%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT128^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 08:44:52 AM UTC 2026
% Result : Theorem 70.62s 11.28s
% Output : Refutation 70.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : DAT128^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 06:08:15 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : DAT128^1 : TPTP v9.2.1. Released v7.0.0.
% 0.07/0.32 % Domain : Data Structures
% 0.07/0.32 % Problem : Coinductive list 3119
% 0.07/0.32 % Version : [Bla16] axioms : Especial.
% 0.07/0.32 % English :
% 0.07/0.32
% 0.07/0.32 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.07/0.32 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.07/0.32 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.07/0.32 % Source : [Bla16]
% 0.07/0.32 % Names : coinductive_list__3119.p [Bla16]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.67 v8.2.0, 0.33 v8.1.0, 0.75 v7.5.0, 1.00 v7.1.0
% 0.07/0.32 % Syntax : Number of formulae : 330 ( 111 unt; 44 typ; 0 def)
% 0.07/0.32 % Number of atoms : 797 ( 203 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 13 ( 2 avg)
% 0.07/0.32 % Number of connectives : 3427 ( 89 ~; 15 |; 47 &;2877 @)
% 0.07/0.32 % ( 0 <=>; 399 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 22 ( 8 avg)
% 0.07/0.32 % Number of types : 5 ( 4 usr)
% 0.07/0.32 % Number of type conns : 175 ( 175 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 41 ( 40 usr; 4 con; 0-5 aty)
% 0.07/0.32 % Number of variables : 1007 ( 36 ^; 907 !; 31 ?;1007 :)
% 0.07/0.32 % ( 33 !>; 0 ?*; 0 @-; 0 @+)
% 0.07/0.32 % SPC : TH1_THM_EQU_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.07/0.32 % 2016-07-13 14:59:56.275
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 %----Could-be-implicit typings (6)
% 0.07/0.32 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 0.07/0.32 coindu1593790203_llist: $tType > $tType ).
% 0.07/0.32
% 0.07/0.32 thf(ty_t_Extended__Nat_Oenat,type,
% 0.07/0.32 extended_enat: $tType ).
% 0.07/0.32
% 0.07/0.32 thf(ty_t_Nat_Onat,type,
% 0.07/0.32 nat: $tType ).
% 0.07/0.32
% 0.07/0.32 thf(ty_t_itself,type,
% 0.07/0.32 itself: $tType > $tType ).
% 0.07/0.32
% 0.07/0.32 thf(ty_tf_b,type,
% 0.07/0.32 b: $tType ).
% 0.07/0.32
% 0.07/0.32 thf(ty_tf_a,type,
% 0.07/0.32 a: $tType ).
% 0.07/0.32
% 0.07/0.32 %----Explicit typings (38)
% 0.07/0.32 thf(sy_cl_HOL_Otype,type,
% 0.07/0.32 type:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Orderings_Oord,type,
% 0.07/0.32 ord:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Orderings_Oorder,type,
% 0.07/0.32 order:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Groups_Ogroup__add,type,
% 0.07/0.32 group_add:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Orderings_Ono__bot,type,
% 0.07/0.32 no_bot:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Orderings_Ono__top,type,
% 0.07/0.32 no_top:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Orderings_Olinorder,type,
% 0.07/0.32 linorder:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Orderings_Opreorder,type,
% 0.07/0.32 preorder:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Orderings_Owellorder,type,
% 0.07/0.32 wellorder:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.07/0.32 semigroup_add:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Orderings_Odense__order,type,
% 0.07/0.32 dense_order:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.07/0.32 ab_semigroup_add:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.07/0.32 cancel_semigroup_add:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.07/0.32 ordere779506340up_add:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.07/0.32 canoni770627133id_add:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.07/0.32 ordere236663937imp_le:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 0.07/0.32 ordere223160158up_add:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 0.07/0.32 strict2144017051up_add:
% 0.07/0.32 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__llength,type,
% 0.07/0.32 coindu493225792length:
% 0.07/0.32 !>[A: $tType] : ( nat > ( coindu1593790203_llist @ A ) > extended_enat ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oiterates,type,
% 0.07/0.32 coindu1529956631erates:
% 0.07/0.32 !>[A: $tType] : ( ( A > A ) > A > ( coindu1593790203_llist @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 0.07/0.32 coindu268472904append:
% 0.07/0.32 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite,type,
% 0.07/0.32 coindu1213758845finite:
% 0.07/0.32 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollength,type,
% 0.07/0.32 coindu1018505716length:
% 0.07/0.32 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > extended_enat ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 0.07/0.32 coindu1121789889_LCons:
% 0.07/0.32 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 0.07/0.32 coindu1598213697e_LNil:
% 0.07/0.32 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ollist__all2,type,
% 0.07/0.32 coindu987187967t_all2:
% 0.07/0.32 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 0.07/0.32 coindu335574135_lnull:
% 0.07/0.32 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olnth,type,
% 0.07/0.32 coindu749330388e_lnth:
% 0.07/0.32 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > nat > A ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Extended__Nat_Oenat,type,
% 0.07/0.32 extended_enat2: nat > extended_enat ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.07/0.32 plus_plus:
% 0.07/0.32 !>[A: $tType] : ( A > A > A ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.07/0.32 ord_less:
% 0.07/0.32 !>[A: $tType] : ( A > A > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.07/0.32 ord_less_eq:
% 0.07/0.32 !>[A: $tType] : ( A > A > $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_c_Pure_Otype,type,
% 0.07/0.32 type2:
% 0.07/0.32 !>[A: $tType] : ( itself @ A ) ).
% 0.07/0.32
% 0.07/0.32 thf(sy_v_P,type,
% 0.07/0.32 p: a > b > $o ).
% 0.07/0.32
% 0.07/0.32 thf(sy_v_n____,type,
% 0.07/0.32 n: nat ).
% 0.07/0.32
% 0.07/0.32 thf(sy_v_xs,type,
% 0.07/0.32 xs: coindu1593790203_llist @ a ).
% 0.07/0.32
% 0.07/0.32 thf(sy_v_xs_H,type,
% 0.07/0.32 xs2: coindu1593790203_llist @ a ).
% 0.07/0.32
% 0.07/0.32 thf(sy_v_ys,type,
% 0.07/0.32 ys: coindu1593790203_llist @ b ).
% 0.07/0.32
% 0.07/0.32 %----Relevant facts (254)
% 0.07/0.32 thf(fact_0_assms,axiom,
% 0.07/0.32 coindu987187967t_all2 @ a @ b @ p @ ( coindu268472904append @ a @ xs @ xs2 ) @ ys ).
% 0.07/0.32
% 0.07/0.32 % assms
% 0.07/0.32 thf(fact_1_lappend__assoc,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 0.07/0.32 = ( coindu268472904append @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lappend_assoc
% 0.07/0.32 thf(fact_2__092_060open_062llength_Axs_A_092_060le_062_Allength_A_Ilappend_Axs_Axs_H_J_092_060close_062,axiom,
% 0.07/0.32 ord_less_eq @ extended_enat @ ( coindu1018505716length @ a @ xs ) @ ( coindu1018505716length @ a @ ( coindu268472904append @ a @ xs @ xs2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % \<open>llength xs \<le> llength (lappend xs xs')\<close>
% 0.07/0.32 thf(fact_3_n,axiom,
% 0.07/0.32 ord_less @ extended_enat @ ( extended_enat2 @ n ) @ ( coindu1018505716length @ a @ xs ) ).
% 0.07/0.32
% 0.07/0.32 % n
% 0.07/0.32 thf(fact_4_len,axiom,
% 0.07/0.32 ( ( plus_plus @ extended_enat @ ( coindu1018505716length @ a @ xs ) @ ( coindu1018505716length @ a @ xs2 ) )
% 0.07/0.32 = ( coindu1018505716length @ b @ ys ) ) ).
% 0.07/0.32
% 0.07/0.32 % len
% 0.07/0.32 thf(fact_5_len__xs_H,axiom,
% 0.07/0.32 ord_less_eq @ extended_enat @ ( coindu1018505716length @ a @ xs2 ) @ ( coindu1018505716length @ b @ ys ) ).
% 0.07/0.32
% 0.07/0.32 % len_xs'
% 0.07/0.32 thf(fact_6_len__xs,axiom,
% 0.07/0.32 ord_less_eq @ extended_enat @ ( coindu1018505716length @ a @ xs ) @ ( coindu1018505716length @ b @ ys ) ).
% 0.07/0.32
% 0.07/0.32 % len_xs
% 0.07/0.32 thf(fact_7_lappend__code_I1_J,axiom,
% 0.07/0.32 ! [A: $tType,Ys: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ Ys )
% 0.07/0.32 = Ys ) ).
% 0.07/0.32
% 0.07/0.32 % lappend_code(1)
% 0.07/0.32 thf(fact_8_lappend__LNil2,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu268472904append @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.07/0.32 = Xs ) ).
% 0.07/0.32
% 0.07/0.32 % lappend_LNil2
% 0.07/0.32 thf(fact_9_lappend__iterates,axiom,
% 0.07/0.32 ! [A: $tType,F: A > A,X: A,Xs: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu268472904append @ A @ ( coindu1529956631erates @ A @ F @ X ) @ Xs )
% 0.07/0.32 = ( coindu1529956631erates @ A @ F @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % lappend_iterates
% 0.07/0.32 thf(fact_10_lappend_Odisc__iff_I2_J,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 0.07/0.32 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.07/0.32 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lappend.disc_iff(2)
% 0.07/0.32 thf(fact_11_lnull__lappend,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.07/0.32 = ( ( coindu335574135_lnull @ A @ Xs )
% 0.07/0.32 & ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lnull_lappend
% 0.07/0.32 thf(fact_12_lappend__code_I2_J,axiom,
% 0.07/0.32 ! [A: $tType,Xa: A,X: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu268472904append @ A @ ( coindu1121789889_LCons @ A @ Xa @ X ) @ Ys )
% 0.07/0.32 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu268472904append @ A @ X @ Ys ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lappend_code(2)
% 0.07/0.32 thf(fact_13_lfinite__lappend,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu1213758845finite @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.07/0.32 = ( ( coindu1213758845finite @ A @ Xs )
% 0.07/0.32 & ( coindu1213758845finite @ A @ Ys ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lfinite_lappend
% 0.07/0.32 thf(fact_14_llist_Oinject,axiom,
% 0.07/0.32 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 0.07/0.32 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 0.07/0.32 = ( ( X21 = Y21 )
% 0.07/0.32 & ( X22 = Y22 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist.inject
% 0.07/0.32 thf(fact_15_llist__all2__LCons__LCons,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,X22: coindu1593790203_llist @ A,Y21: B,Y22: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) )
% 0.07/0.32 = ( ( R @ X21 @ Y21 )
% 0.07/0.32 & ( coindu987187967t_all2 @ A @ B @ R @ X22 @ Y22 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_LCons_LCons
% 0.07/0.32 thf(fact_16_lfinite__code_I2_J,axiom,
% 0.07/0.32 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ( coindu1213758845finite @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) )
% 0.07/0.32 = ( coindu1213758845finite @ B @ Xs ) ) ).
% 0.07/0.32
% 0.07/0.32 % lfinite_code(2)
% 0.07/0.32 thf(fact_17_lfinite__LCons,axiom,
% 0.07/0.32 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.07/0.32 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.07/0.32
% 0.07/0.32 % lfinite_LCons
% 0.07/0.32 thf(fact_18_llist__all2__LNil1,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ( coindu987187967t_all2 @ A @ B @ P @ ( coindu1598213697e_LNil @ A ) @ Xs )
% 0.07/0.32 = ( Xs
% 0.07/0.32 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_LNil1
% 0.07/0.32 thf(fact_19_llist__all2__LNil2,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ ( coindu1598213697e_LNil @ B ) )
% 0.07/0.32 = ( Xs
% 0.07/0.32 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_LNil2
% 0.07/0.32 thf(fact_20_lfinite__code_I1_J,axiom,
% 0.07/0.32 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 % lfinite_code(1)
% 0.07/0.32 thf(fact_21_llength__lappend,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu1018505716length @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.07/0.32 = ( plus_plus @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ ( coindu1018505716length @ A @ Ys ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llength_lappend
% 0.07/0.32 thf(fact_22_llist_Odisc_I2_J,axiom,
% 0.07/0.32 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.07/0.32 ~ ( coindu335574135_lnull @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist.disc(2)
% 0.07/0.32 thf(fact_23_llist_Odisc_I1_J,axiom,
% 0.07/0.32 ! [A: $tType] : ( coindu335574135_lnull @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist.disc(1)
% 0.07/0.32 thf(fact_24_llist_OdiscI_I2_J,axiom,
% 0.07/0.32 ! [A: $tType,Llist: coindu1593790203_llist @ A,X21: A,X22: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( Llist
% 0.07/0.32 = ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.07/0.32 => ~ ( coindu335574135_lnull @ A @ Llist ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist.discI(2)
% 0.07/0.32 thf(fact_25_llist_OdiscI_I1_J,axiom,
% 0.07/0.32 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( Llist
% 0.07/0.32 = ( coindu1598213697e_LNil @ A ) )
% 0.07/0.32 => ( coindu335574135_lnull @ A @ Llist ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist.discI(1)
% 0.07/0.32 thf(fact_26_llist_Ocollapse_I1_J,axiom,
% 0.07/0.32 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu335574135_lnull @ A @ Llist )
% 0.07/0.32 => ( Llist
% 0.07/0.32 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist.collapse(1)
% 0.07/0.32 thf(fact_27_llist_Odistinct_I1_J,axiom,
% 0.07/0.32 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu1598213697e_LNil @ A )
% 0.07/0.32 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist.distinct(1)
% 0.07/0.32 thf(fact_28_llist_Orel__intros_I2_J,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,Y21: B,X22: coindu1593790203_llist @ A,Y22: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ( R @ X21 @ Y21 )
% 0.07/0.32 => ( ( coindu987187967t_all2 @ A @ B @ R @ X22 @ Y22 )
% 0.07/0.32 => ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist.rel_intros(2)
% 0.07/0.32 thf(fact_29_lzip_Oexhaust,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 0.07/0.32 | ( coindu335574135_lnull @ B @ Ys ) )
% 0.07/0.32 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.07/0.32 => ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lzip.exhaust
% 0.07/0.32 thf(fact_30_iterates_Ocode,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( coindu1529956631erates @ A )
% 0.07/0.32 = ( ^ [F2: A > A,X2: A] : ( coindu1121789889_LCons @ A @ X2 @ ( coindu1529956631erates @ A @ F2 @ ( F2 @ X2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % iterates.code
% 0.07/0.32 thf(fact_31_lfinite_Ocases,axiom,
% 0.07/0.32 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu1213758845finite @ A @ A2 )
% 0.07/0.32 => ( ( A2
% 0.07/0.32 != ( coindu1598213697e_LNil @ A ) )
% 0.07/0.32 => ~ ! [Xs2: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ? [X3: A] :
% 0.07/0.32 ( A2
% 0.07/0.32 = ( coindu1121789889_LCons @ A @ X3 @ Xs2 ) )
% 0.07/0.32 => ~ ( coindu1213758845finite @ A @ Xs2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lfinite.cases
% 0.07/0.32 thf(fact_32_lfinite_Osimps,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( coindu1213758845finite @ A )
% 0.07/0.32 = ( ^ [A3: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( A3
% 0.07/0.32 = ( coindu1598213697e_LNil @ A ) )
% 0.07/0.32 | ? [Xs3: coindu1593790203_llist @ A,X2: A] :
% 0.07/0.32 ( ( A3
% 0.07/0.32 = ( coindu1121789889_LCons @ A @ X2 @ Xs3 ) )
% 0.07/0.32 & ( coindu1213758845finite @ A @ Xs3 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lfinite.simps
% 0.07/0.32 thf(fact_33_llist_Oexhaust,axiom,
% 0.07/0.32 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( Y
% 0.07/0.32 != ( coindu1598213697e_LNil @ A ) )
% 0.07/0.32 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 0.07/0.32 ( Y
% 0.07/0.32 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist.exhaust
% 0.07/0.32 thf(fact_34_neq__LNil__conv,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( Xs
% 0.07/0.32 != ( coindu1598213697e_LNil @ A ) )
% 0.07/0.32 = ( ? [X2: A,Xs4: coindu1593790203_llist @ A] :
% 0.07/0.32 ( Xs
% 0.07/0.32 = ( coindu1121789889_LCons @ A @ X2 @ Xs4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % neq_LNil_conv
% 0.07/0.32 thf(fact_35_not__lnull__conv,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( ~ ( coindu335574135_lnull @ A @ Xs ) )
% 0.07/0.32 = ( ? [X2: A,Xs4: coindu1593790203_llist @ A] :
% 0.07/0.32 ( Xs
% 0.07/0.32 = ( coindu1121789889_LCons @ A @ X2 @ Xs4 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % not_lnull_conv
% 0.07/0.32 thf(fact_36_lappend_Oexhaust,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.07/0.32 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.07/0.32 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.07/0.32 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lappend.exhaust
% 0.07/0.32 thf(fact_37_lfinite_Oinducts,axiom,
% 0.07/0.32 ! [A: $tType,X: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.07/0.32 ( ( coindu1213758845finite @ A @ X )
% 0.07/0.32 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.07/0.32 => ( ! [Xs2: coindu1593790203_llist @ A,X3: A] :
% 0.07/0.32 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.07/0.32 => ( ( P @ Xs2 )
% 0.07/0.32 => ( P @ ( coindu1121789889_LCons @ A @ X3 @ Xs2 ) ) ) )
% 0.07/0.32 => ( P @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lfinite.inducts
% 0.07/0.32 thf(fact_38_lnull__def,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( coindu335574135_lnull @ A )
% 0.07/0.32 = ( ^ [Llist2: coindu1593790203_llist @ A] :
% 0.07/0.32 ( Llist2
% 0.07/0.32 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lnull_def
% 0.07/0.32 thf(fact_39_llist_Orel__cases,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,R: A > B > $o,A2: coindu1593790203_llist @ A,B2: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ( coindu987187967t_all2 @ A @ B @ R @ A2 @ B2 )
% 0.07/0.32 => ( ( ( A2
% 0.07/0.32 = ( coindu1598213697e_LNil @ A ) )
% 0.07/0.32 => ( B2
% 0.07/0.32 != ( coindu1598213697e_LNil @ B ) ) )
% 0.07/0.32 => ~ ! [X1: A,X23: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( A2
% 0.07/0.32 = ( coindu1121789889_LCons @ A @ X1 @ X23 ) )
% 0.07/0.32 => ! [Y1: B,Y2: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ( B2
% 0.07/0.32 = ( coindu1121789889_LCons @ B @ Y1 @ Y2 ) )
% 0.07/0.32 => ( ( R @ X1 @ Y1 )
% 0.07/0.32 => ~ ( coindu987187967t_all2 @ A @ B @ R @ X23 @ Y2 ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist.rel_cases
% 0.07/0.32 thf(fact_40_lfinite__iterates,axiom,
% 0.07/0.32 ! [A: $tType,F: A > A,X: A] :
% 0.07/0.32 ~ ( coindu1213758845finite @ A @ ( coindu1529956631erates @ A @ F @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % lfinite_iterates
% 0.07/0.32 thf(fact_41_llist__all2__cases,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.07/0.32 => ( ( ( Xs
% 0.07/0.32 = ( coindu1598213697e_LNil @ A ) )
% 0.07/0.32 => ( Ys
% 0.07/0.32 != ( coindu1598213697e_LNil @ B ) ) )
% 0.07/0.32 => ~ ! [X3: A,Xs5: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( Xs
% 0.07/0.32 = ( coindu1121789889_LCons @ A @ X3 @ Xs5 ) )
% 0.07/0.32 => ! [Y3: B,Ys2: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ( Ys
% 0.07/0.32 = ( coindu1121789889_LCons @ B @ Y3 @ Ys2 ) )
% 0.07/0.32 => ( ( P @ X3 @ Y3 )
% 0.07/0.32 => ~ ( coindu987187967t_all2 @ A @ B @ P @ Xs5 @ Ys2 ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_cases
% 0.07/0.32 thf(fact_42_llist__all2__lnthD,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B,N: nat] :
% 0.07/0.32 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.07/0.32 => ( ( ord_less @ extended_enat @ ( extended_enat2 @ N ) @ ( coindu1018505716length @ A @ Xs ) )
% 0.07/0.32 => ( P @ ( coindu749330388e_lnth @ A @ Xs @ N ) @ ( coindu749330388e_lnth @ B @ Ys @ N ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_lnthD
% 0.07/0.32 thf(fact_43_wlog__linorder__le,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [P: A > A > $o,B2: A,A2: A] :
% 0.07/0.32 ( ! [A4: A,B3: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.07/0.32 => ( P @ A4 @ B3 ) )
% 0.07/0.32 => ( ( ( P @ B2 @ A2 )
% 0.07/0.32 => ( P @ A2 @ B2 ) )
% 0.07/0.32 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % wlog_linorder_le
% 0.07/0.32 thf(fact_44_ext,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.07/0.32 ( ! [X3: A] :
% 0.07/0.32 ( ( F @ X3 )
% 0.07/0.32 = ( G @ X3 ) )
% 0.07/0.32 => ( F = G ) ) ).
% 0.07/0.32
% 0.07/0.32 % ext
% 0.07/0.32 thf(fact_45_iterates_Odisc__iff,axiom,
% 0.07/0.32 ! [A: $tType,F: A > A,X: A] :
% 0.07/0.32 ~ ( coindu335574135_lnull @ A @ ( coindu1529956631erates @ A @ F @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % iterates.disc_iff
% 0.07/0.32 thf(fact_46_llist__all2__LCons1,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,P: A > B > $o,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ( coindu987187967t_all2 @ A @ B @ P @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ Ys )
% 0.07/0.32 = ( ? [Y4: B,Ys3: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ( Ys
% 0.07/0.32 = ( coindu1121789889_LCons @ B @ Y4 @ Ys3 ) )
% 0.07/0.32 & ( P @ X @ Y4 )
% 0.07/0.32 & ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_LCons1
% 0.07/0.32 thf(fact_47_llist__all2__LCons2,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Y: B,Ys: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ ( coindu1121789889_LCons @ B @ Y @ Ys ) )
% 0.07/0.32 = ( ? [X2: A,Xs4: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( Xs
% 0.07/0.32 = ( coindu1121789889_LCons @ A @ X2 @ Xs4 ) )
% 0.07/0.32 & ( P @ X2 @ Y )
% 0.07/0.32 & ( coindu987187967t_all2 @ A @ B @ P @ Xs4 @ Ys ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_LCons2
% 0.07/0.32 thf(fact_48_llist__all2__lnthD2,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B,N: nat] :
% 0.07/0.32 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.07/0.32 => ( ( ord_less @ extended_enat @ ( extended_enat2 @ N ) @ ( coindu1018505716length @ B @ Ys ) )
% 0.07/0.32 => ( P @ ( coindu749330388e_lnth @ A @ Xs @ N ) @ ( coindu749330388e_lnth @ B @ Ys @ N ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_lnthD2
% 0.07/0.32 thf(fact_49_llist__all2__lnullD,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.07/0.32 => ( ( coindu335574135_lnull @ A @ Xs )
% 0.07/0.32 = ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_lnullD
% 0.07/0.32 thf(fact_50_lnull__imp__lfinite,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu335574135_lnull @ A @ Xs )
% 0.07/0.32 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.07/0.32
% 0.07/0.32 % lnull_imp_lfinite
% 0.07/0.32 thf(fact_51_lfinite__rev__induct,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.07/0.32 ( ( coindu1213758845finite @ A @ Xs )
% 0.07/0.32 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.07/0.32 => ( ! [X3: A,Xs2: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.07/0.32 => ( ( P @ Xs2 )
% 0.07/0.32 => ( P @ ( coindu268472904append @ A @ Xs2 @ ( coindu1121789889_LCons @ A @ X3 @ ( coindu1598213697e_LNil @ A ) ) ) ) ) )
% 0.07/0.32 => ( P @ Xs ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lfinite_rev_induct
% 0.07/0.32 thf(fact_52_llist__all2__lfiniteD,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.07/0.32 => ( ( coindu1213758845finite @ A @ Xs )
% 0.07/0.32 = ( coindu1213758845finite @ B @ Ys ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_lfiniteD
% 0.07/0.32 thf(fact_53_llist__all2__llengthD,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.07/0.32 => ( ( coindu1018505716length @ A @ Xs )
% 0.07/0.32 = ( coindu1018505716length @ B @ Ys ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_llengthD
% 0.07/0.32 thf(fact_54_lfinite__LNil,axiom,
% 0.07/0.32 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 % lfinite_LNil
% 0.07/0.32 thf(fact_55_lfinite__llength__enat,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu1213758845finite @ A @ Xs )
% 0.07/0.32 => ? [N2: nat] :
% 0.07/0.32 ( ( coindu1018505716length @ A @ Xs )
% 0.07/0.32 = ( extended_enat2 @ N2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lfinite_llength_enat
% 0.07/0.32 thf(fact_56_llist__all2__LNil__LNil,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,R: A > B > $o] : ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_LNil_LNil
% 0.07/0.32 thf(fact_57_llist__all2__all__lnthI,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B,P: A > B > $o] :
% 0.07/0.32 ( ( ( coindu1018505716length @ A @ Xs )
% 0.07/0.32 = ( coindu1018505716length @ B @ Ys ) )
% 0.07/0.32 => ( ! [N2: nat] :
% 0.07/0.32 ( ( ord_less @ extended_enat @ ( extended_enat2 @ N2 ) @ ( coindu1018505716length @ A @ Xs ) )
% 0.07/0.32 => ( P @ ( coindu749330388e_lnth @ A @ Xs @ N2 ) @ ( coindu749330388e_lnth @ B @ Ys @ N2 ) ) )
% 0.07/0.32 => ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_all_lnthI
% 0.07/0.32 thf(fact_58_llist__all2__LCons__LNil,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,R: A > B > $o,Y21: A,Y22: coindu1593790203_llist @ A] :
% 0.07/0.32 ~ ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_LCons_LNil
% 0.07/0.32 thf(fact_59_llist__all2__LNil__LCons,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,R: A > B > $o,Y21: B,Y22: coindu1593790203_llist @ B] :
% 0.07/0.32 ~ ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1598213697e_LNil @ A ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_LNil_LCons
% 0.07/0.32 thf(fact_60_lfinite__LConsI,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 0.07/0.32 ( ( coindu1213758845finite @ A @ Xs )
% 0.07/0.32 => ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lfinite_LConsI
% 0.07/0.32 thf(fact_61_llength__eq__enat__lfiniteD,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,N: nat] :
% 0.07/0.32 ( ( ( coindu1018505716length @ A @ Xs )
% 0.07/0.32 = ( extended_enat2 @ N ) )
% 0.07/0.32 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.07/0.32
% 0.07/0.32 % llength_eq_enat_lfiniteD
% 0.07/0.32 thf(fact_62_llist__all2__conv__all__lnth,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType] :
% 0.07/0.32 ( ( coindu987187967t_all2 @ A @ B )
% 0.07/0.32 = ( ^ [P2: A > B > $o,Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ( ( coindu1018505716length @ A @ Xs3 )
% 0.07/0.32 = ( coindu1018505716length @ B @ Ys4 ) )
% 0.07/0.32 & ! [N3: nat] :
% 0.07/0.32 ( ( ord_less @ extended_enat @ ( extended_enat2 @ N3 ) @ ( coindu1018505716length @ B @ Ys4 ) )
% 0.07/0.32 => ( P2 @ ( coindu749330388e_lnth @ A @ Xs3 @ N3 ) @ ( coindu749330388e_lnth @ B @ Ys4 @ N3 ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_conv_all_lnth
% 0.07/0.32 thf(fact_63_lfinite__conv__llength__enat,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( coindu1213758845finite @ A )
% 0.07/0.32 = ( ^ [Xs3: coindu1593790203_llist @ A] :
% 0.07/0.32 ? [N3: nat] :
% 0.07/0.32 ( ( coindu1018505716length @ A @ Xs3 )
% 0.07/0.32 = ( extended_enat2 @ N3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lfinite_conv_llength_enat
% 0.07/0.32 thf(fact_64_lappend__eq__lappend__conv,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,Us: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Vs: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( ( coindu1018505716length @ A @ Xs )
% 0.07/0.32 = ( coindu1018505716length @ A @ Us ) )
% 0.07/0.32 => ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.07/0.32 = ( coindu268472904append @ A @ Us @ Vs ) )
% 0.07/0.32 = ( ( Xs = Us )
% 0.07/0.32 & ( ( coindu1213758845finite @ A @ Xs )
% 0.07/0.32 => ( Ys = Vs ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lappend_eq_lappend_conv
% 0.07/0.32 thf(fact_65_lappend__snocL1__conv__LCons2,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ ( coindu1598213697e_LNil @ A ) ) ) @ Ys )
% 0.07/0.32 = ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lappend_snocL1_conv_LCons2
% 0.07/0.32 thf(fact_66_lappend_Octr_I1_J,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu335574135_lnull @ A @ Xs )
% 0.07/0.32 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.07/0.32 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.07/0.32 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lappend.ctr(1)
% 0.07/0.32 thf(fact_67_lnth__lappend1,axiom,
% 0.07/0.32 ! [A: $tType,N: nat,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( ord_less @ extended_enat @ ( extended_enat2 @ N ) @ ( coindu1018505716length @ A @ Xs ) )
% 0.07/0.32 => ( ( coindu749330388e_lnth @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ N )
% 0.07/0.32 = ( coindu749330388e_lnth @ A @ Xs @ N ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lnth_lappend1
% 0.07/0.32 thf(fact_68_llist__all2__lappendI,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B,Xs6: coindu1593790203_llist @ A,Ys5: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.07/0.32 => ( ( ( coindu1213758845finite @ A @ Xs )
% 0.07/0.32 => ( ( coindu1213758845finite @ B @ Ys )
% 0.07/0.32 => ( coindu987187967t_all2 @ A @ B @ P @ Xs6 @ Ys5 ) ) )
% 0.07/0.32 => ( coindu987187967t_all2 @ A @ B @ P @ ( coindu268472904append @ A @ Xs @ Xs6 ) @ ( coindu268472904append @ B @ Ys @ Ys5 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_lappendI
% 0.07/0.32 thf(fact_69_llist_Orel__refl,axiom,
% 0.07/0.32 ! [B: $tType,Ra: B > B > $o,X: coindu1593790203_llist @ B] :
% 0.07/0.32 ( ! [X3: B] : ( Ra @ X3 @ X3 )
% 0.07/0.32 => ( coindu987187967t_all2 @ B @ B @ Ra @ X @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist.rel_refl
% 0.07/0.32 thf(fact_70_llist_Orel__eq,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( coindu987187967t_all2 @ A @ A
% 0.07/0.32 @ ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 0.07/0.32 = ( ^ [Y5: coindu1593790203_llist @ A,Z: coindu1593790203_llist @ A] : ( Y5 = Z ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist.rel_eq
% 0.07/0.32 thf(fact_71_llist__all2__mono,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B,P3: A > B > $o] :
% 0.07/0.32 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.07/0.32 => ( ! [X3: A,Y3: B] :
% 0.07/0.32 ( ( P @ X3 @ Y3 )
% 0.07/0.32 => ( P3 @ X3 @ Y3 ) )
% 0.07/0.32 => ( coindu987187967t_all2 @ A @ B @ P3 @ Xs @ Ys ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist_all2_mono
% 0.07/0.32 thf(fact_72_lappend__inf,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.07/0.32 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.07/0.32 = Xs ) ) ).
% 0.07/0.32
% 0.07/0.32 % lappend_inf
% 0.07/0.32 thf(fact_73_lappend__lnull2,axiom,
% 0.07/0.32 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu335574135_lnull @ A @ Ys )
% 0.07/0.32 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.07/0.32 = Xs ) ) ).
% 0.07/0.32
% 0.07/0.32 % lappend_lnull2
% 0.07/0.32 thf(fact_74_lappend__lnull1,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu335574135_lnull @ A @ Xs )
% 0.07/0.32 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.07/0.32 = Ys ) ) ).
% 0.07/0.32
% 0.07/0.32 % lappend_lnull1
% 0.07/0.32 thf(fact_75_lappend_Odisc_I1_J,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( coindu335574135_lnull @ A @ Xs )
% 0.07/0.32 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.07/0.32 => ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lappend.disc(1)
% 0.07/0.32 thf(fact_76_lappend_Odisc_I2_J,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.07/0.32 | ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.07/0.32 => ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lappend.disc(2)
% 0.07/0.32 thf(fact_77_lappend__eq__LNil__iff,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.07/0.32 = ( coindu1598213697e_LNil @ A ) )
% 0.07/0.32 = ( ( Xs
% 0.07/0.32 = ( coindu1598213697e_LNil @ A ) )
% 0.07/0.32 & ( Ys
% 0.07/0.32 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % lappend_eq_LNil_iff
% 0.07/0.32 thf(fact_78_LNil__eq__lappend__iff,axiom,
% 0.07/0.32 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.07/0.32 ( ( ( coindu1598213697e_LNil @ A )
% 0.07/0.32 = ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.07/0.32 = ( ( Xs
% 0.07/0.32 = ( coindu1598213697e_LNil @ A ) )
% 0.07/0.32 & ( Ys
% 0.07/0.32 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % LNil_eq_lappend_iff
% 0.07/0.32 thf(fact_79_lappend__LNil__LNil,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) )
% 0.07/0.32 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.07/0.32
% 0.07/0.32 % lappend_LNil_LNil
% 0.07/0.32 thf(fact_80_enat__add__mono,axiom,
% 0.07/0.32 ! [X: nat,Y: extended_enat,Z2: extended_enat] :
% 0.07/0.32 ( ( ord_less @ extended_enat @ ( plus_plus @ extended_enat @ ( extended_enat2 @ X ) @ Y ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ X ) @ Z2 ) )
% 0.07/0.32 = ( ord_less @ extended_enat @ Y @ Z2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % enat_add_mono
% 0.07/0.32 thf(fact_81_enat__add1__eq,axiom,
% 0.07/0.32 ! [X: nat,Y: extended_enat,Z2: extended_enat] :
% 0.07/0.32 ( ( ( plus_plus @ extended_enat @ ( extended_enat2 @ X ) @ Y )
% 0.07/0.32 = ( plus_plus @ extended_enat @ ( extended_enat2 @ X ) @ Z2 ) )
% 0.07/0.32 = ( Y = Z2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % enat_add1_eq
% 0.07/0.32 thf(fact_82_enat__add2__eq,axiom,
% 0.07/0.32 ! [Y: extended_enat,X: nat,Z2: extended_enat] :
% 0.07/0.32 ( ( ( plus_plus @ extended_enat @ Y @ ( extended_enat2 @ X ) )
% 0.07/0.32 = ( plus_plus @ extended_enat @ Z2 @ ( extended_enat2 @ X ) ) )
% 0.07/0.32 = ( Y = Z2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % enat_add2_eq
% 0.07/0.32 thf(fact_83_add__less__cancel__left,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [C: A,A2: A,B2: A] :
% 0.07/0.32 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 0.07/0.32 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_less_cancel_left
% 0.07/0.32 thf(fact_84_add__less__cancel__right,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,C: A,B2: A] :
% 0.07/0.32 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 0.07/0.32 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_less_cancel_right
% 0.07/0.32 thf(fact_85_add__le__cancel__left,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [C: A,A2: A,B2: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 0.07/0.32 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_le_cancel_left
% 0.07/0.32 thf(fact_86_add__le__cancel__right,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,C: A,B2: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 0.07/0.32 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_le_cancel_right
% 0.07/0.32 thf(fact_87_enat__less__imp__le,axiom,
% 0.07/0.32 ! [N: extended_enat,M: extended_enat] :
% 0.07/0.32 ( ! [K: nat] :
% 0.07/0.32 ( ( ord_less @ extended_enat @ N @ ( extended_enat2 @ K ) )
% 0.07/0.32 => ( ord_less @ extended_enat @ M @ ( extended_enat2 @ K ) ) )
% 0.07/0.32 => ( ord_less_eq @ extended_enat @ M @ N ) ) ).
% 0.07/0.32
% 0.07/0.32 % enat_less_imp_le
% 0.07/0.32 thf(fact_88_add__mono__thms__linordered__field_I4_J,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [I: A,J: A,K2: A,L: A] :
% 0.07/0.32 ( ( ( ord_less_eq @ A @ I @ J )
% 0.07/0.32 & ( ord_less @ A @ K2 @ L ) )
% 0.07/0.32 => ( ord_less @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_mono_thms_linordered_field(4)
% 0.07/0.32 thf(fact_89_add__mono__thms__linordered__field_I3_J,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [I: A,J: A,K2: A,L: A] :
% 0.07/0.32 ( ( ( ord_less @ A @ I @ J )
% 0.07/0.32 & ( ord_less_eq @ A @ K2 @ L ) )
% 0.07/0.32 => ( ord_less @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_mono_thms_linordered_field(3)
% 0.07/0.32 thf(fact_90_add__le__less__mono,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A,D: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less @ A @ C @ D )
% 0.07/0.32 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_le_less_mono
% 0.07/0.32 thf(fact_91_add__right__cancel,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [B2: A,A2: A,C: A] :
% 0.07/0.32 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.07/0.32 = ( plus_plus @ A @ C @ A2 ) )
% 0.07/0.32 = ( B2 = C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_right_cancel
% 0.07/0.32 thf(fact_92_add__left__cancel,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A] :
% 0.07/0.32 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.07/0.32 = ( plus_plus @ A @ A2 @ C ) )
% 0.07/0.32 = ( B2 = C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_left_cancel
% 0.07/0.32 thf(fact_93_llist_Orel__mono,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,R: A > B > $o,Ra: A > B > $o] :
% 0.07/0.32 ( ( ord_less_eq @ ( A > B > $o ) @ R @ Ra )
% 0.07/0.32 => ( ord_less_eq @ ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o ) @ ( coindu987187967t_all2 @ A @ B @ R ) @ ( coindu987187967t_all2 @ A @ B @ Ra ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % llist.rel_mono
% 0.07/0.32 thf(fact_94_enat__less__enat__plusI2,axiom,
% 0.07/0.32 ! [Y: nat,Z2: extended_enat,X: nat] :
% 0.07/0.32 ( ( ord_less @ extended_enat @ ( extended_enat2 @ Y ) @ Z2 )
% 0.07/0.32 => ( ord_less @ extended_enat @ ( extended_enat2 @ ( plus_plus @ nat @ X @ Y ) ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ X ) @ Z2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % enat_less_enat_plusI2
% 0.07/0.32 thf(fact_95_enat__less__enat__plusI,axiom,
% 0.07/0.32 ! [X: nat,Y: nat,Z2: extended_enat] :
% 0.07/0.32 ( ( ord_less @ nat @ X @ Y )
% 0.07/0.32 => ( ord_less @ extended_enat @ ( extended_enat2 @ X ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ Y ) @ Z2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % enat_less_enat_plusI
% 0.07/0.32 thf(fact_96_add__right__imp__eq,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [B2: A,A2: A,C: A] :
% 0.07/0.32 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.07/0.32 = ( plus_plus @ A @ C @ A2 ) )
% 0.07/0.32 => ( B2 = C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_right_imp_eq
% 0.07/0.32 thf(fact_97_add__left__imp__eq,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A] :
% 0.07/0.32 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.07/0.32 = ( plus_plus @ A @ A2 @ C ) )
% 0.07/0.32 => ( B2 = C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_left_imp_eq
% 0.07/0.32 thf(fact_98_add_Oleft__commute,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [B2: A,A2: A,C: A] :
% 0.07/0.32 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C ) )
% 0.07/0.32 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add.left_commute
% 0.07/0.32 thf(fact_99_add_Ocommute,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ( ( plus_plus @ A )
% 0.07/0.32 = ( ^ [A3: A,B4: A] : ( plus_plus @ A @ B4 @ A3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add.commute
% 0.07/0.32 thf(fact_100_add_Oright__cancel,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( group_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [B2: A,A2: A,C: A] :
% 0.07/0.32 ( ( ( plus_plus @ A @ B2 @ A2 )
% 0.07/0.32 = ( plus_plus @ A @ C @ A2 ) )
% 0.07/0.32 = ( B2 = C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add.right_cancel
% 0.07/0.32 thf(fact_101_add_Oleft__cancel,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( group_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A] :
% 0.07/0.32 ( ( ( plus_plus @ A @ A2 @ B2 )
% 0.07/0.32 = ( plus_plus @ A @ A2 @ C ) )
% 0.07/0.32 = ( B2 = C ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add.left_cancel
% 0.07/0.32 thf(fact_102_add_Oassoc,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( semigroup_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A] :
% 0.07/0.32 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C )
% 0.07/0.32 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add.assoc
% 0.07/0.32 thf(fact_103_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [I: A,J: A,K2: A,L: A] :
% 0.07/0.32 ( ( ( I = J )
% 0.07/0.32 & ( K2 = L ) )
% 0.07/0.32 => ( ( plus_plus @ A @ I @ K2 )
% 0.07/0.32 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_mono_thms_linordered_semiring(4)
% 0.07/0.32 thf(fact_104_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A] :
% 0.07/0.32 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C )
% 0.07/0.32 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ab_semigroup_add_class.add_ac(1)
% 0.07/0.32 thf(fact_105_add__le__imp__le__right,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,C: A,B2: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 0.07/0.32 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_le_imp_le_right
% 0.07/0.32 thf(fact_106_add__le__imp__le__left,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [C: A,A2: A,B2: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 0.07/0.32 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_le_imp_le_left
% 0.07/0.32 thf(fact_107_le__iff__add,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ( ( ord_less_eq @ A )
% 0.07/0.32 = ( ^ [A3: A,B4: A] :
% 0.07/0.32 ? [C2: A] :
% 0.07/0.32 ( B4
% 0.07/0.32 = ( plus_plus @ A @ A3 @ C2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_iff_add
% 0.07/0.32 thf(fact_108_add__right__mono,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.07/0.32 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_right_mono
% 0.07/0.32 thf(fact_109_add__left__mono,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.07/0.32 => ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_left_mono
% 0.07/0.32 thf(fact_110_add__mono,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A,D: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less_eq @ A @ C @ D )
% 0.07/0.32 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_mono
% 0.07/0.32 thf(fact_111_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [I: A,J: A,K2: A,L: A] :
% 0.07/0.32 ( ( ( ord_less_eq @ A @ I @ J )
% 0.07/0.32 & ( ord_less_eq @ A @ K2 @ L ) )
% 0.07/0.32 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_mono_thms_linordered_semiring(1)
% 0.07/0.32 thf(fact_112_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [I: A,J: A,K2: A,L: A] :
% 0.07/0.32 ( ( ( I = J )
% 0.07/0.32 & ( ord_less_eq @ A @ K2 @ L ) )
% 0.07/0.32 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_mono_thms_linordered_semiring(2)
% 0.07/0.32 thf(fact_113_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [I: A,J: A,K2: A,L: A] :
% 0.07/0.32 ( ( ( ord_less_eq @ A @ I @ J )
% 0.07/0.32 & ( K2 = L ) )
% 0.07/0.32 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_mono_thms_linordered_semiring(3)
% 0.07/0.32 thf(fact_114_add__less__imp__less__right,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,C: A,B2: A] :
% 0.07/0.32 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 0.07/0.32 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_less_imp_less_right
% 0.07/0.32 thf(fact_115_add__less__imp__less__left,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [C: A,A2: A,B2: A] :
% 0.07/0.32 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 0.07/0.32 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_less_imp_less_left
% 0.07/0.32 thf(fact_116_add__strict__right__mono,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A] :
% 0.07/0.32 ( ( ord_less @ A @ A2 @ B2 )
% 0.07/0.32 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_strict_right_mono
% 0.07/0.32 thf(fact_117_add__strict__left__mono,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A] :
% 0.07/0.32 ( ( ord_less @ A @ A2 @ B2 )
% 0.07/0.32 => ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_strict_left_mono
% 0.07/0.32 thf(fact_118_add__strict__mono,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( strict2144017051up_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A,D: A] :
% 0.07/0.32 ( ( ord_less @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less @ A @ C @ D )
% 0.07/0.32 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_strict_mono
% 0.07/0.32 thf(fact_119_add__mono__thms__linordered__field_I1_J,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [I: A,J: A,K2: A,L: A] :
% 0.07/0.32 ( ( ( ord_less @ A @ I @ J )
% 0.07/0.32 & ( K2 = L ) )
% 0.07/0.32 => ( ord_less @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_mono_thms_linordered_field(1)
% 0.07/0.32 thf(fact_120_add__mono__thms__linordered__field_I2_J,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [I: A,J: A,K2: A,L: A] :
% 0.07/0.32 ( ( ( I = J )
% 0.07/0.32 & ( ord_less @ A @ K2 @ L ) )
% 0.07/0.32 => ( ord_less @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_mono_thms_linordered_field(2)
% 0.07/0.32 thf(fact_121_add__mono__thms__linordered__field_I5_J,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [I: A,J: A,K2: A,L: A] :
% 0.07/0.32 ( ( ( ord_less @ A @ I @ J )
% 0.07/0.32 & ( ord_less @ A @ K2 @ L ) )
% 0.07/0.32 => ( ord_less @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_mono_thms_linordered_field(5)
% 0.07/0.32 thf(fact_122_enat__le__plus__same_I1_J,axiom,
% 0.07/0.32 ! [X: extended_enat,Y: extended_enat] : ( ord_less_eq @ extended_enat @ X @ ( plus_plus @ extended_enat @ X @ Y ) ) ).
% 0.07/0.32
% 0.07/0.32 % enat_le_plus_same(1)
% 0.07/0.32 thf(fact_123_enat__le__plus__same_I2_J,axiom,
% 0.07/0.32 ! [X: extended_enat,Y: extended_enat] : ( ord_less_eq @ extended_enat @ X @ ( plus_plus @ extended_enat @ Y @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % enat_le_plus_same(2)
% 0.07/0.32 thf(fact_124_add__less__le__mono,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A,D: A] :
% 0.07/0.32 ( ( ord_less @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less_eq @ A @ C @ D )
% 0.07/0.32 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_less_le_mono
% 0.07/0.32 thf(fact_125_plus__enat__simps_I1_J,axiom,
% 0.07/0.32 ! [M: nat,N: nat] :
% 0.07/0.32 ( ( plus_plus @ extended_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 0.07/0.32 = ( extended_enat2 @ ( plus_plus @ nat @ M @ N ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % plus_enat_simps(1)
% 0.07/0.32 thf(fact_126_enat__ord__simps_I2_J,axiom,
% 0.07/0.32 ! [M: nat,N: nat] :
% 0.07/0.32 ( ( ord_less @ extended_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 0.07/0.32 = ( ord_less @ nat @ M @ N ) ) ).
% 0.07/0.32
% 0.07/0.32 % enat_ord_simps(2)
% 0.07/0.32 thf(fact_127_enat__ord__simps_I1_J,axiom,
% 0.07/0.32 ! [M: nat,N: nat] :
% 0.07/0.32 ( ( ord_less_eq @ extended_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 0.07/0.32 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.07/0.32
% 0.07/0.32 % enat_ord_simps(1)
% 0.07/0.32 thf(fact_128_iadd__le__enat__iff,axiom,
% 0.07/0.32 ! [X: extended_enat,Y: extended_enat,N: nat] :
% 0.07/0.32 ( ( ord_less_eq @ extended_enat @ ( plus_plus @ extended_enat @ X @ Y ) @ ( extended_enat2 @ N ) )
% 0.07/0.32 = ( ? [Y6: nat,X4: nat] :
% 0.07/0.32 ( ( X
% 0.07/0.32 = ( extended_enat2 @ X4 ) )
% 0.07/0.32 & ( Y
% 0.07/0.32 = ( extended_enat2 @ Y6 ) )
% 0.07/0.32 & ( ord_less_eq @ nat @ ( plus_plus @ nat @ X4 @ Y6 ) @ N ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % iadd_le_enat_iff
% 0.07/0.32 thf(fact_129_enat_Oinject,axiom,
% 0.07/0.32 ! [Nat: nat,Nat2: nat] :
% 0.07/0.32 ( ( ( extended_enat2 @ Nat )
% 0.07/0.32 = ( extended_enat2 @ Nat2 ) )
% 0.07/0.32 = ( Nat = Nat2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % enat.inject
% 0.07/0.32 thf(fact_130_enat__less__induct,axiom,
% 0.07/0.32 ! [P: extended_enat > $o,N: extended_enat] :
% 0.07/0.32 ( ! [N2: extended_enat] :
% 0.07/0.32 ( ! [M2: extended_enat] :
% 0.07/0.32 ( ( ord_less @ extended_enat @ M2 @ N2 )
% 0.07/0.32 => ( P @ M2 ) )
% 0.07/0.32 => ( P @ N2 ) )
% 0.07/0.32 => ( P @ N ) ) ).
% 0.07/0.32
% 0.07/0.32 % enat_less_induct
% 0.07/0.32 thf(fact_131_enat__ile,axiom,
% 0.07/0.32 ! [N: extended_enat,M: nat] :
% 0.07/0.32 ( ( ord_less_eq @ extended_enat @ N @ ( extended_enat2 @ M ) )
% 0.07/0.32 => ? [K: nat] :
% 0.07/0.32 ( N
% 0.07/0.32 = ( extended_enat2 @ K ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % enat_ile
% 0.07/0.32 thf(fact_132_chain__incr,axiom,
% 0.07/0.32 ! [A: $tType,Y7: A > extended_enat,K2: nat] :
% 0.07/0.32 ( ! [I2: A] :
% 0.07/0.32 ? [J2: A] : ( ord_less @ extended_enat @ ( Y7 @ I2 ) @ ( Y7 @ J2 ) )
% 0.07/0.32 => ? [J3: A] : ( ord_less @ extended_enat @ ( extended_enat2 @ K2 ) @ ( Y7 @ J3 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % chain_incr
% 0.07/0.32 thf(fact_133_enat__iless,axiom,
% 0.07/0.32 ! [N: extended_enat,M: nat] :
% 0.07/0.32 ( ( ord_less @ extended_enat @ N @ ( extended_enat2 @ M ) )
% 0.07/0.32 => ? [K: nat] :
% 0.07/0.32 ( N
% 0.07/0.32 = ( extended_enat2 @ K ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % enat_iless
% 0.07/0.32 thf(fact_134_less__enatE,axiom,
% 0.07/0.32 ! [N: extended_enat,M: nat] :
% 0.07/0.32 ( ( ord_less @ extended_enat @ N @ ( extended_enat2 @ M ) )
% 0.07/0.32 => ~ ! [K: nat] :
% 0.07/0.32 ( ( N
% 0.07/0.32 = ( extended_enat2 @ K ) )
% 0.07/0.32 => ~ ( ord_less @ nat @ K @ M ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_enatE
% 0.07/0.32 thf(fact_135_nat__add__left__cancel__le,axiom,
% 0.07/0.32 ! [K2: nat,M: nat,N: nat] :
% 0.07/0.32 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ K2 @ M ) @ ( plus_plus @ nat @ K2 @ N ) )
% 0.07/0.32 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.07/0.32
% 0.07/0.32 % nat_add_left_cancel_le
% 0.07/0.32 thf(fact_136_nat__add__left__cancel__less,axiom,
% 0.07/0.32 ! [K2: nat,M: nat,N: nat] :
% 0.07/0.32 ( ( ord_less @ nat @ ( plus_plus @ nat @ K2 @ M ) @ ( plus_plus @ nat @ K2 @ N ) )
% 0.07/0.32 = ( ord_less @ nat @ M @ N ) ) ).
% 0.07/0.32
% 0.07/0.32 % nat_add_left_cancel_less
% 0.07/0.32 thf(fact_137_mono__nat__linear__lb,axiom,
% 0.07/0.32 ! [F: nat > nat,M: nat,K2: nat] :
% 0.07/0.32 ( ! [M3: nat,N2: nat] :
% 0.07/0.32 ( ( ord_less @ nat @ M3 @ N2 )
% 0.07/0.32 => ( ord_less @ nat @ ( F @ M3 ) @ ( F @ N2 ) ) )
% 0.07/0.32 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( F @ M ) @ K2 ) @ ( F @ ( plus_plus @ nat @ M @ K2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % mono_nat_linear_lb
% 0.07/0.32 thf(fact_138_ex__has__greatest__nat__lemma,axiom,
% 0.07/0.32 ! [A: $tType,P: A > $o,K2: A,M: A > nat,N: nat] :
% 0.07/0.32 ( ( P @ K2 )
% 0.07/0.32 => ( ! [X3: A] :
% 0.07/0.32 ( ( P @ X3 )
% 0.07/0.32 => ? [Y8: A] :
% 0.07/0.32 ( ( P @ Y8 )
% 0.07/0.32 & ~ ( ord_less_eq @ nat @ ( M @ Y8 ) @ ( M @ X3 ) ) ) )
% 0.07/0.32 => ? [Y3: A] :
% 0.07/0.32 ( ( P @ Y3 )
% 0.07/0.32 & ~ ( ord_less @ nat @ ( M @ Y3 ) @ ( plus_plus @ nat @ ( M @ K2 ) @ N ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ex_has_greatest_nat_lemma
% 0.07/0.32 thf(fact_139_infinite__descent__measure,axiom,
% 0.07/0.32 ! [A: $tType,P: A > $o,V: A > nat,X: A] :
% 0.07/0.32 ( ! [X3: A] :
% 0.07/0.32 ( ~ ( P @ X3 )
% 0.07/0.32 => ? [Y8: A] :
% 0.07/0.32 ( ( ord_less @ nat @ ( V @ Y8 ) @ ( V @ X3 ) )
% 0.07/0.32 & ~ ( P @ Y8 ) ) )
% 0.07/0.32 => ( P @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % infinite_descent_measure
% 0.07/0.32 thf(fact_140_measure__induct__rule,axiom,
% 0.07/0.32 ! [A: $tType,F: A > nat,P: A > $o,A2: A] :
% 0.07/0.32 ( ! [X3: A] :
% 0.07/0.32 ( ! [Y8: A] :
% 0.07/0.32 ( ( ord_less @ nat @ ( F @ Y8 ) @ ( F @ X3 ) )
% 0.07/0.32 => ( P @ Y8 ) )
% 0.07/0.32 => ( P @ X3 ) )
% 0.07/0.32 => ( P @ A2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % measure_induct_rule
% 0.07/0.32 thf(fact_141_linorder__neqE__nat,axiom,
% 0.07/0.32 ! [X: nat,Y: nat] :
% 0.07/0.32 ( ( X != Y )
% 0.07/0.32 => ( ~ ( ord_less @ nat @ X @ Y )
% 0.07/0.32 => ( ord_less @ nat @ Y @ X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % linorder_neqE_nat
% 0.07/0.32 thf(fact_142_infinite__descent,axiom,
% 0.07/0.32 ! [P: nat > $o,N: nat] :
% 0.07/0.32 ( ! [N2: nat] :
% 0.07/0.32 ( ~ ( P @ N2 )
% 0.07/0.32 => ? [M2: nat] :
% 0.07/0.32 ( ( ord_less @ nat @ M2 @ N2 )
% 0.07/0.32 & ~ ( P @ M2 ) ) )
% 0.07/0.32 => ( P @ N ) ) ).
% 0.07/0.32
% 0.07/0.32 % infinite_descent
% 0.07/0.32 thf(fact_143_nat__less__induct,axiom,
% 0.07/0.32 ! [P: nat > $o,N: nat] :
% 0.07/0.32 ( ! [N2: nat] :
% 0.07/0.32 ( ! [M2: nat] :
% 0.07/0.32 ( ( ord_less @ nat @ M2 @ N2 )
% 0.07/0.32 => ( P @ M2 ) )
% 0.07/0.32 => ( P @ N2 ) )
% 0.07/0.32 => ( P @ N ) ) ).
% 0.07/0.32
% 0.07/0.32 % nat_less_induct
% 0.07/0.32 thf(fact_144_less__irrefl__nat,axiom,
% 0.07/0.32 ! [N: nat] :
% 0.07/0.32 ~ ( ord_less @ nat @ N @ N ) ).
% 0.07/0.32
% 0.07/0.32 % less_irrefl_nat
% 0.07/0.32 thf(fact_145_measure__induct,axiom,
% 0.07/0.32 ! [A: $tType,F: A > nat,P: A > $o,A2: A] :
% 0.07/0.32 ( ! [X3: A] :
% 0.07/0.32 ( ! [Y8: A] :
% 0.07/0.32 ( ( ord_less @ nat @ ( F @ Y8 ) @ ( F @ X3 ) )
% 0.07/0.32 => ( P @ Y8 ) )
% 0.07/0.32 => ( P @ X3 ) )
% 0.07/0.32 => ( P @ A2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % measure_induct
% 0.07/0.32 thf(fact_146_less__not__refl3,axiom,
% 0.07/0.32 ! [S: nat,T: nat] :
% 0.07/0.32 ( ( ord_less @ nat @ S @ T )
% 0.07/0.32 => ( S != T ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_not_refl3
% 0.07/0.32 thf(fact_147_less__not__refl2,axiom,
% 0.07/0.32 ! [N: nat,M: nat] :
% 0.07/0.32 ( ( ord_less @ nat @ N @ M )
% 0.07/0.32 => ( M != N ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_not_refl2
% 0.07/0.32 thf(fact_148_less__not__refl,axiom,
% 0.07/0.32 ! [N: nat] :
% 0.07/0.32 ~ ( ord_less @ nat @ N @ N ) ).
% 0.07/0.32
% 0.07/0.32 % less_not_refl
% 0.07/0.32 thf(fact_149_nat__neq__iff,axiom,
% 0.07/0.32 ! [M: nat,N: nat] :
% 0.07/0.32 ( ( M != N )
% 0.07/0.32 = ( ( ord_less @ nat @ M @ N )
% 0.07/0.32 | ( ord_less @ nat @ N @ M ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % nat_neq_iff
% 0.07/0.32 thf(fact_150_ex__has__least__nat,axiom,
% 0.07/0.32 ! [A: $tType,P: A > $o,K2: A,M: A > nat] :
% 0.07/0.32 ( ( P @ K2 )
% 0.07/0.32 => ? [X3: A] :
% 0.07/0.32 ( ( P @ X3 )
% 0.07/0.32 & ! [Y8: A] :
% 0.07/0.32 ( ( P @ Y8 )
% 0.07/0.32 => ( ord_less_eq @ nat @ ( M @ X3 ) @ ( M @ Y8 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ex_has_least_nat
% 0.07/0.32 thf(fact_151_nat__le__linear,axiom,
% 0.07/0.32 ! [M: nat,N: nat] :
% 0.07/0.32 ( ( ord_less_eq @ nat @ M @ N )
% 0.07/0.32 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.07/0.32
% 0.07/0.32 % nat_le_linear
% 0.07/0.32 thf(fact_152_le__antisym,axiom,
% 0.07/0.32 ! [M: nat,N: nat] :
% 0.07/0.32 ( ( ord_less_eq @ nat @ M @ N )
% 0.07/0.32 => ( ( ord_less_eq @ nat @ N @ M )
% 0.07/0.32 => ( M = N ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_antisym
% 0.07/0.32 thf(fact_153_eq__imp__le,axiom,
% 0.07/0.32 ! [M: nat,N: nat] :
% 0.07/0.32 ( ( M = N )
% 0.07/0.32 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_imp_le
% 0.07/0.32 thf(fact_154_le__trans,axiom,
% 0.07/0.32 ! [I: nat,J: nat,K2: nat] :
% 0.07/0.32 ( ( ord_less_eq @ nat @ I @ J )
% 0.07/0.32 => ( ( ord_less_eq @ nat @ J @ K2 )
% 0.07/0.32 => ( ord_less_eq @ nat @ I @ K2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_trans
% 0.07/0.32 thf(fact_155_le__refl,axiom,
% 0.07/0.32 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 0.07/0.32
% 0.07/0.32 % le_refl
% 0.07/0.32 thf(fact_156_nat__add__right__cancel,axiom,
% 0.07/0.32 ! [M: nat,K2: nat,N: nat] :
% 0.07/0.32 ( ( ( plus_plus @ nat @ M @ K2 )
% 0.07/0.32 = ( plus_plus @ nat @ N @ K2 ) )
% 0.07/0.32 = ( M = N ) ) ).
% 0.07/0.32
% 0.07/0.32 % nat_add_right_cancel
% 0.07/0.32 thf(fact_157_nat__add__left__cancel,axiom,
% 0.07/0.32 ! [K2: nat,M: nat,N: nat] :
% 0.07/0.32 ( ( ( plus_plus @ nat @ K2 @ M )
% 0.07/0.32 = ( plus_plus @ nat @ K2 @ N ) )
% 0.07/0.32 = ( M = N ) ) ).
% 0.07/0.32
% 0.07/0.32 % nat_add_left_cancel
% 0.07/0.32 thf(fact_158_ex__has__greatest__nat,axiom,
% 0.07/0.32 ! [A: $tType,P: A > $o,K2: A,M: A > nat,B2: nat] :
% 0.07/0.32 ( ( P @ K2 )
% 0.07/0.32 => ( ! [Y3: A] :
% 0.07/0.32 ( ( P @ Y3 )
% 0.07/0.32 => ( ord_less @ nat @ ( M @ Y3 ) @ B2 ) )
% 0.07/0.32 => ? [X3: A] :
% 0.07/0.32 ( ( P @ X3 )
% 0.07/0.32 & ! [Y8: A] :
% 0.07/0.32 ( ( P @ Y8 )
% 0.07/0.32 => ( ord_less_eq @ nat @ ( M @ Y8 ) @ ( M @ X3 ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ex_has_greatest_nat
% 0.07/0.32 thf(fact_159_less__mono__imp__le__mono,axiom,
% 0.07/0.32 ! [F: nat > nat,I: nat,J: nat] :
% 0.07/0.32 ( ! [I2: nat,J3: nat] :
% 0.07/0.32 ( ( ord_less @ nat @ I2 @ J3 )
% 0.07/0.32 => ( ord_less @ nat @ ( F @ I2 ) @ ( F @ J3 ) ) )
% 0.07/0.32 => ( ( ord_less_eq @ nat @ I @ J )
% 0.07/0.32 => ( ord_less_eq @ nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_mono_imp_le_mono
% 0.07/0.32 thf(fact_160_le__neq__implies__less,axiom,
% 0.07/0.32 ! [M: nat,N: nat] :
% 0.07/0.32 ( ( ord_less_eq @ nat @ M @ N )
% 0.07/0.32 => ( ( M != N )
% 0.07/0.32 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_neq_implies_less
% 0.07/0.32 thf(fact_161_less__or__eq__imp__le,axiom,
% 0.07/0.32 ! [M: nat,N: nat] :
% 0.07/0.32 ( ( ( ord_less @ nat @ M @ N )
% 0.07/0.32 | ( M = N ) )
% 0.07/0.32 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_or_eq_imp_le
% 0.07/0.32 thf(fact_162_le__eq__less__or__eq,axiom,
% 0.07/0.32 ( ( ord_less_eq @ nat )
% 0.07/0.32 = ( ^ [M4: nat,N3: nat] :
% 0.07/0.32 ( ( ord_less @ nat @ M4 @ N3 )
% 0.07/0.32 | ( M4 = N3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_eq_less_or_eq
% 0.07/0.32 thf(fact_163_less__imp__le__nat,axiom,
% 0.07/0.32 ! [M: nat,N: nat] :
% 0.07/0.32 ( ( ord_less @ nat @ M @ N )
% 0.07/0.32 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_imp_le_nat
% 0.07/0.32 thf(fact_164_nat__less__le,axiom,
% 0.07/0.32 ( ( ord_less @ nat )
% 0.07/0.32 = ( ^ [M4: nat,N3: nat] :
% 0.07/0.32 ( ( ord_less_eq @ nat @ M4 @ N3 )
% 0.07/0.32 & ( M4 != N3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % nat_less_le
% 0.07/0.32 thf(fact_165_less__add__eq__less,axiom,
% 0.07/0.32 ! [K2: nat,L: nat,M: nat,N: nat] :
% 0.07/0.32 ( ( ord_less @ nat @ K2 @ L )
% 0.07/0.32 => ( ( ( plus_plus @ nat @ M @ L )
% 0.07/0.32 = ( plus_plus @ nat @ K2 @ N ) )
% 0.07/0.32 => ( ord_less @ nat @ M @ N ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_add_eq_less
% 0.07/0.32 thf(fact_166_trans__less__add2,axiom,
% 0.07/0.32 ! [I: nat,J: nat,M: nat] :
% 0.07/0.32 ( ( ord_less @ nat @ I @ J )
% 0.07/0.32 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % trans_less_add2
% 0.07/0.32 thf(fact_167_trans__less__add1,axiom,
% 0.07/0.32 ! [I: nat,J: nat,M: nat] :
% 0.07/0.32 ( ( ord_less @ nat @ I @ J )
% 0.07/0.32 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % trans_less_add1
% 0.07/0.32 thf(fact_168_add__less__mono1,axiom,
% 0.07/0.32 ! [I: nat,J: nat,K2: nat] :
% 0.07/0.32 ( ( ord_less @ nat @ I @ J )
% 0.07/0.32 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K2 ) @ ( plus_plus @ nat @ J @ K2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_less_mono1
% 0.07/0.32 thf(fact_169_not__add__less2,axiom,
% 0.07/0.32 ! [J: nat,I: nat] :
% 0.07/0.32 ~ ( ord_less @ nat @ ( plus_plus @ nat @ J @ I ) @ I ) ).
% 0.07/0.32
% 0.07/0.32 % not_add_less2
% 0.07/0.32 thf(fact_170_not__add__less1,axiom,
% 0.07/0.32 ! [I: nat,J: nat] :
% 0.07/0.32 ~ ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ I ) ).
% 0.07/0.32
% 0.07/0.32 % not_add_less1
% 0.07/0.32 thf(fact_171_add__less__mono,axiom,
% 0.07/0.32 ! [I: nat,J: nat,K2: nat,L: nat] :
% 0.07/0.32 ( ( ord_less @ nat @ I @ J )
% 0.07/0.32 => ( ( ord_less @ nat @ K2 @ L )
% 0.07/0.32 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K2 ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_less_mono
% 0.07/0.32 thf(fact_172_add__lessD1,axiom,
% 0.07/0.32 ! [I: nat,J: nat,K2: nat] :
% 0.07/0.32 ( ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ K2 )
% 0.07/0.32 => ( ord_less @ nat @ I @ K2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_lessD1
% 0.07/0.32 thf(fact_173_nat__le__iff__add,axiom,
% 0.07/0.32 ( ( ord_less_eq @ nat )
% 0.07/0.32 = ( ^ [M4: nat,N3: nat] :
% 0.07/0.32 ? [K3: nat] :
% 0.07/0.32 ( N3
% 0.07/0.32 = ( plus_plus @ nat @ M4 @ K3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % nat_le_iff_add
% 0.07/0.32 thf(fact_174_trans__le__add2,axiom,
% 0.07/0.32 ! [I: nat,J: nat,M: nat] :
% 0.07/0.32 ( ( ord_less_eq @ nat @ I @ J )
% 0.07/0.32 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % trans_le_add2
% 0.07/0.32 thf(fact_175_trans__le__add1,axiom,
% 0.07/0.32 ! [I: nat,J: nat,M: nat] :
% 0.07/0.32 ( ( ord_less_eq @ nat @ I @ J )
% 0.07/0.32 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % trans_le_add1
% 0.07/0.32 thf(fact_176_add__le__mono1,axiom,
% 0.07/0.32 ! [I: nat,J: nat,K2: nat] :
% 0.07/0.32 ( ( ord_less_eq @ nat @ I @ J )
% 0.07/0.32 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K2 ) @ ( plus_plus @ nat @ J @ K2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_le_mono1
% 0.07/0.32 thf(fact_177_add__le__mono,axiom,
% 0.07/0.32 ! [I: nat,J: nat,K2: nat,L: nat] :
% 0.07/0.32 ( ( ord_less_eq @ nat @ I @ J )
% 0.07/0.32 => ( ( ord_less_eq @ nat @ K2 @ L )
% 0.07/0.32 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K2 ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_le_mono
% 0.07/0.32 thf(fact_178_le__Suc__ex,axiom,
% 0.07/0.32 ! [K2: nat,L: nat] :
% 0.07/0.32 ( ( ord_less_eq @ nat @ K2 @ L )
% 0.07/0.32 => ? [N2: nat] :
% 0.07/0.32 ( L
% 0.07/0.32 = ( plus_plus @ nat @ K2 @ N2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_Suc_ex
% 0.07/0.32 thf(fact_179_add__leD2,axiom,
% 0.07/0.32 ! [M: nat,K2: nat,N: nat] :
% 0.07/0.32 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K2 ) @ N )
% 0.07/0.32 => ( ord_less_eq @ nat @ K2 @ N ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_leD2
% 0.07/0.32 thf(fact_180_add__leD1,axiom,
% 0.07/0.32 ! [M: nat,K2: nat,N: nat] :
% 0.07/0.32 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K2 ) @ N )
% 0.07/0.32 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_leD1
% 0.07/0.32 thf(fact_181_le__add2,axiom,
% 0.07/0.32 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ M @ N ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_add2
% 0.07/0.32 thf(fact_182_le__add1,axiom,
% 0.07/0.32 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ N @ M ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_add1
% 0.07/0.32 thf(fact_183_add__leE,axiom,
% 0.07/0.32 ! [M: nat,K2: nat,N: nat] :
% 0.07/0.32 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K2 ) @ N )
% 0.07/0.32 => ~ ( ( ord_less_eq @ nat @ M @ N )
% 0.07/0.32 => ~ ( ord_less_eq @ nat @ K2 @ N ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % add_leE
% 0.07/0.32 thf(fact_184_predicate2I,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType,P: A > B > $o,Q: A > B > $o] :
% 0.07/0.32 ( ! [X3: A,Y3: B] :
% 0.07/0.32 ( ( P @ X3 @ Y3 )
% 0.07/0.32 => ( Q @ X3 @ Y3 ) )
% 0.07/0.32 => ( ord_less_eq @ ( A > B > $o ) @ P @ Q ) ) ).
% 0.07/0.32
% 0.07/0.32 % predicate2I
% 0.07/0.32 thf(fact_185_order__refl,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( preorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_refl
% 0.07/0.32 thf(fact_186_gen__llength__def,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( coindu493225792length @ A )
% 0.07/0.32 = ( ^ [N3: nat,Xs3: coindu1593790203_llist @ A] : ( plus_plus @ extended_enat @ ( extended_enat2 @ N3 ) @ ( coindu1018505716length @ A @ Xs3 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % gen_llength_def
% 0.07/0.32 thf(fact_187_le__fun__def,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType] :
% 0.07/0.32 ( ( ord @ B @ ( type2 @ B ) )
% 0.07/0.32 => ( ( ord_less_eq @ ( A > B ) )
% 0.07/0.32 = ( ^ [F2: A > B,G2: A > B] :
% 0.07/0.32 ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_fun_def
% 0.07/0.32 thf(fact_188_order__subst1,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType] :
% 0.07/0.32 ( ( ( order @ B @ ( type2 @ B ) )
% 0.07/0.32 & ( order @ A @ ( type2 @ A ) ) )
% 0.07/0.32 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.07/0.32 => ( ! [X3: B,Y3: B] :
% 0.07/0.32 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 0.07/0.32 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst1
% 0.07/0.32 thf(fact_189_order__subst2,axiom,
% 0.07/0.32 ! [A: $tType,C3: $tType] :
% 0.07/0.32 ( ( ( order @ C3 @ ( type2 @ C3 ) )
% 0.07/0.32 & ( order @ A @ ( type2 @ A ) ) )
% 0.07/0.32 => ! [A2: A,B2: A,F: A > C3,C: C3] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less_eq @ C3 @ ( F @ B2 ) @ C )
% 0.07/0.32 => ( ! [X3: A,Y3: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.07/0.32 => ( ord_less_eq @ C3 @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq @ C3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_subst2
% 0.07/0.32 thf(fact_190_ord__eq__le__subst,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType] :
% 0.07/0.32 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.07/0.32 & ( ord @ A @ ( type2 @ A ) ) )
% 0.07/0.32 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.07/0.32 ( ( A2
% 0.07/0.32 = ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.07/0.32 => ( ! [X3: B,Y3: B] :
% 0.07/0.32 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 0.07/0.32 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_subst
% 0.07/0.32 thf(fact_191_ord__le__eq__subst,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType] :
% 0.07/0.32 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.07/0.32 & ( ord @ A @ ( type2 @ A ) ) )
% 0.07/0.32 => ! [A2: A,B2: A,F: A > B,C: B] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( ( F @ B2 )
% 0.07/0.32 = C )
% 0.07/0.32 => ( ! [X3: A,Y3: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.07/0.32 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less_eq @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_subst
% 0.07/0.32 thf(fact_192_eq__iff,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ( ( ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 0.07/0.32 = ( ^ [X2: A,Y4: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.07/0.32 & ( ord_less_eq @ A @ Y4 @ X2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_iff
% 0.07/0.32 thf(fact_193_antisym,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ X @ Y )
% 0.07/0.32 => ( ( ord_less_eq @ A @ Y @ X )
% 0.07/0.32 => ( X = Y ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym
% 0.07/0.32 thf(fact_194_linear,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ X @ Y )
% 0.07/0.32 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % linear
% 0.07/0.32 thf(fact_195_eq__refl,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( preorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ( X = Y )
% 0.07/0.32 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % eq_refl
% 0.07/0.32 thf(fact_196_le__cases,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.07/0.32 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_cases
% 0.07/0.32 thf(fact_197_order_Otrans,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.07/0.32 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.trans
% 0.07/0.32 thf(fact_198_le__cases3,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A,Z2: A] :
% 0.07/0.32 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.07/0.32 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 0.07/0.32 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.07/0.32 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 0.07/0.32 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 0.07/0.32 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 0.07/0.32 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 0.07/0.32 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.07/0.32 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.07/0.32 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 0.07/0.32 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 0.07/0.32 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_cases3
% 0.07/0.32 thf(fact_199_antisym__conv,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [Y: A,X: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ Y @ X )
% 0.07/0.32 => ( ( ord_less_eq @ A @ X @ Y )
% 0.07/0.32 = ( X = Y ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym_conv
% 0.07/0.32 thf(fact_200_ord__eq__le__trans,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ord @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A] :
% 0.07/0.32 ( ( A2 = B2 )
% 0.07/0.32 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.07/0.32 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_le_trans
% 0.07/0.32 thf(fact_201_ord__le__eq__trans,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ord @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( B2 = C )
% 0.07/0.32 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_le_eq_trans
% 0.07/0.32 thf(fact_202_order__class_Oorder_Oantisym,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.07/0.32 => ( A2 = B2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_class.order.antisym
% 0.07/0.32 thf(fact_203_order__trans,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( preorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A,Z2: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ X @ Y )
% 0.07/0.32 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.07/0.32 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_trans
% 0.07/0.32 thf(fact_204_dual__order_Orefl,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.refl
% 0.07/0.32 thf(fact_205_linorder__wlog,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.07/0.32 ( ! [A4: A,B3: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.07/0.32 => ( P @ A4 @ B3 ) )
% 0.07/0.32 => ( ! [A4: A,B3: A] :
% 0.07/0.32 ( ( P @ B3 @ A4 )
% 0.07/0.32 => ( P @ A4 @ B3 ) )
% 0.07/0.32 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % linorder_wlog
% 0.07/0.32 thf(fact_206_dual__order_Otrans,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [B2: A,A2: A,C: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.07/0.32 => ( ( ord_less_eq @ A @ C @ B2 )
% 0.07/0.32 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.trans
% 0.07/0.32 thf(fact_207_dual__order_Oantisym,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [B2: A,A2: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.07/0.32 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.07/0.32 => ( A2 = B2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.antisym
% 0.07/0.32 thf(fact_208_ord__eq__less__subst,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType] :
% 0.07/0.32 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.07/0.32 & ( ord @ A @ ( type2 @ A ) ) )
% 0.07/0.32 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.07/0.32 ( ( A2
% 0.07/0.32 = ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_less @ B @ B2 @ C )
% 0.07/0.32 => ( ! [X3: B,Y3: B] :
% 0.07/0.32 ( ( ord_less @ B @ X3 @ Y3 )
% 0.07/0.32 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_less_subst
% 0.07/0.32 thf(fact_209_ord__less__eq__subst,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType] :
% 0.07/0.32 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.07/0.32 & ( ord @ A @ ( type2 @ A ) ) )
% 0.07/0.32 => ! [A2: A,B2: A,F: A > B,C: B] :
% 0.07/0.32 ( ( ord_less @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( ( F @ B2 )
% 0.07/0.32 = C )
% 0.07/0.32 => ( ! [X3: A,Y3: A] :
% 0.07/0.32 ( ( ord_less @ A @ X3 @ Y3 )
% 0.07/0.32 => ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_less_eq_subst
% 0.07/0.32 thf(fact_210_order__less__subst1,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType] :
% 0.07/0.32 ( ( ( order @ B @ ( type2 @ B ) )
% 0.07/0.32 & ( order @ A @ ( type2 @ A ) ) )
% 0.07/0.32 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.07/0.32 ( ( ord_less @ A @ A2 @ ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_less @ B @ B2 @ C )
% 0.07/0.32 => ( ! [X3: B,Y3: B] :
% 0.07/0.32 ( ( ord_less @ B @ X3 @ Y3 )
% 0.07/0.32 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_less_subst1
% 0.07/0.32 thf(fact_211_order__less__subst2,axiom,
% 0.07/0.32 ! [A: $tType,C3: $tType] :
% 0.07/0.32 ( ( ( order @ C3 @ ( type2 @ C3 ) )
% 0.07/0.32 & ( order @ A @ ( type2 @ A ) ) )
% 0.07/0.32 => ! [A2: A,B2: A,F: A > C3,C: C3] :
% 0.07/0.32 ( ( ord_less @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less @ C3 @ ( F @ B2 ) @ C )
% 0.07/0.32 => ( ! [X3: A,Y3: A] :
% 0.07/0.32 ( ( ord_less @ A @ X3 @ Y3 )
% 0.07/0.32 => ( ord_less @ C3 @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less @ C3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_less_subst2
% 0.07/0.32 thf(fact_212_lt__ex,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( no_bot @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A] :
% 0.07/0.32 ? [Y3: A] : ( ord_less @ A @ Y3 @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % lt_ex
% 0.07/0.32 thf(fact_213_gt__ex,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( no_top @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A] :
% 0.07/0.32 ? [X1: A] : ( ord_less @ A @ X @ X1 ) ) ).
% 0.07/0.32
% 0.07/0.32 % gt_ex
% 0.07/0.32 thf(fact_214_neqE,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ( X != Y )
% 0.07/0.32 => ( ~ ( ord_less @ A @ X @ Y )
% 0.07/0.32 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % neqE
% 0.07/0.32 thf(fact_215_neq__iff,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ( X != Y )
% 0.07/0.32 = ( ( ord_less @ A @ X @ Y )
% 0.07/0.32 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % neq_iff
% 0.07/0.32 thf(fact_216_order_Oasym,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A] :
% 0.07/0.32 ( ( ord_less @ A @ A2 @ B2 )
% 0.07/0.32 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.asym
% 0.07/0.32 thf(fact_217_dense,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( dense_order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ( ord_less @ A @ X @ Y )
% 0.07/0.32 => ? [Z3: A] :
% 0.07/0.32 ( ( ord_less @ A @ X @ Z3 )
% 0.07/0.32 & ( ord_less @ A @ Z3 @ Y ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dense
% 0.07/0.32 thf(fact_218_less__imp__neq,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ( ord_less @ A @ X @ Y )
% 0.07/0.32 => ( X != Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_imp_neq
% 0.07/0.32 thf(fact_219_less__asym,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( preorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ( ord_less @ A @ X @ Y )
% 0.07/0.32 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_asym
% 0.07/0.32 thf(fact_220_less__asym_H,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( preorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A] :
% 0.07/0.32 ( ( ord_less @ A @ A2 @ B2 )
% 0.07/0.32 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_asym'
% 0.07/0.32 thf(fact_221_less__trans,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( preorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A,Z2: A] :
% 0.07/0.32 ( ( ord_less @ A @ X @ Y )
% 0.07/0.32 => ( ( ord_less @ A @ Y @ Z2 )
% 0.07/0.32 => ( ord_less @ A @ X @ Z2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_trans
% 0.07/0.32 thf(fact_222_less__linear,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ( ord_less @ A @ X @ Y )
% 0.07/0.32 | ( X = Y )
% 0.07/0.32 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_linear
% 0.07/0.32 thf(fact_223_less__irrefl,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( preorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A] :
% 0.07/0.32 ~ ( ord_less @ A @ X @ X ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_irrefl
% 0.07/0.32 thf(fact_224_ord__eq__less__trans,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ord @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A] :
% 0.07/0.32 ( ( A2 = B2 )
% 0.07/0.32 => ( ( ord_less @ A @ B2 @ C )
% 0.07/0.32 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_eq_less_trans
% 0.07/0.32 thf(fact_225_ord__less__eq__trans,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( ord @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A] :
% 0.07/0.32 ( ( ord_less @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( B2 = C )
% 0.07/0.32 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % ord_less_eq_trans
% 0.07/0.32 thf(fact_226_dual__order_Oasym,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [B2: A,A2: A] :
% 0.07/0.32 ( ( ord_less @ A @ B2 @ A2 )
% 0.07/0.32 => ~ ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.asym
% 0.07/0.32 thf(fact_227_less__imp__not__eq,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ( ord_less @ A @ X @ Y )
% 0.07/0.32 => ( X != Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_imp_not_eq
% 0.07/0.32 thf(fact_228_less__not__sym,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( preorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ( ord_less @ A @ X @ Y )
% 0.07/0.32 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_not_sym
% 0.07/0.32 thf(fact_229_less__induct,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [P: A > $o,A2: A] :
% 0.07/0.32 ( ! [X3: A] :
% 0.07/0.32 ( ! [Y8: A] :
% 0.07/0.32 ( ( ord_less @ A @ Y8 @ X3 )
% 0.07/0.32 => ( P @ Y8 ) )
% 0.07/0.32 => ( P @ X3 ) )
% 0.07/0.32 => ( P @ A2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_induct
% 0.07/0.32 thf(fact_230_antisym__conv3,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [Y: A,X: A] :
% 0.07/0.32 ( ~ ( ord_less @ A @ Y @ X )
% 0.07/0.32 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.07/0.32 = ( X = Y ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % antisym_conv3
% 0.07/0.32 thf(fact_231_less__imp__not__eq2,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ( ord_less @ A @ X @ Y )
% 0.07/0.32 => ( Y != X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_imp_not_eq2
% 0.07/0.32 thf(fact_232_less__imp__triv,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( preorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A,P: $o] :
% 0.07/0.32 ( ( ord_less @ A @ X @ Y )
% 0.07/0.32 => ( ( ord_less @ A @ Y @ X )
% 0.07/0.32 => P ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_imp_triv
% 0.07/0.32 thf(fact_233_linorder__cases,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ~ ( ord_less @ A @ X @ Y )
% 0.07/0.32 => ( ( X != Y )
% 0.07/0.32 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % linorder_cases
% 0.07/0.32 thf(fact_234_dual__order_Oirrefl,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A] :
% 0.07/0.32 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.irrefl
% 0.07/0.32 thf(fact_235_order_Ostrict__trans,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A,C: A] :
% 0.07/0.32 ( ( ord_less @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less @ A @ B2 @ C )
% 0.07/0.32 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.strict_trans
% 0.07/0.32 thf(fact_236_less__imp__not__less,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( preorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ( ord_less @ A @ X @ Y )
% 0.07/0.32 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_imp_not_less
% 0.07/0.32 thf(fact_237_dual__order_Ostrict__trans,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [B2: A,A2: A,C: A] :
% 0.07/0.32 ( ( ord_less @ A @ B2 @ A2 )
% 0.07/0.32 => ( ( ord_less @ A @ C @ B2 )
% 0.07/0.32 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.strict_trans
% 0.07/0.32 thf(fact_238_not__less__iff__gr__or__eq,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.07/0.32 = ( ( ord_less @ A @ Y @ X )
% 0.07/0.32 | ( X = Y ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % not_less_iff_gr_or_eq
% 0.07/0.32 thf(fact_239_order_Ostrict__implies__not__eq,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [A2: A,B2: A] :
% 0.07/0.32 ( ( ord_less @ A @ A2 @ B2 )
% 0.07/0.32 => ( A2 != B2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order.strict_implies_not_eq
% 0.07/0.32 thf(fact_240_dual__order_Ostrict__implies__not__eq,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [B2: A,A2: A] :
% 0.07/0.32 ( ( ord_less @ A @ B2 @ A2 )
% 0.07/0.32 => ( A2 != B2 ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % dual_order.strict_implies_not_eq
% 0.07/0.32 thf(fact_241_less__fun__def,axiom,
% 0.07/0.32 ! [B: $tType,A: $tType] :
% 0.07/0.32 ( ( ord @ B @ ( type2 @ B ) )
% 0.07/0.32 => ( ( ord_less @ ( A > B ) )
% 0.07/0.32 = ( ^ [F2: A > B,G2: A > B] :
% 0.07/0.32 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.07/0.32 & ~ ( ord_less_eq @ ( A > B ) @ G2 @ F2 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_fun_def
% 0.07/0.32 thf(fact_242_predicate2D,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,X: A,Y: B] :
% 0.07/0.32 ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.07/0.32 => ( ( P @ X @ Y )
% 0.07/0.32 => ( Q @ X @ Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % predicate2D
% 0.07/0.32 thf(fact_243_rev__predicate2D,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType,P: A > B > $o,X: A,Y: B,Q: A > B > $o] :
% 0.07/0.32 ( ( P @ X @ Y )
% 0.07/0.32 => ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.07/0.32 => ( Q @ X @ Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % rev_predicate2D
% 0.07/0.32 thf(fact_244_gen__llength__code_I1_J,axiom,
% 0.07/0.32 ! [A: $tType,N: nat] :
% 0.07/0.32 ( ( coindu493225792length @ A @ N @ ( coindu1598213697e_LNil @ A ) )
% 0.07/0.32 = ( extended_enat2 @ N ) ) ).
% 0.07/0.32
% 0.07/0.32 % gen_llength_code(1)
% 0.07/0.32 thf(fact_245_leD,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [Y: A,X: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ Y @ X )
% 0.07/0.32 => ~ ( ord_less @ A @ X @ Y ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % leD
% 0.07/0.32 thf(fact_246_leI,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ~ ( ord_less @ A @ X @ Y )
% 0.07/0.32 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % leI
% 0.07/0.32 thf(fact_247_le__less,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ( ( ord_less_eq @ A )
% 0.07/0.32 = ( ^ [X2: A,Y4: A] :
% 0.07/0.32 ( ( ord_less @ A @ X2 @ Y4 )
% 0.07/0.32 | ( X2 = Y4 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % le_less
% 0.07/0.32 thf(fact_248_less__le,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( order @ A @ ( type2 @ A ) )
% 0.07/0.32 => ( ( ord_less @ A )
% 0.07/0.32 = ( ^ [X2: A,Y4: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.07/0.32 & ( X2 != Y4 ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % less_le
% 0.07/0.32 thf(fact_249_order__le__less__subst1,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType] :
% 0.07/0.32 ( ( ( order @ B @ ( type2 @ B ) )
% 0.07/0.32 & ( order @ A @ ( type2 @ A ) ) )
% 0.07/0.32 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_less @ B @ B2 @ C )
% 0.07/0.32 => ( ! [X3: B,Y3: B] :
% 0.07/0.32 ( ( ord_less @ B @ X3 @ Y3 )
% 0.07/0.32 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_le_less_subst1
% 0.07/0.32 thf(fact_250_order__le__less__subst2,axiom,
% 0.07/0.32 ! [A: $tType,C3: $tType] :
% 0.07/0.32 ( ( ( order @ C3 @ ( type2 @ C3 ) )
% 0.07/0.32 & ( order @ A @ ( type2 @ A ) ) )
% 0.07/0.32 => ! [A2: A,B2: A,F: A > C3,C: C3] :
% 0.07/0.32 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less @ C3 @ ( F @ B2 ) @ C )
% 0.07/0.32 => ( ! [X3: A,Y3: A] :
% 0.07/0.32 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 0.07/0.32 => ( ord_less_eq @ C3 @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less @ C3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_le_less_subst2
% 0.07/0.32 thf(fact_251_order__less__le__subst1,axiom,
% 0.07/0.32 ! [A: $tType,B: $tType] :
% 0.07/0.32 ( ( ( order @ B @ ( type2 @ B ) )
% 0.07/0.32 & ( order @ A @ ( type2 @ A ) ) )
% 0.07/0.32 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.07/0.32 ( ( ord_less @ A @ A2 @ ( F @ B2 ) )
% 0.07/0.32 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.07/0.32 => ( ! [X3: B,Y3: B] :
% 0.07/0.32 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 0.07/0.32 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_less_le_subst1
% 0.07/0.32 thf(fact_252_order__less__le__subst2,axiom,
% 0.07/0.32 ! [A: $tType,C3: $tType] :
% 0.07/0.32 ( ( ( order @ C3 @ ( type2 @ C3 ) )
% 0.07/0.32 & ( order @ A @ ( type2 @ A ) ) )
% 0.07/0.32 => ! [A2: A,B2: A,F: A > C3,C: C3] :
% 0.07/0.32 ( ( ord_less @ A @ A2 @ B2 )
% 0.07/0.32 => ( ( ord_less_eq @ C3 @ ( F @ B2 ) @ C )
% 0.07/0.32 => ( ! [X3: A,Y3: A] :
% 0.07/0.32 ( ( ord_less @ A @ X3 @ Y3 )
% 0.07/0.32 => ( ord_less @ C3 @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 0.07/0.32 => ( ord_less @ C3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % order_less_le_subst2
% 0.07/0.32 thf(fact_253_not__le,axiom,
% 0.07/0.32 ! [A: $tType] :
% 0.07/0.32 ( ( linorder @ A @ ( type2 @ A ) )
% 0.07/0.32 => ! [X: A,Y: A] :
% 0.07/0.32 ( ( ~ ( ord_less_eq @ A @ X @ Y ) )
% 0.07/0.32 = ( ord_less @ A @ Y @ X ) ) ) ).
% 0.07/0.32
% 0.07/0.32 % not_le
% 0.07/0.32
% 0.07/0.32 %----Type constructors (31)
% 0.07/0.32 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.07/0.32 ! [A5: $tType,A6: $tType] :
% 0.07/0.32 ( ( preorder @ A6 @ ( type2 @ A6 ) )
% 0.07/0.32 => ( preorder @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.07/0.32 ! [A5: $tType,A6: $tType] :
% 0.07/0.32 ( ( order @ A6 @ ( type2 @ A6 ) )
% 0.07/0.32 => ( order @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_fun___Orderings_Oord,axiom,
% 0.07/0.32 ! [A5: $tType,A6: $tType] :
% 0.07/0.32 ( ( ord @ A6 @ ( type2 @ A6 ) )
% 0.07/0.32 => ( ord @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 0.07/0.32 strict2144017051up_add @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 0.07/0.32 ordere223160158up_add @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.07/0.32 ordere236663937imp_le @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.07/0.32 canoni770627133id_add @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 0.07/0.32 ordere779506340up_add @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 0.07/0.32 cancel_semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 0.07/0.32 ab_semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 0.07/0.32 semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.07/0.32 wellorder @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.07/0.32 preorder @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.07/0.32 linorder @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.07/0.32 no_top @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.07/0.32 order @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.07/0.32 ord @ nat @ ( type2 @ nat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_HOL_Obool___Orderings_Opreorder_4,axiom,
% 0.07/0.32 preorder @ $o @ ( type2 @ $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_HOL_Obool___Orderings_Olinorder_5,axiom,
% 0.07/0.32 linorder @ $o @ ( type2 @ $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_HOL_Obool___Orderings_Oorder_6,axiom,
% 0.07/0.32 order @ $o @ ( type2 @ $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_HOL_Obool___Orderings_Oord_7,axiom,
% 0.07/0.32 ord @ $o @ ( type2 @ $o ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add_8,axiom,
% 0.07/0.32 strict2144017051up_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_9,axiom,
% 0.07/0.32 canoni770627133id_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add_10,axiom,
% 0.07/0.32 ordere779506340up_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add_11,axiom,
% 0.07/0.32 ab_semigroup_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Extended__Nat_Oenat___Groups_Osemigroup__add_12,axiom,
% 0.07/0.32 semigroup_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Extended__Nat_Oenat___Orderings_Owellorder_13,axiom,
% 0.07/0.32 wellorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Extended__Nat_Oenat___Orderings_Opreorder_14,axiom,
% 0.07/0.32 preorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Extended__Nat_Oenat___Orderings_Olinorder_15,axiom,
% 0.07/0.32 linorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Extended__Nat_Oenat___Orderings_Oorder_16,axiom,
% 0.07/0.32 order @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.07/0.32
% 0.07/0.32 thf(tcon_Extended__Nat_Oenat___Orderings_Oord_17,axiom,
% 0.07/0.32 ord @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.07/0.32
% 0.07/0.32 %----Conjectures (1)
% 0.07/0.32 thf(conj_0,conjecture,
% 0.07/0.32 p @ ( coindu749330388e_lnth @ a @ ( coindu268472904append @ a @ xs @ xs2 ) @ n ) @ ( coindu749330388e_lnth @ b @ ys @ n ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 2.08/1.17 ---- Embedded in THF ---
% 2.08/1.17 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.08/1.17 %%% Generated on Tue Feb 24 06:08:16 EST 2026
% 2.08/1.17 %%% using '$$dhol' embedding, version 1.3.0.
% 2.08/1.17 %%% Logic specification used:
% 2.08/1.17 %%% thf(spec, logic, $$dhol).
% 2.08/1.17
% 2.08/1.17 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.YAJWcH1y2A/DTF2DTF20469.p
% 2.08/1.17 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist, type, coindu1593790203_llist: ($tType > $tType)).
% 2.08/1.17 thf(ty_t_Extended__Nat_Oenat, type, extended_enat: $tType).
% 2.08/1.17 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.08/1.17 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.08/1.17 thf(ty_tf_b, type, b: $tType).
% 2.08/1.17 thf(ty_tf_a, type, a: $tType).
% 2.08/1.17 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_cl_Groups_Osemigroup__add, type, semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_cl_Groups_Oab__semigroup__add, type, ab_semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le, type, ordere236663937imp_le: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add, type, ordere223160158up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add, type, strict2144017051up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.08/1.17 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__llength, type, coindu493225792length: (!> [A:$tType]: ((nat > ((coindu1593790203_llist @ A) > extended_enat))))).
% 2.08/1.17 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oiterates, type, coindu1529956631erates: (!> [A:$tType]: (((A > A) > (A > (coindu1593790203_llist @ A)))))).
% 2.08/1.17 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend, type, coindu268472904append: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 2.08/1.17 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite, type, coindu1213758845finite: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 2.08/1.17 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollength, type, coindu1018505716length: (!> [A:$tType]: (((coindu1593790203_llist @ A) > extended_enat)))).
% 2.08/1.17 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons, type, coindu1121789889_LCons: (!> [A:$tType]: ((A > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 2.08/1.17 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil, type, coindu1598213697e_LNil: (!> [A:$tType]: ((coindu1593790203_llist @ A)))).
% 2.08/1.17 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ollist__all2, type, coindu987187967t_all2: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ B) > $o)))))).
% 2.08/1.17 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull, type, coindu335574135_lnull: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 2.08/1.17 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olnth, type, coindu749330388e_lnth: (!> [A:$tType]: (((coindu1593790203_llist @ A) > (nat > A))))).
% 2.08/1.17 thf(sy_c_Extended__Nat_Oenat, type, extended_enat2: (nat > extended_enat)).
% 2.08/1.17 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 2.08/1.17 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.08/1.17 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.08/1.17 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.08/1.17 thf(sy_v_P, type, p: (a > (b > $o))).
% 2.08/1.17 thf(sy_v_n____, type, n: nat).
% 2.08/1.17 thf(sy_v_xs, type, xs: (coindu1593790203_llist @ a)).
% 2.08/1.17 thf(sy_v_xs_H, type, xs2: (coindu1593790203_llist @ a)).
% 2.08/1.17 thf(sy_v_ys, type, ys: (coindu1593790203_llist @ b)).
% 2.08/1.17 thf(fact_0_assms, axiom, (((((coindu987187967t_all2 @ a) @ b) @ p) @ (((coindu268472904append @ a) @ xs) @ xs2)) @ ys)).
% 2.08/1.17 thf(fact_1_lappend__assoc, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) @ Zs) = (((coindu268472904append @ A) @ Xs) @ (((coindu268472904append @ A) @ Ys) @ Zs)))))).
% 2.08/1.17 thf(fact_2__092_060open_062llength_Axs_A_092_060le_062_Allength_A_Ilappend_Axs_Axs_H_J_092_060close_062, axiom, (((ord_less_eq @ extended_enat) @ ((coindu1018505716length @ a) @ xs)) @ ((coindu1018505716length @ a) @ (((coindu268472904append @ a) @ xs) @ xs2)))).
% 2.08/1.17 thf(fact_3_n, axiom, (((ord_less @ extended_enat) @ (extended_enat2 @ n)) @ ((coindu1018505716length @ a) @ xs))).
% 2.08/1.17 thf(fact_4_len, axiom, ((((plus_plus @ extended_enat) @ ((coindu1018505716length @ a) @ xs)) @ ((coindu1018505716length @ a) @ xs2)) = ((coindu1018505716length @ b) @ ys))).
% 2.08/1.17 thf(fact_5_len__xs_H, axiom, (((ord_less_eq @ extended_enat) @ ((coindu1018505716length @ a) @ xs2)) @ ((coindu1018505716length @ b) @ ys))).
% 2.08/1.17 thf(fact_6_len__xs, axiom, (((ord_less_eq @ extended_enat) @ ((coindu1018505716length @ a) @ xs)) @ ((coindu1018505716length @ b) @ ys))).
% 2.08/1.17 thf(fact_7_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (coindu1598213697e_LNil @ A)) @ Ys) = Ys)))).
% 2.08/1.17 thf(fact_8_lappend__LNil2, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = Xs)))).
% 2.08/1.17 thf(fact_9_lappend__iterates, axiom, (! [A:$tType,F:(A > A),X:A,Xs:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu1529956631erates @ A) @ F) @ X)) @ Xs) = (((coindu1529956631erates @ A) @ F) @ X))))).
% 2.08/1.17 thf(fact_10_lappend_Odisc__iff_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)))) = ((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 2.08/1.17 thf(fact_11_lnull__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu335574135_lnull @ A) @ Xs) & ((coindu335574135_lnull @ A) @ Ys)))))).
% 2.08/1.17 thf(fact_12_lappend__code_I2_J, axiom, (! [A:$tType,Xa:A,X:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu1121789889_LCons @ A) @ Xa) @ X)) @ Ys) = (((coindu1121789889_LCons @ A) @ Xa) @ (((coindu268472904append @ A) @ X) @ Ys)))))).
% 2.08/1.17 thf(fact_13_lfinite__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu1213758845finite @ A) @ Xs) & ((coindu1213758845finite @ A) @ Ys)))))).
% 2.08/1.17 thf(fact_14_llist_Oinject, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A),Y21:A,Y22:(coindu1593790203_llist @ A)]: ((((((coindu1121789889_LCons @ A) @ X21) @ X22) = (((coindu1121789889_LCons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.08/1.17 thf(fact_15_llist__all2__LCons__LCons, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X21:A,X22:(coindu1593790203_llist @ A),Y21:B,Y22:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ R) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) @ (((coindu1121789889_LCons @ B) @ Y21) @ Y22)) = (((R @ X21) @ Y21) & (((((coindu987187967t_all2 @ A) @ B) @ R) @ X22) @ Y22)))))).
% 2.08/1.17 thf(fact_16_lfinite__code_I2_J, axiom, (! [B:$tType,X:B,Xs:(coindu1593790203_llist @ B)]: ((((coindu1213758845finite @ B) @ (((coindu1121789889_LCons @ B) @ X) @ Xs)) = ((coindu1213758845finite @ B) @ Xs))))).
% 2.08/1.17 thf(fact_17_lfinite__LCons, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) = ((coindu1213758845finite @ A) @ Xs))))).
% 2.08/1.17 thf(fact_18_llist__all2__LNil1, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ P) @ (coindu1598213697e_LNil @ A)) @ Xs) = (Xs = (coindu1598213697e_LNil @ B)))))).
% 2.08/1.17 thf(fact_19_llist__all2__LNil2, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o)),Xs:(coindu1593790203_llist @ A)]: (((((((coindu987187967t_all2 @ A) @ B) @ P) @ Xs) @ (coindu1598213697e_LNil @ B)) = (Xs = (coindu1598213697e_LNil @ A)))))).
% 2.08/1.17 thf(fact_20_lfinite__code_I1_J, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) @ (coindu1598213697e_LNil @ A))))).
% 2.08/1.17 thf(fact_21_llength__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1018505716length @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((plus_plus @ extended_enat) @ ((coindu1018505716length @ A) @ Xs)) @ ((coindu1018505716length @ A) @ Ys)))))).
% 2.08/1.17 thf(fact_22_llist_Odisc_I2_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: ((~ (((coindu335574135_lnull @ A) @ (((coindu1121789889_LCons @ A) @ X21) @ X22))))))).
% 2.08/1.17 thf(fact_23_llist_Odisc_I1_J, axiom, (! [A:$tType]: (((coindu335574135_lnull @ A) @ (coindu1598213697e_LNil @ A))))).
% 2.08/1.17 thf(fact_24_llist_OdiscI_I2_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A),X21:A,X22:(coindu1593790203_llist @ A)]: (((Llist = (((coindu1121789889_LCons @ A) @ X21) @ X22)) => (~ (((coindu335574135_lnull @ A) @ Llist))))))).
% 2.08/1.17 thf(fact_25_llist_OdiscI_I1_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: (((Llist = (coindu1598213697e_LNil @ A)) => ((coindu335574135_lnull @ A) @ Llist))))).
% 2.08/1.17 thf(fact_26_llist_Ocollapse_I1_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Llist) => (Llist = (coindu1598213697e_LNil @ A)))))).
% 2.08/1.17 thf(fact_27_llist_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: (((coindu1598213697e_LNil @ A) != (((coindu1121789889_LCons @ A) @ X21) @ X22))))).
% 2.08/1.17 thf(fact_28_llist_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X21:A,Y21:B,X22:(coindu1593790203_llist @ A),Y22:(coindu1593790203_llist @ B)]: ((((R @ X21) @ Y21) => ((((((coindu987187967t_all2 @ A) @ B) @ R) @ X22) @ Y22) => (((((coindu987187967t_all2 @ A) @ B) @ R) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) @ (((coindu1121789889_LCons @ B) @ Y21) @ Y22))))))).
% 2.08/1.17 thf(fact_29_lzip_Oexhaust, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((~ ((((coindu335574135_lnull @ A) @ Xs) | ((coindu335574135_lnull @ B) @ Ys)))) => (~ (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((coindu335574135_lnull @ B) @ Ys)))))))).
% 2.08/1.17 thf(fact_30_iterates_Ocode, axiom, (! [A:$tType]: (((coindu1529956631erates @ A) = (^ [F2:(A > A),X2:A]: ((((coindu1121789889_LCons @ A) @ X2) @ (((coindu1529956631erates @ A) @ F2) @ (F2 @ X2))))))))).
% 2.08/1.17 thf(fact_31_lfinite_Ocases, axiom, (! [A:$tType,A2:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ A2) => ((A2 != (coindu1598213697e_LNil @ A)) => (~ ((! [Xs2:(coindu1593790203_llist @ A)]: (((? [X3:A]: ((A2 = (((coindu1121789889_LCons @ A) @ X3) @ Xs2)))) => (~ (((coindu1213758845finite @ A) @ Xs2))))))))))))).
% 2.08/1.17 thf(fact_32_lfinite_Osimps, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) = (^ [A3:(coindu1593790203_llist @ A)]: (((A3 = (coindu1598213697e_LNil @ A)) | (? [Xs3:(coindu1593790203_llist @ A),X2:A]: (((A3 = (((coindu1121789889_LCons @ A) @ X2) @ Xs3)) & ((coindu1213758845finite @ A) @ Xs3))))))))))).
% 2.08/1.17 thf(fact_33_llist_Oexhaust, axiom, (! [A:$tType,Y:(coindu1593790203_llist @ A)]: (((Y != (coindu1598213697e_LNil @ A)) => (~ ((! [X212:A,X222:(coindu1593790203_llist @ A)]: ((Y != (((coindu1121789889_LCons @ A) @ X212) @ X222)))))))))).
% 2.08/1.17 thf(fact_34_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((Xs != (coindu1598213697e_LNil @ A)) = (? [X2:A,Xs4:(coindu1593790203_llist @ A)]: ((Xs = (((coindu1121789889_LCons @ A) @ X2) @ Xs4)))))))).
% 2.08/1.17 thf(fact_35_not__lnull__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) = (? [X2:A,Xs4:(coindu1593790203_llist @ A)]: ((Xs = (((coindu1121789889_LCons @ A) @ X2) @ Xs4)))))))).
% 2.08/1.17 thf(fact_36_lappend_Oexhaust, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Xs) => (~ (((coindu335574135_lnull @ A) @ Ys)))) => ((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 2.08/1.17 thf(fact_37_lfinite_Oinducts, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: ((((coindu1213758845finite @ A) @ X) => ((P @ (coindu1598213697e_LNil @ A)) => ((! [Xs2:(coindu1593790203_llist @ A),X3:A]: ((((coindu1213758845finite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X3) @ Xs2)))))) => (P @ X))))))).
% 2.08/1.17 thf(fact_38_lnull__def, axiom, (! [A:$tType]: (((coindu335574135_lnull @ A) = (^ [Llist2:(coindu1593790203_llist @ A)]: ((Llist2 = (coindu1598213697e_LNil @ A)))))))).
% 2.08/1.17 thf(fact_39_llist_Orel__cases, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),A2:(coindu1593790203_llist @ A),B2:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ R) @ A2) @ B2) => (((A2 = (coindu1598213697e_LNil @ A)) => (B2 != (coindu1598213697e_LNil @ B))) => (~ ((! [X1:A,X23:(coindu1593790203_llist @ A)]: (((A2 = (((coindu1121789889_LCons @ A) @ X1) @ X23)) => (! [Y1:B,Y2:(coindu1593790203_llist @ B)]: (((B2 = (((coindu1121789889_LCons @ B) @ Y1) @ Y2)) => (((R @ X1) @ Y1) => (~ ((((((coindu987187967t_all2 @ A) @ B) @ R) @ X23) @ Y2))))))))))))))))).
% 2.08/1.17 thf(fact_40_lfinite__iterates, axiom, (! [A:$tType,F:(A > A),X:A]: ((~ (((coindu1213758845finite @ A) @ (((coindu1529956631erates @ A) @ F) @ X))))))).
% 2.08/1.17 thf(fact_41_llist__all2__cases, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => (((Xs = (coindu1598213697e_LNil @ A)) => (Ys != (coindu1598213697e_LNil @ B))) => (~ ((! [X3:A,Xs5:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ X3) @ Xs5)) => (! [Y3:B,Ys2:(coindu1593790203_llist @ B)]: (((Ys = (((coindu1121789889_LCons @ B) @ Y3) @ Ys2)) => (((P @ X3) @ Y3) => (~ ((((((coindu987187967t_all2 @ A) @ B) @ P) @ Xs5) @ Ys2))))))))))))))))).
% 2.08/1.17 thf(fact_42_llist__all2__lnthD, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B),N:nat]: (((((((coindu987187967t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => ((((ord_less @ extended_enat) @ (extended_enat2 @ N)) @ ((coindu1018505716length @ A) @ Xs)) => ((P @ (((coindu749330388e_lnth @ A) @ Xs) @ N)) @ (((coindu749330388e_lnth @ B) @ Ys) @ N))))))).
% 2.08/1.17 thf(fact_43_wlog__linorder__le, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),B2:A,A2:A]: (((! [A4:A,B3:A]: (((((ord_less_eq @ A) @ A4) @ B3) => ((P @ A4) @ B3)))) => ((((P @ B2) @ A2) => ((P @ A2) @ B2)) => ((P @ A2) @ B2))))))))).
% 2.08/1.17 thf(fact_44_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.08/1.17 thf(fact_45_iterates_Odisc__iff, axiom, (! [A:$tType,F:(A > A),X:A]: ((~ (((coindu335574135_lnull @ A) @ (((coindu1529956631erates @ A) @ F) @ X))))))).
% 2.08/1.17 thf(fact_46_llist__all2__LCons1, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),X:A,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ P) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ Ys) = (? [Y4:B,Ys3:(coindu1593790203_llist @ B)]: (((Ys = (((coindu1121789889_LCons @ B) @ Y4) @ Ys3)) & (((P @ X) @ Y4) & (((((coindu987187967t_all2 @ A) @ B) @ P) @ Xs) @ Ys3))))))))).
% 2.08/1.17 thf(fact_47_llist__all2__LCons2, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o)),Xs:(coindu1593790203_llist @ A),Y:B,Ys:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ P) @ Xs) @ (((coindu1121789889_LCons @ B) @ Y) @ Ys)) = (? [X2:A,Xs4:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ X2) @ Xs4)) & (((P @ X2) @ Y) & (((((coindu987187967t_all2 @ A) @ B) @ P) @ Xs4) @ Ys))))))))).
% 2.08/1.17 thf(fact_48_llist__all2__lnthD2, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B),N:nat]: (((((((coindu987187967t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => ((((ord_less @ extended_enat) @ (extended_enat2 @ N)) @ ((coindu1018505716length @ B) @ Ys)) => ((P @ (((coindu749330388e_lnth @ A) @ Xs) @ N)) @ (((coindu749330388e_lnth @ B) @ Ys) @ N))))))).
% 2.08/1.17 thf(fact_49_llist__all2__lnullD, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => (((coindu335574135_lnull @ A) @ Xs) = ((coindu335574135_lnull @ B) @ Ys)))))).
% 2.08/1.17 thf(fact_50_lnull__imp__lfinite, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((coindu1213758845finite @ A) @ Xs))))).
% 2.08/1.17 thf(fact_51_lfinite__rev__induct, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: ((((coindu1213758845finite @ A) @ Xs) => ((P @ (coindu1598213697e_LNil @ A)) => ((! [X3:A,Xs2:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coindu268472904append @ A) @ Xs2) @ (((coindu1121789889_LCons @ A) @ X3) @ (coindu1598213697e_LNil @ A)))))))) => (P @ Xs))))))).
% 2.08/1.17 thf(fact_52_llist__all2__lfiniteD, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => (((coindu1213758845finite @ A) @ Xs) = ((coindu1213758845finite @ B) @ Ys)))))).
% 2.08/1.17 thf(fact_53_llist__all2__llengthD, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => (((coindu1018505716length @ A) @ Xs) = ((coindu1018505716length @ B) @ Ys)))))).
% 2.08/1.17 thf(fact_54_lfinite__LNil, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) @ (coindu1598213697e_LNil @ A))))).
% 2.08/1.17 thf(fact_55_lfinite__llength__enat, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs) => (? [N2:nat]: ((((coindu1018505716length @ A) @ Xs) = (extended_enat2 @ N2)))))))).
% 2.08/1.17 thf(fact_56_llist__all2__LNil__LNil, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: ((((((coindu987187967t_all2 @ A) @ B) @ R) @ (coindu1598213697e_LNil @ A)) @ (coindu1598213697e_LNil @ B))))).
% 2.08/1.17 thf(fact_57_llist__all2__all__lnthI, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B),P:(A > (B > $o))]: (((((coindu1018505716length @ A) @ Xs) = ((coindu1018505716length @ B) @ Ys)) => ((! [N2:nat]: (((((ord_less @ extended_enat) @ (extended_enat2 @ N2)) @ ((coindu1018505716length @ A) @ Xs)) => ((P @ (((coindu749330388e_lnth @ A) @ Xs) @ N2)) @ (((coindu749330388e_lnth @ B) @ Ys) @ N2))))) => (((((coindu987187967t_all2 @ A) @ B) @ P) @ Xs) @ Ys)))))).
% 2.08/1.17 thf(fact_58_llist__all2__LCons__LNil, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),Y21:A,Y22:(coindu1593790203_llist @ A)]: ((~ ((((((coindu987187967t_all2 @ A) @ B) @ R) @ (((coindu1121789889_LCons @ A) @ Y21) @ Y22)) @ (coindu1598213697e_LNil @ B))))))).
% 2.08/1.17 thf(fact_59_llist__all2__LNil__LCons, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),Y21:B,Y22:(coindu1593790203_llist @ B)]: ((~ ((((((coindu987187967t_all2 @ A) @ B) @ R) @ (coindu1598213697e_LNil @ A)) @ (((coindu1121789889_LCons @ B) @ Y21) @ Y22))))))).
% 2.08/1.17 thf(fact_60_lfinite__LConsI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),X:A]: ((((coindu1213758845finite @ A) @ Xs) => ((coindu1213758845finite @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)))))).
% 2.08/1.17 thf(fact_61_llength__eq__enat__lfiniteD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),N:nat]: (((((coindu1018505716length @ A) @ Xs) = (extended_enat2 @ N)) => ((coindu1213758845finite @ A) @ Xs))))).
% 2.08/1.17 thf(fact_62_llist__all2__conv__all__lnth, axiom, (! [B:$tType,A:$tType]: ((((coindu987187967t_all2 @ A) @ B) = (^ [P2:(A > (B > $o)),Xs3:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ B)]: (((((coindu1018505716length @ A) @ Xs3) = ((coindu1018505716length @ B) @ Ys4)) & (! [N3:nat]: (((((ord_less @ extended_enat) @ (extended_enat2 @ N3)) @ ((coindu1018505716length @ B) @ Ys4)) => ((P2 @ (((coindu749330388e_lnth @ A) @ Xs3) @ N3)) @ (((coindu749330388e_lnth @ B) @ Ys4) @ N3)))))))))))).
% 2.08/1.17 thf(fact_63_lfinite__conv__llength__enat, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) = (^ [Xs3:(coindu1593790203_llist @ A)]: ((? [N3:nat]: ((((coindu1018505716length @ A) @ Xs3) = (extended_enat2 @ N3)))))))))).
% 2.08/1.17 thf(fact_64_lappend__eq__lappend__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Us:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Vs:(coindu1593790203_llist @ A)]: (((((coindu1018505716length @ A) @ Xs) = ((coindu1018505716length @ A) @ Us)) => (((((coindu268472904append @ A) @ Xs) @ Ys) = (((coindu268472904append @ A) @ Us) @ Vs)) = ((Xs = Us) & (((coindu1213758845finite @ A) @ Xs) => (Ys = Vs)))))))).
% 2.08/1.17 thf(fact_65_lappend__snocL1__conv__LCons2, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu268472904append @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ (coindu1598213697e_LNil @ A)))) @ Ys) = (((coindu268472904append @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)))))).
% 2.08/1.17 thf(fact_66_lappend_Octr_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu335574135_lnull @ A) @ Ys) => ((((coindu268472904append @ A) @ Xs) @ Ys) = (coindu1598213697e_LNil @ A))))))).
% 2.08/1.17 thf(fact_67_lnth__lappend1, axiom, (! [A:$tType,N:nat,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((ord_less @ extended_enat) @ (extended_enat2 @ N)) @ ((coindu1018505716length @ A) @ Xs)) => ((((coindu749330388e_lnth @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) @ N) = (((coindu749330388e_lnth @ A) @ Xs) @ N)))))).
% 2.08/1.17 thf(fact_68_llist__all2__lappendI, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B),Xs6:(coindu1593790203_llist @ A),Ys5:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => ((((coindu1213758845finite @ A) @ Xs) => (((coindu1213758845finite @ B) @ Ys) => (((((coindu987187967t_all2 @ A) @ B) @ P) @ Xs6) @ Ys5))) => (((((coindu987187967t_all2 @ A) @ B) @ P) @ (((coindu268472904append @ A) @ Xs) @ Xs6)) @ (((coindu268472904append @ B) @ Ys) @ Ys5))))))).
% 2.08/1.17 thf(fact_69_llist_Orel__refl, axiom, (! [B:$tType,Ra:(B > (B > $o)),X:(coindu1593790203_llist @ B)]: (((! [X3:B]: (((Ra @ X3) @ X3))) => (((((coindu987187967t_all2 @ B) @ B) @ Ra) @ X) @ X))))).
% 2.08/1.17 thf(fact_70_llist_Orel__eq, axiom, (! [A:$tType]: (((((coindu987187967t_all2 @ A) @ A) @ (^ [Y5:A,Z:A]: ((Y5 = Z)))) = (^ [Y5:(coindu1593790203_llist @ A),Z:(coindu1593790203_llist @ A)]: ((Y5 = Z))))))).
% 2.08/1.17 thf(fact_71_llist__all2__mono, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B),P3:(A > (B > $o))]: (((((((coindu987187967t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => ((! [X3:A,Y3:B]: ((((P @ X3) @ Y3) => ((P3 @ X3) @ Y3)))) => (((((coindu987187967t_all2 @ A) @ B) @ P3) @ Xs) @ Ys)))))).
% 2.08/1.17 thf(fact_72_lappend__inf, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu1213758845finite @ A) @ Xs))) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Xs))))).
% 2.08/1.17 thf(fact_73_lappend__lnull2, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Ys) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Xs))))).
% 2.08/1.17 thf(fact_74_lappend__lnull1, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Ys))))).
% 2.08/1.17 thf(fact_75_lappend_Odisc_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu335574135_lnull @ A) @ Ys) => ((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys))))))).
% 2.08/1.17 thf(fact_76_lappend_Odisc_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))) => (~ (((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)))))))).
% 2.08/1.17 thf(fact_77_lappend__eq__LNil__iff, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((((coindu268472904append @ A) @ Xs) @ Ys) = (coindu1598213697e_LNil @ A)) = ((Xs = (coindu1598213697e_LNil @ A)) & (Ys = (coindu1598213697e_LNil @ A))))))).
% 2.08/1.17 thf(fact_78_LNil__eq__lappend__iff, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1598213697e_LNil @ A) = (((coindu268472904append @ A) @ Xs) @ Ys)) = ((Xs = (coindu1598213697e_LNil @ A)) & (Ys = (coindu1598213697e_LNil @ A))))))).
% 2.08/1.17 thf(fact_79_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coindu268472904append @ A) @ (coindu1598213697e_LNil @ A)) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 2.08/1.17 thf(fact_80_enat__add__mono, axiom, (! [X:nat,Y:extended_enat,Z2:extended_enat]: (((((ord_less @ extended_enat) @ (((plus_plus @ extended_enat) @ (extended_enat2 @ X)) @ Y)) @ (((plus_plus @ extended_enat) @ (extended_enat2 @ X)) @ Z2)) = (((ord_less @ extended_enat) @ Y) @ Z2))))).
% 2.08/1.17 thf(fact_81_enat__add1__eq, axiom, (! [X:nat,Y:extended_enat,Z2:extended_enat]: ((((((plus_plus @ extended_enat) @ (extended_enat2 @ X)) @ Y) = (((plus_plus @ extended_enat) @ (extended_enat2 @ X)) @ Z2)) = (Y = Z2))))).
% 2.08/1.17 thf(fact_82_enat__add2__eq, axiom, (! [Y:extended_enat,X:nat,Z2:extended_enat]: ((((((plus_plus @ extended_enat) @ Y) @ (extended_enat2 @ X)) = (((plus_plus @ extended_enat) @ Z2) @ (extended_enat2 @ X))) = (Y = Z2))))).
% 2.08/1.17 thf(fact_83_add__less__cancel__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C:A,A2:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2)) = (((ord_less @ A) @ A2) @ B2)))))))).
% 2.08/1.17 thf(fact_84_add__less__cancel__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C)) = (((ord_less @ A) @ A2) @ B2)))))))).
% 2.08/1.17 thf(fact_85_add__le__cancel__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.08/1.17 thf(fact_86_add__le__cancel__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.08/1.17 thf(fact_87_enat__less__imp__le, axiom, (! [N:extended_enat,M:extended_enat]: (((! [K:nat]: (((((ord_less @ extended_enat) @ N) @ (extended_enat2 @ K)) => (((ord_less @ extended_enat) @ M) @ (extended_enat2 @ K))))) => (((ord_less_eq @ extended_enat) @ M) @ N))))).
% 2.08/1.17 thf(fact_88_add__mono__thms__linordered__field_I4_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K2:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (((ord_less @ A) @ K2) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K2)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.08/1.17 thf(fact_89_add__mono__thms__linordered__field_I3_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K2:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (((ord_less_eq @ A) @ K2) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K2)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.08/1.17 thf(fact_90_add__le__less__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A,D:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less @ A) @ C) @ D) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ D)))))))))).
% 2.08/1.17 thf(fact_91_add__right__cancel, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C) @ A2)) = (B2 = C)))))))).
% 2.08/1.17 thf(fact_92_add__left__cancel, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C)) = (B2 = C)))))))).
% 2.08/1.17 thf(fact_93_llist_Orel__mono, axiom, (! [B:$tType,A:$tType,R:(A > (B > $o)),Ra:(A > (B > $o))]: (((((ord_less_eq @ (A > (B > $o))) @ R) @ Ra) => (((ord_less_eq @ ((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ B) > $o))) @ (((coindu987187967t_all2 @ A) @ B) @ R)) @ (((coindu987187967t_all2 @ A) @ B) @ Ra)))))).
% 2.08/1.17 thf(fact_94_enat__less__enat__plusI2, axiom, (! [Y:nat,Z2:extended_enat,X:nat]: (((((ord_less @ extended_enat) @ (extended_enat2 @ Y)) @ Z2) => (((ord_less @ extended_enat) @ (extended_enat2 @ (((plus_plus @ nat) @ X) @ Y))) @ (((plus_plus @ extended_enat) @ (extended_enat2 @ X)) @ Z2)))))).
% 2.08/1.17 thf(fact_95_enat__less__enat__plusI, axiom, (! [X:nat,Y:nat,Z2:extended_enat]: (((((ord_less @ nat) @ X) @ Y) => (((ord_less @ extended_enat) @ (extended_enat2 @ X)) @ (((plus_plus @ extended_enat) @ (extended_enat2 @ Y)) @ Z2)))))).
% 2.08/1.17 thf(fact_96_add__right__imp__eq, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C) @ A2)) => (B2 = C)))))))).
% 2.08/1.17 thf(fact_97_add__left__imp__eq, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C)) => (B2 = C)))))))).
% 2.08/1.17 thf(fact_98_add_Oleft__commute, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C:A]: (((((plus_plus @ A) @ B2) @ (((plus_plus @ A) @ A2) @ C)) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C))))))))).
% 2.08/1.17 thf(fact_99_add_Ocommute, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A3:A,B4:A]: ((((plus_plus @ A) @ B4) @ A3)))))))).
% 2.08/1.17 thf(fact_100_add_Oright__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C:A]: ((((((plus_plus @ A) @ B2) @ A2) = (((plus_plus @ A) @ C) @ A2)) = (B2 = C)))))))).
% 2.08/1.17 thf(fact_101_add_Oleft__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: ((((((plus_plus @ A) @ A2) @ B2) = (((plus_plus @ A) @ A2) @ C)) = (B2 = C)))))))).
% 2.08/1.17 thf(fact_102_add_Oassoc, axiom, (! [A:$tType]: ((((semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C))))))))).
% 2.08/1.17 thf(fact_103_add__mono__thms__linordered__semiring_I4_J, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K2:A,L:A]: ((((I = J) & (K2 = L)) => ((((plus_plus @ A) @ I) @ K2) = (((plus_plus @ A) @ J) @ L))))))))).
% 2.08/1.17 thf(fact_104_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A2) @ B2)) @ C) = (((plus_plus @ A) @ A2) @ (((plus_plus @ A) @ B2) @ C))))))))).
% 2.08/1.17 thf(fact_105_add__le__imp__le__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.08/1.17 thf(fact_106_add__le__imp__le__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 2.08/1.17 thf(fact_107_le__iff__add, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [A3:A,B4:A]: ((? [C2:A]: ((B4 = (((plus_plus @ A) @ A3) @ C2))))))))))).
% 2.08/1.17 thf(fact_108_add__right__mono, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C))))))))).
% 2.08/1.17 thf(fact_109_add__left__mono, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2))))))))).
% 2.08/1.17 thf(fact_110_add__mono, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A,D:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C) @ D) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ D)))))))))).
% 2.08/1.17 thf(fact_111_add__mono__thms__linordered__semiring_I1_J, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K2:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (((ord_less_eq @ A) @ K2) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K2)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.08/1.17 thf(fact_112_add__mono__thms__linordered__semiring_I2_J, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K2:A,L:A]: ((((I = J) & (((ord_less_eq @ A) @ K2) @ L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K2)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.08/1.17 thf(fact_113_add__mono__thms__linordered__semiring_I3_J, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K2:A,L:A]: ((((((ord_less_eq @ A) @ I) @ J) & (K2 = L)) => (((ord_less_eq @ A) @ (((plus_plus @ A) @ I) @ K2)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.08/1.17 thf(fact_114_add__less__imp__less__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A2:A,C:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C)) => (((ord_less @ A) @ A2) @ B2)))))))).
% 2.08/1.17 thf(fact_115_add__less__imp__less__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C:A,A2:A,B2:A]: (((((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2)) => (((ord_less @ A) @ A2) @ B2)))))))).
% 2.08/1.17 thf(fact_116_add__strict__right__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ C))))))))).
% 2.08/1.17 thf(fact_117_add__strict__left__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => (((ord_less @ A) @ (((plus_plus @ A) @ C) @ A2)) @ (((plus_plus @ A) @ C) @ B2))))))))).
% 2.08/1.17 thf(fact_118_add__strict__mono, axiom, (! [A:$tType]: ((((strict2144017051up_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A,D:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ C) @ D) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ D)))))))))).
% 2.08/1.17 thf(fact_119_add__mono__thms__linordered__field_I1_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K2:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (K2 = L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K2)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.08/1.17 thf(fact_120_add__mono__thms__linordered__field_I2_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K2:A,L:A]: ((((I = J) & (((ord_less @ A) @ K2) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K2)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.08/1.17 thf(fact_121_add__mono__thms__linordered__field_I5_J, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K2:A,L:A]: ((((((ord_less @ A) @ I) @ J) & (((ord_less @ A) @ K2) @ L)) => (((ord_less @ A) @ (((plus_plus @ A) @ I) @ K2)) @ (((plus_plus @ A) @ J) @ L))))))))).
% 2.08/1.17 thf(fact_122_enat__le__plus__same_I1_J, axiom, (! [X:extended_enat,Y:extended_enat]: ((((ord_less_eq @ extended_enat) @ X) @ (((plus_plus @ extended_enat) @ X) @ Y))))).
% 2.08/1.17 thf(fact_123_enat__le__plus__same_I2_J, axiom, (! [X:extended_enat,Y:extended_enat]: ((((ord_less_eq @ extended_enat) @ X) @ (((plus_plus @ extended_enat) @ Y) @ X))))).
% 2.08/1.17 thf(fact_124_add__less__le__mono, axiom, (! [A:$tType]: ((((ordere223160158up_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A,D:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ C) @ D) => (((ord_less @ A) @ (((plus_plus @ A) @ A2) @ C)) @ (((plus_plus @ A) @ B2) @ D)))))))))).
% 2.08/1.17 thf(fact_125_plus__enat__simps_I1_J, axiom, (! [M:nat,N:nat]: (((((plus_plus @ extended_enat) @ (extended_enat2 @ M)) @ (extended_enat2 @ N)) = (extended_enat2 @ (((plus_plus @ nat) @ M) @ N)))))).
% 2.08/1.17 thf(fact_126_enat__ord__simps_I2_J, axiom, (! [M:nat,N:nat]: (((((ord_less @ extended_enat) @ (extended_enat2 @ M)) @ (extended_enat2 @ N)) = (((ord_less @ nat) @ M) @ N))))).
% 2.08/1.17 thf(fact_127_enat__ord__simps_I1_J, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ extended_enat) @ (extended_enat2 @ M)) @ (extended_enat2 @ N)) = (((ord_less_eq @ nat) @ M) @ N))))).
% 2.08/1.17 thf(fact_128_iadd__le__enat__iff, axiom, (! [X:extended_enat,Y:extended_enat,N:nat]: (((((ord_less_eq @ extended_enat) @ (((plus_plus @ extended_enat) @ X) @ Y)) @ (extended_enat2 @ N)) = (? [Y6:nat,X4:nat]: (((X = (extended_enat2 @ X4)) & ((Y = (extended_enat2 @ Y6)) & (((ord_less_eq @ nat) @ (((plus_plus @ nat) @ X4) @ Y6)) @ N))))))))).
% 2.08/1.17 thf(fact_129_enat_Oinject, axiom, (! [Nat:nat,Nat2:nat]: ((((extended_enat2 @ Nat) = (extended_enat2 @ Nat2)) = (Nat = Nat2))))).
% 2.08/1.17 thf(fact_130_enat__less__induct, axiom, (! [P:(extended_enat > $o),N:extended_enat]: (((! [N2:extended_enat]: (((! [M2:extended_enat]: (((((ord_less @ extended_enat) @ M2) @ N2) => (P @ M2)))) => (P @ N2)))) => (P @ N))))).
% 2.08/1.17 thf(fact_131_enat__ile, axiom, (! [N:extended_enat,M:nat]: (((((ord_less_eq @ extended_enat) @ N) @ (extended_enat2 @ M)) => (? [K:nat]: ((N = (extended_enat2 @ K)))))))).
% 2.08/1.17 thf(fact_132_chain__incr, axiom, (! [A:$tType,Y7:(A > extended_enat),K2:nat]: (((! [I2:A]: ((? [J2:A]: ((((ord_less @ extended_enat) @ (Y7 @ I2)) @ (Y7 @ J2)))))) => (? [J3:A]: ((((ord_less @ extended_enat) @ (extended_enat2 @ K2)) @ (Y7 @ J3)))))))).
% 2.08/1.17 thf(fact_133_enat__iless, axiom, (! [N:extended_enat,M:nat]: (((((ord_less @ extended_enat) @ N) @ (extended_enat2 @ M)) => (? [K:nat]: ((N = (extended_enat2 @ K)))))))).
% 2.08/1.17 thf(fact_134_less__enatE, axiom, (! [N:extended_enat,M:nat]: (((((ord_less @ extended_enat) @ N) @ (extended_enat2 @ M)) => (~ ((! [K:nat]: (((N = (extended_enat2 @ K)) => (~ ((((ord_less @ nat) @ K) @ M)))))))))))).
% 2.08/1.17 thf(fact_135_nat__add__left__cancel__le, axiom, (! [K2:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ K2) @ M)) @ (((plus_plus @ nat) @ K2) @ N)) = (((ord_less_eq @ nat) @ M) @ N))))).
% 2.08/1.17 thf(fact_136_nat__add__left__cancel__less, axiom, (! [K2:nat,M:nat,N:nat]: (((((ord_less @ nat) @ (((plus_plus @ nat) @ K2) @ M)) @ (((plus_plus @ nat) @ K2) @ N)) = (((ord_less @ nat) @ M) @ N))))).
% 2.08/1.17 thf(fact_137_mono__nat__linear__lb, axiom, (! [F:(nat > nat),M:nat,K2:nat]: (((! [M3:nat,N2:nat]: (((((ord_less @ nat) @ M3) @ N2) => (((ord_less @ nat) @ (F @ M3)) @ (F @ N2))))) => (((ord_less_eq @ nat) @ (((plus_plus @ nat) @ (F @ M)) @ K2)) @ (F @ (((plus_plus @ nat) @ M) @ K2))))))).
% 2.08/1.17 thf(fact_138_ex__has__greatest__nat__lemma, axiom, (! [A:$tType,P:(A > $o),K2:A,M:(A > nat),N:nat]: (((P @ K2) => ((! [X3:A]: (((P @ X3) => (? [Y8:A]: (((P @ Y8) & (~ ((((ord_less_eq @ nat) @ (M @ Y8)) @ (M @ X3)))))))))) => (? [Y3:A]: (((P @ Y3) & (~ ((((ord_less @ nat) @ (M @ Y3)) @ (((plus_plus @ nat) @ (M @ K2)) @ N)))))))))))).
% 2.08/1.17 thf(fact_139_infinite__descent__measure, axiom, (! [A:$tType,P:(A > $o),V:(A > nat),X:A]: (((! [X3:A]: (((~ ((P @ X3))) => (? [Y8:A]: (((((ord_less @ nat) @ (V @ Y8)) @ (V @ X3)) & (~ ((P @ Y8))))))))) => (P @ X))))).
% 2.08/1.17 thf(fact_140_measure__induct__rule, axiom, (! [A:$tType,F:(A > nat),P:(A > $o),A2:A]: (((! [X3:A]: (((! [Y8:A]: (((((ord_less @ nat) @ (F @ Y8)) @ (F @ X3)) => (P @ Y8)))) => (P @ X3)))) => (P @ A2))))).
% 2.08/1.17 thf(fact_141_linorder__neqE__nat, axiom, (! [X:nat,Y:nat]: (((X != Y) => ((~ ((((ord_less @ nat) @ X) @ Y))) => (((ord_less @ nat) @ Y) @ X)))))).
% 2.08/1.17 thf(fact_142_infinite__descent, axiom, (! [P:(nat > $o),N:nat]: (((! [N2:nat]: (((~ ((P @ N2))) => (? [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) & (~ ((P @ M2))))))))) => (P @ N))))).
% 2.08/1.17 thf(fact_143_nat__less__induct, axiom, (! [P:(nat > $o),N:nat]: (((! [N2:nat]: (((! [M2:nat]: (((((ord_less @ nat) @ M2) @ N2) => (P @ M2)))) => (P @ N2)))) => (P @ N))))).
% 2.08/1.17 thf(fact_144_less__irrefl__nat, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.08/1.17 thf(fact_145_measure__induct, axiom, (! [A:$tType,F:(A > nat),P:(A > $o),A2:A]: (((! [X3:A]: (((! [Y8:A]: (((((ord_less @ nat) @ (F @ Y8)) @ (F @ X3)) => (P @ Y8)))) => (P @ X3)))) => (P @ A2))))).
% 2.08/1.17 thf(fact_146_less__not__refl3, axiom, (! [S:nat,T:nat]: (((((ord_less @ nat) @ S) @ T) => (S != T))))).
% 2.08/1.17 thf(fact_147_less__not__refl2, axiom, (! [N:nat,M:nat]: (((((ord_less @ nat) @ N) @ M) => (M != N))))).
% 2.08/1.17 thf(fact_148_less__not__refl, axiom, (! [N:nat]: ((~ ((((ord_less @ nat) @ N) @ N)))))).
% 2.08/1.17 thf(fact_149_nat__neq__iff, axiom, (! [M:nat,N:nat]: (((M != N) = ((((ord_less @ nat) @ M) @ N) | (((ord_less @ nat) @ N) @ M)))))).
% 2.08/1.17 thf(fact_150_ex__has__least__nat, axiom, (! [A:$tType,P:(A > $o),K2:A,M:(A > nat)]: (((P @ K2) => (? [X3:A]: (((P @ X3) & (! [Y8:A]: (((P @ Y8) => (((ord_less_eq @ nat) @ (M @ X3)) @ (M @ Y8)))))))))))).
% 2.08/1.17 thf(fact_151_nat__le__linear, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) | (((ord_less_eq @ nat) @ N) @ M))))).
% 2.08/1.17 thf(fact_152_le__antisym, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((ord_less_eq @ nat) @ N) @ M) => (M = N)))))).
% 2.08/1.17 thf(fact_153_eq__imp__le, axiom, (! [M:nat,N:nat]: (((M = N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.08/1.17 thf(fact_154_le__trans, axiom, (! [I:nat,J:nat,K2:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((ord_less_eq @ nat) @ J) @ K2) => (((ord_less_eq @ nat) @ I) @ K2)))))).
% 2.08/1.17 thf(fact_155_le__refl, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ N) @ N)))).
% 2.08/1.17 thf(fact_156_nat__add__right__cancel, axiom, (! [M:nat,K2:nat,N:nat]: ((((((plus_plus @ nat) @ M) @ K2) = (((plus_plus @ nat) @ N) @ K2)) = (M = N))))).
% 2.08/1.17 thf(fact_157_nat__add__left__cancel, axiom, (! [K2:nat,M:nat,N:nat]: ((((((plus_plus @ nat) @ K2) @ M) = (((plus_plus @ nat) @ K2) @ N)) = (M = N))))).
% 2.08/1.17 thf(fact_158_ex__has__greatest__nat, axiom, (! [A:$tType,P:(A > $o),K2:A,M:(A > nat),B2:nat]: (((P @ K2) => ((! [Y3:A]: (((P @ Y3) => (((ord_less @ nat) @ (M @ Y3)) @ B2)))) => (? [X3:A]: (((P @ X3) & (! [Y8:A]: (((P @ Y8) => (((ord_less_eq @ nat) @ (M @ Y8)) @ (M @ X3))))))))))))).
% 2.08/1.17 thf(fact_159_less__mono__imp__le__mono, axiom, (! [F:(nat > nat),I:nat,J:nat]: (((! [I2:nat,J3:nat]: (((((ord_less @ nat) @ I2) @ J3) => (((ord_less @ nat) @ (F @ I2)) @ (F @ J3))))) => ((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (F @ I)) @ (F @ J))))))).
% 2.08/1.17 thf(fact_160_le__neq__implies__less, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((M != N) => (((ord_less @ nat) @ M) @ N)))))).
% 2.08/1.17 thf(fact_161_less__or__eq__imp__le, axiom, (! [M:nat,N:nat]: ((((((ord_less @ nat) @ M) @ N) | (M = N)) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.08/1.17 thf(fact_162_le__eq__less__or__eq, axiom, ((ord_less_eq @ nat) = (^ [M4:nat,N3:nat]: (((((ord_less @ nat) @ M4) @ N3) | (M4 = N3)))))).
% 2.08/1.17 thf(fact_163_less__imp__le__nat, axiom, (! [M:nat,N:nat]: (((((ord_less @ nat) @ M) @ N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.08/1.17 thf(fact_164_nat__less__le, axiom, ((ord_less @ nat) = (^ [M4:nat,N3:nat]: (((((ord_less_eq @ nat) @ M4) @ N3) & (M4 != N3)))))).
% 2.08/1.17 thf(fact_165_less__add__eq__less, axiom, (! [K2:nat,L:nat,M:nat,N:nat]: (((((ord_less @ nat) @ K2) @ L) => (((((plus_plus @ nat) @ M) @ L) = (((plus_plus @ nat) @ K2) @ N)) => (((ord_less @ nat) @ M) @ N)))))).
% 2.08/1.17 thf(fact_166_trans__less__add2, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ I) @ (((plus_plus @ nat) @ M) @ J)))))).
% 2.08/1.17 thf(fact_167_trans__less__add1, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ I) @ (((plus_plus @ nat) @ J) @ M)))))).
% 2.08/1.17 thf(fact_168_add__less__mono1, axiom, (! [I:nat,J:nat,K2:nat]: (((((ord_less @ nat) @ I) @ J) => (((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ K2)) @ (((plus_plus @ nat) @ J) @ K2)))))).
% 2.08/1.17 thf(fact_169_not__add__less2, axiom, (! [J:nat,I:nat]: ((~ ((((ord_less @ nat) @ (((plus_plus @ nat) @ J) @ I)) @ I)))))).
% 2.08/1.17 thf(fact_170_not__add__less1, axiom, (! [I:nat,J:nat]: ((~ ((((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ J)) @ I)))))).
% 2.08/1.17 thf(fact_171_add__less__mono, axiom, (! [I:nat,J:nat,K2:nat,L:nat]: (((((ord_less @ nat) @ I) @ J) => ((((ord_less @ nat) @ K2) @ L) => (((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ K2)) @ (((plus_plus @ nat) @ J) @ L))))))).
% 2.08/1.17 thf(fact_172_add__lessD1, axiom, (! [I:nat,J:nat,K2:nat]: (((((ord_less @ nat) @ (((plus_plus @ nat) @ I) @ J)) @ K2) => (((ord_less @ nat) @ I) @ K2))))).
% 2.08/1.17 thf(fact_173_nat__le__iff__add, axiom, ((ord_less_eq @ nat) = (^ [M4:nat,N3:nat]: ((? [K3:nat]: ((N3 = (((plus_plus @ nat) @ M4) @ K3)))))))).
% 2.08/1.17 thf(fact_174_trans__le__add2, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ I) @ (((plus_plus @ nat) @ M) @ J)))))).
% 2.08/1.17 thf(fact_175_trans__le__add1, axiom, (! [I:nat,J:nat,M:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ I) @ (((plus_plus @ nat) @ J) @ M)))))).
% 2.08/1.17 thf(fact_176_add__le__mono1, axiom, (! [I:nat,J:nat,K2:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (((plus_plus @ nat) @ I) @ K2)) @ (((plus_plus @ nat) @ J) @ K2)))))).
% 2.08/1.17 thf(fact_177_add__le__mono, axiom, (! [I:nat,J:nat,K2:nat,L:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((ord_less_eq @ nat) @ K2) @ L) => (((ord_less_eq @ nat) @ (((plus_plus @ nat) @ I) @ K2)) @ (((plus_plus @ nat) @ J) @ L))))))).
% 2.08/1.17 thf(fact_178_le__Suc__ex, axiom, (! [K2:nat,L:nat]: (((((ord_less_eq @ nat) @ K2) @ L) => (? [N2:nat]: ((L = (((plus_plus @ nat) @ K2) @ N2)))))))).
% 2.08/1.17 thf(fact_179_add__leD2, axiom, (! [M:nat,K2:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ M) @ K2)) @ N) => (((ord_less_eq @ nat) @ K2) @ N))))).
% 2.08/1.17 thf(fact_180_add__leD1, axiom, (! [M:nat,K2:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ M) @ K2)) @ N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 2.08/1.17 thf(fact_181_le__add2, axiom, (! [N:nat,M:nat]: ((((ord_less_eq @ nat) @ N) @ (((plus_plus @ nat) @ M) @ N))))).
% 2.08/1.17 thf(fact_182_le__add1, axiom, (! [N:nat,M:nat]: ((((ord_less_eq @ nat) @ N) @ (((plus_plus @ nat) @ N) @ M))))).
% 2.08/1.17 thf(fact_183_add__leE, axiom, (! [M:nat,K2:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ M) @ K2)) @ N) => (~ (((((ord_less_eq @ nat) @ M) @ N) => (~ ((((ord_less_eq @ nat) @ K2) @ N)))))))))).
% 2.08/1.17 thf(fact_184_predicate2I, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o)),Q:(A > (B > $o))]: (((! [X3:A,Y3:B]: ((((P @ X3) @ Y3) => ((Q @ X3) @ Y3)))) => (((ord_less_eq @ (A > (B > $o))) @ P) @ Q))))).
% 2.08/1.17 thf(fact_185_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 2.08/1.17 thf(fact_186_gen__llength__def, axiom, (! [A:$tType]: (((coindu493225792length @ A) = (^ [N3:nat,Xs3:(coindu1593790203_llist @ A)]: ((((plus_plus @ extended_enat) @ (extended_enat2 @ N3)) @ ((coindu1018505716length @ A) @ Xs3)))))))).
% 2.08/1.17 thf(fact_187_le__fun__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: ((! [X2:A]: ((((ord_less_eq @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))))).
% 2.08/1.17 thf(fact_188_order__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B2:B,C:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X3:B,Y3:B]: (((((ord_less_eq @ B) @ X3) @ Y3) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 2.08/1.17 thf(fact_189_order__subst2, axiom, (! [A:$tType,C3:$tType]: (((((order @ C3) @ (type2 @ C3)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B2:A,F:(A > C3),C:C3]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C3) @ (F @ B2)) @ C) => ((! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => (((ord_less_eq @ C3) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less_eq @ C3) @ (F @ A2)) @ C)))))))))).
% 2.08/1.17 thf(fact_190_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B2:B,C:B]: (((A2 = (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X3:B,Y3:B]: (((((ord_less_eq @ B) @ X3) @ Y3) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 2.08/1.17 thf(fact_191_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,B2:A,F:(A > B),C:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F @ B2) = C) => ((! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => (((ord_less_eq @ B) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less_eq @ B) @ (F @ A2)) @ C)))))))))).
% 2.08/1.17 thf(fact_192_eq__iff, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((^ [Y5:A,Z:A]: ((Y5 = Z))) = (^ [X2:A,Y4:A]: (((((ord_less_eq @ A) @ X2) @ Y4) & (((ord_less_eq @ A) @ Y4) @ X2))))))))).
% 2.08/1.17 thf(fact_193_antisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 2.08/1.17 thf(fact_194_linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.08/1.17 thf(fact_195_eq__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X = Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 2.08/1.17 thf(fact_196_le__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.08/1.17 thf(fact_197_order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 2.08/1.17 thf(fact_198_le__cases3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z2:A]: ((((((ord_less_eq @ A) @ X) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z2)))) => (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z2)))) => (((((ord_less_eq @ A) @ X) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y)))) => (((((ord_less_eq @ A) @ Z2) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X)))) => (((((ord_less_eq @ A) @ Y) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y))))))))))))))))).
% 2.08/1.17 thf(fact_199_antisym__conv, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 2.08/1.17 thf(fact_200_ord__eq__le__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 2.08/1.17 thf(fact_201_ord__le__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 2.08/1.17 thf(fact_202_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 2.08/1.17 thf(fact_203_order__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z2:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z2) => (((ord_less_eq @ A) @ X) @ Z2))))))))).
% 2.08/1.17 thf(fact_204_dual__order_Orefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 2.08/1.17 thf(fact_205_linorder__wlog, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A4:A,B3:A]: (((((ord_less_eq @ A) @ A4) @ B3) => ((P @ A4) @ B3)))) => ((! [A4:A,B3:A]: ((((P @ B3) @ A4) => ((P @ A4) @ B3)))) => ((P @ A2) @ B2))))))))).
% 2.08/1.17 thf(fact_206_dual__order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C) @ B2) => (((ord_less_eq @ A) @ C) @ A2))))))))).
% 2.08/1.17 thf(fact_207_dual__order_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 2.08/1.17 thf(fact_208_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B2:B,C:B]: (((A2 = (F @ B2)) => ((((ord_less @ B) @ B2) @ C) => ((! [X3:B,Y3:B]: (((((ord_less @ B) @ X3) @ Y3) => (((ord_less @ A) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 2.08/1.17 thf(fact_209_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,B2:A,F:(A > B),C:B]: (((((ord_less @ A) @ A2) @ B2) => (((F @ B2) = C) => ((! [X3:A,Y3:A]: (((((ord_less @ A) @ X3) @ Y3) => (((ord_less @ B) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less @ B) @ (F @ A2)) @ C)))))))))).
% 2.08/1.17 thf(fact_210_order__less__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B2:B,C:B]: (((((ord_less @ A) @ A2) @ (F @ B2)) => ((((ord_less @ B) @ B2) @ C) => ((! [X3:B,Y3:B]: (((((ord_less @ B) @ X3) @ Y3) => (((ord_less @ A) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 2.08/1.17 thf(fact_211_order__less__subst2, axiom, (! [A:$tType,C3:$tType]: (((((order @ C3) @ (type2 @ C3)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B2:A,F:(A > C3),C:C3]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ C3) @ (F @ B2)) @ C) => ((! [X3:A,Y3:A]: (((((ord_less @ A) @ X3) @ Y3) => (((ord_less @ C3) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less @ C3) @ (F @ A2)) @ C)))))))))).
% 2.08/1.17 thf(fact_212_lt__ex, axiom, (! [A:$tType]: ((((no_bot @ A) @ (type2 @ A)) => (! [X:A]: ((? [Y3:A]: ((((ord_less @ A) @ Y3) @ X))))))))).
% 2.08/1.17 thf(fact_213_gt__ex, axiom, (! [A:$tType]: ((((no_top @ A) @ (type2 @ A)) => (! [X:A]: ((? [X1:A]: ((((ord_less @ A) @ X) @ X1))))))))).
% 2.08/1.17 thf(fact_214_neqE, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X != Y) => ((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less @ A) @ Y) @ X))))))))).
% 2.08/1.17 thf(fact_215_neq__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X != Y) = ((((ord_less @ A) @ X) @ Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 2.08/1.17 thf(fact_216_order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (~ ((((ord_less @ A) @ B2) @ A2)))))))))).
% 2.08/1.17 thf(fact_217_dense, axiom, (! [A:$tType]: ((((dense_order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (? [Z3:A]: (((((ord_less @ A) @ X) @ Z3) & (((ord_less @ A) @ Z3) @ Y))))))))))).
% 2.08/1.17 thf(fact_218_less__imp__neq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 2.08/1.17 thf(fact_219_less__asym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 2.08/1.17 thf(fact_220_less__asym_H, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (~ ((((ord_less @ A) @ B2) @ A2)))))))))).
% 2.08/1.17 thf(fact_221_less__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z2:A]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ Z2) => (((ord_less @ A) @ X) @ Z2))))))))).
% 2.08/1.17 thf(fact_222_less__linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) | ((X = Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 2.08/1.17 thf(fact_223_less__irrefl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((~ ((((ord_less @ A) @ X) @ X))))))))).
% 2.08/1.17 thf(fact_224_ord__eq__less__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((A2 = B2) => ((((ord_less @ A) @ B2) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 2.08/1.17 thf(fact_225_ord__less__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => ((B2 = C) => (((ord_less @ A) @ A2) @ C))))))))).
% 2.08/1.17 thf(fact_226_dual__order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: (((((ord_less @ A) @ B2) @ A2) => (~ ((((ord_less @ A) @ A2) @ B2)))))))))).
% 2.08/1.17 thf(fact_227_less__imp__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 2.08/1.17 thf(fact_228_less__not__sym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 2.08/1.17 thf(fact_229_less__induct, axiom, (! [A:$tType]: ((((wellorder @ A) @ (type2 @ A)) => (! [P:(A > $o),A2:A]: (((! [X3:A]: (((! [Y8:A]: (((((ord_less @ A) @ Y8) @ X3) => (P @ Y8)))) => (P @ X3)))) => (P @ A2)))))))).
% 2.08/1.17 thf(fact_230_antisym__conv3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((~ ((((ord_less @ A) @ Y) @ X))) => ((~ ((((ord_less @ A) @ X) @ Y))) = (X = Y))))))))).
% 2.08/1.17 thf(fact_231_less__imp__not__eq2, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (Y != X)))))))).
% 2.08/1.17 thf(fact_232_less__imp__triv, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,P:$o]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ X) => P)))))))).
% 2.08/1.17 thf(fact_233_linorder__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) => ((X != Y) => (((ord_less @ A) @ Y) @ X))))))))).
% 2.08/1.17 thf(fact_234_dual__order_Oirrefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A]: ((~ ((((ord_less @ A) @ A2) @ A2))))))))).
% 2.08/1.17 thf(fact_235_order_Ostrict__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less @ A) @ B2) @ C) => (((ord_less @ A) @ A2) @ C))))))))).
% 2.08/1.17 thf(fact_236_less__imp__not__less, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 2.08/1.17 thf(fact_237_dual__order_Ostrict__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C:A]: (((((ord_less @ A) @ B2) @ A2) => ((((ord_less @ A) @ C) @ B2) => (((ord_less @ A) @ C) @ A2))))))))).
% 2.08/1.17 thf(fact_238_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) = ((((ord_less @ A) @ Y) @ X) | (X = Y))))))))).
% 2.08/1.17 thf(fact_239_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less @ A) @ A2) @ B2) => (A2 != B2)))))))).
% 2.08/1.17 thf(fact_240_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: (((((ord_less @ A) @ B2) @ A2) => (A2 != B2)))))))).
% 2.08/1.17 thf(fact_241_less__fun__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => ((ord_less @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: (((((ord_less_eq @ (A > B)) @ F2) @ G2) & (~ ((((ord_less_eq @ (A > B)) @ G2) @ F2))))))))))).
% 2.08/1.17 thf(fact_242_predicate2D, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Q:(A > (B > $o)),X:A,Y:B]: (((((ord_less_eq @ (A > (B > $o))) @ P) @ Q) => (((P @ X) @ Y) => ((Q @ X) @ Y)))))).
% 2.08/1.17 thf(fact_243_rev__predicate2D, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),X:A,Y:B,Q:(A > (B > $o))]: ((((P @ X) @ Y) => ((((ord_less_eq @ (A > (B > $o))) @ P) @ Q) => ((Q @ X) @ Y)))))).
% 2.08/1.17 thf(fact_244_gen__llength__code_I1_J, axiom, (! [A:$tType,N:nat]: (((((coindu493225792length @ A) @ N) @ (coindu1598213697e_LNil @ A)) = (extended_enat2 @ N))))).
% 2.08/1.17 thf(fact_245_leD, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less @ A) @ X) @ Y)))))))))).
% 2.08/1.17 thf(fact_246_leI, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.08/1.17 thf(fact_247_le__less, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [X2:A,Y4:A]: (((((ord_less @ A) @ X2) @ Y4) | (X2 = Y4))))))))).
% 2.08/1.17 thf(fact_248_less__le, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [X2:A,Y4:A]: (((((ord_less_eq @ A) @ X2) @ Y4) & (X2 != Y4))))))))).
% 2.08/1.17 thf(fact_249_order__le__less__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B2:B,C:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B2)) => ((((ord_less @ B) @ B2) @ C) => ((! [X3:B,Y3:B]: (((((ord_less @ B) @ X3) @ Y3) => (((ord_less @ A) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 2.08/1.17 thf(fact_250_order__le__less__subst2, axiom, (! [A:$tType,C3:$tType]: (((((order @ C3) @ (type2 @ C3)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B2:A,F:(A > C3),C:C3]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less @ C3) @ (F @ B2)) @ C) => ((! [X3:A,Y3:A]: (((((ord_less_eq @ A) @ X3) @ Y3) => (((ord_less_eq @ C3) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less @ C3) @ (F @ A2)) @ C)))))))))).
% 2.08/1.17 thf(fact_251_order__less__le__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B2:B,C:B]: (((((ord_less @ A) @ A2) @ (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X3:B,Y3:B]: (((((ord_less_eq @ B) @ X3) @ Y3) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less @ A) @ A2) @ (F @ C))))))))))).
% 2.08/1.17 thf(fact_252_order__less__le__subst2, axiom, (! [A:$tType,C3:$tType]: (((((order @ C3) @ (type2 @ C3)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B2:A,F:(A > C3),C:C3]: (((((ord_less @ A) @ A2) @ B2) => ((((ord_less_eq @ C3) @ (F @ B2)) @ C) => ((! [X3:A,Y3:A]: (((((ord_less @ A) @ X3) @ Y3) => (((ord_less @ C3) @ (F @ X3)) @ (F @ Y3))))) => (((ord_less @ C3) @ (F @ A2)) @ C)))))))))).
% 2.08/1.17 thf(fact_253_not__le, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) = (((ord_less @ A) @ Y) @ X)))))))).
% 2.08/1.17 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A5:$tType,A6:$tType]: ((((preorder @ A6) @ (type2 @ A6)) => ((preorder @ (A5 > A6)) @ (type2 @ (A5 > A6))))))).
% 2.08/1.17 thf(tcon_fun___Orderings_Oorder, axiom, (! [A5:$tType,A6:$tType]: ((((order @ A6) @ (type2 @ A6)) => ((order @ (A5 > A6)) @ (type2 @ (A5 > A6))))))).
% 2.08/1.17 thf(tcon_fun___Orderings_Oord, axiom, (! [A5:$tType,A6:$tType]: ((((ord @ A6) @ (type2 @ A6)) => ((ord @ (A5 > A6)) @ (type2 @ (A5 > A6))))))).
% 2.08/1.17 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add, axiom, ((strict2144017051up_add @ nat) @ (type2 @ nat))).
% 2.08/1.17 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, axiom, ((ordere223160158up_add @ nat) @ (type2 @ nat))).
% 2.08/1.17 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, axiom, ((ordere236663937imp_le @ nat) @ (type2 @ nat))).
% 2.08/1.17 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, ((canoni770627133id_add @ nat) @ (type2 @ nat))).
% 2.08/1.17 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, axiom, ((ordere779506340up_add @ nat) @ (type2 @ nat))).
% 2.08/1.17 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add, axiom, ((cancel_semigroup_add @ nat) @ (type2 @ nat))).
% 2.08/1.17 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add, axiom, ((ab_semigroup_add @ nat) @ (type2 @ nat))).
% 2.08/1.17 thf(tcon_Nat_Onat___Groups_Osemigroup__add, axiom, ((semigroup_add @ nat) @ (type2 @ nat))).
% 2.08/1.17 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, ((wellorder @ nat) @ (type2 @ nat))).
% 2.08/1.17 thf(tcon_Nat_Onat___Orderings_Opreorder_1, axiom, ((preorder @ nat) @ (type2 @ nat))).
% 2.08/1.17 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, ((linorder @ nat) @ (type2 @ nat))).
% 2.08/1.17 thf(tcon_Nat_Onat___Orderings_Ono__top, axiom, ((no_top @ nat) @ (type2 @ nat))).
% 2.08/1.17 thf(tcon_Nat_Onat___Orderings_Oorder_2, axiom, ((order @ nat) @ (type2 @ nat))).
% 2.08/1.17 thf(tcon_Nat_Onat___Orderings_Oord_3, axiom, ((ord @ nat) @ (type2 @ nat))).
% 2.08/1.17 thf(tcon_HOL_Obool___Orderings_Opreorder_4, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 2.08/1.17 thf(tcon_HOL_Obool___Orderings_Olinorder_5, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.08/1.17 thf(tcon_HOL_Obool___Orderings_Oorder_6, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.08/1.17 thf(tcon_HOL_Obool___Orderings_Oord_7, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.08/1.17 thf(tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add_8, axiom, ((strict2144017051up_add @ extended_enat) @ (type2 @ extended_enat))).
% 2.08/1.17 thf(tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_9, axiom, ((canoni770627133id_add @ extended_enat) @ (type2 @ extended_enat))).
% 2.08/1.17 thf(tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add_10, axiom, ((ordere779506340up_add @ extended_enat) @ (type2 @ extended_enat))).
% 2.08/1.17 thf(tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add_11, axiom, ((ab_semigroup_add @ extended_enat) @ (type2 @ extended_enat))).
% 2.08/1.17 thf(tcon_Extended__Nat_Oenat___Groups_Osemigroup__add_12, axiom, ((semigroup_add @ extended_enat) @ (type2 @ extended_enat))).
% 2.08/1.17 thf(tcon_Extended__Nat_Oenat___Orderings_Owellorder_13, axiom, ((wellorder @ extended_enat) @ (type2 @ extended_enat))).
% 2.08/1.17 thf(tcon_Extended__Nat_Oenat___Orderings_Opreorder_14, axiom, ((preorder @ extended_enat) @ (type2 @ extended_enat))).
% 2.08/1.17 thf(tcon_Extended__Nat_Oenat___Orderings_Olinorder_15, axiom, ((linorder @ extended_enat) @ (type2 @ extended_enat))).
% 2.08/1.17 thf(tcon_Extended__Nat_Oenat___Orderings_Oorder_16, axiom, ((order @ extended_enat) @ (type2 @ extended_enat))).
% 2.08/1.17 thf(tcon_Extended__Nat_Oenat___Orderings_Oord_17, axiom, ((ord @ extended_enat) @ (type2 @ extended_enat))).
% 2.08/1.17 thf(conj_0, conjecture, ((p @ (((coindu749330388e_lnth @ a) @ (((coindu268472904append @ a) @ xs) @ xs2)) @ n)) @ (((coindu749330388e_lnth @ b) @ ys) @ n))).
% 2.08/1.17 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.YAJWcH1y2A/DTF2DTF20469.p
% 2.08/1.17 ------------------------
% 2.27/1.20 ---- Cleaned THF ---
% 2.27/1.20 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 2.27/1.20 coindu1593790203_llist: $tType > $tType ).
% 2.27/1.20
% 2.27/1.20 thf(ty_t_Extended__Nat_Oenat,type,
% 2.27/1.20 extended_enat: $tType ).
% 2.27/1.20
% 2.27/1.20 thf(ty_t_Nat_Onat,type,
% 2.27/1.20 nat: $tType ).
% 2.27/1.20
% 2.27/1.20 thf(ty_t_itself,type,
% 2.27/1.20 itself: $tType > $tType ).
% 2.27/1.20
% 2.27/1.20 thf(ty_tf_b,type,
% 2.27/1.20 b: $tType ).
% 2.27/1.20
% 2.27/1.20 thf(ty_tf_a,type,
% 2.27/1.20 a: $tType ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_HOL_Otype,type,
% 2.27/1.20 type:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_Orderings_Oord,type,
% 2.27/1.20 ord:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_Orderings_Oorder,type,
% 2.27/1.20 order:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_Groups_Ogroup__add,type,
% 2.27/1.20 group_add:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_Orderings_Ono__bot,type,
% 2.27/1.20 no_bot:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_Orderings_Ono__top,type,
% 2.27/1.20 no_top:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_Orderings_Olinorder,type,
% 2.27/1.20 linorder:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_Orderings_Opreorder,type,
% 2.27/1.20 preorder:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_Orderings_Owellorder,type,
% 2.27/1.20 wellorder:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_Groups_Osemigroup__add,type,
% 2.27/1.20 semigroup_add:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_Orderings_Odense__order,type,
% 2.27/1.20 dense_order:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 2.27/1.20 ab_semigroup_add:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 2.27/1.20 cancel_semigroup_add:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 2.27/1.20 ordere779506340up_add:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.27/1.20 canoni770627133id_add:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 2.27/1.20 ordere236663937imp_le:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_Groups_Oordered__cancel__ab__semigroup__add,type,
% 2.27/1.20 ordere223160158up_add:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_cl_Groups_Ostrict__ordered__ab__semigroup__add,type,
% 2.27/1.20 strict2144017051up_add:
% 2.27/1.20 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__llength,type,
% 2.27/1.20 coindu493225792length:
% 2.27/1.20 !>[A: $tType] : ( nat > ( coindu1593790203_llist @ A ) > extended_enat ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oiterates,type,
% 2.27/1.20 coindu1529956631erates:
% 2.27/1.20 !>[A: $tType] : ( ( A > A ) > A > ( coindu1593790203_llist @ A ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 2.27/1.20 coindu268472904append:
% 2.27/1.20 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite,type,
% 2.27/1.20 coindu1213758845finite:
% 2.27/1.20 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollength,type,
% 2.27/1.20 coindu1018505716length:
% 2.27/1.20 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > extended_enat ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 2.27/1.20 coindu1121789889_LCons:
% 2.27/1.20 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 2.27/1.20 coindu1598213697e_LNil:
% 2.27/1.20 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ollist__all2,type,
% 2.27/1.20 coindu987187967t_all2:
% 2.27/1.20 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 2.27/1.20 coindu335574135_lnull:
% 2.27/1.20 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olnth,type,
% 2.27/1.20 coindu749330388e_lnth:
% 2.27/1.20 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > nat > A ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_c_Extended__Nat_Oenat,type,
% 2.27/1.20 extended_enat2: nat > extended_enat ).
% 2.27/1.20
% 2.27/1.20 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 2.27/1.20 plus_plus:
% 2.27/1.20 !>[A: $tType] : ( A > A > A ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.27/1.20 ord_less:
% 2.27/1.20 !>[A: $tType] : ( A > A > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.27/1.20 ord_less_eq:
% 2.27/1.20 !>[A: $tType] : ( A > A > $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_c_Pure_Otype,type,
% 2.27/1.20 type2:
% 2.27/1.20 !>[A: $tType] : ( itself @ A ) ).
% 2.27/1.20
% 2.27/1.20 thf(sy_v_P,type,
% 2.27/1.20 p: a > b > $o ).
% 2.27/1.20
% 2.27/1.20 thf(sy_v_n____,type,
% 2.27/1.20 n: nat ).
% 2.27/1.20
% 2.27/1.20 thf(sy_v_xs,type,
% 2.27/1.20 xs: coindu1593790203_llist @ a ).
% 2.27/1.20
% 2.27/1.20 thf(sy_v_xs_H,type,
% 2.27/1.20 xs2: coindu1593790203_llist @ a ).
% 2.27/1.20
% 2.27/1.20 thf(sy_v_ys,type,
% 2.27/1.20 ys: coindu1593790203_llist @ b ).
% 2.27/1.20
% 2.27/1.20 thf(fact_0_assms,axiom,
% 2.27/1.20 coindu987187967t_all2 @ a @ b @ p @ ( coindu268472904append @ a @ xs @ xs2 ) @ ys ).
% 2.27/1.20
% 2.27/1.20 thf(fact_1_lappend__assoc,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 2.27/1.20 = ( coindu268472904append @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_2__092_060open_062llength_Axs_A_092_060le_062_Allength_A_Ilappend_Axs_Axs_H_J_092_060close_062,axiom,
% 2.27/1.20 ord_less_eq @ extended_enat @ ( coindu1018505716length @ a @ xs ) @ ( coindu1018505716length @ a @ ( coindu268472904append @ a @ xs @ xs2 ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_3_n,axiom,
% 2.27/1.20 ord_less @ extended_enat @ ( extended_enat2 @ n ) @ ( coindu1018505716length @ a @ xs ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_4_len,axiom,
% 2.27/1.20 ( ( plus_plus @ extended_enat @ ( coindu1018505716length @ a @ xs ) @ ( coindu1018505716length @ a @ xs2 ) )
% 2.27/1.20 = ( coindu1018505716length @ b @ ys ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_5_len__xs_H,axiom,
% 2.27/1.20 ord_less_eq @ extended_enat @ ( coindu1018505716length @ a @ xs2 ) @ ( coindu1018505716length @ b @ ys ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_6_len__xs,axiom,
% 2.27/1.20 ord_less_eq @ extended_enat @ ( coindu1018505716length @ a @ xs ) @ ( coindu1018505716length @ b @ ys ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_7_lappend__code_I1_J,axiom,
% 2.27/1.20 ! [A: $tType,Ys: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ Ys )
% 2.27/1.20 = Ys ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_8_lappend__LNil2,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu268472904append @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 2.27/1.20 = Xs ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_9_lappend__iterates,axiom,
% 2.27/1.20 ! [A: $tType,F: A > A,X: A,Xs: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu268472904append @ A @ ( coindu1529956631erates @ A @ F @ X ) @ Xs )
% 2.27/1.20 = ( coindu1529956631erates @ A @ F @ X ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_10_lappend_Odisc__iff_I2_J,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 2.27/1.20 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.27/1.20 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_11_lnull__lappend,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.27/1.20 = ( ( coindu335574135_lnull @ A @ Xs )
% 2.27/1.20 & ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_12_lappend__code_I2_J,axiom,
% 2.27/1.20 ! [A: $tType,Xa: A,X: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu268472904append @ A @ ( coindu1121789889_LCons @ A @ Xa @ X ) @ Ys )
% 2.27/1.20 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu268472904append @ A @ X @ Ys ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_13_lfinite__lappend,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu1213758845finite @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.27/1.20 = ( ( coindu1213758845finite @ A @ Xs )
% 2.27/1.20 & ( coindu1213758845finite @ A @ Ys ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_14_llist_Oinject,axiom,
% 2.27/1.20 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 2.27/1.20 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 2.27/1.20 = ( ( X21 = Y21 )
% 2.27/1.20 & ( X22 = Y22 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_15_llist__all2__LCons__LCons,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,X22: coindu1593790203_llist @ A,Y21: B,Y22: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) )
% 2.27/1.20 = ( ( R @ X21 @ Y21 )
% 2.27/1.20 & ( coindu987187967t_all2 @ A @ B @ R @ X22 @ Y22 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_16_lfinite__code_I2_J,axiom,
% 2.27/1.20 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ( coindu1213758845finite @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) )
% 2.27/1.20 = ( coindu1213758845finite @ B @ Xs ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_17_lfinite__LCons,axiom,
% 2.27/1.20 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 2.27/1.20 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_18_llist__all2__LNil1,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ( coindu987187967t_all2 @ A @ B @ P @ ( coindu1598213697e_LNil @ A ) @ Xs )
% 2.27/1.20 = ( Xs
% 2.27/1.20 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_19_llist__all2__LNil2,axiom,
% 2.27/1.20 ! [B: $tType,A: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ ( coindu1598213697e_LNil @ B ) )
% 2.27/1.20 = ( Xs
% 2.27/1.20 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_20_lfinite__code_I1_J,axiom,
% 2.27/1.20 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_21_llength__lappend,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu1018505716length @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.27/1.20 = ( plus_plus @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ ( coindu1018505716length @ A @ Ys ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_22_llist_Odisc_I2_J,axiom,
% 2.27/1.20 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 2.27/1.20 ~ ( coindu335574135_lnull @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_23_llist_Odisc_I1_J,axiom,
% 2.27/1.20 ! [A: $tType] : ( coindu335574135_lnull @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_24_llist_OdiscI_I2_J,axiom,
% 2.27/1.20 ! [A: $tType,Llist: coindu1593790203_llist @ A,X21: A,X22: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( Llist
% 2.27/1.20 = ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 2.27/1.20 => ~ ( coindu335574135_lnull @ A @ Llist ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_25_llist_OdiscI_I1_J,axiom,
% 2.27/1.20 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( Llist
% 2.27/1.20 = ( coindu1598213697e_LNil @ A ) )
% 2.27/1.20 => ( coindu335574135_lnull @ A @ Llist ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_26_llist_Ocollapse_I1_J,axiom,
% 2.27/1.20 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu335574135_lnull @ A @ Llist )
% 2.27/1.20 => ( Llist
% 2.27/1.20 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_27_llist_Odistinct_I1_J,axiom,
% 2.27/1.20 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu1598213697e_LNil @ A )
% 2.27/1.20 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_28_llist_Orel__intros_I2_J,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,R: A > B > $o,X21: A,Y21: B,X22: coindu1593790203_llist @ A,Y22: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ( R @ X21 @ Y21 )
% 2.27/1.20 => ( ( coindu987187967t_all2 @ A @ B @ R @ X22 @ Y22 )
% 2.27/1.20 => ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_29_lzip_Oexhaust,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 2.27/1.20 | ( coindu335574135_lnull @ B @ Ys ) )
% 2.27/1.20 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.27/1.20 => ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_30_iterates_Ocode,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( coindu1529956631erates @ A )
% 2.27/1.20 = ( ^ [F2: A > A,X2: A] : ( coindu1121789889_LCons @ A @ X2 @ ( coindu1529956631erates @ A @ F2 @ ( F2 @ X2 ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_31_lfinite_Ocases,axiom,
% 2.27/1.20 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu1213758845finite @ A @ A2 )
% 2.27/1.20 => ( ( A2
% 2.27/1.20 != ( coindu1598213697e_LNil @ A ) )
% 2.27/1.20 => ~ ! [Xs2: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ? [X3: A] :
% 2.27/1.20 ( A2
% 2.27/1.20 = ( coindu1121789889_LCons @ A @ X3 @ Xs2 ) )
% 2.27/1.20 => ~ ( coindu1213758845finite @ A @ Xs2 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_32_lfinite_Osimps,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( coindu1213758845finite @ A )
% 2.27/1.20 = ( ^ [A3: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( A3
% 2.27/1.20 = ( coindu1598213697e_LNil @ A ) )
% 2.27/1.20 | ? [Xs3: coindu1593790203_llist @ A,X2: A] :
% 2.27/1.20 ( ( A3
% 2.27/1.20 = ( coindu1121789889_LCons @ A @ X2 @ Xs3 ) )
% 2.27/1.20 & ( coindu1213758845finite @ A @ Xs3 ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_33_llist_Oexhaust,axiom,
% 2.27/1.20 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( Y
% 2.27/1.20 != ( coindu1598213697e_LNil @ A ) )
% 2.27/1.20 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 2.27/1.20 ( Y
% 2.27/1.20 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_34_neq__LNil__conv,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( Xs
% 2.27/1.20 != ( coindu1598213697e_LNil @ A ) )
% 2.27/1.20 = ( ? [X2: A,Xs4: coindu1593790203_llist @ A] :
% 2.27/1.20 ( Xs
% 2.27/1.20 = ( coindu1121789889_LCons @ A @ X2 @ Xs4 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_35_not__lnull__conv,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( ~ ( coindu335574135_lnull @ A @ Xs ) )
% 2.27/1.20 = ( ? [X2: A,Xs4: coindu1593790203_llist @ A] :
% 2.27/1.20 ( Xs
% 2.27/1.20 = ( coindu1121789889_LCons @ A @ X2 @ Xs4 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_36_lappend_Oexhaust,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( ( coindu335574135_lnull @ A @ Xs )
% 2.27/1.20 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 2.27/1.20 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.27/1.20 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_37_lfinite_Oinducts,axiom,
% 2.27/1.20 ! [A: $tType,X: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 2.27/1.20 ( ( coindu1213758845finite @ A @ X )
% 2.27/1.20 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 2.27/1.20 => ( ! [Xs2: coindu1593790203_llist @ A,X3: A] :
% 2.27/1.20 ( ( coindu1213758845finite @ A @ Xs2 )
% 2.27/1.20 => ( ( P @ Xs2 )
% 2.27/1.20 => ( P @ ( coindu1121789889_LCons @ A @ X3 @ Xs2 ) ) ) )
% 2.27/1.20 => ( P @ X ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_38_lnull__def,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( coindu335574135_lnull @ A )
% 2.27/1.20 = ( ^ [Llist2: coindu1593790203_llist @ A] :
% 2.27/1.20 ( Llist2
% 2.27/1.20 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_39_llist_Orel__cases,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,R: A > B > $o,A2: coindu1593790203_llist @ A,B2: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ( coindu987187967t_all2 @ A @ B @ R @ A2 @ B2 )
% 2.27/1.20 => ( ( ( A2
% 2.27/1.20 = ( coindu1598213697e_LNil @ A ) )
% 2.27/1.20 => ( B2
% 2.27/1.20 != ( coindu1598213697e_LNil @ B ) ) )
% 2.27/1.20 => ~ ! [X1: A,X23: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( A2
% 2.27/1.20 = ( coindu1121789889_LCons @ A @ X1 @ X23 ) )
% 2.27/1.20 => ! [Y1: B,Y2: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ( B2
% 2.27/1.20 = ( coindu1121789889_LCons @ B @ Y1 @ Y2 ) )
% 2.27/1.20 => ( ( R @ X1 @ Y1 )
% 2.27/1.20 => ~ ( coindu987187967t_all2 @ A @ B @ R @ X23 @ Y2 ) ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_40_lfinite__iterates,axiom,
% 2.27/1.20 ! [A: $tType,F: A > A,X: A] :
% 2.27/1.20 ~ ( coindu1213758845finite @ A @ ( coindu1529956631erates @ A @ F @ X ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_41_llist__all2__cases,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys )
% 2.27/1.20 => ( ( ( Xs
% 2.27/1.20 = ( coindu1598213697e_LNil @ A ) )
% 2.27/1.20 => ( Ys
% 2.27/1.20 != ( coindu1598213697e_LNil @ B ) ) )
% 2.27/1.20 => ~ ! [X3: A,Xs5: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( Xs
% 2.27/1.20 = ( coindu1121789889_LCons @ A @ X3 @ Xs5 ) )
% 2.27/1.20 => ! [Y3: B,Ys2: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ( Ys
% 2.27/1.20 = ( coindu1121789889_LCons @ B @ Y3 @ Ys2 ) )
% 2.27/1.20 => ( ( P @ X3 @ Y3 )
% 2.27/1.20 => ~ ( coindu987187967t_all2 @ A @ B @ P @ Xs5 @ Ys2 ) ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_42_llist__all2__lnthD,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B,N: nat] :
% 2.27/1.20 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys )
% 2.27/1.20 => ( ( ord_less @ extended_enat @ ( extended_enat2 @ N ) @ ( coindu1018505716length @ A @ Xs ) )
% 2.27/1.20 => ( P @ ( coindu749330388e_lnth @ A @ Xs @ N ) @ ( coindu749330388e_lnth @ B @ Ys @ N ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_43_wlog__linorder__le,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( linorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [P: A > A > $o,B2: A,A2: A] :
% 2.27/1.20 ( ! [A4: A,B3: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.27/1.20 => ( P @ A4 @ B3 ) )
% 2.27/1.20 => ( ( ( P @ B2 @ A2 )
% 2.27/1.20 => ( P @ A2 @ B2 ) )
% 2.27/1.20 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_44_ext,axiom,
% 2.27/1.20 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.27/1.20 ( ! [X3: A] :
% 2.27/1.20 ( ( F @ X3 )
% 2.27/1.20 = ( G @ X3 ) )
% 2.27/1.20 => ( F = G ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_45_iterates_Odisc__iff,axiom,
% 2.27/1.20 ! [A: $tType,F: A > A,X: A] :
% 2.27/1.20 ~ ( coindu335574135_lnull @ A @ ( coindu1529956631erates @ A @ F @ X ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_46_llist__all2__LCons1,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,P: A > B > $o,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ( coindu987187967t_all2 @ A @ B @ P @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ Ys )
% 2.27/1.20 = ( ? [Y4: B,Ys3: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ( Ys
% 2.27/1.20 = ( coindu1121789889_LCons @ B @ Y4 @ Ys3 ) )
% 2.27/1.20 & ( P @ X @ Y4 )
% 2.27/1.20 & ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys3 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_47_llist__all2__LCons2,axiom,
% 2.27/1.20 ! [B: $tType,A: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Y: B,Ys: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ ( coindu1121789889_LCons @ B @ Y @ Ys ) )
% 2.27/1.20 = ( ? [X2: A,Xs4: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( Xs
% 2.27/1.20 = ( coindu1121789889_LCons @ A @ X2 @ Xs4 ) )
% 2.27/1.20 & ( P @ X2 @ Y )
% 2.27/1.20 & ( coindu987187967t_all2 @ A @ B @ P @ Xs4 @ Ys ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_48_llist__all2__lnthD2,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B,N: nat] :
% 2.27/1.20 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys )
% 2.27/1.20 => ( ( ord_less @ extended_enat @ ( extended_enat2 @ N ) @ ( coindu1018505716length @ B @ Ys ) )
% 2.27/1.20 => ( P @ ( coindu749330388e_lnth @ A @ Xs @ N ) @ ( coindu749330388e_lnth @ B @ Ys @ N ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_49_llist__all2__lnullD,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys )
% 2.27/1.20 => ( ( coindu335574135_lnull @ A @ Xs )
% 2.27/1.20 = ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_50_lnull__imp__lfinite,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu335574135_lnull @ A @ Xs )
% 2.27/1.20 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_51_lfinite__rev__induct,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 2.27/1.20 ( ( coindu1213758845finite @ A @ Xs )
% 2.27/1.20 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 2.27/1.20 => ( ! [X3: A,Xs2: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu1213758845finite @ A @ Xs2 )
% 2.27/1.20 => ( ( P @ Xs2 )
% 2.27/1.20 => ( P @ ( coindu268472904append @ A @ Xs2 @ ( coindu1121789889_LCons @ A @ X3 @ ( coindu1598213697e_LNil @ A ) ) ) ) ) )
% 2.27/1.20 => ( P @ Xs ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_52_llist__all2__lfiniteD,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys )
% 2.27/1.20 => ( ( coindu1213758845finite @ A @ Xs )
% 2.27/1.20 = ( coindu1213758845finite @ B @ Ys ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_53_llist__all2__llengthD,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys )
% 2.27/1.20 => ( ( coindu1018505716length @ A @ Xs )
% 2.27/1.20 = ( coindu1018505716length @ B @ Ys ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_54_lfinite__LNil,axiom,
% 2.27/1.20 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_55_lfinite__llength__enat,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu1213758845finite @ A @ Xs )
% 2.27/1.20 => ? [N2: nat] :
% 2.27/1.20 ( ( coindu1018505716length @ A @ Xs )
% 2.27/1.20 = ( extended_enat2 @ N2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_56_llist__all2__LNil__LNil,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,R: A > B > $o] : ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_57_llist__all2__all__lnthI,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B,P: A > B > $o] :
% 2.27/1.20 ( ( ( coindu1018505716length @ A @ Xs )
% 2.27/1.20 = ( coindu1018505716length @ B @ Ys ) )
% 2.27/1.20 => ( ! [N2: nat] :
% 2.27/1.20 ( ( ord_less @ extended_enat @ ( extended_enat2 @ N2 ) @ ( coindu1018505716length @ A @ Xs ) )
% 2.27/1.20 => ( P @ ( coindu749330388e_lnth @ A @ Xs @ N2 ) @ ( coindu749330388e_lnth @ B @ Ys @ N2 ) ) )
% 2.27/1.20 => ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_58_llist__all2__LCons__LNil,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,R: A > B > $o,Y21: A,Y22: coindu1593790203_llist @ A] :
% 2.27/1.20 ~ ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_59_llist__all2__LNil__LCons,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,R: A > B > $o,Y21: B,Y22: coindu1593790203_llist @ B] :
% 2.27/1.20 ~ ( coindu987187967t_all2 @ A @ B @ R @ ( coindu1598213697e_LNil @ A ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_60_lfinite__LConsI,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 2.27/1.20 ( ( coindu1213758845finite @ A @ Xs )
% 2.27/1.20 => ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_61_llength__eq__enat__lfiniteD,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,N: nat] :
% 2.27/1.20 ( ( ( coindu1018505716length @ A @ Xs )
% 2.27/1.20 = ( extended_enat2 @ N ) )
% 2.27/1.20 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_62_llist__all2__conv__all__lnth,axiom,
% 2.27/1.20 ! [B: $tType,A: $tType] :
% 2.27/1.20 ( ( coindu987187967t_all2 @ A @ B )
% 2.27/1.20 = ( ^ [P2: A > B > $o,Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ( ( coindu1018505716length @ A @ Xs3 )
% 2.27/1.20 = ( coindu1018505716length @ B @ Ys4 ) )
% 2.27/1.20 & ! [N3: nat] :
% 2.27/1.20 ( ( ord_less @ extended_enat @ ( extended_enat2 @ N3 ) @ ( coindu1018505716length @ B @ Ys4 ) )
% 2.27/1.20 => ( P2 @ ( coindu749330388e_lnth @ A @ Xs3 @ N3 ) @ ( coindu749330388e_lnth @ B @ Ys4 @ N3 ) ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_63_lfinite__conv__llength__enat,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( coindu1213758845finite @ A )
% 2.27/1.20 = ( ^ [Xs3: coindu1593790203_llist @ A] :
% 2.27/1.20 ? [N3: nat] :
% 2.27/1.20 ( ( coindu1018505716length @ A @ Xs3 )
% 2.27/1.20 = ( extended_enat2 @ N3 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_64_lappend__eq__lappend__conv,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,Us: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Vs: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( ( coindu1018505716length @ A @ Xs )
% 2.27/1.20 = ( coindu1018505716length @ A @ Us ) )
% 2.27/1.20 => ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.27/1.20 = ( coindu268472904append @ A @ Us @ Vs ) )
% 2.27/1.20 = ( ( Xs = Us )
% 2.27/1.20 & ( ( coindu1213758845finite @ A @ Xs )
% 2.27/1.20 => ( Ys = Vs ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_65_lappend__snocL1__conv__LCons2,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ ( coindu1598213697e_LNil @ A ) ) ) @ Ys )
% 2.27/1.20 = ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_66_lappend_Octr_I1_J,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu335574135_lnull @ A @ Xs )
% 2.27/1.20 => ( ( coindu335574135_lnull @ A @ Ys )
% 2.27/1.20 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.27/1.20 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_67_lnth__lappend1,axiom,
% 2.27/1.20 ! [A: $tType,N: nat,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( ord_less @ extended_enat @ ( extended_enat2 @ N ) @ ( coindu1018505716length @ A @ Xs ) )
% 2.27/1.20 => ( ( coindu749330388e_lnth @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ N )
% 2.27/1.20 = ( coindu749330388e_lnth @ A @ Xs @ N ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_68_llist__all2__lappendI,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B,Xs6: coindu1593790203_llist @ A,Ys5: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys )
% 2.27/1.20 => ( ( ( coindu1213758845finite @ A @ Xs )
% 2.27/1.20 => ( ( coindu1213758845finite @ B @ Ys )
% 2.27/1.20 => ( coindu987187967t_all2 @ A @ B @ P @ Xs6 @ Ys5 ) ) )
% 2.27/1.20 => ( coindu987187967t_all2 @ A @ B @ P @ ( coindu268472904append @ A @ Xs @ Xs6 ) @ ( coindu268472904append @ B @ Ys @ Ys5 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_69_llist_Orel__refl,axiom,
% 2.27/1.20 ! [B: $tType,Ra: B > B > $o,X: coindu1593790203_llist @ B] :
% 2.27/1.20 ( ! [X3: B] : ( Ra @ X3 @ X3 )
% 2.27/1.20 => ( coindu987187967t_all2 @ B @ B @ Ra @ X @ X ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_70_llist_Orel__eq,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( coindu987187967t_all2 @ A @ A
% 2.27/1.20 @ ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 2.27/1.20 = ( ^ [Y5: coindu1593790203_llist @ A,Z: coindu1593790203_llist @ A] : ( Y5 = Z ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_71_llist__all2__mono,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B,P3: A > B > $o] :
% 2.27/1.20 ( ( coindu987187967t_all2 @ A @ B @ P @ Xs @ Ys )
% 2.27/1.20 => ( ! [X3: A,Y3: B] :
% 2.27/1.20 ( ( P @ X3 @ Y3 )
% 2.27/1.20 => ( P3 @ X3 @ Y3 ) )
% 2.27/1.20 => ( coindu987187967t_all2 @ A @ B @ P3 @ Xs @ Ys ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_72_lappend__inf,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ~ ( coindu1213758845finite @ A @ Xs )
% 2.27/1.20 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.27/1.20 = Xs ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_73_lappend__lnull2,axiom,
% 2.27/1.20 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu335574135_lnull @ A @ Ys )
% 2.27/1.20 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.27/1.20 = Xs ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_74_lappend__lnull1,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu335574135_lnull @ A @ Xs )
% 2.27/1.20 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.27/1.20 = Ys ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_75_lappend_Odisc_I1_J,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( coindu335574135_lnull @ A @ Xs )
% 2.27/1.20 => ( ( coindu335574135_lnull @ A @ Ys )
% 2.27/1.20 => ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_76_lappend_Odisc_I2_J,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.27/1.20 | ~ ( coindu335574135_lnull @ A @ Ys ) )
% 2.27/1.20 => ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_77_lappend__eq__LNil__iff,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.27/1.20 = ( coindu1598213697e_LNil @ A ) )
% 2.27/1.20 = ( ( Xs
% 2.27/1.20 = ( coindu1598213697e_LNil @ A ) )
% 2.27/1.20 & ( Ys
% 2.27/1.20 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_78_LNil__eq__lappend__iff,axiom,
% 2.27/1.20 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.27/1.20 ( ( ( coindu1598213697e_LNil @ A )
% 2.27/1.20 = ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.27/1.20 = ( ( Xs
% 2.27/1.20 = ( coindu1598213697e_LNil @ A ) )
% 2.27/1.20 & ( Ys
% 2.27/1.20 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_79_lappend__LNil__LNil,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) )
% 2.27/1.20 = ( coindu1598213697e_LNil @ A ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_80_enat__add__mono,axiom,
% 2.27/1.20 ! [X: nat,Y: extended_enat,Z2: extended_enat] :
% 2.27/1.20 ( ( ord_less @ extended_enat @ ( plus_plus @ extended_enat @ ( extended_enat2 @ X ) @ Y ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ X ) @ Z2 ) )
% 2.27/1.20 = ( ord_less @ extended_enat @ Y @ Z2 ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_81_enat__add1__eq,axiom,
% 2.27/1.20 ! [X: nat,Y: extended_enat,Z2: extended_enat] :
% 2.27/1.20 ( ( ( plus_plus @ extended_enat @ ( extended_enat2 @ X ) @ Y )
% 2.27/1.20 = ( plus_plus @ extended_enat @ ( extended_enat2 @ X ) @ Z2 ) )
% 2.27/1.20 = ( Y = Z2 ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_82_enat__add2__eq,axiom,
% 2.27/1.20 ! [Y: extended_enat,X: nat,Z2: extended_enat] :
% 2.27/1.20 ( ( ( plus_plus @ extended_enat @ Y @ ( extended_enat2 @ X ) )
% 2.27/1.20 = ( plus_plus @ extended_enat @ Z2 @ ( extended_enat2 @ X ) ) )
% 2.27/1.20 = ( Y = Z2 ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_83_add__less__cancel__left,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [C: A,A2: A,B2: A] :
% 2.27/1.20 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 2.27/1.20 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_84_add__less__cancel__right,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,C: A,B2: A] :
% 2.27/1.20 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 2.27/1.20 = ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_85_add__le__cancel__left,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [C: A,A2: A,B2: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 2.27/1.20 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_86_add__le__cancel__right,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,C: A,B2: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 2.27/1.20 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_87_enat__less__imp__le,axiom,
% 2.27/1.20 ! [N: extended_enat,M: extended_enat] :
% 2.27/1.20 ( ! [K: nat] :
% 2.27/1.20 ( ( ord_less @ extended_enat @ N @ ( extended_enat2 @ K ) )
% 2.27/1.20 => ( ord_less @ extended_enat @ M @ ( extended_enat2 @ K ) ) )
% 2.27/1.20 => ( ord_less_eq @ extended_enat @ M @ N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_88_add__mono__thms__linordered__field_I4_J,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [I: A,J: A,K2: A,L: A] :
% 2.27/1.20 ( ( ( ord_less_eq @ A @ I @ J )
% 2.27/1.20 & ( ord_less @ A @ K2 @ L ) )
% 2.27/1.20 => ( ord_less @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_89_add__mono__thms__linordered__field_I3_J,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [I: A,J: A,K2: A,L: A] :
% 2.27/1.20 ( ( ( ord_less @ A @ I @ J )
% 2.27/1.20 & ( ord_less_eq @ A @ K2 @ L ) )
% 2.27/1.20 => ( ord_less @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_90_add__le__less__mono,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A,D: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.27/1.20 => ( ( ord_less @ A @ C @ D )
% 2.27/1.20 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_91_add__right__cancel,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [B2: A,A2: A,C: A] :
% 2.27/1.20 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.27/1.20 = ( plus_plus @ A @ C @ A2 ) )
% 2.27/1.20 = ( B2 = C ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_92_add__left__cancel,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A] :
% 2.27/1.20 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.27/1.20 = ( plus_plus @ A @ A2 @ C ) )
% 2.27/1.20 = ( B2 = C ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_93_llist_Orel__mono,axiom,
% 2.27/1.20 ! [B: $tType,A: $tType,R: A > B > $o,Ra: A > B > $o] :
% 2.27/1.20 ( ( ord_less_eq @ ( A > B > $o ) @ R @ Ra )
% 2.27/1.20 => ( ord_less_eq @ ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o ) @ ( coindu987187967t_all2 @ A @ B @ R ) @ ( coindu987187967t_all2 @ A @ B @ Ra ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_94_enat__less__enat__plusI2,axiom,
% 2.27/1.20 ! [Y: nat,Z2: extended_enat,X: nat] :
% 2.27/1.20 ( ( ord_less @ extended_enat @ ( extended_enat2 @ Y ) @ Z2 )
% 2.27/1.20 => ( ord_less @ extended_enat @ ( extended_enat2 @ ( plus_plus @ nat @ X @ Y ) ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ X ) @ Z2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_95_enat__less__enat__plusI,axiom,
% 2.27/1.20 ! [X: nat,Y: nat,Z2: extended_enat] :
% 2.27/1.20 ( ( ord_less @ nat @ X @ Y )
% 2.27/1.20 => ( ord_less @ extended_enat @ ( extended_enat2 @ X ) @ ( plus_plus @ extended_enat @ ( extended_enat2 @ Y ) @ Z2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_96_add__right__imp__eq,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [B2: A,A2: A,C: A] :
% 2.27/1.20 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.27/1.20 = ( plus_plus @ A @ C @ A2 ) )
% 2.27/1.20 => ( B2 = C ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_97_add__left__imp__eq,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A] :
% 2.27/1.20 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.27/1.20 = ( plus_plus @ A @ A2 @ C ) )
% 2.27/1.20 => ( B2 = C ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_98_add_Oleft__commute,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [B2: A,A2: A,C: A] :
% 2.27/1.20 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A2 @ C ) )
% 2.27/1.20 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_99_add_Ocommute,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ( ( plus_plus @ A )
% 2.27/1.20 = ( ^ [A3: A,B4: A] : ( plus_plus @ A @ B4 @ A3 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_100_add_Oright__cancel,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( group_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [B2: A,A2: A,C: A] :
% 2.27/1.20 ( ( ( plus_plus @ A @ B2 @ A2 )
% 2.27/1.20 = ( plus_plus @ A @ C @ A2 ) )
% 2.27/1.20 = ( B2 = C ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_101_add_Oleft__cancel,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( group_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A] :
% 2.27/1.20 ( ( ( plus_plus @ A @ A2 @ B2 )
% 2.27/1.20 = ( plus_plus @ A @ A2 @ C ) )
% 2.27/1.20 = ( B2 = C ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_102_add_Oassoc,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( semigroup_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A] :
% 2.27/1.20 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C )
% 2.27/1.20 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_103_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [I: A,J: A,K2: A,L: A] :
% 2.27/1.20 ( ( ( I = J )
% 2.27/1.20 & ( K2 = L ) )
% 2.27/1.20 => ( ( plus_plus @ A @ I @ K2 )
% 2.27/1.20 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_104_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A] :
% 2.27/1.20 ( ( plus_plus @ A @ ( plus_plus @ A @ A2 @ B2 ) @ C )
% 2.27/1.20 = ( plus_plus @ A @ A2 @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_105_add__le__imp__le__right,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,C: A,B2: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 2.27/1.20 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_106_add__le__imp__le__left,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [C: A,A2: A,B2: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 2.27/1.20 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_107_le__iff__add,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ( ( ord_less_eq @ A )
% 2.27/1.20 = ( ^ [A3: A,B4: A] :
% 2.27/1.20 ? [C2: A] :
% 2.27/1.20 ( B4
% 2.27/1.20 = ( plus_plus @ A @ A3 @ C2 ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_108_add__right__mono,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.27/1.20 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_109_add__left__mono,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.27/1.20 => ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_110_add__mono,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A,D: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.27/1.20 => ( ( ord_less_eq @ A @ C @ D )
% 2.27/1.20 => ( ord_less_eq @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_111_add__mono__thms__linordered__semiring_I1_J,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [I: A,J: A,K2: A,L: A] :
% 2.27/1.20 ( ( ( ord_less_eq @ A @ I @ J )
% 2.27/1.20 & ( ord_less_eq @ A @ K2 @ L ) )
% 2.27/1.20 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_112_add__mono__thms__linordered__semiring_I2_J,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [I: A,J: A,K2: A,L: A] :
% 2.27/1.20 ( ( ( I = J )
% 2.27/1.20 & ( ord_less_eq @ A @ K2 @ L ) )
% 2.27/1.20 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_113_add__mono__thms__linordered__semiring_I3_J,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [I: A,J: A,K2: A,L: A] :
% 2.27/1.20 ( ( ( ord_less_eq @ A @ I @ J )
% 2.27/1.20 & ( K2 = L ) )
% 2.27/1.20 => ( ord_less_eq @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_114_add__less__imp__less__right,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,C: A,B2: A] :
% 2.27/1.20 ( ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) )
% 2.27/1.20 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_115_add__less__imp__less__left,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [C: A,A2: A,B2: A] :
% 2.27/1.20 ( ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) )
% 2.27/1.20 => ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_116_add__strict__right__mono,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A] :
% 2.27/1.20 ( ( ord_less @ A @ A2 @ B2 )
% 2.27/1.20 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ C ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_117_add__strict__left__mono,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A] :
% 2.27/1.20 ( ( ord_less @ A @ A2 @ B2 )
% 2.27/1.20 => ( ord_less @ A @ ( plus_plus @ A @ C @ A2 ) @ ( plus_plus @ A @ C @ B2 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_118_add__strict__mono,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( strict2144017051up_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A,D: A] :
% 2.27/1.20 ( ( ord_less @ A @ A2 @ B2 )
% 2.27/1.20 => ( ( ord_less @ A @ C @ D )
% 2.27/1.20 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_119_add__mono__thms__linordered__field_I1_J,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [I: A,J: A,K2: A,L: A] :
% 2.27/1.20 ( ( ( ord_less @ A @ I @ J )
% 2.27/1.20 & ( K2 = L ) )
% 2.27/1.20 => ( ord_less @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_120_add__mono__thms__linordered__field_I2_J,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [I: A,J: A,K2: A,L: A] :
% 2.27/1.20 ( ( ( I = J )
% 2.27/1.20 & ( ord_less @ A @ K2 @ L ) )
% 2.27/1.20 => ( ord_less @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_121_add__mono__thms__linordered__field_I5_J,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [I: A,J: A,K2: A,L: A] :
% 2.27/1.20 ( ( ( ord_less @ A @ I @ J )
% 2.27/1.20 & ( ord_less @ A @ K2 @ L ) )
% 2.27/1.20 => ( ord_less @ A @ ( plus_plus @ A @ I @ K2 ) @ ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_122_enat__le__plus__same_I1_J,axiom,
% 2.27/1.20 ! [X: extended_enat,Y: extended_enat] : ( ord_less_eq @ extended_enat @ X @ ( plus_plus @ extended_enat @ X @ Y ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_123_enat__le__plus__same_I2_J,axiom,
% 2.27/1.20 ! [X: extended_enat,Y: extended_enat] : ( ord_less_eq @ extended_enat @ X @ ( plus_plus @ extended_enat @ Y @ X ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_124_add__less__le__mono,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ordere223160158up_add @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A,D: A] :
% 2.27/1.20 ( ( ord_less @ A @ A2 @ B2 )
% 2.27/1.20 => ( ( ord_less_eq @ A @ C @ D )
% 2.27/1.20 => ( ord_less @ A @ ( plus_plus @ A @ A2 @ C ) @ ( plus_plus @ A @ B2 @ D ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_125_plus__enat__simps_I1_J,axiom,
% 2.27/1.20 ! [M: nat,N: nat] :
% 2.27/1.20 ( ( plus_plus @ extended_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 2.27/1.20 = ( extended_enat2 @ ( plus_plus @ nat @ M @ N ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_126_enat__ord__simps_I2_J,axiom,
% 2.27/1.20 ! [M: nat,N: nat] :
% 2.27/1.20 ( ( ord_less @ extended_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 2.27/1.20 = ( ord_less @ nat @ M @ N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_127_enat__ord__simps_I1_J,axiom,
% 2.27/1.20 ! [M: nat,N: nat] :
% 2.27/1.20 ( ( ord_less_eq @ extended_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 2.27/1.20 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_128_iadd__le__enat__iff,axiom,
% 2.27/1.20 ! [X: extended_enat,Y: extended_enat,N: nat] :
% 2.27/1.20 ( ( ord_less_eq @ extended_enat @ ( plus_plus @ extended_enat @ X @ Y ) @ ( extended_enat2 @ N ) )
% 2.27/1.20 = ( ? [Y6: nat,X4: nat] :
% 2.27/1.20 ( ( X
% 2.27/1.20 = ( extended_enat2 @ X4 ) )
% 2.27/1.20 & ( Y
% 2.27/1.20 = ( extended_enat2 @ Y6 ) )
% 2.27/1.20 & ( ord_less_eq @ nat @ ( plus_plus @ nat @ X4 @ Y6 ) @ N ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_129_enat_Oinject,axiom,
% 2.27/1.20 ! [Nat: nat,Nat2: nat] :
% 2.27/1.20 ( ( ( extended_enat2 @ Nat )
% 2.27/1.20 = ( extended_enat2 @ Nat2 ) )
% 2.27/1.20 = ( Nat = Nat2 ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_130_enat__less__induct,axiom,
% 2.27/1.20 ! [P: extended_enat > $o,N: extended_enat] :
% 2.27/1.20 ( ! [N2: extended_enat] :
% 2.27/1.20 ( ! [M2: extended_enat] :
% 2.27/1.20 ( ( ord_less @ extended_enat @ M2 @ N2 )
% 2.27/1.20 => ( P @ M2 ) )
% 2.27/1.20 => ( P @ N2 ) )
% 2.27/1.20 => ( P @ N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_131_enat__ile,axiom,
% 2.27/1.20 ! [N: extended_enat,M: nat] :
% 2.27/1.20 ( ( ord_less_eq @ extended_enat @ N @ ( extended_enat2 @ M ) )
% 2.27/1.20 => ? [K: nat] :
% 2.27/1.20 ( N
% 2.27/1.20 = ( extended_enat2 @ K ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_132_chain__incr,axiom,
% 2.27/1.20 ! [A: $tType,Y7: A > extended_enat,K2: nat] :
% 2.27/1.20 ( ! [I2: A] :
% 2.27/1.20 ? [J2: A] : ( ord_less @ extended_enat @ ( Y7 @ I2 ) @ ( Y7 @ J2 ) )
% 2.27/1.20 => ? [J3: A] : ( ord_less @ extended_enat @ ( extended_enat2 @ K2 ) @ ( Y7 @ J3 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_133_enat__iless,axiom,
% 2.27/1.20 ! [N: extended_enat,M: nat] :
% 2.27/1.20 ( ( ord_less @ extended_enat @ N @ ( extended_enat2 @ M ) )
% 2.27/1.20 => ? [K: nat] :
% 2.27/1.20 ( N
% 2.27/1.20 = ( extended_enat2 @ K ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_134_less__enatE,axiom,
% 2.27/1.20 ! [N: extended_enat,M: nat] :
% 2.27/1.20 ( ( ord_less @ extended_enat @ N @ ( extended_enat2 @ M ) )
% 2.27/1.20 => ~ ! [K: nat] :
% 2.27/1.20 ( ( N
% 2.27/1.20 = ( extended_enat2 @ K ) )
% 2.27/1.20 => ~ ( ord_less @ nat @ K @ M ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_135_nat__add__left__cancel__le,axiom,
% 2.27/1.20 ! [K2: nat,M: nat,N: nat] :
% 2.27/1.20 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ K2 @ M ) @ ( plus_plus @ nat @ K2 @ N ) )
% 2.27/1.20 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_136_nat__add__left__cancel__less,axiom,
% 2.27/1.20 ! [K2: nat,M: nat,N: nat] :
% 2.27/1.20 ( ( ord_less @ nat @ ( plus_plus @ nat @ K2 @ M ) @ ( plus_plus @ nat @ K2 @ N ) )
% 2.27/1.20 = ( ord_less @ nat @ M @ N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_137_mono__nat__linear__lb,axiom,
% 2.27/1.20 ! [F: nat > nat,M: nat,K2: nat] :
% 2.27/1.20 ( ! [M3: nat,N2: nat] :
% 2.27/1.20 ( ( ord_less @ nat @ M3 @ N2 )
% 2.27/1.20 => ( ord_less @ nat @ ( F @ M3 ) @ ( F @ N2 ) ) )
% 2.27/1.20 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( F @ M ) @ K2 ) @ ( F @ ( plus_plus @ nat @ M @ K2 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_138_ex__has__greatest__nat__lemma,axiom,
% 2.27/1.20 ! [A: $tType,P: A > $o,K2: A,M: A > nat,N: nat] :
% 2.27/1.20 ( ( P @ K2 )
% 2.27/1.20 => ( ! [X3: A] :
% 2.27/1.20 ( ( P @ X3 )
% 2.27/1.20 => ? [Y8: A] :
% 2.27/1.20 ( ( P @ Y8 )
% 2.27/1.20 & ~ ( ord_less_eq @ nat @ ( M @ Y8 ) @ ( M @ X3 ) ) ) )
% 2.27/1.20 => ? [Y3: A] :
% 2.27/1.20 ( ( P @ Y3 )
% 2.27/1.20 & ~ ( ord_less @ nat @ ( M @ Y3 ) @ ( plus_plus @ nat @ ( M @ K2 ) @ N ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_139_infinite__descent__measure,axiom,
% 2.27/1.20 ! [A: $tType,P: A > $o,V: A > nat,X: A] :
% 2.27/1.20 ( ! [X3: A] :
% 2.27/1.20 ( ~ ( P @ X3 )
% 2.27/1.20 => ? [Y8: A] :
% 2.27/1.20 ( ( ord_less @ nat @ ( V @ Y8 ) @ ( V @ X3 ) )
% 2.27/1.20 & ~ ( P @ Y8 ) ) )
% 2.27/1.20 => ( P @ X ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_140_measure__induct__rule,axiom,
% 2.27/1.20 ! [A: $tType,F: A > nat,P: A > $o,A2: A] :
% 2.27/1.20 ( ! [X3: A] :
% 2.27/1.20 ( ! [Y8: A] :
% 2.27/1.20 ( ( ord_less @ nat @ ( F @ Y8 ) @ ( F @ X3 ) )
% 2.27/1.20 => ( P @ Y8 ) )
% 2.27/1.20 => ( P @ X3 ) )
% 2.27/1.20 => ( P @ A2 ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_141_linorder__neqE__nat,axiom,
% 2.27/1.20 ! [X: nat,Y: nat] :
% 2.27/1.20 ( ( X != Y )
% 2.27/1.20 => ( ~ ( ord_less @ nat @ X @ Y )
% 2.27/1.20 => ( ord_less @ nat @ Y @ X ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_142_infinite__descent,axiom,
% 2.27/1.20 ! [P: nat > $o,N: nat] :
% 2.27/1.20 ( ! [N2: nat] :
% 2.27/1.20 ( ~ ( P @ N2 )
% 2.27/1.20 => ? [M2: nat] :
% 2.27/1.20 ( ( ord_less @ nat @ M2 @ N2 )
% 2.27/1.20 & ~ ( P @ M2 ) ) )
% 2.27/1.20 => ( P @ N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_143_nat__less__induct,axiom,
% 2.27/1.20 ! [P: nat > $o,N: nat] :
% 2.27/1.20 ( ! [N2: nat] :
% 2.27/1.20 ( ! [M2: nat] :
% 2.27/1.20 ( ( ord_less @ nat @ M2 @ N2 )
% 2.27/1.20 => ( P @ M2 ) )
% 2.27/1.20 => ( P @ N2 ) )
% 2.27/1.20 => ( P @ N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_144_less__irrefl__nat,axiom,
% 2.27/1.20 ! [N: nat] :
% 2.27/1.20 ~ ( ord_less @ nat @ N @ N ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_145_measure__induct,axiom,
% 2.27/1.20 ! [A: $tType,F: A > nat,P: A > $o,A2: A] :
% 2.27/1.20 ( ! [X3: A] :
% 2.27/1.20 ( ! [Y8: A] :
% 2.27/1.20 ( ( ord_less @ nat @ ( F @ Y8 ) @ ( F @ X3 ) )
% 2.27/1.20 => ( P @ Y8 ) )
% 2.27/1.20 => ( P @ X3 ) )
% 2.27/1.20 => ( P @ A2 ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_146_less__not__refl3,axiom,
% 2.27/1.20 ! [S: nat,T: nat] :
% 2.27/1.20 ( ( ord_less @ nat @ S @ T )
% 2.27/1.20 => ( S != T ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_147_less__not__refl2,axiom,
% 2.27/1.20 ! [N: nat,M: nat] :
% 2.27/1.20 ( ( ord_less @ nat @ N @ M )
% 2.27/1.20 => ( M != N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_148_less__not__refl,axiom,
% 2.27/1.20 ! [N: nat] :
% 2.27/1.20 ~ ( ord_less @ nat @ N @ N ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_149_nat__neq__iff,axiom,
% 2.27/1.20 ! [M: nat,N: nat] :
% 2.27/1.20 ( ( M != N )
% 2.27/1.20 = ( ( ord_less @ nat @ M @ N )
% 2.27/1.20 | ( ord_less @ nat @ N @ M ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_150_ex__has__least__nat,axiom,
% 2.27/1.20 ! [A: $tType,P: A > $o,K2: A,M: A > nat] :
% 2.27/1.20 ( ( P @ K2 )
% 2.27/1.20 => ? [X3: A] :
% 2.27/1.20 ( ( P @ X3 )
% 2.27/1.20 & ! [Y8: A] :
% 2.27/1.20 ( ( P @ Y8 )
% 2.27/1.20 => ( ord_less_eq @ nat @ ( M @ X3 ) @ ( M @ Y8 ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_151_nat__le__linear,axiom,
% 2.27/1.20 ! [M: nat,N: nat] :
% 2.27/1.20 ( ( ord_less_eq @ nat @ M @ N )
% 2.27/1.20 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_152_le__antisym,axiom,
% 2.27/1.20 ! [M: nat,N: nat] :
% 2.27/1.20 ( ( ord_less_eq @ nat @ M @ N )
% 2.27/1.20 => ( ( ord_less_eq @ nat @ N @ M )
% 2.27/1.20 => ( M = N ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_153_eq__imp__le,axiom,
% 2.27/1.20 ! [M: nat,N: nat] :
% 2.27/1.20 ( ( M = N )
% 2.27/1.20 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_154_le__trans,axiom,
% 2.27/1.20 ! [I: nat,J: nat,K2: nat] :
% 2.27/1.20 ( ( ord_less_eq @ nat @ I @ J )
% 2.27/1.20 => ( ( ord_less_eq @ nat @ J @ K2 )
% 2.27/1.20 => ( ord_less_eq @ nat @ I @ K2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_155_le__refl,axiom,
% 2.27/1.20 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_156_nat__add__right__cancel,axiom,
% 2.27/1.20 ! [M: nat,K2: nat,N: nat] :
% 2.27/1.20 ( ( ( plus_plus @ nat @ M @ K2 )
% 2.27/1.20 = ( plus_plus @ nat @ N @ K2 ) )
% 2.27/1.20 = ( M = N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_157_nat__add__left__cancel,axiom,
% 2.27/1.20 ! [K2: nat,M: nat,N: nat] :
% 2.27/1.20 ( ( ( plus_plus @ nat @ K2 @ M )
% 2.27/1.20 = ( plus_plus @ nat @ K2 @ N ) )
% 2.27/1.20 = ( M = N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_158_ex__has__greatest__nat,axiom,
% 2.27/1.20 ! [A: $tType,P: A > $o,K2: A,M: A > nat,B2: nat] :
% 2.27/1.20 ( ( P @ K2 )
% 2.27/1.20 => ( ! [Y3: A] :
% 2.27/1.20 ( ( P @ Y3 )
% 2.27/1.20 => ( ord_less @ nat @ ( M @ Y3 ) @ B2 ) )
% 2.27/1.20 => ? [X3: A] :
% 2.27/1.20 ( ( P @ X3 )
% 2.27/1.20 & ! [Y8: A] :
% 2.27/1.20 ( ( P @ Y8 )
% 2.27/1.20 => ( ord_less_eq @ nat @ ( M @ Y8 ) @ ( M @ X3 ) ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_159_less__mono__imp__le__mono,axiom,
% 2.27/1.20 ! [F: nat > nat,I: nat,J: nat] :
% 2.27/1.20 ( ! [I2: nat,J3: nat] :
% 2.27/1.20 ( ( ord_less @ nat @ I2 @ J3 )
% 2.27/1.20 => ( ord_less @ nat @ ( F @ I2 ) @ ( F @ J3 ) ) )
% 2.27/1.20 => ( ( ord_less_eq @ nat @ I @ J )
% 2.27/1.20 => ( ord_less_eq @ nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_160_le__neq__implies__less,axiom,
% 2.27/1.20 ! [M: nat,N: nat] :
% 2.27/1.20 ( ( ord_less_eq @ nat @ M @ N )
% 2.27/1.20 => ( ( M != N )
% 2.27/1.20 => ( ord_less @ nat @ M @ N ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_161_less__or__eq__imp__le,axiom,
% 2.27/1.20 ! [M: nat,N: nat] :
% 2.27/1.20 ( ( ( ord_less @ nat @ M @ N )
% 2.27/1.20 | ( M = N ) )
% 2.27/1.20 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_162_le__eq__less__or__eq,axiom,
% 2.27/1.20 ( ( ord_less_eq @ nat )
% 2.27/1.20 = ( ^ [M4: nat,N3: nat] :
% 2.27/1.20 ( ( ord_less @ nat @ M4 @ N3 )
% 2.27/1.20 | ( M4 = N3 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_163_less__imp__le__nat,axiom,
% 2.27/1.20 ! [M: nat,N: nat] :
% 2.27/1.20 ( ( ord_less @ nat @ M @ N )
% 2.27/1.20 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_164_nat__less__le,axiom,
% 2.27/1.20 ( ( ord_less @ nat )
% 2.27/1.20 = ( ^ [M4: nat,N3: nat] :
% 2.27/1.20 ( ( ord_less_eq @ nat @ M4 @ N3 )
% 2.27/1.20 & ( M4 != N3 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_165_less__add__eq__less,axiom,
% 2.27/1.20 ! [K2: nat,L: nat,M: nat,N: nat] :
% 2.27/1.20 ( ( ord_less @ nat @ K2 @ L )
% 2.27/1.20 => ( ( ( plus_plus @ nat @ M @ L )
% 2.27/1.20 = ( plus_plus @ nat @ K2 @ N ) )
% 2.27/1.20 => ( ord_less @ nat @ M @ N ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_166_trans__less__add2,axiom,
% 2.27/1.20 ! [I: nat,J: nat,M: nat] :
% 2.27/1.20 ( ( ord_less @ nat @ I @ J )
% 2.27/1.20 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_167_trans__less__add1,axiom,
% 2.27/1.20 ! [I: nat,J: nat,M: nat] :
% 2.27/1.20 ( ( ord_less @ nat @ I @ J )
% 2.27/1.20 => ( ord_less @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_168_add__less__mono1,axiom,
% 2.27/1.20 ! [I: nat,J: nat,K2: nat] :
% 2.27/1.20 ( ( ord_less @ nat @ I @ J )
% 2.27/1.20 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K2 ) @ ( plus_plus @ nat @ J @ K2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_169_not__add__less2,axiom,
% 2.27/1.20 ! [J: nat,I: nat] :
% 2.27/1.20 ~ ( ord_less @ nat @ ( plus_plus @ nat @ J @ I ) @ I ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_170_not__add__less1,axiom,
% 2.27/1.20 ! [I: nat,J: nat] :
% 2.27/1.20 ~ ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ I ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_171_add__less__mono,axiom,
% 2.27/1.20 ! [I: nat,J: nat,K2: nat,L: nat] :
% 2.27/1.20 ( ( ord_less @ nat @ I @ J )
% 2.27/1.20 => ( ( ord_less @ nat @ K2 @ L )
% 2.27/1.20 => ( ord_less @ nat @ ( plus_plus @ nat @ I @ K2 ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_172_add__lessD1,axiom,
% 2.27/1.20 ! [I: nat,J: nat,K2: nat] :
% 2.27/1.20 ( ( ord_less @ nat @ ( plus_plus @ nat @ I @ J ) @ K2 )
% 2.27/1.20 => ( ord_less @ nat @ I @ K2 ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_173_nat__le__iff__add,axiom,
% 2.27/1.20 ( ( ord_less_eq @ nat )
% 2.27/1.20 = ( ^ [M4: nat,N3: nat] :
% 2.27/1.20 ? [K3: nat] :
% 2.27/1.20 ( N3
% 2.27/1.20 = ( plus_plus @ nat @ M4 @ K3 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_174_trans__le__add2,axiom,
% 2.27/1.20 ! [I: nat,J: nat,M: nat] :
% 2.27/1.20 ( ( ord_less_eq @ nat @ I @ J )
% 2.27/1.20 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ M @ J ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_175_trans__le__add1,axiom,
% 2.27/1.20 ! [I: nat,J: nat,M: nat] :
% 2.27/1.20 ( ( ord_less_eq @ nat @ I @ J )
% 2.27/1.20 => ( ord_less_eq @ nat @ I @ ( plus_plus @ nat @ J @ M ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_176_add__le__mono1,axiom,
% 2.27/1.20 ! [I: nat,J: nat,K2: nat] :
% 2.27/1.20 ( ( ord_less_eq @ nat @ I @ J )
% 2.27/1.20 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K2 ) @ ( plus_plus @ nat @ J @ K2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_177_add__le__mono,axiom,
% 2.27/1.20 ! [I: nat,J: nat,K2: nat,L: nat] :
% 2.27/1.20 ( ( ord_less_eq @ nat @ I @ J )
% 2.27/1.20 => ( ( ord_less_eq @ nat @ K2 @ L )
% 2.27/1.20 => ( ord_less_eq @ nat @ ( plus_plus @ nat @ I @ K2 ) @ ( plus_plus @ nat @ J @ L ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_178_le__Suc__ex,axiom,
% 2.27/1.20 ! [K2: nat,L: nat] :
% 2.27/1.20 ( ( ord_less_eq @ nat @ K2 @ L )
% 2.27/1.20 => ? [N2: nat] :
% 2.27/1.20 ( L
% 2.27/1.20 = ( plus_plus @ nat @ K2 @ N2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_179_add__leD2,axiom,
% 2.27/1.20 ! [M: nat,K2: nat,N: nat] :
% 2.27/1.20 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K2 ) @ N )
% 2.27/1.20 => ( ord_less_eq @ nat @ K2 @ N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_180_add__leD1,axiom,
% 2.27/1.20 ! [M: nat,K2: nat,N: nat] :
% 2.27/1.20 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K2 ) @ N )
% 2.27/1.20 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_181_le__add2,axiom,
% 2.27/1.20 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ M @ N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_182_le__add1,axiom,
% 2.27/1.20 ! [N: nat,M: nat] : ( ord_less_eq @ nat @ N @ ( plus_plus @ nat @ N @ M ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_183_add__leE,axiom,
% 2.27/1.20 ! [M: nat,K2: nat,N: nat] :
% 2.27/1.20 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ M @ K2 ) @ N )
% 2.27/1.20 => ~ ( ( ord_less_eq @ nat @ M @ N )
% 2.27/1.20 => ~ ( ord_less_eq @ nat @ K2 @ N ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_184_predicate2I,axiom,
% 2.27/1.20 ! [B: $tType,A: $tType,P: A > B > $o,Q: A > B > $o] :
% 2.27/1.20 ( ! [X3: A,Y3: B] :
% 2.27/1.20 ( ( P @ X3 @ Y3 )
% 2.27/1.20 => ( Q @ X3 @ Y3 ) )
% 2.27/1.20 => ( ord_less_eq @ ( A > B > $o ) @ P @ Q ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_185_order__refl,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( preorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_186_gen__llength__def,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( coindu493225792length @ A )
% 2.27/1.20 = ( ^ [N3: nat,Xs3: coindu1593790203_llist @ A] : ( plus_plus @ extended_enat @ ( extended_enat2 @ N3 ) @ ( coindu1018505716length @ A @ Xs3 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_187_le__fun__def,axiom,
% 2.27/1.20 ! [B: $tType,A: $tType] :
% 2.27/1.20 ( ( ord @ B @ ( type2 @ B ) )
% 2.27/1.20 => ( ( ord_less_eq @ ( A > B ) )
% 2.27/1.20 = ( ^ [F2: A > B,G2: A > B] :
% 2.27/1.20 ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_188_order__subst1,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType] :
% 2.27/1.20 ( ( ( order @ B @ ( type2 @ B ) )
% 2.27/1.20 & ( order @ A @ ( type2 @ A ) ) )
% 2.27/1.20 => ! [A2: A,F: B > A,B2: B,C: B] :
% 2.27/1.20 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 2.27/1.20 => ( ( ord_less_eq @ B @ B2 @ C )
% 2.27/1.20 => ( ! [X3: B,Y3: B] :
% 2.27/1.20 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 2.27/1.20 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.27/1.20 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_189_order__subst2,axiom,
% 2.27/1.20 ! [A: $tType,C3: $tType] :
% 2.27/1.20 ( ( ( order @ C3 @ ( type2 @ C3 ) )
% 2.27/1.20 & ( order @ A @ ( type2 @ A ) ) )
% 2.27/1.20 => ! [A2: A,B2: A,F: A > C3,C: C3] :
% 2.27/1.20 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.27/1.20 => ( ( ord_less_eq @ C3 @ ( F @ B2 ) @ C )
% 2.27/1.20 => ( ! [X3: A,Y3: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.27/1.20 => ( ord_less_eq @ C3 @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.27/1.20 => ( ord_less_eq @ C3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_190_ord__eq__le__subst,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType] :
% 2.27/1.20 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.27/1.20 & ( ord @ A @ ( type2 @ A ) ) )
% 2.27/1.20 => ! [A2: A,F: B > A,B2: B,C: B] :
% 2.27/1.20 ( ( A2
% 2.27/1.20 = ( F @ B2 ) )
% 2.27/1.20 => ( ( ord_less_eq @ B @ B2 @ C )
% 2.27/1.20 => ( ! [X3: B,Y3: B] :
% 2.27/1.20 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 2.27/1.20 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.27/1.20 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_191_ord__le__eq__subst,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType] :
% 2.27/1.20 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.27/1.20 & ( ord @ A @ ( type2 @ A ) ) )
% 2.27/1.20 => ! [A2: A,B2: A,F: A > B,C: B] :
% 2.27/1.20 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.27/1.20 => ( ( ( F @ B2 )
% 2.27/1.20 = C )
% 2.27/1.20 => ( ! [X3: A,Y3: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.27/1.20 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.27/1.20 => ( ord_less_eq @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_192_eq__iff,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ( ( ^ [Y5: A,Z: A] : ( Y5 = Z ) )
% 2.27/1.20 = ( ^ [X2: A,Y4: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 2.27/1.20 & ( ord_less_eq @ A @ Y4 @ X2 ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_193_antisym,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ X @ Y )
% 2.27/1.20 => ( ( ord_less_eq @ A @ Y @ X )
% 2.27/1.20 => ( X = Y ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_194_linear,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( linorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ X @ Y )
% 2.27/1.20 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_195_eq__refl,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( preorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ( X = Y )
% 2.27/1.20 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_196_le__cases,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( linorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ~ ( ord_less_eq @ A @ X @ Y )
% 2.27/1.20 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_197_order_Otrans,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.27/1.20 => ( ( ord_less_eq @ A @ B2 @ C )
% 2.27/1.20 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_198_le__cases3,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( linorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A,Z2: A] :
% 2.27/1.20 ( ( ( ord_less_eq @ A @ X @ Y )
% 2.27/1.20 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 2.27/1.20 => ( ( ( ord_less_eq @ A @ Y @ X )
% 2.27/1.20 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 2.27/1.20 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 2.27/1.20 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 2.27/1.20 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 2.27/1.20 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 2.27/1.20 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.27/1.20 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 2.27/1.20 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 2.27/1.20 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_199_antisym__conv,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [Y: A,X: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ Y @ X )
% 2.27/1.20 => ( ( ord_less_eq @ A @ X @ Y )
% 2.27/1.20 = ( X = Y ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_200_ord__eq__le__trans,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ord @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A] :
% 2.27/1.20 ( ( A2 = B2 )
% 2.27/1.20 => ( ( ord_less_eq @ A @ B2 @ C )
% 2.27/1.20 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_201_ord__le__eq__trans,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ord @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.27/1.20 => ( ( B2 = C )
% 2.27/1.20 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_202_order__class_Oorder_Oantisym,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.27/1.20 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.27/1.20 => ( A2 = B2 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_203_order__trans,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( preorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A,Z2: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ X @ Y )
% 2.27/1.20 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.27/1.20 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_204_dual__order_Orefl,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_205_linorder__wlog,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( linorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [P: A > A > $o,A2: A,B2: A] :
% 2.27/1.20 ( ! [A4: A,B3: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ A4 @ B3 )
% 2.27/1.20 => ( P @ A4 @ B3 ) )
% 2.27/1.20 => ( ! [A4: A,B3: A] :
% 2.27/1.20 ( ( P @ B3 @ A4 )
% 2.27/1.20 => ( P @ A4 @ B3 ) )
% 2.27/1.20 => ( P @ A2 @ B2 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_206_dual__order_Otrans,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [B2: A,A2: A,C: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.27/1.20 => ( ( ord_less_eq @ A @ C @ B2 )
% 2.27/1.20 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_207_dual__order_Oantisym,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [B2: A,A2: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ B2 @ A2 )
% 2.27/1.20 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.27/1.20 => ( A2 = B2 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_208_ord__eq__less__subst,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType] :
% 2.27/1.20 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.27/1.20 & ( ord @ A @ ( type2 @ A ) ) )
% 2.27/1.20 => ! [A2: A,F: B > A,B2: B,C: B] :
% 2.27/1.20 ( ( A2
% 2.27/1.20 = ( F @ B2 ) )
% 2.27/1.20 => ( ( ord_less @ B @ B2 @ C )
% 2.27/1.20 => ( ! [X3: B,Y3: B] :
% 2.27/1.20 ( ( ord_less @ B @ X3 @ Y3 )
% 2.27/1.20 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.27/1.20 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_209_ord__less__eq__subst,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType] :
% 2.27/1.20 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.27/1.20 & ( ord @ A @ ( type2 @ A ) ) )
% 2.27/1.20 => ! [A2: A,B2: A,F: A > B,C: B] :
% 2.27/1.20 ( ( ord_less @ A @ A2 @ B2 )
% 2.27/1.20 => ( ( ( F @ B2 )
% 2.27/1.20 = C )
% 2.27/1.20 => ( ! [X3: A,Y3: A] :
% 2.27/1.20 ( ( ord_less @ A @ X3 @ Y3 )
% 2.27/1.20 => ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.27/1.20 => ( ord_less @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_210_order__less__subst1,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType] :
% 2.27/1.20 ( ( ( order @ B @ ( type2 @ B ) )
% 2.27/1.20 & ( order @ A @ ( type2 @ A ) ) )
% 2.27/1.20 => ! [A2: A,F: B > A,B2: B,C: B] :
% 2.27/1.20 ( ( ord_less @ A @ A2 @ ( F @ B2 ) )
% 2.27/1.20 => ( ( ord_less @ B @ B2 @ C )
% 2.27/1.20 => ( ! [X3: B,Y3: B] :
% 2.27/1.20 ( ( ord_less @ B @ X3 @ Y3 )
% 2.27/1.20 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.27/1.20 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_211_order__less__subst2,axiom,
% 2.27/1.20 ! [A: $tType,C3: $tType] :
% 2.27/1.20 ( ( ( order @ C3 @ ( type2 @ C3 ) )
% 2.27/1.20 & ( order @ A @ ( type2 @ A ) ) )
% 2.27/1.20 => ! [A2: A,B2: A,F: A > C3,C: C3] :
% 2.27/1.20 ( ( ord_less @ A @ A2 @ B2 )
% 2.27/1.20 => ( ( ord_less @ C3 @ ( F @ B2 ) @ C )
% 2.27/1.20 => ( ! [X3: A,Y3: A] :
% 2.27/1.20 ( ( ord_less @ A @ X3 @ Y3 )
% 2.27/1.20 => ( ord_less @ C3 @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.27/1.20 => ( ord_less @ C3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_212_lt__ex,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( no_bot @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A] :
% 2.27/1.20 ? [Y3: A] : ( ord_less @ A @ Y3 @ X ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_213_gt__ex,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( no_top @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A] :
% 2.27/1.20 ? [X1: A] : ( ord_less @ A @ X @ X1 ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_214_neqE,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( linorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ( X != Y )
% 2.27/1.20 => ( ~ ( ord_less @ A @ X @ Y )
% 2.27/1.20 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_215_neq__iff,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( linorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ( X != Y )
% 2.27/1.20 = ( ( ord_less @ A @ X @ Y )
% 2.27/1.20 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_216_order_Oasym,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A] :
% 2.27/1.20 ( ( ord_less @ A @ A2 @ B2 )
% 2.27/1.20 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_217_dense,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( dense_order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ( ord_less @ A @ X @ Y )
% 2.27/1.20 => ? [Z3: A] :
% 2.27/1.20 ( ( ord_less @ A @ X @ Z3 )
% 2.27/1.20 & ( ord_less @ A @ Z3 @ Y ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_218_less__imp__neq,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ( ord_less @ A @ X @ Y )
% 2.27/1.20 => ( X != Y ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_219_less__asym,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( preorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ( ord_less @ A @ X @ Y )
% 2.27/1.20 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_220_less__asym_H,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( preorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A] :
% 2.27/1.20 ( ( ord_less @ A @ A2 @ B2 )
% 2.27/1.20 => ~ ( ord_less @ A @ B2 @ A2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_221_less__trans,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( preorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A,Z2: A] :
% 2.27/1.20 ( ( ord_less @ A @ X @ Y )
% 2.27/1.20 => ( ( ord_less @ A @ Y @ Z2 )
% 2.27/1.20 => ( ord_less @ A @ X @ Z2 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_222_less__linear,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( linorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ( ord_less @ A @ X @ Y )
% 2.27/1.20 | ( X = Y )
% 2.27/1.20 | ( ord_less @ A @ Y @ X ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_223_less__irrefl,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( preorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A] :
% 2.27/1.20 ~ ( ord_less @ A @ X @ X ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_224_ord__eq__less__trans,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ord @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A] :
% 2.27/1.20 ( ( A2 = B2 )
% 2.27/1.20 => ( ( ord_less @ A @ B2 @ C )
% 2.27/1.20 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_225_ord__less__eq__trans,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( ord @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A] :
% 2.27/1.20 ( ( ord_less @ A @ A2 @ B2 )
% 2.27/1.20 => ( ( B2 = C )
% 2.27/1.20 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_226_dual__order_Oasym,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [B2: A,A2: A] :
% 2.27/1.20 ( ( ord_less @ A @ B2 @ A2 )
% 2.27/1.20 => ~ ( ord_less @ A @ A2 @ B2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_227_less__imp__not__eq,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ( ord_less @ A @ X @ Y )
% 2.27/1.20 => ( X != Y ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_228_less__not__sym,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( preorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ( ord_less @ A @ X @ Y )
% 2.27/1.20 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_229_less__induct,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( wellorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [P: A > $o,A2: A] :
% 2.27/1.20 ( ! [X3: A] :
% 2.27/1.20 ( ! [Y8: A] :
% 2.27/1.20 ( ( ord_less @ A @ Y8 @ X3 )
% 2.27/1.20 => ( P @ Y8 ) )
% 2.27/1.20 => ( P @ X3 ) )
% 2.27/1.20 => ( P @ A2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_230_antisym__conv3,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( linorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [Y: A,X: A] :
% 2.27/1.20 ( ~ ( ord_less @ A @ Y @ X )
% 2.27/1.20 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 2.27/1.20 = ( X = Y ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_231_less__imp__not__eq2,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ( ord_less @ A @ X @ Y )
% 2.27/1.20 => ( Y != X ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_232_less__imp__triv,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( preorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A,P: $o] :
% 2.27/1.20 ( ( ord_less @ A @ X @ Y )
% 2.27/1.20 => ( ( ord_less @ A @ Y @ X )
% 2.27/1.20 => P ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_233_linorder__cases,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( linorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ~ ( ord_less @ A @ X @ Y )
% 2.27/1.20 => ( ( X != Y )
% 2.27/1.20 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_234_dual__order_Oirrefl,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A] :
% 2.27/1.20 ~ ( ord_less @ A @ A2 @ A2 ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_235_order_Ostrict__trans,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A,C: A] :
% 2.27/1.20 ( ( ord_less @ A @ A2 @ B2 )
% 2.27/1.20 => ( ( ord_less @ A @ B2 @ C )
% 2.27/1.20 => ( ord_less @ A @ A2 @ C ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_236_less__imp__not__less,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( preorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ( ord_less @ A @ X @ Y )
% 2.27/1.20 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_237_dual__order_Ostrict__trans,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [B2: A,A2: A,C: A] :
% 2.27/1.20 ( ( ord_less @ A @ B2 @ A2 )
% 2.27/1.20 => ( ( ord_less @ A @ C @ B2 )
% 2.27/1.20 => ( ord_less @ A @ C @ A2 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_238_not__less__iff__gr__or__eq,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( linorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 2.27/1.20 = ( ( ord_less @ A @ Y @ X )
% 2.27/1.20 | ( X = Y ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_239_order_Ostrict__implies__not__eq,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [A2: A,B2: A] :
% 2.27/1.20 ( ( ord_less @ A @ A2 @ B2 )
% 2.27/1.20 => ( A2 != B2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_240_dual__order_Ostrict__implies__not__eq,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [B2: A,A2: A] :
% 2.27/1.20 ( ( ord_less @ A @ B2 @ A2 )
% 2.27/1.20 => ( A2 != B2 ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_241_less__fun__def,axiom,
% 2.27/1.20 ! [B: $tType,A: $tType] :
% 2.27/1.20 ( ( ord @ B @ ( type2 @ B ) )
% 2.27/1.20 => ( ( ord_less @ ( A > B ) )
% 2.27/1.20 = ( ^ [F2: A > B,G2: A > B] :
% 2.27/1.20 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 2.27/1.20 & ~ ( ord_less_eq @ ( A > B ) @ G2 @ F2 ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_242_predicate2D,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,X: A,Y: B] :
% 2.27/1.20 ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 2.27/1.20 => ( ( P @ X @ Y )
% 2.27/1.20 => ( Q @ X @ Y ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_243_rev__predicate2D,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType,P: A > B > $o,X: A,Y: B,Q: A > B > $o] :
% 2.27/1.20 ( ( P @ X @ Y )
% 2.27/1.20 => ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 2.27/1.20 => ( Q @ X @ Y ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_244_gen__llength__code_I1_J,axiom,
% 2.27/1.20 ! [A: $tType,N: nat] :
% 2.27/1.20 ( ( coindu493225792length @ A @ N @ ( coindu1598213697e_LNil @ A ) )
% 2.27/1.20 = ( extended_enat2 @ N ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_245_leD,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( linorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [Y: A,X: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ Y @ X )
% 2.27/1.20 => ~ ( ord_less @ A @ X @ Y ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_246_leI,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( linorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ~ ( ord_less @ A @ X @ Y )
% 2.27/1.20 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_247_le__less,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ( ( ord_less_eq @ A )
% 2.27/1.20 = ( ^ [X2: A,Y4: A] :
% 2.27/1.20 ( ( ord_less @ A @ X2 @ Y4 )
% 2.27/1.20 | ( X2 = Y4 ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_248_less__le,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( order @ A @ ( type2 @ A ) )
% 2.27/1.20 => ( ( ord_less @ A )
% 2.27/1.20 = ( ^ [X2: A,Y4: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 2.27/1.20 & ( X2 != Y4 ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_249_order__le__less__subst1,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType] :
% 2.27/1.20 ( ( ( order @ B @ ( type2 @ B ) )
% 2.27/1.20 & ( order @ A @ ( type2 @ A ) ) )
% 2.27/1.20 => ! [A2: A,F: B > A,B2: B,C: B] :
% 2.27/1.20 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 2.27/1.20 => ( ( ord_less @ B @ B2 @ C )
% 2.27/1.20 => ( ! [X3: B,Y3: B] :
% 2.27/1.20 ( ( ord_less @ B @ X3 @ Y3 )
% 2.27/1.20 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.27/1.20 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_250_order__le__less__subst2,axiom,
% 2.27/1.20 ! [A: $tType,C3: $tType] :
% 2.27/1.20 ( ( ( order @ C3 @ ( type2 @ C3 ) )
% 2.27/1.20 & ( order @ A @ ( type2 @ A ) ) )
% 2.27/1.20 => ! [A2: A,B2: A,F: A > C3,C: C3] :
% 2.27/1.20 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.27/1.20 => ( ( ord_less @ C3 @ ( F @ B2 ) @ C )
% 2.27/1.20 => ( ! [X3: A,Y3: A] :
% 2.27/1.20 ( ( ord_less_eq @ A @ X3 @ Y3 )
% 2.27/1.20 => ( ord_less_eq @ C3 @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.27/1.20 => ( ord_less @ C3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_251_order__less__le__subst1,axiom,
% 2.27/1.20 ! [A: $tType,B: $tType] :
% 2.27/1.20 ( ( ( order @ B @ ( type2 @ B ) )
% 2.27/1.20 & ( order @ A @ ( type2 @ A ) ) )
% 2.27/1.20 => ! [A2: A,F: B > A,B2: B,C: B] :
% 2.27/1.20 ( ( ord_less @ A @ A2 @ ( F @ B2 ) )
% 2.27/1.20 => ( ( ord_less_eq @ B @ B2 @ C )
% 2.27/1.20 => ( ! [X3: B,Y3: B] :
% 2.27/1.20 ( ( ord_less_eq @ B @ X3 @ Y3 )
% 2.27/1.20 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.27/1.20 => ( ord_less @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_252_order__less__le__subst2,axiom,
% 2.27/1.20 ! [A: $tType,C3: $tType] :
% 2.27/1.20 ( ( ( order @ C3 @ ( type2 @ C3 ) )
% 2.27/1.20 & ( order @ A @ ( type2 @ A ) ) )
% 2.27/1.20 => ! [A2: A,B2: A,F: A > C3,C: C3] :
% 2.27/1.20 ( ( ord_less @ A @ A2 @ B2 )
% 2.27/1.20 => ( ( ord_less_eq @ C3 @ ( F @ B2 ) @ C )
% 2.27/1.20 => ( ! [X3: A,Y3: A] :
% 2.27/1.20 ( ( ord_less @ A @ X3 @ Y3 )
% 2.27/1.20 => ( ord_less @ C3 @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 2.27/1.20 => ( ord_less @ C3 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(fact_253_not__le,axiom,
% 2.27/1.20 ! [A: $tType] :
% 2.27/1.20 ( ( linorder @ A @ ( type2 @ A ) )
% 2.27/1.20 => ! [X: A,Y: A] :
% 2.27/1.20 ( ( ~ ( ord_less_eq @ A @ X @ Y ) )
% 2.27/1.20 = ( ord_less @ A @ Y @ X ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.27/1.20 ! [A5: $tType,A6: $tType] :
% 2.27/1.20 ( ( preorder @ A6 @ ( type2 @ A6 ) )
% 2.27/1.20 => ( preorder @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.27/1.20 ! [A5: $tType,A6: $tType] :
% 2.27/1.20 ( ( order @ A6 @ ( type2 @ A6 ) )
% 2.27/1.20 => ( order @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_fun___Orderings_Oord,axiom,
% 2.27/1.20 ! [A5: $tType,A6: $tType] :
% 2.27/1.20 ( ( ord @ A6 @ ( type2 @ A6 ) )
% 2.27/1.20 => ( ord @ ( A5 > A6 ) @ ( type2 @ ( A5 > A6 ) ) ) ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add,axiom,
% 2.27/1.20 strict2144017051up_add @ nat @ ( type2 @ nat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 2.27/1.20 ordere223160158up_add @ nat @ ( type2 @ nat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.27/1.20 ordere236663937imp_le @ nat @ ( type2 @ nat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 2.27/1.20 canoni770627133id_add @ nat @ ( type2 @ nat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 2.27/1.20 ordere779506340up_add @ nat @ ( type2 @ nat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 2.27/1.20 cancel_semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 2.27/1.20 ab_semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 2.27/1.20 semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 2.27/1.20 wellorder @ nat @ ( type2 @ nat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 2.27/1.20 preorder @ nat @ ( type2 @ nat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.27/1.20 linorder @ nat @ ( type2 @ nat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 2.27/1.20 no_top @ nat @ ( type2 @ nat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 2.27/1.20 order @ nat @ ( type2 @ nat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 2.27/1.20 ord @ nat @ ( type2 @ nat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_HOL_Obool___Orderings_Opreorder_4,axiom,
% 2.27/1.20 preorder @ $o @ ( type2 @ $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_HOL_Obool___Orderings_Olinorder_5,axiom,
% 2.27/1.20 linorder @ $o @ ( type2 @ $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_HOL_Obool___Orderings_Oorder_6,axiom,
% 2.27/1.20 order @ $o @ ( type2 @ $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_HOL_Obool___Orderings_Oord_7,axiom,
% 2.27/1.20 ord @ $o @ ( type2 @ $o ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Extended__Nat_Oenat___Groups_Ostrict__ordered__ab__semigroup__add_8,axiom,
% 2.27/1.20 strict2144017051up_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_9,axiom,
% 2.27/1.20 canoni770627133id_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Extended__Nat_Oenat___Groups_Oordered__ab__semigroup__add_10,axiom,
% 2.27/1.20 ordere779506340up_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__add_11,axiom,
% 2.27/1.20 ab_semigroup_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Extended__Nat_Oenat___Groups_Osemigroup__add_12,axiom,
% 2.27/1.20 semigroup_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Extended__Nat_Oenat___Orderings_Owellorder_13,axiom,
% 2.27/1.20 wellorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Extended__Nat_Oenat___Orderings_Opreorder_14,axiom,
% 2.27/1.20 preorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Extended__Nat_Oenat___Orderings_Olinorder_15,axiom,
% 2.27/1.20 linorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Extended__Nat_Oenat___Orderings_Oorder_16,axiom,
% 2.27/1.20 order @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.27/1.20
% 2.27/1.20 thf(tcon_Extended__Nat_Oenat___Orderings_Oord_17,axiom,
% 2.27/1.20 ord @ extended_enat @ ( type2 @ extended_enat ) ).
% 2.27/1.20
% 2.27/1.20 thf(conj_0,conjecture,
% 2.27/1.20 p @ ( coindu749330388e_lnth @ a @ ( coindu268472904append @ a @ xs @ xs2 ) @ n ) @ ( coindu749330388e_lnth @ b @ ys @ n ) ).
% 2.27/1.20 ------------------------
% 2.27/1.23 % (20690)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_20469 for (2999ds/27Mi)
% 2.27/1.23 % (20688)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20469 for (2999ds/183Mi)
% 2.27/1.23 % (20692)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_20469 for (2999ds/2Mi)
% 2.27/1.23 % (20692)Instruction limit reached!
% 2.27/1.23 % (20692)------------------------------
% 2.27/1.23 % (20692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.23 % (20692)Termination reason: Unknown
% 2.27/1.23 % (20692)Termination phase: shuffling
% 2.27/1.23
% 2.27/1.23 % (20692)Memory used [KB]: 1407
% 2.27/1.23 % (20692)Time elapsed: 0.002 s
% 2.27/1.23 % (20692)Instructions burned: 3 (million)
% 2.27/1.23 % (20692)------------------------------
% 2.27/1.23 % (20692)------------------------------
% 2.27/1.23 % (20691)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20469 for (2999ds/2Mi)
% 2.27/1.23 % (20695)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20469 for (2999ds/18Mi)
% 2.27/1.23 % (20694)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_20469 for (2999ds/275Mi)
% 2.27/1.24 % (20691)Instruction limit reached!
% 2.27/1.24 % (20691)------------------------------
% 2.27/1.24 % (20691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.24 % (20691)Termination reason: Unknown
% 2.27/1.24 % (20691)Termination phase: shuffling
% 2.27/1.24
% 2.27/1.24 % (20691)Memory used [KB]: 1407
% 2.27/1.24 % (20691)Time elapsed: 0.003 s
% 2.27/1.24 % (20691)Instructions burned: 3 (million)
% 2.27/1.24 % (20691)------------------------------
% 2.27/1.24 % (20691)------------------------------
% 2.27/1.24 % (20698)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20469 for (2999ds/3Mi)
% 2.27/1.24 % (20689)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_20469 for (2999ds/4Mi)
% 2.27/1.24 % (20698)Instruction limit reached!
% 2.27/1.24 % (20698)------------------------------
% 2.27/1.24 % (20698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.24 % (20698)Termination reason: Unknown
% 2.27/1.24 % (20698)Termination phase: shuffling
% 2.27/1.24
% 2.27/1.24 % (20698)Memory used [KB]: 1407
% 2.27/1.24 % (20698)Time elapsed: 0.002 s
% 2.27/1.24 % (20698)Instructions burned: 3 (million)
% 2.27/1.24 % (20698)------------------------------
% 2.27/1.24 % (20698)------------------------------
% 2.27/1.24 % (20690)Instruction limit reached!
% 2.27/1.24 % (20690)------------------------------
% 2.27/1.24 % (20690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.24 % (20690)Termination reason: Unknown
% 2.27/1.24 % (20690)Termination phase: Property scanning
% 2.27/1.24
% 2.27/1.24 % (20690)Memory used [KB]: 1663
% 2.27/1.24 % (20690)Time elapsed: 0.014 s
% 2.27/1.24 % (20690)Instructions burned: 27 (million)
% 2.27/1.24 % (20690)------------------------------
% 2.27/1.24 % (20690)------------------------------
% 2.27/1.24 % (20689)Instruction limit reached!
% 2.27/1.24 % (20689)------------------------------
% 2.27/1.24 % (20689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.24 % (20689)Termination reason: Unknown
% 2.27/1.24 % (20689)Termination phase: shuffling
% 2.27/1.24
% 2.27/1.24 % (20689)Memory used [KB]: 1407
% 2.27/1.24 % (20689)Time elapsed: 0.003 s
% 2.27/1.24 % (20689)Instructions burned: 6 (million)
% 2.27/1.24 % (20689)------------------------------
% 2.27/1.24 % (20689)------------------------------
% 2.27/1.24 % (20695)Instruction limit reached!
% 2.27/1.24 % (20695)------------------------------
% 2.27/1.24 % (20695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.24 % (20695)Termination reason: Unknown
% 2.27/1.24 % (20695)Termination phase: shuffling
% 2.27/1.24
% 2.27/1.24 % (20695)Memory used [KB]: 1663
% 2.27/1.24 % (20695)Time elapsed: 0.011 s
% 2.27/1.24 % (20695)Instructions burned: 19 (million)
% 2.27/1.24 % (20695)------------------------------
% 2.27/1.24 % (20695)------------------------------
% 2.27/1.25 % (20701)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_20469 for (2999ds/37Mi)
% 2.27/1.25 % (20702)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_20469 for (2999ds/15Mi)
% 2.27/1.26 % (20703)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_20469 for (2999ds/3Mi)
% 2.27/1.26 % (20702)Instruction limit reached!
% 2.27/1.26 % (20702)------------------------------
% 2.27/1.26 % (20702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.26 % (20702)Termination reason: Unknown
% 2.27/1.26 % (20702)Termination phase: shuffling
% 2.27/1.26
% 2.27/1.26 % (20702)Memory used [KB]: 1663
% 2.27/1.26 % (20702)Time elapsed: 0.007 s
% 2.27/1.26 % (20702)Instructions burned: 17 (million)
% 2.27/1.26 % (20702)------------------------------
% 2.27/1.26 % (20702)------------------------------
% 2.27/1.26 % (20704)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_20469 for (2999ds/1041Mi)
% 2.27/1.26 % (20703)Instruction limit reached!
% 2.27/1.26 % (20703)------------------------------
% 2.27/1.26 % (20703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.26 % (20703)Termination reason: Unknown
% 2.27/1.26 % (20703)Termination phase: shuffling
% 2.27/1.26
% 2.27/1.26 % (20703)Memory used [KB]: 1407
% 2.27/1.26 % (20703)Time elapsed: 0.003 s
% 2.27/1.26 % (20703)Instructions burned: 4 (million)
% 2.27/1.26 % (20703)------------------------------
% 2.27/1.26 % (20703)------------------------------
% 2.27/1.26 % (20705)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20469 for (2999ds/7Mi)
% 2.27/1.26 % (20705)Instruction limit reached!
% 2.27/1.26 % (20705)------------------------------
% 2.27/1.26 % (20705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.26 % (20705)Termination reason: Unknown
% 2.27/1.26 % (20705)Termination phase: shuffling
% 2.27/1.26
% 2.27/1.26 % (20705)Memory used [KB]: 1407
% 2.27/1.26 % (20705)Time elapsed: 0.005 s
% 2.27/1.26 % (20705)Instructions burned: 7 (million)
% 2.27/1.26 % (20705)------------------------------
% 2.27/1.26 % (20705)------------------------------
% 2.27/1.27 % (20710)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20469 for (2999ds/16Mi)
% 2.27/1.27 % (20701)Instruction limit reached!
% 2.27/1.27 % (20701)------------------------------
% 2.27/1.27 % (20701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.27 % (20701)Termination reason: Unknown
% 2.27/1.27 % (20701)Termination phase: shuffling
% 2.27/1.27
% 2.27/1.27 % (20701)Memory used [KB]: 2046
% 2.27/1.27 % (20701)Time elapsed: 0.019 s
% 2.27/1.27 % (20701)Instructions burned: 38 (million)
% 2.27/1.27 % (20701)------------------------------
% 2.27/1.27 % (20701)------------------------------
% 2.27/1.27 % (20710)Instruction limit reached!
% 2.27/1.27 % (20710)------------------------------
% 2.27/1.27 % (20710)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.27 % (20710)Termination reason: Unknown
% 2.27/1.27 % (20710)Termination phase: shuffling
% 2.27/1.27
% 2.27/1.27 % (20710)Memory used [KB]: 1663
% 2.27/1.27 % (20710)Time elapsed: 0.007 s
% 2.27/1.27 % (20710)Instructions burned: 17 (million)
% 2.27/1.27 % (20710)------------------------------
% 2.27/1.27 % (20710)------------------------------
% 2.27/1.27 % (20711)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_20469 for (2999ds/3Mi)
% 2.27/1.28 % (20711)Instruction limit reached!
% 2.27/1.28 % (20711)------------------------------
% 2.27/1.28 % (20711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.28 % (20711)Termination reason: Unknown
% 2.27/1.28 % (20711)Termination phase: shuffling
% 2.27/1.28
% 2.27/1.28 % (20711)Memory used [KB]: 1407
% 2.27/1.28 % (20711)Time elapsed: 0.003 s
% 2.27/1.28 % (20711)Instructions burned: 3 (million)
% 2.27/1.28 % (20711)------------------------------
% 2.27/1.28 % (20711)------------------------------
% 2.27/1.28 % (20694)Refutation not found, incomplete strategy
% 2.27/1.28 % (20694)------------------------------
% 2.27/1.28 % (20694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.28 % (20694)Termination reason: Refutation not found, incomplete strategy
% 2.27/1.28
% 2.27/1.28
% 2.27/1.28 % (20694)Memory used [KB]: 6780
% 2.27/1.28 % (20694)Time elapsed: 0.044 s
% 2.27/1.28 % (20694)Instructions burned: 87 (million)
% 2.27/1.28 % (20694)------------------------------
% 2.27/1.28 % (20694)------------------------------
% 2.27/1.28 % (20713)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_20469 for (2999ds/3Mi)
% 2.27/1.28 % (20713)Instruction limit reached!
% 2.27/1.28 % (20713)------------------------------
% 2.27/1.28 % (20713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.28 % (20713)Termination reason: Unknown
% 2.27/1.28 % (20713)Termination phase: shuffling
% 2.27/1.28
% 2.27/1.28 % (20713)Memory used [KB]: 1407
% 2.27/1.28 % (20713)Time elapsed: 0.003 s
% 2.27/1.28 % (20713)Instructions burned: 3 (million)
% 2.27/1.28 % (20713)------------------------------
% 2.27/1.28 % (20713)------------------------------
% 2.27/1.28 % (20716)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20469 for (2999ds/3Mi)
% 2.27/1.28 % (20716)Instruction limit reached!
% 2.27/1.28 % (20716)------------------------------
% 2.27/1.28 % (20716)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.28 % (20716)Termination reason: Unknown
% 2.27/1.28 % (20716)Termination phase: shuffling
% 2.27/1.28
% 2.27/1.28 % (20716)Memory used [KB]: 1407
% 2.27/1.28 % (20716)Time elapsed: 0.002 s
% 2.27/1.28 % (20716)Instructions burned: 3 (million)
% 2.27/1.28 % (20716)------------------------------
% 2.27/1.28 % (20716)------------------------------
% 2.27/1.29 % (20715)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20469 for (2999ds/7Mi)
% 2.27/1.29 % (20715)Instruction limit reached!
% 2.27/1.29 % (20715)------------------------------
% 2.27/1.29 % (20715)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.29 % (20715)Termination reason: Unknown
% 2.27/1.29 % (20715)Termination phase: shuffling
% 2.27/1.29
% 2.27/1.29 % (20715)Memory used [KB]: 1407
% 2.27/1.29 % (20715)Time elapsed: 0.005 s
% 2.27/1.29 % (20715)Instructions burned: 7 (million)
% 2.27/1.29 % (20715)------------------------------
% 2.27/1.29 % (20715)------------------------------
% 2.27/1.29 % (20717)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_20469 for (2999ds/4Mi)
% 2.27/1.29 % (20720)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20469 for (2999ds/6Mi)
% 2.27/1.29 % (20717)Instruction limit reached!
% 2.27/1.29 % (20717)------------------------------
% 2.27/1.29 % (20717)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.29 % (20717)Termination reason: Unknown
% 2.27/1.29 % (20717)Termination phase: shuffling
% 2.27/1.29
% 2.27/1.29 % (20717)Memory used [KB]: 1407
% 2.27/1.29 % (20717)Time elapsed: 0.004 s
% 2.27/1.29 % (20717)Instructions burned: 5 (million)
% 2.27/1.29 % (20717)------------------------------
% 2.27/1.29 % (20717)------------------------------
% 2.27/1.29 % (20720)Instruction limit reached!
% 2.27/1.29 % (20720)------------------------------
% 2.27/1.29 % (20720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.27/1.29 % (20720)Termination reason: Unknown
% 2.27/1.29 % (20720)Termination phase: shuffling
% 2.27/1.29
% 2.27/1.29 % (20720)Memory used [KB]: 1407
% 2.27/1.29 % (20720)Time elapsed: 0.003 s
% 2.27/1.29 % (20720)Instructions burned: 6 (million)
% 2.27/1.29 % (20720)------------------------------
% 2.27/1.29 % (20720)------------------------------
% 2.27/1.29 % (20718)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_20469 for (2999ds/18Mi)
% 2.29/1.30 % (20719)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_20469 for (2999ds/710Mi)
% 2.29/1.30 % (20724)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_20469 for (2999ds/5Mi)
% 2.29/1.30 % (20718)Instruction limit reached!
% 2.29/1.30 % (20718)------------------------------
% 2.29/1.30 % (20718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.30 % (20718)Termination reason: Unknown
% 2.29/1.30 % (20718)Termination phase: shuffling
% 2.29/1.30
% 2.29/1.30 % (20718)Memory used [KB]: 1663
% 2.29/1.30 % (20718)Time elapsed: 0.011 s
% 2.29/1.30 % (20718)Instructions burned: 19 (million)
% 2.29/1.30 % (20718)------------------------------
% 2.29/1.30 % (20718)------------------------------
% 2.29/1.31 % (20722)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_20469 for (2999ds/902Mi)
% 2.29/1.31 % (20724)Instruction limit reached!
% 2.29/1.31 % (20724)------------------------------
% 2.29/1.31 % (20724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.31 % (20724)Termination reason: Unknown
% 2.29/1.31 % (20724)Termination phase: shuffling
% 2.29/1.31
% 2.29/1.31 % (20724)Memory used [KB]: 1407
% 2.29/1.31 % (20724)Time elapsed: 0.003 s
% 2.29/1.31 % (20724)Instructions burned: 7 (million)
% 2.29/1.31 % (20724)------------------------------
% 2.29/1.31 % (20724)------------------------------
% 2.29/1.31 % (20723)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_20469 for (2999ds/21Mi)
% 2.29/1.32 % (20726)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_20469 for (2998ds/377Mi)
% 2.29/1.32 % (20688)Instruction limit reached!
% 2.29/1.32 % (20688)------------------------------
% 2.29/1.32 % (20688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.32 % (20688)Termination reason: Unknown
% 2.29/1.32 % (20688)Termination phase: Saturation
% 2.29/1.32
% 2.29/1.32 % (20688)Memory used [KB]: 7291
% 2.29/1.32 % (20688)Time elapsed: 0.084 s
% 2.29/1.32 % (20688)Instructions burned: 184 (million)
% 2.29/1.32 % (20688)------------------------------
% 2.29/1.32 % (20688)------------------------------
% 2.29/1.32 % (20723)Instruction limit reached!
% 2.29/1.32 % (20723)------------------------------
% 2.29/1.32 % (20723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.32 % (20723)Termination reason: Unknown
% 2.29/1.32 % (20723)Termination phase: shuffling
% 2.29/1.32
% 2.29/1.32 % (20723)Memory used [KB]: 1663
% 2.29/1.32 % (20723)Time elapsed: 0.012 s
% 2.29/1.32 % (20723)Instructions burned: 21 (million)
% 2.29/1.32 % (20723)------------------------------
% 2.29/1.32 % (20723)------------------------------
% 2.29/1.32 % (20725)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_20469 for (2998ds/6Mi)
% 2.29/1.32 % (20725)Instruction limit reached!
% 2.29/1.32 % (20725)------------------------------
% 2.29/1.32 % (20725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.32 % (20725)Termination reason: Unknown
% 2.29/1.32 % (20725)Termination phase: shuffling
% 2.29/1.32
% 2.29/1.32 % (20725)Memory used [KB]: 1407
% 2.29/1.32 % (20725)Time elapsed: 0.005 s
% 2.29/1.32 % (20725)Instructions burned: 8 (million)
% 2.29/1.32 % (20725)------------------------------
% 2.29/1.32 % (20725)------------------------------
% 2.29/1.33 % (20730)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_20469 for (2998ds/779Mi)
% 2.29/1.34 % (20731)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_20469 for (2998ds/19Mi)
% 2.29/1.34 % (20732)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_20469 for (2998ds/879Mi)
% 2.29/1.35 % (20731)Instruction limit reached!
% 2.29/1.35 % (20731)------------------------------
% 2.29/1.35 % (20731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.35 % (20731)Termination reason: Unknown
% 2.29/1.35 % (20731)Termination phase: shuffling
% 2.29/1.35
% 2.29/1.35 % (20731)Memory used [KB]: 1663
% 2.29/1.35 % (20731)Time elapsed: 0.011 s
% 2.29/1.35 % (20731)Instructions burned: 20 (million)
% 2.29/1.35 % (20731)------------------------------
% 2.29/1.35 % (20731)------------------------------
% 2.29/1.36 % (20734)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_20469 for (2998ds/17Mi)
% 2.29/1.37 % (20734)Instruction limit reached!
% 2.29/1.37 % (20734)------------------------------
% 2.29/1.37 % (20734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.37 % (20734)Termination reason: Unknown
% 2.29/1.37 % (20734)Termination phase: shuffling
% 2.29/1.37
% 2.29/1.37 % (20734)Memory used [KB]: 1663
% 2.29/1.37 % (20734)Time elapsed: 0.011 s
% 2.29/1.37 % (20734)Instructions burned: 17 (million)
% 2.29/1.37 % (20734)------------------------------
% 2.29/1.37 % (20734)------------------------------
% 2.29/1.39 % (20735)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_20469 for (2998ds/3Mi)
% 2.29/1.39 % (20735)Instruction limit reached!
% 2.29/1.39 % (20735)------------------------------
% 2.29/1.39 % (20735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.39 % (20735)Termination reason: Unknown
% 2.29/1.39 % (20735)Termination phase: shuffling
% 2.29/1.39
% 2.29/1.39 % (20735)Memory used [KB]: 1407
% 2.29/1.39 % (20735)Time elapsed: 0.004 s
% 2.29/1.39 % (20735)Instructions burned: 4 (million)
% 2.29/1.39 % (20735)------------------------------
% 2.29/1.39 % (20735)------------------------------
% 2.29/1.41 % (20736)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_20469 for (2998ds/30Mi)
% 2.29/1.42 % (20736)Instruction limit reached!
% 2.29/1.42 % (20736)------------------------------
% 2.29/1.42 % (20736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.42 % (20736)Termination reason: Unknown
% 2.29/1.42 % (20736)Termination phase: Property scanning
% 2.29/1.42
% 2.29/1.42 % (20736)Memory used [KB]: 1791
% 2.29/1.42 % (20736)Time elapsed: 0.017 s
% 2.29/1.42 % (20736)Instructions burned: 30 (million)
% 2.29/1.42 % (20736)------------------------------
% 2.29/1.42 % (20736)------------------------------
% 2.29/1.44 % (20740)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_20469 for (2997ds/127Mi)
% 2.29/1.46 % (20726)Instruction limit reached!
% 2.29/1.46 % (20726)------------------------------
% 2.29/1.46 % (20726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.46 % (20726)Termination reason: Unknown
% 2.29/1.46 % (20726)Termination phase: Saturation
% 2.29/1.46
% 2.29/1.46 % (20726)Memory used [KB]: 8187
% 2.29/1.46 % (20726)Time elapsed: 0.142 s
% 2.29/1.46 % (20726)Instructions burned: 377 (million)
% 2.29/1.46 % (20726)------------------------------
% 2.29/1.46 % (20726)------------------------------
% 2.29/1.47 % (20743)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_20469 for (2997ds/100Mi)
% 2.29/1.49 % (20743)Instruction limit reached!
% 2.29/1.49 % (20743)------------------------------
% 2.29/1.49 % (20743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.49 % (20743)Termination reason: Unknown
% 2.29/1.49 % (20743)Termination phase: Property scanning
% 2.29/1.49
% 2.29/1.49 % (20743)Memory used [KB]: 2302
% 2.29/1.49 % (20743)Time elapsed: 0.028 s
% 2.29/1.49 % (20743)Instructions burned: 100 (million)
% 2.29/1.49 % (20743)------------------------------
% 2.29/1.49 % (20743)------------------------------
% 2.29/1.50 % (20740)Instruction limit reached!
% 2.29/1.50 % (20740)------------------------------
% 2.29/1.50 % (20740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.50 % (20740)Termination reason: Unknown
% 2.29/1.50 % (20740)Termination phase: Saturation
% 2.29/1.50
% 2.29/1.50 % (20740)Memory used [KB]: 6780
% 2.29/1.50 % (20740)Time elapsed: 0.062 s
% 2.29/1.50 % (20740)Instructions burned: 128 (million)
% 2.29/1.50 % (20740)------------------------------
% 2.29/1.50 % (20740)------------------------------
% 2.29/1.50 % (20746)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_20469 for (2997ds/3Mi)
% 2.29/1.50 % (20746)Instruction limit reached!
% 2.29/1.50 % (20746)------------------------------
% 2.29/1.50 % (20746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.50 % (20746)Termination reason: Unknown
% 2.29/1.50 % (20746)Termination phase: shuffling
% 2.29/1.50
% 2.29/1.50 % (20746)Memory used [KB]: 1407
% 2.29/1.50 % (20746)Time elapsed: 0.003 s
% 2.29/1.50 % (20746)Instructions burned: 4 (million)
% 2.29/1.50 % (20746)------------------------------
% 2.29/1.50 % (20746)------------------------------
% 2.29/1.52 % (20747)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_20469 for (2997ds/20Mi)
% 2.29/1.52 % (20749)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_20469 for (2997ds/86Mi)
% 2.29/1.53 % (20747)Instruction limit reached!
% 2.29/1.53 % (20747)------------------------------
% 2.29/1.53 % (20747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.53 % (20747)Termination reason: Unknown
% 2.29/1.53 % (20747)Termination phase: Property scanning
% 2.29/1.53
% 2.29/1.53 % (20747)Memory used [KB]: 1663
% 2.29/1.53 % (20747)Time elapsed: 0.012 s
% 2.29/1.53 % (20747)Instructions burned: 20 (million)
% 2.29/1.53 % (20747)------------------------------
% 2.29/1.53 % (20747)------------------------------
% 2.29/1.54 % (20749)Instruction limit reached!
% 2.29/1.54 % (20749)------------------------------
% 2.29/1.54 % (20749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.54 % (20749)Termination reason: Unknown
% 2.29/1.54 % (20749)Termination phase: Property scanning
% 2.29/1.54
% 2.29/1.54 % (20749)Memory used [KB]: 2174
% 2.29/1.54 % (20749)Time elapsed: 0.026 s
% 2.29/1.54 % (20749)Instructions burned: 86 (million)
% 2.29/1.54 % (20749)------------------------------
% 2.29/1.54 % (20749)------------------------------
% 2.29/1.54 % (20751)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_20469 for (2996ds/107Mi)
% 2.29/1.55 % (20753)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_20469 for (2996ds/39Mi)
% 2.29/1.56 % (20753)Instruction limit reached!
% 2.29/1.56 % (20753)------------------------------
% 2.29/1.56 % (20753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.56 % (20753)Termination reason: Unknown
% 2.29/1.56 % (20753)Termination phase: Property scanning
% 2.29/1.56
% 2.29/1.56 % (20753)Memory used [KB]: 2174
% 2.29/1.56 % (20753)Time elapsed: 0.012 s
% 2.29/1.56 % (20753)Instructions burned: 39 (million)
% 2.29/1.56 % (20753)------------------------------
% 2.29/1.56 % (20753)------------------------------
% 2.29/1.57 % (20754)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_20469 for (2996ds/448Mi)
% 2.29/1.59 % (20751)Instruction limit reached!
% 2.29/1.59 % (20751)------------------------------
% 2.29/1.59 % (20751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.59 % (20751)Termination reason: Unknown
% 2.29/1.59 % (20751)Termination phase: Saturation
% 2.29/1.59
% 2.29/1.59 % (20751)Memory used [KB]: 6780
% 2.29/1.59 % (20751)Time elapsed: 0.044 s
% 2.29/1.59 % (20751)Instructions burned: 109 (million)
% 2.29/1.59 % (20751)------------------------------
% 2.29/1.59 % (20751)------------------------------
% 2.29/1.60 % (20756)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_20469 for (2996ds/46Mi)
% 2.29/1.62 % (20756)Instruction limit reached!
% 2.29/1.62 % (20756)------------------------------
% 2.29/1.62 % (20756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.62 % (20756)Termination reason: Unknown
% 2.29/1.62 % (20756)Termination phase: Preprocessing 3
% 2.29/1.62
% 2.29/1.62 % (20756)Memory used [KB]: 2046
% 2.29/1.62 % (20756)Time elapsed: 0.021 s
% 2.29/1.62 % (20756)Instructions burned: 47 (million)
% 2.29/1.62 % (20756)------------------------------
% 2.29/1.62 % (20756)------------------------------
% 2.29/1.64 % (20761)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_20469 for (2995ds/98Mi)
% 2.29/1.64 % (20719)Instruction limit reached!
% 2.29/1.64 % (20719)------------------------------
% 2.29/1.64 % (20719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.64 % (20719)Termination reason: Unknown
% 2.29/1.64 % (20719)Termination phase: Saturation
% 2.29/1.64
% 2.29/1.64 % (20719)Memory used [KB]: 8315
% 2.29/1.64 % (20719)Time elapsed: 0.346 s
% 2.29/1.64 % (20719)Instructions burned: 710 (million)
% 2.29/1.64 % (20719)------------------------------
% 2.29/1.64 % (20719)------------------------------
% 2.29/1.66 % (20763)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_20469 for (2995ds/507Mi)
% 2.29/1.68 % (20730)Instruction limit reached!
% 2.29/1.68 % (20730)------------------------------
% 2.29/1.68 % (20730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.68 % (20730)Termination reason: Unknown
% 2.29/1.68 % (20730)Termination phase: Saturation
% 2.29/1.68
% 2.29/1.68 % (20730)Memory used [KB]: 8059
% 2.29/1.68 % (20730)Time elapsed: 0.354 s
% 2.29/1.68 % (20730)Instructions burned: 780 (million)
% 2.29/1.68 % (20730)------------------------------
% 2.29/1.68 % (20730)------------------------------
% 2.29/1.69 % (20761)Instruction limit reached!
% 2.29/1.69 % (20761)------------------------------
% 2.29/1.69 % (20761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.69 % (20761)Termination reason: Unknown
% 2.29/1.69 % (20761)Termination phase: Property scanning
% 2.29/1.69
% 2.29/1.69 % (20761)Memory used [KB]: 2302
% 2.29/1.69 % (20761)Time elapsed: 0.044 s
% 2.29/1.69 % (20761)Instructions burned: 98 (million)
% 2.29/1.69 % (20761)------------------------------
% 2.29/1.69 % (20761)------------------------------
% 2.29/1.70 % (20770)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_20469 for (2995ds/39Mi)
% 2.29/1.71 % (20768)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_20469 for (2995ds/149Mi)
% 2.29/1.72 % (20770)Instruction limit reached!
% 2.29/1.72 % (20770)------------------------------
% 2.29/1.72 % (20770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.72 % (20770)Termination reason: Unknown
% 2.29/1.72 % (20770)Termination phase: Preprocessing 3
% 2.29/1.72
% 2.29/1.72 % (20770)Memory used [KB]: 1918
% 2.29/1.72 % (20770)Time elapsed: 0.021 s
% 2.29/1.72 % (20770)Instructions burned: 39 (million)
% 2.29/1.72 % (20770)------------------------------
% 2.29/1.72 % (20770)------------------------------
% 2.29/1.73 % (20704)Instruction limit reached!
% 2.29/1.73 % (20704)------------------------------
% 2.29/1.73 % (20704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.73 % (20704)Termination reason: Unknown
% 2.29/1.73 % (20704)Termination phase: Saturation
% 2.29/1.73
% 2.29/1.73 % (20704)Memory used [KB]: 9850
% 2.29/1.73 % (20704)Time elapsed: 0.470 s
% 2.29/1.73 % (20704)Instructions burned: 1042 (million)
% 2.29/1.73 % (20704)------------------------------
% 2.29/1.73 % (20704)------------------------------
% 2.29/1.73 % (20763)Refutation not found, incomplete strategy
% 2.29/1.73 % (20763)------------------------------
% 2.29/1.73 % (20763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.73 % (20763)Termination reason: Refutation not found, incomplete strategy
% 2.29/1.73
% 2.29/1.73
% 2.29/1.73 % (20763)Memory used [KB]: 7419
% 2.29/1.73 % (20763)Time elapsed: 0.072 s
% 2.29/1.73 % (20763)Instructions burned: 144 (million)
% 2.29/1.73 % (20763)------------------------------
% 2.29/1.73 % (20763)------------------------------
% 2.29/1.73 % (20754)Instruction limit reached!
% 2.29/1.73 % (20754)------------------------------
% 2.29/1.73 % (20754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.73 % (20754)Termination reason: Unknown
% 2.29/1.73 % (20754)Termination phase: Saturation
% 2.29/1.73
% 2.29/1.73 % (20754)Memory used [KB]: 8571
% 2.29/1.73 % (20754)Time elapsed: 0.176 s
% 2.29/1.73 % (20754)Instructions burned: 449 (million)
% 2.29/1.73 % (20754)------------------------------
% 2.29/1.73 % (20754)------------------------------
% 2.29/1.74 % (20722)Instruction limit reached!
% 2.29/1.74 % (20722)------------------------------
% 2.29/1.74 % (20722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.74 % (20722)Termination reason: Unknown
% 2.29/1.74 % (20722)Termination phase: Saturation
% 2.29/1.74
% 2.29/1.74 % (20722)Memory used [KB]: 8699
% 2.29/1.74 % (20722)Time elapsed: 0.433 s
% 2.29/1.74 % (20722)Instructions burned: 903 (million)
% 2.29/1.74 % (20722)------------------------------
% 2.29/1.74 % (20722)------------------------------
% 2.29/1.74 % (20778)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_20469 for (2994ds/44Mi)
% 2.29/1.74 % (20775)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_20469 for (2994ds/1087Mi)
% 2.29/1.75 % (20773)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_20469 for (2994ds/6Mi)
% 2.29/1.75 % (20776)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_20469 for (2994ds/47Mi)
% 2.29/1.75 % (20773)Instruction limit reached!
% 2.29/1.75 % (20773)------------------------------
% 2.29/1.75 % (20773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.75 % (20773)Termination reason: Unknown
% 2.29/1.75 % (20773)Termination phase: shuffling
% 2.29/1.75
% 2.29/1.75 % (20773)Memory used [KB]: 1407
% 2.29/1.75 % (20773)Time elapsed: 0.004 s
% 2.29/1.75 % (20773)Instructions burned: 6 (million)
% 2.29/1.75 % (20773)------------------------------
% 2.29/1.75 % (20773)------------------------------
% 2.29/1.75 % (20732)Instruction limit reached!
% 2.29/1.75 % (20732)------------------------------
% 2.29/1.75 % (20732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.75 % (20732)Termination reason: Unknown
% 2.29/1.75 % (20732)Termination phase: Saturation
% 2.29/1.75
% 2.29/1.75 % (20732)Memory used [KB]: 7931
% 2.29/1.75 % (20732)Time elapsed: 0.396 s
% 2.29/1.75 % (20732)Instructions burned: 879 (million)
% 2.29/1.75 % (20732)------------------------------
% 2.29/1.75 % (20732)------------------------------
% 2.29/1.75 % (20779)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_20469 for (2994ds/432Mi)
% 2.29/1.76 % (20778)Instruction limit reached!
% 2.29/1.76 % (20778)------------------------------
% 2.29/1.76 % (20778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.76 % (20778)Termination reason: Unknown
% 2.29/1.76 % (20778)Termination phase: Property scanning
% 2.29/1.76
% 2.29/1.76 % (20778)Memory used [KB]: 2174
% 2.29/1.76 % (20778)Time elapsed: 0.014 s
% 2.29/1.76 % (20778)Instructions burned: 45 (million)
% 2.29/1.76 % (20778)------------------------------
% 2.29/1.76 % (20778)------------------------------
% 2.29/1.76 % (20781)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_20469 for (2994ds/31Mi)
% 2.29/1.77 % (20780)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_20469 for (2994ds/62Mi)
% 2.29/1.77 % (20776)Instruction limit reached!
% 2.29/1.77 % (20776)------------------------------
% 2.29/1.77 % (20776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.77 % (20776)Termination reason: Unknown
% 2.29/1.77 % (20776)Termination phase: Property scanning
% 2.29/1.77
% 2.29/1.77 % (20776)Memory used [KB]: 2174
% 2.29/1.77 % (20776)Time elapsed: 0.025 s
% 2.29/1.77 % (20776)Instructions burned: 48 (million)
% 2.29/1.77 % (20776)------------------------------
% 2.29/1.77 % (20776)------------------------------
% 2.29/1.77 % (20768)Instruction limit reached!
% 2.29/1.77 % (20768)------------------------------
% 2.29/1.77 % (20768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.77 % (20768)Termination reason: Unknown
% 2.29/1.77 % (20768)Termination phase: Saturation
% 2.29/1.77
% 2.29/1.77 % (20768)Memory used [KB]: 7036
% 2.29/1.77 % (20768)Time elapsed: 0.053 s
% 2.29/1.77 % (20768)Instructions burned: 150 (million)
% 2.29/1.77 % (20768)------------------------------
% 2.29/1.77 % (20768)------------------------------
% 2.29/1.77 % (20784)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_20469 for (2994ds/96Mi)
% 2.29/1.78 % (20781)Instruction limit reached!
% 2.29/1.78 % (20781)------------------------------
% 2.29/1.78 % (20781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.78 % (20781)Termination reason: Unknown
% 2.29/1.78 % (20781)Termination phase: Preprocessing 1
% 2.29/1.78
% 2.29/1.78 % (20781)Memory used [KB]: 1663
% 2.29/1.78 % (20781)Time elapsed: 0.017 s
% 2.29/1.78 % (20781)Instructions burned: 32 (million)
% 2.29/1.78 % (20781)------------------------------
% 2.29/1.78 % (20781)------------------------------
% 2.29/1.79 % (20787)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_20469 for (2994ds/453Mi)
% 2.29/1.79 % (20788)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_20469 for (2994ds/71Mi)
% 2.29/1.80 % (20780)Instruction limit reached!
% 2.29/1.80 % (20780)------------------------------
% 2.29/1.80 % (20780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.80 % (20780)Termination reason: Unknown
% 2.29/1.80 % (20780)Termination phase: Property scanning
% 2.29/1.80
% 2.29/1.80 % (20780)Memory used [KB]: 2174
% 2.29/1.80 % (20780)Time elapsed: 0.030 s
% 2.29/1.80 % (20780)Instructions burned: 63 (million)
% 2.29/1.80 % (20780)------------------------------
% 2.29/1.80 % (20780)------------------------------
% 2.29/1.80 % (20789)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_20469 for (2994ds/83Mi)
% 2.29/1.81 % (20784)Instruction limit reached!
% 2.29/1.81 % (20784)------------------------------
% 2.29/1.81 % (20784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.81 % (20784)Termination reason: Unknown
% 2.29/1.81 % (20784)Termination phase: Saturation
% 2.29/1.81
% 2.29/1.81 % (20784)Memory used [KB]: 6652
% 2.29/1.81 % (20784)Time elapsed: 0.045 s
% 2.29/1.81 % (20784)Instructions burned: 97 (million)
% 2.29/1.81 % (20784)------------------------------
% 2.29/1.81 % (20784)------------------------------
% 2.29/1.82 % (20790)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_20469 for (2994ds/11Mi)
% 2.29/1.82 % (20788)Instruction limit reached!
% 2.29/1.82 % (20788)------------------------------
% 2.29/1.82 % (20788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.82 % (20788)Termination reason: Unknown
% 2.29/1.82 % (20788)Termination phase: Property scanning
% 2.29/1.82
% 2.29/1.82 % (20788)Memory used [KB]: 2174
% 2.29/1.82 % (20788)Time elapsed: 0.036 s
% 2.29/1.82 % (20788)Instructions burned: 73 (million)
% 2.29/1.82 % (20788)------------------------------
% 2.29/1.82 % (20788)------------------------------
% 2.29/1.82 % (20790)Instruction limit reached!
% 2.29/1.82 % (20790)------------------------------
% 2.29/1.82 % (20790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.82 % (20790)Termination reason: Unknown
% 2.29/1.82 % (20790)Termination phase: shuffling
% 2.29/1.82
% 2.29/1.82 % (20790)Memory used [KB]: 1535
% 2.29/1.82 % (20790)Time elapsed: 0.004 s
% 2.29/1.82 % (20790)Instructions burned: 11 (million)
% 2.29/1.82 % (20790)------------------------------
% 2.29/1.82 % (20790)------------------------------
% 2.29/1.83 % (20791)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_20469 for (2994ds/41Mi)
% 2.29/1.83 % (20794)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_20469 for (2993ds/150Mi)
% 2.29/1.84 % (20793)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20469 for (2993ds/6Mi)
% 2.29/1.84 % (20789)Instruction limit reached!
% 2.29/1.84 % (20789)------------------------------
% 2.29/1.84 % (20789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.84 % (20789)Termination reason: Unknown
% 2.29/1.84 % (20789)Termination phase: Saturation
% 2.29/1.84
% 2.29/1.84 % (20789)Memory used [KB]: 6652
% 2.29/1.84 % (20789)Time elapsed: 0.066 s
% 2.29/1.84 % (20789)Instructions burned: 83 (million)
% 2.29/1.84 % (20789)------------------------------
% 2.29/1.84 % (20789)------------------------------
% 2.29/1.84 % (20793)Instruction limit reached!
% 2.29/1.84 % (20793)------------------------------
% 2.29/1.84 % (20793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.84 % (20793)Termination reason: Unknown
% 2.29/1.84 % (20793)Termination phase: shuffling
% 2.29/1.84
% 2.29/1.84 % (20793)Memory used [KB]: 1407
% 2.29/1.84 % (20793)Time elapsed: 0.005 s
% 2.29/1.84 % (20793)Instructions burned: 7 (million)
% 2.29/1.84 % (20793)------------------------------
% 2.29/1.84 % (20793)------------------------------
% 2.29/1.85 % (20791)Instruction limit reached!
% 2.29/1.85 % (20791)------------------------------
% 2.29/1.85 % (20791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.85 % (20791)Termination reason: Unknown
% 2.29/1.85 % (20791)Termination phase: Property scanning
% 2.29/1.85
% 2.29/1.85 % (20791)Memory used [KB]: 2174
% 2.29/1.85 % (20791)Time elapsed: 0.021 s
% 2.29/1.85 % (20791)Instructions burned: 42 (million)
% 2.29/1.85 % (20791)------------------------------
% 2.29/1.85 % (20791)------------------------------
% 2.29/1.85 % (20797)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_20469 for (2993ds/343Mi)
% 2.29/1.86 % (20798)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_20469 for (2993ds/109Mi)
% 2.29/1.87 % (20799)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_20469 for (2993ds/253Mi)
% 2.29/1.90 % (20794)Instruction limit reached!
% 2.29/1.90 % (20794)------------------------------
% 2.29/1.90 % (20794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.90 % (20794)Termination reason: Unknown
% 2.29/1.90 % (20794)Termination phase: Saturation
% 2.29/1.90
% 2.29/1.90 % (20794)Memory used [KB]: 7164
% 2.29/1.90 % (20794)Time elapsed: 0.096 s
% 2.29/1.90 % (20794)Instructions burned: 150 (million)
% 2.29/1.90 % (20794)------------------------------
% 2.29/1.90 % (20794)------------------------------
% 2.29/1.91 % (20798)Instruction limit reached!
% 2.29/1.91 % (20798)------------------------------
% 2.29/1.91 % (20798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.91 % (20798)Termination reason: Unknown
% 2.29/1.91 % (20798)Termination phase: Saturation
% 2.29/1.91
% 2.29/1.91 % (20798)Memory used [KB]: 6652
% 2.29/1.91 % (20798)Time elapsed: 0.053 s
% 2.29/1.91 % (20798)Instructions burned: 110 (million)
% 2.29/1.91 % (20798)------------------------------
% 2.29/1.91 % (20798)------------------------------
% 2.29/1.92 % (20805)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_20469 for (2992ds/614Mi)
% 2.29/1.92 % (20804)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_20469 for (2993ds/140Mi)
% 2.29/1.97 % (20779)Instruction limit reached!
% 2.29/1.97 % (20779)------------------------------
% 2.29/1.97 % (20779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.97 % (20779)Termination reason: Unknown
% 2.29/1.97 % (20779)Termination phase: Saturation
% 2.29/1.97
% 2.29/1.97 % (20779)Memory used [KB]: 3582
% 2.29/1.97 % (20779)Time elapsed: 0.214 s
% 2.29/1.97 % (20779)Instructions burned: 433 (million)
% 2.29/1.97 % (20779)------------------------------
% 2.29/1.97 % (20779)------------------------------
% 2.29/1.97 % (20799)Instruction limit reached!
% 2.29/1.97 % (20799)------------------------------
% 2.29/1.97 % (20799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.97 % (20799)Termination reason: Unknown
% 2.29/1.97 % (20799)Termination phase: Saturation
% 2.29/1.97
% 2.29/1.97 % (20799)Memory used [KB]: 7547
% 2.29/1.97 % (20799)Time elapsed: 0.128 s
% 2.29/1.97 % (20799)Instructions burned: 256 (million)
% 2.29/1.97 % (20799)------------------------------
% 2.29/1.97 % (20799)------------------------------
% 2.29/1.97 % (20787)Instruction limit reached!
% 2.29/1.97 % (20787)------------------------------
% 2.29/1.97 % (20787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.97 % (20787)Termination reason: Unknown
% 2.29/1.97 % (20787)Termination phase: Saturation
% 2.29/1.97
% 2.29/1.97 % (20787)Memory used [KB]: 7675
% 2.29/1.97 % (20787)Time elapsed: 0.212 s
% 2.29/1.97 % (20787)Instructions burned: 453 (million)
% 2.29/1.97 % (20787)------------------------------
% 2.29/1.97 % (20787)------------------------------
% 2.29/1.99 % (20808)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_20469 for (2992ds/339Mi)
% 2.29/1.99 % (20807)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_20469 for (2992ds/202Mi)
% 2.29/1.99 % (20810)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_20469 for (2992ds/283Mi)
% 2.29/1.99 % (20804)Instruction limit reached!
% 2.29/1.99 % (20804)------------------------------
% 2.29/1.99 % (20804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.99 % (20804)Termination reason: Unknown
% 2.29/1.99 % (20804)Termination phase: Saturation
% 2.29/1.99
% 2.29/1.99 % (20804)Memory used [KB]: 6780
% 2.29/1.99 % (20804)Time elapsed: 0.097 s
% 2.29/1.99 % (20804)Instructions burned: 140 (million)
% 2.29/1.99 % (20804)------------------------------
% 2.29/1.99 % (20804)------------------------------
% 2.29/2.01 % (20797)Instruction limit reached!
% 2.29/2.01 % (20797)------------------------------
% 2.29/2.01 % (20797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/2.01 % (20797)Termination reason: Unknown
% 2.29/2.01 % (20797)Termination phase: Saturation
% 2.29/2.01
% 2.29/2.01 % (20797)Memory used [KB]: 7547
% 2.29/2.01 % (20797)Time elapsed: 0.180 s
% 2.29/2.01 % (20797)Instructions burned: 344 (million)
% 2.29/2.01 % (20797)------------------------------
% 2.29/2.01 % (20797)------------------------------
% 2.29/2.01 % (20811)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_20469 for (2992ds/134Mi)
% 7.72/2.03 % (20812)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_20469 for (2992ds/298Mi)
% 7.72/2.07 % (20811)Instruction limit reached!
% 7.72/2.07 % (20811)------------------------------
% 7.72/2.07 % (20811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.07 % (20811)Termination reason: Unknown
% 7.72/2.07 % (20811)Termination phase: Saturation
% 7.72/2.07
% 7.72/2.07 % (20811)Memory used [KB]: 7036
% 7.72/2.07 % (20811)Time elapsed: 0.064 s
% 7.72/2.07 % (20811)Instructions burned: 134 (million)
% 7.72/2.07 % (20811)------------------------------
% 7.72/2.07 % (20811)------------------------------
% 7.72/2.08 % (20807)Instruction limit reached!
% 7.72/2.08 % (20807)------------------------------
% 7.72/2.08 % (20807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.08 % (20807)Termination reason: Unknown
% 7.72/2.08 % (20807)Termination phase: Saturation
% 7.72/2.08
% 7.72/2.08 % (20807)Memory used [KB]: 6908
% 7.72/2.08 % (20807)Time elapsed: 0.100 s
% 7.72/2.08 % (20807)Instructions burned: 202 (million)
% 7.72/2.08 % (20807)------------------------------
% 7.72/2.08 % (20807)------------------------------
% 7.72/2.09 % (20818)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_20469 for (2991ds/192Mi)
% 7.72/2.10 % (20819)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_20469 for (2991ds/258Mi)
% 7.72/2.10 % (20808)Instruction limit reached!
% 7.72/2.10 % (20808)------------------------------
% 7.72/2.10 % (20808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.72/2.10 % (20808)Termination reason: Unknown
% 7.72/2.10 % (20808)Termination phase: Saturation
% 7.72/2.10
% 7.72/2.10 % (20808)Memory used [KB]: 7419
% 7.72/2.10 % (20808)Time elapsed: 0.120 s
% 7.72/2.10 % (20808)Instructions burned: 339 (million)
% 7.72/2.10 % (20808)------------------------------
% 7.72/2.10 % (20808)------------------------------
% 7.72/2.11 % (20821)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_20469 for (2991ds/90Mi)
% 8.23/2.13 % (20810)Instruction limit reached!
% 8.23/2.13 % (20810)------------------------------
% 8.23/2.13 % (20810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.13 % (20810)Termination reason: Unknown
% 8.23/2.13 % (20810)Termination phase: Saturation
% 8.23/2.13
% 8.23/2.13 % (20810)Memory used [KB]: 7547
% 8.23/2.13 % (20810)Time elapsed: 0.141 s
% 8.23/2.13 % (20810)Instructions burned: 284 (million)
% 8.23/2.13 % (20810)------------------------------
% 8.23/2.13 % (20810)------------------------------
% 8.23/2.15 % (20823)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_20469 for (2990ds/231Mi)
% 8.23/2.16 % (20812)Instruction limit reached!
% 8.23/2.16 % (20812)------------------------------
% 8.23/2.16 % (20812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.16 % (20812)Termination reason: Unknown
% 8.23/2.16 % (20812)Termination phase: Saturation
% 8.23/2.16
% 8.23/2.16 % (20812)Memory used [KB]: 8059
% 8.23/2.16 % (20812)Time elapsed: 0.131 s
% 8.23/2.16 % (20812)Instructions burned: 299 (million)
% 8.23/2.16 % (20812)------------------------------
% 8.23/2.16 % (20812)------------------------------
% 8.23/2.16 % (20821)Instruction limit reached!
% 8.23/2.16 % (20821)------------------------------
% 8.23/2.16 % (20821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.16 % (20821)Termination reason: Unknown
% 8.23/2.16 % (20821)Termination phase: Saturation
% 8.23/2.16
% 8.23/2.16 % (20821)Memory used [KB]: 2174
% 8.23/2.16 % (20821)Time elapsed: 0.044 s
% 8.23/2.16 % (20821)Instructions burned: 91 (million)
% 8.23/2.16 % (20821)------------------------------
% 8.23/2.16 % (20821)------------------------------
% 8.23/2.17 % (20826)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_20469 for (2990ds/458Mi)
% 8.23/2.17 % (20775)Instruction limit reached!
% 8.23/2.17 % (20775)------------------------------
% 8.23/2.17 % (20775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.17 % (20775)Termination reason: Unknown
% 8.23/2.17 % (20775)Termination phase: Saturation
% 8.23/2.17
% 8.23/2.17 % (20775)Memory used [KB]: 7675
% 8.23/2.17 % (20775)Time elapsed: 0.439 s
% 8.23/2.17 % (20775)Instructions burned: 1087 (million)
% 8.23/2.17 % (20775)------------------------------
% 8.23/2.17 % (20775)------------------------------
% 8.23/2.17 % (20827)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_20469 for (2990ds/31Mi)
% 8.23/2.18 % (20818)Instruction limit reached!
% 8.23/2.18 % (20818)------------------------------
% 8.23/2.18 % (20818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.18 % (20818)Termination reason: Unknown
% 8.23/2.18 % (20818)Termination phase: Saturation
% 8.23/2.18
% 8.23/2.18 % (20818)Memory used [KB]: 7803
% 8.23/2.18 % (20818)Time elapsed: 0.096 s
% 8.23/2.18 % (20818)Instructions burned: 192 (million)
% 8.23/2.18 % (20818)------------------------------
% 8.23/2.18 % (20818)------------------------------
% 8.23/2.19 % (20829)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_20469 for (2990ds/297Mi)
% 8.23/2.19 % (20827)Instruction limit reached!
% 8.23/2.19 % (20827)------------------------------
% 8.23/2.19 % (20827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.23/2.19 % (20827)Termination reason: Unknown
% 8.23/2.19 % (20827)Termination phase: Property scanning
% 8.23/2.19
% 8.23/2.19 % (20827)Memory used [KB]: 1663
% 8.23/2.19 % (20827)Time elapsed: 0.017 s
% 8.23/2.19 % (20827)Instructions burned: 31 (million)
% 8.23/2.19 % (20827)------------------------------
% 8.23/2.19 % (20827)------------------------------
% 8.71/2.20 % (20830)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_20469 for (2990ds/987Mi)
% 8.71/2.21 % (20831)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_20469 for (2990ds/182Mi)
% 8.71/2.22 % (20805)Instruction limit reached!
% 8.71/2.22 % (20805)------------------------------
% 8.71/2.22 % (20805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.71/2.22 % (20805)Termination reason: Unknown
% 8.71/2.22 % (20805)Termination phase: Saturation
% 8.71/2.22
% 8.71/2.22 % (20805)Memory used [KB]: 8955
% 8.71/2.22 % (20805)Time elapsed: 0.300 s
% 8.71/2.22 % (20805)Instructions burned: 614 (million)
% 8.71/2.22 % (20805)------------------------------
% 8.71/2.22 % (20805)------------------------------
% 8.71/2.23 % (20819)Instruction limit reached!
% 8.71/2.23 % (20819)------------------------------
% 8.71/2.23 % (20819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.71/2.23 % (20819)Termination reason: Unknown
% 8.71/2.23 % (20819)Termination phase: Saturation
% 8.71/2.23
% 8.71/2.23 % (20819)Memory used [KB]: 7547
% 8.71/2.23 % (20819)Time elapsed: 0.150 s
% 8.71/2.23 % (20819)Instructions burned: 258 (million)
% 8.71/2.23 % (20819)------------------------------
% 8.71/2.23 % (20819)------------------------------
% 8.71/2.24 % (20836)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_20469 for (2989ds/182Mi)
% 8.71/2.25 % (20823)Instruction limit reached!
% 8.71/2.25 % (20823)------------------------------
% 8.71/2.25 % (20823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.71/2.25 % (20823)Termination reason: Unknown
% 8.71/2.25 % (20823)Termination phase: Saturation
% 8.71/2.25
% 8.71/2.25 % (20823)Memory used [KB]: 6908
% 8.71/2.25 % (20823)Time elapsed: 0.103 s
% 8.71/2.25 % (20823)Instructions burned: 231 (million)
% 8.71/2.25 % (20823)------------------------------
% 8.71/2.25 % (20823)------------------------------
% 8.71/2.25 % (20837)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_20469 for (2989ds/154Mi)
% 8.71/2.27 % (20839)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_20469 for (2989ds/79Mi)
% 8.71/2.29 % (20831)Instruction limit reached!
% 8.71/2.29 % (20831)------------------------------
% 8.71/2.29 % (20831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.71/2.29 % (20831)Termination reason: Unknown
% 8.71/2.29 % (20831)Termination phase: Saturation
% 8.71/2.29
% 8.71/2.29 % (20831)Memory used [KB]: 7291
% 8.71/2.29 % (20831)Time elapsed: 0.088 s
% 8.71/2.29 % (20831)Instructions burned: 183 (million)
% 8.71/2.29 % (20831)------------------------------
% 8.71/2.29 % (20831)------------------------------
% 9.11/2.31 % (20839)Instruction limit reached!
% 9.11/2.31 % (20839)------------------------------
% 9.11/2.31 % (20839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.31 % (20839)Termination reason: Unknown
% 9.11/2.31 % (20839)Termination phase: Property scanning
% 9.11/2.31
% 9.11/2.31 % (20839)Memory used [KB]: 2174
% 9.11/2.31 % (20839)Time elapsed: 0.040 s
% 9.11/2.31 % (20839)Instructions burned: 80 (million)
% 9.11/2.31 % (20839)------------------------------
% 9.11/2.31 % (20839)------------------------------
% 9.11/2.31 % (20842)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_20469 for (2989ds/216Mi)
% 9.11/2.32 % (20826)Instruction limit reached!
% 9.11/2.32 % (20826)------------------------------
% 9.11/2.32 % (20826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.32 % (20826)Termination reason: Unknown
% 9.11/2.32 % (20826)Termination phase: Saturation
% 9.11/2.32
% 9.11/2.32 % (20826)Memory used [KB]: 8187
% 9.11/2.32 % (20826)Time elapsed: 0.151 s
% 9.11/2.32 % (20826)Instructions burned: 458 (million)
% 9.11/2.32 % (20826)------------------------------
% 9.11/2.32 % (20826)------------------------------
% 9.11/2.32 % (20836)Instruction limit reached!
% 9.11/2.32 % (20836)------------------------------
% 9.11/2.32 % (20836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.32 % (20836)Termination reason: Unknown
% 9.11/2.32 % (20836)Termination phase: Saturation
% 9.11/2.32
% 9.11/2.32 % (20836)Memory used [KB]: 7291
% 9.11/2.32 % (20836)Time elapsed: 0.083 s
% 9.11/2.32 % (20836)Instructions burned: 182 (million)
% 9.11/2.32 % (20836)------------------------------
% 9.11/2.32 % (20836)------------------------------
% 9.11/2.32 % (20837)Instruction limit reached!
% 9.11/2.32 % (20837)------------------------------
% 9.11/2.32 % (20837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.32 % (20837)Termination reason: Unknown
% 9.11/2.32 % (20837)Termination phase: Saturation
% 9.11/2.32
% 9.11/2.32 % (20837)Memory used [KB]: 2686
% 9.11/2.32 % (20837)Time elapsed: 0.072 s
% 9.11/2.32 % (20837)Instructions burned: 154 (million)
% 9.11/2.32 % (20837)------------------------------
% 9.11/2.32 % (20837)------------------------------
% 9.11/2.33 % (20829)Instruction limit reached!
% 9.11/2.33 % (20829)------------------------------
% 9.11/2.33 % (20829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.33 % (20829)Termination reason: Unknown
% 9.11/2.33 % (20829)Termination phase: Saturation
% 9.11/2.33
% 9.11/2.33 % (20829)Memory used [KB]: 7419
% 9.11/2.33 % (20829)Time elapsed: 0.143 s
% 9.11/2.33 % (20829)Instructions burned: 298 (million)
% 9.11/2.33 % (20829)------------------------------
% 9.11/2.33 % (20829)------------------------------
% 9.11/2.33 % (20845)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_20469 for (2988ds/114Mi)
% 9.11/2.34 % (20849)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_20469 for (2988ds/164Mi)
% 9.11/2.34 % (20846)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_20469 for (2988ds/922Mi)
% 9.11/2.34 % (20847)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_20469 for (2988ds/182Mi)
% 9.11/2.34 % (20850)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_20469 for (2988ds/50Mi)
% 9.11/2.37 % (20850)Instruction limit reached!
% 9.11/2.37 % (20850)------------------------------
% 9.11/2.37 % (20850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.37 % (20850)Termination reason: Unknown
% 9.11/2.37 % (20850)Termination phase: Property scanning
% 9.11/2.37
% 9.11/2.37 % (20850)Memory used [KB]: 2174
% 9.11/2.37 % (20850)Time elapsed: 0.025 s
% 9.11/2.37 % (20850)Instructions burned: 51 (million)
% 9.11/2.37 % (20850)------------------------------
% 9.11/2.37 % (20850)------------------------------
% 9.11/2.38 % (20845)Instruction limit reached!
% 9.11/2.38 % (20845)------------------------------
% 9.11/2.38 % (20845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.38 % (20845)Termination reason: Unknown
% 9.11/2.38 % (20845)Termination phase: Saturation
% 9.11/2.38
% 9.11/2.38 % (20845)Memory used [KB]: 6780
% 9.11/2.38 % (20845)Time elapsed: 0.056 s
% 9.11/2.38 % (20845)Instructions burned: 115 (million)
% 9.11/2.38 % (20845)------------------------------
% 9.11/2.38 % (20845)------------------------------
% 9.11/2.38 % (20853)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_20469 for (2988ds/368Mi)
% 9.11/2.39 % (20849)Instruction limit reached!
% 9.11/2.39 % (20849)------------------------------
% 9.11/2.39 % (20849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.11/2.39 % (20849)Termination reason: Unknown
% 9.11/2.39 % (20849)Termination phase: Saturation
% 9.11/2.39
% 9.11/2.39 % (20849)Memory used [KB]: 2558
% 9.11/2.39 % (20849)Time elapsed: 0.059 s
% 9.11/2.39 % (20849)Instructions burned: 165 (million)
% 9.11/2.39 % (20849)------------------------------
% 9.11/2.39 % (20849)------------------------------
% 9.85/2.40 % (20854)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_20469 for (2988ds/1021Mi)
% 9.85/2.41 % (20842)Instruction limit reached!
% 9.85/2.41 % (20842)------------------------------
% 9.85/2.41 % (20842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.85/2.41 % (20842)Termination reason: Unknown
% 9.85/2.41 % (20842)Termination phase: Saturation
% 9.85/2.41
% 9.85/2.41 % (20842)Memory used [KB]: 7419
% 9.85/2.41 % (20842)Time elapsed: 0.102 s
% 9.85/2.41 % (20842)Instructions burned: 217 (million)
% 9.85/2.41 % (20842)------------------------------
% 9.85/2.41 % (20842)------------------------------
% 9.85/2.41 % (20856)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_20469 for (2988ds/267Mi)
% 9.85/2.42 % (20847)Instruction limit reached!
% 9.85/2.42 % (20847)------------------------------
% 9.85/2.42 % (20847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.85/2.42 % (20847)Termination reason: Unknown
% 9.85/2.42 % (20847)Termination phase: Saturation
% 9.85/2.42
% 9.85/2.42 % (20847)Memory used [KB]: 7291
% 9.85/2.42 % (20847)Time elapsed: 0.085 s
% 9.85/2.42 % (20847)Instructions burned: 182 (million)
% 9.85/2.42 % (20847)------------------------------
% 9.85/2.42 % (20847)------------------------------
% 9.85/2.43 % (20857)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_20469 for (2987ds/204Mi)
% 9.85/2.44 % (20859)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_20469 for (2987ds/26Mi)
% 9.85/2.45 % (20859)Instruction limit reached!
% 9.85/2.45 % (20859)------------------------------
% 9.85/2.45 % (20859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.85/2.45 % (20859)Termination reason: Unknown
% 9.85/2.45 % (20859)Termination phase: shuffling
% 9.85/2.45
% 9.85/2.45 % (20859)Memory used [KB]: 1918
% 9.85/2.45 % (20859)Time elapsed: 0.014 s
% 9.85/2.45 % (20859)Instructions burned: 27 (million)
% 9.85/2.45 % (20859)------------------------------
% 9.85/2.45 % (20859)------------------------------
% 9.85/2.46 % (20860)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_20469 for (2987ds/53Mi)
% 9.85/2.49 % (20860)Instruction limit reached!
% 9.85/2.49 % (20860)------------------------------
% 9.85/2.49 % (20860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.85/2.49 % (20860)Termination reason: Unknown
% 9.85/2.49 % (20860)Termination phase: Property scanning
% 9.85/2.49
% 9.85/2.49 % (20860)Memory used [KB]: 2174
% 9.85/2.49 % (20860)Time elapsed: 0.026 s
% 9.85/2.49 % (20860)Instructions burned: 54 (million)
% 9.85/2.49 % (20860)------------------------------
% 9.85/2.49 % (20860)------------------------------
% 10.14/2.50 % (20857)Instruction limit reached!
% 10.14/2.50 % (20857)------------------------------
% 10.14/2.50 % (20857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.14/2.50 % (20857)Termination reason: Unknown
% 10.14/2.50 % (20857)Termination phase: Saturation
% 10.14/2.50
% 10.14/2.50 % (20857)Memory used [KB]: 7291
% 10.14/2.50 % (20857)Time elapsed: 0.078 s
% 10.14/2.50 % (20857)Instructions burned: 204 (million)
% 10.14/2.50 % (20857)------------------------------
% 10.14/2.50 % (20857)------------------------------
% 10.14/2.51 % (20864)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_20469 for (2987ds/4436Mi)
% 10.14/2.51 % (20856)Instruction limit reached!
% 10.14/2.51 % (20856)------------------------------
% 10.14/2.51 % (20856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.14/2.51 % (20856)Termination reason: Unknown
% 10.14/2.51 % (20856)Termination phase: Saturation
% 10.14/2.51
% 10.14/2.51 % (20856)Memory used [KB]: 7547
% 10.14/2.51 % (20856)Time elapsed: 0.103 s
% 10.14/2.51 % (20856)Instructions burned: 267 (million)
% 10.14/2.51 % (20856)------------------------------
% 10.14/2.51 % (20856)------------------------------
% 10.14/2.51 % (20865)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_20469 for (2987ds/1539Mi)
% 10.14/2.53 % (20866)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_20469 for (2986ds/408Mi)
% 10.14/2.55 % (20853)Instruction limit reached!
% 10.14/2.55 % (20853)------------------------------
% 10.14/2.55 % (20853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.14/2.55 % (20853)Termination reason: Unknown
% 10.14/2.55 % (20853)Termination phase: Saturation
% 10.14/2.55
% 10.14/2.55 % (20853)Memory used [KB]: 8187
% 10.14/2.55 % (20853)Time elapsed: 0.166 s
% 10.14/2.55 % (20853)Instructions burned: 368 (million)
% 10.14/2.55 % (20853)------------------------------
% 10.14/2.55 % (20853)------------------------------
% 10.14/2.56 % (20867)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_20469 for (2986ds/5205Mi)
% 10.54/2.65 % (20830)Instruction limit reached!
% 10.54/2.65 % (20830)------------------------------
% 10.54/2.65 % (20830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.54/2.65 % (20830)Termination reason: Unknown
% 10.54/2.65 % (20830)Termination phase: Saturation
% 10.54/2.65
% 10.54/2.65 % (20830)Memory used [KB]: 8955
% 10.54/2.65 % (20830)Time elapsed: 0.447 s
% 10.54/2.65 % (20830)Instructions burned: 988 (million)
% 10.54/2.65 % (20830)------------------------------
% 10.54/2.65 % (20830)------------------------------
% 10.54/2.66 % (20868)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_20469 for (2985ds/1913Mi)
% 11.01/2.73 % (20866)Instruction limit reached!
% 11.01/2.73 % (20866)------------------------------
% 11.01/2.73 % (20866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.01/2.73 % (20866)Termination reason: Unknown
% 11.01/2.73 % (20866)Termination phase: Saturation
% 11.01/2.73
% 11.01/2.73 % (20866)Memory used [KB]: 8059
% 11.01/2.73 % (20866)Time elapsed: 0.200 s
% 11.01/2.73 % (20866)Instructions burned: 408 (million)
% 11.01/2.73 % (20866)------------------------------
% 11.01/2.73 % (20866)------------------------------
% 11.01/2.75 % (20872)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_20469 for (2984ds/4350Mi)
% 11.01/2.79 % (20846)Instruction limit reached!
% 11.01/2.79 % (20846)------------------------------
% 11.01/2.79 % (20846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.01/2.79 % (20846)Termination reason: Unknown
% 11.01/2.79 % (20846)Termination phase: Saturation
% 11.01/2.79
% 11.01/2.79 % (20846)Memory used [KB]: 8443
% 11.01/2.79 % (20846)Time elapsed: 0.460 s
% 11.01/2.79 % (20846)Instructions burned: 922 (million)
% 11.01/2.79 % (20846)------------------------------
% 11.01/2.79 % (20846)------------------------------
% 11.69/2.81 % (20874)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_20469 for (2984ds/68Mi)
% 11.69/2.84 % (20874)Instruction limit reached!
% 11.69/2.84 % (20874)------------------------------
% 11.69/2.84 % (20874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.69/2.84 % (20874)Termination reason: Unknown
% 11.69/2.84 % (20874)Termination phase: Function definition elimination
% 11.69/2.84
% 11.69/2.84 % (20874)Memory used [KB]: 2046
% 11.69/2.84 % (20874)Time elapsed: 0.035 s
% 11.69/2.84 % (20874)Instructions burned: 69 (million)
% 11.69/2.84 % (20874)------------------------------
% 11.69/2.84 % (20874)------------------------------
% 11.69/2.86 % (20876)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_20469 for (2983ds/358Mi)
% 11.69/2.87 % (20854)Instruction limit reached!
% 11.69/2.87 % (20854)------------------------------
% 11.69/2.87 % (20854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.69/2.87 % (20854)Termination reason: Unknown
% 11.69/2.87 % (20854)Termination phase: Saturation
% 11.69/2.87
% 11.69/2.87 % (20854)Memory used [KB]: 9466
% 11.69/2.87 % (20854)Time elapsed: 0.468 s
% 11.69/2.87 % (20854)Instructions burned: 1023 (million)
% 11.69/2.87 % (20854)------------------------------
% 11.69/2.87 % (20854)------------------------------
% 11.69/2.88 % (20877)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_20469 for (2983ds/31Mi)
% 11.69/2.89 % (20877)Instruction limit reached!
% 11.69/2.89 % (20877)------------------------------
% 11.69/2.89 % (20877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.69/2.89 % (20877)Termination reason: Unknown
% 11.69/2.89 % (20877)Termination phase: Property scanning
% 11.69/2.89
% 11.69/2.89 % (20877)Memory used [KB]: 1663
% 11.69/2.89 % (20877)Time elapsed: 0.011 s
% 11.69/2.89 % (20877)Instructions burned: 31 (million)
% 11.69/2.89 % (20877)------------------------------
% 11.69/2.89 % (20877)------------------------------
% 12.24/2.90 % (20879)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_20469 for (2983ds/279Mi)
% 12.24/2.93 % (20879)Refutation not found, incomplete strategy
% 12.24/2.93 % (20879)------------------------------
% 12.24/2.93 % (20879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.24/2.93 % (20879)Termination reason: Refutation not found, incomplete strategy
% 12.24/2.93
% 12.24/2.93
% 12.24/2.93 % (20879)Memory used [KB]: 6908
% 12.24/2.93 % (20879)Time elapsed: 0.033 s
% 12.24/2.93 % (20879)Instructions burned: 113 (million)
% 12.24/2.93 % (20879)------------------------------
% 12.24/2.93 % (20879)------------------------------
% 12.24/2.94 % (20882)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_20469 for (2982ds/258Mi)
% 14.62/3.03 % (20882)Instruction limit reached!
% 14.62/3.03 % (20882)------------------------------
% 14.62/3.03 % (20882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.62/3.03 % (20882)Termination reason: Unknown
% 14.62/3.03 % (20882)Termination phase: Saturation
% 14.62/3.03
% 14.62/3.03 % (20882)Memory used [KB]: 7419
% 14.62/3.03 % (20882)Time elapsed: 0.093 s
% 14.62/3.03 % (20882)Instructions burned: 258 (million)
% 14.62/3.03 % (20882)------------------------------
% 14.62/3.03 % (20882)------------------------------
% 14.62/3.04 % (20884)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_20469 for (2981ds/26Mi)
% 14.62/3.05 % (20876)Instruction limit reached!
% 14.62/3.05 % (20876)------------------------------
% 14.62/3.05 % (20876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.62/3.05 % (20876)Termination reason: Unknown
% 14.62/3.05 % (20876)Termination phase: Saturation
% 14.62/3.05
% 14.62/3.05 % (20876)Memory used [KB]: 7291
% 14.62/3.05 % (20876)Time elapsed: 0.205 s
% 14.62/3.05 % (20876)Instructions burned: 359 (million)
% 14.62/3.05 % (20876)------------------------------
% 14.62/3.05 % (20876)------------------------------
% 14.62/3.05 % (20884)Instruction limit reached!
% 14.62/3.05 % (20884)------------------------------
% 14.62/3.05 % (20884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.62/3.05 % (20884)Termination reason: Unknown
% 14.62/3.05 % (20884)Termination phase: shuffling
% 14.62/3.05
% 14.62/3.05 % (20884)Memory used [KB]: 1918
% 14.62/3.05 % (20884)Time elapsed: 0.010 s
% 14.62/3.05 % (20884)Instructions burned: 27 (million)
% 14.62/3.05 % (20884)------------------------------
% 14.62/3.05 % (20884)------------------------------
% 14.62/3.06 % (20885)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_20469 for (2981ds/995Mi)
% 14.62/3.07 % (20886)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_20469 for (2981ds/373Mi)
% 15.54/3.23 % (20865)Instruction limit reached!
% 15.54/3.23 % (20865)------------------------------
% 15.54/3.23 % (20865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/3.23 % (20865)Termination reason: Unknown
% 15.54/3.23 % (20865)Termination phase: Saturation
% 15.54/3.23
% 15.54/3.23 % (20865)Memory used [KB]: 10490
% 15.54/3.23 % (20865)Time elapsed: 0.720 s
% 15.54/3.23 % (20865)Instructions burned: 1539 (million)
% 15.54/3.23 % (20865)------------------------------
% 15.54/3.23 % (20865)------------------------------
% 15.54/3.24 % (20889)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_20469 for (2979ds/253Mi)
% 15.54/3.25 % (20886)Instruction limit reached!
% 15.54/3.25 % (20886)------------------------------
% 15.54/3.25 % (20886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.54/3.25 % (20886)Termination reason: Unknown
% 15.54/3.25 % (20886)Termination phase: Saturation
% 15.54/3.25
% 15.54/3.25 % (20886)Memory used [KB]: 7931
% 15.54/3.25 % (20886)Time elapsed: 0.205 s
% 15.54/3.25 % (20886)Instructions burned: 373 (million)
% 15.54/3.25 % (20886)------------------------------
% 15.54/3.25 % (20886)------------------------------
% 15.54/3.27 % (20890)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_20469 for (2979ds/832Mi)
% 16.18/3.34 % (20889)Instruction limit reached!
% 16.18/3.34 % (20889)------------------------------
% 16.18/3.34 % (20889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.18/3.34 % (20889)Termination reason: Unknown
% 16.18/3.34 % (20889)Termination phase: Saturation
% 16.18/3.34
% 16.18/3.34 % (20889)Memory used [KB]: 7547
% 16.18/3.34 % (20889)Time elapsed: 0.103 s
% 16.18/3.34 % (20889)Instructions burned: 254 (million)
% 16.18/3.34 % (20889)------------------------------
% 16.18/3.34 % (20889)------------------------------
% 16.18/3.36 % (20895)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_20469 for (2978ds/668Mi)
% 16.69/3.43 % (20885)Instruction limit reached!
% 16.69/3.43 % (20885)------------------------------
% 16.69/3.43 % (20885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.69/3.43 % (20885)Termination reason: Unknown
% 16.69/3.43 % (20885)Termination phase: Saturation
% 16.69/3.43
% 16.69/3.43 % (20885)Memory used [KB]: 9466
% 16.69/3.43 % (20885)Time elapsed: 0.373 s
% 16.69/3.43 % (20885)Instructions burned: 996 (million)
% 16.69/3.43 % (20885)------------------------------
% 16.69/3.43 % (20885)------------------------------
% 16.69/3.45 % (20898)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_20469 for (2977ds/40Mi)
% 16.69/3.46 % (20898)Instruction limit reached!
% 16.69/3.46 % (20898)------------------------------
% 16.69/3.46 % (20898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.69/3.46 % (20898)Termination reason: Unknown
% 16.69/3.46 % (20898)Termination phase: Property scanning
% 16.69/3.46
% 16.69/3.46 % (20898)Memory used [KB]: 2174
% 16.69/3.46 % (20898)Time elapsed: 0.020 s
% 16.69/3.46 % (20898)Instructions burned: 40 (million)
% 16.69/3.46 % (20898)------------------------------
% 16.69/3.46 % (20898)------------------------------
% 16.69/3.48 % (20900)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_20469 for (2977ds/294Mi)
% 17.51/3.52 % (20900)Refutation not found, incomplete strategy
% 17.51/3.52 % (20900)------------------------------
% 17.51/3.52 % (20900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.51/3.52 % (20900)Termination reason: Refutation not found, incomplete strategy
% 17.51/3.52
% 17.51/3.52
% 17.51/3.52 % (20900)Memory used [KB]: 6780
% 17.51/3.52 % (20900)Time elapsed: 0.041 s
% 17.51/3.52 % (20900)Instructions burned: 86 (million)
% 17.51/3.52 % (20900)------------------------------
% 17.51/3.52 % (20900)------------------------------
% 17.51/3.54 % (20903)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_20469 for (2976ds/187Mi)
% 17.51/3.54 % (20868)Instruction limit reached!
% 17.51/3.54 % (20868)------------------------------
% 17.51/3.54 % (20868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.51/3.54 % (20868)Termination reason: Unknown
% 17.51/3.54 % (20868)Termination phase: Saturation
% 17.51/3.54
% 17.51/3.54 % (20868)Memory used [KB]: 3326
% 17.51/3.54 % (20868)Time elapsed: 0.878 s
% 17.51/3.54 % (20868)Instructions burned: 1914 (million)
% 17.51/3.54 % (20868)------------------------------
% 17.51/3.54 % (20868)------------------------------
% 17.51/3.56 % (20904)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_20469 for (2976ds/371Mi)
% 17.91/3.62 % (20903)Instruction limit reached!
% 17.91/3.62 % (20903)------------------------------
% 17.91/3.62 % (20903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.91/3.62 % (20903)Termination reason: Unknown
% 17.91/3.62 % (20903)Termination phase: Saturation
% 17.91/3.62
% 17.91/3.62 % (20903)Memory used [KB]: 7291
% 17.91/3.62 % (20903)Time elapsed: 0.080 s
% 17.91/3.62 % (20903)Instructions burned: 187 (million)
% 17.91/3.62 % (20903)------------------------------
% 17.91/3.62 % (20903)------------------------------
% 17.91/3.63 % (20907)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_20469 for (2975ds/1827Mi)
% 17.91/3.65 % (20895)Instruction limit reached!
% 17.91/3.65 % (20895)------------------------------
% 17.91/3.65 % (20895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.91/3.65 % (20895)Termination reason: Unknown
% 17.91/3.65 % (20895)Termination phase: Saturation
% 17.91/3.65
% 17.91/3.65 % (20895)Memory used [KB]: 13944
% 17.91/3.65 % (20895)Time elapsed: 0.290 s
% 17.91/3.65 % (20895)Instructions burned: 668 (million)
% 17.91/3.65 % (20895)------------------------------
% 17.91/3.65 % (20895)------------------------------
% 17.91/3.66 % (20908)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_20469 for (2975ds/70Mi)
% 17.91/3.67 % (20890)Instruction limit reached!
% 17.91/3.67 % (20890)------------------------------
% 17.91/3.67 % (20890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.91/3.67 % (20890)Termination reason: Unknown
% 17.91/3.67 % (20890)Termination phase: Saturation
% 17.91/3.67
% 17.91/3.67 % (20890)Memory used [KB]: 8059
% 17.91/3.67 % (20890)Time elapsed: 0.430 s
% 17.91/3.67 % (20890)Instructions burned: 834 (million)
% 17.91/3.67 % (20890)------------------------------
% 17.91/3.67 % (20890)------------------------------
% 17.91/3.68 % (20910)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_20469 for (2975ds/316Mi)
% 17.91/3.69 % (20908)Instruction limit reached!
% 17.91/3.69 % (20908)------------------------------
% 17.91/3.69 % (20908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.91/3.69 % (20908)Termination reason: Unknown
% 17.91/3.69 % (20908)Termination phase: Preprocessing 3
% 17.91/3.69
% 17.91/3.69 % (20908)Memory used [KB]: 2174
% 17.91/3.69 % (20908)Time elapsed: 0.028 s
% 17.91/3.69 % (20908)Instructions burned: 70 (million)
% 17.91/3.69 % (20908)------------------------------
% 17.91/3.69 % (20908)------------------------------
% 19.07/3.71 % (20911)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_20469 for (2975ds/932Mi)
% 19.07/3.73 % (20910)Refutation not found, incomplete strategy
% 19.07/3.73 % (20910)------------------------------
% 19.07/3.73 % (20910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.07/3.73 % (20910)Termination reason: Refutation not found, incomplete strategy
% 19.07/3.73
% 19.07/3.73
% 19.07/3.73 % (20910)Memory used [KB]: 7419
% 19.07/3.73 % (20910)Time elapsed: 0.053 s
% 19.07/3.73 % (20910)Instructions burned: 190 (million)
% 19.07/3.73 % (20910)------------------------------
% 19.07/3.73 % (20910)------------------------------
% 19.07/3.74 % (20913)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_20469 for (2974ds/4714Mi)
% 19.07/3.75 % (20904)Instruction limit reached!
% 19.07/3.75 % (20904)------------------------------
% 19.07/3.75 % (20904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.07/3.75 % (20904)Termination reason: Unknown
% 19.07/3.75 % (20904)Termination phase: Saturation
% 19.07/3.75
% 19.07/3.75 % (20904)Memory used [KB]: 7419
% 19.07/3.75 % (20904)Time elapsed: 0.186 s
% 19.07/3.75 % (20904)Instructions burned: 371 (million)
% 19.07/3.75 % (20904)------------------------------
% 19.07/3.75 % (20904)------------------------------
% 19.07/3.76 % (20914)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_20469 for (2974ds/8250Mi)
% 19.64/3.80 % (20913)Refutation not found, incomplete strategy
% 19.64/3.80 % (20913)------------------------------
% 19.64/3.80 % (20913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.64/3.80 % (20913)Termination reason: Refutation not found, incomplete strategy
% 19.64/3.80
% 19.64/3.80
% 19.64/3.80 % (20913)Memory used [KB]: 7675
% 19.64/3.80 % (20913)Time elapsed: 0.053 s
% 19.64/3.80 % (20913)Instructions burned: 186 (million)
% 19.64/3.80 % (20913)------------------------------
% 19.64/3.80 % (20913)------------------------------
% 19.64/3.81 % (20915)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_20469 for (2974ds/770Mi)
% 19.64/3.82 % (20915)Refutation not found, incomplete strategy
% 19.64/3.82 % (20915)------------------------------
% 19.64/3.82 % (20915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.64/3.82 % (20915)Termination reason: Refutation not found, incomplete strategy
% 19.64/3.82
% 19.64/3.82
% 19.64/3.82 % (20915)Memory used [KB]: 6396
% 19.64/3.82 % (20915)Time elapsed: 0.015 s
% 19.64/3.82 % (20915)Instructions burned: 44 (million)
% 19.64/3.82 % (20915)------------------------------
% 19.64/3.82 % (20915)------------------------------
% 19.64/3.83 % (20916)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_20469 for (2973ds/794Mi)
% 21.54/4.10 % (20911)Instruction limit reached!
% 21.54/4.10 % (20911)------------------------------
% 21.54/4.10 % (20911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.54/4.10 % (20911)Termination reason: Unknown
% 21.54/4.10 % (20911)Termination phase: Saturation
% 21.54/4.10
% 21.54/4.10 % (20911)Memory used [KB]: 9978
% 21.54/4.10 % (20911)Time elapsed: 0.390 s
% 21.54/4.10 % (20911)Instructions burned: 933 (million)
% 21.54/4.10 % (20911)------------------------------
% 21.54/4.10 % (20911)------------------------------
% 21.54/4.12 % (20919)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_20469 for (2970ds/464Mi)
% 22.27/4.16 % (20916)Instruction limit reached!
% 22.27/4.16 % (20916)------------------------------
% 22.27/4.16 % (20916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.27/4.16 % (20916)Termination reason: Unknown
% 22.27/4.16 % (20916)Termination phase: Saturation
% 22.27/4.16
% 22.27/4.16 % (20916)Memory used [KB]: 6396
% 22.27/4.16 % (20916)Time elapsed: 0.333 s
% 22.27/4.16 % (20916)Instructions burned: 794 (million)
% 22.27/4.16 % (20916)------------------------------
% 22.27/4.16 % (20916)------------------------------
% 22.27/4.18 % (20921)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_20469 for (2970ds/1376Mi)
% 22.66/4.28 % (20919)Instruction limit reached!
% 22.66/4.28 % (20919)------------------------------
% 22.66/4.28 % (20919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.66/4.28 % (20919)Termination reason: Unknown
% 22.66/4.28 % (20919)Termination phase: Saturation
% 22.66/4.28
% 22.66/4.28 % (20919)Memory used [KB]: 7547
% 22.66/4.28 % (20919)Time elapsed: 0.157 s
% 22.66/4.28 % (20919)Instructions burned: 466 (million)
% 22.66/4.28 % (20919)------------------------------
% 22.66/4.28 % (20919)------------------------------
% 23.33/4.32 % (20923)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_20469 for (2969ds/906Mi)
% 24.32/4.52 % (20907)Instruction limit reached!
% 24.32/4.52 % (20907)------------------------------
% 24.32/4.52 % (20907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.32/4.52 % (20907)Termination reason: Unknown
% 24.32/4.52 % (20907)Termination phase: Saturation
% 24.32/4.52
% 24.32/4.52 % (20907)Memory used [KB]: 8699
% 24.32/4.52 % (20907)Time elapsed: 0.887 s
% 24.32/4.52 % (20907)Instructions burned: 1827 (million)
% 24.32/4.52 % (20907)------------------------------
% 24.32/4.52 % (20907)------------------------------
% 24.32/4.53 % (20926)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_20469 for (2966ds/434Mi)
% 24.77/4.65 % (20864)Instruction limit reached!
% 24.77/4.65 % (20864)------------------------------
% 24.77/4.65 % (20864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.77/4.65 % (20864)Termination reason: Unknown
% 24.77/4.65 % (20864)Termination phase: Saturation
% 24.77/4.65
% 24.77/4.65 % (20864)Memory used [KB]: 11001
% 24.77/4.65 % (20864)Time elapsed: 2.143 s
% 24.77/4.65 % (20864)Instructions burned: 4437 (million)
% 24.77/4.65 % (20864)------------------------------
% 24.77/4.65 % (20864)------------------------------
% 24.77/4.65 % (20926)Instruction limit reached!
% 24.77/4.65 % (20926)------------------------------
% 24.77/4.65 % (20926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.77/4.65 % (20926)Termination reason: Unknown
% 24.77/4.65 % (20926)Termination phase: Saturation
% 24.77/4.65
% 24.77/4.65 % (20926)Memory used [KB]: 7803
% 24.77/4.65 % (20926)Time elapsed: 0.129 s
% 24.77/4.65 % (20926)Instructions burned: 436 (million)
% 24.77/4.65 % (20926)------------------------------
% 24.77/4.65 % (20926)------------------------------
% 24.77/4.66 % (20921)Instruction limit reached!
% 24.77/4.66 % (20921)------------------------------
% 24.77/4.66 % (20921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.77/4.66 % (20921)Termination reason: Unknown
% 24.77/4.66 % (20921)Termination phase: Saturation
% 24.77/4.66
% 24.77/4.66 % (20921)Memory used [KB]: 10874
% 24.77/4.66 % (20921)Time elapsed: 0.490 s
% 24.77/4.66 % (20921)Instructions burned: 1377 (million)
% 24.77/4.66 % (20921)------------------------------
% 24.77/4.66 % (20921)------------------------------
% 24.77/4.66 % (20930)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_20469 for (2965ds/593Mi)
% 24.77/4.66 % (20929)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_20469 for (2965ds/865Mi)
% 24.77/4.68 % (20932)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_20469 for (2965ds/443Mi)
% 25.71/4.74 % (20872)Instruction limit reached!
% 25.71/4.74 % (20872)------------------------------
% 25.71/4.74 % (20872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.71/4.74 % (20872)Termination reason: Unknown
% 25.71/4.74 % (20872)Termination phase: Saturation
% 25.71/4.74
% 25.71/4.74 % (20872)Memory used [KB]: 13432
% 25.71/4.74 % (20872)Time elapsed: 2.002 s
% 25.71/4.74 % (20872)Instructions burned: 4350 (million)
% 25.71/4.74 % (20872)------------------------------
% 25.71/4.74 % (20872)------------------------------
% 25.71/4.76 % (20933)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_20469 for (2964ds/594Mi)
% 25.97/4.80 % (20923)Instruction limit reached!
% 25.97/4.80 % (20923)------------------------------
% 25.97/4.80 % (20923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.97/4.80 % (20923)Termination reason: Unknown
% 25.97/4.80 % (20923)Termination phase: Saturation
% 25.97/4.80
% 25.97/4.80 % (20923)Memory used [KB]: 12281
% 25.97/4.80 % (20923)Time elapsed: 0.510 s
% 25.97/4.80 % (20923)Instructions burned: 908 (million)
% 25.97/4.80 % (20923)------------------------------
% 25.97/4.80 % (20923)------------------------------
% 25.97/4.82 % (20935)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_20469 for (2964ds/327Mi)
% 25.97/4.86 % (20930)Instruction limit reached!
% 25.97/4.86 % (20930)------------------------------
% 25.97/4.86 % (20930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.97/4.86 % (20930)Termination reason: Unknown
% 25.97/4.86 % (20930)Termination phase: Saturation
% 25.97/4.86
% 25.97/4.86 % (20930)Memory used [KB]: 9083
% 25.97/4.86 % (20930)Time elapsed: 0.196 s
% 25.97/4.86 % (20930)Instructions burned: 594 (million)
% 25.97/4.86 % (20930)------------------------------
% 25.97/4.86 % (20930)------------------------------
% 25.97/4.87 % (20939)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_20469 for (2963ds/5411Mi)
% 25.97/4.87 % (20867)Instruction limit reached!
% 25.97/4.87 % (20867)------------------------------
% 25.97/4.87 % (20867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.97/4.87 % (20867)Termination reason: Unknown
% 25.97/4.87 % (20867)Termination phase: Saturation
% 25.97/4.87
% 25.97/4.87 % (20867)Memory used [KB]: 14583
% 25.97/4.87 % (20867)Time elapsed: 2.323 s
% 25.97/4.87 % (20867)Instructions burned: 5205 (million)
% 25.97/4.87 % (20867)------------------------------
% 25.97/4.87 % (20867)------------------------------
% 25.97/4.89 % (20932)Instruction limit reached!
% 25.97/4.89 % (20932)------------------------------
% 25.97/4.89 % (20932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.97/4.89 % (20932)Termination reason: Unknown
% 25.97/4.89 % (20932)Termination phase: Saturation
% 25.97/4.89
% 25.97/4.89 % (20932)Memory used [KB]: 7931
% 25.97/4.89 % (20932)Time elapsed: 0.208 s
% 25.97/4.89 % (20932)Instructions burned: 444 (million)
% 25.97/4.89 % (20932)------------------------------
% 25.97/4.89 % (20932)------------------------------
% 25.97/4.89 % (20942)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_20469 for (2963ds/1762Mi)
% 27.04/4.90 % (20943)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_20469 for (2963ds/96Mi)
% 27.04/4.91 % (20939)Refutation not found, incomplete strategy
% 27.04/4.91 % (20939)------------------------------
% 27.04/4.91 % (20939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.04/4.91 % (20939)Termination reason: Refutation not found, incomplete strategy
% 27.04/4.91
% 27.04/4.91
% 27.04/4.91 % (20939)Memory used [KB]: 6780
% 27.04/4.91 % (20939)Time elapsed: 0.045 s
% 27.04/4.91 % (20939)Instructions burned: 86 (million)
% 27.04/4.91 % (20939)------------------------------
% 27.04/4.91 % (20939)------------------------------
% 27.04/4.93 % (20946)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_20469 for (2962ds/503Mi)
% 27.04/4.95 % (20943)Instruction limit reached!
% 27.04/4.95 % (20943)------------------------------
% 27.04/4.95 % (20943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.04/4.95 % (20943)Termination reason: Unknown
% 27.04/4.95 % (20943)Termination phase: Property scanning
% 27.04/4.95
% 27.04/4.95 % (20943)Memory used [KB]: 2302
% 27.04/4.95 % (20943)Time elapsed: 0.045 s
% 27.04/4.95 % (20943)Instructions burned: 96 (million)
% 27.04/4.95 % (20943)------------------------------
% 27.04/4.95 % (20943)------------------------------
% 27.04/4.96 % (20948)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_20469 for (2962ds/90Mi)
% 27.04/4.98 % (20946)Refutation not found, incomplete strategy
% 27.04/4.98 % (20946)------------------------------
% 27.04/4.98 % (20946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.04/4.98 % (20946)Termination reason: Refutation not found, incomplete strategy
% 27.04/4.98
% 27.04/4.98
% 27.04/4.98 % (20946)Memory used [KB]: 6908
% 27.04/4.98 % (20946)Time elapsed: 0.048 s
% 27.04/4.98 % (20946)Instructions burned: 95 (million)
% 27.04/4.98 % (20946)------------------------------
% 27.04/4.98 % (20946)------------------------------
% 27.04/4.98 % (20935)Instruction limit reached!
% 27.04/4.98 % (20935)------------------------------
% 27.04/4.98 % (20935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.04/4.98 % (20935)Termination reason: Unknown
% 27.04/4.98 % (20935)Termination phase: Saturation
% 27.04/4.98
% 27.04/4.98 % (20935)Memory used [KB]: 7675
% 27.04/4.98 % (20935)Time elapsed: 0.163 s
% 27.04/4.98 % (20935)Instructions burned: 328 (million)
% 27.04/4.98 % (20935)------------------------------
% 27.04/4.98 % (20935)------------------------------
% 27.04/4.99 % (20933)Instruction limit reached!
% 27.04/4.99 % (20933)------------------------------
% 27.04/4.99 % (20933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.04/4.99 % (20933)Termination reason: Unknown
% 27.04/4.99 % (20933)Termination phase: Saturation
% 27.04/4.99
% 27.04/4.99 % (20933)Memory used [KB]: 7803
% 27.04/4.99 % (20933)Time elapsed: 0.233 s
% 27.04/4.99 % (20933)Instructions burned: 595 (million)
% 27.04/4.99 % (20933)------------------------------
% 27.04/4.99 % (20933)------------------------------
% 27.04/4.99 % (20950)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_20469 for (2962ds/593Mi)
% 27.04/5.00 % (20951)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_20469 for (2962ds/1512Mi)
% 27.04/5.00 % (20952)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_20469 for (2962ds/569Mi)
% 27.04/5.01 % (20948)Instruction limit reached!
% 27.04/5.01 % (20948)------------------------------
% 27.04/5.01 % (20948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.04/5.01 % (20948)Termination reason: Unknown
% 27.04/5.01 % (20948)Termination phase: Property scanning
% 27.04/5.01
% 27.04/5.01 % (20948)Memory used [KB]: 2174
% 27.04/5.01 % (20948)Time elapsed: 0.044 s
% 27.04/5.01 % (20948)Instructions burned: 91 (million)
% 27.04/5.01 % (20948)------------------------------
% 27.04/5.01 % (20948)------------------------------
% 27.04/5.02 % (20953)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_20469 for (2962ds/501Mi)
% 28.42/5.06 % (20929)Instruction limit reached!
% 28.42/5.06 % (20929)------------------------------
% 28.42/5.06 % (20929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.42/5.06 % (20929)Termination reason: Unknown
% 28.42/5.06 % (20929)Termination phase: Saturation
% 28.42/5.06
% 28.42/5.06 % (20929)Memory used [KB]: 8443
% 28.42/5.06 % (20929)Time elapsed: 0.390 s
% 28.42/5.06 % (20929)Instructions burned: 866 (million)
% 28.42/5.06 % (20929)------------------------------
% 28.42/5.06 % (20929)------------------------------
% 28.42/5.08 % (20955)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_20469 for (2961ds/562Mi)
% 29.33/5.22 % (20953)Instruction limit reached!
% 29.33/5.22 % (20953)------------------------------
% 29.33/5.22 % (20953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.33/5.22 % (20953)Termination reason: Unknown
% 29.33/5.22 % (20953)Termination phase: Saturation
% 29.33/5.22
% 29.33/5.22 % (20953)Memory used [KB]: 8187
% 29.33/5.22 % (20953)Time elapsed: 0.201 s
% 29.33/5.22 % (20953)Instructions burned: 501 (million)
% 29.33/5.22 % (20953)------------------------------
% 29.33/5.22 % (20953)------------------------------
% 29.33/5.24 % (20960)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_20469 for (2959ds/406Mi)
% 29.33/5.27 % (20952)Instruction limit reached!
% 29.33/5.27 % (20952)------------------------------
% 29.33/5.27 % (20952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.33/5.27 % (20952)Termination reason: Unknown
% 29.33/5.27 % (20952)Termination phase: Saturation
% 29.33/5.27
% 29.33/5.27 % (20952)Memory used [KB]: 7931
% 29.33/5.28 % (20952)Time elapsed: 0.272 s
% 29.33/5.28 % (20952)Instructions burned: 569 (million)
% 29.33/5.28 % (20952)------------------------------
% 29.33/5.28 % (20952)------------------------------
% 29.33/5.29 % (20955)Instruction limit reached!
% 29.33/5.29 % (20955)------------------------------
% 29.33/5.29 % (20955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.33/5.29 % (20955)Termination reason: Unknown
% 29.33/5.29 % (20955)Termination phase: Saturation
% 29.33/5.29
% 29.33/5.29 % (20955)Memory used [KB]: 7931
% 29.33/5.29 % (20955)Time elapsed: 0.211 s
% 29.33/5.29 % (20955)Instructions burned: 563 (million)
% 29.33/5.29 % (20955)------------------------------
% 29.33/5.29 % (20955)------------------------------
% 29.33/5.29 % (20950)Instruction limit reached!
% 29.33/5.29 % (20950)------------------------------
% 29.33/5.29 % (20950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.33/5.29 % (20950)Termination reason: Unknown
% 29.33/5.29 % (20950)Termination phase: Saturation
% 29.33/5.29
% 29.33/5.29 % (20950)Memory used [KB]: 8571
% 29.33/5.29 % (20950)Time elapsed: 0.296 s
% 29.33/5.29 % (20950)Instructions burned: 594 (million)
% 29.33/5.29 % (20950)------------------------------
% 29.33/5.29 % (20950)------------------------------
% 29.33/5.29 % (20962)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_20469 for (2959ds/582Mi)
% 30.27/5.30 % (20963)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_20469 for (2959ds/456Mi)
% 30.27/5.32 % (20964)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_20469 for (2959ds/393Mi)
% 30.57/5.45 % (20960)Instruction limit reached!
% 30.57/5.45 % (20960)------------------------------
% 30.57/5.45 % (20960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.57/5.45 % (20960)Termination reason: Unknown
% 30.57/5.45 % (20960)Termination phase: Saturation
% 30.57/5.45
% 30.57/5.45 % (20960)Memory used [KB]: 7931
% 30.57/5.45 % (20960)Time elapsed: 0.209 s
% 30.57/5.45 % (20960)Instructions burned: 406 (million)
% 30.57/5.45 % (20960)------------------------------
% 30.57/5.45 % (20960)------------------------------
% 30.57/5.45 % (20963)Instruction limit reached!
% 30.57/5.45 % (20963)------------------------------
% 30.57/5.45 % (20963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.57/5.45 % (20963)Termination reason: Unknown
% 30.57/5.45 % (20963)Termination phase: Saturation
% 30.57/5.45
% 30.57/5.45 % (20963)Memory used [KB]: 8315
% 30.57/5.45 % (20963)Time elapsed: 0.153 s
% 30.57/5.45 % (20963)Instructions burned: 457 (million)
% 30.57/5.45 % (20963)------------------------------
% 30.57/5.45 % (20963)------------------------------
% 30.57/5.46 % (20969)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_20469 for (2957ds/3373Mi)
% 30.57/5.47 % (20964)Instruction limit reached!
% 30.57/5.47 % (20964)------------------------------
% 30.57/5.47 % (20964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.57/5.47 % (20964)Termination reason: Unknown
% 30.57/5.47 % (20964)Termination phase: Saturation
% 30.57/5.47
% 30.57/5.47 % (20964)Memory used [KB]: 7547
% 30.57/5.47 % (20964)Time elapsed: 0.155 s
% 30.57/5.47 % (20964)Instructions burned: 395 (million)
% 30.57/5.47 % (20964)------------------------------
% 30.57/5.47 % (20964)------------------------------
% 30.57/5.47 % (20968)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_20469 for (2957ds/1335Mi)
% 30.57/5.48 % (20971)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_20469 for (2957ds/474Mi)
% 31.42/5.58 % (20962)Instruction limit reached!
% 31.42/5.58 % (20962)------------------------------
% 31.42/5.58 % (20962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.42/5.58 % (20962)Termination reason: Unknown
% 31.42/5.58 % (20962)Termination phase: Saturation
% 31.42/5.58
% 31.42/5.58 % (20962)Memory used [KB]: 7803
% 31.42/5.58 % (20962)Time elapsed: 0.288 s
% 31.42/5.58 % (20962)Instructions burned: 582 (million)
% 31.42/5.58 % (20962)------------------------------
% 31.42/5.58 % (20962)------------------------------
% 32.02/5.61 % (20974)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_20469 for (2956ds/157Mi)
% 32.02/5.65 % (20971)Instruction limit reached!
% 32.02/5.65 % (20971)------------------------------
% 32.02/5.65 % (20971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.02/5.65 % (20971)Termination reason: Unknown
% 32.02/5.65 % (20971)Termination phase: Saturation
% 32.02/5.65
% 32.02/5.65 % (20971)Memory used [KB]: 8059
% 32.02/5.65 % (20971)Time elapsed: 0.177 s
% 32.02/5.65 % (20971)Instructions burned: 476 (million)
% 32.02/5.65 % (20971)------------------------------
% 32.02/5.65 % (20971)------------------------------
% 32.02/5.67 % (20951)Instruction limit reached!
% 32.02/5.67 % (20951)------------------------------
% 32.02/5.67 % (20951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.02/5.67 % (20951)Termination reason: Unknown
% 32.02/5.67 % (20951)Termination phase: Saturation
% 32.02/5.67
% 32.02/5.67 % (20951)Memory used [KB]: 8187
% 32.02/5.67 % (20951)Time elapsed: 0.688 s
% 32.02/5.67 % (20951)Instructions burned: 1512 (million)
% 32.02/5.67 % (20951)------------------------------
% 32.02/5.67 % (20951)------------------------------
% 32.02/5.67 % (20976)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_20469 for (2955ds/590Mi)
% 32.02/5.68 % (20977)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_20469 for (2955ds/104Mi)
% 32.02/5.68 % (20974)Instruction limit reached!
% 32.02/5.68 % (20974)------------------------------
% 32.02/5.68 % (20974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.02/5.68 % (20974)Termination reason: Unknown
% 32.02/5.68 % (20974)Termination phase: Saturation
% 32.02/5.68
% 32.02/5.68 % (20974)Memory used [KB]: 6908
% 32.02/5.68 % (20974)Time elapsed: 0.045 s
% 32.02/5.68 % (20974)Instructions burned: 157 (million)
% 32.02/5.68 % (20974)------------------------------
% 32.02/5.68 % (20974)------------------------------
% 32.02/5.69 % (20978)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_20469 for (2955ds/414Mi)
% 32.02/5.70 % (20942)Instruction limit reached!
% 32.02/5.70 % (20942)------------------------------
% 32.02/5.70 % (20942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.02/5.70 % (20942)Termination reason: Unknown
% 32.02/5.70 % (20942)Termination phase: Saturation
% 32.02/5.70
% 32.02/5.70 % (20942)Memory used [KB]: 9978
% 32.02/5.70 % (20942)Time elapsed: 0.809 s
% 32.02/5.70 % (20942)Instructions burned: 1762 (million)
% 32.02/5.70 % (20942)------------------------------
% 32.02/5.70 % (20942)------------------------------
% 31.69/5.71 % (20977)Instruction limit reached!
% 31.69/5.71 % (20977)------------------------------
% 31.69/5.71 % (20977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.69/5.71 % (20977)Termination reason: Unknown
% 31.69/5.72 % (20977)Termination phase: Saturation
% 31.69/5.72
% 31.69/5.72 % (20977)Memory used [KB]: 2430
% 31.69/5.72 % (20977)Time elapsed: 0.039 s
% 31.69/5.72 % (20977)Instructions burned: 105 (million)
% 31.69/5.72 % (20977)------------------------------
% 31.69/5.72 % (20977)------------------------------
% 31.69/5.72 % (20979)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_20469 for (2955ds/715Mi)
% 31.69/5.74 % (20982)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_20469 for (2955ds/961Mi)
% 32.71/5.90 % (20978)Instruction limit reached!
% 32.71/5.90 % (20978)------------------------------
% 32.71/5.90 % (20978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.71/5.90 % (20978)Termination reason: Unknown
% 32.71/5.90 % (20978)Termination phase: Saturation
% 32.71/5.90
% 32.71/5.90 % (20978)Memory used [KB]: 7675
% 32.71/5.90 % (20978)Time elapsed: 0.221 s
% 32.71/5.90 % (20978)Instructions burned: 414 (million)
% 32.71/5.90 % (20978)------------------------------
% 32.71/5.90 % (20978)------------------------------
% 32.71/5.92 % (20984)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_20469 for (2953ds/1213Mi)
% 32.71/5.95 % (20976)Instruction limit reached!
% 32.71/5.95 % (20976)------------------------------
% 32.71/5.95 % (20976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.71/5.95 % (20976)Termination reason: Unknown
% 32.71/5.95 % (20976)Termination phase: Saturation
% 32.71/5.95
% 32.71/5.95 % (20976)Memory used [KB]: 8443
% 32.71/5.95 % (20976)Time elapsed: 0.279 s
% 32.71/5.95 % (20976)Instructions burned: 591 (million)
% 32.71/5.95 % (20976)------------------------------
% 32.71/5.95 % (20976)------------------------------
% 32.71/5.97 % (20986)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_20469 for (2952ds/1979Mi)
% 34.97/6.08 % (20979)Instruction limit reached!
% 34.97/6.08 % (20979)------------------------------
% 34.97/6.08 % (20979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.97/6.08 % (20979)Termination reason: Unknown
% 34.97/6.08 % (20979)Termination phase: Saturation
% 34.97/6.08
% 34.97/6.08 % (20979)Memory used [KB]: 4093
% 34.97/6.08 % (20979)Time elapsed: 0.393 s
% 34.97/6.08 % (20979)Instructions burned: 716 (million)
% 34.97/6.08 % (20979)------------------------------
% 34.97/6.08 % (20979)------------------------------
% 34.97/6.09 % (20988)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_20469 for (2951ds/481Mi)
% 34.97/6.11 % (20968)Instruction limit reached!
% 34.97/6.11 % (20968)------------------------------
% 34.97/6.11 % (20968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.97/6.11 % (20968)Termination reason: Unknown
% 34.97/6.11 % (20968)Termination phase: Saturation
% 34.97/6.11
% 34.97/6.11 % (20968)Memory used [KB]: 9083
% 34.97/6.11 % (20968)Time elapsed: 0.659 s
% 34.97/6.11 % (20968)Instructions burned: 1336 (million)
% 34.97/6.11 % (20968)------------------------------
% 34.97/6.11 % (20968)------------------------------
% 34.97/6.12 % (20989)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_20469 for (2950ds/783Mi)
% 36.00/6.20 % (20982)Instruction limit reached!
% 36.00/6.20 % (20982)------------------------------
% 36.00/6.20 % (20982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.00/6.20 % (20982)Termination reason: Unknown
% 36.00/6.20 % (20982)Termination phase: Saturation
% 36.00/6.20
% 36.00/6.20 % (20982)Memory used [KB]: 7803
% 36.00/6.20 % (20982)Time elapsed: 0.482 s
% 36.00/6.20 % (20982)Instructions burned: 961 (million)
% 36.00/6.20 % (20982)------------------------------
% 36.00/6.20 % (20982)------------------------------
% 36.00/6.22 % (20991)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_20469 for (2949ds/432Mi)
% 36.40/6.34 % (20988)Instruction limit reached!
% 36.40/6.34 % (20988)------------------------------
% 36.40/6.34 % (20988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.40/6.34 % (20988)Termination reason: Unknown
% 36.40/6.34 % (20988)Termination phase: Saturation
% 36.40/6.34
% 36.40/6.34 % (20988)Memory used [KB]: 7931
% 36.40/6.34 % (20988)Time elapsed: 0.244 s
% 36.40/6.34 % (20988)Instructions burned: 481 (million)
% 36.40/6.34 % (20988)------------------------------
% 36.40/6.34 % (20988)------------------------------
% 36.40/6.35 % (20996)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_20469 for (2948ds/1670Mi)
% 36.40/6.37 % (20991)Instruction limit reached!
% 36.40/6.37 % (20991)------------------------------
% 36.40/6.37 % (20991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.40/6.37 % (20991)Termination reason: Unknown
% 36.40/6.37 % (20991)Termination phase: Saturation
% 36.40/6.37
% 36.40/6.37 % (20991)Memory used [KB]: 7803
% 36.40/6.37 % (20991)Time elapsed: 0.150 s
% 36.40/6.37 % (20991)Instructions burned: 433 (million)
% 36.40/6.37 % (20991)------------------------------
% 36.40/6.37 % (20991)------------------------------
% 36.40/6.38 % (20997)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_20469 for (2948ds/90Mi)
% 36.40/6.38 % (20989)Instruction limit reached!
% 36.40/6.38 % (20989)------------------------------
% 36.40/6.38 % (20989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.40/6.38 % (20989)Termination reason: Unknown
% 36.40/6.38 % (20989)Termination phase: Saturation
% 36.40/6.38
% 36.40/6.38 % (20989)Memory used [KB]: 9083
% 36.40/6.38 % (20989)Time elapsed: 0.263 s
% 36.40/6.38 % (20989)Instructions burned: 784 (million)
% 36.40/6.38 % (20989)------------------------------
% 36.40/6.38 % (20989)------------------------------
% 37.51/6.40 % (20998)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_20469 for (2948ds/346Mi)
% 37.51/6.41 % (20997)Instruction limit reached!
% 37.51/6.41 % (20997)------------------------------
% 37.51/6.41 % (20997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.51/6.41 % (20997)Termination reason: Unknown
% 37.51/6.41 % (20997)Termination phase: Property scanning
% 37.51/6.41
% 37.51/6.41 % (20997)Memory used [KB]: 2174
% 37.51/6.41 % (20997)Time elapsed: 0.033 s
% 37.51/6.41 % (20997)Instructions burned: 90 (million)
% 37.51/6.41 % (20997)------------------------------
% 37.51/6.41 % (20997)------------------------------
% 37.51/6.43 % (20999)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_20469 for (2947ds/401Mi)
% 37.94/6.52 % (20984)Instruction limit reached!
% 37.94/6.52 % (20984)------------------------------
% 37.94/6.52 % (20984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.94/6.52 % (20984)Termination reason: Unknown
% 37.94/6.52 % (20984)Termination phase: Saturation
% 37.94/6.52
% 37.94/6.52 % (20984)Memory used [KB]: 9850
% 37.94/6.52 % (20984)Time elapsed: 0.630 s
% 37.94/6.52 % (20984)Instructions burned: 1214 (million)
% 37.94/6.52 % (20984)------------------------------
% 37.94/6.52 % (20984)------------------------------
% 37.94/6.53 % (20998)Instruction limit reached!
% 37.94/6.53 % (20998)------------------------------
% 37.94/6.53 % (20998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.94/6.53 % (20998)Termination reason: Unknown
% 37.94/6.53 % (20998)Termination phase: Saturation
% 37.94/6.53
% 37.94/6.53 % (20998)Memory used [KB]: 7675
% 37.94/6.53 % (20998)Time elapsed: 0.129 s
% 37.94/6.53 % (20998)Instructions burned: 347 (million)
% 37.94/6.53 % (20998)------------------------------
% 37.94/6.53 % (20998)------------------------------
% 37.94/6.53 % (21002)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_20469 for (2946ds/6454Mi)
% 37.94/6.54 % (21003)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_20469 for (2946ds/283Mi)
% 38.43/6.62 % (20999)Instruction limit reached!
% 38.43/6.62 % (20999)------------------------------
% 38.43/6.62 % (20999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.43/6.62 % (20999)Termination reason: Unknown
% 38.43/6.62 % (20999)Termination phase: Saturation
% 38.43/6.62
% 38.43/6.62 % (20999)Memory used [KB]: 8187
% 38.43/6.62 % (20999)Time elapsed: 0.194 s
% 38.43/6.62 % (20999)Instructions burned: 402 (million)
% 38.43/6.62 % (20999)------------------------------
% 38.43/6.62 % (20999)------------------------------
% 38.43/6.64 % (21004)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_20469 for (2945ds/865Mi)
% 38.43/6.68 % (21003)Instruction limit reached!
% 38.43/6.68 % (21003)------------------------------
% 38.43/6.68 % (21003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.43/6.68 % (21003)Termination reason: Unknown
% 38.43/6.68 % (21003)Termination phase: Saturation
% 38.43/6.68
% 38.43/6.68 % (21003)Memory used [KB]: 7547
% 38.43/6.68 % (21003)Time elapsed: 0.141 s
% 38.43/6.68 % (21003)Instructions burned: 283 (million)
% 38.43/6.68 % (21003)------------------------------
% 38.43/6.68 % (21003)------------------------------
% 39.09/6.71 % (21008)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_20469 for (2945ds/4528Mi)
% 39.09/6.74 % (21008)Refutation not found, incomplete strategy
% 39.09/6.74 % (21008)------------------------------
% 39.09/6.74 % (21008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.09/6.74 % (21008)Termination reason: Refutation not found, incomplete strategy
% 39.09/6.74
% 39.09/6.74
% 39.09/6.74 % (21008)Memory used [KB]: 2046
% 39.09/6.74 % (21008)Time elapsed: 0.054 s
% 39.09/6.74 % (21008)Instructions burned: 50 (million)
% 39.09/6.74 % (21008)------------------------------
% 39.09/6.74 % (21008)------------------------------
% 39.09/6.75 % (21009)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_20469 for (2944ds/1001Mi)
% 39.39/6.89 % (20986)Instruction limit reached!
% 39.39/6.89 % (20986)------------------------------
% 39.39/6.89 % (20986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.39/6.89 % (20986)Termination reason: Unknown
% 39.39/6.89 % (20986)Termination phase: Saturation
% 39.39/6.89
% 39.39/6.89 % (20986)Memory used [KB]: 8059
% 39.39/6.89 % (20986)Time elapsed: 0.953 s
% 39.39/6.89 % (20986)Instructions burned: 1980 (million)
% 39.39/6.89 % (20986)------------------------------
% 39.39/6.89 % (20986)------------------------------
% 39.69/6.91 % (21013)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_20469 for (2943ds/102Mi)
% 39.69/6.95 % (21013)Instruction limit reached!
% 39.69/6.95 % (21013)------------------------------
% 39.69/6.95 % (21013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.69/6.95 % (21013)Termination reason: Unknown
% 39.69/6.95 % (21013)Termination phase: Saturation
% 39.69/6.95
% 39.69/6.95 % (21013)Memory used [KB]: 6780
% 39.69/6.95 % (21013)Time elapsed: 0.038 s
% 39.69/6.95 % (21013)Instructions burned: 103 (million)
% 39.69/6.95 % (21013)------------------------------
% 39.69/6.95 % (21013)------------------------------
% 39.69/6.96 % (21015)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_20469 for (2942ds/952Mi)
% 41.90/7.07 % (21004)Instruction limit reached!
% 41.90/7.07 % (21004)------------------------------
% 41.90/7.07 % (21004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.90/7.07 % (21004)Termination reason: Unknown
% 41.90/7.07 % (21004)Termination phase: Saturation
% 41.90/7.07
% 41.90/7.07 % (21004)Memory used [KB]: 9466
% 41.90/7.07 % (21004)Time elapsed: 0.434 s
% 41.90/7.07 % (21004)Instructions burned: 865 (million)
% 41.90/7.07 % (21004)------------------------------
% 41.90/7.07 % (21004)------------------------------
% 41.90/7.08 % (21016)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_20469 for (2941ds/578Mi)
% 41.90/7.09 % (20969)Instruction limit reached!
% 41.90/7.09 % (20969)------------------------------
% 41.90/7.09 % (20969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.90/7.09 % (20969)Termination reason: Unknown
% 41.90/7.09 % (20969)Termination phase: Saturation
% 41.90/7.09
% 41.90/7.09 % (20969)Memory used [KB]: 12409
% 41.90/7.09 % (20969)Time elapsed: 1.628 s
% 41.90/7.09 % (20969)Instructions burned: 3373 (million)
% 41.90/7.09 % (20969)------------------------------
% 41.90/7.09 % (20969)------------------------------
% 41.90/7.11 % (21017)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_20469 for (2941ds/643Mi)
% 42.54/7.14 % (20996)Instruction limit reached!
% 42.54/7.14 % (20996)------------------------------
% 42.54/7.14 % (20996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.54/7.14 % (20996)Termination reason: Unknown
% 42.54/7.14 % (20996)Termination phase: Saturation
% 42.54/7.14
% 42.54/7.14 % (20996)Memory used [KB]: 9850
% 42.54/7.14 % (20996)Time elapsed: 0.790 s
% 42.54/7.14 % (20996)Instructions burned: 1671 (million)
% 42.54/7.14 % (20996)------------------------------
% 42.54/7.14 % (20996)------------------------------
% 42.54/7.16 % (21021)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_20469 for (2940ds/865Mi)
% 42.54/7.16 % (21009)Instruction limit reached!
% 42.54/7.16 % (21009)------------------------------
% 42.54/7.16 % (21009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.54/7.16 % (21009)Termination reason: Unknown
% 42.54/7.16 % (21009)Termination phase: Saturation
% 42.54/7.16
% 42.54/7.16 % (21009)Memory used [KB]: 8187
% 42.54/7.16 % (21009)Time elapsed: 0.410 s
% 42.54/7.16 % (21009)Instructions burned: 1003 (million)
% 42.54/7.16 % (21009)------------------------------
% 42.54/7.16 % (21009)------------------------------
% 42.54/7.17 % (21022)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_20469 for (2940ds/1174Mi)
% 43.13/7.35 % (21016)Instruction limit reached!
% 43.13/7.35 % (21016)------------------------------
% 43.13/7.35 % (21016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.13/7.35 % (21016)Termination reason: Unknown
% 43.13/7.35 % (21016)Termination phase: Saturation
% 43.13/7.35
% 43.13/7.35 % (21016)Memory used [KB]: 8315
% 43.13/7.35 % (21016)Time elapsed: 0.296 s
% 43.13/7.35 % (21016)Instructions burned: 578 (million)
% 43.13/7.35 % (21016)------------------------------
% 43.13/7.35 % (21016)------------------------------
% 43.13/7.37 % (21026)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_20469 for (2938ds/644Mi)
% 43.72/7.41 % (21017)Instruction limit reached!
% 43.72/7.41 % (21017)------------------------------
% 43.72/7.41 % (21017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.72/7.41 % (21017)Termination reason: Unknown
% 43.72/7.41 % (21017)Termination phase: Saturation
% 43.72/7.41
% 43.72/7.41 % (21017)Memory used [KB]: 8955
% 43.72/7.41 % (21017)Time elapsed: 0.323 s
% 43.72/7.41 % (21017)Instructions burned: 646 (million)
% 43.72/7.41 % (21017)------------------------------
% 43.72/7.41 % (21017)------------------------------
% 43.72/7.42 % (21029)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_20469 for (2937ds/1201Mi)
% 43.72/7.43 % (21015)Instruction limit reached!
% 43.72/7.43 % (21015)------------------------------
% 43.72/7.43 % (21015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.72/7.43 % (21015)Termination reason: Unknown
% 43.72/7.43 % (21015)Termination phase: Saturation
% 43.72/7.43
% 43.72/7.43 % (21015)Memory used [KB]: 10106
% 43.72/7.43 % (21015)Time elapsed: 0.489 s
% 43.72/7.43 % (21015)Instructions burned: 953 (million)
% 43.72/7.43 % (21015)------------------------------
% 43.72/7.43 % (21015)------------------------------
% 43.72/7.45 % (21031)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_20469 for (2937ds/1046Mi)
% 44.28/7.54 % (20914)Instruction limit reached!
% 44.28/7.54 % (20914)------------------------------
% 44.28/7.54 % (20914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.28/7.54 % (20914)Termination reason: Unknown
% 44.28/7.54 % (20914)Termination phase: Saturation
% 44.28/7.54
% 44.28/7.54 % (20914)Memory used [KB]: 14967
% 44.28/7.54 % (20914)Time elapsed: 3.784 s
% 44.28/7.54 % (20914)Instructions burned: 8251 (million)
% 44.28/7.54 % (20914)------------------------------
% 44.28/7.54 % (20914)------------------------------
% 44.28/7.56 % (21034)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_20469 for (2936ds/222Mi)
% 44.28/7.59 % (21021)Instruction limit reached!
% 44.28/7.59 % (21021)------------------------------
% 44.28/7.59 % (21021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.28/7.59 % (21021)Termination reason: Unknown
% 44.28/7.59 % (21021)Termination phase: Saturation
% 44.28/7.59
% 44.28/7.59 % (21021)Memory used [KB]: 9466
% 44.28/7.59 % (21021)Time elapsed: 0.454 s
% 44.28/7.59 % (21021)Instructions burned: 866 (million)
% 44.28/7.59 % (21021)------------------------------
% 44.28/7.59 % (21021)------------------------------
% 44.28/7.59 % (21022)Instruction limit reached!
% 44.28/7.59 % (21022)------------------------------
% 44.28/7.59 % (21022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.28/7.59 % (21022)Termination reason: Unknown
% 44.28/7.59 % (21022)Termination phase: Saturation
% 44.28/7.59
% 44.28/7.59 % (21022)Memory used [KB]: 9594
% 44.28/7.59 % (21022)Time elapsed: 0.442 s
% 44.28/7.59 % (21022)Instructions burned: 1176 (million)
% 44.28/7.59 % (21022)------------------------------
% 44.28/7.59 % (21022)------------------------------
% 45.30/7.61 % (21038)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_20469 for (2936ds/454Mi)
% 45.30/7.62 % (21037)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_20469 for (2936ds/68Mi)
% 45.30/7.66 % (21034)Instruction limit reached!
% 45.30/7.66 % (21034)------------------------------
% 45.30/7.66 % (21034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.30/7.66 % (21034)Termination reason: Unknown
% 45.30/7.66 % (21034)Termination phase: Saturation
% 45.30/7.66
% 45.30/7.66 % (21034)Memory used [KB]: 7291
% 45.30/7.66 % (21034)Time elapsed: 0.106 s
% 45.30/7.66 % (21034)Instructions burned: 223 (million)
% 45.30/7.66 % (21034)------------------------------
% 45.30/7.66 % (21034)------------------------------
% 45.30/7.66 % (21037)Instruction limit reached!
% 45.30/7.66 % (21037)------------------------------
% 45.30/7.66 % (21037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.30/7.66 % (21037)Termination reason: Unknown
% 45.30/7.66 % (21037)Termination phase: Property scanning
% 45.30/7.66
% 45.30/7.66 % (21037)Memory used [KB]: 2174
% 45.30/7.66 % (21037)Time elapsed: 0.024 s
% 45.30/7.66 % (21037)Instructions burned: 71 (million)
% 45.30/7.66 % (21037)------------------------------
% 45.30/7.66 % (21037)------------------------------
% 45.30/7.67 % (21040)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_20469 for (2935ds/360Mi)
% 45.30/7.68 % (21041)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_20469 for (2935ds/157Mi)
% 45.30/7.69 % (21026)Instruction limit reached!
% 45.30/7.69 % (21026)------------------------------
% 45.30/7.69 % (21026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.30/7.69 % (21026)Termination reason: Unknown
% 45.30/7.69 % (21026)Termination phase: Saturation
% 45.30/7.69
% 45.30/7.69 % (21026)Memory used [KB]: 8827
% 45.30/7.69 % (21026)Time elapsed: 0.346 s
% 45.30/7.69 % (21026)Instructions burned: 645 (million)
% 45.30/7.69 % (21026)------------------------------
% 45.30/7.69 % (21026)------------------------------
% 45.89/7.71 % (21042)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_20469 for (2935ds/5061Mi)
% 45.89/7.75 % (21041)Instruction limit reached!
% 45.89/7.75 % (21041)------------------------------
% 45.89/7.75 % (21041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.89/7.75 % (21041)Termination reason: Unknown
% 45.89/7.75 % (21041)Termination phase: Saturation
% 45.89/7.75
% 45.89/7.75 % (21041)Memory used [KB]: 6908
% 45.89/7.75 % (21041)Time elapsed: 0.075 s
% 45.89/7.75 % (21041)Instructions burned: 158 (million)
% 45.89/7.75 % (21041)------------------------------
% 45.89/7.75 % (21041)------------------------------
% 45.89/7.78 % (21044)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_20469 for (2934ds/2401Mi)
% 45.89/7.79 % (21040)Instruction limit reached!
% 45.89/7.79 % (21040)------------------------------
% 45.89/7.79 % (21040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.89/7.79 % (21040)Termination reason: Unknown
% 45.89/7.79 % (21040)Termination phase: Saturation
% 45.89/7.79
% 45.89/7.79 % (21040)Memory used [KB]: 8059
% 45.89/7.79 % (21040)Time elapsed: 0.108 s
% 45.89/7.79 % (21040)Instructions burned: 363 (million)
% 45.89/7.79 % (21040)------------------------------
% 45.89/7.79 % (21040)------------------------------
% 46.20/7.81 % (21038)Instruction limit reached!
% 46.20/7.81 % (21038)------------------------------
% 46.20/7.81 % (21038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.20/7.81 % (21038)Termination reason: Unknown
% 46.20/7.81 % (21038)Termination phase: Saturation
% 46.20/7.81
% 46.20/7.81 % (21038)Memory used [KB]: 12537
% 46.20/7.81 % (21038)Time elapsed: 0.202 s
% 46.20/7.81 % (21038)Instructions burned: 455 (million)
% 46.20/7.81 % (21038)------------------------------
% 46.20/7.81 % (21038)------------------------------
% 46.20/7.81 % (21046)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_20469 for (2934ds/5798Mi)
% 46.20/7.82 % (21047)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_20469 for (2933ds/346Mi)
% 46.20/7.86 % (21031)Instruction limit reached!
% 46.20/7.86 % (21031)------------------------------
% 46.20/7.86 % (21031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.20/7.86 % (21031)Termination reason: Unknown
% 46.20/7.86 % (21031)Termination phase: Saturation
% 46.20/7.86
% 46.20/7.86 % (21031)Memory used [KB]: 9338
% 46.20/7.86 % (21031)Time elapsed: 0.384 s
% 46.20/7.86 % (21031)Instructions burned: 1047 (million)
% 46.20/7.86 % (21031)------------------------------
% 46.20/7.86 % (21031)------------------------------
% 46.20/7.88 % (21048)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_20469 for (2933ds/1321Mi)
% 46.92/7.96 % (21029)Instruction limit reached!
% 46.92/7.96 % (21029)------------------------------
% 46.92/7.96 % (21029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.92/7.96 % (21029)Termination reason: Unknown
% 46.92/7.96 % (21029)Termination phase: Saturation
% 46.92/7.96
% 46.92/7.96 % (21029)Memory used [KB]: 9722
% 46.92/7.96 % (21029)Time elapsed: 0.548 s
% 46.92/7.96 % (21029)Instructions burned: 1202 (million)
% 46.92/7.96 % (21029)------------------------------
% 46.92/7.96 % (21029)------------------------------
% 46.92/7.96 % (21047)Instruction limit reached!
% 46.92/7.96 % (21047)------------------------------
% 46.92/7.96 % (21047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.92/7.96 % (21047)Termination reason: Unknown
% 46.92/7.96 % (21047)Termination phase: Saturation
% 46.92/7.96
% 46.92/7.96 % (21047)Memory used [KB]: 7675
% 46.92/7.96 % (21047)Time elapsed: 0.148 s
% 46.92/7.96 % (21047)Instructions burned: 346 (million)
% 46.92/7.96 % (21047)------------------------------
% 46.92/7.96 % (21047)------------------------------
% 46.92/7.98 % (21049)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_20469 for (2932ds/1312Mi)
% 46.92/7.98 % (21050)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_20469 for (2932ds/672Mi)
% 46.92/7.98 % (21048)Refutation not found, incomplete strategy
% 46.92/7.98 % (21048)------------------------------
% 46.92/7.98 % (21048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.92/7.98 % (21048)Termination reason: Refutation not found, incomplete strategy
% 46.92/7.98
% 46.92/7.98
% 46.92/7.98 % (21048)Memory used [KB]: 3070
% 46.92/7.98 % (21048)Time elapsed: 0.114 s
% 46.92/7.98 % (21048)Instructions burned: 148 (million)
% 46.92/7.98 % (21048)------------------------------
% 46.92/7.98 % (21048)------------------------------
% 46.92/8.00 % (21051)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_20469 for (2932ds/1897Mi)
% 50.56/8.30 % (21050)Instruction limit reached!
% 50.56/8.30 % (21050)------------------------------
% 50.56/8.30 % (21050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.56/8.30 % (21050)Termination reason: Unknown
% 50.56/8.30 % (21050)Termination phase: Saturation
% 50.56/8.30
% 50.56/8.30 % (21050)Memory used [KB]: 8699
% 50.56/8.30 % (21050)Time elapsed: 0.324 s
% 50.56/8.30 % (21050)Instructions burned: 673 (million)
% 50.56/8.30 % (21050)------------------------------
% 50.56/8.30 % (21050)------------------------------
% 50.56/8.31 % (21054)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_20469 for (2929ds/1202Mi)
% 51.78/8.58 % (21049)Instruction limit reached!
% 51.78/8.58 % (21049)------------------------------
% 51.78/8.58 % (21049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.78/8.58 % (21049)Termination reason: Unknown
% 51.78/8.58 % (21049)Termination phase: Saturation
% 51.78/8.58
% 51.78/8.58 % (21049)Memory used [KB]: 9466
% 51.78/8.58 % (21049)Time elapsed: 0.600 s
% 51.78/8.58 % (21049)Instructions burned: 1315 (million)
% 51.78/8.58 % (21049)------------------------------
% 51.78/8.58 % (21049)------------------------------
% 51.78/8.59 % (21057)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_20469 for (2926ds/1493Mi)
% 52.37/8.62 % (21057)Refutation not found, incomplete strategy
% 52.37/8.62 % (21057)------------------------------
% 52.37/8.62 % (21057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.37/8.62 % (21057)Termination reason: Refutation not found, incomplete strategy
% 52.37/8.62
% 52.37/8.62
% 52.37/8.62 % (21057)Memory used [KB]: 6908
% 52.37/8.62 % (21057)Time elapsed: 0.034 s
% 52.37/8.62 % (21057)Instructions burned: 112 (million)
% 52.37/8.62 % (21057)------------------------------
% 52.37/8.62 % (21057)------------------------------
% 52.37/8.63 % (21058)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_20469 for (2925ds/7679Mi)
% 53.42/8.84 % (21054)Instruction limit reached!
% 53.42/8.84 % (21054)------------------------------
% 53.42/8.84 % (21054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.42/8.84 % (21054)Termination reason: Unknown
% 53.42/8.84 % (21054)Termination phase: Saturation
% 53.42/8.84
% 53.42/8.84 % (21054)Memory used [KB]: 5245
% 53.42/8.84 % (21054)Time elapsed: 0.527 s
% 53.42/8.84 % (21054)Instructions burned: 1202 (million)
% 53.42/8.84 % (21054)------------------------------
% 53.42/8.84 % (21054)------------------------------
% 53.42/8.86 % (21061)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_20469 for (2923ds/340Mi)
% 54.44/8.93 % (21044)Instruction limit reached!
% 54.44/8.93 % (21044)------------------------------
% 54.44/8.93 % (21044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.44/8.93 % (21044)Termination reason: Unknown
% 54.44/8.93 % (21044)Termination phase: Saturation
% 54.44/8.93
% 54.44/8.93 % (21044)Memory used [KB]: 7803
% 54.44/8.93 % (21044)Time elapsed: 1.161 s
% 54.44/8.93 % (21044)Instructions burned: 2401 (million)
% 54.44/8.93 % (21044)------------------------------
% 54.44/8.93 % (21044)------------------------------
% 54.44/8.95 % (21063)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_20469 for (2922ds/3672Mi)
% 54.44/8.96 % (21051)Instruction limit reached!
% 54.44/8.96 % (21051)------------------------------
% 54.44/8.96 % (21051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.44/8.96 % (21051)Termination reason: Unknown
% 54.44/8.96 % (21051)Termination phase: Saturation
% 54.44/8.96
% 54.44/8.96 % (21051)Memory used [KB]: 10234
% 54.44/8.96 % (21051)Time elapsed: 0.957 s
% 54.44/8.96 % (21051)Instructions burned: 1897 (million)
% 54.44/8.96 % (21051)------------------------------
% 54.44/8.96 % (21051)------------------------------
% 54.44/8.98 % (21064)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_20469 for (2922ds/1535Mi)
% 54.44/8.99 % (21002)Instruction limit reached!
% 54.44/8.99 % (21002)------------------------------
% 54.44/8.99 % (21002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.44/8.99 % (21002)Termination reason: Unknown
% 54.44/8.99 % (21002)Termination phase: Saturation
% 54.44/8.99
% 54.44/8.99 % (21002)Memory used [KB]: 10234
% 54.44/8.99 % (21002)Time elapsed: 2.447 s
% 54.44/8.99 % (21002)Instructions burned: 6457 (million)
% 54.44/8.99 % (21002)------------------------------
% 54.44/8.99 % (21002)------------------------------
% 54.44/9.01 % (21061)Instruction limit reached!
% 54.44/9.01 % (21061)------------------------------
% 54.44/9.01 % (21061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.44/9.01 % (21061)Termination reason: Unknown
% 54.44/9.01 % (21061)Termination phase: Saturation
% 54.44/9.01
% 54.44/9.01 % (21061)Memory used [KB]: 7547
% 54.44/9.01 % (21061)Time elapsed: 0.158 s
% 54.44/9.01 % (21061)Instructions burned: 342 (million)
% 54.44/9.01 % (21061)------------------------------
% 54.44/9.01 % (21061)------------------------------
% 54.44/9.01 % (21066)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_20469 for (2922ds/4637Mi)
% 55.61/9.03 % (21067)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_20469 for (2921ds/3174Mi)
% 59.63/9.73 % (21064)Instruction limit reached!
% 59.63/9.73 % (21064)------------------------------
% 59.63/9.73 % (21064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.63/9.73 % (21064)Termination reason: Unknown
% 59.63/9.73 % (21064)Termination phase: Saturation
% 59.63/9.73
% 59.63/9.73 % (21064)Memory used [KB]: 12153
% 59.63/9.73 % (21064)Time elapsed: 0.771 s
% 59.63/9.73 % (21064)Instructions burned: 1537 (million)
% 59.63/9.73 % (21064)------------------------------
% 59.63/9.73 % (21064)------------------------------
% 59.63/9.74 % (21071)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_20469 for (2914ds/307Mi)
% 60.17/9.89 % (21071)Instruction limit reached!
% 60.17/9.89 % (21071)------------------------------
% 60.17/9.89 % (21071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.17/9.89 % (21071)Termination reason: Unknown
% 60.17/9.89 % (21071)Termination phase: Saturation
% 60.17/9.89
% 60.17/9.89 % (21071)Memory used [KB]: 7419
% 60.17/9.89 % (21071)Time elapsed: 0.145 s
% 60.17/9.89 % (21071)Instructions burned: 308 (million)
% 60.17/9.89 % (21071)------------------------------
% 60.17/9.89 % (21071)------------------------------
% 60.82/9.92 % (21042)Instruction limit reached!
% 60.82/9.92 % (21042)------------------------------
% 60.82/9.92 % (21042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.82/9.92 % (21042)Termination reason: Unknown
% 60.82/9.92 % (21042)Termination phase: Saturation
% 60.82/9.92
% 60.82/9.92 % (21042)Memory used [KB]: 10746
% 60.82/9.92 % (21042)Time elapsed: 2.210 s
% 60.82/9.92 % (21042)Instructions burned: 5062 (million)
% 60.82/9.92 % (21042)------------------------------
% 60.82/9.92 % (21042)------------------------------
% 60.82/9.92 % (21074)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_20469 for (2913ds/3619Mi)
% 60.82/9.93 % (21076)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_20469 for (2912ds/2325Mi)
% 65.18/10.48 % (21067)Instruction limit reached!
% 65.18/10.48 % (21067)------------------------------
% 65.18/10.48 % (21067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.18/10.48 % (21067)Termination reason: Unknown
% 65.18/10.48 % (21067)Termination phase: Saturation
% 65.18/10.48
% 65.18/10.48 % (21067)Memory used [KB]: 9722
% 65.18/10.48 % (21067)Time elapsed: 1.451 s
% 65.18/10.48 % (21067)Instructions burned: 3175 (million)
% 65.18/10.48 % (21067)------------------------------
% 65.18/10.48 % (21067)------------------------------
% 65.18/10.50 % (21078)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_20469 for (2907ds/2341Mi)
% 65.87/10.54 % (21046)Instruction limit reached!
% 65.87/10.54 % (21046)------------------------------
% 65.87/10.54 % (21046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.87/10.54 % (21046)Termination reason: Unknown
% 65.87/10.54 % (21046)Termination phase: Saturation
% 65.87/10.54
% 65.87/10.54 % (21046)Memory used [KB]: 10746
% 65.87/10.54 % (21046)Time elapsed: 2.737 s
% 65.87/10.54 % (21046)Instructions burned: 5798 (million)
% 65.87/10.54 % (21046)------------------------------
% 65.87/10.54 % (21046)------------------------------
% 65.87/10.56 % (21063)Instruction limit reached!
% 65.87/10.56 % (21063)------------------------------
% 65.87/10.56 % (21063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.87/10.56 % (21063)Termination reason: Unknown
% 65.87/10.56 % (21063)Termination phase: Saturation
% 65.87/10.56
% 65.87/10.56 % (21063)Memory used [KB]: 11513
% 65.87/10.56 % (21063)Time elapsed: 1.624 s
% 65.87/10.56 % (21063)Instructions burned: 3672 (million)
% 65.87/10.56 % (21063)------------------------------
% 65.87/10.56 % (21063)------------------------------
% 65.87/10.56 % (21080)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_20469 for (2906ds/7257Mi)
% 65.87/10.58 % (21081)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_20469 for (2906ds/3710Mi)
% 66.80/10.76 % (21066)Instruction limit reached!
% 66.80/10.76 % (21066)------------------------------
% 66.80/10.76 % (21066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.80/10.76 % (21066)Termination reason: Unknown
% 66.80/10.76 % (21066)Termination phase: Saturation
% 66.80/10.76
% 66.80/10.76 % (21066)Memory used [KB]: 10362
% 66.80/10.76 % (21066)Time elapsed: 1.763 s
% 66.80/10.76 % (21066)Instructions burned: 4637 (million)
% 66.80/10.76 % (21066)------------------------------
% 66.80/10.76 % (21066)------------------------------
% 66.80/10.78 % (21084)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_20469 for (2904ds/326Mi)
% 67.16/10.89 % (21084)Instruction limit reached!
% 67.16/10.89 % (21084)------------------------------
% 67.16/10.89 % (21084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.16/10.89 % (21084)Termination reason: Unknown
% 67.16/10.89 % (21084)Termination phase: Saturation
% 67.16/10.89
% 67.16/10.89 % (21084)Memory used [KB]: 7419
% 67.16/10.89 % (21084)Time elapsed: 0.147 s
% 67.16/10.89 % (21084)Instructions burned: 327 (million)
% 67.16/10.89 % (21084)------------------------------
% 67.16/10.89 % (21084)------------------------------
% 67.57/10.91 % (21086)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_20469 for (2903ds/1100Mi)
% 67.57/10.95 % (21076)Instruction limit reached!
% 67.57/10.95 % (21076)------------------------------
% 67.57/10.95 % (21076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.57/10.95 % (21076)Termination reason: Unknown
% 67.57/10.95 % (21076)Termination phase: Saturation
% 67.57/10.95
% 67.57/10.95 % (21076)Memory used [KB]: 9722
% 67.57/10.95 % (21076)Time elapsed: 1.045 s
% 67.57/10.95 % (21076)Instructions burned: 2327 (million)
% 67.57/10.95 % (21076)------------------------------
% 67.57/10.95 % (21076)------------------------------
% 67.57/10.96 % (21088)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_20469 for (2902ds/406Mi)
% 69.49/11.11 % (21088)Instruction limit reached!
% 69.49/11.11 % (21088)------------------------------
% 69.49/11.11 % (21088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.49/11.11 % (21088)Termination reason: Unknown
% 69.49/11.11 % (21088)Termination phase: Saturation
% 69.49/11.11
% 69.49/11.11 % (21088)Memory used [KB]: 7931
% 69.49/11.11 % (21088)Time elapsed: 0.146 s
% 69.49/11.11 % (21088)Instructions burned: 406 (million)
% 69.49/11.11 % (21088)------------------------------
% 69.49/11.11 % (21088)------------------------------
% 69.49/11.12 % (21091)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_20469 for (2900ds/1871Mi)
% 70.62/11.28 % (21074)First to succeed.
% 70.62/11.28 % (21074)Refutation found. Thanks to Tanya!
% 70.62/11.28 % SZS status Theorem for DTF2THF_20469
% 70.62/11.28 % SZS output start Proof for DTF2THF_20469
% 70.62/11.28 thf(type_def_5, type, itself: ($tType) > $tType).
% 70.62/11.28 thf(type_def_7, type, nat: $tType).
% 70.62/11.28 thf(type_def_8, type, coindu1593790203_llist: ($tType) > $tType).
% 70.62/11.28 thf(type_def_9, type, extended_enat: $tType).
% 70.62/11.28 thf(type_def_10, type, a: $tType).
% 70.62/11.28 thf(type_def_11, type, b: $tType).
% 70.62/11.28 thf(func_def_0, type, coindu1593790203_llist: ($tType) > $tType).
% 70.62/11.28 thf(func_def_1, type, extended_enat: $tType).
% 70.62/11.28 thf(func_def_2, type, nat: $tType).
% 70.62/11.28 thf(func_def_3, type, itself: ($tType) > $tType).
% 70.62/11.28 thf(func_def_4, type, b: $tType).
% 70.62/11.28 thf(func_def_5, type, a: $tType).
% 70.62/11.28 thf(func_def_6, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_7, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_8, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_9, type, group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_10, type, no_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_11, type, no_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_12, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_13, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_14, type, wellorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_15, type, semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_16, type, dense_order: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_17, type, ab_semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_18, type, cancel_semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_19, type, ordere779506340up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_20, type, canoni770627133id_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_21, type, ordere236663937imp_le: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_22, type, ordere223160158up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_23, type, strict2144017051up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 70.62/11.28 thf(func_def_24, type, coindu493225792length: !>[X0: $tType]:(nat > coindu1593790203_llist @ X0 > extended_enat)).
% 70.62/11.28 thf(func_def_25, type, coindu1529956631erates: !>[X0: $tType]:((X0 > X0) > X0 > coindu1593790203_llist @ X0)).
% 70.62/11.28 thf(func_def_26, type, coindu268472904append: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 70.62/11.28 thf(func_def_27, type, coindu1213758845finite: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 70.62/11.28 thf(func_def_28, type, coindu1018505716length: !>[X0: $tType]:(coindu1593790203_llist @ X0 > extended_enat)).
% 70.62/11.28 thf(func_def_29, type, coindu1121789889_LCons: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 70.62/11.28 thf(func_def_30, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 70.62/11.28 thf(func_def_31, type, coindu987187967t_all2: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > $o)).
% 70.62/11.28 thf(func_def_32, type, coindu335574135_lnull: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 70.62/11.28 thf(func_def_33, type, coindu749330388e_lnth: !>[X0: $tType]:(coindu1593790203_llist @ X0 > nat > X0)).
% 70.62/11.28 thf(func_def_34, type, extended_enat2: nat > extended_enat).
% 70.62/11.28 thf(func_def_35, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 70.62/11.28 thf(func_def_36, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 70.62/11.28 thf(func_def_37, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 70.62/11.28 thf(func_def_38, type, type2: !>[X0: $tType]:(itself @ X0)).
% 70.62/11.28 thf(func_def_39, type, p: a > b > $o).
% 70.62/11.28 thf(func_def_40, type, n: nat).
% 70.62/11.28 thf(func_def_41, type, xs: coindu1593790203_llist @ a).
% 70.62/11.28 thf(func_def_42, type, xs2: coindu1593790203_llist @ a).
% 70.62/11.28 thf(func_def_43, type, ys: coindu1593790203_llist @ b).
% 70.62/11.28 thf(func_def_59, type, sP0: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 70.62/11.28 thf(func_def_60, type, sP1: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 70.62/11.28 thf(func_def_61, type, sP2: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 70.62/11.28 thf(func_def_62, type, sK3: nat > extended_enat > nat).
% 70.62/11.28 thf(func_def_63, type, sK4: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 70.62/11.28 thf(func_def_64, type, sK5: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 70.62/11.29 thf(func_def_65, type, sK6: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 70.62/11.29 thf(func_def_66, type, sK7: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 70.62/11.29 thf(func_def_67, type, sK8: !>[X0: $tType, X1: $tType]:(coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > X0 > (X0 > X1 > $o) > X1)).
% 70.62/11.29 thf(func_def_68, type, sK9: !>[X0: $tType, X1: $tType]:(coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > X0 > (X0 > X1 > $o) > coindu1593790203_llist @ X1)).
% 70.62/11.29 thf(func_def_69, type, sK10: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 70.62/11.29 thf(func_def_70, type, sK11: !>[X0: $tType]:((X0 > $o) > X0)).
% 70.62/11.29 thf(func_def_71, type, sK12: nat > nat > nat).
% 70.62/11.29 thf(func_def_72, type, sK13: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 70.62/11.29 thf(func_def_73, type, sK14: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 70.62/11.29 thf(func_def_74, type, sK15: !>[X0: $tType]:(nat > (X0 > nat) > (X0 > $o) > X0)).
% 70.62/11.29 thf(func_def_75, type, sK16: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 70.62/11.29 thf(func_def_76, type, sK17: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 70.62/11.29 thf(func_def_77, type, sK18: !>[X0: $tType]:(coindu1593790203_llist @ X0 > nat)).
% 70.62/11.29 thf(func_def_78, type, sK19: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 70.62/11.29 thf(func_def_79, type, sK20: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 70.62/11.29 thf(func_def_80, type, sK21: !>[X0: $tType, X1: $tType]:(coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > X0)).
% 70.62/11.29 thf(func_def_81, type, sK22: !>[X0: $tType, X1: $tType]:(coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > coindu1593790203_llist @ X0)).
% 70.62/11.29 thf(func_def_82, type, sK23: !>[X0: $tType, X1: $tType]:(coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > X1)).
% 70.62/11.29 thf(func_def_83, type, sK24: !>[X0: $tType, X1: $tType]:(coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > coindu1593790203_llist @ X1)).
% 70.62/11.29 thf(func_def_84, type, sK25: extended_enat > nat).
% 70.62/11.29 thf(func_def_85, type, sK26: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 70.62/11.29 thf(func_def_86, type, sK27: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 70.62/11.29 thf(func_def_87, type, sK28: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 70.62/11.29 thf(func_def_88, type, sK29: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > X0)).
% 70.62/11.29 thf(func_def_89, type, sK30: !>[X0: $tType]:(nat > (X0 > nat) > X0 > (X0 > $o) > X0)).
% 70.62/11.29 thf(func_def_90, type, sK31: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 70.62/11.29 thf(func_def_91, type, sK32: !>[X0: $tType]:(X0 > X0 > X0)).
% 70.62/11.29 thf(func_def_92, type, sK33: !>[X0: $tType, X1: $tType]:(coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > X0)).
% 70.62/11.29 thf(func_def_93, type, sK34: !>[X0: $tType, X1: $tType]:(coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > coindu1593790203_llist @ X0)).
% 70.62/11.29 thf(func_def_94, type, sK35: !>[X0: $tType, X1: $tType]:(coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > X1)).
% 70.62/11.29 thf(func_def_95, type, sK36: !>[X0: $tType, X1: $tType]:(coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > (X0 > X1 > $o) > coindu1593790203_llist @ X1)).
% 70.62/11.29 thf(func_def_96, type, sK37: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 70.62/11.29 thf(func_def_97, type, sK38: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 70.62/11.29 thf(func_def_98, type, sK39: (nat > nat) > nat).
% 70.62/11.29 thf(func_def_99, type, sK40: (nat > nat) > nat).
% 70.62/11.29 thf(func_def_100, type, sK41: !>[X0: $tType]:(X0 > X0)).
% 70.62/11.29 thf(func_def_101, type, sK42: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 70.62/11.29 thf(func_def_102, type, sK43: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 70.62/11.29 thf(func_def_103, type, sK44: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 70.62/11.29 thf(func_def_104, type, sK45: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 70.62/11.29 thf(func_def_105, type, sK46: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 70.62/11.29 thf(func_def_106, type, sK47: (nat > $o) > nat).
% 70.62/11.29 thf(func_def_107, type, sK48: !>[X0: $tType]:((X0 > $o) > (X0 > nat) > X0)).
% 70.62/11.29 thf(func_def_108, type, sK49: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 70.62/11.29 thf(func_def_109, type, sK50: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 70.62/11.29 thf(func_def_110, type, sK51: nat > extended_enat > extended_enat > nat).
% 70.62/11.29 thf(func_def_111, type, sK52: nat > extended_enat > extended_enat > nat).
% 70.62/11.29 thf(func_def_112, type, sK53: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 70.62/11.29 thf(func_def_113, type, sK54: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 70.62/11.29 thf(func_def_114, type, sK55: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X1)).
% 70.62/11.29 thf(func_def_115, type, sK56: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X0)).
% 70.62/11.29 thf(func_def_116, type, sK57: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 70.62/11.29 thf(func_def_117, type, sK58: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 70.62/11.29 thf(func_def_118, type, sK59: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X0)).
% 70.62/11.29 thf(func_def_119, type, sK60: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X1)).
% 70.62/11.29 thf(func_def_120, type, sK61: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 70.62/11.29 thf(func_def_121, type, sK62: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 70.62/11.29 thf(func_def_122, type, sK63: extended_enat > nat).
% 70.62/11.29 thf(func_def_123, type, sK64: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > X0)).
% 70.62/11.29 thf(func_def_124, type, sK65: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 70.62/11.29 thf(func_def_125, type, sK66: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 70.62/11.29 thf(func_def_126, type, sK67: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 70.62/11.29 thf(func_def_127, type, sK68: !>[X0: $tType]:(X0 > X0)).
% 70.62/11.29 thf(func_def_128, type, sK69: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 70.62/11.29 thf(func_def_129, type, sK70: extended_enat > extended_enat > nat).
% 70.62/11.29 thf(func_def_130, type, sK71: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 70.62/11.29 thf(func_def_131, type, sK72: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 70.62/11.29 thf(func_def_132, type, sK73: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 70.62/11.29 thf(func_def_133, type, sK74: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 70.62/11.29 thf(func_def_134, type, sK75: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 70.62/11.29 thf(func_def_135, type, sK76: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 70.62/11.29 thf(func_def_136, type, sK77: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 70.62/11.29 thf(func_def_137, type, sK78: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 70.62/11.29 thf(func_def_138, type, sK79: (nat > $o) > nat).
% 70.62/11.29 thf(func_def_139, type, sK80: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 70.62/11.29 thf(func_def_140, type, sK81: !>[X0: $tType]:((X0 > extended_enat) > X0)).
% 70.62/11.29 thf(func_def_141, type, sK82: !>[X0: $tType]:(nat > (X0 > extended_enat) > X0)).
% 70.62/11.29 thf(func_def_142, type, sK83: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 70.62/11.29 thf(func_def_143, type, sK84: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 70.62/11.29 thf(func_def_144, type, sK85: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 70.62/11.29 thf(func_def_145, type, sK86: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 70.62/11.29 thf(func_def_146, type, sK87: (nat > nat) > nat).
% 70.62/11.29 thf(func_def_147, type, sK88: (nat > nat) > nat).
% 70.62/11.29 thf(func_def_148, type, sK89: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > coindu1593790203_llist @ X1 > coindu1593790203_llist @ X0 > nat)).
% 70.62/11.29 thf(func_def_149, type, sK90: (extended_enat > $o) > extended_enat).
% 70.62/11.29 thf(func_def_150, type, sK91: !>[X0: $tType, X1: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X1 > (X1 > X0 > $o) > X1)).
% 70.62/11.29 thf(func_def_151, type, sK92: !>[X0: $tType, X1: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X1 > (X1 > X0 > $o) > coindu1593790203_llist @ X1)).
% 70.62/11.29 thf(func_def_153, type, ph94: !>[X0: $tType]:(X0)).
% 70.62/11.29 thf(f18725,plain,(
% 70.62/11.29 $false),
% 70.62/11.29 inference(avatar_sat_refutation,[status(thm)],[f1824,f1981,f2300,f2575,f3405,f18563,f18713])).
% 70.62/11.29 thf(f18713,plain,(
% 70.62/11.29 ~spl93_21 | spl93_2 | ~spl93_45),
% 70.62/11.29 inference(avatar_split_clause,[status(thm)],[f18569,f2565,f1808,f2112])).
% 70.62/11.29 thf(f2112,definition,(
% 70.62/11.29 spl93_21 <=> ((ord_less @ extended_enat @ (extended_enat2 @ n) @ (coindu1018505716length @ a @ xs)) = $true)),
% 70.62/11.29 introduced(definition,[new_symbols(naming,[spl93_21])],[avatar_definition])).
% 70.62/11.29 thf(f1808,definition,(
% 70.62/11.29 spl93_2 <=> ((ord_less @ extended_enat @ (extended_enat2 @ n) @ (coindu1018505716length @ b @ ys)) = $true)),
% 70.62/11.29 introduced(definition,[new_symbols(naming,[spl93_2])],[avatar_definition])).
% 70.62/11.29 thf(f2565,definition,(
% 70.62/11.29 spl93_45 <=> ((coindu1018505716length @ a @ xs) = (coindu1018505716length @ b @ ys))),
% 70.62/11.29 introduced(definition,[new_symbols(naming,[spl93_45])],[avatar_definition])).
% 70.62/11.29 thf(f18569,plain,(
% 70.62/11.29 ((ord_less @ extended_enat @ (extended_enat2 @ n) @ (coindu1018505716length @ a @ xs)) != $true) | (spl93_2 | ~spl93_45)),
% 70.62/11.29 inference(superposition,[status(thm)],[f1810,f2567])).
% 70.62/11.29 thf(f2567,plain,(
% 70.62/11.29 ((coindu1018505716length @ a @ xs) = (coindu1018505716length @ b @ ys)) | ~spl93_45),
% 70.62/11.29 inference(avatar_component_clause,[status(thm)],[f2565])).
% 70.62/11.29 thf(f1810,plain,(
% 70.62/11.29 ((ord_less @ extended_enat @ (extended_enat2 @ n) @ (coindu1018505716length @ b @ ys)) != $true) | spl93_2),
% 70.62/11.29 inference(avatar_component_clause,[status(thm)],[f1808])).
% 70.62/11.29 thf(f18563,plain,(
% 70.62/11.29 ~spl93_21 | ~spl93_1 | spl93_5 | spl93_58),
% 70.62/11.29 inference(avatar_split_clause,[status(thm)],[f18528,f3393,f1821,f1804,f2112])).
% 70.62/11.29 thf(f1804,definition,(
% 70.62/11.29 spl93_1 <=> ((coindu987187967t_all2 @ a @ b @ p @ (coindu268472904append @ a @ xs @ xs2) @ ys) = $true)),
% 70.62/11.29 introduced(definition,[new_symbols(naming,[spl93_1])],[avatar_definition])).
% 70.62/11.29 thf(f1821,definition,(
% 70.62/11.29 spl93_5 <=> ((ord_less @ extended_enat @ (extended_enat2 @ n) @ (coindu1018505716length @ a @ (coindu268472904append @ a @ xs @ xs2))) = $true)),
% 70.62/11.29 introduced(definition,[new_symbols(naming,[spl93_5])],[avatar_definition])).
% 70.62/11.29 thf(f3393,definition,(
% 70.62/11.29 spl93_58 <=> ((ord_less_eq @ extended_enat @ (coindu1018505716length @ b @ ys) @ (coindu1018505716length @ a @ xs)) = $true)),
% 70.62/11.29 introduced(definition,[new_symbols(naming,[spl93_58])],[avatar_definition])).
% 70.62/11.29 thf(f18528,plain,(
% 70.62/11.29 ((ord_less @ extended_enat @ (extended_enat2 @ n) @ (coindu1018505716length @ a @ xs)) != $true) | (~spl93_1 | spl93_5 | spl93_58)),
% 70.62/11.29 inference(trivial_inequality_removal,[status(thm)],[f18518])).
% 70.62/11.29 thf(f18518,plain,(
% 70.62/11.29 ((ord_less @ extended_enat @ (extended_enat2 @ n) @ (coindu1018505716length @ a @ xs)) != $true) | ($true != $true) | (~spl93_1 | spl93_5 | spl93_58)),
% 70.62/11.29 inference(superposition,[status(thm)],[f3395,f2979])).
% 70.62/11.29 thf(f2979,plain,(
% 70.62/11.29 ( ! [X0 : extended_enat] : (((ord_less_eq @ extended_enat @ (coindu1018505716length @ b @ ys) @ X0) = $true) | ($true != (ord_less @ extended_enat @ (extended_enat2 @ n) @ X0))) ) | (~spl93_1 | spl93_5)),
% 70.62/11.29 inference(trivial_inequality_removal,[status(thm)],[f2978])).
% 70.62/11.29 thf(f2978,plain,(
% 70.62/11.29 ( ! [X0 : extended_enat] : (((ord_less_eq @ extended_enat @ (coindu1018505716length @ b @ ys) @ X0) = $true) | ($true != (ord_less @ extended_enat @ (extended_enat2 @ n) @ X0)) | ($true != $true)) ) | (~spl93_1 | spl93_5)),
% 70.62/11.29 inference(forward_demodulation,[status(thm)],[f2964,f1312])).
% 70.62/11.29 thf(f1312,plain,(
% 70.62/11.29 ((linorder @ extended_enat @ type2 @ extended_enat) = $true)),
% 70.62/11.29 inference(cnf_transformation,[status(thm)],[f698])).
% 70.62/11.29 thf(f698,plain,(
% 70.62/11.29 ((linorder @ extended_enat @ type2 @ extended_enat) = $true)),
% 70.62/11.29 inference(fool_elimination,[status(thm)],[f697])).
% 70.62/11.29 thf(f697,plain,(
% 70.62/11.29 (linorder @ extended_enat @ type2 @ extended_enat)),
% 70.62/11.29 inference(rectify,[status(thm)],[f283])).
% 70.62/11.29 thf(f283,axiom,(
% 70.62/11.29 (linorder @ extended_enat @ type2 @ extended_enat)),
% 70.62/11.29 file('/export/starexec/sandbox/tmp/tmp.YAJWcH1y2A/DTF2THF_20469.p',tcon_Extended__Nat_Oenat___Orderings_Olinorder_15)).
% 70.62/11.29 thf(f2964,plain,(
% 70.62/11.29 ( ! [X0 : extended_enat] : (($true != (ord_less @ extended_enat @ (extended_enat2 @ n) @ X0)) | ((ord_less_eq @ extended_enat @ (coindu1018505716length @ b @ ys) @ X0) = $true) | ((linorder @ extended_enat @ type2 @ extended_enat) != $true)) ) | (~spl93_1 | spl93_5)),
% 70.62/11.29 inference(trivial_inequality_removal,[status(thm)],[f2946])).
% 70.62/11.29 thf(f2946,plain,(
% 70.62/11.29 ( ! [X0 : extended_enat] : (((ord_less_eq @ extended_enat @ (coindu1018505716length @ b @ ys) @ X0) = $true) | ($true != (ord_less @ extended_enat @ (extended_enat2 @ n) @ X0)) | ((linorder @ extended_enat @ type2 @ extended_enat) != $true) | ($true != $true)) ) | (~spl93_1 | spl93_5)),
% 70.62/11.29 inference(superposition,[status(thm)],[f2939,f1455])).
% 70.62/11.29 thf(f1455,plain,(
% 70.62/11.29 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = (ord_less @ X0 @ X1 @ X2)) | ((ord_less_eq @ X0 @ X2 @ X1) = $true) | ((linorder @ X0 @ type2 @ X0) != $true)) )),
% 70.62/11.29 inference(cnf_transformation,[status(thm)],[f1096])).
% 70.62/11.29 thf(f1096,plain,(
% 70.62/11.29 ! [X0 : $tType] : (((linorder @ X0 @ type2 @ X0) != $true) | ! [X1 : X0,X2 : X0] : (($true = (ord_less @ X0 @ X1 @ X2)) | ((ord_less_eq @ X0 @ X2 @ X1) = $true)))),
% 70.62/11.29 inference(ennf_transformation,[status(thm)],[f847])).
% 70.62/11.29 thf(f847,plain,(
% 70.62/11.29 ! [X0 : $tType] : (((linorder @ X0 @ type2 @ X0) = $true) => ! [X1 : X0,X2 : X0] : (($true != (ord_less @ X0 @ X1 @ X2)) => ((ord_less_eq @ X0 @ X2 @ X1) = $true)))),
% 70.62/11.29 inference(flattening,[status(thm)],[f508])).
% 70.62/11.29 thf(f508,plain,(
% 70.62/11.29 ! [X0 : $tType] : (((linorder @ X0 @ type2 @ X0) = $true) => ! [X1 : X0,X2 : X0] : (~($true = (ord_less @ X0 @ X1 @ X2)) => ((ord_less_eq @ X0 @ X2 @ X1) = $true)))),
% 70.62/11.29 inference(fool_elimination,[status(thm)],[f507])).
% 70.62/11.29 thf(f507,plain,(
% 70.62/11.29 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : X0] : (~(ord_less @ X0 @ X1 @ X2) => (ord_less_eq @ X0 @ X2 @ X1)))),
% 70.62/11.29 inference(rectify,[status(thm)],[f247])).
% 70.62/11.29 thf(f247,axiom,(
% 70.62/11.29 ! [X0 : $tType] : ((linorder @ X0 @ type2 @ X0) => ! [X6 : X0,X22 : X0] : (~(ord_less @ X0 @ X6 @ X22) => (ord_less_eq @ X0 @ X22 @ X6)))),
% 70.62/11.29 file('/export/starexec/sandbox/tmp/tmp.YAJWcH1y2A/DTF2THF_20469.p',fact_246_leI)).
% 70.62/11.29 thf(f2939,plain,(
% 70.62/11.29 ( ! [X0 : extended_enat] : (($true != (ord_less @ extended_enat @ X0 @ (coindu1018505716length @ b @ ys))) | ($true != (ord_less @ extended_enat @ (extended_enat2 @ n) @ X0))) ) | (~spl93_1 | spl93_5)),
% 70.62/11.29 inference(forward_demodulation,[status(thm)],[f2127,f2148])).
% 70.62/11.29 thf(f2148,plain,(
% 70.62/11.29 ((coindu1018505716length @ a @ (coindu268472904append @ a @ xs @ xs2)) = (coindu1018505716length @ b @ ys)) | ~spl93_1),
% 70.62/11.29 inference(trivial_inequality_removal,[status(thm)],[f2144])).
% 70.62/11.29 thf(f2144,plain,(
% 70.62/11.29 ($true != $true) | ((coindu1018505716length @ a @ (coindu268472904append @ a @ xs @ xs2)) = (coindu1018505716length @ b @ ys)) | ~spl93_1),
% 70.62/11.29 inference(superposition,[status(thm)],[f1435,f1805])).
% 70.62/11.29 thf(f1805,plain,(
% 70.62/11.29 ((coindu987187967t_all2 @ a @ b @ p @ (coindu268472904append @ a @ xs @ xs2) @ ys) = $true) | ~spl93_1),
% 70.62/11.29 inference(avatar_component_clause,[status(thm)],[f1804])).
% 70.62/11.29 thf(f1435,plain,(
% 70.62/11.29 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : coindu1593790203_llist @ X0,X4 : coindu1593790203_llist @ X1] : (((coindu987187967t_all2 @ X0 @ X1 @ X2 @ X3 @ X4) != $true) | ((coindu1018505716length @ X0 @ X3) = (coindu1018505716length @ X1 @ X4))) )),
% 70.62/11.29 inference(cnf_transformation,[status(thm)],[f939])).
% 70.62/11.29 thf(f939,plain,(
% 70.62/11.29 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : coindu1593790203_llist @ X0,X4 : coindu1593790203_llist @ X1] : (((coindu987187967t_all2 @ X0 @ X1 @ X2 @ X3 @ X4) != $true) | ((coindu1018505716length @ X0 @ X3) = (coindu1018505716length @ X1 @ X4)))),
% 70.62/11.29 inference(ennf_transformation,[status(thm)],[f696])).
% 70.62/11.29 thf(f696,plain,(
% 70.62/11.29 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : coindu1593790203_llist @ X0,X4 : coindu1593790203_llist @ X1] : (((coindu987187967t_all2 @ X0 @ X1 @ X2 @ X3 @ X4) = $true) => ((coindu1018505716length @ X0 @ X3) = (coindu1018505716length @ X1 @ X4)))),
% 70.62/11.29 inference(fool_elimination,[status(thm)],[f695])).
% 70.62/11.29 thf(f695,plain,(
% 70.62/11.29 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : coindu1593790203_llist @ X0,X4 : coindu1593790203_llist @ X1] : ((coindu987187967t_all2 @ X0 @ X1 @ X2 @ X3 @ X4) => ((coindu1018505716length @ X0 @ X3) = (coindu1018505716length @ X1 @ X4)))),
% 70.62/11.29 inference(rectify,[status(thm)],[f54])).
% 70.62/11.29 thf(f54,axiom,(
% 70.62/11.29 ! [X0 : $tType,X1 : $tType,X13 : X0 > X1 > $o,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X1] : ((coindu987187967t_all2 @ X0 @ X1 @ X13 @ X2 @ X3) => ((coindu1018505716length @ X0 @ X2) = (coindu1018505716length @ X1 @ X3)))),
% 70.62/11.29 file('/export/starexec/sandbox/tmp/tmp.YAJWcH1y2A/DTF2THF_20469.p',fact_53_llist__all2__llengthD)).
% 70.62/11.29 thf(f2127,plain,(
% 70.62/11.29 ( ! [X0 : extended_enat] : (((ord_less @ extended_enat @ X0 @ (coindu1018505716length @ a @ (coindu268472904append @ a @ xs @ xs2))) != $true) | ($true != (ord_less @ extended_enat @ (extended_enat2 @ n) @ X0))) ) | spl93_5),
% 70.62/11.29 inference(trivial_inequality_removal,[status(thm)],[f2126])).
% 70.62/11.29 thf(f2126,plain,(
% 70.62/11.29 ( ! [X0 : extended_enat] : (($true != $true) | ((ord_less @ extended_enat @ X0 @ (coindu1018505716length @ a @ (coindu268472904append @ a @ xs @ xs2))) != $true) | ($true != (ord_less @ extended_enat @ (extended_enat2 @ n) @ X0))) ) | spl93_5),
% 70.62/11.29 inference(forward_demodulation,[status(thm)],[f2075,f1529])).
% 70.62/11.29 thf(f1529,plain,(
% 70.62/11.29 ((preorder @ extended_enat @ type2 @ extended_enat) = $true)),
% 70.62/11.29 inference(cnf_transformation,[status(thm)],[f724])).
% 70.62/11.29 thf(f724,plain,(
% 70.62/11.29 ((preorder @ extended_enat @ type2 @ extended_enat) = $true)),
% 70.62/11.29 inference(fool_elimination,[status(thm)],[f723])).
% 70.62/11.29 thf(f723,plain,(
% 70.62/11.29 (preorder @ extended_enat @ type2 @ extended_enat)),
% 70.62/11.29 inference(rectify,[status(thm)],[f282])).
% 70.62/11.29 thf(f282,axiom,(
% 70.62/11.29 (preorder @ extended_enat @ type2 @ extended_enat)),
% 70.62/11.29 file('/export/starexec/sandbox/tmp/tmp.YAJWcH1y2A/DTF2THF_20469.p',tcon_Extended__Nat_Oenat___Orderings_Opreorder_14)).
% 70.62/11.29 thf(f2075,plain,(
% 70.62/11.29 ( ! [X0 : extended_enat] : (($true != (ord_less @ extended_enat @ (extended_enat2 @ n) @ X0)) | ((ord_less @ extended_enat @ X0 @ (coindu1018505716length @ a @ (coindu268472904append @ a @ xs @ xs2))) != $true) | ((preorder @ extended_enat @ type2 @ extended_enat) != $true)) ) | spl93_5),
% 70.62/11.29 inference(trivial_inequality_removal,[status(thm)],[f2069])).
% 70.62/11.29 thf(f2069,plain,(
% 70.62/11.29 ( ! [X0 : extended_enat] : (((ord_less @ extended_enat @ X0 @ (coindu1018505716length @ a @ (coindu268472904append @ a @ xs @ xs2))) != $true) | ($true != (ord_less @ extended_enat @ (extended_enat2 @ n) @ X0)) | ($true != $true) | ((preorder @ extended_enat @ type2 @ extended_enat) != $true)) ) | spl93_5),
% 70.62/11.29 inference(superposition,[status(thm)],[f1823,f1573])).
% 70.62/11.29 thf(f1573,plain,(
% 70.62/11.29 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (((ord_less @ X0 @ X1 @ X3) = $true) | ((ord_less @ X0 @ X2 @ X3) != $true) | ($true != (ord_less @ X0 @ X1 @ X2)) | ((preorder @ X0 @ type2 @ X0) != $true)) )),
% 70.62/11.29 inference(cnf_transformation,[status(thm)],[f1058])).
% 70.62/11.29 thf(f1058,plain,(
% 70.62/11.29 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (((ord_less @ X0 @ X2 @ X3) != $true) | ((ord_less @ X0 @ X1 @ X3) = $true) | ($true != (ord_less @ X0 @ X1 @ X2))) | ((preorder @ X0 @ type2 @ X0) != $true))),
% 70.62/11.29 inference(flattening,[status(thm)],[f1057])).
% 70.62/11.29 thf(f1057,plain,(
% 70.62/11.29 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((((ord_less @ X0 @ X1 @ X3) = $true) | ((ord_less @ X0 @ X2 @ X3) != $true)) | ($true != (ord_less @ X0 @ X1 @ X2))) | ((preorder @ X0 @ type2 @ X0) != $true))),
% 70.62/11.29 inference(ennf_transformation,[status(thm)],[f578])).
% 70.62/11.29 thf(f578,plain,(
% 70.62/11.29 ! [X0 : $tType] : (((preorder @ X0 @ type2 @ X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = (ord_less @ X0 @ X1 @ X2)) => (((ord_less @ X0 @ X2 @ X3) = $true) => ((ord_less @ X0 @ X1 @ X3) = $true))))),
% 70.62/11.29 inference(fool_elimination,[status(thm)],[f577])).
% 70.62/11.29 thf(f577,plain,(
% 70.62/11.29 ! [X0 : $tType] : ((preorder @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((ord_less @ X0 @ X1 @ X2) => ((ord_less @ X0 @ X2 @ X3) => (ord_less @ X0 @ X1 @ X3))))),
% 70.62/11.29 inference(rectify,[status(thm)],[f222])).
% 70.62/11.29 thf(f222,axiom,(
% 70.62/11.29 ! [X0 : $tType] : ((preorder @ X0 @ type2 @ X0) => ! [X6 : X0,X22 : X0,X53 : X0] : ((ord_less @ X0 @ X6 @ X22) => ((ord_less @ X0 @ X22 @ X53) => (ord_less @ X0 @ X6 @ X53))))),
% 70.62/11.29 file('/export/starexec/sandbox/tmp/tmp.YAJWcH1y2A/DTF2THF_20469.p',fact_221_less__trans)).
% 70.62/11.29 thf(f1823,plain,(
% 70.62/11.29 ((ord_less @ extended_enat @ (extended_enat2 @ n) @ (coindu1018505716length @ a @ (coindu268472904append @ a @ xs @ xs2))) != $true) | spl93_5),
% 70.62/11.29 inference(avatar_component_clause,[status(thm)],[f1821])).
% 70.62/11.29 thf(f3395,plain,(
% 70.62/11.29 ((ord_less_eq @ extended_enat @ (coindu1018505716length @ b @ ys) @ (coindu1018505716length @ a @ xs)) != $true) | spl93_58),
% 70.62/11.29 inference(avatar_component_clause,[status(thm)],[f3393])).
% 70.62/11.29 thf(f3405,plain,(
% 70.62/11.29 spl93_45 | ~spl93_58 | ~spl93_1),
% 70.62/11.29 inference(avatar_split_clause,[status(thm)],[f3404,f1804,f3393,f2565])).
% 70.62/11.29 thf(f3404,plain,(
% 70.62/11.29 ((coindu1018505716length @ a @ xs) = (coindu1018505716length @ b @ ys)) | ((ord_less_eq @ extended_enat @ (coindu1018505716length @ b @ ys) @ (coindu1018505716length @ a @ xs)) != $true) | ~spl93_1),
% 70.62/11.29 inference(trivial_inequality_removal,[status(thm)],[f3403])).
% 70.62/11.29 thf(f3403,plain,(
% 70.62/11.29 ((ord_less_eq @ extended_enat @ (coindu1018505716length @ b @ ys) @ (coindu1018505716length @ a @ xs)) != $true) | ($true != $true) | ((coindu1018505716length @ a @ xs) = (coindu1018505716length @ b @ ys)) | ~spl93_1),
% 70.62/11.29 inference(forward_demodulation,[status(thm)],[f3386,f1329])).
% 70.62/11.29 thf(f1329,plain,(
% 70.62/11.29 ((order @ extended_enat @ type2 @ extended_enat) = $true)),
% 70.62/11.29 inference(cnf_transformation,[status(thm)],[f812])).
% 70.62/11.29 thf(f812,plain,(
% 70.62/11.29 ((order @ extended_enat @ type2 @ extended_enat) = $true)),
% 70.62/11.29 inference(fool_elimination,[status(thm)],[f811])).
% 70.62/11.29 thf(f811,plain,(
% 70.62/11.29 (order @ extended_enat @ type2 @ extended_enat)),
% 70.62/11.29 inference(rectify,[status(thm)],[f284])).
% 70.62/11.29 thf(f284,axiom,(
% 70.62/11.29 (order @ extended_enat @ type2 @ extended_enat)),
% 70.62/11.29 file('/export/starexec/sandbox/tmp/tmp.YAJWcH1y2A/DTF2THF_20469.p',tcon_Extended__Nat_Oenat___Orderings_Oorder_16)).
% 70.62/11.29 thf(f3386,plain,(
% 70.62/11.29 ((coindu1018505716length @ a @ xs) = (coindu1018505716length @ b @ ys)) | ((order @ extended_enat @ type2 @ extended_enat) != $true) | ((ord_less_eq @ extended_enat @ (coindu1018505716length @ b @ ys) @ (coindu1018505716length @ a @ xs)) != $true) | ~spl93_1),
% 70.62/11.29 inference(trivial_inequality_removal,[status(thm)],[f3384])).
% 70.62/11.29 thf(f3384,plain,(
% 70.62/11.29 ((ord_less_eq @ extended_enat @ (coindu1018505716length @ b @ ys) @ (coindu1018505716length @ a @ xs)) != $true) | ((order @ extended_enat @ type2 @ extended_enat) != $true) | ((coindu1018505716length @ a @ xs) = (coindu1018505716length @ b @ ys)) | ($true != $true) | ~spl93_1),
% 70.62/11.29 inference(superposition,[status(thm)],[f1616,f2554])).
% 70.62/11.29 thf(f2554,plain,(
% 70.62/11.29 ((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ (coindu1018505716length @ b @ ys)) = $true) | ~spl93_1),
% 70.62/11.29 inference(superposition,[status(thm)],[f1468,f2148])).
% 70.62/11.29 thf(f1468,plain,(
% 70.62/11.29 ((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ (coindu1018505716length @ a @ (coindu268472904append @ a @ xs @ xs2))) = $true)),
% 70.62/11.29 inference(cnf_transformation,[status(thm)],[f348])).
% 70.62/11.29 thf(f348,plain,(
% 70.62/11.29 ((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ (coindu1018505716length @ a @ (coindu268472904append @ a @ xs @ xs2))) = $true)),
% 70.62/11.29 inference(fool_elimination,[status(thm)],[f347])).
% 70.62/11.29 thf(f347,plain,(
% 70.62/11.29 (ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ (coindu1018505716length @ a @ (coindu268472904append @ a @ xs @ xs2)))),
% 70.62/11.29 inference(rectify,[status(thm)],[f3])).
% 70.62/11.29 thf(f3,axiom,(
% 70.62/11.29 (ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ (coindu1018505716length @ a @ (coindu268472904append @ a @ xs @ xs2)))),
% 70.62/11.29 file('/export/starexec/sandbox/tmp/tmp.YAJWcH1y2A/DTF2THF_20469.p',fact_2__092_060open_062llength_Axs_A_092_060le_062_Allength_A_Ilappend_Axs_Axs_H_J_092_060close_062)).
% 70.62/11.29 thf(f1616,plain,(
% 70.62/11.29 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((ord_less_eq @ X0 @ X2 @ X1) != $true) | (X1 = X2) | ((ord_less_eq @ X0 @ X1 @ X2) != $true) | ((order @ X0 @ type2 @ X0) != $true)) )),
% 70.62/11.29 inference(cnf_transformation,[status(thm)],[f1107])).
% 70.62/11.29 thf(f1107,plain,(
% 70.62/11.29 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (((ord_less_eq @ X0 @ X1 @ X2) != $true) | (X1 = X2) | ((ord_less_eq @ X0 @ X2 @ X1) != $true)) | ((order @ X0 @ type2 @ X0) != $true))),
% 70.62/11.29 inference(flattening,[status(thm)],[f1106])).
% 70.62/11.29 thf(f1106,plain,(
% 70.62/11.29 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (((X1 = X2) | ((ord_less_eq @ X0 @ X2 @ X1) != $true)) | ((ord_less_eq @ X0 @ X1 @ X2) != $true)) | ((order @ X0 @ type2 @ X0) != $true))),
% 70.62/11.29 inference(ennf_transformation,[status(thm)],[f542])).
% 70.62/11.29 thf(f542,plain,(
% 70.62/11.29 ! [X0 : $tType] : (((order @ X0 @ type2 @ X0) = $true) => ! [X1 : X0,X2 : X0] : (((ord_less_eq @ X0 @ X1 @ X2) = $true) => (((ord_less_eq @ X0 @ X2 @ X1) = $true) => (X1 = X2))))),
% 70.62/11.29 inference(fool_elimination,[status(thm)],[f541])).
% 70.62/11.29 thf(f541,plain,(
% 70.62/11.29 ! [X0 : $tType] : ((order @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : X0] : ((ord_less_eq @ X0 @ X1 @ X2) => ((ord_less_eq @ X0 @ X2 @ X1) => (X1 = X2))))),
% 70.62/11.29 inference(rectify,[status(thm)],[f194])).
% 70.62/11.29 thf(f194,axiom,(
% 70.62/11.29 ! [X0 : $tType] : ((order @ X0 @ type2 @ X0) => ! [X6 : X0,X22 : X0] : ((ord_less_eq @ X0 @ X6 @ X22) => ((ord_less_eq @ X0 @ X22 @ X6) => (X6 = X22))))),
% 70.62/11.29 file('/export/starexec/sandbox/tmp/tmp.YAJWcH1y2A/DTF2THF_20469.p',fact_193_antisym)).
% 70.62/11.29 thf(f2575,plain,(
% 70.62/11.29 ~spl93_2 | ~spl93_1 | spl93_5),
% 70.62/11.29 inference(avatar_split_clause,[status(thm)],[f2553,f1821,f1804,f1808])).
% 70.62/11.29 thf(f2553,plain,(
% 70.62/11.29 ((ord_less @ extended_enat @ (extended_enat2 @ n) @ (coindu1018505716length @ b @ ys)) != $true) | (~spl93_1 | spl93_5)),
% 70.62/11.29 inference(superposition,[status(thm)],[f1823,f2148])).
% 70.62/11.29 thf(f2300,plain,(
% 70.62/11.29 spl93_21),
% 70.62/11.29 inference(avatar_contradiction_clause,[status(thm)],[f2299])).
% 70.62/11.29 thf(f2299,plain,(
% 70.62/11.29 $false | spl93_21),
% 70.62/11.29 inference(trivial_inequality_removal,[status(thm)],[f2287])).
% 70.62/11.29 thf(f2287,plain,(
% 70.62/11.29 ($true != $true) | spl93_21),
% 70.62/11.29 inference(superposition,[status(thm)],[f2114,f1689])).
% 70.62/11.29 thf(f1689,plain,(
% 70.62/11.29 ((ord_less @ extended_enat @ (extended_enat2 @ n) @ (coindu1018505716length @ a @ xs)) = $true)),
% 70.62/11.29 inference(cnf_transformation,[status(thm)],[f466])).
% 70.62/11.29 thf(f466,plain,(
% 70.62/11.29 ((ord_less @ extended_enat @ (extended_enat2 @ n) @ (coindu1018505716length @ a @ xs)) = $true)),
% 70.62/11.29 inference(fool_elimination,[status(thm)],[f465])).
% 70.62/11.29 thf(f465,plain,(
% 70.62/11.29 (ord_less @ extended_enat @ (extended_enat2 @ n) @ (coindu1018505716length @ a @ xs))),
% 70.62/11.29 inference(rectify,[status(thm)],[f4])).
% 70.62/11.29 thf(f4,axiom,(
% 70.62/11.29 (ord_less @ extended_enat @ (extended_enat2 @ n) @ (coindu1018505716length @ a @ xs))),
% 70.62/11.29 file('/export/starexec/sandbox/tmp/tmp.YAJWcH1y2A/DTF2THF_20469.p',fact_3_n)).
% 70.62/11.29 thf(f2114,plain,(
% 70.62/11.29 ((ord_less @ extended_enat @ (extended_enat2 @ n) @ (coindu1018505716length @ a @ xs)) != $true) | spl93_21),
% 70.62/11.29 inference(avatar_component_clause,[status(thm)],[f2112])).
% 70.62/11.29 thf(f1981,plain,(
% 70.62/11.29 spl93_1),
% 70.62/11.29 inference(avatar_contradiction_clause,[status(thm)],[f1980])).
% 70.62/11.29 thf(f1980,plain,(
% 70.62/11.29 $false | spl93_1),
% 70.62/11.29 inference(trivial_inequality_removal,[status(thm)],[f1979])).
% 70.62/11.29 thf(f1979,plain,(
% 70.62/11.29 ($true != $true) | spl93_1),
% 70.62/11.29 inference(superposition,[status(thm)],[f1806,f1444])).
% 70.62/11.29 thf(f1444,plain,(
% 70.62/11.29 ((coindu987187967t_all2 @ a @ b @ p @ (coindu268472904append @ a @ xs @ xs2) @ ys) = $true)),
% 70.62/11.29 inference(cnf_transformation,[status(thm)],[f716])).
% 70.62/11.29 thf(f716,plain,(
% 70.62/11.29 ((coindu987187967t_all2 @ a @ b @ p @ (coindu268472904append @ a @ xs @ xs2) @ ys) = $true)),
% 70.62/11.29 inference(fool_elimination,[status(thm)],[f715])).
% 70.62/11.29 thf(f715,plain,(
% 70.62/11.29 (coindu987187967t_all2 @ a @ b @ p @ (coindu268472904append @ a @ xs @ xs2) @ ys)),
% 70.62/11.29 inference(rectify,[status(thm)],[f1])).
% 70.62/11.29 thf(f1,axiom,(
% 70.62/11.29 (coindu987187967t_all2 @ a @ b @ p @ (coindu268472904append @ a @ xs @ xs2) @ ys)),
% 70.62/11.29 file('/export/starexec/sandbox/tmp/tmp.YAJWcH1y2A/DTF2THF_20469.p',fact_0_assms)).
% 70.62/11.29 thf(f1806,plain,(
% 70.62/11.29 ((coindu987187967t_all2 @ a @ b @ p @ (coindu268472904append @ a @ xs @ xs2) @ ys) != $true) | spl93_1),
% 70.62/11.29 inference(avatar_component_clause,[status(thm)],[f1804])).
% 70.62/11.29 thf(f1824,plain,(
% 70.62/11.29 ~spl93_5 | ~spl93_1),
% 70.62/11.29 inference(avatar_split_clause,[status(thm)],[f1801,f1804,f1821])).
% 70.62/11.29 thf(f1801,plain,(
% 70.62/11.29 ((coindu987187967t_all2 @ a @ b @ p @ (coindu268472904append @ a @ xs @ xs2) @ ys) != $true) | ((ord_less @ extended_enat @ (extended_enat2 @ n) @ (coindu1018505716length @ a @ (coindu268472904append @ a @ xs @ xs2))) != $true)),
% 70.62/11.29 inference(trivial_inequality_removal,[status(thm)],[f1800])).
% 70.62/11.29 thf(f1800,plain,(
% 70.62/11.29 ((ord_less @ extended_enat @ (extended_enat2 @ n) @ (coindu1018505716length @ a @ (coindu268472904append @ a @ xs @ xs2))) != $true) | ((coindu987187967t_all2 @ a @ b @ p @ (coindu268472904append @ a @ xs @ xs2) @ ys) != $true) | ($true != $true)),
% 70.62/11.29 inference(superposition,[status(thm)],[f1663,f1574])).
% 70.62/11.29 thf(f1574,plain,(
% 70.62/11.29 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : coindu1593790203_llist @ X0,X4 : coindu1593790203_llist @ X1,X5 : nat] : (((X2 @ (coindu749330388e_lnth @ X0 @ X3 @ X5) @ (coindu749330388e_lnth @ X1 @ X4 @ X5)) = $true) | ($true != (ord_less @ extended_enat @ (extended_enat2 @ X5) @ (coindu1018505716length @ X0 @ X3))) | ((coindu987187967t_all2 @ X0 @ X1 @ X2 @ X3 @ X4) != $true)) )),
% 70.62/11.29 inference(cnf_transformation,[status(thm)],[f1134])).
% 70.62/11.29 thf(f1134,plain,(
% 70.62/11.29 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : coindu1593790203_llist @ X0,X4 : coindu1593790203_llist @ X1,X5 : nat] : (($true != (ord_less @ extended_enat @ (extended_enat2 @ X5) @ (coindu1018505716length @ X0 @ X3))) | ((coindu987187967t_all2 @ X0 @ X1 @ X2 @ X3 @ X4) != $true) | ((X2 @ (coindu749330388e_lnth @ X0 @ X3 @ X5) @ (coindu749330388e_lnth @ X1 @ X4 @ X5)) = $true))),
% 70.62/11.29 inference(flattening,[status(thm)],[f1133])).
% 70.62/11.29 thf(f1133,plain,(
% 70.62/11.29 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : coindu1593790203_llist @ X0,X4 : coindu1593790203_llist @ X1,X5 : nat] : ((((X2 @ (coindu749330388e_lnth @ X0 @ X3 @ X5) @ (coindu749330388e_lnth @ X1 @ X4 @ X5)) = $true) | ($true != (ord_less @ extended_enat @ (extended_enat2 @ X5) @ (coindu1018505716length @ X0 @ X3)))) | ((coindu987187967t_all2 @ X0 @ X1 @ X2 @ X3 @ X4) != $true))),
% 70.62/11.29 inference(ennf_transformation,[status(thm)],[f552])).
% 70.62/11.29 thf(f552,plain,(
% 70.62/11.29 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : coindu1593790203_llist @ X0,X4 : coindu1593790203_llist @ X1,X5 : nat] : (((coindu987187967t_all2 @ X0 @ X1 @ X2 @ X3 @ X4) = $true) => (($true = (ord_less @ extended_enat @ (extended_enat2 @ X5) @ (coindu1018505716length @ X0 @ X3))) => ((X2 @ (coindu749330388e_lnth @ X0 @ X3 @ X5) @ (coindu749330388e_lnth @ X1 @ X4 @ X5)) = $true)))),
% 70.62/11.29 inference(fool_elimination,[status(thm)],[f551])).
% 70.62/11.29 thf(f551,plain,(
% 70.62/11.29 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : coindu1593790203_llist @ X0,X4 : coindu1593790203_llist @ X1,X5 : nat] : ((coindu987187967t_all2 @ X0 @ X1 @ X2 @ X3 @ X4) => ((ord_less @ extended_enat @ (extended_enat2 @ X5) @ (coindu1018505716length @ X0 @ X3)) => (X2 @ (coindu749330388e_lnth @ X0 @ X3 @ X5) @ (coindu749330388e_lnth @ X1 @ X4 @ X5))))),
% 70.62/11.29 inference(rectify,[status(thm)],[f43])).
% 70.62/11.29 thf(f43,axiom,(
% 70.62/11.29 ! [X0 : $tType,X1 : $tType,X13 : X0 > X1 > $o,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X1,X35 : nat] : ((coindu987187967t_all2 @ X0 @ X1 @ X13 @ X2 @ X3) => ((ord_less @ extended_enat @ (extended_enat2 @ X35) @ (coindu1018505716length @ X0 @ X2)) => (X13 @ (coindu749330388e_lnth @ X0 @ X2 @ X35) @ (coindu749330388e_lnth @ X1 @ X3 @ X35))))),
% 70.62/11.29 file('/export/starexec/sandbox/tmp/tmp.YAJWcH1y2A/DTF2THF_20469.p',fact_42_llist__all2__lnthD)).
% 70.62/11.29 thf(f1663,plain,(
% 70.62/11.29 ((p @ (coindu749330388e_lnth @ a @ (coindu268472904append @ a @ xs @ xs2) @ n) @ (coindu749330388e_lnth @ b @ ys @ n)) != $true)),
% 70.62/11.29 inference(cnf_transformation,[status(thm)],[f822])).
% 70.62/11.29 thf(f822,plain,(
% 70.62/11.29 ((p @ (coindu749330388e_lnth @ a @ (coindu268472904append @ a @ xs @ xs2) @ n) @ (coindu749330388e_lnth @ b @ ys @ n)) != $true)),
% 70.62/11.29 inference(flattening,[status(thm)],[f300])).
% 70.62/11.29 thf(f300,plain,(
% 70.62/11.29 ~((p @ (coindu749330388e_lnth @ a @ (coindu268472904append @ a @ xs @ xs2) @ n) @ (coindu749330388e_lnth @ b @ ys @ n)) = $true)),
% 70.62/11.29 inference(fool_elimination,[status(thm)],[f299])).
% 70.62/11.29 thf(f299,plain,(
% 70.62/11.29 ~(p @ (coindu749330388e_lnth @ a @ (coindu268472904append @ a @ xs @ xs2) @ n) @ (coindu749330388e_lnth @ b @ ys @ n))),
% 70.62/11.29 inference(rectify,[status(thm)],[f287])).
% 70.62/11.29 thf(f287,negated_conjecture,(
% 70.62/11.29 ~(p @ (coindu749330388e_lnth @ a @ (coindu268472904append @ a @ xs @ xs2) @ n) @ (coindu749330388e_lnth @ b @ ys @ n))),
% 70.62/11.29 inference(negated_conjecture,[status(cth)],[f286])).
% 70.62/11.29 thf(f286,conjecture,(
% 70.62/11.29 (p @ (coindu749330388e_lnth @ a @ (coindu268472904append @ a @ xs @ xs2) @ n) @ (coindu749330388e_lnth @ b @ ys @ n))),
% 70.62/11.29 file('/export/starexec/sandbox/tmp/tmp.YAJWcH1y2A/DTF2THF_20469.p',conj_0)).
% 70.62/11.29 % SZS output end Proof for DTF2THF_20469
% 70.62/11.29 % (21074)------------------------------
% 70.62/11.29 % (21074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.62/11.29 % (21074)Termination reason: Refutation
% 70.62/11.29
% 70.62/11.29 % (21074)Memory used [KB]: 12537
% 70.62/11.29 % (21074)Time elapsed: 1.378 s
% 70.62/11.29 % (21074)Instructions burned: 3048 (million)
% 70.62/11.29 % (21074)------------------------------
% 70.62/11.29 % (21074)------------------------------
% 70.62/11.29 % (20681)Success in time 10.089 s
%------------------------------------------------------------------------------