 for (2994ds/134Mi)
% 6.11/2.09 % (32452)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_32065 for (2994ds/298Mi)
% 6.11/2.10 % (32408)Instruction limit reached!
% 6.11/2.10 % (32408)------------------------------
% 6.11/2.10 % (32408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.11/2.10 % (32408)Termination reason: Unknown
% 6.11/2.10 % (32408)Termination phase: Saturation
% 6.11/2.10
% 6.11/2.10 % (32408)Memory used [KB]: 7547
% 6.11/2.10 % (32408)Time elapsed: 0.112 s
% 6.11/2.10 % (32408)Instructions burned: 343 (million)
% 6.11/2.10 % (32408)------------------------------
% 6.11/2.10 % (32408)------------------------------
% 6.62/2.11 % (32468)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_32065 for (2994ds/192Mi)
% 6.62/2.13 % (32450)Instruction limit reached!
% 6.62/2.13 % (32450)------------------------------
% 6.62/2.13 % (32450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.13 % (32450)Termination reason: Unknown
% 6.62/2.13 % (32450)Termination phase: Saturation
% 6.62/2.13
% 6.62/2.13 % (32450)Memory used [KB]: 6908
% 6.62/2.13 % (32450)Time elapsed: 0.043 s
% 6.62/2.13 % (32450)Instructions burned: 137 (million)
% 6.62/2.13 % (32450)------------------------------
% 6.62/2.13 % (32450)------------------------------
% 6.62/2.14 % (32477)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_32065 for (2994ds/258Mi)
% 6.62/2.16 % (32449)Instruction limit reached!
% 6.62/2.16 % (32449)------------------------------
% 6.62/2.16 % (32449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.16 % (32449)Termination reason: Unknown
% 6.62/2.16 % (32449)Termination phase: Saturation
% 6.62/2.16
% 6.62/2.16 % (32449)Memory used [KB]: 7547
% 6.62/2.16 % (32449)Time elapsed: 0.088 s
% 6.62/2.16 % (32449)Instructions burned: 284 (million)
% 6.62/2.16 % (32449)------------------------------
% 6.62/2.16 % (32449)------------------------------
% 6.62/2.17 % (32468)Instruction limit reached!
% 6.62/2.17 % (32468)------------------------------
% 6.62/2.17 % (32468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.17 % (32468)Termination reason: Unknown
% 6.62/2.17 % (32468)Termination phase: Saturation
% 6.62/2.17
% 6.62/2.17 % (32468)Memory used [KB]: 7419
% 6.62/2.17 % (32468)Time elapsed: 0.059 s
% 6.62/2.17 % (32468)Instructions burned: 196 (million)
% 6.62/2.17 % (32468)------------------------------
% 6.62/2.17 % (32468)------------------------------
% 6.62/2.17 % (32496)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_32065 for (2993ds/90Mi)
% 6.62/2.18 % (32443)Instruction limit reached!
% 6.62/2.18 % (32443)------------------------------
% 6.62/2.18 % (32443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.18 % (32443)Termination reason: Unknown
% 6.62/2.18 % (32443)Termination phase: Saturation
% 6.62/2.18
% 6.62/2.18 % (32443)Memory used [KB]: 7547
% 6.62/2.18 % (32443)Time elapsed: 0.108 s
% 6.62/2.18 % (32443)Instructions burned: 340 (million)
% 6.62/2.18 % (32443)------------------------------
% 6.62/2.18 % (32443)------------------------------
% 6.62/2.18 % (32452)Instruction limit reached!
% 6.62/2.18 % (32452)------------------------------
% 6.62/2.18 % (32452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.18 % (32452)Termination reason: Unknown
% 6.62/2.18 % (32452)Termination phase: Saturation
% 6.62/2.18
% 6.62/2.18 % (32452)Memory used [KB]: 7803
% 6.62/2.18 % (32452)Time elapsed: 0.088 s
% 6.62/2.18 % (32452)Instructions burned: 299 (million)
% 6.62/2.18 % (32452)------------------------------
% 6.62/2.18 % (32452)------------------------------
% 6.62/2.18 % (32500)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_32065 for (2993ds/231Mi)
% 6.62/2.18 % (32477)Refutation not found, incomplete strategy
% 6.62/2.18 % (32477)------------------------------
% 6.62/2.18 % (32477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.18 % (32477)Termination reason: Refutation not found, incomplete strategy
% 6.62/2.18
% 6.62/2.18
% 6.62/2.18 % (32477)Memory used [KB]: 7164
% 6.62/2.18 % (32477)Time elapsed: 0.039 s
% 6.62/2.18 % (32477)Instructions burned: 129 (million)
% 6.62/2.18 % (32477)------------------------------
% 6.62/2.18 % (32477)------------------------------
% 6.62/2.19 % (32504)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_32065 for (2993ds/458Mi)
% 6.62/2.19 % (32508)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_32065 for (2993ds/31Mi)
% 6.62/2.19 % (32509)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_32065 for (2993ds/297Mi)
% 7.18/2.20 % (32496)Instruction limit reached!
% 7.18/2.20 % (32496)------------------------------
% 7.18/2.20 % (32496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.20 % (32496)Termination reason: Unknown
% 7.18/2.20 % (32496)Termination phase: Saturation
% 7.18/2.20
% 7.18/2.20 % (32496)Memory used [KB]: 6780
% 7.18/2.20 % (32496)Time elapsed: 0.028 s
% 7.18/2.20 % (32496)Instructions burned: 92 (million)
% 7.18/2.20 % (32496)------------------------------
% 7.18/2.20 % (32496)------------------------------
% 7.18/2.20 % (32508)Instruction limit reached!
% 7.18/2.20 % (32508)------------------------------
% 7.18/2.20 % (32508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.20 % (32508)Termination reason: Unknown
% 7.18/2.20 % (32508)Termination phase: Preprocessing 2
% 7.18/2.20
% 7.18/2.20 % (32508)Memory used [KB]: 1791
% 7.18/2.20 % (32508)Time elapsed: 0.012 s
% 7.18/2.20 % (32508)Instructions burned: 33 (million)
% 7.18/2.20 % (32508)------------------------------
% 7.18/2.20 % (32508)------------------------------
% 7.18/2.21 % (32515)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_32065 for (2993ds/987Mi)
% 7.18/2.21 % (32516)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_32065 for (2993ds/182Mi)
% 7.18/2.23 % (32426)Instruction limit reached!
% 7.18/2.23 % (32426)------------------------------
% 7.18/2.23 % (32426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.23 % (32426)Termination reason: Unknown
% 7.18/2.23 % (32426)Termination phase: Saturation
% 7.18/2.23
% 7.18/2.23 % (32426)Memory used [KB]: 8315
% 7.18/2.23 % (32426)Time elapsed: 0.196 s
% 7.18/2.23 % (32426)Instructions burned: 615 (million)
% 7.18/2.23 % (32426)------------------------------
% 7.18/2.23 % (32426)------------------------------
% 7.18/2.24 % (32500)Instruction limit reached!
% 7.18/2.24 % (32500)------------------------------
% 7.18/2.24 % (32500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.24 % (32500)Termination reason: Unknown
% 7.18/2.24 % (32500)Termination phase: Saturation
% 7.18/2.24
% 7.18/2.24 % (32500)Memory used [KB]: 6780
% 7.18/2.24 % (32500)Time elapsed: 0.063 s
% 7.18/2.24 % (32500)Instructions burned: 232 (million)
% 7.18/2.24 % (32500)------------------------------
% 7.18/2.24 % (32500)------------------------------
% 7.18/2.24 % (32530)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_32065 for (2993ds/182Mi)
% 7.18/2.25 % (32361)Instruction limit reached!
% 7.18/2.25 % (32361)------------------------------
% 7.18/2.25 % (32361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.25 % (32361)Termination reason: Unknown
% 7.18/2.25 % (32361)Termination phase: Saturation
% 7.18/2.25
% 7.18/2.25 % (32361)Memory used [KB]: 8315
% 7.18/2.25 % (32361)Time elapsed: 0.343 s
% 7.18/2.25 % (32361)Instructions burned: 1087 (million)
% 7.18/2.25 % (32361)------------------------------
% 7.18/2.25 % (32361)------------------------------
% 7.18/2.25 % (32532)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_32065 for (2992ds/154Mi)
% 7.18/2.26 % (32536)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_32065 for (2992ds/79Mi)
% 7.18/2.27 % (32516)Instruction limit reached!
% 7.18/2.27 % (32516)------------------------------
% 7.18/2.27 % (32516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.27 % (32516)Termination reason: Unknown
% 7.18/2.27 % (32516)Termination phase: Saturation
% 7.18/2.27
% 7.18/2.27 % (32516)Memory used [KB]: 7036
% 7.18/2.27 % (32516)Time elapsed: 0.058 s
% 7.18/2.27 % (32516)Instructions burned: 182 (million)
% 7.18/2.27 % (32516)------------------------------
% 7.18/2.27 % (32516)------------------------------
% 7.18/2.28 % (32544)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_32065 for (2992ds/216Mi)
% 7.18/2.28 % (32509)Instruction limit reached!
% 7.18/2.28 % (32509)------------------------------
% 7.18/2.28 % (32509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.28 % (32509)Termination reason: Unknown
% 7.18/2.28 % (32509)Termination phase: Saturation
% 7.18/2.28
% 7.18/2.28 % (32509)Memory used [KB]: 7291
% 7.18/2.28 % (32509)Time elapsed: 0.090 s
% 7.18/2.28 % (32509)Instructions burned: 297 (million)
% 7.18/2.28 % (32509)------------------------------
% 7.18/2.28 % (32509)------------------------------
% 7.18/2.29 % (32536)Instruction limit reached!
% 7.18/2.29 % (32536)------------------------------
% 7.18/2.29 % (32536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.18/2.29 % (32536)Termination reason: Unknown
% 7.18/2.29 % (32536)Termination phase: Saturation
% 7.18/2.29
% 7.18/2.29 % (32536)Memory used [KB]: 6652
% 7.18/2.29 % (32536)Time elapsed: 0.025 s
% 7.18/2.29 % (32536)Instructions burned: 80 (million)
% 7.18/2.29 % (32536)------------------------------
% 7.18/2.29 % (32536)------------------------------
% 7.18/2.29 % (32548)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_32065 for (2992ds/114Mi)
% 7.18/2.30 % (32551)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_32065 for (2992ds/922Mi)
% 7.77/2.30 % (32532)Instruction limit reached!
% 7.77/2.30 % (32532)------------------------------
% 7.77/2.30 % (32532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.30 % (32532)Termination reason: Unknown
% 7.77/2.30 % (32532)Termination phase: Saturation
% 7.77/2.30
% 7.77/2.30 % (32532)Memory used [KB]: 2686
% 7.77/2.30 % (32532)Time elapsed: 0.046 s
% 7.77/2.30 % (32532)Instructions burned: 155 (million)
% 7.77/2.30 % (32532)------------------------------
% 7.77/2.30 % (32532)------------------------------
% 7.77/2.30 % (32530)Instruction limit reached!
% 7.77/2.30 % (32530)------------------------------
% 7.77/2.30 % (32530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.30 % (32530)Termination reason: Unknown
% 7.77/2.30 % (32530)Termination phase: Saturation
% 7.77/2.30
% 7.77/2.30 % (32530)Memory used [KB]: 7164
% 7.77/2.30 % (32530)Time elapsed: 0.059 s
% 7.77/2.30 % (32530)Instructions burned: 182 (million)
% 7.77/2.30 % (32530)------------------------------
% 7.77/2.30 % (32530)------------------------------
% 7.77/2.31 % (32555)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_32065 for (2992ds/182Mi)
% 7.77/2.31 % (32557)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_32065 for (2992ds/164Mi)
% 7.77/2.32 % (32548)Instruction limit reached!
% 7.77/2.32 % (32548)------------------------------
% 7.77/2.32 % (32548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.32 % (32548)Termination reason: Unknown
% 7.77/2.32 % (32548)Termination phase: Saturation
% 7.77/2.32
% 7.77/2.32 % (32548)Memory used [KB]: 6908
% 7.77/2.32 % (32548)Time elapsed: 0.035 s
% 7.77/2.32 % (32548)Instructions burned: 114 (million)
% 7.77/2.32 % (32548)------------------------------
% 7.77/2.32 % (32548)------------------------------
% 7.77/2.33 % (32565)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_32065 for (2992ds/50Mi)
% 7.77/2.34 % (32504)Instruction limit reached!
% 7.77/2.34 % (32504)------------------------------
% 7.77/2.34 % (32504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.34 % (32504)Termination reason: Unknown
% 7.77/2.34 % (32504)Termination phase: Saturation
% 7.77/2.34
% 7.77/2.34 % (32504)Memory used [KB]: 7803
% 7.77/2.34 % (32504)Time elapsed: 0.151 s
% 7.77/2.34 % (32504)Instructions burned: 459 (million)
% 7.77/2.34 % (32504)------------------------------
% 7.77/2.34 % (32504)------------------------------
% 7.77/2.34 % (32544)Instruction limit reached!
% 7.77/2.34 % (32544)------------------------------
% 7.77/2.34 % (32544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.34 % (32544)Termination reason: Unknown
% 7.77/2.34 % (32544)Termination phase: Saturation
% 7.77/2.34
% 7.77/2.34 % (32544)Memory used [KB]: 7291
% 7.77/2.34 % (32544)Time elapsed: 0.063 s
% 7.77/2.34 % (32544)Instructions burned: 217 (million)
% 7.77/2.34 % (32544)------------------------------
% 7.77/2.34 % (32544)------------------------------
% 7.77/2.35 % (32568)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_32065 for (2992ds/368Mi)
% 7.77/2.35 % (32565)Instruction limit reached!
% 7.77/2.35 % (32565)------------------------------
% 7.77/2.35 % (32565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.35 % (32565)Termination reason: Unknown
% 7.77/2.35 % (32565)Termination phase: Property scanning
% 7.77/2.35
% 7.77/2.35 % (32565)Memory used [KB]: 2046
% 7.77/2.35 % (32565)Time elapsed: 0.015 s
% 7.77/2.35 % (32565)Instructions burned: 52 (million)
% 7.77/2.35 % (32565)------------------------------
% 7.77/2.35 % (32565)------------------------------
% 7.77/2.35 % (32571)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_32065 for (2992ds/1021Mi)
% 7.77/2.36 % (32575)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_32065 for (2991ds/267Mi)
% 7.77/2.36 % (32555)Instruction limit reached!
% 7.77/2.36 % (32555)------------------------------
% 7.77/2.36 % (32555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.36 % (32555)Termination reason: Unknown
% 7.77/2.36 % (32555)Termination phase: Saturation
% 7.77/2.36
% 7.77/2.36 % (32555)Memory used [KB]: 6908
% 7.77/2.36 % (32555)Time elapsed: 0.052 s
% 7.77/2.36 % (32555)Instructions burned: 182 (million)
% 7.77/2.36 % (32555)------------------------------
% 7.77/2.36 % (32555)------------------------------
% 7.77/2.36 % (32557)Instruction limit reached!
% 7.77/2.36 % (32557)------------------------------
% 7.77/2.36 % (32557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.36 % (32557)Termination reason: Unknown
% 7.77/2.36 % (32557)Termination phase: Saturation
% 7.77/2.36
% 7.77/2.36 % (32557)Memory used [KB]: 2430
% 7.77/2.36 % (32557)Time elapsed: 0.048 s
% 7.77/2.36 % (32557)Instructions burned: 165 (million)
% 7.77/2.36 % (32557)------------------------------
% 7.77/2.36 % (32557)------------------------------
% 7.77/2.37 % (32577)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_32065 for (2991ds/204Mi)
% 7.77/2.37 % (32579)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_32065 for (2991ds/26Mi)
% 7.77/2.38 % (32579)Instruction limit reached!
% 7.77/2.38 % (32579)------------------------------
% 7.77/2.38 % (32579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.77/2.38 % (32579)Termination reason: Unknown
% 7.77/2.38 % (32579)Termination phase: shuffling
% 7.77/2.38
% 7.77/2.38 % (32579)Memory used [KB]: 1791
% 7.77/2.38 % (32579)Time elapsed: 0.008 s
% 7.77/2.38 % (32579)Instructions burned: 26 (million)
% 7.77/2.38 % (32579)------------------------------
% 7.77/2.38 % (32579)------------------------------
% 7.77/2.39 % (32583)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_32065 for (2991ds/53Mi)
% 8.33/2.40 % (32583)Instruction limit reached!
% 8.33/2.40 % (32583)------------------------------
% 8.33/2.40 % (32583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.40 % (32583)Termination reason: Unknown
% 8.33/2.40 % (32583)Termination phase: Property scanning
% 8.33/2.40
% 8.33/2.40 % (32583)Memory used [KB]: 2046
% 8.33/2.40 % (32583)Time elapsed: 0.016 s
% 8.33/2.40 % (32583)Instructions burned: 53 (million)
% 8.33/2.40 % (32583)------------------------------
% 8.33/2.40 % (32583)------------------------------
% 8.33/2.41 % (32597)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_32065 for (2991ds/4436Mi)
% 8.33/2.43 % (32577)Instruction limit reached!
% 8.33/2.43 % (32577)------------------------------
% 8.33/2.43 % (32577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.43 % (32577)Termination reason: Unknown
% 8.33/2.43 % (32577)Termination phase: Saturation
% 8.33/2.43
% 8.33/2.43 % (32577)Memory used [KB]: 7036
% 8.33/2.43 % (32577)Time elapsed: 0.088 s
% 8.33/2.43 % (32577)Instructions burned: 204 (million)
% 8.33/2.43 % (32577)------------------------------
% 8.33/2.43 % (32577)------------------------------
% 8.33/2.44 % (32575)Instruction limit reached!
% 8.33/2.44 % (32575)------------------------------
% 8.33/2.44 % (32575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.44 % (32575)Termination reason: Unknown
% 8.33/2.44 % (32575)Termination phase: Saturation
% 8.33/2.44
% 8.33/2.44 % (32575)Memory used [KB]: 7547
% 8.33/2.44 % (32575)Time elapsed: 0.106 s
% 8.33/2.44 % (32575)Instructions burned: 269 (million)
% 8.33/2.44 % (32575)------------------------------
% 8.33/2.44 % (32575)------------------------------
% 8.33/2.44 % (32616)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_32065 for (2990ds/1539Mi)
% 8.33/2.45 % (32619)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_32065 for (2990ds/408Mi)
% 8.33/2.46 % (32568)Instruction limit reached!
% 8.33/2.46 % (32568)------------------------------
% 8.33/2.46 % (32568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.46 % (32568)Termination reason: Unknown
% 8.33/2.46 % (32568)Termination phase: Saturation
% 8.33/2.46
% 8.33/2.46 % (32568)Memory used [KB]: 8571
% 8.33/2.46 % (32568)Time elapsed: 0.118 s
% 8.33/2.46 % (32568)Instructions burned: 368 (million)
% 8.33/2.46 % (32568)------------------------------
% 8.33/2.46 % (32568)------------------------------
% 8.33/2.47 % (32625)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_32065 for (2990ds/5205Mi)
% 8.33/2.48 % (32619)Refutation not found, incomplete strategy
% 8.33/2.48 % (32619)------------------------------
% 8.33/2.48 % (32619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.33/2.48 % (32619)Termination reason: Refutation not found, incomplete strategy
% 8.33/2.48
% 8.33/2.48
% 8.33/2.48 % (32619)Memory used [KB]: 7164
% 8.33/2.48 % (32619)Time elapsed: 0.034 s
% 8.33/2.48 % (32619)Instructions burned: 107 (million)
% 8.33/2.48 % (32619)------------------------------
% 8.33/2.48 % (32619)------------------------------
% 8.33/2.49 % (32626)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_32065 for (2990ds/1913Mi)
% 8.70/2.51 % (32515)Instruction limit reached!
% 8.70/2.51 % (32515)------------------------------
% 8.70/2.51 % (32515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/2.51 % (32515)Termination reason: Unknown
% 8.70/2.51 % (32515)Termination phase: Saturation
% 8.70/2.51
% 8.70/2.51 % (32515)Memory used [KB]: 9466
% 8.70/2.51 % (32515)Time elapsed: 0.299 s
% 8.70/2.51 % (32515)Instructions burned: 988 (million)
% 8.70/2.51 % (32515)------------------------------
% 8.70/2.51 % (32515)------------------------------
% 8.70/2.52 % (32627)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_32065 for (2990ds/4350Mi)
% 8.70/2.53 % (32627)Refutation not found, incomplete strategy
% 8.70/2.53 % (32627)------------------------------
% 8.70/2.53 % (32627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/2.53 % (32627)Termination reason: Refutation not found, incomplete strategy
% 8.70/2.53
% 8.70/2.53
% 8.70/2.53 % (32627)Memory used [KB]: 6396
% 8.70/2.53 % (32627)Time elapsed: 0.015 s
% 8.70/2.53 % (32627)Instructions burned: 47 (million)
% 8.70/2.53 % (32627)------------------------------
% 8.70/2.53 % (32627)------------------------------
% 8.70/2.54 % (32628)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_32065 for (2989ds/68Mi)
% 8.70/2.56 % (32628)Instruction limit reached!
% 8.70/2.56 % (32628)------------------------------
% 8.70/2.56 % (32628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/2.56 % (32628)Termination reason: Unknown
% 8.70/2.56 % (32628)Termination phase: Property scanning
% 8.70/2.56
% 8.70/2.56 % (32628)Memory used [KB]: 2174
% 8.70/2.56 % (32628)Time elapsed: 0.022 s
% 8.70/2.56 % (32628)Instructions burned: 69 (million)
% 8.70/2.56 % (32628)------------------------------
% 8.70/2.56 % (32628)------------------------------
% 8.70/2.57 % (32629)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_32065 for (2989ds/358Mi)
% 8.70/2.59 % (32551)Instruction limit reached!
% 8.70/2.59 % (32551)------------------------------
% 8.70/2.59 % (32551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.70/2.59 % (32551)Termination reason: Unknown
% 8.70/2.59 % (32551)Termination phase: Saturation
% 8.70/2.59
% 8.70/2.59 % (32551)Memory used [KB]: 7931
% 8.70/2.59 % (32551)Time elapsed: 0.295 s
% 8.70/2.59 % (32551)Instructions burned: 924 (million)
% 8.70/2.59 % (32551)------------------------------
% 8.70/2.59 % (32551)------------------------------
% 9.36/2.60 % (32630)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_32065 for (2989ds/31Mi)
% 9.36/2.61 % (32630)Instruction limit reached!
% 9.36/2.61 % (32630)------------------------------
% 9.36/2.61 % (32630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.36/2.61 % (32630)Termination reason: Unknown
% 9.36/2.61 % (32630)Termination phase: Preprocessing 1
% 9.36/2.61
% 9.36/2.61 % (32630)Memory used [KB]: 1791
% 9.36/2.61 % (32630)Time elapsed: 0.011 s
% 9.36/2.61 % (32630)Instructions burned: 31 (million)
% 9.36/2.61 % (32630)------------------------------
% 9.36/2.61 % (32630)------------------------------
% 9.36/2.62 % (32631)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_32065 for (2989ds/279Mi)
% 9.36/2.65 % (32631)Refutation not found, incomplete strategy
% 9.36/2.65 % (32631)------------------------------
% 9.36/2.65 % (32631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.36/2.65 % (32631)Termination reason: Refutation not found, incomplete strategy
% 9.36/2.65
% 9.36/2.65
% 9.36/2.65 % (32631)Memory used [KB]: 6908
% 9.36/2.65 % (32631)Time elapsed: 0.031 s
% 9.36/2.65 % (32631)Instructions burned: 110 (million)
% 9.36/2.65 % (32631)------------------------------
% 9.36/2.65 % (32631)------------------------------
% 9.36/2.66 % (32632)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_32065 for (2988ds/258Mi)
% 9.36/2.68 % (32571)Instruction limit reached!
% 9.36/2.68 % (32571)------------------------------
% 9.36/2.68 % (32571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.36/2.68 % (32571)Termination reason: Unknown
% 9.36/2.68 % (32571)Termination phase: Saturation
% 9.36/2.68
% 9.36/2.68 % (32571)Memory used [KB]: 8699
% 9.36/2.68 % (32571)Time elapsed: 0.328 s
% 9.36/2.68 % (32571)Instructions burned: 1021 (million)
% 9.36/2.68 % (32571)------------------------------
% 9.36/2.68 % (32571)------------------------------
% 9.36/2.68 % (32629)Instruction limit reached!
% 9.36/2.68 % (32629)------------------------------
% 9.36/2.68 % (32629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.36/2.68 % (32629)Termination reason: Unknown
% 9.36/2.68 % (32629)Termination phase: Saturation
% 9.36/2.68
% 9.36/2.68 % (32629)Memory used [KB]: 7419
% 9.36/2.68 % (32629)Time elapsed: 0.112 s
% 9.36/2.68 % (32629)Instructions burned: 358 (million)
% 9.36/2.68 % (32629)------------------------------
% 9.36/2.68 % (32629)------------------------------
% 9.36/2.69 % (32633)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_32065 for (2988ds/26Mi)
% 9.36/2.69 % (32634)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_32065 for (2988ds/995Mi)
% 9.36/2.69 % (32633)Instruction limit reached!
% 9.36/2.69 % (32633)------------------------------
% 9.36/2.69 % (32633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.36/2.69 % (32633)Termination reason: Unknown
% 9.36/2.69 % (32633)Termination phase: shuffling
% 9.36/2.69
% 9.36/2.69 % (32633)Memory used [KB]: 1918
% 9.36/2.69 % (32633)Time elapsed: 0.009 s
% 9.36/2.69 % (32633)Instructions burned: 29 (million)
% 9.36/2.69 % (32633)------------------------------
% 9.36/2.69 % (32633)------------------------------
% 9.90/2.70 % (32635)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_32065 for (2988ds/373Mi)
% 9.90/2.74 % (32632)Instruction limit reached!
% 9.90/2.74 % (32632)------------------------------
% 9.90/2.74 % (32632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.90/2.74 % (32632)Termination reason: Unknown
% 9.90/2.74 % (32632)Termination phase: Saturation
% 9.90/2.74
% 9.90/2.74 % (32632)Memory used [KB]: 7419
% 9.90/2.74 % (32632)Time elapsed: 0.081 s
% 9.90/2.74 % (32632)Instructions burned: 259 (million)
% 9.90/2.74 % (32632)------------------------------
% 9.90/2.74 % (32632)------------------------------
% 9.90/2.75 % (32636)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_32065 for (2987ds/253Mi)
% 9.98/2.82 % (32635)Instruction limit reached!
% 9.98/2.82 % (32635)------------------------------
% 9.98/2.82 % (32635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.82 % (32635)Termination reason: Unknown
% 9.98/2.82 % (32635)Termination phase: Saturation
% 9.98/2.82
% 9.98/2.82 % (32635)Memory used [KB]: 8187
% 9.98/2.82 % (32635)Time elapsed: 0.119 s
% 9.98/2.82 % (32635)Instructions burned: 373 (million)
% 9.98/2.82 % (32635)------------------------------
% 9.98/2.82 % (32635)------------------------------
% 9.98/2.82 % (32636)Instruction limit reached!
% 9.98/2.82 % (32636)------------------------------
% 9.98/2.82 % (32636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.82 % (32636)Termination reason: Unknown
% 9.98/2.82 % (32636)Termination phase: Saturation
% 9.98/2.82
% 9.98/2.82 % (32636)Memory used [KB]: 7547
% 9.98/2.82 % (32636)Time elapsed: 0.075 s
% 9.98/2.82 % (32636)Instructions burned: 253 (million)
% 9.98/2.82 % (32636)------------------------------
% 9.98/2.82 % (32636)------------------------------
% 9.98/2.83 % (32637)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_32065 for (2987ds/832Mi)
% 9.98/2.83 % (32638)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_32065 for (2987ds/668Mi)
% 9.98/2.86 % (32637)Refutation not found, incomplete strategy
% 9.98/2.86 % (32637)------------------------------
% 9.98/2.86 % (32637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.86 % (32637)Termination reason: Refutation not found, incomplete strategy
% 9.98/2.86
% 9.98/2.86
% 9.98/2.86 % (32637)Memory used [KB]: 7164
% 9.98/2.86 % (32637)Time elapsed: 0.033 s
% 9.98/2.86 % (32637)Instructions burned: 109 (million)
% 9.98/2.86 % (32637)------------------------------
% 9.98/2.86 % (32637)------------------------------
% 9.98/2.87 % (32639)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_32065 for (2986ds/40Mi)
% 9.98/2.88 % (32639)Instruction limit reached!
% 9.98/2.88 % (32639)------------------------------
% 9.98/2.88 % (32639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.88 % (32639)Termination reason: Unknown
% 9.98/2.88 % (32639)Termination phase: Property scanning
% 9.98/2.88
% 9.98/2.88 % (32639)Memory used [KB]: 2046
% 9.98/2.88 % (32639)Time elapsed: 0.012 s
% 9.98/2.88 % (32639)Instructions burned: 42 (million)
% 9.98/2.88 % (32639)------------------------------
% 9.98/2.88 % (32639)------------------------------
% 9.98/2.89 % (32640)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_32065 for (2986ds/294Mi)
% 10.25/2.92 % (32640)Refutation not found, incomplete strategy
% 10.25/2.92 % (32640)------------------------------
% 10.25/2.92 % (32640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.25/2.92 % (32640)Termination reason: Refutation not found, incomplete strategy
% 10.25/2.92
% 10.25/2.92
% 10.25/2.92 % (32640)Memory used [KB]: 6780
% 10.25/2.92 % (32640)Time elapsed: 0.025 s
% 10.25/2.92 % (32640)Instructions burned: 84 (million)
% 10.25/2.92 % (32640)------------------------------
% 10.25/2.92 % (32640)------------------------------
% 10.25/2.93 % (32641)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_32065 for (2986ds/187Mi)
% 10.25/2.93 % (32616)Instruction limit reached!
% 10.25/2.93 % (32616)------------------------------
% 10.25/2.93 % (32616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.25/2.93 % (32616)Termination reason: Unknown
% 10.25/2.93 % (32616)Termination phase: Saturation
% 10.25/2.93
% 10.25/2.93 % (32616)Memory used [KB]: 10490
% 10.25/2.93 % (32616)Time elapsed: 0.489 s
% 10.25/2.93 % (32616)Instructions burned: 1541 (million)
% 10.25/2.93 % (32616)------------------------------
% 10.25/2.93 % (32616)------------------------------
% 10.25/2.94 % (32642)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_32065 for (2986ds/371Mi)
% 10.25/2.99 % (32641)Instruction limit reached!
% 10.25/2.99 % (32641)------------------------------
% 10.25/2.99 % (32641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.25/2.99 % (32641)Termination reason: Unknown
% 10.25/2.99 % (32641)Termination phase: Saturation
% 10.25/2.99
% 10.25/2.99 % (32641)Memory used [KB]: 7419
% 10.25/2.99 % (32641)Time elapsed: 0.059 s
% 10.25/2.99 % (32641)Instructions burned: 189 (million)
% 10.25/2.99 % (32641)------------------------------
% 10.25/2.99 % (32641)------------------------------
% 10.25/2.99 % (32634)Instruction limit reached!
% 10.25/2.99 % (32634)------------------------------
% 10.25/2.99 % (32634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.25/2.99 % (32634)Termination reason: Unknown
% 10.25/2.99 % (32634)Termination phase: Saturation
% 10.25/2.99
% 10.25/2.99 % (32634)Memory used [KB]: 9210
% 10.25/2.99 % (32634)Time elapsed: 0.303 s
% 10.25/2.99 % (32634)Instructions burned: 995 (million)
% 10.25/2.99 % (32634)------------------------------
% 10.25/2.99 % (32634)------------------------------
% 10.25/3.00 % (32643)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_32065 for (2985ds/1827Mi)
% 10.25/3.00 % (32644)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_32065 for (2985ds/70Mi)
% 13.11/3.02 % (32644)Instruction limit reached!
% 13.11/3.02 % (32644)------------------------------
% 13.11/3.02 % (32644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.11/3.02 % (32644)Termination reason: Unknown
% 13.11/3.02 % (32644)Termination phase: Property scanning
% 13.11/3.02
% 13.11/3.02 % (32644)Memory used [KB]: 2174
% 13.11/3.02 % (32644)Time elapsed: 0.020 s
% 13.11/3.02 % (32644)Instructions burned: 71 (million)
% 13.11/3.02 % (32644)------------------------------
% 13.11/3.02 % (32644)------------------------------
% 13.11/3.03 % (32645)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_32065 for (2985ds/316Mi)
% 13.11/3.03 % (32638)Instruction limit reached!
% 13.11/3.03 % (32638)------------------------------
% 13.11/3.03 % (32638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.11/3.03 % (32638)Termination reason: Unknown
% 13.11/3.03 % (32638)Termination phase: Saturation
% 13.11/3.03
% 13.11/3.03 % (32638)Memory used [KB]: 13944
% 13.11/3.03 % (32638)Time elapsed: 0.203 s
% 13.11/3.03 % (32638)Instructions burned: 668 (million)
% 13.11/3.03 % (32638)------------------------------
% 13.11/3.03 % (32638)------------------------------
% 13.11/3.04 % (32646)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_32065 for (2985ds/932Mi)
% 13.11/3.06 % (32642)Instruction limit reached!
% 13.11/3.06 % (32642)------------------------------
% 13.11/3.06 % (32642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.11/3.06 % (32642)Termination reason: Unknown
% 13.11/3.06 % (32642)Termination phase: Saturation
% 13.11/3.06
% 13.11/3.06 % (32642)Memory used [KB]: 7675
% 13.11/3.06 % (32642)Time elapsed: 0.121 s
% 13.11/3.06 % (32642)Instructions burned: 371 (million)
% 13.11/3.06 % (32642)------------------------------
% 13.11/3.06 % (32642)------------------------------
% 13.11/3.07 % (32647)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_32065 for (2984ds/4714Mi)
% 13.11/3.08 % (32645)Refutation not found, incomplete strategy
% 13.11/3.08 % (32645)------------------------------
% 13.11/3.08 % (32645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.11/3.08 % (32645)Termination reason: Refutation not found, incomplete strategy
% 13.11/3.08
% 13.11/3.08
% 13.11/3.08 % (32645)Memory used [KB]: 7164
% 13.11/3.08 % (32645)Time elapsed: 0.048 s
% 13.11/3.08 % (32645)Instructions burned: 166 (million)
% 13.11/3.08 % (32645)------------------------------
% 13.11/3.08 % (32645)------------------------------
% 13.11/3.09 % (32648)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_32065 for (2984ds/8250Mi)
% 13.11/3.10 % (32626)Instruction limit reached!
% 13.11/3.10 % (32626)------------------------------
% 13.11/3.10 % (32626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.11/3.10 % (32626)Termination reason: Unknown
% 13.11/3.10 % (32626)Termination phase: Saturation
% 13.11/3.10
% 13.11/3.10 % (32626)Memory used [KB]: 4605
% 13.11/3.10 % (32626)Time elapsed: 0.607 s
% 13.11/3.10 % (32626)Instructions burned: 1914 (million)
% 13.11/3.10 % (32626)------------------------------
% 13.11/3.10 % (32626)------------------------------
% 13.11/3.11 % (32649)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_32065 for (2984ds/770Mi)
% 13.68/3.11 % (32647)Refutation not found, incomplete strategy
% 13.68/3.11 % (32647)------------------------------
% 13.68/3.11 % (32647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.68/3.11 % (32647)Termination reason: Refutation not found, incomplete strategy
% 13.68/3.11
% 13.68/3.11
% 13.68/3.11 % (32647)Memory used [KB]: 7164
% 13.68/3.11 % (32647)Time elapsed: 0.045 s
% 13.68/3.11 % (32647)Instructions burned: 158 (million)
% 13.68/3.11 % (32647)------------------------------
% 13.68/3.11 % (32647)------------------------------
% 13.68/3.12 % (32649)Refutation not found, incomplete strategy
% 13.68/3.12 % (32649)------------------------------
% 13.68/3.12 % (32649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.68/3.12 % (32649)Termination reason: Refutation not found, incomplete strategy
% 13.68/3.12
% 13.68/3.12
% 13.68/3.12 % (32649)Memory used [KB]: 6396
% 13.68/3.12 % (32649)Time elapsed: 0.014 s
% 13.68/3.12 % (32649)Instructions burned: 42 (million)
% 13.68/3.12 % (32649)------------------------------
% 13.68/3.12 % (32649)------------------------------
% 13.68/3.12 % (32650)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_32065 for (2984ds/794Mi)
% 13.68/3.13 % (32651)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_32065 for (2984ds/464Mi)
% 14.01/3.27 % (32651)Instruction limit reached!
% 14.01/3.27 % (32651)------------------------------
% 14.01/3.27 % (32651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.01/3.27 % (32651)Termination reason: Unknown
% 14.01/3.27 % (32651)Termination phase: Saturation
% 14.01/3.27
% 14.01/3.27 % (32651)Memory used [KB]: 7036
% 14.01/3.27 % (32651)Time elapsed: 0.138 s
% 14.01/3.27 % (32651)Instructions burned: 464 (million)
% 14.01/3.27 % (32651)------------------------------
% 14.01/3.27 % (32651)------------------------------
% 14.01/3.28 % (32652)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_32065 for (2982ds/1376Mi)
% 14.45/3.32 % (32646)Instruction limit reached!
% 14.45/3.32 % (32646)------------------------------
% 14.45/3.32 % (32646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.45/3.32 % (32646)Termination reason: Unknown
% 14.45/3.32 % (32646)Termination phase: Saturation
% 14.45/3.32
% 14.45/3.32 % (32646)Memory used [KB]: 9978
% 14.45/3.32 % (32646)Time elapsed: 0.306 s
% 14.45/3.32 % (32646)Instructions burned: 932 (million)
% 14.45/3.32 % (32646)------------------------------
% 14.45/3.32 % (32646)------------------------------
% 14.45/3.33 % (32653)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_32065 for (2982ds/906Mi)
% 14.45/3.37 % (32650)Instruction limit reached!
% 14.45/3.37 % (32650)------------------------------
% 14.45/3.37 % (32650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.45/3.37 % (32650)Termination reason: Unknown
% 14.45/3.37 % (32650)Termination phase: Saturation
% 14.45/3.37
% 14.45/3.37 % (32650)Memory used [KB]: 6140
% 14.45/3.37 % (32650)Time elapsed: 0.244 s
% 14.45/3.37 % (32650)Instructions burned: 794 (million)
% 14.45/3.37 % (32650)------------------------------
% 14.45/3.37 % (32650)------------------------------
% 14.45/3.38 % (32654)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_32065 for (2981ds/434Mi)
% 15.30/3.40 % (32654)Refutation not found, incomplete strategy
% 15.30/3.40 % (32654)------------------------------
% 15.30/3.40 % (32654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.30/3.40 % (32654)Termination reason: Refutation not found, incomplete strategy
% 15.30/3.40
% 15.30/3.40
% 15.30/3.40 % (32654)Memory used [KB]: 6908
% 15.30/3.40 % (32654)Time elapsed: 0.024 s
% 15.30/3.40 % (32654)Instructions burned: 78 (million)
% 15.30/3.40 % (32654)------------------------------
% 15.30/3.40 % (32654)------------------------------
% 15.30/3.41 % (32655)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_32065 for (2981ds/865Mi)
% 15.93/3.65 % (32653)Instruction limit reached!
% 15.93/3.65 % (32653)------------------------------
% 15.93/3.65 % (32653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.93/3.65 % (32653)Termination reason: Unknown
% 15.93/3.65 % (32653)Termination phase: Saturation
% 15.93/3.65
% 15.93/3.65 % (32653)Memory used [KB]: 11257
% 15.93/3.65 % (32653)Time elapsed: 0.316 s
% 15.93/3.65 % (32653)Instructions burned: 906 (million)
% 15.93/3.65 % (32653)------------------------------
% 15.93/3.65 % (32653)------------------------------
% 15.93/3.66 % (32643)Instruction limit reached!
% 15.93/3.66 % (32643)------------------------------
% 15.93/3.66 % (32643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.93/3.66 % (32643)Termination reason: Unknown
% 15.93/3.66 % (32643)Termination phase: Saturation
% 15.93/3.66
% 15.93/3.66 % (32643)Memory used [KB]: 10106
% 15.93/3.66 % (32643)Time elapsed: 0.664 s
% 15.93/3.66 % (32643)Instructions burned: 1827 (million)
% 15.93/3.66 % (32643)------------------------------
% 15.93/3.66 % (32643)------------------------------
% 15.93/3.66 % (32656)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_32065 for (2978ds/593Mi)
% 15.93/3.67 % (32657)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_32065 for (2978ds/443Mi)
% 15.93/3.67 % (32655)Instruction limit reached!
% 15.93/3.67 % (32655)------------------------------
% 15.93/3.67 % (32655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.93/3.67 % (32655)Termination reason: Unknown
% 15.93/3.67 % (32655)Termination phase: Saturation
% 15.93/3.67
% 15.93/3.67 % (32655)Memory used [KB]: 9466
% 15.93/3.67 % (32655)Time elapsed: 0.262 s
% 15.93/3.67 % (32655)Instructions burned: 867 (million)
% 15.93/3.67 % (32655)------------------------------
% 15.93/3.67 % (32655)------------------------------
% 15.93/3.68 % (32658)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_32065 for (2978ds/594Mi)
% 16.80/3.70 % (32652)Instruction limit reached!
% 16.80/3.70 % (32652)------------------------------
% 16.80/3.70 % (32652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.80/3.70 % (32652)Termination reason: Unknown
% 16.80/3.70 % (32652)Termination phase: Saturation
% 16.80/3.70
% 16.80/3.70 % (32652)Memory used [KB]: 12281
% 16.80/3.70 % (32652)Time elapsed: 0.423 s
% 16.80/3.70 % (32652)Instructions burned: 1378 (million)
% 16.80/3.70 % (32652)------------------------------
% 16.80/3.70 % (32652)------------------------------
% 16.80/3.71 % (32659)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_32065 for (2978ds/327Mi)
% 17.44/3.80 % (32597)Instruction limit reached!
% 17.44/3.80 % (32597)------------------------------
% 17.44/3.80 % (32597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.80 % (32597)Termination reason: Unknown
% 17.44/3.80 % (32597)Termination phase: Saturation
% 17.44/3.80
% 17.44/3.80 % (32597)Memory used [KB]: 13176
% 17.44/3.80 % (32597)Time elapsed: 1.396 s
% 17.44/3.80 % (32597)Instructions burned: 4436 (million)
% 17.44/3.80 % (32597)------------------------------
% 17.44/3.80 % (32597)------------------------------
% 17.44/3.81 % (32657)Instruction limit reached!
% 17.44/3.81 % (32657)------------------------------
% 17.44/3.81 % (32657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.81 % (32657)Termination reason: Unknown
% 17.44/3.81 % (32657)Termination phase: Saturation
% 17.44/3.81
% 17.44/3.81 % (32657)Memory used [KB]: 8187
% 17.44/3.81 % (32657)Time elapsed: 0.139 s
% 17.44/3.81 % (32657)Instructions burned: 443 (million)
% 17.44/3.81 % (32657)------------------------------
% 17.44/3.81 % (32657)------------------------------
% 17.44/3.81 % (32659)Instruction limit reached!
% 17.44/3.81 % (32659)------------------------------
% 17.44/3.81 % (32659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.81 % (32659)Termination reason: Unknown
% 17.44/3.81 % (32659)Termination phase: Saturation
% 17.44/3.81
% 17.44/3.81 % (32659)Memory used [KB]: 7931
% 17.44/3.81 % (32659)Time elapsed: 0.104 s
% 17.44/3.81 % (32659)Instructions burned: 329 (million)
% 17.44/3.81 % (32659)------------------------------
% 17.44/3.81 % (32659)------------------------------
% 17.44/3.81 % (32660)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_32065 for (2977ds/5411Mi)
% 17.44/3.82 % (32661)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_32065 for (2977ds/1762Mi)
% 17.44/3.82 % (32662)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_32065 for (2977ds/96Mi)
% 17.44/3.84 % (32660)Refutation not found, incomplete strategy
% 17.44/3.84 % (32660)------------------------------
% 17.44/3.84 % (32660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.84 % (32660)Termination reason: Refutation not found, incomplete strategy
% 17.44/3.84
% 17.44/3.84
% 17.44/3.84 % (32660)Memory used [KB]: 6780
% 17.44/3.84 % (32660)Time elapsed: 0.025 s
% 17.44/3.84 % (32660)Instructions burned: 74 (million)
% 17.44/3.84 % (32660)------------------------------
% 17.44/3.84 % (32660)------------------------------
% 17.44/3.84 % (32656)Instruction limit reached!
% 17.44/3.84 % (32656)------------------------------
% 17.44/3.84 % (32656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.84 % (32656)Termination reason: Unknown
% 17.44/3.84 % (32656)Termination phase: Saturation
% 17.44/3.84
% 17.44/3.84 % (32656)Memory used [KB]: 8315
% 17.44/3.84 % (32656)Time elapsed: 0.183 s
% 17.44/3.84 % (32656)Instructions burned: 593 (million)
% 17.44/3.84 % (32656)------------------------------
% 17.44/3.84 % (32656)------------------------------
% 17.44/3.85 % (32663)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_32065 for (2976ds/503Mi)
% 17.44/3.85 % (32664)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_32065 for (2976ds/90Mi)
% 17.44/3.85 % (32662)Instruction limit reached!
% 17.44/3.85 % (32662)------------------------------
% 17.44/3.85 % (32662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.85 % (32662)Termination reason: Unknown
% 17.44/3.85 % (32662)Termination phase: Saturation
% 17.44/3.85
% 17.44/3.85 % (32662)Memory used [KB]: 6652
% 17.44/3.85 % (32662)Time elapsed: 0.027 s
% 17.44/3.85 % (32662)Instructions burned: 96 (million)
% 17.44/3.85 % (32662)------------------------------
% 17.44/3.85 % (32662)------------------------------
% 17.44/3.86 % (32665)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_32065 for (2976ds/593Mi)
% 17.44/3.87 % (32658)Instruction limit reached!
% 17.44/3.87 % (32658)------------------------------
% 17.44/3.87 % (32658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.87 % (32658)Termination reason: Unknown
% 17.44/3.87 % (32658)Termination phase: Saturation
% 17.44/3.87
% 17.44/3.87 % (32658)Memory used [KB]: 8315
% 17.44/3.87 % (32658)Time elapsed: 0.186 s
% 17.44/3.87 % (32658)Instructions burned: 595 (million)
% 17.44/3.87 % (32658)------------------------------
% 17.44/3.87 % (32658)------------------------------
% 17.44/3.87 % (32663)Refutation not found, incomplete strategy
% 17.44/3.87 % (32663)------------------------------
% 17.44/3.87 % (32663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.87 % (32663)Termination reason: Refutation not found, incomplete strategy
% 17.44/3.87
% 17.44/3.87
% 17.44/3.87 % (32663)Memory used [KB]: 6780
% 17.44/3.87 % (32663)Time elapsed: 0.026 s
% 17.44/3.87 % (32663)Instructions burned: 80 (million)
% 17.44/3.87 % (32663)------------------------------
% 17.44/3.87 % (32663)------------------------------
% 17.44/3.88 % (32664)Instruction limit reached!
% 17.44/3.88 % (32664)------------------------------
% 17.44/3.88 % (32664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.88 % (32664)Termination reason: Unknown
% 17.44/3.88 % (32664)Termination phase: Saturation
% 17.44/3.88
% 17.44/3.88 % (32664)Memory used [KB]: 6780
% 17.44/3.88 % (32664)Time elapsed: 0.027 s
% 17.44/3.88 % (32664)Instructions burned: 90 (million)
% 17.44/3.88 % (32664)------------------------------
% 17.44/3.88 % (32664)------------------------------
% 17.44/3.88 % (32666)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_32065 for (2976ds/1512Mi)
% 17.44/3.88 % (32667)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_32065 for (2976ds/569Mi)
% 17.44/3.89 % (32668)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_32065 for (2976ds/501Mi)
% 18.34/3.91 % (32666)Refutation not found, incomplete strategy
% 18.34/3.91 % (32666)------------------------------
% 18.34/3.91 % (32666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.34/3.91 % (32666)Termination reason: Refutation not found, incomplete strategy
% 18.34/3.91
% 18.34/3.91
% 18.34/3.91 % (32666)Memory used [KB]: 7164
% 18.34/3.91 % (32666)Time elapsed: 0.034 s
% 18.34/3.91 % (32666)Instructions burned: 111 (million)
% 18.34/3.91 % (32666)------------------------------
% 18.34/3.91 % (32666)------------------------------
% 18.34/3.92 % (32668)Refutation not found, incomplete strategy
% 18.34/3.92 % (32668)------------------------------
% 18.34/3.92 % (32668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.34/3.92 % (32668)Termination reason: Refutation not found, incomplete strategy
% 18.34/3.92
% 18.34/3.92
% 18.34/3.92 % (32668)Memory used [KB]: 7164
% 18.34/3.92 % (32668)Time elapsed: 0.034 s
% 18.34/3.92 % (32668)Instructions burned: 109 (million)
% 18.34/3.92 % (32668)------------------------------
% 18.34/3.92 % (32668)------------------------------
% 18.34/3.92 % (32669)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_32065 for (2976ds/562Mi)
% 18.34/3.93 % (32670)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_32065 for (2976ds/406Mi)
% 18.34/3.99 % (32625)Instruction limit reached!
% 18.34/3.99 % (32625)------------------------------
% 18.34/3.99 % (32625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.34/3.99 % (32625)Termination reason: Unknown
% 18.34/3.99 % (32625)Termination phase: Saturation
% 18.34/3.99
% 18.34/3.99 % (32625)Memory used [KB]: 14967
% 18.34/3.99 % (32625)Time elapsed: 1.522 s
% 18.34/3.99 % (32625)Instructions burned: 5208 (million)
% 18.34/3.99 % (32625)------------------------------
% 18.34/3.99 % (32625)------------------------------
% 18.34/4.00 % (32671)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_32065 for (2975ds/582Mi)
% 20.22/4.02 % (32665)Instruction limit reached!
% 20.22/4.02 % (32665)------------------------------
% 20.22/4.02 % (32665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.22/4.02 % (32665)Termination reason: Unknown
% 20.22/4.02 % (32665)Termination phase: Saturation
% 20.22/4.02
% 20.22/4.02 % (32665)Memory used [KB]: 7803
% 20.22/4.02 % (32665)Time elapsed: 0.166 s
% 20.22/4.02 % (32665)Instructions burned: 594 (million)
% 20.22/4.02 % (32665)------------------------------
% 20.22/4.02 % (32665)------------------------------
% 20.22/4.03 % (32672)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_32065 for (2975ds/456Mi)
% 20.22/4.05 % (32667)Instruction limit reached!
% 20.22/4.05 % (32667)------------------------------
% 20.22/4.05 % (32667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.22/4.05 % (32667)Termination reason: Unknown
% 20.22/4.05 % (32667)Termination phase: Saturation
% 20.22/4.05
% 20.22/4.05 % (32667)Memory used [KB]: 7931
% 20.22/4.05 % (32667)Time elapsed: 0.169 s
% 20.22/4.05 % (32667)Instructions burned: 571 (million)
% 20.22/4.05 % (32667)------------------------------
% 20.22/4.05 % (32667)------------------------------
% 20.22/4.05 % (32670)Refutation not found, non-redundant clauses discarded% (32670)------------------------------
% 20.22/4.05 % (32670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.22/4.05 % (32670)Termination reason: Refutation not found, non-redundant clauses discarded
% 20.22/4.05
% 20.22/4.05 % (32670)Memory used [KB]: 7675
% 20.22/4.05 % (32670)Time elapsed: 0.126 s
% 20.22/4.05 % (32670)Instructions burned: 394 (million)
% 20.22/4.05 % (32670)------------------------------
% 20.22/4.05 % (32670)------------------------------
% 20.22/4.06 % (32673)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_32065 for (2974ds/393Mi)
% 20.22/4.06 % (32674)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_32065 for (2974ds/1335Mi)
% 20.22/4.07 % (32672)Refutation not found, incomplete strategy
% 20.22/4.07 % (32672)------------------------------
% 20.22/4.07 % (32672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.22/4.07 % (32672)Termination reason: Refutation not found, incomplete strategy
% 20.22/4.07
% 20.22/4.07
% 20.22/4.07 % (32672)Memory used [KB]: 7291
% 20.22/4.07 % (32672)Time elapsed: 0.040 s
% 20.22/4.07 % (32672)Instructions burned: 125 (million)
% 20.22/4.07 % (32672)------------------------------
% 20.22/4.07 % (32672)------------------------------
% 20.22/4.08 % (32675)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_32065 for (2974ds/3373Mi)
% 20.22/4.09 % (32669)Instruction limit reached!
% 20.22/4.09 % (32669)------------------------------
% 20.22/4.09 % (32669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.22/4.09 % (32669)Termination reason: Unknown
% 20.22/4.09 % (32669)Termination phase: Saturation
% 20.22/4.09
% 20.22/4.09 % (32669)Memory used [KB]: 8059
% 20.22/4.09 % (32669)Time elapsed: 0.171 s
% 20.22/4.09 % (32669)Instructions burned: 562 (million)
% 20.22/4.09 % (32669)------------------------------
% 20.22/4.09 % (32669)------------------------------
% 20.22/4.10 % (32676)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_32065 for (2974ds/474Mi)
% 20.73/4.17 % (32673)Instruction limit reached!
% 20.73/4.17 % (32673)------------------------------
% 20.73/4.17 % (32673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.73/4.17 % (32673)Termination reason: Unknown
% 20.73/4.17 % (32673)Termination phase: Saturation
% 20.73/4.17
% 20.73/4.17 % (32673)Memory used [KB]: 7419
% 20.73/4.17 % (32673)Time elapsed: 0.113 s
% 20.73/4.17 % (32673)Instructions burned: 393 (million)
% 20.73/4.17 % (32673)------------------------------
% 20.73/4.17 % (32673)------------------------------
% 20.73/4.18 % (32677)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_32065 for (2973ds/157Mi)
% 20.73/4.19 % (32671)Instruction limit reached!
% 20.73/4.19 % (32671)------------------------------
% 20.73/4.19 % (32671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.73/4.19 % (32671)Termination reason: Unknown
% 20.73/4.19 % (32671)Termination phase: Saturation
% 20.73/4.19
% 20.73/4.19 % (32671)Memory used [KB]: 8187
% 20.73/4.19 % (32671)Time elapsed: 0.182 s
% 20.73/4.19 % (32671)Instructions burned: 583 (million)
% 20.73/4.19 % (32671)------------------------------
% 20.73/4.19 % (32671)------------------------------
% 20.73/4.20 % (32678)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_32065 for (2973ds/590Mi)
% 21.06/4.23 % (32677)Instruction limit reached!
% 21.06/4.23 % (32677)------------------------------
% 21.06/4.23 % (32677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.06/4.23 % (32677)Termination reason: Unknown
% 21.06/4.23 % (32677)Termination phase: Saturation
% 21.06/4.23
% 21.06/4.23 % (32677)Memory used [KB]: 6908
% 21.06/4.23 % (32677)Time elapsed: 0.046 s
% 21.06/4.23 % (32677)Instructions burned: 160 (million)
% 21.06/4.23 % (32677)------------------------------
% 21.06/4.23 % (32677)------------------------------
% 21.06/4.24 % (32679)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_32065 for (2973ds/104Mi)
% 21.06/4.24 % (32676)Instruction limit reached!
% 21.06/4.24 % (32676)------------------------------
% 21.06/4.24 % (32676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.06/4.24 % (32676)Termination reason: Unknown
% 21.06/4.24 % (32676)Termination phase: Saturation
% 21.06/4.24
% 21.06/4.24 % (32676)Memory used [KB]: 8059
% 21.06/4.24 % (32676)Time elapsed: 0.144 s
% 21.06/4.24 % (32676)Instructions burned: 474 (million)
% 21.06/4.24 % (32676)------------------------------
% 21.06/4.24 % (32676)------------------------------
% 21.06/4.25 % (32680)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_32065 for (2972ds/414Mi)
% 21.06/4.27 % (32679)Instruction limit reached!
% 21.06/4.27 % (32679)------------------------------
% 21.06/4.27 % (32679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.06/4.27 % (32679)Termination reason: Unknown
% 21.06/4.27 % (32679)Termination phase: Saturation
% 21.06/4.27
% 21.06/4.27 % (32679)Memory used [KB]: 2558
% 21.06/4.27 % (32679)Time elapsed: 0.032 s
% 21.06/4.27 % (32679)Instructions burned: 104 (million)
% 21.06/4.27 % (32679)------------------------------
% 21.06/4.27 % (32679)------------------------------
% 21.06/4.28 % (32681)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_32065 for (2972ds/715Mi)
% 21.51/4.31 % (32661)Instruction limit reached!
% 21.51/4.31 % (32661)------------------------------
% 21.51/4.31 % (32661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.51/4.31 % (32661)Termination reason: Unknown
% 21.51/4.31 % (32661)Termination phase: Saturation
% 21.51/4.31
% 21.51/4.31 % (32661)Memory used [KB]: 9210
% 21.51/4.31 % (32661)Time elapsed: 0.499 s
% 21.51/4.31 % (32661)Instructions burned: 1764 (million)
% 21.51/4.31 % (32661)------------------------------
% 21.51/4.31 % (32661)------------------------------
% 21.51/4.32 % (32682)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_32065 for (2972ds/961Mi)
% 21.51/4.37 % (32678)Instruction limit reached!
% 21.51/4.37 % (32678)------------------------------
% 21.51/4.37 % (32678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.51/4.37 % (32678)Termination reason: Unknown
% 21.51/4.37 % (32678)Termination phase: Saturation
% 21.51/4.37
% 21.51/4.37 % (32678)Memory used [KB]: 7803
% 21.51/4.37 % (32678)Time elapsed: 0.179 s
% 21.51/4.37 % (32678)Instructions burned: 590 (million)
% 21.51/4.37 % (32678)------------------------------
% 21.51/4.37 % (32678)------------------------------
% 21.51/4.37 % (32680)Instruction limit reached!
% 21.51/4.37 % (32680)------------------------------
% 21.51/4.37 % (32680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.51/4.37 % (32680)Termination reason: Unknown
% 21.51/4.37 % (32680)Termination phase: Saturation
% 21.51/4.37
% 21.51/4.37 % (32680)Memory used [KB]: 7419
% 21.51/4.37 % (32680)Time elapsed: 0.124 s
% 21.51/4.37 % (32680)Instructions burned: 415 (million)
% 21.51/4.37 % (32680)------------------------------
% 21.51/4.37 % (32680)------------------------------
% 21.51/4.38 % (32683)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_32065 for (2971ds/1213Mi)
% 21.51/4.38 % (32684)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_32065 for (2971ds/1979Mi)
% 21.96/4.42 % (32674)Instruction limit reached!
% 21.96/4.42 % (32674)------------------------------
% 21.96/4.42 % (32674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.96/4.42 % (32674)Termination reason: Unknown
% 21.96/4.42 % (32674)Termination phase: Saturation
% 21.96/4.42
% 21.96/4.42 % (32674)Memory used [KB]: 8315
% 21.96/4.42 % (32674)Time elapsed: 0.361 s
% 21.96/4.42 % (32674)Instructions burned: 1335 (million)
% 21.96/4.42 % (32674)------------------------------
% 21.96/4.42 % (32674)------------------------------
% 21.96/4.43 % (32685)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_32065 for (2971ds/481Mi)
% 22.43/4.50 % (32681)Instruction limit reached!
% 22.43/4.50 % (32681)------------------------------
% 22.43/4.50 % (32681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.43/4.50 % (32681)Termination reason: Unknown
% 22.43/4.50 % (32681)Termination phase: Saturation
% 22.43/4.50
% 22.43/4.50 % (32681)Memory used [KB]: 4861
% 22.43/4.50 % (32681)Time elapsed: 0.226 s
% 22.43/4.50 % (32681)Instructions burned: 717 (million)
% 22.43/4.50 % (32681)------------------------------
% 22.43/4.50 % (32681)------------------------------
% 22.43/4.51 % (32686)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_32065 for (2970ds/783Mi)
% 22.43/4.58 % (32685)Instruction limit reached!
% 22.43/4.58 % (32685)------------------------------
% 22.43/4.58 % (32685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.43/4.58 % (32685)Termination reason: Unknown
% 22.43/4.58 % (32685)Termination phase: Saturation
% 22.43/4.58
% 22.43/4.58 % (32685)Memory used [KB]: 7931
% 22.43/4.58 % (32685)Time elapsed: 0.152 s
% 22.43/4.58 % (32685)Instructions burned: 482 (million)
% 22.43/4.58 % (32685)------------------------------
% 22.43/4.58 % (32685)------------------------------
% 22.43/4.59 % (32687)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_32065 for (2969ds/432Mi)
% 22.94/4.63 % (32682)Instruction limit reached!
% 22.94/4.63 % (32682)------------------------------
% 22.94/4.63 % (32682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.94/4.63 % (32682)Termination reason: Unknown
% 22.94/4.63 % (32682)Termination phase: Saturation
% 22.94/4.63
% 22.94/4.63 % (32682)Memory used [KB]: 7803
% 22.94/4.63 % (32682)Time elapsed: 0.305 s
% 22.94/4.63 % (32682)Instructions burned: 963 (million)
% 22.94/4.63 % (32682)------------------------------
% 22.94/4.63 % (32682)------------------------------
% 22.94/4.64 % (32688)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_32065 for (2969ds/1670Mi)
% 23.36/4.73 % (32687)Instruction limit reached!
% 23.36/4.73 % (32687)------------------------------
% 23.36/4.73 % (32687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.36/4.73 % (32687)Termination reason: Unknown
% 23.36/4.73 % (32687)Termination phase: Saturation
% 23.36/4.73
% 23.36/4.73 % (32687)Memory used [KB]: 7675
% 23.36/4.73 % (32687)Time elapsed: 0.137 s
% 23.36/4.73 % (32687)Instructions burned: 434 (million)
% 23.36/4.73 % (32687)------------------------------
% 23.36/4.73 % (32687)------------------------------
% 23.36/4.74 % (32689)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_32065 for (2968ds/90Mi)
% 23.36/4.76 % (32686)Instruction limit reached!
% 23.36/4.76 % (32686)------------------------------
% 23.36/4.76 % (32686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.36/4.76 % (32686)Termination reason: Unknown
% 23.36/4.76 % (32686)Termination phase: Saturation
% 23.36/4.76
% 23.36/4.76 % (32686)Memory used [KB]: 8315
% 23.36/4.76 % (32686)Time elapsed: 0.247 s
% 23.36/4.76 % (32686)Instructions burned: 786 (million)
% 23.36/4.76 % (32686)------------------------------
% 23.36/4.76 % (32686)------------------------------
% 23.36/4.76 % (32683)Instruction limit reached!
% 23.36/4.76 % (32683)------------------------------
% 23.36/4.76 % (32683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.36/4.76 % (32683)Termination reason: Unknown
% 23.36/4.76 % (32683)Termination phase: Saturation
% 23.36/4.76
% 23.36/4.76 % (32683)Memory used [KB]: 8699
% 23.36/4.76 % (32683)Time elapsed: 0.378 s
% 23.36/4.76 % (32683)Instructions burned: 1213 (million)
% 23.36/4.76 % (32683)------------------------------
% 23.36/4.76 % (32683)------------------------------
% 23.36/4.77 % (32689)Instruction limit reached!
% 23.36/4.77 % (32689)------------------------------
% 23.36/4.77 % (32689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.36/4.77 % (32689)Termination reason: Unknown
% 23.36/4.77 % (32689)Termination phase: Saturation
% 23.36/4.77
% 23.36/4.77 % (32689)Memory used [KB]: 6780
% 23.36/4.77 % (32689)Time elapsed: 0.027 s
% 23.36/4.77 % (32689)Instructions burned: 91 (million)
% 23.36/4.77 % (32689)------------------------------
% 23.36/4.77 % (32689)------------------------------
% 23.36/4.77 % (32690)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_32065 for (2967ds/346Mi)
% 23.36/4.77 % (32691)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_32065 for (2967ds/401Mi)
% 23.36/4.77 % (32692)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_32065 for (2967ds/6454Mi)
% 24.27/4.88 % (32690)Instruction limit reached!
% 24.27/4.88 % (32690)------------------------------
% 24.27/4.88 % (32690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.27/4.88 % (32690)Termination reason: Unknown
% 24.27/4.88 % (32690)Termination phase: Saturation
% 24.27/4.88
% 24.27/4.88 % (32690)Memory used [KB]: 7675
% 24.27/4.88 % (32690)Time elapsed: 0.111 s
% 24.27/4.88 % (32690)Instructions burned: 346 (million)
% 24.27/4.88 % (32690)------------------------------
% 24.27/4.88 % (32690)------------------------------
% 24.27/4.89 % (32693)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_32065 for (2966ds/283Mi)
% 24.27/4.89 % (32691)Instruction limit reached!
% 24.27/4.89 % (32691)------------------------------
% 24.27/4.89 % (32691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.27/4.89 % (32691)Termination reason: Unknown
% 24.27/4.89 % (32691)Termination phase: Saturation
% 24.27/4.89
% 24.27/4.89 % (32691)Memory used [KB]: 8059
% 24.27/4.89 % (32691)Time elapsed: 0.125 s
% 24.27/4.89 % (32691)Instructions burned: 403 (million)
% 24.27/4.89 % (32691)------------------------------
% 24.27/4.89 % (32691)------------------------------
% 24.63/4.90 % (32694)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_32065 for (2966ds/865Mi)
% 24.63/4.94 % (32694)Refutation not found, incomplete strategy
% 24.63/4.94 % (32694)------------------------------
% 24.63/4.94 % (32694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.63/4.94 % (32694)Termination reason: Refutation not found, incomplete strategy
% 24.63/4.94
% 24.63/4.94
% 24.63/4.94 % (32694)Memory used [KB]: 7419
% 24.63/4.94 % (32694)Time elapsed: 0.039 s
% 24.63/4.94 % (32694)Instructions burned: 119 (million)
% 24.63/4.94 % (32694)------------------------------
% 24.63/4.94 % (32694)------------------------------
% 24.63/4.95 % (32695)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_32065 for (2965ds/4528Mi)
% 24.63/4.97 % (32695)Refutation not found, incomplete strategy
% 24.63/4.97 % (32695)------------------------------
% 24.63/4.97 % (32695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.63/4.97 % (32695)Termination reason: Refutation not found, incomplete strategy
% 24.63/4.97
% 24.63/4.97
% 24.63/4.97 % (32695)Memory used [KB]: 1918
% 24.63/4.97 % (32695)Time elapsed: 0.016 s
% 24.63/4.97 % (32695)Instructions burned: 44 (million)
% 24.63/4.97 % (32695)------------------------------
% 24.63/4.97 % (32695)------------------------------
% 24.63/4.98 % (32696)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_32065 for (2965ds/1001Mi)
% 24.63/4.98 % (32693)Instruction limit reached!
% 24.63/4.98 % (32693)------------------------------
% 24.63/4.98 % (32693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.63/4.98 % (32693)Termination reason: Unknown
% 24.63/4.98 % (32693)Termination phase: Saturation
% 24.63/4.98
% 24.63/4.98 % (32693)Memory used [KB]: 7931
% 24.63/4.98 % (32693)Time elapsed: 0.091 s
% 24.63/4.98 % (32693)Instructions burned: 285 (million)
% 24.63/4.98 % (32693)------------------------------
% 24.63/4.98 % (32693)------------------------------
% 24.63/4.99 % (32697)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_32065 for (2965ds/102Mi)
% 24.63/5.00 % (32684)Instruction limit reached!
% 24.63/5.00 % (32684)------------------------------
% 24.63/5.00 % (32684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.63/5.00 % (32684)Termination reason: Unknown
% 24.63/5.00 % (32684)Termination phase: Saturation
% 24.63/5.00
% 24.63/5.00 % (32684)Memory used [KB]: 7803
% 24.63/5.00 % (32684)Time elapsed: 0.616 s
% 24.63/5.00 % (32684)Instructions burned: 1981 (million)
% 24.63/5.00 % (32684)------------------------------
% 24.63/5.00 % (32684)------------------------------
% 24.63/5.01 % (32698)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_32065 for (2965ds/952Mi)
% 24.63/5.01 % (32697)Instruction limit reached!
% 24.63/5.01 % (32697)------------------------------
% 24.63/5.01 % (32697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.63/5.01 % (32697)Termination reason: Unknown
% 24.63/5.01 % (32697)Termination phase: Saturation
% 24.63/5.01
% 24.63/5.01 % (32697)Memory used [KB]: 6652
% 24.63/5.01 % (32697)Time elapsed: 0.028 s
% 24.63/5.01 % (32697)Instructions burned: 103 (million)
% 24.63/5.01 % (32697)------------------------------
% 24.63/5.01 % (32697)------------------------------
% 24.63/5.02 % (32699)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_32065 for (2965ds/578Mi)
% 27.72/5.16 % (32675)Instruction limit reached!
% 27.72/5.16 % (32675)------------------------------
% 27.72/5.16 % (32675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.72/5.16 % (32675)Termination reason: Unknown
% 27.72/5.16 % (32675)Termination phase: Saturation
% 27.72/5.16
% 27.72/5.16 % (32675)Memory used [KB]: 11897
% 27.72/5.16 % (32675)Time elapsed: 1.073 s
% 27.72/5.16 % (32675)Instructions burned: 3373 (million)
% 27.72/5.16 % (32675)------------------------------
% 27.72/5.16 % (32675)------------------------------
% 27.72/5.16 % (32688)Instruction limit reached!
% 27.72/5.16 % (32688)------------------------------
% 27.72/5.16 % (32688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.72/5.16 % (32688)Termination reason: Unknown
% 27.72/5.16 % (32688)Termination phase: Saturation
% 27.72/5.16
% 27.72/5.16 % (32688)Memory used [KB]: 9594
% 27.72/5.16 % (32688)Time elapsed: 0.519 s
% 27.72/5.16 % (32688)Instructions burned: 1670 (million)
% 27.72/5.16 % (32688)------------------------------
% 27.72/5.16 % (32688)------------------------------
% 27.72/5.17 % (32701)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_32065 for (2963ds/865Mi)
% 27.72/5.17 % (32700)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_32065 for (2963ds/643Mi)
% 27.72/5.20 % (32699)Instruction limit reached!
% 27.72/5.20 % (32699)------------------------------
% 27.72/5.20 % (32699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.72/5.20 % (32699)Termination reason: Unknown
% 27.72/5.20 % (32699)Termination phase: Saturation
% 27.72/5.20
% 27.72/5.20 % (32699)Memory used [KB]: 8315
% 27.72/5.20 % (32699)Time elapsed: 0.196 s
% 27.72/5.20 % (32699)Instructions burned: 580 (million)
% 27.72/5.20 % (32699)------------------------------
% 27.72/5.20 % (32699)------------------------------
% 28.21/5.21 % (32702)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_32065 for (2963ds/1174Mi)
% 28.21/5.29 % (32696)Instruction limit reached!
% 28.21/5.29 % (32696)------------------------------
% 28.21/5.29 % (32696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.21/5.29 % (32696)Termination reason: Unknown
% 28.21/5.29 % (32696)Termination phase: Saturation
% 28.21/5.29
% 28.21/5.29 % (32696)Memory used [KB]: 9338
% 28.21/5.29 % (32696)Time elapsed: 0.316 s
% 28.21/5.29 % (32696)Instructions burned: 1001 (million)
% 28.21/5.29 % (32696)------------------------------
% 28.21/5.29 % (32696)------------------------------
% 28.51/5.30 % (32703)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_32065 for (2962ds/644Mi)
% 28.51/5.32 % (32698)Instruction limit reached!
% 28.51/5.32 % (32698)------------------------------
% 28.51/5.32 % (32698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.51/5.32 % (32698)Termination reason: Unknown
% 28.51/5.32 % (32698)Termination phase: Saturation
% 28.51/5.32
% 28.51/5.32 % (32698)Memory used [KB]: 9210
% 28.51/5.32 % (32698)Time elapsed: 0.330 s
% 28.51/5.32 % (32698)Instructions burned: 952 (million)
% 28.51/5.32 % (32698)------------------------------
% 28.51/5.32 % (32698)------------------------------
% 28.51/5.33 % (32704)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_32065 for (2962ds/1201Mi)
% 28.51/5.34 % (32703)Refutation not found, incomplete strategy
% 28.51/5.34 % (32703)------------------------------
% 28.51/5.34 % (32703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.51/5.34 % (32703)Termination reason: Refutation not found, incomplete strategy
% 28.51/5.34
% 28.51/5.34
% 28.51/5.34 % (32703)Memory used [KB]: 7419
% 28.51/5.34 % (32703)Time elapsed: 0.059 s
% 28.51/5.34 % (32703)Instructions burned: 119 (million)
% 28.51/5.34 % (32703)------------------------------
% 28.51/5.34 % (32703)------------------------------
% 28.51/5.35 % (32705)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_32065 for (2962ds/1046Mi)
% 28.51/5.37 % (32700)Instruction limit reached!
% 28.51/5.37 % (32700)------------------------------
% 28.51/5.37 % (32700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.51/5.37 % (32700)Termination reason: Unknown
% 28.51/5.37 % (32700)Termination phase: Saturation
% 28.51/5.37
% 28.51/5.37 % (32700)Memory used [KB]: 8187
% 28.51/5.37 % (32700)Time elapsed: 0.224 s
% 28.51/5.37 % (32700)Instructions burned: 644 (million)
% 28.51/5.37 % (32700)------------------------------
% 28.51/5.37 % (32700)------------------------------
% 28.51/5.38 % (32706)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_32065 for (2961ds/222Mi)
% 29.29/5.44 % (32706)Instruction limit reached!
% 29.29/5.44 % (32706)------------------------------
% 29.29/5.44 % (32706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.29/5.44 % (32706)Termination reason: Unknown
% 29.29/5.44 % (32706)Termination phase: Saturation
% 29.29/5.44
% 29.29/5.44 % (32706)Memory used [KB]: 7291
% 29.29/5.44 % (32706)Time elapsed: 0.067 s
% 29.29/5.44 % (32706)Instructions burned: 223 (million)
% 29.29/5.44 % (32706)------------------------------
% 29.29/5.44 % (32706)------------------------------
% 29.29/5.44 % (32701)Instruction limit reached!
% 29.29/5.44 % (32701)------------------------------
% 29.29/5.44 % (32701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.29/5.44 % (32701)Termination reason: Unknown
% 29.29/5.44 % (32701)Termination phase: Saturation
% 29.29/5.44
% 29.29/5.44 % (32701)Memory used [KB]: 9338
% 29.29/5.44 % (32701)Time elapsed: 0.302 s
% 29.29/5.44 % (32701)Instructions burned: 866 (million)
% 29.29/5.44 % (32701)------------------------------
% 29.29/5.44 % (32701)------------------------------
% 29.29/5.45 % (32707)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_32065 for (2960ds/68Mi)
% 29.29/5.45 % (32708)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_32065 for (2960ds/454Mi)
% 29.29/5.46 % (32702)Instruction limit reached!
% 29.29/5.46 % (32702)------------------------------
% 29.29/5.46 % (32702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.29/5.46 % (32702)Termination reason: Unknown
% 29.29/5.46 % (32702)Termination phase: Saturation
% 29.29/5.46
% 29.29/5.46 % (32702)Memory used [KB]: 7547
% 29.29/5.46 % (32702)Time elapsed: 0.276 s
% 29.29/5.46 % (32702)Instructions burned: 1176 (million)
% 29.29/5.46 % (32702)------------------------------
% 29.29/5.46 % (32702)------------------------------
% 29.29/5.47 % (32709)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_32065 for (2960ds/360Mi)
% 29.29/5.47 % (32707)Instruction limit reached!
% 29.29/5.47 % (32707)------------------------------
% 29.29/5.47 % (32707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.29/5.47 % (32707)Termination reason: Unknown
% 29.29/5.47 % (32707)Termination phase: Property scanning
% 29.29/5.47
% 29.29/5.47 % (32707)Memory used [KB]: 2174
% 29.29/5.47 % (32707)Time elapsed: 0.021 s
% 29.29/5.47 % (32707)Instructions burned: 69 (million)
% 29.29/5.47 % (32707)------------------------------
% 29.29/5.47 % (32707)------------------------------
% 29.29/5.48 % (32710)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_32065 for (2960ds/157Mi)
% 30.14/5.53 % (32710)Instruction limit reached!
% 30.14/5.53 % (32710)------------------------------
% 30.14/5.53 % (32710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.14/5.53 % (32710)Termination reason: Unknown
% 30.14/5.53 % (32710)Termination phase: Saturation
% 30.14/5.53
% 30.14/5.53 % (32710)Memory used [KB]: 6908
% 30.14/5.53 % (32710)Time elapsed: 0.046 s
% 30.14/5.53 % (32710)Instructions burned: 158 (million)
% 30.14/5.53 % (32710)------------------------------
% 30.14/5.53 % (32710)------------------------------
% 30.14/5.54 % (32711)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_32065 for (2960ds/5061Mi)
% 30.14/5.58 % (32709)Instruction limit reached!
% 30.14/5.58 % (32709)------------------------------
% 30.14/5.58 % (32709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.14/5.58 % (32709)Termination reason: Unknown
% 30.14/5.58 % (32709)Termination phase: Saturation
% 30.14/5.58
% 30.14/5.58 % (32709)Memory used [KB]: 7931
% 30.14/5.58 % (32709)Time elapsed: 0.109 s
% 30.14/5.58 % (32709)Instructions burned: 362 (million)
% 30.14/5.58 % (32709)------------------------------
% 30.14/5.58 % (32709)------------------------------
% 30.14/5.59 % (32712)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_32065 for (2959ds/2401Mi)
% 30.14/5.59 % (32708)Instruction limit reached!
% 30.14/5.59 % (32708)------------------------------
% 30.14/5.59 % (32708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.14/5.59 % (32708)Termination reason: Unknown
% 30.14/5.59 % (32708)Termination phase: Saturation
% 30.14/5.59
% 30.14/5.59 % (32708)Memory used [KB]: 12665
% 30.14/5.59 % (32708)Time elapsed: 0.139 s
% 30.14/5.59 % (32708)Instructions burned: 456 (million)
% 30.14/5.59 % (32708)------------------------------
% 30.14/5.59 % (32708)------------------------------
% 30.67/5.60 % (32713)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_32065 for (2959ds/5798Mi)
% 30.67/5.67 % (32705)Instruction limit reached!
% 30.67/5.67 % (32705)------------------------------
% 30.67/5.67 % (32705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.67/5.67 % (32705)Termination reason: Unknown
% 30.67/5.67 % (32705)Termination phase: Saturation
% 30.67/5.67
% 30.67/5.67 % (32705)Memory used [KB]: 8955
% 30.67/5.67 % (32705)Time elapsed: 0.324 s
% 30.67/5.67 % (32705)Instructions burned: 1047 (million)
% 30.67/5.67 % (32705)------------------------------
% 30.67/5.67 % (32705)------------------------------
% 30.67/5.68 % (32714)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_32065 for (2958ds/346Mi)
% 31.20/5.70 % (32704)Refutation not found, non-redundant clauses discarded% (32704)------------------------------
% 31.20/5.70 % (32704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.20/5.70 % (32704)Termination reason: Refutation not found, non-redundant clauses discarded
% 31.20/5.70
% 31.20/5.70 % (32704)Memory used [KB]: 8955
% 31.20/5.70 % (32704)Time elapsed: 0.400 s
% 31.20/5.70 % (32704)Instructions burned: 1153 (million)
% 31.20/5.70 % (32704)------------------------------
% 31.20/5.70 % (32704)------------------------------
% 31.20/5.71 % (32648)Instruction limit reached!
% 31.20/5.71 % (32648)------------------------------
% 31.20/5.71 % (32648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.20/5.71 % (32648)Termination reason: Unknown
% 31.20/5.71 % (32648)Termination phase: Saturation
% 31.20/5.71
% 31.20/5.71 % (32648)Memory used [KB]: 16630
% 31.20/5.71 % (32648)Time elapsed: 2.643 s
% 31.20/5.71 % (32648)Instructions burned: 8251 (million)
% 31.20/5.71 % (32648)------------------------------
% 31.20/5.71 % (32648)------------------------------
% 31.20/5.71 % (32715)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_32065 for (2958ds/1321Mi)
% 31.20/5.72 % (32716)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_32065 for (2958ds/1312Mi)
% 31.20/5.75 % (32715)Refutation not found, incomplete strategy
% 31.20/5.75 % (32715)------------------------------
% 31.20/5.75 % (32715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.20/5.75 % (32715)Termination reason: Refutation not found, incomplete strategy
% 31.20/5.75
% 31.20/5.75
% 31.20/5.75 % (32715)Memory used [KB]: 2686
% 31.20/5.75 % (32715)Time elapsed: 0.034 s
% 31.20/5.75 % (32715)Instructions burned: 108 (million)
% 31.20/5.75 % (32715)------------------------------
% 31.20/5.75 % (32715)------------------------------
% 31.20/5.76 % (32717)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_32065 for (2957ds/672Mi)
% 31.20/5.79 % (32714)Instruction limit reached!
% 31.20/5.79 % (32714)------------------------------
% 31.20/5.79 % (32714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.20/5.79 % (32714)Termination reason: Unknown
% 31.20/5.79 % (32714)Termination phase: Saturation
% 31.20/5.79
% 31.20/5.79 % (32714)Memory used [KB]: 7675
% 31.20/5.79 % (32714)Time elapsed: 0.107 s
% 31.20/5.79 % (32714)Instructions burned: 346 (million)
% 31.20/5.79 % (32714)------------------------------
% 31.20/5.79 % (32714)------------------------------
% 31.20/5.80 % (32718)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_32065 for (2957ds/1897Mi)
% 31.87/5.83 % (32718)Refutation not found, incomplete strategy
% 31.87/5.83 % (32718)------------------------------
% 31.87/5.83 % (32718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.87/5.83 % (32718)Termination reason: Refutation not found, incomplete strategy
% 31.87/5.83
% 31.87/5.83
% 31.87/5.83 % (32718)Memory used [KB]: 7036
% 31.87/5.83 % (32718)Time elapsed: 0.031 s
% 31.87/5.83 % (32718)Instructions burned: 97 (million)
% 31.87/5.83 % (32718)------------------------------
% 31.87/5.83 % (32718)------------------------------
% 31.87/5.84 % (32719)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_32065 for (2957ds/1202Mi)
% 32.01/5.97 % (32717)Instruction limit reached!
% 32.01/5.97 % (32717)------------------------------
% 32.01/5.97 % (32717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.01/5.97 % (32717)Termination reason: Unknown
% 32.01/5.97 % (32717)Termination phase: Saturation
% 32.01/5.97
% 32.01/5.97 % (32717)Memory used [KB]: 8315
% 32.01/5.97 % (32717)Time elapsed: 0.212 s
% 32.01/5.97 % (32717)Instructions burned: 672 (million)
% 32.01/5.97 % (32717)------------------------------
% 32.01/5.97 % (32717)------------------------------
% 32.01/5.98 % (32720)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_32065 for (2955ds/1493Mi)
% 32.01/6.01 % (32720)Refutation not found, incomplete strategy
% 32.01/6.01 % (32720)------------------------------
% 32.01/6.01 % (32720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.01/6.01 % (32720)Termination reason: Refutation not found, incomplete strategy
% 32.01/6.01
% 32.01/6.01
% 32.01/6.01 % (32720)Memory used [KB]: 6908
% 32.01/6.01 % (32720)Time elapsed: 0.031 s
% 32.01/6.01 % (32720)Instructions burned: 111 (million)
% 32.01/6.01 % (32720)------------------------------
% 32.01/6.01 % (32720)------------------------------
% 32.01/6.02 % (32721)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_32065 for (2955ds/7679Mi)
% 34.24/6.11 % (32716)Instruction limit reached!
% 34.24/6.11 % (32716)------------------------------
% 34.24/6.11 % (32716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.24/6.11 % (32716)Termination reason: Unknown
% 34.24/6.11 % (32716)Termination phase: Saturation
% 34.24/6.11
% 34.24/6.11 % (32716)Memory used [KB]: 8699
% 34.24/6.11 % (32716)Time elapsed: 0.393 s
% 34.24/6.11 % (32716)Instructions burned: 1314 (million)
% 34.24/6.11 % (32716)------------------------------
% 34.24/6.11 % (32716)------------------------------
% 34.24/6.12 % (32722)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_32065 for (2954ds/340Mi)
% 35.20/6.21 % (32719)Instruction limit reached!
% 35.20/6.21 % (32719)------------------------------
% 35.20/6.21 % (32719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.20/6.21 % (32719)Termination reason: Unknown
% 35.20/6.21 % (32719)Termination phase: Saturation
% 35.20/6.21
% 35.20/6.21 % (32719)Memory used [KB]: 4221
% 35.20/6.21 % (32719)Time elapsed: 0.370 s
% 35.20/6.21 % (32719)Instructions burned: 1204 (million)
% 35.20/6.21 % (32719)------------------------------
% 35.20/6.21 % (32719)------------------------------
% 35.20/6.22 % (32723)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_32065 for (2953ds/3672Mi)
% 35.20/6.23 % (32722)Instruction limit reached!
% 35.20/6.23 % (32722)------------------------------
% 35.20/6.23 % (32722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.20/6.23 % (32722)Termination reason: Unknown
% 35.20/6.23 % (32722)Termination phase: Saturation
% 35.20/6.23
% 35.20/6.23 % (32722)Memory used [KB]: 8315
% 35.20/6.23 % (32722)Time elapsed: 0.108 s
% 35.20/6.23 % (32722)Instructions burned: 342 (million)
% 35.20/6.23 % (32722)------------------------------
% 35.20/6.23 % (32722)------------------------------
% 35.20/6.24 % (32724)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_32065 for (2953ds/1535Mi)
% 35.74/6.34 % (32712)Instruction limit reached!
% 35.74/6.34 % (32712)------------------------------
% 35.74/6.34 % (32712)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.74/6.34 % (32712)Termination reason: Unknown
% 35.74/6.34 % (32712)Termination phase: Saturation
% 35.74/6.34
% 35.74/6.34 % (32712)Memory used [KB]: 6524
% 35.74/6.34 % (32712)Time elapsed: 0.753 s
% 35.74/6.34 % (32712)Instructions burned: 2404 (million)
% 35.74/6.34 % (32712)------------------------------
% 35.74/6.34 % (32712)------------------------------
% 35.74/6.35 % (32725)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_32065 for (2951ds/4637Mi)
% 36.99/6.72 % (32724)Instruction limit reached!
% 36.99/6.72 % (32724)------------------------------
% 36.99/6.72 % (32724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.99/6.72 % (32724)Termination reason: Unknown
% 36.99/6.72 % (32724)Termination phase: Saturation
% 36.99/6.72
% 36.99/6.72 % (32724)Memory used [KB]: 11129
% 36.99/6.72 % (32724)Time elapsed: 0.484 s
% 36.99/6.72 % (32724)Instructions burned: 1536 (million)
% 36.99/6.72 % (32724)------------------------------
% 36.99/6.72 % (32724)------------------------------
% 36.99/6.73 % (32726)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_32065 for (2948ds/3174Mi)
% 37.78/6.84 % (32692)Refutation not found, non-redundant clauses discarded% (32692)------------------------------
% 37.78/6.84 % (32692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.78/6.84 % (32692)Termination reason: Refutation not found, non-redundant clauses discarded
% 37.78/6.84
% 37.78/6.84 % (32692)Memory used [KB]: 12792
% 37.78/6.84 % (32692)Time elapsed: 2.066 s
% 37.78/6.84 % (32692)Instructions burned: 6446 (million)
% 37.78/6.84 % (32692)------------------------------
% 37.78/6.84 % (32692)------------------------------
% 37.78/6.85 % (32727)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_32065 for (2946ds/307Mi)
% 38.05/6.94 % (32727)Instruction limit reached!
% 38.05/6.94 % (32727)------------------------------
% 38.05/6.94 % (32727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.05/6.94 % (32727)Termination reason: Unknown
% 38.05/6.94 % (32727)Termination phase: Saturation
% 38.05/6.94
% 38.05/6.94 % (32727)Memory used [KB]: 7291
% 38.05/6.94 % (32727)Time elapsed: 0.091 s
% 38.05/6.94 % (32727)Instructions burned: 309 (million)
% 38.05/6.94 % (32727)------------------------------
% 38.05/6.94 % (32727)------------------------------
% 38.05/6.95 % (32728)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_32065 for (2945ds/3619Mi)
% 38.05/6.98 % (32728)Refutation not found, incomplete strategy
% 38.05/6.98 % (32728)------------------------------
% 38.05/6.98 % (32728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.05/6.98 % (32728)Termination reason: Refutation not found, incomplete strategy
% 38.05/6.98
% 38.05/6.98
% 38.05/6.98 % (32728)Memory used [KB]: 6908
% 38.05/6.98 % (32728)Time elapsed: 0.030 s
% 38.05/6.98 % (32728)Instructions burned: 99 (million)
% 38.05/6.98 % (32728)------------------------------
% 38.05/6.98 % (32728)------------------------------
% 38.05/6.99 % (32729)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_32065 for (2945ds/2325Mi)
% 41.28/7.09 % (32711)Instruction limit reached!
% 41.28/7.09 % (32711)------------------------------
% 41.28/7.09 % (32711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.28/7.09 % (32711)Termination reason: Unknown
% 41.28/7.09 % (32711)Termination phase: Saturation
% 41.28/7.09
% 41.28/7.09 % (32711)Memory used [KB]: 11129
% 41.28/7.09 % (32711)Time elapsed: 1.556 s
% 41.28/7.09 % (32711)Instructions burned: 5063 (million)
% 41.28/7.09 % (32711)------------------------------
% 41.28/7.09 % (32711)------------------------------
% 41.28/7.10 % (32730)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_32065 for (2944ds/2341Mi)
% 43.01/7.39 % (32723)Instruction limit reached!
% 43.01/7.39 % (32723)------------------------------
% 43.01/7.39 % (32723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.01/7.39 % (32723)Termination reason: Unknown
% 43.01/7.39 % (32723)Termination phase: Saturation
% 43.01/7.39
% 43.01/7.39 % (32723)Memory used [KB]: 11001
% 43.01/7.39 % (32723)Time elapsed: 1.173 s
% 43.01/7.39 % (32723)Instructions burned: 3674 (million)
% 43.01/7.39 % (32723)------------------------------
% 43.01/7.39 % (32723)------------------------------
% 43.61/7.40 % (32731)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_32065 for (2941ds/7257Mi)
% 43.61/7.40 % (32713)Instruction limit reached!
% 43.61/7.40 % (32713)------------------------------
% 43.61/7.40 % (32713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.61/7.40 % (32713)Termination reason: Unknown
% 43.61/7.40 % (32713)Termination phase: Saturation
% 43.61/7.40
% 43.61/7.40 % (32713)Memory used [KB]: 13944
% 43.61/7.40 % (32713)Time elapsed: 1.798 s
% 43.61/7.40 % (32713)Instructions burned: 5801 (million)
% 43.61/7.40 % (32713)------------------------------
% 43.61/7.40 % (32713)------------------------------
% 43.61/7.41 % (32732)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_32065 for (2941ds/3710Mi)
% 43.61/7.42 % (32731)Refutation not found, incomplete strategy
% 43.61/7.42 % (32731)------------------------------
% 43.61/7.42 % (32731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.61/7.42 % (32731)Termination reason: Refutation not found, incomplete strategy
% 43.61/7.42
% 43.61/7.42
% 43.61/7.42 % (32731)Memory used [KB]: 6908
% 43.61/7.42 % (32731)Time elapsed: 0.027 s
% 43.61/7.42 % (32731)Instructions burned: 85 (million)
% 43.61/7.42 % (32731)------------------------------
% 43.61/7.42 % (32731)------------------------------
% 43.61/7.43 % (32733)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_32065 for (2941ds/326Mi)
% 44.05/7.53 % (32733)Instruction limit reached!
% 44.05/7.53 % (32733)------------------------------
% 44.05/7.53 % (32733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.05/7.53 % (32733)Termination reason: Unknown
% 44.05/7.53 % (32733)Termination phase: Saturation
% 44.05/7.53
% 44.05/7.53 % (32733)Memory used [KB]: 7291
% 44.05/7.53 % (32733)Time elapsed: 0.126 s
% 44.05/7.53 % (32733)Instructions burned: 327 (million)
% 44.05/7.53 % (32733)------------------------------
% 44.05/7.53 % (32733)------------------------------
% 44.05/7.54 % (32734)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_32065 for (2939ds/1100Mi)
% 44.97/7.73 % (32729)Instruction limit reached!
% 44.97/7.73 % (32729)------------------------------
% 44.97/7.73 % (32729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.97/7.73 % (32729)Termination reason: Unknown
% 44.97/7.73 % (32729)Termination phase: Saturation
% 44.97/7.73
% 44.97/7.73 % (32729)Memory used [KB]: 11001
% 44.97/7.73 % (32729)Time elapsed: 0.737 s
% 44.97/7.73 % (32729)Instructions burned: 2326 (million)
% 44.97/7.73 % (32729)------------------------------
% 44.97/7.73 % (32729)------------------------------
% 44.97/7.74 % (32735)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_32065 for (2937ds/406Mi)
% 44.97/7.74 % (32726)Instruction limit reached!
% 44.97/7.74 % (32726)------------------------------
% 44.97/7.74 % (32726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.97/7.74 % (32726)Termination reason: Unknown
% 44.97/7.74 % (32726)Termination phase: Saturation
% 44.97/7.74
% 44.97/7.74 % (32726)Memory used [KB]: 11385
% 44.97/7.74 % (32726)Time elapsed: 1.012 s
% 44.97/7.74 % (32726)Instructions burned: 3175 (million)
% 44.97/7.74 % (32726)------------------------------
% 44.97/7.74 % (32726)------------------------------
% 44.97/7.75 % (32736)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_32065 for (2937ds/1871Mi)
% 45.26/7.80 % (32725)Instruction limit reached!
% 45.26/7.80 % (32725)------------------------------
% 45.26/7.80 % (32725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.26/7.80 % (32725)Termination reason: Unknown
% 45.26/7.80 % (32725)Termination phase: Saturation
% 45.26/7.80
% 45.26/7.80 % (32725)Memory used [KB]: 12665
% 45.26/7.80 % (32725)Time elapsed: 1.453 s
% 45.26/7.80 % (32725)Instructions burned: 4638 (million)
% 45.26/7.80 % (32725)------------------------------
% 45.26/7.80 % (32725)------------------------------
% 45.26/7.81 % (32737)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_32065 for (2937ds/1194Mi)
% 45.26/7.82 % (32730)Instruction limit reached!
% 45.26/7.82 % (32730)------------------------------
% 45.26/7.82 % (32730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.26/7.82 % (32730)Termination reason: Unknown
% 45.26/7.82 % (32730)Termination phase: Saturation
% 45.26/7.82
% 45.26/7.82 % (32730)Memory used [KB]: 8315
% 45.26/7.82 % (32730)Time elapsed: 0.744 s
% 45.26/7.82 % (32730)Instructions burned: 2341 (million)
% 45.26/7.82 % (32730)------------------------------
% 45.26/7.82 % (32730)------------------------------
% 45.26/7.83 % (32738)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_32065 for (2937ds/474Mi)
% 45.26/7.86 % (32735)Refutation not found, non-redundant clauses discarded% (32735)------------------------------
% 45.26/7.86 % (32735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.26/7.86 % (32735)Termination reason: Refutation not found, non-redundant clauses discarded
% 45.26/7.86
% 45.26/7.86 % (32735)Memory used [KB]: 7675
% 45.26/7.86 % (32735)Time elapsed: 0.128 s
% 45.26/7.86 % (32735)Instructions burned: 394 (million)
% 45.26/7.86 % (32735)------------------------------
% 45.26/7.86 % (32735)------------------------------
% 45.26/7.87 % (32739)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_32065 for (2936ds/3115Mi)
% 45.26/7.89 % (32734)Instruction limit reached!
% 45.26/7.89 % (32734)------------------------------
% 45.26/7.89 % (32734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.26/7.89 % (32734)Termination reason: Unknown
% 45.26/7.89 % (32734)Termination phase: Saturation
% 45.26/7.89
% 45.26/7.89 % (32734)Memory used [KB]: 9850
% 45.26/7.89 % (32734)Time elapsed: 0.348 s
% 45.26/7.89 % (32734)Instructions burned: 1101 (million)
% 45.26/7.89 % (32734)------------------------------
% 45.26/7.89 % (32734)------------------------------
% 46.60/7.90 % (32740)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_32065 for (2936ds/831Mi)
% 46.60/7.95 % (32740)Refutation not found, incomplete strategy
% 46.60/7.95 % (32740)------------------------------
% 46.60/7.95 % (32740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.60/7.95 % (32740)Termination reason: Refutation not found, incomplete strategy
% 46.60/7.95
% 46.60/7.95
% 46.60/7.95 % (32740)Memory used [KB]: 7547
% 46.60/7.95 % (32740)Time elapsed: 0.045 s
% 46.60/7.95 % (32740)Instructions burned: 137 (million)
% 46.60/7.95 % (32740)------------------------------
% 46.60/7.95 % (32740)------------------------------
% 46.60/7.96 % (32741)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_32065 for (2935ds/1188Mi)
% 46.60/7.98 % (32738)Instruction limit reached!
% 46.60/7.98 % (32738)------------------------------
% 46.60/7.98 % (32738)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.60/7.98 % (32738)Termination reason: Unknown
% 46.60/7.98 % (32738)Termination phase: Saturation
% 46.60/7.98
% 46.60/7.98 % (32738)Memory used [KB]: 8059
% 46.60/7.98 % (32738)Time elapsed: 0.146 s
% 46.60/7.98 % (32738)Instructions burned: 476 (million)
% 46.60/7.98 % (32738)------------------------------
% 46.60/7.98 % (32738)------------------------------
% 46.60/7.99 % (32742)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_32065 for (2935ds/2868Mi)
% 48.29/8.03 % (32742)Refutation not found, incomplete strategy
% 48.29/8.03 % (32742)------------------------------
% 48.29/8.03 % (32742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.29/8.03 % (32742)Termination reason: Refutation not found, incomplete strategy
% 48.29/8.03
% 48.29/8.03
% 48.29/8.03 % (32742)Memory used [KB]: 7291
% 48.29/8.03 % (32742)Time elapsed: 0.045 s
% 48.29/8.03 % (32742)Instructions burned: 162 (million)
% 48.29/8.03 % (32742)------------------------------
% 48.29/8.03 % (32742)------------------------------
% 48.29/8.04 % (32743)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_32065 for (2935ds/1516Mi)
% 48.91/8.19 % (32737)Instruction limit reached!
% 48.91/8.19 % (32737)------------------------------
% 48.91/8.19 % (32737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.91/8.19 % (32737)Termination reason: Unknown
% 48.91/8.19 % (32737)Termination phase: Saturation
% 48.91/8.19
% 48.91/8.19 % (32737)Memory used [KB]: 8699
% 48.91/8.19 % (32737)Time elapsed: 0.377 s
% 48.91/8.19 % (32737)Instructions burned: 1195 (million)
% 48.91/8.19 % (32737)------------------------------
% 48.91/8.19 % (32737)------------------------------
% 48.91/8.20 % (32744)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_32065 for (2933ds/2321Mi)
% 49.34/8.24 % (32744)Refutation not found, incomplete strategy
% 49.34/8.24 % (32744)------------------------------
% 49.34/8.24 % (32744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.34/8.24 % (32744)Termination reason: Refutation not found, incomplete strategy
% 49.34/8.24
% 49.34/8.24
% 49.34/8.24 % (32744)Memory used [KB]: 7291
% 49.34/8.24 % (32744)Time elapsed: 0.048 s
% 49.34/8.24 % (32744)Instructions burned: 167 (million)
% 49.34/8.24 % (32744)------------------------------
% 49.34/8.24 % (32744)------------------------------
% 49.34/8.25 % (32745)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_32065 for (2932ds/2812Mi)
% 49.90/8.32 % (32741)Instruction limit reached!
% 49.90/8.32 % (32741)------------------------------
% 49.90/8.32 % (32741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.90/8.32 % (32741)Termination reason: Unknown
% 49.90/8.32 % (32741)Termination phase: Saturation
% 49.90/8.32
% 49.90/8.32 % (32741)Memory used [KB]: 9210
% 49.90/8.32 % (32741)Time elapsed: 0.364 s
% 49.90/8.32 % (32741)Instructions burned: 1188 (million)
% 49.90/8.32 % (32741)------------------------------
% 49.90/8.32 % (32741)------------------------------
% 49.90/8.33 % (32721)Instruction limit reached!
% 49.90/8.33 % (32721)------------------------------
% 49.90/8.33 % (32721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.90/8.33 % (32721)Termination reason: Unknown
% 49.90/8.33 % (32721)Termination phase: Saturation
% 49.90/8.33
% 49.90/8.33 % (32721)Memory used [KB]: 20852
% 49.90/8.33 % (32721)Time elapsed: 2.332 s
% 49.90/8.33 % (32721)Instructions burned: 7679 (million)
% 49.90/8.33 % (32721)------------------------------
% 49.90/8.33 % (32721)------------------------------
% 49.90/8.33 % (32746)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_32065 for (2932ds/4604Mi)
% 49.90/8.34 % (32747)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_32065 for (2932ds/2678Mi)
% 49.90/8.35 % (32736)Instruction limit reached!
% 49.90/8.35 % (32736)------------------------------
% 49.90/8.35 % (32736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.90/8.35 % (32736)Termination reason: Unknown
% 49.90/8.35 % (32736)Termination phase: Saturation
% 49.90/8.35
% 49.90/8.35 % (32736)Memory used [KB]: 11001
% 49.90/8.35 % (32736)Time elapsed: 0.598 s
% 49.90/8.35 % (32736)Instructions burned: 1873 (million)
% 49.90/8.35 % (32736)------------------------------
% 49.90/8.35 % (32736)------------------------------
% 49.90/8.36 % (32748)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_32065 for (2931ds/643Mi)
% 50.44/8.50 % (32743)Instruction limit reached!
% 50.44/8.50 % (32743)------------------------------
% 50.44/8.50 % (32743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.44/8.50 % (32743)Termination reason: Unknown
% 50.44/8.50 % (32743)Termination phase: Saturation
% 50.44/8.50
% 50.44/8.50 % (32743)Memory used [KB]: 9978
% 50.44/8.50 % (32743)Time elapsed: 0.459 s
% 50.44/8.50 % (32743)Instructions burned: 1518 (million)
% 50.44/8.50 % (32743)------------------------------
% 50.44/8.50 % (32743)------------------------------
% 50.44/8.51 % (32749)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_32065 for (2930ds/458Mi)
% 50.44/8.54 % (32732)Instruction limit reached!
% 50.44/8.54 % (32732)------------------------------
% 50.44/8.54 % (32732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.44/8.54 % (32732)Termination reason: Unknown
% 50.44/8.54 % (32732)Termination phase: Saturation
% 50.44/8.54
% 50.44/8.54 % (32732)Memory used [KB]: 18677
% 50.44/8.54 % (32732)Time elapsed: 1.151 s
% 50.44/8.54 % (32732)Instructions burned: 3710 (million)
% 50.44/8.54 % (32732)------------------------------
% 50.44/8.54 % (32732)------------------------------
% 50.44/8.55 % (32750)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_32065 for (2930ds/2546Mi)
% 50.44/8.55 % (32748)Instruction limit reached!
% 50.44/8.55 % (32748)------------------------------
% 50.44/8.55 % (32748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.44/8.55 % (32748)Termination reason: Unknown
% 50.44/8.55 % (32748)Termination phase: Saturation
% 50.44/8.55
% 50.44/8.55 % (32748)Memory used [KB]: 8187
% 50.44/8.55 % (32748)Time elapsed: 0.220 s
% 50.44/8.55 % (32748)Instructions burned: 644 (million)
% 50.44/8.55 % (32748)------------------------------
% 50.44/8.55 % (32748)------------------------------
% 50.44/8.56 % (32751)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_32065 for (2929ds/1432Mi)
% 51.28/8.64 % (32749)Instruction limit reached!
% 51.28/8.64 % (32749)------------------------------
% 51.28/8.64 % (32749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.28/8.64 % (32749)Termination reason: Unknown
% 51.28/8.64 % (32749)Termination phase: Saturation
% 51.28/8.64
% 51.28/8.64 % (32749)Memory used [KB]: 7547
% 51.28/8.64 % (32749)Time elapsed: 0.134 s
% 51.28/8.64 % (32749)Instructions burned: 458 (million)
% 51.28/8.64 % (32749)------------------------------
% 51.28/8.64 % (32749)------------------------------
% 51.28/8.65 % (32752)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_32065 for (2928ds/386Mi)
% 51.52/8.77 % (32752)Instruction limit reached!
% 51.52/8.77 % (32752)------------------------------
% 51.52/8.77 % (32752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.52/8.77 % (32752)Termination reason: Unknown
% 51.52/8.77 % (32752)Termination phase: Saturation
% 51.52/8.77
% 51.52/8.77 % (32752)Memory used [KB]: 8059
% 51.52/8.77 % (32752)Time elapsed: 0.117 s
% 51.52/8.77 % (32752)Instructions burned: 388 (million)
% 51.52/8.77 % (32752)------------------------------
% 51.52/8.77 % (32752)------------------------------
% 51.52/8.78 % (32753)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_32065 for (2927ds/360Mi)
% 51.52/8.78 % (32739)Instruction limit reached!
% 51.52/8.78 % (32739)------------------------------
% 51.52/8.78 % (32739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.52/8.78 % (32739)Termination reason: Unknown
% 51.52/8.78 % (32739)Termination phase: Saturation
% 51.52/8.78
% 51.52/8.78 % (32739)Memory used [KB]: 13176
% 51.52/8.78 % (32739)Time elapsed: 0.907 s
% 51.52/8.78 % (32739)Instructions burned: 3115 (million)
% 51.52/8.78 % (32739)------------------------------
% 51.52/8.78 % (32739)------------------------------
% 51.52/8.79 % (32754)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_32065 for (2927ds/5446Mi)
% 51.75/8.89 % (32753)Instruction limit reached!
% 51.75/8.89 % (32753)------------------------------
% 51.75/8.89 % (32753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.75/8.89 % (32753)Termination reason: Unknown
% 51.75/8.89 % (32753)Termination phase: Saturation
% 51.75/8.89
% 51.75/8.89 % (32753)Memory used [KB]: 7931
% 51.75/8.89 % (32753)Time elapsed: 0.112 s
% 51.75/8.89 % (32753)Instructions burned: 362 (million)
% 51.75/8.89 % (32753)------------------------------
% 51.75/8.89 % (32753)------------------------------
% 51.87/8.90 % (32755)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_32065 for (2926ds/2573Mi)
% 51.87/8.92 % (32751)Instruction limit reached!
% 51.87/8.92 % (32751)------------------------------
% 51.87/8.92 % (32751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.87/8.92 % (32751)Termination reason: Unknown
% 51.87/8.92 % (32751)Termination phase: Saturation
% 51.87/8.92
% 51.87/8.92 % (32751)Memory used [KB]: 9466
% 51.87/8.92 % (32751)Time elapsed: 0.361 s
% 51.87/8.92 % (32751)Instructions burned: 1434 (million)
% 51.87/8.92 % (32751)------------------------------
% 51.87/8.92 % (32751)------------------------------
% 51.87/8.93 % (32756)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=2655:si=on:rtra=on_0 on DTF2THF_32065 for (2926ds/2655Mi)
% 56.04/9.17 % (32745)Instruction limit reached!
% 56.04/9.17 % (32745)------------------------------
% 56.04/9.17 % (32745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.04/9.17 % (32745)Termination reason: Unknown
% 56.04/9.17 % (32745)Termination phase: Saturation
% 56.04/9.17
% 56.04/9.17 % (32745)Memory used [KB]: 10362
% 56.04/9.17 % (32745)Time elapsed: 0.916 s
% 56.04/9.17 % (32745)Instructions burned: 2812 (million)
% 56.04/9.17 % (32745)------------------------------
% 56.04/9.17 % (32745)------------------------------
% 56.04/9.18 % (32757)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_32065 for (2923ds/2781Mi)
% 56.04/9.19 % (32747)Instruction limit reached!
% 56.04/9.19 % (32747)------------------------------
% 56.04/9.19 % (32747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.04/9.19 % (32747)Termination reason: Unknown
% 56.04/9.19 % (32747)Termination phase: Saturation
% 56.04/9.19
% 56.04/9.19 % (32747)Memory used [KB]: 12409
% 56.04/9.19 % (32747)Time elapsed: 0.854 s
% 56.04/9.19 % (32747)Instructions burned: 2679 (million)
% 56.04/9.19 % (32747)------------------------------
% 56.04/9.19 % (32747)------------------------------
% 56.54/9.20 % (32758)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_32065 for (2923ds/307Mi)
% 56.54/9.29 % (32758)Instruction limit reached!
% 56.54/9.29 % (32758)------------------------------
% 56.54/9.29 % (32758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.54/9.29 % (32758)Termination reason: Unknown
% 56.54/9.29 % (32758)Termination phase: Saturation
% 56.54/9.29
% 56.54/9.29 % (32758)Memory used [KB]: 7291
% 56.54/9.29 % (32758)Time elapsed: 0.090 s
% 56.54/9.29 % (32758)Instructions burned: 308 (million)
% 56.54/9.29 % (32758)------------------------------
% 56.54/9.29 % (32758)------------------------------
% 57.14/9.30 % (32759)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_32065 for (2922ds/1548Mi)
% 57.14/9.38 % (32750)Instruction limit reached!
% 57.14/9.38 % (32750)------------------------------
% 57.14/9.38 % (32750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.14/9.38 % (32750)Termination reason: Unknown
% 57.14/9.38 % (32750)Termination phase: Saturation
% 57.14/9.38
% 57.14/9.38 % (32750)Memory used [KB]: 11129
% 57.14/9.38 % (32750)Time elapsed: 0.857 s
% 57.14/9.38 % (32750)Instructions burned: 2546 (million)
% 57.14/9.38 % (32750)------------------------------
% 57.14/9.38 % (32750)------------------------------
% 57.14/9.39 % (32760)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_32065 for (2921ds/5214Mi)
% 58.41/9.67 % (32755)Instruction limit reached!
% 58.41/9.67 % (32755)------------------------------
% 58.41/9.67 % (32755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.41/9.67 % (32755)Termination reason: Unknown
% 58.41/9.67 % (32755)Termination phase: Saturation
% 58.41/9.67
% 58.41/9.67 % (32755)Memory used [KB]: 12025
% 58.41/9.67 % (32755)Time elapsed: 0.775 s
% 58.41/9.67 % (32755)Instructions burned: 2574 (million)
% 58.41/9.67 % (32755)------------------------------
% 58.41/9.67 % (32755)------------------------------
% 58.41/9.68 % (32761)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_32065 for (2918ds/3201Mi)
% 58.80/9.73 % (32756)Instruction limit reached!
% 58.80/9.73 % (32756)------------------------------
% 58.80/9.73 % (32756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.80/9.73 % (32756)Termination reason: Unknown
% 58.80/9.73 % (32756)Termination phase: Saturation
% 58.80/9.73
% 58.80/9.73 % (32756)Memory used [KB]: 11513
% 58.80/9.73 % (32756)Time elapsed: 0.801 s
% 58.80/9.73 % (32756)Instructions burned: 2657 (million)
% 58.80/9.73 % (32756)------------------------------
% 58.80/9.73 % (32756)------------------------------
% 58.80/9.74 % (32762)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_32065 for (2918ds/454Mi)
% 58.80/9.75 % (32746)Instruction limit reached!
% 58.80/9.75 % (32746)------------------------------
% 58.80/9.75 % (32746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.80/9.75 % (32746)Termination reason: Unknown
% 58.80/9.75 % (32746)Termination phase: Saturation
% 58.80/9.75
% 58.80/9.75 % (32746)Memory used [KB]: 13432
% 58.80/9.75 % (32746)Time elapsed: 1.419 s
% 58.80/9.75 % (32746)Instructions burned: 4606 (million)
% 58.80/9.75 % (32746)------------------------------
% 58.80/9.75 % (32746)------------------------------
% 58.80/9.76 % (32763)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_32065 for (2917ds/3049Mi)
% 58.80/9.79 % (32759)Instruction limit reached!
% 58.80/9.79 % (32759)------------------------------
% 58.80/9.79 % (32759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.80/9.79 % (32759)Termination reason: Unknown
% 58.80/9.79 % (32759)Termination phase: Saturation
% 58.80/9.79
% 58.80/9.79 % (32759)Memory used [KB]: 9978
% 58.80/9.79 % (32759)Time elapsed: 0.488 s
% 58.80/9.79 % (32759)Instructions burned: 1549 (million)
% 58.80/9.79 % (32759)------------------------------
% 58.80/9.79 % (32759)------------------------------
% 59.51/9.80 % (32764)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_32065 for (2917ds/7311Mi)
% 59.51/9.88 % (32762)Instruction limit reached!
% 59.51/9.88 % (32762)------------------------------
% 59.51/9.88 % (32762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.51/9.88 % (32762)Termination reason: Unknown
% 59.51/9.88 % (32762)Termination phase: Saturation
% 59.51/9.88
% 59.51/9.88 % (32762)Memory used [KB]: 12665
% 59.51/9.88 % (32762)Time elapsed: 0.140 s
% 59.51/9.88 % (32762)Instructions burned: 454 (million)
% 59.51/9.88 % (32762)------------------------------
% 59.51/9.88 % (32762)------------------------------
% 59.51/9.89 % (32765)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_32065 for (2916ds/6804Mi)
% 59.76/9.93 % (32765)Refutation not found, incomplete strategy
% 59.76/9.93 % (32765)------------------------------
% 59.76/9.93 % (32765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.76/9.93 % (32765)Termination reason: Refutation not found, incomplete strategy
% 59.76/9.93
% 59.76/9.93
% 59.76/9.93 % (32765)Memory used [KB]: 7164
% 59.76/9.93 % (32765)Time elapsed: 0.035 s
% 59.76/9.93 % (32765)Instructions burned: 108 (million)
% 59.76/9.93 % (32765)------------------------------
% 59.76/9.93 % (32765)------------------------------
% 59.76/9.94 % (32766)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_32065 for (2916ds/1683Mi)
% 62.35/10.07 % (32757)Instruction limit reached!
% 62.35/10.07 % (32757)------------------------------
% 62.35/10.07 % (32757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.35/10.07 % (32757)Termination reason: Unknown
% 62.35/10.07 % (32757)Termination phase: Saturation
% 62.35/10.07
% 62.35/10.07 % (32757)Memory used [KB]: 4861
% 62.35/10.07 % (32757)Time elapsed: 0.889 s
% 62.35/10.07 % (32757)Instructions burned: 2781 (million)
% 62.35/10.07 % (32757)------------------------------
% 62.35/10.07 % (32757)------------------------------
% 62.35/10.08 % (32767)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_32065 for (2914ds/4688Mi)
% 64.62/10.47 % (32766)Instruction limit reached!
% 64.62/10.47 % (32766)------------------------------
% 64.62/10.47 % (32766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.62/10.47 % (32766)Termination reason: Unknown
% 64.62/10.47 % (32766)Termination phase: Saturation
% 64.62/10.47
% 64.62/10.47 % (32766)Memory used [KB]: 10106
% 64.62/10.47 % (32766)Time elapsed: 0.554 s
% 64.62/10.47 % (32766)Instructions burned: 1683 (million)
% 64.62/10.47 % (32766)------------------------------
% 64.62/10.47 % (32766)------------------------------
% 64.62/10.48 % (300)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_32065 for (2910ds/2207Mi)
% 65.21/10.58 % (32754)Instruction limit reached!
% 65.21/10.58 % (32754)------------------------------
% 65.21/10.58 % (32754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.21/10.58 % (32754)Termination reason: Unknown
% 65.21/10.58 % (32754)Termination phase: Saturation
% 65.21/10.58
% 65.21/10.58 % (32754)Memory used [KB]: 14200
% 65.21/10.58 % (32754)Time elapsed: 1.791 s
% 65.21/10.58 % (32754)Instructions burned: 5446 (million)
% 65.21/10.58 % (32754)------------------------------
% 65.21/10.58 % (32754)------------------------------
% 65.21/10.59 % (301)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=8216:si=on:rtra=on_0 on DTF2THF_32065 for (2909ds/8216Mi)
% 65.71/10.68 % (32761)Instruction limit reached!
% 65.71/10.68 % (32761)------------------------------
% 65.71/10.68 % (32761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.71/10.68 % (32761)Termination reason: Unknown
% 65.71/10.68 % (32761)Termination phase: Saturation
% 65.71/10.68
% 65.71/10.68 % (32761)Memory used [KB]: 12665
% 65.71/10.68 % (32761)Time elapsed: 1.001 s
% 65.71/10.68 % (32761)Instructions burned: 3203 (million)
% 65.71/10.68 % (32761)------------------------------
% 65.71/10.68 % (32761)------------------------------
% 65.71/10.69 % (302)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_32065 for (2908ds/430Mi)
% 65.71/10.69 % (32763)Instruction limit reached!
% 65.71/10.69 % (32763)------------------------------
% 65.71/10.69 % (32763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.71/10.69 % (32763)Termination reason: Unknown
% 65.71/10.69 % (32763)Termination phase: Saturation
% 65.71/10.69
% 65.71/10.69 % (32763)Memory used [KB]: 8059
% 65.71/10.69 % (32763)Time elapsed: 0.939 s
% 65.71/10.69 % (32763)Instructions burned: 3050 (million)
% 65.71/10.69 % (32763)------------------------------
% 65.71/10.69 % (32763)------------------------------
% 66.11/10.70 % (303)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_32065 for (2908ds/2012Mi)
% 66.32/10.82 % (302)Instruction limit reached!
% 66.32/10.82 % (302)------------------------------
% 66.32/10.82 % (302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.32/10.82 % (302)Termination reason: Unknown
% 66.32/10.82 % (302)Termination phase: Saturation
% 66.32/10.82
% 66.32/10.82 % (302)Memory used [KB]: 7803
% 66.32/10.82 % (302)Time elapsed: 0.133 s
% 66.32/10.82 % (302)Instructions burned: 432 (million)
% 66.32/10.82 % (302)------------------------------
% 66.32/10.82 % (302)------------------------------
% 66.32/10.83 % (304)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_32065 for (2907ds/631Mi)
% 66.32/10.87 % (304)Refutation not found, incomplete strategy
% 66.32/10.87 % (304)------------------------------
% 66.32/10.87 % (304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.32/10.87 % (304)Termination reason: Refutation not found, incomplete strategy
% 66.32/10.87
% 66.32/10.87
% 66.32/10.87 % (304)Memory used [KB]: 7291
% 66.32/10.87 % (304)Time elapsed: 0.038 s
% 66.32/10.87 % (304)Instructions burned: 118 (million)
% 66.32/10.87 % (304)------------------------------
% 66.32/10.87 % (304)------------------------------
% 66.32/10.88 % (305)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_32065 for (2906ds/8785Mi)
% 66.71/11.00 % (32760)Instruction limit reached!
% 66.71/11.00 % (32760)------------------------------
% 66.71/11.00 % (32760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.71/11.00 % (32760)Termination reason: Unknown
% 66.71/11.00 % (32760)Termination phase: Saturation
% 66.71/11.00
% 66.71/11.00 % (32760)Memory used [KB]: 19701
% 66.71/11.00 % (32760)Time elapsed: 1.609 s
% 66.71/11.00 % (32760)Instructions burned: 5214 (million)
% 66.71/11.00 % (32760)------------------------------
% 66.71/11.00 % (32760)------------------------------
% 66.71/11.01 % (306)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_32065 for (2905ds/739Mi)
% 69.94/11.19 % (300)Instruction limit reached!
% 69.94/11.19 % (300)------------------------------
% 69.94/11.19 % (300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.94/11.19 % (300)Termination reason: Unknown
% 69.94/11.19 % (300)Termination phase: Saturation
% 69.94/11.19
% 69.94/11.19 % (300)Memory used [KB]: 9466
% 69.94/11.19 % (300)Time elapsed: 0.716 s
% 69.94/11.19 % (300)Instructions burned: 2209 (million)
% 69.94/11.19 % (300)------------------------------
% 69.94/11.19 % (300)------------------------------
% 70.40/11.20 % (307)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_32065 for (2903ds/5473Mi)
% 70.40/11.24 % (306)Instruction limit reached!
% 70.40/11.24 % (306)------------------------------
% 70.40/11.24 % (306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.40/11.24 % (306)Termination reason: Unknown
% 70.40/11.24 % (306)Termination phase: Saturation
% 70.40/11.24
% 70.40/11.24 % (306)Memory used [KB]: 8187
% 70.40/11.24 % (306)Time elapsed: 0.234 s
% 70.40/11.24 % (306)Instructions burned: 741 (million)
% 70.40/11.24 % (306)------------------------------
% 70.40/11.24 % (306)------------------------------
% 70.40/11.25 % (308)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_32065 for (2902ds/43570Mi)
% 70.40/11.27 % (308)Refutation not found, incomplete strategy
% 70.40/11.27 % (308)------------------------------
% 70.40/11.27 % (308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.40/11.27 % (308)Termination reason: Refutation not found, incomplete strategy
% 70.40/11.27
% 70.40/11.27
% 70.40/11.27 % (308)Memory used [KB]: 6780
% 70.40/11.27 % (308)Time elapsed: 0.023 s
% 70.40/11.27 % (308)Instructions burned: 75 (million)
% 70.40/11.27 % (308)------------------------------
% 70.40/11.27 % (308)------------------------------
% 70.40/11.28 % (309)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_32065 for (2902ds/8382Mi)
% 71.17/11.32 % (303)Instruction limit reached!
% 71.17/11.32 % (303)------------------------------
% 71.17/11.32 % (303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.17/11.32 % (303)Termination reason: Unknown
% 71.17/11.32 % (303)Termination phase: Saturation
% 71.17/11.32
% 71.17/11.32 % (303)Memory used [KB]: 16886
% 71.17/11.32 % (303)Time elapsed: 0.621 s
% 71.17/11.32 % (303)Instructions burned: 2012 (million)
% 71.17/11.32 % (303)------------------------------
% 71.17/11.32 % (303)------------------------------
% 71.17/11.33 % (310)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_32065 for (2902ds/407Mi)
% 71.62/11.47 % (310)Instruction limit reached!
% 71.62/11.47 % (310)------------------------------
% 71.62/11.47 % (310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.62/11.47 % (310)Termination reason: Unknown
% 71.62/11.47 % (310)Termination phase: Saturation
% 71.62/11.47
% 71.62/11.47 % (310)Memory used [KB]: 8699
% 71.62/11.47 % (310)Time elapsed: 0.134 s
% 71.62/11.47 % (310)Instructions burned: 407 (million)
% 71.62/11.47 % (310)------------------------------
% 71.62/11.47 % (310)------------------------------
% 71.62/11.48 % (311)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_32065 for (2900ds/2971Mi)
% 72.16/11.52 % (311)Refutation not found, incomplete strategy
% 72.16/11.52 % (311)------------------------------
% 72.16/11.52 % (311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.16/11.52 % (311)Termination reason: Refutation not found, incomplete strategy
% 72.16/11.52
% 72.16/11.52
% 72.16/11.52 % (311)Memory used [KB]: 7291
% 72.16/11.52 % (311)Time elapsed: 0.046 s
% 72.16/11.52 % (311)Instructions burned: 161 (million)
% 72.16/11.52 % (311)------------------------------
% 72.16/11.52 % (311)------------------------------
% 72.16/11.53 % (312)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_32065 for (2900ds/9822Mi)
% 72.16/11.56 % (312)Refutation not found, incomplete strategy
% 72.16/11.56 % (312)------------------------------
% 72.16/11.56 % (312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.16/11.56 % (312)Termination reason: Refutation not found, incomplete strategy
% 72.16/11.56
% 72.16/11.56
% 72.16/11.56 % (312)Memory used [KB]: 7164
% 72.16/11.56 % (312)Time elapsed: 0.034 s
% 72.16/11.56 % (312)Instructions burned: 109 (million)
% 72.16/11.56 % (312)------------------------------
% 72.16/11.56 % (312)------------------------------
% 72.16/11.57 % (32767)Instruction limit reached!
% 72.16/11.57 % (32767)------------------------------
% 72.16/11.57 % (32767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.16/11.57 % (32767)Termination reason: Unknown
% 72.16/11.57 % (32767)Termination phase: Saturation
% 72.16/11.57
% 72.16/11.57 % (32767)Memory used [KB]: 6780
% 72.16/11.57 % (32767)Time elapsed: 1.495 s
% 72.16/11.57 % (32767)Instructions burned: 4690 (million)
% 72.16/11.57 % (32767)------------------------------
% 72.16/11.57 % (32767)------------------------------
% 72.16/11.57 % (313)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_32065 for (2899ds/8425Mi)
% 72.16/11.58 % (314)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_32065 for (2899ds/3107Mi)
% 72.64/11.62 % (314)Refutation not found, incomplete strategy
% 72.64/11.62 % (314)------------------------------
% 72.64/11.62 % (314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.64/11.62 % (314)Termination reason: Refutation not found, incomplete strategy
% 72.64/11.62
% 72.64/11.62
% 72.64/11.62 % (314)Memory used [KB]: 7547
% 72.64/11.62 % (314)Time elapsed: 0.038 s
% 72.64/11.62 % (314)Instructions burned: 124 (million)
% 72.64/11.62 % (314)------------------------------
% 72.64/11.62 % (314)------------------------------
% 72.64/11.63 % (315)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_32065 for (2899ds/7967Mi)
% 72.64/11.67 % (315)Refutation not found, incomplete strategy
% 72.64/11.67 % (315)------------------------------
% 72.64/11.67 % (315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.64/11.67 % (315)Termination reason: Refutation not found, incomplete strategy
% 72.64/11.67
% 72.64/11.67
% 72.64/11.67 % (315)Memory used [KB]: 7291
% 72.64/11.67 % (315)Time elapsed: 0.047 s
% 72.64/11.67 % (315)Instructions burned: 162 (million)
% 72.64/11.67 % (315)------------------------------
% 72.64/11.67 % (315)------------------------------
% 72.64/11.68 % (317)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_32065 for (2898ds/3629Mi)
% 77.08/12.13 % (32764)Refutation not found, non-redundant clauses discarded% (32764)------------------------------
% 77.08/12.13 % (32764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.08/12.13 % (32764)Termination reason: Refutation not found, non-redundant clauses discarded
% 77.08/12.13
% 77.08/12.13 % (32764)Memory used [KB]: 15095
% 77.08/12.13 % (32764)Time elapsed: 2.353 s
% 77.08/12.13 % (32764)Instructions burned: 7266 (million)
% 77.08/12.13 % (32764)------------------------------
% 77.08/12.13 % (32764)------------------------------
% 77.08/12.14 % (318)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_32065 for (2894ds/939Mi)
% 78.73/12.43 % (318)Instruction limit reached!
% 78.73/12.43 % (318)------------------------------
% 78.73/12.43 % (318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.73/12.43 % (318)Termination reason: Unknown
% 78.73/12.43 % (318)Termination phase: Saturation
% 78.73/12.43
% 78.73/12.43 % (318)Memory used [KB]: 8059
% 78.73/12.43 % (318)Time elapsed: 0.295 s
% 78.73/12.43 % (318)Instructions burned: 941 (million)
% 78.73/12.43 % (318)------------------------------
% 78.73/12.43 % (318)------------------------------
% 78.73/12.44 % (320)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_32065 for (2890ds/1188Mi)
% 80.82/12.78 % (317)Instruction limit reached!
% 80.82/12.78 % (317)------------------------------
% 80.82/12.78 % (317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.82/12.78 % (317)Termination reason: Unknown
% 80.82/12.78 % (317)Termination phase: Saturation
% 80.82/12.78
% 80.82/12.78 % (317)Memory used [KB]: 9466
% 80.82/12.78 % (317)Time elapsed: 1.099 s
% 80.82/12.78 % (317)Instructions burned: 3631 (million)
% 80.82/12.78 % (317)------------------------------
% 80.82/12.78 % (317)------------------------------
% 80.82/12.79 % (321)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_32065 for (2887ds/3205Mi)
% 81.44/12.80 % (320)Instruction limit reached!
% 81.44/12.80 % (320)------------------------------
% 81.44/12.80 % (320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.44/12.80 % (320)Termination reason: Unknown
% 81.44/12.80 % (320)Termination phase: Saturation
% 81.44/12.80
% 81.44/12.80 % (320)Memory used [KB]: 9210
% 81.44/12.80 % (320)Time elapsed: 0.362 s
% 81.44/12.80 % (320)Instructions burned: 1189 (million)
% 81.44/12.80 % (320)------------------------------
% 81.44/12.80 % (320)------------------------------
% 81.44/12.81 % (322)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_32065 for (2887ds/865Mi)
% 81.44/12.85 % (307)Instruction limit reached!
% 81.44/12.85 % (307)------------------------------
% 81.44/12.85 % (307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.44/12.85 % (307)Termination reason: Unknown
% 81.44/12.85 % (307)Termination phase: Saturation
% 81.44/12.85
% 81.44/12.85 % (307)Memory used [KB]: 9722
% 81.44/12.85 % (307)Time elapsed: 1.651 s
% 81.44/12.85 % (307)Instructions burned: 5475 (million)
% 81.44/12.85 % (307)------------------------------
% 81.44/12.85 % (307)------------------------------
% 81.44/12.86 % (323)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_32065 for (2886ds/7469Mi)
% 83.31/13.09 % (322)Instruction limit reached!
% 83.31/13.09 % (322)------------------------------
% 83.31/13.09 % (322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.31/13.09 % (322)Termination reason: Unknown
% 83.31/13.09 % (322)Termination phase: Saturation
% 83.31/13.09
% 83.31/13.09 % (322)Memory used [KB]: 9210
% 83.31/13.09 % (322)Time elapsed: 0.273 s
% 83.31/13.09 % (322)Instructions burned: 865 (million)
% 83.31/13.09 % (322)------------------------------
% 83.31/13.09 % (322)------------------------------
% 83.31/13.09 % (301)Instruction limit reached!
% 83.31/13.09 % (301)------------------------------
% 83.31/13.09 % (301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.31/13.09 % (301)Termination reason: Unknown
% 83.31/13.09 % (301)Termination phase: Saturation
% 83.31/13.09
% 83.31/13.09 % (301)Memory used [KB]: 14328
% 83.31/13.09 % (301)Time elapsed: 2.498 s
% 83.31/13.09 % (301)Instructions burned: 8217 (million)
% 83.31/13.09 % (301)------------------------------
% 83.31/13.09 % (301)------------------------------
% 83.31/13.10 % (324)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_32065 for (2884ds/4165Mi)
% 83.31/13.10 % (325)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_32065 for (2884ds/13468Mi)
% 86.41/13.64 % (305)Instruction limit reached!
% 86.41/13.64 % (305)------------------------------
% 86.41/13.64 % (305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.41/13.64 % (305)Termination reason: Unknown
% 86.41/13.64 % (305)Termination phase: Saturation
% 86.41/13.64
% 86.41/13.64 % (305)Memory used [KB]: 16502
% 86.41/13.64 % (305)Time elapsed: 2.758 s
% 86.41/13.64 % (305)Instructions burned: 8787 (million)
% 86.41/13.64 % (305)------------------------------
% 86.41/13.64 % (305)------------------------------
% 86.41/13.65 % (326)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_32065 for (2878ds/2635Mi)
% 86.41/13.70 % (326)Refutation not found, incomplete strategy
% 86.41/13.70 % (326)------------------------------
% 86.41/13.70 % (326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.41/13.70 % (326)Termination reason: Refutation not found, incomplete strategy
% 86.41/13.70
% 86.41/13.70
% 86.41/13.70 % (326)Memory used [KB]: 7675
% 86.41/13.70 % (326)Time elapsed: 0.049 s
% 86.41/13.70 % (326)Instructions burned: 155 (million)
% 86.41/13.70 % (326)------------------------------
% 86.41/13.70 % (326)------------------------------
% 86.88/13.71 % (327)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=631:si=on:rtra=on_0 on DTF2THF_32065 for (2878ds/631Mi)
% 86.88/13.78 % (321)Instruction limit reached!
% 86.88/13.78 % (321)------------------------------
% 86.88/13.78 % (321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.88/13.78 % (321)Termination reason: Unknown
% 86.88/13.78 % (321)Termination phase: Saturation
% 86.88/13.78
% 86.88/13.78 % (321)Memory used [KB]: 12665
% 86.88/13.78 % (321)Time elapsed: 0.993 s
% 86.88/13.78 % (321)Instructions burned: 3206 (million)
% 86.88/13.78 % (321)------------------------------
% 86.88/13.78 % (321)------------------------------
% 86.88/13.79 % (328)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on DTF2THF_32065 for (2877ds/15557Mi)
% 87.34/13.88 % (309)Instruction limit reached!
% 87.34/13.88 % (309)------------------------------
% 87.34/13.88 % (309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.34/13.88 % (309)Termination reason: Unknown
% 87.34/13.88 % (309)Termination phase: Saturation
% 87.34/13.88
% 87.34/13.88 % (309)Memory used [KB]: 15095
% 87.34/13.88 % (309)Time elapsed: 2.592 s
% 87.34/13.88 % (309)Instructions burned: 8383 (million)
% 87.34/13.88 % (309)------------------------------
% 87.34/13.88 % (309)------------------------------
% 87.34/13.89 % (329)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on DTF2THF_32065 for (2876ds/2142Mi)
% 87.63/13.90 % (327)Instruction limit reached!
% 87.63/13.90 % (327)------------------------------
% 87.63/13.90 % (327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.63/13.90 % (327)Termination reason: Unknown
% 87.63/13.90 % (327)Termination phase: Saturation
% 87.63/13.90
% 87.63/13.90 % (327)Memory used [KB]: 8187
% 87.63/13.90 % (327)Time elapsed: 0.195 s
% 87.63/13.90 % (327)Instructions burned: 633 (million)
% 87.63/13.90 % (327)------------------------------
% 87.63/13.90 % (327)------------------------------
% 87.63/13.91 % (330)dis+1002_1:1_aac=none:au=on:bd=off:cnfonf=conj_eager:nwc=5.0:sgt=5:sp=reverse_arity:ss=axioms:i=5624:si=on:rtra=on_0 on DTF2THF_32065 for (2876ds/5624Mi)
% 90.33/14.11 % (313)Instruction limit reached!
% 90.33/14.11 % (313)------------------------------
% 90.33/14.11 % (313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.33/14.11 % (313)Termination reason: Unknown
% 90.33/14.11 % (313)Termination phase: Saturation
% 90.33/14.11
% 90.33/14.11 % (313)Memory used [KB]: 15351
% 90.33/14.11 % (313)Time elapsed: 2.533 s
% 90.33/14.11 % (313)Instructions burned: 8427 (million)
% 90.33/14.11 % (313)------------------------------
% 90.33/14.11 % (313)------------------------------
% 90.33/14.12 % (331)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=1665:si=on:rtra=on_0 on DTF2THF_32065 for (2874ds/1665Mi)
% 92.18/14.37 % (324)Instruction limit reached!
% 92.18/14.37 % (324)------------------------------
% 92.18/14.37 % (324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.18/14.37 % (324)Termination reason: Unknown
% 92.18/14.37 % (324)Termination phase: Saturation
% 92.18/14.37
% 92.18/14.37 % (324)Memory used [KB]: 16502
% 92.18/14.37 % (324)Time elapsed: 1.275 s
% 92.18/14.37 % (324)Instructions burned: 4166 (million)
% 92.18/14.37 % (324)------------------------------
% 92.18/14.37 % (324)------------------------------
% 92.18/14.38 % (381)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=64912:si=on:rtra=on_0 on DTF2THF_32065 for (2871ds/64912Mi)
% 92.18/14.39 % (381)Refutation not found, incomplete strategy
% 92.18/14.39 % (381)------------------------------
% 92.18/14.39 % (381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.18/14.39 % (381)Termination reason: Refutation not found, incomplete strategy
% 92.18/14.39
% 92.18/14.39
% 92.18/14.39 % (381)Memory used [KB]: 1918
% 92.18/14.39 % (381)Time elapsed: 0.014 s
% 92.18/14.39 % (381)Instructions burned: 42 (million)
% 92.18/14.39 % (381)------------------------------
% 92.18/14.39 % (381)------------------------------
% 92.79/14.40 % (398)lrs+10_1:32_atotf=0.1:avsq=on:bsr=on:cnfonf=lazy_gen:fde=unused:i=7801:si=on:rtra=on_0 on DTF2THF_32065 for (2871ds/7801Mi)
% 93.28/14.55 % (329)Instruction limit reached!
% 93.28/14.55 % (329)------------------------------
% 93.28/14.55 % (329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.28/14.55 % (329)Termination reason: Unknown
% 93.28/14.55 % (329)Termination phase: Saturation
% 93.28/14.55
% 93.28/14.55 % (329)Memory used [KB]: 8059
% 93.28/14.55 % (329)Time elapsed: 0.668 s
% 93.28/14.55 % (329)Instructions burned: 2144 (million)
% 93.28/14.55 % (329)------------------------------
% 93.28/14.55 % (329)------------------------------
% 93.28/14.56 % (464)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15194:si=on:rtra=on_0 on DTF2THF_32065 for (2869ds/15194Mi)
% 93.73/14.63 % (331)Instruction limit reached!
% 93.73/14.63 % (331)------------------------------
% 93.73/14.63 % (331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.73/14.63 % (331)Termination reason: Unknown
% 93.73/14.63 % (331)Termination phase: Saturation
% 93.73/14.63
% 93.73/14.63 % (331)Memory used [KB]: 9594
% 93.73/14.63 % (331)Time elapsed: 0.516 s
% 93.73/14.63 % (331)Instructions burned: 1667 (million)
% 93.73/14.63 % (331)------------------------------
% 93.73/14.63 % (331)------------------------------
% 93.73/14.64 % (488)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=6753:si=on:rtra=on_0 on DTF2THF_32065 for (2869ds/6753Mi)
% 93.73/14.68 % (488)Refutation not found, incomplete strategy
% 93.73/14.68 % (488)------------------------------
% 93.73/14.68 % (488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 93.73/14.68 % (488)Termination reason: Refutation not found, incomplete strategy
% 93.73/14.68
% 93.73/14.68
% 93.73/14.68 % (488)Memory used [KB]: 7164
% 93.73/14.68 % (488)Time elapsed: 0.037 s
% 93.73/14.68 % (488)Instructions burned: 111 (million)
% 93.73/14.68 % (488)------------------------------
% 93.73/14.68 % (488)------------------------------
% 93.73/14.69 % (519)lrs+1002_1:28_bd=off:cnfonf=lazy_simp:plsq=on:plsqr=1,1:prag=on:i=1003:si=on:rtra=on_0 on DTF2THF_32065 for (2868ds/1003Mi)
% 95.52/14.99 % (519)Instruction limit reached!
% 95.52/14.99 % (519)------------------------------
% 95.52/14.99 % (519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 95.52/14.99 % (519)Termination reason: Unknown
% 95.52/14.99 % (519)Termination phase: Saturation
% 95.52/14.99
% 95.52/14.99 % (519)Memory used [KB]: 8699
% 95.52/14.99 % (519)Time elapsed: 0.303 s
% 95.52/14.99 % (519)Instructions burned: 1004 (million)
% 95.52/14.99 % (519)------------------------------
% 95.52/14.99 % (519)------------------------------
% 95.52/15.00 % (618)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=13018:si=on:rtra=on_0 on DTF2THF_32065 for (2865ds/13018Mi)
% 98.15/15.13 % (323)Instruction limit reached!
% 98.15/15.13 % (323)------------------------------
% 98.15/15.13 % (323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.15/15.13 % (323)Termination reason: Unknown
% 98.15/15.13 % (323)Termination phase: Saturation
% 98.15/15.13
% 98.15/15.13 % (323)Memory used [KB]: 9338
% 98.15/15.13 % (323)Time elapsed: 2.268 s
% 98.15/15.13 % (323)Instructions burned: 7471 (million)
% 98.15/15.13 % (323)------------------------------
% 98.15/15.13 % (323)------------------------------
% 98.15/15.14 % (717)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1267:si=on:rtra=on_0 on DTF2THF_32065 for (2864ds/1267Mi)
% 100.43/15.55 % (717)Instruction limit reached!
% 100.43/15.55 % (717)------------------------------
% 100.43/15.55 % (717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.43/15.55 % (717)Termination reason: Unknown
% 100.43/15.55 % (717)Termination phase: Saturation
% 100.43/15.55
% 100.43/15.55 % (717)Memory used [KB]: 9466
% 100.43/15.55 % (717)Time elapsed: 0.415 s
% 100.43/15.55 % (717)Instructions burned: 1268 (million)
% 100.43/15.55 % (717)------------------------------
% 100.43/15.55 % (717)------------------------------
% 100.43/15.57 % (865)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=2570:si=on:rtra=on_0 on DTF2THF_32065 for (2859ds/2570Mi)
% 100.43/15.58 % (325)Instruction limit reached!
% 100.43/15.58 % (325)------------------------------
% 100.43/15.58 % (325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 100.43/15.58 % (325)Termination reason: Unknown
% 100.43/15.58 % (325)Termination phase: Saturation
% 100.43/15.58
% 100.43/15.58 % (325)Memory used [KB]: 9338
% 100.43/15.58 % (325)Time elapsed: 2.486 s
% 100.43/15.58 % (325)Instructions burned: 13469 (million)
% 100.43/15.58 % (325)------------------------------
% 100.43/15.58 % (325)------------------------------
% 100.43/15.59 % (869)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_32065 for (2859ds/13163Mi)
% 101.44/15.68 % (330)Instruction limit reached!
% 101.44/15.68 % (330)------------------------------
% 101.44/15.68 % (330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 101.44/15.68 % (330)Termination reason: Unknown
% 101.44/15.68 % (330)Termination phase: Saturation
% 101.44/15.68
% 101.44/15.68 % (330)Memory used [KB]: 12153
% 101.44/15.68 % (330)Time elapsed: 1.773 s
% 101.44/15.68 % (330)Instructions burned: 5625 (million)
% 101.44/15.68 % (330)------------------------------
% 101.44/15.68 % (330)------------------------------
% 101.44/15.69 % (870)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_32065 for (2858ds/5087Mi)
% 107.04/16.41 % (865)Instruction limit reached!
% 107.04/16.41 % (865)------------------------------
% 107.04/16.41 % (865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 107.04/16.41 % (865)Termination reason: Unknown
% 107.04/16.41 % (865)Termination phase: Saturation
% 107.04/16.41
% 107.04/16.41 % (865)Memory used [KB]: 9722
% 107.04/16.41 % (865)Time elapsed: 0.849 s
% 107.04/16.41 % (865)Instructions burned: 2571 (million)
% 107.04/16.41 % (865)------------------------------
% 107.04/16.41 % (865)------------------------------
% 107.04/16.42 % (873)lrs+1002_1:1_aac=none:au=on:bd=off:cnfonf=lazy_pi_sigma_gen:s2a=on:sac=on:sd=1:sgt=20:ss=axioms:i=10380:si=on:rtra=on_0 on DTF2THF_32065 for (2851ds/10380Mi)
% 110.08/16.90 % (398)Instruction limit reached!
% 110.08/16.90 % (398)------------------------------
% 110.08/16.90 % (398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 110.08/16.90 % (398)Termination reason: Unknown
% 110.08/16.90 % (398)Termination phase: Saturation
% 110.08/16.90
% 110.08/16.90 % (398)Memory used [KB]: 19445
% 110.08/16.90 % (398)Time elapsed: 2.501 s
% 110.08/16.90 % (398)Instructions burned: 7804 (million)
% 110.08/16.90 % (398)------------------------------
% 110.08/16.90 % (398)------------------------------
% 110.08/16.91 % (944)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4218:si=on:rtra=on_0 on DTF2THF_32065 for (2846ds/4218Mi)
% 110.08/16.93 % (944)Refutation not found, incomplete strategy
% 110.08/16.93 % (944)------------------------------
% 110.08/16.93 % (944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 110.08/16.93 % (944)Termination reason: Refutation not found, incomplete strategy
% 110.08/16.93
% 110.08/16.93
% 110.08/16.93 % (944)Memory used [KB]: 6396
% 110.08/16.93 % (944)Time elapsed: 0.016 s
% 110.08/16.93 % (944)Instructions burned: 48 (million)
% 110.08/16.93 % (944)------------------------------
% 110.08/16.93 % (944)------------------------------
% 110.08/16.94 % (955)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3971:si=on:rtra=on_0 on DTF2THF_32065 for (2846ds/3971Mi)
% 114.76/17.50 % (870)Instruction limit reached!
% 114.76/17.50 % (870)------------------------------
% 114.76/17.50 % (870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.76/17.50 % (870)Termination reason: Unknown
% 114.76/17.50 % (870)Termination phase: Saturation
% 114.76/17.50
% 114.76/17.50 % (870)Memory used [KB]: 10874
% 114.76/17.50 % (870)Time elapsed: 1.808 s
% 114.76/17.50 % (870)Instructions burned: 5087 (million)
% 114.76/17.50 % (870)------------------------------
% 114.76/17.50 % (870)------------------------------
% 114.76/17.51 % (1184)dis+1010_1:1_anc=all_dependent:au=on:bs=on:sd=5:sp=occurrence:ss=axioms:st=2.0:i=14014:si=on:rtra=on_0 on DTF2THF_32065 for (2840ds/14014Mi)
% 115.99/17.79 % (328)First to succeed.
% 115.99/17.79 % (328)Refutation found. Thanks to Tanya!
% 115.99/17.79 % SZS status Theorem for DTF2THF_32065
% 115.99/17.79 % SZS output start Proof for DTF2THF_32065
% 115.99/17.79 thf(type_def_5, type, product_unit: $tType).
% 115.99/17.79 thf(type_def_6, type, configuration_ext: ($tType * $tType * $tType * $tType) > $tType).
% 115.99/17.79 thf(type_def_7, type, message: ($tType * $tType) > $tType).
% 115.99/17.79 thf(type_def_9, type, list: ($tType) > $tType).
% 115.99/17.79 thf(type_def_10, type, nat: $tType).
% 115.99/17.79 thf(type_def_11, type, set: ($tType) > $tType).
% 115.99/17.79 thf(type_def_12, type, p: $tType).
% 115.99/17.79 thf(type_def_13, type, v: $tType).
% 115.99/17.79 thf(type_def_14, type, s: $tType).
% 115.99/17.79 thf(func_def_0, type, configuration_ext: ($tType * $tType * $tType * $tType) > $tType).
% 115.99/17.79 thf(func_def_1, type, message: ($tType * $tType) > $tType).
% 115.99/17.79 thf(func_def_2, type, product_unit: $tType).
% 115.99/17.79 thf(func_def_3, type, list: ($tType) > $tType).
% 115.99/17.79 thf(func_def_4, type, set: ($tType) > $tType).
% 115.99/17.79 thf(func_def_5, type, nat: $tType).
% 115.99/17.79 thf(func_def_6, type, v: $tType).
% 115.99/17.79 thf(func_def_7, type, s: $tType).
% 115.99/17.79 thf(func_def_8, type, p: $tType).
% 115.99/17.79 thf(func_def_9, type, type: !>[X0: $tType]:($o)).
% 115.99/17.79 thf(func_def_10, type, size: !>[X0: $tType]:($o)).
% 115.99/17.79 thf(func_def_11, type, one: !>[X0: $tType]:($o)).
% 115.99/17.79 thf(func_def_12, type, minus: !>[X0: $tType]:($o)).
% 115.99/17.79 thf(func_def_13, type, ord: !>[X0: $tType]:($o)).
% 115.99/17.79 thf(func_def_14, type, order: !>[X0: $tType]:($o)).
% 115.99/17.79 thf(func_def_15, type, group_add: !>[X0: $tType]:($o)).
% 115.99/17.79 thf(func_def_16, type, no_bot: !>[X0: $tType]:($o)).
% 115.99/17.79 thf(func_def_17, type, no_top: !>[X0: $tType]:($o)).
% 115.99/17.79 thf(func_def_18, type, linorder: !>[X0: $tType]:($o)).
% 115.99/17.79 thf(func_def_19, type, preorder: !>[X0: $tType]:($o)).
% 115.99/17.79 thf(func_def_20, type, wellorder: !>[X0: $tType]:($o)).
% 115.99/17.79 thf(func_def_21, type, dense_order: !>[X0: $tType]:($o)).
% 115.99/17.79 thf(func_def_22, type, dense_linorder: !>[X0: $tType]:($o)).
% 115.99/17.79 thf(func_def_23, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 115.99/17.79 thf(func_def_24, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 115.99/17.79 thf(func_def_25, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 115.99/17.79 thf(func_def_26, type, enabled: !>[X0: $tType, X1: $tType, X2: $tType]:(configuration_ext @ X0 @ X1 @ X2 @ product_unit > message @ X0 @ X1 > $o)).
% 115.99/17.79 thf(func_def_27, type, isReceiverOf: !>[X0: $tType, X1: $tType]:(X0 > message @ X0 @ X1 > $o)).
% 115.99/17.79 thf(func_def_28, type, firstOccurrence: !>[X0: $tType, X1: $tType, X2: $tType]:(list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit > list @ message @ X0 @ X1 > message @ X0 @ X1 > nat > $o)).
% 115.99/17.79 thf(func_def_29, type, minimalEnabled: !>[X0: $tType, X1: $tType, X2: $tType]:(list @ configuration_ext @ X0 @ X1 @ X2 @ product_unit > list @ message @ X0 @ X1 > message @ X0 @ X1 > $o)).
% 115.99/17.79 thf(func_def_30, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 115.99/17.79 thf(func_def_31, type, one_one: !>[X0: $tType]:(X0)).
% 115.99/17.79 thf(func_def_32, type, prefixList: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 115.99/17.79 thf(func_def_33, type, nil: !>[X0: $tType]:(list @ X0)).
% 115.99/17.79 thf(func_def_34, type, nth: !>[X0: $tType]:(list @ X0 > nat > X0)).
% 115.99/17.79 thf(func_def_35, type, suc: nat > nat).
% 115.99/17.79 thf(func_def_36, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 115.99/17.79 thf(func_def_37, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 115.99/17.79 thf(func_def_38, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 115.99/17.79 thf(func_def_39, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 115.99/17.79 thf(func_def_40, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 115.99/17.79 thf(func_def_41, type, occM: nat).
% 115.99/17.79 thf(func_def_42, type, occM2: nat).
% 115.99/17.79 thf(func_def_43, type, consumedMsg: message @ p @ v).
% 115.99/17.79 thf(func_def_44, type, fe: nat > list @ configuration_ext @ p @ v @ s @ product_unit).
% 115.99/17.79 thf(func_def_45, type, firstOccSet: nat > set @ message @ p @ v).
% 115.99/17.79 thf(func_def_46, type, ft: nat > list @ message @ p @ v).
% 115.99/17.79 thf(func_def_47, type, index: nat).
% 115.99/17.79 thf(func_def_48, type, msg: message @ p @ v).
% 115.99/17.79 thf(func_def_49, type, msg2: message @ p @ v).
% 115.99/17.79 thf(func_def_50, type, msga: message @ p @ v).
% 115.99/17.79 thf(func_def_51, type, n0: nat).
% 115.99/17.79 thf(func_def_52, type, n: nat).
% 115.99/17.79 thf(func_def_53, type, p2: p).
% 115.99/17.79 thf(func_def_72, type, ph1: !>[X0: $tType]:(X0)).
% 115.99/17.79 thf(func_def_73, type, sK2: p).
% 115.99/17.79 thf(func_def_74, type, sK3: p).
% 115.99/17.79 thf(func_def_75, type, sK4: !>[X0: $tType]:(nat > list @ X0)).
% 115.99/17.79 thf(func_def_76, type, sK5: nat > nat).
% 115.99/17.79 thf(func_def_77, type, sK6: nat > nat).
% 115.99/17.79 thf(func_def_78, type, sK7: nat > nat).
% 115.99/17.79 thf(func_def_79, type, sK8: nat).
% 115.99/17.79 thf(func_def_80, type, sK9: nat).
% 115.99/17.79 thf(func_def_81, type, sK10: nat > nat).
% 115.99/17.79 thf(func_def_82, type, sK11: nat > nat).
% 115.99/17.79 thf(func_def_83, type, sK12: nat).
% 115.99/17.79 thf(f25855,plain,(
% 115.99/17.79 $false),
% 115.99/17.79 inference(trivial_inequality_removal,[status(thm)],[f25854])).
% 115.99/17.79 thf(f25854,plain,(
% 115.99/17.79 ($true = $false)),
% 115.99/17.79 inference(forward_demodulation,[status(thm)],[f25745,f24880])).
% 115.99/17.79 thf(f24880,plain,(
% 115.99/17.79 ((ord_less_eq @ nat @ occM2 @ sK12) = $false)),
% 115.99/17.79 inference(forward_demodulation,[status(thm)],[f24679,f1699])).
% 115.99/17.79 thf(f1699,plain,(
% 115.99/17.79 ( ! [X1 : nat] : (((minus_minus @ nat @ (suc @ X1) @ one_one @ nat) = X1)) )),
% 115.99/17.79 inference(equality_proxy_clausification,[status(thm)],[f1690])).
% 115.99/17.79 thf(f1690,plain,(
% 115.99/17.79 ( ! [X1 : nat] : (($true = ((minus_minus @ nat @ (suc @ X1) @ one_one @ nat) = X1))) )),
% 115.99/17.79 inference(beta_eta_normalization,[status(thm)],[f1689])).
% 115.99/17.79 thf(f1689,plain,(
% 115.99/17.79 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: ((minus_minus @ nat @ (suc @ Y0) @ one_one @ nat) = Y0)) @ X1))) )),
% 115.99/17.79 inference(pi_clausification,[status(thm)],[f1157])).
% 115.99/17.79 thf(f1157,plain,(
% 115.99/17.79 ($true = (!! @ nat @ (^[Y0 : nat]: ((minus_minus @ nat @ (suc @ Y0) @ one_one @ nat) = Y0))))),
% 115.99/17.79 inference(cnf_transformation,[status(thm)],[f551])).
% 115.99/17.79 thf(f551,plain,(
% 115.99/17.79 ($true = (!! @ nat @ (^[Y0 : nat]: ((minus_minus @ nat @ (suc @ Y0) @ one_one @ nat) = Y0))))),
% 115.99/17.79 inference(fool_elimination,[status(thm)],[f550])).
% 115.99/17.79 thf(f550,plain,(
% 115.99/17.79 ! [X0 : nat] : ((minus_minus @ nat @ (suc @ X0) @ one_one @ nat) = X0)),
% 115.99/17.79 inference(rectify,[status(thm)],[f25])).
% 115.99/17.79 thf(f25,axiom,(
% 115.99/17.79 ! [X11 : nat] : ((minus_minus @ nat @ (suc @ X11) @ one_one @ nat) = X11)),
% 115.99/17.79 file('/export/starexec/sandbox/tmp/tmp.0mkoVbkNSb/DTF2THF_32065.p',fact_24_diff__Suc__1)).
% 115.99/17.79 thf(f24679,plain,(
% 115.99/17.79 ((ord_less_eq @ nat @ occM2 @ (minus_minus @ nat @ (suc @ sK12) @ one_one @ nat)) = $false)),
% 115.99/17.79 inference(backward_demodulation,[status(thm)],[f5687,f24659])).
% 115.99/17.79 thf(f24659,plain,(
% 115.99/17.79 ((size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) = (suc @ sK12))),
% 115.99/17.79 inference(equality_proxy_clausification,[status(thm)],[f24642])).
% 115.99/17.79 thf(f24642,plain,(
% 115.99/17.79 ($true = ((suc @ sK12) = (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))))),
% 115.99/17.79 inference(beta_eta_normalization,[status(thm)],[f24641])).
% 115.99/17.79 thf(f24641,plain,(
% 115.99/17.79 ($true = ((^[Y0 : nat]: ((suc @ Y0) = (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))) @ sK12))),
% 115.99/17.79 inference(sigma_clausification,[status(thm)],[f4415])).
% 115.99/17.79 thf(f4415,plain,(
% 115.99/17.79 ($true = (?? @ nat @ (^[Y0 : nat]: ((suc @ Y0) = (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))))))),
% 115.99/17.79 inference(boolean_simplification,[status(thm)],[f4401])).
% 115.99/17.79 thf(f4401,plain,(
% 115.99/17.79 ($true = ($true => (?? @ nat @ (^[Y0 : nat]: ((suc @ Y0) = (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))))))),
% 115.99/17.79 inference(superposition,[status(thm)],[f4379,f1217])).
% 115.99/17.79 thf(f1217,plain,(
% 115.99/17.79 ((ord_less @ nat @ occM @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) = $true)),
% 115.99/17.79 inference(cnf_transformation,[status(thm)],[f852])).
% 115.99/17.79 thf(f852,plain,(
% 115.99/17.79 ((ord_less @ nat @ occM @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) = $true)),
% 115.99/17.79 inference(fool_elimination,[status(thm)],[f851])).
% 115.99/17.79 thf(f851,plain,(
% 115.99/17.79 (ord_less @ nat @ occM @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))),
% 115.99/17.79 inference(rectify,[status(thm)],[f3])).
% 115.99/17.79 thf(f3,axiom,(
% 115.99/17.79 (ord_less @ nat @ occM @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))),
% 115.99/17.79 file('/export/starexec/sandbox/tmp/tmp.0mkoVbkNSb/DTF2THF_32065.p',fact_2_OccM_H_I3_J)).
% 115.99/17.79 thf(f4379,plain,(
% 115.99/17.79 ( ! [X2 : nat,X1 : nat] : (($true = ((ord_less @ nat @ X2 @ X1) => (?? @ nat @ (^[Y0 : nat]: ((suc @ Y0) = X1)))))) )),
% 115.99/17.79 inference(forward_demodulation,[status(thm)],[f4378,f2408])).
% 115.99/17.79 thf(f2408,plain,(
% 115.99/17.79 ( ! [X2 : nat,X1 : nat] : (((ord_less @ nat @ X2 @ X1) = (ord_less_eq @ nat @ (suc @ X2) @ X1))) )),
% 115.99/17.79 inference(equality_proxy_clausification,[status(thm)],[f2399])).
% 115.99/17.79 thf(f2399,plain,(
% 115.99/17.79 ( ! [X2 : nat,X1 : nat] : ((((ord_less @ nat @ X2 @ X1) = (ord_less_eq @ nat @ (suc @ X2) @ X1)) = $true)) )),
% 115.99/17.79 inference(beta_eta_normalization,[status(thm)],[f2398])).
% 115.99/17.79 thf(f2398,plain,(
% 115.99/17.79 ( ! [X2 : nat,X1 : nat] : (($true = ((^[Y0 : nat]: ((ord_less @ nat @ Y0 @ X1) = (ord_less_eq @ nat @ (suc @ Y0) @ X1))) @ X2))) )),
% 115.99/17.79 inference(pi_clausification,[status(thm)],[f2393])).
% 115.99/17.79 thf(f2393,plain,(
% 115.99/17.79 ( ! [X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((ord_less @ nat @ Y0 @ X1) = (ord_less_eq @ nat @ (suc @ Y0) @ X1)))))) )),
% 115.99/17.79 inference(beta_eta_normalization,[status(thm)],[f2392])).
% 115.99/17.79 thf(f2392,plain,(
% 115.99/17.79 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less @ nat @ Y1 @ Y0) = (ord_less_eq @ nat @ (suc @ Y1) @ Y0))))) @ X1))) )),
% 115.99/17.79 inference(pi_clausification,[status(thm)],[f1219])).
% 115.99/17.79 thf(f1219,plain,(
% 115.99/17.79 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less @ nat @ Y1 @ Y0) = (ord_less_eq @ nat @ (suc @ Y1) @ Y0)))))))),
% 115.99/17.79 inference(cnf_transformation,[status(thm)],[f469])).
% 115.99/17.79 thf(f469,plain,(
% 115.99/17.79 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less @ nat @ Y1 @ Y0) = (ord_less_eq @ nat @ (suc @ Y1) @ Y0)))))))),
% 115.99/17.79 inference(fool_elimination,[status(thm)],[f468])).
% 115.99/17.79 thf(f468,plain,(
% 115.99/17.79 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ X0 @ X1) = (ord_less_eq @ nat @ (suc @ X0) @ X1))),
% 115.99/17.79 inference(rectify,[status(thm)],[f34])).
% 115.99/17.79 thf(f34,axiom,(
% 115.99/17.79 ! [X25 : nat,X11 : nat] : ((ord_less @ nat @ X25 @ X11) = (ord_less_eq @ nat @ (suc @ X25) @ X11))),
% 115.99/17.79 file('/export/starexec/sandbox/tmp/tmp.0mkoVbkNSb/DTF2THF_32065.p',fact_33_Suc__le__eq)).
% 115.99/17.79 thf(f4378,plain,(
% 115.99/17.79 ( ! [X2 : nat,X1 : nat] : (($true = ((ord_less_eq @ nat @ (suc @ X2) @ X1) => (?? @ nat @ (^[Y0 : nat]: ((suc @ Y0) = X1)))))) )),
% 115.99/17.79 inference(beta_eta_normalization,[status(thm)],[f4377])).
% 115.99/17.79 thf(f4377,plain,(
% 115.99/17.79 ( ! [X2 : nat,X1 : nat] : (($true = ((^[Y0 : nat]: ((ord_less_eq @ nat @ (suc @ Y0) @ X1) => (?? @ nat @ (^[Y1 : nat]: ((suc @ Y1) = X1))))) @ X2))) )),
% 115.99/17.79 inference(pi_clausification,[status(thm)],[f4360])).
% 115.99/17.79 thf(f4360,plain,(
% 115.99/17.79 ( ! [X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((ord_less_eq @ nat @ (suc @ Y0) @ X1) => (?? @ nat @ (^[Y1 : nat]: ((suc @ Y1) = X1)))))))) )),
% 115.99/17.79 inference(beta_eta_normalization,[status(thm)],[f4359])).
% 115.99/17.79 thf(f4359,plain,(
% 115.99/17.79 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_eq @ nat @ (suc @ Y1) @ Y0) => (?? @ nat @ (^[Y2 : nat]: ((suc @ Y2) = Y0))))))) @ X1))) )),
% 115.99/17.79 inference(pi_clausification,[status(thm)],[f1155])).
% 115.99/17.79 thf(f1155,plain,(
% 115.99/17.79 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_eq @ nat @ (suc @ Y1) @ Y0) => (?? @ nat @ (^[Y2 : nat]: ((suc @ Y2) = Y0)))))))))),
% 115.99/17.79 inference(cnf_transformation,[status(thm)],[f428])).
% 115.99/17.79 thf(f428,plain,(
% 115.99/17.79 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_eq @ nat @ (suc @ Y1) @ Y0) => (?? @ nat @ (^[Y2 : nat]: ((suc @ Y2) = Y0)))))))))),
% 115.99/17.79 inference(fool_elimination,[status(thm)],[f427])).
% 115.99/17.79 thf(f427,plain,(
% 115.99/17.79 ! [X0 : nat,X1 : nat] : ((ord_less_eq @ nat @ (suc @ X0) @ X1) => ? [X2 : nat] : ((suc @ X2) = X1))),
% 115.99/17.79 inference(rectify,[status(thm)],[f32])).
% 115.99/17.79 thf(f32,axiom,(
% 115.99/17.79 ! [X11 : nat,X27 : nat] : ((ord_less_eq @ nat @ (suc @ X11) @ X27) => ? [X28 : nat] : ((suc @ X28) = X27))),
% 115.99/17.79 file('/export/starexec/sandbox/tmp/tmp.0mkoVbkNSb/DTF2THF_32065.p',fact_31_Suc__le__D)).
% 115.99/17.79 thf(f5687,plain,(
% 115.99/17.79 ((ord_less_eq @ nat @ occM2 @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ one_one @ nat)) = $false)),
% 115.99/17.79 inference(forward_demodulation,[status(thm)],[f5656,f2876])).
% 115.99/17.79 thf(f2876,plain,(
% 115.99/17.79 ((ord_less @ nat @ occM2 @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ one_one @ nat)) = $false)),
% 115.99/17.79 inference(boolean_simplification,[status(thm)],[f2872])).
% 115.99/17.79 thf(f2872,plain,(
% 115.99/17.79 ((~ $true) = (ord_less @ nat @ occM2 @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ one_one @ nat)))),
% 115.99/17.79 inference(superposition,[status(thm)],[f2801,f1099])).
% 115.99/17.79 thf(f1099,plain,(
% 115.99/17.79 ((ord_less_eq @ nat @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ one_one @ nat) @ occM2) = $true)),
% 115.99/17.79 inference(cnf_transformation,[status(thm)],[f661])).
% 115.99/17.79 thf(f661,plain,(
% 115.99/17.79 ((ord_less_eq @ nat @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ one_one @ nat) @ occM2) = $true)),
% 115.99/17.79 inference(fool_elimination,[status(thm)],[f660])).
% 115.99/17.79 thf(f660,plain,(
% 115.99/17.79 (ord_less_eq @ nat @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ one_one @ nat) @ occM2)),
% 115.99/17.79 inference(rectify,[status(thm)],[f2])).
% 115.99/17.79 thf(f2,axiom,(
% 115.99/17.79 (ord_less_eq @ nat @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ one_one @ nat) @ occM2)),
% 115.99/17.79 file('/export/starexec/sandbox/tmp/tmp.0mkoVbkNSb/DTF2THF_32065.p',fact_1__092_060open_062length_A_Ife_Aindex_J_A_N_A1_A_092_060le_062_AOccM_092_060close_062)).
% 115.99/17.79 thf(f2801,plain,(
% 115.99/17.79 ( ! [X2 : nat,X1 : nat] : (((~ (ord_less_eq @ nat @ X2 @ X1)) = (ord_less @ nat @ X1 @ X2))) )),
% 115.99/17.79 inference(equality_proxy_clausification,[status(thm)],[f2790])).
% 115.99/17.79 thf(f2790,plain,(
% 115.99/17.79 ( ! [X2 : nat,X1 : nat] : (($true = ((ord_less @ nat @ X1 @ X2) = (~ (ord_less_eq @ nat @ X2 @ X1))))) )),
% 115.99/17.79 inference(forward_demodulation,[status(thm)],[f2789,f2408])).
% 115.99/17.79 thf(f2789,plain,(
% 115.99/17.79 ( ! [X2 : nat,X1 : nat] : (($true = ((ord_less_eq @ nat @ (suc @ X1) @ X2) = (~ (ord_less_eq @ nat @ X2 @ X1))))) )),
% 115.99/17.79 inference(beta_eta_normalization,[status(thm)],[f2788])).
% 115.99/17.79 thf(f2788,plain,(
% 115.99/17.79 ( ! [X2 : nat,X1 : nat] : (($true = ((^[Y0 : nat]: ((ord_less_eq @ nat @ (suc @ X1) @ Y0) = (~ (ord_less_eq @ nat @ Y0 @ X1)))) @ X2))) )),
% 115.99/17.79 inference(pi_clausification,[status(thm)],[f2783])).
% 115.99/17.79 thf(f2783,plain,(
% 115.99/17.79 ( ! [X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((ord_less_eq @ nat @ (suc @ X1) @ Y0) = (~ (ord_less_eq @ nat @ Y0 @ X1))))))) )),
% 115.99/17.79 inference(beta_eta_normalization,[status(thm)],[f2782])).
% 115.99/17.79 thf(f2782,plain,(
% 115.99/17.79 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_eq @ nat @ (suc @ Y0) @ Y1) = (~ (ord_less_eq @ nat @ Y1 @ Y0)))))) @ X1))) )),
% 115.99/17.79 inference(pi_clausification,[status(thm)],[f1209])).
% 115.99/17.79 thf(f1209,plain,(
% 115.99/17.79 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_eq @ nat @ (suc @ Y0) @ Y1) = (~ (ord_less_eq @ nat @ Y1 @ Y0))))))))),
% 115.99/17.79 inference(cnf_transformation,[status(thm)],[f414])).
% 115.99/17.79 thf(f414,plain,(
% 115.99/17.79 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_eq @ nat @ (suc @ Y0) @ Y1) = (~ (ord_less_eq @ nat @ Y1 @ Y0))))))))),
% 115.99/17.79 inference(fool_elimination,[status(thm)],[f413])).
% 115.99/17.79 thf(f413,plain,(
% 115.99/17.79 ! [X0 : nat,X1 : nat] : ((ord_less_eq @ nat @ (suc @ X1) @ X0) = ~(ord_less_eq @ nat @ X0 @ X1))),
% 115.99/17.79 inference(rectify,[status(thm)],[f71])).
% 115.99/17.79 thf(f71,axiom,(
% 115.99/17.79 ! [X25 : nat,X11 : nat] : ((ord_less_eq @ nat @ (suc @ X11) @ X25) = ~(ord_less_eq @ nat @ X25 @ X11))),
% 115.99/17.79 file('/export/starexec/sandbox/tmp/tmp.0mkoVbkNSb/DTF2THF_32065.p',fact_70_not__less__eq__eq)).
% 115.99/17.79 thf(f5656,plain,(
% 115.99/17.79 ((ord_less_eq @ nat @ occM2 @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ one_one @ nat)) = (ord_less @ nat @ occM2 @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ one_one @ nat)))),
% 115.99/17.79 inference(boolean_simplification,[status(thm)],[f5631])).
% 115.99/17.79 thf(f5631,plain,(
% 115.99/17.79 ((ord_less_eq @ nat @ occM2 @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ one_one @ nat)) = ((ord_less @ nat @ occM2 @ (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ one_one @ nat)) | $false))),
% 115.99/17.79 inference(superposition,[status(thm)],[f5488,f1808])).
% 115.99/17.79 thf(f1808,plain,(
% 115.99/17.79 ((occM2 = (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ one_one @ nat)) = $false)),
% 115.99/17.79 inference(not_proxy_clausification,[status(thm)],[f1226])).
% 115.99/17.79 thf(f1226,plain,(
% 115.99/17.79 ($true = (~ (occM2 = (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ one_one @ nat))))),
% 115.99/17.79 inference(cnf_transformation,[status(thm)],[f788])).
% 115.99/17.79 thf(f788,plain,(
% 115.99/17.79 ($true = (~ (occM2 = (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ one_one @ nat))))),
% 115.99/17.79 inference(fool_elimination,[status(thm)],[f287])).
% 115.99/17.79 thf(f287,negated_conjecture,(
% 115.99/17.79 ~(occM2 = (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ one_one @ nat))),
% 115.99/17.79 inference(negated_conjecture,[status(cth)],[f286])).
% 115.99/17.79 thf(f286,conjecture,(
% 115.99/17.79 (occM2 = (minus_minus @ nat @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)) @ one_one @ nat))),
% 115.99/17.79 file('/export/starexec/sandbox/tmp/tmp.0mkoVbkNSb/DTF2THF_32065.p',conj_0)).
% 115.99/17.79 thf(f5488,plain,(
% 115.99/17.79 ( ! [X2 : nat,X1 : nat] : ((((ord_less @ nat @ X2 @ X1) | (X2 = X1)) = (ord_less_eq @ nat @ X2 @ X1))) )),
% 115.99/17.79 inference(equality_proxy_clausification,[status(thm)],[f5483])).
% 115.99/17.79 thf(f5483,plain,(
% 115.99/17.79 ( ! [X2 : nat,X1 : nat] : (($true = ((ord_less_eq @ nat @ X2 @ X1) = ((ord_less @ nat @ X2 @ X1) | (X2 = X1))))) )),
% 115.99/17.79 inference(forward_demodulation,[status(thm)],[f5482,f2507])).
% 115.99/17.79 thf(f2507,plain,(
% 115.99/17.79 ( ! [X2 : nat,X1 : nat] : (((ord_less_eq @ nat @ X2 @ X1) = (ord_less @ nat @ X2 @ (suc @ X1)))) )),
% 115.99/17.79 inference(equality_proxy_clausification,[status(thm)],[f2498])).
% 115.99/17.79 thf(f2498,plain,(
% 115.99/17.79 ( ! [X2 : nat,X1 : nat] : (($true = ((ord_less_eq @ nat @ X2 @ X1) = (ord_less @ nat @ X2 @ (suc @ X1))))) )),
% 115.99/17.79 inference(beta_eta_normalization,[status(thm)],[f2497])).
% 115.99/17.79 thf(f2497,plain,(
% 115.99/17.79 ( ! [X2 : nat,X1 : nat] : (($true = ((^[Y0 : nat]: ((ord_less_eq @ nat @ Y0 @ X1) = (ord_less @ nat @ Y0 @ (suc @ X1)))) @ X2))) )),
% 115.99/17.79 inference(pi_clausification,[status(thm)],[f2488])).
% 115.99/17.79 thf(f2488,plain,(
% 115.99/17.79 ( ! [X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((ord_less_eq @ nat @ Y0 @ X1) = (ord_less @ nat @ Y0 @ (suc @ X1))))))) )),
% 115.99/17.79 inference(beta_eta_normalization,[status(thm)],[f2487])).
% 115.99/17.79 thf(f2487,plain,(
% 115.99/17.79 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_eq @ nat @ Y1 @ Y0) = (ord_less @ nat @ Y1 @ (suc @ Y0)))))) @ X1))) )),
% 115.99/17.79 inference(pi_clausification,[status(thm)],[f1242])).
% 115.99/17.79 thf(f1242,plain,(
% 115.99/17.79 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_eq @ nat @ Y1 @ Y0) = (ord_less @ nat @ Y1 @ (suc @ Y0))))))) = $true)),
% 115.99/17.79 inference(cnf_transformation,[status(thm)],[f386])).
% 115.99/17.79 thf(f386,plain,(
% 115.99/17.79 ((!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less_eq @ nat @ Y1 @ Y0) = (ord_less @ nat @ Y1 @ (suc @ Y0))))))) = $true)),
% 115.99/17.79 inference(fool_elimination,[status(thm)],[f385])).
% 115.99/17.79 thf(f385,plain,(
% 115.99/17.79 ! [X0 : nat,X1 : nat] : ((ord_less_eq @ nat @ X0 @ X1) = (ord_less @ nat @ X0 @ (suc @ X1)))),
% 115.99/17.79 inference(rectify,[status(thm)],[f65])).
% 115.99/17.79 thf(f65,axiom,(
% 115.99/17.79 ! [X25 : nat,X11 : nat] : ((ord_less_eq @ nat @ X25 @ X11) = (ord_less @ nat @ X25 @ (suc @ X11)))),
% 115.99/17.79 file('/export/starexec/sandbox/tmp/tmp.0mkoVbkNSb/DTF2THF_32065.p',fact_64_less__Suc__eq__le)).
% 115.99/17.79 thf(f5482,plain,(
% 115.99/17.79 ( ! [X2 : nat,X1 : nat] : (($true = ((ord_less @ nat @ X2 @ (suc @ X1)) = ((ord_less @ nat @ X2 @ X1) | (X2 = X1))))) )),
% 115.99/17.79 inference(beta_eta_normalization,[status(thm)],[f5481])).
% 115.99/17.79 thf(f5481,plain,(
% 115.99/17.79 ( ! [X2 : nat,X1 : nat] : (($true = ((^[Y0 : nat]: ((ord_less @ nat @ Y0 @ (suc @ X1)) = ((ord_less @ nat @ Y0 @ X1) | (Y0 = X1)))) @ X2))) )),
% 115.99/17.79 inference(pi_clausification,[status(thm)],[f5476])).
% 115.99/17.79 thf(f5476,plain,(
% 115.99/17.79 ( ! [X1 : nat] : (($true = (!! @ nat @ (^[Y0 : nat]: ((ord_less @ nat @ Y0 @ (suc @ X1)) = ((ord_less @ nat @ Y0 @ X1) | (Y0 = X1))))))) )),
% 115.99/17.79 inference(beta_eta_normalization,[status(thm)],[f5475])).
% 115.99/17.79 thf(f5475,plain,(
% 115.99/17.79 ( ! [X1 : nat] : (($true = ((^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less @ nat @ Y1 @ (suc @ Y0)) = ((ord_less @ nat @ Y1 @ Y0) | (Y1 = Y0)))))) @ X1))) )),
% 115.99/17.79 inference(pi_clausification,[status(thm)],[f1150])).
% 115.99/17.79 thf(f1150,plain,(
% 115.99/17.79 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less @ nat @ Y1 @ (suc @ Y0)) = ((ord_less @ nat @ Y1 @ Y0) | (Y1 = Y0))))))))),
% 115.99/17.79 inference(cnf_transformation,[status(thm)],[f318])).
% 115.99/17.79 thf(f318,plain,(
% 115.99/17.79 ($true = (!! @ nat @ (^[Y0 : nat]: (!! @ nat @ (^[Y1 : nat]: ((ord_less @ nat @ Y1 @ (suc @ Y0)) = ((ord_less @ nat @ Y1 @ Y0) | (Y1 = Y0))))))))),
% 115.99/17.79 inference(fool_elimination,[status(thm)],[f317])).
% 115.99/17.79 thf(f317,plain,(
% 115.99/17.79 ! [X0 : nat,X1 : nat] : ((ord_less @ nat @ X0 @ (suc @ X1)) = (X0 = X1) | (ord_less @ nat @ X0 @ X1))),
% 115.99/17.79 inference(rectify,[status(thm)],[f51])).
% 115.99/17.79 thf(f51,axiom,(
% 115.99/17.79 ! [X25 : nat,X11 : nat] : ((ord_less @ nat @ X25 @ (suc @ X11)) = (X11 = X25) | (ord_less @ nat @ X25 @ X11))),
% 115.99/17.79 file('/export/starexec/sandbox/tmp/tmp.0mkoVbkNSb/DTF2THF_32065.p',fact_50_less__Suc__eq)).
% 115.99/17.79 thf(f25745,plain,(
% 115.99/17.79 ((ord_less_eq @ nat @ occM2 @ sK12) = $true)),
% 115.99/17.79 inference(superposition,[status(thm)],[f24662,f2507])).
% 115.99/17.79 thf(f24662,plain,(
% 115.99/17.79 ((ord_less @ nat @ occM2 @ (suc @ sK12)) = $true)),
% 115.99/17.79 inference(backward_demodulation,[status(thm)],[f1109,f24659])).
% 115.99/17.79 thf(f1109,plain,(
% 115.99/17.79 ((ord_less @ nat @ occM2 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) = $true)),
% 115.99/17.79 inference(cnf_transformation,[status(thm)],[f435])).
% 115.99/17.79 thf(f435,plain,(
% 115.99/17.79 ((ord_less @ nat @ occM2 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index))) = $true)),
% 115.99/17.79 inference(fool_elimination,[status(thm)],[f434])).
% 115.99/17.79 thf(f434,plain,(
% 115.99/17.79 (ord_less @ nat @ occM2 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))),
% 115.99/17.79 inference(rectify,[status(thm)],[f1])).
% 115.99/17.79 thf(f1,axiom,(
% 115.99/17.79 (ord_less @ nat @ occM2 @ (size_size @ list @ configuration_ext @ p @ v @ s @ product_unit @ (fe @ index)))),
% 115.99/17.79 file('/export/starexec/sandbox/tmp/tmp.0mkoVbkNSb/DTF2THF_32065.p',fact_0_AssumpOccMFirstOccurrence_I3_J)).
% 115.99/17.79 % SZS output end Proof for DTF2THF_32065
% 115.99/17.79 % (328)------------------------------
% 115.99/17.79 % (328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 115.99/17.79 % (328)Termination reason: Refutation
% 115.99/17.79
% 115.99/17.79 % (328)Memory used [KB]: 31726
% 115.99/17.79 % (328)Time elapsed: 3.994 s
% 115.99/17.79 % (328)Instructions burned: 13588 (million)
% 115.99/17.79 % (328)------------------------------
% 115.99/17.79 % (328)------------------------------
% 115.99/17.79 % (32257)Success in time 16.244 s
%------------------------------------------------------------------------------