%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT120^1 : 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 : n015.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 08:44:50 AM UTC 2026
% Result : Theorem 161.19s 24.52s
% Output : Refutation 161.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT120^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n015.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 06:07:46 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.34/0.49 ---- Original DTF file ---
% 0.34/0.49 thf(spec,logic,$$dhol).
% 0.34/0.49 %------------------------------------------------------------------------------
% 0.34/0.49 % File : DAT120^1 : TPTP v9.2.1. Released v7.0.0.
% 0.34/0.49 % Domain : Data Structures
% 0.34/0.49 % Problem : Coinductive list 1483
% 0.34/0.49 % Version : [Bla16] axioms : Especial.
% 0.34/0.49 % English :
% 0.34/0.49
% 0.34/0.49 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.34/0.49 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.34/0.49 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.34/0.49 % Source : [Bla16]
% 0.34/0.49 % Names : coinductive_list__1483.p [Bla16]
% 0.34/0.49
% 0.34/0.49 % Status : Theorem
% 0.34/0.49 % Rating : 0.67 v9.1.0, 0.33 v8.1.0, 0.25 v7.5.0, 1.00 v7.3.0, 0.67 v7.2.0, 0.75 v7.1.0
% 0.34/0.49 % Syntax : Number of formulae : 347 ( 128 unt; 56 typ; 0 def)
% 0.34/0.49 % Number of atoms : 794 ( 284 equ; 0 cnn)
% 0.34/0.49 % Maximal formula atoms : 13 ( 2 avg)
% 0.34/0.49 % Number of connectives : 3537 ( 102 ~; 39 |; 49 &;3017 @)
% 0.34/0.49 % ( 0 <=>; 330 =>; 0 <=; 0 <~>)
% 0.34/0.49 % Maximal formula depth : 24 ( 7 avg)
% 0.34/0.49 % Number of types : 4 ( 3 usr)
% 0.34/0.49 % Number of type conns : 207 ( 207 >; 0 *; 0 +; 0 <<)
% 0.34/0.49 % Number of symbols : 56 ( 53 usr; 5 con; 0-6 aty)
% 0.34/0.49 % Number of variables : 991 ( 51 ^; 850 !; 40 ?; 991 :)
% 0.34/0.49 % ( 50 !>; 0 ?*; 0 @-; 0 @+)
% 0.34/0.49 % SPC : TH1_THM_EQU_NAR
% 0.34/0.49
% 0.34/0.49 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.34/0.49 % 2016-07-13 14:50:34.804
% 0.34/0.49 %------------------------------------------------------------------------------
% 0.34/0.49 %----Could-be-implicit typings (7)
% 0.34/0.49 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 0.34/0.49 coindu1593790203_llist: $tType > $tType ).
% 0.34/0.49
% 0.34/0.49 thf(ty_t_Product__Type_Oprod,type,
% 0.34/0.49 product_prod: $tType > $tType > $tType ).
% 0.34/0.49
% 0.34/0.49 thf(ty_t_Extended__Nat_Oenat,type,
% 0.34/0.49 extended_enat: $tType ).
% 0.34/0.49
% 0.34/0.49 thf(ty_t_Set_Oset,type,
% 0.34/0.49 set: $tType > $tType ).
% 0.34/0.49
% 0.34/0.49 thf(ty_t_Nat_Onat,type,
% 0.34/0.49 nat: $tType ).
% 0.34/0.49
% 0.34/0.49 thf(ty_t_itself,type,
% 0.34/0.49 itself: $tType > $tType ).
% 0.34/0.49
% 0.34/0.49 thf(ty_tf_a,type,
% 0.34/0.49 a: $tType ).
% 0.34/0.49
% 0.34/0.49 %----Explicit typings (49)
% 0.34/0.49 thf(sy_cl_HOL_Otype,type,
% 0.34/0.49 type:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Ozero,type,
% 0.34/0.49 zero:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Ominus,type,
% 0.34/0.49 minus:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Orderings_Oord,type,
% 0.34/0.49 ord:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Orderings_Oorder,type,
% 0.34/0.49 order:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Ogroup__add,type,
% 0.34/0.49 group_add:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Orderings_Olinorder,type,
% 0.34/0.49 linorder:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Orderings_Opreorder,type,
% 0.34/0.49 preorder:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Ocomm__monoid__diff,type,
% 0.34/0.49 comm_monoid_diff:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Rings_Olinordered__semidom,type,
% 0.34/0.49 linordered_semidom:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.34/0.49 ordered_ab_group_add:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.34/0.49 cancel1352612707id_add:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.34/0.49 cancel146912293up_add:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Complete__Lattices_Ocomplete__lattice,type,
% 0.34/0.49 comple187826305attice:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.34/0.49 canoni770627133id_add:
% 0.34/0.49 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__llength,type,
% 0.34/0.49 coindu493225792length:
% 0.34/0.49 !>[A: $tType] : ( nat > ( coindu1593790203_llist @ A ) > extended_enat ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 0.34/0.49 coindu268472904append:
% 0.34/0.49 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite,type,
% 0.34/0.49 coindu1213758845finite:
% 0.34/0.49 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollength,type,
% 0.34/0.49 coindu1018505716length:
% 0.34/0.49 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > extended_enat ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollexord,type,
% 0.34/0.49 coindu300403952lexord:
% 0.34/0.49 !>[A: $tType] : ( ( A > A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 0.34/0.49 coindu1121789889_LCons:
% 0.34/0.49 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 0.34/0.49 coindu1598213697e_LNil:
% 0.34/0.49 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd,type,
% 0.34/0.49 coindu1046438764le_lhd:
% 0.34/0.49 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ollist__all2,type,
% 0.34/0.49 coindu987187967t_all2:
% 0.34/0.49 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olmap,type,
% 0.34/0.49 coindu1062782156e_lmap:
% 0.34/0.49 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ Aa ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 0.34/0.49 coindu335574135_lnull:
% 0.34/0.49 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Oltl,type,
% 0.34/0.49 coindu1047225960le_ltl:
% 0.34/0.49 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember,type,
% 0.34/0.49 coindu567634248member:
% 0.34/0.49 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix,type,
% 0.34/0.49 coindu1696667936prefix:
% 0.34/0.49 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix,type,
% 0.34/0.49 coindu574146665prefix:
% 0.34/0.49 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oltake,type,
% 0.34/0.49 coindu1802687541_ltake:
% 0.34/0.49 !>[A: $tType] : ( extended_enat > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_OltakeWhile,type,
% 0.34/0.49 coindu721411036eWhile:
% 0.34/0.49 !>[A: $tType] : ( ( A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olzip,type,
% 0.34/0.49 coindu847746867e_lzip:
% 0.34/0.49 !>[A: $tType,B: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > ( coindu1593790203_llist @ ( product_prod @ A @ B ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Extended__Nat_Oenat_Ocase__enat,type,
% 0.34/0.49 extended_case_enat:
% 0.34/0.49 !>[T: $tType] : ( ( nat > T ) > T > extended_enat > T ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Extended__Nat_Othe__enat,type,
% 0.34/0.49 extended_the_enat: extended_enat > nat ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.34/0.49 minus_minus:
% 0.34/0.49 !>[A: $tType] : ( A > A > A ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.34/0.49 zero_zero:
% 0.34/0.49 !>[A: $tType] : A ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_If,type,
% 0.34/0.49 if:
% 0.34/0.49 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.34/0.49 ord_less_eq:
% 0.34/0.49 !>[A: $tType] : ( A > A > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Orderings_Oord__class_Omin,type,
% 0.34/0.49 ord_min:
% 0.34/0.49 !>[A: $tType] : ( A > A > A ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Product__Type_OPair,type,
% 0.34/0.49 product_Pair:
% 0.34/0.49 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Pure_Otype,type,
% 0.34/0.49 type2:
% 0.34/0.49 !>[A: $tType] : ( itself @ A ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Relation_Oinv__imagep,type,
% 0.34/0.49 inv_imagep:
% 0.34/0.49 !>[B: $tType,A: $tType] : ( ( B > B > $o ) > ( A > B ) > A > A > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Relation_Otransp,type,
% 0.34/0.49 transp:
% 0.34/0.49 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_Set_OCollect,type,
% 0.34/0.49 collect:
% 0.34/0.49 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_c_member,type,
% 0.34/0.49 member:
% 0.34/0.49 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(sy_v_m,type,
% 0.34/0.49 m: extended_enat ).
% 0.34/0.49
% 0.34/0.49 thf(sy_v_n,type,
% 0.34/0.49 n: extended_enat ).
% 0.34/0.49
% 0.34/0.49 thf(sy_v_xs,type,
% 0.34/0.49 xs: coindu1593790203_llist @ a ).
% 0.34/0.49
% 0.34/0.49 %----Relevant facts (252)
% 0.34/0.49 thf(fact_0_lprefix__refl,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ Xs ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix_refl
% 0.34/0.49 thf(fact_1_llist_Oleq__refl,axiom,
% 0.34/0.49 ! [A: $tType,X: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ X @ X ) ).
% 0.34/0.49
% 0.34/0.49 % llist.leq_refl
% 0.34/0.49 thf(fact_2__092_060open_062n_A_092_060le_062_Am_A_092_060or_062_Allength_Axs_A_092_060le_062_Am_092_060close_062,axiom,
% 0.34/0.49 ( ( ord_less_eq @ extended_enat @ n @ m )
% 0.34/0.49 | ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ a @ xs ) @ m ) ) ).
% 0.34/0.49
% 0.34/0.49 % \<open>n \<le> m \<or> llength xs \<le> m\<close>
% 0.34/0.49 thf(fact_3_ltake__is__lprefix,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) @ Xs ) ).
% 0.34/0.49
% 0.34/0.49 % ltake_is_lprefix
% 0.34/0.49 thf(fact_4_lprefix__trans,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.34/0.49 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.34/0.49 => ( coindu1696667936prefix @ A @ Xs @ Zs ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix_trans
% 0.34/0.49 thf(fact_5_llist_Oleq__trans,axiom,
% 0.34/0.49 ! [A: $tType,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A,Z: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A @ X @ Y )
% 0.34/0.49 => ( ( coindu1696667936prefix @ A @ Y @ Z )
% 0.34/0.49 => ( coindu1696667936prefix @ A @ X @ Z ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.leq_trans
% 0.34/0.49 thf(fact_6_lprefix__antisym,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.34/0.49 => ( ( coindu1696667936prefix @ A @ Ys @ Xs )
% 0.34/0.49 => ( Xs = Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix_antisym
% 0.34/0.49 thf(fact_7_llist_Oleq__antisym,axiom,
% 0.34/0.49 ! [A: $tType,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A @ X @ Y )
% 0.34/0.49 => ( ( coindu1696667936prefix @ A @ Y @ X )
% 0.34/0.49 => ( X = Y ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.leq_antisym
% 0.34/0.49 thf(fact_8_lprefix__down__linear,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A @ Xs @ Zs )
% 0.34/0.49 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.34/0.49 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.34/0.49 | ( coindu1696667936prefix @ A @ Ys @ Xs ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix_down_linear
% 0.34/0.49 thf(fact_9_lstrict__prefix__def,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( coindu574146665prefix @ A )
% 0.34/0.49 = ( ^ [Xs2: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A @ Xs2 @ Ys2 )
% 0.34/0.49 & ( Xs2 != Ys2 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lstrict_prefix_def
% 0.34/0.49 thf(fact_10_ltake__eq__ltake__antimono,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,M: extended_enat] :
% 0.34/0.49 ( ( ( coindu1802687541_ltake @ A @ N @ Xs )
% 0.34/0.49 = ( coindu1802687541_ltake @ A @ N @ Ys ) )
% 0.34/0.49 => ( ( ord_less_eq @ extended_enat @ M @ N )
% 0.34/0.49 => ( ( coindu1802687541_ltake @ A @ M @ Xs )
% 0.34/0.49 = ( coindu1802687541_ltake @ A @ M @ Ys ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltake_eq_ltake_antimono
% 0.34/0.49 thf(fact_11_ltake__all,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,M: extended_enat] :
% 0.34/0.49 ( ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ M )
% 0.34/0.49 => ( ( coindu1802687541_ltake @ A @ M @ Xs )
% 0.34/0.49 = Xs ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltake_all
% 0.34/0.49 thf(fact_12_ltake__lmap,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,N: extended_enat,F: B > A,Xs: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ( coindu1802687541_ltake @ A @ N @ ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) )
% 0.34/0.49 = ( coindu1062782156e_lmap @ B @ A @ F @ ( coindu1802687541_ltake @ B @ N @ Xs ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltake_lmap
% 0.34/0.49 thf(fact_13_ltake__LNil,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat] :
% 0.34/0.49 ( ( coindu1802687541_ltake @ A @ N @ ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltake_LNil
% 0.34/0.49 thf(fact_14_ltake__ltake,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat,M: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1802687541_ltake @ A @ N @ ( coindu1802687541_ltake @ A @ M @ Xs ) )
% 0.34/0.49 = ( coindu1802687541_ltake @ A @ ( ord_min @ extended_enat @ N @ M ) @ Xs ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltake_ltake
% 0.34/0.49 thf(fact_15_lprefix__code_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix_code(1)
% 0.34/0.49 thf(fact_16_wlog__linorder__le,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [P: A > A > $o,B2: A,A2: A] :
% 0.34/0.49 ( ! [A3: A,B3: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.34/0.49 => ( P @ A3 @ B3 ) )
% 0.34/0.49 => ( ( ( P @ B2 @ A2 )
% 0.34/0.49 => ( P @ A2 @ B2 ) )
% 0.34/0.49 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % wlog_linorder_le
% 0.34/0.49 thf(fact_17_LCons__lprefix__LCons,axiom,
% 0.34/0.49 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.34/0.49 = ( ( X = Y )
% 0.34/0.49 & ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % LCons_lprefix_LCons
% 0.34/0.49 thf(fact_18_llist_Otransp__le,axiom,
% 0.34/0.49 ! [A: $tType] : ( transp @ ( coindu1593790203_llist @ A ) @ ( coindu1696667936prefix @ A ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.transp_le
% 0.34/0.49 thf(fact_19_lprefix__lappend,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix_lappend
% 0.34/0.49 thf(fact_20_lprefix__lappend__sameI,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.34/0.49 => ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Zs @ Xs ) @ ( coindu268472904append @ A @ Zs @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix_lappend_sameI
% 0.34/0.49 thf(fact_21_llist_Oinject,axiom,
% 0.34/0.49 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 0.34/0.49 = ( ( X21 = Y21 )
% 0.34/0.49 & ( X22 = Y22 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.inject
% 0.34/0.49 thf(fact_22_lappend__code_I2_J,axiom,
% 0.34/0.49 ! [A: $tType,Xa: A,X: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu268472904append @ A @ ( coindu1121789889_LCons @ A @ Xa @ X ) @ Ys )
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu268472904append @ A @ X @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lappend_code(2)
% 0.34/0.49 thf(fact_23_lappend__code_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ Ys )
% 0.34/0.49 = Ys ) ).
% 0.34/0.49
% 0.34/0.49 % lappend_code(1)
% 0.34/0.49 thf(fact_24_lappend__LNil2,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu268472904append @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 = Xs ) ).
% 0.34/0.49
% 0.34/0.49 % lappend_LNil2
% 0.34/0.49 thf(fact_25_llength__lmap,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ( coindu1018505716length @ A @ ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) )
% 0.34/0.49 = ( coindu1018505716length @ B @ Xs ) ) ).
% 0.34/0.49
% 0.34/0.49 % llength_lmap
% 0.34/0.49 thf(fact_26_llength__ltake,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1018505716length @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 0.34/0.49 = ( ord_min @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llength_ltake
% 0.34/0.49 thf(fact_27_llist_Osimps_I13_J,axiom,
% 0.34/0.49 ! [B: $tType,A: $tType,F: A > B,X21: A,X22: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1062782156e_lmap @ A @ B @ F @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.34/0.49 = ( coindu1121789889_LCons @ B @ ( F @ X21 ) @ ( coindu1062782156e_lmap @ A @ B @ F @ X22 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.simps(13)
% 0.34/0.49 thf(fact_28_llist_Osimps_I12_J,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,F: A > B] :
% 0.34/0.49 ( ( coindu1062782156e_lmap @ A @ B @ F @ ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 = ( coindu1598213697e_LNil @ B ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.simps(12)
% 0.34/0.49 thf(fact_29_llist_Odistinct_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1598213697e_LNil @ A )
% 0.34/0.49 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.distinct(1)
% 0.34/0.49 thf(fact_30_LNil__eq__lmap,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ( ( coindu1598213697e_LNil @ A )
% 0.34/0.49 = ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) )
% 0.34/0.49 = ( Xs
% 0.34/0.49 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % LNil_eq_lmap
% 0.34/0.49 thf(fact_31_lmap__eq__LNil,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ( ( coindu1062782156e_lmap @ B @ A @ F @ Xs )
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 = ( Xs
% 0.34/0.49 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lmap_eq_LNil
% 0.34/0.49 thf(fact_32_lappend__assoc,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 0.34/0.49 = ( coindu268472904append @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lappend_assoc
% 0.34/0.49 thf(fact_33_llist_Oexhaust,axiom,
% 0.34/0.49 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( Y
% 0.34/0.49 != ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 0.34/0.49 ( Y
% 0.34/0.49 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.exhaust
% 0.34/0.49 thf(fact_34_neq__LNil__conv,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( Xs
% 0.34/0.49 != ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 = ( ? [X2: A,Xs3: coindu1593790203_llist @ A] :
% 0.34/0.49 ( Xs
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X2 @ Xs3 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % neq_LNil_conv
% 0.34/0.49 thf(fact_35_lappend__LNil__LNil,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.34/0.49
% 0.34/0.49 % lappend_LNil_LNil
% 0.34/0.49 thf(fact_36_lmap__eq__LCons__conv,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ( coindu1062782156e_lmap @ B @ A @ F @ Xs )
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.34/0.49 = ( ? [X2: B,Xs3: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ( Xs
% 0.34/0.49 = ( coindu1121789889_LCons @ B @ X2 @ Xs3 ) )
% 0.34/0.49 & ( Y
% 0.34/0.49 = ( F @ X2 ) )
% 0.34/0.49 & ( Ys
% 0.34/0.49 = ( coindu1062782156e_lmap @ B @ A @ F @ Xs3 ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lmap_eq_LCons_conv
% 0.34/0.49 thf(fact_37_LNil__eq__lappend__iff,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ( coindu1598213697e_LNil @ A )
% 0.34/0.49 = ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.34/0.49 = ( ( Xs
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 & ( Ys
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % LNil_eq_lappend_iff
% 0.34/0.49 thf(fact_38_lappend__eq__LNil__iff,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 = ( ( Xs
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 & ( Ys
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lappend_eq_LNil_iff
% 0.34/0.49 thf(fact_39_lmap__lappend__distrib,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B,Ys: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ( coindu1062782156e_lmap @ B @ A @ F @ ( coindu268472904append @ B @ Xs @ Ys ) )
% 0.34/0.49 = ( coindu268472904append @ A @ ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) @ ( coindu1062782156e_lmap @ B @ A @ F @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lmap_lappend_distrib
% 0.34/0.49 thf(fact_40_lappend__snocL1__conv__LCons2,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ ( coindu1598213697e_LNil @ A ) ) ) @ Ys )
% 0.34/0.49 = ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lappend_snocL1_conv_LCons2
% 0.34/0.49 thf(fact_41_lprefix__LCons__conv,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.34/0.49 = ( ( Xs
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 | ? [Xs3: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( Xs
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ Y @ Xs3 ) )
% 0.34/0.49 & ( coindu1696667936prefix @ A @ Xs3 @ Ys ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix_LCons_conv
% 0.34/0.49 thf(fact_42_lprefix_Ocoinduct,axiom,
% 0.34/0.49 ! [A: $tType,X3: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( X3 @ X @ Xa )
% 0.34/0.49 => ( ! [X4: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( X3 @ X4 @ Xa2 )
% 0.34/0.49 => ( ? [Xs4: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( X4
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 & ( Xa2 = Xs4 ) )
% 0.34/0.49 | ? [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,Xb: A] :
% 0.34/0.49 ( ( X4
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ Xb @ Xs4 ) )
% 0.34/0.49 & ( Xa2
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ Xb @ Ys3 ) )
% 0.34/0.49 & ( ( X3 @ Xs4 @ Ys3 )
% 0.34/0.49 | ( coindu1696667936prefix @ A @ Xs4 @ Ys3 ) ) ) ) )
% 0.34/0.49 => ( coindu1696667936prefix @ A @ X @ Xa ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix.coinduct
% 0.34/0.49 thf(fact_43_lprefix_Osimps,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A )
% 0.34/0.49 = ( ^ [A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ? [Xs2: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( A1
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 & ( A22 = Xs2 ) )
% 0.34/0.49 | ? [Xs2: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A,X2: A] :
% 0.34/0.49 ( ( A1
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.34/0.49 & ( A22
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X2 @ Ys2 ) )
% 0.34/0.49 & ( coindu1696667936prefix @ A @ Xs2 @ Ys2 ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix.simps
% 0.34/0.49 thf(fact_44_lprefix_Ocases,axiom,
% 0.34/0.49 ! [A: $tType,A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A @ A12 @ A23 )
% 0.34/0.49 => ( ( ( A12
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 => ! [Xs5: coindu1593790203_llist @ A] : ( A23 != Xs5 ) )
% 0.34/0.49 => ~ ! [Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,X4: A] :
% 0.34/0.49 ( ( A12
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X4 @ Xs5 ) )
% 0.34/0.49 => ( ( A23
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X4 @ Ys4 ) )
% 0.34/0.49 => ~ ( coindu1696667936prefix @ A @ Xs5 @ Ys4 ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix.cases
% 0.34/0.49 thf(fact_45_mem__Collect__eq,axiom,
% 0.34/0.49 ! [A: $tType,A2: A,P: A > $o] :
% 0.34/0.49 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.34/0.49 = ( P @ A2 ) ) ).
% 0.34/0.49
% 0.34/0.49 % mem_Collect_eq
% 0.34/0.49 thf(fact_46_Collect__mem__eq,axiom,
% 0.34/0.49 ! [A: $tType,A4: set @ A] :
% 0.34/0.49 ( ( collect @ A
% 0.34/0.49 @ ^ [X2: A] : ( member @ A @ X2 @ A4 ) )
% 0.34/0.49 = A4 ) ).
% 0.34/0.49
% 0.34/0.49 % Collect_mem_eq
% 0.34/0.49 thf(fact_47_Collect__cong,axiom,
% 0.34/0.49 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.34/0.49 ( ! [X4: A] :
% 0.34/0.49 ( ( P @ X4 )
% 0.34/0.49 = ( Q @ X4 ) )
% 0.34/0.49 => ( ( collect @ A @ P )
% 0.34/0.49 = ( collect @ A @ Q ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % Collect_cong
% 0.34/0.49 thf(fact_48_ext,axiom,
% 0.34/0.49 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.34/0.49 ( ! [X4: A] :
% 0.34/0.49 ( ( F @ X4 )
% 0.34/0.49 = ( G @ X4 ) )
% 0.34/0.49 => ( F = G ) ) ).
% 0.34/0.49
% 0.34/0.49 % ext
% 0.34/0.49 thf(fact_49_lprefix__code_I2_J,axiom,
% 0.34/0.49 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ~ ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix_code(2)
% 0.34/0.49 thf(fact_50_ltake__lappend1,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ord_less_eq @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) )
% 0.34/0.49 => ( ( coindu1802687541_ltake @ A @ N @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.34/0.49 = ( coindu1802687541_ltake @ A @ N @ Xs ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltake_lappend1
% 0.34/0.49 thf(fact_51_LCons__lprefix__conv,axiom,
% 0.34/0.49 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ Ys )
% 0.34/0.49 = ( ? [Ys5: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( Ys
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X @ Ys5 ) )
% 0.34/0.49 & ( coindu1696667936prefix @ A @ Xs @ Ys5 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % LCons_lprefix_conv
% 0.34/0.49 thf(fact_52_Le__LCons,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.34/0.49 => ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % Le_LCons
% 0.34/0.49 thf(fact_53_LNil__lprefix,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 0.34/0.49
% 0.34/0.49 % LNil_lprefix
% 0.34/0.49 thf(fact_54_min_Obounded__iff,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A,C: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ A2 @ ( ord_min @ A @ B2 @ C ) )
% 0.34/0.49 = ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.34/0.49 & ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.bounded_iff
% 0.34/0.49 thf(fact_55_min_Oidem,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A] :
% 0.34/0.49 ( ( ord_min @ A @ A2 @ A2 )
% 0.34/0.49 = A2 ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.idem
% 0.34/0.49 thf(fact_56_min_Oleft__idem,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A] :
% 0.34/0.49 ( ( ord_min @ A @ A2 @ ( ord_min @ A @ A2 @ B2 ) )
% 0.34/0.49 = ( ord_min @ A @ A2 @ B2 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.left_idem
% 0.34/0.49 thf(fact_57_min_Oright__idem,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A] :
% 0.34/0.49 ( ( ord_min @ A @ ( ord_min @ A @ A2 @ B2 ) @ B2 )
% 0.34/0.49 = ( ord_min @ A @ A2 @ B2 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.right_idem
% 0.34/0.49 thf(fact_58_order__refl,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( preorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.34/0.49
% 0.34/0.49 % order_refl
% 0.34/0.49 thf(fact_59_lfp_Otransp__le,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.34/0.49 => ( transp @ A @ ( ord_less_eq @ A ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lfp.transp_le
% 0.34/0.49 thf(fact_60_preorder__class_Otransp__le,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( preorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ( transp @ A @ ( ord_less_eq @ A ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % preorder_class.transp_le
% 0.34/0.49 thf(fact_61_min__absorb1,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [X: A,Y: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ X @ Y )
% 0.34/0.49 => ( ( ord_min @ A @ X @ Y )
% 0.34/0.49 = X ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min_absorb1
% 0.34/0.49 thf(fact_62_min__absorb2,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [Y: A,X: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ Y @ X )
% 0.34/0.49 => ( ( ord_min @ A @ X @ Y )
% 0.34/0.49 = Y ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min_absorb2
% 0.34/0.49 thf(fact_63_min__def,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.34/0.49 => ( ( ord_min @ A )
% 0.34/0.49 = ( ^ [A5: A,B4: A] : ( if @ A @ ( ord_less_eq @ A @ A5 @ B4 ) @ A5 @ B4 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min_def
% 0.34/0.49 thf(fact_64_dual__order_Oantisym,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [B2: A,A2: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.34/0.49 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.34/0.49 => ( A2 = B2 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % dual_order.antisym
% 0.34/0.49 thf(fact_65_lfp_Oleq__antisym,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [X: A,Y: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ X @ Y )
% 0.34/0.49 => ( ( ord_less_eq @ A @ Y @ X )
% 0.34/0.49 => ( X = Y ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lfp.leq_antisym
% 0.34/0.49 thf(fact_66_gfp_Oleq__antisym,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [Y: A,X: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ Y @ X )
% 0.34/0.49 => ( ( ord_less_eq @ A @ X @ Y )
% 0.34/0.49 => ( X = Y ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % gfp.leq_antisym
% 0.34/0.49 thf(fact_67_dual__order_Otrans,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [B2: A,A2: A,C: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.34/0.49 => ( ( ord_less_eq @ A @ C @ B2 )
% 0.34/0.49 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % dual_order.trans
% 0.34/0.49 thf(fact_68_linorder__wlog,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.34/0.49 ( ! [A3: A,B3: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.34/0.49 => ( P @ A3 @ B3 ) )
% 0.34/0.49 => ( ! [A3: A,B3: A] :
% 0.34/0.49 ( ( P @ B3 @ A3 )
% 0.34/0.49 => ( P @ A3 @ B3 ) )
% 0.34/0.49 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % linorder_wlog
% 0.34/0.49 thf(fact_69_dual__order_Orefl,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.34/0.49
% 0.34/0.49 % dual_order.refl
% 0.34/0.49 thf(fact_70_lfp_Oleq__trans,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [X: A,Y: A,Z: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ X @ Y )
% 0.34/0.49 => ( ( ord_less_eq @ A @ Y @ Z )
% 0.34/0.49 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lfp.leq_trans
% 0.34/0.49 thf(fact_71_gfp_Oleq__trans,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [Y: A,X: A,Z: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ Y @ X )
% 0.34/0.49 => ( ( ord_less_eq @ A @ Z @ Y )
% 0.34/0.49 => ( ord_less_eq @ A @ Z @ X ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % gfp.leq_trans
% 0.34/0.49 thf(fact_72_order__trans,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( preorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [X: A,Y: A,Z: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ X @ Y )
% 0.34/0.49 => ( ( ord_less_eq @ A @ Y @ Z )
% 0.34/0.49 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % order_trans
% 0.34/0.49 thf(fact_73_lfp_Oleq__refl,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.34/0.49
% 0.34/0.49 % lfp.leq_refl
% 0.34/0.49 thf(fact_74_order__class_Oorder_Oantisym,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.34/0.49 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.34/0.49 => ( A2 = B2 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % order_class.order.antisym
% 0.34/0.49 thf(fact_75_ord__le__eq__trans,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A,C: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.34/0.49 => ( ( B2 = C )
% 0.34/0.49 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ord_le_eq_trans
% 0.34/0.49 thf(fact_76_ord__eq__le__trans,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A,C: A] :
% 0.34/0.49 ( ( A2 = B2 )
% 0.34/0.49 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.34/0.49 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ord_eq_le_trans
% 0.34/0.49 thf(fact_77_antisym__conv,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [Y: A,X: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ Y @ X )
% 0.34/0.49 => ( ( ord_less_eq @ A @ X @ Y )
% 0.34/0.49 = ( X = Y ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % antisym_conv
% 0.34/0.49 thf(fact_78_le__cases3,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [X: A,Y: A,Z: A] :
% 0.34/0.49 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.34/0.49 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 0.34/0.49 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.34/0.49 => ~ ( ord_less_eq @ A @ X @ Z ) )
% 0.34/0.49 => ( ( ( ord_less_eq @ A @ X @ Z )
% 0.34/0.49 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 0.34/0.49 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 0.34/0.49 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.34/0.49 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 0.34/0.49 => ~ ( ord_less_eq @ A @ Z @ X ) )
% 0.34/0.49 => ~ ( ( ord_less_eq @ A @ Z @ X )
% 0.34/0.49 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % le_cases3
% 0.34/0.49 thf(fact_79_order_Otrans,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A,C: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.34/0.49 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.34/0.49 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % order.trans
% 0.34/0.49 thf(fact_80_le__cases,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [X: A,Y: A] :
% 0.34/0.49 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.34/0.49 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % le_cases
% 0.34/0.49 thf(fact_81_eq__refl,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( preorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [X: A,Y: A] :
% 0.34/0.49 ( ( X = Y )
% 0.34/0.49 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % eq_refl
% 0.34/0.49 thf(fact_82_linear,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [X: A,Y: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ X @ Y )
% 0.34/0.49 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % linear
% 0.34/0.49 thf(fact_83_antisym,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [X: A,Y: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ X @ Y )
% 0.34/0.49 => ( ( ord_less_eq @ A @ Y @ X )
% 0.34/0.49 => ( X = Y ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % antisym
% 0.34/0.49 thf(fact_84_eq__iff,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( order @ A @ ( type2 @ A ) )
% 0.34/0.49 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 0.34/0.49 = ( ^ [X2: A,Y3: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.34/0.49 & ( ord_less_eq @ A @ Y3 @ X2 ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % eq_iff
% 0.34/0.49 thf(fact_85_ord__le__eq__subst,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType] :
% 0.34/0.49 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.34/0.49 & ( ord @ A @ ( type2 @ A ) ) )
% 0.34/0.49 => ! [A2: A,B2: A,F: A > B,C: B] :
% 0.34/0.49 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.34/0.49 => ( ( ( F @ B2 )
% 0.34/0.49 = C )
% 0.34/0.49 => ( ! [X4: A,Y4: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ X4 @ Y4 )
% 0.34/0.49 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.34/0.49 => ( ord_less_eq @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ord_le_eq_subst
% 0.34/0.49 thf(fact_86_ord__eq__le__subst,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType] :
% 0.34/0.49 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.34/0.49 & ( ord @ A @ ( type2 @ A ) ) )
% 0.34/0.49 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.34/0.49 ( ( A2
% 0.34/0.49 = ( F @ B2 ) )
% 0.34/0.49 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.34/0.49 => ( ! [X4: B,Y4: B] :
% 0.34/0.49 ( ( ord_less_eq @ B @ X4 @ Y4 )
% 0.34/0.49 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.34/0.49 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ord_eq_le_subst
% 0.34/0.49 thf(fact_87_order__subst2,axiom,
% 0.34/0.49 ! [A: $tType,C2: $tType] :
% 0.34/0.49 ( ( ( order @ C2 @ ( type2 @ C2 ) )
% 0.34/0.49 & ( order @ A @ ( type2 @ A ) ) )
% 0.34/0.49 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 0.34/0.49 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.34/0.49 => ( ( ord_less_eq @ C2 @ ( F @ B2 ) @ C )
% 0.34/0.49 => ( ! [X4: A,Y4: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ X4 @ Y4 )
% 0.34/0.49 => ( ord_less_eq @ C2 @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.34/0.49 => ( ord_less_eq @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % order_subst2
% 0.34/0.49 thf(fact_88_order__subst1,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType] :
% 0.34/0.49 ( ( ( order @ B @ ( type2 @ B ) )
% 0.34/0.49 & ( order @ A @ ( type2 @ A ) ) )
% 0.34/0.49 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.34/0.49 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.34/0.49 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.34/0.49 => ( ! [X4: B,Y4: B] :
% 0.34/0.49 ( ( ord_less_eq @ B @ X4 @ Y4 )
% 0.34/0.49 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 0.34/0.49 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % order_subst1
% 0.34/0.49 thf(fact_89_le__fun__def,axiom,
% 0.34/0.49 ! [B: $tType,A: $tType] :
% 0.34/0.49 ( ( ord @ B @ ( type2 @ B ) )
% 0.34/0.49 => ( ( ord_less_eq @ ( A > B ) )
% 0.34/0.49 = ( ^ [F2: A > B,G2: A > B] :
% 0.34/0.49 ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % le_fun_def
% 0.34/0.49 thf(fact_90_le__funI,axiom,
% 0.34/0.49 ! [B: $tType,A: $tType] :
% 0.34/0.49 ( ( ord @ B @ ( type2 @ B ) )
% 0.34/0.49 => ! [F: A > B,G: A > B] :
% 0.34/0.49 ( ! [X4: A] : ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.34/0.49 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % le_funI
% 0.34/0.49 thf(fact_91_le__funE,axiom,
% 0.34/0.49 ! [B: $tType,A: $tType] :
% 0.34/0.49 ( ( ord @ B @ ( type2 @ B ) )
% 0.34/0.49 => ! [F: A > B,G: A > B,X: A] :
% 0.34/0.49 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.34/0.49 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % le_funE
% 0.34/0.49 thf(fact_92_le__funD,axiom,
% 0.34/0.49 ! [B: $tType,A: $tType] :
% 0.34/0.49 ( ( ord @ B @ ( type2 @ B ) )
% 0.34/0.49 => ! [F: A > B,G: A > B,X: A] :
% 0.34/0.49 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.34/0.49 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % le_funD
% 0.34/0.49 thf(fact_93_min_Oleft__commute,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [B2: A,A2: A,C: A] :
% 0.34/0.49 ( ( ord_min @ A @ B2 @ ( ord_min @ A @ A2 @ C ) )
% 0.34/0.49 = ( ord_min @ A @ A2 @ ( ord_min @ A @ B2 @ C ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.left_commute
% 0.34/0.49 thf(fact_94_min_Ocommute,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ( ( ord_min @ A )
% 0.34/0.49 = ( ^ [A5: A,B4: A] : ( ord_min @ A @ B4 @ A5 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.commute
% 0.34/0.49 thf(fact_95_min_Oassoc,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A,C: A] :
% 0.34/0.49 ( ( ord_min @ A @ ( ord_min @ A @ A2 @ B2 ) @ C )
% 0.34/0.49 = ( ord_min @ A @ A2 @ ( ord_min @ A @ B2 @ C ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.assoc
% 0.34/0.49 thf(fact_96_min__le__iff__disj,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [X: A,Y: A,Z: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ ( ord_min @ A @ X @ Y ) @ Z )
% 0.34/0.49 = ( ( ord_less_eq @ A @ X @ Z )
% 0.34/0.49 | ( ord_less_eq @ A @ Y @ Z ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min_le_iff_disj
% 0.34/0.49 thf(fact_97_min_OcoboundedI2,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [B2: A,C: A,A2: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ B2 @ C )
% 0.34/0.49 => ( ord_less_eq @ A @ ( ord_min @ A @ A2 @ B2 ) @ C ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.coboundedI2
% 0.34/0.49 thf(fact_98_min_OcoboundedI1,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,C: A,B2: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ A2 @ C )
% 0.34/0.49 => ( ord_less_eq @ A @ ( ord_min @ A @ A2 @ B2 ) @ C ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.coboundedI1
% 0.34/0.49 thf(fact_99_min_Oabsorb__iff2,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ( ( ord_less_eq @ A )
% 0.34/0.49 = ( ^ [B4: A,A5: A] :
% 0.34/0.49 ( ( ord_min @ A @ A5 @ B4 )
% 0.34/0.49 = B4 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.absorb_iff2
% 0.34/0.49 thf(fact_100_min_Oabsorb__iff1,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ( ( ord_less_eq @ A )
% 0.34/0.49 = ( ^ [A5: A,B4: A] :
% 0.34/0.49 ( ( ord_min @ A @ A5 @ B4 )
% 0.34/0.49 = A5 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.absorb_iff1
% 0.34/0.49 thf(fact_101_min_Ocobounded2,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ ( ord_min @ A @ A2 @ B2 ) @ B2 ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.cobounded2
% 0.34/0.49 thf(fact_102_min_Ocobounded1,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ ( ord_min @ A @ A2 @ B2 ) @ A2 ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.cobounded1
% 0.34/0.49 thf(fact_103_min_Oorder__iff,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ( ( ord_less_eq @ A )
% 0.34/0.49 = ( ^ [A5: A,B4: A] :
% 0.34/0.49 ( A5
% 0.34/0.49 = ( ord_min @ A @ A5 @ B4 ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.order_iff
% 0.34/0.49 thf(fact_104_min_OboundedI,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A,C: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.34/0.49 => ( ( ord_less_eq @ A @ A2 @ C )
% 0.34/0.49 => ( ord_less_eq @ A @ A2 @ ( ord_min @ A @ B2 @ C ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.boundedI
% 0.34/0.49 thf(fact_105_min_OboundedE,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A,C: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ A2 @ ( ord_min @ A @ B2 @ C ) )
% 0.34/0.49 => ~ ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.34/0.49 => ~ ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.boundedE
% 0.34/0.49 thf(fact_106_min_Oabsorb2,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [B2: A,A2: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.34/0.49 => ( ( ord_min @ A @ A2 @ B2 )
% 0.34/0.49 = B2 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.absorb2
% 0.34/0.49 thf(fact_107_min_Oabsorb1,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.34/0.49 => ( ( ord_min @ A @ A2 @ B2 )
% 0.34/0.49 = A2 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.absorb1
% 0.34/0.49 thf(fact_108_min_OorderI,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A] :
% 0.34/0.49 ( ( A2
% 0.34/0.49 = ( ord_min @ A @ A2 @ B2 ) )
% 0.34/0.49 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.orderI
% 0.34/0.49 thf(fact_109_min_OorderE,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.34/0.49 => ( A2
% 0.34/0.49 = ( ord_min @ A @ A2 @ B2 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.orderE
% 0.34/0.49 thf(fact_110_min_Omono,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,C: A,B2: A,D: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ A2 @ C )
% 0.34/0.49 => ( ( ord_less_eq @ A @ B2 @ D )
% 0.34/0.49 => ( ord_less_eq @ A @ ( ord_min @ A @ A2 @ B2 ) @ ( ord_min @ A @ C @ D ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min.mono
% 0.34/0.49 thf(fact_111_ltake__lappend2,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,N: extended_enat,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ N )
% 0.34/0.49 => ( ( coindu1802687541_ltake @ A @ N @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.34/0.49 = ( coindu268472904append @ A @ Xs @ ( coindu1802687541_ltake @ A @ ( minus_minus @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) ) @ Ys ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltake_lappend2
% 0.34/0.49 thf(fact_112_DEADID_Orel__transp,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( transp @ A
% 0.34/0.49 @ ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) ) ).
% 0.34/0.49
% 0.34/0.49 % DEADID.rel_transp
% 0.34/0.49 thf(fact_113_transp__def,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( transp @ A )
% 0.34/0.49 = ( ^ [R: A > A > $o] :
% 0.34/0.49 ! [X2: A,Y3: A,Z3: A] :
% 0.34/0.49 ( ( R @ X2 @ Y3 )
% 0.34/0.49 => ( ( R @ Y3 @ Z3 )
% 0.34/0.49 => ( R @ X2 @ Z3 ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % transp_def
% 0.34/0.49 thf(fact_114_transpI,axiom,
% 0.34/0.49 ! [A: $tType,R2: A > A > $o] :
% 0.34/0.49 ( ! [X4: A,Y4: A,Z4: A] :
% 0.34/0.49 ( ( R2 @ X4 @ Y4 )
% 0.34/0.49 => ( ( R2 @ Y4 @ Z4 )
% 0.34/0.49 => ( R2 @ X4 @ Z4 ) ) )
% 0.34/0.49 => ( transp @ A @ R2 ) ) ).
% 0.34/0.49
% 0.34/0.49 % transpI
% 0.34/0.49 thf(fact_115_transpE,axiom,
% 0.34/0.49 ! [A: $tType,R2: A > A > $o,X: A,Y: A,Z: A] :
% 0.34/0.49 ( ( transp @ A @ R2 )
% 0.34/0.49 => ( ( R2 @ X @ Y )
% 0.34/0.49 => ( ( R2 @ Y @ Z )
% 0.34/0.49 => ( R2 @ X @ Z ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % transpE
% 0.34/0.49 thf(fact_116_transpD,axiom,
% 0.34/0.49 ! [A: $tType,R2: A > A > $o,X: A,Y: A,Z: A] :
% 0.34/0.49 ( ( transp @ A @ R2 )
% 0.34/0.49 => ( ( R2 @ X @ Y )
% 0.34/0.49 => ( ( R2 @ Y @ Z )
% 0.34/0.49 => ( R2 @ X @ Z ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % transpD
% 0.34/0.49 thf(fact_117_llexord_Ocoinduct,axiom,
% 0.34/0.49 ! [A: $tType,X3: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A,R2: A > A > $o] :
% 0.34/0.49 ( ( X3 @ X @ Xa )
% 0.34/0.49 => ( ! [X4: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( X3 @ X4 @ Xa2 )
% 0.34/0.49 => ( ? [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,Xb: A] :
% 0.34/0.49 ( ( X4
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ Xb @ Xs4 ) )
% 0.34/0.49 & ( Xa2
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ Xb @ Ys3 ) )
% 0.34/0.49 & ( ( X3 @ Xs4 @ Ys3 )
% 0.34/0.49 | ( coindu300403952lexord @ A @ R2 @ Xs4 @ Ys3 ) ) )
% 0.34/0.49 | ? [Xb: A,Y5: A,Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( X4
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ Xb @ Xs4 ) )
% 0.34/0.49 & ( Xa2
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ Y5 @ Ys3 ) )
% 0.34/0.49 & ( R2 @ Xb @ Y5 ) )
% 0.34/0.49 | ? [Ys3: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( X4
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 & ( Xa2 = Ys3 ) ) ) )
% 0.34/0.49 => ( coindu300403952lexord @ A @ R2 @ X @ Xa ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llexord.coinduct
% 0.34/0.49 thf(fact_118_minus__apply,axiom,
% 0.34/0.49 ! [B: $tType,A: $tType] :
% 0.34/0.49 ( ( minus @ B @ ( type2 @ B ) )
% 0.34/0.49 => ( ( minus_minus @ ( A > B ) )
% 0.34/0.49 = ( ^ [A6: A > B,B5: A > B,X2: A] : ( minus_minus @ B @ ( A6 @ X2 ) @ ( B5 @ X2 ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % minus_apply
% 0.34/0.49 thf(fact_119_fun__diff__def,axiom,
% 0.34/0.49 ! [B: $tType,A: $tType] :
% 0.34/0.49 ( ( minus @ B @ ( type2 @ B ) )
% 0.34/0.49 => ( ( minus_minus @ ( A > B ) )
% 0.34/0.49 = ( ^ [A6: A > B,B5: A > B,X2: A] : ( minus_minus @ B @ ( A6 @ X2 ) @ ( B5 @ X2 ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % fun_diff_def
% 0.34/0.49 thf(fact_120_llexord__LCons__eq,axiom,
% 0.34/0.49 ! [A: $tType,R2: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 0.34/0.49 ( ( coindu300403952lexord @ A @ R2 @ Xs @ Ys )
% 0.34/0.49 => ( coindu300403952lexord @ A @ R2 @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llexord_LCons_eq
% 0.34/0.49 thf(fact_121_llexord__LCons__less,axiom,
% 0.34/0.49 ! [A: $tType,R2: A > A > $o,X: A,Y: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( R2 @ X @ Y )
% 0.34/0.49 => ( coindu300403952lexord @ A @ R2 @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llexord_LCons_less
% 0.34/0.49 thf(fact_122_llexord__LNil,axiom,
% 0.34/0.49 ! [A: $tType,R2: A > A > $o,Ys: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R2 @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 0.34/0.49
% 0.34/0.49 % llexord_LNil
% 0.34/0.49 thf(fact_123_ltake__lappend,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1802687541_ltake @ A @ N @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.34/0.49 = ( coindu268472904append @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) @ ( coindu1802687541_ltake @ A @ ( minus_minus @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) ) @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltake_lappend
% 0.34/0.49 thf(fact_124_llexord_Ocases,axiom,
% 0.34/0.49 ! [A: $tType,R2: A > A > $o,A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu300403952lexord @ A @ R2 @ A12 @ A23 )
% 0.34/0.49 => ( ! [Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,X4: A] :
% 0.34/0.49 ( ( A12
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X4 @ Xs5 ) )
% 0.34/0.49 => ( ( A23
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X4 @ Ys4 ) )
% 0.34/0.49 => ~ ( coindu300403952lexord @ A @ R2 @ Xs5 @ Ys4 ) ) )
% 0.34/0.49 => ( ! [X4: A] :
% 0.34/0.49 ( ? [Xs5: coindu1593790203_llist @ A] :
% 0.34/0.49 ( A12
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X4 @ Xs5 ) )
% 0.34/0.49 => ! [Y4: A] :
% 0.34/0.49 ( ? [Ys4: coindu1593790203_llist @ A] :
% 0.34/0.49 ( A23
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ Y4 @ Ys4 ) )
% 0.34/0.49 => ~ ( R2 @ X4 @ Y4 ) ) )
% 0.34/0.49 => ~ ( ( A12
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 => ! [Ys4: coindu1593790203_llist @ A] : ( A23 != Ys4 ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llexord.cases
% 0.34/0.49 thf(fact_125_llexord_Osimps,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( coindu300403952lexord @ A )
% 0.34/0.49 = ( ^ [R: A > A > $o,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ? [Xs2: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A,X2: A] :
% 0.34/0.49 ( ( A1
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.34/0.49 & ( A22
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X2 @ Ys2 ) )
% 0.34/0.49 & ( coindu300403952lexord @ A @ R @ Xs2 @ Ys2 ) )
% 0.34/0.49 | ? [X2: A,Y3: A,Xs2: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( A1
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.34/0.49 & ( A22
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ Y3 @ Ys2 ) )
% 0.34/0.49 & ( R @ X2 @ Y3 ) )
% 0.34/0.49 | ? [Ys2: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( A1
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 & ( A22 = Ys2 ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llexord.simps
% 0.34/0.49 thf(fact_126_enat__diff__cancel__left,axiom,
% 0.34/0.49 ! [M: extended_enat,X: extended_enat,Y: extended_enat] :
% 0.34/0.49 ( ( ord_less_eq @ extended_enat @ M @ X )
% 0.34/0.49 => ( ( ord_less_eq @ extended_enat @ M @ Y )
% 0.34/0.49 => ( ( ( minus_minus @ extended_enat @ X @ M )
% 0.34/0.49 = ( minus_minus @ extended_enat @ Y @ M ) )
% 0.34/0.49 = ( X = Y ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % enat_diff_cancel_left
% 0.34/0.49 thf(fact_127_enat__minus__mono1,axiom,
% 0.34/0.49 ! [X: extended_enat,Y: extended_enat,M: extended_enat] :
% 0.34/0.49 ( ( ord_less_eq @ extended_enat @ X @ Y )
% 0.34/0.49 => ( ord_less_eq @ extended_enat @ ( minus_minus @ extended_enat @ X @ M ) @ ( minus_minus @ extended_enat @ Y @ M ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % enat_minus_mono1
% 0.34/0.49 thf(fact_128_min__diff__distrib__left,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [X: A,Y: A,Z: A] :
% 0.34/0.49 ( ( minus_minus @ A @ ( ord_min @ A @ X @ Y ) @ Z )
% 0.34/0.49 = ( ord_min @ A @ ( minus_minus @ A @ X @ Z ) @ ( minus_minus @ A @ Y @ Z ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % min_diff_distrib_left
% 0.34/0.49 thf(fact_129_diff__eq__diff__less__eq,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A,C: A,D: A] :
% 0.34/0.49 ( ( ( minus_minus @ A @ A2 @ B2 )
% 0.34/0.49 = ( minus_minus @ A @ C @ D ) )
% 0.34/0.49 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.34/0.49 = ( ord_less_eq @ A @ C @ D ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % diff_eq_diff_less_eq
% 0.34/0.49 thf(fact_130_diff__right__commute,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,C: A,B2: A] :
% 0.34/0.49 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C ) @ B2 )
% 0.34/0.49 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B2 ) @ C ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % diff_right_commute
% 0.34/0.49 thf(fact_131_diff__eq__diff__eq,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( group_add @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A,C: A,D: A] :
% 0.34/0.49 ( ( ( minus_minus @ A @ A2 @ B2 )
% 0.34/0.49 = ( minus_minus @ A @ C @ D ) )
% 0.34/0.49 => ( ( A2 = B2 )
% 0.34/0.49 = ( C = D ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % diff_eq_diff_eq
% 0.34/0.49 thf(fact_132_diff__mono,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A,D: A,C: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.34/0.49 => ( ( ord_less_eq @ A @ D @ C )
% 0.34/0.49 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B2 @ D ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % diff_mono
% 0.34/0.49 thf(fact_133_diff__left__mono,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [B2: A,A2: A,C: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.34/0.49 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A2 ) @ ( minus_minus @ A @ C @ B2 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % diff_left_mono
% 0.34/0.49 thf(fact_134_diff__right__mono,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A,C: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.34/0.49 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B2 @ C ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % diff_right_mono
% 0.34/0.49 thf(fact_135_lmember__code_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,X: A] :
% 0.34/0.49 ~ ( coindu567634248member @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.34/0.49
% 0.34/0.49 % lmember_code(1)
% 0.34/0.49 thf(fact_136_lmember__code_I2_J,axiom,
% 0.34/0.49 ! [A: $tType,X: A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu567634248member @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.34/0.49 = ( ( X = Y )
% 0.34/0.49 | ( coindu567634248member @ A @ X @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lmember_code(2)
% 0.34/0.49 thf(fact_137_lfinite__rev__induct,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.34/0.49 ( ( coindu1213758845finite @ A @ Xs )
% 0.34/0.49 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 => ( ! [X4: A,Xs5: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1213758845finite @ A @ Xs5 )
% 0.34/0.49 => ( ( P @ Xs5 )
% 0.34/0.49 => ( P @ ( coindu268472904append @ A @ Xs5 @ ( coindu1121789889_LCons @ A @ X4 @ ( coindu1598213697e_LNil @ A ) ) ) ) ) )
% 0.34/0.49 => ( P @ Xs ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lfinite_rev_induct
% 0.34/0.49 thf(fact_138_llist_Orel__transp,axiom,
% 0.34/0.49 ! [A: $tType,R3: A > A > $o] :
% 0.34/0.49 ( ( transp @ A @ R3 )
% 0.34/0.49 => ( transp @ ( coindu1593790203_llist @ A ) @ ( coindu987187967t_all2 @ A @ A @ R3 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.rel_transp
% 0.34/0.49 thf(fact_139_lfinite__LCons,axiom,
% 0.34/0.49 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.34/0.49 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.34/0.49
% 0.34/0.49 % lfinite_LCons
% 0.34/0.49 thf(fact_140_lfinite__code_I2_J,axiom,
% 0.34/0.49 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ( coindu1213758845finite @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) )
% 0.34/0.49 = ( coindu1213758845finite @ B @ Xs ) ) ).
% 0.34/0.49
% 0.34/0.49 % lfinite_code(2)
% 0.34/0.49 thf(fact_141_llist_Orel__inject_I2_J,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,R3: A > B > $o,X21: A,X22: coindu1593790203_llist @ A,Y21: B,Y22: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ( coindu987187967t_all2 @ A @ B @ R3 @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) )
% 0.34/0.49 = ( ( R3 @ X21 @ Y21 )
% 0.34/0.49 & ( coindu987187967t_all2 @ A @ B @ R3 @ X22 @ Y22 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.rel_inject(2)
% 0.34/0.49 thf(fact_142_lfinite__code_I1_J,axiom,
% 0.34/0.49 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.34/0.49
% 0.34/0.49 % lfinite_code(1)
% 0.34/0.49 thf(fact_143_lfinite__lappend,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1213758845finite @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.34/0.49 = ( ( coindu1213758845finite @ A @ Xs )
% 0.34/0.49 & ( coindu1213758845finite @ A @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lfinite_lappend
% 0.34/0.49 thf(fact_144_lfinite__lmap,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ( coindu1213758845finite @ A @ ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) )
% 0.34/0.49 = ( coindu1213758845finite @ B @ Xs ) ) ).
% 0.34/0.49
% 0.34/0.49 % lfinite_lmap
% 0.34/0.49 thf(fact_145_lprefix__lappend__same,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ ( coindu268472904append @ A @ Xs @ Zs ) )
% 0.34/0.49 = ( ( coindu1213758845finite @ A @ Xs )
% 0.34/0.49 => ( coindu1696667936prefix @ A @ Ys @ Zs ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix_lappend_same
% 0.34/0.49 thf(fact_146_llist_Orel__eq,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( coindu987187967t_all2 @ A @ A
% 0.34/0.49 @ ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 0.34/0.49 = ( ^ [Y2: coindu1593790203_llist @ A,Z2: coindu1593790203_llist @ A] : ( Y2 = Z2 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.rel_eq
% 0.34/0.49 thf(fact_147_llist_Orel__refl,axiom,
% 0.34/0.49 ! [B: $tType,Ra: B > B > $o,X: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ! [X4: B] : ( Ra @ X4 @ X4 )
% 0.34/0.49 => ( coindu987187967t_all2 @ B @ B @ Ra @ X @ X ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.rel_refl
% 0.34/0.49 thf(fact_148_lappend__inf,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.34/0.49 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.34/0.49 = Xs ) ) ).
% 0.34/0.49
% 0.34/0.49 % lappend_inf
% 0.34/0.49 thf(fact_149_lfinite__LNil,axiom,
% 0.34/0.49 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.34/0.49
% 0.34/0.49 % lfinite_LNil
% 0.34/0.49 thf(fact_150_lfinite__LConsI,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 0.34/0.49 ( ( coindu1213758845finite @ A @ Xs )
% 0.34/0.49 => ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lfinite_LConsI
% 0.34/0.49 thf(fact_151_llist_Octr__transfer_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,R3: A > B > $o] : ( coindu987187967t_all2 @ A @ B @ R3 @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.ctr_transfer(1)
% 0.34/0.49 thf(fact_152_llist_Orel__intros_I2_J,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,R3: A > B > $o,X21: A,Y21: B,X22: coindu1593790203_llist @ A,Y22: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ( R3 @ X21 @ Y21 )
% 0.34/0.49 => ( ( coindu987187967t_all2 @ A @ B @ R3 @ X22 @ Y22 )
% 0.34/0.49 => ( coindu987187967t_all2 @ A @ B @ R3 @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.rel_intros(2)
% 0.34/0.49 thf(fact_153_not__lfinite__lprefix__conv__eq,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.34/0.49 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.34/0.49 = ( Xs = Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % not_lfinite_lprefix_conv_eq
% 0.34/0.49 thf(fact_154_llist_Orel__mono,axiom,
% 0.34/0.49 ! [B: $tType,A: $tType,R3: A > B > $o,Ra: A > B > $o] :
% 0.34/0.49 ( ( ord_less_eq @ ( A > B > $o ) @ R3 @ Ra )
% 0.34/0.49 => ( ord_less_eq @ ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o ) @ ( coindu987187967t_all2 @ A @ B @ R3 ) @ ( coindu987187967t_all2 @ A @ B @ Ra ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.rel_mono
% 0.34/0.49 thf(fact_155_llist_Orel__distinct_I2_J,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,R3: A > B > $o,Y21: A,Y22: coindu1593790203_llist @ A] :
% 0.34/0.49 ~ ( coindu987187967t_all2 @ A @ B @ R3 @ ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.rel_distinct(2)
% 0.34/0.49 thf(fact_156_llist_Orel__distinct_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,R3: A > B > $o,Y21: B,Y22: coindu1593790203_llist @ B] :
% 0.34/0.49 ~ ( coindu987187967t_all2 @ A @ B @ R3 @ ( coindu1598213697e_LNil @ A ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.rel_distinct(1)
% 0.34/0.49 thf(fact_157_llist_Orel__cases,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,R3: A > B > $o,A2: coindu1593790203_llist @ A,B2: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ( coindu987187967t_all2 @ A @ B @ R3 @ A2 @ B2 )
% 0.34/0.49 => ( ( ( A2
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 => ( B2
% 0.34/0.49 != ( coindu1598213697e_LNil @ B ) ) )
% 0.34/0.49 => ~ ! [X1: A,X23: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( A2
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X1 @ X23 ) )
% 0.34/0.49 => ! [Y1: B,Y23: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ( B2
% 0.34/0.49 = ( coindu1121789889_LCons @ B @ Y1 @ Y23 ) )
% 0.34/0.49 => ( ( R3 @ X1 @ Y1 )
% 0.34/0.49 => ~ ( coindu987187967t_all2 @ A @ B @ R3 @ X23 @ Y23 ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.rel_cases
% 0.34/0.49 thf(fact_158_lfinite_Ocases,axiom,
% 0.34/0.49 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1213758845finite @ A @ A2 )
% 0.34/0.49 => ( ( A2
% 0.34/0.49 != ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 => ~ ! [Xs5: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ? [X4: A] :
% 0.34/0.49 ( A2
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X4 @ Xs5 ) )
% 0.34/0.49 => ~ ( coindu1213758845finite @ A @ Xs5 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lfinite.cases
% 0.34/0.49 thf(fact_159_lfinite_Osimps,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( coindu1213758845finite @ A )
% 0.34/0.49 = ( ^ [A5: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( A5
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 | ? [Xs2: coindu1593790203_llist @ A,X2: A] :
% 0.34/0.49 ( ( A5
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.34/0.49 & ( coindu1213758845finite @ A @ Xs2 ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lfinite.simps
% 0.34/0.49 thf(fact_160_lfinite_Oinducts,axiom,
% 0.34/0.49 ! [A: $tType,X: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.34/0.49 ( ( coindu1213758845finite @ A @ X )
% 0.34/0.49 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 => ( ! [Xs5: coindu1593790203_llist @ A,X4: A] :
% 0.34/0.49 ( ( coindu1213758845finite @ A @ Xs5 )
% 0.34/0.49 => ( ( P @ Xs5 )
% 0.34/0.49 => ( P @ ( coindu1121789889_LCons @ A @ X4 @ Xs5 ) ) ) )
% 0.34/0.49 => ( P @ X ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lfinite.inducts
% 0.34/0.49 thf(fact_161_llength__LNil,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( coindu1018505716length @ A @ ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 = ( zero_zero @ extended_enat ) ) ).
% 0.34/0.49
% 0.34/0.49 % llength_LNil
% 0.34/0.49 thf(fact_162_in__inv__imagep,axiom,
% 0.34/0.49 ! [B: $tType,A: $tType] :
% 0.34/0.49 ( ( inv_imagep @ A @ B )
% 0.34/0.49 = ( ^ [R: A > A > $o,F2: B > A,X2: B,Y3: B] : ( R @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % in_inv_imagep
% 0.34/0.49 thf(fact_163_LNil__eq__ltake__iff,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ( coindu1598213697e_LNil @ A )
% 0.34/0.49 = ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 0.34/0.49 = ( ( Xs
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 | ( N
% 0.34/0.49 = ( zero_zero @ extended_enat ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % LNil_eq_ltake_iff
% 0.34/0.49 thf(fact_164_ltake__0,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1802687541_ltake @ A @ ( zero_zero @ extended_enat ) @ Xs )
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltake_0
% 0.34/0.49 thf(fact_165_le__zero__eq,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [N: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 0.34/0.49 = ( N
% 0.34/0.49 = ( zero_zero @ A ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % le_zero_eq
% 0.34/0.49 thf(fact_166_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A] :
% 0.34/0.49 ( ( minus_minus @ A @ A2 @ A2 )
% 0.34/0.49 = ( zero_zero @ A ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % cancel_comm_monoid_add_class.diff_cancel
% 0.34/0.49 thf(fact_167_diff__zero,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A] :
% 0.34/0.49 ( ( minus_minus @ A @ A2 @ ( zero_zero @ A ) )
% 0.34/0.49 = A2 ) ) ).
% 0.34/0.49
% 0.34/0.49 % diff_zero
% 0.34/0.49 thf(fact_168_zero__diff,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( comm_monoid_diff @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A] :
% 0.34/0.49 ( ( minus_minus @ A @ ( zero_zero @ A ) @ A2 )
% 0.34/0.49 = ( zero_zero @ A ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % zero_diff
% 0.34/0.49 thf(fact_169_diff__0__right,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( group_add @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A] :
% 0.34/0.49 ( ( minus_minus @ A @ A2 @ ( zero_zero @ A ) )
% 0.34/0.49 = A2 ) ) ).
% 0.34/0.49
% 0.34/0.49 % diff_0_right
% 0.34/0.49 thf(fact_170_diff__self,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( group_add @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A] :
% 0.34/0.49 ( ( minus_minus @ A @ A2 @ A2 )
% 0.34/0.49 = ( zero_zero @ A ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % diff_self
% 0.34/0.49 thf(fact_171_diff__ge__0__iff__ge,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [A2: A,B2: A] :
% 0.34/0.49 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A2 @ B2 ) )
% 0.34/0.49 = ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % diff_ge_0_iff_ge
% 0.34/0.49 thf(fact_172_enat__min__eq__0__iff,axiom,
% 0.34/0.49 ! [A2: extended_enat,B2: extended_enat] :
% 0.34/0.49 ( ( ( ord_min @ extended_enat @ A2 @ B2 )
% 0.34/0.49 = ( zero_zero @ extended_enat ) )
% 0.34/0.49 = ( ( A2
% 0.34/0.49 = ( zero_zero @ extended_enat ) )
% 0.34/0.49 | ( B2
% 0.34/0.49 = ( zero_zero @ extended_enat ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % enat_min_eq_0_iff
% 0.34/0.49 thf(fact_173_zero__reorient,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( zero @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [X: A] :
% 0.34/0.49 ( ( ( zero_zero @ A )
% 0.34/0.49 = X )
% 0.34/0.49 = ( X
% 0.34/0.49 = ( zero_zero @ A ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % zero_reorient
% 0.34/0.49 thf(fact_174_eq__iff__diff__eq__0,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( group_add @ A @ ( type2 @ A ) )
% 0.34/0.49 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 0.34/0.49 = ( ^ [A5: A,B4: A] :
% 0.34/0.49 ( ( minus_minus @ A @ A5 @ B4 )
% 0.34/0.49 = ( zero_zero @ A ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % eq_iff_diff_eq_0
% 0.34/0.49 thf(fact_175_zero__le,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.34/0.49 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 0.34/0.49
% 0.34/0.49 % zero_le
% 0.34/0.49 thf(fact_176_le__iff__diff__le__0,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.34/0.49 => ( ( ord_less_eq @ A )
% 0.34/0.49 = ( ^ [A5: A,B4: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ A5 @ B4 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % le_iff_diff_le_0
% 0.34/0.49 thf(fact_177_ltake__eq__LNil__iff,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ( coindu1802687541_ltake @ A @ N @ Xs )
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 = ( ( Xs
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 | ( N
% 0.34/0.49 = ( zero_zero @ extended_enat ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltake_eq_LNil_iff
% 0.34/0.49 thf(fact_178_min__enat__simps_I3_J,axiom,
% 0.34/0.49 ! [Q2: extended_enat] :
% 0.34/0.49 ( ( ord_min @ extended_enat @ ( zero_zero @ extended_enat ) @ Q2 )
% 0.34/0.49 = ( zero_zero @ extended_enat ) ) ).
% 0.34/0.49
% 0.34/0.49 % min_enat_simps(3)
% 0.34/0.49 thf(fact_179_min__enat__simps_I2_J,axiom,
% 0.34/0.49 ! [Q2: extended_enat] :
% 0.34/0.49 ( ( ord_min @ extended_enat @ Q2 @ ( zero_zero @ extended_enat ) )
% 0.34/0.49 = ( zero_zero @ extended_enat ) ) ).
% 0.34/0.49
% 0.34/0.49 % min_enat_simps(2)
% 0.34/0.49 thf(fact_180_idiff__0__right,axiom,
% 0.34/0.49 ! [N: extended_enat] :
% 0.34/0.49 ( ( minus_minus @ extended_enat @ N @ ( zero_zero @ extended_enat ) )
% 0.34/0.49 = N ) ).
% 0.34/0.49
% 0.34/0.49 % idiff_0_right
% 0.34/0.49 thf(fact_181_idiff__0,axiom,
% 0.34/0.49 ! [N: extended_enat] :
% 0.34/0.49 ( ( minus_minus @ extended_enat @ ( zero_zero @ extended_enat ) @ N )
% 0.34/0.49 = ( zero_zero @ extended_enat ) ) ).
% 0.34/0.49
% 0.34/0.49 % idiff_0
% 0.34/0.49 thf(fact_182_i0__lb,axiom,
% 0.34/0.49 ! [N: extended_enat] : ( ord_less_eq @ extended_enat @ ( zero_zero @ extended_enat ) @ N ) ).
% 0.34/0.49
% 0.34/0.49 % i0_lb
% 0.34/0.49 thf(fact_183_ile0__eq,axiom,
% 0.34/0.49 ! [N: extended_enat] :
% 0.34/0.49 ( ( ord_less_eq @ extended_enat @ N @ ( zero_zero @ extended_enat ) )
% 0.34/0.49 = ( N
% 0.34/0.49 = ( zero_zero @ extended_enat ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ile0_eq
% 0.34/0.49 thf(fact_184_le__numeral__extra_I3_J,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.34/0.49 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % le_numeral_extra(3)
% 0.34/0.49 thf(fact_185_the__enat__0,axiom,
% 0.34/0.49 ( ( extended_the_enat @ ( zero_zero @ extended_enat ) )
% 0.34/0.49 = ( zero_zero @ nat ) ) ).
% 0.34/0.49
% 0.34/0.49 % the_enat_0
% 0.34/0.49 thf(fact_186_case__enat__0,axiom,
% 0.34/0.49 ! [A: $tType,F: nat > A,I: A] :
% 0.34/0.49 ( ( extended_case_enat @ A @ F @ I @ ( zero_zero @ extended_enat ) )
% 0.34/0.49 = ( F @ ( zero_zero @ nat ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % case_enat_0
% 0.34/0.49 thf(fact_187_llength__code,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( coindu1018505716length @ A )
% 0.34/0.49 = ( coindu493225792length @ A @ ( zero_zero @ nat ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llength_code
% 0.34/0.49 thf(fact_188_ltake_Octr_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ( N
% 0.34/0.49 = ( zero_zero @ extended_enat ) )
% 0.34/0.49 | ( coindu335574135_lnull @ A @ Xs ) )
% 0.34/0.49 => ( ( coindu1802687541_ltake @ A @ N @ Xs )
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltake.ctr(1)
% 0.34/0.49 thf(fact_189_lnull__lappend,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.34/0.49 = ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 & ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lnull_lappend
% 0.34/0.49 thf(fact_190_lappend_Odisc__iff_I2_J,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 0.34/0.49 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lappend.disc_iff(2)
% 0.34/0.49 thf(fact_191_llist_Omap__disc__iff,axiom,
% 0.34/0.49 ! [B: $tType,A: $tType,F: A > B,A2: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu335574135_lnull @ B @ ( coindu1062782156e_lmap @ A @ B @ F @ A2 ) )
% 0.34/0.49 = ( coindu335574135_lnull @ A @ A2 ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.map_disc_iff
% 0.34/0.49 thf(fact_192_lprefix__LNil,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix_LNil
% 0.34/0.49 thf(fact_193_ltake_Odisc__iff_I2_J,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) ) )
% 0.34/0.49 = ( ( N
% 0.34/0.49 != ( zero_zero @ extended_enat ) )
% 0.34/0.49 & ~ ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltake.disc_iff(2)
% 0.34/0.49 thf(fact_194_ltake_Odisc__iff_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 0.34/0.49 = ( ( N
% 0.34/0.49 = ( zero_zero @ extended_enat ) )
% 0.34/0.49 | ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltake.disc_iff(1)
% 0.34/0.49 thf(fact_195_lnull__ltake,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 0.34/0.49 = ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 | ( N
% 0.34/0.49 = ( zero_zero @ extended_enat ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lnull_ltake
% 0.34/0.49 thf(fact_196_llength__lnull,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( ( coindu1018505716length @ A @ Xs )
% 0.34/0.49 = ( zero_zero @ extended_enat ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llength_lnull
% 0.34/0.49 thf(fact_197_llength__eq__0,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ( coindu1018505716length @ A @ Xs )
% 0.34/0.49 = ( zero_zero @ extended_enat ) )
% 0.34/0.49 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 0.34/0.49
% 0.34/0.49 % llength_eq_0
% 0.34/0.49 thf(fact_198_ltake_Oexhaust,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ~ ( ( N
% 0.34/0.49 = ( zero_zero @ extended_enat ) )
% 0.34/0.49 | ( coindu335574135_lnull @ A @ Xs ) )
% 0.34/0.49 => ~ ( ( N
% 0.34/0.49 != ( zero_zero @ extended_enat ) )
% 0.34/0.49 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltake.exhaust
% 0.34/0.49 thf(fact_199_lappend_Octr_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.34/0.49 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lappend.ctr(1)
% 0.34/0.49 thf(fact_200_ltake_Odisc_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ( N
% 0.34/0.49 = ( zero_zero @ extended_enat ) )
% 0.34/0.49 | ( coindu335574135_lnull @ A @ Xs ) )
% 0.34/0.49 => ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltake.disc(1)
% 0.34/0.49 thf(fact_201_ltake_Odisc_I2_J,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( N
% 0.34/0.49 != ( zero_zero @ extended_enat ) )
% 0.34/0.49 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ~ ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltake.disc(2)
% 0.34/0.49 thf(fact_202_lzip_Oexhaust,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 | ( coindu335574135_lnull @ B @ Ys ) )
% 0.34/0.49 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lzip.exhaust
% 0.34/0.49 thf(fact_203_lappend_Oexhaust,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.34/0.49 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lappend.exhaust
% 0.34/0.49 thf(fact_204_lappend__lnull2,axiom,
% 0.34/0.49 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu335574135_lnull @ A @ Ys )
% 0.34/0.49 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.34/0.49 = Xs ) ) ).
% 0.34/0.49
% 0.34/0.49 % lappend_lnull2
% 0.34/0.49 thf(fact_205_lappend__lnull1,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.34/0.49 = Ys ) ) ).
% 0.34/0.49
% 0.34/0.49 % lappend_lnull1
% 0.34/0.49 thf(fact_206_lappend_Odisc_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.34/0.49 => ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lappend.disc(1)
% 0.34/0.49 thf(fact_207_lappend_Odisc_I2_J,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 | ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.34/0.49 => ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lappend.disc(2)
% 0.34/0.49 thf(fact_208_lnull__def,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( coindu335574135_lnull @ A )
% 0.34/0.49 = ( ^ [Llist: coindu1593790203_llist @ A] :
% 0.34/0.49 ( Llist
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lnull_def
% 0.34/0.49 thf(fact_209_llist_Ocollapse_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,Llist2: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu335574135_lnull @ A @ Llist2 )
% 0.34/0.49 => ( Llist2
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.collapse(1)
% 0.34/0.49 thf(fact_210_llist_OdiscI_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,Llist2: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( Llist2
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) )
% 0.34/0.49 => ( coindu335574135_lnull @ A @ Llist2 ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.discI(1)
% 0.34/0.49 thf(fact_211_llist_Odisc_I1_J,axiom,
% 0.34/0.49 ! [A: $tType] : ( coindu335574135_lnull @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.disc(1)
% 0.34/0.49 thf(fact_212_not__lnull__conv,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ~ ( coindu335574135_lnull @ A @ Xs ) )
% 0.34/0.49 = ( ? [X2: A,Xs3: coindu1593790203_llist @ A] :
% 0.34/0.49 ( Xs
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X2 @ Xs3 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % not_lnull_conv
% 0.34/0.49 thf(fact_213_llist_OdiscI_I2_J,axiom,
% 0.34/0.49 ! [A: $tType,Llist2: coindu1593790203_llist @ A,X21: A,X22: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( Llist2
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.34/0.49 => ~ ( coindu335574135_lnull @ A @ Llist2 ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.discI(2)
% 0.34/0.49 thf(fact_214_llist_Odisc_I2_J,axiom,
% 0.34/0.49 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.34/0.49 ~ ( coindu335574135_lnull @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.disc(2)
% 0.34/0.49 thf(fact_215_lnull__lprefix,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 0.34/0.49
% 0.34/0.49 % lnull_lprefix
% 0.34/0.49 thf(fact_216_lprefix__lnull,axiom,
% 0.34/0.49 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu335574135_lnull @ A @ Ys )
% 0.34/0.49 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.34/0.49 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix_lnull
% 0.34/0.49 thf(fact_217_lprefix__lnullD,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.34/0.49 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.34/0.49 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix_lnullD
% 0.34/0.49 thf(fact_218_lprefix__not__lnullD,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.34/0.49 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix_not_lnullD
% 0.34/0.49 thf(fact_219_lnull__imp__lfinite,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.34/0.49
% 0.34/0.49 % lnull_imp_lfinite
% 0.34/0.49 thf(fact_220_lprefixI,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X3: set @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) )] :
% 0.34/0.49 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs @ Ys ) @ X3 )
% 0.34/0.49 => ( ! [Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs5 @ Ys4 ) @ X3 )
% 0.34/0.49 => ( ( coindu335574135_lnull @ A @ Xs5 )
% 0.34/0.49 | ? [X5: A,Xs6: coindu1593790203_llist @ A,Ys6: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( Xs5
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X5 @ Xs6 ) )
% 0.34/0.49 & ( Ys4
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ X5 @ Ys6 ) )
% 0.34/0.49 & ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs6 @ Ys6 ) @ X3 )
% 0.34/0.49 | ( coindu1696667936prefix @ A @ Xs6 @ Ys6 ) ) ) ) )
% 0.34/0.49 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefixI
% 0.34/0.49 thf(fact_221_ltake_Osimps_I3_J,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( N
% 0.34/0.49 != ( zero_zero @ extended_enat ) )
% 0.34/0.49 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( ( coindu1046438764le_lhd @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 0.34/0.49 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltake.simps(3)
% 0.34/0.49 thf(fact_222_lhd__lappend,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.34/0.49 = ( coindu1046438764le_lhd @ A @ Ys ) ) )
% 0.34/0.49 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.34/0.49 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lhd_lappend
% 0.34/0.49 thf(fact_223_llist_Omap__sel_I1_J,axiom,
% 0.34/0.49 ! [B: $tType,A: $tType,A2: coindu1593790203_llist @ A,F: A > B] :
% 0.34/0.49 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 0.34/0.49 => ( ( coindu1046438764le_lhd @ B @ ( coindu1062782156e_lmap @ A @ B @ F @ A2 ) )
% 0.34/0.49 = ( F @ ( coindu1046438764le_lhd @ A @ A2 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.map_sel(1)
% 0.34/0.49 thf(fact_224_lhd__ltake,axiom,
% 0.34/0.49 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( N
% 0.34/0.49 != ( zero_zero @ extended_enat ) )
% 0.34/0.49 => ( ( coindu1046438764le_lhd @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 0.34/0.49 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lhd_ltake
% 0.34/0.49 thf(fact_225_ltakeWhile_Oexhaust,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.34/0.49 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 0.34/0.49 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltakeWhile.exhaust
% 0.34/0.49 thf(fact_226_lprefix__lhdD,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.34/0.49 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.34/0.49 = ( coindu1046438764le_lhd @ A @ Ys ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix_lhdD
% 0.34/0.49 thf(fact_227_lhd__LCons,axiom,
% 0.34/0.49 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1046438764le_lhd @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.34/0.49 = X21 ) ).
% 0.34/0.49
% 0.34/0.49 % lhd_LCons
% 0.34/0.49 thf(fact_228_subrelI,axiom,
% 0.34/0.49 ! [B: $tType,A: $tType,R2: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.34/0.49 ( ! [X4: A,Y4: B] :
% 0.34/0.49 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y4 ) @ R2 )
% 0.34/0.49 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y4 ) @ S ) )
% 0.34/0.49 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R2 @ S ) ) ).
% 0.34/0.49
% 0.34/0.49 % subrelI
% 0.34/0.49 thf(fact_229_lzip_Osimps_I3_J,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( ~ ( coindu335574135_lnull @ B @ Ys )
% 0.34/0.49 => ( ( coindu1046438764le_lhd @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) )
% 0.34/0.49 = ( product_Pair @ A @ B @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu1046438764le_lhd @ B @ Ys ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lzip.simps(3)
% 0.34/0.49 thf(fact_230_ltakeWhile_Octr_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.34/0.49 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 0.34/0.49 => ( ( coindu721411036eWhile @ A @ P @ Xs )
% 0.34/0.49 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltakeWhile.ctr(1)
% 0.34/0.49 thf(fact_231_lzip_Odisc__iff_I2_J,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ( ~ ( coindu335574135_lnull @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) ) )
% 0.34/0.49 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 & ~ ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lzip.disc_iff(2)
% 0.34/0.49 thf(fact_232_lzip_Odisc__iff_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ( coindu335574135_lnull @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) )
% 0.34/0.49 = ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 | ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lzip.disc_iff(1)
% 0.34/0.49 thf(fact_233_ltakeWhile_Odisc__iff_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.34/0.49 = ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltakeWhile.disc_iff(1)
% 0.34/0.49 thf(fact_234_ltakeWhile_Odisc__iff_I2_J,axiom,
% 0.34/0.49 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) )
% 0.34/0.49 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 & ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltakeWhile.disc_iff(2)
% 0.34/0.49 thf(fact_235_lzip_Octr_I1_J,axiom,
% 0.34/0.49 ! [B: $tType,A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 | ( coindu335574135_lnull @ B @ Ys ) )
% 0.34/0.49 => ( ( coindu847746867e_lzip @ A @ B @ Xs @ Ys )
% 0.34/0.49 = ( coindu1598213697e_LNil @ ( product_prod @ A @ B ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lzip.ctr(1)
% 0.34/0.49 thf(fact_236_lzip_Odisc_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 | ( coindu335574135_lnull @ B @ Ys ) )
% 0.34/0.49 => ( coindu335574135_lnull @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lzip.disc(1)
% 0.34/0.49 thf(fact_237_lzip_Odisc_I2_J,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( ~ ( coindu335574135_lnull @ B @ Ys )
% 0.34/0.49 => ~ ( coindu335574135_lnull @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lzip.disc(2)
% 0.34/0.49 thf(fact_238_ltakeWhile_Osimps_I3_J,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.34/0.49 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.34/0.49 => ( ( coindu1046438764le_lhd @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 0.34/0.49 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltakeWhile.simps(3)
% 0.34/0.49 thf(fact_239_ltakeWhile_Odisc_I1_J,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.34/0.49 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 0.34/0.49 => ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltakeWhile.disc(1)
% 0.34/0.49 thf(fact_240_ltakeWhile_Odisc_I2_J,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.34/0.49 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.34/0.49 => ~ ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltakeWhile.disc(2)
% 0.34/0.49 thf(fact_241_ltakeWhile_Ocode,axiom,
% 0.34/0.49 ! [A: $tType] :
% 0.34/0.49 ( ( coindu721411036eWhile @ A )
% 0.34/0.49 = ( ^ [P2: A > $o,Xs2: coindu1593790203_llist @ A] :
% 0.34/0.49 ( if @ ( coindu1593790203_llist @ A )
% 0.34/0.49 @ ( ( coindu335574135_lnull @ A @ Xs2 )
% 0.34/0.49 | ~ ( P2 @ ( coindu1046438764le_lhd @ A @ Xs2 ) ) )
% 0.34/0.49 @ ( coindu1598213697e_LNil @ A )
% 0.34/0.49 @ ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Xs2 ) @ ( coindu721411036eWhile @ A @ P2 @ ( coindu1047225960le_ltl @ A @ Xs2 ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltakeWhile.code
% 0.34/0.49 thf(fact_242_ltakeWhile_Octr_I2_J,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 0.34/0.49 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 0.34/0.49 => ( ( coindu721411036eWhile @ A @ P @ Xs )
% 0.34/0.49 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu721411036eWhile @ A @ P @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltakeWhile.ctr(2)
% 0.34/0.49 thf(fact_243_lfinite__ltl,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( coindu1213758845finite @ A @ ( coindu1047225960le_ltl @ A @ Xs ) )
% 0.34/0.49 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.34/0.49
% 0.34/0.49 % lfinite_ltl
% 0.34/0.49 thf(fact_244_ltl__lmap,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ( coindu1047225960le_ltl @ A @ ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) )
% 0.34/0.49 = ( coindu1062782156e_lmap @ B @ A @ F @ ( coindu1047225960le_ltl @ B @ Xs ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltl_lmap
% 0.34/0.49 thf(fact_245_ltl__lappend,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.34/0.49 = ( coindu1047225960le_ltl @ A @ Ys ) ) )
% 0.34/0.49 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.34/0.49 = ( coindu268472904append @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ Ys ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % ltl_lappend
% 0.34/0.49 thf(fact_246_lhd__LCons__ltl,axiom,
% 0.34/0.49 ! [A: $tType,Llist2: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ~ ( coindu335574135_lnull @ A @ Llist2 )
% 0.34/0.49 => ( ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist2 ) @ ( coindu1047225960le_ltl @ A @ Llist2 ) )
% 0.34/0.49 = Llist2 ) ) ).
% 0.34/0.49
% 0.34/0.49 % lhd_LCons_ltl
% 0.34/0.49 thf(fact_247_llist_Oexpand,axiom,
% 0.34/0.49 ! [A: $tType,Llist2: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ( coindu335574135_lnull @ A @ Llist2 )
% 0.34/0.49 = ( coindu335574135_lnull @ A @ Llist3 ) )
% 0.34/0.49 => ( ( ~ ( coindu335574135_lnull @ A @ Llist2 )
% 0.34/0.49 => ( ~ ( coindu335574135_lnull @ A @ Llist3 )
% 0.34/0.49 => ( ( ( coindu1046438764le_lhd @ A @ Llist2 )
% 0.34/0.49 = ( coindu1046438764le_lhd @ A @ Llist3 ) )
% 0.34/0.49 & ( ( coindu1047225960le_ltl @ A @ Llist2 )
% 0.34/0.49 = ( coindu1047225960le_ltl @ A @ Llist3 ) ) ) ) )
% 0.34/0.49 => ( Llist2 = Llist3 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.expand
% 0.34/0.49 thf(fact_248_llist_Ocoinduct,axiom,
% 0.34/0.49 ! [A: $tType,R3: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist2: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( R3 @ Llist2 @ Llist3 )
% 0.34/0.49 => ( ! [Llist4: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( R3 @ Llist4 @ Llist5 )
% 0.34/0.49 => ( ( ( coindu335574135_lnull @ A @ Llist4 )
% 0.34/0.49 = ( coindu335574135_lnull @ A @ Llist5 ) )
% 0.34/0.49 & ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 0.34/0.49 => ( ~ ( coindu335574135_lnull @ A @ Llist5 )
% 0.34/0.49 => ( ( ( coindu1046438764le_lhd @ A @ Llist4 )
% 0.34/0.49 = ( coindu1046438764le_lhd @ A @ Llist5 ) )
% 0.34/0.49 & ( R3 @ ( coindu1047225960le_ltl @ A @ Llist4 ) @ ( coindu1047225960le_ltl @ A @ Llist5 ) ) ) ) ) ) )
% 0.34/0.49 => ( Llist2 = Llist3 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.coinduct
% 0.34/0.49 thf(fact_249_llist_Ocoinduct__strong,axiom,
% 0.34/0.49 ! [A: $tType,R3: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist2: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( R3 @ Llist2 @ Llist3 )
% 0.34/0.49 => ( ! [Llist4: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( R3 @ Llist4 @ Llist5 )
% 0.34/0.49 => ( ( ( coindu335574135_lnull @ A @ Llist4 )
% 0.34/0.49 = ( coindu335574135_lnull @ A @ Llist5 ) )
% 0.34/0.49 & ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 0.34/0.49 => ( ~ ( coindu335574135_lnull @ A @ Llist5 )
% 0.34/0.49 => ( ( ( coindu1046438764le_lhd @ A @ Llist4 )
% 0.34/0.49 = ( coindu1046438764le_lhd @ A @ Llist5 ) )
% 0.34/0.49 & ( ( R3 @ ( coindu1047225960le_ltl @ A @ Llist4 ) @ ( coindu1047225960le_ltl @ A @ Llist5 ) )
% 0.34/0.49 | ( ( coindu1047225960le_ltl @ A @ Llist4 )
% 0.34/0.49 = ( coindu1047225960le_ltl @ A @ Llist5 ) ) ) ) ) ) ) )
% 0.34/0.49 => ( Llist2 = Llist3 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % llist.coinduct_strong
% 0.34/0.49 thf(fact_250_lzip_Osimps_I4_J,axiom,
% 0.34/0.49 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.34/0.49 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( ~ ( coindu335574135_lnull @ B @ Ys )
% 0.34/0.49 => ( ( coindu1047225960le_ltl @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) )
% 0.34/0.49 = ( coindu847746867e_lzip @ A @ B @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ B @ Ys ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 % lzip.simps(4)
% 0.34/0.49 thf(fact_251_lprefix__expand,axiom,
% 0.34/0.49 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.34/0.49 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.34/0.49 => ( ~ ( coindu335574135_lnull @ A @ Ys )
% 0.34/0.49 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 0.34/0.49 = ( coindu1046438764le_lhd @ A @ Ys ) )
% 0.34/0.49 & ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) )
% 0.34/0.49 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 0.34/0.49
% 0.34/0.49 % lprefix_expand
% 0.34/0.49
% 0.34/0.49 %----Type constructors (35)
% 0.34/0.49 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice,axiom,
% 0.34/0.49 ! [A7: $tType,A8: $tType] :
% 0.34/0.49 ( ( comple187826305attice @ A8 @ ( type2 @ A8 ) )
% 0.34/0.49 => ( comple187826305attice @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.34/0.49 ! [A7: $tType,A8: $tType] :
% 0.34/0.49 ( ( preorder @ A8 @ ( type2 @ A8 ) )
% 0.34/0.49 => ( preorder @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.34/0.49 ! [A7: $tType,A8: $tType] :
% 0.34/0.49 ( ( order @ A8 @ ( type2 @ A8 ) )
% 0.34/0.49 => ( order @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_fun___Orderings_Oord,axiom,
% 0.34/0.49 ! [A7: $tType,A8: $tType] :
% 0.34/0.49 ( ( ord @ A8 @ ( type2 @ A8 ) )
% 0.34/0.49 => ( ord @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_fun___Groups_Ominus,axiom,
% 0.34/0.49 ! [A7: $tType,A8: $tType] :
% 0.34/0.49 ( ( minus @ A8 @ ( type2 @ A8 ) )
% 0.34/0.49 => ( minus @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.34/0.49 canoni770627133id_add @ nat @ ( type2 @ nat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 0.34/0.49 cancel146912293up_add @ nat @ ( type2 @ nat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 0.34/0.49 cancel1352612707id_add @ nat @ ( type2 @ nat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 0.34/0.49 linordered_semidom @ nat @ ( type2 @ nat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff,axiom,
% 0.34/0.49 comm_monoid_diff @ nat @ ( type2 @ nat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.34/0.49 preorder @ nat @ ( type2 @ nat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.34/0.49 linorder @ nat @ ( type2 @ nat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.34/0.49 order @ nat @ ( type2 @ nat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.34/0.49 ord @ nat @ ( type2 @ nat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Nat_Onat___Groups_Ominus_4,axiom,
% 0.34/0.49 minus @ nat @ ( type2 @ nat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.34/0.49 zero @ nat @ ( type2 @ nat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_5,axiom,
% 0.34/0.49 ! [A7: $tType] : ( comple187826305attice @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Set_Oset___Orderings_Opreorder_6,axiom,
% 0.34/0.49 ! [A7: $tType] : ( preorder @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Set_Oset___Orderings_Oorder_7,axiom,
% 0.34/0.49 ! [A7: $tType] : ( order @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Set_Oset___Orderings_Oord_8,axiom,
% 0.34/0.49 ! [A7: $tType] : ( ord @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Set_Oset___Groups_Ominus_9,axiom,
% 0.34/0.49 ! [A7: $tType] : ( minus @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_10,axiom,
% 0.34/0.49 comple187826305attice @ $o @ ( type2 @ $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_HOL_Obool___Orderings_Opreorder_11,axiom,
% 0.34/0.49 preorder @ $o @ ( type2 @ $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_HOL_Obool___Orderings_Olinorder_12,axiom,
% 0.34/0.49 linorder @ $o @ ( type2 @ $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_HOL_Obool___Orderings_Oorder_13,axiom,
% 0.34/0.49 order @ $o @ ( type2 @ $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_HOL_Obool___Orderings_Oord_14,axiom,
% 0.34/0.49 ord @ $o @ ( type2 @ $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_HOL_Obool___Groups_Ominus_15,axiom,
% 0.34/0.49 minus @ $o @ ( type2 @ $o ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_16,axiom,
% 0.34/0.49 canoni770627133id_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Extended__Nat_Oenat___Complete__Lattices_Ocomplete__lattice_17,axiom,
% 0.34/0.49 comple187826305attice @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Extended__Nat_Oenat___Orderings_Opreorder_18,axiom,
% 0.34/0.49 preorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Extended__Nat_Oenat___Orderings_Olinorder_19,axiom,
% 0.34/0.49 linorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Extended__Nat_Oenat___Orderings_Oorder_20,axiom,
% 0.34/0.49 order @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Extended__Nat_Oenat___Orderings_Oord_21,axiom,
% 0.34/0.49 ord @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Extended__Nat_Oenat___Groups_Ominus_22,axiom,
% 0.34/0.49 minus @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.34/0.49
% 0.34/0.49 thf(tcon_Extended__Nat_Oenat___Groups_Ozero_23,axiom,
% 0.34/0.49 zero @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.34/0.49
% 0.34/0.49 %----Helper facts (3)
% 0.34/0.49 thf(help_If_3_1_T,axiom,
% 0.34/0.49 ! [P: $o] :
% 0.34/0.49 ( ( P = $true )
% 0.34/0.49 | ( P = $false ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(help_If_2_1_T,axiom,
% 0.34/0.49 ! [A: $tType,X: A,Y: A] :
% 0.34/0.49 ( ( if @ A @ $false @ X @ Y )
% 0.34/0.49 = Y ) ).
% 0.34/0.49
% 0.34/0.49 thf(help_If_1_1_T,axiom,
% 0.34/0.49 ! [A: $tType,X: A,Y: A] :
% 0.34/0.49 ( ( if @ A @ $true @ X @ Y )
% 0.34/0.49 = X ) ).
% 0.34/0.49
% 0.34/0.49 %----Conjectures (1)
% 0.34/0.49 thf(conj_0,conjecture,
% 0.34/0.49 coindu1696667936prefix @ a @ ( coindu1802687541_ltake @ a @ n @ xs ) @ ( coindu1802687541_ltake @ a @ m @ xs ) ).
% 0.34/0.49
% 0.34/0.49 %------------------------------------------------------------------------------
% 0.34/0.49 ------------------------
% 3.20/1.76 ---- Embedded in THF ---
% 3.20/1.76 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.20/1.76 %%% Generated on Tue Feb 24 06:07:48 EST 2026
% 3.20/1.76 %%% using '$$dhol' embedding, version 1.3.0.
% 3.20/1.76 %%% Logic specification used:
% 3.20/1.76 %%% thf(spec, logic, $$dhol).
% 3.20/1.76
% 3.20/1.76 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ZCwsuNV1cP/DTF2DTF21964.p
% 3.20/1.76 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist, type, coindu1593790203_llist: ($tType > $tType)).
% 3.20/1.76 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 3.20/1.76 thf(ty_t_Extended__Nat_Oenat, type, extended_enat: $tType).
% 3.20/1.76 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.20/1.76 thf(ty_t_Nat_Onat, type, nat: $tType).
% 3.20/1.76 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 3.20/1.76 thf(ty_tf_a, type, a: $tType).
% 3.20/1.76 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.76 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.76 thf(sy_cl_Groups_Ominus, type, minus: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.76 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.76 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.76 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.76 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.76 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.76 thf(sy_cl_Groups_Ocomm__monoid__diff, type, comm_monoid_diff: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.76 thf(sy_cl_Rings_Olinordered__semidom, type, linordered_semidom: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.76 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.76 thf(sy_cl_Groups_Ocancel__comm__monoid__add, type, cancel1352612707id_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.76 thf(sy_cl_Groups_Ocancel__ab__semigroup__add, type, cancel146912293up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.76 thf(sy_cl_Complete__Lattices_Ocomplete__lattice, type, comple187826305attice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.76 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.76 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__llength, type, coindu493225792length: (!> [A:$tType]: ((nat > ((coindu1593790203_llist @ A) > extended_enat))))).
% 3.20/1.76 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend, type, coindu268472904append: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 3.20/1.76 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite, type, coindu1213758845finite: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 3.20/1.76 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollength, type, coindu1018505716length: (!> [A:$tType]: (((coindu1593790203_llist @ A) > extended_enat)))).
% 3.20/1.76 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollexord, type, coindu300403952lexord: (!> [A:$tType]: (((A > (A > $o)) > ((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)))))).
% 3.20/1.76 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons, type, coindu1121789889_LCons: (!> [A:$tType]: ((A > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 3.20/1.76 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil, type, coindu1598213697e_LNil: (!> [A:$tType]: ((coindu1593790203_llist @ A)))).
% 3.20/1.76 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd, type, coindu1046438764le_lhd: (!> [A:$tType]: (((coindu1593790203_llist @ A) > A)))).
% 3.20/1.76 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) > $o)))))).
% 3.20/1.76 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olmap, type, coindu1062782156e_lmap: (!> [A:$tType,Aa:$tType]: (((A > Aa) > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ Aa)))))).
% 3.20/1.76 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull, type, coindu335574135_lnull: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 3.20/1.76 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Oltl, type, coindu1047225960le_ltl: (!> [A:$tType]: (((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A))))).
% 3.20/1.76 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember, type, coindu567634248member: (!> [A:$tType]: ((A > ((coindu1593790203_llist @ A) > $o))))).
% 3.20/1.76 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix, type, coindu1696667936prefix: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o))))).
% 3.20/1.76 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix, type, coindu574146665prefix: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o))))).
% 3.20/1.76 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oltake, type, coindu1802687541_ltake: (!> [A:$tType]: ((extended_enat > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 3.20/1.76 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_OltakeWhile, type, coindu721411036eWhile: (!> [A:$tType]: (((A > $o) > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 3.20/1.76 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olzip, type, coindu847746867e_lzip: (!> [A:$tType,B:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ B) > (coindu1593790203_llist @ ((product_prod @ A) @ B))))))).
% 3.20/1.76 thf(sy_c_Extended__Nat_Oenat_Ocase__enat, type, extended_case_enat: (!> [T:$tType]: (((nat > T) > (T > (extended_enat > T)))))).
% 3.20/1.76 thf(sy_c_Extended__Nat_Othe__enat, type, extended_the_enat: (extended_enat > nat)).
% 3.20/1.76 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 3.20/1.76 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 3.20/1.76 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 3.20/1.76 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 3.20/1.76 thf(sy_c_Orderings_Oord__class_Omin, type, ord_min: (!> [A:$tType]: ((A > (A > A))))).
% 3.20/1.76 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 3.20/1.76 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 3.20/1.76 thf(sy_c_Relation_Oinv__imagep, type, inv_imagep: (!> [B:$tType,A:$tType]: (((B > (B > $o)) > ((A > B) > (A > (A > $o))))))).
% 3.20/1.76 thf(sy_c_Relation_Otransp, type, transp: (!> [A:$tType]: (((A > (A > $o)) > $o)))).
% 3.20/1.76 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.20/1.76 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.20/1.76 thf(sy_v_m, type, m: extended_enat).
% 3.20/1.76 thf(sy_v_n, type, n: extended_enat).
% 3.20/1.76 thf(sy_v_xs, type, xs: (coindu1593790203_llist @ a)).
% 3.20/1.76 thf(fact_0_lprefix__refl, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ Xs) @ Xs)))).
% 3.20/1.76 thf(fact_1_llist_Oleq__refl, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ X) @ X)))).
% 3.20/1.76 thf(fact_2__092_060open_062n_A_092_060le_062_Am_A_092_060or_062_Allength_Axs_A_092_060le_062_Am_092_060close_062, axiom, ((((ord_less_eq @ extended_enat) @ n) @ m) | (((ord_less_eq @ extended_enat) @ ((coindu1018505716length @ a) @ xs)) @ m))).
% 3.20/1.76 thf(fact_3_ltake__is__lprefix, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) @ Xs)))).
% 3.20/1.76 thf(fact_4_lprefix__trans, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((((coindu1696667936prefix @ A) @ Ys) @ Zs) => (((coindu1696667936prefix @ A) @ Xs) @ Zs)))))).
% 3.20/1.76 thf(fact_5_llist_Oleq__trans, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A),Y:(coindu1593790203_llist @ A),Z:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ X) @ Y) => ((((coindu1696667936prefix @ A) @ Y) @ Z) => (((coindu1696667936prefix @ A) @ X) @ Z)))))).
% 3.20/1.76 thf(fact_6_lprefix__antisym, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((((coindu1696667936prefix @ A) @ Ys) @ Xs) => (Xs = Ys)))))).
% 3.20/1.76 thf(fact_7_llist_Oleq__antisym, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A),Y:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ X) @ Y) => ((((coindu1696667936prefix @ A) @ Y) @ X) => (X = Y)))))).
% 3.20/1.76 thf(fact_8_lprefix__down__linear, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Zs) => ((((coindu1696667936prefix @ A) @ Ys) @ Zs) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) | (((coindu1696667936prefix @ A) @ Ys) @ Xs))))))).
% 3.20/1.76 thf(fact_9_lstrict__prefix__def, axiom, (! [A:$tType]: (((coindu574146665prefix @ A) = (^ [Xs2:(coindu1593790203_llist @ A),Ys2:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs2) @ Ys2) & (Xs2 != Ys2)))))))).
% 3.20/1.76 thf(fact_10_ltake__eq__ltake__antimono, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),M:extended_enat]: ((((((coindu1802687541_ltake @ A) @ N) @ Xs) = (((coindu1802687541_ltake @ A) @ N) @ Ys)) => ((((ord_less_eq @ extended_enat) @ M) @ N) => ((((coindu1802687541_ltake @ A) @ M) @ Xs) = (((coindu1802687541_ltake @ A) @ M) @ Ys))))))).
% 3.20/1.76 thf(fact_11_ltake__all, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),M:extended_enat]: (((((ord_less_eq @ extended_enat) @ ((coindu1018505716length @ A) @ Xs)) @ M) => ((((coindu1802687541_ltake @ A) @ M) @ Xs) = Xs))))).
% 3.20/1.76 thf(fact_12_ltake__lmap, axiom, (! [A:$tType,B:$tType,N:extended_enat,F:(B > A),Xs:(coindu1593790203_llist @ B)]: (((((coindu1802687541_ltake @ A) @ N) @ ((((coindu1062782156e_lmap @ B) @ A) @ F) @ Xs)) = ((((coindu1062782156e_lmap @ B) @ A) @ F) @ (((coindu1802687541_ltake @ B) @ N) @ Xs)))))).
% 3.20/1.76 thf(fact_13_ltake__LNil, axiom, (! [A:$tType,N:extended_enat]: (((((coindu1802687541_ltake @ A) @ N) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 3.20/1.76 thf(fact_14_ltake__ltake, axiom, (! [A:$tType,N:extended_enat,M:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((((coindu1802687541_ltake @ A) @ N) @ (((coindu1802687541_ltake @ A) @ M) @ Xs)) = (((coindu1802687541_ltake @ A) @ (((ord_min @ extended_enat) @ N) @ M)) @ Xs))))).
% 3.20/1.76 thf(fact_15_lprefix__code_I1_J, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (coindu1598213697e_LNil @ A)) @ Ys)))).
% 3.20/1.76 thf(fact_16_wlog__linorder__le, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),B2:A,A2:A]: (((! [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((P @ A3) @ B3)))) => ((((P @ B2) @ A2) => ((P @ A2) @ B2)) => ((P @ A2) @ B2))))))))).
% 3.20/1.76 thf(fact_17_LCons__lprefix__LCons, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((X = Y) & (((coindu1696667936prefix @ A) @ Xs) @ Ys)))))).
% 3.20/1.76 thf(fact_18_llist_Otransp__le, axiom, (! [A:$tType]: (((transp @ (coindu1593790203_llist @ A)) @ (coindu1696667936prefix @ A))))).
% 3.20/1.76 thf(fact_19_lprefix__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ Xs) @ (((coindu268472904append @ A) @ Xs) @ Ys))))).
% 3.20/1.76 thf(fact_20_lprefix__lappend__sameI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu1696667936prefix @ A) @ (((coindu268472904append @ A) @ Zs) @ Xs)) @ (((coindu268472904append @ A) @ Zs) @ Ys)))))).
% 3.20/1.76 thf(fact_21_llist_Oinject, axiom, (! [A:$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)))))).
% 3.20/1.76 thf(fact_22_lappend__code_I2_J, axiom, (! [A:$tType,Xa:A,X:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu1121789889_LCons @ A) @ Xa) @ X)) @ Ys) = (((coindu1121789889_LCons @ A) @ Xa) @ (((coindu268472904append @ A) @ X) @ Ys)))))).
% 3.20/1.76 thf(fact_23_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (coindu1598213697e_LNil @ A)) @ Ys) = Ys)))).
% 3.20/1.76 thf(fact_24_lappend__LNil2, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = Xs)))).
% 3.20/1.76 thf(fact_25_llength__lmap, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coindu1593790203_llist @ B)]: ((((coindu1018505716length @ A) @ ((((coindu1062782156e_lmap @ B) @ A) @ F) @ Xs)) = ((coindu1018505716length @ B) @ Xs))))).
% 3.20/1.76 thf(fact_26_llength__ltake, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((coindu1018505716length @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) = (((ord_min @ extended_enat) @ N) @ ((coindu1018505716length @ A) @ Xs)))))).
% 3.20/1.76 thf(fact_27_llist_Osimps_I13_J, axiom, (! [B:$tType,A:$tType,F:(A > B),X21:A,X22:(coindu1593790203_llist @ A)]: ((((((coindu1062782156e_lmap @ A) @ B) @ F) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) = (((coindu1121789889_LCons @ B) @ (F @ X21)) @ ((((coindu1062782156e_lmap @ A) @ B) @ F) @ X22)))))).
% 3.20/1.76 thf(fact_28_llist_Osimps_I12_J, axiom, (! [A:$tType,B:$tType,F:(A > B)]: ((((((coindu1062782156e_lmap @ A) @ B) @ F) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ B))))).
% 3.20/1.76 thf(fact_29_llist_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: (((coindu1598213697e_LNil @ A) != (((coindu1121789889_LCons @ A) @ X21) @ X22))))).
% 3.20/1.76 thf(fact_30_LNil__eq__lmap, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coindu1593790203_llist @ B)]: ((((coindu1598213697e_LNil @ A) = ((((coindu1062782156e_lmap @ B) @ A) @ F) @ Xs)) = (Xs = (coindu1598213697e_LNil @ B)))))).
% 3.20/1.76 thf(fact_31_lmap__eq__LNil, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coindu1593790203_llist @ B)]: (((((((coindu1062782156e_lmap @ B) @ A) @ F) @ Xs) = (coindu1598213697e_LNil @ A)) = (Xs = (coindu1598213697e_LNil @ B)))))).
% 3.20/1.76 thf(fact_32_lappend__assoc, axiom, (! [A:$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)))))).
% 3.20/1.76 thf(fact_33_llist_Oexhaust, axiom, (! [A:$tType,Y:(coindu1593790203_llist @ A)]: (((Y != (coindu1598213697e_LNil @ A)) => (~ ((! [X212:A,X222:(coindu1593790203_llist @ A)]: ((Y != (((coindu1121789889_LCons @ A) @ X212) @ X222)))))))))).
% 3.20/1.76 thf(fact_34_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((Xs != (coindu1598213697e_LNil @ A)) = (? [X2:A,Xs3:(coindu1593790203_llist @ A)]: ((Xs = (((coindu1121789889_LCons @ A) @ X2) @ Xs3)))))))).
% 3.20/1.76 thf(fact_35_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coindu268472904append @ A) @ (coindu1598213697e_LNil @ A)) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 3.20/1.76 thf(fact_36_lmap__eq__LCons__conv, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coindu1593790203_llist @ B),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((((coindu1062782156e_lmap @ B) @ A) @ F) @ Xs) = (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = (? [X2:B,Xs3:(coindu1593790203_llist @ B)]: (((Xs = (((coindu1121789889_LCons @ B) @ X2) @ Xs3)) & ((Y = (F @ X2)) & (Ys = ((((coindu1062782156e_lmap @ B) @ A) @ F) @ Xs3)))))))))).
% 3.20/1.76 thf(fact_37_LNil__eq__lappend__iff, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1598213697e_LNil @ A) = (((coindu268472904append @ A) @ Xs) @ Ys)) = ((Xs = (coindu1598213697e_LNil @ A)) & (Ys = (coindu1598213697e_LNil @ A))))))).
% 3.20/1.76 thf(fact_38_lappend__eq__LNil__iff, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((((coindu268472904append @ A) @ Xs) @ Ys) = (coindu1598213697e_LNil @ A)) = ((Xs = (coindu1598213697e_LNil @ A)) & (Ys = (coindu1598213697e_LNil @ A))))))).
% 3.20/1.76 thf(fact_39_lmap__lappend__distrib, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coindu1593790203_llist @ B),Ys:(coindu1593790203_llist @ B)]: ((((((coindu1062782156e_lmap @ B) @ A) @ F) @ (((coindu268472904append @ B) @ Xs) @ Ys)) = (((coindu268472904append @ A) @ ((((coindu1062782156e_lmap @ B) @ A) @ F) @ Xs)) @ ((((coindu1062782156e_lmap @ B) @ A) @ F) @ Ys)))))).
% 3.20/1.76 thf(fact_40_lappend__snocL1__conv__LCons2, axiom, (! [A:$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)))))).
% 3.20/1.76 thf(fact_41_lprefix__LCons__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((Xs = (coindu1598213697e_LNil @ A)) | (? [Xs3:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ Y) @ Xs3)) & (((coindu1696667936prefix @ A) @ Xs3) @ Ys))))))))).
% 3.20/1.76 thf(fact_42_lprefix_Ocoinduct, axiom, (! [A:$tType,X3:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),X:(coindu1593790203_llist @ A),Xa:(coindu1593790203_llist @ A)]: ((((X3 @ X) @ Xa) => ((! [X4:(coindu1593790203_llist @ A),Xa2:(coindu1593790203_llist @ A)]: ((((X3 @ X4) @ Xa2) => ((? [Xs4:(coindu1593790203_llist @ A)]: (((X4 = (coindu1598213697e_LNil @ A)) & (Xa2 = Xs4)))) | (? [Xs4:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A),Xb:A]: (((X4 = (((coindu1121789889_LCons @ A) @ Xb) @ Xs4)) & ((Xa2 = (((coindu1121789889_LCons @ A) @ Xb) @ Ys3)) & (((X3 @ Xs4) @ Ys3) | (((coindu1696667936prefix @ A) @ Xs4) @ Ys3)))))))))) => (((coindu1696667936prefix @ A) @ X) @ Xa)))))).
% 3.20/1.76 thf(fact_43_lprefix_Osimps, axiom, (! [A:$tType]: (((coindu1696667936prefix @ A) = (^ [A1:(coindu1593790203_llist @ A),A22:(coindu1593790203_llist @ A)]: (((? [Xs2:(coindu1593790203_llist @ A)]: (((A1 = (coindu1598213697e_LNil @ A)) & (A22 = Xs2)))) | (? [Xs2:(coindu1593790203_llist @ A),Ys2:(coindu1593790203_llist @ A),X2:A]: (((A1 = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)) & ((A22 = (((coindu1121789889_LCons @ A) @ X2) @ Ys2)) & (((coindu1696667936prefix @ A) @ Xs2) @ Ys2)))))))))))).
% 3.20/1.76 thf(fact_44_lprefix_Ocases, axiom, (! [A:$tType,A12:(coindu1593790203_llist @ A),A23:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ A12) @ A23) => (((A12 = (coindu1598213697e_LNil @ A)) => (! [Xs5:(coindu1593790203_llist @ A)]: ((A23 != Xs5)))) => (~ ((! [Xs5:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A),X4:A]: (((A12 = (((coindu1121789889_LCons @ A) @ X4) @ Xs5)) => ((A23 = (((coindu1121789889_LCons @ A) @ X4) @ Ys4)) => (~ ((((coindu1696667936prefix @ A) @ Xs5) @ Ys4)))))))))))))).
% 3.20/1.76 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 3.20/1.76 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A4)))) = A4)))).
% 3.20/1.76 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 3.20/1.76 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X4:A]: (((F @ X4) = (G @ X4)))) => (F = G))))).
% 3.20/1.76 thf(fact_49_lprefix__code_I2_J, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: ((~ ((((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (coindu1598213697e_LNil @ A))))))).
% 3.20/1.76 thf(fact_50_ltake__lappend1, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((ord_less_eq @ extended_enat) @ N) @ ((coindu1018505716length @ A) @ Xs)) => ((((coindu1802687541_ltake @ A) @ N) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu1802687541_ltake @ A) @ N) @ Xs)))))).
% 3.20/1.76 thf(fact_51_LCons__lprefix__conv, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ Ys) = (? [Ys5:(coindu1593790203_llist @ A)]: (((Ys = (((coindu1121789889_LCons @ A) @ X) @ Ys5)) & (((coindu1696667936prefix @ A) @ Xs) @ Ys5)))))))).
% 3.20/1.76 thf(fact_52_Le__LCons, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),X:A]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ X) @ Ys)))))).
% 3.20/1.76 thf(fact_53_LNil__lprefix, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (coindu1598213697e_LNil @ A)) @ Xs)))).
% 3.20/1.76 thf(fact_54_min_Obounded__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ (((ord_min @ A) @ B2) @ C)) = ((((ord_less_eq @ A) @ A2) @ B2) & (((ord_less_eq @ A) @ A2) @ C))))))))).
% 3.20/1.76 thf(fact_55_min_Oidem, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A]: (((((ord_min @ A) @ A2) @ A2) = A2))))))).
% 3.20/1.76 thf(fact_56_min_Oleft__idem, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_min @ A) @ A2) @ (((ord_min @ A) @ A2) @ B2)) = (((ord_min @ A) @ A2) @ B2)))))))).
% 3.20/1.76 thf(fact_57_min_Oright__idem, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_min @ A) @ (((ord_min @ A) @ A2) @ B2)) @ B2) = (((ord_min @ A) @ A2) @ B2)))))))).
% 3.20/1.76 thf(fact_58_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 3.20/1.76 thf(fact_59_lfp_Otransp__le, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => ((transp @ A) @ (ord_less_eq @ A)))))).
% 3.20/1.76 thf(fact_60_preorder__class_Otransp__le, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => ((transp @ A) @ (ord_less_eq @ A)))))).
% 3.20/1.76 thf(fact_61_min__absorb1, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_min @ A) @ X) @ Y) = X)))))))).
% 3.20/1.76 thf(fact_62_min__absorb2, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_min @ A) @ X) @ Y) = Y)))))))).
% 3.20/1.76 thf(fact_63_min__def, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => ((ord_min @ A) = (^ [A5:A,B4:A]: (((((if @ A) @ (((ord_less_eq @ A) @ A5) @ B4)) @ A5) @ B4)))))))).
% 3.20/1.76 thf(fact_64_dual__order_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 3.20/1.76 thf(fact_65_lfp_Oleq__antisym, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 3.20/1.76 thf(fact_66_gfp_Oleq__antisym, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) => (X = Y))))))))).
% 3.20/1.76 thf(fact_67_dual__order_Otrans, axiom, (! [A:$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))))))))).
% 3.20/1.76 thf(fact_68_linorder__wlog, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((P @ A3) @ B3)))) => ((! [A3:A,B3:A]: ((((P @ B3) @ A3) => ((P @ A3) @ B3)))) => ((P @ A2) @ B2))))))))).
% 3.20/1.76 thf(fact_69_dual__order_Orefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 3.20/1.76 thf(fact_70_lfp_Oleq__trans, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z) => (((ord_less_eq @ A) @ X) @ Z))))))))).
% 3.20/1.76 thf(fact_71_gfp_Oleq__trans, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [Y:A,X:A,Z:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ Z) @ Y) => (((ord_less_eq @ A) @ Z) @ X))))))))).
% 3.20/1.76 thf(fact_72_order__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z) => (((ord_less_eq @ A) @ X) @ Z))))))))).
% 3.20/1.76 thf(fact_73_lfp_Oleq__refl, axiom, (! [A:$tType]: ((((comple187826305attice @ A) @ (type2 @ A)) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 3.20/1.76 thf(fact_74_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 3.20/1.76 thf(fact_75_ord__le__eq__trans, axiom, (! [A:$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))))))))).
% 3.20/1.76 thf(fact_76_ord__eq__le__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 3.20/1.76 thf(fact_77_antisym__conv, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 3.20/1.76 thf(fact_78_le__cases3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: ((((((ord_less_eq @ A) @ X) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z)))) => (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z)))) => (((((ord_less_eq @ A) @ X) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ Y)))) => (((((ord_less_eq @ A) @ Z) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X)))) => (((((ord_less_eq @ A) @ Y) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ X)))) => (~ (((((ord_less_eq @ A) @ Z) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y))))))))))))))))).
% 3.20/1.76 thf(fact_79_order_Otrans, axiom, (! [A:$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))))))))).
% 3.20/1.76 thf(fact_80_le__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 3.20/1.76 thf(fact_81_eq__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X = Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 3.20/1.76 thf(fact_82_linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less_eq @ A) @ Y) @ X)))))))).
% 3.20/1.76 thf(fact_83_antisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 3.20/1.76 thf(fact_84_eq__iff, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((^ [Y2:A,Z2:A]: ((Y2 = Z2))) = (^ [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) & (((ord_less_eq @ A) @ Y3) @ X2))))))))).
% 3.20/1.76 thf(fact_85_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,B2:A,F:(A > B),C:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F @ B2) = C) => ((! [X4:A,Y4:A]: (((((ord_less_eq @ A) @ X4) @ Y4) => (((ord_less_eq @ B) @ (F @ X4)) @ (F @ Y4))))) => (((ord_less_eq @ B) @ (F @ A2)) @ C)))))))))).
% 3.20/1.76 thf(fact_86_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B2:B,C:B]: (((A2 = (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X4:B,Y4:B]: (((((ord_less_eq @ B) @ X4) @ Y4) => (((ord_less_eq @ A) @ (F @ X4)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 3.20/1.76 thf(fact_87_order__subst2, axiom, (! [A:$tType,C2:$tType]: (((((order @ C2) @ (type2 @ C2)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B2:A,F:(A > C2),C:C2]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C2) @ (F @ B2)) @ C) => ((! [X4:A,Y4:A]: (((((ord_less_eq @ A) @ X4) @ Y4) => (((ord_less_eq @ C2) @ (F @ X4)) @ (F @ Y4))))) => (((ord_less_eq @ C2) @ (F @ A2)) @ C)))))))))).
% 3.20/1.76 thf(fact_88_order__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B2:B,C:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X4:B,Y4:B]: (((((ord_less_eq @ B) @ X4) @ Y4) => (((ord_less_eq @ A) @ (F @ X4)) @ (F @ Y4))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 3.20/1.76 thf(fact_89_le__fun__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: ((! [X2:A]: ((((ord_less_eq @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))))).
% 3.20/1.76 thf(fact_90_le__funI, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B)]: (((! [X4:A]: ((((ord_less_eq @ B) @ (F @ X4)) @ (G @ X4)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 3.20/1.76 thf(fact_91_le__funE, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 3.20/1.76 thf(fact_92_le__funD, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 3.20/1.76 thf(fact_93_min_Oleft__commute, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C:A]: (((((ord_min @ A) @ B2) @ (((ord_min @ A) @ A2) @ C)) = (((ord_min @ A) @ A2) @ (((ord_min @ A) @ B2) @ C))))))))).
% 3.20/1.76 thf(fact_94_min_Ocommute, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((ord_min @ A) = (^ [A5:A,B4:A]: ((((ord_min @ A) @ B4) @ A5)))))))).
% 3.20/1.76 thf(fact_95_min_Oassoc, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_min @ A) @ (((ord_min @ A) @ A2) @ B2)) @ C) = (((ord_min @ A) @ A2) @ (((ord_min @ A) @ B2) @ C))))))))).
% 3.20/1.76 thf(fact_96_min__le__iff__disj, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ (((ord_min @ A) @ X) @ Y)) @ Z) = ((((ord_less_eq @ A) @ X) @ Z) | (((ord_less_eq @ A) @ Y) @ Z))))))))).
% 3.20/1.76 thf(fact_97_min_OcoboundedI2, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B2:A,C:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ (((ord_min @ A) @ A2) @ B2)) @ C)))))))).
% 3.20/1.76 thf(fact_98_min_OcoboundedI1, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,C:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ C) => (((ord_less_eq @ A) @ (((ord_min @ A) @ A2) @ B2)) @ C)))))))).
% 3.20/1.76 thf(fact_99_min_Oabsorb__iff2, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [B4:A,A5:A]: (((((ord_min @ A) @ A5) @ B4) = B4)))))))).
% 3.20/1.76 thf(fact_100_min_Oabsorb__iff1, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [A5:A,B4:A]: (((((ord_min @ A) @ A5) @ B4) = A5)))))))).
% 3.20/1.76 thf(fact_101_min_Ocobounded2, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: ((((ord_less_eq @ A) @ (((ord_min @ A) @ A2) @ B2)) @ B2))))))).
% 3.20/1.76 thf(fact_102_min_Ocobounded1, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: ((((ord_less_eq @ A) @ (((ord_min @ A) @ A2) @ B2)) @ A2))))))).
% 3.20/1.76 thf(fact_103_min_Oorder__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [A5:A,B4:A]: ((A5 = (((ord_min @ A) @ A5) @ B4))))))))).
% 3.20/1.76 thf(fact_104_min_OboundedI, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ A2) @ C) => (((ord_less_eq @ A) @ A2) @ (((ord_min @ A) @ B2) @ C)))))))))).
% 3.20/1.76 thf(fact_105_min_OboundedE, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ (((ord_min @ A) @ B2) @ C)) => (~ (((((ord_less_eq @ A) @ A2) @ B2) => (~ ((((ord_less_eq @ A) @ A2) @ C))))))))))))).
% 3.20/1.76 thf(fact_106_min_Oabsorb2, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_min @ A) @ A2) @ B2) = B2)))))))).
% 3.20/1.76 thf(fact_107_min_Oabsorb1, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_min @ A) @ A2) @ B2) = A2)))))))).
% 3.20/1.76 thf(fact_108_min_OorderI, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((A2 = (((ord_min @ A) @ A2) @ B2)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 3.20/1.76 thf(fact_109_min_OorderE, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (A2 = (((ord_min @ A) @ A2) @ B2))))))))).
% 3.20/1.76 thf(fact_110_min_Omono, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A2:A,C:A,B2:A,D:A]: (((((ord_less_eq @ A) @ A2) @ C) => ((((ord_less_eq @ A) @ B2) @ D) => (((ord_less_eq @ A) @ (((ord_min @ A) @ A2) @ B2)) @ (((ord_min @ A) @ C) @ D)))))))))).
% 3.20/1.76 thf(fact_111_ltake__lappend2, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),N:extended_enat,Ys:(coindu1593790203_llist @ A)]: (((((ord_less_eq @ extended_enat) @ ((coindu1018505716length @ A) @ Xs)) @ N) => ((((coindu1802687541_ltake @ A) @ N) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu268472904append @ A) @ Xs) @ (((coindu1802687541_ltake @ A) @ (((minus_minus @ extended_enat) @ N) @ ((coindu1018505716length @ A) @ Xs))) @ Ys))))))).
% 3.20/1.76 thf(fact_112_DEADID_Orel__transp, axiom, (! [A:$tType]: (((transp @ A) @ (^ [Y2:A,Z2:A]: ((Y2 = Z2))))))).
% 3.20/1.76 thf(fact_113_transp__def, axiom, (! [A:$tType]: (((transp @ A) = (^ [R:(A > (A > $o))]: ((! [X2:A,Y3:A,Z3:A]: ((((R @ X2) @ Y3) => (((R @ Y3) @ Z3) => ((R @ X2) @ Z3))))))))))).
% 3.20/1.76 thf(fact_114_transpI, axiom, (! [A:$tType,R2:(A > (A > $o))]: (((! [X4:A,Y4:A,Z4:A]: ((((R2 @ X4) @ Y4) => (((R2 @ Y4) @ Z4) => ((R2 @ X4) @ Z4))))) => ((transp @ A) @ R2))))).
% 3.20/1.76 thf(fact_115_transpE, axiom, (! [A:$tType,R2:(A > (A > $o)),X:A,Y:A,Z:A]: ((((transp @ A) @ R2) => (((R2 @ X) @ Y) => (((R2 @ Y) @ Z) => ((R2 @ X) @ Z))))))).
% 3.20/1.76 thf(fact_116_transpD, axiom, (! [A:$tType,R2:(A > (A > $o)),X:A,Y:A,Z:A]: ((((transp @ A) @ R2) => (((R2 @ X) @ Y) => (((R2 @ Y) @ Z) => ((R2 @ X) @ Z))))))).
% 3.20/1.76 thf(fact_117_llexord_Ocoinduct, axiom, (! [A:$tType,X3:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),X:(coindu1593790203_llist @ A),Xa:(coindu1593790203_llist @ A),R2:(A > (A > $o))]: ((((X3 @ X) @ Xa) => ((! [X4:(coindu1593790203_llist @ A),Xa2:(coindu1593790203_llist @ A)]: ((((X3 @ X4) @ Xa2) => ((? [Xs4:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A),Xb:A]: (((X4 = (((coindu1121789889_LCons @ A) @ Xb) @ Xs4)) & ((Xa2 = (((coindu1121789889_LCons @ A) @ Xb) @ Ys3)) & (((X3 @ Xs4) @ Ys3) | ((((coindu300403952lexord @ A) @ R2) @ Xs4) @ Ys3)))))) | ((? [Xb:A,Y5:A,Xs4:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A)]: (((X4 = (((coindu1121789889_LCons @ A) @ Xb) @ Xs4)) & ((Xa2 = (((coindu1121789889_LCons @ A) @ Y5) @ Ys3)) & ((R2 @ Xb) @ Y5))))) | (? [Ys3:(coindu1593790203_llist @ A)]: (((X4 = (coindu1598213697e_LNil @ A)) & (Xa2 = Ys3))))))))) => ((((coindu300403952lexord @ A) @ R2) @ X) @ Xa)))))).
% 3.20/1.76 thf(fact_118_minus__apply, axiom, (! [B:$tType,A:$tType]: ((((minus @ B) @ (type2 @ B)) => ((minus_minus @ (A > B)) = (^ [A6:(A > B),B5:(A > B),X2:A]: ((((minus_minus @ B) @ (A6 @ X2)) @ (B5 @ X2))))))))).
% 3.20/1.76 thf(fact_119_fun__diff__def, axiom, (! [B:$tType,A:$tType]: ((((minus @ B) @ (type2 @ B)) => ((minus_minus @ (A > B)) = (^ [A6:(A > B),B5:(A > B),X2:A]: ((((minus_minus @ B) @ (A6 @ X2)) @ (B5 @ X2))))))))).
% 3.20/1.76 thf(fact_120_llexord__LCons__eq, axiom, (! [A:$tType,R2:(A > (A > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),X:A]: ((((((coindu300403952lexord @ A) @ R2) @ Xs) @ Ys) => ((((coindu300403952lexord @ A) @ R2) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ X) @ Ys)))))).
% 3.20/1.76 thf(fact_121_llexord__LCons__less, axiom, (! [A:$tType,R2:(A > (A > $o)),X:A,Y:A,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((R2 @ X) @ Y) => ((((coindu300403952lexord @ A) @ R2) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)))))).
% 3.20/1.76 thf(fact_122_llexord__LNil, axiom, (! [A:$tType,R2:(A > (A > $o)),Ys:(coindu1593790203_llist @ A)]: (((((coindu300403952lexord @ A) @ R2) @ (coindu1598213697e_LNil @ A)) @ Ys)))).
% 3.20/1.76 thf(fact_123_ltake__lappend, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1802687541_ltake @ A) @ N) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu268472904append @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) @ (((coindu1802687541_ltake @ A) @ (((minus_minus @ extended_enat) @ N) @ ((coindu1018505716length @ A) @ Xs))) @ Ys)))))).
% 3.20/1.76 thf(fact_124_llexord_Ocases, axiom, (! [A:$tType,R2:(A > (A > $o)),A12:(coindu1593790203_llist @ A),A23:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ R2) @ A12) @ A23) => ((! [Xs5:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A),X4:A]: (((A12 = (((coindu1121789889_LCons @ A) @ X4) @ Xs5)) => ((A23 = (((coindu1121789889_LCons @ A) @ X4) @ Ys4)) => (~ (((((coindu300403952lexord @ A) @ R2) @ Xs5) @ Ys4))))))) => ((! [X4:A]: (((? [Xs5:(coindu1593790203_llist @ A)]: ((A12 = (((coindu1121789889_LCons @ A) @ X4) @ Xs5)))) => (! [Y4:A]: (((? [Ys4:(coindu1593790203_llist @ A)]: ((A23 = (((coindu1121789889_LCons @ A) @ Y4) @ Ys4)))) => (~ (((R2 @ X4) @ Y4))))))))) => (~ (((A12 = (coindu1598213697e_LNil @ A)) => (! [Ys4:(coindu1593790203_llist @ A)]: ((A23 != Ys4)))))))))))).
% 3.20/1.76 thf(fact_125_llexord_Osimps, axiom, (! [A:$tType]: (((coindu300403952lexord @ A) = (^ [R:(A > (A > $o)),A1:(coindu1593790203_llist @ A),A22:(coindu1593790203_llist @ A)]: (((? [Xs2:(coindu1593790203_llist @ A),Ys2:(coindu1593790203_llist @ A),X2:A]: (((A1 = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)) & ((A22 = (((coindu1121789889_LCons @ A) @ X2) @ Ys2)) & ((((coindu300403952lexord @ A) @ R) @ Xs2) @ Ys2))))) | ((? [X2:A,Y3:A,Xs2:(coindu1593790203_llist @ A),Ys2:(coindu1593790203_llist @ A)]: (((A1 = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)) & ((A22 = (((coindu1121789889_LCons @ A) @ Y3) @ Ys2)) & ((R @ X2) @ Y3))))) | (? [Ys2:(coindu1593790203_llist @ A)]: (((A1 = (coindu1598213697e_LNil @ A)) & (A22 = Ys2)))))))))))).
% 3.20/1.76 thf(fact_126_enat__diff__cancel__left, axiom, (! [M:extended_enat,X:extended_enat,Y:extended_enat]: (((((ord_less_eq @ extended_enat) @ M) @ X) => ((((ord_less_eq @ extended_enat) @ M) @ Y) => (((((minus_minus @ extended_enat) @ X) @ M) = (((minus_minus @ extended_enat) @ Y) @ M)) = (X = Y))))))).
% 3.20/1.76 thf(fact_127_enat__minus__mono1, axiom, (! [X:extended_enat,Y:extended_enat,M:extended_enat]: (((((ord_less_eq @ extended_enat) @ X) @ Y) => (((ord_less_eq @ extended_enat) @ (((minus_minus @ extended_enat) @ X) @ M)) @ (((minus_minus @ extended_enat) @ Y) @ M)))))).
% 3.20/1.76 thf(fact_128_min__diff__distrib__left, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((minus_minus @ A) @ (((ord_min @ A) @ X) @ Y)) @ Z) = (((ord_min @ A) @ (((minus_minus @ A) @ X) @ Z)) @ (((minus_minus @ A) @ Y) @ Z))))))))).
% 3.20/1.76 thf(fact_129_diff__eq__diff__less__eq, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A,D:A]: ((((((minus_minus @ A) @ A2) @ B2) = (((minus_minus @ A) @ C) @ D)) => ((((ord_less_eq @ A) @ A2) @ B2) = (((ord_less_eq @ A) @ C) @ D))))))))).
% 3.20/1.76 thf(fact_130_diff__right__commute, axiom, (! [A:$tType]: ((((cancel146912293up_add @ A) @ (type2 @ A)) => (! [A2:A,C:A,B2:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ C)) @ B2) = (((minus_minus @ A) @ (((minus_minus @ A) @ A2) @ B2)) @ C)))))))).
% 3.20/1.76 thf(fact_131_diff__eq__diff__eq, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A,D:A]: ((((((minus_minus @ A) @ A2) @ B2) = (((minus_minus @ A) @ C) @ D)) => ((A2 = B2) = (C = D))))))))).
% 3.20/1.76 thf(fact_132_diff__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,D:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ D) @ C) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A2) @ C)) @ (((minus_minus @ A) @ B2) @ D)))))))))).
% 3.20/1.76 thf(fact_133_diff__left__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A2) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ C) @ A2)) @ (((minus_minus @ A) @ C) @ B2))))))))).
% 3.20/1.76 thf(fact_134_diff__right__mono, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ (((minus_minus @ A) @ A2) @ C)) @ (((minus_minus @ A) @ B2) @ C))))))))).
% 3.20/1.76 thf(fact_135_lmember__code_I1_J, axiom, (! [A:$tType,X:A]: ((~ ((((coindu567634248member @ A) @ X) @ (coindu1598213697e_LNil @ A))))))).
% 3.20/1.76 thf(fact_136_lmember__code_I2_J, axiom, (! [A:$tType,X:A,Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu567634248member @ A) @ X) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((X = Y) | (((coindu567634248member @ A) @ X) @ Ys)))))).
% 3.20/1.76 thf(fact_137_lfinite__rev__induct, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: ((((coindu1213758845finite @ A) @ Xs) => ((P @ (coindu1598213697e_LNil @ A)) => ((! [X4:A,Xs5:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs5) => ((P @ Xs5) => (P @ (((coindu268472904append @ A) @ Xs5) @ (((coindu1121789889_LCons @ A) @ X4) @ (coindu1598213697e_LNil @ A)))))))) => (P @ Xs))))))).
% 3.20/1.76 thf(fact_138_llist_Orel__transp, axiom, (! [A:$tType,R3:(A > (A > $o))]: ((((transp @ A) @ R3) => ((transp @ (coindu1593790203_llist @ A)) @ (((coindu987187967t_all2 @ A) @ A) @ R3)))))).
% 3.20/1.76 thf(fact_139_lfinite__LCons, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) = ((coindu1213758845finite @ A) @ Xs))))).
% 3.20/1.76 thf(fact_140_lfinite__code_I2_J, axiom, (! [B:$tType,X:B,Xs:(coindu1593790203_llist @ B)]: ((((coindu1213758845finite @ B) @ (((coindu1121789889_LCons @ B) @ X) @ Xs)) = ((coindu1213758845finite @ B) @ Xs))))).
% 3.20/1.76 thf(fact_141_llist_Orel__inject_I2_J, axiom, (! [A:$tType,B:$tType,R3:(A > (B > $o)),X21:A,X22:(coindu1593790203_llist @ A),Y21:B,Y22:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ R3) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) @ (((coindu1121789889_LCons @ B) @ Y21) @ Y22)) = (((R3 @ X21) @ Y21) & (((((coindu987187967t_all2 @ A) @ B) @ R3) @ X22) @ Y22)))))).
% 3.20/1.76 thf(fact_142_lfinite__code_I1_J, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) @ (coindu1598213697e_LNil @ A))))).
% 3.20/1.76 thf(fact_143_lfinite__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu1213758845finite @ A) @ Xs) & ((coindu1213758845finite @ A) @ Ys)))))).
% 3.20/1.76 thf(fact_144_lfinite__lmap, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coindu1593790203_llist @ B)]: ((((coindu1213758845finite @ A) @ ((((coindu1062782156e_lmap @ B) @ A) @ F) @ Xs)) = ((coindu1213758845finite @ B) @ Xs))))).
% 3.20/1.76 thf(fact_145_lprefix__lappend__same, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) @ (((coindu268472904append @ A) @ Xs) @ Zs)) = (((coindu1213758845finite @ A) @ Xs) => (((coindu1696667936prefix @ A) @ Ys) @ Zs)))))).
% 3.20/1.76 thf(fact_146_llist_Orel__eq, axiom, (! [A:$tType]: (((((coindu987187967t_all2 @ A) @ A) @ (^ [Y2:A,Z2:A]: ((Y2 = Z2)))) = (^ [Y2:(coindu1593790203_llist @ A),Z2:(coindu1593790203_llist @ A)]: ((Y2 = Z2))))))).
% 3.20/1.76 thf(fact_147_llist_Orel__refl, axiom, (! [B:$tType,Ra:(B > (B > $o)),X:(coindu1593790203_llist @ B)]: (((! [X4:B]: (((Ra @ X4) @ X4))) => (((((coindu987187967t_all2 @ B) @ B) @ Ra) @ X) @ X))))).
% 3.20/1.76 thf(fact_148_lappend__inf, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu1213758845finite @ A) @ Xs))) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Xs))))).
% 3.20/1.76 thf(fact_149_lfinite__LNil, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) @ (coindu1598213697e_LNil @ A))))).
% 3.20/1.76 thf(fact_150_lfinite__LConsI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),X:A]: ((((coindu1213758845finite @ A) @ Xs) => ((coindu1213758845finite @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)))))).
% 3.20/1.76 thf(fact_151_llist_Octr__transfer_I1_J, axiom, (! [A:$tType,B:$tType,R3:(A > (B > $o))]: ((((((coindu987187967t_all2 @ A) @ B) @ R3) @ (coindu1598213697e_LNil @ A)) @ (coindu1598213697e_LNil @ B))))).
% 3.20/1.76 thf(fact_152_llist_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,R3:(A > (B > $o)),X21:A,Y21:B,X22:(coindu1593790203_llist @ A),Y22:(coindu1593790203_llist @ B)]: ((((R3 @ X21) @ Y21) => ((((((coindu987187967t_all2 @ A) @ B) @ R3) @ X22) @ Y22) => (((((coindu987187967t_all2 @ A) @ B) @ R3) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) @ (((coindu1121789889_LCons @ B) @ Y21) @ Y22))))))).
% 3.20/1.76 thf(fact_153_not__lfinite__lprefix__conv__eq, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu1213758845finite @ A) @ Xs))) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) = (Xs = Ys)))))).
% 3.20/1.76 thf(fact_154_llist_Orel__mono, axiom, (! [B:$tType,A:$tType,R3:(A > (B > $o)),Ra:(A > (B > $o))]: (((((ord_less_eq @ (A > (B > $o))) @ R3) @ Ra) => (((ord_less_eq @ ((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ B) > $o))) @ (((coindu987187967t_all2 @ A) @ B) @ R3)) @ (((coindu987187967t_all2 @ A) @ B) @ Ra)))))).
% 3.20/1.76 thf(fact_155_llist_Orel__distinct_I2_J, axiom, (! [A:$tType,B:$tType,R3:(A > (B > $o)),Y21:A,Y22:(coindu1593790203_llist @ A)]: ((~ ((((((coindu987187967t_all2 @ A) @ B) @ R3) @ (((coindu1121789889_LCons @ A) @ Y21) @ Y22)) @ (coindu1598213697e_LNil @ B))))))).
% 3.20/1.76 thf(fact_156_llist_Orel__distinct_I1_J, axiom, (! [A:$tType,B:$tType,R3:(A > (B > $o)),Y21:B,Y22:(coindu1593790203_llist @ B)]: ((~ ((((((coindu987187967t_all2 @ A) @ B) @ R3) @ (coindu1598213697e_LNil @ A)) @ (((coindu1121789889_LCons @ B) @ Y21) @ Y22))))))).
% 3.20/1.76 thf(fact_157_llist_Orel__cases, axiom, (! [A:$tType,B:$tType,R3:(A > (B > $o)),A2:(coindu1593790203_llist @ A),B2:(coindu1593790203_llist @ B)]: (((((((coindu987187967t_all2 @ A) @ B) @ R3) @ A2) @ B2) => (((A2 = (coindu1598213697e_LNil @ A)) => (B2 != (coindu1598213697e_LNil @ B))) => (~ ((! [X1:A,X23:(coindu1593790203_llist @ A)]: (((A2 = (((coindu1121789889_LCons @ A) @ X1) @ X23)) => (! [Y1:B,Y23:(coindu1593790203_llist @ B)]: (((B2 = (((coindu1121789889_LCons @ B) @ Y1) @ Y23)) => (((R3 @ X1) @ Y1) => (~ ((((((coindu987187967t_all2 @ A) @ B) @ R3) @ X23) @ Y23))))))))))))))))).
% 3.20/1.76 thf(fact_158_lfinite_Ocases, axiom, (! [A:$tType,A2:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ A2) => ((A2 != (coindu1598213697e_LNil @ A)) => (~ ((! [Xs5:(coindu1593790203_llist @ A)]: (((? [X4:A]: ((A2 = (((coindu1121789889_LCons @ A) @ X4) @ Xs5)))) => (~ (((coindu1213758845finite @ A) @ Xs5))))))))))))).
% 3.20/1.76 thf(fact_159_lfinite_Osimps, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) = (^ [A5:(coindu1593790203_llist @ A)]: (((A5 = (coindu1598213697e_LNil @ A)) | (? [Xs2:(coindu1593790203_llist @ A),X2:A]: (((A5 = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)) & ((coindu1213758845finite @ A) @ Xs2))))))))))).
% 3.20/1.76 thf(fact_160_lfinite_Oinducts, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: ((((coindu1213758845finite @ A) @ X) => ((P @ (coindu1598213697e_LNil @ A)) => ((! [Xs5:(coindu1593790203_llist @ A),X4:A]: ((((coindu1213758845finite @ A) @ Xs5) => ((P @ Xs5) => (P @ (((coindu1121789889_LCons @ A) @ X4) @ Xs5)))))) => (P @ X))))))).
% 3.20/1.76 thf(fact_161_llength__LNil, axiom, (! [A:$tType]: ((((coindu1018505716length @ A) @ (coindu1598213697e_LNil @ A)) = (zero_zero @ extended_enat))))).
% 3.20/1.76 thf(fact_162_in__inv__imagep, axiom, (! [B:$tType,A:$tType]: ((((inv_imagep @ A) @ B) = (^ [R:(A > (A > $o)),F2:(B > A),X2:B,Y3:B]: (((R @ (F2 @ X2)) @ (F2 @ Y3)))))))).
% 3.20/1.76 thf(fact_163_LNil__eq__ltake__iff, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((coindu1598213697e_LNil @ A) = (((coindu1802687541_ltake @ A) @ N) @ Xs)) = ((Xs = (coindu1598213697e_LNil @ A)) | (N = (zero_zero @ extended_enat))))))).
% 3.20/1.76 thf(fact_164_ltake__0, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu1802687541_ltake @ A) @ (zero_zero @ extended_enat)) @ Xs) = (coindu1598213697e_LNil @ A))))).
% 3.20/1.76 thf(fact_165_le__zero__eq, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [N:A]: (((((ord_less_eq @ A) @ N) @ (zero_zero @ A)) = (N = (zero_zero @ A))))))))).
% 3.20/1.76 thf(fact_166_cancel__comm__monoid__add__class_Odiff__cancel, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((minus_minus @ A) @ A2) @ A2) = (zero_zero @ A)))))))).
% 3.20/1.76 thf(fact_167_diff__zero, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((minus_minus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 3.20/1.76 thf(fact_168_zero__diff, axiom, (! [A:$tType]: ((((comm_monoid_diff @ A) @ (type2 @ A)) => (! [A2:A]: (((((minus_minus @ A) @ (zero_zero @ A)) @ A2) = (zero_zero @ A)))))))).
% 3.20/1.76 thf(fact_169_diff__0__right, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((minus_minus @ A) @ A2) @ (zero_zero @ A)) = A2))))))).
% 3.20/1.76 thf(fact_170_diff__self, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A]: (((((minus_minus @ A) @ A2) @ A2) = (zero_zero @ A)))))))).
% 3.20/1.76 thf(fact_171_diff__ge__0__iff__ge, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((minus_minus @ A) @ A2) @ B2)) = (((ord_less_eq @ A) @ B2) @ A2)))))))).
% 3.20/1.76 thf(fact_172_enat__min__eq__0__iff, axiom, (! [A2:extended_enat,B2:extended_enat]: ((((((ord_min @ extended_enat) @ A2) @ B2) = (zero_zero @ extended_enat)) = ((A2 = (zero_zero @ extended_enat)) | (B2 = (zero_zero @ extended_enat))))))).
% 3.20/1.76 thf(fact_173_zero__reorient, axiom, (! [A:$tType]: ((((zero @ A) @ (type2 @ A)) => (! [X:A]: ((((zero_zero @ A) = X) = (X = (zero_zero @ A))))))))).
% 3.20/1.76 thf(fact_174_eq__iff__diff__eq__0, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => ((^ [Y2:A,Z2:A]: ((Y2 = Z2))) = (^ [A5:A,B4:A]: (((((minus_minus @ A) @ A5) @ B4) = (zero_zero @ A))))))))).
% 3.20/1.76 thf(fact_175_zero__le, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [X:A]: ((((ord_less_eq @ A) @ (zero_zero @ A)) @ X))))))).
% 3.20/1.76 thf(fact_176_le__iff__diff__le__0, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [A5:A,B4:A]: ((((ord_less_eq @ A) @ (((minus_minus @ A) @ A5) @ B4)) @ (zero_zero @ A))))))))).
% 3.20/1.76 thf(fact_177_ltake__eq__LNil__iff, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((((coindu1802687541_ltake @ A) @ N) @ Xs) = (coindu1598213697e_LNil @ A)) = ((Xs = (coindu1598213697e_LNil @ A)) | (N = (zero_zero @ extended_enat))))))).
% 3.20/1.76 thf(fact_178_min__enat__simps_I3_J, axiom, (! [Q2:extended_enat]: (((((ord_min @ extended_enat) @ (zero_zero @ extended_enat)) @ Q2) = (zero_zero @ extended_enat))))).
% 3.20/1.76 thf(fact_179_min__enat__simps_I2_J, axiom, (! [Q2:extended_enat]: (((((ord_min @ extended_enat) @ Q2) @ (zero_zero @ extended_enat)) = (zero_zero @ extended_enat))))).
% 3.20/1.76 thf(fact_180_idiff__0__right, axiom, (! [N:extended_enat]: (((((minus_minus @ extended_enat) @ N) @ (zero_zero @ extended_enat)) = N)))).
% 3.20/1.76 thf(fact_181_idiff__0, axiom, (! [N:extended_enat]: (((((minus_minus @ extended_enat) @ (zero_zero @ extended_enat)) @ N) = (zero_zero @ extended_enat))))).
% 3.20/1.76 thf(fact_182_i0__lb, axiom, (! [N:extended_enat]: ((((ord_less_eq @ extended_enat) @ (zero_zero @ extended_enat)) @ N)))).
% 3.20/1.76 thf(fact_183_ile0__eq, axiom, (! [N:extended_enat]: (((((ord_less_eq @ extended_enat) @ N) @ (zero_zero @ extended_enat)) = (N = (zero_zero @ extended_enat)))))).
% 3.20/1.76 thf(fact_184_le__numeral__extra_I3_J, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (((ord_less_eq @ A) @ (zero_zero @ A)) @ (zero_zero @ A)))))).
% 3.20/1.76 thf(fact_185_the__enat__0, axiom, ((extended_the_enat @ (zero_zero @ extended_enat)) = (zero_zero @ nat))).
% 3.20/1.76 thf(fact_186_case__enat__0, axiom, (! [A:$tType,F:(nat > A),I:A]: ((((((extended_case_enat @ A) @ F) @ I) @ (zero_zero @ extended_enat)) = (F @ (zero_zero @ nat)))))).
% 3.20/1.76 thf(fact_187_llength__code, axiom, (! [A:$tType]: (((coindu1018505716length @ A) = ((coindu493225792length @ A) @ (zero_zero @ nat)))))).
% 3.20/1.76 thf(fact_188_ltake_Octr_I1_J, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((N = (zero_zero @ extended_enat)) | ((coindu335574135_lnull @ A) @ Xs)) => ((((coindu1802687541_ltake @ A) @ N) @ Xs) = (coindu1598213697e_LNil @ A)))))).
% 3.20/1.76 thf(fact_189_lnull__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu335574135_lnull @ A) @ Xs) & ((coindu335574135_lnull @ A) @ Ys)))))).
% 3.20/1.76 thf(fact_190_lappend_Odisc__iff_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)))) = ((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 3.20/1.76 thf(fact_191_llist_Omap__disc__iff, axiom, (! [B:$tType,A:$tType,F:(A > B),A2:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ B) @ ((((coindu1062782156e_lmap @ A) @ B) @ F) @ A2)) = ((coindu335574135_lnull @ A) @ A2))))).
% 3.20/1.76 thf(fact_192_lprefix__LNil, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = ((coindu335574135_lnull @ A) @ Xs))))).
% 3.20/1.76 thf(fact_193_ltake_Odisc__iff_I2_J, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)))) = ((N != (zero_zero @ extended_enat)) & (~ (((coindu335574135_lnull @ A) @ Xs)))))))).
% 3.20/1.76 thf(fact_194_ltake_Odisc__iff_I1_J, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) = ((N = (zero_zero @ extended_enat)) | ((coindu335574135_lnull @ A) @ Xs)))))).
% 3.20/1.76 thf(fact_195_lnull__ltake, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) = (((coindu335574135_lnull @ A) @ Xs) | (N = (zero_zero @ extended_enat))))))).
% 3.20/1.76 thf(fact_196_llength__lnull, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu1018505716length @ A) @ Xs) = (zero_zero @ extended_enat)))))).
% 3.20/1.76 thf(fact_197_llength__eq__0, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu1018505716length @ A) @ Xs) = (zero_zero @ extended_enat)) = ((coindu335574135_lnull @ A) @ Xs))))).
% 3.20/1.76 thf(fact_198_ltake_Oexhaust, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((~ (((N = (zero_zero @ extended_enat)) | ((coindu335574135_lnull @ A) @ Xs)))) => (~ (((N != (zero_zero @ extended_enat)) => ((coindu335574135_lnull @ A) @ Xs)))))))).
% 3.20/1.76 thf(fact_199_lappend_Octr_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu335574135_lnull @ A) @ Ys) => ((((coindu268472904append @ A) @ Xs) @ Ys) = (coindu1598213697e_LNil @ A))))))).
% 3.20/1.76 thf(fact_200_ltake_Odisc_I1_J, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: ((((N = (zero_zero @ extended_enat)) | ((coindu335574135_lnull @ A) @ Xs)) => ((coindu335574135_lnull @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)))))).
% 3.20/1.76 thf(fact_201_ltake_Odisc_I2_J, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((N != (zero_zero @ extended_enat)) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (~ (((coindu335574135_lnull @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs))))))))).
% 3.20/1.76 thf(fact_202_lzip_Oexhaust, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((~ ((((coindu335574135_lnull @ A) @ Xs) | ((coindu335574135_lnull @ B) @ Ys)))) => (~ (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((coindu335574135_lnull @ B) @ Ys)))))))).
% 3.20/1.76 thf(fact_203_lappend_Oexhaust, axiom, (! [A:$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)))))))).
% 3.20/1.76 thf(fact_204_lappend__lnull2, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Ys) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Xs))))).
% 3.20/1.76 thf(fact_205_lappend__lnull1, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Ys))))).
% 3.20/1.76 thf(fact_206_lappend_Odisc_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu335574135_lnull @ A) @ Ys) => ((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys))))))).
% 3.20/1.76 thf(fact_207_lappend_Odisc_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))) => (~ (((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)))))))).
% 3.20/1.76 thf(fact_208_lnull__def, axiom, (! [A:$tType]: (((coindu335574135_lnull @ A) = (^ [Llist:(coindu1593790203_llist @ A)]: ((Llist = (coindu1598213697e_LNil @ A)))))))).
% 3.20/1.76 thf(fact_209_llist_Ocollapse_I1_J, axiom, (! [A:$tType,Llist2:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Llist2) => (Llist2 = (coindu1598213697e_LNil @ A)))))).
% 3.20/1.76 thf(fact_210_llist_OdiscI_I1_J, axiom, (! [A:$tType,Llist2:(coindu1593790203_llist @ A)]: (((Llist2 = (coindu1598213697e_LNil @ A)) => ((coindu335574135_lnull @ A) @ Llist2))))).
% 3.20/1.76 thf(fact_211_llist_Odisc_I1_J, axiom, (! [A:$tType]: (((coindu335574135_lnull @ A) @ (coindu1598213697e_LNil @ A))))).
% 3.20/1.76 thf(fact_212_not__lnull__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) = (? [X2:A,Xs3:(coindu1593790203_llist @ A)]: ((Xs = (((coindu1121789889_LCons @ A) @ X2) @ Xs3)))))))).
% 3.20/1.76 thf(fact_213_llist_OdiscI_I2_J, axiom, (! [A:$tType,Llist2:(coindu1593790203_llist @ A),X21:A,X22:(coindu1593790203_llist @ A)]: (((Llist2 = (((coindu1121789889_LCons @ A) @ X21) @ X22)) => (~ (((coindu335574135_lnull @ A) @ Llist2))))))).
% 3.20/1.76 thf(fact_214_llist_Odisc_I2_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: ((~ (((coindu335574135_lnull @ A) @ (((coindu1121789889_LCons @ A) @ X21) @ X22))))))).
% 3.20/1.76 thf(fact_215_lnull__lprefix, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu1696667936prefix @ A) @ Xs) @ Ys))))).
% 3.20/1.76 thf(fact_216_lprefix__lnull, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Ys) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) = ((coindu335574135_lnull @ A) @ Xs)))))).
% 3.20/1.76 thf(fact_217_lprefix__lnullD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu335574135_lnull @ A) @ Ys) => ((coindu335574135_lnull @ A) @ Xs)))))).
% 3.20/1.76 thf(fact_218_lprefix__not__lnullD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 3.20/1.76 thf(fact_219_lnull__imp__lfinite, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((coindu1213758845finite @ A) @ Xs))))).
% 3.20/1.76 thf(fact_220_lprefixI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),X3:(set @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)))]: (((((member @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A))) @ ((((product_Pair @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)) @ Xs) @ Ys)) @ X3) => ((! [Xs5:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A)]: (((((member @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A))) @ ((((product_Pair @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)) @ Xs5) @ Ys4)) @ X3) => (((coindu335574135_lnull @ A) @ Xs5) | (? [X5:A,Xs6:(coindu1593790203_llist @ A),Ys6:(coindu1593790203_llist @ A)]: (((Xs5 = (((coindu1121789889_LCons @ A) @ X5) @ Xs6)) & ((Ys4 = (((coindu1121789889_LCons @ A) @ X5) @ Ys6)) & ((((member @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A))) @ ((((product_Pair @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)) @ Xs6) @ Ys6)) @ X3) | (((coindu1696667936prefix @ A) @ Xs6) @ Ys6)))))))))) => (((coindu1696667936prefix @ A) @ Xs) @ Ys)))))).
% 3.20/1.76 thf(fact_221_ltake_Osimps_I3_J, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((N != (zero_zero @ extended_enat)) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (((coindu1046438764le_lhd @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) = ((coindu1046438764le_lhd @ A) @ Xs))))))).
% 3.20/1.76 thf(fact_222_lhd__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Xs) => (((coindu1046438764le_lhd @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = ((coindu1046438764le_lhd @ A) @ Ys))) & ((~ (((coindu335574135_lnull @ A) @ Xs))) => (((coindu1046438764le_lhd @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = ((coindu1046438764le_lhd @ A) @ Xs))))))).
% 3.20/1.76 thf(fact_223_llist_Omap__sel_I1_J, axiom, (! [B:$tType,A:$tType,A2:(coindu1593790203_llist @ A),F:(A > B)]: (((~ (((coindu335574135_lnull @ A) @ A2))) => (((coindu1046438764le_lhd @ B) @ ((((coindu1062782156e_lmap @ A) @ B) @ F) @ A2)) = (F @ ((coindu1046438764le_lhd @ A) @ A2))))))).
% 3.20/1.76 thf(fact_224_lhd__ltake, axiom, (! [A:$tType,N:extended_enat,Xs:(coindu1593790203_llist @ A)]: (((N != (zero_zero @ extended_enat)) => (((coindu1046438764le_lhd @ A) @ (((coindu1802687541_ltake @ A) @ N) @ Xs)) = ((coindu1046438764le_lhd @ A) @ Xs)))))).
% 3.20/1.76 thf(fact_225_ltakeWhile_Oexhaust, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((~ ((((coindu335574135_lnull @ A) @ Xs) | (~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs))))))) => (~ (((~ (((coindu335574135_lnull @ A) @ Xs))) => (~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs))))))))))).
% 3.20/1.76 thf(fact_226_lprefix__lhdD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (((coindu1046438764le_lhd @ A) @ Xs) = ((coindu1046438764le_lhd @ A) @ Ys))))))).
% 3.20/1.76 thf(fact_227_lhd__LCons, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: ((((coindu1046438764le_lhd @ A) @ (((coindu1121789889_LCons @ A) @ X21) @ X22)) = X21)))).
% 3.20/1.76 thf(fact_228_subrelI, axiom, (! [B:$tType,A:$tType,R2:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: (((! [X4:A,Y4:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X4) @ Y4)) @ R2) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X4) @ Y4)) @ S)))) => (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R2) @ S))))).
% 3.20/1.76 thf(fact_229_lzip_Osimps_I3_J, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((~ (((coindu335574135_lnull @ B) @ Ys))) => (((coindu1046438764le_lhd @ ((product_prod @ A) @ B)) @ ((((coindu847746867e_lzip @ A) @ B) @ Xs) @ Ys)) = ((((product_Pair @ A) @ B) @ ((coindu1046438764le_lhd @ A) @ Xs)) @ ((coindu1046438764le_lhd @ B) @ Ys)))))))).
% 3.20/1.76 thf(fact_230_ltakeWhile_Octr_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((((coindu335574135_lnull @ A) @ Xs) | (~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs))))) => ((((coindu721411036eWhile @ A) @ P) @ Xs) = (coindu1598213697e_LNil @ A)))))).
% 3.20/1.76 thf(fact_231_lzip_Odisc__iff_I2_J, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((~ (((coindu335574135_lnull @ ((product_prod @ A) @ B)) @ ((((coindu847746867e_lzip @ A) @ B) @ Xs) @ Ys)))) = ((~ (((coindu335574135_lnull @ A) @ Xs))) & (~ (((coindu335574135_lnull @ B) @ Ys)))))))).
% 3.20/1.76 thf(fact_232_lzip_Odisc__iff_I1_J, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: ((((coindu335574135_lnull @ ((product_prod @ A) @ B)) @ ((((coindu847746867e_lzip @ A) @ B) @ Xs) @ Ys)) = (((coindu335574135_lnull @ A) @ Xs) | ((coindu335574135_lnull @ B) @ Ys)))))).
% 3.20/1.76 thf(fact_233_ltakeWhile_Odisc__iff_I1_J, axiom, (! [A:$tType,P:(A > $o),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)) = (((coindu335574135_lnull @ A) @ Xs) | (~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs))))))))).
% 3.20/1.76 thf(fact_234_ltakeWhile_Odisc__iff_I2_J, axiom, (! [A:$tType,P:(A > $o),Xs:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)))) = ((~ (((coindu335574135_lnull @ A) @ Xs))) & (P @ ((coindu1046438764le_lhd @ A) @ Xs))))))).
% 3.20/1.76 thf(fact_235_lzip_Octr_I1_J, axiom, (! [B:$tType,A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((((coindu335574135_lnull @ A) @ Xs) | ((coindu335574135_lnull @ B) @ Ys)) => (((((coindu847746867e_lzip @ A) @ B) @ Xs) @ Ys) = (coindu1598213697e_LNil @ ((product_prod @ A) @ B))))))).
% 3.20/1.76 thf(fact_236_lzip_Odisc_I1_J, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((((coindu335574135_lnull @ A) @ Xs) | ((coindu335574135_lnull @ B) @ Ys)) => ((coindu335574135_lnull @ ((product_prod @ A) @ B)) @ ((((coindu847746867e_lzip @ A) @ B) @ Xs) @ Ys)))))).
% 3.20/1.76 thf(fact_237_lzip_Odisc_I2_J, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((~ (((coindu335574135_lnull @ B) @ Ys))) => (~ (((coindu335574135_lnull @ ((product_prod @ A) @ B)) @ ((((coindu847746867e_lzip @ A) @ B) @ Xs) @ Ys))))))))).
% 3.20/1.76 thf(fact_238_ltakeWhile_Osimps_I3_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((P @ ((coindu1046438764le_lhd @ A) @ Xs)) => (((coindu1046438764le_lhd @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)) = ((coindu1046438764le_lhd @ A) @ Xs))))))).
% 3.20/1.76 thf(fact_239_ltakeWhile_Odisc_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((((coindu335574135_lnull @ A) @ Xs) | (~ ((P @ ((coindu1046438764le_lhd @ A) @ Xs))))) => ((coindu335574135_lnull @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)))))).
% 3.20/1.76 thf(fact_240_ltakeWhile_Odisc_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((P @ ((coindu1046438764le_lhd @ A) @ Xs)) => (~ (((coindu335574135_lnull @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs))))))))).
% 3.20/1.76 thf(fact_241_ltakeWhile_Ocode, axiom, (! [A:$tType]: (((coindu721411036eWhile @ A) = (^ [P2:(A > $o),Xs2:(coindu1593790203_llist @ A)]: (((((if @ (coindu1593790203_llist @ A)) @ (((coindu335574135_lnull @ A) @ Xs2) | (~ ((P2 @ ((coindu1046438764le_lhd @ A) @ Xs2)))))) @ (coindu1598213697e_LNil @ A)) @ (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Xs2)) @ (((coindu721411036eWhile @ A) @ P2) @ ((coindu1047225960le_ltl @ A) @ Xs2)))))))))).
% 3.20/1.76 thf(fact_242_ltakeWhile_Octr_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:(A > $o)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((P @ ((coindu1046438764le_lhd @ A) @ Xs)) => ((((coindu721411036eWhile @ A) @ P) @ Xs) = (((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Xs)) @ (((coindu721411036eWhile @ A) @ P) @ ((coindu1047225960le_ltl @ A) @ Xs))))))))).
% 3.20/1.76 thf(fact_243_lfinite__ltl, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)) = ((coindu1213758845finite @ A) @ Xs))))).
% 3.20/1.76 thf(fact_244_ltl__lmap, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coindu1593790203_llist @ B)]: ((((coindu1047225960le_ltl @ A) @ ((((coindu1062782156e_lmap @ B) @ A) @ F) @ Xs)) = ((((coindu1062782156e_lmap @ B) @ A) @ F) @ ((coindu1047225960le_ltl @ B) @ Xs)))))).
% 3.20/1.76 thf(fact_245_ltl__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Xs) => (((coindu1047225960le_ltl @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = ((coindu1047225960le_ltl @ A) @ Ys))) & ((~ (((coindu335574135_lnull @ A) @ Xs))) => (((coindu1047225960le_ltl @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu268472904append @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)) @ Ys))))))).
% 3.20/1.76 thf(fact_246_lhd__LCons__ltl, axiom, (! [A:$tType,Llist2:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Llist2))) => ((((coindu1121789889_LCons @ A) @ ((coindu1046438764le_lhd @ A) @ Llist2)) @ ((coindu1047225960le_ltl @ A) @ Llist2)) = Llist2))))).
% 3.20/1.76 thf(fact_247_llist_Oexpand, axiom, (! [A:$tType,Llist2:(coindu1593790203_llist @ A),Llist3:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Llist2) = ((coindu335574135_lnull @ A) @ Llist3)) => (((~ (((coindu335574135_lnull @ A) @ Llist2))) => ((~ (((coindu335574135_lnull @ A) @ Llist3))) => ((((coindu1046438764le_lhd @ A) @ Llist2) = ((coindu1046438764le_lhd @ A) @ Llist3)) & (((coindu1047225960le_ltl @ A) @ Llist2) = ((coindu1047225960le_ltl @ A) @ Llist3))))) => (Llist2 = Llist3)))))).
% 3.20/1.76 thf(fact_248_llist_Ocoinduct, axiom, (! [A:$tType,R3:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),Llist2:(coindu1593790203_llist @ A),Llist3:(coindu1593790203_llist @ A)]: ((((R3 @ Llist2) @ Llist3) => ((! [Llist4:(coindu1593790203_llist @ A),Llist5:(coindu1593790203_llist @ A)]: ((((R3 @ Llist4) @ Llist5) => ((((coindu335574135_lnull @ A) @ Llist4) = ((coindu335574135_lnull @ A) @ Llist5)) & ((~ (((coindu335574135_lnull @ A) @ Llist4))) => ((~ (((coindu335574135_lnull @ A) @ Llist5))) => ((((coindu1046438764le_lhd @ A) @ Llist4) = ((coindu1046438764le_lhd @ A) @ Llist5)) & ((R3 @ ((coindu1047225960le_ltl @ A) @ Llist4)) @ ((coindu1047225960le_ltl @ A) @ Llist5))))))))) => (Llist2 = Llist3)))))).
% 3.20/1.76 thf(fact_249_llist_Ocoinduct__strong, axiom, (! [A:$tType,R3:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),Llist2:(coindu1593790203_llist @ A),Llist3:(coindu1593790203_llist @ A)]: ((((R3 @ Llist2) @ Llist3) => ((! [Llist4:(coindu1593790203_llist @ A),Llist5:(coindu1593790203_llist @ A)]: ((((R3 @ Llist4) @ Llist5) => ((((coindu335574135_lnull @ A) @ Llist4) = ((coindu335574135_lnull @ A) @ Llist5)) & ((~ (((coindu335574135_lnull @ A) @ Llist4))) => ((~ (((coindu335574135_lnull @ A) @ Llist5))) => ((((coindu1046438764le_lhd @ A) @ Llist4) = ((coindu1046438764le_lhd @ A) @ Llist5)) & (((R3 @ ((coindu1047225960le_ltl @ A) @ Llist4)) @ ((coindu1047225960le_ltl @ A) @ Llist5)) | (((coindu1047225960le_ltl @ A) @ Llist4) = ((coindu1047225960le_ltl @ A) @ Llist5)))))))))) => (Llist2 = Llist3)))))).
% 3.20/1.76 thf(fact_250_lzip_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((~ (((coindu335574135_lnull @ B) @ Ys))) => (((coindu1047225960le_ltl @ ((product_prod @ A) @ B)) @ ((((coindu847746867e_lzip @ A) @ B) @ Xs) @ Ys)) = ((((coindu847746867e_lzip @ A) @ B) @ ((coindu1047225960le_ltl @ A) @ Xs)) @ ((coindu1047225960le_ltl @ B) @ Ys)))))))).
% 3.20/1.76 thf(fact_251_lprefix__expand, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((~ (((coindu335574135_lnull @ A) @ Xs))) => ((~ (((coindu335574135_lnull @ A) @ Ys))) & ((((coindu1046438764le_lhd @ A) @ Xs) = ((coindu1046438764le_lhd @ A) @ Ys)) & (((coindu1696667936prefix @ A) @ ((coindu1047225960le_ltl @ A) @ Xs)) @ ((coindu1047225960le_ltl @ A) @ Ys))))) => (((coindu1696667936prefix @ A) @ Xs) @ Ys))))).
% 3.20/1.76 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice, axiom, (! [A7:$tType,A8:$tType]: ((((comple187826305attice @ A8) @ (type2 @ A8)) => ((comple187826305attice @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 3.20/1.76 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A7:$tType,A8:$tType]: ((((preorder @ A8) @ (type2 @ A8)) => ((preorder @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 3.20/1.76 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: ((((order @ A8) @ (type2 @ A8)) => ((order @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 3.20/1.76 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: ((((ord @ A8) @ (type2 @ A8)) => ((ord @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 3.20/1.76 thf(tcon_fun___Groups_Ominus, axiom, (! [A7:$tType,A8:$tType]: ((((minus @ A8) @ (type2 @ A8)) => ((minus @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 3.20/1.76 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, ((canoni770627133id_add @ nat) @ (type2 @ nat))).
% 3.20/1.76 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add, axiom, ((cancel146912293up_add @ nat) @ (type2 @ nat))).
% 3.20/1.76 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add, axiom, ((cancel1352612707id_add @ nat) @ (type2 @ nat))).
% 3.20/1.76 thf(tcon_Nat_Onat___Rings_Olinordered__semidom, axiom, ((linordered_semidom @ nat) @ (type2 @ nat))).
% 3.20/1.76 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff, axiom, ((comm_monoid_diff @ nat) @ (type2 @ nat))).
% 3.20/1.76 thf(tcon_Nat_Onat___Orderings_Opreorder_1, axiom, ((preorder @ nat) @ (type2 @ nat))).
% 3.20/1.76 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, ((linorder @ nat) @ (type2 @ nat))).
% 3.20/1.76 thf(tcon_Nat_Onat___Orderings_Oorder_2, axiom, ((order @ nat) @ (type2 @ nat))).
% 3.20/1.76 thf(tcon_Nat_Onat___Orderings_Oord_3, axiom, ((ord @ nat) @ (type2 @ nat))).
% 3.20/1.76 thf(tcon_Nat_Onat___Groups_Ominus_4, axiom, ((minus @ nat) @ (type2 @ nat))).
% 3.20/1.76 thf(tcon_Nat_Onat___Groups_Ozero, axiom, ((zero @ nat) @ (type2 @ nat))).
% 3.20/1.76 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_5, axiom, (! [A7:$tType]: (((comple187826305attice @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 3.20/1.76 thf(tcon_Set_Oset___Orderings_Opreorder_6, axiom, (! [A7:$tType]: (((preorder @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 3.20/1.76 thf(tcon_Set_Oset___Orderings_Oorder_7, axiom, (! [A7:$tType]: (((order @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 3.20/1.76 thf(tcon_Set_Oset___Orderings_Oord_8, axiom, (! [A7:$tType]: (((ord @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 3.20/1.76 thf(tcon_Set_Oset___Groups_Ominus_9, axiom, (! [A7:$tType]: (((minus @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 3.20/1.76 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_10, axiom, ((comple187826305attice @ $o) @ (type2 @ $o))).
% 3.20/1.76 thf(tcon_HOL_Obool___Orderings_Opreorder_11, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 3.20/1.76 thf(tcon_HOL_Obool___Orderings_Olinorder_12, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 3.20/1.76 thf(tcon_HOL_Obool___Orderings_Oorder_13, axiom, ((order @ $o) @ (type2 @ $o))).
% 3.20/1.76 thf(tcon_HOL_Obool___Orderings_Oord_14, axiom, ((ord @ $o) @ (type2 @ $o))).
% 3.20/1.76 thf(tcon_HOL_Obool___Groups_Ominus_15, axiom, ((minus @ $o) @ (type2 @ $o))).
% 3.20/1.76 thf(tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_16, axiom, ((canoni770627133id_add @ extended_enat) @ (type2 @ extended_enat))).
% 3.20/1.76 thf(tcon_Extended__Nat_Oenat___Complete__Lattices_Ocomplete__lattice_17, axiom, ((comple187826305attice @ extended_enat) @ (type2 @ extended_enat))).
% 3.20/1.76 thf(tcon_Extended__Nat_Oenat___Orderings_Opreorder_18, axiom, ((preorder @ extended_enat) @ (type2 @ extended_enat))).
% 3.20/1.76 thf(tcon_Extended__Nat_Oenat___Orderings_Olinorder_19, axiom, ((linorder @ extended_enat) @ (type2 @ extended_enat))).
% 3.20/1.76 thf(tcon_Extended__Nat_Oenat___Orderings_Oorder_20, axiom, ((order @ extended_enat) @ (type2 @ extended_enat))).
% 3.20/1.76 thf(tcon_Extended__Nat_Oenat___Orderings_Oord_21, axiom, ((ord @ extended_enat) @ (type2 @ extended_enat))).
% 3.20/1.76 thf(tcon_Extended__Nat_Oenat___Groups_Ominus_22, axiom, ((minus @ extended_enat) @ (type2 @ extended_enat))).
% 3.20/1.76 thf(tcon_Extended__Nat_Oenat___Groups_Ozero_23, axiom, ((zero @ extended_enat) @ (type2 @ extended_enat))).
% 3.20/1.76 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 3.20/1.76 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 3.20/1.76 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 3.20/1.76 thf(conj_0, conjecture, (((coindu1696667936prefix @ a) @ (((coindu1802687541_ltake @ a) @ n) @ xs)) @ (((coindu1802687541_ltake @ a) @ m) @ xs))).
% 3.20/1.76 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.ZCwsuNV1cP/DTF2DTF21964.p
% 3.20/1.76 ------------------------
% 3.39/1.80 ---- Cleaned THF ---
% 3.39/1.80 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 3.39/1.80 coindu1593790203_llist: $tType > $tType ).
% 3.39/1.80
% 3.39/1.80 thf(ty_t_Product__Type_Oprod,type,
% 3.39/1.80 product_prod: $tType > $tType > $tType ).
% 3.39/1.80
% 3.39/1.80 thf(ty_t_Extended__Nat_Oenat,type,
% 3.39/1.80 extended_enat: $tType ).
% 3.39/1.80
% 3.39/1.80 thf(ty_t_Set_Oset,type,
% 3.39/1.80 set: $tType > $tType ).
% 3.39/1.80
% 3.39/1.80 thf(ty_t_Nat_Onat,type,
% 3.39/1.80 nat: $tType ).
% 3.39/1.80
% 3.39/1.80 thf(ty_t_itself,type,
% 3.39/1.80 itself: $tType > $tType ).
% 3.39/1.80
% 3.39/1.80 thf(ty_tf_a,type,
% 3.39/1.80 a: $tType ).
% 3.39/1.80
% 3.39/1.80 thf(sy_cl_HOL_Otype,type,
% 3.39/1.80 type:
% 3.39/1.80 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_cl_Groups_Ozero,type,
% 3.39/1.80 zero:
% 3.39/1.80 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_cl_Groups_Ominus,type,
% 3.39/1.80 minus:
% 3.39/1.80 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_cl_Orderings_Oord,type,
% 3.39/1.80 ord:
% 3.39/1.80 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_cl_Orderings_Oorder,type,
% 3.39/1.80 order:
% 3.39/1.80 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_cl_Groups_Ogroup__add,type,
% 3.39/1.80 group_add:
% 3.39/1.80 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_cl_Orderings_Olinorder,type,
% 3.39/1.80 linorder:
% 3.39/1.80 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_cl_Orderings_Opreorder,type,
% 3.39/1.80 preorder:
% 3.39/1.80 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_cl_Groups_Ocomm__monoid__diff,type,
% 3.39/1.80 comm_monoid_diff:
% 3.39/1.80 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_cl_Rings_Olinordered__semidom,type,
% 3.39/1.80 linordered_semidom:
% 3.39/1.80 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 3.39/1.80 ordered_ab_group_add:
% 3.39/1.80 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 3.39/1.80 cancel1352612707id_add:
% 3.39/1.80 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 3.39/1.80 cancel146912293up_add:
% 3.39/1.80 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_cl_Complete__Lattices_Ocomplete__lattice,type,
% 3.39/1.80 comple187826305attice:
% 3.39/1.80 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 3.39/1.80 canoni770627133id_add:
% 3.39/1.80 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__llength,type,
% 3.39/1.80 coindu493225792length:
% 3.39/1.80 !>[A: $tType] : ( nat > ( coindu1593790203_llist @ A ) > extended_enat ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 3.39/1.80 coindu268472904append:
% 3.39/1.80 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite,type,
% 3.39/1.80 coindu1213758845finite:
% 3.39/1.80 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollength,type,
% 3.39/1.80 coindu1018505716length:
% 3.39/1.80 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > extended_enat ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollexord,type,
% 3.39/1.80 coindu300403952lexord:
% 3.39/1.80 !>[A: $tType] : ( ( A > A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 3.39/1.80 coindu1121789889_LCons:
% 3.39/1.80 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 3.39/1.80 coindu1598213697e_LNil:
% 3.39/1.80 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olhd,type,
% 3.39/1.80 coindu1046438764le_lhd:
% 3.39/1.80 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ollist__all2,type,
% 3.39/1.80 coindu987187967t_all2:
% 3.39/1.80 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olmap,type,
% 3.39/1.80 coindu1062782156e_lmap:
% 3.39/1.80 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ Aa ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 3.39/1.80 coindu335574135_lnull:
% 3.39/1.80 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Oltl,type,
% 3.39/1.80 coindu1047225960le_ltl:
% 3.39/1.80 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember,type,
% 3.39/1.80 coindu567634248member:
% 3.39/1.80 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix,type,
% 3.39/1.80 coindu1696667936prefix:
% 3.39/1.80 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix,type,
% 3.39/1.80 coindu574146665prefix:
% 3.39/1.80 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oltake,type,
% 3.39/1.80 coindu1802687541_ltake:
% 3.39/1.80 !>[A: $tType] : ( extended_enat > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_OltakeWhile,type,
% 3.39/1.80 coindu721411036eWhile:
% 3.39/1.80 !>[A: $tType] : ( ( A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olzip,type,
% 3.39/1.80 coindu847746867e_lzip:
% 3.39/1.80 !>[A: $tType,B: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > ( coindu1593790203_llist @ ( product_prod @ A @ B ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Extended__Nat_Oenat_Ocase__enat,type,
% 3.39/1.80 extended_case_enat:
% 3.39/1.80 !>[T: $tType] : ( ( nat > T ) > T > extended_enat > T ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Extended__Nat_Othe__enat,type,
% 3.39/1.80 extended_the_enat: extended_enat > nat ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 3.39/1.80 minus_minus:
% 3.39/1.80 !>[A: $tType] : ( A > A > A ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 3.39/1.80 zero_zero:
% 3.39/1.80 !>[A: $tType] : A ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_If,type,
% 3.39/1.80 if:
% 3.39/1.80 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 3.39/1.80 ord_less_eq:
% 3.39/1.80 !>[A: $tType] : ( A > A > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Orderings_Oord__class_Omin,type,
% 3.39/1.80 ord_min:
% 3.39/1.80 !>[A: $tType] : ( A > A > A ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Product__Type_OPair,type,
% 3.39/1.80 product_Pair:
% 3.39/1.80 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Pure_Otype,type,
% 3.39/1.80 type2:
% 3.39/1.80 !>[A: $tType] : ( itself @ A ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Relation_Oinv__imagep,type,
% 3.39/1.80 inv_imagep:
% 3.39/1.80 !>[B: $tType,A: $tType] : ( ( B > B > $o ) > ( A > B ) > A > A > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Relation_Otransp,type,
% 3.39/1.80 transp:
% 3.39/1.80 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_Set_OCollect,type,
% 3.39/1.80 collect:
% 3.39/1.80 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_c_member,type,
% 3.39/1.80 member:
% 3.39/1.80 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.39/1.80
% 3.39/1.80 thf(sy_v_m,type,
% 3.39/1.80 m: extended_enat ).
% 3.39/1.80
% 3.39/1.80 thf(sy_v_n,type,
% 3.39/1.80 n: extended_enat ).
% 3.39/1.80
% 3.39/1.80 thf(sy_v_xs,type,
% 3.39/1.80 xs: coindu1593790203_llist @ a ).
% 3.39/1.80
% 3.39/1.80 thf(fact_0_lprefix__refl,axiom,
% 3.39/1.80 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ Xs ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_1_llist_Oleq__refl,axiom,
% 3.39/1.80 ! [A: $tType,X: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ X @ X ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_2__092_060open_062n_A_092_060le_062_Am_A_092_060or_062_Allength_Axs_A_092_060le_062_Am_092_060close_062,axiom,
% 3.39/1.80 ( ( ord_less_eq @ extended_enat @ n @ m )
% 3.39/1.80 | ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ a @ xs ) @ m ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_3_ltake__is__lprefix,axiom,
% 3.39/1.80 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) @ Xs ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_4_lprefix__trans,axiom,
% 3.39/1.80 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.39/1.80 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 3.39/1.80 => ( coindu1696667936prefix @ A @ Xs @ Zs ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_5_llist_Oleq__trans,axiom,
% 3.39/1.80 ! [A: $tType,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A,Z: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu1696667936prefix @ A @ X @ Y )
% 3.39/1.80 => ( ( coindu1696667936prefix @ A @ Y @ Z )
% 3.39/1.80 => ( coindu1696667936prefix @ A @ X @ Z ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_6_lprefix__antisym,axiom,
% 3.39/1.80 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.39/1.80 => ( ( coindu1696667936prefix @ A @ Ys @ Xs )
% 3.39/1.80 => ( Xs = Ys ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_7_llist_Oleq__antisym,axiom,
% 3.39/1.80 ! [A: $tType,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu1696667936prefix @ A @ X @ Y )
% 3.39/1.80 => ( ( coindu1696667936prefix @ A @ Y @ X )
% 3.39/1.80 => ( X = Y ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_8_lprefix__down__linear,axiom,
% 3.39/1.80 ! [A: $tType,Xs: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu1696667936prefix @ A @ Xs @ Zs )
% 3.39/1.80 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 3.39/1.80 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.39/1.80 | ( coindu1696667936prefix @ A @ Ys @ Xs ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_9_lstrict__prefix__def,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( coindu574146665prefix @ A )
% 3.39/1.80 = ( ^ [Xs2: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu1696667936prefix @ A @ Xs2 @ Ys2 )
% 3.39/1.80 & ( Xs2 != Ys2 ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_10_ltake__eq__ltake__antimono,axiom,
% 3.39/1.80 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,M: extended_enat] :
% 3.39/1.80 ( ( ( coindu1802687541_ltake @ A @ N @ Xs )
% 3.39/1.80 = ( coindu1802687541_ltake @ A @ N @ Ys ) )
% 3.39/1.80 => ( ( ord_less_eq @ extended_enat @ M @ N )
% 3.39/1.80 => ( ( coindu1802687541_ltake @ A @ M @ Xs )
% 3.39/1.80 = ( coindu1802687541_ltake @ A @ M @ Ys ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_11_ltake__all,axiom,
% 3.39/1.80 ! [A: $tType,Xs: coindu1593790203_llist @ A,M: extended_enat] :
% 3.39/1.80 ( ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ M )
% 3.39/1.80 => ( ( coindu1802687541_ltake @ A @ M @ Xs )
% 3.39/1.80 = Xs ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_12_ltake__lmap,axiom,
% 3.39/1.80 ! [A: $tType,B: $tType,N: extended_enat,F: B > A,Xs: coindu1593790203_llist @ B] :
% 3.39/1.80 ( ( coindu1802687541_ltake @ A @ N @ ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) )
% 3.39/1.80 = ( coindu1062782156e_lmap @ B @ A @ F @ ( coindu1802687541_ltake @ B @ N @ Xs ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_13_ltake__LNil,axiom,
% 3.39/1.80 ! [A: $tType,N: extended_enat] :
% 3.39/1.80 ( ( coindu1802687541_ltake @ A @ N @ ( coindu1598213697e_LNil @ A ) )
% 3.39/1.80 = ( coindu1598213697e_LNil @ A ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_14_ltake__ltake,axiom,
% 3.39/1.80 ! [A: $tType,N: extended_enat,M: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu1802687541_ltake @ A @ N @ ( coindu1802687541_ltake @ A @ M @ Xs ) )
% 3.39/1.80 = ( coindu1802687541_ltake @ A @ ( ord_min @ extended_enat @ N @ M ) @ Xs ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_15_lprefix__code_I1_J,axiom,
% 3.39/1.80 ! [A: $tType,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_16_wlog__linorder__le,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [P: A > A > $o,B2: A,A2: A] :
% 3.39/1.80 ( ! [A3: A,B3: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ A3 @ B3 )
% 3.39/1.80 => ( P @ A3 @ B3 ) )
% 3.39/1.80 => ( ( ( P @ B2 @ A2 )
% 3.39/1.80 => ( P @ A2 @ B2 ) )
% 3.39/1.80 => ( P @ A2 @ B2 ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_17_LCons__lprefix__LCons,axiom,
% 3.39/1.80 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 3.39/1.80 = ( ( X = Y )
% 3.39/1.80 & ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_18_llist_Otransp__le,axiom,
% 3.39/1.80 ! [A: $tType] : ( transp @ ( coindu1593790203_llist @ A ) @ ( coindu1696667936prefix @ A ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_19_lprefix__lappend,axiom,
% 3.39/1.80 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_20_lprefix__lappend__sameI,axiom,
% 3.39/1.80 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.39/1.80 => ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Zs @ Xs ) @ ( coindu268472904append @ A @ Zs @ Ys ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_21_llist_Oinject,axiom,
% 3.39/1.80 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 3.39/1.80 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 3.39/1.80 = ( ( X21 = Y21 )
% 3.39/1.80 & ( X22 = Y22 ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_22_lappend__code_I2_J,axiom,
% 3.39/1.80 ! [A: $tType,Xa: A,X: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu268472904append @ A @ ( coindu1121789889_LCons @ A @ Xa @ X ) @ Ys )
% 3.39/1.80 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu268472904append @ A @ X @ Ys ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_23_lappend__code_I1_J,axiom,
% 3.39/1.80 ! [A: $tType,Ys: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ Ys )
% 3.39/1.80 = Ys ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_24_lappend__LNil2,axiom,
% 3.39/1.80 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu268472904append @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 3.39/1.80 = Xs ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_25_llength__lmap,axiom,
% 3.39/1.80 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B] :
% 3.39/1.80 ( ( coindu1018505716length @ A @ ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) )
% 3.39/1.80 = ( coindu1018505716length @ B @ Xs ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_26_llength__ltake,axiom,
% 3.39/1.80 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu1018505716length @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 3.39/1.80 = ( ord_min @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_27_llist_Osimps_I13_J,axiom,
% 3.39/1.80 ! [B: $tType,A: $tType,F: A > B,X21: A,X22: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu1062782156e_lmap @ A @ B @ F @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 3.39/1.80 = ( coindu1121789889_LCons @ B @ ( F @ X21 ) @ ( coindu1062782156e_lmap @ A @ B @ F @ X22 ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_28_llist_Osimps_I12_J,axiom,
% 3.39/1.80 ! [A: $tType,B: $tType,F: A > B] :
% 3.39/1.80 ( ( coindu1062782156e_lmap @ A @ B @ F @ ( coindu1598213697e_LNil @ A ) )
% 3.39/1.80 = ( coindu1598213697e_LNil @ B ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_29_llist_Odistinct_I1_J,axiom,
% 3.39/1.80 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu1598213697e_LNil @ A )
% 3.39/1.80 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_30_LNil__eq__lmap,axiom,
% 3.39/1.80 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B] :
% 3.39/1.80 ( ( ( coindu1598213697e_LNil @ A )
% 3.39/1.80 = ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) )
% 3.39/1.80 = ( Xs
% 3.39/1.80 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_31_lmap__eq__LNil,axiom,
% 3.39/1.80 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B] :
% 3.39/1.80 ( ( ( coindu1062782156e_lmap @ B @ A @ F @ Xs )
% 3.39/1.80 = ( coindu1598213697e_LNil @ A ) )
% 3.39/1.80 = ( Xs
% 3.39/1.80 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_32_lappend__assoc,axiom,
% 3.39/1.80 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 3.39/1.80 = ( coindu268472904append @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_33_llist_Oexhaust,axiom,
% 3.39/1.80 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( Y
% 3.39/1.80 != ( coindu1598213697e_LNil @ A ) )
% 3.39/1.80 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 3.39/1.80 ( Y
% 3.39/1.80 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_34_neq__LNil__conv,axiom,
% 3.39/1.80 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( Xs
% 3.39/1.80 != ( coindu1598213697e_LNil @ A ) )
% 3.39/1.80 = ( ? [X2: A,Xs3: coindu1593790203_llist @ A] :
% 3.39/1.80 ( Xs
% 3.39/1.80 = ( coindu1121789889_LCons @ A @ X2 @ Xs3 ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_35_lappend__LNil__LNil,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) )
% 3.39/1.80 = ( coindu1598213697e_LNil @ A ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_36_lmap__eq__LCons__conv,axiom,
% 3.39/1.80 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B,Y: A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( ( coindu1062782156e_lmap @ B @ A @ F @ Xs )
% 3.39/1.80 = ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 3.39/1.80 = ( ? [X2: B,Xs3: coindu1593790203_llist @ B] :
% 3.39/1.80 ( ( Xs
% 3.39/1.80 = ( coindu1121789889_LCons @ B @ X2 @ Xs3 ) )
% 3.39/1.80 & ( Y
% 3.39/1.80 = ( F @ X2 ) )
% 3.39/1.80 & ( Ys
% 3.39/1.80 = ( coindu1062782156e_lmap @ B @ A @ F @ Xs3 ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_37_LNil__eq__lappend__iff,axiom,
% 3.39/1.80 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( ( coindu1598213697e_LNil @ A )
% 3.39/1.80 = ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.39/1.80 = ( ( Xs
% 3.39/1.80 = ( coindu1598213697e_LNil @ A ) )
% 3.39/1.80 & ( Ys
% 3.39/1.80 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_38_lappend__eq__LNil__iff,axiom,
% 3.39/1.80 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 3.39/1.80 = ( coindu1598213697e_LNil @ A ) )
% 3.39/1.80 = ( ( Xs
% 3.39/1.80 = ( coindu1598213697e_LNil @ A ) )
% 3.39/1.80 & ( Ys
% 3.39/1.80 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_39_lmap__lappend__distrib,axiom,
% 3.39/1.80 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B,Ys: coindu1593790203_llist @ B] :
% 3.39/1.80 ( ( coindu1062782156e_lmap @ B @ A @ F @ ( coindu268472904append @ B @ Xs @ Ys ) )
% 3.39/1.80 = ( coindu268472904append @ A @ ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) @ ( coindu1062782156e_lmap @ B @ A @ F @ Ys ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_40_lappend__snocL1__conv__LCons2,axiom,
% 3.39/1.80 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ ( coindu1598213697e_LNil @ A ) ) ) @ Ys )
% 3.39/1.80 = ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_41_lprefix__LCons__conv,axiom,
% 3.39/1.80 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 3.39/1.80 = ( ( Xs
% 3.39/1.80 = ( coindu1598213697e_LNil @ A ) )
% 3.39/1.80 | ? [Xs3: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( Xs
% 3.39/1.80 = ( coindu1121789889_LCons @ A @ Y @ Xs3 ) )
% 3.39/1.80 & ( coindu1696667936prefix @ A @ Xs3 @ Ys ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_42_lprefix_Ocoinduct,axiom,
% 3.39/1.80 ! [A: $tType,X3: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( X3 @ X @ Xa )
% 3.39/1.80 => ( ! [X4: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( X3 @ X4 @ Xa2 )
% 3.39/1.80 => ( ? [Xs4: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( X4
% 3.39/1.80 = ( coindu1598213697e_LNil @ A ) )
% 3.39/1.80 & ( Xa2 = Xs4 ) )
% 3.39/1.80 | ? [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,Xb: A] :
% 3.39/1.80 ( ( X4
% 3.39/1.80 = ( coindu1121789889_LCons @ A @ Xb @ Xs4 ) )
% 3.39/1.80 & ( Xa2
% 3.39/1.80 = ( coindu1121789889_LCons @ A @ Xb @ Ys3 ) )
% 3.39/1.80 & ( ( X3 @ Xs4 @ Ys3 )
% 3.39/1.80 | ( coindu1696667936prefix @ A @ Xs4 @ Ys3 ) ) ) ) )
% 3.39/1.80 => ( coindu1696667936prefix @ A @ X @ Xa ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_43_lprefix_Osimps,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( coindu1696667936prefix @ A )
% 3.39/1.80 = ( ^ [A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ? [Xs2: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( A1
% 3.39/1.80 = ( coindu1598213697e_LNil @ A ) )
% 3.39/1.80 & ( A22 = Xs2 ) )
% 3.39/1.80 | ? [Xs2: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A,X2: A] :
% 3.39/1.80 ( ( A1
% 3.39/1.80 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 3.39/1.80 & ( A22
% 3.39/1.80 = ( coindu1121789889_LCons @ A @ X2 @ Ys2 ) )
% 3.39/1.80 & ( coindu1696667936prefix @ A @ Xs2 @ Ys2 ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_44_lprefix_Ocases,axiom,
% 3.39/1.80 ! [A: $tType,A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu1696667936prefix @ A @ A12 @ A23 )
% 3.39/1.80 => ( ( ( A12
% 3.39/1.80 = ( coindu1598213697e_LNil @ A ) )
% 3.39/1.80 => ! [Xs5: coindu1593790203_llist @ A] : ( A23 != Xs5 ) )
% 3.39/1.80 => ~ ! [Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,X4: A] :
% 3.39/1.80 ( ( A12
% 3.39/1.80 = ( coindu1121789889_LCons @ A @ X4 @ Xs5 ) )
% 3.39/1.80 => ( ( A23
% 3.39/1.80 = ( coindu1121789889_LCons @ A @ X4 @ Ys4 ) )
% 3.39/1.80 => ~ ( coindu1696667936prefix @ A @ Xs5 @ Ys4 ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_45_mem__Collect__eq,axiom,
% 3.39/1.80 ! [A: $tType,A2: A,P: A > $o] :
% 3.39/1.80 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 3.39/1.80 = ( P @ A2 ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_46_Collect__mem__eq,axiom,
% 3.39/1.80 ! [A: $tType,A4: set @ A] :
% 3.39/1.80 ( ( collect @ A
% 3.39/1.80 @ ^ [X2: A] : ( member @ A @ X2 @ A4 ) )
% 3.39/1.80 = A4 ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_47_Collect__cong,axiom,
% 3.39/1.80 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.39/1.80 ( ! [X4: A] :
% 3.39/1.80 ( ( P @ X4 )
% 3.39/1.80 = ( Q @ X4 ) )
% 3.39/1.80 => ( ( collect @ A @ P )
% 3.39/1.80 = ( collect @ A @ Q ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_48_ext,axiom,
% 3.39/1.80 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 3.39/1.80 ( ! [X4: A] :
% 3.39/1.80 ( ( F @ X4 )
% 3.39/1.80 = ( G @ X4 ) )
% 3.39/1.80 => ( F = G ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_49_lprefix__code_I2_J,axiom,
% 3.39/1.80 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 3.39/1.80 ~ ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_50_ltake__lappend1,axiom,
% 3.39/1.80 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( ord_less_eq @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) )
% 3.39/1.80 => ( ( coindu1802687541_ltake @ A @ N @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.39/1.80 = ( coindu1802687541_ltake @ A @ N @ Xs ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_51_LCons__lprefix__conv,axiom,
% 3.39/1.80 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ Ys )
% 3.39/1.80 = ( ? [Ys5: coindu1593790203_llist @ A] :
% 3.39/1.80 ( ( Ys
% 3.39/1.80 = ( coindu1121789889_LCons @ A @ X @ Ys5 ) )
% 3.39/1.80 & ( coindu1696667936prefix @ A @ Xs @ Ys5 ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_52_Le__LCons,axiom,
% 3.39/1.80 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 3.39/1.80 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.39/1.80 => ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_53_LNil__lprefix,axiom,
% 3.39/1.80 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_54_min_Obounded__iff,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [A2: A,B2: A,C: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ A2 @ ( ord_min @ A @ B2 @ C ) )
% 3.39/1.80 = ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.39/1.80 & ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_55_min_Oidem,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [A2: A] :
% 3.39/1.80 ( ( ord_min @ A @ A2 @ A2 )
% 3.39/1.80 = A2 ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_56_min_Oleft__idem,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [A2: A,B2: A] :
% 3.39/1.80 ( ( ord_min @ A @ A2 @ ( ord_min @ A @ A2 @ B2 ) )
% 3.39/1.80 = ( ord_min @ A @ A2 @ B2 ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_57_min_Oright__idem,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [A2: A,B2: A] :
% 3.39/1.80 ( ( ord_min @ A @ ( ord_min @ A @ A2 @ B2 ) @ B2 )
% 3.39/1.80 = ( ord_min @ A @ A2 @ B2 ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_58_order__refl,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( preorder @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_59_lfp_Otransp__le,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.39/1.80 => ( transp @ A @ ( ord_less_eq @ A ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_60_preorder__class_Otransp__le,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( preorder @ A @ ( type2 @ A ) )
% 3.39/1.80 => ( transp @ A @ ( ord_less_eq @ A ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_61_min__absorb1,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( ord @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [X: A,Y: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ X @ Y )
% 3.39/1.80 => ( ( ord_min @ A @ X @ Y )
% 3.39/1.80 = X ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_62_min__absorb2,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( order @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [Y: A,X: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ Y @ X )
% 3.39/1.80 => ( ( ord_min @ A @ X @ Y )
% 3.39/1.80 = Y ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_63_min__def,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( ord @ A @ ( type2 @ A ) )
% 3.39/1.80 => ( ( ord_min @ A )
% 3.39/1.80 = ( ^ [A5: A,B4: A] : ( if @ A @ ( ord_less_eq @ A @ A5 @ B4 ) @ A5 @ B4 ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_64_dual__order_Oantisym,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( order @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [B2: A,A2: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.39/1.80 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.39/1.80 => ( A2 = B2 ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_65_lfp_Oleq__antisym,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [X: A,Y: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ X @ Y )
% 3.39/1.80 => ( ( ord_less_eq @ A @ Y @ X )
% 3.39/1.80 => ( X = Y ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_66_gfp_Oleq__antisym,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [Y: A,X: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ Y @ X )
% 3.39/1.80 => ( ( ord_less_eq @ A @ X @ Y )
% 3.39/1.80 => ( X = Y ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_67_dual__order_Otrans,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( order @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [B2: A,A2: A,C: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.39/1.80 => ( ( ord_less_eq @ A @ C @ B2 )
% 3.39/1.80 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_68_linorder__wlog,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [P: A > A > $o,A2: A,B2: A] :
% 3.39/1.80 ( ! [A3: A,B3: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ A3 @ B3 )
% 3.39/1.80 => ( P @ A3 @ B3 ) )
% 3.39/1.80 => ( ! [A3: A,B3: A] :
% 3.39/1.80 ( ( P @ B3 @ A3 )
% 3.39/1.80 => ( P @ A3 @ B3 ) )
% 3.39/1.80 => ( P @ A2 @ B2 ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_69_dual__order_Orefl,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( order @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_70_lfp_Oleq__trans,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [X: A,Y: A,Z: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ X @ Y )
% 3.39/1.80 => ( ( ord_less_eq @ A @ Y @ Z )
% 3.39/1.80 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_71_gfp_Oleq__trans,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [Y: A,X: A,Z: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ Y @ X )
% 3.39/1.80 => ( ( ord_less_eq @ A @ Z @ Y )
% 3.39/1.80 => ( ord_less_eq @ A @ Z @ X ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_72_order__trans,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( preorder @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [X: A,Y: A,Z: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ X @ Y )
% 3.39/1.80 => ( ( ord_less_eq @ A @ Y @ Z )
% 3.39/1.80 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_73_lfp_Oleq__refl,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( comple187826305attice @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_74_order__class_Oorder_Oantisym,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( order @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [A2: A,B2: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.39/1.80 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.39/1.80 => ( A2 = B2 ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_75_ord__le__eq__trans,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( ord @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [A2: A,B2: A,C: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.39/1.80 => ( ( B2 = C )
% 3.39/1.80 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_76_ord__eq__le__trans,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( ord @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [A2: A,B2: A,C: A] :
% 3.39/1.80 ( ( A2 = B2 )
% 3.39/1.80 => ( ( ord_less_eq @ A @ B2 @ C )
% 3.39/1.80 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_77_antisym__conv,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( order @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [Y: A,X: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ Y @ X )
% 3.39/1.80 => ( ( ord_less_eq @ A @ X @ Y )
% 3.39/1.80 = ( X = Y ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_78_le__cases3,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [X: A,Y: A,Z: A] :
% 3.39/1.80 ( ( ( ord_less_eq @ A @ X @ Y )
% 3.39/1.80 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 3.39/1.80 => ( ( ( ord_less_eq @ A @ Y @ X )
% 3.39/1.80 => ~ ( ord_less_eq @ A @ X @ Z ) )
% 3.39/1.80 => ( ( ( ord_less_eq @ A @ X @ Z )
% 3.39/1.80 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 3.39/1.80 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 3.39/1.80 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 3.39/1.80 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 3.39/1.80 => ~ ( ord_less_eq @ A @ Z @ X ) )
% 3.39/1.80 => ~ ( ( ord_less_eq @ A @ Z @ X )
% 3.39/1.80 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_79_order_Otrans,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( order @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [A2: A,B2: A,C: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.39/1.80 => ( ( ord_less_eq @ A @ B2 @ C )
% 3.39/1.80 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_80_le__cases,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [X: A,Y: A] :
% 3.39/1.80 ( ~ ( ord_less_eq @ A @ X @ Y )
% 3.39/1.80 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_81_eq__refl,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( preorder @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [X: A,Y: A] :
% 3.39/1.80 ( ( X = Y )
% 3.39/1.80 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_82_linear,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [X: A,Y: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ X @ Y )
% 3.39/1.80 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_83_antisym,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( order @ A @ ( type2 @ A ) )
% 3.39/1.80 => ! [X: A,Y: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ X @ Y )
% 3.39/1.80 => ( ( ord_less_eq @ A @ Y @ X )
% 3.39/1.80 => ( X = Y ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_84_eq__iff,axiom,
% 3.39/1.80 ! [A: $tType] :
% 3.39/1.80 ( ( order @ A @ ( type2 @ A ) )
% 3.39/1.80 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 3.39/1.80 = ( ^ [X2: A,Y3: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 3.39/1.80 & ( ord_less_eq @ A @ Y3 @ X2 ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_85_ord__le__eq__subst,axiom,
% 3.39/1.80 ! [A: $tType,B: $tType] :
% 3.39/1.80 ( ( ( ord @ B @ ( type2 @ B ) )
% 3.39/1.80 & ( ord @ A @ ( type2 @ A ) ) )
% 3.39/1.80 => ! [A2: A,B2: A,F: A > B,C: B] :
% 3.39/1.80 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.39/1.80 => ( ( ( F @ B2 )
% 3.39/1.80 = C )
% 3.39/1.80 => ( ! [X4: A,Y4: A] :
% 3.39/1.80 ( ( ord_less_eq @ A @ X4 @ Y4 )
% 3.39/1.80 => ( ord_less_eq @ B @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.39/1.80 => ( ord_less_eq @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_86_ord__eq__le__subst,axiom,
% 3.39/1.80 ! [A: $tType,B: $tType] :
% 3.39/1.80 ( ( ( ord @ B @ ( type2 @ B ) )
% 3.39/1.80 & ( ord @ A @ ( type2 @ A ) ) )
% 3.39/1.80 => ! [A2: A,F: B > A,B2: B,C: B] :
% 3.39/1.80 ( ( A2
% 3.39/1.80 = ( F @ B2 ) )
% 3.39/1.80 => ( ( ord_less_eq @ B @ B2 @ C )
% 3.39/1.80 => ( ! [X4: B,Y4: B] :
% 3.39/1.80 ( ( ord_less_eq @ B @ X4 @ Y4 )
% 3.39/1.80 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.39/1.80 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 3.39/1.80
% 3.39/1.80 thf(fact_87_order__subst2,axiom,
% 3.39/1.80 ! [A: $tType,C2: $tType] :
% 3.39/1.80 ( ( ( order @ C2 @ ( type2 @ C2 ) )
% 3.39/1.80 & ( order @ A @ ( type2 @ A ) ) )
% 3.39/1.80 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 3.39/1.80 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.39/1.81 => ( ( ord_less_eq @ C2 @ ( F @ B2 ) @ C )
% 3.39/1.81 => ( ! [X4: A,Y4: A] :
% 3.39/1.81 ( ( ord_less_eq @ A @ X4 @ Y4 )
% 3.39/1.81 => ( ord_less_eq @ C2 @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.39/1.81 => ( ord_less_eq @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_88_order__subst1,axiom,
% 3.39/1.81 ! [A: $tType,B: $tType] :
% 3.39/1.81 ( ( ( order @ B @ ( type2 @ B ) )
% 3.39/1.81 & ( order @ A @ ( type2 @ A ) ) )
% 3.39/1.81 => ! [A2: A,F: B > A,B2: B,C: B] :
% 3.39/1.81 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 3.39/1.81 => ( ( ord_less_eq @ B @ B2 @ C )
% 3.39/1.81 => ( ! [X4: B,Y4: B] :
% 3.39/1.81 ( ( ord_less_eq @ B @ X4 @ Y4 )
% 3.39/1.81 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y4 ) ) )
% 3.39/1.81 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_89_le__fun__def,axiom,
% 3.39/1.81 ! [B: $tType,A: $tType] :
% 3.39/1.81 ( ( ord @ B @ ( type2 @ B ) )
% 3.39/1.81 => ( ( ord_less_eq @ ( A > B ) )
% 3.39/1.81 = ( ^ [F2: A > B,G2: A > B] :
% 3.39/1.81 ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_90_le__funI,axiom,
% 3.39/1.81 ! [B: $tType,A: $tType] :
% 3.39/1.81 ( ( ord @ B @ ( type2 @ B ) )
% 3.39/1.81 => ! [F: A > B,G: A > B] :
% 3.39/1.81 ( ! [X4: A] : ( ord_less_eq @ B @ ( F @ X4 ) @ ( G @ X4 ) )
% 3.39/1.81 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_91_le__funE,axiom,
% 3.39/1.81 ! [B: $tType,A: $tType] :
% 3.39/1.81 ( ( ord @ B @ ( type2 @ B ) )
% 3.39/1.81 => ! [F: A > B,G: A > B,X: A] :
% 3.39/1.81 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 3.39/1.81 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_92_le__funD,axiom,
% 3.39/1.81 ! [B: $tType,A: $tType] :
% 3.39/1.81 ( ( ord @ B @ ( type2 @ B ) )
% 3.39/1.81 => ! [F: A > B,G: A > B,X: A] :
% 3.39/1.81 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 3.39/1.81 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_93_min_Oleft__commute,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [B2: A,A2: A,C: A] :
% 3.39/1.81 ( ( ord_min @ A @ B2 @ ( ord_min @ A @ A2 @ C ) )
% 3.39/1.81 = ( ord_min @ A @ A2 @ ( ord_min @ A @ B2 @ C ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_94_min_Ocommute,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ( ( ord_min @ A )
% 3.39/1.81 = ( ^ [A5: A,B4: A] : ( ord_min @ A @ B4 @ A5 ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_95_min_Oassoc,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A,B2: A,C: A] :
% 3.39/1.81 ( ( ord_min @ A @ ( ord_min @ A @ A2 @ B2 ) @ C )
% 3.39/1.81 = ( ord_min @ A @ A2 @ ( ord_min @ A @ B2 @ C ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_96_min__le__iff__disj,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [X: A,Y: A,Z: A] :
% 3.39/1.81 ( ( ord_less_eq @ A @ ( ord_min @ A @ X @ Y ) @ Z )
% 3.39/1.81 = ( ( ord_less_eq @ A @ X @ Z )
% 3.39/1.81 | ( ord_less_eq @ A @ Y @ Z ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_97_min_OcoboundedI2,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [B2: A,C: A,A2: A] :
% 3.39/1.81 ( ( ord_less_eq @ A @ B2 @ C )
% 3.39/1.81 => ( ord_less_eq @ A @ ( ord_min @ A @ A2 @ B2 ) @ C ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_98_min_OcoboundedI1,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A,C: A,B2: A] :
% 3.39/1.81 ( ( ord_less_eq @ A @ A2 @ C )
% 3.39/1.81 => ( ord_less_eq @ A @ ( ord_min @ A @ A2 @ B2 ) @ C ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_99_min_Oabsorb__iff2,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ( ( ord_less_eq @ A )
% 3.39/1.81 = ( ^ [B4: A,A5: A] :
% 3.39/1.81 ( ( ord_min @ A @ A5 @ B4 )
% 3.39/1.81 = B4 ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_100_min_Oabsorb__iff1,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ( ( ord_less_eq @ A )
% 3.39/1.81 = ( ^ [A5: A,B4: A] :
% 3.39/1.81 ( ( ord_min @ A @ A5 @ B4 )
% 3.39/1.81 = A5 ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_101_min_Ocobounded2,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ ( ord_min @ A @ A2 @ B2 ) @ B2 ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_102_min_Ocobounded1,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ ( ord_min @ A @ A2 @ B2 ) @ A2 ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_103_min_Oorder__iff,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ( ( ord_less_eq @ A )
% 3.39/1.81 = ( ^ [A5: A,B4: A] :
% 3.39/1.81 ( A5
% 3.39/1.81 = ( ord_min @ A @ A5 @ B4 ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_104_min_OboundedI,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A,B2: A,C: A] :
% 3.39/1.81 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.39/1.81 => ( ( ord_less_eq @ A @ A2 @ C )
% 3.39/1.81 => ( ord_less_eq @ A @ A2 @ ( ord_min @ A @ B2 @ C ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_105_min_OboundedE,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A,B2: A,C: A] :
% 3.39/1.81 ( ( ord_less_eq @ A @ A2 @ ( ord_min @ A @ B2 @ C ) )
% 3.39/1.81 => ~ ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.39/1.81 => ~ ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_106_min_Oabsorb2,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [B2: A,A2: A] :
% 3.39/1.81 ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.39/1.81 => ( ( ord_min @ A @ A2 @ B2 )
% 3.39/1.81 = B2 ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_107_min_Oabsorb1,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A,B2: A] :
% 3.39/1.81 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.39/1.81 => ( ( ord_min @ A @ A2 @ B2 )
% 3.39/1.81 = A2 ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_108_min_OorderI,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A,B2: A] :
% 3.39/1.81 ( ( A2
% 3.39/1.81 = ( ord_min @ A @ A2 @ B2 ) )
% 3.39/1.81 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_109_min_OorderE,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A,B2: A] :
% 3.39/1.81 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.39/1.81 => ( A2
% 3.39/1.81 = ( ord_min @ A @ A2 @ B2 ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_110_min_Omono,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A,C: A,B2: A,D: A] :
% 3.39/1.81 ( ( ord_less_eq @ A @ A2 @ C )
% 3.39/1.81 => ( ( ord_less_eq @ A @ B2 @ D )
% 3.39/1.81 => ( ord_less_eq @ A @ ( ord_min @ A @ A2 @ B2 ) @ ( ord_min @ A @ C @ D ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_111_ltake__lappend2,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,N: extended_enat,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( ord_less_eq @ extended_enat @ ( coindu1018505716length @ A @ Xs ) @ N )
% 3.39/1.81 => ( ( coindu1802687541_ltake @ A @ N @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.39/1.81 = ( coindu268472904append @ A @ Xs @ ( coindu1802687541_ltake @ A @ ( minus_minus @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) ) @ Ys ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_112_DEADID_Orel__transp,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( transp @ A
% 3.39/1.81 @ ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_113_transp__def,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( transp @ A )
% 3.39/1.81 = ( ^ [R: A > A > $o] :
% 3.39/1.81 ! [X2: A,Y3: A,Z3: A] :
% 3.39/1.81 ( ( R @ X2 @ Y3 )
% 3.39/1.81 => ( ( R @ Y3 @ Z3 )
% 3.39/1.81 => ( R @ X2 @ Z3 ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_114_transpI,axiom,
% 3.39/1.81 ! [A: $tType,R2: A > A > $o] :
% 3.39/1.81 ( ! [X4: A,Y4: A,Z4: A] :
% 3.39/1.81 ( ( R2 @ X4 @ Y4 )
% 3.39/1.81 => ( ( R2 @ Y4 @ Z4 )
% 3.39/1.81 => ( R2 @ X4 @ Z4 ) ) )
% 3.39/1.81 => ( transp @ A @ R2 ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_115_transpE,axiom,
% 3.39/1.81 ! [A: $tType,R2: A > A > $o,X: A,Y: A,Z: A] :
% 3.39/1.81 ( ( transp @ A @ R2 )
% 3.39/1.81 => ( ( R2 @ X @ Y )
% 3.39/1.81 => ( ( R2 @ Y @ Z )
% 3.39/1.81 => ( R2 @ X @ Z ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_116_transpD,axiom,
% 3.39/1.81 ! [A: $tType,R2: A > A > $o,X: A,Y: A,Z: A] :
% 3.39/1.81 ( ( transp @ A @ R2 )
% 3.39/1.81 => ( ( R2 @ X @ Y )
% 3.39/1.81 => ( ( R2 @ Y @ Z )
% 3.39/1.81 => ( R2 @ X @ Z ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_117_llexord_Ocoinduct,axiom,
% 3.39/1.81 ! [A: $tType,X3: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A,R2: A > A > $o] :
% 3.39/1.81 ( ( X3 @ X @ Xa )
% 3.39/1.81 => ( ! [X4: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( X3 @ X4 @ Xa2 )
% 3.39/1.81 => ( ? [Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,Xb: A] :
% 3.39/1.81 ( ( X4
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ Xb @ Xs4 ) )
% 3.39/1.81 & ( Xa2
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ Xb @ Ys3 ) )
% 3.39/1.81 & ( ( X3 @ Xs4 @ Ys3 )
% 3.39/1.81 | ( coindu300403952lexord @ A @ R2 @ Xs4 @ Ys3 ) ) )
% 3.39/1.81 | ? [Xb: A,Y5: A,Xs4: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( X4
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ Xb @ Xs4 ) )
% 3.39/1.81 & ( Xa2
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ Y5 @ Ys3 ) )
% 3.39/1.81 & ( R2 @ Xb @ Y5 ) )
% 3.39/1.81 | ? [Ys3: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( X4
% 3.39/1.81 = ( coindu1598213697e_LNil @ A ) )
% 3.39/1.81 & ( Xa2 = Ys3 ) ) ) )
% 3.39/1.81 => ( coindu300403952lexord @ A @ R2 @ X @ Xa ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_118_minus__apply,axiom,
% 3.39/1.81 ! [B: $tType,A: $tType] :
% 3.39/1.81 ( ( minus @ B @ ( type2 @ B ) )
% 3.39/1.81 => ( ( minus_minus @ ( A > B ) )
% 3.39/1.81 = ( ^ [A6: A > B,B5: A > B,X2: A] : ( minus_minus @ B @ ( A6 @ X2 ) @ ( B5 @ X2 ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_119_fun__diff__def,axiom,
% 3.39/1.81 ! [B: $tType,A: $tType] :
% 3.39/1.81 ( ( minus @ B @ ( type2 @ B ) )
% 3.39/1.81 => ( ( minus_minus @ ( A > B ) )
% 3.39/1.81 = ( ^ [A6: A > B,B5: A > B,X2: A] : ( minus_minus @ B @ ( A6 @ X2 ) @ ( B5 @ X2 ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_120_llexord__LCons__eq,axiom,
% 3.39/1.81 ! [A: $tType,R2: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 3.39/1.81 ( ( coindu300403952lexord @ A @ R2 @ Xs @ Ys )
% 3.39/1.81 => ( coindu300403952lexord @ A @ R2 @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_121_llexord__LCons__less,axiom,
% 3.39/1.81 ! [A: $tType,R2: A > A > $o,X: A,Y: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( R2 @ X @ Y )
% 3.39/1.81 => ( coindu300403952lexord @ A @ R2 @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_122_llexord__LNil,axiom,
% 3.39/1.81 ! [A: $tType,R2: A > A > $o,Ys: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R2 @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_123_ltake__lappend,axiom,
% 3.39/1.81 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu1802687541_ltake @ A @ N @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.39/1.81 = ( coindu268472904append @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) @ ( coindu1802687541_ltake @ A @ ( minus_minus @ extended_enat @ N @ ( coindu1018505716length @ A @ Xs ) ) @ Ys ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_124_llexord_Ocases,axiom,
% 3.39/1.81 ! [A: $tType,R2: A > A > $o,A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu300403952lexord @ A @ R2 @ A12 @ A23 )
% 3.39/1.81 => ( ! [Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,X4: A] :
% 3.39/1.81 ( ( A12
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ X4 @ Xs5 ) )
% 3.39/1.81 => ( ( A23
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ X4 @ Ys4 ) )
% 3.39/1.81 => ~ ( coindu300403952lexord @ A @ R2 @ Xs5 @ Ys4 ) ) )
% 3.39/1.81 => ( ! [X4: A] :
% 3.39/1.81 ( ? [Xs5: coindu1593790203_llist @ A] :
% 3.39/1.81 ( A12
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ X4 @ Xs5 ) )
% 3.39/1.81 => ! [Y4: A] :
% 3.39/1.81 ( ? [Ys4: coindu1593790203_llist @ A] :
% 3.39/1.81 ( A23
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ Y4 @ Ys4 ) )
% 3.39/1.81 => ~ ( R2 @ X4 @ Y4 ) ) )
% 3.39/1.81 => ~ ( ( A12
% 3.39/1.81 = ( coindu1598213697e_LNil @ A ) )
% 3.39/1.81 => ! [Ys4: coindu1593790203_llist @ A] : ( A23 != Ys4 ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_125_llexord_Osimps,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( coindu300403952lexord @ A )
% 3.39/1.81 = ( ^ [R: A > A > $o,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ? [Xs2: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A,X2: A] :
% 3.39/1.81 ( ( A1
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 3.39/1.81 & ( A22
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ X2 @ Ys2 ) )
% 3.39/1.81 & ( coindu300403952lexord @ A @ R @ Xs2 @ Ys2 ) )
% 3.39/1.81 | ? [X2: A,Y3: A,Xs2: coindu1593790203_llist @ A,Ys2: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( A1
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 3.39/1.81 & ( A22
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ Y3 @ Ys2 ) )
% 3.39/1.81 & ( R @ X2 @ Y3 ) )
% 3.39/1.81 | ? [Ys2: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( A1
% 3.39/1.81 = ( coindu1598213697e_LNil @ A ) )
% 3.39/1.81 & ( A22 = Ys2 ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_126_enat__diff__cancel__left,axiom,
% 3.39/1.81 ! [M: extended_enat,X: extended_enat,Y: extended_enat] :
% 3.39/1.81 ( ( ord_less_eq @ extended_enat @ M @ X )
% 3.39/1.81 => ( ( ord_less_eq @ extended_enat @ M @ Y )
% 3.39/1.81 => ( ( ( minus_minus @ extended_enat @ X @ M )
% 3.39/1.81 = ( minus_minus @ extended_enat @ Y @ M ) )
% 3.39/1.81 = ( X = Y ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_127_enat__minus__mono1,axiom,
% 3.39/1.81 ! [X: extended_enat,Y: extended_enat,M: extended_enat] :
% 3.39/1.81 ( ( ord_less_eq @ extended_enat @ X @ Y )
% 3.39/1.81 => ( ord_less_eq @ extended_enat @ ( minus_minus @ extended_enat @ X @ M ) @ ( minus_minus @ extended_enat @ Y @ M ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_128_min__diff__distrib__left,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [X: A,Y: A,Z: A] :
% 3.39/1.81 ( ( minus_minus @ A @ ( ord_min @ A @ X @ Y ) @ Z )
% 3.39/1.81 = ( ord_min @ A @ ( minus_minus @ A @ X @ Z ) @ ( minus_minus @ A @ Y @ Z ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_129_diff__eq__diff__less__eq,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A,B2: A,C: A,D: A] :
% 3.39/1.81 ( ( ( minus_minus @ A @ A2 @ B2 )
% 3.39/1.81 = ( minus_minus @ A @ C @ D ) )
% 3.39/1.81 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.39/1.81 = ( ord_less_eq @ A @ C @ D ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_130_diff__right__commute,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A,C: A,B2: A] :
% 3.39/1.81 ( ( minus_minus @ A @ ( minus_minus @ A @ A2 @ C ) @ B2 )
% 3.39/1.81 = ( minus_minus @ A @ ( minus_minus @ A @ A2 @ B2 ) @ C ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_131_diff__eq__diff__eq,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( group_add @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A,B2: A,C: A,D: A] :
% 3.39/1.81 ( ( ( minus_minus @ A @ A2 @ B2 )
% 3.39/1.81 = ( minus_minus @ A @ C @ D ) )
% 3.39/1.81 => ( ( A2 = B2 )
% 3.39/1.81 = ( C = D ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_132_diff__mono,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A,B2: A,D: A,C: A] :
% 3.39/1.81 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.39/1.81 => ( ( ord_less_eq @ A @ D @ C )
% 3.39/1.81 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B2 @ D ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_133_diff__left__mono,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [B2: A,A2: A,C: A] :
% 3.39/1.81 ( ( ord_less_eq @ A @ B2 @ A2 )
% 3.39/1.81 => ( ord_less_eq @ A @ ( minus_minus @ A @ C @ A2 ) @ ( minus_minus @ A @ C @ B2 ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_134_diff__right__mono,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A,B2: A,C: A] :
% 3.39/1.81 ( ( ord_less_eq @ A @ A2 @ B2 )
% 3.39/1.81 => ( ord_less_eq @ A @ ( minus_minus @ A @ A2 @ C ) @ ( minus_minus @ A @ B2 @ C ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_135_lmember__code_I1_J,axiom,
% 3.39/1.81 ! [A: $tType,X: A] :
% 3.39/1.81 ~ ( coindu567634248member @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_136_lmember__code_I2_J,axiom,
% 3.39/1.81 ! [A: $tType,X: A,Y: A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu567634248member @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 3.39/1.81 = ( ( X = Y )
% 3.39/1.81 | ( coindu567634248member @ A @ X @ Ys ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_137_lfinite__rev__induct,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 3.39/1.81 ( ( coindu1213758845finite @ A @ Xs )
% 3.39/1.81 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 3.39/1.81 => ( ! [X4: A,Xs5: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu1213758845finite @ A @ Xs5 )
% 3.39/1.81 => ( ( P @ Xs5 )
% 3.39/1.81 => ( P @ ( coindu268472904append @ A @ Xs5 @ ( coindu1121789889_LCons @ A @ X4 @ ( coindu1598213697e_LNil @ A ) ) ) ) ) )
% 3.39/1.81 => ( P @ Xs ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_138_llist_Orel__transp,axiom,
% 3.39/1.81 ! [A: $tType,R3: A > A > $o] :
% 3.39/1.81 ( ( transp @ A @ R3 )
% 3.39/1.81 => ( transp @ ( coindu1593790203_llist @ A ) @ ( coindu987187967t_all2 @ A @ A @ R3 ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_139_lfinite__LCons,axiom,
% 3.39/1.81 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 3.39/1.81 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_140_lfinite__code_I2_J,axiom,
% 3.39/1.81 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B] :
% 3.39/1.81 ( ( coindu1213758845finite @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) )
% 3.39/1.81 = ( coindu1213758845finite @ B @ Xs ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_141_llist_Orel__inject_I2_J,axiom,
% 3.39/1.81 ! [A: $tType,B: $tType,R3: A > B > $o,X21: A,X22: coindu1593790203_llist @ A,Y21: B,Y22: coindu1593790203_llist @ B] :
% 3.39/1.81 ( ( coindu987187967t_all2 @ A @ B @ R3 @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) )
% 3.39/1.81 = ( ( R3 @ X21 @ Y21 )
% 3.39/1.81 & ( coindu987187967t_all2 @ A @ B @ R3 @ X22 @ Y22 ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_142_lfinite__code_I1_J,axiom,
% 3.39/1.81 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_143_lfinite__lappend,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu1213758845finite @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.39/1.81 = ( ( coindu1213758845finite @ A @ Xs )
% 3.39/1.81 & ( coindu1213758845finite @ A @ Ys ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_144_lfinite__lmap,axiom,
% 3.39/1.81 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B] :
% 3.39/1.81 ( ( coindu1213758845finite @ A @ ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) )
% 3.39/1.81 = ( coindu1213758845finite @ B @ Xs ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_145_lprefix__lappend__same,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ ( coindu268472904append @ A @ Xs @ Zs ) )
% 3.39/1.81 = ( ( coindu1213758845finite @ A @ Xs )
% 3.39/1.81 => ( coindu1696667936prefix @ A @ Ys @ Zs ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_146_llist_Orel__eq,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( coindu987187967t_all2 @ A @ A
% 3.39/1.81 @ ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 3.39/1.81 = ( ^ [Y2: coindu1593790203_llist @ A,Z2: coindu1593790203_llist @ A] : ( Y2 = Z2 ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_147_llist_Orel__refl,axiom,
% 3.39/1.81 ! [B: $tType,Ra: B > B > $o,X: coindu1593790203_llist @ B] :
% 3.39/1.81 ( ! [X4: B] : ( Ra @ X4 @ X4 )
% 3.39/1.81 => ( coindu987187967t_all2 @ B @ B @ Ra @ X @ X ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_148_lappend__inf,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ~ ( coindu1213758845finite @ A @ Xs )
% 3.39/1.81 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 3.39/1.81 = Xs ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_149_lfinite__LNil,axiom,
% 3.39/1.81 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_150_lfinite__LConsI,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 3.39/1.81 ( ( coindu1213758845finite @ A @ Xs )
% 3.39/1.81 => ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_151_llist_Octr__transfer_I1_J,axiom,
% 3.39/1.81 ! [A: $tType,B: $tType,R3: A > B > $o] : ( coindu987187967t_all2 @ A @ B @ R3 @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_152_llist_Orel__intros_I2_J,axiom,
% 3.39/1.81 ! [A: $tType,B: $tType,R3: A > B > $o,X21: A,Y21: B,X22: coindu1593790203_llist @ A,Y22: coindu1593790203_llist @ B] :
% 3.39/1.81 ( ( R3 @ X21 @ Y21 )
% 3.39/1.81 => ( ( coindu987187967t_all2 @ A @ B @ R3 @ X22 @ Y22 )
% 3.39/1.81 => ( coindu987187967t_all2 @ A @ B @ R3 @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_153_not__lfinite__lprefix__conv__eq,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ~ ( coindu1213758845finite @ A @ Xs )
% 3.39/1.81 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.39/1.81 = ( Xs = Ys ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_154_llist_Orel__mono,axiom,
% 3.39/1.81 ! [B: $tType,A: $tType,R3: A > B > $o,Ra: A > B > $o] :
% 3.39/1.81 ( ( ord_less_eq @ ( A > B > $o ) @ R3 @ Ra )
% 3.39/1.81 => ( ord_less_eq @ ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ B ) > $o ) @ ( coindu987187967t_all2 @ A @ B @ R3 ) @ ( coindu987187967t_all2 @ A @ B @ Ra ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_155_llist_Orel__distinct_I2_J,axiom,
% 3.39/1.81 ! [A: $tType,B: $tType,R3: A > B > $o,Y21: A,Y22: coindu1593790203_llist @ A] :
% 3.39/1.81 ~ ( coindu987187967t_all2 @ A @ B @ R3 @ ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_156_llist_Orel__distinct_I1_J,axiom,
% 3.39/1.81 ! [A: $tType,B: $tType,R3: A > B > $o,Y21: B,Y22: coindu1593790203_llist @ B] :
% 3.39/1.81 ~ ( coindu987187967t_all2 @ A @ B @ R3 @ ( coindu1598213697e_LNil @ A ) @ ( coindu1121789889_LCons @ B @ Y21 @ Y22 ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_157_llist_Orel__cases,axiom,
% 3.39/1.81 ! [A: $tType,B: $tType,R3: A > B > $o,A2: coindu1593790203_llist @ A,B2: coindu1593790203_llist @ B] :
% 3.39/1.81 ( ( coindu987187967t_all2 @ A @ B @ R3 @ A2 @ B2 )
% 3.39/1.81 => ( ( ( A2
% 3.39/1.81 = ( coindu1598213697e_LNil @ A ) )
% 3.39/1.81 => ( B2
% 3.39/1.81 != ( coindu1598213697e_LNil @ B ) ) )
% 3.39/1.81 => ~ ! [X1: A,X23: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( A2
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ X1 @ X23 ) )
% 3.39/1.81 => ! [Y1: B,Y23: coindu1593790203_llist @ B] :
% 3.39/1.81 ( ( B2
% 3.39/1.81 = ( coindu1121789889_LCons @ B @ Y1 @ Y23 ) )
% 3.39/1.81 => ( ( R3 @ X1 @ Y1 )
% 3.39/1.81 => ~ ( coindu987187967t_all2 @ A @ B @ R3 @ X23 @ Y23 ) ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_158_lfinite_Ocases,axiom,
% 3.39/1.81 ! [A: $tType,A2: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu1213758845finite @ A @ A2 )
% 3.39/1.81 => ( ( A2
% 3.39/1.81 != ( coindu1598213697e_LNil @ A ) )
% 3.39/1.81 => ~ ! [Xs5: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ? [X4: A] :
% 3.39/1.81 ( A2
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ X4 @ Xs5 ) )
% 3.39/1.81 => ~ ( coindu1213758845finite @ A @ Xs5 ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_159_lfinite_Osimps,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( coindu1213758845finite @ A )
% 3.39/1.81 = ( ^ [A5: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( A5
% 3.39/1.81 = ( coindu1598213697e_LNil @ A ) )
% 3.39/1.81 | ? [Xs2: coindu1593790203_llist @ A,X2: A] :
% 3.39/1.81 ( ( A5
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 3.39/1.81 & ( coindu1213758845finite @ A @ Xs2 ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_160_lfinite_Oinducts,axiom,
% 3.39/1.81 ! [A: $tType,X: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 3.39/1.81 ( ( coindu1213758845finite @ A @ X )
% 3.39/1.81 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 3.39/1.81 => ( ! [Xs5: coindu1593790203_llist @ A,X4: A] :
% 3.39/1.81 ( ( coindu1213758845finite @ A @ Xs5 )
% 3.39/1.81 => ( ( P @ Xs5 )
% 3.39/1.81 => ( P @ ( coindu1121789889_LCons @ A @ X4 @ Xs5 ) ) ) )
% 3.39/1.81 => ( P @ X ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_161_llength__LNil,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( coindu1018505716length @ A @ ( coindu1598213697e_LNil @ A ) )
% 3.39/1.81 = ( zero_zero @ extended_enat ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_162_in__inv__imagep,axiom,
% 3.39/1.81 ! [B: $tType,A: $tType] :
% 3.39/1.81 ( ( inv_imagep @ A @ B )
% 3.39/1.81 = ( ^ [R: A > A > $o,F2: B > A,X2: B,Y3: B] : ( R @ ( F2 @ X2 ) @ ( F2 @ Y3 ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_163_LNil__eq__ltake__iff,axiom,
% 3.39/1.81 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( ( coindu1598213697e_LNil @ A )
% 3.39/1.81 = ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 3.39/1.81 = ( ( Xs
% 3.39/1.81 = ( coindu1598213697e_LNil @ A ) )
% 3.39/1.81 | ( N
% 3.39/1.81 = ( zero_zero @ extended_enat ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_164_ltake__0,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu1802687541_ltake @ A @ ( zero_zero @ extended_enat ) @ Xs )
% 3.39/1.81 = ( coindu1598213697e_LNil @ A ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_165_le__zero__eq,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [N: A] :
% 3.39/1.81 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 3.39/1.81 = ( N
% 3.39/1.81 = ( zero_zero @ A ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_166_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A] :
% 3.39/1.81 ( ( minus_minus @ A @ A2 @ A2 )
% 3.39/1.81 = ( zero_zero @ A ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_167_diff__zero,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A] :
% 3.39/1.81 ( ( minus_minus @ A @ A2 @ ( zero_zero @ A ) )
% 3.39/1.81 = A2 ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_168_zero__diff,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( comm_monoid_diff @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A] :
% 3.39/1.81 ( ( minus_minus @ A @ ( zero_zero @ A ) @ A2 )
% 3.39/1.81 = ( zero_zero @ A ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_169_diff__0__right,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( group_add @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A] :
% 3.39/1.81 ( ( minus_minus @ A @ A2 @ ( zero_zero @ A ) )
% 3.39/1.81 = A2 ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_170_diff__self,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( group_add @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A] :
% 3.39/1.81 ( ( minus_minus @ A @ A2 @ A2 )
% 3.39/1.81 = ( zero_zero @ A ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_171_diff__ge__0__iff__ge,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [A2: A,B2: A] :
% 3.39/1.81 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A2 @ B2 ) )
% 3.39/1.81 = ( ord_less_eq @ A @ B2 @ A2 ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_172_enat__min__eq__0__iff,axiom,
% 3.39/1.81 ! [A2: extended_enat,B2: extended_enat] :
% 3.39/1.81 ( ( ( ord_min @ extended_enat @ A2 @ B2 )
% 3.39/1.81 = ( zero_zero @ extended_enat ) )
% 3.39/1.81 = ( ( A2
% 3.39/1.81 = ( zero_zero @ extended_enat ) )
% 3.39/1.81 | ( B2
% 3.39/1.81 = ( zero_zero @ extended_enat ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_173_zero__reorient,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( zero @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [X: A] :
% 3.39/1.81 ( ( ( zero_zero @ A )
% 3.39/1.81 = X )
% 3.39/1.81 = ( X
% 3.39/1.81 = ( zero_zero @ A ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_174_eq__iff__diff__eq__0,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( group_add @ A @ ( type2 @ A ) )
% 3.39/1.81 => ( ( ^ [Y2: A,Z2: A] : ( Y2 = Z2 ) )
% 3.39/1.81 = ( ^ [A5: A,B4: A] :
% 3.39/1.81 ( ( minus_minus @ A @ A5 @ B4 )
% 3.39/1.81 = ( zero_zero @ A ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_175_zero__le,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 3.39/1.81 => ! [X: A] : ( ord_less_eq @ A @ ( zero_zero @ A ) @ X ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_176_le__iff__diff__le__0,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 3.39/1.81 => ( ( ord_less_eq @ A )
% 3.39/1.81 = ( ^ [A5: A,B4: A] : ( ord_less_eq @ A @ ( minus_minus @ A @ A5 @ B4 ) @ ( zero_zero @ A ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_177_ltake__eq__LNil__iff,axiom,
% 3.39/1.81 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( ( coindu1802687541_ltake @ A @ N @ Xs )
% 3.39/1.81 = ( coindu1598213697e_LNil @ A ) )
% 3.39/1.81 = ( ( Xs
% 3.39/1.81 = ( coindu1598213697e_LNil @ A ) )
% 3.39/1.81 | ( N
% 3.39/1.81 = ( zero_zero @ extended_enat ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_178_min__enat__simps_I3_J,axiom,
% 3.39/1.81 ! [Q2: extended_enat] :
% 3.39/1.81 ( ( ord_min @ extended_enat @ ( zero_zero @ extended_enat ) @ Q2 )
% 3.39/1.81 = ( zero_zero @ extended_enat ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_179_min__enat__simps_I2_J,axiom,
% 3.39/1.81 ! [Q2: extended_enat] :
% 3.39/1.81 ( ( ord_min @ extended_enat @ Q2 @ ( zero_zero @ extended_enat ) )
% 3.39/1.81 = ( zero_zero @ extended_enat ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_180_idiff__0__right,axiom,
% 3.39/1.81 ! [N: extended_enat] :
% 3.39/1.81 ( ( minus_minus @ extended_enat @ N @ ( zero_zero @ extended_enat ) )
% 3.39/1.81 = N ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_181_idiff__0,axiom,
% 3.39/1.81 ! [N: extended_enat] :
% 3.39/1.81 ( ( minus_minus @ extended_enat @ ( zero_zero @ extended_enat ) @ N )
% 3.39/1.81 = ( zero_zero @ extended_enat ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_182_i0__lb,axiom,
% 3.39/1.81 ! [N: extended_enat] : ( ord_less_eq @ extended_enat @ ( zero_zero @ extended_enat ) @ N ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_183_ile0__eq,axiom,
% 3.39/1.81 ! [N: extended_enat] :
% 3.39/1.81 ( ( ord_less_eq @ extended_enat @ N @ ( zero_zero @ extended_enat ) )
% 3.39/1.81 = ( N
% 3.39/1.81 = ( zero_zero @ extended_enat ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_184_le__numeral__extra_I3_J,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 3.39/1.81 => ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( zero_zero @ A ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_185_the__enat__0,axiom,
% 3.39/1.81 ( ( extended_the_enat @ ( zero_zero @ extended_enat ) )
% 3.39/1.81 = ( zero_zero @ nat ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_186_case__enat__0,axiom,
% 3.39/1.81 ! [A: $tType,F: nat > A,I: A] :
% 3.39/1.81 ( ( extended_case_enat @ A @ F @ I @ ( zero_zero @ extended_enat ) )
% 3.39/1.81 = ( F @ ( zero_zero @ nat ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_187_llength__code,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( coindu1018505716length @ A )
% 3.39/1.81 = ( coindu493225792length @ A @ ( zero_zero @ nat ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_188_ltake_Octr_I1_J,axiom,
% 3.39/1.81 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( ( N
% 3.39/1.81 = ( zero_zero @ extended_enat ) )
% 3.39/1.81 | ( coindu335574135_lnull @ A @ Xs ) )
% 3.39/1.81 => ( ( coindu1802687541_ltake @ A @ N @ Xs )
% 3.39/1.81 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_189_lnull__lappend,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.39/1.81 = ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 & ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_190_lappend_Odisc__iff_I2_J,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 3.39/1.81 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_191_llist_Omap__disc__iff,axiom,
% 3.39/1.81 ! [B: $tType,A: $tType,F: A > B,A2: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu335574135_lnull @ B @ ( coindu1062782156e_lmap @ A @ B @ F @ A2 ) )
% 3.39/1.81 = ( coindu335574135_lnull @ A @ A2 ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_192_lprefix__LNil,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 3.39/1.81 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_193_ltake_Odisc__iff_I2_J,axiom,
% 3.39/1.81 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) ) )
% 3.39/1.81 = ( ( N
% 3.39/1.81 != ( zero_zero @ extended_enat ) )
% 3.39/1.81 & ~ ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_194_ltake_Odisc__iff_I1_J,axiom,
% 3.39/1.81 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 3.39/1.81 = ( ( N
% 3.39/1.81 = ( zero_zero @ extended_enat ) )
% 3.39/1.81 | ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_195_lnull__ltake,axiom,
% 3.39/1.81 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 3.39/1.81 = ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 | ( N
% 3.39/1.81 = ( zero_zero @ extended_enat ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_196_llength__lnull,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( ( coindu1018505716length @ A @ Xs )
% 3.39/1.81 = ( zero_zero @ extended_enat ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_197_llength__eq__0,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( ( coindu1018505716length @ A @ Xs )
% 3.39/1.81 = ( zero_zero @ extended_enat ) )
% 3.39/1.81 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_198_ltake_Oexhaust,axiom,
% 3.39/1.81 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ~ ( ( N
% 3.39/1.81 = ( zero_zero @ extended_enat ) )
% 3.39/1.81 | ( coindu335574135_lnull @ A @ Xs ) )
% 3.39/1.81 => ~ ( ( N
% 3.39/1.81 != ( zero_zero @ extended_enat ) )
% 3.39/1.81 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_199_lappend_Octr_I1_J,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( ( coindu335574135_lnull @ A @ Ys )
% 3.39/1.81 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 3.39/1.81 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_200_ltake_Odisc_I1_J,axiom,
% 3.39/1.81 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( ( N
% 3.39/1.81 = ( zero_zero @ extended_enat ) )
% 3.39/1.81 | ( coindu335574135_lnull @ A @ Xs ) )
% 3.39/1.81 => ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_201_ltake_Odisc_I2_J,axiom,
% 3.39/1.81 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( N
% 3.39/1.81 != ( zero_zero @ extended_enat ) )
% 3.39/1.81 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ~ ( coindu335574135_lnull @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_202_lzip_Oexhaust,axiom,
% 3.39/1.81 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 3.39/1.81 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 | ( coindu335574135_lnull @ B @ Ys ) )
% 3.39/1.81 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_203_lappend_Oexhaust,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 3.39/1.81 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_204_lappend__lnull2,axiom,
% 3.39/1.81 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu335574135_lnull @ A @ Ys )
% 3.39/1.81 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 3.39/1.81 = Xs ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_205_lappend__lnull1,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 3.39/1.81 = Ys ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_206_lappend_Odisc_I1_J,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( ( coindu335574135_lnull @ A @ Ys )
% 3.39/1.81 => ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_207_lappend_Odisc_I2_J,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 | ~ ( coindu335574135_lnull @ A @ Ys ) )
% 3.39/1.81 => ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_208_lnull__def,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( coindu335574135_lnull @ A )
% 3.39/1.81 = ( ^ [Llist: coindu1593790203_llist @ A] :
% 3.39/1.81 ( Llist
% 3.39/1.81 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_209_llist_Ocollapse_I1_J,axiom,
% 3.39/1.81 ! [A: $tType,Llist2: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu335574135_lnull @ A @ Llist2 )
% 3.39/1.81 => ( Llist2
% 3.39/1.81 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_210_llist_OdiscI_I1_J,axiom,
% 3.39/1.81 ! [A: $tType,Llist2: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( Llist2
% 3.39/1.81 = ( coindu1598213697e_LNil @ A ) )
% 3.39/1.81 => ( coindu335574135_lnull @ A @ Llist2 ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_211_llist_Odisc_I1_J,axiom,
% 3.39/1.81 ! [A: $tType] : ( coindu335574135_lnull @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_212_not__lnull__conv,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( ~ ( coindu335574135_lnull @ A @ Xs ) )
% 3.39/1.81 = ( ? [X2: A,Xs3: coindu1593790203_llist @ A] :
% 3.39/1.81 ( Xs
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ X2 @ Xs3 ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_213_llist_OdiscI_I2_J,axiom,
% 3.39/1.81 ! [A: $tType,Llist2: coindu1593790203_llist @ A,X21: A,X22: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( Llist2
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 3.39/1.81 => ~ ( coindu335574135_lnull @ A @ Llist2 ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_214_llist_Odisc_I2_J,axiom,
% 3.39/1.81 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 3.39/1.81 ~ ( coindu335574135_lnull @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_215_lnull__lprefix,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_216_lprefix__lnull,axiom,
% 3.39/1.81 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu335574135_lnull @ A @ Ys )
% 3.39/1.81 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.39/1.81 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_217_lprefix__lnullD,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.39/1.81 => ( ( coindu335574135_lnull @ A @ Ys )
% 3.39/1.81 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_218_lprefix__not__lnullD,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.39/1.81 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_219_lnull__imp__lfinite,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_220_lprefixI,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X3: set @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) )] :
% 3.39/1.81 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs @ Ys ) @ X3 )
% 3.39/1.81 => ( ! [Xs5: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs5 @ Ys4 ) @ X3 )
% 3.39/1.81 => ( ( coindu335574135_lnull @ A @ Xs5 )
% 3.39/1.81 | ? [X5: A,Xs6: coindu1593790203_llist @ A,Ys6: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( Xs5
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ X5 @ Xs6 ) )
% 3.39/1.81 & ( Ys4
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ X5 @ Ys6 ) )
% 3.39/1.81 & ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs6 @ Ys6 ) @ X3 )
% 3.39/1.81 | ( coindu1696667936prefix @ A @ Xs6 @ Ys6 ) ) ) ) )
% 3.39/1.81 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_221_ltake_Osimps_I3_J,axiom,
% 3.39/1.81 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( N
% 3.39/1.81 != ( zero_zero @ extended_enat ) )
% 3.39/1.81 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( ( coindu1046438764le_lhd @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 3.39/1.81 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_222_lhd__lappend,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.39/1.81 = ( coindu1046438764le_lhd @ A @ Ys ) ) )
% 3.39/1.81 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( ( coindu1046438764le_lhd @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.39/1.81 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_223_llist_Omap__sel_I1_J,axiom,
% 3.39/1.81 ! [B: $tType,A: $tType,A2: coindu1593790203_llist @ A,F: A > B] :
% 3.39/1.81 ( ~ ( coindu335574135_lnull @ A @ A2 )
% 3.39/1.81 => ( ( coindu1046438764le_lhd @ B @ ( coindu1062782156e_lmap @ A @ B @ F @ A2 ) )
% 3.39/1.81 = ( F @ ( coindu1046438764le_lhd @ A @ A2 ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_224_lhd__ltake,axiom,
% 3.39/1.81 ! [A: $tType,N: extended_enat,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( N
% 3.39/1.81 != ( zero_zero @ extended_enat ) )
% 3.39/1.81 => ( ( coindu1046438764le_lhd @ A @ ( coindu1802687541_ltake @ A @ N @ Xs ) )
% 3.39/1.81 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_225_ltakeWhile_Oexhaust,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 3.39/1.81 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 3.39/1.81 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_226_lprefix__lhdD,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 3.39/1.81 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( ( coindu1046438764le_lhd @ A @ Xs )
% 3.39/1.81 = ( coindu1046438764le_lhd @ A @ Ys ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_227_lhd__LCons,axiom,
% 3.39/1.81 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu1046438764le_lhd @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 3.39/1.81 = X21 ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_228_subrelI,axiom,
% 3.39/1.81 ! [B: $tType,A: $tType,R2: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 3.39/1.81 ( ! [X4: A,Y4: B] :
% 3.39/1.81 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y4 ) @ R2 )
% 3.39/1.81 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X4 @ Y4 ) @ S ) )
% 3.39/1.81 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R2 @ S ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_229_lzip_Osimps_I3_J,axiom,
% 3.39/1.81 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 3.39/1.81 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( ~ ( coindu335574135_lnull @ B @ Ys )
% 3.39/1.81 => ( ( coindu1046438764le_lhd @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) )
% 3.39/1.81 = ( product_Pair @ A @ B @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu1046438764le_lhd @ B @ Ys ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_230_ltakeWhile_Octr_I1_J,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 3.39/1.81 ( ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 3.39/1.81 => ( ( coindu721411036eWhile @ A @ P @ Xs )
% 3.39/1.81 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_231_lzip_Odisc__iff_I2_J,axiom,
% 3.39/1.81 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 3.39/1.81 ( ( ~ ( coindu335574135_lnull @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) ) )
% 3.39/1.81 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 & ~ ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_232_lzip_Odisc__iff_I1_J,axiom,
% 3.39/1.81 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 3.39/1.81 ( ( coindu335574135_lnull @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) )
% 3.39/1.81 = ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 | ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_233_ltakeWhile_Odisc__iff_I1_J,axiom,
% 3.39/1.81 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 3.39/1.81 = ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_234_ltakeWhile_Odisc__iff_I2_J,axiom,
% 3.39/1.81 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) )
% 3.39/1.81 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 & ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_235_lzip_Octr_I1_J,axiom,
% 3.39/1.81 ! [B: $tType,A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 3.39/1.81 ( ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 | ( coindu335574135_lnull @ B @ Ys ) )
% 3.39/1.81 => ( ( coindu847746867e_lzip @ A @ B @ Xs @ Ys )
% 3.39/1.81 = ( coindu1598213697e_LNil @ ( product_prod @ A @ B ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_236_lzip_Odisc_I1_J,axiom,
% 3.39/1.81 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 3.39/1.81 ( ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 | ( coindu335574135_lnull @ B @ Ys ) )
% 3.39/1.81 => ( coindu335574135_lnull @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_237_lzip_Odisc_I2_J,axiom,
% 3.39/1.81 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 3.39/1.81 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( ~ ( coindu335574135_lnull @ B @ Ys )
% 3.39/1.81 => ~ ( coindu335574135_lnull @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_238_ltakeWhile_Osimps_I3_J,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 3.39/1.81 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 3.39/1.81 => ( ( coindu1046438764le_lhd @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) )
% 3.39/1.81 = ( coindu1046438764le_lhd @ A @ Xs ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_239_ltakeWhile_Odisc_I1_J,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 3.39/1.81 ( ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 | ~ ( P @ ( coindu1046438764le_lhd @ A @ Xs ) ) )
% 3.39/1.81 => ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_240_ltakeWhile_Odisc_I2_J,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 3.39/1.81 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 3.39/1.81 => ~ ( coindu335574135_lnull @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_241_ltakeWhile_Ocode,axiom,
% 3.39/1.81 ! [A: $tType] :
% 3.39/1.81 ( ( coindu721411036eWhile @ A )
% 3.39/1.81 = ( ^ [P2: A > $o,Xs2: coindu1593790203_llist @ A] :
% 3.39/1.81 ( if @ ( coindu1593790203_llist @ A )
% 3.39/1.81 @ ( ( coindu335574135_lnull @ A @ Xs2 )
% 3.39/1.81 | ~ ( P2 @ ( coindu1046438764le_lhd @ A @ Xs2 ) ) )
% 3.39/1.81 @ ( coindu1598213697e_LNil @ A )
% 3.39/1.81 @ ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Xs2 ) @ ( coindu721411036eWhile @ A @ P2 @ ( coindu1047225960le_ltl @ A @ Xs2 ) ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_242_ltakeWhile_Octr_I2_J,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: A > $o] :
% 3.39/1.81 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( ( P @ ( coindu1046438764le_lhd @ A @ Xs ) )
% 3.39/1.81 => ( ( coindu721411036eWhile @ A @ P @ Xs )
% 3.39/1.81 = ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Xs ) @ ( coindu721411036eWhile @ A @ P @ ( coindu1047225960le_ltl @ A @ Xs ) ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_243_lfinite__ltl,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( coindu1213758845finite @ A @ ( coindu1047225960le_ltl @ A @ Xs ) )
% 3.39/1.81 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_244_ltl__lmap,axiom,
% 3.39/1.81 ! [A: $tType,B: $tType,F: B > A,Xs: coindu1593790203_llist @ B] :
% 3.39/1.81 ( ( coindu1047225960le_ltl @ A @ ( coindu1062782156e_lmap @ B @ A @ F @ Xs ) )
% 3.39/1.81 = ( coindu1062782156e_lmap @ B @ A @ F @ ( coindu1047225960le_ltl @ B @ Xs ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_245_ltl__lappend,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.39/1.81 = ( coindu1047225960le_ltl @ A @ Ys ) ) )
% 3.39/1.81 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( ( coindu1047225960le_ltl @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 3.39/1.81 = ( coindu268472904append @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ Ys ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_246_lhd__LCons__ltl,axiom,
% 3.39/1.81 ! [A: $tType,Llist2: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ~ ( coindu335574135_lnull @ A @ Llist2 )
% 3.39/1.81 => ( ( coindu1121789889_LCons @ A @ ( coindu1046438764le_lhd @ A @ Llist2 ) @ ( coindu1047225960le_ltl @ A @ Llist2 ) )
% 3.39/1.81 = Llist2 ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_247_llist_Oexpand,axiom,
% 3.39/1.81 ! [A: $tType,Llist2: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( ( coindu335574135_lnull @ A @ Llist2 )
% 3.39/1.81 = ( coindu335574135_lnull @ A @ Llist3 ) )
% 3.39/1.81 => ( ( ~ ( coindu335574135_lnull @ A @ Llist2 )
% 3.39/1.81 => ( ~ ( coindu335574135_lnull @ A @ Llist3 )
% 3.39/1.81 => ( ( ( coindu1046438764le_lhd @ A @ Llist2 )
% 3.39/1.81 = ( coindu1046438764le_lhd @ A @ Llist3 ) )
% 3.39/1.81 & ( ( coindu1047225960le_ltl @ A @ Llist2 )
% 3.39/1.81 = ( coindu1047225960le_ltl @ A @ Llist3 ) ) ) ) )
% 3.39/1.81 => ( Llist2 = Llist3 ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_248_llist_Ocoinduct,axiom,
% 3.39/1.81 ! [A: $tType,R3: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist2: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( R3 @ Llist2 @ Llist3 )
% 3.39/1.81 => ( ! [Llist4: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( R3 @ Llist4 @ Llist5 )
% 3.39/1.81 => ( ( ( coindu335574135_lnull @ A @ Llist4 )
% 3.39/1.81 = ( coindu335574135_lnull @ A @ Llist5 ) )
% 3.39/1.81 & ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 3.39/1.81 => ( ~ ( coindu335574135_lnull @ A @ Llist5 )
% 3.39/1.81 => ( ( ( coindu1046438764le_lhd @ A @ Llist4 )
% 3.39/1.81 = ( coindu1046438764le_lhd @ A @ Llist5 ) )
% 3.39/1.81 & ( R3 @ ( coindu1047225960le_ltl @ A @ Llist4 ) @ ( coindu1047225960le_ltl @ A @ Llist5 ) ) ) ) ) ) )
% 3.39/1.81 => ( Llist2 = Llist3 ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_249_llist_Ocoinduct__strong,axiom,
% 3.39/1.81 ! [A: $tType,R3: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,Llist2: coindu1593790203_llist @ A,Llist3: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( R3 @ Llist2 @ Llist3 )
% 3.39/1.81 => ( ! [Llist4: coindu1593790203_llist @ A,Llist5: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( R3 @ Llist4 @ Llist5 )
% 3.39/1.81 => ( ( ( coindu335574135_lnull @ A @ Llist4 )
% 3.39/1.81 = ( coindu335574135_lnull @ A @ Llist5 ) )
% 3.39/1.81 & ( ~ ( coindu335574135_lnull @ A @ Llist4 )
% 3.39/1.81 => ( ~ ( coindu335574135_lnull @ A @ Llist5 )
% 3.39/1.81 => ( ( ( coindu1046438764le_lhd @ A @ Llist4 )
% 3.39/1.81 = ( coindu1046438764le_lhd @ A @ Llist5 ) )
% 3.39/1.81 & ( ( R3 @ ( coindu1047225960le_ltl @ A @ Llist4 ) @ ( coindu1047225960le_ltl @ A @ Llist5 ) )
% 3.39/1.81 | ( ( coindu1047225960le_ltl @ A @ Llist4 )
% 3.39/1.81 = ( coindu1047225960le_ltl @ A @ Llist5 ) ) ) ) ) ) ) )
% 3.39/1.81 => ( Llist2 = Llist3 ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_250_lzip_Osimps_I4_J,axiom,
% 3.39/1.81 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 3.39/1.81 ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( ~ ( coindu335574135_lnull @ B @ Ys )
% 3.39/1.81 => ( ( coindu1047225960le_ltl @ ( product_prod @ A @ B ) @ ( coindu847746867e_lzip @ A @ B @ Xs @ Ys ) )
% 3.39/1.81 = ( coindu847746867e_lzip @ A @ B @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ B @ Ys ) ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(fact_251_lprefix__expand,axiom,
% 3.39/1.81 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 3.39/1.81 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 3.39/1.81 => ( ~ ( coindu335574135_lnull @ A @ Ys )
% 3.39/1.81 & ( ( coindu1046438764le_lhd @ A @ Xs )
% 3.39/1.81 = ( coindu1046438764le_lhd @ A @ Ys ) )
% 3.39/1.81 & ( coindu1696667936prefix @ A @ ( coindu1047225960le_ltl @ A @ Xs ) @ ( coindu1047225960le_ltl @ A @ Ys ) ) ) )
% 3.39/1.81 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_fun___Complete__Lattices_Ocomplete__lattice,axiom,
% 3.39/1.81 ! [A7: $tType,A8: $tType] :
% 3.39/1.81 ( ( comple187826305attice @ A8 @ ( type2 @ A8 ) )
% 3.39/1.81 => ( comple187826305attice @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_fun___Orderings_Opreorder,axiom,
% 3.39/1.81 ! [A7: $tType,A8: $tType] :
% 3.39/1.81 ( ( preorder @ A8 @ ( type2 @ A8 ) )
% 3.39/1.81 => ( preorder @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_fun___Orderings_Oorder,axiom,
% 3.39/1.81 ! [A7: $tType,A8: $tType] :
% 3.39/1.81 ( ( order @ A8 @ ( type2 @ A8 ) )
% 3.39/1.81 => ( order @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_fun___Orderings_Oord,axiom,
% 3.39/1.81 ! [A7: $tType,A8: $tType] :
% 3.39/1.81 ( ( ord @ A8 @ ( type2 @ A8 ) )
% 3.39/1.81 => ( ord @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_fun___Groups_Ominus,axiom,
% 3.39/1.81 ! [A7: $tType,A8: $tType] :
% 3.39/1.81 ( ( minus @ A8 @ ( type2 @ A8 ) )
% 3.39/1.81 => ( minus @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 3.39/1.81 canoni770627133id_add @ nat @ ( type2 @ nat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 3.39/1.81 cancel146912293up_add @ nat @ ( type2 @ nat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 3.39/1.81 cancel1352612707id_add @ nat @ ( type2 @ nat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 3.39/1.81 linordered_semidom @ nat @ ( type2 @ nat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff,axiom,
% 3.39/1.81 comm_monoid_diff @ nat @ ( type2 @ nat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 3.39/1.81 preorder @ nat @ ( type2 @ nat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 3.39/1.81 linorder @ nat @ ( type2 @ nat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 3.39/1.81 order @ nat @ ( type2 @ nat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 3.39/1.81 ord @ nat @ ( type2 @ nat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Nat_Onat___Groups_Ominus_4,axiom,
% 3.39/1.81 minus @ nat @ ( type2 @ nat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 3.39/1.81 zero @ nat @ ( type2 @ nat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Set_Oset___Complete__Lattices_Ocomplete__lattice_5,axiom,
% 3.39/1.81 ! [A7: $tType] : ( comple187826305attice @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Set_Oset___Orderings_Opreorder_6,axiom,
% 3.39/1.81 ! [A7: $tType] : ( preorder @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Set_Oset___Orderings_Oorder_7,axiom,
% 3.39/1.81 ! [A7: $tType] : ( order @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Set_Oset___Orderings_Oord_8,axiom,
% 3.39/1.81 ! [A7: $tType] : ( ord @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Set_Oset___Groups_Ominus_9,axiom,
% 3.39/1.81 ! [A7: $tType] : ( minus @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_HOL_Obool___Complete__Lattices_Ocomplete__lattice_10,axiom,
% 3.39/1.81 comple187826305attice @ $o @ ( type2 @ $o ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_HOL_Obool___Orderings_Opreorder_11,axiom,
% 3.39/1.81 preorder @ $o @ ( type2 @ $o ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_HOL_Obool___Orderings_Olinorder_12,axiom,
% 3.39/1.81 linorder @ $o @ ( type2 @ $o ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_HOL_Obool___Orderings_Oorder_13,axiom,
% 3.39/1.81 order @ $o @ ( type2 @ $o ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_HOL_Obool___Orderings_Oord_14,axiom,
% 3.39/1.81 ord @ $o @ ( type2 @ $o ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_HOL_Obool___Groups_Ominus_15,axiom,
% 3.39/1.81 minus @ $o @ ( type2 @ $o ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_16,axiom,
% 3.39/1.81 canoni770627133id_add @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Extended__Nat_Oenat___Complete__Lattices_Ocomplete__lattice_17,axiom,
% 3.39/1.81 comple187826305attice @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Extended__Nat_Oenat___Orderings_Opreorder_18,axiom,
% 3.39/1.81 preorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Extended__Nat_Oenat___Orderings_Olinorder_19,axiom,
% 3.39/1.81 linorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Extended__Nat_Oenat___Orderings_Oorder_20,axiom,
% 3.39/1.81 order @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Extended__Nat_Oenat___Orderings_Oord_21,axiom,
% 3.39/1.81 ord @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Extended__Nat_Oenat___Groups_Ominus_22,axiom,
% 3.39/1.81 minus @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.39/1.81
% 3.39/1.81 thf(tcon_Extended__Nat_Oenat___Groups_Ozero_23,axiom,
% 3.39/1.81 zero @ extended_enat @ ( type2 @ extended_enat ) ).
% 3.39/1.81
% 3.39/1.81 thf(help_If_3_1_T,axiom,
% 3.39/1.81 ! [P: $o] :
% 3.39/1.81 ( ( P = $true )
% 3.39/1.81 | ( P = $false ) ) ).
% 3.39/1.81
% 3.39/1.81 thf(help_If_2_1_T,axiom,
% 3.39/1.81 ! [A: $tType,X: A,Y: A] :
% 3.39/1.81 ( ( if @ A @ $false @ X @ Y )
% 3.39/1.81 = Y ) ).
% 3.39/1.81
% 3.39/1.81 thf(help_If_1_1_T,axiom,
% 3.39/1.81 ! [A: $tType,X: A,Y: A] :
% 3.39/1.81 ( ( if @ A @ $true @ X @ Y )
% 3.39/1.81 = X ) ).
% 3.39/1.81
% 3.39/1.81 thf(conj_0,conjecture,
% 3.39/1.81 coindu1696667936prefix @ a @ ( coindu1802687541_ltake @ a @ n @ xs ) @ ( coindu1802687541_ltake @ a @ m @ xs ) ).
% 3.39/1.81 ------------------------
% 3.39/1.84 % (22079)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21964 for (2999ds/183Mi)
% 3.39/1.84 % (22084)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_21964 for (2999ds/275Mi)
% 3.39/1.84 % (22082)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21964 for (2999ds/2Mi)
% 3.39/1.84 % (22080)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_21964 for (2999ds/4Mi)
% 3.39/1.84 % (22081)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_21964 for (2999ds/27Mi)
% 3.39/1.84 % (22083)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_21964 for (2999ds/2Mi)
% 3.39/1.84 % (22085)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21964 for (2999ds/18Mi)
% 3.39/1.84 % (22082)Instruction limit reached!
% 3.39/1.84 % (22082)------------------------------
% 3.39/1.84 % (22082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.84 % (22082)Termination reason: Unknown
% 3.39/1.84 % (22083)Instruction limit reached!
% 3.39/1.84 % (22083)------------------------------
% 3.39/1.84 % (22083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.84 % (22082)Termination phase: shuffling
% 3.39/1.84
% 3.39/1.84 % (22082)Memory used [KB]: 1279
% 3.39/1.84 % (22082)Time elapsed: 0.003 s
% 3.39/1.84 % (22082)Instructions burned: 2 (million)
% 3.39/1.84 % (22082)------------------------------
% 3.39/1.84 % (22082)------------------------------
% 3.39/1.84 % (22083)Termination reason: Unknown
% 3.39/1.84 % (22083)Termination phase: shuffling
% 3.39/1.84
% 3.39/1.84 % (22083)Memory used [KB]: 1279
% 3.39/1.84 % (22083)Time elapsed: 0.003 s
% 3.39/1.84 % (22083)Instructions burned: 3 (million)
% 3.39/1.84 % (22083)------------------------------
% 3.39/1.84 % (22083)------------------------------
% 3.39/1.84 % (22080)Instruction limit reached!
% 3.39/1.84 % (22080)------------------------------
% 3.39/1.84 % (22080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.84 % (22080)Termination reason: Unknown
% 3.39/1.84 % (22080)Termination phase: shuffling
% 3.39/1.84
% 3.39/1.84 % (22080)Memory used [KB]: 1407
% 3.39/1.84 % (22080)Time elapsed: 0.004 s
% 3.39/1.84 % (22080)Instructions burned: 4 (million)
% 3.39/1.84 % (22080)------------------------------
% 3.39/1.84 % (22080)------------------------------
% 3.39/1.85 % (22085)Instruction limit reached!
% 3.39/1.85 % (22085)------------------------------
% 3.39/1.85 % (22085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.85 % (22085)Termination reason: Unknown
% 3.39/1.85 % (22085)Termination phase: shuffling
% 3.39/1.85
% 3.39/1.85 % (22085)Memory used [KB]: 1663
% 3.39/1.85 % (22085)Time elapsed: 0.011 s
% 3.39/1.85 % (22085)Instructions burned: 18 (million)
% 3.39/1.85 % (22085)------------------------------
% 3.39/1.85 % (22085)------------------------------
% 3.39/1.85 % (22081)Instruction limit reached!
% 3.39/1.85 % (22081)------------------------------
% 3.39/1.85 % (22081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.85 % (22081)Termination reason: Unknown
% 3.39/1.85 % (22081)Termination phase: Property scanning
% 3.39/1.85
% 3.39/1.85 % (22081)Memory used [KB]: 1663
% 3.39/1.85 % (22081)Time elapsed: 0.016 s
% 3.39/1.85 % (22081)Instructions burned: 29 (million)
% 3.39/1.85 % (22081)------------------------------
% 3.39/1.85 % (22081)------------------------------
% 3.39/1.86 % (22086)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21964 for (2999ds/3Mi)
% 3.39/1.86 % (22087)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_21964 for (2999ds/37Mi)
% 3.39/1.86 % (22088)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_21964 for (2999ds/15Mi)
% 3.39/1.86 % (22086)Instruction limit reached!
% 3.39/1.86 % (22086)------------------------------
% 3.39/1.86 % (22086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.86 % (22086)Termination reason: Unknown
% 3.39/1.86 % (22086)Termination phase: shuffling
% 3.39/1.86
% 3.39/1.86 % (22086)Memory used [KB]: 1407
% 3.39/1.86 % (22086)Time elapsed: 0.003 s
% 3.39/1.86 % (22086)Instructions burned: 3 (million)
% 3.39/1.86 % (22086)------------------------------
% 3.39/1.86 % (22086)------------------------------
% 3.39/1.87 % (22088)Instruction limit reached!
% 3.39/1.87 % (22088)------------------------------
% 3.39/1.87 % (22088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.87 % (22088)Termination reason: Unknown
% 3.39/1.87 % (22088)Termination phase: shuffling
% 3.39/1.87
% 3.39/1.87 % (22088)Memory used [KB]: 1663
% 3.39/1.87 % (22088)Time elapsed: 0.009 s
% 3.39/1.87 % (22088)Instructions burned: 15 (million)
% 3.39/1.87 % (22088)------------------------------
% 3.39/1.87 % (22088)------------------------------
% 3.39/1.87 % (22089)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_21964 for (2999ds/3Mi)
% 3.39/1.87 % (22089)Instruction limit reached!
% 3.39/1.87 % (22089)------------------------------
% 3.39/1.87 % (22089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.87 % (22089)Termination reason: Unknown
% 3.39/1.87 % (22089)Termination phase: shuffling
% 3.39/1.87
% 3.39/1.87 % (22089)Memory used [KB]: 1407
% 3.39/1.87 % (22089)Time elapsed: 0.003 s
% 3.39/1.87 % (22089)Instructions burned: 3 (million)
% 3.39/1.87 % (22089)------------------------------
% 3.39/1.87 % (22089)------------------------------
% 3.39/1.87 % (22090)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_21964 for (2999ds/1041Mi)
% 3.39/1.88 % (22091)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_21964 for (2999ds/7Mi)
% 3.39/1.88 % (22087)Instruction limit reached!
% 3.39/1.88 % (22087)------------------------------
% 3.39/1.88 % (22087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.88 % (22087)Termination reason: Unknown
% 3.39/1.88 % (22087)Termination phase: Property scanning
% 3.39/1.88
% 3.39/1.88 % (22087)Memory used [KB]: 2046
% 3.39/1.88 % (22087)Time elapsed: 0.019 s
% 3.39/1.88 % (22087)Instructions burned: 38 (million)
% 3.39/1.88 % (22087)------------------------------
% 3.39/1.88 % (22087)------------------------------
% 3.39/1.88 % (22091)Instruction limit reached!
% 3.39/1.88 % (22091)------------------------------
% 3.39/1.88 % (22091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.88 % (22091)Termination reason: Unknown
% 3.39/1.88 % (22091)Termination phase: shuffling
% 3.39/1.88
% 3.39/1.88 % (22091)Memory used [KB]: 1407
% 3.39/1.88 % (22091)Time elapsed: 0.005 s
% 3.39/1.88 % (22091)Instructions burned: 7 (million)
% 3.39/1.88 % (22091)------------------------------
% 3.39/1.88 % (22091)------------------------------
% 3.39/1.88 % (22092)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_21964 for (2999ds/16Mi)
% 3.39/1.88 % (22093)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_21964 for (2999ds/3Mi)
% 3.39/1.89 % (22093)Instruction limit reached!
% 3.39/1.89 % (22093)------------------------------
% 3.39/1.89 % (22093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.89 % (22093)Termination reason: Unknown
% 3.39/1.89 % (22093)Termination phase: shuffling
% 3.39/1.89
% 3.39/1.89 % (22093)Memory used [KB]: 1407
% 3.39/1.89 % (22093)Time elapsed: 0.003 s
% 3.39/1.89 % (22093)Instructions burned: 3 (million)
% 3.39/1.89 % (22093)------------------------------
% 3.39/1.89 % (22093)------------------------------
% 3.39/1.89 % (22092)Instruction limit reached!
% 3.39/1.89 % (22092)------------------------------
% 3.39/1.89 % (22092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.89 % (22092)Termination reason: Unknown
% 3.39/1.89 % (22092)Termination phase: shuffling
% 3.39/1.89
% 3.39/1.89 % (22092)Memory used [KB]: 1663
% 3.39/1.89 % (22092)Time elapsed: 0.010 s
% 3.39/1.89 % (22092)Instructions burned: 17 (million)
% 3.39/1.89 % (22092)------------------------------
% 3.39/1.89 % (22092)------------------------------
% 3.39/1.89 % (22094)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_21964 for (2999ds/3Mi)
% 3.39/1.89 % (22094)Instruction limit reached!
% 3.39/1.89 % (22094)------------------------------
% 3.39/1.89 % (22094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.89 % (22094)Termination reason: Unknown
% 3.39/1.89 % (22094)Termination phase: shuffling
% 3.39/1.89
% 3.39/1.89 % (22094)Memory used [KB]: 1407
% 3.39/1.89 % (22094)Time elapsed: 0.003 s
% 3.39/1.89 % (22094)Instructions burned: 3 (million)
% 3.39/1.89 % (22094)------------------------------
% 3.39/1.89 % (22094)------------------------------
% 3.39/1.90 % (22095)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_21964 for (2999ds/7Mi)
% 3.43/1.90 % (22095)Instruction limit reached!
% 3.43/1.90 % (22095)------------------------------
% 3.43/1.90 % (22095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.43/1.90 % (22095)Termination reason: Unknown
% 3.43/1.90 % (22095)Termination phase: shuffling
% 3.43/1.90
% 3.43/1.90 % (22095)Memory used [KB]: 1407
% 3.43/1.90 % (22095)Time elapsed: 0.005 s
% 3.43/1.90 % (22095)Instructions burned: 7 (million)
% 3.43/1.90 % (22095)------------------------------
% 3.43/1.90 % (22095)------------------------------
% 3.43/1.90 % (22096)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_21964 for (2999ds/3Mi)
% 3.43/1.90 % (22096)Instruction limit reached!
% 3.43/1.90 % (22096)------------------------------
% 3.43/1.90 % (22096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.43/1.90 % (22096)Termination reason: Unknown
% 3.43/1.90 % (22096)Termination phase: shuffling
% 3.43/1.90
% 3.43/1.90 % (22096)Memory used [KB]: 1407
% 3.43/1.90 % (22096)Time elapsed: 0.003 s
% 3.43/1.90 % (22096)Instructions burned: 3 (million)
% 3.43/1.90 % (22096)------------------------------
% 3.43/1.90 % (22096)------------------------------
% 3.43/1.91 % (22097)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_21964 for (2999ds/4Mi)
% 3.43/1.91 % (22098)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_21964 for (2999ds/18Mi)
% 3.43/1.91 % (22097)Instruction limit reached!
% 3.43/1.91 % (22097)------------------------------
% 3.43/1.91 % (22097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.43/1.91 % (22097)Termination reason: Unknown
% 3.43/1.91 % (22097)Termination phase: shuffling
% 3.43/1.91
% 3.43/1.91 % (22097)Memory used [KB]: 1407
% 3.43/1.91 % (22097)Time elapsed: 0.004 s
% 3.43/1.91 % (22097)Instructions burned: 5 (million)
% 3.43/1.91 % (22097)------------------------------
% 3.43/1.91 % (22097)------------------------------
% 3.43/1.91 % (22099)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_21964 for (2999ds/710Mi)
% 3.43/1.92 % (22098)Instruction limit reached!
% 3.43/1.92 % (22098)------------------------------
% 3.43/1.92 % (22098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.43/1.92 % (22098)Termination reason: Unknown
% 3.43/1.92 % (22098)Termination phase: shuffling
% 3.43/1.92
% 3.43/1.92 % (22098)Memory used [KB]: 1663
% 3.43/1.92 % (22098)Time elapsed: 0.011 s
% 3.43/1.92 % (22098)Instructions burned: 18 (million)
% 3.43/1.92 % (22098)------------------------------
% 3.43/1.92 % (22098)------------------------------
% 3.43/1.92 % (22100)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21964 for (2999ds/6Mi)
% 3.43/1.92 % (22100)Instruction limit reached!
% 3.43/1.92 % (22100)------------------------------
% 3.43/1.92 % (22100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.43/1.92 % (22100)Termination reason: Unknown
% 3.43/1.92 % (22100)Termination phase: shuffling
% 3.43/1.92
% 3.43/1.92 % (22100)Memory used [KB]: 1407
% 3.43/1.92 % (22100)Time elapsed: 0.005 s
% 3.43/1.92 % (22100)Instructions burned: 7 (million)
% 3.43/1.92 % (22100)------------------------------
% 3.43/1.92 % (22100)------------------------------
% 3.43/1.93 % (22101)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_21964 for (2999ds/902Mi)
% 3.43/1.93 % (22079)Instruction limit reached!
% 3.43/1.93 % (22079)------------------------------
% 3.43/1.93 % (22079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.43/1.93 % (22079)Termination reason: Unknown
% 3.43/1.93 % (22079)Termination phase: Saturation
% 3.43/1.93
% 3.43/1.93 % (22079)Memory used [KB]: 7164
% 3.43/1.93 % (22079)Time elapsed: 0.090 s
% 3.43/1.93 % (22079)Instructions burned: 184 (million)
% 3.43/1.93 % (22079)------------------------------
% 3.43/1.93 % (22079)------------------------------
% 3.43/1.93 % (22102)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_21964 for (2998ds/21Mi)
% 3.43/1.94 % (22103)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_21964 for (2998ds/5Mi)
% 3.43/1.94 % (22103)Instruction limit reached!
% 3.43/1.94 % (22103)------------------------------
% 3.43/1.94 % (22103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.43/1.94 % (22103)Termination reason: Unknown
% 3.43/1.94 % (22103)Termination phase: shuffling
% 3.43/1.94
% 3.43/1.94 % (22103)Memory used [KB]: 1407
% 3.43/1.94 % (22103)Time elapsed: 0.004 s
% 3.43/1.94 % (22103)Instructions burned: 5 (million)
% 3.43/1.94 % (22103)------------------------------
% 3.43/1.94 % (22103)------------------------------
% 3.43/1.94 % (22102)Instruction limit reached!
% 3.43/1.94 % (22102)------------------------------
% 3.43/1.94 % (22102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.43/1.94 % (22102)Termination reason: Unknown
% 3.43/1.94 % (22102)Termination phase: shuffling
% 3.43/1.94
% 3.43/1.94 % (22102)Memory used [KB]: 1791
% 3.43/1.94 % (22102)Time elapsed: 0.012 s
% 3.43/1.94 % (22102)Instructions burned: 21 (million)
% 3.43/1.94 % (22102)------------------------------
% 3.43/1.94 % (22102)------------------------------
% 3.43/1.95 % (22104)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_21964 for (2998ds/6Mi)
% 3.43/1.95 % (22104)Instruction limit reached!
% 3.43/1.95 % (22104)------------------------------
% 3.43/1.95 % (22104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.43/1.95 % (22104)Termination reason: Unknown
% 3.43/1.95 % (22104)Termination phase: shuffling
% 3.43/1.95
% 3.43/1.95 % (22104)Memory used [KB]: 1407
% 3.43/1.95 % (22104)Time elapsed: 0.005 s
% 3.43/1.95 % (22104)Instructions burned: 7 (million)
% 3.43/1.95 % (22104)------------------------------
% 3.43/1.95 % (22104)------------------------------
% 3.43/1.96 % (22105)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_21964 for (2998ds/377Mi)
% 3.43/1.96 % (22106)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_21964 for (2998ds/779Mi)
% 3.43/1.96 % (22107)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_21964 for (2998ds/19Mi)
% 3.43/1.97 % (22107)Instruction limit reached!
% 3.43/1.97 % (22107)------------------------------
% 3.43/1.97 % (22107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.43/1.97 % (22107)Termination reason: Unknown
% 3.43/1.97 % (22107)Termination phase: shuffling
% 3.43/1.97
% 3.43/1.97 % (22107)Memory used [KB]: 1663
% 3.43/1.97 % (22107)Time elapsed: 0.010 s
% 3.43/1.97 % (22107)Instructions burned: 19 (million)
% 3.43/1.97 % (22107)------------------------------
% 3.43/1.97 % (22107)------------------------------
% 3.43/1.98 % (22084)Instruction limit reached!
% 3.43/1.98 % (22084)------------------------------
% 3.43/1.98 % (22084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.43/1.98 % (22084)Termination reason: Unknown
% 3.43/1.98 % (22084)Termination phase: Saturation
% 3.43/1.98
% 3.43/1.98 % (22084)Memory used [KB]: 6780
% 3.43/1.98 % (22084)Time elapsed: 0.136 s
% 3.43/1.98 % (22084)Instructions burned: 275 (million)
% 3.43/1.98 % (22084)------------------------------
% 3.43/1.98 % (22084)------------------------------
% 3.43/1.99 % (22108)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_21964 for (2998ds/879Mi)
% 3.43/1.99 % (22109)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_21964 for (2998ds/17Mi)
% 3.43/2.00 % (22109)Instruction limit reached!
% 3.43/2.00 % (22109)------------------------------
% 3.43/2.00 % (22109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.43/2.00 % (22109)Termination reason: Unknown
% 3.43/2.00 % (22109)Termination phase: shuffling
% 3.43/2.00
% 3.43/2.00 % (22109)Memory used [KB]: 1663
% 3.43/2.00 % (22109)Time elapsed: 0.010 s
% 3.43/2.00 % (22109)Instructions burned: 17 (million)
% 3.43/2.00 % (22109)------------------------------
% 3.43/2.00 % (22109)------------------------------
% 3.43/2.02 % (22110)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_21964 for (2998ds/3Mi)
% 3.43/2.02 % (22110)Instruction limit reached!
% 3.43/2.02 % (22110)------------------------------
% 3.43/2.02 % (22110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.43/2.02 % (22110)Termination reason: Unknown
% 3.43/2.02 % (22110)Termination phase: shuffling
% 3.43/2.02
% 3.43/2.02 % (22110)Memory used [KB]: 1407
% 3.43/2.02 % (22110)Time elapsed: 0.004 s
% 3.43/2.02 % (22110)Instructions burned: 4 (million)
% 3.43/2.02 % (22110)------------------------------
% 3.43/2.02 % (22110)------------------------------
% 4.77/2.04 % (22111)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_21964 for (2998ds/30Mi)
% 4.77/2.05 % (22111)Instruction limit reached!
% 4.77/2.05 % (22111)------------------------------
% 4.77/2.05 % (22111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.05 % (22111)Termination reason: Unknown
% 4.77/2.05 % (22111)Termination phase: Property scanning
% 4.77/2.05
% 4.77/2.05 % (22111)Memory used [KB]: 1791
% 4.77/2.05 % (22111)Time elapsed: 0.017 s
% 4.77/2.05 % (22111)Instructions burned: 30 (million)
% 4.77/2.05 % (22111)------------------------------
% 4.77/2.05 % (22111)------------------------------
% 4.77/2.07 % (22112)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_21964 for (2997ds/127Mi)
% 5.42/2.13 % (22112)Instruction limit reached!
% 5.42/2.13 % (22112)------------------------------
% 5.42/2.13 % (22112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.13 % (22112)Termination reason: Unknown
% 5.42/2.13 % (22112)Termination phase: Saturation
% 5.42/2.13
% 5.42/2.13 % (22112)Memory used [KB]: 6780
% 5.42/2.13 % (22112)Time elapsed: 0.086 s
% 5.42/2.13 % (22112)Instructions burned: 127 (million)
% 5.42/2.13 % (22112)------------------------------
% 5.42/2.13 % (22112)------------------------------
% 5.42/2.15 % (22113)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_21964 for (2996ds/100Mi)
% 5.42/2.15 % (22105)Instruction limit reached!
% 5.42/2.15 % (22105)------------------------------
% 5.42/2.15 % (22105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.15 % (22105)Termination reason: Unknown
% 5.42/2.15 % (22105)Termination phase: Saturation
% 5.42/2.15
% 5.42/2.15 % (22105)Memory used [KB]: 7803
% 5.42/2.15 % (22105)Time elapsed: 0.193 s
% 5.42/2.15 % (22105)Instructions burned: 378 (million)
% 5.42/2.15 % (22105)------------------------------
% 5.42/2.15 % (22105)------------------------------
% 5.42/2.17 % (22114)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_21964 for (2996ds/3Mi)
% 5.42/2.17 % (22114)Instruction limit reached!
% 5.42/2.17 % (22114)------------------------------
% 5.42/2.17 % (22114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.17 % (22114)Termination reason: Unknown
% 5.42/2.17 % (22114)Termination phase: shuffling
% 5.42/2.17
% 5.42/2.17 % (22114)Memory used [KB]: 1407
% 5.42/2.17 % (22114)Time elapsed: 0.003 s
% 5.42/2.17 % (22114)Instructions burned: 3 (million)
% 5.42/2.17 % (22114)------------------------------
% 5.42/2.17 % (22114)------------------------------
% 5.42/2.18 % (22115)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_21964 for (2996ds/20Mi)
% 5.42/2.19 % (22113)Instruction limit reached!
% 5.42/2.19 % (22113)------------------------------
% 5.42/2.19 % (22113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.19 % (22113)Termination reason: Unknown
% 5.42/2.19 % (22113)Termination phase: Saturation
% 5.42/2.19
% 5.42/2.19 % (22113)Memory used [KB]: 6780
% 5.42/2.19 % (22113)Time elapsed: 0.048 s
% 5.42/2.19 % (22113)Instructions burned: 101 (million)
% 5.42/2.19 % (22113)------------------------------
% 5.42/2.19 % (22113)------------------------------
% 5.42/2.19 % (22115)Instruction limit reached!
% 5.42/2.19 % (22115)------------------------------
% 5.42/2.19 % (22115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.42/2.19 % (22115)Termination reason: Unknown
% 5.42/2.19 % (22115)Termination phase: Property scanning
% 5.42/2.19
% 5.42/2.19 % (22115)Memory used [KB]: 1663
% 5.42/2.19 % (22115)Time elapsed: 0.012 s
% 5.42/2.19 % (22115)Instructions burned: 20 (million)
% 5.42/2.19 % (22115)------------------------------
% 5.42/2.19 % (22115)------------------------------
% 5.97/2.21 % (22116)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_21964 for (2996ds/86Mi)
% 5.97/2.21 % (22117)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_21964 for (2996ds/107Mi)
% 5.97/2.25 % (22116)Instruction limit reached!
% 5.97/2.25 % (22116)------------------------------
% 5.97/2.25 % (22116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.25 % (22116)Termination reason: Unknown
% 5.97/2.25 % (22116)Termination phase: Saturation
% 5.97/2.25
% 5.97/2.25 % (22116)Memory used [KB]: 6652
% 5.97/2.25 % (22116)Time elapsed: 0.043 s
% 5.97/2.25 % (22116)Instructions burned: 87 (million)
% 5.97/2.25 % (22116)------------------------------
% 5.97/2.25 % (22116)------------------------------
% 5.97/2.26 % (22117)Instruction limit reached!
% 5.97/2.26 % (22117)------------------------------
% 5.97/2.26 % (22117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.26 % (22117)Termination reason: Unknown
% 5.97/2.26 % (22117)Termination phase: Saturation
% 5.97/2.26
% 5.97/2.26 % (22117)Memory used [KB]: 6780
% 5.97/2.26 % (22117)Time elapsed: 0.053 s
% 5.97/2.26 % (22117)Instructions burned: 107 (million)
% 5.97/2.26 % (22117)------------------------------
% 5.97/2.26 % (22117)------------------------------
% 5.97/2.26 % (22099)Instruction limit reached!
% 5.97/2.26 % (22099)------------------------------
% 5.97/2.26 % (22099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.26 % (22099)Termination reason: Unknown
% 5.97/2.26 % (22099)Termination phase: Saturation
% 5.97/2.26
% 5.97/2.26 % (22099)Memory used [KB]: 7291
% 5.97/2.26 % (22099)Time elapsed: 0.350 s
% 5.97/2.26 % (22099)Instructions burned: 710 (million)
% 5.97/2.26 % (22099)------------------------------
% 5.97/2.26 % (22099)------------------------------
% 5.97/2.27 % (22118)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_21964 for (2995ds/39Mi)
% 5.97/2.28 % (22119)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_21964 for (2995ds/448Mi)
% 5.97/2.28 % (22120)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_21964 for (2995ds/46Mi)
% 5.97/2.28 % (22118)Instruction limit reached!
% 5.97/2.28 % (22118)------------------------------
% 5.97/2.28 % (22118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.28 % (22118)Termination reason: Unknown
% 5.97/2.28 % (22118)Termination phase: Property scanning
% 5.97/2.28
% 5.97/2.28 % (22118)Memory used [KB]: 2046
% 5.97/2.28 % (22118)Time elapsed: 0.020 s
% 5.97/2.28 % (22118)Instructions burned: 39 (million)
% 5.97/2.28 % (22118)------------------------------
% 5.97/2.28 % (22118)------------------------------
% 6.61/2.30 % (22121)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_21964 for (2995ds/98Mi)
% 6.61/2.30 % (22120)Instruction limit reached!
% 6.61/2.30 % (22120)------------------------------
% 6.61/2.30 % (22120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.30 % (22120)Termination reason: Unknown
% 6.61/2.30 % (22120)Termination phase: Preprocessing 3
% 6.61/2.30
% 6.61/2.30 % (22120)Memory used [KB]: 1918
% 6.61/2.30 % (22120)Time elapsed: 0.024 s
% 6.61/2.30 % (22120)Instructions burned: 46 (million)
% 6.61/2.30 % (22120)------------------------------
% 6.61/2.30 % (22120)------------------------------
% 6.61/2.32 % (22122)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_21964 for (2995ds/507Mi)
% 6.61/2.34 % (22121)Instruction limit reached!
% 6.61/2.34 % (22121)------------------------------
% 6.61/2.34 % (22121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.35 % (22121)Termination reason: Unknown
% 6.61/2.35 % (22121)Termination phase: Property scanning
% 6.61/2.35 % (22106)Instruction limit reached!
% 6.61/2.35 % (22106)------------------------------
% 6.61/2.35 % (22106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.35 % (22106)Termination reason: Unknown
% 6.61/2.35 % (22106)Termination phase: Saturation
% 6.61/2.35
% 6.61/2.35 % (22106)Memory used [KB]: 8315
% 6.61/2.35 % (22106)Time elapsed: 0.386 s
% 6.61/2.35 % (22106)Instructions burned: 779 (million)
% 6.61/2.35 % (22106)------------------------------
% 6.61/2.35 % (22106)------------------------------
% 6.61/2.35
% 6.61/2.35 % (22121)Memory used [KB]: 2302
% 6.61/2.35 % (22121)Time elapsed: 0.046 s
% 6.61/2.35 % (22121)Instructions burned: 98 (million)
% 6.61/2.35 % (22121)------------------------------
% 6.61/2.35 % (22121)------------------------------
% 6.61/2.36 % (22123)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_21964 for (2994ds/149Mi)
% 6.61/2.36 % (22124)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_21964 for (2994ds/39Mi)
% 6.61/2.36 % (22101)Instruction limit reached!
% 6.61/2.36 % (22101)------------------------------
% 6.61/2.36 % (22101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.36 % (22101)Termination reason: Unknown
% 6.61/2.36 % (22101)Termination phase: Saturation
% 6.61/2.36
% 6.61/2.36 % (22101)Memory used [KB]: 8571
% 6.61/2.36 % (22101)Time elapsed: 0.438 s
% 6.61/2.36 % (22101)Instructions burned: 903 (million)
% 6.61/2.36 % (22101)------------------------------
% 6.61/2.36 % (22101)------------------------------
% 6.61/2.38 % (22125)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_21964 for (2994ds/6Mi)
% 6.61/2.38 % (22124)Instruction limit reached!
% 6.61/2.38 % (22124)------------------------------
% 6.61/2.38 % (22124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.38 % (22124)Termination reason: Unknown
% 6.61/2.38 % (22124)Termination phase: Preprocessing 3
% 6.61/2.38
% 6.61/2.38 % (22124)Memory used [KB]: 2046
% 6.61/2.38 % (22124)Time elapsed: 0.021 s
% 6.61/2.38 % (22124)Instructions burned: 39 (million)
% 6.61/2.38 % (22124)------------------------------
% 6.61/2.38 % (22124)------------------------------
% 6.61/2.38 % (22125)Instruction limit reached!
% 6.61/2.38 % (22125)------------------------------
% 6.61/2.38 % (22125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.38 % (22125)Termination reason: Unknown
% 6.61/2.38 % (22125)Termination phase: shuffling
% 6.61/2.38
% 6.61/2.38 % (22125)Memory used [KB]: 1407
% 6.61/2.38 % (22125)Time elapsed: 0.005 s
% 6.61/2.38 % (22125)Instructions burned: 7 (million)
% 6.61/2.38 % (22125)------------------------------
% 6.61/2.38 % (22125)------------------------------
% 6.61/2.40 % (22090)Instruction limit reached!
% 6.61/2.40 % (22090)------------------------------
% 6.61/2.40 % (22090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.61/2.40 % (22090)Termination reason: Unknown
% 6.61/2.40 % (22090)Termination phase: Saturation
% 6.61/2.40
% 6.61/2.40 % (22090)Memory used [KB]: 10234
% 6.61/2.40 % (22090)Time elapsed: 0.526 s
% 6.61/2.40 % (22090)Instructions burned: 1042 (million)
% 6.61/2.40 % (22090)------------------------------
% 6.61/2.40 % (22090)------------------------------
% 7.13/2.40 % (22126)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_21964 for (2994ds/1087Mi)
% 7.13/2.40 % (22127)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_21964 for (2994ds/47Mi)
% 7.13/2.41 % (22128)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_21964 for (2994ds/44Mi)
% 7.13/2.42 % (22108)Instruction limit reached!
% 7.13/2.42 % (22108)------------------------------
% 7.13/2.42 % (22108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.13/2.42 % (22108)Termination reason: Unknown
% 7.13/2.42 % (22108)Termination phase: Saturation
% 7.13/2.42
% 7.13/2.42 % (22108)Memory used [KB]: 7547
% 7.13/2.42 % (22108)Time elapsed: 0.433 s
% 7.13/2.42 % (22108)Instructions burned: 880 (million)
% 7.13/2.42 % (22108)------------------------------
% 7.13/2.42 % (22108)------------------------------
% 7.13/2.42 % (22127)Instruction limit reached!
% 7.13/2.42 % (22127)------------------------------
% 7.13/2.42 % (22127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.13/2.42 % (22127)Termination reason: Unknown
% 7.13/2.42 % (22127)Termination phase: Property scanning
% 7.13/2.42
% 7.13/2.42 % (22127)Memory used [KB]: 2046
% 7.13/2.42 % (22127)Time elapsed: 0.025 s
% 7.13/2.42 % (22127)Instructions burned: 48 (million)
% 7.13/2.42 % (22127)------------------------------
% 7.13/2.42 % (22127)------------------------------
% 7.13/2.43 % (22128)Instruction limit reached!
% 7.13/2.43 % (22128)------------------------------
% 7.13/2.43 % (22128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.13/2.43 % (22128)Termination reason: Unknown
% 7.13/2.43 % (22128)Termination phase: Property scanning
% 7.13/2.43
% 7.13/2.43 % (22123)Instruction limit reached!
% 7.13/2.43 % (22123)------------------------------
% 7.13/2.43 % (22123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.13/2.43 % (22123)Termination reason: Unknown
% 7.13/2.43 % (22123)Termination phase: Saturation
% 7.13/2.43
% 7.13/2.43 % (22123)Memory used [KB]: 6908
% 7.13/2.43 % (22123)Time elapsed: 0.074 s
% 7.13/2.43 % (22123)Instructions burned: 150 (million)
% 7.13/2.43 % (22123)------------------------------
% 7.13/2.43 % (22123)------------------------------
% 7.13/2.43 % (22128)Memory used [KB]: 2046
% 7.13/2.43 % (22128)Time elapsed: 0.023 s
% 7.13/2.43 % (22128)Instructions burned: 45 (million)
% 7.13/2.43 % (22128)------------------------------
% 7.13/2.43 % (22128)------------------------------
% 7.13/2.44 % (22129)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_21964 for (2993ds/432Mi)
% 7.13/2.44 % (22130)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_21964 for (2993ds/62Mi)
% 7.13/2.45 % (22131)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_21964 for (2993ds/31Mi)
% 7.13/2.45 % (22132)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_21964 for (2993ds/96Mi)
% 7.13/2.47 % (22131)Instruction limit reached!
% 7.13/2.47 % (22131)------------------------------
% 7.13/2.47 % (22131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.13/2.47 % (22131)Termination reason: Unknown
% 7.13/2.47 % (22131)Termination phase: Property scanning
% 7.13/2.47
% 7.13/2.47 % (22131)Memory used [KB]: 1663
% 7.13/2.47 % (22131)Time elapsed: 0.017 s
% 7.13/2.47 % (22131)Instructions burned: 31 (million)
% 7.13/2.47 % (22131)------------------------------
% 7.13/2.47 % (22131)------------------------------
% 7.13/2.47 % (22130)Instruction limit reached!
% 7.13/2.47 % (22130)------------------------------
% 7.13/2.47 % (22130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.13/2.47 % (22130)Termination reason: Unknown
% 7.13/2.47 % (22130)Termination phase: Preprocessing 1
% 7.13/2.47
% 7.13/2.47 % (22130)Memory used [KB]: 2174
% 7.13/2.47 % (22130)Time elapsed: 0.030 s
% 7.13/2.47 % (22130)Instructions burned: 62 (million)
% 7.13/2.47 % (22130)------------------------------
% 7.13/2.47 % (22130)------------------------------
% 7.13/2.48 % (22133)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_21964 for (2993ds/453Mi)
% 7.13/2.48 % (22134)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_21964 for (2993ds/71Mi)
% 7.13/2.49 % (22119)Instruction limit reached!
% 7.13/2.49 % (22119)------------------------------
% 7.13/2.49 % (22119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.13/2.49 % (22119)Termination reason: Unknown
% 7.13/2.49 % (22119)Termination phase: Saturation
% 7.13/2.49
% 7.13/2.49 % (22119)Memory used [KB]: 7931
% 7.13/2.49 % (22119)Time elapsed: 0.216 s
% 7.13/2.49 % (22119)Instructions burned: 448 (million)
% 7.13/2.49 % (22119)------------------------------
% 7.13/2.49 % (22119)------------------------------
% 7.63/2.50 % (22132)Instruction limit reached!
% 7.63/2.50 % (22132)------------------------------
% 7.63/2.50 % (22132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.50 % (22132)Termination reason: Unknown
% 7.63/2.50 % (22132)Termination phase: Saturation
% 7.63/2.50
% 7.63/2.50 % (22132)Memory used [KB]: 6652
% 7.63/2.50 % (22132)Time elapsed: 0.048 s
% 7.63/2.50 % (22132)Instructions burned: 97 (million)
% 7.63/2.50 % (22132)------------------------------
% 7.63/2.50 % (22132)------------------------------
% 7.63/2.51 % (22135)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_21964 for (2993ds/83Mi)
% 7.63/2.51 % (22136)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_21964 for (2993ds/11Mi)
% 7.63/2.52 % (22134)Instruction limit reached!
% 7.63/2.52 % (22134)------------------------------
% 7.63/2.52 % (22134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.52 % (22134)Termination reason: Unknown
% 7.63/2.52 % (22134)Termination phase: Property scanning
% 7.63/2.52
% 7.63/2.52 % (22134)Memory used [KB]: 2174
% 7.63/2.52 % (22134)Time elapsed: 0.036 s
% 7.63/2.52 % (22134)Instructions burned: 72 (million)
% 7.63/2.52 % (22134)------------------------------
% 7.63/2.52 % (22134)------------------------------
% 7.63/2.52 % (22136)Instruction limit reached!
% 7.63/2.52 % (22136)------------------------------
% 7.63/2.52 % (22136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.52 % (22136)Termination reason: Unknown
% 7.63/2.52 % (22136)Termination phase: shuffling
% 7.63/2.52
% 7.63/2.52 % (22136)Memory used [KB]: 1535
% 7.63/2.52 % (22136)Time elapsed: 0.007 s
% 7.63/2.52 % (22136)Instructions burned: 12 (million)
% 7.63/2.52 % (22136)------------------------------
% 7.63/2.52 % (22136)------------------------------
% 7.63/2.53 % (22137)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_21964 for (2993ds/41Mi)
% 7.63/2.53 % (22138)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_21964 for (2993ds/6Mi)
% 7.63/2.54 % (22138)Instruction limit reached!
% 7.63/2.54 % (22138)------------------------------
% 7.63/2.54 % (22138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.54 % (22138)Termination reason: Unknown
% 7.63/2.54 % (22138)Termination phase: shuffling
% 7.63/2.54
% 7.63/2.54 % (22138)Memory used [KB]: 1407
% 7.63/2.54 % (22138)Time elapsed: 0.005 s
% 7.63/2.54 % (22138)Instructions burned: 7 (million)
% 7.63/2.54 % (22138)------------------------------
% 7.63/2.54 % (22138)------------------------------
% 7.63/2.55 % (22135)Instruction limit reached!
% 7.63/2.55 % (22135)------------------------------
% 7.63/2.55 % (22135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.55 % (22135)Termination reason: Unknown
% 7.63/2.55 % (22135)Termination phase: Saturation
% 7.63/2.55
% 7.63/2.55 % (22135)Memory used [KB]: 6524
% 7.63/2.55 % (22135)Time elapsed: 0.044 s
% 7.63/2.55 % (22135)Instructions burned: 84 (million)
% 7.63/2.55 % (22135)------------------------------
% 7.63/2.55 % (22135)------------------------------
% 7.63/2.55 % (22137)Instruction limit reached!
% 7.63/2.55 % (22137)------------------------------
% 7.63/2.55 % (22137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.55 % (22137)Termination reason: Unknown
% 7.63/2.55 % (22137)Termination phase: Property scanning
% 7.63/2.55
% 7.63/2.55 % (22137)Memory used [KB]: 2046
% 7.63/2.55 % (22137)Time elapsed: 0.021 s
% 7.63/2.55 % (22137)Instructions burned: 41 (million)
% 7.63/2.55 % (22137)------------------------------
% 7.63/2.55 % (22137)------------------------------
% 7.63/2.55 % (22139)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_21964 for (2992ds/150Mi)
% 7.63/2.57 % (22140)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_21964 for (2992ds/343Mi)
% 7.63/2.57 % (22141)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_21964 for (2992ds/109Mi)
% 7.63/2.57 % (22122)Instruction limit reached!
% 7.63/2.57 % (22122)------------------------------
% 7.63/2.57 % (22122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.63/2.57 % (22122)Termination reason: Unknown
% 7.63/2.57 % (22122)Termination phase: Saturation
% 7.63/2.57
% 7.63/2.57 % (22122)Memory used [KB]: 7931
% 7.63/2.57 % (22122)Time elapsed: 0.253 s
% 7.63/2.57 % (22122)Instructions burned: 507 (million)
% 7.63/2.57 % (22122)------------------------------
% 7.63/2.57 % (22122)------------------------------
% 7.63/2.59 % (22142)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_21964 for (2992ds/253Mi)
% 8.14/2.62 % (22141)Instruction limit reached!
% 8.14/2.62 % (22141)------------------------------
% 8.14/2.62 % (22141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.14/2.62 % (22141)Termination reason: Unknown
% 8.14/2.62 % (22141)Termination phase: Saturation
% 8.14/2.62
% 8.14/2.62 % (22141)Memory used [KB]: 6780
% 8.14/2.62 % (22141)Time elapsed: 0.054 s
% 8.14/2.62 % (22141)Instructions burned: 110 (million)
% 8.14/2.62 % (22141)------------------------------
% 8.14/2.62 % (22141)------------------------------
% 8.14/2.63 % (22139)Instruction limit reached!
% 8.14/2.63 % (22139)------------------------------
% 8.14/2.63 % (22139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.14/2.63 % (22139)Termination reason: Unknown
% 8.14/2.63 % (22139)Termination phase: Saturation
% 8.14/2.63
% 8.14/2.63 % (22139)Memory used [KB]: 7036
% 8.14/2.63 % (22139)Time elapsed: 0.075 s
% 8.14/2.63 % (22139)Instructions burned: 150 (million)
% 8.14/2.63 % (22139)------------------------------
% 8.14/2.63 % (22139)------------------------------
% 8.14/2.64 % (22143)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_21964 for (2992ds/140Mi)
% 8.14/2.64 % (22144)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_21964 for (2991ds/614Mi)
% 8.14/2.65 % (22129)Instruction limit reached!
% 8.14/2.65 % (22129)------------------------------
% 8.14/2.65 % (22129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.14/2.65 % (22129)Termination reason: Unknown
% 8.14/2.65 % (22129)Termination phase: Saturation
% 8.14/2.65
% 8.14/2.65 % (22129)Memory used [KB]: 3582
% 8.14/2.65 % (22129)Time elapsed: 0.218 s
% 8.14/2.65 % (22129)Instructions burned: 433 (million)
% 8.14/2.65 % (22129)------------------------------
% 8.14/2.65 % (22129)------------------------------
% 8.14/2.67 % (22145)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_21964 for (2991ds/202Mi)
% 8.53/2.70 % (22133)Instruction limit reached!
% 8.53/2.70 % (22133)------------------------------
% 8.53/2.70 % (22133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.70 % (22133)Termination reason: Unknown
% 8.53/2.70 % (22133)Termination phase: Saturation
% 8.53/2.70
% 8.53/2.70 % (22133)Memory used [KB]: 7803
% 8.53/2.70 % (22133)Time elapsed: 0.218 s
% 8.53/2.70 % (22133)Instructions burned: 454 (million)
% 8.53/2.70 % (22133)------------------------------
% 8.53/2.70 % (22133)------------------------------
% 8.53/2.71 % (22143)Instruction limit reached!
% 8.53/2.71 % (22143)------------------------------
% 8.53/2.71 % (22143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.71 % (22143)Termination reason: Unknown
% 8.53/2.71 % (22143)Termination phase: Saturation
% 8.53/2.71
% 8.53/2.71 % (22143)Memory used [KB]: 6652
% 8.53/2.71 % (22143)Time elapsed: 0.096 s
% 8.53/2.71 % (22143)Instructions burned: 140 (million)
% 8.53/2.71 % (22143)------------------------------
% 8.53/2.71 % (22143)------------------------------
% 8.53/2.71 % (22142)Instruction limit reached!
% 8.53/2.71 % (22142)------------------------------
% 8.53/2.71 % (22142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.71 % (22142)Termination reason: Unknown
% 8.53/2.71 % (22142)Termination phase: Saturation
% 8.53/2.71
% 8.53/2.71 % (22142)Memory used [KB]: 7164
% 8.53/2.71 % (22142)Time elapsed: 0.127 s
% 8.53/2.71 % (22142)Instructions burned: 253 (million)
% 8.53/2.71 % (22142)------------------------------
% 8.53/2.71 % (22142)------------------------------
% 8.53/2.71 % (22146)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_21964 for (2991ds/339Mi)
% 8.53/2.73 % (22147)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_21964 for (2990ds/283Mi)
% 8.53/2.73 % (22148)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_21964 for (2990ds/134Mi)
% 8.53/2.74 % (22140)Instruction limit reached!
% 8.53/2.74 % (22140)------------------------------
% 8.53/2.74 % (22140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.74 % (22140)Termination reason: Unknown
% 8.53/2.74 % (22140)Termination phase: Saturation
% 8.53/2.74
% 8.53/2.74 % (22140)Memory used [KB]: 7419
% 8.53/2.74 % (22140)Time elapsed: 0.175 s
% 8.53/2.74 % (22140)Instructions burned: 343 (million)
% 8.53/2.74 % (22140)------------------------------
% 8.53/2.74 % (22140)------------------------------
% 8.53/2.76 % (22149)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_21964 for (2990ds/298Mi)
% 8.53/2.77 % (22145)Instruction limit reached!
% 8.53/2.77 % (22145)------------------------------
% 8.53/2.77 % (22145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.77 % (22145)Termination reason: Unknown
% 8.53/2.77 % (22145)Termination phase: Saturation
% 8.53/2.77
% 8.53/2.77 % (22145)Memory used [KB]: 6780
% 8.53/2.77 % (22145)Time elapsed: 0.124 s
% 8.53/2.77 % (22145)Instructions burned: 202 (million)
% 8.53/2.77 % (22145)------------------------------
% 8.53/2.77 % (22145)------------------------------
% 8.53/2.79 % (22150)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_21964 for (2990ds/192Mi)
% 8.53/2.79 % (22148)Instruction limit reached!
% 8.53/2.79 % (22148)------------------------------
% 8.53/2.79 % (22148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.53/2.79 % (22148)Termination reason: Unknown
% 8.53/2.79 % (22148)Termination phase: Saturation
% 8.53/2.79
% 8.53/2.79 % (22148)Memory used [KB]: 6908
% 8.53/2.79 % (22148)Time elapsed: 0.067 s
% 8.53/2.79 % (22148)Instructions burned: 135 (million)
% 8.53/2.79 % (22148)------------------------------
% 8.53/2.79 % (22148)------------------------------
% 9.38/2.81 % (22151)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_21964 for (2990ds/258Mi)
% 9.38/2.87 % (22147)Instruction limit reached!
% 9.38/2.87 % (22147)------------------------------
% 9.38/2.87 % (22147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.38/2.87 % (22147)Termination reason: Unknown
% 9.38/2.87 % (22147)Termination phase: Saturation
% 9.38/2.87
% 9.38/2.87 % (22147)Memory used [KB]: 7547
% 9.38/2.87 % (22147)Time elapsed: 0.145 s
% 9.38/2.87 % (22147)Instructions burned: 283 (million)
% 9.38/2.87 % (22147)------------------------------
% 9.38/2.87 % (22147)------------------------------
% 9.38/2.88 % (22150)Instruction limit reached!
% 9.38/2.88 % (22150)------------------------------
% 9.38/2.88 % (22150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.38/2.88 % (22150)Termination reason: Unknown
% 9.38/2.88 % (22150)Termination phase: Saturation
% 9.38/2.88
% 9.38/2.88 % (22150)Memory used [KB]: 7803
% 9.38/2.88 % (22150)Time elapsed: 0.096 s
% 9.38/2.88 % (22150)Instructions burned: 192 (million)
% 9.38/2.88 % (22150)------------------------------
% 9.38/2.88 % (22150)------------------------------
% 9.38/2.89 % (22146)Instruction limit reached!
% 9.38/2.89 % (22146)------------------------------
% 9.38/2.89 % (22146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.38/2.89 % (22146)Termination reason: Unknown
% 9.38/2.89 % (22146)Termination phase: Saturation
% 9.38/2.89
% 9.38/2.89 % (22146)Memory used [KB]: 7419
% 9.38/2.89 % (22146)Time elapsed: 0.194 s
% 9.38/2.89 % (22146)Instructions burned: 339 (million)
% 9.38/2.89 % (22146)------------------------------
% 9.38/2.89 % (22146)------------------------------
% 9.38/2.89 % (22152)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_21964 for (2989ds/90Mi)
% 9.38/2.90 % (22149)Instruction limit reached!
% 9.38/2.90 % (22149)------------------------------
% 9.38/2.90 % (22149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.38/2.90 % (22149)Termination reason: Unknown
% 9.38/2.90 % (22149)Termination phase: Saturation
% 9.38/2.90
% 9.38/2.90 % (22149)Memory used [KB]: 7931
% 9.38/2.90 % (22149)Time elapsed: 0.141 s
% 9.38/2.90 % (22149)Instructions burned: 298 (million)
% 9.38/2.90 % (22149)------------------------------
% 9.38/2.90 % (22149)------------------------------
% 9.84/2.90 % (22157)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_21964 for (2989ds/231Mi)
% 9.84/2.90 % (22160)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_21964 for (2989ds/458Mi)
% 9.84/2.91 % (22172)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_21964 for (2989ds/31Mi)
% 9.84/2.93 % (22172)Instruction limit reached!
% 9.84/2.93 % (22172)------------------------------
% 9.84/2.93 % (22172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/2.93 % (22172)Termination reason: Unknown
% 9.84/2.93 % (22172)Termination phase: Property scanning
% 9.84/2.93
% 9.84/2.93 % (22172)Memory used [KB]: 1663
% 9.84/2.93 % (22172)Time elapsed: 0.017 s
% 9.84/2.93 % (22172)Instructions burned: 31 (million)
% 9.84/2.93 % (22172)------------------------------
% 9.84/2.93 % (22172)------------------------------
% 9.84/2.93 % (22152)Instruction limit reached!
% 9.84/2.93 % (22152)------------------------------
% 9.84/2.93 % (22152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/2.93 % (22152)Termination reason: Unknown
% 9.84/2.93 % (22152)Termination phase: Saturation
% 9.84/2.93
% 9.84/2.93 % (22152)Memory used [KB]: 6652
% 9.84/2.93 % (22152)Time elapsed: 0.045 s
% 9.84/2.93 % (22152)Instructions burned: 90 (million)
% 9.84/2.93 % (22152)------------------------------
% 9.84/2.93 % (22152)------------------------------
% 9.84/2.94 % (22151)Instruction limit reached!
% 9.84/2.94 % (22151)------------------------------
% 9.84/2.94 % (22151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/2.94 % (22151)Termination reason: Unknown
% 9.84/2.94 % (22151)Termination phase: Saturation
% 9.84/2.94
% 9.84/2.94 % (22151)Memory used [KB]: 7291
% 9.84/2.94 % (22151)Time elapsed: 0.130 s
% 9.84/2.94 % (22151)Instructions burned: 259 (million)
% 9.84/2.94 % (22151)------------------------------
% 9.84/2.94 % (22151)------------------------------
% 9.84/2.94 % (22126)Instruction limit reached!
% 9.84/2.94 % (22126)------------------------------
% 9.84/2.94 % (22126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/2.94 % (22126)Termination reason: Unknown
% 9.84/2.94 % (22126)Termination phase: Saturation
% 9.84/2.94
% 9.84/2.94 % (22126)Memory used [KB]: 7803
% 9.84/2.94 % (22126)Time elapsed: 0.546 s
% 9.84/2.94 % (22126)Instructions burned: 1087 (million)
% 9.84/2.94 % (22126)------------------------------
% 9.84/2.94 % (22126)------------------------------
% 9.84/2.94 % (22144)Instruction limit reached!
% 9.84/2.94 % (22144)------------------------------
% 9.84/2.94 % (22144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/2.94 % (22144)Termination reason: Unknown
% 9.84/2.94 % (22144)Termination phase: Saturation
% 9.84/2.94
% 9.84/2.94 % (22144)Memory used [KB]: 8059
% 9.84/2.94 % (22144)Time elapsed: 0.321 s
% 9.84/2.94 % (22144)Instructions burned: 615 (million)
% 9.84/2.94 % (22144)------------------------------
% 9.84/2.94 % (22144)------------------------------
% 9.84/2.94 % (22186)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_21964 for (2988ds/297Mi)
% 9.84/2.95 % (22187)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_21964 for (2988ds/987Mi)
% 9.84/2.95 % (22188)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_21964 for (2988ds/182Mi)
% 9.84/2.96 % (22189)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_21964 for (2988ds/182Mi)
% 9.84/2.96 % (22190)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_21964 for (2988ds/154Mi)
% 9.84/3.00 % (22157)Instruction limit reached!
% 9.84/3.00 % (22157)------------------------------
% 9.84/3.00 % (22157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.84/3.00 % (22157)Termination reason: Unknown
% 9.84/3.00 % (22157)Termination phase: Saturation
% 9.84/3.00
% 9.84/3.00 % (22157)Memory used [KB]: 6908
% 9.84/3.00 % (22157)Time elapsed: 0.106 s
% 9.84/3.00 % (22157)Instructions burned: 232 (million)
% 9.84/3.00 % (22157)------------------------------
% 9.84/3.00 % (22157)------------------------------
% 9.84/3.02 % (22191)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_21964 for (2988ds/79Mi)
% 11.75/3.03 % (22190)Instruction limit reached!
% 11.75/3.03 % (22190)------------------------------
% 11.75/3.03 % (22190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.75/3.03 % (22190)Termination reason: Unknown
% 11.75/3.03 % (22190)Termination phase: Saturation
% 11.75/3.03
% 11.75/3.03 % (22190)Memory used [KB]: 3070
% 11.75/3.03 % (22190)Time elapsed: 0.073 s
% 11.75/3.03 % (22190)Instructions burned: 155 (million)
% 11.75/3.03 % (22190)------------------------------
% 11.75/3.03 % (22190)------------------------------
% 11.75/3.04 % (22188)Instruction limit reached!
% 11.75/3.04 % (22188)------------------------------
% 11.75/3.04 % (22188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.75/3.04 % (22188)Termination reason: Unknown
% 11.75/3.04 % (22188)Termination phase: Saturation
% 11.75/3.04
% 11.75/3.04 % (22188)Memory used [KB]: 7164
% 11.75/3.04 % (22188)Time elapsed: 0.090 s
% 11.75/3.04 % (22188)Instructions burned: 183 (million)
% 11.75/3.04 % (22188)------------------------------
% 11.75/3.04 % (22188)------------------------------
% 11.75/3.05 % (22192)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_21964 for (2987ds/216Mi)
% 11.75/3.05 % (22189)Instruction limit reached!
% 11.75/3.05 % (22189)------------------------------
% 11.75/3.05 % (22189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.75/3.05 % (22189)Termination reason: Unknown
% 11.75/3.05 % (22189)Termination phase: Saturation
% 11.75/3.05
% 11.75/3.05 % (22189)Memory used [KB]: 7036
% 11.75/3.05 % (22189)Time elapsed: 0.093 s
% 11.75/3.05 % (22189)Instructions burned: 182 (million)
% 11.75/3.05 % (22189)------------------------------
% 11.75/3.05 % (22189)------------------------------
% 11.75/3.06 % (22191)Instruction limit reached!
% 11.75/3.06 % (22191)------------------------------
% 11.75/3.06 % (22191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.75/3.06 % (22191)Termination reason: Unknown
% 11.75/3.06 % (22191)Termination phase: Property scanning
% 11.75/3.06
% 11.75/3.06 % (22191)Memory used [KB]: 2174
% 11.75/3.06 % (22191)Time elapsed: 0.040 s
% 11.75/3.06 % (22191)Instructions burned: 79 (million)
% 11.75/3.06 % (22191)------------------------------
% 11.75/3.06 % (22191)------------------------------
% 11.75/3.06 % (22193)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_21964 for (2987ds/114Mi)
% 11.75/3.07 % (22194)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_21964 for (2987ds/922Mi)
% 11.75/3.07 % (22195)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_21964 for (2987ds/182Mi)
% 11.75/3.09 % (22186)Instruction limit reached!
% 11.75/3.09 % (22186)------------------------------
% 11.75/3.09 % (22186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.75/3.09 % (22186)Termination reason: Unknown
% 11.75/3.09 % (22186)Termination phase: Saturation
% 11.75/3.09
% 11.75/3.09 % (22186)Memory used [KB]: 7291
% 11.75/3.09 % (22186)Time elapsed: 0.145 s
% 11.75/3.09 % (22186)Instructions burned: 298 (million)
% 11.75/3.09 % (22186)------------------------------
% 11.75/3.09 % (22186)------------------------------
% 11.75/3.11 % (22160)Refutation not found, non-redundant clauses discarded% (22160)------------------------------
% 11.75/3.11 % (22160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.75/3.11 % (22160)Termination reason: Refutation not found, non-redundant clauses discarded
% 11.75/3.11
% 11.75/3.11 % (22160)Memory used [KB]: 7675
% 11.75/3.11 % (22160)Time elapsed: 0.209 s
% 11.75/3.11 % (22160)Instructions burned: 411 (million)
% 11.75/3.11 % (22160)------------------------------
% 11.75/3.11 % (22160)------------------------------
% 11.75/3.11 % (22196)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_21964 for (2987ds/164Mi)
% 11.75/3.11 % (22193)Instruction limit reached!
% 11.75/3.11 % (22193)------------------------------
% 11.75/3.11 % (22193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.75/3.11 % (22193)Termination reason: Unknown
% 11.75/3.11 % (22193)Termination phase: Saturation
% 11.75/3.11
% 11.75/3.11 % (22193)Memory used [KB]: 6780
% 11.75/3.11 % (22193)Time elapsed: 0.057 s
% 11.75/3.11 % (22193)Instructions burned: 115 (million)
% 11.75/3.11 % (22193)------------------------------
% 11.75/3.11 % (22193)------------------------------
% 11.75/3.13 % (22197)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_21964 for (2987ds/50Mi)
% 12.24/3.13 % (22198)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_21964 for (2986ds/368Mi)
% 12.24/3.15 % (22192)Instruction limit reached!
% 12.24/3.15 % (22192)------------------------------
% 12.24/3.15 % (22192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.24/3.15 % (22192)Termination reason: Unknown
% 12.24/3.15 % (22192)Termination phase: Saturation
% 12.24/3.15
% 12.24/3.15 % (22192)Memory used [KB]: 7419
% 12.24/3.15 % (22192)Time elapsed: 0.102 s
% 12.24/3.15 % (22192)Instructions burned: 216 (million)
% 12.24/3.15 % (22192)------------------------------
% 12.24/3.15 % (22192)------------------------------
% 12.24/3.15 % (22197)Instruction limit reached!
% 12.24/3.15 % (22197)------------------------------
% 12.24/3.15 % (22197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.24/3.15 % (22197)Termination reason: Unknown
% 12.24/3.15 % (22197)Termination phase: Property scanning
% 12.24/3.15
% 12.24/3.15 % (22197)Memory used [KB]: 2046
% 12.24/3.15 % (22197)Time elapsed: 0.025 s
% 12.24/3.15 % (22197)Instructions burned: 51 (million)
% 12.24/3.15 % (22197)------------------------------
% 12.24/3.15 % (22197)------------------------------
% 12.24/3.16 % (22195)Instruction limit reached!
% 12.24/3.16 % (22195)------------------------------
% 12.24/3.16 % (22195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.24/3.16 % (22195)Termination reason: Unknown
% 12.24/3.16 % (22195)Termination phase: Saturation
% 12.24/3.16
% 12.24/3.16 % (22195)Memory used [KB]: 7036
% 12.24/3.16 % (22195)Time elapsed: 0.086 s
% 12.24/3.16 % (22195)Instructions burned: 183 (million)
% 12.24/3.16 % (22195)------------------------------
% 12.24/3.16 % (22195)------------------------------
% 12.24/3.16 % (22199)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_21964 for (2986ds/1021Mi)
% 12.24/3.17 % (22200)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_21964 for (2986ds/267Mi)
% 12.24/3.18 % (22201)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_21964 for (2986ds/204Mi)
% 12.24/3.19 % (22196)Instruction limit reached!
% 12.24/3.19 % (22196)------------------------------
% 12.24/3.19 % (22196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.24/3.19 % (22196)Termination reason: Unknown
% 12.24/3.19 % (22196)Termination phase: Saturation
% 12.24/3.19
% 12.24/3.19 % (22196)Memory used [KB]: 2430
% 12.24/3.19 % (22196)Time elapsed: 0.080 s
% 12.24/3.19 % (22196)Instructions burned: 165 (million)
% 12.24/3.19 % (22196)------------------------------
% 12.24/3.19 % (22196)------------------------------
% 12.65/3.20 % (22202)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_21964 for (2986ds/26Mi)
% 12.65/3.22 % (22202)Instruction limit reached!
% 12.65/3.22 % (22202)------------------------------
% 12.65/3.22 % (22202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.65/3.22 % (22202)Termination reason: Unknown
% 12.65/3.22 % (22202)Termination phase: shuffling
% 12.65/3.22
% 12.65/3.22 % (22202)Memory used [KB]: 1791
% 12.65/3.22 % (22202)Time elapsed: 0.014 s
% 12.65/3.22 % (22202)Instructions burned: 27 (million)
% 12.65/3.22 % (22202)------------------------------
% 12.65/3.22 % (22202)------------------------------
% 12.65/3.24 % (22203)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_21964 for (2986ds/53Mi)
% 12.65/3.25 % (22203)Instruction limit reached!
% 12.65/3.25 % (22203)------------------------------
% 12.65/3.25 % (22203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.65/3.25 % (22203)Termination reason: Unknown
% 12.65/3.25 % (22203)Termination phase: Property scanning
% 12.65/3.25
% 12.65/3.25 % (22203)Memory used [KB]: 2046
% 12.65/3.25 % (22203)Time elapsed: 0.016 s
% 12.65/3.25 % (22203)Instructions burned: 55 (million)
% 12.65/3.25 % (22203)------------------------------
% 12.65/3.25 % (22203)------------------------------
% 12.65/3.26 % (22204)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_21964 for (2985ds/4436Mi)
% 12.65/3.27 % (22201)Instruction limit reached!
% 12.65/3.27 % (22201)------------------------------
% 12.65/3.27 % (22201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.65/3.27 % (22201)Termination reason: Unknown
% 12.65/3.27 % (22201)Termination phase: Saturation
% 12.65/3.27
% 12.65/3.27 % (22201)Memory used [KB]: 7036
% 12.65/3.27 % (22201)Time elapsed: 0.094 s
% 12.65/3.27 % (22201)Instructions burned: 205 (million)
% 12.65/3.27 % (22201)------------------------------
% 12.65/3.27 % (22201)------------------------------
% 12.65/3.29 % (22205)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_21964 for (2985ds/1539Mi)
% 12.92/3.30 % (22200)Instruction limit reached!
% 12.92/3.30 % (22200)------------------------------
% 12.92/3.30 % (22200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.92/3.30 % (22200)Termination reason: Unknown
% 12.92/3.30 % (22200)Termination phase: Saturation
% 12.92/3.30
% 12.92/3.30 % (22200)Memory used [KB]: 7547
% 12.92/3.30 % (22200)Time elapsed: 0.136 s
% 12.92/3.30 % (22200)Instructions burned: 267 (million)
% 12.92/3.30 % (22200)------------------------------
% 12.92/3.30 % (22200)------------------------------
% 12.92/3.32 % (22198)Instruction limit reached!
% 12.92/3.32 % (22198)------------------------------
% 12.92/3.32 % (22198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.92/3.32 % (22198)Termination reason: Unknown
% 12.92/3.32 % (22198)Termination phase: Saturation
% 12.92/3.32
% 12.92/3.32 % (22198)Memory used [KB]: 7675
% 12.92/3.32 % (22198)Time elapsed: 0.186 s
% 12.92/3.32 % (22198)Instructions burned: 369 (million)
% 12.92/3.32 % (22198)------------------------------
% 12.92/3.32 % (22198)------------------------------
% 12.92/3.32 % (22206)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_21964 for (2985ds/408Mi)
% 12.92/3.33 % (22207)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_21964 for (2985ds/5205Mi)
% 13.36/3.43 % (22187)Instruction limit reached!
% 13.36/3.43 % (22187)------------------------------
% 13.36/3.43 % (22187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.36/3.43 % (22187)Termination reason: Unknown
% 13.36/3.43 % (22187)Termination phase: Saturation
% 13.36/3.43
% 13.36/3.43 % (22187)Memory used [KB]: 8571
% 13.36/3.43 % (22187)Time elapsed: 0.487 s
% 13.36/3.43 % (22187)Instructions burned: 987 (million)
% 13.36/3.43 % (22187)------------------------------
% 13.36/3.43 % (22187)------------------------------
% 13.36/3.45 % (22208)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_21964 for (2983ds/1913Mi)
% 13.41/3.51 % (22206)Instruction limit reached!
% 13.41/3.51 % (22206)------------------------------
% 13.41/3.51 % (22206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.41/3.51 % (22206)Termination reason: Unknown
% 13.41/3.51 % (22206)Termination phase: Saturation
% 13.41/3.51
% 13.41/3.51 % (22206)Memory used [KB]: 8187
% 13.41/3.51 % (22206)Time elapsed: 0.198 s
% 13.41/3.51 % (22206)Instructions burned: 408 (million)
% 13.41/3.51 % (22206)------------------------------
% 13.41/3.51 % (22206)------------------------------
% 13.41/3.52 % (22194)Instruction limit reached!
% 13.41/3.52 % (22194)------------------------------
% 13.41/3.52 % (22194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.41/3.52 % (22194)Termination reason: Unknown
% 13.41/3.52 % (22194)Termination phase: Saturation
% 13.41/3.52
% 13.41/3.52 % (22194)Memory used [KB]: 7675
% 13.41/3.52 % (22194)Time elapsed: 0.455 s
% 13.41/3.52 % (22194)Instructions burned: 922 (million)
% 13.41/3.52 % (22194)------------------------------
% 13.41/3.52 % (22194)------------------------------
% 13.41/3.53 % (22209)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_21964 for (2983ds/4350Mi)
% 13.41/3.54 % (22210)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_21964 for (2983ds/68Mi)
% 13.41/3.57 % (22210)Instruction limit reached!
% 13.41/3.57 % (22210)------------------------------
% 13.41/3.57 % (22210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.41/3.57 % (22210)Termination reason: Unknown
% 13.41/3.57 % (22210)Termination phase: Function definition elimination
% 13.41/3.57
% 13.41/3.57 % (22210)Memory used [KB]: 2046
% 13.41/3.57 % (22210)Time elapsed: 0.034 s
% 13.41/3.57 % (22210)Instructions burned: 68 (million)
% 13.41/3.57 % (22210)------------------------------
% 13.41/3.57 % (22210)------------------------------
% 13.41/3.58 % (22211)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_21964 for (2982ds/358Mi)
% 14.14/3.67 % (22199)Instruction limit reached!
% 14.14/3.67 % (22199)------------------------------
% 14.14/3.67 % (22199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.14/3.67 % (22199)Termination reason: Unknown
% 14.14/3.67 % (22199)Termination phase: Saturation
% 14.14/3.67
% 14.14/3.67 % (22199)Memory used [KB]: 8699
% 14.14/3.67 % (22199)Time elapsed: 0.508 s
% 14.14/3.67 % (22199)Instructions burned: 1022 (million)
% 14.14/3.67 % (22199)------------------------------
% 14.14/3.67 % (22199)------------------------------
% 14.14/3.69 % (22212)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_21964 for (2981ds/31Mi)
% 14.66/3.70 % (22212)Instruction limit reached!
% 14.66/3.70 % (22212)------------------------------
% 14.66/3.70 % (22212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.66/3.70 % (22212)Termination reason: Unknown
% 14.66/3.70 % (22212)Termination phase: Property scanning
% 14.66/3.70
% 14.66/3.70 % (22212)Memory used [KB]: 1663
% 14.66/3.70 % (22212)Time elapsed: 0.017 s
% 14.66/3.70 % (22212)Instructions burned: 31 (million)
% 14.66/3.70 % (22212)------------------------------
% 14.66/3.70 % (22212)------------------------------
% 14.66/3.72 % (22213)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_21964 for (2981ds/279Mi)
% 14.66/3.76 % (22211)Instruction limit reached!
% 14.66/3.76 % (22211)------------------------------
% 14.66/3.76 % (22211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.66/3.76 % (22211)Termination reason: Unknown
% 14.66/3.76 % (22211)Termination phase: Saturation
% 14.66/3.76
% 14.66/3.76 % (22211)Memory used [KB]: 7291
% 14.66/3.76 % (22211)Time elapsed: 0.203 s
% 14.66/3.76 % (22211)Instructions burned: 359 (million)
% 14.66/3.76 % (22211)------------------------------
% 14.66/3.76 % (22211)------------------------------
% 14.66/3.77 % (22213)Refutation not found, incomplete strategy
% 14.66/3.77 % (22213)------------------------------
% 14.66/3.77 % (22213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.66/3.77 % (22213)Termination reason: Refutation not found, incomplete strategy
% 14.66/3.77
% 14.66/3.77
% 14.66/3.77 % (22213)Memory used [KB]: 6908
% 14.66/3.77 % (22213)Time elapsed: 0.051 s
% 14.66/3.77 % (22213)Instructions burned: 108 (million)
% 14.66/3.77 % (22213)------------------------------
% 14.66/3.77 % (22213)------------------------------
% 14.66/3.78 % (22214)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_21964 for (2980ds/258Mi)
% 14.66/3.79 % (22215)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_21964 for (2980ds/26Mi)
% 14.95/3.80 % (22215)Instruction limit reached!
% 14.95/3.80 % (22215)------------------------------
% 14.95/3.80 % (22215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.95/3.80 % (22215)Termination reason: Unknown
% 14.95/3.80 % (22215)Termination phase: shuffling
% 14.95/3.80
% 14.95/3.80 % (22215)Memory used [KB]: 1791
% 14.95/3.80 % (22215)Time elapsed: 0.014 s
% 14.95/3.80 % (22215)Instructions burned: 26 (million)
% 14.95/3.80 % (22215)------------------------------
% 14.95/3.80 % (22215)------------------------------
% 14.95/3.81 % (22216)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_21964 for (2980ds/995Mi)
% 14.99/3.91 % (22214)Instruction limit reached!
% 14.99/3.91 % (22214)------------------------------
% 14.99/3.91 % (22214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.99/3.91 % (22214)Termination reason: Unknown
% 14.99/3.91 % (22214)Termination phase: Saturation
% 14.99/3.91
% 14.99/3.91 % (22214)Memory used [KB]: 7419
% 14.99/3.91 % (22214)Time elapsed: 0.129 s
% 14.99/3.91 % (22214)Instructions burned: 258 (million)
% 14.99/3.91 % (22214)------------------------------
% 14.99/3.91 % (22214)------------------------------
% 14.99/3.92 % (22217)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_21964 for (2978ds/373Mi)
% 18.75/4.05 % (22205)Instruction limit reached!
% 18.75/4.05 % (22205)------------------------------
% 18.75/4.05 % (22205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.75/4.05 % (22205)Termination reason: Unknown
% 18.75/4.05 % (22205)Termination phase: Saturation
% 18.75/4.05
% 18.75/4.05 % (22205)Memory used [KB]: 9466
% 18.75/4.05 % (22205)Time elapsed: 0.768 s
% 18.75/4.05 % (22205)Instructions burned: 1540 (million)
% 18.75/4.05 % (22205)------------------------------
% 18.75/4.05 % (22205)------------------------------
% 18.75/4.07 % (22218)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_21964 for (2977ds/253Mi)
% 18.75/4.11 % (22217)Instruction limit reached!
% 18.75/4.11 % (22217)------------------------------
% 18.75/4.11 % (22217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.75/4.11 % (22217)Termination reason: Unknown
% 18.75/4.11 % (22217)Termination phase: Saturation
% 18.75/4.11
% 18.75/4.11 % (22217)Memory used [KB]: 7547
% 18.75/4.11 % (22217)Time elapsed: 0.189 s
% 18.75/4.11 % (22217)Instructions burned: 375 (million)
% 18.75/4.11 % (22217)------------------------------
% 18.75/4.11 % (22217)------------------------------
% 19.38/4.13 % (22219)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_21964 for (2976ds/832Mi)
% 19.38/4.19 % (22218)Instruction limit reached!
% 19.38/4.19 % (22218)------------------------------
% 19.38/4.19 % (22218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.38/4.19 % (22218)Termination reason: Unknown
% 19.38/4.19 % (22218)Termination phase: Saturation
% 19.38/4.19
% 19.38/4.19 % (22218)Memory used [KB]: 7547
% 19.38/4.19 % (22218)Time elapsed: 0.120 s
% 19.38/4.19 % (22218)Instructions burned: 253 (million)
% 19.38/4.19 % (22218)------------------------------
% 19.38/4.19 % (22218)------------------------------
% 19.88/4.21 % (22220)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_21964 for (2976ds/668Mi)
% 19.88/4.29 % (22216)Instruction limit reached!
% 19.88/4.29 % (22216)------------------------------
% 19.88/4.29 % (22216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.88/4.29 % (22216)Termination reason: Unknown
% 19.88/4.29 % (22216)Termination phase: Saturation
% 19.88/4.29
% 19.88/4.29 % (22216)Memory used [KB]: 9210
% 19.88/4.29 % (22216)Time elapsed: 0.482 s
% 19.88/4.29 % (22216)Instructions burned: 996 (million)
% 19.88/4.29 % (22216)------------------------------
% 19.88/4.29 % (22216)------------------------------
% 20.38/4.31 % (22221)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_21964 for (2975ds/40Mi)
% 20.38/4.33 % (22221)Instruction limit reached!
% 20.38/4.33 % (22221)------------------------------
% 20.38/4.33 % (22221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.38/4.33 % (22221)Termination reason: Unknown
% 20.38/4.33 % (22221)Termination phase: Property scanning
% 20.38/4.33
% 20.38/4.33 % (22221)Memory used [KB]: 2046
% 20.38/4.33 % (22221)Time elapsed: 0.021 s
% 20.38/4.33 % (22221)Instructions burned: 42 (million)
% 20.38/4.33 % (22221)------------------------------
% 20.38/4.33 % (22221)------------------------------
% 20.38/4.35 % (22208)Instruction limit reached!
% 20.38/4.35 % (22208)------------------------------
% 20.38/4.35 % (22208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.38/4.35 % (22208)Termination reason: Unknown
% 20.38/4.35 % (22208)Termination phase: Saturation
% 20.38/4.35
% 20.38/4.35 % (22208)Memory used [KB]: 3709
% 20.38/4.35 % (22208)Time elapsed: 0.899 s
% 20.38/4.35 % (22208)Instructions burned: 1913 (million)
% 20.38/4.35 % (22208)------------------------------
% 20.38/4.35 % (22208)------------------------------
% 20.38/4.35 % (22222)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_21964 for (2974ds/294Mi)
% 20.38/4.36 % (22223)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_21964 for (2974ds/187Mi)
% 20.38/4.39 % (22222)Refutation not found, incomplete strategy
% 20.38/4.39 % (22222)------------------------------
% 20.38/4.39 % (22222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.38/4.39 % (22222)Termination reason: Refutation not found, incomplete strategy
% 20.38/4.39
% 20.38/4.39
% 20.38/4.39 % (22222)Memory used [KB]: 6652
% 20.38/4.39 % (22222)Time elapsed: 0.039 s
% 20.38/4.39 % (22222)Instructions burned: 81 (million)
% 20.38/4.39 % (22222)------------------------------
% 20.38/4.39 % (22222)------------------------------
% 20.83/4.40 % (22224)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_21964 for (2974ds/371Mi)
% 20.83/4.45 % (22223)Instruction limit reached!
% 20.83/4.45 % (22223)------------------------------
% 20.83/4.45 % (22223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.83/4.45 % (22223)Termination reason: Unknown
% 20.83/4.45 % (22223)Termination phase: Saturation
% 20.83/4.45
% 20.83/4.45 % (22223)Memory used [KB]: 7036
% 20.83/4.46 % (22223)Time elapsed: 0.094 s
% 20.83/4.46 % (22223)Instructions burned: 187 (million)
% 20.83/4.46 % (22223)------------------------------
% 20.83/4.46 % (22223)------------------------------
% 20.83/4.47 % (22225)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_21964 for (2973ds/1827Mi)
% 21.23/4.54 % (22219)Instruction limit reached!
% 21.23/4.54 % (22219)------------------------------
% 21.23/4.54 % (22219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.23/4.54 % (22219)Termination reason: Unknown
% 21.23/4.54 % (22219)Termination phase: Saturation
% 21.23/4.54
% 21.23/4.54 % (22219)Memory used [KB]: 7931
% 21.23/4.54 % (22219)Time elapsed: 0.410 s
% 21.23/4.54 % (22219)Instructions burned: 833 (million)
% 21.23/4.54 % (22219)------------------------------
% 21.23/4.54 % (22219)------------------------------
% 21.23/4.54 % (22220)Instruction limit reached!
% 21.23/4.54 % (22220)------------------------------
% 21.23/4.54 % (22220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.23/4.54 % (22220)Termination reason: Unknown
% 21.23/4.54 % (22220)Termination phase: Saturation
% 21.23/4.54
% 21.23/4.54 % (22220)Memory used [KB]: 13944
% 21.23/4.54 % (22220)Time elapsed: 0.335 s
% 21.23/4.54 % (22220)Instructions burned: 669 (million)
% 21.23/4.54 % (22220)------------------------------
% 21.23/4.54 % (22220)------------------------------
% 21.23/4.55 % (22226)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_21964 for (2972ds/70Mi)
% 21.23/4.55 % (22227)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_21964 for (2972ds/316Mi)
% 21.23/4.59 % (22226)Instruction limit reached!
% 21.23/4.59 % (22226)------------------------------
% 21.23/4.59 % (22226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.23/4.59 % (22226)Termination reason: Unknown
% 21.23/4.59 % (22226)Termination phase: Preprocessing 3
% 21.23/4.59
% 21.23/4.59 % (22226)Memory used [KB]: 2174
% 21.23/4.59 % (22226)Time elapsed: 0.034 s
% 21.23/4.59 % (22226)Instructions burned: 70 (million)
% 21.23/4.59 % (22226)------------------------------
% 21.23/4.59 % (22226)------------------------------
% 21.23/4.59 % (22224)Instruction limit reached!
% 21.23/4.59 % (22224)------------------------------
% 21.23/4.59 % (22224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.23/4.59 % (22224)Termination reason: Unknown
% 21.23/4.59 % (22224)Termination phase: Saturation
% 21.23/4.59
% 21.23/4.59 % (22224)Memory used [KB]: 7419
% 21.23/4.59 % (22224)Time elapsed: 0.193 s
% 21.23/4.59 % (22224)Instructions burned: 372 (million)
% 21.23/4.59 % (22224)------------------------------
% 21.23/4.59 % (22224)------------------------------
% 21.23/4.60 % (22228)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_21964 for (2972ds/932Mi)
% 22.56/4.61 % (22229)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_21964 for (2972ds/4714Mi)
% 22.56/4.65 % (22227)Refutation not found, incomplete strategy
% 22.56/4.65 % (22227)------------------------------
% 22.56/4.65 % (22227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.56/4.65 % (22227)Termination reason: Refutation not found, incomplete strategy
% 22.56/4.65
% 22.56/4.65
% 22.56/4.65 % (22227)Memory used [KB]: 7419
% 22.56/4.65 % (22227)Time elapsed: 0.092 s
% 22.56/4.65 % (22227)Instructions burned: 193 (million)
% 22.56/4.65 % (22227)------------------------------
% 22.56/4.65 % (22227)------------------------------
% 22.56/4.67 % (22230)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_21964 for (2971ds/8250Mi)
% 22.98/4.70 % (22229)Refutation not found, incomplete strategy
% 22.98/4.70 % (22229)------------------------------
% 22.98/4.70 % (22229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.98/4.70 % (22229)Termination reason: Refutation not found, incomplete strategy
% 22.98/4.70
% 22.98/4.70
% 22.98/4.70 % (22229)Memory used [KB]: 7547
% 22.98/4.70 % (22229)Time elapsed: 0.093 s
% 22.98/4.70 % (22229)Instructions burned: 192 (million)
% 22.98/4.70 % (22229)------------------------------
% 22.98/4.70 % (22229)------------------------------
% 22.98/4.73 % (22231)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_21964 for (2971ds/770Mi)
% 23.68/4.98 % (22231)Instruction limit reached!
% 23.68/4.98 % (22231)------------------------------
% 23.68/4.98 % (22231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.68/4.98 % (22231)Termination reason: Unknown
% 23.68/4.98 % (22231)Termination phase: Saturation
% 23.68/4.98
% 23.68/4.98 % (22231)Memory used [KB]: 7419
% 23.68/4.98 % (22231)Time elapsed: 0.269 s
% 23.68/4.98 % (22231)Instructions burned: 770 (million)
% 23.68/4.98 % (22231)------------------------------
% 23.68/4.98 % (22231)------------------------------
% 23.68/4.99 % (22232)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_21964 for (2968ds/794Mi)
% 23.68/5.01 % (22228)Instruction limit reached!
% 23.68/5.01 % (22228)------------------------------
% 23.68/5.01 % (22228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.68/5.01 % (22228)Termination reason: Unknown
% 23.68/5.01 % (22228)Termination phase: Saturation
% 23.68/5.01
% 23.68/5.01 % (22228)Memory used [KB]: 9338
% 23.68/5.01 % (22228)Time elapsed: 0.421 s
% 23.68/5.01 % (22228)Instructions burned: 933 (million)
% 23.68/5.01 % (22228)------------------------------
% 23.68/5.01 % (22228)------------------------------
% 25.57/5.02 % (22233)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_21964 for (2968ds/464Mi)
% 26.65/5.26 % (22233)Instruction limit reached!
% 26.65/5.26 % (22233)------------------------------
% 26.65/5.26 % (22233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.65/5.26 % (22233)Termination reason: Unknown
% 26.65/5.26 % (22233)Termination phase: Saturation
% 26.65/5.26
% 26.65/5.26 % (22233)Memory used [KB]: 7675
% 26.65/5.26 % (22233)Time elapsed: 0.261 s
% 26.65/5.26 % (22233)Instructions burned: 464 (million)
% 26.65/5.26 % (22233)------------------------------
% 26.65/5.26 % (22233)------------------------------
% 26.65/5.28 % (22234)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_21964 for (2965ds/1376Mi)
% 27.49/5.35 % (22232)Instruction limit reached!
% 27.49/5.35 % (22232)------------------------------
% 27.49/5.35 % (22232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.49/5.35 % (22232)Termination reason: Unknown
% 27.49/5.35 % (22232)Termination phase: Saturation
% 27.49/5.35
% 27.49/5.35 % (22232)Memory used [KB]: 5884
% 27.49/5.35 % (22232)Time elapsed: 0.373 s
% 27.49/5.35 % (22232)Instructions burned: 795 (million)
% 27.49/5.35 % (22232)------------------------------
% 27.49/5.35 % (22232)------------------------------
% 27.49/5.37 % (22235)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_21964 for (2964ds/906Mi)
% 27.49/5.39 % (22225)Instruction limit reached!
% 27.49/5.39 % (22225)------------------------------
% 27.49/5.39 % (22225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.49/5.39 % (22225)Termination reason: Unknown
% 27.49/5.39 % (22225)Termination phase: Saturation
% 27.49/5.39
% 27.49/5.39 % (22225)Memory used [KB]: 9722
% 27.49/5.39 % (22225)Time elapsed: 0.921 s
% 27.49/5.39 % (22225)Instructions burned: 1827 (million)
% 27.49/5.39 % (22225)------------------------------
% 27.49/5.39 % (22225)------------------------------
% 28.05/5.41 % (22236)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_21964 for (2964ds/434Mi)
% 28.05/5.47 % (22204)Instruction limit reached!
% 28.05/5.47 % (22204)------------------------------
% 28.05/5.47 % (22204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.05/5.47 % (22204)Termination reason: Unknown
% 28.05/5.47 % (22204)Termination phase: Saturation
% 28.05/5.47
% 28.05/5.47 % (22204)Memory used [KB]: 10362
% 28.05/5.47 % (22204)Time elapsed: 2.207 s
% 28.05/5.47 % (22204)Instructions burned: 4437 (million)
% 28.05/5.47 % (22204)------------------------------
% 28.05/5.47 % (22204)------------------------------
% 28.05/5.49 % (22237)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_21964 for (2963ds/865Mi)
% 28.75/5.62 % (22236)Instruction limit reached!
% 28.75/5.62 % (22236)------------------------------
% 28.75/5.62 % (22236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.75/5.62 % (22236)Termination reason: Unknown
% 28.75/5.62 % (22236)Termination phase: Saturation
% 28.75/5.62
% 28.75/5.62 % (22236)Memory used [KB]: 7419
% 28.75/5.62 % (22236)Time elapsed: 0.217 s
% 28.75/5.62 % (22236)Instructions burned: 435 (million)
% 28.75/5.62 % (22236)------------------------------
% 28.75/5.62 % (22236)------------------------------
% 28.75/5.63 % (22209)Instruction limit reached!
% 28.75/5.63 % (22209)------------------------------
% 28.75/5.63 % (22209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.75/5.63 % (22209)Termination reason: Unknown
% 28.75/5.63 % (22209)Termination phase: Saturation
% 28.75/5.63
% 28.75/5.63 % (22209)Memory used [KB]: 10618
% 28.75/5.63 % (22209)Time elapsed: 2.120 s
% 28.75/5.63 % (22209)Instructions burned: 4351 (million)
% 28.75/5.63 % (22209)------------------------------
% 28.75/5.63 % (22209)------------------------------
% 28.75/5.64 % (22238)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_21964 for (2961ds/593Mi)
% 28.75/5.64 % (22239)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_21964 for (2961ds/443Mi)
% 29.43/5.85 % (22235)Instruction limit reached!
% 29.43/5.85 % (22235)------------------------------
% 29.43/5.85 % (22235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.43/5.85 % (22235)Termination reason: Unknown
% 29.43/5.85 % (22235)Termination phase: Saturation
% 29.43/5.85
% 29.43/5.85 % (22235)Memory used [KB]: 10618
% 29.43/5.85 % (22235)Time elapsed: 0.487 s
% 29.43/5.85 % (22235)Instructions burned: 907 (million)
% 29.43/5.85 % (22235)------------------------------
% 29.43/5.85 % (22235)------------------------------
% 29.43/5.86 % (22207)Instruction limit reached!
% 29.43/5.86 % (22207)------------------------------
% 29.43/5.86 % (22207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.43/5.86 % (22207)Termination reason: Unknown
% 29.43/5.86 % (22207)Termination phase: Saturation
% 29.43/5.86
% 29.43/5.86 % (22207)Memory used [KB]: 15479
% 29.43/5.86 % (22207)Time elapsed: 2.532 s
% 29.43/5.86 % (22207)Instructions burned: 5206 (million)
% 29.43/5.86 % (22207)------------------------------
% 29.43/5.86 % (22207)------------------------------
% 29.43/5.87 % (22239)Instruction limit reached!
% 29.43/5.87 % (22239)------------------------------
% 29.43/5.87 % (22239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.43/5.87 % (22239)Termination reason: Unknown
% 29.43/5.87 % (22239)Termination phase: Saturation
% 29.43/5.87
% 29.43/5.87 % (22239)Memory used [KB]: 7547
% 29.43/5.87 % (22239)Time elapsed: 0.225 s
% 29.43/5.87 % (22239)Instructions burned: 443 (million)
% 29.43/5.87 % (22239)------------------------------
% 29.43/5.87 % (22239)------------------------------
% 29.43/5.87 % (22240)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_21964 for (2959ds/594Mi)
% 29.43/5.88 % (22241)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_21964 for (2959ds/327Mi)
% 29.43/5.88 % (22242)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_21964 for (2959ds/5411Mi)
% 30.34/5.91 % (22237)Instruction limit reached!
% 30.34/5.91 % (22237)------------------------------
% 30.34/5.91 % (22237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.34/5.91 % (22237)Termination reason: Unknown
% 30.34/5.91 % (22237)Termination phase: Saturation
% 30.34/5.91
% 30.34/5.91 % (22237)Memory used [KB]: 8443
% 30.34/5.91 % (22237)Time elapsed: 0.429 s
% 30.34/5.91 % (22237)Instructions burned: 866 (million)
% 30.34/5.91 % (22237)------------------------------
% 30.34/5.91 % (22237)------------------------------
% 30.34/5.93 % (22243)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_21964 for (2958ds/1762Mi)
% 30.34/5.93 % (22238)Instruction limit reached!
% 30.34/5.93 % (22238)------------------------------
% 30.34/5.93 % (22238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.34/5.93 % (22238)Termination reason: Unknown
% 30.34/5.93 % (22238)Termination phase: Saturation
% 30.34/5.93
% 30.34/5.93 % (22238)Memory used [KB]: 9338
% 30.34/5.93 % (22238)Time elapsed: 0.294 s
% 30.34/5.93 % (22238)Instructions burned: 594 (million)
% 30.34/5.93 % (22238)------------------------------
% 30.34/5.93 % (22238)------------------------------
% 30.34/5.95 % (22244)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_21964 for (2958ds/96Mi)
% 30.34/5.96 % (22234)Instruction limit reached!
% 30.34/5.96 % (22234)------------------------------
% 30.34/5.96 % (22234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.34/5.96 % (22234)Termination reason: Unknown
% 30.34/5.96 % (22234)Termination phase: Saturation
% 30.34/5.96
% 30.34/5.96 % (22234)Memory used [KB]: 10874
% 30.34/5.96 % (22234)Time elapsed: 0.681 s
% 30.34/5.96 % (22234)Instructions burned: 1377 (million)
% 30.34/5.96 % (22234)------------------------------
% 30.34/5.96 % (22234)------------------------------
% 30.34/5.97 % (22245)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_21964 for (2958ds/503Mi)
% 30.34/5.99 % (22244)Instruction limit reached!
% 30.34/5.99 % (22244)------------------------------
% 30.34/5.99 % (22244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.34/5.99 % (22244)Termination reason: Unknown
% 30.34/5.99 % (22244)Termination phase: Property scanning
% 30.34/5.99
% 30.34/5.99 % (22244)Memory used [KB]: 2302
% 30.34/5.99 % (22244)Time elapsed: 0.045 s
% 30.34/5.99 % (22244)Instructions burned: 96 (million)
% 30.34/5.99 % (22244)------------------------------
% 30.34/5.99 % (22244)------------------------------
% 30.34/6.01 % (22246)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_21964 for (2958ds/90Mi)
% 30.34/6.02 % (22245)Refutation not found, incomplete strategy
% 30.34/6.02 % (22245)------------------------------
% 30.34/6.02 % (22245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.34/6.02 % (22245)Termination reason: Refutation not found, incomplete strategy
% 30.34/6.02
% 30.34/6.02
% 30.34/6.02 % (22245)Memory used [KB]: 6780
% 30.34/6.02 % (22245)Time elapsed: 0.045 s
% 30.34/6.02 % (22245)Instructions burned: 86 (million)
% 30.34/6.02 % (22245)------------------------------
% 30.34/6.02 % (22245)------------------------------
% 32.62/6.04 % (22247)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_21964 for (2957ds/593Mi)
% 32.62/6.05 % (22241)Instruction limit reached!
% 32.62/6.05 % (22241)------------------------------
% 32.62/6.05 % (22241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.62/6.05 % (22241)Termination reason: Unknown
% 32.62/6.05 % (22241)Termination phase: Saturation
% 32.62/6.05
% 32.62/6.05 % (22241)Memory used [KB]: 7547
% 32.62/6.05 % (22241)Time elapsed: 0.167 s
% 32.62/6.05 % (22241)Instructions burned: 327 (million)
% 32.62/6.05 % (22241)------------------------------
% 32.62/6.05 % (22241)------------------------------
% 32.62/6.05 % (22246)Instruction limit reached!
% 32.62/6.05 % (22246)------------------------------
% 32.62/6.05 % (22246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.62/6.05 % (22246)Termination reason: Unknown
% 32.62/6.05 % (22246)Termination phase: Saturation
% 32.62/6.05
% 32.62/6.05 % (22246)Memory used [KB]: 6652
% 32.62/6.05 % (22246)Time elapsed: 0.045 s
% 32.62/6.05 % (22246)Instructions burned: 90 (million)
% 32.62/6.05 % (22246)------------------------------
% 32.62/6.05 % (22246)------------------------------
% 32.62/6.06 % (22248)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_21964 for (2957ds/1512Mi)
% 32.62/6.07 % (22249)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_21964 for (2957ds/569Mi)
% 33.10/6.16 % (22240)Instruction limit reached!
% 33.10/6.16 % (22240)------------------------------
% 33.10/6.16 % (22240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.10/6.16 % (22240)Termination reason: Unknown
% 33.10/6.16 % (22240)Termination phase: Saturation
% 33.10/6.16
% 33.10/6.16 % (22240)Memory used [KB]: 7803
% 33.10/6.16 % (22240)Time elapsed: 0.297 s
% 33.10/6.16 % (22240)Instructions burned: 595 (million)
% 33.10/6.16 % (22240)------------------------------
% 33.10/6.16 % (22240)------------------------------
% 33.10/6.18 % (22250)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_21964 for (2956ds/501Mi)
% 33.67/6.34 % (22247)Instruction limit reached!
% 33.67/6.34 % (22247)------------------------------
% 33.67/6.34 % (22247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.67/6.34 % (22247)Termination reason: Unknown
% 33.67/6.34 % (22247)Termination phase: Saturation
% 33.67/6.34
% 33.67/6.34 % (22247)Memory used [KB]: 7931
% 33.67/6.34 % (22247)Time elapsed: 0.306 s
% 33.67/6.34 % (22247)Instructions burned: 594 (million)
% 33.67/6.34 % (22247)------------------------------
% 33.67/6.34 % (22247)------------------------------
% 33.67/6.34 % (22249)Instruction limit reached!
% 33.67/6.34 % (22249)------------------------------
% 33.67/6.34 % (22249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.67/6.34 % (22249)Termination reason: Unknown
% 33.67/6.34 % (22249)Termination phase: Saturation
% 33.67/6.34
% 33.67/6.34 % (22249)Memory used [KB]: 7931
% 33.67/6.34 % (22249)Time elapsed: 0.271 s
% 33.67/6.34 % (22249)Instructions burned: 569 (million)
% 33.67/6.34 % (22249)------------------------------
% 33.67/6.34 % (22249)------------------------------
% 33.67/6.36 % (22252)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_21964 for (2954ds/406Mi)
% 33.67/6.36 % (22251)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_21964 for (2954ds/562Mi)
% 34.58/6.43 % (22250)Instruction limit reached!
% 34.58/6.43 % (22250)------------------------------
% 34.58/6.43 % (22250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.58/6.43 % (22250)Termination reason: Unknown
% 34.58/6.43 % (22250)Termination phase: Saturation
% 34.58/6.43
% 34.58/6.43 % (22250)Memory used [KB]: 8315
% 34.58/6.43 % (22250)Time elapsed: 0.248 s
% 34.58/6.43 % (22250)Instructions burned: 501 (million)
% 34.58/6.43 % (22250)------------------------------
% 34.58/6.43 % (22250)------------------------------
% 34.58/6.44 % (22253)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_21964 for (2953ds/582Mi)
% 35.13/6.56 % (22252)Instruction limit reached!
% 35.13/6.56 % (22252)------------------------------
% 35.13/6.56 % (22252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.13/6.56 % (22252)Termination reason: Unknown
% 35.13/6.56 % (22252)Termination phase: Saturation
% 35.13/6.56
% 35.13/6.56 % (22252)Memory used [KB]: 7675
% 35.13/6.56 % (22252)Time elapsed: 0.206 s
% 35.13/6.56 % (22252)Instructions burned: 407 (million)
% 35.13/6.56 % (22252)------------------------------
% 35.13/6.56 % (22252)------------------------------
% 35.13/6.58 % (22254)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_21964 for (2952ds/456Mi)
% 35.66/6.64 % (22251)Instruction limit reached!
% 35.66/6.64 % (22251)------------------------------
% 35.66/6.64 % (22251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.66/6.64 % (22251)Termination reason: Unknown
% 35.66/6.64 % (22251)Termination phase: Saturation
% 35.66/6.64
% 35.66/6.64 % (22251)Memory used [KB]: 7675
% 35.66/6.64 % (22251)Time elapsed: 0.281 s
% 35.66/6.64 % (22251)Instructions burned: 563 (million)
% 35.66/6.64 % (22251)------------------------------
% 35.66/6.64 % (22251)------------------------------
% 35.66/6.65 % (22255)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_21964 for (2951ds/393Mi)
% 36.25/6.73 % (22254)Instruction limit reached!
% 36.25/6.73 % (22254)------------------------------
% 36.25/6.73 % (22254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.25/6.73 % (22254)Termination reason: Unknown
% 36.25/6.73 % (22254)Termination phase: Saturation
% 36.25/6.73
% 36.25/6.73 % (22254)Memory used [KB]: 7931
% 36.25/6.73 % (22254)Time elapsed: 0.150 s
% 36.25/6.73 % (22254)Instructions burned: 458 (million)
% 36.25/6.73 % (22254)------------------------------
% 36.25/6.73 % (22254)------------------------------
% 36.25/6.73 % (22253)Instruction limit reached!
% 36.25/6.73 % (22253)------------------------------
% 36.25/6.73 % (22253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.25/6.73 % (22253)Termination reason: Unknown
% 36.25/6.73 % (22253)Termination phase: Saturation
% 36.25/6.73
% 36.25/6.73 % (22253)Memory used [KB]: 7547
% 36.25/6.73 % (22253)Time elapsed: 0.293 s
% 36.25/6.73 % (22253)Instructions burned: 583 (million)
% 36.25/6.73 % (22253)------------------------------
% 36.25/6.73 % (22253)------------------------------
% 36.25/6.74 % (22256)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_21964 for (2950ds/1335Mi)
% 36.25/6.75 % (22257)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_21964 for (2950ds/3373Mi)
% 36.25/6.76 % (22243)Instruction limit reached!
% 36.25/6.76 % (22243)------------------------------
% 36.25/6.76 % (22243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.25/6.76 % (22243)Termination reason: Unknown
% 36.25/6.76 % (22243)Termination phase: Saturation
% 36.25/6.76
% 36.25/6.76 % (22243)Memory used [KB]: 10618
% 36.25/6.76 % (22243)Time elapsed: 0.834 s
% 36.25/6.76 % (22243)Instructions burned: 1762 (million)
% 36.25/6.76 % (22243)------------------------------
% 36.25/6.76 % (22243)------------------------------
% 36.25/6.79 % (22258)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_21964 for (2950ds/474Mi)
% 37.00/6.81 % (22248)Instruction limit reached!
% 37.00/6.81 % (22248)------------------------------
% 37.00/6.81 % (22248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.00/6.81 % (22248)Termination reason: Unknown
% 37.00/6.81 % (22248)Termination phase: Saturation
% 37.00/6.81
% 37.00/6.81 % (22248)Memory used [KB]: 8187
% 37.00/6.81 % (22248)Time elapsed: 0.753 s
% 37.00/6.81 % (22248)Instructions burned: 1513 (million)
% 37.00/6.81 % (22248)------------------------------
% 37.00/6.81 % (22248)------------------------------
% 37.00/6.83 % (22259)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_21964 for (2950ds/157Mi)
% 37.00/6.83 % (22255)Instruction limit reached!
% 37.00/6.83 % (22255)------------------------------
% 37.00/6.83 % (22255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.00/6.83 % (22255)Termination reason: Unknown
% 37.00/6.83 % (22255)Termination phase: Saturation
% 37.00/6.83
% 37.00/6.83 % (22255)Memory used [KB]: 7419
% 37.00/6.83 % (22255)Time elapsed: 0.184 s
% 37.00/6.83 % (22255)Instructions burned: 394 (million)
% 37.00/6.83 % (22255)------------------------------
% 37.00/6.83 % (22255)------------------------------
% 37.00/6.85 % (22260)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_21964 for (2949ds/590Mi)
% 38.17/6.90 % (22259)Instruction limit reached!
% 38.17/6.90 % (22259)------------------------------
% 38.17/6.90 % (22259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.17/6.90 % (22259)Termination reason: Unknown
% 38.17/6.90 % (22259)Termination phase: Saturation
% 38.17/6.90
% 38.17/6.90 % (22259)Memory used [KB]: 6908
% 38.17/6.90 % (22259)Time elapsed: 0.074 s
% 38.17/6.90 % (22259)Instructions burned: 158 (million)
% 38.17/6.90 % (22259)------------------------------
% 38.17/6.90 % (22259)------------------------------
% 38.17/6.92 % (22261)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_21964 for (2949ds/104Mi)
% 38.17/6.97 % (22261)Instruction limit reached!
% 38.17/6.97 % (22261)------------------------------
% 38.17/6.97 % (22261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.17/6.97 % (22261)Termination reason: Unknown
% 38.17/6.97 % (22261)Termination phase: Saturation
% 38.17/6.97
% 38.17/6.97 % (22261)Memory used [KB]: 2430
% 38.17/6.97 % (22261)Time elapsed: 0.052 s
% 38.17/6.97 % (22261)Instructions burned: 104 (million)
% 38.17/6.97 % (22261)------------------------------
% 38.17/6.97 % (22261)------------------------------
% 38.17/6.99 % (22262)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_21964 for (2948ds/414Mi)
% 39.56/7.03 % (22258)Instruction limit reached!
% 39.56/7.03 % (22258)------------------------------
% 39.56/7.03 % (22258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.56/7.03 % (22258)Termination reason: Unknown
% 39.56/7.03 % (22258)Termination phase: Saturation
% 39.56/7.03
% 39.56/7.03 % (22258)Memory used [KB]: 8187
% 39.56/7.03 % (22258)Time elapsed: 0.257 s
% 39.56/7.03 % (22258)Instructions burned: 475 (million)
% 39.56/7.03 % (22258)------------------------------
% 39.56/7.03 % (22258)------------------------------
% 39.56/7.05 % (22263)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_21964 for (2947ds/715Mi)
% 40.19/7.14 % (22260)Instruction limit reached!
% 40.19/7.14 % (22260)------------------------------
% 40.19/7.14 % (22260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.19/7.14 % (22260)Termination reason: Unknown
% 40.19/7.14 % (22260)Termination phase: Saturation
% 40.19/7.14
% 40.19/7.14 % (22260)Memory used [KB]: 8059
% 40.19/7.14 % (22260)Time elapsed: 0.286 s
% 40.19/7.14 % (22260)Instructions burned: 590 (million)
% 40.19/7.14 % (22260)------------------------------
% 40.19/7.14 % (22260)------------------------------
% 40.19/7.15 % (22264)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_21964 for (2946ds/961Mi)
% 40.19/7.18 % (22262)Instruction limit reached!
% 40.19/7.18 % (22262)------------------------------
% 40.19/7.18 % (22262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.19/7.18 % (22262)Termination reason: Unknown
% 40.19/7.18 % (22262)Termination phase: Saturation
% 40.19/7.18
% 40.19/7.18 % (22262)Memory used [KB]: 7675
% 40.19/7.18 % (22262)Time elapsed: 0.199 s
% 40.19/7.18 % (22262)Instructions burned: 415 (million)
% 40.19/7.18 % (22262)------------------------------
% 40.19/7.18 % (22262)------------------------------
% 40.58/7.20 % (22265)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_21964 for (2946ds/1213Mi)
% 40.98/7.35 % (22256)Instruction limit reached!
% 40.98/7.35 % (22256)------------------------------
% 40.98/7.35 % (22256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.98/7.35 % (22256)Termination reason: Unknown
% 40.98/7.35 % (22256)Termination phase: Saturation
% 40.98/7.35
% 40.98/7.35 % (22256)Memory used [KB]: 9210
% 40.98/7.35 % (22256)Time elapsed: 0.624 s
% 40.98/7.35 % (22256)Instructions burned: 1336 (million)
% 40.98/7.35 % (22256)------------------------------
% 40.98/7.35 % (22256)------------------------------
% 40.98/7.36 % (22266)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_21964 for (2944ds/1979Mi)
% 41.34/7.41 % (22263)Instruction limit reached!
% 41.34/7.41 % (22263)------------------------------
% 41.34/7.41 % (22263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.34/7.41 % (22263)Termination reason: Unknown
% 41.34/7.41 % (22263)Termination phase: Saturation
% 41.34/7.41
% 41.34/7.41 % (22263)Memory used [KB]: 3454
% 41.34/7.41 % (22263)Time elapsed: 0.365 s
% 41.34/7.41 % (22263)Instructions burned: 716 (million)
% 41.34/7.41 % (22263)------------------------------
% 41.34/7.41 % (22263)------------------------------
% 41.34/7.42 % (22267)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_21964 for (2944ds/481Mi)
% 42.02/7.53 % (22264)Instruction limit reached!
% 42.02/7.53 % (22264)------------------------------
% 42.02/7.53 % (22264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.02/7.53 % (22264)Termination reason: Unknown
% 42.02/7.53 % (22264)Termination phase: Saturation
% 42.02/7.53
% 42.02/7.53 % (22264)Memory used [KB]: 7291
% 42.02/7.53 % (22264)Time elapsed: 0.377 s
% 42.02/7.53 % (22264)Instructions burned: 961 (million)
% 42.02/7.53 % (22264)------------------------------
% 42.02/7.53 % (22264)------------------------------
% 42.02/7.54 % (22268)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_21964 for (2942ds/783Mi)
% 42.71/7.66 % (22267)Instruction limit reached!
% 42.71/7.66 % (22267)------------------------------
% 42.71/7.66 % (22267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.71/7.66 % (22267)Termination reason: Unknown
% 42.71/7.66 % (22267)Termination phase: Saturation
% 42.71/7.66
% 42.71/7.66 % (22267)Memory used [KB]: 7803
% 42.71/7.66 % (22267)Time elapsed: 0.240 s
% 42.71/7.66 % (22267)Instructions burned: 481 (million)
% 42.71/7.66 % (22267)------------------------------
% 42.71/7.66 % (22267)------------------------------
% 42.71/7.68 % (22269)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_21964 for (2941ds/432Mi)
% 43.56/7.82 % (22265)Instruction limit reached!
% 43.56/7.82 % (22265)------------------------------
% 43.56/7.82 % (22265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.56/7.82 % (22265)Termination reason: Unknown
% 43.56/7.82 % (22265)Termination phase: Saturation
% 43.56/7.82
% 43.56/7.82 % (22265)Memory used [KB]: 8827
% 43.56/7.82 % (22265)Time elapsed: 0.626 s
% 43.56/7.82 % (22265)Instructions burned: 1214 (million)
% 43.56/7.82 % (22265)------------------------------
% 43.56/7.82 % (22265)------------------------------
% 43.56/7.84 % (22270)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_21964 for (2939ds/1670Mi)
% 44.51/7.90 % (22269)Instruction limit reached!
% 44.51/7.90 % (22269)------------------------------
% 44.51/7.90 % (22269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.51/7.90 % (22269)Termination reason: Unknown
% 44.51/7.90 % (22269)Termination phase: Saturation
% 44.51/7.90
% 44.51/7.90 % (22269)Memory used [KB]: 7164
% 44.51/7.90 % (22269)Time elapsed: 0.239 s
% 44.51/7.90 % (22269)Instructions burned: 432 (million)
% 44.51/7.90 % (22269)------------------------------
% 44.51/7.90 % (22269)------------------------------
% 44.51/7.91 % (22271)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_21964 for (2939ds/90Mi)
% 44.51/7.93 % (22268)Instruction limit reached!
% 44.51/7.93 % (22268)------------------------------
% 44.51/7.93 % (22268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.51/7.93 % (22268)Termination reason: Unknown
% 44.51/7.93 % (22268)Termination phase: Saturation
% 44.51/7.93
% 44.51/7.93 % (22268)Memory used [KB]: 7931
% 44.51/7.93 % (22268)Time elapsed: 0.411 s
% 44.51/7.93 % (22268)Instructions burned: 784 (million)
% 44.51/7.93 % (22268)------------------------------
% 44.51/7.93 % (22268)------------------------------
% 44.51/7.95 % (22272)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_21964 for (2938ds/346Mi)
% 44.51/7.96 % (22271)Instruction limit reached!
% 44.51/7.96 % (22271)------------------------------
% 44.51/7.96 % (22271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.51/7.96 % (22271)Termination reason: Unknown
% 44.51/7.96 % (22271)Termination phase: Saturation
% 44.51/7.96
% 44.51/7.96 % (22271)Memory used [KB]: 6652
% 44.51/7.96 % (22271)Time elapsed: 0.045 s
% 44.51/7.96 % (22271)Instructions burned: 91 (million)
% 44.51/7.96 % (22271)------------------------------
% 44.51/7.96 % (22271)------------------------------
% 44.51/7.97 % (22273)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_21964 for (2938ds/401Mi)
% 46.60/8.12 % (22272)Instruction limit reached!
% 46.60/8.12 % (22272)------------------------------
% 46.60/8.12 % (22272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.60/8.12 % (22272)Termination reason: Unknown
% 46.60/8.12 % (22272)Termination phase: Saturation
% 46.60/8.12
% 46.60/8.12 % (22272)Memory used [KB]: 7675
% 46.60/8.12 % (22272)Time elapsed: 0.174 s
% 46.60/8.12 % (22272)Instructions burned: 346 (million)
% 46.60/8.12 % (22272)------------------------------
% 46.60/8.12 % (22272)------------------------------
% 47.30/8.14 % (22274)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_21964 for (2936ds/6454Mi)
% 47.30/8.16 % (22273)Instruction limit reached!
% 47.30/8.16 % (22273)------------------------------
% 47.30/8.16 % (22273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.30/8.16 % (22273)Termination reason: Unknown
% 47.30/8.16 % (22273)Termination phase: Saturation
% 47.30/8.16
% 47.30/8.16 % (22273)Memory used [KB]: 8187
% 47.30/8.16 % (22273)Time elapsed: 0.193 s
% 47.30/8.16 % (22273)Instructions burned: 402 (million)
% 47.30/8.16 % (22273)------------------------------
% 47.30/8.16 % (22273)------------------------------
% 47.30/8.18 % (22275)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_21964 for (2936ds/283Mi)
% 47.69/8.29 % (22266)Instruction limit reached!
% 47.69/8.29 % (22266)------------------------------
% 47.69/8.29 % (22266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.69/8.29 % (22266)Termination reason: Unknown
% 47.69/8.29 % (22266)Termination phase: Saturation
% 47.69/8.29
% 47.69/8.29 % (22266)Memory used [KB]: 8315
% 47.69/8.29 % (22266)Time elapsed: 0.930 s
% 47.69/8.29 % (22266)Instructions burned: 1980 (million)
% 47.69/8.29 % (22266)------------------------------
% 47.69/8.29 % (22266)------------------------------
% 48.19/8.31 % (22276)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_21964 for (2935ds/865Mi)
% 48.19/8.32 % (22275)Instruction limit reached!
% 48.19/8.32 % (22275)------------------------------
% 48.19/8.32 % (22275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.19/8.32 % (22275)Termination reason: Unknown
% 48.19/8.32 % (22275)Termination phase: Saturation
% 48.19/8.32
% 48.19/8.32 % (22275)Memory used [KB]: 7164
% 48.19/8.32 % (22275)Time elapsed: 0.142 s
% 48.19/8.32 % (22275)Instructions burned: 283 (million)
% 48.19/8.32 % (22275)------------------------------
% 48.19/8.32 % (22275)------------------------------
% 48.19/8.34 % (22277)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_21964 for (2934ds/4528Mi)
% 48.19/8.35 % (22242)Instruction limit reached!
% 48.19/8.35 % (22242)------------------------------
% 48.19/8.35 % (22242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.19/8.35 % (22242)Termination reason: Unknown
% 48.19/8.35 % (22242)Termination phase: Saturation
% 48.19/8.35
% 48.19/8.35 % (22242)Memory used [KB]: 8699
% 48.19/8.35 % (22242)Time elapsed: 2.472 s
% 48.19/8.35 % (22242)Instructions burned: 5411 (million)
% 48.19/8.35 % (22242)------------------------------
% 48.19/8.35 % (22242)------------------------------
% 48.19/8.37 % (22278)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_21964 for (2934ds/1001Mi)
% 48.19/8.38 % (22257)Instruction limit reached!
% 48.19/8.38 % (22257)------------------------------
% 48.19/8.38 % (22257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.19/8.38 % (22257)Termination reason: Unknown
% 48.19/8.38 % (22257)Termination phase: Saturation
% 48.19/8.38
% 48.19/8.38 % (22257)Memory used [KB]: 11129
% 48.19/8.38 % (22257)Time elapsed: 1.636 s
% 48.19/8.38 % (22257)Instructions burned: 3374 (million)
% 48.19/8.38 % (22257)------------------------------
% 48.19/8.38 % (22257)------------------------------
% 48.71/8.40 % (22279)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_21964 for (2934ds/102Mi)
% 48.71/8.45 % (22279)Instruction limit reached!
% 48.71/8.45 % (22279)------------------------------
% 48.71/8.45 % (22279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.71/8.45 % (22279)Termination reason: Unknown
% 48.71/8.45 % (22279)Termination phase: Saturation
% 48.71/8.45
% 48.71/8.45 % (22279)Memory used [KB]: 6780
% 48.71/8.45 % (22279)Time elapsed: 0.048 s
% 48.71/8.45 % (22279)Instructions burned: 103 (million)
% 48.71/8.45 % (22279)------------------------------
% 48.71/8.45 % (22279)------------------------------
% 48.71/8.46 % (22280)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_21964 for (2933ds/952Mi)
% 49.18/8.65 % (22270)Instruction limit reached!
% 49.18/8.65 % (22270)------------------------------
% 49.18/8.65 % (22270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.18/8.65 % (22270)Termination reason: Unknown
% 49.18/8.65 % (22270)Termination phase: Saturation
% 49.18/8.65
% 49.18/8.65 % (22270)Memory used [KB]: 9722
% 49.18/8.65 % (22270)Time elapsed: 0.827 s
% 49.18/8.65 % (22270)Instructions burned: 1670 (million)
% 49.18/8.65 % (22270)------------------------------
% 49.18/8.65 % (22270)------------------------------
% 49.18/8.66 % (22281)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_21964 for (2931ds/578Mi)
% 49.34/8.70 % (22230)Instruction limit reached!
% 49.34/8.70 % (22230)------------------------------
% 49.34/8.70 % (22230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.34/8.70 % (22230)Termination reason: Unknown
% 49.34/8.70 % (22230)Termination phase: Saturation
% 49.34/8.70
% 49.34/8.70 % (22230)Memory used [KB]: 15351
% 49.34/8.70 % (22230)Time elapsed: 4.040 s
% 49.34/8.70 % (22230)Instructions burned: 8250 (million)
% 49.34/8.70 % (22230)------------------------------
% 49.34/8.70 % (22230)------------------------------
% 49.34/8.72 % (22282)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_21964 for (2931ds/643Mi)
% 49.34/8.74 % (22276)Instruction limit reached!
% 49.34/8.74 % (22276)------------------------------
% 49.34/8.74 % (22276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.34/8.74 % (22276)Termination reason: Unknown
% 49.34/8.74 % (22276)Termination phase: Saturation
% 49.34/8.74
% 49.34/8.74 % (22276)Memory used [KB]: 9722
% 49.34/8.74 % (22276)Time elapsed: 0.432 s
% 49.34/8.74 % (22276)Instructions burned: 865 (million)
% 49.34/8.74 % (22276)------------------------------
% 49.34/8.74 % (22276)------------------------------
% 49.34/8.75 % (22283)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_21964 for (2930ds/865Mi)
% 49.81/8.85 % (22278)Instruction limit reached!
% 49.81/8.85 % (22278)------------------------------
% 49.81/8.85 % (22278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.81/8.85 % (22278)Termination reason: Unknown
% 49.81/8.85 % (22278)Termination phase: Saturation
% 49.81/8.85
% 49.81/8.85 % (22278)Memory used [KB]: 8059
% 49.81/8.85 % (22278)Time elapsed: 0.484 s
% 49.81/8.85 % (22278)Instructions burned: 1001 (million)
% 49.81/8.85 % (22278)------------------------------
% 49.81/8.85 % (22278)------------------------------
% 49.81/8.87 % (22284)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_21964 for (2929ds/1174Mi)
% 50.31/8.94 % (22280)Instruction limit reached!
% 50.31/8.94 % (22280)------------------------------
% 50.31/8.94 % (22280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.31/8.94 % (22280)Termination reason: Unknown
% 50.31/8.94 % (22280)Termination phase: Saturation
% 50.31/8.94
% 50.31/8.94 % (22280)Memory used [KB]: 8699
% 50.31/8.94 % (22280)Time elapsed: 0.481 s
% 50.31/8.94 % (22280)Instructions burned: 952 (million)
% 50.31/8.94 % (22280)------------------------------
% 50.31/8.94 % (22280)------------------------------
% 50.31/8.95 % (22281)Instruction limit reached!
% 50.31/8.95 % (22281)------------------------------
% 50.31/8.95 % (22281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.31/8.95 % (22281)Termination reason: Unknown
% 50.31/8.95 % (22281)Termination phase: Saturation
% 50.31/8.95
% 50.31/8.95 % (22281)Memory used [KB]: 8955
% 50.31/8.95 % (22281)Time elapsed: 0.291 s
% 50.31/8.95 % (22281)Instructions burned: 579 (million)
% 50.31/8.95 % (22281)------------------------------
% 50.31/8.95 % (22281)------------------------------
% 50.31/8.96 % (22285)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_21964 for (2928ds/644Mi)
% 50.31/8.97 % (22286)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_21964 for (2928ds/1201Mi)
% 53.57/9.04 % (22282)Instruction limit reached!
% 53.57/9.04 % (22282)------------------------------
% 53.57/9.04 % (22282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.57/9.04 % (22282)Termination reason: Unknown
% 53.57/9.04 % (22282)Termination phase: Saturation
% 53.57/9.04
% 53.57/9.04 % (22282)Memory used [KB]: 8955
% 53.57/9.04 % (22282)Time elapsed: 0.318 s
% 53.57/9.04 % (22282)Instructions burned: 644 (million)
% 53.57/9.04 % (22282)------------------------------
% 53.57/9.04 % (22282)------------------------------
% 53.57/9.05 % (22287)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_21964 for (2927ds/1046Mi)
% 54.20/9.18 % (22283)Instruction limit reached!
% 54.20/9.18 % (22283)------------------------------
% 54.20/9.18 % (22283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.20/9.18 % (22283)Termination reason: Unknown
% 54.20/9.18 % (22283)Termination phase: Saturation
% 54.20/9.18
% 54.20/9.18 % (22283)Memory used [KB]: 9210
% 54.20/9.18 % (22283)Time elapsed: 0.430 s
% 54.20/9.18 % (22283)Instructions burned: 865 (million)
% 54.20/9.18 % (22283)------------------------------
% 54.20/9.18 % (22283)------------------------------
% 54.62/9.20 % (22288)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_21964 for (2926ds/222Mi)
% 54.62/9.28 % (22285)Instruction limit reached!
% 54.62/9.28 % (22285)------------------------------
% 54.62/9.28 % (22285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.62/9.28 % (22285)Termination reason: Unknown
% 54.62/9.28 % (22285)Termination phase: Saturation
% 54.62/9.28
% 54.62/9.28 % (22285)Memory used [KB]: 9083
% 54.62/9.28 % (22285)Time elapsed: 0.320 s
% 54.62/9.28 % (22285)Instructions burned: 644 (million)
% 54.62/9.28 % (22285)------------------------------
% 54.62/9.28 % (22285)------------------------------
% 54.62/9.30 % (22289)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_21964 for (2925ds/68Mi)
% 55.10/9.30 % (22288)Instruction limit reached!
% 55.10/9.30 % (22288)------------------------------
% 55.10/9.30 % (22288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.10/9.30 % (22288)Termination reason: Unknown
% 55.10/9.30 % (22288)Termination phase: Saturation
% 55.10/9.30
% 55.10/9.30 % (22288)Memory used [KB]: 7291
% 55.10/9.30 % (22288)Time elapsed: 0.105 s
% 55.10/9.30 % (22288)Instructions burned: 222 (million)
% 55.10/9.30 % (22288)------------------------------
% 55.10/9.30 % (22288)------------------------------
% 55.10/9.32 % (22290)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_21964 for (2925ds/454Mi)
% 55.10/9.33 % (22289)Instruction limit reached!
% 55.10/9.33 % (22289)------------------------------
% 55.10/9.33 % (22289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.10/9.33 % (22289)Termination reason: Unknown
% 55.10/9.33 % (22289)Termination phase: Function definition elimination
% 55.10/9.33
% 55.10/9.33 % (22289)Memory used [KB]: 2046
% 55.10/9.33 % (22289)Time elapsed: 0.036 s
% 55.10/9.33 % (22289)Instructions burned: 68 (million)
% 55.10/9.33 % (22289)------------------------------
% 55.10/9.33 % (22289)------------------------------
% 55.10/9.35 % (22291)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_21964 for (2924ds/360Mi)
% 55.68/9.45 % (22284)Instruction limit reached!
% 55.68/9.45 % (22284)------------------------------
% 55.68/9.45 % (22284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.68/9.45 % (22284)Termination reason: Unknown
% 55.68/9.45 % (22284)Termination phase: Saturation
% 55.68/9.45
% 55.68/9.45 % (22284)Memory used [KB]: 9083
% 55.68/9.45 % (22284)Time elapsed: 0.581 s
% 55.68/9.45 % (22284)Instructions burned: 1175 (million)
% 55.68/9.45 % (22284)------------------------------
% 55.68/9.45 % (22284)------------------------------
% 55.68/9.47 % (22292)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_21964 for (2923ds/157Mi)
% 56.04/9.52 % (22291)Instruction limit reached!
% 56.04/9.52 % (22291)------------------------------
% 56.04/9.52 % (22291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.04/9.52 % (22291)Termination reason: Unknown
% 56.04/9.52 % (22291)Termination phase: Saturation
% 56.04/9.52
% 56.04/9.52 % (22291)Memory used [KB]: 8059
% 56.04/9.52 % (22291)Time elapsed: 0.174 s
% 56.04/9.52 % (22291)Instructions burned: 360 (million)
% 56.04/9.52 % (22291)------------------------------
% 56.04/9.52 % (22291)------------------------------
% 56.04/9.53 % (22290)Instruction limit reached!
% 56.04/9.53 % (22290)------------------------------
% 56.04/9.53 % (22290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.04/9.53 % (22290)Termination reason: Unknown
% 56.04/9.53 % (22290)Termination phase: Saturation
% 56.04/9.53
% 56.04/9.53 % (22290)Memory used [KB]: 12281
% 56.04/9.53 % (22290)Time elapsed: 0.215 s
% 56.04/9.53 % (22290)Instructions burned: 455 (million)
% 56.04/9.53 % (22290)------------------------------
% 56.04/9.53 % (22290)------------------------------
% 56.04/9.54 % (22293)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_21964 for (2922ds/5061Mi)
% 56.04/9.54 % (22292)Instruction limit reached!
% 56.04/9.54 % (22292)------------------------------
% 56.04/9.54 % (22292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.04/9.54 % (22292)Termination reason: Unknown
% 56.04/9.54 % (22292)Termination phase: Saturation
% 56.04/9.54
% 56.04/9.54 % (22292)Memory used [KB]: 6908
% 56.04/9.54 % (22292)Time elapsed: 0.074 s
% 56.04/9.54 % (22292)Instructions burned: 157 (million)
% 56.04/9.54 % (22292)------------------------------
% 56.04/9.54 % (22292)------------------------------
% 56.04/9.55 % (22294)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_21964 for (2922ds/2401Mi)
% 56.04/9.55 % (22295)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_21964 for (2922ds/5798Mi)
% 56.04/9.55 % (22286)Instruction limit reached!
% 56.04/9.55 % (22286)------------------------------
% 56.04/9.55 % (22286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.04/9.55 % (22286)Termination reason: Unknown
% 56.04/9.55 % (22286)Termination phase: Saturation
% 56.04/9.55
% 56.04/9.55 % (22286)Memory used [KB]: 9338
% 56.04/9.55 % (22286)Time elapsed: 0.588 s
% 56.04/9.55 % (22286)Instructions burned: 1202 (million)
% 56.04/9.55 % (22286)------------------------------
% 56.04/9.55 % (22286)------------------------------
% 56.04/9.56 % (22287)Instruction limit reached!
% 56.04/9.56 % (22287)------------------------------
% 56.04/9.56 % (22287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.04/9.56 % (22287)Termination reason: Unknown
% 56.04/9.56 % (22287)Termination phase: Saturation
% 56.04/9.56
% 56.04/9.56 % (22287)Memory used [KB]: 8955
% 56.04/9.56 % (22287)Time elapsed: 0.507 s
% 56.04/9.56 % (22287)Instructions burned: 1046 (million)
% 56.04/9.56 % (22287)------------------------------
% 56.04/9.56 % (22287)------------------------------
% 56.04/9.57 % (22296)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_21964 for (2922ds/346Mi)
% 56.04/9.58 % (22297)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_21964 for (2922ds/1321Mi)
% 57.54/9.75 % (22296)Instruction limit reached!
% 57.54/9.75 % (22296)------------------------------
% 57.54/9.75 % (22296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.54/9.75 % (22296)Termination reason: Unknown
% 57.54/9.75 % (22296)Termination phase: Saturation
% 57.54/9.75
% 57.54/9.75 % (22296)Memory used [KB]: 7675
% 57.54/9.75 % (22296)Time elapsed: 0.176 s
% 57.54/9.75 % (22296)Instructions burned: 346 (million)
% 57.54/9.75 % (22296)------------------------------
% 57.54/9.75 % (22296)------------------------------
% 57.54/9.76 % (22298)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_21964 for (2920ds/1312Mi)
% 61.75/10.22 % (22297)Instruction limit reached!
% 61.75/10.22 % (22297)------------------------------
% 61.75/10.22 % (22297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.75/10.22 % (22297)Termination reason: Unknown
% 61.75/10.22 % (22297)Termination phase: Saturation
% 61.75/10.22
% 61.75/10.22 % (22297)Memory used [KB]: 4349
% 61.75/10.22 % (22297)Time elapsed: 0.650 s
% 61.75/10.22 % (22297)Instructions burned: 1321 (million)
% 61.75/10.22 % (22297)------------------------------
% 61.75/10.22 % (22297)------------------------------
% 61.75/10.24 % (22299)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_21964 for (2915ds/672Mi)
% 61.75/10.27 % (22277)Instruction limit reached!
% 61.75/10.27 % (22277)------------------------------
% 61.75/10.27 % (22277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.75/10.27 % (22277)Termination reason: Unknown
% 61.75/10.27 % (22277)Termination phase: Saturation
% 61.75/10.27
% 61.75/10.27 % (22277)Memory used [KB]: 3965
% 61.75/10.27 % (22277)Time elapsed: 1.933 s
% 61.75/10.27 % (22277)Instructions burned: 4528 (million)
% 61.75/10.27 % (22277)------------------------------
% 61.75/10.27 % (22277)------------------------------
% 61.75/10.28 % (22300)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_21964 for (2915ds/1897Mi)
% 62.37/10.39 % (22298)Instruction limit reached!
% 62.37/10.39 % (22298)------------------------------
% 62.37/10.39 % (22298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.37/10.39 % (22298)Termination reason: Unknown
% 62.37/10.39 % (22298)Termination phase: Saturation
% 62.37/10.39
% 62.37/10.39 % (22298)Memory used [KB]: 9210
% 62.37/10.39 % (22298)Time elapsed: 0.625 s
% 62.37/10.39 % (22298)Instructions burned: 1313 (million)
% 62.37/10.39 % (22298)------------------------------
% 62.37/10.39 % (22298)------------------------------
% 62.87/10.40 % (22301)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_21964 for (2914ds/1202Mi)
% 63.26/10.58 % (22299)Instruction limit reached!
% 63.26/10.58 % (22299)------------------------------
% 63.26/10.58 % (22299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.26/10.58 % (22299)Termination reason: Unknown
% 63.26/10.58 % (22299)Termination phase: Saturation
% 63.26/10.58
% 63.26/10.58 % (22299)Memory used [KB]: 7419
% 63.26/10.58 % (22299)Time elapsed: 0.362 s
% 63.26/10.58 % (22299)Instructions burned: 673 (million)
% 63.26/10.58 % (22299)------------------------------
% 63.26/10.58 % (22299)------------------------------
% 64.02/10.60 % (22302)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_21964 for (2912ds/1493Mi)
% 64.02/10.65 % (22302)Refutation not found, incomplete strategy
% 64.02/10.65 % (22302)------------------------------
% 64.02/10.65 % (22302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.02/10.65 % (22302)Termination reason: Refutation not found, incomplete strategy
% 64.02/10.65
% 64.02/10.65
% 64.02/10.65 % (22302)Memory used [KB]: 6780
% 64.02/10.65 % (22302)Time elapsed: 0.051 s
% 64.02/10.65 % (22302)Instructions burned: 108 (million)
% 64.02/10.65 % (22302)------------------------------
% 64.02/10.65 % (22302)------------------------------
% 64.02/10.67 % (22303)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_21964 for (2911ds/7679Mi)
% 64.49/10.71 % (22294)Instruction limit reached!
% 64.49/10.71 % (22294)------------------------------
% 64.49/10.71 % (22294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.49/10.71 % (22294)Termination reason: Unknown
% 64.49/10.71 % (22294)Termination phase: Saturation
% 64.49/10.71
% 64.49/10.71 % (22294)Memory used [KB]: 6652
% 64.49/10.71 % (22294)Time elapsed: 1.158 s
% 64.49/10.71 % (22294)Instructions burned: 2402 (million)
% 64.49/10.71 % (22294)------------------------------
% 64.49/10.71 % (22294)------------------------------
% 64.49/10.72 % (22304)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_21964 for (2911ds/340Mi)
% 64.79/10.89 % (22304)Instruction limit reached!
% 64.79/10.89 % (22304)------------------------------
% 64.79/10.89 % (22304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.79/10.89 % (22304)Termination reason: Unknown
% 64.79/10.89 % (22304)Termination phase: Saturation
% 64.79/10.89
% 64.79/10.89 % (22304)Memory used [KB]: 8443
% 64.79/10.89 % (22304)Time elapsed: 0.172 s
% 64.79/10.89 % (22304)Instructions burned: 340 (million)
% 64.79/10.89 % (22304)------------------------------
% 64.79/10.89 % (22304)------------------------------
% 65.28/10.91 % (22305)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_21964 for (2909ds/3672Mi)
% 65.28/10.99 % (22301)Instruction limit reached!
% 65.28/10.99 % (22301)------------------------------
% 65.28/10.99 % (22301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.28/10.99 % (22301)Termination reason: Unknown
% 65.28/10.99 % (22301)Termination phase: Saturation
% 65.28/10.99
% 65.28/10.99 % (22301)Memory used [KB]: 4989
% 65.28/10.99 % (22301)Time elapsed: 0.610 s
% 65.28/10.99 % (22301)Instructions burned: 1202 (million)
% 65.28/10.99 % (22301)------------------------------
% 65.28/10.99 % (22301)------------------------------
% 65.28/11.01 % (22306)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_21964 for (2908ds/1535Mi)
% 68.75/11.21 % (22300)Instruction limit reached!
% 68.75/11.21 % (22300)------------------------------
% 68.75/11.21 % (22300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.75/11.21 % (22300)Termination reason: Unknown
% 68.75/11.21 % (22300)Termination phase: Saturation
% 68.75/11.21
% 68.75/11.21 % (22300)Memory used [KB]: 8955
% 68.75/11.21 % (22300)Time elapsed: 0.931 s
% 68.75/11.21 % (22300)Instructions burned: 1897 (million)
% 68.75/11.21 % (22300)------------------------------
% 68.75/11.21 % (22300)------------------------------
% 68.75/11.23 % (22307)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_21964 for (2906ds/4637Mi)
% 68.75/11.23 % (22274)Refutation not found, non-redundant clauses discarded% (22274)------------------------------
% 68.75/11.23 % (22274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.75/11.23 % (22274)Termination reason: Refutation not found, non-redundant clauses discarded
% 68.75/11.23
% 68.75/11.23 % (22274)Memory used [KB]: 11129
% 68.75/11.23 % (22274)Time elapsed: 3.096 s
% 68.75/11.23 % (22274)Instructions burned: 6425 (million)
% 68.75/11.23 % (22274)------------------------------
% 68.75/11.23 % (22274)------------------------------
% 68.75/11.25 % (22308)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_21964 for (2905ds/3174Mi)
% 71.29/11.74 % (22306)Instruction limit reached!
% 71.29/11.74 % (22306)------------------------------
% 71.29/11.74 % (22306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.29/11.74 % (22306)Termination reason: Unknown
% 71.29/11.74 % (22306)Termination phase: Saturation
% 71.29/11.74
% 71.29/11.74 % (22306)Memory used [KB]: 12409
% 71.29/11.74 % (22306)Time elapsed: 0.762 s
% 71.29/11.74 % (22306)Instructions burned: 1535 (million)
% 71.29/11.74 % (22306)------------------------------
% 71.29/11.74 % (22306)------------------------------
% 71.29/11.76 % (22309)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_21964 for (2900ds/307Mi)
% 72.17/11.90 % (22309)Instruction limit reached!
% 72.17/11.90 % (22309)------------------------------
% 72.17/11.90 % (22309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.17/11.90 % (22309)Termination reason: Unknown
% 72.17/11.90 % (22309)Termination phase: Saturation
% 72.17/11.90
% 72.17/11.90 % (22309)Memory used [KB]: 7419
% 72.17/11.90 % (22309)Time elapsed: 0.146 s
% 72.17/11.90 % (22309)Instructions burned: 307 (million)
% 72.17/11.90 % (22309)------------------------------
% 72.17/11.90 % (22309)------------------------------
% 72.17/11.92 % (22310)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_21964 for (2899ds/3619Mi)
% 72.17/12.01 % (22305)Instruction limit reached!
% 72.17/12.01 % (22305)------------------------------
% 72.17/12.01 % (22305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.17/12.01 % (22305)Termination reason: Unknown
% 72.17/12.01 % (22305)Termination phase: Saturation
% 72.17/12.01
% 72.17/12.01 % (22305)Memory used [KB]: 7931
% 72.17/12.01 % (22305)Time elapsed: 1.126 s
% 72.17/12.01 % (22305)Instructions burned: 3672 (million)
% 72.17/12.01 % (22305)------------------------------
% 72.17/12.01 % (22305)------------------------------
% 74.52/12.03 % (22311)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_21964 for (2897ds/2325Mi)
% 74.52/12.06 % (22293)Instruction limit reached!
% 74.52/12.06 % (22293)------------------------------
% 74.52/12.06 % (22293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.52/12.06 % (22293)Termination reason: Unknown
% 74.52/12.06 % (22293)Termination phase: Saturation
% 74.52/12.06
% 74.52/12.06 % (22293)Memory used [KB]: 14200
% 74.52/12.06 % (22293)Time elapsed: 2.530 s
% 74.52/12.06 % (22293)Instructions burned: 5062 (million)
% 74.52/12.06 % (22293)------------------------------
% 74.52/12.06 % (22293)------------------------------
% 74.52/12.08 % (22312)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_21964 for (2897ds/2341Mi)
% 75.43/12.26 % (22295)Instruction limit reached!
% 75.43/12.26 % (22295)------------------------------
% 75.43/12.26 % (22295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.43/12.26 % (22295)Termination reason: Unknown
% 75.43/12.26 % (22295)Termination phase: Saturation
% 75.43/12.26
% 75.43/12.26 % (22295)Memory used [KB]: 8955
% 75.43/12.26 % (22295)Time elapsed: 2.708 s
% 75.43/12.26 % (22295)Instructions burned: 5799 (million)
% 75.43/12.26 % (22295)------------------------------
% 75.43/12.26 % (22295)------------------------------
% 75.43/12.28 % (22313)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_21964 for (2895ds/7257Mi)
% 75.90/12.32 % (22313)Refutation not found, incomplete strategy
% 75.90/12.32 % (22313)------------------------------
% 75.90/12.32 % (22313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.90/12.32 % (22313)Termination reason: Refutation not found, incomplete strategy
% 75.90/12.32
% 75.90/12.32
% 75.90/12.32 % (22313)Memory used [KB]: 6908
% 75.90/12.32 % (22313)Time elapsed: 0.043 s
% 75.90/12.32 % (22313)Instructions burned: 81 (million)
% 75.90/12.32 % (22313)------------------------------
% 75.90/12.32 % (22313)------------------------------
% 75.90/12.34 % (22314)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_21964 for (2894ds/3710Mi)
% 77.97/12.81 % (22308)Instruction limit reached!
% 77.97/12.81 % (22308)------------------------------
% 77.97/12.81 % (22308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.97/12.81 % (22308)Termination reason: Unknown
% 77.97/12.81 % (22308)Termination phase: Saturation
% 77.97/12.81
% 77.97/12.81 % (22308)Memory used [KB]: 10106
% 77.97/12.81 % (22308)Time elapsed: 1.557 s
% 77.97/12.81 % (22308)Instructions burned: 3175 (million)
% 77.97/12.81 % (22308)------------------------------
% 77.97/12.81 % (22308)------------------------------
% 77.97/12.82 % (22315)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_21964 for (2890ds/326Mi)
% 78.29/12.92 % (22312)Instruction limit reached!
% 78.29/12.92 % (22312)------------------------------
% 78.29/12.92 % (22312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.29/12.92 % (22312)Termination reason: Unknown
% 78.29/12.92 % (22312)Termination phase: Saturation
% 78.29/12.92
% 78.29/12.92 % (22312)Memory used [KB]: 7931
% 78.29/12.92 % (22312)Time elapsed: 0.842 s
% 78.29/12.92 % (22312)Instructions burned: 2343 (million)
% 78.29/12.92 % (22312)------------------------------
% 78.29/12.92 % (22312)------------------------------
% 78.29/12.94 % (22316)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_21964 for (2888ds/1100Mi)
% 78.29/12.98 % (22315)Instruction limit reached!
% 78.29/12.98 % (22315)------------------------------
% 78.29/12.98 % (22315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.29/12.98 % (22315)Termination reason: Unknown
% 78.29/12.98 % (22315)Termination phase: Saturation
% 78.29/12.98
% 78.29/12.98 % (22315)Memory used [KB]: 7036
% 78.29/12.98 % (22315)Time elapsed: 0.163 s
% 78.29/12.98 % (22315)Instructions burned: 327 (million)
% 78.29/12.98 % (22315)------------------------------
% 78.29/12.98 % (22315)------------------------------
% 78.29/13.00 % (22317)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_21964 for (2888ds/406Mi)
% 82.23/13.19 % (22311)Instruction limit reached!
% 82.23/13.19 % (22311)------------------------------
% 82.23/13.19 % (22311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.23/13.19 % (22311)Termination reason: Unknown
% 82.23/13.19 % (22311)Termination phase: Saturation
% 82.23/13.19
% 82.23/13.19 % (22311)Memory used [KB]: 11513
% 82.23/13.19 % (22311)Time elapsed: 1.166 s
% 82.23/13.19 % (22311)Instructions burned: 2326 (million)
% 82.23/13.19 % (22311)------------------------------
% 82.23/13.19 % (22311)------------------------------
% 82.72/13.20 % (22317)Instruction limit reached!
% 82.72/13.20 % (22317)------------------------------
% 82.72/13.20 % (22317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.72/13.20 % (22317)Termination reason: Unknown
% 82.72/13.20 % (22317)Termination phase: Saturation
% 82.72/13.20
% 82.72/13.20 % (22317)Memory used [KB]: 7675
% 82.72/13.20 % (22317)Time elapsed: 0.204 s
% 82.72/13.20 % (22317)Instructions burned: 406 (million)
% 82.72/13.20 % (22317)------------------------------
% 82.72/13.20 % (22317)------------------------------
% 82.72/13.21 % (22318)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_21964 for (2886ds/1871Mi)
% 82.72/13.22 % (22319)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_21964 for (2886ds/1194Mi)
% 83.74/13.48 % (22307)Instruction limit reached!
% 83.74/13.48 % (22307)------------------------------
% 83.74/13.48 % (22307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.74/13.48 % (22307)Termination reason: Unknown
% 83.74/13.48 % (22307)Termination phase: Saturation
% 83.74/13.48
% 83.74/13.48 % (22307)Memory used [KB]: 11769
% 83.74/13.48 % (22307)Time elapsed: 2.279 s
% 83.74/13.48 % (22307)Instructions burned: 4638 (million)
% 83.74/13.48 % (22307)------------------------------
% 83.74/13.48 % (22307)------------------------------
% 83.74/13.48 % (22316)Instruction limit reached!
% 83.74/13.48 % (22316)------------------------------
% 83.74/13.48 % (22316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.74/13.48 % (22316)Termination reason: Unknown
% 83.74/13.48 % (22316)Termination phase: Saturation
% 83.74/13.48
% 83.74/13.48 % (22316)Memory used [KB]: 10618
% 83.74/13.48 % (22316)Time elapsed: 0.548 s
% 83.74/13.48 % (22316)Instructions burned: 1101 (million)
% 83.74/13.48 % (22316)------------------------------
% 83.74/13.48 % (22316)------------------------------
% 84.25/13.50 % (22320)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_21964 for (2883ds/474Mi)
% 84.25/13.50 % (22321)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_21964 for (2883ds/3115Mi)
% 84.55/13.68 % (22310)Instruction limit reached!
% 84.55/13.68 % (22310)------------------------------
% 84.55/13.68 % (22310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.55/13.68 % (22310)Termination reason: Unknown
% 84.55/13.68 % (22310)Termination phase: Saturation
% 84.55/13.68
% 84.55/13.68 % (22310)Memory used [KB]: 12281
% 84.55/13.68 % (22310)Time elapsed: 1.755 s
% 84.55/13.68 % (22310)Instructions burned: 3620 (million)
% 84.55/13.68 % (22310)------------------------------
% 84.55/13.68 % (22310)------------------------------
% 84.55/13.69 % (22322)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_21964 for (2881ds/831Mi)
% 84.83/13.73 % (22320)Instruction limit reached!
% 84.83/13.73 % (22320)------------------------------
% 84.83/13.73 % (22320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.83/13.73 % (22320)Termination reason: Unknown
% 84.83/13.73 % (22320)Termination phase: Saturation
% 84.83/13.73
% 84.83/13.73 % (22320)Memory used [KB]: 8187
% 84.83/13.73 % (22320)Time elapsed: 0.237 s
% 84.83/13.73 % (22320)Instructions burned: 474 (million)
% 84.83/13.73 % (22320)------------------------------
% 84.83/13.73 % (22320)------------------------------
% 84.83/13.75 % (22323)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_21964 for (2880ds/1188Mi)
% 85.29/13.82 % (22319)Instruction limit reached!
% 85.29/13.82 % (22319)------------------------------
% 85.29/13.82 % (22319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.29/13.82 % (22319)Termination reason: Unknown
% 85.29/13.82 % (22319)Termination phase: Saturation
% 85.29/13.82
% 85.29/13.82 % (22319)Memory used [KB]: 8955
% 85.29/13.82 % (22319)Time elapsed: 0.606 s
% 85.29/13.82 % (22319)Instructions burned: 1195 (million)
% 85.29/13.82 % (22319)------------------------------
% 85.29/13.82 % (22319)------------------------------
% 85.29/13.84 % (22324)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_21964 for (2879ds/2868Mi)
% 86.10/13.93 % (22324)Refutation not found, incomplete strategy
% 86.10/13.93 % (22324)------------------------------
% 86.10/13.93 % (22324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.10/13.93 % (22324)Termination reason: Refutation not found, incomplete strategy
% 86.10/13.93
% 86.10/13.93
% 86.10/13.93 % (22324)Memory used [KB]: 7675
% 86.10/13.93 % (22324)Time elapsed: 0.094 s
% 86.10/13.93 % (22324)Instructions burned: 196 (million)
% 86.10/13.93 % (22324)------------------------------
% 86.10/13.93 % (22324)------------------------------
% 86.10/13.95 % (22325)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_21964 for (2878ds/1516Mi)
% 88.51/14.10 % (22322)Instruction limit reached!
% 88.51/14.10 % (22322)------------------------------
% 88.51/14.10 % (22322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 88.51/14.10 % (22322)Termination reason: Unknown
% 88.51/14.10 % (22322)Termination phase: Saturation
% 88.51/14.10
% 88.51/14.10 % (22322)Memory used [KB]: 8699
% 88.51/14.10 % (22322)Time elapsed: 0.409 s
% 88.51/14.10 % (22322)Instructions burned: 831 (million)
% 88.51/14.10 % (22322)------------------------------
% 88.51/14.10 % (22322)------------------------------
% 88.51/14.12 % (22326)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_21964 for (2877ds/2321Mi)
% 89.22/14.13 % (22318)Instruction limit reached!
% 89.22/14.13 % (22318)------------------------------
% 89.22/14.13 % (22318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.22/14.13 % (22318)Termination reason: Unknown
% 89.22/14.13 % (22318)Termination phase: Saturation
% 89.22/14.13
% 89.22/14.13 % (22318)Memory used [KB]: 10234
% 89.22/14.13 % (22318)Time elapsed: 0.921 s
% 89.22/14.13 % (22318)Instructions burned: 1871 (million)
% 89.22/14.13 % (22318)------------------------------
% 89.22/14.13 % (22318)------------------------------
% 89.22/14.13 % (22314)Instruction limit reached!
% 89.22/14.13 % (22314)------------------------------
% 89.22/14.13 % (22314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.22/14.13 % (22314)Termination reason: Unknown
% 89.22/14.13 % (22314)Termination phase: Saturation
% 89.22/14.13
% 89.22/14.13 % (22314)Memory used [KB]: 14072
% 89.22/14.13 % (22314)Time elapsed: 1.798 s
% 89.22/14.13 % (22314)Instructions burned: 3710 (million)
% 89.22/14.13 % (22314)------------------------------
% 89.22/14.13 % (22314)------------------------------
% 89.22/14.15 % (22327)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_21964 for (2876ds/2812Mi)
% 89.22/14.15 % (22328)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_21964 for (2876ds/4604Mi)
% 89.53/14.21 % (22326)Refutation not found, incomplete strategy
% 89.53/14.21 % (22326)------------------------------
% 89.53/14.21 % (22326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.53/14.21 % (22326)Termination reason: Refutation not found, incomplete strategy
% 89.53/14.21
% 89.53/14.21
% 89.53/14.21 % (22326)Memory used [KB]: 7675
% 89.53/14.21 % (22326)Time elapsed: 0.098 s
% 89.53/14.21 % (22326)Instructions burned: 204 (million)
% 89.53/14.21 % (22326)------------------------------
% 89.53/14.21 % (22326)------------------------------
% 89.53/14.23 % (22303)Instruction limit reached!
% 89.53/14.23 % (22303)------------------------------
% 89.53/14.23 % (22303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.53/14.23 % (22303)Termination reason: Unknown
% 89.53/14.23 % (22303)Termination phase: Saturation
% 89.53/14.23
% 89.53/14.23 % (22303)Memory used [KB]: 13176
% 89.53/14.23 % (22303)Time elapsed: 3.584 s
% 89.53/14.23 % (22303)Instructions burned: 7679 (million)
% 89.53/14.23 % (22303)------------------------------
% 89.53/14.23 % (22303)------------------------------
% 89.53/14.23 % (22329)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_21964 for (2876ds/2678Mi)
% 89.53/14.25 % (22330)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_21964 for (2875ds/643Mi)
% 89.98/14.33 % (22323)Instruction limit reached!
% 89.98/14.33 % (22323)------------------------------
% 89.98/14.33 % (22323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.98/14.33 % (22323)Termination reason: Unknown
% 89.98/14.33 % (22323)Termination phase: Saturation
% 89.98/14.33
% 89.98/14.33 % (22323)Memory used [KB]: 9210
% 89.98/14.33 % (22323)Time elapsed: 0.585 s
% 89.98/14.33 % (22323)Instructions burned: 1188 (million)
% 89.98/14.33 % (22323)------------------------------
% 89.98/14.33 % (22323)------------------------------
% 89.98/14.35 % (22331)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_21964 for (2874ds/458Mi)
% 90.43/14.56 % (22330)Instruction limit reached!
% 90.43/14.56 % (22330)------------------------------
% 90.43/14.56 % (22330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.43/14.56 % (22330)Termination reason: Unknown
% 90.43/14.56 % (22330)Termination phase: Saturation
% 90.43/14.56
% 90.43/14.56 % (22330)Memory used [KB]: 8955
% 90.43/14.56 % (22330)Time elapsed: 0.317 s
% 90.43/14.56 % (22330)Instructions burned: 643 (million)
% 90.43/14.56 % (22330)------------------------------
% 90.43/14.56 % (22330)------------------------------
% 90.43/14.58 % (22331)Instruction limit reached!
% 90.43/14.58 % (22331)------------------------------
% 90.43/14.58 % (22331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.43/14.58 % (22331)Termination reason: Unknown
% 90.43/14.58 % (22331)Termination phase: Saturation
% 90.43/14.58
% 90.43/14.58 % (22331)Memory used [KB]: 7803
% 90.43/14.58 % (22331)Time elapsed: 0.226 s
% 90.43/14.58 % (22331)Instructions burned: 458 (million)
% 90.43/14.58 % (22331)------------------------------
% 90.43/14.58 % (22331)------------------------------
% 90.43/14.58 % (22332)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_21964 for (2872ds/2546Mi)
% 90.43/14.59 % (22333)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_21964 for (2872ds/1432Mi)
% 91.40/14.71 % (22325)Instruction limit reached!
% 91.40/14.71 % (22325)------------------------------
% 91.40/14.71 % (22325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.40/14.71 % (22325)Termination reason: Unknown
% 91.40/14.71 % (22325)Termination phase: Saturation
% 91.40/14.71
% 91.40/14.71 % (22325)Memory used [KB]: 8187
% 91.40/14.71 % (22325)Time elapsed: 0.778 s
% 91.40/14.71 % (22325)Instructions burned: 1517 (million)
% 91.40/14.71 % (22325)------------------------------
% 91.40/14.71 % (22325)------------------------------
% 91.40/14.73 % (22334)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_21964 for (2871ds/386Mi)
% 91.62/14.92 % (22334)Instruction limit reached!
% 91.62/14.92 % (22334)------------------------------
% 91.62/14.92 % (22334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.62/14.92 % (22334)Termination reason: Unknown
% 91.62/14.92 % (22334)Termination phase: Saturation
% 91.62/14.92
% 91.62/14.92 % (22334)Memory used [KB]: 8187
% 91.62/14.92 % (22334)Time elapsed: 0.208 s
% 91.62/14.92 % (22334)Instructions burned: 386 (million)
% 91.62/14.92 % (22334)------------------------------
% 91.62/14.92 % (22334)------------------------------
% 91.62/14.93 % (22335)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_21964 for (2869ds/360Mi)
% 95.51/15.03 % (22321)Instruction limit reached!
% 95.51/15.03 % (22321)------------------------------
% 95.51/15.03 % (22321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 95.51/15.03 % (22321)Termination reason: Unknown
% 95.51/15.03 % (22321)Termination phase: Saturation
% 95.51/15.03
% 95.51/15.03 % (22321)Memory used [KB]: 12409
% 95.51/15.03 % (22321)Time elapsed: 1.527 s
% 95.51/15.03 % (22321)Instructions burned: 3115 (million)
% 95.51/15.03 % (22321)------------------------------
% 95.51/15.03 % (22321)------------------------------
% 95.51/15.04 % (22336)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_21964 for (2867ds/5446Mi)
% 95.51/15.10 % (22335)Instruction limit reached!
% 95.51/15.10 % (22335)------------------------------
% 95.51/15.10 % (22335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 95.51/15.10 % (22335)Termination reason: Unknown
% 95.51/15.10 % (22335)Termination phase: Saturation
% 95.51/15.10
% 95.51/15.10 % (22335)Memory used [KB]: 8059
% 95.51/15.10 % (22335)Time elapsed: 0.195 s
% 95.51/15.10 % (22335)Instructions burned: 360 (million)
% 95.51/15.10 % (22335)------------------------------
% 95.51/15.10 % (22335)------------------------------
% 95.51/15.12 % (22337)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_21964 for (2867ds/2573Mi)
% 96.46/15.26 % (22333)Instruction limit reached!
% 96.46/15.26 % (22333)------------------------------
% 96.46/15.26 % (22333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 96.46/15.26 % (22333)Termination reason: Unknown
% 96.46/15.26 % (22333)Termination phase: Saturation
% 96.46/15.26
% 96.46/15.26 % (22333)Memory used [KB]: 11769
% 96.46/15.26 % (22333)Time elapsed: 0.672 s
% 96.46/15.26 % (22333)Instructions burned: 1433 (million)
% 96.46/15.26 % (22333)------------------------------
% 96.46/15.26 % (22333)------------------------------
% 96.46/15.28 % (22338)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_21964 for (2865ds/2655Mi)
% 97.74/15.55 % (22329)Instruction limit reached!
% 97.74/15.55 % (22329)------------------------------
% 97.74/15.55 % (22329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.74/15.55 % (22329)Termination reason: Unknown
% 97.74/15.55 % (22329)Termination phase: Saturation
% 97.74/15.55
% 97.74/15.55 % (22329)Memory used [KB]: 10362
% 97.74/15.55 % (22329)Time elapsed: 1.323 s
% 97.74/15.55 % (22329)Instructions burned: 2680 (million)
% 97.74/15.55 % (22329)------------------------------
% 97.74/15.55 % (22329)------------------------------
% 97.74/15.57 % (22339)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_21964 for (2862ds/2781Mi)
% 97.74/15.57 % (22327)Instruction limit reached!
% 97.74/15.57 % (22327)------------------------------
% 97.74/15.57 % (22327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.74/15.57 % (22327)Termination reason: Unknown
% 97.74/15.57 % (22327)Termination phase: Saturation
% 97.74/15.57
% 97.74/15.57 % (22327)Memory used [KB]: 11513
% 97.74/15.57 % (22327)Time elapsed: 1.424 s
% 97.74/15.57 % (22327)Instructions burned: 2813 (million)
% 97.74/15.57 % (22327)------------------------------
% 97.74/15.57 % (22327)------------------------------
% 97.74/15.59 % (22340)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_21964 for (2862ds/307Mi)
% 98.29/15.73 % (22340)Instruction limit reached!
% 98.29/15.73 % (22340)------------------------------
% 98.29/15.73 % (22340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.29/15.73 % (22340)Termination reason: Unknown
% 98.29/15.73 % (22340)Termination phase: Saturation
% 98.29/15.73
% 98.29/15.73 % (22340)Memory used [KB]: 7419
% 98.29/15.73 % (22340)Time elapsed: 0.144 s
% 98.29/15.73 % (22340)Instructions burned: 308 (million)
% 98.29/15.73 % (22340)------------------------------
% 98.29/15.73 % (22340)------------------------------
% 98.29/15.75 % (22341)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_21964 for (2860ds/1548Mi)
% 98.66/15.88 % (22332)Instruction limit reached!
% 98.66/15.88 % (22332)------------------------------
% 98.66/15.88 % (22332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.66/15.88 % (22332)Termination reason: Unknown
% 98.66/15.88 % (22332)Termination phase: Saturation
% 98.66/15.88
% 98.66/15.88 % (22332)Memory used [KB]: 10746
% 98.66/15.88 % (22332)Time elapsed: 1.297 s
% 98.66/15.88 % (22332)Instructions burned: 2547 (million)
% 98.66/15.88 % (22332)------------------------------
% 98.66/15.88 % (22332)------------------------------
% 98.66/15.89 % (22342)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_21964 for (2859ds/5214Mi)
% 103.61/16.29 % (22328)Instruction limit reached!
% 103.61/16.29 % (22328)------------------------------
% 103.61/16.29 % (22328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 103.61/16.29 % (22328)Termination reason: Unknown
% 103.61/16.29 % (22328)Termination phase: Saturation
% 103.61/16.29
% 103.61/16.29 % (22328)Memory used [KB]: 11769
% 103.61/16.29 % (22328)Time elapsed: 2.140 s
% 103.61/16.29 % (22328)Instructions burned: 4605 (million)
% 103.61/16.29 % (22328)------------------------------
% 103.61/16.29 % (22328)------------------------------
% 104.29/16.31 % (22343)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_21964 for (2855ds/3201Mi)
% 104.29/16.36 % (22337)Instruction limit reached!
% 104.29/16.36 % (22337)------------------------------
% 104.29/16.36 % (22337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.29/16.36 % (22337)Termination reason: Unknown
% 104.29/16.36 % (22337)Termination phase: Saturation
% 104.29/16.36
% 104.29/16.36 % (22337)Memory used [KB]: 12281
% 104.29/16.36 % (22337)Time elapsed: 1.258 s
% 104.29/16.36 % (22337)Instructions burned: 2574 (million)
% 104.29/16.36 % (22337)------------------------------
% 104.29/16.36 % (22337)------------------------------
% 104.29/16.38 % (22344)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_21964 for (2854ds/454Mi)
% 104.87/16.49 % (22341)Instruction limit reached!
% 104.87/16.49 % (22341)------------------------------
% 104.87/16.49 % (22341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.87/16.49 % (22341)Termination reason: Unknown
% 104.87/16.49 % (22341)Termination phase: Saturation
% 104.87/16.49
% 104.87/16.49 % (22341)Memory used [KB]: 9978
% 104.87/16.49 % (22341)Time elapsed: 0.734 s
% 104.87/16.49 % (22341)Instructions burned: 1548 (million)
% 104.87/16.49 % (22341)------------------------------
% 104.87/16.49 % (22341)------------------------------
% 105.38/16.51 % (22345)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_21964 for (2853ds/3049Mi)
% 105.38/16.56 % (22338)Instruction limit reached!
% 105.38/16.56 % (22338)------------------------------
% 105.38/16.56 % (22338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.38/16.56 % (22338)Termination reason: Unknown
% 105.38/16.56 % (22338)Termination phase: Saturation
% 105.38/16.56
% 105.38/16.56 % (22338)Memory used [KB]: 16502
% 105.38/16.56 % (22338)Time elapsed: 1.304 s
% 105.38/16.56 % (22338)Instructions burned: 2656 (million)
% 105.38/16.56 % (22338)------------------------------
% 105.38/16.56 % (22338)------------------------------
% 105.38/16.58 % (22346)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_21964 for (2852ds/7311Mi)
% 105.38/16.59 % (22344)Instruction limit reached!
% 105.38/16.59 % (22344)------------------------------
% 105.38/16.59 % (22344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 105.38/16.59 % (22344)Termination reason: Unknown
% 105.38/16.59 % (22344)Termination phase: Saturation
% 105.38/16.59
% 105.38/16.59 % (22344)Memory used [KB]: 12537
% 105.38/16.59 % (22344)Time elapsed: 0.219 s
% 105.38/16.59 % (22344)Instructions burned: 455 (million)
% 105.38/16.59 % (22344)------------------------------
% 105.38/16.59 % (22344)------------------------------
% 105.99/16.61 % (22347)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_21964 for (2852ds/6804Mi)
% 106.89/16.96 % (22339)Instruction limit reached!
% 106.89/16.96 % (22339)------------------------------
% 106.89/16.96 % (22339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 106.89/16.96 % (22339)Termination reason: Unknown
% 106.89/16.96 % (22339)Termination phase: Saturation
% 106.89/16.96
% 106.89/16.96 % (22339)Memory used [KB]: 4733
% 106.89/16.96 % (22339)Time elapsed: 1.417 s
% 106.89/16.96 % (22339)Instructions burned: 2781 (million)
% 106.89/16.96 % (22339)------------------------------
% 106.89/16.96 % (22339)------------------------------
% 106.89/16.98 % (22348)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_21964 for (2848ds/1683Mi)
% 114.79/17.82 % (22348)Instruction limit reached!
% 114.79/17.82 % (22348)------------------------------
% 114.79/17.82 % (22348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.79/17.82 % (22348)Termination reason: Unknown
% 114.79/17.82 % (22348)Termination phase: Saturation
% 114.79/17.82
% 114.79/17.83 % (22348)Memory used [KB]: 9594
% 114.79/17.83 % (22348)Time elapsed: 0.847 s
% 114.79/17.83 % (22348)Instructions burned: 1683 (million)
% 114.79/17.83 % (22348)------------------------------
% 114.79/17.83 % (22348)------------------------------
% 114.79/17.84 % (22349)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_21964 for (2839ds/4688Mi)
% 114.79/17.86 % (22336)Instruction limit reached!
% 114.79/17.86 % (22336)------------------------------
% 114.79/17.86 % (22336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.79/17.86 % (22336)Termination reason: Unknown
% 114.79/17.86 % (22336)Termination phase: Saturation
% 114.79/17.86
% 114.79/17.86 % (22336)Memory used [KB]: 17270
% 114.79/17.86 % (22336)Time elapsed: 2.835 s
% 114.79/17.86 % (22336)Instructions burned: 5447 (million)
% 114.79/17.86 % (22336)------------------------------
% 114.79/17.86 % (22336)------------------------------
% 114.79/17.88 % (22350)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_21964 for (2839ds/2207Mi)
% 114.79/17.88 % (22343)Instruction limit reached!
% 114.79/17.88 % (22343)------------------------------
% 114.79/17.88 % (22343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 114.79/17.88 % (22343)Termination reason: Unknown
% 114.79/17.88 % (22343)Termination phase: Saturation
% 114.79/17.88
% 114.79/17.88 % (22343)Memory used [KB]: 10490
% 114.79/17.88 % (22343)Time elapsed: 1.578 s
% 114.79/17.88 % (22343)Instructions burned: 3201 (million)
% 114.79/17.88 % (22343)------------------------------
% 114.79/17.88 % (22343)------------------------------
% 115.40/17.90 % (22351)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=8216:si=on:rtra=on_0 on DTF2THF_21964 for (2839ds/8216Mi)
% 115.40/18.04 % (22345)Instruction limit reached!
% 115.40/18.04 % (22345)------------------------------
% 115.40/18.04 % (22345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 115.40/18.04 % (22345)Termination reason: Unknown
% 115.40/18.04 % (22345)Termination phase: Saturation
% 115.40/18.04
% 115.40/18.04 % (22345)Memory used [KB]: 9338
% 115.40/18.04 % (22345)Time elapsed: 1.537 s
% 115.40/18.04 % (22345)Instructions burned: 3049 (million)
% 115.40/18.04 % (22345)------------------------------
% 115.40/18.04 % (22345)------------------------------
% 116.46/18.06 % (22352)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_21964 for (2837ds/430Mi)
% 117.43/18.27 % (22352)Instruction limit reached!
% 117.43/18.27 % (22352)------------------------------
% 117.43/18.27 % (22352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 117.43/18.27 % (22352)Termination reason: Unknown
% 117.43/18.27 % (22352)Termination phase: Saturation
% 117.43/18.27
% 117.43/18.27 % (22352)Memory used [KB]: 7675
% 117.43/18.27 % (22352)Time elapsed: 0.212 s
% 117.43/18.27 % (22352)Instructions burned: 430 (million)
% 117.43/18.27 % (22352)------------------------------
% 117.43/18.27 % (22352)------------------------------
% 117.43/18.29 % (22353)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_21964 for (2835ds/2012Mi)
% 118.85/18.46 % (22342)Instruction limit reached!
% 118.85/18.46 % (22342)------------------------------
% 118.85/18.46 % (22342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 118.85/18.46 % (22342)Termination reason: Unknown
% 118.85/18.46 % (22342)Termination phase: Saturation
% 118.85/18.46
% 118.85/18.46 % (22342)Memory used [KB]: 18805
% 118.85/18.46 % (22342)Time elapsed: 2.566 s
% 118.85/18.46 % (22342)Instructions burned: 5215 (million)
% 118.85/18.46 % (22342)------------------------------
% 118.85/18.46 % (22342)------------------------------
% 118.85/18.47 % (22354)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_21964 for (2833ds/631Mi)
% 120.40/18.79 % (22354)Instruction limit reached!
% 120.40/18.79 % (22354)------------------------------
% 120.40/18.79 % (22354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 120.40/18.79 % (22354)Termination reason: Unknown
% 120.40/18.79 % (22354)Termination phase: Saturation
% 120.40/18.79
% 120.40/18.79 % (22354)Memory used [KB]: 8955
% 120.40/18.79 % (22354)Time elapsed: 0.317 s
% 120.40/18.79 % (22354)Instructions burned: 632 (million)
% 120.40/18.79 % (22354)------------------------------
% 120.40/18.79 % (22354)------------------------------
% 121.24/18.81 % (22355)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_21964 for (2830ds/8785Mi)
% 121.73/18.99 % (22350)Instruction limit reached!
% 121.73/18.99 % (22350)------------------------------
% 121.73/18.99 % (22350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 121.73/18.99 % (22350)Termination reason: Unknown
% 121.73/18.99 % (22350)Termination phase: Saturation
% 121.73/18.99
% 121.73/18.99 % (22350)Memory used [KB]: 9722
% 121.73/18.99 % (22350)Time elapsed: 1.116 s
% 121.73/18.99 % (22350)Instructions burned: 2207 (million)
% 121.73/18.99 % (22350)------------------------------
% 121.73/18.99 % (22350)------------------------------
% 121.73/19.01 % (22356)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_21964 for (2828ds/739Mi)
% 124.56/19.27 % (22353)Instruction limit reached!
% 124.56/19.27 % (22353)------------------------------
% 124.56/19.27 % (22353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 124.56/19.27 % (22353)Termination reason: Unknown
% 124.56/19.27 % (22353)Termination phase: Saturation
% 124.56/19.27
% 124.56/19.27 % (22353)Memory used [KB]: 19829
% 124.56/19.27 % (22353)Time elapsed: 0.991 s
% 124.56/19.27 % (22353)Instructions burned: 2013 (million)
% 124.56/19.27 % (22353)------------------------------
% 124.56/19.27 % (22353)------------------------------
% 124.56/19.29 % (22357)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_21964 for (2825ds/5473Mi)
% 125.25/19.39 % (22356)Instruction limit reached!
% 125.25/19.39 % (22356)------------------------------
% 125.25/19.39 % (22356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 125.25/19.39 % (22356)Termination reason: Unknown
% 125.25/19.39 % (22356)Termination phase: Saturation
% 125.25/19.39
% 125.25/19.39 % (22356)Memory used [KB]: 8315
% 125.25/19.39 % (22356)Time elapsed: 0.380 s
% 125.25/19.39 % (22356)Instructions burned: 739 (million)
% 125.25/19.39 % (22356)------------------------------
% 125.25/19.39 % (22356)------------------------------
% 125.83/19.40 % (22358)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_21964 for (2824ds/43570Mi)
% 128.34/19.93 % (22347)Instruction limit reached!
% 128.34/19.93 % (22347)------------------------------
% 128.34/19.93 % (22347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 128.34/19.93 % (22347)Termination reason: Unknown
% 128.34/19.93 % (22347)Termination phase: Saturation
% 128.34/19.93
% 128.34/19.93 % (22347)Memory used [KB]: 11257
% 128.34/19.93 % (22347)Time elapsed: 3.325 s
% 128.34/19.93 % (22347)Instructions burned: 6805 (million)
% 128.34/19.93 % (22347)------------------------------
% 128.34/19.93 % (22347)------------------------------
% 128.34/19.95 % (22359)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_21964 for (2818ds/8382Mi)
% 131.08/20.17 % (22349)Instruction limit reached!
% 131.08/20.17 % (22349)------------------------------
% 131.08/20.17 % (22349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 131.08/20.17 % (22349)Termination reason: Unknown
% 131.08/20.17 % (22349)Termination phase: Saturation
% 131.08/20.17
% 131.08/20.17 % (22349)Memory used [KB]: 10618
% 131.08/20.17 % (22349)Time elapsed: 2.327 s
% 131.08/20.17 % (22349)Instructions burned: 4689 (million)
% 131.08/20.17 % (22349)------------------------------
% 131.08/20.17 % (22349)------------------------------
% 131.08/20.19 % (22360)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_21964 for (2816ds/407Mi)
% 131.55/20.21 % (22346)Instruction limit reached!
% 131.55/20.21 % (22346)------------------------------
% 131.55/20.21 % (22346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 131.55/20.21 % (22346)Termination reason: Unknown
% 131.55/20.21 % (22346)Termination phase: Saturation
% 131.55/20.21
% 131.55/20.21 % (22346)Memory used [KB]: 10874
% 131.55/20.21 % (22346)Time elapsed: 3.625 s
% 131.55/20.21 % (22346)Instructions burned: 7311 (million)
% 131.55/20.21 % (22346)------------------------------
% 131.55/20.21 % (22346)------------------------------
% 131.55/20.23 % (22361)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_21964 for (2816ds/2971Mi)
% 132.08/20.32 % (22361)Refutation not found, incomplete strategy
% 132.08/20.32 % (22361)------------------------------
% 132.08/20.32 % (22361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 132.08/20.32 % (22361)Termination reason: Refutation not found, incomplete strategy
% 132.08/20.32
% 132.08/20.32
% 132.08/20.32 % (22361)Memory used [KB]: 7675
% 132.08/20.32 % (22361)Time elapsed: 0.096 s
% 132.08/20.32 % (22361)Instructions burned: 196 (million)
% 132.08/20.32 % (22361)------------------------------
% 132.08/20.32 % (22361)------------------------------
% 132.08/20.34 % (22362)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_21964 for (2814ds/9822Mi)
% 132.69/20.42 % (22360)Instruction limit reached!
% 132.69/20.42 % (22360)------------------------------
% 132.69/20.42 % (22360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 132.69/20.42 % (22360)Termination reason: Unknown
% 132.69/20.42 % (22360)Termination phase: Saturation
% 132.69/20.42
% 132.69/20.42 % (22360)Memory used [KB]: 7675
% 132.69/20.42 % (22360)Time elapsed: 0.232 s
% 132.69/20.42 % (22360)Instructions burned: 408 (million)
% 132.69/20.42 % (22360)------------------------------
% 132.69/20.42 % (22360)------------------------------
% 132.69/20.44 % (22363)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_21964 for (2813ds/8425Mi)
% 142.72/21.82 % (22357)Instruction limit reached!
% 142.72/21.82 % (22357)------------------------------
% 142.72/21.82 % (22357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 142.72/21.82 % (22357)Termination reason: Unknown
% 142.72/21.82 % (22357)Termination phase: Saturation
% 142.72/21.82
% 142.72/21.82 % (22357)Memory used [KB]: 10106
% 142.72/21.82 % (22357)Time elapsed: 2.524 s
% 142.72/21.82 % (22357)Instructions burned: 5474 (million)
% 142.72/21.82 % (22357)------------------------------
% 142.72/21.82 % (22357)------------------------------
% 142.72/21.83 % (22364)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_21964 for (2800ds/3107Mi)
% 142.72/21.84 % (22351)Instruction limit reached!
% 142.72/21.84 % (22351)------------------------------
% 142.72/21.84 % (22351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 142.72/21.84 % (22351)Termination reason: Unknown
% 142.72/21.84 % (22351)Termination phase: Saturation
% 142.72/21.84
% 142.72/21.84 % (22351)Memory used [KB]: 12409
% 142.72/21.84 % (22351)Time elapsed: 3.944 s
% 142.72/21.84 % (22351)Instructions burned: 8216 (million)
% 142.72/21.84 % (22351)------------------------------
% 142.72/21.84 % (22351)------------------------------
% 142.72/21.86 % (22365)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_21964 for (2799ds/7967Mi)
% 143.31/21.92 % (22365)Refutation not found, incomplete strategy
% 143.31/21.92 % (22365)------------------------------
% 143.31/21.92 % (22365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 143.31/21.92 % (22365)Termination reason: Refutation not found, incomplete strategy
% 143.31/21.92
% 143.31/21.92
% 143.31/21.92 % (22365)Memory used [KB]: 7547
% 143.31/21.92 % (22365)Time elapsed: 0.059 s
% 143.31/21.92 % (22365)Instructions burned: 191 (million)
% 143.31/21.92 % (22365)------------------------------
% 143.31/21.92 % (22365)------------------------------
% 143.31/21.93 % (22366)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_21964 for (2799ds/3629Mi)
% 146.89/22.46 % (22355)Instruction limit reached!
% 146.89/22.46 % (22355)------------------------------
% 146.89/22.46 % (22355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 146.89/22.46 % (22355)Termination reason: Unknown
% 146.89/22.46 % (22355)Termination phase: Saturation
% 146.89/22.46
% 146.89/22.46 % (22355)Memory used [KB]: 13944
% 146.89/22.46 % (22355)Time elapsed: 3.654 s
% 146.89/22.46 % (22355)Instructions burned: 8787 (million)
% 146.89/22.46 % (22355)------------------------------
% 146.89/22.46 % (22355)------------------------------
% 146.89/22.47 % (22367)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_21964 for (2793ds/939Mi)
% 148.76/22.76 % (22367)Instruction limit reached!
% 148.76/22.76 % (22367)------------------------------
% 148.76/22.76 % (22367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 148.76/22.76 % (22367)Termination reason: Unknown
% 148.76/22.76 % (22367)Termination phase: Saturation
% 148.76/22.76
% 148.76/22.76 % (22367)Memory used [KB]: 7931
% 148.76/22.76 % (22367)Time elapsed: 0.290 s
% 148.76/22.76 % (22367)Instructions burned: 941 (million)
% 148.76/22.76 % (22367)------------------------------
% 148.76/22.76 % (22367)------------------------------
% 148.76/22.77 % (22368)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_21964 for (2790ds/1188Mi)
% 149.67/22.87 % (22364)Instruction limit reached!
% 149.67/22.87 % (22364)------------------------------
% 149.67/22.87 % (22364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 149.67/22.87 % (22364)Termination reason: Unknown
% 149.67/22.87 % (22364)Termination phase: Saturation
% 149.67/22.87
% 149.67/22.87 % (22364)Memory used [KB]: 10746
% 149.67/22.87 % (22364)Time elapsed: 1.045 s
% 149.67/22.87 % (22364)Instructions burned: 3110 (million)
% 149.67/22.87 % (22364)------------------------------
% 149.67/22.87 % (22364)------------------------------
% 149.67/22.88 % (22369)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_21964 for (2789ds/3205Mi)
% 151.19/23.06 % (22366)Instruction limit reached!
% 151.19/23.06 % (22366)------------------------------
% 151.19/23.06 % (22366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 151.19/23.06 % (22366)Termination reason: Unknown
% 151.19/23.06 % (22366)Termination phase: Saturation
% 151.19/23.06
% 151.19/23.06 % (22366)Memory used [KB]: 12537
% 151.19/23.06 % (22366)Time elapsed: 1.138 s
% 151.19/23.06 % (22366)Instructions burned: 3631 (million)
% 151.19/23.06 % (22366)------------------------------
% 151.19/23.06 % (22366)------------------------------
% 151.19/23.07 % (22370)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_21964 for (2787ds/865Mi)
% 151.86/23.13 % (22368)Instruction limit reached!
% 151.86/23.13 % (22368)------------------------------
% 151.86/23.13 % (22368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 151.86/23.13 % (22368)Termination reason: Unknown
% 151.86/23.13 % (22368)Termination phase: Saturation
% 151.86/23.13
% 151.86/23.13 % (22368)Memory used [KB]: 9594
% 151.86/23.13 % (22368)Time elapsed: 0.363 s
% 151.86/23.13 % (22368)Instructions burned: 1190 (million)
% 151.86/23.13 % (22368)------------------------------
% 151.86/23.13 % (22368)------------------------------
% 151.86/23.14 % (22371)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_21964 for (2786ds/7469Mi)
% 152.79/23.34 % (22370)Instruction limit reached!
% 152.79/23.34 % (22370)------------------------------
% 152.79/23.34 % (22370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 152.79/23.34 % (22370)Termination reason: Unknown
% 152.79/23.34 % (22370)Termination phase: Saturation
% 152.79/23.34
% 152.79/23.34 % (22370)Memory used [KB]: 9210
% 152.79/23.34 % (22370)Time elapsed: 0.294 s
% 152.79/23.34 % (22370)Instructions burned: 866 (million)
% 152.79/23.34 % (22370)------------------------------
% 152.79/23.34 % (22370)------------------------------
% 152.79/23.35 % (22372)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_21964 for (2784ds/4165Mi)
% 154.08/23.59 % (22363)Instruction limit reached!
% 154.08/23.59 % (22363)------------------------------
% 154.08/23.59 % (22363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 154.08/23.59 % (22363)Termination reason: Unknown
% 154.08/23.59 % (22363)Termination phase: Saturation
% 154.08/23.59
% 154.08/23.59 % (22363)Memory used [KB]: 13944
% 154.08/23.59 % (22363)Time elapsed: 3.158 s
% 154.08/23.59 % (22363)Instructions burned: 8427 (million)
% 154.08/23.59 % (22363)------------------------------
% 154.08/23.59 % (22363)------------------------------
% 154.58/23.60 % (22450)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_21964 for (2782ds/13468Mi)
% 154.99/23.79 % (22359)Instruction limit reached!
% 154.99/23.79 % (22359)------------------------------
% 154.99/23.79 % (22359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 154.99/23.79 % (22359)Termination reason: Unknown
% 154.99/23.79 % (22359)Termination phase: Saturation
% 154.99/23.79
% 154.99/23.79 % (22359)Memory used [KB]: 19573
% 154.99/23.79 % (22359)Time elapsed: 3.844 s
% 154.99/23.79 % (22359)Instructions burned: 8383 (million)
% 154.99/23.79 % (22359)------------------------------
% 154.99/23.79 % (22359)------------------------------
% 155.39/23.80 % (22538)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_21964 for (2780ds/2635Mi)
% 155.39/23.88 % (22369)Instruction limit reached!
% 155.39/23.88 % (22369)------------------------------
% 155.39/23.88 % (22369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 155.39/23.88 % (22369)Termination reason: Unknown
% 155.39/23.88 % (22369)Termination phase: Saturation
% 155.39/23.88
% 155.39/23.88 % (22369)Memory used [KB]: 10618
% 155.39/23.88 % (22369)Time elapsed: 0.998 s
% 155.39/23.88 % (22369)Instructions burned: 3206 (million)
% 155.39/23.88 % (22369)------------------------------
% 155.39/23.88 % (22369)------------------------------
% 155.39/23.89 % (22556)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=631:si=on:rtra=on_0 on DTF2THF_21964 for (2779ds/631Mi)
% 155.68/23.92 % (22362)Instruction limit reached!
% 155.68/23.92 % (22362)------------------------------
% 155.68/23.92 % (22362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 155.68/23.92 % (22362)Termination reason: Unknown
% 155.68/23.92 % (22362)Termination phase: Saturation
% 155.68/23.92
% 155.68/23.92 % (22362)Memory used [KB]: 14583
% 155.68/23.92 % (22362)Time elapsed: 3.585 s
% 155.68/23.92 % (22362)Instructions burned: 9824 (million)
% 155.68/23.92 % (22362)------------------------------
% 155.68/23.92 % (22362)------------------------------
% 155.68/23.93 % (22569)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on DTF2THF_21964 for (2778ds/15557Mi)
% 158.20/24.08 % (22556)Instruction limit reached!
% 158.20/24.08 % (22556)------------------------------
% 158.20/24.08 % (22556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 158.20/24.08 % (22556)Termination reason: Unknown
% 158.20/24.08 % (22556)Termination phase: Saturation
% 158.20/24.08
% 158.20/24.08 % (22556)Memory used [KB]: 8955
% 158.20/24.08 % (22556)Time elapsed: 0.216 s
% 158.20/24.08 % (22556)Instructions burned: 633 (million)
% 158.20/24.08 % (22556)------------------------------
% 158.20/24.08 % (22556)------------------------------
% 158.20/24.09 % (22606)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on DTF2THF_21964 for (2777ds/2142Mi)
% 161.19/24.52 % (22450)First to succeed.
% 161.19/24.52 % (22450)Refutation found. Thanks to Tanya!
% 161.19/24.52 % SZS status Theorem for DTF2THF_21964
% 161.19/24.52 % SZS output start Proof for DTF2THF_21964
% 161.19/24.52 thf(type_def_5, type, itself: ($tType) > $tType).
% 161.19/24.52 thf(type_def_7, type, nat: $tType).
% 161.19/24.52 thf(type_def_8, type, coindu1593790203_llist: ($tType) > $tType).
% 161.19/24.52 thf(type_def_9, type, extended_enat: $tType).
% 161.19/24.52 thf(type_def_10, type, product_prod: ($tType * $tType) > $tType).
% 161.19/24.52 thf(type_def_11, type, set: ($tType) > $tType).
% 161.19/24.52 thf(type_def_12, type, a: $tType).
% 161.19/24.52 thf(func_def_0, type, coindu1593790203_llist: ($tType) > $tType).
% 161.19/24.52 thf(func_def_1, type, product_prod: ($tType * $tType) > $tType).
% 161.19/24.52 thf(func_def_2, type, extended_enat: $tType).
% 161.19/24.52 thf(func_def_3, type, set: ($tType) > $tType).
% 161.19/24.52 thf(func_def_4, type, nat: $tType).
% 161.19/24.52 thf(func_def_5, type, itself: ($tType) > $tType).
% 161.19/24.52 thf(func_def_6, type, a: $tType).
% 161.19/24.52 thf(func_def_7, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 161.19/24.52 thf(func_def_8, type, zero: !>[X0: $tType]:(itself @ X0 > $o)).
% 161.19/24.52 thf(func_def_9, type, minus: !>[X0: $tType]:(itself @ X0 > $o)).
% 161.19/24.52 thf(func_def_10, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 161.19/24.52 thf(func_def_11, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 161.19/24.52 thf(func_def_12, type, group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 161.19/24.52 thf(func_def_13, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 161.19/24.52 thf(func_def_14, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 161.19/24.52 thf(func_def_15, type, comm_monoid_diff: !>[X0: $tType]:(itself @ X0 > $o)).
% 161.19/24.52 thf(func_def_16, type, linordered_semidom: !>[X0: $tType]:(itself @ X0 > $o)).
% 161.19/24.52 thf(func_def_17, type, ordered_ab_group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 161.19/24.52 thf(func_def_18, type, cancel1352612707id_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 161.19/24.52 thf(func_def_19, type, cancel146912293up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 161.19/24.52 thf(func_def_20, type, comple187826305attice: !>[X0: $tType]:(itself @ X0 > $o)).
% 161.19/24.52 thf(func_def_21, type, canoni770627133id_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 161.19/24.52 thf(func_def_22, type, coindu493225792length: !>[X0: $tType]:(nat > coindu1593790203_llist @ X0 > extended_enat)).
% 161.19/24.52 thf(func_def_23, type, coindu268472904append: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_24, type, coindu1213758845finite: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 161.19/24.52 thf(func_def_25, type, coindu1018505716length: !>[X0: $tType]:(coindu1593790203_llist @ X0 > extended_enat)).
% 161.19/24.52 thf(func_def_26, type, coindu300403952lexord: !>[X0: $tType]:((X0 > X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 161.19/24.52 thf(func_def_27, type, coindu1121789889_LCons: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_28, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_29, type, coindu1046438764le_lhd: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 161.19/24.52 thf(func_def_30, type, coindu987187967t_all2: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > $o)).
% 161.19/24.52 thf(func_def_31, type, coindu1062782156e_lmap: !>[X0: $tType, X1: $tType]:((X0 > X1) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1)).
% 161.19/24.52 thf(func_def_32, type, coindu335574135_lnull: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 161.19/24.52 thf(func_def_33, type, coindu1047225960le_ltl: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_34, type, coindu567634248member: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > $o)).
% 161.19/24.52 thf(func_def_35, type, coindu1696667936prefix: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 161.19/24.52 thf(func_def_36, type, coindu574146665prefix: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 161.19/24.52 thf(func_def_37, type, coindu1802687541_ltake: !>[X0: $tType]:(extended_enat > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_38, type, coindu721411036eWhile: !>[X0: $tType]:((X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_39, type, coindu847746867e_lzip: !>[X0: $tType, X1: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X1 > coindu1593790203_llist @ product_prod @ X0 @ X1)).
% 161.19/24.52 thf(func_def_40, type, extended_case_enat: !>[X0: $tType]:((nat > X0) > X0 > extended_enat > X0)).
% 161.19/24.52 thf(func_def_41, type, extended_the_enat: extended_enat > nat).
% 161.19/24.52 thf(func_def_42, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 161.19/24.52 thf(func_def_43, type, zero_zero: !>[X0: $tType]:(X0)).
% 161.19/24.52 thf(func_def_44, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 161.19/24.52 thf(func_def_45, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 161.19/24.52 thf(func_def_46, type, ord_min: !>[X0: $tType]:(X0 > X0 > X0)).
% 161.19/24.52 thf(func_def_47, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 161.19/24.52 thf(func_def_48, type, type2: !>[X0: $tType]:(itself @ X0)).
% 161.19/24.52 thf(func_def_49, type, inv_imagep: !>[X0: $tType, X1: $tType]:((X0 > X0 > $o) > (X1 > X0) > X1 > X1 > $o)).
% 161.19/24.52 thf(func_def_50, type, transp: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 161.19/24.52 thf(func_def_51, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 161.19/24.52 thf(func_def_52, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 161.19/24.52 thf(func_def_53, type, m: extended_enat).
% 161.19/24.52 thf(func_def_54, type, n: extended_enat).
% 161.19/24.52 thf(func_def_55, type, xs: coindu1593790203_llist @ a).
% 161.19/24.52 thf(func_def_78, type, sK1: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_79, type, sK2: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 161.19/24.52 thf(func_def_80, type, sK3: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_81, type, sK4: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > X0)).
% 161.19/24.52 thf(func_def_82, type, sK5: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0)).
% 161.19/24.52 thf(func_def_83, type, sK6: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_84, type, sK7: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_85, type, sK8: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_86, type, sK9: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 161.19/24.52 thf(func_def_87, type, sK10: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 161.19/24.52 thf(func_def_88, type, sK11: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 161.19/24.52 thf(func_def_89, type, sK12: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 161.19/24.52 thf(func_def_90, type, sK13: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > X1) > X0)).
% 161.19/24.52 thf(func_def_91, type, sK14: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_92, type, sK15: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 161.19/24.52 thf(func_def_93, type, sK16: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_94, type, sK17: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 161.19/24.52 thf(func_def_95, type, sK18: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 161.19/24.52 thf(func_def_96, type, sK19: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 161.19/24.52 thf(func_def_97, type, sK20: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_98, type, sK21: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 161.19/24.52 thf(func_def_99, type, sK22: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_100, type, sK23: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_101, type, sK24: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 161.19/24.52 thf(func_def_102, type, sK25: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 161.19/24.52 thf(func_def_103, type, sK26: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 161.19/24.52 thf(func_def_104, type, sK27: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_105, type, sK28: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_106, type, sK29: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > X0)).
% 161.19/24.52 thf(func_def_107, type, sK30: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_108, type, sK31: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 161.19/24.52 thf(func_def_109, type, sK32: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(func_def_110, type, ph33: !>[X0: $tType]:(X0)).
% 161.19/24.52 thf(func_def_111, type, sK34: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 161.19/24.52 thf(func_def_112, type, sK35: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 161.19/24.52 thf(f10153,plain,(
% 161.19/24.52 $false),
% 161.19/24.52 inference(avatar_sat_refutation,[status(thm)],[f1810,f3928,f10148])).
% 161.19/24.52 thf(f10148,plain,(
% 161.19/24.52 ~spl0_1),
% 161.19/24.52 inference(avatar_contradiction_clause,[status(thm)],[f10147])).
% 161.19/24.52 thf(f10147,plain,(
% 161.19/24.52 $false | ~spl0_1),
% 161.19/24.52 inference(trivial_inequality_removal,[status(thm)],[f10129])).
% 161.19/24.52 thf(f10129,plain,(
% 161.19/24.52 ($true = $false) | ~spl0_1),
% 161.19/24.52 inference(superposition,[status(thm)],[f3163,f10086])).
% 161.19/24.52 thf(f10086,plain,(
% 161.19/24.52 ((coindu1696667936prefix @ a @ (coindu1802687541_ltake @ a @ n @ xs) @ (coindu1802687541_ltake @ a @ n @ xs)) = $false) | ~spl0_1),
% 161.19/24.52 inference(superposition,[status(thm)],[f9836,f3952])).
% 161.19/24.52 thf(f3952,plain,(
% 161.19/24.52 (n = (ord_min @ extended_enat @ n @ m)) | ~spl0_1),
% 161.19/24.52 inference(trivial_inequality_removal,[status(thm)],[f3951])).
% 161.19/24.52 thf(f3951,plain,(
% 161.19/24.52 ($true = $false) | (n = (ord_min @ extended_enat @ n @ m)) | ~spl0_1),
% 161.19/24.52 inference(forward_demodulation,[status(thm)],[f3947,f1282])).
% 161.19/24.52 thf(f1282,plain,(
% 161.19/24.52 ((ord @ extended_enat @ type2 @ extended_enat) = $true)),
% 161.19/24.52 inference(cnf_transformation,[status(thm)],[f620])).
% 161.19/24.52 thf(f620,plain,(
% 161.19/24.52 ((ord @ extended_enat @ type2 @ extended_enat) = $true)),
% 161.19/24.52 inference(fool_elimination,[status(thm)],[f619])).
% 161.19/24.52 thf(f619,plain,(
% 161.19/24.52 (ord @ extended_enat @ type2 @ extended_enat)),
% 161.19/24.52 inference(rectify,[status(thm)],[f285])).
% 161.19/24.52 thf(f285,axiom,(
% 161.19/24.52 (ord @ extended_enat @ type2 @ extended_enat)),
% 161.19/24.52 file('/export/starexec/sandbox/tmp/tmp.ZCwsuNV1cP/DTF2THF_21964.p',tcon_Extended__Nat_Oenat___Orderings_Oord_21)).
% 161.19/24.52 thf(f3947,plain,(
% 161.19/24.52 (n = (ord_min @ extended_enat @ n @ m)) | ((ord @ extended_enat @ type2 @ extended_enat) = $false) | ~spl0_1),
% 161.19/24.52 inference(trivial_inequality_removal,[status(thm)],[f3935])).
% 161.19/24.52 thf(f3935,plain,(
% 161.19/24.52 (n = (ord_min @ extended_enat @ n @ m)) | ($true = $false) | ((ord @ extended_enat @ type2 @ extended_enat) = $false) | ~spl0_1),
% 161.19/24.52 inference(superposition,[status(thm)],[f1805,f1961])).
% 161.19/24.52 thf(f1961,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((ord_less_eq @ X0 @ X2 @ X1) = $false) | ((ord @ X0 @ type2 @ X0) = $false) | ((ord_min @ X0 @ X2 @ X1) = X2)) )),
% 161.19/24.52 inference(equality_proxy_clausification,[status(thm)],[f1960])).
% 161.19/24.52 thf(f1960,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((ord_less_eq @ X0 @ X2 @ X1) = $false) | ($true = ((ord_min @ X0 @ X2 @ X1) = X2)) | ((ord @ X0 @ type2 @ X0) = $false)) )),
% 161.19/24.52 inference(binary_proxy_clausification,[status(thm)],[f1959])).
% 161.19/24.52 thf(f1959,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((ord_less_eq @ X0 @ X2 @ X1) => ((ord_min @ X0 @ X2 @ X1) = X2)) = $true) | ((ord @ X0 @ type2 @ X0) = $false)) )),
% 161.19/24.52 inference(beta_eta_normalization,[status(thm)],[f1958])).
% 161.19/24.52 thf(f1958,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((ord @ X0 @ type2 @ X0) = $false) | (((^[Y0 : X0]: ((ord_less_eq @ X0 @ Y0 @ X1) => ((ord_min @ X0 @ Y0 @ X1) = Y0))) @ X2) = $true)) )),
% 161.19/24.52 inference(pi_clausification,[status(thm)],[f1957])).
% 161.19/24.52 thf(f1957,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X1 : X0] : (((!! @ X0 @ (^[Y0 : X0]: ((ord_less_eq @ X0 @ Y0 @ X1) => ((ord_min @ X0 @ Y0 @ X1) = Y0)))) = $true) | ((ord @ X0 @ type2 @ X0) = $false)) )),
% 161.19/24.52 inference(beta_eta_normalization,[status(thm)],[f1956])).
% 161.19/24.52 thf(f1956,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X1 : X0] : ((((^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less_eq @ X0 @ Y1 @ Y0) => ((ord_min @ X0 @ Y1 @ Y0) = Y1))))) @ X1) = $true) | ((ord @ X0 @ type2 @ X0) = $false)) )),
% 161.19/24.52 inference(pi_clausification,[status(thm)],[f1955])).
% 161.19/24.52 thf(f1955,plain,(
% 161.19/24.52 ( ! [X0 : $tType] : (((ord @ X0 @ type2 @ X0) = $false) | ($true = (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less_eq @ X0 @ Y1 @ Y0) => ((ord_min @ X0 @ Y1 @ Y0) = Y1)))))))) )),
% 161.19/24.52 inference(binary_proxy_clausification,[status(thm)],[f1348])).
% 161.19/24.52 thf(f1348,plain,(
% 161.19/24.52 ( ! [X0 : $tType] : ((((ord @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less_eq @ X0 @ Y1 @ Y0) => ((ord_min @ X0 @ Y1 @ Y0) = Y1))))))) = $true)) )),
% 161.19/24.52 inference(cnf_transformation,[status(thm)],[f1070])).
% 161.19/24.52 thf(f1070,plain,(
% 161.19/24.52 ! [X0 : $tType] : (((ord @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less_eq @ X0 @ Y1 @ Y0) => ((ord_min @ X0 @ Y1 @ Y0) = Y1))))))) = $true)),
% 161.19/24.52 inference(closure,[status(thm)],[f317])).
% 161.19/24.52 thf(f317,plain,(
% 161.19/24.52 ( ! [X0 : $tType] : ((((ord @ X0 @ type2 @ X0) => (!! @ X0 @ (^[Y0 : X0]: (!! @ X0 @ (^[Y1 : X0]: ((ord_less_eq @ X0 @ Y1 @ Y0) => ((ord_min @ X0 @ Y1 @ Y0) = Y1))))))) = $true)) )),
% 161.19/24.52 inference(fool_elimination,[status(thm)],[f316])).
% 161.19/24.52 thf(f316,plain,(
% 161.19/24.52 ! [X0 : $tType] : ((ord @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : X0] : ((ord_less_eq @ X0 @ X1 @ X2) => ((ord_min @ X0 @ X1 @ X2) = X1)))),
% 161.19/24.52 inference(rectify,[status(thm)],[f62])).
% 161.19/24.52 thf(f62,axiom,(
% 161.19/24.52 ! [X0 : $tType] : ((ord @ X0 @ type2 @ X0) => ! [X5 : X0,X9 : X0] : ((ord_less_eq @ X0 @ X5 @ X9) => ((ord_min @ X0 @ X5 @ X9) = X5)))),
% 161.19/24.52 file('/export/starexec/sandbox/tmp/tmp.ZCwsuNV1cP/DTF2THF_21964.p',fact_61_min__absorb1)).
% 161.19/24.52 thf(f1805,plain,(
% 161.19/24.52 ((ord_less_eq @ extended_enat @ n @ m) = $true) | ~spl0_1),
% 161.19/24.52 inference(avatar_component_clause,[status(thm)],[f1803])).
% 161.19/24.52 thf(f1803,definition,(
% 161.19/24.52 spl0_1 <=> ((ord_less_eq @ extended_enat @ n @ m) = $true)),
% 161.19/24.52 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 161.19/24.52 thf(f9836,plain,(
% 161.19/24.52 ( ! [X0 : extended_enat] : (($false = (coindu1696667936prefix @ a @ (coindu1802687541_ltake @ a @ n @ xs) @ (coindu1802687541_ltake @ a @ (ord_min @ extended_enat @ X0 @ m) @ xs)))) )),
% 161.19/24.52 inference(forward_demodulation,[status(thm)],[f9828,f3381])).
% 161.19/24.52 thf(f3381,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : extended_enat,X3 : extended_enat,X1 : coindu1593790203_llist @ X0] : (((coindu1802687541_ltake @ X0 @ (ord_min @ extended_enat @ X3 @ X2) @ X1) = (coindu1802687541_ltake @ X0 @ X3 @ (coindu1802687541_ltake @ X0 @ X2 @ X1)))) )),
% 161.19/24.52 inference(equality_proxy_clausification,[status(thm)],[f3380])).
% 161.19/24.52 thf(f3380,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : extended_enat,X3 : extended_enat,X1 : coindu1593790203_llist @ X0] : (($true = ((coindu1802687541_ltake @ X0 @ (ord_min @ extended_enat @ X3 @ X2) @ X1) = (coindu1802687541_ltake @ X0 @ X3 @ (coindu1802687541_ltake @ X0 @ X2 @ X1))))) )),
% 161.19/24.52 inference(beta_eta_normalization,[status(thm)],[f3379])).
% 161.19/24.52 thf(f3379,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : extended_enat,X3 : extended_enat,X1 : coindu1593790203_llist @ X0] : ((((^[Y0 : extended_enat]: ((coindu1802687541_ltake @ X0 @ (ord_min @ extended_enat @ Y0 @ X2) @ X1) = (coindu1802687541_ltake @ X0 @ Y0 @ (coindu1802687541_ltake @ X0 @ X2 @ X1)))) @ X3) = $true)) )),
% 161.19/24.52 inference(pi_clausification,[status(thm)],[f3378])).
% 161.19/24.52 thf(f3378,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : extended_enat,X1 : coindu1593790203_llist @ X0] : (($true = (!! @ extended_enat @ (^[Y0 : extended_enat]: ((coindu1802687541_ltake @ X0 @ (ord_min @ extended_enat @ Y0 @ X2) @ X1) = (coindu1802687541_ltake @ X0 @ Y0 @ (coindu1802687541_ltake @ X0 @ X2 @ X1))))))) )),
% 161.19/24.52 inference(beta_eta_normalization,[status(thm)],[f3377])).
% 161.19/24.52 thf(f3377,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : extended_enat,X1 : coindu1593790203_llist @ X0] : (($true = ((^[Y0 : extended_enat]: (!! @ extended_enat @ (^[Y1 : extended_enat]: ((coindu1802687541_ltake @ X0 @ (ord_min @ extended_enat @ Y1 @ Y0) @ X1) = (coindu1802687541_ltake @ X0 @ Y1 @ (coindu1802687541_ltake @ X0 @ Y0 @ X1)))))) @ X2))) )),
% 161.19/24.52 inference(pi_clausification,[status(thm)],[f3376])).
% 161.19/24.52 thf(f3376,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (((!! @ extended_enat @ (^[Y0 : extended_enat]: (!! @ extended_enat @ (^[Y1 : extended_enat]: ((coindu1802687541_ltake @ X0 @ (ord_min @ extended_enat @ Y1 @ Y0) @ X1) = (coindu1802687541_ltake @ X0 @ Y1 @ (coindu1802687541_ltake @ X0 @ Y0 @ X1))))))) = $true)) )),
% 161.19/24.52 inference(beta_eta_normalization,[status(thm)],[f3375])).
% 161.19/24.52 thf(f3375,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (($true = ((^[Y0 : coindu1593790203_llist @ X0]: (!! @ extended_enat @ (^[Y1 : extended_enat]: (!! @ extended_enat @ (^[Y2 : extended_enat]: ((coindu1802687541_ltake @ X0 @ (ord_min @ extended_enat @ Y2 @ Y1) @ Y0) = (coindu1802687541_ltake @ X0 @ Y2 @ (coindu1802687541_ltake @ X0 @ Y1 @ Y0)))))))) @ X1))) )),
% 161.19/24.52 inference(pi_clausification,[status(thm)],[f1344])).
% 161.19/24.52 thf(f1344,plain,(
% 161.19/24.52 ( ! [X0 : $tType] : (($true = (!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: (!! @ extended_enat @ (^[Y1 : extended_enat]: (!! @ extended_enat @ (^[Y2 : extended_enat]: ((coindu1802687541_ltake @ X0 @ (ord_min @ extended_enat @ Y2 @ Y1) @ Y0) = (coindu1802687541_ltake @ X0 @ Y2 @ (coindu1802687541_ltake @ X0 @ Y1 @ Y0))))))))))) )),
% 161.19/24.52 inference(cnf_transformation,[status(thm)],[f906])).
% 161.19/24.52 thf(f906,plain,(
% 161.19/24.52 ! [X0 : $tType] : ($true = (!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: (!! @ extended_enat @ (^[Y1 : extended_enat]: (!! @ extended_enat @ (^[Y2 : extended_enat]: ((coindu1802687541_ltake @ X0 @ (ord_min @ extended_enat @ Y2 @ Y1) @ Y0) = (coindu1802687541_ltake @ X0 @ Y2 @ (coindu1802687541_ltake @ X0 @ Y1 @ Y0))))))))))),
% 161.19/24.52 inference(closure,[status(thm)],[f307])).
% 161.19/24.52 thf(f307,plain,(
% 161.19/24.52 ( ! [X0 : $tType] : (($true = (!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: (!! @ extended_enat @ (^[Y1 : extended_enat]: (!! @ extended_enat @ (^[Y2 : extended_enat]: ((coindu1802687541_ltake @ X0 @ (ord_min @ extended_enat @ Y2 @ Y1) @ Y0) = (coindu1802687541_ltake @ X0 @ Y2 @ (coindu1802687541_ltake @ X0 @ Y1 @ Y0))))))))))) )),
% 161.19/24.52 inference(fool_elimination,[status(thm)],[f306])).
% 161.19/24.52 thf(f306,plain,(
% 161.19/24.52 ! [X0 : $tType,X1 : extended_enat,X2 : extended_enat,X3 : coindu1593790203_llist @ X0] : ((coindu1802687541_ltake @ X0 @ (ord_min @ extended_enat @ X1 @ X2) @ X3) = (coindu1802687541_ltake @ X0 @ X1 @ (coindu1802687541_ltake @ X0 @ X2 @ X3)))),
% 161.19/24.52 inference(rectify,[status(thm)],[f15])).
% 161.19/24.52 thf(f15,axiom,(
% 161.19/24.52 ! [X0 : $tType,X6 : extended_enat,X13 : extended_enat,X4 : coindu1593790203_llist @ X0] : ((coindu1802687541_ltake @ X0 @ X6 @ (coindu1802687541_ltake @ X0 @ X13 @ X4)) = (coindu1802687541_ltake @ X0 @ (ord_min @ extended_enat @ X6 @ X13) @ X4))),
% 161.19/24.52 file('/export/starexec/sandbox/tmp/tmp.ZCwsuNV1cP/DTF2THF_21964.p',fact_14_ltake__ltake)).
% 161.19/24.52 thf(f9828,plain,(
% 161.19/24.52 ( ! [X0 : extended_enat] : (((coindu1696667936prefix @ a @ (coindu1802687541_ltake @ a @ n @ xs) @ (coindu1802687541_ltake @ a @ X0 @ (coindu1802687541_ltake @ a @ m @ xs))) = $false)) )),
% 161.19/24.52 inference(trivial_inequality_removal,[status(thm)],[f9810])).
% 161.19/24.52 thf(f9810,plain,(
% 161.19/24.52 ( ! [X0 : extended_enat] : (($true = $false) | ((coindu1696667936prefix @ a @ (coindu1802687541_ltake @ a @ n @ xs) @ (coindu1802687541_ltake @ a @ X0 @ (coindu1802687541_ltake @ a @ m @ xs))) = $false)) )),
% 161.19/24.52 inference(superposition,[status(thm)],[f5072,f2603])).
% 161.19/24.52 thf(f2603,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : extended_enat,X1 : coindu1593790203_llist @ X0] : (($true = (coindu1696667936prefix @ X0 @ (coindu1802687541_ltake @ X0 @ X2 @ X1) @ X1))) )),
% 161.19/24.52 inference(beta_eta_normalization,[status(thm)],[f2602])).
% 161.19/24.52 thf(f2602,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : extended_enat,X1 : coindu1593790203_llist @ X0] : (($true = ((^[Y0 : extended_enat]: (coindu1696667936prefix @ X0 @ (coindu1802687541_ltake @ X0 @ Y0 @ X1) @ X1)) @ X2))) )),
% 161.19/24.52 inference(pi_clausification,[status(thm)],[f2601])).
% 161.19/24.52 thf(f2601,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (($true = (!! @ extended_enat @ (^[Y0 : extended_enat]: (coindu1696667936prefix @ X0 @ (coindu1802687541_ltake @ X0 @ Y0 @ X1) @ X1))))) )),
% 161.19/24.52 inference(beta_eta_normalization,[status(thm)],[f2600])).
% 161.19/24.52 thf(f2600,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : ((((^[Y0 : coindu1593790203_llist @ X0]: (!! @ extended_enat @ (^[Y1 : extended_enat]: (coindu1696667936prefix @ X0 @ (coindu1802687541_ltake @ X0 @ Y1 @ Y0) @ Y0)))) @ X1) = $true)) )),
% 161.19/24.52 inference(pi_clausification,[status(thm)],[f1337])).
% 161.19/24.52 thf(f1337,plain,(
% 161.19/24.52 ( ! [X0 : $tType] : (($true = (!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: (!! @ extended_enat @ (^[Y1 : extended_enat]: (coindu1696667936prefix @ X0 @ (coindu1802687541_ltake @ X0 @ Y1 @ Y0) @ Y0))))))) )),
% 161.19/24.52 inference(cnf_transformation,[status(thm)],[f884])).
% 161.19/24.52 thf(f884,plain,(
% 161.19/24.52 ! [X0 : $tType] : ($true = (!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: (!! @ extended_enat @ (^[Y1 : extended_enat]: (coindu1696667936prefix @ X0 @ (coindu1802687541_ltake @ X0 @ Y1 @ Y0) @ Y0))))))),
% 161.19/24.52 inference(closure,[status(thm)],[f622])).
% 161.19/24.52 thf(f622,plain,(
% 161.19/24.52 ( ! [X0 : $tType] : (($true = (!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: (!! @ extended_enat @ (^[Y1 : extended_enat]: (coindu1696667936prefix @ X0 @ (coindu1802687541_ltake @ X0 @ Y1 @ Y0) @ Y0))))))) )),
% 161.19/24.52 inference(fool_elimination,[status(thm)],[f621])).
% 161.19/24.52 thf(f621,plain,(
% 161.19/24.52 ! [X0 : $tType,X1 : extended_enat,X2 : coindu1593790203_llist @ X0] : (coindu1696667936prefix @ X0 @ (coindu1802687541_ltake @ X0 @ X1 @ X2) @ X2)),
% 161.19/24.52 inference(rectify,[status(thm)],[f4])).
% 161.19/24.52 thf(f4,axiom,(
% 161.19/24.52 ! [X0 : $tType,X6 : extended_enat,X4 : coindu1593790203_llist @ X0] : (coindu1696667936prefix @ X0 @ (coindu1802687541_ltake @ X0 @ X6 @ X4) @ X4)),
% 161.19/24.52 file('/export/starexec/sandbox/tmp/tmp.ZCwsuNV1cP/DTF2THF_21964.p',fact_3_ltake__is__lprefix)).
% 161.19/24.52 thf(f5072,plain,(
% 161.19/24.52 ( ! [X0 : coindu1593790203_llist @ a] : (($false = (coindu1696667936prefix @ a @ X0 @ (coindu1802687541_ltake @ a @ m @ xs))) | ((coindu1696667936prefix @ a @ (coindu1802687541_ltake @ a @ n @ xs) @ X0) = $false)) )),
% 161.19/24.52 inference(trivial_inequality_removal,[status(thm)],[f5057])).
% 161.19/24.52 thf(f5057,plain,(
% 161.19/24.52 ( ! [X0 : coindu1593790203_llist @ a] : (($false = (coindu1696667936prefix @ a @ X0 @ (coindu1802687541_ltake @ a @ m @ xs))) | ($true = $false) | ((coindu1696667936prefix @ a @ (coindu1802687541_ltake @ a @ n @ xs) @ X0) = $false)) )),
% 161.19/24.52 inference(superposition,[status(thm)],[f1451,f2084])).
% 161.19/24.52 thf(f2084,plain,(
% 161.19/24.52 ((coindu1696667936prefix @ a @ (coindu1802687541_ltake @ a @ n @ xs) @ (coindu1802687541_ltake @ a @ m @ xs)) = $false)),
% 161.19/24.52 inference(not_proxy_clausification,[status(thm)],[f1178])).
% 161.19/24.52 thf(f1178,plain,(
% 161.19/24.52 ((~ (coindu1696667936prefix @ a @ (coindu1802687541_ltake @ a @ n @ xs) @ (coindu1802687541_ltake @ a @ m @ xs))) = $true)),
% 161.19/24.52 inference(cnf_transformation,[status(thm)],[f339])).
% 161.19/24.52 thf(f339,plain,(
% 161.19/24.52 ((~ (coindu1696667936prefix @ a @ (coindu1802687541_ltake @ a @ n @ xs) @ (coindu1802687541_ltake @ a @ m @ xs))) = $true)),
% 161.19/24.52 inference(fool_elimination,[status(thm)],[f338])).
% 161.19/24.52 thf(f338,plain,(
% 161.19/24.52 ~(coindu1696667936prefix @ a @ (coindu1802687541_ltake @ a @ n @ xs) @ (coindu1802687541_ltake @ a @ m @ xs))),
% 161.19/24.52 inference(rectify,[status(thm)],[f292])).
% 161.19/24.52 thf(f292,negated_conjecture,(
% 161.19/24.52 ~(coindu1696667936prefix @ a @ (coindu1802687541_ltake @ a @ n @ xs) @ (coindu1802687541_ltake @ a @ m @ xs))),
% 161.19/24.52 inference(negated_conjecture,[status(cth)],[f291])).
% 161.19/24.52 thf(f291,conjecture,(
% 161.19/24.52 (coindu1696667936prefix @ a @ (coindu1802687541_ltake @ a @ n @ xs) @ (coindu1802687541_ltake @ a @ m @ xs))),
% 161.19/24.52 file('/export/starexec/sandbox/tmp/tmp.ZCwsuNV1cP/DTF2THF_21964.p',conj_0)).
% 161.19/24.52 thf(f1451,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : (($true = (coindu1696667936prefix @ X0 @ X3 @ X1)) | ((coindu1696667936prefix @ X0 @ X3 @ X2) = $false) | ($false = (coindu1696667936prefix @ X0 @ X2 @ X1))) )),
% 161.19/24.52 inference(binary_proxy_clausification,[status(thm)],[f1450])).
% 161.19/24.52 thf(f1450,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : (($true = ((coindu1696667936prefix @ X0 @ X2 @ X1) => (coindu1696667936prefix @ X0 @ X3 @ X1))) | ((coindu1696667936prefix @ X0 @ X3 @ X2) = $false)) )),
% 161.19/24.52 inference(binary_proxy_clausification,[status(thm)],[f1449])).
% 161.19/24.52 thf(f1449,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : (($true = ((coindu1696667936prefix @ X0 @ X3 @ X2) => ((coindu1696667936prefix @ X0 @ X2 @ X1) => (coindu1696667936prefix @ X0 @ X3 @ X1))))) )),
% 161.19/24.52 inference(beta_eta_normalization,[status(thm)],[f1448])).
% 161.19/24.52 thf(f1448,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : ((((^[Y0 : coindu1593790203_llist @ X0]: ((coindu1696667936prefix @ X0 @ Y0 @ X2) => ((coindu1696667936prefix @ X0 @ X2 @ X1) => (coindu1696667936prefix @ X0 @ Y0 @ X1)))) @ X3) = $true)) )),
% 161.19/24.52 inference(pi_clausification,[status(thm)],[f1447])).
% 161.19/24.52 thf(f1447,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : (($true = (!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: ((coindu1696667936prefix @ X0 @ Y0 @ X2) => ((coindu1696667936prefix @ X0 @ X2 @ X1) => (coindu1696667936prefix @ X0 @ Y0 @ X1))))))) )),
% 161.19/24.52 inference(beta_eta_normalization,[status(thm)],[f1446])).
% 161.19/24.52 thf(f1446,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : coindu1593790203_llist @ X0] : ((((^[Y0 : coindu1593790203_llist @ X0]: (!! @ coindu1593790203_llist @ X0 @ (^[Y1 : coindu1593790203_llist @ X0]: ((coindu1696667936prefix @ X0 @ Y1 @ Y0) => ((coindu1696667936prefix @ X0 @ Y0 @ X1) => (coindu1696667936prefix @ X0 @ Y1 @ X1)))))) @ X2) = $true)) )),
% 161.19/24.52 inference(pi_clausification,[status(thm)],[f1445])).
% 161.19/24.52 thf(f1445,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (((!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: (!! @ coindu1593790203_llist @ X0 @ (^[Y1 : coindu1593790203_llist @ X0]: ((coindu1696667936prefix @ X0 @ Y1 @ Y0) => ((coindu1696667936prefix @ X0 @ Y0 @ X1) => (coindu1696667936prefix @ X0 @ Y1 @ X1))))))) = $true)) )),
% 161.19/24.52 inference(beta_eta_normalization,[status(thm)],[f1444])).
% 161.19/24.52 thf(f1444,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (($true = ((^[Y0 : coindu1593790203_llist @ X0]: (!! @ coindu1593790203_llist @ X0 @ (^[Y1 : coindu1593790203_llist @ X0]: (!! @ coindu1593790203_llist @ X0 @ (^[Y2 : coindu1593790203_llist @ X0]: ((coindu1696667936prefix @ X0 @ Y2 @ Y1) => ((coindu1696667936prefix @ X0 @ Y1 @ Y0) => (coindu1696667936prefix @ X0 @ Y2 @ Y0)))))))) @ X1))) )),
% 161.19/24.52 inference(pi_clausification,[status(thm)],[f1180])).
% 161.19/24.52 thf(f1180,plain,(
% 161.19/24.52 ( ! [X0 : $tType] : (($true = (!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: (!! @ coindu1593790203_llist @ X0 @ (^[Y1 : coindu1593790203_llist @ X0]: (!! @ coindu1593790203_llist @ X0 @ (^[Y2 : coindu1593790203_llist @ X0]: ((coindu1696667936prefix @ X0 @ Y2 @ Y1) => ((coindu1696667936prefix @ X0 @ Y1 @ Y0) => (coindu1696667936prefix @ X0 @ Y2 @ Y0))))))))))) )),
% 161.19/24.52 inference(cnf_transformation,[status(thm)],[f887])).
% 161.19/24.52 thf(f887,plain,(
% 161.19/24.52 ! [X0 : $tType] : ($true = (!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: (!! @ coindu1593790203_llist @ X0 @ (^[Y1 : coindu1593790203_llist @ X0]: (!! @ coindu1593790203_llist @ X0 @ (^[Y2 : coindu1593790203_llist @ X0]: ((coindu1696667936prefix @ X0 @ Y2 @ Y1) => ((coindu1696667936prefix @ X0 @ Y1 @ Y0) => (coindu1696667936prefix @ X0 @ Y2 @ Y0))))))))))),
% 161.19/24.52 inference(closure,[status(thm)],[f524])).
% 161.19/24.52 thf(f524,plain,(
% 161.19/24.52 ( ! [X0 : $tType] : (($true = (!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: (!! @ coindu1593790203_llist @ X0 @ (^[Y1 : coindu1593790203_llist @ X0]: (!! @ coindu1593790203_llist @ X0 @ (^[Y2 : coindu1593790203_llist @ X0]: ((coindu1696667936prefix @ X0 @ Y2 @ Y1) => ((coindu1696667936prefix @ X0 @ Y1 @ Y0) => (coindu1696667936prefix @ X0 @ Y2 @ Y0))))))))))) )),
% 161.19/24.52 inference(fool_elimination,[status(thm)],[f523])).
% 161.19/24.52 thf(f523,plain,(
% 161.19/24.52 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0] : ((coindu1696667936prefix @ X0 @ X1 @ X2) => ((coindu1696667936prefix @ X0 @ X2 @ X3) => (coindu1696667936prefix @ X0 @ X1 @ X3)))),
% 161.19/24.52 inference(rectify,[status(thm)],[f6])).
% 161.19/24.52 thf(f6,axiom,(
% 161.19/24.52 ! [X0 : $tType,X5 : coindu1593790203_llist @ X0,X9 : coindu1593790203_llist @ X0,X10 : coindu1593790203_llist @ X0] : ((coindu1696667936prefix @ X0 @ X5 @ X9) => ((coindu1696667936prefix @ X0 @ X9 @ X10) => (coindu1696667936prefix @ X0 @ X5 @ X10)))),
% 161.19/24.52 file('/export/starexec/sandbox/tmp/tmp.ZCwsuNV1cP/DTF2THF_21964.p',fact_5_llist_Oleq__trans)).
% 161.19/24.52 thf(f3163,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (($true = (coindu1696667936prefix @ X0 @ X1 @ X1))) )),
% 161.19/24.52 inference(beta_eta_normalization,[status(thm)],[f3162])).
% 161.19/24.52 thf(f3162,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : ((((^[Y0 : coindu1593790203_llist @ X0]: (coindu1696667936prefix @ X0 @ Y0 @ Y0)) @ X1) = $true)) )),
% 161.19/24.52 inference(pi_clausification,[status(thm)],[f1261])).
% 161.19/24.52 thf(f1261,plain,(
% 161.19/24.52 ( ! [X0 : $tType] : (((!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: (coindu1696667936prefix @ X0 @ Y0 @ Y0))) = $true)) )),
% 161.19/24.52 inference(cnf_transformation,[status(thm)],[f889])).
% 161.19/24.52 thf(f889,plain,(
% 161.19/24.52 ! [X0 : $tType] : ((!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: (coindu1696667936prefix @ X0 @ Y0 @ Y0))) = $true)),
% 161.19/24.52 inference(closure,[status(thm)],[f436])).
% 161.19/24.52 thf(f436,plain,(
% 161.19/24.52 ( ! [X0 : $tType] : (((!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: (coindu1696667936prefix @ X0 @ Y0 @ Y0))) = $true)) )),
% 161.19/24.52 inference(fool_elimination,[status(thm)],[f435])).
% 161.19/24.52 thf(f435,plain,(
% 161.19/24.52 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (coindu1696667936prefix @ X0 @ X1 @ X1)),
% 161.19/24.52 inference(rectify,[status(thm)],[f1])).
% 161.19/24.52 thf(f1,axiom,(
% 161.19/24.52 ! [X0 : $tType,X4 : coindu1593790203_llist @ X0] : (coindu1696667936prefix @ X0 @ X4 @ X4)),
% 161.19/24.52 file('/export/starexec/sandbox/tmp/tmp.ZCwsuNV1cP/DTF2THF_21964.p',fact_0_lprefix__refl)).
% 161.19/24.52 thf(f3928,plain,(
% 161.19/24.52 ~spl0_2),
% 161.19/24.52 inference(avatar_contradiction_clause,[status(thm)],[f3927])).
% 161.19/24.52 thf(f3927,plain,(
% 161.19/24.52 $false | ~spl0_2),
% 161.19/24.52 inference(trivial_inequality_removal,[status(thm)],[f3919])).
% 161.19/24.52 thf(f3919,plain,(
% 161.19/24.52 ($true = $false) | ~spl0_2),
% 161.19/24.52 inference(superposition,[status(thm)],[f3911,f2603])).
% 161.19/24.52 thf(f3911,plain,(
% 161.19/24.52 ((coindu1696667936prefix @ a @ (coindu1802687541_ltake @ a @ n @ xs) @ xs) = $false) | ~spl0_2),
% 161.19/24.52 inference(backward_demodulation,[status(thm)],[f2084,f3871])).
% 161.19/24.52 thf(f3871,plain,(
% 161.19/24.52 (xs = (coindu1802687541_ltake @ a @ m @ xs)) | ~spl0_2),
% 161.19/24.52 inference(trivial_inequality_removal,[status(thm)],[f3857])).
% 161.19/24.52 thf(f3857,plain,(
% 161.19/24.52 (xs = (coindu1802687541_ltake @ a @ m @ xs)) | ($true = $false) | ~spl0_2),
% 161.19/24.52 inference(superposition,[status(thm)],[f2889,f1809])).
% 161.19/24.52 thf(f1809,plain,(
% 161.19/24.52 ((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m) = $true) | ~spl0_2),
% 161.19/24.52 inference(avatar_component_clause,[status(thm)],[f1807])).
% 161.19/24.52 thf(f1807,definition,(
% 161.19/24.52 spl0_2 <=> ((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m) = $true)),
% 161.19/24.52 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 161.19/24.52 thf(f2889,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : extended_enat] : (($false = (ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ X2) @ X1)) | ((coindu1802687541_ltake @ X0 @ X1 @ X2) = X2)) )),
% 161.19/24.52 inference(equality_proxy_clausification,[status(thm)],[f2888])).
% 161.19/24.52 thf(f2888,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : extended_enat] : (($false = (ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ X2) @ X1)) | ($true = ((coindu1802687541_ltake @ X0 @ X1 @ X2) = X2))) )),
% 161.19/24.52 inference(binary_proxy_clausification,[status(thm)],[f2887])).
% 161.19/24.52 thf(f2887,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : extended_enat] : ((((ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ X2) @ X1) => ((coindu1802687541_ltake @ X0 @ X1 @ X2) = X2)) = $true)) )),
% 161.19/24.52 inference(beta_eta_normalization,[status(thm)],[f2886])).
% 161.19/24.52 thf(f2886,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : extended_enat] : (($true = ((^[Y0 : coindu1593790203_llist @ X0]: ((ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ Y0) @ X1) => ((coindu1802687541_ltake @ X0 @ X1 @ Y0) = Y0))) @ X2))) )),
% 161.19/24.52 inference(pi_clausification,[status(thm)],[f2885])).
% 161.19/24.52 thf(f2885,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X1 : extended_enat] : (((!! @ coindu1593790203_llist @ X0 @ (^[Y0 : coindu1593790203_llist @ X0]: ((ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ Y0) @ X1) => ((coindu1802687541_ltake @ X0 @ X1 @ Y0) = Y0)))) = $true)) )),
% 161.19/24.52 inference(beta_eta_normalization,[status(thm)],[f2884])).
% 161.19/24.52 thf(f2884,plain,(
% 161.19/24.52 ( ! [X0 : $tType,X1 : extended_enat] : ((((^[Y0 : extended_enat]: (!! @ coindu1593790203_llist @ X0 @ (^[Y1 : coindu1593790203_llist @ X0]: ((ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ Y1) @ Y0) => ((coindu1802687541_ltake @ X0 @ Y0 @ Y1) = Y1))))) @ X1) = $true)) )),
% 161.19/24.52 inference(pi_clausification,[status(thm)],[f1242])).
% 161.19/24.52 thf(f1242,plain,(
% 161.19/24.52 ( ! [X0 : $tType] : (((!! @ extended_enat @ (^[Y0 : extended_enat]: (!! @ coindu1593790203_llist @ X0 @ (^[Y1 : coindu1593790203_llist @ X0]: ((ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ Y1) @ Y0) => ((coindu1802687541_ltake @ X0 @ Y0 @ Y1) = Y1)))))) = $true)) )),
% 161.19/24.52 inference(cnf_transformation,[status(thm)],[f931])).
% 161.19/24.52 thf(f931,plain,(
% 161.19/24.52 ! [X0 : $tType] : ((!! @ extended_enat @ (^[Y0 : extended_enat]: (!! @ coindu1593790203_llist @ X0 @ (^[Y1 : coindu1593790203_llist @ X0]: ((ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ Y1) @ Y0) => ((coindu1802687541_ltake @ X0 @ Y0 @ Y1) = Y1)))))) = $true)),
% 161.19/24.52 inference(closure,[status(thm)],[f313])).
% 161.19/24.52 thf(f313,plain,(
% 161.19/24.52 ( ! [X0 : $tType] : (((!! @ extended_enat @ (^[Y0 : extended_enat]: (!! @ coindu1593790203_llist @ X0 @ (^[Y1 : coindu1593790203_llist @ X0]: ((ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ Y1) @ Y0) => ((coindu1802687541_ltake @ X0 @ Y0 @ Y1) = Y1)))))) = $true)) )),
% 161.19/24.52 inference(fool_elimination,[status(thm)],[f312])).
% 161.19/24.52 thf(f312,plain,(
% 161.19/24.52 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0,X2 : extended_enat] : ((ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ X1) @ X2) => ((coindu1802687541_ltake @ X0 @ X2 @ X1) = X1))),
% 161.19/24.52 inference(rectify,[status(thm)],[f12])).
% 161.19/24.52 thf(f12,axiom,(
% 161.19/24.52 ! [X0 : $tType,X4 : coindu1593790203_llist @ X0,X13 : extended_enat] : ((ord_less_eq @ extended_enat @ (coindu1018505716length @ X0 @ X4) @ X13) => ((coindu1802687541_ltake @ X0 @ X13 @ X4) = X4))),
% 161.19/24.52 file('/export/starexec/sandbox/tmp/tmp.ZCwsuNV1cP/DTF2THF_21964.p',fact_11_ltake__all)).
% 161.19/24.52 thf(f1810,plain,(
% 161.19/24.52 spl0_1 | spl0_2),
% 161.19/24.52 inference(avatar_split_clause,[status(thm)],[f1801,f1807,f1803])).
% 161.19/24.52 thf(f1801,plain,(
% 161.19/24.52 ((ord_less_eq @ extended_enat @ n @ m) = $true) | ((ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m) = $true)),
% 161.19/24.52 inference(binary_proxy_clausification,[status(thm)],[f1213])).
% 161.19/24.52 thf(f1213,plain,(
% 161.19/24.52 (((ord_less_eq @ extended_enat @ n @ m) | (ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m)) = $true)),
% 161.19/24.52 inference(cnf_transformation,[status(thm)],[f516])).
% 161.19/24.52 thf(f516,plain,(
% 161.19/24.52 (((ord_less_eq @ extended_enat @ n @ m) | (ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m)) = $true)),
% 161.19/24.52 inference(fool_elimination,[status(thm)],[f515])).
% 161.19/24.52 thf(f515,plain,(
% 161.19/24.52 (ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m) | (ord_less_eq @ extended_enat @ n @ m)),
% 161.19/24.52 inference(rectify,[status(thm)],[f3])).
% 161.19/24.52 thf(f3,axiom,(
% 161.19/24.52 (ord_less_eq @ extended_enat @ (coindu1018505716length @ a @ xs) @ m) | (ord_less_eq @ extended_enat @ n @ m)),
% 161.19/24.52 file('/export/starexec/sandbox/tmp/tmp.ZCwsuNV1cP/DTF2THF_21964.p',fact_2__092_060open_062n_A_092_060le_062_Am_A_092_060or_062_Allength_Axs_A_092_060le_062_Am_092_060close_062)).
% 161.19/24.52 % SZS output end Proof for DTF2THF_21964
% 161.19/24.52 % (22450)------------------------------
% 161.19/24.52 % (22450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 161.19/24.52 % (22450)Termination reason: Refutation
% 161.19/24.52
% 161.19/24.52 % (22450)Memory used [KB]: 10874
% 161.19/24.52 % (22450)Time elapsed: 0.940 s
% 161.19/24.52 % (22450)Instructions burned: 2680 (million)
% 161.19/24.52 % (22450)------------------------------
% 161.19/24.52 % (22450)------------------------------
% 161.19/24.52 % (22078)Success in time 22.701 s
%------------------------------------------------------------------------------