%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT131^1 : 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 : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:44:52 AM UTC 2026
% Result : Theorem 14.00s 3.56s
% Output : Refutation 14.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : DAT131^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n019.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 06:08:24 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.38 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : DAT131^1 : TPTP v9.2.1. Released v7.0.0.
% 0.16/0.39 % Domain : Data Structures
% 0.16/0.39 % Problem : Coinductive list 3781
% 0.16/0.39 % Version : [Bla16] axioms : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.16/0.39 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.16/0.39 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bla16]
% 0.16/0.39 % Names : coinductive_list__3781.p [Bla16]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.67 v9.1.0, 0.33 v8.1.0, 1.00 v7.1.0
% 0.16/0.39 % Syntax : Number of formulae : 315 ( 136 unt; 46 typ; 0 def)
% 0.16/0.39 % Number of atoms : 736 ( 249 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 13 ( 2 avg)
% 0.16/0.39 % Number of connectives : 3937 ( 104 ~; 39 |; 72 &;3400 @)
% 0.16/0.39 % ( 0 <=>; 322 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 28 ( 9 avg)
% 0.16/0.39 % Number of types : 2 ( 1 usr)
% 0.16/0.39 % Number of type conns : 310 ( 310 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 48 ( 45 usr; 9 con; 0-8 aty)
% 0.16/0.39 % Number of variables : 1224 ( 74 ^;1043 !; 67 ?;1224 :)
% 0.16/0.39 % ( 40 !>; 0 ?*; 0 @-; 0 @+)
% 0.16/0.39 % SPC : TH1_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.16/0.39 % 2016-07-13 15:03:12.383
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 %----Could-be-implicit typings (5)
% 0.16/0.39 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 0.16/0.39 coindu1593790203_llist: $tType > $tType ).
% 0.16/0.39
% 0.16/0.39 thf(ty_t_Product__Type_Oprod,type,
% 0.16/0.39 product_prod: $tType > $tType > $tType ).
% 0.16/0.39
% 0.16/0.39 thf(ty_t_Set_Oset,type,
% 0.16/0.39 set: $tType > $tType ).
% 0.16/0.39
% 0.16/0.39 thf(ty_t_itself,type,
% 0.16/0.39 itself: $tType > $tType ).
% 0.16/0.39
% 0.16/0.39 thf(ty_tf_a,type,
% 0.16/0.39 a: $tType ).
% 0.16/0.39
% 0.16/0.39 %----Explicit typings (41)
% 0.16/0.39 thf(sy_cl_HOL_Otype,type,
% 0.16/0.39 type:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Orderings_Oord,type,
% 0.16/0.39 ord:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Orderings_Oorder,type,
% 0.16/0.39 order:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Orderings_Olinorder,type,
% 0.16/0.39 linorder:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_cl_Orderings_Opreorder,type,
% 0.16/0.39 preorder:
% 0.16/0.39 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix,type,
% 0.16/0.39 coindu1571841457prefix:
% 0.16/0.39 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__lset,type,
% 0.16/0.39 coindu1928975208n_lset:
% 0.16/0.39 !>[A: $tType] : ( ( set @ A ) > ( coindu1593790203_llist @ A ) > ( set @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 0.16/0.39 coindu268472904append:
% 0.16/0.39 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite,type,
% 0.16/0.39 coindu1213758845finite:
% 0.16/0.39 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollast,type,
% 0.16/0.39 coindu2000965700_llast:
% 0.16/0.39 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollexord,type,
% 0.16/0.39 coindu300403952lexord:
% 0.16/0.39 !>[A: $tType] : ( ( A > A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 0.16/0.39 coindu1121789889_LCons:
% 0.16/0.39 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 0.16/0.39 coindu1598213697e_LNil:
% 0.16/0.39 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocorec__llist,type,
% 0.16/0.39 coindu1244876290_llist:
% 0.16/0.39 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( coindu1593790203_llist @ A ) ) > ( C > C ) > C > ( coindu1593790203_llist @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 0.16/0.39 coindu335574135_lnull:
% 0.16/0.39 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Opred__llist,type,
% 0.16/0.39 coindu44415597_llist:
% 0.16/0.39 !>[A: $tType] : ( ( A > $o ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember,type,
% 0.16/0.39 coindu567634248member:
% 0.16/0.39 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix,type,
% 0.16/0.39 coindu1696667936prefix:
% 0.16/0.39 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olsetp,type,
% 0.16/0.39 coindu1055736764_lsetp:
% 0.16/0.39 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix,type,
% 0.16/0.39 coindu574146665prefix:
% 0.16/0.39 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_OltakeWhile,type,
% 0.16/0.39 coindu721411036eWhile:
% 0.16/0.39 !>[A: $tType] : ( ( A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oord_Olsorted,type,
% 0.16/0.39 coindu543932918sorted:
% 0.16/0.39 !>[A: $tType] : ( ( A > A > $o ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oord__class_Olsorted,type,
% 0.16/0.39 coindu48241764sorted:
% 0.16/0.39 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ounfold__llist,type,
% 0.16/0.39 coindu1599971794_llist:
% 0.16/0.39 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > B ) > ( A > A ) > A > ( coindu1593790203_llist @ B ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_HOL_Oundefined,type,
% 0.16/0.39 undefined:
% 0.16/0.39 !>[A: $tType] : A ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_If,type,
% 0.16/0.39 if:
% 0.16/0.39 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.16/0.39 ord_less_eq:
% 0.16/0.39 !>[A: $tType] : ( A > A > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Product__Type_OPair,type,
% 0.16/0.39 product_Pair:
% 0.16/0.39 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.16/0.39 produc2004651681e_prod:
% 0.16/0.39 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.16/0.39 product_rec_prod:
% 0.16/0.39 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Pure_Otype,type,
% 0.16/0.39 type2:
% 0.16/0.39 !>[A: $tType] : ( itself @ A ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_Set_OCollect,type,
% 0.16/0.39 collect:
% 0.16/0.39 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_c_member,type,
% 0.16/0.39 member:
% 0.16/0.39 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_r,type,
% 0.16/0.39 r: a > a > $o ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_thesis____,type,
% 0.16/0.39 thesis: $o ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_x____,type,
% 0.16/0.39 x: a ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_xs,type,
% 0.16/0.39 xs: coindu1593790203_llist @ a ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_xs_H____,type,
% 0.16/0.39 xs2: coindu1593790203_llist @ a ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_xsa____,type,
% 0.16/0.39 xsa: coindu1593790203_llist @ a ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_ys,type,
% 0.16/0.39 ys: coindu1593790203_llist @ a ).
% 0.16/0.39
% 0.16/0.39 thf(sy_v_ysa____,type,
% 0.16/0.39 ysa: coindu1593790203_llist @ a ).
% 0.16/0.39
% 0.16/0.39 %----Relevant facts (254)
% 0.16/0.39 thf(fact_0_local_Olinear,axiom,
% 0.16/0.39 ! [X: a,Y: a] :
% 0.16/0.39 ( ( r @ X @ Y )
% 0.16/0.39 | ( X = Y )
% 0.16/0.39 | ( r @ Y @ X ) ) ).
% 0.16/0.39
% 0.16/0.39 % local.linear
% 0.16/0.39 thf(fact_1__092_060open_062_092_060not_062_Allexord_Ar_Ays_Axs_092_060close_062,axiom,
% 0.16/0.39 ~ ( coindu300403952lexord @ a @ r @ ysa @ xsa ) ).
% 0.16/0.39
% 0.16/0.39 % \<open>\<not> llexord r ys xs\<close>
% 0.16/0.39 thf(fact_2__092_060open_062_092_060not_062_Allexord_Ar_Ays_Axs_092_060close_062,axiom,
% 0.16/0.39 ~ ( coindu300403952lexord @ a @ r @ ys @ xs ) ).
% 0.16/0.39
% 0.16/0.39 % \<open>\<not> llexord r ys xs\<close>
% 0.16/0.39 thf(fact_3_LCons,axiom,
% 0.16/0.39 ( xsa
% 0.16/0.39 = ( coindu1121789889_LCons @ a @ x @ xs2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % LCons
% 0.16/0.39 thf(fact_4_llist_Oinject,axiom,
% 0.16/0.39 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 0.16/0.39 = ( ( X21 = Y21 )
% 0.16/0.39 & ( X22 = Y22 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.inject
% 0.16/0.39 thf(fact_5_llexord__refl,axiom,
% 0.16/0.39 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R @ Xs @ Xs ) ).
% 0.16/0.39
% 0.16/0.39 % llexord_refl
% 0.16/0.39 thf(fact_6_llexord__LCons__LCons,axiom,
% 0.16/0.39 ! [A: $tType,R: A > A > $o,X: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.16/0.39 = ( ( ( X = Y )
% 0.16/0.39 & ( coindu300403952lexord @ A @ R @ Xs @ Ys ) )
% 0.16/0.39 | ( R @ X @ Y ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llexord_LCons_LCons
% 0.16/0.39 thf(fact_7_llexord__trans,axiom,
% 0.16/0.39 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 0.16/0.39 => ( ( coindu300403952lexord @ A @ R @ Ys @ Zs )
% 0.16/0.39 => ( ! [A2: A,B2: A,C2: A] :
% 0.16/0.39 ( ( R @ A2 @ B2 )
% 0.16/0.39 => ( ( R @ B2 @ C2 )
% 0.16/0.39 => ( R @ A2 @ C2 ) ) )
% 0.16/0.39 => ( coindu300403952lexord @ A @ R @ Xs @ Zs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llexord_trans
% 0.16/0.39 thf(fact_8_llexord__antisym,axiom,
% 0.16/0.39 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 0.16/0.39 => ( ( coindu300403952lexord @ A @ R @ Ys @ Xs )
% 0.16/0.39 => ( ! [A2: A,B2: A] :
% 0.16/0.39 ( ( R @ A2 @ B2 )
% 0.16/0.39 => ~ ( R @ B2 @ A2 ) )
% 0.16/0.39 => ( Xs = Ys ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llexord_antisym
% 0.16/0.39 thf(fact_9_llexord__LCons__left,axiom,
% 0.16/0.39 ! [A: $tType,R: A > A > $o,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ Ys )
% 0.16/0.39 = ( ? [Y2: A,Ys2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( Ys
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Y2 @ Ys2 ) )
% 0.16/0.39 & ( ( ( X = Y2 )
% 0.16/0.39 & ( coindu300403952lexord @ A @ R @ Xs @ Ys2 ) )
% 0.16/0.39 | ( R @ X @ Y2 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llexord_LCons_left
% 0.16/0.39 thf(fact_10_llexord__LCons__eq,axiom,
% 0.16/0.39 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 0.16/0.39 ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 0.16/0.39 => ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llexord_LCons_eq
% 0.16/0.39 thf(fact_11_llexord__LCons__less,axiom,
% 0.16/0.39 ! [A: $tType,R: A > A > $o,X: A,Y: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( R @ X @ Y )
% 0.16/0.39 => ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llexord_LCons_less
% 0.16/0.39 thf(fact_12_llexord_I2_J,axiom,
% 0.16/0.39 ~ ( coindu335574135_lnull @ a @ xsa ) ).
% 0.16/0.39
% 0.16/0.39 % llexord(2)
% 0.16/0.39 thf(fact_13_llexord_I1_J,axiom,
% 0.16/0.39 ~ ( coindu300403952lexord @ a @ r @ ysa @ xsa ) ).
% 0.16/0.39
% 0.16/0.39 % llexord(1)
% 0.16/0.39 thf(fact_14_lmember__code_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu567634248member @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.16/0.39 = ( ( X = Y )
% 0.16/0.39 | ( coindu567634248member @ A @ X @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lmember_code(2)
% 0.16/0.39 thf(fact_15_lstrict__prefix__code_I4_J,axiom,
% 0.16/0.39 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B,Y: B,Ys: coindu1593790203_llist @ B] :
% 0.16/0.39 ( ( coindu574146665prefix @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) @ ( coindu1121789889_LCons @ B @ Y @ Ys ) )
% 0.16/0.39 = ( ( X = Y )
% 0.16/0.39 & ( coindu574146665prefix @ B @ Xs @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lstrict_prefix_code(4)
% 0.16/0.39 thf(fact_16_llexord_Ocases,axiom,
% 0.16/0.39 ! [A: $tType,R: A > A > $o,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu300403952lexord @ A @ R @ A1 @ A22 )
% 0.16/0.39 => ( ! [Xs2: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X2: A] :
% 0.16/0.39 ( ( A1
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.16/0.39 => ( ( A22
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X2 @ Ys3 ) )
% 0.16/0.39 => ~ ( coindu300403952lexord @ A @ R @ Xs2 @ Ys3 ) ) )
% 0.16/0.39 => ( ! [X2: A] :
% 0.16/0.39 ( ? [Xs2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( A1
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.16/0.39 => ! [Y3: A] :
% 0.16/0.39 ( ? [Ys3: coindu1593790203_llist @ A] :
% 0.16/0.39 ( A22
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Y3 @ Ys3 ) )
% 0.16/0.39 => ~ ( R @ X2 @ Y3 ) ) )
% 0.16/0.39 => ~ ( ( A1
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 => ! [Ys3: coindu1593790203_llist @ A] : ( A22 != Ys3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llexord.cases
% 0.16/0.39 thf(fact_17_llexord_Osimps,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu300403952lexord @ A )
% 0.16/0.39 = ( ^ [R2: A > A > $o,A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ? [Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,X3: A] :
% 0.16/0.39 ( ( A12
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 0.16/0.39 & ( A23
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X3 @ Ys4 ) )
% 0.16/0.39 & ( coindu300403952lexord @ A @ R2 @ Xs3 @ Ys4 ) )
% 0.16/0.39 | ? [X3: A,Y2: A,Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( A12
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 0.16/0.39 & ( A23
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Y2 @ Ys4 ) )
% 0.16/0.39 & ( R2 @ X3 @ Y2 ) )
% 0.16/0.39 | ? [Ys4: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( A12
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 & ( A23 = Ys4 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llexord.simps
% 0.16/0.39 thf(fact_18_llexord_Ocoinduct,axiom,
% 0.16/0.39 ! [A: $tType,X4: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A,R: A > A > $o] :
% 0.16/0.39 ( ( X4 @ X @ Xa )
% 0.16/0.39 => ( ! [X2: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( X4 @ X2 @ Xa2 )
% 0.16/0.39 => ( ? [Xs4: coindu1593790203_llist @ A,Ys5: coindu1593790203_llist @ A,Xb: A] :
% 0.16/0.39 ( ( X2
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Xb @ Xs4 ) )
% 0.16/0.39 & ( Xa2
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Xb @ Ys5 ) )
% 0.16/0.39 & ( ( X4 @ Xs4 @ Ys5 )
% 0.16/0.39 | ( coindu300403952lexord @ A @ R @ Xs4 @ Ys5 ) ) )
% 0.16/0.39 | ? [Xb: A,Y4: A,Xs4: coindu1593790203_llist @ A,Ys5: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( X2
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Xb @ Xs4 ) )
% 0.16/0.39 & ( Xa2
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Y4 @ Ys5 ) )
% 0.16/0.39 & ( R @ Xb @ Y4 ) )
% 0.16/0.39 | ? [Ys5: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( X2
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 & ( Xa2 = Ys5 ) ) ) )
% 0.16/0.39 => ( coindu300403952lexord @ A @ R @ X @ Xa ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llexord.coinduct
% 0.16/0.39 thf(fact_19_llist_Opred__inject_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,P: A > $o,A3: A,Aa: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu44415597_llist @ A @ P @ ( coindu1121789889_LCons @ A @ A3 @ Aa ) )
% 0.16/0.39 = ( ( P @ A3 )
% 0.16/0.39 & ( coindu44415597_llist @ A @ P @ Aa ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.pred_inject(2)
% 0.16/0.39 thf(fact_20_llast__LCons2,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) )
% 0.16/0.39 = ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llast_LCons2
% 0.16/0.39 thf(fact_21_unfold__llist__eq__LCons,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B3: B,X: A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ B3 )
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.16/0.39 = ( ~ ( IS_LNIL @ B3 )
% 0.16/0.39 & ( X
% 0.16/0.39 = ( LHD @ B3 ) )
% 0.16/0.39 & ( Xs
% 0.16/0.39 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % unfold_llist_eq_LCons
% 0.16/0.39 thf(fact_22_lsetp_Ointros_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A,X5: A] :
% 0.16/0.39 ( ( coindu1055736764_lsetp @ A @ Xs @ X )
% 0.16/0.39 => ( coindu1055736764_lsetp @ A @ ( coindu1121789889_LCons @ A @ X5 @ Xs ) @ X ) ) ).
% 0.16/0.39
% 0.16/0.39 % lsetp.intros(2)
% 0.16/0.39 thf(fact_23_lsetp_Ointros_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] : ( coindu1055736764_lsetp @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ X ) ).
% 0.16/0.39
% 0.16/0.39 % lsetp.intros(1)
% 0.16/0.39 thf(fact_24_llexord__LNil__right,axiom,
% 0.16/0.39 ! [A: $tType,Ys: coindu1593790203_llist @ A,R: A > A > $o,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Ys )
% 0.16/0.39 => ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 0.16/0.39 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llexord_LNil_right
% 0.16/0.39 thf(fact_25_unfold__llist_Odisc__iff_I2_J,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,P2: A > $o,G21: A > B,G22: A > A,A3: A] :
% 0.16/0.39 ( ( ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A3 ) ) )
% 0.16/0.39 = ( ~ ( P2 @ A3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % unfold_llist.disc_iff(2)
% 0.16/0.39 thf(fact_26_unfold__llist_Odisc__iff_I1_J,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,P2: A > $o,G21: A > B,G22: A > A,A3: A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A3 ) )
% 0.16/0.39 = ( P2 @ A3 ) ) ).
% 0.16/0.39
% 0.16/0.39 % unfold_llist.disc_iff(1)
% 0.16/0.39 thf(fact_27_lstrict__prefix__code_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ~ ( coindu574146665prefix @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % lstrict_prefix_code(1)
% 0.16/0.39 thf(fact_28_llast__singleton,axiom,
% 0.16/0.39 ! [A: $tType,X: A] :
% 0.16/0.39 ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X @ ( coindu1598213697e_LNil @ A ) ) )
% 0.16/0.39 = X ) ).
% 0.16/0.39
% 0.16/0.39 % llast_singleton
% 0.16/0.39 thf(fact_29_lstrict__prefix__code_I2_J,axiom,
% 0.16/0.39 ! [B: $tType,Y: B,Ys: coindu1593790203_llist @ B] : ( coindu574146665prefix @ B @ ( coindu1598213697e_LNil @ B ) @ ( coindu1121789889_LCons @ B @ Y @ Ys ) ) ).
% 0.16/0.39
% 0.16/0.39 % lstrict_prefix_code(2)
% 0.16/0.39 thf(fact_30_lstrict__prefix__code_I3_J,axiom,
% 0.16/0.39 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B] :
% 0.16/0.39 ~ ( coindu574146665prefix @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 0.16/0.39
% 0.16/0.39 % lstrict_prefix_code(3)
% 0.16/0.39 thf(fact_31_llist_Odisc_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] : ( coindu335574135_lnull @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.disc(1)
% 0.16/0.39 thf(fact_32_llist_OdiscI_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( Llist
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 => ( coindu335574135_lnull @ A @ Llist ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.discI(1)
% 0.16/0.39 thf(fact_33_lmember__code_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,X: A] :
% 0.16/0.39 ~ ( coindu567634248member @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % lmember_code(1)
% 0.16/0.39 thf(fact_34_llist_Ocollapse_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Llist )
% 0.16/0.39 => ( Llist
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.collapse(1)
% 0.16/0.39 thf(fact_35_unfold__llist_Octr_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,P2: A > $o,A3: A,G21: A > B,G22: A > A] :
% 0.16/0.39 ( ( P2 @ A3 )
% 0.16/0.39 => ( ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A3 )
% 0.16/0.39 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % unfold_llist.ctr(1)
% 0.16/0.39 thf(fact_36_llist_Opred__inject_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,P: A > $o] : ( coindu44415597_llist @ A @ P @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.pred_inject(1)
% 0.16/0.39 thf(fact_37_unfold__llist_Odisc_I2_J,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,P2: A > $o,A3: A,G21: A > B,G22: A > A] :
% 0.16/0.39 ( ~ ( P2 @ A3 )
% 0.16/0.39 => ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % unfold_llist.disc(2)
% 0.16/0.39 thf(fact_38_unfold__llist_Odisc_I1_J,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,P2: A > $o,A3: A,G21: A > B,G22: A > A] :
% 0.16/0.39 ( ( P2 @ A3 )
% 0.16/0.39 => ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % unfold_llist.disc(1)
% 0.16/0.39 thf(fact_39_lzip_Oexhaust,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 0.16/0.39 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 | ( coindu335574135_lnull @ B @ Ys ) )
% 0.16/0.39 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lzip.exhaust
% 0.16/0.39 thf(fact_40_lappend_Oexhaust,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.16/0.39 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend.exhaust
% 0.16/0.39 thf(fact_41_lnull__def,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A )
% 0.16/0.39 = ( ^ [Llist2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( Llist2
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lnull_def
% 0.16/0.39 thf(fact_42_llist_Opred__True,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu44415597_llist @ A
% 0.16/0.39 @ ^ [Uu: A] : $true )
% 0.16/0.39 = ( ^ [Uu: coindu1593790203_llist @ A] : $true ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.pred_True
% 0.16/0.39 thf(fact_43_mem__Collect__eq,axiom,
% 0.16/0.39 ! [A: $tType,A3: A,P: A > $o] :
% 0.16/0.39 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.16/0.39 = ( P @ A3 ) ) ).
% 0.16/0.39
% 0.16/0.39 % mem_Collect_eq
% 0.16/0.39 thf(fact_44_Collect__mem__eq,axiom,
% 0.16/0.39 ! [A: $tType,A4: set @ A] :
% 0.16/0.39 ( ( collect @ A
% 0.16/0.39 @ ^ [X3: A] : ( member @ A @ X3 @ A4 ) )
% 0.16/0.39 = A4 ) ).
% 0.16/0.39
% 0.16/0.39 % Collect_mem_eq
% 0.16/0.39 thf(fact_45_Collect__cong,axiom,
% 0.16/0.39 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.16/0.39 ( ! [X2: A] :
% 0.16/0.39 ( ( P @ X2 )
% 0.16/0.39 = ( Q @ X2 ) )
% 0.16/0.39 => ( ( collect @ A @ P )
% 0.16/0.39 = ( collect @ A @ Q ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Collect_cong
% 0.16/0.39 thf(fact_46_ext,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.16/0.39 ( ! [X2: A] :
% 0.16/0.39 ( ( F @ X2 )
% 0.16/0.39 = ( G @ X2 ) )
% 0.16/0.39 => ( F = G ) ) ).
% 0.16/0.39
% 0.16/0.39 % ext
% 0.16/0.39 thf(fact_47_llist__less__induct,axiom,
% 0.16/0.39 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ! [Xs2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ! [Ys5: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu574146665prefix @ A @ Ys5 @ Xs2 )
% 0.16/0.39 => ( P @ Ys5 ) )
% 0.16/0.39 => ( P @ Xs2 ) )
% 0.16/0.39 => ( P @ Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist_less_induct
% 0.16/0.39 thf(fact_48_llast__LCons,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 0.16/0.39 ( ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.16/0.39 = X ) )
% 0.16/0.39 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.16/0.39 = ( coindu2000965700_llast @ A @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llast_LCons
% 0.16/0.39 thf(fact_49_unfold__llist_Ocode,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType] :
% 0.16/0.39 ( ( coindu1599971794_llist @ A @ B )
% 0.16/0.39 = ( ^ [P3: A > $o,G212: A > B,G222: A > A,A5: A] : ( if @ ( coindu1593790203_llist @ B ) @ ( P3 @ A5 ) @ ( coindu1598213697e_LNil @ B ) @ ( coindu1121789889_LCons @ B @ ( G212 @ A5 ) @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G222 @ ( G222 @ A5 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % unfold_llist.code
% 0.16/0.39 thf(fact_50_not__lnull__conv,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ~ ( coindu335574135_lnull @ A @ Xs ) )
% 0.16/0.39 = ( ? [X3: A,Xs5: coindu1593790203_llist @ A] :
% 0.16/0.39 ( Xs
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X3 @ Xs5 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % not_lnull_conv
% 0.16/0.39 thf(fact_51_llist_OdiscI_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,Llist: coindu1593790203_llist @ A,X21: A,X22: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( Llist
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 0.16/0.39 => ~ ( coindu335574135_lnull @ A @ Llist ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.discI(2)
% 0.16/0.39 thf(fact_52_llist_Odisc_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.16/0.39 ~ ( coindu335574135_lnull @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.disc(2)
% 0.16/0.39 thf(fact_53_neq__LNil__conv,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 != ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( ? [X3: A,Xs5: coindu1593790203_llist @ A] :
% 0.16/0.39 ( Xs
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X3 @ Xs5 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % neq_LNil_conv
% 0.16/0.39 thf(fact_54_llist_Oexhaust,axiom,
% 0.16/0.39 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( Y
% 0.16/0.39 != ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 0.16/0.39 ( Y
% 0.16/0.39 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.exhaust
% 0.16/0.39 thf(fact_55_llist_Odistinct_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1598213697e_LNil @ A )
% 0.16/0.39 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.distinct(1)
% 0.16/0.39 thf(fact_56_lnull__llexord,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,R: A > A > $o,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( coindu300403952lexord @ A @ R @ Xs @ Ys ) ) ).
% 0.16/0.39
% 0.16/0.39 % lnull_llexord
% 0.16/0.39 thf(fact_57_llexord__LNil,axiom,
% 0.16/0.39 ! [A: $tType,R: A > A > $o,Ys: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 0.16/0.39
% 0.16/0.39 % llexord_LNil
% 0.16/0.39 thf(fact_58_unfold__llist_Octr_I2_J,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,P2: A > $o,A3: A,G21: A > B,G22: A > A] :
% 0.16/0.39 ( ~ ( P2 @ A3 )
% 0.16/0.39 => ( ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A3 )
% 0.16/0.39 = ( coindu1121789889_LCons @ B @ ( G21 @ A3 ) @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ ( G22 @ A3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % unfold_llist.ctr(2)
% 0.16/0.39 thf(fact_59_lsetp_Oinducts,axiom,
% 0.16/0.39 ! [A: $tType,X1: coindu1593790203_llist @ A,X23: A,P: ( coindu1593790203_llist @ A ) > A > $o] :
% 0.16/0.39 ( ( coindu1055736764_lsetp @ A @ X1 @ X23 )
% 0.16/0.39 => ( ! [X2: A,Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) @ X2 )
% 0.16/0.39 => ( ! [Xs2: coindu1593790203_llist @ A,X2: A,X6: A] :
% 0.16/0.39 ( ( coindu1055736764_lsetp @ A @ Xs2 @ X2 )
% 0.16/0.39 => ( ( P @ Xs2 @ X2 )
% 0.16/0.39 => ( P @ ( coindu1121789889_LCons @ A @ X6 @ Xs2 ) @ X2 ) ) )
% 0.16/0.39 => ( P @ X1 @ X23 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lsetp.inducts
% 0.16/0.39 thf(fact_60_lsetp_Osimps,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu1055736764_lsetp @ A )
% 0.16/0.39 = ( ^ [A12: coindu1593790203_llist @ A,A23: A] :
% 0.16/0.39 ( ? [X3: A,Xs3: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( A12
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 0.16/0.39 & ( A23 = X3 ) )
% 0.16/0.39 | ? [Xs3: coindu1593790203_llist @ A,X3: A,X7: A] :
% 0.16/0.39 ( ( A12
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X7 @ Xs3 ) )
% 0.16/0.39 & ( A23 = X3 )
% 0.16/0.39 & ( coindu1055736764_lsetp @ A @ Xs3 @ X3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lsetp.simps
% 0.16/0.39 thf(fact_61_lsetp_Ocases,axiom,
% 0.16/0.39 ! [A: $tType,A1: coindu1593790203_llist @ A,A22: A] :
% 0.16/0.39 ( ( coindu1055736764_lsetp @ A @ A1 @ A22 )
% 0.16/0.39 => ( ! [X2: A] :
% 0.16/0.39 ( ? [Xs2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( A1
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.16/0.39 => ( A22 != X2 ) )
% 0.16/0.39 => ~ ! [Xs2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ? [X6: A] :
% 0.16/0.39 ( A1
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X6 @ Xs2 ) )
% 0.16/0.39 => ~ ( coindu1055736764_lsetp @ A @ Xs2 @ A22 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lsetp.cases
% 0.16/0.39 thf(fact_62_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1571841457prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.16/0.39 = ( ( Xs
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 | ? [Xs5: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Y @ Xs5 ) )
% 0.16/0.39 & ( coindu1571841457prefix @ A @ Xs5 @ Ys ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Coinductive_List_Mirabelle_kmikjhschf.finite_lprefix_nitpick_simps(3)
% 0.16/0.39 thf(fact_63_llimit__induct,axiom,
% 0.16/0.39 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 => ( ! [X2: A,Xs2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.16/0.39 => ( ( P @ Xs2 )
% 0.16/0.39 => ( P @ ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) ) ) )
% 0.16/0.39 => ( ( ! [Ys5: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu574146665prefix @ A @ Ys5 @ Xs )
% 0.16/0.39 => ( P @ Ys5 ) )
% 0.16/0.39 => ( P @ Xs ) )
% 0.16/0.39 => ( P @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llimit_induct
% 0.16/0.39 thf(fact_64_lsorted__code_I2_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X: A] : ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lsorted_code(2)
% 0.16/0.39 thf(fact_65_gen__lset__code_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,A4: set @ A] :
% 0.16/0.39 ( ( coindu1928975208n_lset @ A @ A4 @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = A4 ) ).
% 0.16/0.39
% 0.16/0.39 % gen_lset_code(1)
% 0.16/0.39 thf(fact_66_llist_Ocorec__code,axiom,
% 0.16/0.39 ! [A: $tType,C: $tType] :
% 0.16/0.39 ( ( coindu1244876290_llist @ C @ A )
% 0.16/0.39 = ( ^ [P3: C > $o,G212: C > A,Q22: C > $o,G221: C > ( coindu1593790203_llist @ A ),G2222: C > C,A5: C] : ( if @ ( coindu1593790203_llist @ A ) @ ( P3 @ A5 ) @ ( coindu1598213697e_LNil @ A ) @ ( coindu1121789889_LCons @ A @ ( G212 @ A5 ) @ ( if @ ( coindu1593790203_llist @ A ) @ ( Q22 @ A5 ) @ ( G221 @ A5 ) @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q22 @ G221 @ G2222 @ ( G2222 @ A5 ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.corec_code
% 0.16/0.39 thf(fact_67_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1571841457prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 0.16/0.39
% 0.16/0.39 % Coinductive_List_Mirabelle_kmikjhschf.finite_lprefix_nitpick_simps(2)
% 0.16/0.39 thf(fact_68_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1571841457prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( Xs
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Coinductive_List_Mirabelle_kmikjhschf.finite_lprefix_nitpick_simps(1)
% 0.16/0.39 thf(fact_69_lprefix__LNil,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_LNil
% 0.16/0.39 thf(fact_70_ltakeWhile__LCons,axiom,
% 0.16/0.39 ! [A: $tType,P: A > $o,X: A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ( P @ X )
% 0.16/0.39 => ( ( coindu721411036eWhile @ A @ P @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X @ ( coindu721411036eWhile @ A @ P @ Xs ) ) ) )
% 0.16/0.39 & ( ~ ( P @ X )
% 0.16/0.39 => ( ( coindu721411036eWhile @ A @ P @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ltakeWhile_LCons
% 0.16/0.39 thf(fact_71_ord_OSingleton,axiom,
% 0.16/0.39 ! [A: $tType,Less_eq: A > A > $o,X: A] : ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord.Singleton
% 0.16/0.39 thf(fact_72_llist_Oleq__refl,axiom,
% 0.16/0.39 ! [A: $tType,X: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ X @ X ) ).
% 0.16/0.39
% 0.16/0.39 % llist.leq_refl
% 0.16/0.39 thf(fact_73_lprefix__refl,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ Xs ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_refl
% 0.16/0.39 thf(fact_74_ltakeWhile__K__True,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu721411036eWhile @ A
% 0.16/0.39 @ ^ [Uu: A] : $true
% 0.16/0.39 @ Xs )
% 0.16/0.39 = Xs ) ).
% 0.16/0.39
% 0.16/0.39 % ltakeWhile_K_True
% 0.16/0.39 thf(fact_75_LCons__lprefix__LCons,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.16/0.39 = ( ( X = Y )
% 0.16/0.39 & ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % LCons_lprefix_LCons
% 0.16/0.39 thf(fact_76_lprefix__code_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_code(1)
% 0.16/0.39 thf(fact_77_lfinite__code_I2_J,axiom,
% 0.16/0.39 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B] :
% 0.16/0.39 ( ( coindu1213758845finite @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) )
% 0.16/0.39 = ( coindu1213758845finite @ B @ Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % lfinite_code(2)
% 0.16/0.39 thf(fact_78_lfinite__LCons,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 0.16/0.39 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % lfinite_LCons
% 0.16/0.39 thf(fact_79_lfinite__code_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % lfinite_code(1)
% 0.16/0.39 thf(fact_80_ltakeWhile__LNil,axiom,
% 0.16/0.39 ! [A: $tType,P: A > $o] :
% 0.16/0.39 ( ( coindu721411036eWhile @ A @ P @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % ltakeWhile_LNil
% 0.16/0.39 thf(fact_81_lsorted__code_I1_J,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.39 => ( coindu48241764sorted @ A @ ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lsorted_code(1)
% 0.16/0.39 thf(fact_82_llist_Ocorec__disc__iff_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,C: $tType,P2: C > $o,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C,A3: C] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A3 ) )
% 0.16/0.39 = ( P2 @ A3 ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.corec_disc_iff(1)
% 0.16/0.39 thf(fact_83_llist_Ocorec__disc__iff_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,C: $tType,P2: C > $o,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C,A3: C] :
% 0.16/0.39 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A3 ) ) )
% 0.16/0.39 = ( ~ ( P2 @ A3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.corec_disc_iff(2)
% 0.16/0.39 thf(fact_84_ltakeWhile__K__False,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu721411036eWhile @ A
% 0.16/0.39 @ ^ [Uu: A] : $false
% 0.16/0.39 @ Xs )
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % ltakeWhile_K_False
% 0.16/0.39 thf(fact_85_not__lfinite__lprefix__conv__eq,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.16/0.39 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 = ( Xs = Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % not_lfinite_lprefix_conv_eq
% 0.16/0.39 thf(fact_86_lsorted__lprefixD,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( ( coindu48241764sorted @ A @ Ys )
% 0.16/0.39 => ( coindu48241764sorted @ A @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lsorted_lprefixD
% 0.16/0.39 thf(fact_87_Coinductive__List__Mirabelle__kmikjhschf_Olprefix__nitpick__simps,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A )
% 0.16/0.39 = ( ^ [Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ( coindu1213758845finite @ A @ Xs3 )
% 0.16/0.39 => ( coindu1571841457prefix @ A @ Xs3 @ Ys4 ) )
% 0.16/0.39 & ( ~ ( coindu1213758845finite @ A @ Xs3 )
% 0.16/0.39 => ( Xs3 = Ys4 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Coinductive_List_Mirabelle_kmikjhschf.lprefix_nitpick_simps
% 0.16/0.39 thf(fact_88_ord_Olsorted__lprefixD,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Less_eq: A > A > $o] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( ( coindu543932918sorted @ A @ Less_eq @ Ys )
% 0.16/0.39 => ( coindu543932918sorted @ A @ Less_eq @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord.lsorted_lprefixD
% 0.16/0.39 thf(fact_89_lprefix__down__linear,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Zs )
% 0.16/0.39 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.16/0.39 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 | ( coindu1696667936prefix @ A @ Ys @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_down_linear
% 0.16/0.39 thf(fact_90_lprefix__ltakeWhile,axiom,
% 0.16/0.39 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) @ Xs ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_ltakeWhile
% 0.16/0.39 thf(fact_91_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__def,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu1571841457prefix @ A )
% 0.16/0.39 = ( coindu1696667936prefix @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % Coinductive_List_Mirabelle_kmikjhschf.finite_lprefix_def
% 0.16/0.39 thf(fact_92_llist_Oleq__antisym,axiom,
% 0.16/0.39 ! [A: $tType,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ X @ Y )
% 0.16/0.39 => ( ( coindu1696667936prefix @ A @ Y @ X )
% 0.16/0.39 => ( X = Y ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.leq_antisym
% 0.16/0.39 thf(fact_93_lprefix__lfiniteD,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( ( coindu1213758845finite @ A @ Ys )
% 0.16/0.39 => ( coindu1213758845finite @ A @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_lfiniteD
% 0.16/0.39 thf(fact_94_lprefix__antisym,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( ( coindu1696667936prefix @ A @ Ys @ Xs )
% 0.16/0.39 => ( Xs = Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_antisym
% 0.16/0.39 thf(fact_95_llist_Oleq__trans,axiom,
% 0.16/0.39 ! [A: $tType,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A,Z: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ X @ Y )
% 0.16/0.39 => ( ( coindu1696667936prefix @ A @ Y @ Z )
% 0.16/0.39 => ( coindu1696667936prefix @ A @ X @ Z ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.leq_trans
% 0.16/0.39 thf(fact_96_lprefix__trans,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 0.16/0.39 => ( coindu1696667936prefix @ A @ Xs @ Zs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_trans
% 0.16/0.39 thf(fact_97_lfinite__LConsI,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 0.16/0.39 ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.39 => ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lfinite_LConsI
% 0.16/0.39 thf(fact_98_lnull__imp__lfinite,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % lnull_imp_lfinite
% 0.16/0.39 thf(fact_99_lfinite__LNil,axiom,
% 0.16/0.39 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % lfinite_LNil
% 0.16/0.39 thf(fact_100_Le__LCons,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Le_LCons
% 0.16/0.39 thf(fact_101_LCons__lprefix__conv,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ Ys )
% 0.16/0.39 = ( ? [Ys2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( Ys
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X @ Ys2 ) )
% 0.16/0.39 & ( coindu1696667936prefix @ A @ Xs @ Ys2 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % LCons_lprefix_conv
% 0.16/0.39 thf(fact_102_lprefix__not__lnullD,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_not_lnullD
% 0.16/0.39 thf(fact_103_lprefix__lnullD,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.16/0.39 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_lnullD
% 0.16/0.39 thf(fact_104_lprefix__lnull,axiom,
% 0.16/0.39 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Ys )
% 0.16/0.39 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_lnull
% 0.16/0.39 thf(fact_105_lnull__lprefix,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 0.16/0.39
% 0.16/0.39 % lnull_lprefix
% 0.16/0.39 thf(fact_106_LNil__lprefix,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 0.16/0.39
% 0.16/0.39 % LNil_lprefix
% 0.16/0.39 thf(fact_107_lprefix__imp__llexord,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,R: A > A > $o] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( coindu300403952lexord @ A @ R @ Xs @ Ys ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_imp_llexord
% 0.16/0.39 thf(fact_108_lstrict__prefix__lfinite1,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu574146665prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % lstrict_prefix_lfinite1
% 0.16/0.39 thf(fact_109_LNil,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.39 => ( coindu48241764sorted @ A @ ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % LNil
% 0.16/0.39 thf(fact_110_ord_OLCons__LCons,axiom,
% 0.16/0.39 ! [A: $tType,Less_eq: A > A > $o,X: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( Less_eq @ X @ Y )
% 0.16/0.39 => ( ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ Y @ Xs ) )
% 0.16/0.39 => ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord.LCons_LCons
% 0.16/0.39 thf(fact_111_ord_Olsorted__LCons__LCons,axiom,
% 0.16/0.39 ! [A: $tType,Less_eq: A > A > $o,X: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) )
% 0.16/0.39 = ( ( Less_eq @ X @ Y )
% 0.16/0.39 & ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord.lsorted_LCons_LCons
% 0.16/0.39 thf(fact_112_ord_OLNil,axiom,
% 0.16/0.39 ! [A: $tType,Less_eq: A > A > $o] : ( coindu543932918sorted @ A @ Less_eq @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord.LNil
% 0.16/0.39 thf(fact_113_ord_Olsorted__code_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Less_eq: A > A > $o] : ( coindu543932918sorted @ A @ Less_eq @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord.lsorted_code(1)
% 0.16/0.39 thf(fact_114_lstrict__prefix__def,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu574146665prefix @ A )
% 0.16/0.39 = ( ^ [Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs3 @ Ys4 )
% 0.16/0.39 & ( Xs3 != Ys4 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lstrict_prefix_def
% 0.16/0.39 thf(fact_115_llist_Ocorec_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,C: $tType,P2: C > $o,A3: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 0.16/0.39 ( ~ ( P2 @ A3 )
% 0.16/0.39 => ( ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A3 )
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ ( G21 @ A3 ) @ ( if @ ( coindu1593790203_llist @ A ) @ ( Q222 @ A3 ) @ ( G2212 @ A3 ) @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ ( G2223 @ A3 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.corec(2)
% 0.16/0.39 thf(fact_116_llist_Ocorec__disc_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,C: $tType,P2: C > $o,A3: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 0.16/0.39 ( ( P2 @ A3 )
% 0.16/0.39 => ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.corec_disc(1)
% 0.16/0.39 thf(fact_117_llist_Ocorec__disc_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,C: $tType,P2: C > $o,A3: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 0.16/0.39 ( ~ ( P2 @ A3 )
% 0.16/0.39 => ~ ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.corec_disc(2)
% 0.16/0.39 thf(fact_118_llist_Ocorec_I1_J,axiom,
% 0.16/0.39 ! [C: $tType,A: $tType,P2: C > $o,A3: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 0.16/0.39 ( ( P2 @ A3 )
% 0.16/0.39 => ( ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A3 )
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llist.corec(1)
% 0.16/0.39 thf(fact_119_llexord__empty,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu300403952lexord @ A
% 0.16/0.39 @ ^ [X3: A,Y2: A] : $false
% 0.16/0.39 @ Xs
% 0.16/0.39 @ Ys )
% 0.16/0.39 = ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 0.16/0.39
% 0.16/0.39 % llexord_empty
% 0.16/0.39 thf(fact_120_lfinite_Ocases,axiom,
% 0.16/0.39 ! [A: $tType,A3: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1213758845finite @ A @ A3 )
% 0.16/0.39 => ( ( A3
% 0.16/0.39 != ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 => ~ ! [Xs2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ? [X2: A] :
% 0.16/0.39 ( A3
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.16/0.39 => ~ ( coindu1213758845finite @ A @ Xs2 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lfinite.cases
% 0.16/0.39 thf(fact_121_lfinite_Osimps,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu1213758845finite @ A )
% 0.16/0.39 = ( ^ [A5: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( A5
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 | ? [Xs3: coindu1593790203_llist @ A,X3: A] :
% 0.16/0.39 ( ( A5
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 0.16/0.39 & ( coindu1213758845finite @ A @ Xs3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lfinite.simps
% 0.16/0.39 thf(fact_122_lfinite_Oinducts,axiom,
% 0.16/0.39 ! [A: $tType,X: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.16/0.39 ( ( coindu1213758845finite @ A @ X )
% 0.16/0.39 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 => ( ! [Xs2: coindu1593790203_llist @ A,X2: A] :
% 0.16/0.39 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.16/0.39 => ( ( P @ Xs2 )
% 0.16/0.39 => ( P @ ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) ) ) )
% 0.16/0.39 => ( P @ X ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lfinite.inducts
% 0.16/0.39 thf(fact_123_lprefix__code_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ~ ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_code(2)
% 0.16/0.39 thf(fact_124_lprefix_Ocases,axiom,
% 0.16/0.39 ! [A: $tType,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ A1 @ A22 )
% 0.16/0.39 => ( ( ( A1
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 => ! [Xs2: coindu1593790203_llist @ A] : ( A22 != Xs2 ) )
% 0.16/0.39 => ~ ! [Xs2: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X2: A] :
% 0.16/0.39 ( ( A1
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 0.16/0.39 => ( ( A22
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X2 @ Ys3 ) )
% 0.16/0.39 => ~ ( coindu1696667936prefix @ A @ Xs2 @ Ys3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix.cases
% 0.16/0.39 thf(fact_125_lprefix_Osimps,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A )
% 0.16/0.39 = ( ^ [A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ? [Xs3: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( A12
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 & ( A23 = Xs3 ) )
% 0.16/0.39 | ? [Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,X3: A] :
% 0.16/0.39 ( ( A12
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 0.16/0.39 & ( A23
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X3 @ Ys4 ) )
% 0.16/0.39 & ( coindu1696667936prefix @ A @ Xs3 @ Ys4 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix.simps
% 0.16/0.39 thf(fact_126_lprefix_Ocoinduct,axiom,
% 0.16/0.39 ! [A: $tType,X4: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( X4 @ X @ Xa )
% 0.16/0.39 => ( ! [X2: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( X4 @ X2 @ Xa2 )
% 0.16/0.39 => ( ? [Xs4: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( X2
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 & ( Xa2 = Xs4 ) )
% 0.16/0.39 | ? [Xs4: coindu1593790203_llist @ A,Ys5: coindu1593790203_llist @ A,Xb: A] :
% 0.16/0.39 ( ( X2
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Xb @ Xs4 ) )
% 0.16/0.39 & ( Xa2
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Xb @ Ys5 ) )
% 0.16/0.39 & ( ( X4 @ Xs4 @ Ys5 )
% 0.16/0.39 | ( coindu1696667936prefix @ A @ Xs4 @ Ys5 ) ) ) ) )
% 0.16/0.39 => ( coindu1696667936prefix @ A @ X @ Xa ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix.coinduct
% 0.16/0.39 thf(fact_127_lprefix__LCons__conv,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 0.16/0.39 = ( ( Xs
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 | ? [Xs5: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( Xs
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Y @ Xs5 ) )
% 0.16/0.39 & ( coindu1696667936prefix @ A @ Xs5 @ Ys ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_LCons_conv
% 0.16/0.39 thf(fact_128_corec__llist__never__stop,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,MORE: B > ( coindu1593790203_llist @ A ),LTL: B > B,X: B] :
% 0.16/0.39 ( ( coindu1244876290_llist @ B @ A @ IS_LNIL @ LHD
% 0.16/0.39 @ ^ [Uu: B] : $false
% 0.16/0.39 @ MORE
% 0.16/0.39 @ LTL
% 0.16/0.39 @ X )
% 0.16/0.39 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ X ) ) ).
% 0.16/0.39
% 0.16/0.39 % corec_llist_never_stop
% 0.16/0.39 thf(fact_129_Singleton,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X: A] : ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Singleton
% 0.16/0.39 thf(fact_130_ord_Olsorted__code_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,Less_eq: A > A > $o,X: A] : ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord.lsorted_code(2)
% 0.16/0.39 thf(fact_131_ord_Olsorted_Ocases,axiom,
% 0.16/0.39 ! [A: $tType,Less_eq: A > A > $o,A3: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu543932918sorted @ A @ Less_eq @ A3 )
% 0.16/0.39 => ( ( A3
% 0.16/0.39 != ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 => ( ! [X2: A] :
% 0.16/0.39 ( A3
% 0.16/0.39 != ( coindu1121789889_LCons @ A @ X2 @ ( coindu1598213697e_LNil @ A ) ) )
% 0.16/0.39 => ~ ! [X2: A,Y3: A,Xs2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( A3
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X2 @ ( coindu1121789889_LCons @ A @ Y3 @ Xs2 ) ) )
% 0.16/0.39 => ( ( Less_eq @ X2 @ Y3 )
% 0.16/0.39 => ~ ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ Y3 @ Xs2 ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord.lsorted.cases
% 0.16/0.39 thf(fact_132_ord_Olsorted_Osimps,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu543932918sorted @ A )
% 0.16/0.39 = ( ^ [Less_eq2: A > A > $o,A5: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( A5
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 | ? [X3: A] :
% 0.16/0.39 ( A5
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X3 @ ( coindu1598213697e_LNil @ A ) ) )
% 0.16/0.39 | ? [X3: A,Y2: A,Xs3: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( A5
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X3 @ ( coindu1121789889_LCons @ A @ Y2 @ Xs3 ) ) )
% 0.16/0.39 & ( Less_eq2 @ X3 @ Y2 )
% 0.16/0.39 & ( coindu543932918sorted @ A @ Less_eq2 @ ( coindu1121789889_LCons @ A @ Y2 @ Xs3 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord.lsorted.simps
% 0.16/0.39 thf(fact_133_ord_Olsorted_Ocoinduct,axiom,
% 0.16/0.39 ! [A: $tType,X4: ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Less_eq: A > A > $o] :
% 0.16/0.39 ( ( X4 @ X )
% 0.16/0.39 => ( ! [X2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( X4 @ X2 )
% 0.16/0.39 => ( ( X2
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 | ? [Xa3: A] :
% 0.16/0.39 ( X2
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Xa3 @ ( coindu1598213697e_LNil @ A ) ) )
% 0.16/0.39 | ? [Xa3: A,Y4: A,Xs4: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( X2
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Xa3 @ ( coindu1121789889_LCons @ A @ Y4 @ Xs4 ) ) )
% 0.16/0.39 & ( Less_eq @ Xa3 @ Y4 )
% 0.16/0.39 & ( ( X4 @ ( coindu1121789889_LCons @ A @ Y4 @ Xs4 ) )
% 0.16/0.39 | ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ Y4 @ Xs4 ) ) ) ) ) )
% 0.16/0.39 => ( coindu543932918sorted @ A @ Less_eq @ X ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord.lsorted.coinduct
% 0.16/0.39 thf(fact_134_llast__lappend__LCons,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.39 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) )
% 0.16/0.39 = ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llast_lappend_LCons
% 0.16/0.39 thf(fact_135_lsorted_Ocoinduct,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X4: ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( X4 @ X )
% 0.16/0.39 => ( ! [X2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( X4 @ X2 )
% 0.16/0.39 => ( ( X2
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 | ? [Xa3: A] :
% 0.16/0.39 ( X2
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Xa3 @ ( coindu1598213697e_LNil @ A ) ) )
% 0.16/0.39 | ? [Xa3: A,Y4: A,Xs4: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( X2
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Xa3 @ ( coindu1121789889_LCons @ A @ Y4 @ Xs4 ) ) )
% 0.16/0.39 & ( ord_less_eq @ A @ Xa3 @ Y4 )
% 0.16/0.39 & ( ( X4 @ ( coindu1121789889_LCons @ A @ Y4 @ Xs4 ) )
% 0.16/0.39 | ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ Y4 @ Xs4 ) ) ) ) ) )
% 0.16/0.39 => ( coindu48241764sorted @ A @ X ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lsorted.coinduct
% 0.16/0.39 thf(fact_136_lsorted_Osimps,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.39 => ( ( coindu48241764sorted @ A )
% 0.16/0.39 = ( ^ [A5: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( A5
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 | ? [X3: A] :
% 0.16/0.39 ( A5
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X3 @ ( coindu1598213697e_LNil @ A ) ) )
% 0.16/0.39 | ? [X3: A,Y2: A,Xs3: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( A5
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X3 @ ( coindu1121789889_LCons @ A @ Y2 @ Xs3 ) ) )
% 0.16/0.39 & ( ord_less_eq @ A @ X3 @ Y2 )
% 0.16/0.39 & ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ Y2 @ Xs3 ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lsorted.simps
% 0.16/0.39 thf(fact_137_lsorted_Ocases,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A3: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu48241764sorted @ A @ A3 )
% 0.16/0.39 => ( ( A3
% 0.16/0.39 != ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 => ( ! [X2: A] :
% 0.16/0.39 ( A3
% 0.16/0.39 != ( coindu1121789889_LCons @ A @ X2 @ ( coindu1598213697e_LNil @ A ) ) )
% 0.16/0.39 => ~ ! [X2: A,Y3: A,Xs2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( A3
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X2 @ ( coindu1121789889_LCons @ A @ Y3 @ Xs2 ) ) )
% 0.16/0.39 => ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.16/0.39 => ~ ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ Y3 @ Xs2 ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lsorted.cases
% 0.16/0.39 thf(fact_138_lstrict__prefix__lappend__conv,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu574146665prefix @ A @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.39 & ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lstrict_prefix_lappend_conv
% 0.16/0.39 thf(fact_139_lprefixI,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X4: set @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) )] :
% 0.16/0.39 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs @ Ys ) @ X4 )
% 0.16/0.39 => ( ! [Xs2: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs2 @ Ys3 ) @ X4 )
% 0.16/0.39 => ( ( coindu335574135_lnull @ A @ Xs2 )
% 0.16/0.39 | ? [X8: A,Xs6: coindu1593790203_llist @ A,Ys6: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( Xs2
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X8 @ Xs6 ) )
% 0.16/0.39 & ( Ys3
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ X8 @ Ys6 ) )
% 0.16/0.39 & ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs6 @ Ys6 ) @ X4 )
% 0.16/0.39 | ( coindu1696667936prefix @ A @ Xs6 @ Ys6 ) ) ) ) )
% 0.16/0.39 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefixI
% 0.16/0.39 thf(fact_140_lappend__code_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,Xa: A,X: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu268472904append @ A @ ( coindu1121789889_LCons @ A @ Xa @ X ) @ Ys )
% 0.16/0.39 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu268472904append @ A @ X @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_code(2)
% 0.16/0.39 thf(fact_141_lappend_Odisc__iff_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 0.16/0.39 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend.disc_iff(2)
% 0.16/0.39 thf(fact_142_lnull__lappend,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 & ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lnull_lappend
% 0.16/0.39 thf(fact_143_lappend__code_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ Ys )
% 0.16/0.39 = Ys ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_code(1)
% 0.16/0.39 thf(fact_144_lappend__LNil2,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu268472904append @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = Xs ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_LNil2
% 0.16/0.39 thf(fact_145_lfinite__lappend,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1213758845finite @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.39 & ( coindu1213758845finite @ A @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lfinite_lappend
% 0.16/0.39 thf(fact_146_lsorted__LCons__LCons,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) )
% 0.16/0.39 = ( ( ord_less_eq @ A @ X @ Y )
% 0.16/0.39 & ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lsorted_LCons_LCons
% 0.16/0.39 thf(fact_147_lprefix__lappend__same,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ ( coindu268472904append @ A @ Xs @ Zs ) )
% 0.16/0.39 = ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.39 => ( coindu1696667936prefix @ A @ Ys @ Zs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_lappend_same
% 0.16/0.39 thf(fact_148_lappend__assoc,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 0.16/0.39 = ( coindu268472904append @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_assoc
% 0.16/0.39 thf(fact_149_wlog__linorder__le,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [P: A > A > $o,B3: A,A3: A] :
% 0.16/0.39 ( ! [A2: A,B2: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.16/0.39 => ( P @ A2 @ B2 ) )
% 0.16/0.39 => ( ( ( P @ B3 @ A3 )
% 0.16/0.39 => ( P @ A3 @ B3 ) )
% 0.16/0.39 => ( P @ A3 @ B3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % wlog_linorder_le
% 0.16/0.39 thf(fact_150_lprefix__lappend,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_lappend
% 0.16/0.39 thf(fact_151_lappend__lprefixE,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 0.16/0.39 => ~ ! [Zs2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( Zs
% 0.16/0.39 != ( coindu268472904append @ A @ Xs @ Zs2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_lprefixE
% 0.16/0.39 thf(fact_152_lprefix__lappendD,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs ) )
% 0.16/0.39 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 | ( coindu1696667936prefix @ A @ Ys @ Xs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_lappendD
% 0.16/0.39 thf(fact_153_lprefix__conv__lappend,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A )
% 0.16/0.39 = ( ^ [Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 0.16/0.39 ? [Zs3: coindu1593790203_llist @ A] :
% 0.16/0.39 ( Ys4
% 0.16/0.39 = ( coindu268472904append @ A @ Xs3 @ Zs3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_conv_lappend
% 0.16/0.39 thf(fact_154_lprefix__lappend__sameI,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 0.16/0.39 => ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Zs @ Xs ) @ ( coindu268472904append @ A @ Zs @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lprefix_lappend_sameI
% 0.16/0.39 thf(fact_155_lappend_Odisc_I2_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 | ~ ( coindu335574135_lnull @ A @ Ys ) )
% 0.16/0.39 => ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend.disc(2)
% 0.16/0.39 thf(fact_156_lappend_Odisc_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.16/0.39 => ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend.disc(1)
% 0.16/0.39 thf(fact_157_lappend__lnull1,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.16/0.39 = Ys ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_lnull1
% 0.16/0.39 thf(fact_158_lappend__lnull2,axiom,
% 0.16/0.39 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Ys )
% 0.16/0.39 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.16/0.39 = Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_lnull2
% 0.16/0.39 thf(fact_159_lappend__LNil__LNil,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_LNil_LNil
% 0.16/0.39 thf(fact_160_LNil__eq__lappend__iff,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ( coindu1598213697e_LNil @ A )
% 0.16/0.39 = ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( ( Xs
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 & ( Ys
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % LNil_eq_lappend_iff
% 0.16/0.39 thf(fact_161_lappend__eq__LNil__iff,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( ( Xs
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 & ( Ys
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_eq_LNil_iff
% 0.16/0.39 thf(fact_162_lappend__inf,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.16/0.39 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.16/0.39 = Xs ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_inf
% 0.16/0.39 thf(fact_163_llexord__lappend__leftI,axiom,
% 0.16/0.39 ! [A: $tType,R: A > A > $o,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu300403952lexord @ A @ R @ Ys @ Zs )
% 0.16/0.39 => ( coindu300403952lexord @ A @ R @ ( coindu268472904append @ A @ Xs @ Ys ) @ ( coindu268472904append @ A @ Xs @ Zs ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llexord_lappend_leftI
% 0.16/0.39 thf(fact_164_llexord__append__right,axiom,
% 0.16/0.39 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) ) ).
% 0.16/0.39
% 0.16/0.39 % llexord_append_right
% 0.16/0.39 thf(fact_165_lappend__snocL1__conv__LCons2,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ ( coindu1598213697e_LNil @ A ) ) ) @ Ys )
% 0.16/0.39 = ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend_snocL1_conv_LCons2
% 0.16/0.39 thf(fact_166_lappend_Octr_I1_J,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu335574135_lnull @ A @ Xs )
% 0.16/0.39 => ( ( coindu335574135_lnull @ A @ Ys )
% 0.16/0.39 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 0.16/0.39 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lappend.ctr(1)
% 0.16/0.39 thf(fact_167_LCons__LCons,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X @ Y )
% 0.16/0.39 => ( ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ Y @ Xs ) )
% 0.16/0.39 => ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % LCons_LCons
% 0.16/0.39 thf(fact_168_lfinite__rev__induct,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 0.16/0.39 ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.39 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 => ( ! [X2: A,Xs2: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( coindu1213758845finite @ A @ Xs2 )
% 0.16/0.39 => ( ( P @ Xs2 )
% 0.16/0.39 => ( P @ ( coindu268472904append @ A @ Xs2 @ ( coindu1121789889_LCons @ A @ X2 @ ( coindu1598213697e_LNil @ A ) ) ) ) ) )
% 0.16/0.39 => ( P @ Xs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % lfinite_rev_induct
% 0.16/0.39 thf(fact_169_prod_Oinject,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,X1: A,X23: B,Y1: A,Y23: B] :
% 0.16/0.39 ( ( ( product_Pair @ A @ B @ X1 @ X23 )
% 0.16/0.39 = ( product_Pair @ A @ B @ Y1 @ Y23 ) )
% 0.16/0.39 = ( ( X1 = Y1 )
% 0.16/0.39 & ( X23 = Y23 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod.inject
% 0.16/0.39 thf(fact_170_old_Oprod_Oinject,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,A3: A,B3: B,A6: A,B4: B] :
% 0.16/0.39 ( ( ( product_Pair @ A @ B @ A3 @ B3 )
% 0.16/0.39 = ( product_Pair @ A @ B @ A6 @ B4 ) )
% 0.16/0.39 = ( ( A3 = A6 )
% 0.16/0.39 & ( B3 = B4 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % old.prod.inject
% 0.16/0.39 thf(fact_171_order__refl,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.16/0.39
% 0.16/0.39 % order_refl
% 0.16/0.39 thf(fact_172_pred__subset__eq2,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.16/0.39 ( ( ord_less_eq @ ( A > B > $o )
% 0.16/0.39 @ ^ [X3: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y2 ) @ R3 )
% 0.16/0.39 @ ^ [X3: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y2 ) @ S ) )
% 0.16/0.39 = ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R3 @ S ) ) ).
% 0.16/0.39
% 0.16/0.39 % pred_subset_eq2
% 0.16/0.39 thf(fact_173_predicate2I,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,P: A > B > $o,Q: A > B > $o] :
% 0.16/0.39 ( ! [X2: A,Y3: B] :
% 0.16/0.39 ( ( P @ X2 @ Y3 )
% 0.16/0.39 => ( Q @ X2 @ Y3 ) )
% 0.16/0.39 => ( ord_less_eq @ ( A > B > $o ) @ P @ Q ) ) ).
% 0.16/0.39
% 0.16/0.39 % predicate2I
% 0.16/0.39 thf(fact_174_predicate2D,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,X: A,Y: B] :
% 0.16/0.39 ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.16/0.39 => ( ( P @ X @ Y )
% 0.16/0.39 => ( Q @ X @ Y ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % predicate2D
% 0.16/0.39 thf(fact_175_rev__predicate2D,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,P: A > B > $o,X: A,Y: B,Q: A > B > $o] :
% 0.16/0.39 ( ( P @ X @ Y )
% 0.16/0.39 => ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.16/0.39 => ( Q @ X @ Y ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % rev_predicate2D
% 0.16/0.39 thf(fact_176_pred__subset__eq,axiom,
% 0.16/0.39 ! [A: $tType,R3: set @ A,S: set @ A] :
% 0.16/0.39 ( ( ord_less_eq @ ( A > $o )
% 0.16/0.39 @ ^ [X3: A] : ( member @ A @ X3 @ R3 )
% 0.16/0.39 @ ^ [X3: A] : ( member @ A @ X3 @ S ) )
% 0.16/0.39 = ( ord_less_eq @ ( set @ A ) @ R3 @ S ) ) ).
% 0.16/0.39
% 0.16/0.39 % pred_subset_eq
% 0.16/0.39 thf(fact_177_dual__order_Oantisym,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B3: A,A3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.16/0.39 => ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.16/0.39 => ( A3 = B3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % dual_order.antisym
% 0.16/0.39 thf(fact_178_dual__order_Otrans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [B3: A,A3: A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.16/0.39 => ( ( ord_less_eq @ A @ C3 @ B3 )
% 0.16/0.39 => ( ord_less_eq @ A @ C3 @ A3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % dual_order.trans
% 0.16/0.39 thf(fact_179_linorder__wlog,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [P: A > A > $o,A3: A,B3: A] :
% 0.16/0.39 ( ! [A2: A,B2: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.16/0.39 => ( P @ A2 @ B2 ) )
% 0.16/0.39 => ( ! [A2: A,B2: A] :
% 0.16/0.39 ( ( P @ B2 @ A2 )
% 0.16/0.39 => ( P @ A2 @ B2 ) )
% 0.16/0.39 => ( P @ A3 @ B3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % linorder_wlog
% 0.16/0.39 thf(fact_180_dual__order_Orefl,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 0.16/0.39
% 0.16/0.39 % dual_order.refl
% 0.16/0.39 thf(fact_181_order__trans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X: A,Y: A,Z: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X @ Y )
% 0.16/0.39 => ( ( ord_less_eq @ A @ Y @ Z )
% 0.16/0.39 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order_trans
% 0.16/0.39 thf(fact_182_order__class_Oorder_Oantisym,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A3: A,B3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.16/0.39 => ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.16/0.39 => ( A3 = B3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order_class.order.antisym
% 0.16/0.39 thf(fact_183_ord__le__eq__trans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A3: A,B3: A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.16/0.39 => ( ( B3 = C3 )
% 0.16/0.39 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord_le_eq_trans
% 0.16/0.39 thf(fact_184_ord__eq__le__trans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A3: A,B3: A,C3: A] :
% 0.16/0.39 ( ( A3 = B3 )
% 0.16/0.39 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 0.16/0.39 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord_eq_le_trans
% 0.16/0.39 thf(fact_185_antisym__conv,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [Y: A,X: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ Y @ X )
% 0.16/0.39 => ( ( ord_less_eq @ A @ X @ Y )
% 0.16/0.39 = ( X = Y ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % antisym_conv
% 0.16/0.39 thf(fact_186_le__cases3,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X: A,Y: A,Z: A] :
% 0.16/0.39 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.16/0.39 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 0.16/0.39 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.16/0.39 => ~ ( ord_less_eq @ A @ X @ Z ) )
% 0.16/0.39 => ( ( ( ord_less_eq @ A @ X @ Z )
% 0.16/0.39 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 0.16/0.39 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 0.16/0.39 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.16/0.39 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 0.16/0.39 => ~ ( ord_less_eq @ A @ Z @ X ) )
% 0.16/0.39 => ~ ( ( ord_less_eq @ A @ Z @ X )
% 0.16/0.39 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_cases3
% 0.16/0.39 thf(fact_187_order_Otrans,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [A3: A,B3: A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.16/0.39 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 0.16/0.39 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order.trans
% 0.16/0.39 thf(fact_188_le__cases,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X: A,Y: A] :
% 0.16/0.39 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.16/0.39 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_cases
% 0.16/0.39 thf(fact_189_eq__refl,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( preorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X: A,Y: A] :
% 0.16/0.39 ( ( X = Y )
% 0.16/0.39 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % eq_refl
% 0.16/0.39 thf(fact_190_linorder__class_Olinear,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( linorder @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X: A,Y: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X @ Y )
% 0.16/0.39 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % linorder_class.linear
% 0.16/0.39 thf(fact_191_antisym,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ! [X: A,Y: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X @ Y )
% 0.16/0.39 => ( ( ord_less_eq @ A @ Y @ X )
% 0.16/0.39 => ( X = Y ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % antisym
% 0.16/0.39 thf(fact_192_eq__iff,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( order @ A @ ( type2 @ A ) )
% 0.16/0.39 => ( ( ^ [Y5: A,Z2: A] : ( Y5 = Z2 ) )
% 0.16/0.39 = ( ^ [X3: A,Y2: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.16/0.39 & ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % eq_iff
% 0.16/0.39 thf(fact_193_ord__le__eq__subst,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType] :
% 0.16/0.39 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.16/0.39 & ( ord @ A @ ( type2 @ A ) ) )
% 0.16/0.39 => ! [A3: A,B3: A,F: A > B,C3: B] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.16/0.39 => ( ( ( F @ B3 )
% 0.16/0.39 = C3 )
% 0.16/0.39 => ( ! [X2: A,Y3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.16/0.39 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/0.39 => ( ord_less_eq @ B @ ( F @ A3 ) @ C3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord_le_eq_subst
% 0.16/0.39 thf(fact_194_ord__eq__le__subst,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType] :
% 0.16/0.39 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.16/0.39 & ( ord @ A @ ( type2 @ A ) ) )
% 0.16/0.39 => ! [A3: A,F: B > A,B3: B,C3: B] :
% 0.16/0.39 ( ( A3
% 0.16/0.39 = ( F @ B3 ) )
% 0.16/0.39 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 0.16/0.39 => ( ! [X2: B,Y3: B] :
% 0.16/0.39 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 0.16/0.39 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/0.39 => ( ord_less_eq @ A @ A3 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ord_eq_le_subst
% 0.16/0.39 thf(fact_195_order__subst2,axiom,
% 0.16/0.39 ! [A: $tType,C: $tType] :
% 0.16/0.39 ( ( ( order @ C @ ( type2 @ C ) )
% 0.16/0.39 & ( order @ A @ ( type2 @ A ) ) )
% 0.16/0.39 => ! [A3: A,B3: A,F: A > C,C3: C] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.16/0.39 => ( ( ord_less_eq @ C @ ( F @ B3 ) @ C3 )
% 0.16/0.39 => ( ! [X2: A,Y3: A] :
% 0.16/0.39 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 0.16/0.39 => ( ord_less_eq @ C @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/0.39 => ( ord_less_eq @ C @ ( F @ A3 ) @ C3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order_subst2
% 0.16/0.39 thf(fact_196_order__subst1,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType] :
% 0.16/0.39 ( ( ( order @ B @ ( type2 @ B ) )
% 0.16/0.39 & ( order @ A @ ( type2 @ A ) ) )
% 0.16/0.39 => ! [A3: A,F: B > A,B3: B,C3: B] :
% 0.16/0.39 ( ( ord_less_eq @ A @ A3 @ ( F @ B3 ) )
% 0.16/0.39 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 0.16/0.39 => ( ! [X2: B,Y3: B] :
% 0.16/0.39 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 0.16/0.39 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 0.16/0.39 => ( ord_less_eq @ A @ A3 @ ( F @ C3 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % order_subst1
% 0.16/0.39 thf(fact_197_le__fun__def,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType] :
% 0.16/0.39 ( ( ord @ B @ ( type2 @ B ) )
% 0.16/0.39 => ( ( ord_less_eq @ ( A > B ) )
% 0.16/0.39 = ( ^ [F2: A > B,G2: A > B] :
% 0.16/0.39 ! [X3: A] : ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_fun_def
% 0.16/0.39 thf(fact_198_le__funI,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType] :
% 0.16/0.39 ( ( ord @ B @ ( type2 @ B ) )
% 0.16/0.39 => ! [F: A > B,G: A > B] :
% 0.16/0.39 ( ! [X2: A] : ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) )
% 0.16/0.39 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_funI
% 0.16/0.39 thf(fact_199_le__funE,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType] :
% 0.16/0.39 ( ( ord @ B @ ( type2 @ B ) )
% 0.16/0.39 => ! [F: A > B,G: A > B,X: A] :
% 0.16/0.39 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.16/0.39 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_funE
% 0.16/0.39 thf(fact_200_le__funD,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType] :
% 0.16/0.39 ( ( ord @ B @ ( type2 @ B ) )
% 0.16/0.39 => ! [F: A > B,G: A > B,X: A] :
% 0.16/0.39 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.16/0.39 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % le_funD
% 0.16/0.39 thf(fact_201_old_Oprod_Oinducts,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.16/0.39 ( ! [A2: A,B2: B] : ( P @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.16/0.39 => ( P @ Prod ) ) ).
% 0.16/0.39
% 0.16/0.39 % old.prod.inducts
% 0.16/0.39 thf(fact_202_old_Oprod_Oexhaust,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.16/0.39 ~ ! [A2: A,B2: B] :
% 0.16/0.39 ( Y
% 0.16/0.39 != ( product_Pair @ A @ B @ A2 @ B2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % old.prod.exhaust
% 0.16/0.39 thf(fact_203_prod__induct7,axiom,
% 0.16/0.39 ! [G3: $tType,F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) )] :
% 0.16/0.39 ( ! [A2: A,B2: B,C2: C,D2: D,E2: E,F4: F3,G4: G3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) @ A2 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) @ B2 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F3 @ G3 ) @ E2 @ ( product_Pair @ F3 @ G3 @ F4 @ G4 ) ) ) ) ) ) )
% 0.16/0.39 => ( P @ X ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_induct7
% 0.16/0.39 thf(fact_204_prod__induct6,axiom,
% 0.16/0.39 ! [F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 0.16/0.39 ( ! [A2: A,B2: B,C2: C,D2: D,E2: E,F4: F3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A2 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B2 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D2 @ ( product_Pair @ E @ F3 @ E2 @ F4 ) ) ) ) ) )
% 0.16/0.39 => ( P @ X ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_induct6
% 0.16/0.39 thf(fact_205_prod__induct5,axiom,
% 0.16/0.39 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.16/0.39 ( ! [A2: A,B2: B,C2: C,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A2 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B2 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.16/0.39 => ( P @ X ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_induct5
% 0.16/0.39 thf(fact_206_prod__induct4,axiom,
% 0.16/0.39 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.16/0.39 ( ! [A2: A,B2: B,C2: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A2 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B2 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 0.16/0.39 => ( P @ X ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_induct4
% 0.16/0.39 thf(fact_207_prod__induct3,axiom,
% 0.16/0.39 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.16/0.39 ( ! [A2: A,B2: B,C2: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ B2 @ C2 ) ) )
% 0.16/0.39 => ( P @ X ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_induct3
% 0.16/0.39 thf(fact_208_prod__cases7,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,G3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) )] :
% 0.16/0.39 ~ ! [A2: A,B2: B,C2: C,D2: D,E2: E,F4: F3,G4: G3] :
% 0.16/0.39 ( Y
% 0.16/0.39 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) @ A2 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) @ B2 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F3 @ G3 ) @ E2 @ ( product_Pair @ F3 @ G3 @ F4 @ G4 ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_cases7
% 0.16/0.39 thf(fact_209_prod__cases6,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 0.16/0.39 ~ ! [A2: A,B2: B,C2: C,D2: D,E2: E,F4: F3] :
% 0.16/0.39 ( Y
% 0.16/0.39 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A2 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B2 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D2 @ ( product_Pair @ E @ F3 @ E2 @ F4 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_cases6
% 0.16/0.39 thf(fact_210_prod__cases5,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.16/0.39 ~ ! [A2: A,B2: B,C2: C,D2: D,E2: E] :
% 0.16/0.39 ( Y
% 0.16/0.39 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A2 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B2 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_cases5
% 0.16/0.39 thf(fact_211_prod__cases4,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.16/0.39 ~ ! [A2: A,B2: B,C2: C,D2: D] :
% 0.16/0.39 ( Y
% 0.16/0.39 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A2 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B2 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_cases4
% 0.16/0.39 thf(fact_212_prod__cases3,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.16/0.39 ~ ! [A2: A,B2: B,C2: C] :
% 0.16/0.39 ( Y
% 0.16/0.39 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ B2 @ C2 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_cases3
% 0.16/0.39 thf(fact_213_Pair__inject,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,A3: A,B3: B,A6: A,B4: B] :
% 0.16/0.39 ( ( ( product_Pair @ A @ B @ A3 @ B3 )
% 0.16/0.39 = ( product_Pair @ A @ B @ A6 @ B4 ) )
% 0.16/0.39 => ~ ( ( A3 = A6 )
% 0.16/0.39 => ( B3 != B4 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Pair_inject
% 0.16/0.39 thf(fact_214_prod__cases,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 0.16/0.39 ( ! [A2: A,B2: B] : ( P @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.16/0.39 => ( P @ P2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % prod_cases
% 0.16/0.39 thf(fact_215_surj__pair,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 0.16/0.39 ? [X2: A,Y3: B] :
% 0.16/0.39 ( P2
% 0.16/0.39 = ( product_Pair @ A @ B @ X2 @ Y3 ) ) ).
% 0.16/0.39
% 0.16/0.39 % surj_pair
% 0.16/0.39 thf(fact_216_subrelI,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S2: set @ ( product_prod @ A @ B )] :
% 0.16/0.39 ( ! [X2: A,Y3: B] :
% 0.16/0.39 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ R )
% 0.16/0.39 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ S2 ) )
% 0.16/0.39 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S2 ) ) ).
% 0.16/0.39
% 0.16/0.39 % subrelI
% 0.16/0.39 thf(fact_217_pred__equals__eq2,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.16/0.39 ( ( ( ^ [X3: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y2 ) @ R3 ) )
% 0.16/0.39 = ( ^ [X3: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y2 ) @ S ) ) )
% 0.16/0.39 = ( R3 = S ) ) ).
% 0.16/0.39
% 0.16/0.39 % pred_equals_eq2
% 0.16/0.39 thf(fact_218_old_Oprod_Orec,axiom,
% 0.16/0.39 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A3: A,B3: B] :
% 0.16/0.39 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.16/0.39 = ( F1 @ A3 @ B3 ) ) ).
% 0.16/0.39
% 0.16/0.39 % old.prod.rec
% 0.16/0.39 thf(fact_219_subsetI,axiom,
% 0.16/0.39 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.16/0.39 ( ! [X2: A] :
% 0.16/0.39 ( ( member @ A @ X2 @ A4 )
% 0.16/0.39 => ( member @ A @ X2 @ B5 ) )
% 0.16/0.39 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.16/0.39
% 0.16/0.39 % subsetI
% 0.16/0.39 thf(fact_220_subset__antisym,axiom,
% 0.16/0.39 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.16/0.39 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.16/0.39 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 0.16/0.39 => ( A4 = B5 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % subset_antisym
% 0.16/0.39 thf(fact_221_predicate1I,axiom,
% 0.16/0.39 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.16/0.39 ( ! [X2: A] :
% 0.16/0.39 ( ( P @ X2 )
% 0.16/0.39 => ( Q @ X2 ) )
% 0.16/0.39 => ( ord_less_eq @ ( A > $o ) @ P @ Q ) ) ).
% 0.16/0.39
% 0.16/0.39 % predicate1I
% 0.16/0.39 thf(fact_222_predicate1D,axiom,
% 0.16/0.39 ! [A: $tType,P: A > $o,Q: A > $o,X: A] :
% 0.16/0.39 ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 0.16/0.39 => ( ( P @ X )
% 0.16/0.39 => ( Q @ X ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % predicate1D
% 0.16/0.39 thf(fact_223_rev__predicate1D,axiom,
% 0.16/0.39 ! [A: $tType,P: A > $o,X: A,Q: A > $o] :
% 0.16/0.39 ( ( P @ X )
% 0.16/0.39 => ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 0.16/0.39 => ( Q @ X ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % rev_predicate1D
% 0.16/0.39 thf(fact_224_Collect__mono__iff,axiom,
% 0.16/0.39 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.16/0.39 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.16/0.39 = ( ! [X3: A] :
% 0.16/0.39 ( ( P @ X3 )
% 0.16/0.39 => ( Q @ X3 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Collect_mono_iff
% 0.16/0.39 thf(fact_225_contra__subsetD,axiom,
% 0.16/0.39 ! [A: $tType,A4: set @ A,B5: set @ A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.16/0.39 => ( ~ ( member @ A @ C3 @ B5 )
% 0.16/0.39 => ~ ( member @ A @ C3 @ A4 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % contra_subsetD
% 0.16/0.39 thf(fact_226_set__eq__subset,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ^ [Y5: set @ A,Z2: set @ A] : ( Y5 = Z2 ) )
% 0.16/0.39 = ( ^ [A7: set @ A,B6: set @ A] :
% 0.16/0.39 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B6 )
% 0.16/0.39 & ( ord_less_eq @ ( set @ A ) @ B6 @ A7 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % set_eq_subset
% 0.16/0.39 thf(fact_227_subset__trans,axiom,
% 0.16/0.39 ! [A: $tType,A4: set @ A,B5: set @ A,C4: set @ A] :
% 0.16/0.39 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.16/0.39 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C4 )
% 0.16/0.39 => ( ord_less_eq @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % subset_trans
% 0.16/0.39 thf(fact_228_Collect__mono,axiom,
% 0.16/0.39 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.16/0.39 ( ! [X2: A] :
% 0.16/0.39 ( ( P @ X2 )
% 0.16/0.39 => ( Q @ X2 ) )
% 0.16/0.39 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % Collect_mono
% 0.16/0.39 thf(fact_229_subset__refl,axiom,
% 0.16/0.39 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 0.16/0.39
% 0.16/0.39 % subset_refl
% 0.16/0.39 thf(fact_230_rev__subsetD,axiom,
% 0.16/0.39 ! [A: $tType,C3: A,A4: set @ A,B5: set @ A] :
% 0.16/0.39 ( ( member @ A @ C3 @ A4 )
% 0.16/0.39 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.16/0.39 => ( member @ A @ C3 @ B5 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % rev_subsetD
% 0.16/0.39 thf(fact_231_subset__iff,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord_less_eq @ ( set @ A ) )
% 0.16/0.39 = ( ^ [A7: set @ A,B6: set @ A] :
% 0.16/0.39 ! [T2: A] :
% 0.16/0.39 ( ( member @ A @ T2 @ A7 )
% 0.16/0.39 => ( member @ A @ T2 @ B6 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % subset_iff
% 0.16/0.39 thf(fact_232_set__rev__mp,axiom,
% 0.16/0.39 ! [A: $tType,X: A,A4: set @ A,B5: set @ A] :
% 0.16/0.39 ( ( member @ A @ X @ A4 )
% 0.16/0.39 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.16/0.39 => ( member @ A @ X @ B5 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % set_rev_mp
% 0.16/0.39 thf(fact_233_equalityD2,axiom,
% 0.16/0.39 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.16/0.39 ( ( A4 = B5 )
% 0.16/0.39 => ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ).
% 0.16/0.39
% 0.16/0.39 % equalityD2
% 0.16/0.39 thf(fact_234_equalityD1,axiom,
% 0.16/0.39 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.16/0.39 ( ( A4 = B5 )
% 0.16/0.39 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 0.16/0.39
% 0.16/0.39 % equalityD1
% 0.16/0.39 thf(fact_235_subset__eq,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord_less_eq @ ( set @ A ) )
% 0.16/0.39 = ( ^ [A7: set @ A,B6: set @ A] :
% 0.16/0.39 ! [X3: A] :
% 0.16/0.39 ( ( member @ A @ X3 @ A7 )
% 0.16/0.39 => ( member @ A @ X3 @ B6 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % subset_eq
% 0.16/0.39 thf(fact_236_equalityE,axiom,
% 0.16/0.39 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 0.16/0.39 ( ( A4 = B5 )
% 0.16/0.39 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.16/0.39 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % equalityE
% 0.16/0.39 thf(fact_237_subsetCE,axiom,
% 0.16/0.39 ! [A: $tType,A4: set @ A,B5: set @ A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.16/0.39 => ( ( member @ A @ C3 @ A4 )
% 0.16/0.39 => ( member @ A @ C3 @ B5 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % subsetCE
% 0.16/0.39 thf(fact_238_subsetD,axiom,
% 0.16/0.39 ! [A: $tType,A4: set @ A,B5: set @ A,C3: A] :
% 0.16/0.39 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.16/0.39 => ( ( member @ A @ C3 @ A4 )
% 0.16/0.39 => ( member @ A @ C3 @ B5 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % subsetD
% 0.16/0.39 thf(fact_239_in__mono,axiom,
% 0.16/0.39 ! [A: $tType,A4: set @ A,B5: set @ A,X: A] :
% 0.16/0.39 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.16/0.39 => ( ( member @ A @ X @ A4 )
% 0.16/0.39 => ( member @ A @ X @ B5 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % in_mono
% 0.16/0.39 thf(fact_240_set__mp,axiom,
% 0.16/0.39 ! [A: $tType,A4: set @ A,B5: set @ A,X: A] :
% 0.16/0.39 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.16/0.39 => ( ( member @ A @ X @ A4 )
% 0.16/0.39 => ( member @ A @ X @ B5 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % set_mp
% 0.16/0.39 thf(fact_241_less__eq__set__def,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( ord_less_eq @ ( set @ A ) )
% 0.16/0.39 = ( ^ [A7: set @ A,B6: set @ A] :
% 0.16/0.39 ( ord_less_eq @ ( A > $o )
% 0.16/0.39 @ ^ [X3: A] : ( member @ A @ X3 @ A7 )
% 0.16/0.39 @ ^ [X3: A] : ( member @ A @ X3 @ B6 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % less_eq_set_def
% 0.16/0.39 thf(fact_242_eq__subset,axiom,
% 0.16/0.39 ! [A: $tType,P: A > A > $o] :
% 0.16/0.39 ( ord_less_eq @ ( A > A > $o )
% 0.16/0.39 @ ^ [Y5: A,Z2: A] : ( Y5 = Z2 )
% 0.16/0.39 @ ^ [A5: A,B7: A] :
% 0.16/0.39 ( ( P @ A5 @ B7 )
% 0.16/0.39 | ( A5 = B7 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % eq_subset
% 0.16/0.39 thf(fact_243_conj__subset__def,axiom,
% 0.16/0.39 ! [A: $tType,A4: set @ A,P: A > $o,Q: A > $o] :
% 0.16/0.39 ( ( ord_less_eq @ ( set @ A ) @ A4
% 0.16/0.39 @ ( collect @ A
% 0.16/0.39 @ ^ [X3: A] :
% 0.16/0.39 ( ( P @ X3 )
% 0.16/0.39 & ( Q @ X3 ) ) ) )
% 0.16/0.39 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( collect @ A @ P ) )
% 0.16/0.39 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( collect @ A @ Q ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % conj_subset_def
% 0.16/0.39 thf(fact_244_predicate2D__conj,axiom,
% 0.16/0.39 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,R3: $o,X: A,Y: B] :
% 0.16/0.39 ( ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 0.16/0.39 & R3 )
% 0.16/0.39 => ( R3
% 0.16/0.39 & ( ( P @ X @ Y )
% 0.16/0.39 => ( Q @ X @ Y ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % predicate2D_conj
% 0.16/0.39 thf(fact_245_subset__Collect__iff,axiom,
% 0.16/0.39 ! [A: $tType,B5: set @ A,A4: set @ A,P: A > $o] :
% 0.16/0.39 ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 0.16/0.39 => ( ( ord_less_eq @ ( set @ A ) @ B5
% 0.16/0.39 @ ( collect @ A
% 0.16/0.39 @ ^ [X3: A] :
% 0.16/0.39 ( ( member @ A @ X3 @ A4 )
% 0.16/0.39 & ( P @ X3 ) ) ) )
% 0.16/0.39 = ( ! [X3: A] :
% 0.16/0.39 ( ( member @ A @ X3 @ B5 )
% 0.16/0.39 => ( P @ X3 ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % subset_Collect_iff
% 0.16/0.39 thf(fact_246_subset__CollectI,axiom,
% 0.16/0.39 ! [A: $tType,B5: set @ A,A4: set @ A,Q: A > $o,P: A > $o] :
% 0.16/0.39 ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 0.16/0.39 => ( ! [X2: A] :
% 0.16/0.39 ( ( member @ A @ X2 @ B5 )
% 0.16/0.39 => ( ( Q @ X2 )
% 0.16/0.39 => ( P @ X2 ) ) )
% 0.16/0.39 => ( ord_less_eq @ ( set @ A )
% 0.16/0.39 @ ( collect @ A
% 0.16/0.39 @ ^ [X3: A] :
% 0.16/0.39 ( ( member @ A @ X3 @ B5 )
% 0.16/0.39 & ( Q @ X3 ) ) )
% 0.16/0.39 @ ( collect @ A
% 0.16/0.39 @ ^ [X3: A] :
% 0.16/0.39 ( ( member @ A @ X3 @ A4 )
% 0.16/0.39 & ( P @ X3 ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % subset_CollectI
% 0.16/0.39 thf(fact_247_prop__restrict,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Z3: set @ A,X4: set @ A,P: A > $o] :
% 0.16/0.39 ( ( member @ A @ X @ Z3 )
% 0.16/0.39 => ( ( ord_less_eq @ ( set @ A ) @ Z3
% 0.16/0.39 @ ( collect @ A
% 0.16/0.39 @ ^ [X3: A] :
% 0.16/0.39 ( ( member @ A @ X3 @ X4 )
% 0.16/0.39 & ( P @ X3 ) ) ) )
% 0.16/0.39 => ( P @ X ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % prop_restrict
% 0.16/0.39 thf(fact_248_Collect__restrict,axiom,
% 0.16/0.39 ! [A: $tType,X4: set @ A,P: A > $o] :
% 0.16/0.39 ( ord_less_eq @ ( set @ A )
% 0.16/0.39 @ ( collect @ A
% 0.16/0.39 @ ^ [X3: A] :
% 0.16/0.39 ( ( member @ A @ X3 @ X4 )
% 0.16/0.39 & ( P @ X3 ) ) )
% 0.16/0.39 @ X4 ) ).
% 0.16/0.39
% 0.16/0.39 % Collect_restrict
% 0.16/0.39 thf(fact_249_ssubst__Pair__rhs,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,R: A,S2: B,R3: set @ ( product_prod @ A @ B ),S3: B] :
% 0.16/0.39 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R @ S2 ) @ R3 )
% 0.16/0.39 => ( ( S3 = S2 )
% 0.16/0.39 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R @ S3 ) @ R3 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % ssubst_Pair_rhs
% 0.16/0.39 thf(fact_250_internal__case__prod__conv,axiom,
% 0.16/0.39 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A3: B,B3: C] :
% 0.16/0.39 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A3 @ B3 ) )
% 0.16/0.39 = ( C3 @ A3 @ B3 ) ) ).
% 0.16/0.39
% 0.16/0.39 % internal_case_prod_conv
% 0.16/0.39 thf(fact_251_llast__lappend,axiom,
% 0.16/0.39 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ( ( coindu335574135_lnull @ A @ Ys )
% 0.16/0.39 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( coindu2000965700_llast @ A @ Xs ) ) )
% 0.16/0.39 & ( ~ ( coindu335574135_lnull @ A @ Ys )
% 0.16/0.39 => ( ( ( coindu1213758845finite @ A @ Xs )
% 0.16/0.39 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( coindu2000965700_llast @ A @ Ys ) ) )
% 0.16/0.39 & ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.16/0.39 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 0.16/0.39 = ( undefined @ A ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llast_lappend
% 0.16/0.39 thf(fact_252_llast__linfinite,axiom,
% 0.16/0.39 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 0.16/0.39 ( ~ ( coindu1213758845finite @ A @ Xs )
% 0.16/0.39 => ( ( coindu2000965700_llast @ A @ Xs )
% 0.16/0.39 = ( undefined @ A ) ) ) ).
% 0.16/0.39
% 0.16/0.39 % llast_linfinite
% 0.16/0.39 thf(fact_253_llast__LNil,axiom,
% 0.16/0.39 ! [A: $tType] :
% 0.16/0.39 ( ( coindu2000965700_llast @ A @ ( coindu1598213697e_LNil @ A ) )
% 0.16/0.39 = ( undefined @ A ) ) ).
% 0.16/0.39
% 0.16/0.39 % llast_LNil
% 0.16/0.39
% 0.16/0.39 %----Type constructors (10)
% 0.16/0.39 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.16/0.39 ! [A8: $tType,A9: $tType] :
% 0.16/0.39 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 0.16/0.39 => ( preorder @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.16/0.39 ! [A8: $tType,A9: $tType] :
% 0.16/0.39 ( ( order @ A9 @ ( type2 @ A9 ) )
% 0.16/0.39 => ( order @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_fun___Orderings_Oord,axiom,
% 0.16/0.39 ! [A8: $tType,A9: $tType] :
% 0.16/0.39 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 0.16/0.39 => ( ord @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_Set_Oset___Orderings_Opreorder_1,axiom,
% 0.16/0.39 ! [A8: $tType] : ( preorder @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_Set_Oset___Orderings_Oorder_2,axiom,
% 0.16/0.39 ! [A8: $tType] : ( order @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_Set_Oset___Orderings_Oord_3,axiom,
% 0.16/0.39 ! [A8: $tType] : ( ord @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_HOL_Obool___Orderings_Opreorder_4,axiom,
% 0.16/0.39 preorder @ $o @ ( type2 @ $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.16/0.39 linorder @ $o @ ( type2 @ $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_HOL_Obool___Orderings_Oorder_5,axiom,
% 0.16/0.39 order @ $o @ ( type2 @ $o ) ).
% 0.16/0.39
% 0.16/0.39 thf(tcon_HOL_Obool___Orderings_Oord_6,axiom,
% 0.16/0.39 ord @ $o @ ( type2 @ $o ) ).
% 0.16/0.39
% 0.16/0.39 %----Helper facts (3)
% 0.16/0.39 thf(help_If_3_1_T,axiom,
% 0.16/0.39 ! [P: $o] :
% 0.16/0.39 ( ( P = $true )
% 0.16/0.39 | ( P = $false ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(help_If_2_1_T,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Y: A] :
% 0.16/0.39 ( ( if @ A @ $false @ X @ Y )
% 0.16/0.39 = Y ) ).
% 0.16/0.39
% 0.16/0.39 thf(help_If_1_1_T,axiom,
% 0.16/0.39 ! [A: $tType,X: A,Y: A] :
% 0.16/0.39 ( ( if @ A @ $true @ X @ Y )
% 0.16/0.39 = X ) ).
% 0.16/0.39
% 0.16/0.39 %----Conjectures (2)
% 0.16/0.39 thf(conj_0,hypothesis,
% 0.16/0.39 ! [Y4: a,Ys6: coindu1593790203_llist @ a] :
% 0.16/0.39 ( ( ysa
% 0.16/0.39 = ( coindu1121789889_LCons @ a @ Y4 @ Ys6 ) )
% 0.16/0.39 => ( ~ ( r @ Y4 @ x )
% 0.16/0.39 => ( ( ( Y4 != x )
% 0.16/0.39 | ~ ( coindu300403952lexord @ a @ r @ Ys6 @ xs2 ) )
% 0.16/0.39 => thesis ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(conj_1,conjecture,
% 0.16/0.39 thesis ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 2.96/1.61 ---- Embedded in THF ---
% 2.96/1.61 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.96/1.61 %%% Generated on Tue Feb 24 06:08:25 EST 2026
% 2.96/1.61 %%% using '$$dhol' embedding, version 1.3.0.
% 2.96/1.61 %%% Logic specification used:
% 2.96/1.61 %%% thf(spec, logic, $$dhol).
% 2.96/1.61
% 2.96/1.61 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.vsmmhmmsID/DTF2DTF32705.p
% 2.96/1.61 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist, type, coindu1593790203_llist: ($tType > $tType)).
% 2.96/1.61 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.96/1.61 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.96/1.61 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.96/1.61 thf(ty_tf_a, type, a: $tType).
% 2.96/1.61 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.96/1.61 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.96/1.61 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.96/1.61 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.96/1.61 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix, type, coindu1571841457prefix: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o))))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__lset, type, coindu1928975208n_lset: (!> [A:$tType]: (((set @ A) > ((coindu1593790203_llist @ A) > (set @ A)))))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend, type, coindu268472904append: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite, type, coindu1213758845finite: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollast, type, coindu2000965700_llast: (!> [A:$tType]: (((coindu1593790203_llist @ A) > A)))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollexord, type, coindu300403952lexord: (!> [A:$tType]: (((A > (A > $o)) > ((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)))))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons, type, coindu1121789889_LCons: (!> [A:$tType]: ((A > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil, type, coindu1598213697e_LNil: (!> [A:$tType]: ((coindu1593790203_llist @ A)))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocorec__llist, type, coindu1244876290_llist: (!> [C:$tType,A:$tType]: (((C > $o) > ((C > A) > ((C > $o) > ((C > (coindu1593790203_llist @ A)) > ((C > C) > (C > (coindu1593790203_llist @ A)))))))))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull, type, coindu335574135_lnull: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Opred__llist, type, coindu44415597_llist: (!> [A:$tType]: (((A > $o) > ((coindu1593790203_llist @ A) > $o))))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember, type, coindu567634248member: (!> [A:$tType]: ((A > ((coindu1593790203_llist @ A) > $o))))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix, type, coindu1696667936prefix: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o))))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olsetp, type, coindu1055736764_lsetp: (!> [A:$tType]: (((coindu1593790203_llist @ A) > (A > $o))))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix, type, coindu574146665prefix: (!> [A:$tType]: (((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o))))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_OltakeWhile, type, coindu721411036eWhile: (!> [A:$tType]: (((A > $o) > ((coindu1593790203_llist @ A) > (coindu1593790203_llist @ A)))))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oord_Olsorted, type, coindu543932918sorted: (!> [A:$tType]: (((A > (A > $o)) > ((coindu1593790203_llist @ A) > $o))))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oord__class_Olsorted, type, coindu48241764sorted: (!> [A:$tType]: (((coindu1593790203_llist @ A) > $o)))).
% 2.96/1.61 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ounfold__llist, type, coindu1599971794_llist: (!> [A:$tType,B:$tType]: (((A > $o) > ((A > B) > ((A > A) > (A > (coindu1593790203_llist @ B)))))))).
% 2.96/1.61 thf(sy_c_HOL_Oundefined, type, undefined: (!> [A:$tType]: (A))).
% 2.96/1.61 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.96/1.61 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.96/1.61 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.96/1.61 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.96/1.61 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 2.96/1.61 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.96/1.61 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.96/1.61 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.96/1.61 thf(sy_v_r, type, r: (a > (a > $o))).
% 2.96/1.61 thf(sy_v_thesis____, type, thesis: $o).
% 2.96/1.61 thf(sy_v_x____, type, x: a).
% 2.96/1.61 thf(sy_v_xs, type, xs: (coindu1593790203_llist @ a)).
% 2.96/1.61 thf(sy_v_xs_H____, type, xs2: (coindu1593790203_llist @ a)).
% 2.96/1.61 thf(sy_v_xsa____, type, xsa: (coindu1593790203_llist @ a)).
% 2.96/1.61 thf(sy_v_ys, type, ys: (coindu1593790203_llist @ a)).
% 2.96/1.61 thf(sy_v_ysa____, type, ysa: (coindu1593790203_llist @ a)).
% 2.96/1.61 thf(fact_0_local_Olinear, axiom, (! [X:a,Y:a]: ((((r @ X) @ Y) | ((X = Y) | ((r @ Y) @ X)))))).
% 2.96/1.61 thf(fact_1__092_060open_062_092_060not_062_Allexord_Ar_Ays_Axs_092_060close_062, axiom, (~ (((((coindu300403952lexord @ a) @ r) @ ysa) @ xsa)))).
% 2.96/1.61 thf(fact_2__092_060open_062_092_060not_062_Allexord_Ar_Ays_Axs_092_060close_062, axiom, (~ (((((coindu300403952lexord @ a) @ r) @ ys) @ xs)))).
% 2.96/1.61 thf(fact_3_LCons, axiom, (xsa = (((coindu1121789889_LCons @ a) @ x) @ xs2))).
% 2.96/1.61 thf(fact_4_llist_Oinject, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A),Y21:A,Y22:(coindu1593790203_llist @ A)]: ((((((coindu1121789889_LCons @ A) @ X21) @ X22) = (((coindu1121789889_LCons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.96/1.61 thf(fact_5_llexord__refl, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coindu1593790203_llist @ A)]: (((((coindu300403952lexord @ A) @ R) @ Xs) @ Xs)))).
% 2.96/1.61 thf(fact_6_llexord__LCons__LCons, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ R) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = (((X = Y) & ((((coindu300403952lexord @ A) @ R) @ Xs) @ Ys)) | ((R @ X) @ Y)))))).
% 2.96/1.61 thf(fact_7_llexord__trans, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ R) @ Xs) @ Ys) => (((((coindu300403952lexord @ A) @ R) @ Ys) @ Zs) => ((! [A2:A,B2:A,C2:A]: ((((R @ A2) @ B2) => (((R @ B2) @ C2) => ((R @ A2) @ C2))))) => ((((coindu300403952lexord @ A) @ R) @ Xs) @ Zs))))))).
% 2.96/1.61 thf(fact_8_llexord__antisym, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ R) @ Xs) @ Ys) => (((((coindu300403952lexord @ A) @ R) @ Ys) @ Xs) => ((! [A2:A,B2:A]: ((((R @ A2) @ B2) => (~ (((R @ B2) @ A2)))))) => (Xs = Ys))))))).
% 2.96/1.61 thf(fact_9_llexord__LCons__left, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ R) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ Ys) = (? [Y2:A,Ys2:(coindu1593790203_llist @ A)]: (((Ys = (((coindu1121789889_LCons @ A) @ Y2) @ Ys2)) & (((X = Y2) & ((((coindu300403952lexord @ A) @ R) @ Xs) @ Ys2)) | ((R @ X) @ Y2))))))))).
% 2.96/1.61 thf(fact_10_llexord__LCons__eq, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),X:A]: ((((((coindu300403952lexord @ A) @ R) @ Xs) @ Ys) => ((((coindu300403952lexord @ A) @ R) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ X) @ Ys)))))).
% 2.96/1.61 thf(fact_11_llexord__LCons__less, axiom, (! [A:$tType,R:(A > (A > $o)),X:A,Y:A,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((R @ X) @ Y) => ((((coindu300403952lexord @ A) @ R) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)))))).
% 2.96/1.61 thf(fact_12_llexord_I2_J, axiom, (~ (((coindu335574135_lnull @ a) @ xsa)))).
% 2.96/1.61 thf(fact_13_llexord_I1_J, axiom, (~ (((((coindu300403952lexord @ a) @ r) @ ysa) @ xsa)))).
% 2.96/1.61 thf(fact_14_lmember__code_I2_J, axiom, (! [A:$tType,X:A,Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu567634248member @ A) @ X) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((X = Y) | (((coindu567634248member @ A) @ X) @ Ys)))))).
% 2.96/1.61 thf(fact_15_lstrict__prefix__code_I4_J, axiom, (! [B:$tType,X:B,Xs:(coindu1593790203_llist @ B),Y:B,Ys:(coindu1593790203_llist @ B)]: (((((coindu574146665prefix @ B) @ (((coindu1121789889_LCons @ B) @ X) @ Xs)) @ (((coindu1121789889_LCons @ B) @ Y) @ Ys)) = ((X = Y) & (((coindu574146665prefix @ B) @ Xs) @ Ys)))))).
% 2.96/1.61 thf(fact_16_llexord_Ocases, axiom, (! [A:$tType,R:(A > (A > $o)),A1:(coindu1593790203_llist @ A),A22:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ R) @ A1) @ A22) => ((! [Xs2:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A),X2:A]: (((A1 = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)) => ((A22 = (((coindu1121789889_LCons @ A) @ X2) @ Ys3)) => (~ (((((coindu300403952lexord @ A) @ R) @ Xs2) @ Ys3))))))) => ((! [X2:A]: (((? [Xs2:(coindu1593790203_llist @ A)]: ((A1 = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)))) => (! [Y3:A]: (((? [Ys3:(coindu1593790203_llist @ A)]: ((A22 = (((coindu1121789889_LCons @ A) @ Y3) @ Ys3)))) => (~ (((R @ X2) @ Y3))))))))) => (~ (((A1 = (coindu1598213697e_LNil @ A)) => (! [Ys3:(coindu1593790203_llist @ A)]: ((A22 != Ys3)))))))))))).
% 2.96/1.61 thf(fact_17_llexord_Osimps, axiom, (! [A:$tType]: (((coindu300403952lexord @ A) = (^ [R2:(A > (A > $o)),A12:(coindu1593790203_llist @ A),A23:(coindu1593790203_llist @ A)]: (((? [Xs3:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A),X3:A]: (((A12 = (((coindu1121789889_LCons @ A) @ X3) @ Xs3)) & ((A23 = (((coindu1121789889_LCons @ A) @ X3) @ Ys4)) & ((((coindu300403952lexord @ A) @ R2) @ Xs3) @ Ys4))))) | ((? [X3:A,Y2:A,Xs3:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A)]: (((A12 = (((coindu1121789889_LCons @ A) @ X3) @ Xs3)) & ((A23 = (((coindu1121789889_LCons @ A) @ Y2) @ Ys4)) & ((R2 @ X3) @ Y2))))) | (? [Ys4:(coindu1593790203_llist @ A)]: (((A12 = (coindu1598213697e_LNil @ A)) & (A23 = Ys4)))))))))))).
% 2.96/1.61 thf(fact_18_llexord_Ocoinduct, axiom, (! [A:$tType,X4:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),X:(coindu1593790203_llist @ A),Xa:(coindu1593790203_llist @ A),R:(A > (A > $o))]: ((((X4 @ X) @ Xa) => ((! [X2:(coindu1593790203_llist @ A),Xa2:(coindu1593790203_llist @ A)]: ((((X4 @ X2) @ Xa2) => ((? [Xs4:(coindu1593790203_llist @ A),Ys5:(coindu1593790203_llist @ A),Xb:A]: (((X2 = (((coindu1121789889_LCons @ A) @ Xb) @ Xs4)) & ((Xa2 = (((coindu1121789889_LCons @ A) @ Xb) @ Ys5)) & (((X4 @ Xs4) @ Ys5) | ((((coindu300403952lexord @ A) @ R) @ Xs4) @ Ys5)))))) | ((? [Xb:A,Y4:A,Xs4:(coindu1593790203_llist @ A),Ys5:(coindu1593790203_llist @ A)]: (((X2 = (((coindu1121789889_LCons @ A) @ Xb) @ Xs4)) & ((Xa2 = (((coindu1121789889_LCons @ A) @ Y4) @ Ys5)) & ((R @ Xb) @ Y4))))) | (? [Ys5:(coindu1593790203_llist @ A)]: (((X2 = (coindu1598213697e_LNil @ A)) & (Xa2 = Ys5))))))))) => ((((coindu300403952lexord @ A) @ R) @ X) @ Xa)))))).
% 2.96/1.61 thf(fact_19_llist_Opred__inject_I2_J, axiom, (! [A:$tType,P:(A > $o),A3:A,Aa:(coindu1593790203_llist @ A)]: (((((coindu44415597_llist @ A) @ P) @ (((coindu1121789889_LCons @ A) @ A3) @ Aa)) = ((P @ A3) & (((coindu44415597_llist @ A) @ P) @ Aa)))))).
% 2.96/1.61 thf(fact_20_llast__LCons2, axiom, (! [A:$tType,X:A,Y:A,Xs:(coindu1593790203_llist @ A)]: ((((coindu2000965700_llast @ A) @ (((coindu1121789889_LCons @ A) @ X) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs))) = ((coindu2000965700_llast @ A) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs)))))).
% 2.96/1.61 thf(fact_21_unfold__llist__eq__LCons, axiom, (! [A:$tType,B:$tType,IS_LNIL:(B > $o),LHD:(B > A),LTL:(B > B),B3:B,X:A,Xs:(coindu1593790203_llist @ A)]: (((((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ B3) = (((coindu1121789889_LCons @ A) @ X) @ Xs)) = ((~ ((IS_LNIL @ B3))) & ((X = (LHD @ B3)) & (Xs = ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ (LTL @ B3))))))))).
% 2.96/1.61 thf(fact_22_lsetp_Ointros_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),X:A,X5:A]: (((((coindu1055736764_lsetp @ A) @ Xs) @ X) => (((coindu1055736764_lsetp @ A) @ (((coindu1121789889_LCons @ A) @ X5) @ Xs)) @ X))))).
% 2.96/1.61 thf(fact_23_lsetp_Ointros_I1_J, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: ((((coindu1055736764_lsetp @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ X)))).
% 2.96/1.61 thf(fact_24_llexord__LNil__right, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),R:(A > (A > $o)),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Ys) => (((((coindu300403952lexord @ A) @ R) @ Xs) @ Ys) = ((coindu335574135_lnull @ A) @ Xs)))))).
% 2.96/1.61 thf(fact_25_unfold__llist_Odisc__iff_I2_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),G21:(A > B),G22:(A > A),A3:A]: (((~ (((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A3)))) = (~ ((P2 @ A3))))))).
% 2.96/1.61 thf(fact_26_unfold__llist_Odisc__iff_I1_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),G21:(A > B),G22:(A > A),A3:A]: ((((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A3)) = (P2 @ A3))))).
% 2.96/1.61 thf(fact_27_lstrict__prefix__code_I1_J, axiom, (! [A:$tType]: ((~ ((((coindu574146665prefix @ A) @ (coindu1598213697e_LNil @ A)) @ (coindu1598213697e_LNil @ A))))))).
% 2.96/1.61 thf(fact_28_llast__singleton, axiom, (! [A:$tType,X:A]: ((((coindu2000965700_llast @ A) @ (((coindu1121789889_LCons @ A) @ X) @ (coindu1598213697e_LNil @ A))) = X)))).
% 2.96/1.61 thf(fact_29_lstrict__prefix__code_I2_J, axiom, (! [B:$tType,Y:B,Ys:(coindu1593790203_llist @ B)]: ((((coindu574146665prefix @ B) @ (coindu1598213697e_LNil @ B)) @ (((coindu1121789889_LCons @ B) @ Y) @ Ys))))).
% 2.96/1.61 thf(fact_30_lstrict__prefix__code_I3_J, axiom, (! [B:$tType,X:B,Xs:(coindu1593790203_llist @ B)]: ((~ ((((coindu574146665prefix @ B) @ (((coindu1121789889_LCons @ B) @ X) @ Xs)) @ (coindu1598213697e_LNil @ B))))))).
% 2.96/1.61 thf(fact_31_llist_Odisc_I1_J, axiom, (! [A:$tType]: (((coindu335574135_lnull @ A) @ (coindu1598213697e_LNil @ A))))).
% 2.96/1.61 thf(fact_32_llist_OdiscI_I1_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: (((Llist = (coindu1598213697e_LNil @ A)) => ((coindu335574135_lnull @ A) @ Llist))))).
% 2.96/1.61 thf(fact_33_lmember__code_I1_J, axiom, (! [A:$tType,X:A]: ((~ ((((coindu567634248member @ A) @ X) @ (coindu1598213697e_LNil @ A))))))).
% 2.96/1.61 thf(fact_34_llist_Ocollapse_I1_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Llist) => (Llist = (coindu1598213697e_LNil @ A)))))).
% 2.96/1.61 thf(fact_35_unfold__llist_Octr_I1_J, axiom, (! [A:$tType,B:$tType,P2:(A > $o),A3:A,G21:(A > B),G22:(A > A)]: (((P2 @ A3) => (((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A3) = (coindu1598213697e_LNil @ B)))))).
% 2.96/1.61 thf(fact_36_llist_Opred__inject_I1_J, axiom, (! [A:$tType,P:(A > $o)]: ((((coindu44415597_llist @ A) @ P) @ (coindu1598213697e_LNil @ A))))).
% 2.96/1.61 thf(fact_37_unfold__llist_Odisc_I2_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),A3:A,G21:(A > B),G22:(A > A)]: (((~ ((P2 @ A3))) => (~ (((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A3)))))))).
% 2.96/1.61 thf(fact_38_unfold__llist_Odisc_I1_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),A3:A,G21:(A > B),G22:(A > A)]: (((P2 @ A3) => ((coindu335574135_lnull @ B) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A3)))))).
% 2.96/1.61 thf(fact_39_lzip_Oexhaust, axiom, (! [A:$tType,B:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ B)]: (((~ ((((coindu335574135_lnull @ A) @ Xs) | ((coindu335574135_lnull @ B) @ Ys)))) => (~ (((~ (((coindu335574135_lnull @ A) @ Xs))) => ((coindu335574135_lnull @ B) @ Ys)))))))).
% 2.96/1.61 thf(fact_40_lappend_Oexhaust, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Xs) => (~ (((coindu335574135_lnull @ A) @ Ys)))) => ((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 2.96/1.61 thf(fact_41_lnull__def, axiom, (! [A:$tType]: (((coindu335574135_lnull @ A) = (^ [Llist2:(coindu1593790203_llist @ A)]: ((Llist2 = (coindu1598213697e_LNil @ A)))))))).
% 2.96/1.61 thf(fact_42_llist_Opred__True, axiom, (! [A:$tType]: ((((coindu44415597_llist @ A) @ (^ [Uu:A]: ($true))) = (^ [Uu:(coindu1593790203_llist @ A)]: ($true)))))).
% 2.96/1.61 thf(fact_43_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 2.96/1.61 thf(fact_44_Collect__mem__eq, axiom, (! [A:$tType,A4:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A4)))) = A4)))).
% 2.96/1.61 thf(fact_45_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) = (Q @ X2)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.96/1.61 thf(fact_46_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X2:A]: (((F @ X2) = (G @ X2)))) => (F = G))))).
% 2.96/1.61 thf(fact_47_llist__less__induct, axiom, (! [A:$tType,P:((coindu1593790203_llist @ A) > $o),Xs:(coindu1593790203_llist @ A)]: (((! [Xs2:(coindu1593790203_llist @ A)]: (((! [Ys5:(coindu1593790203_llist @ A)]: (((((coindu574146665prefix @ A) @ Ys5) @ Xs2) => (P @ Ys5)))) => (P @ Xs2)))) => (P @ Xs))))).
% 2.96/1.61 thf(fact_48_llast__LCons, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),X:A]: (((((coindu335574135_lnull @ A) @ Xs) => (((coindu2000965700_llast @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) = X)) & ((~ (((coindu335574135_lnull @ A) @ Xs))) => (((coindu2000965700_llast @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) = ((coindu2000965700_llast @ A) @ Xs))))))).
% 2.96/1.61 thf(fact_49_unfold__llist_Ocode, axiom, (! [B:$tType,A:$tType]: ((((coindu1599971794_llist @ A) @ B) = (^ [P3:(A > $o),G212:(A > B),G222:(A > A),A5:A]: (((((if @ (coindu1593790203_llist @ B)) @ (P3 @ A5)) @ (coindu1598213697e_LNil @ B)) @ (((coindu1121789889_LCons @ B) @ (G212 @ A5)) @ ((((((coindu1599971794_llist @ A) @ B) @ P3) @ G212) @ G222) @ (G222 @ A5)))))))))).
% 2.96/1.61 thf(fact_50_not__lnull__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ Xs))) = (? [X3:A,Xs5:(coindu1593790203_llist @ A)]: ((Xs = (((coindu1121789889_LCons @ A) @ X3) @ Xs5)))))))).
% 2.96/1.61 thf(fact_51_llist_OdiscI_I2_J, axiom, (! [A:$tType,Llist:(coindu1593790203_llist @ A),X21:A,X22:(coindu1593790203_llist @ A)]: (((Llist = (((coindu1121789889_LCons @ A) @ X21) @ X22)) => (~ (((coindu335574135_lnull @ A) @ Llist))))))).
% 2.96/1.61 thf(fact_52_llist_Odisc_I2_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: ((~ (((coindu335574135_lnull @ A) @ (((coindu1121789889_LCons @ A) @ X21) @ X22))))))).
% 2.96/1.61 thf(fact_53_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((Xs != (coindu1598213697e_LNil @ A)) = (? [X3:A,Xs5:(coindu1593790203_llist @ A)]: ((Xs = (((coindu1121789889_LCons @ A) @ X3) @ Xs5)))))))).
% 2.96/1.61 thf(fact_54_llist_Oexhaust, axiom, (! [A:$tType,Y:(coindu1593790203_llist @ A)]: (((Y != (coindu1598213697e_LNil @ A)) => (~ ((! [X212:A,X222:(coindu1593790203_llist @ A)]: ((Y != (((coindu1121789889_LCons @ A) @ X212) @ X222)))))))))).
% 2.96/1.61 thf(fact_55_llist_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(coindu1593790203_llist @ A)]: (((coindu1598213697e_LNil @ A) != (((coindu1121789889_LCons @ A) @ X21) @ X22))))).
% 2.96/1.61 thf(fact_56_lnull__llexord, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),R:(A > (A > $o)),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((((coindu300403952lexord @ A) @ R) @ Xs) @ Ys))))).
% 2.96/1.61 thf(fact_57_llexord__LNil, axiom, (! [A:$tType,R:(A > (A > $o)),Ys:(coindu1593790203_llist @ A)]: (((((coindu300403952lexord @ A) @ R) @ (coindu1598213697e_LNil @ A)) @ Ys)))).
% 2.96/1.61 thf(fact_58_unfold__llist_Octr_I2_J, axiom, (! [B:$tType,A:$tType,P2:(A > $o),A3:A,G21:(A > B),G22:(A > A)]: (((~ ((P2 @ A3))) => (((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ A3) = (((coindu1121789889_LCons @ B) @ (G21 @ A3)) @ ((((((coindu1599971794_llist @ A) @ B) @ P2) @ G21) @ G22) @ (G22 @ A3)))))))).
% 2.96/1.61 thf(fact_59_lsetp_Oinducts, axiom, (! [A:$tType,X1:(coindu1593790203_llist @ A),X23:A,P:((coindu1593790203_llist @ A) > (A > $o))]: (((((coindu1055736764_lsetp @ A) @ X1) @ X23) => ((! [X2:A,Xs2:(coindu1593790203_llist @ A)]: (((P @ (((coindu1121789889_LCons @ A) @ X2) @ Xs2)) @ X2))) => ((! [Xs2:(coindu1593790203_llist @ A),X2:A,X6:A]: (((((coindu1055736764_lsetp @ A) @ Xs2) @ X2) => (((P @ Xs2) @ X2) => ((P @ (((coindu1121789889_LCons @ A) @ X6) @ Xs2)) @ X2))))) => ((P @ X1) @ X23))))))).
% 2.96/1.61 thf(fact_60_lsetp_Osimps, axiom, (! [A:$tType]: (((coindu1055736764_lsetp @ A) = (^ [A12:(coindu1593790203_llist @ A),A23:A]: (((? [X3:A,Xs3:(coindu1593790203_llist @ A)]: (((A12 = (((coindu1121789889_LCons @ A) @ X3) @ Xs3)) & (A23 = X3)))) | (? [Xs3:(coindu1593790203_llist @ A),X3:A,X7:A]: (((A12 = (((coindu1121789889_LCons @ A) @ X7) @ Xs3)) & ((A23 = X3) & (((coindu1055736764_lsetp @ A) @ Xs3) @ X3)))))))))))).
% 2.96/1.61 thf(fact_61_lsetp_Ocases, axiom, (! [A:$tType,A1:(coindu1593790203_llist @ A),A22:A]: (((((coindu1055736764_lsetp @ A) @ A1) @ A22) => ((! [X2:A]: (((? [Xs2:(coindu1593790203_llist @ A)]: ((A1 = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)))) => (A22 != X2)))) => (~ ((! [Xs2:(coindu1593790203_llist @ A)]: (((? [X6:A]: ((A1 = (((coindu1121789889_LCons @ A) @ X6) @ Xs2)))) => (~ ((((coindu1055736764_lsetp @ A) @ Xs2) @ A22))))))))))))).
% 2.96/1.61 thf(fact_62_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I3_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu1571841457prefix @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((Xs = (coindu1598213697e_LNil @ A)) | (? [Xs5:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ Y) @ Xs5)) & (((coindu1571841457prefix @ A) @ Xs5) @ Ys))))))))).
% 2.96/1.61 thf(fact_63_llimit__induct, axiom, (! [A:$tType,P:((coindu1593790203_llist @ A) > $o),Xs:(coindu1593790203_llist @ A)]: (((P @ (coindu1598213697e_LNil @ A)) => ((! [X2:A,Xs2:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X2) @ Xs2)))))) => (((! [Ys5:(coindu1593790203_llist @ A)]: (((((coindu574146665prefix @ A) @ Ys5) @ Xs) => (P @ Ys5)))) => (P @ Xs)) => (P @ Xs))))))).
% 2.96/1.61 thf(fact_64_lsorted__code_I2_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A]: (((coindu48241764sorted @ A) @ (((coindu1121789889_LCons @ A) @ X) @ (coindu1598213697e_LNil @ A))))))))).
% 2.96/1.61 thf(fact_65_gen__lset__code_I1_J, axiom, (! [A:$tType,A4:(set @ A)]: (((((coindu1928975208n_lset @ A) @ A4) @ (coindu1598213697e_LNil @ A)) = A4)))).
% 2.96/1.61 thf(fact_66_llist_Ocorec__code, axiom, (! [A:$tType,C:$tType]: ((((coindu1244876290_llist @ C) @ A) = (^ [P3:(C > $o),G212:(C > A),Q22:(C > $o),G221:(C > (coindu1593790203_llist @ A)),G2222:(C > C),A5:C]: (((((if @ (coindu1593790203_llist @ A)) @ (P3 @ A5)) @ (coindu1598213697e_LNil @ A)) @ (((coindu1121789889_LCons @ A) @ (G212 @ A5)) @ ((((if @ (coindu1593790203_llist @ A)) @ (Q22 @ A5)) @ (G221 @ A5)) @ ((((((((coindu1244876290_llist @ C) @ A) @ P3) @ G212) @ Q22) @ G221) @ G2222) @ (G2222 @ A5))))))))))).
% 2.96/1.61 thf(fact_67_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1571841457prefix @ A) @ (coindu1598213697e_LNil @ A)) @ Xs)))).
% 2.96/1.61 thf(fact_68_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu1571841457prefix @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = (Xs = (coindu1598213697e_LNil @ A)))))).
% 2.96/1.61 thf(fact_69_lprefix__LNil, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = ((coindu335574135_lnull @ A) @ Xs))))).
% 2.96/1.61 thf(fact_70_ltakeWhile__LCons, axiom, (! [A:$tType,P:(A > $o),X:A,Xs:(coindu1593790203_llist @ A)]: ((((P @ X) => ((((coindu721411036eWhile @ A) @ P) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) = (((coindu1121789889_LCons @ A) @ X) @ (((coindu721411036eWhile @ A) @ P) @ Xs)))) & ((~ ((P @ X))) => ((((coindu721411036eWhile @ A) @ P) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) = (coindu1598213697e_LNil @ A))))))).
% 2.96/1.61 thf(fact_71_ord_OSingleton, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),X:A]: ((((coindu543932918sorted @ A) @ Less_eq) @ (((coindu1121789889_LCons @ A) @ X) @ (coindu1598213697e_LNil @ A)))))).
% 2.96/1.61 thf(fact_72_llist_Oleq__refl, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ X) @ X)))).
% 2.96/1.61 thf(fact_73_lprefix__refl, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ Xs) @ Xs)))).
% 2.96/1.61 thf(fact_74_ltakeWhile__K__True, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu721411036eWhile @ A) @ (^ [Uu:A]: ($true))) @ Xs) = Xs)))).
% 2.96/1.61 thf(fact_75_LCons__lprefix__LCons, axiom, (! [A:$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)))))).
% 2.96/1.61 thf(fact_76_lprefix__code_I1_J, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (coindu1598213697e_LNil @ A)) @ Ys)))).
% 2.96/1.61 thf(fact_77_lfinite__code_I2_J, axiom, (! [B:$tType,X:B,Xs:(coindu1593790203_llist @ B)]: ((((coindu1213758845finite @ B) @ (((coindu1121789889_LCons @ B) @ X) @ Xs)) = ((coindu1213758845finite @ B) @ Xs))))).
% 2.96/1.61 thf(fact_78_lfinite__LCons, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) = ((coindu1213758845finite @ A) @ Xs))))).
% 2.96/1.61 thf(fact_79_lfinite__code_I1_J, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) @ (coindu1598213697e_LNil @ A))))).
% 2.96/1.61 thf(fact_80_ltakeWhile__LNil, axiom, (! [A:$tType,P:(A > $o)]: (((((coindu721411036eWhile @ A) @ P) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 2.96/1.61 thf(fact_81_lsorted__code_I1_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => ((coindu48241764sorted @ A) @ (coindu1598213697e_LNil @ A)))))).
% 2.96/1.61 thf(fact_82_llist_Ocorec__disc__iff_I1_J, axiom, (! [A:$tType,C:$tType,P2:(C > $o),G21:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2223:(C > C),A3:C]: ((((coindu335574135_lnull @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ A3)) = (P2 @ A3))))).
% 2.96/1.61 thf(fact_83_llist_Ocorec__disc__iff_I2_J, axiom, (! [A:$tType,C:$tType,P2:(C > $o),G21:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2223:(C > C),A3:C]: (((~ (((coindu335574135_lnull @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ A3)))) = (~ ((P2 @ A3))))))).
% 2.96/1.61 thf(fact_84_ltakeWhile__K__False, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu721411036eWhile @ A) @ (^ [Uu:A]: ($false))) @ Xs) = (coindu1598213697e_LNil @ A))))).
% 2.96/1.61 thf(fact_85_not__lfinite__lprefix__conv__eq, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu1213758845finite @ A) @ Xs))) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) = (Xs = Ys)))))).
% 2.96/1.61 thf(fact_86_lsorted__lprefixD, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu48241764sorted @ A) @ Ys) => ((coindu48241764sorted @ A) @ Xs))))))))).
% 2.96/1.61 thf(fact_87_Coinductive__List__Mirabelle__kmikjhschf_Olprefix__nitpick__simps, axiom, (! [A:$tType]: (((coindu1696667936prefix @ A) = (^ [Xs3:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A)]: (((((coindu1213758845finite @ A) @ Xs3) => (((coindu1571841457prefix @ A) @ Xs3) @ Ys4)) & ((~ (((coindu1213758845finite @ A) @ Xs3))) => (Xs3 = Ys4))))))))).
% 2.96/1.61 thf(fact_88_ord_Olsorted__lprefixD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Less_eq:(A > (A > $o))]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((((coindu543932918sorted @ A) @ Less_eq) @ Ys) => (((coindu543932918sorted @ A) @ Less_eq) @ Xs)))))).
% 2.96/1.61 thf(fact_89_lprefix__down__linear, axiom, (! [A:$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))))))).
% 2.96/1.61 thf(fact_90_lprefix__ltakeWhile, axiom, (! [A:$tType,P:(A > $o),Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (((coindu721411036eWhile @ A) @ P) @ Xs)) @ Xs)))).
% 2.96/1.61 thf(fact_91_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__def, axiom, (! [A:$tType]: (((coindu1571841457prefix @ A) = (coindu1696667936prefix @ A))))).
% 2.96/1.61 thf(fact_92_llist_Oleq__antisym, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A),Y:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ X) @ Y) => ((((coindu1696667936prefix @ A) @ Y) @ X) => (X = Y)))))).
% 2.96/1.61 thf(fact_93_lprefix__lfiniteD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu1213758845finite @ A) @ Ys) => ((coindu1213758845finite @ A) @ Xs)))))).
% 2.96/1.61 thf(fact_94_lprefix__antisym, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((((coindu1696667936prefix @ A) @ Ys) @ Xs) => (Xs = Ys)))))).
% 2.96/1.61 thf(fact_95_llist_Oleq__trans, axiom, (! [A:$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)))))).
% 2.96/1.61 thf(fact_96_lprefix__trans, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((((coindu1696667936prefix @ A) @ Ys) @ Zs) => (((coindu1696667936prefix @ A) @ Xs) @ Zs)))))).
% 2.96/1.61 thf(fact_97_lfinite__LConsI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),X:A]: ((((coindu1213758845finite @ A) @ Xs) => ((coindu1213758845finite @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)))))).
% 2.96/1.61 thf(fact_98_lnull__imp__lfinite, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((coindu1213758845finite @ A) @ Xs))))).
% 2.96/1.61 thf(fact_99_lfinite__LNil, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) @ (coindu1598213697e_LNil @ A))))).
% 2.96/1.61 thf(fact_100_Le__LCons, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),X:A]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (((coindu1121789889_LCons @ A) @ X) @ Ys)))))).
% 2.96/1.61 thf(fact_101_LCons__lprefix__conv, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ Ys) = (? [Ys2:(coindu1593790203_llist @ A)]: (((Ys = (((coindu1121789889_LCons @ A) @ X) @ Ys2)) & (((coindu1696667936prefix @ A) @ Xs) @ Ys2)))))))).
% 2.96/1.61 thf(fact_102_lprefix__not__lnullD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((~ (((coindu335574135_lnull @ A) @ Xs))) => (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 2.96/1.61 thf(fact_103_lprefix__lnullD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => (((coindu335574135_lnull @ A) @ Ys) => ((coindu335574135_lnull @ A) @ Xs)))))).
% 2.96/1.61 thf(fact_104_lprefix__lnull, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Ys) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) = ((coindu335574135_lnull @ A) @ Xs)))))).
% 2.96/1.61 thf(fact_105_lnull__lprefix, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu1696667936prefix @ A) @ Xs) @ Ys))))).
% 2.96/1.61 thf(fact_106_LNil__lprefix, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ (coindu1598213697e_LNil @ A)) @ Xs)))).
% 2.96/1.61 thf(fact_107_lprefix__imp__llexord, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),R:(A > (A > $o))]: (((((coindu1696667936prefix @ A) @ Xs) @ Ys) => ((((coindu300403952lexord @ A) @ R) @ Xs) @ Ys))))).
% 2.96/1.61 thf(fact_108_lstrict__prefix__lfinite1, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu574146665prefix @ A) @ Xs) @ Ys) => ((coindu1213758845finite @ A) @ Xs))))).
% 2.96/1.61 thf(fact_109_LNil, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => ((coindu48241764sorted @ A) @ (coindu1598213697e_LNil @ A)))))).
% 2.96/1.61 thf(fact_110_ord_OLCons__LCons, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),X:A,Y:A,Xs:(coindu1593790203_llist @ A)]: ((((Less_eq @ X) @ Y) => ((((coindu543932918sorted @ A) @ Less_eq) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs)) => (((coindu543932918sorted @ A) @ Less_eq) @ (((coindu1121789889_LCons @ A) @ X) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs)))))))).
% 2.96/1.61 thf(fact_111_ord_Olsorted__LCons__LCons, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),X:A,Y:A,Xs:(coindu1593790203_llist @ A)]: (((((coindu543932918sorted @ A) @ Less_eq) @ (((coindu1121789889_LCons @ A) @ X) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs))) = (((Less_eq @ X) @ Y) & (((coindu543932918sorted @ A) @ Less_eq) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs))))))).
% 2.96/1.61 thf(fact_112_ord_OLNil, axiom, (! [A:$tType,Less_eq:(A > (A > $o))]: ((((coindu543932918sorted @ A) @ Less_eq) @ (coindu1598213697e_LNil @ A))))).
% 2.96/1.61 thf(fact_113_ord_Olsorted__code_I1_J, axiom, (! [A:$tType,Less_eq:(A > (A > $o))]: ((((coindu543932918sorted @ A) @ Less_eq) @ (coindu1598213697e_LNil @ A))))).
% 2.96/1.61 thf(fact_114_lstrict__prefix__def, axiom, (! [A:$tType]: (((coindu574146665prefix @ A) = (^ [Xs3:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs3) @ Ys4) & (Xs3 != Ys4)))))))).
% 2.96/1.61 thf(fact_115_llist_Ocorec_I2_J, axiom, (! [A:$tType,C:$tType,P2:(C > $o),A3:C,G21:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2223:(C > C)]: (((~ ((P2 @ A3))) => (((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ A3) = (((coindu1121789889_LCons @ A) @ (G21 @ A3)) @ ((((if @ (coindu1593790203_llist @ A)) @ (Q222 @ A3)) @ (G2212 @ A3)) @ ((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ (G2223 @ A3))))))))).
% 2.96/1.61 thf(fact_116_llist_Ocorec__disc_I1_J, axiom, (! [A:$tType,C:$tType,P2:(C > $o),A3:C,G21:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2223:(C > C)]: (((P2 @ A3) => ((coindu335574135_lnull @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ A3)))))).
% 2.96/1.61 thf(fact_117_llist_Ocorec__disc_I2_J, axiom, (! [A:$tType,C:$tType,P2:(C > $o),A3:C,G21:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2223:(C > C)]: (((~ ((P2 @ A3))) => (~ (((coindu335574135_lnull @ A) @ ((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ A3)))))))).
% 2.96/1.61 thf(fact_118_llist_Ocorec_I1_J, axiom, (! [C:$tType,A:$tType,P2:(C > $o),A3:C,G21:(C > A),Q222:(C > $o),G2212:(C > (coindu1593790203_llist @ A)),G2223:(C > C)]: (((P2 @ A3) => (((((((((coindu1244876290_llist @ C) @ A) @ P2) @ G21) @ Q222) @ G2212) @ G2223) @ A3) = (coindu1598213697e_LNil @ A)))))).
% 2.96/1.61 thf(fact_119_llexord__empty, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ (^ [X3:A,Y2:A]: ($false))) @ Xs) @ Ys) = (((coindu1696667936prefix @ A) @ Xs) @ Ys))))).
% 2.96/1.61 thf(fact_120_lfinite_Ocases, axiom, (! [A:$tType,A3:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ A3) => ((A3 != (coindu1598213697e_LNil @ A)) => (~ ((! [Xs2:(coindu1593790203_llist @ A)]: (((? [X2:A]: ((A3 = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)))) => (~ (((coindu1213758845finite @ A) @ Xs2))))))))))))).
% 2.96/1.61 thf(fact_121_lfinite_Osimps, axiom, (! [A:$tType]: (((coindu1213758845finite @ A) = (^ [A5:(coindu1593790203_llist @ A)]: (((A5 = (coindu1598213697e_LNil @ A)) | (? [Xs3:(coindu1593790203_llist @ A),X3:A]: (((A5 = (((coindu1121789889_LCons @ A) @ X3) @ Xs3)) & ((coindu1213758845finite @ A) @ Xs3))))))))))).
% 2.96/1.61 thf(fact_122_lfinite_Oinducts, axiom, (! [A:$tType,X:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: ((((coindu1213758845finite @ A) @ X) => ((P @ (coindu1598213697e_LNil @ A)) => ((! [Xs2:(coindu1593790203_llist @ A),X2:A]: ((((coindu1213758845finite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coindu1121789889_LCons @ A) @ X2) @ Xs2)))))) => (P @ X))))))).
% 2.96/1.61 thf(fact_123_lprefix__code_I2_J, axiom, (! [A:$tType,X:A,Xs:(coindu1593790203_llist @ A)]: ((~ ((((coindu1696667936prefix @ A) @ (((coindu1121789889_LCons @ A) @ X) @ Xs)) @ (coindu1598213697e_LNil @ A))))))).
% 2.96/1.61 thf(fact_124_lprefix_Ocases, axiom, (! [A:$tType,A1:(coindu1593790203_llist @ A),A22:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ A1) @ A22) => (((A1 = (coindu1598213697e_LNil @ A)) => (! [Xs2:(coindu1593790203_llist @ A)]: ((A22 != Xs2)))) => (~ ((! [Xs2:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A),X2:A]: (((A1 = (((coindu1121789889_LCons @ A) @ X2) @ Xs2)) => ((A22 = (((coindu1121789889_LCons @ A) @ X2) @ Ys3)) => (~ ((((coindu1696667936prefix @ A) @ Xs2) @ Ys3)))))))))))))).
% 2.96/1.61 thf(fact_125_lprefix_Osimps, axiom, (! [A:$tType]: (((coindu1696667936prefix @ A) = (^ [A12:(coindu1593790203_llist @ A),A23:(coindu1593790203_llist @ A)]: (((? [Xs3:(coindu1593790203_llist @ A)]: (((A12 = (coindu1598213697e_LNil @ A)) & (A23 = Xs3)))) | (? [Xs3:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A),X3:A]: (((A12 = (((coindu1121789889_LCons @ A) @ X3) @ Xs3)) & ((A23 = (((coindu1121789889_LCons @ A) @ X3) @ Ys4)) & (((coindu1696667936prefix @ A) @ Xs3) @ Ys4)))))))))))).
% 2.96/1.61 thf(fact_126_lprefix_Ocoinduct, axiom, (! [A:$tType,X4:((coindu1593790203_llist @ A) > ((coindu1593790203_llist @ A) > $o)),X:(coindu1593790203_llist @ A),Xa:(coindu1593790203_llist @ A)]: ((((X4 @ X) @ Xa) => ((! [X2:(coindu1593790203_llist @ A),Xa2:(coindu1593790203_llist @ A)]: ((((X4 @ X2) @ Xa2) => ((? [Xs4:(coindu1593790203_llist @ A)]: (((X2 = (coindu1598213697e_LNil @ A)) & (Xa2 = Xs4)))) | (? [Xs4:(coindu1593790203_llist @ A),Ys5:(coindu1593790203_llist @ A),Xb:A]: (((X2 = (((coindu1121789889_LCons @ A) @ Xb) @ Xs4)) & ((Xa2 = (((coindu1121789889_LCons @ A) @ Xb) @ Ys5)) & (((X4 @ Xs4) @ Ys5) | (((coindu1696667936prefix @ A) @ Xs4) @ Ys5)))))))))) => (((coindu1696667936prefix @ A) @ X) @ Xa)))))).
% 2.96/1.61 thf(fact_127_lprefix__LCons__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)) = ((Xs = (coindu1598213697e_LNil @ A)) | (? [Xs5:(coindu1593790203_llist @ A)]: (((Xs = (((coindu1121789889_LCons @ A) @ Y) @ Xs5)) & (((coindu1696667936prefix @ A) @ Xs5) @ Ys))))))))).
% 2.96/1.61 thf(fact_128_corec__llist__never__stop, axiom, (! [A:$tType,B:$tType,IS_LNIL:(B > $o),LHD:(B > A),MORE:(B > (coindu1593790203_llist @ A)),LTL:(B > B),X:B]: ((((((((((coindu1244876290_llist @ B) @ A) @ IS_LNIL) @ LHD) @ (^ [Uu:B]: ($false))) @ MORE) @ LTL) @ X) = ((((((coindu1599971794_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ X))))).
% 2.96/1.61 thf(fact_129_Singleton, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A]: (((coindu48241764sorted @ A) @ (((coindu1121789889_LCons @ A) @ X) @ (coindu1598213697e_LNil @ A))))))))).
% 2.96/1.61 thf(fact_130_ord_Olsorted__code_I2_J, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),X:A]: ((((coindu543932918sorted @ A) @ Less_eq) @ (((coindu1121789889_LCons @ A) @ X) @ (coindu1598213697e_LNil @ A)))))).
% 2.96/1.61 thf(fact_131_ord_Olsorted_Ocases, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),A3:(coindu1593790203_llist @ A)]: (((((coindu543932918sorted @ A) @ Less_eq) @ A3) => ((A3 != (coindu1598213697e_LNil @ A)) => ((! [X2:A]: ((A3 != (((coindu1121789889_LCons @ A) @ X2) @ (coindu1598213697e_LNil @ A))))) => (~ ((! [X2:A,Y3:A,Xs2:(coindu1593790203_llist @ A)]: (((A3 = (((coindu1121789889_LCons @ A) @ X2) @ (((coindu1121789889_LCons @ A) @ Y3) @ Xs2))) => (((Less_eq @ X2) @ Y3) => (~ ((((coindu543932918sorted @ A) @ Less_eq) @ (((coindu1121789889_LCons @ A) @ Y3) @ Xs2)))))))))))))))).
% 2.96/1.61 thf(fact_132_ord_Olsorted_Osimps, axiom, (! [A:$tType]: (((coindu543932918sorted @ A) = (^ [Less_eq2:(A > (A > $o)),A5:(coindu1593790203_llist @ A)]: (((A5 = (coindu1598213697e_LNil @ A)) | ((? [X3:A]: ((A5 = (((coindu1121789889_LCons @ A) @ X3) @ (coindu1598213697e_LNil @ A))))) | (? [X3:A,Y2:A,Xs3:(coindu1593790203_llist @ A)]: (((A5 = (((coindu1121789889_LCons @ A) @ X3) @ (((coindu1121789889_LCons @ A) @ Y2) @ Xs3))) & (((Less_eq2 @ X3) @ Y2) & (((coindu543932918sorted @ A) @ Less_eq2) @ (((coindu1121789889_LCons @ A) @ Y2) @ Xs3)))))))))))))).
% 2.96/1.61 thf(fact_133_ord_Olsorted_Ocoinduct, axiom, (! [A:$tType,X4:((coindu1593790203_llist @ A) > $o),X:(coindu1593790203_llist @ A),Less_eq:(A > (A > $o))]: (((X4 @ X) => ((! [X2:(coindu1593790203_llist @ A)]: (((X4 @ X2) => ((X2 = (coindu1598213697e_LNil @ A)) | ((? [Xa3:A]: ((X2 = (((coindu1121789889_LCons @ A) @ Xa3) @ (coindu1598213697e_LNil @ A))))) | (? [Xa3:A,Y4:A,Xs4:(coindu1593790203_llist @ A)]: (((X2 = (((coindu1121789889_LCons @ A) @ Xa3) @ (((coindu1121789889_LCons @ A) @ Y4) @ Xs4))) & (((Less_eq @ Xa3) @ Y4) & ((X4 @ (((coindu1121789889_LCons @ A) @ Y4) @ Xs4)) | (((coindu543932918sorted @ A) @ Less_eq) @ (((coindu1121789889_LCons @ A) @ Y4) @ Xs4)))))))))))) => (((coindu543932918sorted @ A) @ Less_eq) @ X)))))).
% 2.96/1.61 thf(fact_134_llast__lappend__LCons, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs) => (((coindu2000965700_llast @ A) @ (((coindu268472904append @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys))) = ((coindu2000965700_llast @ A) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys))))))).
% 2.96/1.61 thf(fact_135_lsorted_Ocoinduct, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X4:((coindu1593790203_llist @ A) > $o),X:(coindu1593790203_llist @ A)]: (((X4 @ X) => ((! [X2:(coindu1593790203_llist @ A)]: (((X4 @ X2) => ((X2 = (coindu1598213697e_LNil @ A)) | ((? [Xa3:A]: ((X2 = (((coindu1121789889_LCons @ A) @ Xa3) @ (coindu1598213697e_LNil @ A))))) | (? [Xa3:A,Y4:A,Xs4:(coindu1593790203_llist @ A)]: (((X2 = (((coindu1121789889_LCons @ A) @ Xa3) @ (((coindu1121789889_LCons @ A) @ Y4) @ Xs4))) & ((((ord_less_eq @ A) @ Xa3) @ Y4) & ((X4 @ (((coindu1121789889_LCons @ A) @ Y4) @ Xs4)) | ((coindu48241764sorted @ A) @ (((coindu1121789889_LCons @ A) @ Y4) @ Xs4)))))))))))) => ((coindu48241764sorted @ A) @ X))))))))).
% 2.96/1.61 thf(fact_136_lsorted_Osimps, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => ((coindu48241764sorted @ A) = (^ [A5:(coindu1593790203_llist @ A)]: (((A5 = (coindu1598213697e_LNil @ A)) | ((? [X3:A]: ((A5 = (((coindu1121789889_LCons @ A) @ X3) @ (coindu1598213697e_LNil @ A))))) | (? [X3:A,Y2:A,Xs3:(coindu1593790203_llist @ A)]: (((A5 = (((coindu1121789889_LCons @ A) @ X3) @ (((coindu1121789889_LCons @ A) @ Y2) @ Xs3))) & ((((ord_less_eq @ A) @ X3) @ Y2) & ((coindu48241764sorted @ A) @ (((coindu1121789889_LCons @ A) @ Y2) @ Xs3))))))))))))))).
% 2.96/1.61 thf(fact_137_lsorted_Ocases, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A3:(coindu1593790203_llist @ A)]: ((((coindu48241764sorted @ A) @ A3) => ((A3 != (coindu1598213697e_LNil @ A)) => ((! [X2:A]: ((A3 != (((coindu1121789889_LCons @ A) @ X2) @ (coindu1598213697e_LNil @ A))))) => (~ ((! [X2:A,Y3:A,Xs2:(coindu1593790203_llist @ A)]: (((A3 = (((coindu1121789889_LCons @ A) @ X2) @ (((coindu1121789889_LCons @ A) @ Y3) @ Xs2))) => ((((ord_less_eq @ A) @ X2) @ Y3) => (~ (((coindu48241764sorted @ A) @ (((coindu1121789889_LCons @ A) @ Y3) @ Xs2))))))))))))))))))).
% 2.96/1.61 thf(fact_138_lstrict__prefix__lappend__conv, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu574146665prefix @ A) @ Xs) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu1213758845finite @ A) @ Xs) & (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 2.96/1.61 thf(fact_139_lprefixI, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),X4:(set @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)))]: (((((member @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A))) @ ((((product_Pair @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)) @ Xs) @ Ys)) @ X4) => ((! [Xs2:(coindu1593790203_llist @ A),Ys3:(coindu1593790203_llist @ A)]: (((((member @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A))) @ ((((product_Pair @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)) @ Xs2) @ Ys3)) @ X4) => (((coindu335574135_lnull @ A) @ Xs2) | (? [X8:A,Xs6:(coindu1593790203_llist @ A),Ys6:(coindu1593790203_llist @ A)]: (((Xs2 = (((coindu1121789889_LCons @ A) @ X8) @ Xs6)) & ((Ys3 = (((coindu1121789889_LCons @ A) @ X8) @ Ys6)) & ((((member @ ((product_prod @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A))) @ ((((product_Pair @ (coindu1593790203_llist @ A)) @ (coindu1593790203_llist @ A)) @ Xs6) @ Ys6)) @ X4) | (((coindu1696667936prefix @ A) @ Xs6) @ Ys6)))))))))) => (((coindu1696667936prefix @ A) @ Xs) @ Ys)))))).
% 2.96/1.61 thf(fact_140_lappend__code_I2_J, axiom, (! [A:$tType,Xa:A,X:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu1121789889_LCons @ A) @ Xa) @ X)) @ Ys) = (((coindu1121789889_LCons @ A) @ Xa) @ (((coindu268472904append @ A) @ X) @ Ys)))))).
% 2.96/1.61 thf(fact_141_lappend_Odisc__iff_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)))) = ((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))))))).
% 2.96/1.61 thf(fact_142_lnull__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu335574135_lnull @ A) @ Xs) & ((coindu335574135_lnull @ A) @ Ys)))))).
% 2.96/1.61 thf(fact_143_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (coindu1598213697e_LNil @ A)) @ Ys) = Ys)))).
% 2.96/1.61 thf(fact_144_lappend__LNil2, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ Xs) @ (coindu1598213697e_LNil @ A)) = Xs)))).
% 2.96/1.61 thf(fact_145_lfinite__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (((coindu1213758845finite @ A) @ Xs) & ((coindu1213758845finite @ A) @ Ys)))))).
% 2.96/1.61 thf(fact_146_lsorted__LCons__LCons, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Y:A,Xs:(coindu1593790203_llist @ A)]: ((((coindu48241764sorted @ A) @ (((coindu1121789889_LCons @ A) @ X) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs))) = ((((ord_less_eq @ A) @ X) @ Y) & ((coindu48241764sorted @ A) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs)))))))))).
% 2.96/1.61 thf(fact_147_lprefix__lappend__same, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) @ (((coindu268472904append @ A) @ Xs) @ Zs)) = (((coindu1213758845finite @ A) @ Xs) => (((coindu1696667936prefix @ A) @ Ys) @ Zs)))))).
% 2.96/1.61 thf(fact_148_lappend__assoc, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) @ Zs) = (((coindu268472904append @ A) @ Xs) @ (((coindu268472904append @ A) @ Ys) @ Zs)))))).
% 2.96/1.61 thf(fact_149_wlog__linorder__le, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),B3:A,A3:A]: (((! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((P @ A2) @ B2)))) => ((((P @ B3) @ A3) => ((P @ A3) @ B3)) => ((P @ A3) @ B3))))))))).
% 2.96/1.61 thf(fact_150_lprefix__lappend, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1696667936prefix @ A) @ Xs) @ (((coindu268472904append @ A) @ Xs) @ Ys))))).
% 2.96/1.61 thf(fact_151_lappend__lprefixE, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) @ Zs) => (~ ((! [Zs2:(coindu1593790203_llist @ A)]: ((Zs != (((coindu268472904append @ A) @ Xs) @ Zs2)))))))))).
% 2.96/1.61 thf(fact_152_lprefix__lappendD, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A)]: (((((coindu1696667936prefix @ A) @ Xs) @ (((coindu268472904append @ A) @ Ys) @ Zs)) => ((((coindu1696667936prefix @ A) @ Xs) @ Ys) | (((coindu1696667936prefix @ A) @ Ys) @ Xs)))))).
% 2.96/1.61 thf(fact_153_lprefix__conv__lappend, axiom, (! [A:$tType]: (((coindu1696667936prefix @ A) = (^ [Xs3:(coindu1593790203_llist @ A),Ys4:(coindu1593790203_llist @ A)]: ((? [Zs3:(coindu1593790203_llist @ A)]: ((Ys4 = (((coindu268472904append @ A) @ Xs3) @ Zs3)))))))))).
% 2.96/1.61 thf(fact_154_lprefix__lappend__sameI, axiom, (! [A:$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)))))).
% 2.96/1.61 thf(fact_155_lappend_Odisc_I2_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((~ (((coindu335574135_lnull @ A) @ Xs))) | (~ (((coindu335574135_lnull @ A) @ Ys)))) => (~ (((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)))))))).
% 2.96/1.61 thf(fact_156_lappend_Odisc_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu335574135_lnull @ A) @ Ys) => ((coindu335574135_lnull @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys))))))).
% 2.96/1.61 thf(fact_157_lappend__lnull1, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Ys))))).
% 2.96/1.61 thf(fact_158_lappend__lnull2, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Ys) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Xs))))).
% 2.96/1.61 thf(fact_159_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coindu268472904append @ A) @ (coindu1598213697e_LNil @ A)) @ (coindu1598213697e_LNil @ A)) = (coindu1598213697e_LNil @ A))))).
% 2.96/1.61 thf(fact_160_LNil__eq__lappend__iff, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu1598213697e_LNil @ A) = (((coindu268472904append @ A) @ Xs) @ Ys)) = ((Xs = (coindu1598213697e_LNil @ A)) & (Ys = (coindu1598213697e_LNil @ A))))))).
% 2.96/1.61 thf(fact_161_lappend__eq__LNil__iff, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((((coindu268472904append @ A) @ Xs) @ Ys) = (coindu1598213697e_LNil @ A)) = ((Xs = (coindu1598213697e_LNil @ A)) & (Ys = (coindu1598213697e_LNil @ A))))))).
% 2.96/1.61 thf(fact_162_lappend__inf, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((~ (((coindu1213758845finite @ A) @ Xs))) => ((((coindu268472904append @ A) @ Xs) @ Ys) = Xs))))).
% 2.96/1.61 thf(fact_163_llexord__lappend__leftI, axiom, (! [A:$tType,R:(A > (A > $o)),Ys:(coindu1593790203_llist @ A),Zs:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: ((((((coindu300403952lexord @ A) @ R) @ Ys) @ Zs) => ((((coindu300403952lexord @ A) @ R) @ (((coindu268472904append @ A) @ Xs) @ Ys)) @ (((coindu268472904append @ A) @ Xs) @ Zs)))))).
% 2.96/1.61 thf(fact_164_llexord__append__right, axiom, (! [A:$tType,R:(A > (A > $o)),Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: (((((coindu300403952lexord @ A) @ R) @ Xs) @ (((coindu268472904append @ A) @ Xs) @ Ys))))).
% 2.96/1.61 thf(fact_165_lappend__snocL1__conv__LCons2, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Y:A,Ys:(coindu1593790203_llist @ A)]: (((((coindu268472904append @ A) @ (((coindu268472904append @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ (coindu1598213697e_LNil @ A)))) @ Ys) = (((coindu268472904append @ A) @ Xs) @ (((coindu1121789889_LCons @ A) @ Y) @ Ys)))))).
% 2.96/1.61 thf(fact_166_lappend_Octr_I1_J, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),Ys:(coindu1593790203_llist @ A)]: ((((coindu335574135_lnull @ A) @ Xs) => (((coindu335574135_lnull @ A) @ Ys) => ((((coindu268472904append @ A) @ Xs) @ Ys) = (coindu1598213697e_LNil @ A))))))).
% 2.96/1.61 thf(fact_167_LCons__LCons, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Y:A,Xs:(coindu1593790203_llist @ A)]: (((((ord_less_eq @ A) @ X) @ Y) => (((coindu48241764sorted @ A) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs)) => ((coindu48241764sorted @ A) @ (((coindu1121789889_LCons @ A) @ X) @ (((coindu1121789889_LCons @ A) @ Y) @ Xs))))))))))).
% 2.96/1.61 thf(fact_168_lfinite__rev__induct, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A),P:((coindu1593790203_llist @ A) > $o)]: ((((coindu1213758845finite @ A) @ Xs) => ((P @ (coindu1598213697e_LNil @ A)) => ((! [X2:A,Xs2:(coindu1593790203_llist @ A)]: ((((coindu1213758845finite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coindu268472904append @ A) @ Xs2) @ (((coindu1121789889_LCons @ A) @ X2) @ (coindu1598213697e_LNil @ A)))))))) => (P @ Xs))))))).
% 2.96/1.61 thf(fact_169_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X23:B,Y1:A,Y23:B]: (((((((product_Pair @ A) @ B) @ X1) @ X23) = ((((product_Pair @ A) @ B) @ Y1) @ Y23)) = ((X1 = Y1) & (X23 = Y23)))))).
% 2.96/1.61 thf(fact_170_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A3:A,B3:B,A6:A,B4:B]: (((((((product_Pair @ A) @ B) @ A3) @ B3) = ((((product_Pair @ A) @ B) @ A6) @ B4)) = ((A3 = A6) & (B3 = B4)))))).
% 2.96/1.61 thf(fact_171_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 2.96/1.61 thf(fact_172_pred__subset__eq2, axiom, (! [B:$tType,A:$tType,R3:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: (((((ord_less_eq @ (A > (B > $o))) @ (^ [X3:A,Y2:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y2)) @ R3)))) @ (^ [X3:A,Y2:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y2)) @ S)))) = (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R3) @ S))))).
% 2.96/1.61 thf(fact_173_predicate2I, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o)),Q:(A > (B > $o))]: (((! [X2:A,Y3:B]: ((((P @ X2) @ Y3) => ((Q @ X2) @ Y3)))) => (((ord_less_eq @ (A > (B > $o))) @ P) @ Q))))).
% 2.96/1.61 thf(fact_174_predicate2D, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Q:(A > (B > $o)),X:A,Y:B]: (((((ord_less_eq @ (A > (B > $o))) @ P) @ Q) => (((P @ X) @ Y) => ((Q @ X) @ Y)))))).
% 2.96/1.61 thf(fact_175_rev__predicate2D, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),X:A,Y:B,Q:(A > (B > $o))]: ((((P @ X) @ Y) => ((((ord_less_eq @ (A > (B > $o))) @ P) @ Q) => ((Q @ X) @ Y)))))).
% 2.96/1.61 thf(fact_176_pred__subset__eq, axiom, (! [A:$tType,R3:(set @ A),S:(set @ A)]: (((((ord_less_eq @ (A > $o)) @ (^ [X3:A]: ((((member @ A) @ X3) @ R3)))) @ (^ [X3:A]: ((((member @ A) @ X3) @ S)))) = (((ord_less_eq @ (set @ A)) @ R3) @ S))))).
% 2.96/1.61 thf(fact_177_dual__order_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A3:A]: (((((ord_less_eq @ A) @ B3) @ A3) => ((((ord_less_eq @ A) @ A3) @ B3) => (A3 = B3))))))))).
% 2.96/1.61 thf(fact_178_dual__order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A3:A,C3:A]: (((((ord_less_eq @ A) @ B3) @ A3) => ((((ord_less_eq @ A) @ C3) @ B3) => (((ord_less_eq @ A) @ C3) @ A3))))))))).
% 2.96/1.61 thf(fact_179_linorder__wlog, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),A3:A,B3:A]: (((! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((P @ A2) @ B2)))) => ((! [A2:A,B2:A]: ((((P @ B2) @ A2) => ((P @ A2) @ B2)))) => ((P @ A3) @ B3))))))))).
% 2.96/1.61 thf(fact_180_dual__order_Orefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A3:A]: ((((ord_less_eq @ A) @ A3) @ A3))))))).
% 2.96/1.61 thf(fact_181_order__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z) => (((ord_less_eq @ A) @ X) @ Z))))))))).
% 2.96/1.61 thf(fact_182_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less_eq @ A) @ B3) @ A3) => (A3 = B3))))))))).
% 2.96/1.61 thf(fact_183_ord__le__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C3:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((B3 = C3) => (((ord_less_eq @ A) @ A3) @ C3))))))))).
% 2.96/1.61 thf(fact_184_ord__eq__le__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C3:A]: (((A3 = B3) => ((((ord_less_eq @ A) @ B3) @ C3) => (((ord_less_eq @ A) @ A3) @ C3))))))))).
% 2.96/1.61 thf(fact_185_antisym__conv, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 2.96/1.61 thf(fact_186_le__cases3, axiom, (! [A:$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))))))))))))))))).
% 2.96/1.61 thf(fact_187_order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C3:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less_eq @ A) @ B3) @ C3) => (((ord_less_eq @ A) @ A3) @ C3))))))))).
% 2.96/1.61 thf(fact_188_le__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.96/1.61 thf(fact_189_eq__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X = Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 2.96/1.61 thf(fact_190_linorder__class_Olinear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.96/1.61 thf(fact_191_antisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 2.96/1.61 thf(fact_192_eq__iff, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((^ [Y5:A,Z2:A]: ((Y5 = Z2))) = (^ [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) & (((ord_less_eq @ A) @ Y2) @ X3))))))))).
% 2.96/1.61 thf(fact_193_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A3:A,B3:A,F:(A > B),C3:B]: (((((ord_less_eq @ A) @ A3) @ B3) => (((F @ B3) = C3) => ((! [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) => (((ord_less_eq @ B) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less_eq @ B) @ (F @ A3)) @ C3)))))))))).
% 2.96/1.61 thf(fact_194_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A3:A,F:(B > A),B3:B,C3:B]: (((A3 = (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C3) => ((! [X2:B,Y3:B]: (((((ord_less_eq @ B) @ X2) @ Y3) => (((ord_less_eq @ A) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less_eq @ A) @ A3) @ (F @ C3))))))))))).
% 2.96/1.61 thf(fact_195_order__subst2, axiom, (! [A:$tType,C:$tType]: (((((order @ C) @ (type2 @ C)) & ((order @ A) @ (type2 @ A))) => (! [A3:A,B3:A,F:(A > C),C3:C]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less_eq @ C) @ (F @ B3)) @ C3) => ((! [X2:A,Y3:A]: (((((ord_less_eq @ A) @ X2) @ Y3) => (((ord_less_eq @ C) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less_eq @ C) @ (F @ A3)) @ C3)))))))))).
% 2.96/1.61 thf(fact_196_order__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A3:A,F:(B > A),B3:B,C3:B]: (((((ord_less_eq @ A) @ A3) @ (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C3) => ((! [X2:B,Y3:B]: (((((ord_less_eq @ B) @ X2) @ Y3) => (((ord_less_eq @ A) @ (F @ X2)) @ (F @ Y3))))) => (((ord_less_eq @ A) @ A3) @ (F @ C3))))))))))).
% 2.96/1.61 thf(fact_197_le__fun__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: ((! [X3:A]: ((((ord_less_eq @ B) @ (F2 @ X3)) @ (G2 @ X3))))))))))).
% 2.96/1.61 thf(fact_198_le__funI, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B)]: (((! [X2:A]: ((((ord_less_eq @ B) @ (F @ X2)) @ (G @ X2)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 2.96/1.61 thf(fact_199_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))))))))).
% 2.96/1.61 thf(fact_200_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))))))))).
% 2.96/1.61 thf(fact_201_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A2:A,B2:B]: ((P @ ((((product_Pair @ A) @ B) @ A2) @ B2)))) => (P @ Prod))))).
% 2.96/1.61 thf(fact_202_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A2:A,B2:B]: ((Y != ((((product_Pair @ A) @ B) @ A2) @ B2))))))))).
% 2.96/1.61 thf(fact_203_prod__induct7, axiom, (! [G3:$tType,F3:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))))))]: (((! [A2:A,B2:B,C2:C,D2:D,E2:E,F4:F3,G4:G3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))))) @ A2) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))))) @ B2) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F3) @ G3)) @ E2) @ ((((product_Pair @ F3) @ G3) @ F4) @ G4))))))))) => (P @ X))))).
% 2.96/1.61 thf(fact_204_prod__induct6, axiom, (! [F3:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))))]: (((! [A2:A,B2:B,C2:C,D2:D,E2:E,F4:F3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))))) @ A2) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))) @ B2) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F3)) @ D2) @ ((((product_Pair @ E) @ F3) @ E2) @ F4)))))))) => (P @ X))))).
% 2.96/1.61 thf(fact_205_prod__induct5, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: (((! [A2:A,B2:B,C2:C,D2:D,E2:E]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A2) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B2) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C2) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P @ X))))).
% 2.96/1.61 thf(fact_206_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A2:A,B2:B,C2:C,D2:D]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A2) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B2) @ ((((product_Pair @ C) @ D) @ C2) @ D2)))))) => (P @ X))))).
% 2.96/1.61 thf(fact_207_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A2:A,B2:B,C2:C]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A2) @ ((((product_Pair @ B) @ C) @ B2) @ C2))))) => (P @ X))))).
% 2.96/1.61 thf(fact_208_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F3:$tType,G3:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))))))]: ((~ ((! [A2:A,B2:B,C2:C,D2:D,E2:E,F4:F3,G4:G3]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))))) @ A2) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))))) @ B2) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F3) @ G3)) @ E2) @ ((((product_Pair @ F3) @ G3) @ F4) @ G4)))))))))))))).
% 2.96/1.61 thf(fact_209_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F3:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))))]: ((~ ((! [A2:A,B2:B,C2:C,D2:D,E2:E,F4:F3]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))))) @ A2) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))) @ B2) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F3)) @ D2) @ ((((product_Pair @ E) @ F3) @ E2) @ F4))))))))))))).
% 2.96/1.61 thf(fact_210_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: ((~ ((! [A2:A,B2:B,C2:C,D2:D,E2:E]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A2) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B2) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C2) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 2.96/1.61 thf(fact_211_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A2:A,B2:B,C2:C,D2:D]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A2) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B2) @ ((((product_Pair @ C) @ D) @ C2) @ D2))))))))))).
% 2.96/1.61 thf(fact_212_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A2:A,B2:B,C2:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A2) @ ((((product_Pair @ B) @ C) @ B2) @ C2)))))))))).
% 2.96/1.61 thf(fact_213_Pair__inject, axiom, (! [A:$tType,B:$tType,A3:A,B3:B,A6:A,B4:B]: (((((((product_Pair @ A) @ B) @ A3) @ B3) = ((((product_Pair @ A) @ B) @ A6) @ B4)) => (~ (((A3 = A6) => (B3 != B4)))))))).
% 2.96/1.61 thf(fact_214_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P2:((product_prod @ A) @ B)]: (((! [A2:A,B2:B]: ((P @ ((((product_Pair @ A) @ B) @ A2) @ B2)))) => (P @ P2))))).
% 2.96/1.61 thf(fact_215_surj__pair, axiom, (! [A:$tType,B:$tType,P2:((product_prod @ A) @ B)]: ((? [X2:A,Y3:B]: ((P2 = ((((product_Pair @ A) @ B) @ X2) @ Y3))))))).
% 2.96/1.61 thf(fact_216_subrelI, axiom, (! [B:$tType,A:$tType,R:(set @ ((product_prod @ A) @ B)),S2:(set @ ((product_prod @ A) @ B))]: (((! [X2:A,Y3:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y3)) @ R) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X2) @ Y3)) @ S2)))) => (((ord_less_eq @ (set @ ((product_prod @ A) @ B))) @ R) @ S2))))).
% 2.96/1.61 thf(fact_217_pred__equals__eq2, axiom, (! [B:$tType,A:$tType,R3:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: ((((^ [X3:A,Y2:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y2)) @ R3))) = (^ [X3:A,Y2:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y2)) @ S)))) = (R3 = S))))).
% 2.96/1.61 thf(fact_218_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A3:A,B3:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A3) @ B3)) = ((F1 @ A3) @ B3))))).
% 2.96/1.61 thf(fact_219_subsetI, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((! [X2:A]: (((((member @ A) @ X2) @ A4) => (((member @ A) @ X2) @ B5)))) => (((ord_less_eq @ (set @ A)) @ A4) @ B5))))).
% 2.96/1.61 thf(fact_220_subset__antisym, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ A4) => (A4 = B5)))))).
% 2.96/1.61 thf(fact_221_predicate1I, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) => (Q @ X2)))) => (((ord_less_eq @ (A > $o)) @ P) @ Q))))).
% 2.96/1.61 thf(fact_222_predicate1D, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o),X:A]: (((((ord_less_eq @ (A > $o)) @ P) @ Q) => ((P @ X) => (Q @ X)))))).
% 2.96/1.61 thf(fact_223_rev__predicate1D, axiom, (! [A:$tType,P:(A > $o),X:A,Q:(A > $o)]: (((P @ X) => ((((ord_less_eq @ (A > $o)) @ P) @ Q) => (Q @ X)))))).
% 2.96/1.61 thf(fact_224_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X3:A]: (((P @ X3) => (Q @ X3)))))))).
% 2.96/1.61 thf(fact_225_contra__subsetD, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C3:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((~ ((((member @ A) @ C3) @ B5))) => (~ ((((member @ A) @ C3) @ A4)))))))).
% 2.96/1.61 thf(fact_226_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y5:(set @ A),Z2:(set @ A)]: ((Y5 = Z2))) = (^ [A7:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A7) @ B6) & (((ord_less_eq @ (set @ A)) @ B6) @ A7)))))))).
% 2.96/1.61 thf(fact_227_subset__trans, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((ord_less_eq @ (set @ A)) @ B5) @ C4) => (((ord_less_eq @ (set @ A)) @ A4) @ C4)))))).
% 2.96/1.61 thf(fact_228_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) => (Q @ X2)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.96/1.61 thf(fact_229_subset__refl, axiom, (! [A:$tType,A4:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A4) @ A4)))).
% 2.96/1.61 thf(fact_230_rev__subsetD, axiom, (! [A:$tType,C3:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ C3) @ A4) => ((((ord_less_eq @ (set @ A)) @ A4) @ B5) => (((member @ A) @ C3) @ B5)))))).
% 2.96/1.61 thf(fact_231_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B6:(set @ A)]: ((! [T2:A]: (((((member @ A) @ T2) @ A7) => (((member @ A) @ T2) @ B6)))))))))).
% 2.96/1.61 thf(fact_232_set__rev__mp, axiom, (! [A:$tType,X:A,A4:(set @ A),B5:(set @ A)]: (((((member @ A) @ X) @ A4) => ((((ord_less_eq @ (set @ A)) @ A4) @ B5) => (((member @ A) @ X) @ B5)))))).
% 2.96/1.61 thf(fact_233_equalityD2, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((A4 = B5) => (((ord_less_eq @ (set @ A)) @ B5) @ A4))))).
% 2.96/1.61 thf(fact_234_equalityD1, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((A4 = B5) => (((ord_less_eq @ (set @ A)) @ A4) @ B5))))).
% 2.96/1.61 thf(fact_235_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B6:(set @ A)]: ((! [X3:A]: (((((member @ A) @ X3) @ A7) => (((member @ A) @ X3) @ B6)))))))))).
% 2.96/1.61 thf(fact_236_equalityE, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A)]: (((A4 = B5) => (~ (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => (~ ((((ord_less_eq @ (set @ A)) @ B5) @ A4)))))))))).
% 2.96/1.61 thf(fact_237_subsetCE, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C3:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((member @ A) @ C3) @ A4) => (((member @ A) @ C3) @ B5)))))).
% 2.96/1.61 thf(fact_238_subsetD, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),C3:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((member @ A) @ C3) @ A4) => (((member @ A) @ C3) @ B5)))))).
% 2.96/1.61 thf(fact_239_in__mono, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((member @ A) @ X) @ A4) => (((member @ A) @ X) @ B5)))))).
% 2.96/1.61 thf(fact_240_set__mp, axiom, (! [A:$tType,A4:(set @ A),B5:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) => ((((member @ A) @ X) @ A4) => (((member @ A) @ X) @ B5)))))).
% 2.96/1.61 thf(fact_241_less__eq__set__def, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A7:(set @ A),B6:(set @ A)]: ((((ord_less_eq @ (A > $o)) @ (^ [X3:A]: ((((member @ A) @ X3) @ A7)))) @ (^ [X3:A]: ((((member @ A) @ X3) @ B6)))))))))).
% 2.96/1.61 thf(fact_242_eq__subset, axiom, (! [A:$tType,P:(A > (A > $o))]: ((((ord_less_eq @ (A > (A > $o))) @ (^ [Y5:A,Z2:A]: ((Y5 = Z2)))) @ (^ [A5:A,B7:A]: ((((P @ A5) @ B7) | (A5 = B7)))))))).
% 2.96/1.61 thf(fact_243_conj__subset__def, axiom, (! [A:$tType,A4:(set @ A),P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ A4) @ ((collect @ A) @ (^ [X3:A]: (((P @ X3) & (Q @ X3)))))) = ((((ord_less_eq @ (set @ A)) @ A4) @ ((collect @ A) @ P)) & (((ord_less_eq @ (set @ A)) @ A4) @ ((collect @ A) @ Q))))))).
% 2.96/1.61 thf(fact_244_predicate2D__conj, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Q:(A > (B > $o)),R3:$o,X:A,Y:B]: ((((((ord_less_eq @ (A > (B > $o))) @ P) @ Q) & R3) => (R3 & (((P @ X) @ Y) => ((Q @ X) @ Y))))))).
% 2.96/1.61 thf(fact_245_subset__Collect__iff, axiom, (! [A:$tType,B5:(set @ A),A4:(set @ A),P:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B5) @ A4) => ((((ord_less_eq @ (set @ A)) @ B5) @ ((collect @ A) @ (^ [X3:A]: (((((member @ A) @ X3) @ A4) & (P @ X3)))))) = (! [X3:A]: (((((member @ A) @ X3) @ B5) => (P @ X3))))))))).
% 2.96/1.61 thf(fact_246_subset__CollectI, axiom, (! [A:$tType,B5:(set @ A),A4:(set @ A),Q:(A > $o),P:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ B5) @ A4) => ((! [X2:A]: (((((member @ A) @ X2) @ B5) => ((Q @ X2) => (P @ X2))))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X3:A]: (((((member @ A) @ X3) @ B5) & (Q @ X3)))))) @ ((collect @ A) @ (^ [X3:A]: (((((member @ A) @ X3) @ A4) & (P @ X3))))))))))).
% 2.96/1.61 thf(fact_247_prop__restrict, axiom, (! [A:$tType,X:A,Z3:(set @ A),X4:(set @ A),P:(A > $o)]: (((((member @ A) @ X) @ Z3) => ((((ord_less_eq @ (set @ A)) @ Z3) @ ((collect @ A) @ (^ [X3:A]: (((((member @ A) @ X3) @ X4) & (P @ X3)))))) => (P @ X)))))).
% 2.96/1.61 thf(fact_248_Collect__restrict, axiom, (! [A:$tType,X4:(set @ A),P:(A > $o)]: ((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ (^ [X3:A]: (((((member @ A) @ X3) @ X4) & (P @ X3)))))) @ X4)))).
% 2.96/1.61 thf(fact_249_ssubst__Pair__rhs, axiom, (! [B:$tType,A:$tType,R:A,S2:B,R3:(set @ ((product_prod @ A) @ B)),S3:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R) @ S2)) @ R3) => ((S3 = S2) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R) @ S3)) @ R3)))))).
% 2.96/1.61 thf(fact_250_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C3:(B > (C > A)),A3:B,B3:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C3) @ ((((product_Pair @ B) @ C) @ A3) @ B3)) = ((C3 @ A3) @ B3))))).
% 2.96/1.61 thf(fact_251_llast__lappend, axiom, (! [A:$tType,Ys:(coindu1593790203_llist @ A),Xs:(coindu1593790203_llist @ A)]: (((((coindu335574135_lnull @ A) @ Ys) => (((coindu2000965700_llast @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = ((coindu2000965700_llast @ A) @ Xs))) & ((~ (((coindu335574135_lnull @ A) @ Ys))) => ((((coindu1213758845finite @ A) @ Xs) => (((coindu2000965700_llast @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = ((coindu2000965700_llast @ A) @ Ys))) & ((~ (((coindu1213758845finite @ A) @ Xs))) => (((coindu2000965700_llast @ A) @ (((coindu268472904append @ A) @ Xs) @ Ys)) = (undefined @ A))))))))).
% 2.96/1.61 thf(fact_252_llast__linfinite, axiom, (! [A:$tType,Xs:(coindu1593790203_llist @ A)]: (((~ (((coindu1213758845finite @ A) @ Xs))) => (((coindu2000965700_llast @ A) @ Xs) = (undefined @ A)))))).
% 2.96/1.61 thf(fact_253_llast__LNil, axiom, (! [A:$tType]: ((((coindu2000965700_llast @ A) @ (coindu1598213697e_LNil @ A)) = (undefined @ A))))).
% 2.96/1.61 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: ((((preorder @ A9) @ (type2 @ A9)) => ((preorder @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.96/1.61 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: ((((order @ A9) @ (type2 @ A9)) => ((order @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.96/1.61 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: ((((ord @ A9) @ (type2 @ A9)) => ((ord @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.96/1.61 thf(tcon_Set_Oset___Orderings_Opreorder_1, axiom, (! [A8:$tType]: (((preorder @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.96/1.61 thf(tcon_Set_Oset___Orderings_Oorder_2, axiom, (! [A8:$tType]: (((order @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.96/1.61 thf(tcon_Set_Oset___Orderings_Oord_3, axiom, (! [A8:$tType]: (((ord @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.96/1.61 thf(tcon_HOL_Obool___Orderings_Opreorder_4, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 2.96/1.61 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.96/1.61 thf(tcon_HOL_Obool___Orderings_Oorder_5, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.96/1.61 thf(tcon_HOL_Obool___Orderings_Oord_6, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.96/1.61 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.96/1.61 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.96/1.61 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.96/1.61 thf(conj_0, hypothesis, (! [Y4:a,Ys6:(coindu1593790203_llist @ a)]: (((ysa = (((coindu1121789889_LCons @ a) @ Y4) @ Ys6)) => ((~ (((r @ Y4) @ x))) => (((Y4 != x) | (~ (((((coindu300403952lexord @ a) @ r) @ Ys6) @ xs2)))) => thesis)))))).
% 2.96/1.61 thf(conj_1, conjecture, thesis).
% 2.96/1.61 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.vsmmhmmsID/DTF2DTF32705.p
% 2.96/1.61 ------------------------
% 2.96/1.66 ---- Cleaned THF ---
% 2.96/1.66 thf(ty_t_Coinductive__List__Mirabelle__kmikjhschf_Ollist,type,
% 2.96/1.66 coindu1593790203_llist: $tType > $tType ).
% 2.96/1.66
% 2.96/1.66 thf(ty_t_Product__Type_Oprod,type,
% 2.96/1.66 product_prod: $tType > $tType > $tType ).
% 2.96/1.66
% 2.96/1.66 thf(ty_t_Set_Oset,type,
% 2.96/1.66 set: $tType > $tType ).
% 2.96/1.66
% 2.96/1.66 thf(ty_t_itself,type,
% 2.96/1.66 itself: $tType > $tType ).
% 2.96/1.66
% 2.96/1.66 thf(ty_tf_a,type,
% 2.96/1.66 a: $tType ).
% 2.96/1.66
% 2.96/1.66 thf(sy_cl_HOL_Otype,type,
% 2.96/1.66 type:
% 2.96/1.66 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_cl_Orderings_Oord,type,
% 2.96/1.66 ord:
% 2.96/1.66 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_cl_Orderings_Oorder,type,
% 2.96/1.66 order:
% 2.96/1.66 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_cl_Orderings_Olinorder,type,
% 2.96/1.66 linorder:
% 2.96/1.66 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_cl_Orderings_Opreorder,type,
% 2.96/1.66 preorder:
% 2.96/1.66 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix,type,
% 2.96/1.66 coindu1571841457prefix:
% 2.96/1.66 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ogen__lset,type,
% 2.96/1.66 coindu1928975208n_lset:
% 2.96/1.66 !>[A: $tType] : ( ( set @ A ) > ( coindu1593790203_llist @ A ) > ( set @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olappend,type,
% 2.96/1.66 coindu268472904append:
% 2.96/1.66 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olfinite,type,
% 2.96/1.66 coindu1213758845finite:
% 2.96/1.66 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollast,type,
% 2.96/1.66 coindu2000965700_llast:
% 2.96/1.66 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollexord,type,
% 2.96/1.66 coindu300403952lexord:
% 2.96/1.66 !>[A: $tType] : ( ( A > A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLCons,type,
% 2.96/1.66 coindu1121789889_LCons:
% 2.96/1.66 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_OLNil,type,
% 2.96/1.66 coindu1598213697e_LNil:
% 2.96/1.66 !>[A: $tType] : ( coindu1593790203_llist @ A ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Ocorec__llist,type,
% 2.96/1.66 coindu1244876290_llist:
% 2.96/1.66 !>[C: $tType,A: $tType] : ( ( C > $o ) > ( C > A ) > ( C > $o ) > ( C > ( coindu1593790203_llist @ A ) ) > ( C > C ) > C > ( coindu1593790203_llist @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Olnull,type,
% 2.96/1.66 coindu335574135_lnull:
% 2.96/1.66 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ollist_Opred__llist,type,
% 2.96/1.66 coindu44415597_llist:
% 2.96/1.66 !>[A: $tType] : ( ( A > $o ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olmember,type,
% 2.96/1.66 coindu567634248member:
% 2.96/1.66 !>[A: $tType] : ( A > ( coindu1593790203_llist @ A ) > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olprefix,type,
% 2.96/1.66 coindu1696667936prefix:
% 2.96/1.66 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olsetp,type,
% 2.96/1.66 coindu1055736764_lsetp:
% 2.96/1.66 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > A > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Olstrict__prefix,type,
% 2.96/1.66 coindu574146665prefix:
% 2.96/1.66 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_OltakeWhile,type,
% 2.96/1.66 coindu721411036eWhile:
% 2.96/1.66 !>[A: $tType] : ( ( A > $o ) > ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oord_Olsorted,type,
% 2.96/1.66 coindu543932918sorted:
% 2.96/1.66 !>[A: $tType] : ( ( A > A > $o ) > ( coindu1593790203_llist @ A ) > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Oord__class_Olsorted,type,
% 2.96/1.66 coindu48241764sorted:
% 2.96/1.66 !>[A: $tType] : ( ( coindu1593790203_llist @ A ) > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Coinductive__List__Mirabelle__kmikjhschf_Ounfold__llist,type,
% 2.96/1.66 coindu1599971794_llist:
% 2.96/1.66 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > B ) > ( A > A ) > A > ( coindu1593790203_llist @ B ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_HOL_Oundefined,type,
% 2.96/1.66 undefined:
% 2.96/1.66 !>[A: $tType] : A ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_If,type,
% 2.96/1.66 if:
% 2.96/1.66 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.96/1.66 ord_less_eq:
% 2.96/1.66 !>[A: $tType] : ( A > A > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Product__Type_OPair,type,
% 2.96/1.66 product_Pair:
% 2.96/1.66 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 2.96/1.66 produc2004651681e_prod:
% 2.96/1.66 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 2.96/1.66 product_rec_prod:
% 2.96/1.66 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Pure_Otype,type,
% 2.96/1.66 type2:
% 2.96/1.66 !>[A: $tType] : ( itself @ A ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_Set_OCollect,type,
% 2.96/1.66 collect:
% 2.96/1.66 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_c_member,type,
% 2.96/1.66 member:
% 2.96/1.66 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.96/1.66
% 2.96/1.66 thf(sy_v_r,type,
% 2.96/1.66 r: a > a > $o ).
% 2.96/1.66
% 2.96/1.66 thf(sy_v_thesis____,type,
% 2.96/1.66 thesis: $o ).
% 2.96/1.66
% 2.96/1.66 thf(sy_v_x____,type,
% 2.96/1.66 x: a ).
% 2.96/1.66
% 2.96/1.66 thf(sy_v_xs,type,
% 2.96/1.66 xs: coindu1593790203_llist @ a ).
% 2.96/1.66
% 2.96/1.66 thf(sy_v_xs_H____,type,
% 2.96/1.66 xs2: coindu1593790203_llist @ a ).
% 2.96/1.66
% 2.96/1.66 thf(sy_v_xsa____,type,
% 2.96/1.66 xsa: coindu1593790203_llist @ a ).
% 2.96/1.66
% 2.96/1.66 thf(sy_v_ys,type,
% 2.96/1.66 ys: coindu1593790203_llist @ a ).
% 2.96/1.66
% 2.96/1.66 thf(sy_v_ysa____,type,
% 2.96/1.66 ysa: coindu1593790203_llist @ a ).
% 2.96/1.66
% 2.96/1.66 thf(fact_0_local_Olinear,axiom,
% 2.96/1.66 ! [X: a,Y: a] :
% 2.96/1.66 ( ( r @ X @ Y )
% 2.96/1.66 | ( X = Y )
% 2.96/1.66 | ( r @ Y @ X ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_1__092_060open_062_092_060not_062_Allexord_Ar_Ays_Axs_092_060close_062,axiom,
% 2.96/1.66 ~ ( coindu300403952lexord @ a @ r @ ysa @ xsa ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_2__092_060open_062_092_060not_062_Allexord_Ar_Ays_Axs_092_060close_062,axiom,
% 2.96/1.66 ~ ( coindu300403952lexord @ a @ r @ ys @ xs ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_3_LCons,axiom,
% 2.96/1.66 ( xsa
% 2.96/1.66 = ( coindu1121789889_LCons @ a @ x @ xs2 ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_4_llist_Oinject,axiom,
% 2.96/1.66 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A,Y21: A,Y22: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( ( coindu1121789889_LCons @ A @ X21 @ X22 )
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ Y21 @ Y22 ) )
% 2.96/1.66 = ( ( X21 = Y21 )
% 2.96/1.66 & ( X22 = Y22 ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_5_llexord__refl,axiom,
% 2.96/1.66 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R @ Xs @ Xs ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_6_llexord__LCons__LCons,axiom,
% 2.96/1.66 ! [A: $tType,R: A > A > $o,X: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.96/1.66 = ( ( ( X = Y )
% 2.96/1.66 & ( coindu300403952lexord @ A @ R @ Xs @ Ys ) )
% 2.96/1.66 | ( R @ X @ Y ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_7_llexord__trans,axiom,
% 2.96/1.66 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 2.96/1.66 => ( ( coindu300403952lexord @ A @ R @ Ys @ Zs )
% 2.96/1.66 => ( ! [A2: A,B2: A,C2: A] :
% 2.96/1.66 ( ( R @ A2 @ B2 )
% 2.96/1.66 => ( ( R @ B2 @ C2 )
% 2.96/1.66 => ( R @ A2 @ C2 ) ) )
% 2.96/1.66 => ( coindu300403952lexord @ A @ R @ Xs @ Zs ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_8_llexord__antisym,axiom,
% 2.96/1.66 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 2.96/1.66 => ( ( coindu300403952lexord @ A @ R @ Ys @ Xs )
% 2.96/1.66 => ( ! [A2: A,B2: A] :
% 2.96/1.66 ( ( R @ A2 @ B2 )
% 2.96/1.66 => ~ ( R @ B2 @ A2 ) )
% 2.96/1.66 => ( Xs = Ys ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_9_llexord__LCons__left,axiom,
% 2.96/1.66 ! [A: $tType,R: A > A > $o,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ Ys )
% 2.96/1.66 = ( ? [Y2: A,Ys2: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( Ys
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ Y2 @ Ys2 ) )
% 2.96/1.66 & ( ( ( X = Y2 )
% 2.96/1.66 & ( coindu300403952lexord @ A @ R @ Xs @ Ys2 ) )
% 2.96/1.66 | ( R @ X @ Y2 ) ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_10_llexord__LCons__eq,axiom,
% 2.96/1.66 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 2.96/1.66 ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 2.96/1.66 => ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_11_llexord__LCons__less,axiom,
% 2.96/1.66 ! [A: $tType,R: A > A > $o,X: A,Y: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( R @ X @ Y )
% 2.96/1.66 => ( coindu300403952lexord @ A @ R @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_12_llexord_I2_J,axiom,
% 2.96/1.66 ~ ( coindu335574135_lnull @ a @ xsa ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_13_llexord_I1_J,axiom,
% 2.96/1.66 ~ ( coindu300403952lexord @ a @ r @ ysa @ xsa ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_14_lmember__code_I2_J,axiom,
% 2.96/1.66 ! [A: $tType,X: A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu567634248member @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.96/1.66 = ( ( X = Y )
% 2.96/1.66 | ( coindu567634248member @ A @ X @ Ys ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_15_lstrict__prefix__code_I4_J,axiom,
% 2.96/1.66 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B,Y: B,Ys: coindu1593790203_llist @ B] :
% 2.96/1.66 ( ( coindu574146665prefix @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) @ ( coindu1121789889_LCons @ B @ Y @ Ys ) )
% 2.96/1.66 = ( ( X = Y )
% 2.96/1.66 & ( coindu574146665prefix @ B @ Xs @ Ys ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_16_llexord_Ocases,axiom,
% 2.96/1.66 ! [A: $tType,R: A > A > $o,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu300403952lexord @ A @ R @ A1 @ A22 )
% 2.96/1.66 => ( ! [Xs2: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X2: A] :
% 2.96/1.66 ( ( A1
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 2.96/1.66 => ( ( A22
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X2 @ Ys3 ) )
% 2.96/1.66 => ~ ( coindu300403952lexord @ A @ R @ Xs2 @ Ys3 ) ) )
% 2.96/1.66 => ( ! [X2: A] :
% 2.96/1.66 ( ? [Xs2: coindu1593790203_llist @ A] :
% 2.96/1.66 ( A1
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 2.96/1.66 => ! [Y3: A] :
% 2.96/1.66 ( ? [Ys3: coindu1593790203_llist @ A] :
% 2.96/1.66 ( A22
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ Y3 @ Ys3 ) )
% 2.96/1.66 => ~ ( R @ X2 @ Y3 ) ) )
% 2.96/1.66 => ~ ( ( A1
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 => ! [Ys3: coindu1593790203_llist @ A] : ( A22 != Ys3 ) ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_17_llexord_Osimps,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ( ( coindu300403952lexord @ A )
% 2.96/1.66 = ( ^ [R2: A > A > $o,A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ? [Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,X3: A] :
% 2.96/1.66 ( ( A12
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 2.96/1.66 & ( A23
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X3 @ Ys4 ) )
% 2.96/1.66 & ( coindu300403952lexord @ A @ R2 @ Xs3 @ Ys4 ) )
% 2.96/1.66 | ? [X3: A,Y2: A,Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( A12
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 2.96/1.66 & ( A23
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ Y2 @ Ys4 ) )
% 2.96/1.66 & ( R2 @ X3 @ Y2 ) )
% 2.96/1.66 | ? [Ys4: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( A12
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 & ( A23 = Ys4 ) ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_18_llexord_Ocoinduct,axiom,
% 2.96/1.66 ! [A: $tType,X4: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A,R: A > A > $o] :
% 2.96/1.66 ( ( X4 @ X @ Xa )
% 2.96/1.66 => ( ! [X2: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( X4 @ X2 @ Xa2 )
% 2.96/1.66 => ( ? [Xs4: coindu1593790203_llist @ A,Ys5: coindu1593790203_llist @ A,Xb: A] :
% 2.96/1.66 ( ( X2
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ Xb @ Xs4 ) )
% 2.96/1.66 & ( Xa2
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ Xb @ Ys5 ) )
% 2.96/1.66 & ( ( X4 @ Xs4 @ Ys5 )
% 2.96/1.66 | ( coindu300403952lexord @ A @ R @ Xs4 @ Ys5 ) ) )
% 2.96/1.66 | ? [Xb: A,Y4: A,Xs4: coindu1593790203_llist @ A,Ys5: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( X2
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ Xb @ Xs4 ) )
% 2.96/1.66 & ( Xa2
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ Y4 @ Ys5 ) )
% 2.96/1.66 & ( R @ Xb @ Y4 ) )
% 2.96/1.66 | ? [Ys5: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( X2
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 & ( Xa2 = Ys5 ) ) ) )
% 2.96/1.66 => ( coindu300403952lexord @ A @ R @ X @ Xa ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_19_llist_Opred__inject_I2_J,axiom,
% 2.96/1.66 ! [A: $tType,P: A > $o,A3: A,Aa: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu44415597_llist @ A @ P @ ( coindu1121789889_LCons @ A @ A3 @ Aa ) )
% 2.96/1.66 = ( ( P @ A3 )
% 2.96/1.66 & ( coindu44415597_llist @ A @ P @ Aa ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_20_llast__LCons2,axiom,
% 2.96/1.66 ! [A: $tType,X: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) )
% 2.96/1.66 = ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_21_unfold__llist__eq__LCons,axiom,
% 2.96/1.66 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B3: B,X: A,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ B3 )
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 2.96/1.66 = ( ~ ( IS_LNIL @ B3 )
% 2.96/1.66 & ( X
% 2.96/1.66 = ( LHD @ B3 ) )
% 2.96/1.66 & ( Xs
% 2.96/1.66 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B3 ) ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_22_lsetp_Ointros_I2_J,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A,X5: A] :
% 2.96/1.66 ( ( coindu1055736764_lsetp @ A @ Xs @ X )
% 2.96/1.66 => ( coindu1055736764_lsetp @ A @ ( coindu1121789889_LCons @ A @ X5 @ Xs ) @ X ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_23_lsetp_Ointros_I1_J,axiom,
% 2.96/1.66 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] : ( coindu1055736764_lsetp @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ X ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_24_llexord__LNil__right,axiom,
% 2.96/1.66 ! [A: $tType,Ys: coindu1593790203_llist @ A,R: A > A > $o,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu335574135_lnull @ A @ Ys )
% 2.96/1.66 => ( ( coindu300403952lexord @ A @ R @ Xs @ Ys )
% 2.96/1.66 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_25_unfold__llist_Odisc__iff_I2_J,axiom,
% 2.96/1.66 ! [B: $tType,A: $tType,P2: A > $o,G21: A > B,G22: A > A,A3: A] :
% 2.96/1.66 ( ( ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A3 ) ) )
% 2.96/1.66 = ( ~ ( P2 @ A3 ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_26_unfold__llist_Odisc__iff_I1_J,axiom,
% 2.96/1.66 ! [B: $tType,A: $tType,P2: A > $o,G21: A > B,G22: A > A,A3: A] :
% 2.96/1.66 ( ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A3 ) )
% 2.96/1.66 = ( P2 @ A3 ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_27_lstrict__prefix__code_I1_J,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ~ ( coindu574146665prefix @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_28_llast__singleton,axiom,
% 2.96/1.66 ! [A: $tType,X: A] :
% 2.96/1.66 ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X @ ( coindu1598213697e_LNil @ A ) ) )
% 2.96/1.66 = X ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_29_lstrict__prefix__code_I2_J,axiom,
% 2.96/1.66 ! [B: $tType,Y: B,Ys: coindu1593790203_llist @ B] : ( coindu574146665prefix @ B @ ( coindu1598213697e_LNil @ B ) @ ( coindu1121789889_LCons @ B @ Y @ Ys ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_30_lstrict__prefix__code_I3_J,axiom,
% 2.96/1.66 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B] :
% 2.96/1.66 ~ ( coindu574146665prefix @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) @ ( coindu1598213697e_LNil @ B ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_31_llist_Odisc_I1_J,axiom,
% 2.96/1.66 ! [A: $tType] : ( coindu335574135_lnull @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_32_llist_OdiscI_I1_J,axiom,
% 2.96/1.66 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( Llist
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 => ( coindu335574135_lnull @ A @ Llist ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_33_lmember__code_I1_J,axiom,
% 2.96/1.66 ! [A: $tType,X: A] :
% 2.96/1.66 ~ ( coindu567634248member @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_34_llist_Ocollapse_I1_J,axiom,
% 2.96/1.66 ! [A: $tType,Llist: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu335574135_lnull @ A @ Llist )
% 2.96/1.66 => ( Llist
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_35_unfold__llist_Octr_I1_J,axiom,
% 2.96/1.66 ! [A: $tType,B: $tType,P2: A > $o,A3: A,G21: A > B,G22: A > A] :
% 2.96/1.66 ( ( P2 @ A3 )
% 2.96/1.66 => ( ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A3 )
% 2.96/1.66 = ( coindu1598213697e_LNil @ B ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_36_llist_Opred__inject_I1_J,axiom,
% 2.96/1.66 ! [A: $tType,P: A > $o] : ( coindu44415597_llist @ A @ P @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_37_unfold__llist_Odisc_I2_J,axiom,
% 2.96/1.66 ! [B: $tType,A: $tType,P2: A > $o,A3: A,G21: A > B,G22: A > A] :
% 2.96/1.66 ( ~ ( P2 @ A3 )
% 2.96/1.66 => ~ ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A3 ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_38_unfold__llist_Odisc_I1_J,axiom,
% 2.96/1.66 ! [B: $tType,A: $tType,P2: A > $o,A3: A,G21: A > B,G22: A > A] :
% 2.96/1.66 ( ( P2 @ A3 )
% 2.96/1.66 => ( coindu335574135_lnull @ B @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A3 ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_39_lzip_Oexhaust,axiom,
% 2.96/1.66 ! [A: $tType,B: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ B] :
% 2.96/1.66 ( ~ ( ( coindu335574135_lnull @ A @ Xs )
% 2.96/1.66 | ( coindu335574135_lnull @ B @ Ys ) )
% 2.96/1.66 => ~ ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.96/1.66 => ( coindu335574135_lnull @ B @ Ys ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_40_lappend_Oexhaust,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( ( coindu335574135_lnull @ A @ Xs )
% 2.96/1.66 => ~ ( coindu335574135_lnull @ A @ Ys ) )
% 2.96/1.66 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.96/1.66 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_41_lnull__def,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ( ( coindu335574135_lnull @ A )
% 2.96/1.66 = ( ^ [Llist2: coindu1593790203_llist @ A] :
% 2.96/1.66 ( Llist2
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_42_llist_Opred__True,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ( ( coindu44415597_llist @ A
% 2.96/1.66 @ ^ [Uu: A] : $true )
% 2.96/1.66 = ( ^ [Uu: coindu1593790203_llist @ A] : $true ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_43_mem__Collect__eq,axiom,
% 2.96/1.66 ! [A: $tType,A3: A,P: A > $o] :
% 2.96/1.66 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 2.96/1.66 = ( P @ A3 ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_44_Collect__mem__eq,axiom,
% 2.96/1.66 ! [A: $tType,A4: set @ A] :
% 2.96/1.66 ( ( collect @ A
% 2.96/1.66 @ ^ [X3: A] : ( member @ A @ X3 @ A4 ) )
% 2.96/1.66 = A4 ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_45_Collect__cong,axiom,
% 2.96/1.66 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.96/1.66 ( ! [X2: A] :
% 2.96/1.66 ( ( P @ X2 )
% 2.96/1.66 = ( Q @ X2 ) )
% 2.96/1.66 => ( ( collect @ A @ P )
% 2.96/1.66 = ( collect @ A @ Q ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_46_ext,axiom,
% 2.96/1.66 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.96/1.66 ( ! [X2: A] :
% 2.96/1.66 ( ( F @ X2 )
% 2.96/1.66 = ( G @ X2 ) )
% 2.96/1.66 => ( F = G ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_47_llist__less__induct,axiom,
% 2.96/1.66 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ! [Xs2: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ! [Ys5: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu574146665prefix @ A @ Ys5 @ Xs2 )
% 2.96/1.66 => ( P @ Ys5 ) )
% 2.96/1.66 => ( P @ Xs2 ) )
% 2.96/1.66 => ( P @ Xs ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_48_llast__LCons,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 2.96/1.66 ( ( ( coindu335574135_lnull @ A @ Xs )
% 2.96/1.66 => ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 2.96/1.66 = X ) )
% 2.96/1.66 & ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.96/1.66 => ( ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 2.96/1.66 = ( coindu2000965700_llast @ A @ Xs ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_49_unfold__llist_Ocode,axiom,
% 2.96/1.66 ! [B: $tType,A: $tType] :
% 2.96/1.66 ( ( coindu1599971794_llist @ A @ B )
% 2.96/1.66 = ( ^ [P3: A > $o,G212: A > B,G222: A > A,A5: A] : ( if @ ( coindu1593790203_llist @ B ) @ ( P3 @ A5 ) @ ( coindu1598213697e_LNil @ B ) @ ( coindu1121789889_LCons @ B @ ( G212 @ A5 ) @ ( coindu1599971794_llist @ A @ B @ P3 @ G212 @ G222 @ ( G222 @ A5 ) ) ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_50_not__lnull__conv,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( ~ ( coindu335574135_lnull @ A @ Xs ) )
% 2.96/1.66 = ( ? [X3: A,Xs5: coindu1593790203_llist @ A] :
% 2.96/1.66 ( Xs
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X3 @ Xs5 ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_51_llist_OdiscI_I2_J,axiom,
% 2.96/1.66 ! [A: $tType,Llist: coindu1593790203_llist @ A,X21: A,X22: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( Llist
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X21 @ X22 ) )
% 2.96/1.66 => ~ ( coindu335574135_lnull @ A @ Llist ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_52_llist_Odisc_I2_J,axiom,
% 2.96/1.66 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 2.96/1.66 ~ ( coindu335574135_lnull @ A @ ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_53_neq__LNil__conv,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( Xs
% 2.96/1.66 != ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 = ( ? [X3: A,Xs5: coindu1593790203_llist @ A] :
% 2.96/1.66 ( Xs
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X3 @ Xs5 ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_54_llist_Oexhaust,axiom,
% 2.96/1.66 ! [A: $tType,Y: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( Y
% 2.96/1.66 != ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 => ~ ! [X212: A,X222: coindu1593790203_llist @ A] :
% 2.96/1.66 ( Y
% 2.96/1.66 != ( coindu1121789889_LCons @ A @ X212 @ X222 ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_55_llist_Odistinct_I1_J,axiom,
% 2.96/1.66 ! [A: $tType,X21: A,X22: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1598213697e_LNil @ A )
% 2.96/1.66 != ( coindu1121789889_LCons @ A @ X21 @ X22 ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_56_lnull__llexord,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,R: A > A > $o,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu335574135_lnull @ A @ Xs )
% 2.96/1.66 => ( coindu300403952lexord @ A @ R @ Xs @ Ys ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_57_llexord__LNil,axiom,
% 2.96/1.66 ! [A: $tType,R: A > A > $o,Ys: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_58_unfold__llist_Octr_I2_J,axiom,
% 2.96/1.66 ! [B: $tType,A: $tType,P2: A > $o,A3: A,G21: A > B,G22: A > A] :
% 2.96/1.66 ( ~ ( P2 @ A3 )
% 2.96/1.66 => ( ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ A3 )
% 2.96/1.66 = ( coindu1121789889_LCons @ B @ ( G21 @ A3 ) @ ( coindu1599971794_llist @ A @ B @ P2 @ G21 @ G22 @ ( G22 @ A3 ) ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_59_lsetp_Oinducts,axiom,
% 2.96/1.66 ! [A: $tType,X1: coindu1593790203_llist @ A,X23: A,P: ( coindu1593790203_llist @ A ) > A > $o] :
% 2.96/1.66 ( ( coindu1055736764_lsetp @ A @ X1 @ X23 )
% 2.96/1.66 => ( ! [X2: A,Xs2: coindu1593790203_llist @ A] : ( P @ ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) @ X2 )
% 2.96/1.66 => ( ! [Xs2: coindu1593790203_llist @ A,X2: A,X6: A] :
% 2.96/1.66 ( ( coindu1055736764_lsetp @ A @ Xs2 @ X2 )
% 2.96/1.66 => ( ( P @ Xs2 @ X2 )
% 2.96/1.66 => ( P @ ( coindu1121789889_LCons @ A @ X6 @ Xs2 ) @ X2 ) ) )
% 2.96/1.66 => ( P @ X1 @ X23 ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_60_lsetp_Osimps,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ( ( coindu1055736764_lsetp @ A )
% 2.96/1.66 = ( ^ [A12: coindu1593790203_llist @ A,A23: A] :
% 2.96/1.66 ( ? [X3: A,Xs3: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( A12
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 2.96/1.66 & ( A23 = X3 ) )
% 2.96/1.66 | ? [Xs3: coindu1593790203_llist @ A,X3: A,X7: A] :
% 2.96/1.66 ( ( A12
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X7 @ Xs3 ) )
% 2.96/1.66 & ( A23 = X3 )
% 2.96/1.66 & ( coindu1055736764_lsetp @ A @ Xs3 @ X3 ) ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_61_lsetp_Ocases,axiom,
% 2.96/1.66 ! [A: $tType,A1: coindu1593790203_llist @ A,A22: A] :
% 2.96/1.66 ( ( coindu1055736764_lsetp @ A @ A1 @ A22 )
% 2.96/1.66 => ( ! [X2: A] :
% 2.96/1.66 ( ? [Xs2: coindu1593790203_llist @ A] :
% 2.96/1.66 ( A1
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 2.96/1.66 => ( A22 != X2 ) )
% 2.96/1.66 => ~ ! [Xs2: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ? [X6: A] :
% 2.96/1.66 ( A1
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X6 @ Xs2 ) )
% 2.96/1.66 => ~ ( coindu1055736764_lsetp @ A @ Xs2 @ A22 ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_62_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1571841457prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.96/1.66 = ( ( Xs
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 | ? [Xs5: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( Xs
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ Y @ Xs5 ) )
% 2.96/1.66 & ( coindu1571841457prefix @ A @ Xs5 @ Ys ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_63_llimit__induct,axiom,
% 2.96/1.66 ! [A: $tType,P: ( coindu1593790203_llist @ A ) > $o,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 => ( ! [X2: A,Xs2: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1213758845finite @ A @ Xs2 )
% 2.96/1.66 => ( ( P @ Xs2 )
% 2.96/1.66 => ( P @ ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) ) ) )
% 2.96/1.66 => ( ( ! [Ys5: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu574146665prefix @ A @ Ys5 @ Xs )
% 2.96/1.66 => ( P @ Ys5 ) )
% 2.96/1.66 => ( P @ Xs ) )
% 2.96/1.66 => ( P @ Xs ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_64_lsorted__code_I2_J,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ( ( ord @ A @ ( type2 @ A ) )
% 2.96/1.66 => ! [X: A] : ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_65_gen__lset__code_I1_J,axiom,
% 2.96/1.66 ! [A: $tType,A4: set @ A] :
% 2.96/1.66 ( ( coindu1928975208n_lset @ A @ A4 @ ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 = A4 ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_66_llist_Ocorec__code,axiom,
% 2.96/1.66 ! [A: $tType,C: $tType] :
% 2.96/1.66 ( ( coindu1244876290_llist @ C @ A )
% 2.96/1.66 = ( ^ [P3: C > $o,G212: C > A,Q22: C > $o,G221: C > ( coindu1593790203_llist @ A ),G2222: C > C,A5: C] : ( if @ ( coindu1593790203_llist @ A ) @ ( P3 @ A5 ) @ ( coindu1598213697e_LNil @ A ) @ ( coindu1121789889_LCons @ A @ ( G212 @ A5 ) @ ( if @ ( coindu1593790203_llist @ A ) @ ( Q22 @ A5 ) @ ( G221 @ A5 ) @ ( coindu1244876290_llist @ C @ A @ P3 @ G212 @ Q22 @ G221 @ G2222 @ ( G2222 @ A5 ) ) ) ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_67_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1571841457prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_68_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1571841457prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 = ( Xs
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_69_lprefix__LNil,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 = ( coindu335574135_lnull @ A @ Xs ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_70_ltakeWhile__LCons,axiom,
% 2.96/1.66 ! [A: $tType,P: A > $o,X: A,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( ( P @ X )
% 2.96/1.66 => ( ( coindu721411036eWhile @ A @ P @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X @ ( coindu721411036eWhile @ A @ P @ Xs ) ) ) )
% 2.96/1.66 & ( ~ ( P @ X )
% 2.96/1.66 => ( ( coindu721411036eWhile @ A @ P @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_71_ord_OSingleton,axiom,
% 2.96/1.66 ! [A: $tType,Less_eq: A > A > $o,X: A] : ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_72_llist_Oleq__refl,axiom,
% 2.96/1.66 ! [A: $tType,X: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ X @ X ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_73_lprefix__refl,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ Xs ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_74_ltakeWhile__K__True,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu721411036eWhile @ A
% 2.96/1.66 @ ^ [Uu: A] : $true
% 2.96/1.66 @ Xs )
% 2.96/1.66 = Xs ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_75_LCons__lprefix__LCons,axiom,
% 2.96/1.66 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.96/1.66 = ( ( X = Y )
% 2.96/1.66 & ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_76_lprefix__code_I1_J,axiom,
% 2.96/1.66 ! [A: $tType,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Ys ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_77_lfinite__code_I2_J,axiom,
% 2.96/1.66 ! [B: $tType,X: B,Xs: coindu1593790203_llist @ B] :
% 2.96/1.66 ( ( coindu1213758845finite @ B @ ( coindu1121789889_LCons @ B @ X @ Xs ) )
% 2.96/1.66 = ( coindu1213758845finite @ B @ Xs ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_78_lfinite__LCons,axiom,
% 2.96/1.66 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) )
% 2.96/1.66 = ( coindu1213758845finite @ A @ Xs ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_79_lfinite__code_I1_J,axiom,
% 2.96/1.66 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_80_ltakeWhile__LNil,axiom,
% 2.96/1.66 ! [A: $tType,P: A > $o] :
% 2.96/1.66 ( ( coindu721411036eWhile @ A @ P @ ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_81_lsorted__code_I1_J,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ( ( ord @ A @ ( type2 @ A ) )
% 2.96/1.66 => ( coindu48241764sorted @ A @ ( coindu1598213697e_LNil @ A ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_82_llist_Ocorec__disc__iff_I1_J,axiom,
% 2.96/1.66 ! [A: $tType,C: $tType,P2: C > $o,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C,A3: C] :
% 2.96/1.66 ( ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A3 ) )
% 2.96/1.66 = ( P2 @ A3 ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_83_llist_Ocorec__disc__iff_I2_J,axiom,
% 2.96/1.66 ! [A: $tType,C: $tType,P2: C > $o,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C,A3: C] :
% 2.96/1.66 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A3 ) ) )
% 2.96/1.66 = ( ~ ( P2 @ A3 ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_84_ltakeWhile__K__False,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu721411036eWhile @ A
% 2.96/1.66 @ ^ [Uu: A] : $false
% 2.96/1.66 @ Xs )
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_85_not__lfinite__lprefix__conv__eq,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ~ ( coindu1213758845finite @ A @ Xs )
% 2.96/1.66 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.96/1.66 = ( Xs = Ys ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_86_lsorted__lprefixD,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ( ( ord @ A @ ( type2 @ A ) )
% 2.96/1.66 => ! [Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.96/1.66 => ( ( coindu48241764sorted @ A @ Ys )
% 2.96/1.66 => ( coindu48241764sorted @ A @ Xs ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_87_Coinductive__List__Mirabelle__kmikjhschf_Olprefix__nitpick__simps,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A )
% 2.96/1.66 = ( ^ [Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( ( coindu1213758845finite @ A @ Xs3 )
% 2.96/1.66 => ( coindu1571841457prefix @ A @ Xs3 @ Ys4 ) )
% 2.96/1.66 & ( ~ ( coindu1213758845finite @ A @ Xs3 )
% 2.96/1.66 => ( Xs3 = Ys4 ) ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_88_ord_Olsorted__lprefixD,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Less_eq: A > A > $o] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.96/1.66 => ( ( coindu543932918sorted @ A @ Less_eq @ Ys )
% 2.96/1.66 => ( coindu543932918sorted @ A @ Less_eq @ Xs ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_89_lprefix__down__linear,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ Xs @ Zs )
% 2.96/1.66 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 2.96/1.66 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.96/1.66 | ( coindu1696667936prefix @ A @ Ys @ Xs ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_90_lprefix__ltakeWhile,axiom,
% 2.96/1.66 ! [A: $tType,P: A > $o,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu721411036eWhile @ A @ P @ Xs ) @ Xs ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_91_Coinductive__List__Mirabelle__kmikjhschf_Ofinite__lprefix__def,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ( ( coindu1571841457prefix @ A )
% 2.96/1.66 = ( coindu1696667936prefix @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_92_llist_Oleq__antisym,axiom,
% 2.96/1.66 ! [A: $tType,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ X @ Y )
% 2.96/1.66 => ( ( coindu1696667936prefix @ A @ Y @ X )
% 2.96/1.66 => ( X = Y ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_93_lprefix__lfiniteD,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.96/1.66 => ( ( coindu1213758845finite @ A @ Ys )
% 2.96/1.66 => ( coindu1213758845finite @ A @ Xs ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_94_lprefix__antisym,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.96/1.66 => ( ( coindu1696667936prefix @ A @ Ys @ Xs )
% 2.96/1.66 => ( Xs = Ys ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_95_llist_Oleq__trans,axiom,
% 2.96/1.66 ! [A: $tType,X: coindu1593790203_llist @ A,Y: coindu1593790203_llist @ A,Z: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ X @ Y )
% 2.96/1.66 => ( ( coindu1696667936prefix @ A @ Y @ Z )
% 2.96/1.66 => ( coindu1696667936prefix @ A @ X @ Z ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_96_lprefix__trans,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.96/1.66 => ( ( coindu1696667936prefix @ A @ Ys @ Zs )
% 2.96/1.66 => ( coindu1696667936prefix @ A @ Xs @ Zs ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_97_lfinite__LConsI,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,X: A] :
% 2.96/1.66 ( ( coindu1213758845finite @ A @ Xs )
% 2.96/1.66 => ( coindu1213758845finite @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_98_lnull__imp__lfinite,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu335574135_lnull @ A @ Xs )
% 2.96/1.66 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_99_lfinite__LNil,axiom,
% 2.96/1.66 ! [A: $tType] : ( coindu1213758845finite @ A @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_100_Le__LCons,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X: A] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.96/1.66 => ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1121789889_LCons @ A @ X @ Ys ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_101_LCons__lprefix__conv,axiom,
% 2.96/1.66 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ Ys )
% 2.96/1.66 = ( ? [Ys2: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( Ys
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X @ Ys2 ) )
% 2.96/1.66 & ( coindu1696667936prefix @ A @ Xs @ Ys2 ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_102_lprefix__not__lnullD,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.96/1.66 => ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.96/1.66 => ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_103_lprefix__lnullD,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.96/1.66 => ( ( coindu335574135_lnull @ A @ Ys )
% 2.96/1.66 => ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_104_lprefix__lnull,axiom,
% 2.96/1.66 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu335574135_lnull @ A @ Ys )
% 2.96/1.66 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.96/1.66 = ( coindu335574135_lnull @ A @ Xs ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_105_lnull__lprefix,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu335574135_lnull @ A @ Xs )
% 2.96/1.66 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_106_LNil__lprefix,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ ( coindu1598213697e_LNil @ A ) @ Xs ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_107_lprefix__imp__llexord,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,R: A > A > $o] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.96/1.66 => ( coindu300403952lexord @ A @ R @ Xs @ Ys ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_108_lstrict__prefix__lfinite1,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu574146665prefix @ A @ Xs @ Ys )
% 2.96/1.66 => ( coindu1213758845finite @ A @ Xs ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_109_LNil,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ( ( ord @ A @ ( type2 @ A ) )
% 2.96/1.66 => ( coindu48241764sorted @ A @ ( coindu1598213697e_LNil @ A ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_110_ord_OLCons__LCons,axiom,
% 2.96/1.66 ! [A: $tType,Less_eq: A > A > $o,X: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( Less_eq @ X @ Y )
% 2.96/1.66 => ( ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ Y @ Xs ) )
% 2.96/1.66 => ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_111_ord_Olsorted__LCons__LCons,axiom,
% 2.96/1.66 ! [A: $tType,Less_eq: A > A > $o,X: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) )
% 2.96/1.66 = ( ( Less_eq @ X @ Y )
% 2.96/1.66 & ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_112_ord_OLNil,axiom,
% 2.96/1.66 ! [A: $tType,Less_eq: A > A > $o] : ( coindu543932918sorted @ A @ Less_eq @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_113_ord_Olsorted__code_I1_J,axiom,
% 2.96/1.66 ! [A: $tType,Less_eq: A > A > $o] : ( coindu543932918sorted @ A @ Less_eq @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_114_lstrict__prefix__def,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ( ( coindu574146665prefix @ A )
% 2.96/1.66 = ( ^ [Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ Xs3 @ Ys4 )
% 2.96/1.66 & ( Xs3 != Ys4 ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_115_llist_Ocorec_I2_J,axiom,
% 2.96/1.66 ! [A: $tType,C: $tType,P2: C > $o,A3: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 2.96/1.66 ( ~ ( P2 @ A3 )
% 2.96/1.66 => ( ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A3 )
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ ( G21 @ A3 ) @ ( if @ ( coindu1593790203_llist @ A ) @ ( Q222 @ A3 ) @ ( G2212 @ A3 ) @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ ( G2223 @ A3 ) ) ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_116_llist_Ocorec__disc_I1_J,axiom,
% 2.96/1.66 ! [A: $tType,C: $tType,P2: C > $o,A3: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 2.96/1.66 ( ( P2 @ A3 )
% 2.96/1.66 => ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A3 ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_117_llist_Ocorec__disc_I2_J,axiom,
% 2.96/1.66 ! [A: $tType,C: $tType,P2: C > $o,A3: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 2.96/1.66 ( ~ ( P2 @ A3 )
% 2.96/1.66 => ~ ( coindu335574135_lnull @ A @ ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A3 ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_118_llist_Ocorec_I1_J,axiom,
% 2.96/1.66 ! [C: $tType,A: $tType,P2: C > $o,A3: C,G21: C > A,Q222: C > $o,G2212: C > ( coindu1593790203_llist @ A ),G2223: C > C] :
% 2.96/1.66 ( ( P2 @ A3 )
% 2.96/1.66 => ( ( coindu1244876290_llist @ C @ A @ P2 @ G21 @ Q222 @ G2212 @ G2223 @ A3 )
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_119_llexord__empty,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu300403952lexord @ A
% 2.96/1.66 @ ^ [X3: A,Y2: A] : $false
% 2.96/1.66 @ Xs
% 2.96/1.66 @ Ys )
% 2.96/1.66 = ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_120_lfinite_Ocases,axiom,
% 2.96/1.66 ! [A: $tType,A3: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1213758845finite @ A @ A3 )
% 2.96/1.66 => ( ( A3
% 2.96/1.66 != ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 => ~ ! [Xs2: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ? [X2: A] :
% 2.96/1.66 ( A3
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 2.96/1.66 => ~ ( coindu1213758845finite @ A @ Xs2 ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_121_lfinite_Osimps,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ( ( coindu1213758845finite @ A )
% 2.96/1.66 = ( ^ [A5: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( A5
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 | ? [Xs3: coindu1593790203_llist @ A,X3: A] :
% 2.96/1.66 ( ( A5
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 2.96/1.66 & ( coindu1213758845finite @ A @ Xs3 ) ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_122_lfinite_Oinducts,axiom,
% 2.96/1.66 ! [A: $tType,X: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 2.96/1.66 ( ( coindu1213758845finite @ A @ X )
% 2.96/1.66 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 => ( ! [Xs2: coindu1593790203_llist @ A,X2: A] :
% 2.96/1.66 ( ( coindu1213758845finite @ A @ Xs2 )
% 2.96/1.66 => ( ( P @ Xs2 )
% 2.96/1.66 => ( P @ ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) ) ) )
% 2.96/1.66 => ( P @ X ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_123_lprefix__code_I2_J,axiom,
% 2.96/1.66 ! [A: $tType,X: A,Xs: coindu1593790203_llist @ A] :
% 2.96/1.66 ~ ( coindu1696667936prefix @ A @ ( coindu1121789889_LCons @ A @ X @ Xs ) @ ( coindu1598213697e_LNil @ A ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_124_lprefix_Ocases,axiom,
% 2.96/1.66 ! [A: $tType,A1: coindu1593790203_llist @ A,A22: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ A1 @ A22 )
% 2.96/1.66 => ( ( ( A1
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 => ! [Xs2: coindu1593790203_llist @ A] : ( A22 != Xs2 ) )
% 2.96/1.66 => ~ ! [Xs2: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A,X2: A] :
% 2.96/1.66 ( ( A1
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X2 @ Xs2 ) )
% 2.96/1.66 => ( ( A22
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X2 @ Ys3 ) )
% 2.96/1.66 => ~ ( coindu1696667936prefix @ A @ Xs2 @ Ys3 ) ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_125_lprefix_Osimps,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A )
% 2.96/1.66 = ( ^ [A12: coindu1593790203_llist @ A,A23: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ? [Xs3: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( A12
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 & ( A23 = Xs3 ) )
% 2.96/1.66 | ? [Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A,X3: A] :
% 2.96/1.66 ( ( A12
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X3 @ Xs3 ) )
% 2.96/1.66 & ( A23
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X3 @ Ys4 ) )
% 2.96/1.66 & ( coindu1696667936prefix @ A @ Xs3 @ Ys4 ) ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_126_lprefix_Ocoinduct,axiom,
% 2.96/1.66 ! [A: $tType,X4: ( coindu1593790203_llist @ A ) > ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Xa: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( X4 @ X @ Xa )
% 2.96/1.66 => ( ! [X2: coindu1593790203_llist @ A,Xa2: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( X4 @ X2 @ Xa2 )
% 2.96/1.66 => ( ? [Xs4: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( X2
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 & ( Xa2 = Xs4 ) )
% 2.96/1.66 | ? [Xs4: coindu1593790203_llist @ A,Ys5: coindu1593790203_llist @ A,Xb: A] :
% 2.96/1.66 ( ( X2
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ Xb @ Xs4 ) )
% 2.96/1.66 & ( Xa2
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ Xb @ Ys5 ) )
% 2.96/1.66 & ( ( X4 @ Xs4 @ Ys5 )
% 2.96/1.66 | ( coindu1696667936prefix @ A @ Xs4 @ Ys5 ) ) ) ) )
% 2.96/1.66 => ( coindu1696667936prefix @ A @ X @ Xa ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_127_lprefix__LCons__conv,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) )
% 2.96/1.66 = ( ( Xs
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 | ? [Xs5: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( Xs
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ Y @ Xs5 ) )
% 2.96/1.66 & ( coindu1696667936prefix @ A @ Xs5 @ Ys ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_128_corec__llist__never__stop,axiom,
% 2.96/1.66 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,MORE: B > ( coindu1593790203_llist @ A ),LTL: B > B,X: B] :
% 2.96/1.66 ( ( coindu1244876290_llist @ B @ A @ IS_LNIL @ LHD
% 2.96/1.66 @ ^ [Uu: B] : $false
% 2.96/1.66 @ MORE
% 2.96/1.66 @ LTL
% 2.96/1.66 @ X )
% 2.96/1.66 = ( coindu1599971794_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ X ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_129_Singleton,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ( ( ord @ A @ ( type2 @ A ) )
% 2.96/1.66 => ! [X: A] : ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_130_ord_Olsorted__code_I2_J,axiom,
% 2.96/1.66 ! [A: $tType,Less_eq: A > A > $o,X: A] : ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ X @ ( coindu1598213697e_LNil @ A ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_131_ord_Olsorted_Ocases,axiom,
% 2.96/1.66 ! [A: $tType,Less_eq: A > A > $o,A3: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu543932918sorted @ A @ Less_eq @ A3 )
% 2.96/1.66 => ( ( A3
% 2.96/1.66 != ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 => ( ! [X2: A] :
% 2.96/1.66 ( A3
% 2.96/1.66 != ( coindu1121789889_LCons @ A @ X2 @ ( coindu1598213697e_LNil @ A ) ) )
% 2.96/1.66 => ~ ! [X2: A,Y3: A,Xs2: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( A3
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X2 @ ( coindu1121789889_LCons @ A @ Y3 @ Xs2 ) ) )
% 2.96/1.66 => ( ( Less_eq @ X2 @ Y3 )
% 2.96/1.66 => ~ ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ Y3 @ Xs2 ) ) ) ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_132_ord_Olsorted_Osimps,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ( ( coindu543932918sorted @ A )
% 2.96/1.66 = ( ^ [Less_eq2: A > A > $o,A5: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( A5
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 | ? [X3: A] :
% 2.96/1.66 ( A5
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X3 @ ( coindu1598213697e_LNil @ A ) ) )
% 2.96/1.66 | ? [X3: A,Y2: A,Xs3: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( A5
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ X3 @ ( coindu1121789889_LCons @ A @ Y2 @ Xs3 ) ) )
% 2.96/1.66 & ( Less_eq2 @ X3 @ Y2 )
% 2.96/1.66 & ( coindu543932918sorted @ A @ Less_eq2 @ ( coindu1121789889_LCons @ A @ Y2 @ Xs3 ) ) ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_133_ord_Olsorted_Ocoinduct,axiom,
% 2.96/1.66 ! [A: $tType,X4: ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A,Less_eq: A > A > $o] :
% 2.96/1.66 ( ( X4 @ X )
% 2.96/1.66 => ( ! [X2: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( X4 @ X2 )
% 2.96/1.66 => ( ( X2
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 | ? [Xa3: A] :
% 2.96/1.66 ( X2
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ Xa3 @ ( coindu1598213697e_LNil @ A ) ) )
% 2.96/1.66 | ? [Xa3: A,Y4: A,Xs4: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( X2
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ Xa3 @ ( coindu1121789889_LCons @ A @ Y4 @ Xs4 ) ) )
% 2.96/1.66 & ( Less_eq @ Xa3 @ Y4 )
% 2.96/1.66 & ( ( X4 @ ( coindu1121789889_LCons @ A @ Y4 @ Xs4 ) )
% 2.96/1.66 | ( coindu543932918sorted @ A @ Less_eq @ ( coindu1121789889_LCons @ A @ Y4 @ Xs4 ) ) ) ) ) )
% 2.96/1.66 => ( coindu543932918sorted @ A @ Less_eq @ X ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_134_llast__lappend__LCons,axiom,
% 2.96/1.66 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( coindu1213758845finite @ A @ Xs )
% 2.96/1.66 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) )
% 2.96/1.66 = ( coindu2000965700_llast @ A @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_135_lsorted_Ocoinduct,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ( ( ord @ A @ ( type2 @ A ) )
% 2.96/1.66 => ! [X4: ( coindu1593790203_llist @ A ) > $o,X: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( X4 @ X )
% 2.96/1.66 => ( ! [X2: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( X4 @ X2 )
% 2.96/1.66 => ( ( X2
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) )
% 2.96/1.66 | ? [Xa3: A] :
% 2.96/1.66 ( X2
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ Xa3 @ ( coindu1598213697e_LNil @ A ) ) )
% 2.96/1.66 | ? [Xa3: A,Y4: A,Xs4: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( X2
% 2.96/1.66 = ( coindu1121789889_LCons @ A @ Xa3 @ ( coindu1121789889_LCons @ A @ Y4 @ Xs4 ) ) )
% 2.96/1.66 & ( ord_less_eq @ A @ Xa3 @ Y4 )
% 2.96/1.66 & ( ( X4 @ ( coindu1121789889_LCons @ A @ Y4 @ Xs4 ) )
% 2.96/1.66 | ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ Y4 @ Xs4 ) ) ) ) ) )
% 2.96/1.66 => ( coindu48241764sorted @ A @ X ) ) ) ) ).
% 2.96/1.66
% 2.96/1.66 thf(fact_136_lsorted_Osimps,axiom,
% 2.96/1.66 ! [A: $tType] :
% 2.96/1.66 ( ( ord @ A @ ( type2 @ A ) )
% 2.96/1.66 => ( ( coindu48241764sorted @ A )
% 2.96/1.66 = ( ^ [A5: coindu1593790203_llist @ A] :
% 2.96/1.66 ( ( A5
% 2.96/1.66 = ( coindu1598213697e_LNil @ A ) )
% 2.96/1.67 | ? [X3: A] :
% 2.96/1.67 ( A5
% 2.96/1.67 = ( coindu1121789889_LCons @ A @ X3 @ ( coindu1598213697e_LNil @ A ) ) )
% 2.96/1.67 | ? [X3: A,Y2: A,Xs3: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( A5
% 2.96/1.67 = ( coindu1121789889_LCons @ A @ X3 @ ( coindu1121789889_LCons @ A @ Y2 @ Xs3 ) ) )
% 2.96/1.67 & ( ord_less_eq @ A @ X3 @ Y2 )
% 2.96/1.67 & ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ Y2 @ Xs3 ) ) ) ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_137_lsorted_Ocases,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( ord @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [A3: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu48241764sorted @ A @ A3 )
% 2.96/1.67 => ( ( A3
% 2.96/1.67 != ( coindu1598213697e_LNil @ A ) )
% 2.96/1.67 => ( ! [X2: A] :
% 2.96/1.67 ( A3
% 2.96/1.67 != ( coindu1121789889_LCons @ A @ X2 @ ( coindu1598213697e_LNil @ A ) ) )
% 2.96/1.67 => ~ ! [X2: A,Y3: A,Xs2: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( A3
% 2.96/1.67 = ( coindu1121789889_LCons @ A @ X2 @ ( coindu1121789889_LCons @ A @ Y3 @ Xs2 ) ) )
% 2.96/1.67 => ( ( ord_less_eq @ A @ X2 @ Y3 )
% 2.96/1.67 => ~ ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ Y3 @ Xs2 ) ) ) ) ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_138_lstrict__prefix__lappend__conv,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu574146665prefix @ A @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.96/1.67 = ( ( coindu1213758845finite @ A @ Xs )
% 2.96/1.67 & ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_139_lprefixI,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,X4: set @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) )] :
% 2.96/1.67 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs @ Ys ) @ X4 )
% 2.96/1.67 => ( ! [Xs2: coindu1593790203_llist @ A,Ys3: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs2 @ Ys3 ) @ X4 )
% 2.96/1.67 => ( ( coindu335574135_lnull @ A @ Xs2 )
% 2.96/1.67 | ? [X8: A,Xs6: coindu1593790203_llist @ A,Ys6: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( Xs2
% 2.96/1.67 = ( coindu1121789889_LCons @ A @ X8 @ Xs6 ) )
% 2.96/1.67 & ( Ys3
% 2.96/1.67 = ( coindu1121789889_LCons @ A @ X8 @ Ys6 ) )
% 2.96/1.67 & ( ( member @ ( product_prod @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) ) @ ( product_Pair @ ( coindu1593790203_llist @ A ) @ ( coindu1593790203_llist @ A ) @ Xs6 @ Ys6 ) @ X4 )
% 2.96/1.67 | ( coindu1696667936prefix @ A @ Xs6 @ Ys6 ) ) ) ) )
% 2.96/1.67 => ( coindu1696667936prefix @ A @ Xs @ Ys ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_140_lappend__code_I2_J,axiom,
% 2.96/1.67 ! [A: $tType,Xa: A,X: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu268472904append @ A @ ( coindu1121789889_LCons @ A @ Xa @ X ) @ Ys )
% 2.96/1.67 = ( coindu1121789889_LCons @ A @ Xa @ ( coindu268472904append @ A @ X @ Ys ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_141_lappend_Odisc__iff_I2_J,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) )
% 2.96/1.67 = ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.96/1.67 | ~ ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_142_lnull__lappend,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.96/1.67 = ( ( coindu335574135_lnull @ A @ Xs )
% 2.96/1.67 & ( coindu335574135_lnull @ A @ Ys ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_143_lappend__code_I1_J,axiom,
% 2.96/1.67 ! [A: $tType,Ys: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ Ys )
% 2.96/1.67 = Ys ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_144_lappend__LNil2,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu268472904append @ A @ Xs @ ( coindu1598213697e_LNil @ A ) )
% 2.96/1.67 = Xs ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_145_lfinite__lappend,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu1213758845finite @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.96/1.67 = ( ( coindu1213758845finite @ A @ Xs )
% 2.96/1.67 & ( coindu1213758845finite @ A @ Ys ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_146_lsorted__LCons__LCons,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( ord @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [X: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) )
% 2.96/1.67 = ( ( ord_less_eq @ A @ X @ Y )
% 2.96/1.67 & ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_147_lprefix__lappend__same,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ ( coindu268472904append @ A @ Xs @ Zs ) )
% 2.96/1.67 = ( ( coindu1213758845finite @ A @ Xs )
% 2.96/1.67 => ( coindu1696667936prefix @ A @ Ys @ Zs ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_148_lappend__assoc,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 2.96/1.67 = ( coindu268472904append @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_149_wlog__linorder__le,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( linorder @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [P: A > A > $o,B3: A,A3: A] :
% 2.96/1.67 ( ! [A2: A,B2: A] :
% 2.96/1.67 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.96/1.67 => ( P @ A2 @ B2 ) )
% 2.96/1.67 => ( ( ( P @ B3 @ A3 )
% 2.96/1.67 => ( P @ A3 @ B3 ) )
% 2.96/1.67 => ( P @ A3 @ B3 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_150_lprefix__lappend,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( coindu1696667936prefix @ A @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_151_lappend__lprefixE,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Xs @ Ys ) @ Zs )
% 2.96/1.67 => ~ ! [Zs2: coindu1593790203_llist @ A] :
% 2.96/1.67 ( Zs
% 2.96/1.67 != ( coindu268472904append @ A @ Xs @ Zs2 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_152_lprefix__lappendD,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu1696667936prefix @ A @ Xs @ ( coindu268472904append @ A @ Ys @ Zs ) )
% 2.96/1.67 => ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.96/1.67 | ( coindu1696667936prefix @ A @ Ys @ Xs ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_153_lprefix__conv__lappend,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( coindu1696667936prefix @ A )
% 2.96/1.67 = ( ^ [Xs3: coindu1593790203_llist @ A,Ys4: coindu1593790203_llist @ A] :
% 2.96/1.67 ? [Zs3: coindu1593790203_llist @ A] :
% 2.96/1.67 ( Ys4
% 2.96/1.67 = ( coindu268472904append @ A @ Xs3 @ Zs3 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_154_lprefix__lappend__sameI,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu1696667936prefix @ A @ Xs @ Ys )
% 2.96/1.67 => ( coindu1696667936prefix @ A @ ( coindu268472904append @ A @ Zs @ Xs ) @ ( coindu268472904append @ A @ Zs @ Ys ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_155_lappend_Odisc_I2_J,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( ~ ( coindu335574135_lnull @ A @ Xs )
% 2.96/1.67 | ~ ( coindu335574135_lnull @ A @ Ys ) )
% 2.96/1.67 => ~ ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_156_lappend_Odisc_I1_J,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu335574135_lnull @ A @ Xs )
% 2.96/1.67 => ( ( coindu335574135_lnull @ A @ Ys )
% 2.96/1.67 => ( coindu335574135_lnull @ A @ ( coindu268472904append @ A @ Xs @ Ys ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_157_lappend__lnull1,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu335574135_lnull @ A @ Xs )
% 2.96/1.67 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.96/1.67 = Ys ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_158_lappend__lnull2,axiom,
% 2.96/1.67 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu335574135_lnull @ A @ Ys )
% 2.96/1.67 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.96/1.67 = Xs ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_159_lappend__LNil__LNil,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( coindu268472904append @ A @ ( coindu1598213697e_LNil @ A ) @ ( coindu1598213697e_LNil @ A ) )
% 2.96/1.67 = ( coindu1598213697e_LNil @ A ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_160_LNil__eq__lappend__iff,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( ( coindu1598213697e_LNil @ A )
% 2.96/1.67 = ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.96/1.67 = ( ( Xs
% 2.96/1.67 = ( coindu1598213697e_LNil @ A ) )
% 2.96/1.67 & ( Ys
% 2.96/1.67 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_161_lappend__eq__LNil__iff,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.96/1.67 = ( coindu1598213697e_LNil @ A ) )
% 2.96/1.67 = ( ( Xs
% 2.96/1.67 = ( coindu1598213697e_LNil @ A ) )
% 2.96/1.67 & ( Ys
% 2.96/1.67 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_162_lappend__inf,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ~ ( coindu1213758845finite @ A @ Xs )
% 2.96/1.67 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.96/1.67 = Xs ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_163_llexord__lappend__leftI,axiom,
% 2.96/1.67 ! [A: $tType,R: A > A > $o,Ys: coindu1593790203_llist @ A,Zs: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu300403952lexord @ A @ R @ Ys @ Zs )
% 2.96/1.67 => ( coindu300403952lexord @ A @ R @ ( coindu268472904append @ A @ Xs @ Ys ) @ ( coindu268472904append @ A @ Xs @ Zs ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_164_llexord__append__right,axiom,
% 2.96/1.67 ! [A: $tType,R: A > A > $o,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] : ( coindu300403952lexord @ A @ R @ Xs @ ( coindu268472904append @ A @ Xs @ Ys ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_165_lappend__snocL1__conv__LCons2,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Y: A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu268472904append @ A @ ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ ( coindu1598213697e_LNil @ A ) ) ) @ Ys )
% 2.96/1.67 = ( coindu268472904append @ A @ Xs @ ( coindu1121789889_LCons @ A @ Y @ Ys ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_166_lappend_Octr_I1_J,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,Ys: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu335574135_lnull @ A @ Xs )
% 2.96/1.67 => ( ( coindu335574135_lnull @ A @ Ys )
% 2.96/1.67 => ( ( coindu268472904append @ A @ Xs @ Ys )
% 2.96/1.67 = ( coindu1598213697e_LNil @ A ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_167_LCons__LCons,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( ord @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [X: A,Y: A,Xs: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( ord_less_eq @ A @ X @ Y )
% 2.96/1.67 => ( ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ Y @ Xs ) )
% 2.96/1.67 => ( coindu48241764sorted @ A @ ( coindu1121789889_LCons @ A @ X @ ( coindu1121789889_LCons @ A @ Y @ Xs ) ) ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_168_lfinite__rev__induct,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A,P: ( coindu1593790203_llist @ A ) > $o] :
% 2.96/1.67 ( ( coindu1213758845finite @ A @ Xs )
% 2.96/1.67 => ( ( P @ ( coindu1598213697e_LNil @ A ) )
% 2.96/1.67 => ( ! [X2: A,Xs2: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( coindu1213758845finite @ A @ Xs2 )
% 2.96/1.67 => ( ( P @ Xs2 )
% 2.96/1.67 => ( P @ ( coindu268472904append @ A @ Xs2 @ ( coindu1121789889_LCons @ A @ X2 @ ( coindu1598213697e_LNil @ A ) ) ) ) ) )
% 2.96/1.67 => ( P @ Xs ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_169_prod_Oinject,axiom,
% 2.96/1.67 ! [A: $tType,B: $tType,X1: A,X23: B,Y1: A,Y23: B] :
% 2.96/1.67 ( ( ( product_Pair @ A @ B @ X1 @ X23 )
% 2.96/1.67 = ( product_Pair @ A @ B @ Y1 @ Y23 ) )
% 2.96/1.67 = ( ( X1 = Y1 )
% 2.96/1.67 & ( X23 = Y23 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_170_old_Oprod_Oinject,axiom,
% 2.96/1.67 ! [A: $tType,B: $tType,A3: A,B3: B,A6: A,B4: B] :
% 2.96/1.67 ( ( ( product_Pair @ A @ B @ A3 @ B3 )
% 2.96/1.67 = ( product_Pair @ A @ B @ A6 @ B4 ) )
% 2.96/1.67 = ( ( A3 = A6 )
% 2.96/1.67 & ( B3 = B4 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_171_order__refl,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( preorder @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_172_pred__subset__eq2,axiom,
% 2.96/1.67 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 2.96/1.67 ( ( ord_less_eq @ ( A > B > $o )
% 2.96/1.67 @ ^ [X3: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y2 ) @ R3 )
% 2.96/1.67 @ ^ [X3: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y2 ) @ S ) )
% 2.96/1.67 = ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R3 @ S ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_173_predicate2I,axiom,
% 2.96/1.67 ! [B: $tType,A: $tType,P: A > B > $o,Q: A > B > $o] :
% 2.96/1.67 ( ! [X2: A,Y3: B] :
% 2.96/1.67 ( ( P @ X2 @ Y3 )
% 2.96/1.67 => ( Q @ X2 @ Y3 ) )
% 2.96/1.67 => ( ord_less_eq @ ( A > B > $o ) @ P @ Q ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_174_predicate2D,axiom,
% 2.96/1.67 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,X: A,Y: B] :
% 2.96/1.67 ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 2.96/1.67 => ( ( P @ X @ Y )
% 2.96/1.67 => ( Q @ X @ Y ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_175_rev__predicate2D,axiom,
% 2.96/1.67 ! [A: $tType,B: $tType,P: A > B > $o,X: A,Y: B,Q: A > B > $o] :
% 2.96/1.67 ( ( P @ X @ Y )
% 2.96/1.67 => ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 2.96/1.67 => ( Q @ X @ Y ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_176_pred__subset__eq,axiom,
% 2.96/1.67 ! [A: $tType,R3: set @ A,S: set @ A] :
% 2.96/1.67 ( ( ord_less_eq @ ( A > $o )
% 2.96/1.67 @ ^ [X3: A] : ( member @ A @ X3 @ R3 )
% 2.96/1.67 @ ^ [X3: A] : ( member @ A @ X3 @ S ) )
% 2.96/1.67 = ( ord_less_eq @ ( set @ A ) @ R3 @ S ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_177_dual__order_Oantisym,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( order @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [B3: A,A3: A] :
% 2.96/1.67 ( ( ord_less_eq @ A @ B3 @ A3 )
% 2.96/1.67 => ( ( ord_less_eq @ A @ A3 @ B3 )
% 2.96/1.67 => ( A3 = B3 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_178_dual__order_Otrans,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( order @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [B3: A,A3: A,C3: A] :
% 2.96/1.67 ( ( ord_less_eq @ A @ B3 @ A3 )
% 2.96/1.67 => ( ( ord_less_eq @ A @ C3 @ B3 )
% 2.96/1.67 => ( ord_less_eq @ A @ C3 @ A3 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_179_linorder__wlog,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( linorder @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [P: A > A > $o,A3: A,B3: A] :
% 2.96/1.67 ( ! [A2: A,B2: A] :
% 2.96/1.67 ( ( ord_less_eq @ A @ A2 @ B2 )
% 2.96/1.67 => ( P @ A2 @ B2 ) )
% 2.96/1.67 => ( ! [A2: A,B2: A] :
% 2.96/1.67 ( ( P @ B2 @ A2 )
% 2.96/1.67 => ( P @ A2 @ B2 ) )
% 2.96/1.67 => ( P @ A3 @ B3 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_180_dual__order_Orefl,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( order @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_181_order__trans,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( preorder @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [X: A,Y: A,Z: A] :
% 2.96/1.67 ( ( ord_less_eq @ A @ X @ Y )
% 2.96/1.67 => ( ( ord_less_eq @ A @ Y @ Z )
% 2.96/1.67 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_182_order__class_Oorder_Oantisym,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( order @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [A3: A,B3: A] :
% 2.96/1.67 ( ( ord_less_eq @ A @ A3 @ B3 )
% 2.96/1.67 => ( ( ord_less_eq @ A @ B3 @ A3 )
% 2.96/1.67 => ( A3 = B3 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_183_ord__le__eq__trans,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( ord @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [A3: A,B3: A,C3: A] :
% 2.96/1.67 ( ( ord_less_eq @ A @ A3 @ B3 )
% 2.96/1.67 => ( ( B3 = C3 )
% 2.96/1.67 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_184_ord__eq__le__trans,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( ord @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [A3: A,B3: A,C3: A] :
% 2.96/1.67 ( ( A3 = B3 )
% 2.96/1.67 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 2.96/1.67 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_185_antisym__conv,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( order @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [Y: A,X: A] :
% 2.96/1.67 ( ( ord_less_eq @ A @ Y @ X )
% 2.96/1.67 => ( ( ord_less_eq @ A @ X @ Y )
% 2.96/1.67 = ( X = Y ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_186_le__cases3,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( linorder @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [X: A,Y: A,Z: A] :
% 2.96/1.67 ( ( ( ord_less_eq @ A @ X @ Y )
% 2.96/1.67 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 2.96/1.67 => ( ( ( ord_less_eq @ A @ Y @ X )
% 2.96/1.67 => ~ ( ord_less_eq @ A @ X @ Z ) )
% 2.96/1.67 => ( ( ( ord_less_eq @ A @ X @ Z )
% 2.96/1.67 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 2.96/1.67 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 2.96/1.67 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 2.96/1.67 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 2.96/1.67 => ~ ( ord_less_eq @ A @ Z @ X ) )
% 2.96/1.67 => ~ ( ( ord_less_eq @ A @ Z @ X )
% 2.96/1.67 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_187_order_Otrans,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( order @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [A3: A,B3: A,C3: A] :
% 2.96/1.67 ( ( ord_less_eq @ A @ A3 @ B3 )
% 2.96/1.67 => ( ( ord_less_eq @ A @ B3 @ C3 )
% 2.96/1.67 => ( ord_less_eq @ A @ A3 @ C3 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_188_le__cases,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( linorder @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [X: A,Y: A] :
% 2.96/1.67 ( ~ ( ord_less_eq @ A @ X @ Y )
% 2.96/1.67 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_189_eq__refl,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( preorder @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [X: A,Y: A] :
% 2.96/1.67 ( ( X = Y )
% 2.96/1.67 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_190_linorder__class_Olinear,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( linorder @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [X: A,Y: A] :
% 2.96/1.67 ( ( ord_less_eq @ A @ X @ Y )
% 2.96/1.67 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_191_antisym,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( order @ A @ ( type2 @ A ) )
% 2.96/1.67 => ! [X: A,Y: A] :
% 2.96/1.67 ( ( ord_less_eq @ A @ X @ Y )
% 2.96/1.67 => ( ( ord_less_eq @ A @ Y @ X )
% 2.96/1.67 => ( X = Y ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_192_eq__iff,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( order @ A @ ( type2 @ A ) )
% 2.96/1.67 => ( ( ^ [Y5: A,Z2: A] : ( Y5 = Z2 ) )
% 2.96/1.67 = ( ^ [X3: A,Y2: A] :
% 2.96/1.67 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 2.96/1.67 & ( ord_less_eq @ A @ Y2 @ X3 ) ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_193_ord__le__eq__subst,axiom,
% 2.96/1.67 ! [A: $tType,B: $tType] :
% 2.96/1.67 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.96/1.67 & ( ord @ A @ ( type2 @ A ) ) )
% 2.96/1.67 => ! [A3: A,B3: A,F: A > B,C3: B] :
% 2.96/1.67 ( ( ord_less_eq @ A @ A3 @ B3 )
% 2.96/1.67 => ( ( ( F @ B3 )
% 2.96/1.67 = C3 )
% 2.96/1.67 => ( ! [X2: A,Y3: A] :
% 2.96/1.67 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 2.96/1.67 => ( ord_less_eq @ B @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 2.96/1.67 => ( ord_less_eq @ B @ ( F @ A3 ) @ C3 ) ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_194_ord__eq__le__subst,axiom,
% 2.96/1.67 ! [A: $tType,B: $tType] :
% 2.96/1.67 ( ( ( ord @ B @ ( type2 @ B ) )
% 2.96/1.67 & ( ord @ A @ ( type2 @ A ) ) )
% 2.96/1.67 => ! [A3: A,F: B > A,B3: B,C3: B] :
% 2.96/1.67 ( ( A3
% 2.96/1.67 = ( F @ B3 ) )
% 2.96/1.67 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 2.96/1.67 => ( ! [X2: B,Y3: B] :
% 2.96/1.67 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 2.96/1.67 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 2.96/1.67 => ( ord_less_eq @ A @ A3 @ ( F @ C3 ) ) ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_195_order__subst2,axiom,
% 2.96/1.67 ! [A: $tType,C: $tType] :
% 2.96/1.67 ( ( ( order @ C @ ( type2 @ C ) )
% 2.96/1.67 & ( order @ A @ ( type2 @ A ) ) )
% 2.96/1.67 => ! [A3: A,B3: A,F: A > C,C3: C] :
% 2.96/1.67 ( ( ord_less_eq @ A @ A3 @ B3 )
% 2.96/1.67 => ( ( ord_less_eq @ C @ ( F @ B3 ) @ C3 )
% 2.96/1.67 => ( ! [X2: A,Y3: A] :
% 2.96/1.67 ( ( ord_less_eq @ A @ X2 @ Y3 )
% 2.96/1.67 => ( ord_less_eq @ C @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 2.96/1.67 => ( ord_less_eq @ C @ ( F @ A3 ) @ C3 ) ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_196_order__subst1,axiom,
% 2.96/1.67 ! [A: $tType,B: $tType] :
% 2.96/1.67 ( ( ( order @ B @ ( type2 @ B ) )
% 2.96/1.67 & ( order @ A @ ( type2 @ A ) ) )
% 2.96/1.67 => ! [A3: A,F: B > A,B3: B,C3: B] :
% 2.96/1.67 ( ( ord_less_eq @ A @ A3 @ ( F @ B3 ) )
% 2.96/1.67 => ( ( ord_less_eq @ B @ B3 @ C3 )
% 2.96/1.67 => ( ! [X2: B,Y3: B] :
% 2.96/1.67 ( ( ord_less_eq @ B @ X2 @ Y3 )
% 2.96/1.67 => ( ord_less_eq @ A @ ( F @ X2 ) @ ( F @ Y3 ) ) )
% 2.96/1.67 => ( ord_less_eq @ A @ A3 @ ( F @ C3 ) ) ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_197_le__fun__def,axiom,
% 2.96/1.67 ! [B: $tType,A: $tType] :
% 2.96/1.67 ( ( ord @ B @ ( type2 @ B ) )
% 2.96/1.67 => ( ( ord_less_eq @ ( A > B ) )
% 2.96/1.67 = ( ^ [F2: A > B,G2: A > B] :
% 2.96/1.67 ! [X3: A] : ( ord_less_eq @ B @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_198_le__funI,axiom,
% 2.96/1.67 ! [B: $tType,A: $tType] :
% 2.96/1.67 ( ( ord @ B @ ( type2 @ B ) )
% 2.96/1.67 => ! [F: A > B,G: A > B] :
% 2.96/1.67 ( ! [X2: A] : ( ord_less_eq @ B @ ( F @ X2 ) @ ( G @ X2 ) )
% 2.96/1.67 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_199_le__funE,axiom,
% 2.96/1.67 ! [B: $tType,A: $tType] :
% 2.96/1.67 ( ( ord @ B @ ( type2 @ B ) )
% 2.96/1.67 => ! [F: A > B,G: A > B,X: A] :
% 2.96/1.67 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.96/1.67 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_200_le__funD,axiom,
% 2.96/1.67 ! [B: $tType,A: $tType] :
% 2.96/1.67 ( ( ord @ B @ ( type2 @ B ) )
% 2.96/1.67 => ! [F: A > B,G: A > B,X: A] :
% 2.96/1.67 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.96/1.67 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_201_old_Oprod_Oinducts,axiom,
% 2.96/1.67 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 2.96/1.67 ( ! [A2: A,B2: B] : ( P @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.96/1.67 => ( P @ Prod ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_202_old_Oprod_Oexhaust,axiom,
% 2.96/1.67 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 2.96/1.67 ~ ! [A2: A,B2: B] :
% 2.96/1.67 ( Y
% 2.96/1.67 != ( product_Pair @ A @ B @ A2 @ B2 ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_203_prod__induct7,axiom,
% 2.96/1.67 ! [G3: $tType,F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) )] :
% 2.96/1.67 ( ! [A2: A,B2: B,C2: C,D2: D,E2: E,F4: F3,G4: G3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) @ A2 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) @ B2 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F3 @ G3 ) @ E2 @ ( product_Pair @ F3 @ G3 @ F4 @ G4 ) ) ) ) ) ) )
% 2.96/1.67 => ( P @ X ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_204_prod__induct6,axiom,
% 2.96/1.67 ! [F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 2.96/1.67 ( ! [A2: A,B2: B,C2: C,D2: D,E2: E,F4: F3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A2 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B2 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D2 @ ( product_Pair @ E @ F3 @ E2 @ F4 ) ) ) ) ) )
% 2.96/1.67 => ( P @ X ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_205_prod__induct5,axiom,
% 2.96/1.67 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 2.96/1.67 ( ! [A2: A,B2: B,C2: C,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A2 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B2 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 2.96/1.67 => ( P @ X ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_206_prod__induct4,axiom,
% 2.96/1.67 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.96/1.67 ( ! [A2: A,B2: B,C2: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A2 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B2 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 2.96/1.67 => ( P @ X ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_207_prod__induct3,axiom,
% 2.96/1.67 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.96/1.67 ( ! [A2: A,B2: B,C2: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ B2 @ C2 ) ) )
% 2.96/1.67 => ( P @ X ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_208_prod__cases7,axiom,
% 2.96/1.67 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,G3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) )] :
% 2.96/1.67 ~ ! [A2: A,B2: B,C2: C,D2: D,E2: E,F4: F3,G4: G3] :
% 2.96/1.67 ( Y
% 2.96/1.67 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) @ A2 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) @ B2 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F3 @ G3 ) @ E2 @ ( product_Pair @ F3 @ G3 @ F4 @ G4 ) ) ) ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_209_prod__cases6,axiom,
% 2.96/1.67 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 2.96/1.67 ~ ! [A2: A,B2: B,C2: C,D2: D,E2: E,F4: F3] :
% 2.96/1.67 ( Y
% 2.96/1.67 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A2 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B2 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D2 @ ( product_Pair @ E @ F3 @ E2 @ F4 ) ) ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_210_prod__cases5,axiom,
% 2.96/1.67 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 2.96/1.67 ~ ! [A2: A,B2: B,C2: C,D2: D,E2: E] :
% 2.96/1.67 ( Y
% 2.96/1.67 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A2 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B2 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_211_prod__cases4,axiom,
% 2.96/1.67 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.96/1.67 ~ ! [A2: A,B2: B,C2: C,D2: D] :
% 2.96/1.67 ( Y
% 2.96/1.67 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A2 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B2 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_212_prod__cases3,axiom,
% 2.96/1.67 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.96/1.67 ~ ! [A2: A,B2: B,C2: C] :
% 2.96/1.67 ( Y
% 2.96/1.67 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A2 @ ( product_Pair @ B @ C @ B2 @ C2 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_213_Pair__inject,axiom,
% 2.96/1.67 ! [A: $tType,B: $tType,A3: A,B3: B,A6: A,B4: B] :
% 2.96/1.67 ( ( ( product_Pair @ A @ B @ A3 @ B3 )
% 2.96/1.67 = ( product_Pair @ A @ B @ A6 @ B4 ) )
% 2.96/1.67 => ~ ( ( A3 = A6 )
% 2.96/1.67 => ( B3 != B4 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_214_prod__cases,axiom,
% 2.96/1.67 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P2: product_prod @ A @ B] :
% 2.96/1.67 ( ! [A2: A,B2: B] : ( P @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 2.96/1.67 => ( P @ P2 ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_215_surj__pair,axiom,
% 2.96/1.67 ! [A: $tType,B: $tType,P2: product_prod @ A @ B] :
% 2.96/1.67 ? [X2: A,Y3: B] :
% 2.96/1.67 ( P2
% 2.96/1.67 = ( product_Pair @ A @ B @ X2 @ Y3 ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_216_subrelI,axiom,
% 2.96/1.67 ! [B: $tType,A: $tType,R: set @ ( product_prod @ A @ B ),S2: set @ ( product_prod @ A @ B )] :
% 2.96/1.67 ( ! [X2: A,Y3: B] :
% 2.96/1.67 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ R )
% 2.96/1.67 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X2 @ Y3 ) @ S2 ) )
% 2.96/1.67 => ( ord_less_eq @ ( set @ ( product_prod @ A @ B ) ) @ R @ S2 ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_217_pred__equals__eq2,axiom,
% 2.96/1.67 ! [B: $tType,A: $tType,R3: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 2.96/1.67 ( ( ( ^ [X3: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y2 ) @ R3 ) )
% 2.96/1.67 = ( ^ [X3: A,Y2: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y2 ) @ S ) ) )
% 2.96/1.67 = ( R3 = S ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_218_old_Oprod_Orec,axiom,
% 2.96/1.67 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A3: A,B3: B] :
% 2.96/1.67 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A3 @ B3 ) )
% 2.96/1.67 = ( F1 @ A3 @ B3 ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_219_subsetI,axiom,
% 2.96/1.67 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.96/1.67 ( ! [X2: A] :
% 2.96/1.67 ( ( member @ A @ X2 @ A4 )
% 2.96/1.67 => ( member @ A @ X2 @ B5 ) )
% 2.96/1.67 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_220_subset__antisym,axiom,
% 2.96/1.67 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.96/1.67 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.96/1.67 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 2.96/1.67 => ( A4 = B5 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_221_predicate1I,axiom,
% 2.96/1.67 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.96/1.67 ( ! [X2: A] :
% 2.96/1.67 ( ( P @ X2 )
% 2.96/1.67 => ( Q @ X2 ) )
% 2.96/1.67 => ( ord_less_eq @ ( A > $o ) @ P @ Q ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_222_predicate1D,axiom,
% 2.96/1.67 ! [A: $tType,P: A > $o,Q: A > $o,X: A] :
% 2.96/1.67 ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 2.96/1.67 => ( ( P @ X )
% 2.96/1.67 => ( Q @ X ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_223_rev__predicate1D,axiom,
% 2.96/1.67 ! [A: $tType,P: A > $o,X: A,Q: A > $o] :
% 2.96/1.67 ( ( P @ X )
% 2.96/1.67 => ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 2.96/1.67 => ( Q @ X ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_224_Collect__mono__iff,axiom,
% 2.96/1.67 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.96/1.67 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 2.96/1.67 = ( ! [X3: A] :
% 2.96/1.67 ( ( P @ X3 )
% 2.96/1.67 => ( Q @ X3 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_225_contra__subsetD,axiom,
% 2.96/1.67 ! [A: $tType,A4: set @ A,B5: set @ A,C3: A] :
% 2.96/1.67 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.96/1.67 => ( ~ ( member @ A @ C3 @ B5 )
% 2.96/1.67 => ~ ( member @ A @ C3 @ A4 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_226_set__eq__subset,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( ^ [Y5: set @ A,Z2: set @ A] : ( Y5 = Z2 ) )
% 2.96/1.67 = ( ^ [A7: set @ A,B6: set @ A] :
% 2.96/1.67 ( ( ord_less_eq @ ( set @ A ) @ A7 @ B6 )
% 2.96/1.67 & ( ord_less_eq @ ( set @ A ) @ B6 @ A7 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_227_subset__trans,axiom,
% 2.96/1.67 ! [A: $tType,A4: set @ A,B5: set @ A,C4: set @ A] :
% 2.96/1.67 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.96/1.67 => ( ( ord_less_eq @ ( set @ A ) @ B5 @ C4 )
% 2.96/1.67 => ( ord_less_eq @ ( set @ A ) @ A4 @ C4 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_228_Collect__mono,axiom,
% 2.96/1.67 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.96/1.67 ( ! [X2: A] :
% 2.96/1.67 ( ( P @ X2 )
% 2.96/1.67 => ( Q @ X2 ) )
% 2.96/1.67 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_229_subset__refl,axiom,
% 2.96/1.67 ! [A: $tType,A4: set @ A] : ( ord_less_eq @ ( set @ A ) @ A4 @ A4 ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_230_rev__subsetD,axiom,
% 2.96/1.67 ! [A: $tType,C3: A,A4: set @ A,B5: set @ A] :
% 2.96/1.67 ( ( member @ A @ C3 @ A4 )
% 2.96/1.67 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.96/1.67 => ( member @ A @ C3 @ B5 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_231_subset__iff,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( ord_less_eq @ ( set @ A ) )
% 2.96/1.67 = ( ^ [A7: set @ A,B6: set @ A] :
% 2.96/1.67 ! [T2: A] :
% 2.96/1.67 ( ( member @ A @ T2 @ A7 )
% 2.96/1.67 => ( member @ A @ T2 @ B6 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_232_set__rev__mp,axiom,
% 2.96/1.67 ! [A: $tType,X: A,A4: set @ A,B5: set @ A] :
% 2.96/1.67 ( ( member @ A @ X @ A4 )
% 2.96/1.67 => ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.96/1.67 => ( member @ A @ X @ B5 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_233_equalityD2,axiom,
% 2.96/1.67 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.96/1.67 ( ( A4 = B5 )
% 2.96/1.67 => ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_234_equalityD1,axiom,
% 2.96/1.67 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.96/1.67 ( ( A4 = B5 )
% 2.96/1.67 => ( ord_less_eq @ ( set @ A ) @ A4 @ B5 ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_235_subset__eq,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( ord_less_eq @ ( set @ A ) )
% 2.96/1.67 = ( ^ [A7: set @ A,B6: set @ A] :
% 2.96/1.67 ! [X3: A] :
% 2.96/1.67 ( ( member @ A @ X3 @ A7 )
% 2.96/1.67 => ( member @ A @ X3 @ B6 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_236_equalityE,axiom,
% 2.96/1.67 ! [A: $tType,A4: set @ A,B5: set @ A] :
% 2.96/1.67 ( ( A4 = B5 )
% 2.96/1.67 => ~ ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.96/1.67 => ~ ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_237_subsetCE,axiom,
% 2.96/1.67 ! [A: $tType,A4: set @ A,B5: set @ A,C3: A] :
% 2.96/1.67 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.96/1.67 => ( ( member @ A @ C3 @ A4 )
% 2.96/1.67 => ( member @ A @ C3 @ B5 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_238_subsetD,axiom,
% 2.96/1.67 ! [A: $tType,A4: set @ A,B5: set @ A,C3: A] :
% 2.96/1.67 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.96/1.67 => ( ( member @ A @ C3 @ A4 )
% 2.96/1.67 => ( member @ A @ C3 @ B5 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_239_in__mono,axiom,
% 2.96/1.67 ! [A: $tType,A4: set @ A,B5: set @ A,X: A] :
% 2.96/1.67 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.96/1.67 => ( ( member @ A @ X @ A4 )
% 2.96/1.67 => ( member @ A @ X @ B5 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_240_set__mp,axiom,
% 2.96/1.67 ! [A: $tType,A4: set @ A,B5: set @ A,X: A] :
% 2.96/1.67 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.96/1.67 => ( ( member @ A @ X @ A4 )
% 2.96/1.67 => ( member @ A @ X @ B5 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_241_less__eq__set__def,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( ord_less_eq @ ( set @ A ) )
% 2.96/1.67 = ( ^ [A7: set @ A,B6: set @ A] :
% 2.96/1.67 ( ord_less_eq @ ( A > $o )
% 2.96/1.67 @ ^ [X3: A] : ( member @ A @ X3 @ A7 )
% 2.96/1.67 @ ^ [X3: A] : ( member @ A @ X3 @ B6 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_242_eq__subset,axiom,
% 2.96/1.67 ! [A: $tType,P: A > A > $o] :
% 2.96/1.67 ( ord_less_eq @ ( A > A > $o )
% 2.96/1.67 @ ^ [Y5: A,Z2: A] : ( Y5 = Z2 )
% 2.96/1.67 @ ^ [A5: A,B7: A] :
% 2.96/1.67 ( ( P @ A5 @ B7 )
% 2.96/1.67 | ( A5 = B7 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_243_conj__subset__def,axiom,
% 2.96/1.67 ! [A: $tType,A4: set @ A,P: A > $o,Q: A > $o] :
% 2.96/1.67 ( ( ord_less_eq @ ( set @ A ) @ A4
% 2.96/1.67 @ ( collect @ A
% 2.96/1.67 @ ^ [X3: A] :
% 2.96/1.67 ( ( P @ X3 )
% 2.96/1.67 & ( Q @ X3 ) ) ) )
% 2.96/1.67 = ( ( ord_less_eq @ ( set @ A ) @ A4 @ ( collect @ A @ P ) )
% 2.96/1.67 & ( ord_less_eq @ ( set @ A ) @ A4 @ ( collect @ A @ Q ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_244_predicate2D__conj,axiom,
% 2.96/1.67 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,R3: $o,X: A,Y: B] :
% 2.96/1.67 ( ( ( ord_less_eq @ ( A > B > $o ) @ P @ Q )
% 2.96/1.67 & R3 )
% 2.96/1.67 => ( R3
% 2.96/1.67 & ( ( P @ X @ Y )
% 2.96/1.67 => ( Q @ X @ Y ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_245_subset__Collect__iff,axiom,
% 2.96/1.67 ! [A: $tType,B5: set @ A,A4: set @ A,P: A > $o] :
% 2.96/1.67 ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 2.96/1.67 => ( ( ord_less_eq @ ( set @ A ) @ B5
% 2.96/1.67 @ ( collect @ A
% 2.96/1.67 @ ^ [X3: A] :
% 2.96/1.67 ( ( member @ A @ X3 @ A4 )
% 2.96/1.67 & ( P @ X3 ) ) ) )
% 2.96/1.67 = ( ! [X3: A] :
% 2.96/1.67 ( ( member @ A @ X3 @ B5 )
% 2.96/1.67 => ( P @ X3 ) ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_246_subset__CollectI,axiom,
% 2.96/1.67 ! [A: $tType,B5: set @ A,A4: set @ A,Q: A > $o,P: A > $o] :
% 2.96/1.67 ( ( ord_less_eq @ ( set @ A ) @ B5 @ A4 )
% 2.96/1.67 => ( ! [X2: A] :
% 2.96/1.67 ( ( member @ A @ X2 @ B5 )
% 2.96/1.67 => ( ( Q @ X2 )
% 2.96/1.67 => ( P @ X2 ) ) )
% 2.96/1.67 => ( ord_less_eq @ ( set @ A )
% 2.96/1.67 @ ( collect @ A
% 2.96/1.67 @ ^ [X3: A] :
% 2.96/1.67 ( ( member @ A @ X3 @ B5 )
% 2.96/1.67 & ( Q @ X3 ) ) )
% 2.96/1.67 @ ( collect @ A
% 2.96/1.67 @ ^ [X3: A] :
% 2.96/1.67 ( ( member @ A @ X3 @ A4 )
% 2.96/1.67 & ( P @ X3 ) ) ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_247_prop__restrict,axiom,
% 2.96/1.67 ! [A: $tType,X: A,Z3: set @ A,X4: set @ A,P: A > $o] :
% 2.96/1.67 ( ( member @ A @ X @ Z3 )
% 2.96/1.67 => ( ( ord_less_eq @ ( set @ A ) @ Z3
% 2.96/1.67 @ ( collect @ A
% 2.96/1.67 @ ^ [X3: A] :
% 2.96/1.67 ( ( member @ A @ X3 @ X4 )
% 2.96/1.67 & ( P @ X3 ) ) ) )
% 2.96/1.67 => ( P @ X ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_248_Collect__restrict,axiom,
% 2.96/1.67 ! [A: $tType,X4: set @ A,P: A > $o] :
% 2.96/1.67 ( ord_less_eq @ ( set @ A )
% 2.96/1.67 @ ( collect @ A
% 2.96/1.67 @ ^ [X3: A] :
% 2.96/1.67 ( ( member @ A @ X3 @ X4 )
% 2.96/1.67 & ( P @ X3 ) ) )
% 2.96/1.67 @ X4 ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_249_ssubst__Pair__rhs,axiom,
% 2.96/1.67 ! [B: $tType,A: $tType,R: A,S2: B,R3: set @ ( product_prod @ A @ B ),S3: B] :
% 2.96/1.67 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R @ S2 ) @ R3 )
% 2.96/1.67 => ( ( S3 = S2 )
% 2.96/1.67 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R @ S3 ) @ R3 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_250_internal__case__prod__conv,axiom,
% 2.96/1.67 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A3: B,B3: C] :
% 2.96/1.67 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A3 @ B3 ) )
% 2.96/1.67 = ( C3 @ A3 @ B3 ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_251_llast__lappend,axiom,
% 2.96/1.67 ! [A: $tType,Ys: coindu1593790203_llist @ A,Xs: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ( ( coindu335574135_lnull @ A @ Ys )
% 2.96/1.67 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.96/1.67 = ( coindu2000965700_llast @ A @ Xs ) ) )
% 2.96/1.67 & ( ~ ( coindu335574135_lnull @ A @ Ys )
% 2.96/1.67 => ( ( ( coindu1213758845finite @ A @ Xs )
% 2.96/1.67 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.96/1.67 = ( coindu2000965700_llast @ A @ Ys ) ) )
% 2.96/1.67 & ( ~ ( coindu1213758845finite @ A @ Xs )
% 2.96/1.67 => ( ( coindu2000965700_llast @ A @ ( coindu268472904append @ A @ Xs @ Ys ) )
% 2.96/1.67 = ( undefined @ A ) ) ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_252_llast__linfinite,axiom,
% 2.96/1.67 ! [A: $tType,Xs: coindu1593790203_llist @ A] :
% 2.96/1.67 ( ~ ( coindu1213758845finite @ A @ Xs )
% 2.96/1.67 => ( ( coindu2000965700_llast @ A @ Xs )
% 2.96/1.67 = ( undefined @ A ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(fact_253_llast__LNil,axiom,
% 2.96/1.67 ! [A: $tType] :
% 2.96/1.67 ( ( coindu2000965700_llast @ A @ ( coindu1598213697e_LNil @ A ) )
% 2.96/1.67 = ( undefined @ A ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.96/1.67 ! [A8: $tType,A9: $tType] :
% 2.96/1.67 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 2.96/1.67 => ( preorder @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.96/1.67 ! [A8: $tType,A9: $tType] :
% 2.96/1.67 ( ( order @ A9 @ ( type2 @ A9 ) )
% 2.96/1.67 => ( order @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(tcon_fun___Orderings_Oord,axiom,
% 2.96/1.67 ! [A8: $tType,A9: $tType] :
% 2.96/1.67 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 2.96/1.67 => ( ord @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(tcon_Set_Oset___Orderings_Opreorder_1,axiom,
% 2.96/1.67 ! [A8: $tType] : ( preorder @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(tcon_Set_Oset___Orderings_Oorder_2,axiom,
% 2.96/1.67 ! [A8: $tType] : ( order @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(tcon_Set_Oset___Orderings_Oord_3,axiom,
% 2.96/1.67 ! [A8: $tType] : ( ord @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(tcon_HOL_Obool___Orderings_Opreorder_4,axiom,
% 2.96/1.67 preorder @ $o @ ( type2 @ $o ) ).
% 2.96/1.67
% 2.96/1.67 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.96/1.67 linorder @ $o @ ( type2 @ $o ) ).
% 2.96/1.67
% 2.96/1.67 thf(tcon_HOL_Obool___Orderings_Oorder_5,axiom,
% 2.96/1.67 order @ $o @ ( type2 @ $o ) ).
% 2.96/1.67
% 2.96/1.67 thf(tcon_HOL_Obool___Orderings_Oord_6,axiom,
% 2.96/1.67 ord @ $o @ ( type2 @ $o ) ).
% 2.96/1.67
% 2.96/1.67 thf(help_If_3_1_T,axiom,
% 2.96/1.67 ! [P: $o] :
% 2.96/1.67 ( ( P = $true )
% 2.96/1.67 | ( P = $false ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(help_If_2_1_T,axiom,
% 2.96/1.67 ! [A: $tType,X: A,Y: A] :
% 2.96/1.67 ( ( if @ A @ $false @ X @ Y )
% 2.96/1.67 = Y ) ).
% 2.96/1.67
% 2.96/1.67 thf(help_If_1_1_T,axiom,
% 2.96/1.67 ! [A: $tType,X: A,Y: A] :
% 2.96/1.67 ( ( if @ A @ $true @ X @ Y )
% 2.96/1.67 = X ) ).
% 2.96/1.67
% 2.96/1.67 thf(conj_0,hypothesis,
% 2.96/1.67 ! [Y4: a,Ys6: coindu1593790203_llist @ a] :
% 2.96/1.67 ( ( ysa
% 2.96/1.67 = ( coindu1121789889_LCons @ a @ Y4 @ Ys6 ) )
% 2.96/1.67 => ( ~ ( r @ Y4 @ x )
% 2.96/1.67 => ( ( ( Y4 != x )
% 2.96/1.67 | ~ ( coindu300403952lexord @ a @ r @ Ys6 @ xs2 ) )
% 2.96/1.67 => thesis ) ) ) ).
% 2.96/1.67
% 2.96/1.67 thf(conj_1,conjecture,
% 2.96/1.67 thesis ).
% 2.96/1.67 ------------------------
% 3.04/1.70 % (341)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_32705 for (2999ds/2Mi)
% 3.04/1.70 % (342)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_32705 for (2999ds/275Mi)
% 3.04/1.70 % (337)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32705 for (2999ds/183Mi)
% 3.04/1.70 % (338)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_32705 for (2999ds/4Mi)
% 3.04/1.70 % (343)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32705 for (2999ds/18Mi)
% 3.04/1.70 % (339)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_32705 for (2999ds/27Mi)
% 3.04/1.70 % (340)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32705 for (2999ds/2Mi)
% 3.04/1.70 % (340)Instruction limit reached!
% 3.04/1.70 % (340)------------------------------
% 3.04/1.70 % (340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.70 % (340)Termination reason: Unknown
% 3.04/1.70 % (340)Termination phase: shuffling
% 3.04/1.70
% 3.04/1.70 % (340)Memory used [KB]: 1407
% 3.04/1.70 % (341)Instruction limit reached!
% 3.04/1.70 % (341)------------------------------
% 3.04/1.70 % (341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.70 % (341)Termination reason: Unknown
% 3.04/1.70 % (341)Termination phase: shuffling
% 3.04/1.70
% 3.04/1.70 % (341)Memory used [KB]: 1407
% 3.04/1.70 % (341)Time elapsed: 0.003 s
% 3.04/1.70 % (341)Instructions burned: 2 (million)
% 3.04/1.70 % (341)------------------------------
% 3.04/1.70 % (341)------------------------------
% 3.04/1.70 % (340)Time elapsed: 0.003 s
% 3.04/1.70 % (340)Instructions burned: 2 (million)
% 3.04/1.70 % (340)------------------------------
% 3.04/1.70 % (340)------------------------------
% 3.04/1.70 % (338)Instruction limit reached!
% 3.04/1.70 % (338)------------------------------
% 3.04/1.70 % (338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.70 % (338)Termination reason: Unknown
% 3.04/1.70 % (338)Termination phase: shuffling
% 3.04/1.70
% 3.04/1.70 % (338)Memory used [KB]: 1407
% 3.04/1.70 % (338)Time elapsed: 0.004 s
% 3.04/1.70 % (338)Instructions burned: 4 (million)
% 3.04/1.70 % (338)------------------------------
% 3.04/1.70 % (338)------------------------------
% 3.04/1.71 % (343)Instruction limit reached!
% 3.04/1.71 % (343)------------------------------
% 3.04/1.71 % (343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.71 % (343)Termination reason: Unknown
% 3.04/1.71 % (343)Termination phase: shuffling
% 3.04/1.71
% 3.04/1.71 % (343)Memory used [KB]: 1791
% 3.04/1.71 % (343)Time elapsed: 0.011 s
% 3.04/1.71 % (343)Instructions burned: 18 (million)
% 3.04/1.71 % (343)------------------------------
% 3.04/1.71 % (343)------------------------------
% 3.04/1.72 % (339)Instruction limit reached!
% 3.04/1.72 % (339)------------------------------
% 3.04/1.72 % (339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.72 % (339)Termination reason: Unknown
% 3.04/1.72 % (339)Termination phase: Property scanning
% 3.04/1.72
% 3.04/1.72 % (339)Memory used [KB]: 1918
% 3.04/1.72 % (339)Time elapsed: 0.016 s
% 3.04/1.72 % (339)Instructions burned: 28 (million)
% 3.04/1.72 % (339)------------------------------
% 3.04/1.72 % (339)------------------------------
% 3.04/1.72 % (344)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32705 for (2999ds/3Mi)
% 3.04/1.72 % (345)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_32705 for (2999ds/37Mi)
% 3.04/1.72 % (346)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_32705 for (2999ds/15Mi)
% 3.04/1.72 % (344)Instruction limit reached!
% 3.04/1.72 % (344)------------------------------
% 3.04/1.72 % (344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.72 % (344)Termination reason: Unknown
% 3.04/1.72 % (344)Termination phase: shuffling
% 3.04/1.72
% 3.04/1.72 % (344)Memory used [KB]: 1407
% 3.04/1.72 % (344)Time elapsed: 0.003 s
% 3.04/1.72 % (344)Instructions burned: 3 (million)
% 3.04/1.72 % (344)------------------------------
% 3.04/1.72 % (344)------------------------------
% 3.04/1.73 % (347)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_32705 for (2999ds/3Mi)
% 3.04/1.73 % (346)Instruction limit reached!
% 3.04/1.73 % (346)------------------------------
% 3.04/1.73 % (346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.73 % (346)Termination reason: Unknown
% 3.04/1.73 % (346)Termination phase: shuffling
% 3.04/1.73
% 3.04/1.73 % (346)Memory used [KB]: 1663
% 3.04/1.73 % (346)Time elapsed: 0.009 s
% 3.04/1.73 % (346)Instructions burned: 16 (million)
% 3.04/1.73 % (346)------------------------------
% 3.04/1.73 % (346)------------------------------
% 3.04/1.73 % (347)Instruction limit reached!
% 3.04/1.73 % (347)------------------------------
% 3.04/1.73 % (347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.73 % (347)Termination reason: Unknown
% 3.04/1.73 % (347)Termination phase: shuffling
% 3.04/1.73
% 3.04/1.73 % (347)Memory used [KB]: 1407
% 3.04/1.73 % (347)Time elapsed: 0.003 s
% 3.04/1.73 % (347)Instructions burned: 3 (million)
% 3.04/1.73 % (347)------------------------------
% 3.04/1.73 % (347)------------------------------
% 3.04/1.73 % (348)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_32705 for (2999ds/1041Mi)
% 3.04/1.74 % (345)Instruction limit reached!
% 3.04/1.74 % (345)------------------------------
% 3.04/1.74 % (345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.74 % (345)Termination reason: Unknown
% 3.04/1.74 % (345)Termination phase: shuffling
% 3.04/1.74
% 3.04/1.74 % (345)Memory used [KB]: 2174
% 3.04/1.74 % (345)Time elapsed: 0.018 s
% 3.04/1.74 % (345)Instructions burned: 37 (million)
% 3.04/1.74 % (345)------------------------------
% 3.04/1.74 % (345)------------------------------
% 3.04/1.74 % (349)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_32705 for (2999ds/7Mi)
% 3.04/1.74 % (349)Instruction limit reached!
% 3.04/1.74 % (349)------------------------------
% 3.04/1.74 % (349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.74 % (349)Termination reason: Unknown
% 3.04/1.74 % (349)Termination phase: shuffling
% 3.04/1.74
% 3.04/1.74 % (349)Memory used [KB]: 1535
% 3.04/1.74 % (349)Time elapsed: 0.005 s
% 3.04/1.74 % (349)Instructions burned: 7 (million)
% 3.04/1.74 % (349)------------------------------
% 3.04/1.74 % (349)------------------------------
% 3.04/1.74 % (350)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_32705 for (2999ds/16Mi)
% 3.04/1.74 % (351)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_32705 for (2999ds/3Mi)
% 3.04/1.75 % (351)Instruction limit reached!
% 3.04/1.75 % (351)------------------------------
% 3.04/1.75 % (351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.75 % (351)Termination reason: Unknown
% 3.04/1.75 % (351)Termination phase: shuffling
% 3.04/1.75
% 3.04/1.75 % (351)Memory used [KB]: 1407
% 3.04/1.75 % (351)Time elapsed: 0.003 s
% 3.04/1.75 % (351)Instructions burned: 4 (million)
% 3.04/1.75 % (351)------------------------------
% 3.04/1.75 % (351)------------------------------
% 3.04/1.75 % (350)Instruction limit reached!
% 3.04/1.75 % (350)------------------------------
% 3.04/1.75 % (350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.75 % (350)Termination reason: Unknown
% 3.04/1.75 % (350)Termination phase: shuffling
% 3.04/1.75
% 3.04/1.75 % (350)Memory used [KB]: 1663
% 3.04/1.75 % (350)Time elapsed: 0.009 s
% 3.04/1.75 % (350)Instructions burned: 16 (million)
% 3.04/1.75 % (350)------------------------------
% 3.04/1.75 % (350)------------------------------
% 3.04/1.75 % (352)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_32705 for (2999ds/3Mi)
% 3.04/1.75 % (352)Instruction limit reached!
% 3.04/1.75 % (352)------------------------------
% 3.04/1.75 % (352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.75 % (352)Termination reason: Unknown
% 3.04/1.75 % (352)Termination phase: shuffling
% 3.04/1.75
% 3.04/1.75 % (352)Memory used [KB]: 1407
% 3.04/1.75 % (352)Time elapsed: 0.003 s
% 3.04/1.75 % (352)Instructions burned: 3 (million)
% 3.04/1.75 % (352)------------------------------
% 3.04/1.75 % (352)------------------------------
% 3.04/1.76 % (353)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_32705 for (2999ds/7Mi)
% 3.04/1.76 % (353)Instruction limit reached!
% 3.04/1.76 % (353)------------------------------
% 3.04/1.76 % (353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.76 % (353)Termination reason: Unknown
% 3.04/1.76 % (353)Termination phase: shuffling
% 3.04/1.76
% 3.04/1.76 % (353)Memory used [KB]: 1535
% 3.04/1.76 % (353)Time elapsed: 0.005 s
% 3.04/1.76 % (353)Instructions burned: 7 (million)
% 3.04/1.76 % (353)------------------------------
% 3.04/1.76 % (353)------------------------------
% 3.04/1.76 % (354)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_32705 for (2999ds/3Mi)
% 3.04/1.76 % (354)Instruction limit reached!
% 3.04/1.76 % (354)------------------------------
% 3.04/1.76 % (354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.76 % (354)Termination reason: Unknown
% 3.04/1.76 % (354)Termination phase: shuffling
% 3.04/1.76
% 3.04/1.76 % (354)Memory used [KB]: 1407
% 3.04/1.76 % (354)Time elapsed: 0.003 s
% 3.04/1.76 % (354)Instructions burned: 4 (million)
% 3.04/1.76 % (354)------------------------------
% 3.04/1.76 % (354)------------------------------
% 3.04/1.77 % (355)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_32705 for (2999ds/4Mi)
% 3.04/1.77 % (356)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_32705 for (2999ds/18Mi)
% 3.04/1.77 % (355)Instruction limit reached!
% 3.04/1.77 % (355)------------------------------
% 3.04/1.77 % (355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.77 % (355)Termination reason: Unknown
% 3.04/1.77 % (355)Termination phase: shuffling
% 3.04/1.77
% 3.04/1.77 % (355)Memory used [KB]: 1535
% 3.04/1.77 % (355)Time elapsed: 0.004 s
% 3.04/1.77 % (355)Instructions burned: 6 (million)
% 3.04/1.77 % (355)------------------------------
% 3.04/1.77 % (355)------------------------------
% 3.04/1.78 % (357)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_32705 for (2999ds/710Mi)
% 3.04/1.78 % (356)Instruction limit reached!
% 3.04/1.78 % (356)------------------------------
% 3.04/1.78 % (356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.78 % (356)Termination reason: Unknown
% 3.04/1.78 % (356)Termination phase: shuffling
% 3.04/1.78
% 3.04/1.78 % (356)Memory used [KB]: 1791
% 3.04/1.78 % (356)Time elapsed: 0.010 s
% 3.04/1.78 % (356)Instructions burned: 18 (million)
% 3.04/1.78 % (356)------------------------------
% 3.04/1.78 % (356)------------------------------
% 3.04/1.78 % (358)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32705 for (2999ds/6Mi)
% 3.04/1.78 % (358)Instruction limit reached!
% 3.04/1.78 % (358)------------------------------
% 3.04/1.78 % (358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.78 % (358)Termination reason: Unknown
% 3.04/1.78 % (358)Termination phase: shuffling
% 3.04/1.78
% 3.04/1.78 % (358)Memory used [KB]: 1535
% 3.04/1.78 % (358)Time elapsed: 0.005 s
% 3.04/1.78 % (358)Instructions burned: 6 (million)
% 3.04/1.78 % (358)------------------------------
% 3.04/1.78 % (358)------------------------------
% 3.04/1.78 % (359)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_32705 for (2999ds/902Mi)
% 3.04/1.79 % (337)Instruction limit reached!
% 3.04/1.79 % (337)------------------------------
% 3.04/1.79 % (337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.79 % (337)Termination reason: Unknown
% 3.04/1.79 % (337)Termination phase: Saturation
% 3.04/1.79
% 3.04/1.79 % (337)Memory used [KB]: 7419
% 3.04/1.79 % (337)Time elapsed: 0.089 s
% 3.04/1.79 % (337)Instructions burned: 183 (million)
% 3.04/1.79 % (337)------------------------------
% 3.04/1.79 % (337)------------------------------
% 3.04/1.79 % (360)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_32705 for (2999ds/21Mi)
% 3.04/1.80 % (361)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_32705 for (2998ds/5Mi)
% 3.04/1.80 % (361)Instruction limit reached!
% 3.04/1.80 % (361)------------------------------
% 3.04/1.80 % (361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.80 % (361)Termination reason: Unknown
% 3.04/1.80 % (361)Termination phase: shuffling
% 3.04/1.80
% 3.04/1.80 % (361)Memory used [KB]: 1407
% 3.04/1.80 % (361)Time elapsed: 0.004 s
% 3.04/1.80 % (361)Instructions burned: 6 (million)
% 3.04/1.80 % (361)------------------------------
% 3.04/1.80 % (361)------------------------------
% 3.04/1.80 % (360)Instruction limit reached!
% 3.04/1.80 % (360)------------------------------
% 3.04/1.80 % (360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.80 % (360)Termination reason: Unknown
% 3.04/1.80 % (360)Termination phase: shuffling
% 3.04/1.80
% 3.04/1.80 % (360)Memory used [KB]: 1918
% 3.04/1.80 % (360)Time elapsed: 0.012 s
% 3.04/1.80 % (360)Instructions burned: 21 (million)
% 3.04/1.80 % (360)------------------------------
% 3.04/1.80 % (360)------------------------------
% 3.04/1.80 % (362)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_32705 for (2998ds/6Mi)
% 3.04/1.81 % (362)Instruction limit reached!
% 3.04/1.81 % (362)------------------------------
% 3.04/1.81 % (362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.81 % (362)Termination reason: Unknown
% 3.04/1.81 % (362)Termination phase: shuffling
% 3.04/1.81
% 3.04/1.81 % (362)Memory used [KB]: 1535
% 3.04/1.81 % (362)Time elapsed: 0.005 s
% 3.04/1.81 % (362)Instructions burned: 7 (million)
% 3.04/1.81 % (362)------------------------------
% 3.04/1.81 % (362)------------------------------
% 3.04/1.82 % (363)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_32705 for (2998ds/377Mi)
% 3.04/1.82 % (364)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_32705 for (2998ds/779Mi)
% 3.04/1.82 % (365)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_32705 for (2998ds/19Mi)
% 3.04/1.83 % (342)Instruction limit reached!
% 3.04/1.83 % (342)------------------------------
% 3.04/1.83 % (342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.83 % (365)Instruction limit reached!
% 3.04/1.83 % (365)------------------------------
% 3.04/1.83 % (365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.83 % (365)Termination reason: Unknown
% 3.04/1.83 % (365)Termination phase: shuffling
% 3.04/1.83
% 3.04/1.83 % (365)Memory used [KB]: 1791
% 3.04/1.83 % (365)Time elapsed: 0.011 s
% 3.04/1.83 % (365)Instructions burned: 20 (million)
% 3.04/1.83 % (365)------------------------------
% 3.04/1.83 % (365)------------------------------
% 3.04/1.83 % (342)Termination reason: Unknown
% 3.04/1.83 % (342)Termination phase: Saturation
% 3.04/1.83
% 3.04/1.83 % (342)Memory used [KB]: 7036
% 3.04/1.83 % (342)Time elapsed: 0.134 s
% 3.04/1.83 % (342)Instructions burned: 276 (million)
% 3.04/1.83 % (342)------------------------------
% 3.04/1.83 % (342)------------------------------
% 3.04/1.85 % (367)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_32705 for (2998ds/17Mi)
% 3.04/1.85 % (366)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_32705 for (2998ds/879Mi)
% 3.04/1.86 % (367)Instruction limit reached!
% 3.04/1.86 % (367)------------------------------
% 3.04/1.86 % (367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.86 % (367)Termination reason: Unknown
% 3.04/1.86 % (367)Termination phase: shuffling
% 3.04/1.86
% 3.04/1.86 % (367)Memory used [KB]: 1791
% 3.04/1.86 % (367)Time elapsed: 0.011 s
% 3.04/1.86 % (367)Instructions burned: 18 (million)
% 3.04/1.86 % (367)------------------------------
% 3.04/1.86 % (367)------------------------------
% 3.04/1.88 % (368)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_32705 for (2998ds/3Mi)
% 3.04/1.88 % (368)Instruction limit reached!
% 3.04/1.88 % (368)------------------------------
% 3.04/1.88 % (368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.88 % (368)Termination reason: Unknown
% 3.04/1.88 % (368)Termination phase: shuffling
% 3.04/1.88
% 3.04/1.88 % (368)Memory used [KB]: 1407
% 3.04/1.88 % (368)Time elapsed: 0.004 s
% 3.04/1.88 % (368)Instructions burned: 4 (million)
% 3.04/1.88 % (368)------------------------------
% 3.04/1.88 % (368)------------------------------
% 3.04/1.89 % (369)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_32705 for (2998ds/30Mi)
% 3.04/1.91 % (369)Instruction limit reached!
% 3.04/1.91 % (369)------------------------------
% 3.04/1.91 % (369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.91 % (369)Termination reason: Unknown
% 3.04/1.91 % (369)Termination phase: Property scanning
% 3.04/1.91
% 3.04/1.91 % (369)Memory used [KB]: 2046
% 3.04/1.91 % (369)Time elapsed: 0.017 s
% 3.04/1.91 % (369)Instructions burned: 30 (million)
% 3.04/1.91 % (369)------------------------------
% 3.04/1.91 % (369)------------------------------
% 3.04/1.93 % (370)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_32705 for (2997ds/127Mi)
% 3.04/1.99 % (370)Instruction limit reached!
% 3.04/1.99 % (370)------------------------------
% 3.04/1.99 % (370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.99 % (370)Termination reason: Unknown
% 3.04/1.99 % (370)Termination phase: Saturation
% 3.04/1.99
% 3.04/1.99 % (370)Memory used [KB]: 6908
% 3.04/1.99 % (370)Time elapsed: 0.062 s
% 3.04/1.99 % (370)Instructions burned: 128 (million)
% 3.04/1.99 % (370)------------------------------
% 3.04/1.99 % (370)------------------------------
% 3.04/2.00 % (363)Instruction limit reached!
% 3.04/2.00 % (363)------------------------------
% 3.04/2.00 % (363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/2.00 % (363)Termination reason: Unknown
% 3.04/2.00 % (363)Termination phase: Saturation
% 3.04/2.00
% 3.04/2.00 % (363)Memory used [KB]: 8571
% 3.04/2.00 % (363)Time elapsed: 0.186 s
% 3.04/2.00 % (363)Instructions burned: 378 (million)
% 3.04/2.00 % (363)------------------------------
% 3.04/2.00 % (363)------------------------------
% 3.04/2.00 % (371)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_32705 for (2997ds/100Mi)
% 3.04/2.02 % (372)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_32705 for (2996ds/3Mi)
% 3.04/2.02 % (372)Instruction limit reached!
% 3.04/2.02 % (372)------------------------------
% 3.04/2.02 % (372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/2.02 % (372)Termination reason: Unknown
% 3.04/2.02 % (372)Termination phase: shuffling
% 3.04/2.02
% 3.04/2.02 % (372)Memory used [KB]: 1407
% 3.04/2.02 % (372)Time elapsed: 0.004 s
% 3.04/2.02 % (372)Instructions burned: 3 (million)
% 3.04/2.02 % (372)------------------------------
% 3.04/2.02 % (372)------------------------------
% 5.25/2.04 % (373)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_32705 for (2996ds/20Mi)
% 5.25/2.05 % (373)Instruction limit reached!
% 5.25/2.05 % (373)------------------------------
% 5.25/2.05 % (373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.25/2.05 % (373)Termination reason: Unknown
% 5.25/2.05 % (373)Termination phase: shuffling
% 5.25/2.05
% 5.25/2.05 % (373)Memory used [KB]: 1918
% 5.25/2.05 % (373)Time elapsed: 0.013 s
% 5.25/2.05 % (373)Instructions burned: 21 (million)
% 5.25/2.05 % (373)------------------------------
% 5.25/2.05 % (373)------------------------------
% 5.25/2.05 % (371)Instruction limit reached!
% 5.25/2.05 % (371)------------------------------
% 5.25/2.05 % (371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.25/2.05 % (371)Termination reason: Unknown
% 5.25/2.05 % (371)Termination phase: Property scanning
% 5.25/2.05
% 5.25/2.05 % (371)Memory used [KB]: 2430
% 5.25/2.05 % (371)Time elapsed: 0.048 s
% 5.25/2.05 % (371)Instructions burned: 102 (million)
% 5.25/2.05 % (371)------------------------------
% 5.25/2.05 % (371)------------------------------
% 5.25/2.06 % (374)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_32705 for (2996ds/86Mi)
% 5.25/2.07 % (375)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_32705 for (2996ds/107Mi)
% 5.25/2.11 % (374)Instruction limit reached!
% 5.25/2.11 % (374)------------------------------
% 5.25/2.11 % (374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.25/2.11 % (374)Termination reason: Unknown
% 5.25/2.11 % (374)Termination phase: Property scanning
% 5.25/2.11
% 5.25/2.11 % (374)Memory used [KB]: 2430
% 5.25/2.11 % (374)Time elapsed: 0.043 s
% 5.25/2.11 % (374)Instructions burned: 87 (million)
% 5.25/2.11 % (374)------------------------------
% 5.25/2.11 % (374)------------------------------
% 5.25/2.11 % (357)Instruction limit reached!
% 5.25/2.11 % (357)------------------------------
% 5.25/2.11 % (357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.25/2.11 % (357)Termination reason: Unknown
% 5.25/2.11 % (357)Termination phase: Saturation
% 5.25/2.11
% 5.25/2.11 % (357)Memory used [KB]: 8187
% 5.25/2.11 % (357)Time elapsed: 0.335 s
% 5.25/2.11 % (357)Instructions burned: 710 (million)
% 5.25/2.11 % (357)------------------------------
% 5.25/2.11 % (357)------------------------------
% 5.25/2.12 % (375)Instruction limit reached!
% 5.25/2.12 % (375)------------------------------
% 5.25/2.12 % (375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.25/2.12 % (375)Termination reason: Unknown
% 5.25/2.12 % (375)Termination phase: Saturation
% 5.25/2.12
% 5.25/2.12 % (375)Memory used [KB]: 6780
% 5.25/2.12 % (375)Time elapsed: 0.053 s
% 5.25/2.12 % (375)Instructions burned: 109 (million)
% 5.25/2.12 % (375)------------------------------
% 5.25/2.12 % (375)------------------------------
% 5.25/2.12 % (376)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_32705 for (2995ds/39Mi)
% 6.04/2.12 % (377)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_32705 for (2995ds/448Mi)
% 6.04/2.13 % (378)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_32705 for (2995ds/46Mi)
% 6.04/2.14 % (376)Instruction limit reached!
% 6.04/2.14 % (376)------------------------------
% 6.04/2.14 % (376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.14 % (376)Termination reason: Unknown
% 6.04/2.14 % (376)Termination phase: shuffling
% 6.04/2.14
% 6.04/2.14 % (376)Memory used [KB]: 2174
% 6.04/2.14 % (376)Time elapsed: 0.020 s
% 6.04/2.14 % (376)Instructions burned: 39 (million)
% 6.04/2.14 % (376)------------------------------
% 6.04/2.14 % (376)------------------------------
% 6.04/2.16 % (378)Instruction limit reached!
% 6.04/2.16 % (378)------------------------------
% 6.04/2.16 % (378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.16 % (378)Termination reason: Unknown
% 6.04/2.16 % (378)Termination phase: Preprocessing 1
% 6.04/2.16
% 6.04/2.16 % (378)Memory used [KB]: 1918
% 6.04/2.16 % (378)Time elapsed: 0.024 s
% 6.04/2.16 % (378)Instructions burned: 47 (million)
% 6.04/2.16 % (378)------------------------------
% 6.04/2.16 % (378)------------------------------
% 6.04/2.16 % (379)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_32705 for (2995ds/98Mi)
% 6.04/2.17 % (380)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_32705 for (2995ds/507Mi)
% 6.04/2.19 % (364)Instruction limit reached!
% 6.04/2.19 % (364)------------------------------
% 6.04/2.19 % (364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.19 % (364)Termination reason: Unknown
% 6.04/2.19 % (364)Termination phase: Saturation
% 6.04/2.19
% 6.04/2.19 % (364)Memory used [KB]: 8187
% 6.04/2.19 % (364)Time elapsed: 0.374 s
% 6.04/2.19 % (364)Instructions burned: 779 (million)
% 6.04/2.19 % (364)------------------------------
% 6.04/2.19 % (364)------------------------------
% 6.40/2.20 % (359)Instruction limit reached!
% 6.40/2.20 % (359)------------------------------
% 6.40/2.20 % (359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.20 % (359)Termination reason: Unknown
% 6.40/2.20 % (359)Termination phase: Saturation
% 6.40/2.20
% 6.40/2.20 % (359)Memory used [KB]: 8699
% 6.40/2.20 % (359)Time elapsed: 0.418 s
% 6.40/2.20 % (359)Instructions burned: 902 (million)
% 6.40/2.20 % (359)------------------------------
% 6.40/2.20 % (359)------------------------------
% 6.40/2.20 % (379)Instruction limit reached!
% 6.40/2.20 % (379)------------------------------
% 6.40/2.20 % (379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.20 % (379)Termination reason: Unknown
% 6.40/2.20 % (379)Termination phase: Property scanning
% 6.40/2.20
% 6.40/2.20 % (379)Memory used [KB]: 2430
% 6.40/2.20 % (379)Time elapsed: 0.047 s
% 6.40/2.20 % (379)Instructions burned: 99 (million)
% 6.40/2.20 % (379)------------------------------
% 6.40/2.20 % (379)------------------------------
% 6.40/2.21 % (381)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_32705 for (2994ds/149Mi)
% 6.40/2.22 % (383)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_32705 for (2994ds/6Mi)
% 6.40/2.22 % (382)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_32705 for (2994ds/39Mi)
% 6.40/2.22 % (383)Instruction limit reached!
% 6.40/2.22 % (383)------------------------------
% 6.40/2.22 % (383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.22 % (383)Termination reason: Unknown
% 6.40/2.22 % (383)Termination phase: shuffling
% 6.40/2.22
% 6.40/2.22 % (383)Memory used [KB]: 1535
% 6.40/2.22 % (383)Time elapsed: 0.005 s
% 6.40/2.22 % (383)Instructions burned: 7 (million)
% 6.40/2.22 % (383)------------------------------
% 6.40/2.22 % (383)------------------------------
% 6.40/2.23 % (348)Instruction limit reached!
% 6.40/2.23 % (348)------------------------------
% 6.40/2.23 % (348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.23 % (348)Termination reason: Unknown
% 6.40/2.23 % (348)Termination phase: Saturation
% 6.40/2.23
% 6.40/2.23 % (348)Memory used [KB]: 9722
% 6.40/2.23 % (348)Time elapsed: 0.497 s
% 6.40/2.23 % (348)Instructions burned: 1041 (million)
% 6.40/2.23 % (348)------------------------------
% 6.40/2.23 % (348)------------------------------
% 6.40/2.24 % (382)Instruction limit reached!
% 6.40/2.24 % (382)------------------------------
% 6.40/2.24 % (382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.24 % (382)Termination reason: Unknown
% 6.40/2.24 % (382)Termination phase: Preprocessing 1
% 6.40/2.24
% 6.40/2.24 % (382)Memory used [KB]: 2046
% 6.40/2.24 % (382)Time elapsed: 0.021 s
% 6.40/2.24 % (382)Instructions burned: 40 (million)
% 6.40/2.24 % (382)------------------------------
% 6.40/2.24 % (382)------------------------------
% 6.40/2.24 % (384)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_32705 for (2994ds/1087Mi)
% 6.40/2.24 % (385)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_32705 for (2994ds/47Mi)
% 6.40/2.25 % (386)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_32705 for (2994ds/44Mi)
% 6.40/2.26 % (366)Instruction limit reached!
% 6.40/2.26 % (366)------------------------------
% 6.40/2.26 % (366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.26 % (366)Termination reason: Unknown
% 6.40/2.26 % (366)Termination phase: Saturation
% 6.40/2.26
% 6.40/2.26 % (366)Memory used [KB]: 7803
% 6.40/2.26 % (366)Time elapsed: 0.412 s
% 6.40/2.26 % (366)Instructions burned: 879 (million)
% 6.40/2.26 % (366)------------------------------
% 6.40/2.26 % (366)------------------------------
% 6.40/2.27 % (385)Instruction limit reached!
% 6.40/2.27 % (385)------------------------------
% 6.40/2.27 % (385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.27 % (385)Termination reason: Unknown
% 6.40/2.27 % (385)Termination phase: Preprocessing 3
% 6.40/2.27
% 6.40/2.27 % (385)Memory used [KB]: 2174
% 6.40/2.27 % (385)Time elapsed: 0.024 s
% 6.40/2.27 % (385)Instructions burned: 47 (million)
% 6.40/2.27 % (385)------------------------------
% 6.40/2.27 % (385)------------------------------
% 6.40/2.27 % (386)Instruction limit reached!
% 6.40/2.27 % (386)------------------------------
% 6.40/2.27 % (386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.27 % (386)Termination reason: Unknown
% 6.40/2.27 % (386)Termination phase: shuffling
% 6.40/2.27
% 6.40/2.27 % (386)Memory used [KB]: 2302
% 6.40/2.27 % (386)Time elapsed: 0.022 s
% 6.40/2.27 % (386)Instructions burned: 44 (million)
% 6.40/2.27 % (386)------------------------------
% 6.40/2.27 % (386)------------------------------
% 6.40/2.28 % (387)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_32705 for (2994ds/432Mi)
% 6.40/2.28 % (381)Instruction limit reached!
% 6.40/2.28 % (381)------------------------------
% 6.40/2.28 % (381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.40/2.28 % (381)Termination reason: Unknown
% 6.40/2.28 % (381)Termination phase: Saturation
% 6.40/2.28
% 6.40/2.28 % (381)Memory used [KB]: 7164
% 6.40/2.28 % (381)Time elapsed: 0.071 s
% 6.40/2.28 % (381)Instructions burned: 149 (million)
% 6.40/2.28 % (381)------------------------------
% 6.40/2.28 % (381)------------------------------
% 6.40/2.28 % (388)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_32705 for (2994ds/62Mi)
% 6.40/2.29 % (389)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_32705 for (2994ds/31Mi)
% 6.40/2.29 % (390)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_32705 for (2993ds/96Mi)
% 6.82/2.31 % (389)Instruction limit reached!
% 6.82/2.31 % (389)------------------------------
% 6.82/2.31 % (389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.31 % (389)Termination reason: Unknown
% 6.82/2.31 % (389)Termination phase: Property scanning
% 6.82/2.31
% 6.82/2.31 % (389)Memory used [KB]: 2046
% 6.82/2.31 % (389)Time elapsed: 0.017 s
% 6.82/2.31 % (389)Instructions burned: 32 (million)
% 6.82/2.31 % (389)------------------------------
% 6.82/2.31 % (389)------------------------------
% 6.82/2.31 % (388)Instruction limit reached!
% 6.82/2.31 % (388)------------------------------
% 6.82/2.31 % (388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.31 % (388)Termination reason: Unknown
% 6.82/2.31 % (388)Termination phase: Property scanning
% 6.82/2.31
% 6.82/2.31 % (388)Memory used [KB]: 2302
% 6.82/2.31 % (388)Time elapsed: 0.030 s
% 6.82/2.31 % (388)Instructions burned: 64 (million)
% 6.82/2.31 % (388)------------------------------
% 6.82/2.31 % (388)------------------------------
% 6.82/2.32 % (391)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_32705 for (2993ds/453Mi)
% 6.82/2.33 % (392)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_32705 for (2993ds/71Mi)
% 6.82/2.34 % (377)Instruction limit reached!
% 6.82/2.34 % (377)------------------------------
% 6.82/2.34 % (377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.34 % (377)Termination reason: Unknown
% 6.82/2.34 % (377)Termination phase: Saturation
% 6.82/2.34
% 6.82/2.34 % (377)Memory used [KB]: 8187
% 6.82/2.34 % (377)Time elapsed: 0.213 s
% 6.82/2.34 % (377)Instructions burned: 448 (million)
% 6.82/2.34 % (377)------------------------------
% 6.82/2.34 % (377)------------------------------
% 6.82/2.34 % (390)Instruction limit reached!
% 6.82/2.34 % (390)------------------------------
% 6.82/2.34 % (390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.34 % (390)Termination reason: Unknown
% 6.82/2.34 % (390)Termination phase: Property scanning
% 6.82/2.34
% 6.82/2.34 % (390)Memory used [KB]: 2430
% 6.82/2.34 % (390)Time elapsed: 0.046 s
% 6.82/2.34 % (390)Instructions burned: 96 (million)
% 6.82/2.34 % (390)------------------------------
% 6.82/2.34 % (390)------------------------------
% 6.82/2.35 % (393)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_32705 for (2993ds/83Mi)
% 6.82/2.36 % (394)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_32705 for (2993ds/11Mi)
% 6.82/2.36 % (392)Instruction limit reached!
% 6.82/2.36 % (392)------------------------------
% 6.82/2.36 % (392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.36 % (392)Termination reason: Unknown
% 6.82/2.36 % (392)Termination phase: Property scanning
% 6.82/2.36
% 6.82/2.36 % (392)Memory used [KB]: 2302
% 6.82/2.36 % (392)Time elapsed: 0.035 s
% 6.82/2.36 % (392)Instructions burned: 71 (million)
% 6.82/2.36 % (392)------------------------------
% 6.82/2.36 % (392)------------------------------
% 6.82/2.36 % (394)Instruction limit reached!
% 6.82/2.36 % (394)------------------------------
% 6.82/2.36 % (394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.36 % (394)Termination reason: Unknown
% 6.82/2.36 % (394)Termination phase: shuffling
% 6.82/2.36
% 6.82/2.36 % (394)Memory used [KB]: 1663
% 6.82/2.36 % (394)Time elapsed: 0.007 s
% 6.82/2.36 % (394)Instructions burned: 12 (million)
% 6.82/2.36 % (394)------------------------------
% 6.82/2.36 % (394)------------------------------
% 6.82/2.38 % (396)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_32705 for (2993ds/6Mi)
% 6.82/2.38 % (395)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_32705 for (2993ds/41Mi)
% 6.82/2.38 % (396)Instruction limit reached!
% 6.82/2.38 % (396)------------------------------
% 6.82/2.38 % (396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.38 % (396)Termination reason: Unknown
% 6.82/2.38 % (396)Termination phase: shuffling
% 6.82/2.38
% 6.82/2.38 % (396)Memory used [KB]: 1535
% 6.82/2.38 % (396)Time elapsed: 0.005 s
% 6.82/2.38 % (396)Instructions burned: 7 (million)
% 6.82/2.38 % (396)------------------------------
% 6.82/2.38 % (396)------------------------------
% 6.82/2.39 % (393)Instruction limit reached!
% 6.82/2.39 % (393)------------------------------
% 6.82/2.39 % (393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.39 % (393)Termination reason: Unknown
% 6.82/2.39 % (393)Termination phase: Saturation
% 6.82/2.39
% 6.82/2.39 % (393)Memory used [KB]: 6652
% 6.82/2.39 % (393)Time elapsed: 0.043 s
% 6.82/2.39 % (393)Instructions burned: 84 (million)
% 6.82/2.39 % (393)------------------------------
% 6.82/2.39 % (393)------------------------------
% 6.82/2.40 % (395)Instruction limit reached!
% 6.82/2.40 % (395)------------------------------
% 6.82/2.40 % (395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.82/2.40 % (395)Termination reason: Unknown
% 6.82/2.40 % (395)Termination phase: shuffling
% 6.82/2.40
% 6.82/2.40 % (395)Memory used [KB]: 2174
% 6.82/2.40 % (395)Time elapsed: 0.021 s
% 6.82/2.40 % (395)Instructions burned: 42 (million)
% 6.82/2.40 % (395)------------------------------
% 6.82/2.40 % (395)------------------------------
% 7.33/2.40 % (397)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_32705 for (2993ds/150Mi)
% 7.33/2.41 % (398)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_32705 for (2992ds/343Mi)
% 7.33/2.41 % (399)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_32705 for (2992ds/109Mi)
% 7.33/2.42 % (380)Instruction limit reached!
% 7.33/2.42 % (380)------------------------------
% 7.33/2.42 % (380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.42 % (380)Termination reason: Unknown
% 7.33/2.42 % (380)Termination phase: Saturation
% 7.33/2.42
% 7.33/2.42 % (380)Memory used [KB]: 8827
% 7.33/2.42 % (380)Time elapsed: 0.252 s
% 7.33/2.42 % (380)Instructions burned: 508 (million)
% 7.33/2.42 % (380)------------------------------
% 7.33/2.42 % (380)------------------------------
% 7.33/2.44 % (400)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_32705 for (2992ds/253Mi)
% 7.33/2.46 % (399)Instruction limit reached!
% 7.33/2.46 % (399)------------------------------
% 7.33/2.46 % (399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.46 % (399)Termination reason: Unknown
% 7.33/2.46 % (399)Termination phase: Saturation
% 7.33/2.46
% 7.33/2.46 % (399)Memory used [KB]: 6780
% 7.33/2.46 % (399)Time elapsed: 0.052 s
% 7.33/2.46 % (399)Instructions burned: 109 (million)
% 7.33/2.46 % (399)------------------------------
% 7.33/2.46 % (399)------------------------------
% 7.33/2.47 % (397)Instruction limit reached!
% 7.33/2.47 % (397)------------------------------
% 7.33/2.47 % (397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.47 % (397)Termination reason: Unknown
% 7.33/2.47 % (397)Termination phase: Saturation
% 7.33/2.47
% 7.33/2.47 % (397)Memory used [KB]: 7164
% 7.33/2.47 % (397)Time elapsed: 0.072 s
% 7.33/2.47 % (397)Instructions burned: 151 (million)
% 7.33/2.47 % (397)------------------------------
% 7.33/2.47 % (397)------------------------------
% 7.33/2.48 % (401)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_32705 for (2992ds/140Mi)
% 7.33/2.48 % (402)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_32705 for (2992ds/614Mi)
% 7.33/2.48 % (387)Instruction limit reached!
% 7.33/2.48 % (387)------------------------------
% 7.33/2.48 % (387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.48 % (387)Termination reason: Unknown
% 7.33/2.48 % (387)Termination phase: Saturation
% 7.33/2.48
% 7.33/2.48 % (387)Memory used [KB]: 3454
% 7.33/2.48 % (387)Time elapsed: 0.210 s
% 7.33/2.48 % (387)Instructions burned: 434 (million)
% 7.33/2.48 % (387)------------------------------
% 7.33/2.48 % (387)------------------------------
% 8.02/2.50 % (403)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_32705 for (2991ds/202Mi)
% 8.02/2.53 % (391)Instruction limit reached!
% 8.02/2.53 % (391)------------------------------
% 8.02/2.53 % (391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.53 % (391)Termination reason: Unknown
% 8.02/2.53 % (391)Termination phase: Saturation
% 8.02/2.53
% 8.02/2.53 % (391)Memory used [KB]: 8059
% 8.02/2.53 % (391)Time elapsed: 0.210 s
% 8.02/2.53 % (391)Instructions burned: 453 (million)
% 8.02/2.53 % (391)------------------------------
% 8.02/2.53 % (391)------------------------------
% 8.02/2.55 % (401)Instruction limit reached!
% 8.02/2.55 % (401)------------------------------
% 8.02/2.55 % (401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.55 % (401)Termination reason: Unknown
% 8.02/2.55 % (401)Termination phase: Saturation
% 8.02/2.55
% 8.02/2.55 % (401)Memory used [KB]: 7036
% 8.02/2.55 % (401)Time elapsed: 0.070 s
% 8.02/2.55 % (401)Instructions burned: 140 (million)
% 8.02/2.55 % (401)------------------------------
% 8.02/2.55 % (401)------------------------------
% 8.02/2.55 % (404)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_32705 for (2991ds/339Mi)
% 8.02/2.56 % (405)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_32705 for (2991ds/283Mi)
% 8.02/2.56 % (400)Instruction limit reached!
% 8.02/2.56 % (400)------------------------------
% 8.02/2.56 % (400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.56 % (400)Termination reason: Unknown
% 8.02/2.56 % (400)Termination phase: Saturation
% 8.02/2.56
% 8.02/2.56 % (400)Memory used [KB]: 7419
% 8.02/2.56 % (400)Time elapsed: 0.126 s
% 8.02/2.56 % (400)Instructions burned: 254 (million)
% 8.02/2.56 % (400)------------------------------
% 8.02/2.56 % (400)------------------------------
% 8.02/2.58 % (398)Instruction limit reached!
% 8.02/2.58 % (398)------------------------------
% 8.02/2.58 % (398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.58 % (398)Termination reason: Unknown
% 8.02/2.58 % (398)Termination phase: Saturation
% 8.02/2.58
% 8.02/2.58 % (398)Memory used [KB]: 7803
% 8.02/2.58 % (398)Time elapsed: 0.168 s
% 8.02/2.58 % (398)Instructions burned: 344 (million)
% 8.02/2.58 % (398)------------------------------
% 8.02/2.58 % (398)------------------------------
% 8.02/2.58 % (406)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_32705 for (2991ds/134Mi)
% 8.02/2.59 % (407)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_32705 for (2991ds/298Mi)
% 8.64/2.60 % (403)Instruction limit reached!
% 8.64/2.60 % (403)------------------------------
% 8.64/2.60 % (403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.60 % (403)Termination reason: Unknown
% 8.64/2.60 % (403)Termination phase: Saturation
% 8.64/2.60
% 8.64/2.60 % (403)Memory used [KB]: 7164
% 8.64/2.60 % (403)Time elapsed: 0.099 s
% 8.64/2.60 % (403)Instructions burned: 202 (million)
% 8.64/2.60 % (403)------------------------------
% 8.64/2.60 % (403)------------------------------
% 8.64/2.62 % (408)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_32705 for (2990ds/192Mi)
% 8.64/2.64 % (406)Instruction limit reached!
% 8.64/2.64 % (406)------------------------------
% 8.64/2.64 % (406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.64/2.64 % (406)Termination reason: Unknown
% 8.64/2.64 % (406)Termination phase: Saturation
% 8.64/2.64
% 8.64/2.64 % (406)Memory used [KB]: 6908
% 8.64/2.64 % (406)Time elapsed: 0.064 s
% 8.64/2.64 % (406)Instructions burned: 135 (million)
% 8.64/2.64 % (406)------------------------------
% 8.64/2.64 % (406)------------------------------
% 8.64/2.66 % (409)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_32705 for (2990ds/258Mi)
% 8.83/2.70 % (405)Instruction limit reached!
% 8.83/2.70 % (405)------------------------------
% 8.83/2.70 % (405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.70 % (405)Termination reason: Unknown
% 8.83/2.70 % (405)Termination phase: Saturation
% 8.83/2.70
% 8.83/2.70 % (405)Memory used [KB]: 7547
% 8.83/2.70 % (405)Time elapsed: 0.159 s
% 8.83/2.70 % (405)Instructions burned: 283 (million)
% 8.83/2.70 % (405)------------------------------
% 8.83/2.70 % (405)------------------------------
% 8.83/2.71 % (404)Instruction limit reached!
% 8.83/2.71 % (404)------------------------------
% 8.83/2.71 % (404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.71 % (404)Termination reason: Unknown
% 8.83/2.71 % (404)Termination phase: Saturation
% 8.83/2.71
% 8.83/2.71 % (404)Memory used [KB]: 7675
% 8.83/2.71 % (404)Time elapsed: 0.160 s
% 8.83/2.71 % (404)Instructions burned: 340 (million)
% 8.83/2.71 % (404)------------------------------
% 8.83/2.71 % (404)------------------------------
% 8.83/2.71 % (408)Instruction limit reached!
% 8.83/2.71 % (408)------------------------------
% 8.83/2.71 % (408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.71 % (408)Termination reason: Unknown
% 8.83/2.71 % (408)Termination phase: Saturation
% 8.83/2.71
% 8.83/2.71 % (408)Memory used [KB]: 3582
% 8.83/2.71 % (408)Time elapsed: 0.095 s
% 8.83/2.71 % (408)Instructions burned: 193 (million)
% 8.83/2.71 % (408)------------------------------
% 8.83/2.71 % (408)------------------------------
% 8.83/2.72 % (410)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_32705 for (2989ds/90Mi)
% 8.83/2.72 % (411)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_32705 for (2989ds/231Mi)
% 8.83/2.72 % (412)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_32705 for (2989ds/458Mi)
% 8.83/2.73 % (407)Instruction limit reached!
% 8.83/2.73 % (407)------------------------------
% 8.83/2.73 % (407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.73 % (407)Termination reason: Unknown
% 8.83/2.73 % (407)Termination phase: Saturation
% 8.83/2.73
% 8.83/2.73 % (407)Memory used [KB]: 7931
% 8.83/2.73 % (407)Time elapsed: 0.137 s
% 8.83/2.73 % (407)Instructions burned: 298 (million)
% 8.83/2.73 % (407)------------------------------
% 8.83/2.73 % (407)------------------------------
% 8.83/2.75 % (413)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_32705 for (2989ds/31Mi)
% 8.83/2.76 % (410)Instruction limit reached!
% 8.83/2.76 % (410)------------------------------
% 8.83/2.76 % (410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.76 % (410)Termination reason: Unknown
% 8.83/2.76 % (410)Termination phase: Property scanning
% 8.83/2.76
% 8.83/2.76 % (384)Instruction limit reached!
% 8.83/2.76 % (384)------------------------------
% 8.83/2.76 % (384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.76 % (384)Termination reason: Unknown
% 8.83/2.76 % (384)Termination phase: Saturation
% 8.83/2.76
% 8.83/2.76 % (384)Memory used [KB]: 8059
% 8.83/2.76 % (384)Time elapsed: 0.523 s
% 8.83/2.76 % (384)Instructions burned: 1087 (million)
% 8.83/2.76 % (384)------------------------------
% 8.83/2.76 % (384)------------------------------
% 8.83/2.76 % (410)Memory used [KB]: 2302
% 8.83/2.76 % (410)Time elapsed: 0.044 s
% 8.83/2.76 % (410)Instructions burned: 90 (million)
% 8.83/2.76 % (410)------------------------------
% 8.83/2.76 % (410)------------------------------
% 8.83/2.76 % (413)Instruction limit reached!
% 8.83/2.76 % (413)------------------------------
% 8.83/2.76 % (413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.76 % (413)Termination reason: Unknown
% 8.83/2.76 % (413)Termination phase: Property scanning
% 8.83/2.76
% 8.83/2.76 % (413)Memory used [KB]: 1918
% 8.83/2.76 % (413)Time elapsed: 0.018 s
% 8.83/2.76 % (413)Instructions burned: 32 (million)
% 8.83/2.76 % (413)------------------------------
% 8.83/2.76 % (413)------------------------------
% 8.83/2.78 % (415)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_32705 for (2989ds/987Mi)
% 8.83/2.78 % (414)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_32705 for (2989ds/297Mi)
% 8.83/2.78 % (416)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_32705 for (2989ds/182Mi)
% 8.83/2.78 % (409)Instruction limit reached!
% 8.83/2.78 % (409)------------------------------
% 8.83/2.78 % (409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.78 % (409)Termination reason: Unknown
% 8.83/2.78 % (409)Termination phase: Saturation
% 8.83/2.78
% 8.83/2.78 % (409)Memory used [KB]: 7291
% 8.83/2.78 % (409)Time elapsed: 0.145 s
% 8.83/2.78 % (409)Instructions burned: 258 (million)
% 8.83/2.78 % (409)------------------------------
% 8.83/2.78 % (409)------------------------------
% 8.83/2.78 % (402)Instruction limit reached!
% 8.83/2.78 % (402)------------------------------
% 8.83/2.78 % (402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.78 % (402)Termination reason: Unknown
% 8.83/2.78 % (402)Termination phase: Saturation
% 8.83/2.78
% 8.83/2.78 % (402)Memory used [KB]: 8571
% 8.83/2.78 % (402)Time elapsed: 0.302 s
% 8.83/2.78 % (402)Instructions burned: 614 (million)
% 8.83/2.78 % (402)------------------------------
% 8.83/2.78 % (402)------------------------------
% 10.51/2.80 % (417)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_32705 for (2988ds/182Mi)
% 10.51/2.80 % (418)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_32705 for (2988ds/154Mi)
% 10.51/2.83 % (411)Instruction limit reached!
% 10.51/2.83 % (411)------------------------------
% 10.51/2.83 % (411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.51/2.83 % (411)Termination reason: Unknown
% 10.51/2.83 % (411)Termination phase: Saturation
% 10.51/2.83
% 10.51/2.83 % (411)Memory used [KB]: 7164
% 10.51/2.83 % (411)Time elapsed: 0.105 s
% 10.51/2.83 % (411)Instructions burned: 232 (million)
% 10.51/2.83 % (411)------------------------------
% 10.51/2.83 % (411)------------------------------
% 10.51/2.84 % (419)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_32705 for (2988ds/79Mi)
% 10.51/2.86 % (416)Instruction limit reached!
% 10.51/2.86 % (416)------------------------------
% 10.51/2.86 % (416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.51/2.86 % (416)Termination reason: Unknown
% 10.51/2.86 % (416)Termination phase: Saturation
% 10.51/2.86
% 10.51/2.86 % (416)Memory used [KB]: 7291
% 10.51/2.86 % (416)Time elapsed: 0.086 s
% 10.51/2.86 % (416)Instructions burned: 184 (million)
% 10.51/2.86 % (416)------------------------------
% 10.51/2.86 % (416)------------------------------
% 10.51/2.87 % (418)Instruction limit reached!
% 10.51/2.87 % (418)------------------------------
% 10.51/2.87 % (418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.51/2.87 % (418)Termination reason: Unknown
% 10.51/2.87 % (418)Termination phase: Saturation
% 10.51/2.87
% 10.51/2.87 % (418)Memory used [KB]: 2558
% 10.51/2.87 % (418)Time elapsed: 0.070 s
% 10.51/2.87 % (418)Instructions burned: 155 (million)
% 10.51/2.87 % (418)------------------------------
% 10.51/2.87 % (418)------------------------------
% 10.51/2.88 % (420)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_32705 for (2988ds/216Mi)
% 10.51/2.88 % (419)Instruction limit reached!
% 10.51/2.88 % (419)------------------------------
% 10.51/2.88 % (419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.51/2.88 % (419)Termination reason: Unknown
% 10.51/2.88 % (419)Termination phase: Function definition elimination
% 10.51/2.88
% 10.51/2.88 % (419)Memory used [KB]: 2302
% 10.51/2.88 % (419)Time elapsed: 0.040 s
% 10.51/2.88 % (419)Instructions burned: 79 (million)
% 10.51/2.88 % (419)------------------------------
% 10.51/2.88 % (419)------------------------------
% 10.51/2.88 % (421)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_32705 for (2988ds/114Mi)
% 10.51/2.89 % (417)Instruction limit reached!
% 10.51/2.89 % (417)------------------------------
% 10.51/2.89 % (417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.51/2.89 % (417)Termination reason: Unknown
% 10.51/2.89 % (417)Termination phase: Saturation
% 10.51/2.89
% 10.51/2.89 % (417)Memory used [KB]: 7291
% 10.51/2.89 % (417)Time elapsed: 0.091 s
% 10.51/2.89 % (417)Instructions burned: 183 (million)
% 10.51/2.89 % (417)------------------------------
% 10.51/2.89 % (417)------------------------------
% 10.98/2.90 % (422)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_32705 for (2987ds/922Mi)
% 10.98/2.90 % (423)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_32705 for (2987ds/182Mi)
% 10.98/2.91 % (414)Instruction limit reached!
% 10.98/2.91 % (414)------------------------------
% 10.98/2.91 % (414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.98/2.91 % (414)Termination reason: Unknown
% 10.98/2.91 % (414)Termination phase: Saturation
% 10.98/2.91
% 10.98/2.91 % (414)Memory used [KB]: 7547
% 10.98/2.91 % (414)Time elapsed: 0.138 s
% 10.98/2.91 % (414)Instructions burned: 297 (million)
% 10.98/2.91 % (414)------------------------------
% 10.98/2.91 % (414)------------------------------
% 10.98/2.93 % (424)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_32705 for (2987ds/164Mi)
% 10.98/2.94 % (421)Instruction limit reached!
% 10.98/2.94 % (421)------------------------------
% 10.98/2.94 % (421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.98/2.94 % (421)Termination reason: Unknown
% 10.98/2.94 % (421)Termination phase: Saturation
% 10.98/2.94
% 10.98/2.94 % (421)Memory used [KB]: 6908
% 10.98/2.94 % (421)Time elapsed: 0.055 s
% 10.98/2.94 % (421)Instructions burned: 115 (million)
% 10.98/2.94 % (421)------------------------------
% 10.98/2.94 % (421)------------------------------
% 10.98/2.94 % (412)Instruction limit reached!
% 10.98/2.94 % (412)------------------------------
% 10.98/2.94 % (412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.98/2.94 % (412)Termination reason: Unknown
% 10.98/2.94 % (412)Termination phase: Saturation
% 10.98/2.94
% 10.98/2.94 % (412)Memory used [KB]: 8059
% 10.98/2.94 % (412)Time elapsed: 0.220 s
% 10.98/2.94 % (412)Instructions burned: 458 (million)
% 10.98/2.94 % (412)------------------------------
% 10.98/2.94 % (412)------------------------------
% 10.98/2.96 % (425)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_32705 for (2987ds/50Mi)
% 10.98/2.96 % (426)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_32705 for (2987ds/368Mi)
% 10.98/2.98 % (420)Instruction limit reached!
% 10.98/2.98 % (420)------------------------------
% 10.98/2.98 % (420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.98/2.98 % (420)Termination reason: Unknown
% 10.98/2.98 % (420)Termination phase: Saturation
% 10.98/2.98
% 10.98/2.98 % (420)Memory used [KB]: 7547
% 10.98/2.98 % (420)Time elapsed: 0.100 s
% 10.98/2.98 % (420)Instructions burned: 216 (million)
% 10.98/2.98 % (420)------------------------------
% 10.98/2.98 % (420)------------------------------
% 10.98/2.98 % (425)Instruction limit reached!
% 10.98/2.98 % (425)------------------------------
% 10.98/2.98 % (425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.98/2.98 % (425)Termination reason: Unknown
% 10.98/2.98 % (425)Termination phase: Property scanning
% 10.98/2.98
% 10.98/2.98 % (425)Memory used [KB]: 2302
% 10.98/2.98 % (425)Time elapsed: 0.025 s
% 10.98/2.98 % (425)Instructions burned: 51 (million)
% 10.98/2.98 % (425)------------------------------
% 10.98/2.98 % (425)------------------------------
% 10.98/2.98 % (423)Instruction limit reached!
% 10.98/2.98 % (423)------------------------------
% 10.98/2.98 % (423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.98/2.98 % (423)Termination reason: Unknown
% 10.98/2.98 % (423)Termination phase: Saturation
% 10.98/2.98
% 10.98/2.98 % (423)Memory used [KB]: 7291
% 10.98/2.98 % (423)Time elapsed: 0.082 s
% 10.98/2.98 % (423)Instructions burned: 182 (million)
% 10.98/2.98 % (423)------------------------------
% 10.98/2.98 % (423)------------------------------
% 10.98/2.99 % (428)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_32705 for (2986ds/267Mi)
% 10.98/2.99 % (427)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_32705 for (2986ds/1021Mi)
% 10.98/3.00 % (429)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_32705 for (2986ds/204Mi)
% 10.98/3.00 % (424)Instruction limit reached!
% 10.98/3.00 % (424)------------------------------
% 10.98/3.00 % (424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.98/3.00 % (424)Termination reason: Unknown
% 10.98/3.00 % (424)Termination phase: Saturation
% 10.98/3.00
% 10.98/3.00 % (424)Memory used [KB]: 2558
% 10.98/3.00 % (424)Time elapsed: 0.077 s
% 10.98/3.00 % (424)Instructions burned: 164 (million)
% 10.98/3.00 % (424)------------------------------
% 10.98/3.00 % (424)------------------------------
% 10.98/3.02 % (430)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_32705 for (2986ds/26Mi)
% 12.25/3.03 % (430)Instruction limit reached!
% 12.25/3.03 % (430)------------------------------
% 12.25/3.03 % (430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.25/3.03 % (430)Termination reason: Unknown
% 12.25/3.03 % (430)Termination phase: shuffling
% 12.25/3.03
% 12.25/3.03 % (430)Memory used [KB]: 2046
% 12.25/3.03 % (430)Time elapsed: 0.015 s
% 12.25/3.03 % (430)Instructions burned: 27 (million)
% 12.25/3.03 % (430)------------------------------
% 12.25/3.03 % (430)------------------------------
% 12.25/3.05 % (431)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_32705 for (2986ds/53Mi)
% 12.25/3.08 % (431)Instruction limit reached!
% 12.25/3.08 % (431)------------------------------
% 12.25/3.08 % (431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.25/3.08 % (431)Termination reason: Unknown
% 12.25/3.08 % (431)Termination phase: Property scanning
% 12.25/3.08
% 12.25/3.08 % (431)Memory used [KB]: 2302
% 12.25/3.08 % (431)Time elapsed: 0.027 s
% 12.25/3.08 % (431)Instructions burned: 53 (million)
% 12.25/3.08 % (431)------------------------------
% 12.25/3.08 % (431)------------------------------
% 12.25/3.09 % (432)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_32705 for (2986ds/4436Mi)
% 12.25/3.10 % (429)Instruction limit reached!
% 12.25/3.10 % (429)------------------------------
% 12.25/3.10 % (429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.25/3.10 % (429)Termination reason: Unknown
% 12.25/3.10 % (429)Termination phase: Saturation
% 12.25/3.10
% 12.25/3.10 % (429)Memory used [KB]: 7419
% 12.25/3.10 % (429)Time elapsed: 0.099 s
% 12.25/3.10 % (429)Instructions burned: 204 (million)
% 12.25/3.10 % (429)------------------------------
% 12.25/3.10 % (429)------------------------------
% 12.25/3.11 % (433)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_32705 for (2985ds/1539Mi)
% 12.25/3.12 % (428)Instruction limit reached!
% 12.25/3.12 % (428)------------------------------
% 12.25/3.12 % (428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.25/3.12 % (428)Termination reason: Unknown
% 12.25/3.12 % (428)Termination phase: Saturation
% 12.25/3.12
% 12.25/3.12 % (428)Memory used [KB]: 7547
% 12.25/3.12 % (428)Time elapsed: 0.129 s
% 12.25/3.12 % (428)Instructions burned: 267 (million)
% 12.25/3.12 % (428)------------------------------
% 12.25/3.12 % (428)------------------------------
% 13.00/3.13 % (426)Instruction limit reached!
% 13.00/3.13 % (426)------------------------------
% 13.00/3.13 % (426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.00/3.13 % (426)Termination reason: Unknown
% 13.00/3.13 % (426)Termination phase: Saturation
% 13.00/3.13
% 13.00/3.13 % (426)Memory used [KB]: 7803
% 13.00/3.13 % (426)Time elapsed: 0.174 s
% 13.00/3.13 % (426)Instructions burned: 368 (million)
% 13.00/3.13 % (426)------------------------------
% 13.00/3.13 % (426)------------------------------
% 13.00/3.14 % (434)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_32705 for (2985ds/408Mi)
% 13.00/3.15 % (435)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_32705 for (2985ds/5205Mi)
% 13.22/3.25 % (415)Instruction limit reached!
% 13.22/3.25 % (415)------------------------------
% 13.22/3.25 % (415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.22/3.25 % (415)Termination reason: Unknown
% 13.22/3.25 % (415)Termination phase: Saturation
% 13.22/3.25
% 13.22/3.25 % (415)Memory used [KB]: 8699
% 13.22/3.25 % (415)Time elapsed: 0.474 s
% 13.22/3.25 % (415)Instructions burned: 987 (million)
% 13.22/3.25 % (415)------------------------------
% 13.22/3.25 % (415)------------------------------
% 13.22/3.27 % (436)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_32705 for (2984ds/1913Mi)
% 13.50/3.34 % (434)Instruction limit reached!
% 13.50/3.34 % (434)------------------------------
% 13.50/3.34 % (434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.50/3.34 % (434)Termination reason: Unknown
% 13.50/3.34 % (434)Termination phase: Saturation
% 13.50/3.34
% 13.50/3.34 % (434)Memory used [KB]: 8443
% 13.50/3.34 % (434)Time elapsed: 0.200 s
% 13.50/3.34 % (434)Instructions burned: 409 (million)
% 13.50/3.34 % (434)------------------------------
% 13.50/3.34 % (434)------------------------------
% 13.50/3.34 % (422)Instruction limit reached!
% 13.50/3.34 % (422)------------------------------
% 13.50/3.34 % (422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.50/3.34 % (422)Termination reason: Unknown
% 13.50/3.34 % (422)Termination phase: Saturation
% 13.50/3.34
% 13.50/3.34 % (422)Memory used [KB]: 7675
% 13.50/3.34 % (422)Time elapsed: 0.444 s
% 13.50/3.34 % (422)Instructions burned: 922 (million)
% 13.50/3.34 % (422)------------------------------
% 13.50/3.34 % (422)------------------------------
% 13.50/3.35 % (437)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_32705 for (2983ds/4350Mi)
% 13.50/3.36 % (438)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_32705 for (2983ds/68Mi)
% 13.86/3.40 % (438)Instruction limit reached!
% 13.86/3.40 % (438)------------------------------
% 13.86/3.40 % (438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.86/3.40 % (438)Termination reason: Unknown
% 13.86/3.40 % (438)Termination phase: Property scanning
% 13.86/3.40
% 13.86/3.40 % (438)Memory used [KB]: 2302
% 13.86/3.40 % (438)Time elapsed: 0.036 s
% 13.86/3.40 % (438)Instructions burned: 70 (million)
% 13.86/3.40 % (438)------------------------------
% 13.86/3.40 % (438)------------------------------
% 13.86/3.41 % (439)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_32705 for (2982ds/358Mi)
% 13.86/3.47 % (427)Instruction limit reached!
% 13.86/3.47 % (427)------------------------------
% 13.86/3.47 % (427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.86/3.47 % (427)Termination reason: Unknown
% 13.86/3.47 % (427)Termination phase: Saturation
% 13.86/3.47
% 13.86/3.47 % (427)Memory used [KB]: 8315
% 13.86/3.47 % (427)Time elapsed: 0.482 s
% 13.86/3.47 % (427)Instructions burned: 1022 (million)
% 13.86/3.47 % (427)------------------------------
% 13.86/3.47 % (427)------------------------------
% 13.86/3.49 % (440)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_32705 for (2982ds/31Mi)
% 14.00/3.51 % (440)Instruction limit reached!
% 14.00/3.51 % (440)------------------------------
% 14.00/3.51 % (440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.00/3.51 % (440)Termination reason: Unknown
% 14.00/3.51 % (440)Termination phase: Property scanning
% 14.00/3.51
% 14.00/3.51 % (440)Memory used [KB]: 2046
% 14.00/3.51 % (440)Time elapsed: 0.018 s
% 14.00/3.51 % (440)Instructions burned: 32 (million)
% 14.00/3.51 % (440)------------------------------
% 14.00/3.51 % (440)------------------------------
% 14.00/3.52 % (441)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_32705 for (2981ds/279Mi)
% 14.00/3.55 % (439)First to succeed.
% 14.00/3.56 % (439)Refutation found. Thanks to Tanya!
% 14.00/3.56 % SZS status Theorem for DTF2THF_32705
% 14.00/3.56 % SZS output start Proof for DTF2THF_32705
% 14.00/3.56 thf(type_def_5, type, itself: ($tType) > $tType).
% 14.00/3.56 thf(type_def_7, type, coindu1593790203_llist: ($tType) > $tType).
% 14.00/3.56 thf(type_def_8, type, set: ($tType) > $tType).
% 14.00/3.56 thf(type_def_9, type, product_prod: ($tType * $tType) > $tType).
% 14.00/3.56 thf(type_def_10, type, a: $tType).
% 14.00/3.56 thf(func_def_0, type, coindu1593790203_llist: ($tType) > $tType).
% 14.00/3.56 thf(func_def_1, type, product_prod: ($tType * $tType) > $tType).
% 14.00/3.56 thf(func_def_2, type, set: ($tType) > $tType).
% 14.00/3.56 thf(func_def_3, type, itself: ($tType) > $tType).
% 14.00/3.56 thf(func_def_4, type, a: $tType).
% 14.00/3.56 thf(func_def_5, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 14.00/3.56 thf(func_def_6, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 14.00/3.56 thf(func_def_7, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 14.00/3.56 thf(func_def_8, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 14.00/3.56 thf(func_def_9, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 14.00/3.56 thf(func_def_10, type, coindu1571841457prefix: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 14.00/3.56 thf(func_def_11, type, coindu1928975208n_lset: !>[X0: $tType]:(set @ X0 > coindu1593790203_llist @ X0 > set @ X0)).
% 14.00/3.56 thf(func_def_12, type, coindu268472904append: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_13, type, coindu1213758845finite: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 14.00/3.56 thf(func_def_14, type, coindu2000965700_llast: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 14.00/3.56 thf(func_def_15, type, coindu300403952lexord: !>[X0: $tType]:((X0 > X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 14.00/3.56 thf(func_def_16, type, coindu1121789889_LCons: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_17, type, coindu1598213697e_LNil: !>[X0: $tType]:(coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_18, type, coindu1244876290_llist: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > $o) > (X0 > coindu1593790203_llist @ X1) > (X0 > X0) > X0 > coindu1593790203_llist @ X1)).
% 14.00/3.56 thf(func_def_19, type, coindu335574135_lnull: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 14.00/3.56 thf(func_def_20, type, coindu44415597_llist: !>[X0: $tType]:((X0 > $o) > coindu1593790203_llist @ X0 > $o)).
% 14.00/3.56 thf(func_def_21, type, coindu567634248member: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > $o)).
% 14.00/3.56 thf(func_def_22, type, coindu1696667936prefix: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 14.00/3.56 thf(func_def_23, type, coindu1055736764_lsetp: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > $o)).
% 14.00/3.56 thf(func_def_24, type, coindu574146665prefix: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o)).
% 14.00/3.56 thf(func_def_25, type, coindu721411036eWhile: !>[X0: $tType]:((X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_26, type, coindu543932918sorted: !>[X0: $tType]:((X0 > X0 > $o) > coindu1593790203_llist @ X0 > $o)).
% 14.00/3.56 thf(func_def_27, type, coindu48241764sorted: !>[X0: $tType]:(coindu1593790203_llist @ X0 > $o)).
% 14.00/3.56 thf(func_def_28, type, coindu1599971794_llist: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coindu1593790203_llist @ X1)).
% 14.00/3.56 thf(func_def_29, type, undefined: !>[X0: $tType]:(X0)).
% 14.00/3.56 thf(func_def_30, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 14.00/3.56 thf(func_def_31, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 14.00/3.56 thf(func_def_32, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 14.00/3.56 thf(func_def_33, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 14.00/3.56 thf(func_def_34, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 14.00/3.56 thf(func_def_35, type, type2: !>[X0: $tType]:(itself @ X0)).
% 14.00/3.56 thf(func_def_36, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 14.00/3.56 thf(func_def_37, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 14.00/3.56 thf(func_def_38, type, r: a > a > $o).
% 14.00/3.56 thf(func_def_40, type, x: a).
% 14.00/3.56 thf(func_def_41, type, xs: coindu1593790203_llist @ a).
% 14.00/3.56 thf(func_def_42, type, xs2: coindu1593790203_llist @ a).
% 14.00/3.56 thf(func_def_43, type, xsa: coindu1593790203_llist @ a).
% 14.00/3.56 thf(func_def_44, type, ys: coindu1593790203_llist @ a).
% 14.00/3.56 thf(func_def_45, type, ysa: coindu1593790203_llist @ a).
% 14.00/3.56 thf(func_def_64, type, sP0: !>[X0: $tType]:(coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0 > $o)).
% 14.00/3.56 thf(func_def_65, type, sK1: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_66, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0)).
% 14.00/3.56 thf(func_def_67, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1)).
% 14.00/3.56 thf(func_def_68, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2)).
% 14.00/3.56 thf(func_def_69, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3)).
% 14.00/3.56 thf(func_def_70, type, sK6: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4)).
% 14.00/3.56 thf(func_def_71, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5)).
% 14.00/3.56 thf(func_def_72, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6)).
% 14.00/3.56 thf(func_def_73, type, sK9: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_74, type, sK10: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 14.00/3.56 thf(func_def_75, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 14.00/3.56 thf(func_def_76, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 14.00/3.56 thf(func_def_77, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 14.00/3.56 thf(func_def_78, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 14.00/3.56 thf(func_def_79, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 14.00/3.56 thf(func_def_80, type, sK16: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 14.00/3.56 thf(func_def_81, type, sK17: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 14.00/3.56 thf(func_def_82, type, sK18: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 14.00/3.56 thf(func_def_83, type, sK19: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 14.00/3.56 thf(func_def_84, type, sK20: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 14.00/3.56 thf(func_def_85, type, sK21: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 14.00/3.56 thf(func_def_86, type, sK22: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_87, type, sK23: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_88, type, sK24: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_89, type, sK25: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 14.00/3.56 thf(func_def_90, type, sK26: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_91, type, sK27: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 14.00/3.56 thf(func_def_92, type, sK28: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 14.00/3.56 thf(func_def_93, type, sK29: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 14.00/3.56 thf(func_def_94, type, sK30: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_95, type, sK31: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X1)).
% 14.00/3.56 thf(func_def_96, type, sK32: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_97, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 14.00/3.56 thf(func_def_98, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 14.00/3.56 thf(func_def_99, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 14.00/3.56 thf(func_def_100, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_101, type, sK37: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 14.00/3.56 thf(func_def_102, type, sK38: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_103, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6)).
% 14.00/3.56 thf(func_def_104, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 14.00/3.56 thf(func_def_105, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 14.00/3.56 thf(func_def_106, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 14.00/3.56 thf(func_def_107, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 14.00/3.56 thf(func_def_108, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 14.00/3.56 thf(func_def_109, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_110, type, sK46: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 14.00/3.56 thf(func_def_111, type, sK47: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 14.00/3.56 thf(func_def_112, type, sK48: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_113, type, sK49: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 14.00/3.56 thf(func_def_114, type, sK50: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 14.00/3.56 thf(func_def_115, type, sK51: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_116, type, sK52: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 14.00/3.56 thf(func_def_117, type, sK53: !>[X0: $tType]:(coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_118, type, sK54: !>[X0: $tType]:(coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_119, type, sK55: !>[X0: $tType]:(coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_120, type, sK56: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_121, type, sK57: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > X0)).
% 14.00/3.56 thf(func_def_122, type, sK58: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > X0)).
% 14.00/3.56 thf(func_def_123, type, sK59: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_124, type, sK60: !>[X0: $tType]:((X0 > X0 > $o) > (coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_125, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0)).
% 14.00/3.56 thf(func_def_126, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1)).
% 14.00/3.56 thf(func_def_127, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2)).
% 14.00/3.56 thf(func_def_128, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3)).
% 14.00/3.56 thf(func_def_129, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4)).
% 14.00/3.56 thf(func_def_130, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5)).
% 14.00/3.56 thf(func_def_131, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 14.00/3.56 thf(func_def_132, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 14.00/3.56 thf(func_def_133, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_134, type, sK70: !>[X0: $tType]:(coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_135, type, sK71: !>[X0: $tType]:(coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_136, type, sK72: !>[X0: $tType]:(coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0 > X0)).
% 14.00/3.56 thf(func_def_137, type, sK73: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_138, type, sK74: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_139, type, sK75: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_140, type, sK76: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > (X0 > X0 > $o) > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_141, type, sK77: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_142, type, sK78: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_143, type, sK79: !>[X0: $tType]:(set @ product_prod @ coindu1593790203_llist @ X0 @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_144, type, sK80: !>[X0: $tType]:(set @ product_prod @ coindu1593790203_llist @ X0 @ coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_145, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 14.00/3.56 thf(func_def_146, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 14.00/3.56 thf(func_def_147, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 14.00/3.56 thf(func_def_148, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 14.00/3.56 thf(func_def_149, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 14.00/3.56 thf(func_def_150, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_151, type, sK87: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_152, type, sK88: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_153, type, sK89: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_154, type, sK90: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_155, type, sK91: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0)).
% 14.00/3.56 thf(func_def_156, type, sK92: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > set @ X0 > X0)).
% 14.00/3.56 thf(func_def_157, type, sK93: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_158, type, sK94: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_159, type, sK95: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_160, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 14.00/3.56 thf(func_def_161, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 14.00/3.56 thf(func_def_162, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 14.00/3.56 thf(func_def_163, type, sK99: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 14.00/3.56 thf(func_def_164, type, sK100: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_165, type, sK101: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 14.00/3.56 thf(func_def_166, type, sK102: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 14.00/3.56 thf(func_def_167, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 14.00/3.56 thf(func_def_168, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 14.00/3.56 thf(func_def_169, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_170, type, sK106: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_171, type, sK107: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_172, type, sK108: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1)).
% 14.00/3.56 thf(func_def_173, type, sK109: !>[X0: $tType, X1: $tType]:(set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0)).
% 14.00/3.56 thf(func_def_174, type, sK110: !>[X0: $tType]:((X0 > X0 > $o) > (coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_175, type, sK111: !>[X0: $tType]:((X0 > X0 > $o) > (coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_176, type, sK112: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 14.00/3.56 thf(func_def_177, type, sK113: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 14.00/3.56 thf(func_def_178, type, sK114: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 14.00/3.56 thf(func_def_179, type, sK115: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_180, type, sK116: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_181, type, sK117: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 14.00/3.56 thf(func_def_182, type, sK118: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 14.00/3.56 thf(func_def_183, type, sK119: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_184, type, sK120: !>[X0: $tType]:((coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_185, type, sK121: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_186, type, sK122: !>[X0: $tType]:((coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > $o) > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_187, type, sK123: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 14.00/3.56 thf(func_def_188, type, sK124: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 14.00/3.56 thf(func_def_189, type, sK125: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 14.00/3.56 thf(func_def_190, type, sK126: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 14.00/3.56 thf(func_def_191, type, sK127: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_192, type, sK128: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > $o) > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_193, type, sK129: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > $o) > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_194, type, sK130: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_195, type, sK131: !>[X0: $tType]:((coindu1593790203_llist @ X0 > X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_197, type, sK133: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_198, type, sK134: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_199, type, sK135: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_200, type, sK136: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_201, type, sK137: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 14.00/3.56 thf(func_def_202, type, sK138: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_203, type, sK139: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_204, type, sK140: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_205, type, sK141: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_206, type, sK142: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_207, type, sK143: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_208, type, sK144: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_209, type, sK145: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_210, type, sK146: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_211, type, sK147: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_212, type, sK148: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_213, type, sK149: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_214, type, sK150: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_215, type, sK151: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_216, type, sK152: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_217, type, sK153: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_218, type, sK154: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_219, type, sK155: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_220, type, sK156: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_221, type, sK157: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_222, type, sK158: !>[X0: $tType]:(X0 > X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_223, type, sK159: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_224, type, sK160: !>[X0: $tType]:((X0 > X0 > $o) > X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_225, type, sK161: !>[X0: $tType]:((X0 > X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0 > X0)).
% 14.00/3.56 thf(func_def_226, type, sK162: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_227, type, sK163: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_228, type, sK164: !>[X0: $tType]:(X0 > X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_229, type, sK165: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_230, type, sK166: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_231, type, sK167: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_232, type, sK168: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_233, type, sK169: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_234, type, sK170: !>[X0: $tType]:(coindu1593790203_llist @ X0 > X0)).
% 14.00/3.56 thf(func_def_235, type, sK171: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_236, type, sK172: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_237, type, sK173: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_238, type, sK174: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_239, type, sK175: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_240, type, sK176: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_241, type, sK177: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_242, type, sK178: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_243, type, sK179: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_244, type, sK180: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_245, type, sK181: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_246, type, sK182: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_247, type, sK183: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_248, type, sK184: !>[X0: $tType]:((X0 > $o) > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_249, type, sK185: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_250, type, sK186: !>[X0: $tType]:(X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_251, type, sK187: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_252, type, sK188: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 14.00/3.56 thf(func_def_253, type, sK189: !>[X0: $tType]:(coindu1593790203_llist @ X0 > coindu1593790203_llist @ X0)).
% 14.00/3.56 thf(func_def_254, type, ph190: !>[X0: $tType]:(X0)).
% 14.00/3.56 thf(f2744,plain,(
% 14.00/3.56 $false),
% 14.00/3.56 inference(avatar_sat_refutation,[status(thm)],[f2417,f2429,f2479,f2540,f2610,f2741])).
% 14.00/3.56 thf(f2741,plain,(
% 14.00/3.56 ~spl132_1 | spl132_2),
% 14.00/3.56 inference(avatar_contradiction_clause,[status(thm)],[f2740])).
% 14.00/3.56 thf(f2740,plain,(
% 14.00/3.56 $false | (~spl132_1 | spl132_2)),
% 14.00/3.56 inference(trivial_inequality_removal,[status(thm)],[f2721])).
% 14.00/3.56 thf(f2721,plain,(
% 14.00/3.56 ($true != $true) | (~spl132_1 | spl132_2)),
% 14.00/3.56 inference(superposition,[status(thm)],[f1482,f2719])).
% 14.00/3.56 thf(f2719,plain,(
% 14.00/3.56 ( ! [X0 : coindu1593790203_llist @ a] : (((coindu300403952lexord @ a @ r @ ysa @ (coindu1121789889_LCons @ a @ x @ X0)) = $true)) ) | (~spl132_1 | spl132_2)),
% 14.00/3.56 inference(subsumption_resolution,[status(thm)],[f2698,f2411])).
% 14.00/3.56 thf(f2411,plain,(
% 14.00/3.56 (ysa != coindu1598213697e_LNil @ a) | spl132_2),
% 14.00/3.56 inference(avatar_component_clause,[status(thm)],[f2410])).
% 14.00/3.56 thf(f2410,definition,(
% 14.00/3.56 spl132_2 <=> (ysa = coindu1598213697e_LNil @ a)),
% 14.00/3.56 introduced(definition,[new_symbols(naming,[spl132_2])],[avatar_definition])).
% 14.00/3.56 thf(f2698,plain,(
% 14.00/3.56 ( ! [X0 : coindu1593790203_llist @ a] : (((coindu300403952lexord @ a @ r @ ysa @ (coindu1121789889_LCons @ a @ x @ X0)) = $true) | (ysa = coindu1598213697e_LNil @ a)) ) | ~spl132_1),
% 14.00/3.56 inference(superposition,[status(thm)],[f2644,f1174])).
% 14.00/3.56 thf(f1174,plain,(
% 14.00/3.56 ( ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (((coindu1121789889_LCons @ X0 @ (sK29 @ X0 @ X1) @ (sK30 @ X0 @ X1)) = X1) | (coindu1598213697e_LNil @ X0 = X1)) )),
% 14.00/3.56 inference(cnf_transformation,[status(thm)],[f1026])).
% 14.00/3.56 thf(f1026,plain,(
% 14.00/3.56 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : ((coindu1598213697e_LNil @ X0 = X1) | ((coindu1121789889_LCons @ X0 @ (sK29 @ X0 @ X1) @ (sK30 @ X0 @ X1)) = X1))),
% 14.00/3.56 inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30])],[f881,f1025])).
% 14.00/3.56 thf(f1025,plain,(
% 14.00/3.56 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : (? [X2 : X0,X3 : coindu1593790203_llist @ X0] : ((coindu1121789889_LCons @ X0 @ X2 @ X3) = X1) => ((coindu1121789889_LCons @ X0 @ (sK29 @ X0 @ X1) @ (sK30 @ X0 @ X1)) = X1))),
% 14.00/3.56 introduced(definition,[],[choice_axiom])).
% 14.00/3.56 thf(f881,plain,(
% 14.00/3.56 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : ((coindu1598213697e_LNil @ X0 = X1) | ? [X2 : X0,X3 : coindu1593790203_llist @ X0] : ((coindu1121789889_LCons @ X0 @ X2 @ X3) = X1))),
% 14.00/3.56 inference(ennf_transformation,[status(thm)],[f755])).
% 14.00/3.56 thf(f755,plain,(
% 14.00/3.56 ! [X0 : $tType,X1 : coindu1593790203_llist @ X0] : ((coindu1598213697e_LNil @ X0 != X1) => ~! [X2 : X0,X3 : coindu1593790203_llist @ X0] : ((coindu1121789889_LCons @ X0 @ X2 @ X3) != X1))),
% 14.00/3.56 inference(rectify,[status(thm)],[f55])).
% 14.00/3.56 thf(f55,axiom,(
% 14.00/3.56 ! [X0 : $tType,X5 : coindu1593790203_llist @ X0] : ((coindu1598213697e_LNil @ X0 != X5) => ~! [X61 : X0,X62 : coindu1593790203_llist @ X0] : ((coindu1121789889_LCons @ X0 @ X61 @ X62) != X5))),
% 14.00/3.56 file('/export/starexec/sandbox/tmp/tmp.vsmmhmmsID/DTF2THF_32705.p',fact_54_llist_Oexhaust)).
% 14.00/3.56 thf(f2644,plain,(
% 14.00/3.56 ( ! [X0 : coindu1593790203_llist @ a,X1 : coindu1593790203_llist @ a] : (((coindu300403952lexord @ a @ r @ (coindu1121789889_LCons @ a @ (sK29 @ a @ ysa) @ X0) @ (coindu1121789889_LCons @ a @ x @ X1)) = $true)) ) | ~spl132_1),
% 14.00/3.56 inference(trivial_inequality_removal,[status(thm)],[f2643])).
% 14.00/3.56 thf(f2643,plain,(
% 14.00/3.56 ( ! [X0 : coindu1593790203_llist @ a,X1 : coindu1593790203_llist @ a] : (((coindu300403952lexord @ a @ r @ (coindu1121789889_LCons @ a @ (sK29 @ a @ ysa) @ X0) @ (coindu1121789889_LCons @ a @ x @ X1)) = $true) | ($true != $true)) ) | ~spl132_1),
% 14.00/3.56 inference(superposition,[status(thm)],[f1364,f2408])).
% 14.00/3.56 thf(f2408,plain,(
% 14.00/3.56 ((r @ (sK29 @ a @ ysa) @ x) = $true) | ~spl132_1),
% 14.00/3.56 inference(avatar_component_clause,[status(thm)],[f2406])).
% 14.00/3.56 thf(f2406,definition,(
% 14.00/3.56 spl132_1 <=> ((r @ (sK29 @ a @ ysa) @ x) = $true)),
% 14.00/3.56 introduced(definition,[new_symbols(naming,[spl132_1])],[avatar_definition])).
% 14.00/3.56 thf(f1364,plain,(
% 14.00/3.56 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o,X4 : coindu1593790203_llist @ X0,X5 : coindu1593790203_llist @ X0] : (((X1 @ X2 @ X3) != $true) | ((coindu300403952lexord @ X0 @ X1 @ (coindu1121789889_LCons @ X0 @ X2 @ X4) @ (coindu1121789889_LCons @ X0 @ X3 @ X5)) = $true)) )),
% 14.00/3.56 inference(cnf_transformation,[status(thm)],[f997])).
% 14.00/3.56 thf(f997,plain,(
% 14.00/3.56 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0,X3 : X0,X4 : coindu1593790203_llist @ X0,X5 : coindu1593790203_llist @ X0] : (((coindu300403952lexord @ X0 @ X1 @ (coindu1121789889_LCons @ X0 @ X2 @ X4) @ (coindu1121789889_LCons @ X0 @ X3 @ X5)) = $true) | ((X1 @ X2 @ X3) != $true))),
% 14.00/3.56 inference(ennf_transformation,[status(thm)],[f395])).
% 14.00/3.56 thf(f395,plain,(
% 14.00/3.56 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0,X3 : X0,X4 : coindu1593790203_llist @ X0,X5 : coindu1593790203_llist @ X0] : (((X1 @ X2 @ X3) = $true) => ((coindu300403952lexord @ X0 @ X1 @ (coindu1121789889_LCons @ X0 @ X2 @ X4) @ (coindu1121789889_LCons @ X0 @ X3 @ X5)) = $true))),
% 14.00/3.56 inference(fool_elimination,[status(thm)],[f394])).
% 14.00/3.56 thf(f394,plain,(
% 14.00/3.56 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0,X3 : X0,X4 : coindu1593790203_llist @ X0,X5 : coindu1593790203_llist @ X0] : ((X1 @ X2 @ X3) => (coindu300403952lexord @ X0 @ X1 @ (coindu1121789889_LCons @ X0 @ X2 @ X4) @ (coindu1121789889_LCons @ X0 @ X3 @ X5)))),
% 14.00/3.56 inference(rectify,[status(thm)],[f12])).
% 14.00/3.56 thf(f12,axiom,(
% 14.00/3.56 ! [X0 : $tType,X10 : X0 > X0 > $o,X4 : X0,X5 : X0,X11 : coindu1593790203_llist @ X0,X12 : coindu1593790203_llist @ X0] : ((X10 @ X4 @ X5) => (coindu300403952lexord @ X0 @ X10 @ (coindu1121789889_LCons @ X0 @ X4 @ X11) @ (coindu1121789889_LCons @ X0 @ X5 @ X12)))),
% 14.00/3.56 file('/export/starexec/sandbox/tmp/tmp.vsmmhmmsID/DTF2THF_32705.p',fact_11_llexord__LCons__less)).
% 14.00/3.56 thf(f1482,plain,(
% 14.00/3.56 ((coindu300403952lexord @ a @ r @ ysa @ (coindu1121789889_LCons @ a @ x @ xs2)) != $true)),
% 14.00/3.56 inference(definition_unfolding,[status(thm)],[f1294,f1124])).
% 14.00/3.56 thf(f1124,plain,(
% 14.00/3.56 (xsa = (coindu1121789889_LCons @ a @ x @ xs2))),
% 14.00/3.56 inference(cnf_transformation,[status(thm)],[f4])).
% 14.00/3.56 thf(f4,axiom,(
% 14.00/3.56 (xsa = (coindu1121789889_LCons @ a @ x @ xs2))),
% 14.00/3.56 file('/export/starexec/sandbox/tmp/tmp.vsmmhmmsID/DTF2THF_32705.p',fact_3_LCons)).
% 14.00/3.56 thf(f1294,plain,(
% 14.00/3.56 ((coindu300403952lexord @ a @ r @ ysa @ xsa) != $true)),
% 14.00/3.56 inference(cnf_transformation,[status(thm)],[f756])).
% 14.00/3.56 thf(f756,plain,(
% 14.00/3.56 ((coindu300403952lexord @ a @ r @ ysa @ xsa) != $true)),
% 14.00/3.56 inference(flattening,[status(thm)],[f575])).
% 14.00/3.56 thf(f575,plain,(
% 14.00/3.56 ~((coindu300403952lexord @ a @ r @ ysa @ xsa) = $true)),
% 14.00/3.56 inference(fool_elimination,[status(thm)],[f574])).
% 14.00/3.56 thf(f574,plain,(
% 14.00/3.56 ~(coindu300403952lexord @ a @ r @ ysa @ xsa)),
% 14.00/3.56 inference(rectify,[status(thm)],[f2])).
% 14.00/3.56 thf(f2,axiom,(
% 14.00/3.56 ~(coindu300403952lexord @ a @ r @ ysa @ xsa)),
% 14.00/3.56 file('/export/starexec/sandbox/tmp/tmp.vsmmhmmsID/DTF2THF_32705.p',fact_1__092_060open_062_092_060not_062_Allexord_Ar_Ays_Axs_092_060close_062)).
% 14.00/3.56 thf(f2610,plain,(
% 14.00/3.56 spl132_2 | ~spl132_3 | ~spl132_5),
% 14.00/3.56 inference(avatar_contradiction_clause,[status(thm)],[f2609])).
% 14.00/3.56 thf(f2609,plain,(
% 14.00/3.56 $false | (spl132_2 | ~spl132_3 | ~spl132_5)),
% 14.00/3.56 inference(subsumption_resolution,[status(thm)],[f2591,f1482])).
% 14.00/3.56 thf(f2591,plain,(
% 14.00/3.56 ((coindu300403952lexord @ a @ r @ ysa @ (coindu1121789889_LCons @ a @ x @ xs2)) = $true) | (spl132_2 | ~spl132_3 | ~spl132_5)),
% 14.00/3.56 inference(superposition,[status(thm)],[f2577,f2432])).
% 14.00/3.56 thf(f2432,plain,(
% 14.00/3.56 (ysa = (coindu1121789889_LCons @ a @ x @ (sK30 @ a @ ysa))) | (spl132_2 | ~spl132_3)),
% 14.00/3.56 inference(subsumption_resolution,[status(thm)],[f2431,f2411])).
% 14.00/3.56 thf(f2431,plain,(
% 14.00/3.56 (ysa = coindu1598213697e_LNil @ a) | (ysa = (coindu1121789889_LCons @ a @ x @ (sK30 @ a @ ysa))) | ~spl132_3),
% 14.00/3.56 inference(superposition,[status(thm)],[f1174,f2416])).
% 14.00/3.56 thf(f2416,plain,(
% 14.00/3.56 (x = (sK29 @ a @ ysa)) | ~spl132_3),
% 14.00/3.56 inference(avatar_component_clause,[status(thm)],[f2414])).
% 14.00/3.56 thf(f2414,definition,(
% 14.00/3.56 spl132_3 <=> (x = (sK29 @ a @ ysa))),
% 14.00/3.56 introduced(definition,[new_symbols(naming,[spl132_3])],[avatar_definition])).
% 14.00/3.56 thf(f2577,plain,(
% 14.00/3.56 ( ! [X0 : a] : (((coindu300403952lexord @ a @ r @ (coindu1121789889_LCons @ a @ X0 @ (sK30 @ a @ ysa)) @ (coindu1121789889_LCons @ a @ X0 @ xs2)) = $true)) ) | ~spl132_5),
% 14.00/3.56 inference(trivial_inequality_removal,[status(thm)],[f2572])).
% 14.00/3.56 thf(f2572,plain,(
% 14.00/3.56 ( ! [X0 : a] : (($true != $true) | ((coindu300403952lexord @ a @ r @ (coindu1121789889_LCons @ a @ X0 @ (sK30 @ a @ ysa)) @ (coindu1121789889_LCons @ a @ X0 @ xs2)) = $true)) ) | ~spl132_5),
% 14.00/3.56 inference(superposition,[status(thm)],[f1258,f2478])).
% 14.00/3.56 thf(f2478,plain,(
% 14.00/3.56 ($true = (coindu300403952lexord @ a @ r @ (sK30 @ a @ ysa) @ xs2)) | ~spl132_5),
% 14.00/3.56 inference(avatar_component_clause,[status(thm)],[f2476])).
% 14.00/3.56 thf(f2476,definition,(
% 14.00/3.56 spl132_5 <=> ($true = (coindu300403952lexord @ a @ r @ (sK30 @ a @ ysa) @ xs2))),
% 14.00/3.56 introduced(definition,[new_symbols(naming,[spl132_5])],[avatar_definition])).
% 14.00/3.56 thf(f1258,plain,(
% 14.00/3.56 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0,X1 : X0 > X0 > $o,X4 : X0] : (($true != (coindu300403952lexord @ X0 @ X1 @ X2 @ X3)) | ((coindu300403952lexord @ X0 @ X1 @ (coindu1121789889_LCons @ X0 @ X4 @ X2) @ (coindu1121789889_LCons @ X0 @ X4 @ X3)) = $true)) )),
% 14.00/3.56 inference(cnf_transformation,[status(thm)],[f924])).
% 14.00/3.56 thf(f924,plain,(
% 14.00/3.56 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0,X4 : X0] : (((coindu300403952lexord @ X0 @ X1 @ (coindu1121789889_LCons @ X0 @ X4 @ X2) @ (coindu1121789889_LCons @ X0 @ X4 @ X3)) = $true) | ($true != (coindu300403952lexord @ X0 @ X1 @ X2 @ X3)))),
% 14.00/3.56 inference(ennf_transformation,[status(thm)],[f647])).
% 14.00/3.56 thf(f647,plain,(
% 14.00/3.56 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0,X4 : X0] : (($true = (coindu300403952lexord @ X0 @ X1 @ X2 @ X3)) => ((coindu300403952lexord @ X0 @ X1 @ (coindu1121789889_LCons @ X0 @ X4 @ X2) @ (coindu1121789889_LCons @ X0 @ X4 @ X3)) = $true))),
% 14.00/3.56 inference(fool_elimination,[status(thm)],[f646])).
% 14.00/3.56 thf(f646,plain,(
% 14.00/3.56 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : coindu1593790203_llist @ X0,X3 : coindu1593790203_llist @ X0,X4 : X0] : ((coindu300403952lexord @ X0 @ X1 @ X2 @ X3) => (coindu300403952lexord @ X0 @ X1 @ (coindu1121789889_LCons @ X0 @ X4 @ X2) @ (coindu1121789889_LCons @ X0 @ X4 @ X3)))),
% 14.00/3.56 inference(rectify,[status(thm)],[f11])).
% 14.00/3.56 thf(f11,axiom,(
% 14.00/3.56 ! [X0 : $tType,X10 : X0 > X0 > $o,X11 : coindu1593790203_llist @ X0,X12 : coindu1593790203_llist @ X0,X4 : X0] : ((coindu300403952lexord @ X0 @ X10 @ X11 @ X12) => (coindu300403952lexord @ X0 @ X10 @ (coindu1121789889_LCons @ X0 @ X4 @ X11) @ (coindu1121789889_LCons @ X0 @ X4 @ X12)))),
% 14.00/3.56 file('/export/starexec/sandbox/tmp/tmp.vsmmhmmsID/DTF2THF_32705.p',fact_10_llexord__LCons__eq)).
% 14.00/3.56 thf(f2540,plain,(
% 14.00/3.56 spl132_2 | ~spl132_3 | ~spl132_4),
% 14.00/3.56 inference(avatar_contradiction_clause,[status(thm)],[f2539])).
% 14.00/3.56 thf(f2539,plain,(
% 14.00/3.56 $false | (spl132_2 | ~spl132_3 | ~spl132_4)),
% 14.00/3.56 inference(trivial_inequality_removal,[status(thm)],[f2533])).
% 14.00/3.56 thf(f2533,plain,(
% 14.00/3.56 ($true != $true) | (spl132_2 | ~spl132_3 | ~spl132_4)),
% 14.00/3.56 inference(superposition,[status(thm)],[f1482,f2484])).
% 14.00/3.56 thf(f2484,plain,(
% 14.00/3.56 ( ! [X0 : coindu1593790203_llist @ a] : (((coindu300403952lexord @ a @ r @ ysa @ (coindu1121789889_LCons @ a @ x @ X0)) = $true)) ) | (spl132_2 | ~spl132_3 | ~spl132_4)),
% 14.00/3.56 inference(superposition,[status(thm)],[f2482,f2432])).
% 14.00/3.56 thf(f2482,plain,(
% 14.00/3.56 ( ! [X0 : coindu1593790203_llist @ a,X1 : coindu1593790203_llist @ a] : (((coindu300403952lexord @ a @ r @ (coindu1121789889_LCons @ a @ x @ X0) @ (coindu1121789889_LCons @ a @ x @ X1)) = $true)) ) | ~spl132_4),
% 14.00/3.56 inference(trivial_inequality_removal,[status(thm)],[f2481])).
% 14.00/3.56 thf(f2481,plain,(
% 14.00/3.56 ( ! [X0 : coindu1593790203_llist @ a,X1 : coindu1593790203_llist @ a] : (($true != $true) | ((coindu300403952lexord @ a @ r @ (coindu1121789889_LCons @ a @ x @ X0) @ (coindu1121789889_LCons @ a @ x @ X1)) = $true)) ) | ~spl132_4),
% 14.00/3.56 inference(superposition,[status(thm)],[f1364,f2474])).
% 14.00/3.56 thf(f2474,plain,(
% 14.00/3.56 ((r @ x @ x) = $true) | ~spl132_4),
% 14.00/3.56 inference(avatar_component_clause,[status(thm)],[f2472])).
% 14.00/3.56 thf(f2472,definition,(
% 14.00/3.56 spl132_4 <=> ((r @ x @ x) = $true)),
% 14.00/3.56 introduced(definition,[new_symbols(naming,[spl132_4])],[avatar_definition])).
% 14.00/3.56 thf(f2479,plain,(
% 14.00/3.56 spl132_4 | spl132_5 | spl132_2 | ~spl132_3),
% 14.00/3.56 inference(avatar_split_clause,[status(thm)],[f2466,f2414,f2410,f2476,f2472])).
% 14.00/3.56 thf(f2466,plain,(
% 14.00/3.56 ($true = (coindu300403952lexord @ a @ r @ (sK30 @ a @ ysa) @ xs2)) | ((r @ x @ x) = $true) | (spl132_2 | ~spl132_3)),
% 14.00/3.56 inference(trivial_inequality_removal,[status(thm)],[f2462])).
% 14.00/3.56 thf(f2462,plain,(
% 14.00/3.56 ($true = (coindu300403952lexord @ a @ r @ (sK30 @ a @ ysa) @ xs2)) | ((r @ x @ x) = $true) | (ysa != ysa) | (spl132_2 | ~spl132_3)),
% 14.00/3.56 inference(superposition,[status(thm)],[f2382,f2432])).
% 14.00/3.56 thf(f2382,plain,(
% 14.00/3.56 ( ! [X0 : a,X1 : coindu1593790203_llist @ a] : ((ysa != (coindu1121789889_LCons @ a @ X0 @ X1)) | ((coindu300403952lexord @ a @ r @ X1 @ xs2) = $true) | ($true = (r @ X0 @ x))) )),
% 14.00/3.56 inference(subsumption_resolution,[status(thm)],[f1284,f1193])).
% 14.00/3.56 thf(f1193,plain,(
% 14.00/3.56 (thesis != $true)),
% 14.00/3.56 inference(cnf_transformation,[status(thm)],[f745])).
% 14.00/3.56 thf(f745,plain,(
% 14.00/3.56 (thesis != $true)),
% 14.00/3.56 inference(flattening,[status(thm)],[f657])).
% 14.00/3.56 thf(f657,plain,(
% 14.00/3.56 ~(thesis = $true)),
% 14.00/3.56 inference(fool_elimination,[status(thm)],[f656])).
% 14.00/3.56 thf(f656,plain,(
% 14.00/3.56 ~thesis),
% 14.00/3.56 inference(rectify,[status(thm)],[f270])).
% 14.00/3.56 thf(f270,negated_conjecture,(
% 14.00/3.56 ~thesis),
% 14.00/3.56 inference(negated_conjecture,[status(cth)],[f269])).
% 14.00/3.56 thf(f269,conjecture,(
% 14.00/3.56 thesis),
% 14.00/3.56 file('/export/starexec/sandbox/tmp/tmp.vsmmhmmsID/DTF2THF_32705.p',conj_1)).
% 14.00/3.56 thf(f1284,plain,(
% 14.00/3.56 ( ! [X0 : a,X1 : coindu1593790203_llist @ a] : ((ysa != (coindu1121789889_LCons @ a @ X0 @ X1)) | ($true = (r @ X0 @ x)) | (thesis = $true) | ((coindu300403952lexord @ a @ r @ X1 @ xs2) = $true)) )),
% 14.00/3.56 inference(cnf_transformation,[status(thm)],[f859])).
% 14.00/3.56 thf(f859,plain,(
% 14.00/3.56 ! [X0 : a,X1 : coindu1593790203_llist @ a] : ((ysa != (coindu1121789889_LCons @ a @ X0 @ X1)) | (thesis = $true) | ($true = (r @ X0 @ x)) | (((coindu300403952lexord @ a @ r @ X1 @ xs2) = $true) & (x = X0)))),
% 14.00/3.56 inference(flattening,[status(thm)],[f858])).
% 14.00/3.56 thf(f858,plain,(
% 14.00/3.56 ! [X0 : a,X1 : coindu1593790203_llist @ a] : ((((thesis = $true) | (((coindu300403952lexord @ a @ r @ X1 @ xs2) = $true) & (x = X0))) | ($true = (r @ X0 @ x))) | (ysa != (coindu1121789889_LCons @ a @ X0 @ X1)))),
% 14.00/3.56 inference(ennf_transformation,[status(thm)],[f744])).
% 14.00/3.56 thf(f744,plain,(
% 14.00/3.56 ! [X0 : a,X1 : coindu1593790203_llist @ a] : ((ysa = (coindu1121789889_LCons @ a @ X0 @ X1)) => (($true != (r @ X0 @ x)) => ((((coindu300403952lexord @ a @ r @ X1 @ xs2) != $true) | (x != X0)) => (thesis = $true))))),
% 14.00/3.56 inference(flattening,[status(thm)],[f585])).
% 14.00/3.56 thf(f585,plain,(
% 14.00/3.56 ! [X0 : a,X1 : coindu1593790203_llist @ a] : ((ysa = (coindu1121789889_LCons @ a @ X0 @ X1)) => (~($true = (r @ X0 @ x)) => ((~((coindu300403952lexord @ a @ r @ X1 @ xs2) = $true) | (x != X0)) => (thesis = $true))))),
% 14.00/3.56 inference(fool_elimination,[status(thm)],[f584])).
% 14.00/3.56 thf(f584,plain,(
% 14.00/3.56 ! [X0 : a,X1 : coindu1593790203_llist @ a] : ((ysa = (coindu1121789889_LCons @ a @ X0 @ X1)) => (~(r @ X0 @ x) => ((~(coindu300403952lexord @ a @ r @ X1 @ xs2) | (x != X0)) => thesis)))),
% 14.00/3.56 inference(rectify,[status(thm)],[f268])).
% 14.00/3.56 thf(f268,axiom,(
% 14.00/3.56 ! [X37 : a,X80 : coindu1593790203_llist @ a] : ((ysa = (coindu1121789889_LCons @ a @ X37 @ X80)) => (~(r @ X37 @ x) => ((~(coindu300403952lexord @ a @ r @ X80 @ xs2) | (x != X37)) => thesis)))),
% 14.00/3.56 file('/export/starexec/sandbox/tmp/tmp.vsmmhmmsID/DTF2THF_32705.p',conj_0)).
% 14.00/3.56 thf(f2429,plain,(
% 14.00/3.56 ~spl132_2),
% 14.00/3.56 inference(avatar_contradiction_clause,[status(thm)],[f2428])).
% 14.00/3.56 thf(f2428,plain,(
% 14.00/3.56 $false | ~spl132_2),
% 14.00/3.56 inference(trivial_inequality_removal,[status(thm)],[f2427])).
% 14.00/3.56 thf(f2427,plain,(
% 14.00/3.56 ($true != $true) | ~spl132_2),
% 14.00/3.56 inference(superposition,[status(thm)],[f1482,f2423])).
% 14.00/3.56 thf(f2423,plain,(
% 14.00/3.56 ( ! [X0 : a > a > $o,X1 : coindu1593790203_llist @ a] : (((coindu300403952lexord @ a @ X0 @ ysa @ X1) = $true)) ) | ~spl132_2),
% 14.00/3.56 inference(superposition,[status(thm)],[f1145,f2412])).
% 14.00/3.56 thf(f2412,plain,(
% 14.00/3.56 (ysa = coindu1598213697e_LNil @ a) | ~spl132_2),
% 14.00/3.56 inference(avatar_component_clause,[status(thm)],[f2410])).
% 14.00/3.56 thf(f1145,plain,(
% 14.00/3.56 ( ! [X0 : $tType,X2 : coindu1593790203_llist @ X0,X1 : X0 > X0 > $o] : (((coindu300403952lexord @ X0 @ X1 @ coindu1598213697e_LNil @ X0 @ X2) = $true)) )),
% 14.00/3.56 inference(cnf_transformation,[status(thm)],[f381])).
% 14.00/3.56 thf(f381,plain,(
% 14.00/3.56 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : coindu1593790203_llist @ X0] : ((coindu300403952lexord @ X0 @ X1 @ coindu1598213697e_LNil @ X0 @ X2) = $true)),
% 14.00/3.56 inference(fool_elimination,[status(thm)],[f380])).
% 14.00/3.56 thf(f380,plain,(
% 14.00/3.56 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : coindu1593790203_llist @ X0] : (coindu300403952lexord @ X0 @ X1 @ coindu1598213697e_LNil @ X0 @ X2)),
% 14.00/3.56 inference(rectify,[status(thm)],[f58])).
% 14.00/3.56 thf(f58,axiom,(
% 14.00/3.56 ! [X0 : $tType,X10 : X0 > X0 > $o,X12 : coindu1593790203_llist @ X0] : (coindu300403952lexord @ X0 @ X10 @ coindu1598213697e_LNil @ X0 @ X12)),
% 14.00/3.56 file('/export/starexec/sandbox/tmp/tmp.vsmmhmmsID/DTF2THF_32705.p',fact_57_llexord__LNil)).
% 14.00/3.56 thf(f2417,plain,(
% 14.00/3.56 spl132_1 | spl132_2 | spl132_3),
% 14.00/3.56 inference(avatar_split_clause,[status(thm)],[f2403,f2414,f2410,f2406])).
% 14.00/3.56 thf(f2403,plain,(
% 14.00/3.56 ((r @ (sK29 @ a @ ysa) @ x) = $true) | (ysa = coindu1598213697e_LNil @ a) | (x = (sK29 @ a @ ysa))),
% 14.00/3.56 inference(equality_resolution,[status(thm)],[f2401])).
% 14.00/3.56 thf(f2401,plain,(
% 14.00/3.56 ( ! [X0 : coindu1593790203_llist @ a] : ((ysa != X0) | ((r @ (sK29 @ a @ X0) @ x) = $true) | (coindu1598213697e_LNil @ a = X0) | (x = (sK29 @ a @ X0))) )),
% 14.00/3.56 inference(superposition,[status(thm)],[f2381,f1174])).
% 14.00/3.56 thf(f2381,plain,(
% 14.00/3.56 ( ! [X0 : a,X1 : coindu1593790203_llist @ a] : ((ysa != (coindu1121789889_LCons @ a @ X0 @ X1)) | ($true = (r @ X0 @ x)) | (x = X0)) )),
% 14.00/3.56 inference(subsumption_resolution,[status(thm)],[f1283,f1193])).
% 14.00/3.56 thf(f1283,plain,(
% 14.00/3.56 ( ! [X0 : a,X1 : coindu1593790203_llist @ a] : ((thesis = $true) | (ysa != (coindu1121789889_LCons @ a @ X0 @ X1)) | ($true = (r @ X0 @ x)) | (x = X0)) )),
% 14.00/3.56 inference(cnf_transformation,[status(thm)],[f859])).
% 14.00/3.56 % SZS output end Proof for DTF2THF_32705
% 14.00/3.56 % (439)------------------------------
% 14.00/3.56 % (439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.00/3.56 % (439)Termination reason: Refutation
% 14.00/3.56
% 14.00/3.56 % (439)Memory used [KB]: 7547
% 14.00/3.56 % (439)Time elapsed: 0.143 s
% 14.00/3.56 % (439)Instructions burned: 283 (million)
% 14.00/3.56 % (439)------------------------------
% 14.00/3.56 % (439)------------------------------
% 14.00/3.56 % (336)Success in time 1.873 s
%------------------------------------------------------------------------------