%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : COM174^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n029.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 08:41:51 AM UTC 2026
% Result : Theorem 35.60s 6.42s
% Output : Refutation 35.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM174^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 04:16:14 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : COM174^1 : TPTP v9.2.1. Released v7.0.0.
% 0.30/0.46 % Domain : Computing Theory
% 0.30/0.46 % Problem : Koenig's lemma 94
% 0.30/0.46 % Version : [Bla16] axioms : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.30/0.46 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.30/0.46 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bla16]
% 0.30/0.46 % Names : koenigslemma__94.p [Bla16]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.67 v9.1.0, 0.33 v9.0.0, 0.67 v8.1.0, 0.75 v7.5.0, 1.00 v7.1.0
% 0.30/0.46 % Syntax : Number of formulae : 314 ( 152 unt; 56 typ; 0 def)
% 0.30/0.46 % Number of atoms : 621 ( 413 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 11 ( 2 avg)
% 0.30/0.46 % Number of connectives : 3774 ( 113 ~; 20 |; 79 &;3323 @)
% 0.30/0.46 % ( 0 <=>; 239 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 22 ( 7 avg)
% 0.30/0.46 % Number of types : 2 ( 1 usr)
% 0.30/0.46 % Number of type conns : 185 ( 185 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 58 ( 55 usr; 10 con; 0-5 aty)
% 0.30/0.46 % Number of variables : 1031 ( 17 ^; 883 !; 84 ?;1031 :)
% 0.30/0.46 % ( 47 !>; 0 ?*; 0 @-; 0 @+)
% 0.30/0.46 % SPC : TH1_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.30/0.46 % 2016-07-13 14:46:08.257
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 %----Could-be-implicit typings (5)
% 0.30/0.46 thf(ty_t_Coinductive__List_Ollist,type,
% 0.30/0.46 coinductive_llist: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_List_Olist,type,
% 0.30/0.46 list: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_Set_Oset,type,
% 0.30/0.46 set: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_t_itself,type,
% 0.30/0.46 itself: $tType > $tType ).
% 0.30/0.46
% 0.30/0.46 thf(ty_tf_a,type,
% 0.30/0.46 a: $tType ).
% 0.30/0.46
% 0.30/0.46 %----Explicit typings (51)
% 0.30/0.46 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 0.30/0.46 coindu328551480prefix:
% 0.30/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List_Olappend,type,
% 0.30/0.46 coinductive_lappend:
% 0.30/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List_Olfinite,type,
% 0.30/0.46 coinductive_lfinite:
% 0.30/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List_Olist__of,type,
% 0.30/0.46 coinductive_list_of:
% 0.30/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( list @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List_Olist__of__aux,type,
% 0.30/0.46 coindu1384447384of_aux:
% 0.30/0.46 !>[A: $tType] : ( ( list @ A ) > ( coinductive_llist @ A ) > ( list @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List_Ollast,type,
% 0.30/0.46 coinductive_llast:
% 0.30/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.30/0.46 coinductive_LCons:
% 0.30/0.46 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 0.30/0.46 coinductive_LNil:
% 0.30/0.46 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List_Ollist_Olnull,type,
% 0.30/0.46 coinductive_lnull:
% 0.30/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List_Ollist_Olset,type,
% 0.30/0.46 coinductive_lset:
% 0.30/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List_Ollist__of,type,
% 0.30/0.46 coinductive_llist_of:
% 0.30/0.46 !>[A: $tType] : ( ( list @ A ) > ( coinductive_llist @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 0.30/0.46 coindu1478340336prefix:
% 0.30/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_HOL_Oundefined,type,
% 0.30/0.46 undefined:
% 0.30/0.46 !>[A: $tType] : A ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_If,type,
% 0.30/0.46 if:
% 0.30/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Oconnected,type,
% 0.30/0.46 koenig793108494nected:
% 0.30/0.46 !>[Node: $tType] : ( ( Node > Node > $o ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Opaths,type,
% 0.30/0.46 koenig916195507_paths:
% 0.30/0.46 !>[Node: $tType] : ( ( Node > Node > $o ) > ( set @ ( coinductive_llist @ Node ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Oappend,type,
% 0.30/0.46 append:
% 0.30/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Obind,type,
% 0.30/0.46 bind:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Obutlast,type,
% 0.30/0.46 butlast:
% 0.30/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Ocan__select,type,
% 0.30/0.46 can_select:
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Oinsert,type,
% 0.30/0.46 insert:
% 0.30/0.46 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olast,type,
% 0.30/0.46 last:
% 0.30/0.46 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist_OCons,type,
% 0.30/0.46 cons:
% 0.30/0.46 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist_ONil,type,
% 0.30/0.46 nil:
% 0.30/0.46 !>[A: $tType] : ( list @ A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist_Omap,type,
% 0.30/0.46 map:
% 0.30/0.46 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( list @ A ) > ( list @ Aa ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist_Oset,type,
% 0.30/0.46 set2:
% 0.30/0.46 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Olist__ex1,type,
% 0.30/0.46 list_ex1:
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Omap__tailrec,type,
% 0.30/0.46 map_tailrec:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Omap__tailrec__rev,type,
% 0.30/0.46 map_tailrec_rev:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) > ( list @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Omaps,type,
% 0.30/0.46 maps:
% 0.30/0.46 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Oproduct__lists,type,
% 0.30/0.46 product_lists:
% 0.30/0.46 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Orev,type,
% 0.30/0.46 rev:
% 0.30/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Orotate1,type,
% 0.30/0.46 rotate1:
% 0.30/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_List_Osublists,type,
% 0.30/0.46 sublists:
% 0.30/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Pure_Otype,type,
% 0.30/0.46 type:
% 0.30/0.46 !>[A: $tType] : ( itself @ A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_OCollect,type,
% 0.30/0.46 collect:
% 0.30/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Set_Othe__elem,type,
% 0.30/0.46 the_elem:
% 0.30/0.46 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Sublist_Oprefixes,type,
% 0.30/0.46 prefixes:
% 0.30/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Sublist_Oprefixes__rel,type,
% 0.30/0.46 prefixes_rel:
% 0.30/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Sublist_Ostrict__suffix,type,
% 0.30/0.46 strict_suffix:
% 0.30/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_Wellfounded_Oaccp,type,
% 0.30/0.46 accp:
% 0.30/0.46 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_c_member,type,
% 0.30/0.46 member:
% 0.30/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_XS_H____,type,
% 0.30/0.46 xs: list @ a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_graph,type,
% 0.30/0.46 graph: a > a > $o ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_n,type,
% 0.30/0.46 n: a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_x,type,
% 0.30/0.46 x: a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_xs,type,
% 0.30/0.46 xs2: coinductive_llist @ a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_xs_H_H____,type,
% 0.30/0.46 xs3: coinductive_llist @ a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_xs_H____,type,
% 0.30/0.46 xs4: coinductive_llist @ a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_ys____,type,
% 0.30/0.46 ys: list @ a ).
% 0.30/0.46
% 0.30/0.46 thf(sy_v_zs____,type,
% 0.30/0.46 zs: list @ a ).
% 0.30/0.46
% 0.30/0.46 %----Relevant facts (254)
% 0.30/0.46 thf(fact_0_xs_H,axiom,
% 0.30/0.46 ( xs4
% 0.30/0.46 = ( coinductive_llist_of @ a @ xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % xs'
% 0.30/0.46 thf(fact_1_n__neq__x,axiom,
% 0.30/0.46 n != x ).
% 0.30/0.46
% 0.30/0.46 % n_neq_x
% 0.30/0.46 thf(fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062XS_H_O_Axs_H_A_061_Allist__of_AXS_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.30/0.46 ~ ! [XS: list @ a] :
% 0.30/0.46 ( xs4
% 0.30/0.46 != ( coinductive_llist_of @ a @ XS ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>\<And>thesis. (\<And>XS'. xs' = llist_of XS' \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.30/0.46 thf(fact_3_path,axiom,
% 0.30/0.46 member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n @ xs2 ) @ ( koenig916195507_paths @ a @ graph ) ).
% 0.30/0.46
% 0.30/0.46 % path
% 0.30/0.46 thf(fact_4_xs,axiom,
% 0.30/0.46 ( xs2
% 0.30/0.46 = ( coinductive_lappend @ a @ xs4 @ ( coinductive_LCons @ a @ x @ xs3 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % xs
% 0.30/0.46 thf(fact_5_XS_H,axiom,
% 0.30/0.46 ( xs
% 0.30/0.46 = ( append @ a @ ys @ ( cons @ a @ n @ zs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % XS'
% 0.30/0.46 thf(fact_6__092_060open_062n_A_092_060notin_062_Aset_Azs_092_060close_062,axiom,
% 0.30/0.46 ~ ( member @ a @ n @ ( set2 @ a @ zs ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>n \<notin> set zs\<close>
% 0.30/0.46 thf(fact_7_paths_OEmpty,axiom,
% 0.30/0.46 ! [Node: $tType,Graph: Node > Node > $o] : ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LNil @ Node ) @ ( koenig916195507_paths @ Node @ Graph ) ) ).
% 0.30/0.46
% 0.30/0.46 % paths.Empty
% 0.30/0.46 thf(fact_8_paths_OLCons,axiom,
% 0.30/0.46 ! [Node: $tType,Graph: Node > Node > $o,X: Node,Y: Node,Xs: coinductive_llist @ Node] :
% 0.30/0.46 ( ( Graph @ X @ Y )
% 0.30/0.46 => ( ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ Y @ Xs ) @ ( koenig916195507_paths @ Node @ Graph ) )
% 0.30/0.46 => ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ X @ ( coinductive_LCons @ Node @ Y @ Xs ) ) @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % paths.LCons
% 0.30/0.46 thf(fact_9_paths_Ocases,axiom,
% 0.30/0.46 ! [Node: $tType,A2: coinductive_llist @ Node,Graph: Node > Node > $o] :
% 0.30/0.46 ( ( member @ ( coinductive_llist @ Node ) @ A2 @ ( koenig916195507_paths @ Node @ Graph ) )
% 0.30/0.46 => ( ( A2
% 0.30/0.46 != ( coinductive_LNil @ Node ) )
% 0.30/0.46 => ( ! [X2: Node] :
% 0.30/0.46 ( A2
% 0.30/0.46 != ( coinductive_LCons @ Node @ X2 @ ( coinductive_LNil @ Node ) ) )
% 0.30/0.46 => ~ ! [X2: Node,Y2: Node,Xs2: coinductive_llist @ Node] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( coinductive_LCons @ Node @ X2 @ ( coinductive_LCons @ Node @ Y2 @ Xs2 ) ) )
% 0.30/0.46 => ( ( Graph @ X2 @ Y2 )
% 0.30/0.46 => ~ ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ Y2 @ Xs2 ) @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % paths.cases
% 0.30/0.46 thf(fact_10_paths_Osimps,axiom,
% 0.30/0.46 ! [Node: $tType,A2: coinductive_llist @ Node,Graph: Node > Node > $o] :
% 0.30/0.46 ( ( member @ ( coinductive_llist @ Node ) @ A2 @ ( koenig916195507_paths @ Node @ Graph ) )
% 0.30/0.46 = ( ( A2
% 0.30/0.46 = ( coinductive_LNil @ Node ) )
% 0.30/0.46 | ? [X3: Node] :
% 0.30/0.46 ( A2
% 0.30/0.46 = ( coinductive_LCons @ Node @ X3 @ ( coinductive_LNil @ Node ) ) )
% 0.30/0.46 | ? [X3: Node,Y3: Node,Xs3: coinductive_llist @ Node] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( coinductive_LCons @ Node @ X3 @ ( coinductive_LCons @ Node @ Y3 @ Xs3 ) ) )
% 0.30/0.46 & ( Graph @ X3 @ Y3 )
% 0.30/0.46 & ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ Y3 @ Xs3 ) @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % paths.simps
% 0.30/0.46 thf(fact_11_paths_OSingle,axiom,
% 0.30/0.46 ! [Node: $tType,X: Node,Graph: Node > Node > $o] : ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ X @ ( coinductive_LNil @ Node ) ) @ ( koenig916195507_paths @ Node @ Graph ) ) ).
% 0.30/0.46
% 0.30/0.46 % paths.Single
% 0.30/0.46 thf(fact_12_paths__LConsD,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Graph: A > A > $o] :
% 0.30/0.46 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X @ Xs ) @ ( koenig916195507_paths @ A @ Graph ) )
% 0.30/0.46 => ( member @ ( coinductive_llist @ A ) @ Xs @ ( koenig916195507_paths @ A @ Graph ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % paths_LConsD
% 0.30/0.46 thf(fact_13_paths_Ocoinduct,axiom,
% 0.30/0.46 ! [Node: $tType,X4: ( coinductive_llist @ Node ) > $o,X: coinductive_llist @ Node,Graph: Node > Node > $o] :
% 0.30/0.46 ( ( X4 @ X )
% 0.30/0.46 => ( ! [X2: coinductive_llist @ Node] :
% 0.30/0.46 ( ( X4 @ X2 )
% 0.30/0.46 => ( ( X2
% 0.30/0.46 = ( coinductive_LNil @ Node ) )
% 0.30/0.46 | ? [Xa: Node] :
% 0.30/0.46 ( X2
% 0.30/0.46 = ( coinductive_LCons @ Node @ Xa @ ( coinductive_LNil @ Node ) ) )
% 0.30/0.46 | ? [Xa: Node,Y4: Node,Xs4: coinductive_llist @ Node] :
% 0.30/0.46 ( ( X2
% 0.30/0.46 = ( coinductive_LCons @ Node @ Xa @ ( coinductive_LCons @ Node @ Y4 @ Xs4 ) ) )
% 0.30/0.46 & ( Graph @ Xa @ Y4 )
% 0.30/0.46 & ( ( X4 @ ( coinductive_LCons @ Node @ Y4 @ Xs4 ) )
% 0.30/0.46 | ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ Y4 @ Xs4 ) @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ) )
% 0.30/0.46 => ( member @ ( coinductive_llist @ Node ) @ X @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % paths.coinduct
% 0.30/0.46 thf(fact_14_paths__lappendD1,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Graph: A > A > $o] :
% 0.30/0.46 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( koenig916195507_paths @ A @ Graph ) )
% 0.30/0.46 => ( member @ ( coinductive_llist @ A ) @ Xs @ ( koenig916195507_paths @ A @ Graph ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % paths_lappendD1
% 0.30/0.46 thf(fact_15_set,axiom,
% 0.30/0.46 member @ a @ x @ ( coinductive_lset @ a @ xs2 ) ).
% 0.30/0.46
% 0.30/0.46 % set
% 0.30/0.46 thf(fact_16__092_060open_062x_A_092_060notin_062_Alset_Axs_H_092_060close_062,axiom,
% 0.30/0.46 ~ ( member @ a @ x @ ( coinductive_lset @ a @ xs4 ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>x \<notin> lset xs'\<close>
% 0.30/0.46 thf(fact_17_True,axiom,
% 0.30/0.46 member @ a @ n @ ( coinductive_lset @ a @ xs4 ) ).
% 0.30/0.46
% 0.30/0.46 % True
% 0.30/0.46 thf(fact_18_calculation,axiom,
% 0.30/0.46 coinductive_lfinite @ a @ ( coinductive_LCons @ a @ n @ ( coinductive_llist_of @ a @ ys ) ) ).
% 0.30/0.46
% 0.30/0.46 % calculation
% 0.30/0.46 thf(fact_19_lappend__code_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 0.30/0.46 = Ys ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_code(1)
% 0.30/0.46 thf(fact_20_lappend__LNil2,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.30/0.46 = Xs ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_LNil2
% 0.30/0.46 thf(fact_21_lappend__code_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,Xa2: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa2 @ X ) @ Ys )
% 0.30/0.46 = ( coinductive_LCons @ A @ Xa2 @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_code(2)
% 0.30/0.46 thf(fact_22_lappend__snocL1__conv__LCons2,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 0.30/0.46 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_snocL1_conv_LCons2
% 0.30/0.46 thf(fact_23_llist__of__inject,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ( ( ( coinductive_llist_of @ A @ Xs )
% 0.30/0.46 = ( coinductive_llist_of @ A @ Ys ) )
% 0.30/0.46 = ( Xs = Ys ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist_of_inject
% 0.30/0.46 thf(fact_24_llist_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,X21: A,X22: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 0.30/0.46 ( ( ( coinductive_LCons @ A @ X21 @ X22 )
% 0.30/0.46 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 0.30/0.46 = ( ( X21 = Y21 )
% 0.30/0.46 & ( X22 = Y22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.inject
% 0.30/0.46 thf(fact_25_lappend__LNil__LNil,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 0.30/0.46 = ( coinductive_LNil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_LNil_LNil
% 0.30/0.46 thf(fact_26_LNil__eq__lappend__iff,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( ( coinductive_LNil @ A )
% 0.30/0.46 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( ( Xs
% 0.30/0.46 = ( coinductive_LNil @ A ) )
% 0.30/0.46 & ( Ys
% 0.30/0.46 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % LNil_eq_lappend_iff
% 0.30/0.46 thf(fact_27__092_060open_062lfinite_Axs_H_092_060close_062,axiom,
% 0.30/0.46 coinductive_lfinite @ a @ xs4 ).
% 0.30/0.46
% 0.30/0.46 % \<open>lfinite xs'\<close>
% 0.30/0.46 thf(fact_28__092_060open_062n_A_092_060in_062_Aset_AXS_H_092_060close_062,axiom,
% 0.30/0.46 member @ a @ n @ ( set2 @ a @ xs ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>n \<in> set XS'\<close>
% 0.30/0.46 thf(fact_29_lfinite__LCons,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.30/0.46 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite_LCons
% 0.30/0.46 thf(fact_30_lfinite__code_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 0.30/0.46 ( ( coinductive_lfinite @ B @ ( coinductive_LCons @ B @ X @ Xs ) )
% 0.30/0.46 = ( coinductive_lfinite @ B @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite_code(2)
% 0.30/0.46 thf(fact_31_lfinite__code_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite_code(1)
% 0.30/0.46 thf(fact_32_lfinite__lappend,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lfinite @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( ( coinductive_lfinite @ A @ Xs )
% 0.30/0.46 & ( coinductive_lfinite @ A @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite_lappend
% 0.30/0.46 thf(fact_33__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ys_Azs_O_A_092_060lbrakk_062XS_H_A_061_Ays_A_064_An_A_D_Azs_059_An_A_092_060notin_062_Aset_Azs_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.30/0.46 ~ ! [Ys2: list @ a,Zs: list @ a] :
% 0.30/0.46 ( ( xs
% 0.30/0.46 = ( append @ a @ Ys2 @ ( cons @ a @ n @ Zs ) ) )
% 0.30/0.46 => ( member @ a @ n @ ( set2 @ a @ Zs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>\<And>thesis. (\<And>ys zs. \<lbrakk>XS' = ys @ n # zs; n \<notin> set zs\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.30/0.46 thf(fact_34__092_060open_062_092_060exists_062ys_Azs_O_AXS_H_A_061_Ays_A_064_An_A_D_Azs_A_092_060and_062_An_A_092_060notin_062_Aset_Azs_092_060close_062,axiom,
% 0.30/0.46 ? [Ys2: list @ a,Zs: list @ a] :
% 0.30/0.46 ( ( xs
% 0.30/0.46 = ( append @ a @ Ys2 @ ( cons @ a @ n @ Zs ) ) )
% 0.30/0.46 & ~ ( member @ a @ n @ ( set2 @ a @ Zs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>\<exists>ys zs. XS' = ys @ n # zs \<and> n \<notin> set zs\<close>
% 0.30/0.46 thf(fact_35__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_H_Axs_H_H_O_A_092_060lbrakk_062lfinite_Axs_H_059_Axs_A_061_Alappend_Axs_H_A_ILCons_Ax_Axs_H_H_J_059_Ax_A_092_060notin_062_Alset_Axs_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.30/0.46 ~ ! [Xs5: coinductive_llist @ a] :
% 0.30/0.46 ( ( coinductive_lfinite @ a @ Xs5 )
% 0.30/0.46 => ( ? [Xs6: coinductive_llist @ a] :
% 0.30/0.46 ( xs2
% 0.30/0.46 = ( coinductive_lappend @ a @ Xs5 @ ( coinductive_LCons @ a @ x @ Xs6 ) ) )
% 0.30/0.46 => ( member @ a @ x @ ( coinductive_lset @ a @ Xs5 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % \<open>\<And>thesis. (\<And>xs' xs''. \<lbrakk>lfinite xs'; xs = lappend xs' (LCons x xs''); x \<notin> lset xs'\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.30/0.46 thf(fact_36_lset__llist__of,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( coinductive_lset @ A @ ( coinductive_llist_of @ A @ Xs ) )
% 0.30/0.46 = ( set2 @ A @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % lset_llist_of
% 0.30/0.46 thf(fact_37_in__lset__lappend__iff,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) )
% 0.30/0.46 = ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.30/0.46 | ( ( coinductive_lfinite @ A @ Xs )
% 0.30/0.46 & ( member @ A @ X @ ( coinductive_lset @ A @ Ys ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_lset_lappend_iff
% 0.30/0.46 thf(fact_38_lfinite__LConsI,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 0.30/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.30/0.46 => ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite_LConsI
% 0.30/0.46 thf(fact_39_lfinite__LNil,axiom,
% 0.30/0.46 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite_LNil
% 0.30/0.46 thf(fact_40_llist_Oset__induct,axiom,
% 0.30/0.46 ! [A: $tType,X: A,A2: coinductive_llist @ A,P: A > ( coinductive_llist @ A ) > $o] :
% 0.30/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ A2 ) )
% 0.30/0.46 => ( ! [Z1: A,Z2: coinductive_llist @ A] : ( P @ Z1 @ ( coinductive_LCons @ A @ Z1 @ Z2 ) )
% 0.30/0.46 => ( ! [Z1: A,Z2: coinductive_llist @ A,Xa3: A] :
% 0.30/0.46 ( ( member @ A @ Xa3 @ ( coinductive_lset @ A @ Z2 ) )
% 0.30/0.46 => ( ( P @ Xa3 @ Z2 )
% 0.30/0.46 => ( P @ Xa3 @ ( coinductive_LCons @ A @ Z1 @ Z2 ) ) ) )
% 0.30/0.46 => ( P @ X @ A2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.set_induct
% 0.30/0.46 thf(fact_41_llist_Oset__cases,axiom,
% 0.30/0.46 ! [A: $tType,E: A,A2: coinductive_llist @ A] :
% 0.30/0.46 ( ( member @ A @ E @ ( coinductive_lset @ A @ A2 ) )
% 0.30/0.46 => ( ! [Z2: coinductive_llist @ A] :
% 0.30/0.46 ( A2
% 0.30/0.46 != ( coinductive_LCons @ A @ E @ Z2 ) )
% 0.30/0.46 => ~ ! [Z1: A,Z2: coinductive_llist @ A] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( coinductive_LCons @ A @ Z1 @ Z2 ) )
% 0.30/0.46 => ~ ( member @ A @ E @ ( coinductive_lset @ A @ Z2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.set_cases
% 0.30/0.46 thf(fact_42_lset__induct_H,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.30/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.30/0.46 => ( ! [Xs2: coinductive_llist @ A] : ( P @ ( coinductive_LCons @ A @ X @ Xs2 ) )
% 0.30/0.46 => ( ! [X5: A,Xs2: coinductive_llist @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs2 ) )
% 0.30/0.46 => ( ( P @ Xs2 )
% 0.30/0.46 => ( P @ ( coinductive_LCons @ A @ X5 @ Xs2 ) ) ) )
% 0.30/0.46 => ( P @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lset_induct'
% 0.30/0.46 thf(fact_43_lset__induct,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.30/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.30/0.46 => ( ! [Xs2: coinductive_llist @ A] : ( P @ ( coinductive_LCons @ A @ X @ Xs2 ) )
% 0.30/0.46 => ( ! [X5: A,Xs2: coinductive_llist @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs2 ) )
% 0.30/0.46 => ( ( X != X5 )
% 0.30/0.46 => ( ( P @ Xs2 )
% 0.30/0.46 => ( P @ ( coinductive_LCons @ A @ X5 @ Xs2 ) ) ) ) )
% 0.30/0.46 => ( P @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lset_induct
% 0.30/0.46 thf(fact_44_lset__cases,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.30/0.46 => ( ! [Xs5: coinductive_llist @ A] :
% 0.30/0.46 ( Xs
% 0.30/0.46 != ( coinductive_LCons @ A @ X @ Xs5 ) )
% 0.30/0.46 => ~ ! [X5: A,Xs5: coinductive_llist @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( coinductive_LCons @ A @ X5 @ Xs5 ) )
% 0.30/0.46 => ~ ( member @ A @ X @ ( coinductive_lset @ A @ Xs5 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lset_cases
% 0.30/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.30/0.46 ! [A: $tType,A2: A,P: A > $o] :
% 0.30/0.46 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.30/0.46 = ( P @ A2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % mem_Collect_eq
% 0.30/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.30/0.46 ! [A: $tType,A3: set @ A] :
% 0.30/0.46 ( ( collect @ A
% 0.30/0.46 @ ^ [X3: A] : ( member @ A @ X3 @ A3 ) )
% 0.30/0.46 = A3 ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_mem_eq
% 0.30/0.46 thf(fact_47_Collect__cong,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.30/0.46 ( ! [X2: A] :
% 0.30/0.46 ( ( P @ X2 )
% 0.30/0.46 = ( Q @ X2 ) )
% 0.30/0.46 => ( ( collect @ A @ P )
% 0.30/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Collect_cong
% 0.30/0.46 thf(fact_48_ext,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.30/0.46 ( ! [X2: A] :
% 0.30/0.46 ( ( F @ X2 )
% 0.30/0.46 = ( G @ X2 ) )
% 0.30/0.46 => ( F = G ) ) ).
% 0.30/0.46
% 0.30/0.46 % ext
% 0.30/0.46 thf(fact_49_llist_Oset__intros_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,A1: A,A22: coinductive_llist @ A] : ( member @ A @ A1 @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ A1 @ A22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.set_intros(1)
% 0.30/0.46 thf(fact_50_llist_Oset__intros_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,X: A,A22: coinductive_llist @ A,A1: A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ A22 ) )
% 0.30/0.46 => ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ A1 @ A22 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.set_intros(2)
% 0.30/0.46 thf(fact_51_lset__intros_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A] : ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lset_intros(1)
% 0.30/0.46 thf(fact_52_lset__intros_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A,X6: A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.30/0.46 => ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ X6 @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lset_intros(2)
% 0.30/0.46 thf(fact_53_lappend__inf,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.30/0.46 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.30/0.46 = Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_inf
% 0.30/0.46 thf(fact_54_lfinite__llist__of,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] : ( coinductive_lfinite @ A @ ( coinductive_llist_of @ A @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite_llist_of
% 0.30/0.46 thf(fact_55_split__llist__first,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.30/0.46 => ? [Ys2: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( coinductive_lappend @ A @ Ys2 @ ( coinductive_LCons @ A @ X @ Zs ) ) )
% 0.30/0.46 & ( coinductive_lfinite @ A @ Ys2 )
% 0.30/0.46 & ~ ( member @ A @ X @ ( coinductive_lset @ A @ Ys2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_llist_first
% 0.30/0.46 thf(fact_56_split__llist,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.30/0.46 => ? [Ys2: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( coinductive_lappend @ A @ Ys2 @ ( coinductive_LCons @ A @ X @ Zs ) ) )
% 0.30/0.46 & ( coinductive_lfinite @ A @ Ys2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_llist
% 0.30/0.46 thf(fact_57_lfinite_Oinducts,axiom,
% 0.30/0.46 ! [A: $tType,X: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.30/0.46 ( ( coinductive_lfinite @ A @ X )
% 0.30/0.46 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.30/0.46 => ( ! [Xs2: coinductive_llist @ A,X2: A] :
% 0.30/0.46 ( ( coinductive_lfinite @ A @ Xs2 )
% 0.30/0.46 => ( ( P @ Xs2 )
% 0.30/0.46 => ( P @ ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) )
% 0.30/0.46 => ( P @ X ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite.inducts
% 0.30/0.46 thf(fact_58_lfinite_Osimps,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( coinductive_lfinite @ A )
% 0.30/0.46 = ( ^ [A4: coinductive_llist @ A] :
% 0.30/0.46 ( ( A4
% 0.30/0.46 = ( coinductive_LNil @ A ) )
% 0.30/0.46 | ? [Xs3: coinductive_llist @ A,X3: A] :
% 0.30/0.46 ( ( A4
% 0.30/0.46 = ( coinductive_LCons @ A @ X3 @ Xs3 ) )
% 0.30/0.46 & ( coinductive_lfinite @ A @ Xs3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite.simps
% 0.30/0.46 thf(fact_59_lfinite_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,A2: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lfinite @ A @ A2 )
% 0.30/0.46 => ( ( A2
% 0.30/0.46 != ( coinductive_LNil @ A ) )
% 0.30/0.46 => ~ ! [Xs2: coinductive_llist @ A] :
% 0.30/0.46 ( ? [X2: A] :
% 0.30/0.46 ( A2
% 0.30/0.46 = ( coinductive_LCons @ A @ X2 @ Xs2 ) )
% 0.30/0.46 => ~ ( coinductive_lfinite @ A @ Xs2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite.cases
% 0.30/0.46 thf(fact_60_lfinite__rev__induct,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.30/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.30/0.46 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.30/0.46 => ( ! [X2: A,Xs2: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lfinite @ A @ Xs2 )
% 0.30/0.46 => ( ( P @ Xs2 )
% 0.30/0.46 => ( P @ ( coinductive_lappend @ A @ Xs2 @ ( coinductive_LCons @ A @ X2 @ ( coinductive_LNil @ A ) ) ) ) ) )
% 0.30/0.46 => ( P @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lfinite_rev_induct
% 0.30/0.46 thf(fact_61_paths__lappendD2,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Graph: A > A > $o] :
% 0.30/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.30/0.46 => ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( koenig916195507_paths @ A @ Graph ) )
% 0.30/0.46 => ( member @ ( coinductive_llist @ A ) @ Ys @ ( koenig916195507_paths @ A @ Graph ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % paths_lappendD2
% 0.30/0.46 thf(fact_62_lappend__assoc,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs2: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs2 )
% 0.30/0.46 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_assoc
% 0.30/0.46 thf(fact_63_llist__of__eq__LCons__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( ( coinductive_llist_of @ A @ Xs )
% 0.30/0.46 = ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.30/0.46 = ( ? [Xs7: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( cons @ A @ Y @ Xs7 ) )
% 0.30/0.46 & ( Ys
% 0.30/0.46 = ( coinductive_llist_of @ A @ Xs7 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist_of_eq_LCons_conv
% 0.30/0.46 thf(fact_64_llist__of_Osimps_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( coinductive_llist_of @ A @ ( cons @ A @ X @ Xs ) )
% 0.30/0.46 = ( coinductive_LCons @ A @ X @ ( coinductive_llist_of @ A @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist_of.simps(2)
% 0.30/0.46 thf(fact_65_lappend__llist__of__llist__of,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ( ( coinductive_lappend @ A @ ( coinductive_llist_of @ A @ Xs ) @ ( coinductive_llist_of @ A @ Ys ) )
% 0.30/0.46 = ( coinductive_llist_of @ A @ ( append @ A @ Xs @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_llist_of_llist_of
% 0.30/0.46 thf(fact_66_neq__LNil__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 != ( coinductive_LNil @ A ) )
% 0.30/0.46 = ( ? [X3: A,Xs7: coinductive_llist @ A] :
% 0.30/0.46 ( Xs
% 0.30/0.46 = ( coinductive_LCons @ A @ X3 @ Xs7 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % neq_LNil_conv
% 0.30/0.46 thf(fact_67_llist_Oexhaust,axiom,
% 0.30/0.46 ! [A: $tType,Y: coinductive_llist @ A] :
% 0.30/0.46 ( ( Y
% 0.30/0.46 != ( coinductive_LNil @ A ) )
% 0.30/0.46 => ~ ! [X212: A,X222: coinductive_llist @ A] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.exhaust
% 0.30/0.46 thf(fact_68_llist_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_LNil @ A )
% 0.30/0.46 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist.distinct(1)
% 0.30/0.46 thf(fact_69_lappend__eq__LNil__iff,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.30/0.46 = ( coinductive_LNil @ A ) )
% 0.30/0.46 = ( ( Xs
% 0.30/0.46 = ( coinductive_LNil @ A ) )
% 0.30/0.46 & ( Ys
% 0.30/0.46 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_eq_LNil_iff
% 0.30/0.46 thf(fact_70_split__list,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.30/0.46 => ? [Ys2: list @ A,Zs: list @ A] :
% 0.30/0.46 ( Xs
% 0.30/0.46 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_list
% 0.30/0.46 thf(fact_71_split__list__last,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.30/0.46 => ? [Ys2: list @ A,Zs: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.30/0.46 & ~ ( member @ A @ X @ ( set2 @ A @ Zs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_list_last
% 0.30/0.46 thf(fact_72_split__list__prop,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.30/0.46 ( ? [X7: A] :
% 0.30/0.46 ( ( member @ A @ X7 @ ( set2 @ A @ Xs ) )
% 0.30/0.46 & ( P @ X7 ) )
% 0.30/0.46 => ? [Ys2: list @ A,X2: A] :
% 0.30/0.46 ( ? [Zs: list @ A] :
% 0.30/0.46 ( Xs
% 0.30/0.46 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) )
% 0.30/0.46 & ( P @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_list_prop
% 0.30/0.46 thf(fact_73_split__list__first,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.30/0.46 => ? [Ys2: list @ A,Zs: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.30/0.46 & ~ ( member @ A @ X @ ( set2 @ A @ Ys2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_list_first
% 0.30/0.46 thf(fact_74_split__list__propE,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.30/0.46 ( ? [X7: A] :
% 0.30/0.46 ( ( member @ A @ X7 @ ( set2 @ A @ Xs ) )
% 0.30/0.46 & ( P @ X7 ) )
% 0.30/0.46 => ~ ! [Ys2: list @ A,X2: A] :
% 0.30/0.46 ( ? [Zs: list @ A] :
% 0.30/0.46 ( Xs
% 0.30/0.46 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) )
% 0.30/0.46 => ~ ( P @ X2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_list_propE
% 0.30/0.46 thf(fact_75_in__set__conv__decomp,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.30/0.46 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 0.30/0.46 ( Xs
% 0.30/0.46 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_set_conv_decomp
% 0.30/0.46 thf(fact_76_split__list__last__prop,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.30/0.46 ( ? [X7: A] :
% 0.30/0.46 ( ( member @ A @ X7 @ ( set2 @ A @ Xs ) )
% 0.30/0.46 & ( P @ X7 ) )
% 0.30/0.46 => ? [Ys2: list @ A,X2: A,Zs: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) )
% 0.30/0.46 & ( P @ X2 )
% 0.30/0.46 & ! [Xa: A] :
% 0.30/0.46 ( ( member @ A @ Xa @ ( set2 @ A @ Zs ) )
% 0.30/0.46 => ~ ( P @ Xa ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_list_last_prop
% 0.30/0.46 thf(fact_77_split__list__first__prop,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.30/0.46 ( ? [X7: A] :
% 0.30/0.46 ( ( member @ A @ X7 @ ( set2 @ A @ Xs ) )
% 0.30/0.46 & ( P @ X7 ) )
% 0.30/0.46 => ? [Ys2: list @ A,X2: A] :
% 0.30/0.46 ( ? [Zs: list @ A] :
% 0.30/0.46 ( Xs
% 0.30/0.46 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) )
% 0.30/0.46 & ( P @ X2 )
% 0.30/0.46 & ! [Xa: A] :
% 0.30/0.46 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 0.30/0.46 => ~ ( P @ Xa ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_list_first_prop
% 0.30/0.46 thf(fact_78_split__list__last__propE,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.30/0.46 ( ? [X7: A] :
% 0.30/0.46 ( ( member @ A @ X7 @ ( set2 @ A @ Xs ) )
% 0.30/0.46 & ( P @ X7 ) )
% 0.30/0.46 => ~ ! [Ys2: list @ A,X2: A,Zs: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) )
% 0.30/0.46 => ( ( P @ X2 )
% 0.30/0.46 => ~ ! [Xa: A] :
% 0.30/0.46 ( ( member @ A @ Xa @ ( set2 @ A @ Zs ) )
% 0.30/0.46 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_list_last_propE
% 0.30/0.46 thf(fact_79_list_Oinject,axiom,
% 0.30/0.46 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 0.30/0.46 ( ( ( cons @ A @ X21 @ X22 )
% 0.30/0.46 = ( cons @ A @ Y21 @ Y22 ) )
% 0.30/0.46 = ( ( X21 = Y21 )
% 0.30/0.46 & ( X22 = Y22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.inject
% 0.30/0.46 thf(fact_80_same__append__eq,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.30/0.46 ( ( ( append @ A @ Xs @ Ys )
% 0.30/0.46 = ( append @ A @ Xs @ Zs2 ) )
% 0.30/0.46 = ( Ys = Zs2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % same_append_eq
% 0.30/0.46 thf(fact_81_append__same__eq,axiom,
% 0.30/0.46 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs2: list @ A] :
% 0.30/0.46 ( ( ( append @ A @ Ys @ Xs )
% 0.30/0.46 = ( append @ A @ Zs2 @ Xs ) )
% 0.30/0.46 = ( Ys = Zs2 ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_same_eq
% 0.30/0.46 thf(fact_82_append__assoc,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.30/0.46 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs2 )
% 0.30/0.46 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_assoc
% 0.30/0.46 thf(fact_83_not__Cons__self2,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( cons @ A @ X @ Xs )
% 0.30/0.46 != Xs ) ).
% 0.30/0.46
% 0.30/0.46 % not_Cons_self2
% 0.30/0.46 thf(fact_84_append__eq__append__conv2,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A,Ts: list @ A] :
% 0.30/0.46 ( ( ( append @ A @ Xs @ Ys )
% 0.30/0.46 = ( append @ A @ Zs2 @ Ts ) )
% 0.30/0.46 = ( ? [Us: list @ A] :
% 0.30/0.46 ( ( ( Xs
% 0.30/0.46 = ( append @ A @ Zs2 @ Us ) )
% 0.30/0.46 & ( ( append @ A @ Us @ Ys )
% 0.30/0.46 = Ts ) )
% 0.30/0.46 | ( ( ( append @ A @ Xs @ Us )
% 0.30/0.46 = Zs2 )
% 0.30/0.46 & ( Ys
% 0.30/0.46 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_eq_append_conv2
% 0.30/0.46 thf(fact_85_append__eq__appendI,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs2: list @ A,Ys: list @ A,Us2: list @ A] :
% 0.30/0.46 ( ( ( append @ A @ Xs @ Xs1 )
% 0.30/0.46 = Zs2 )
% 0.30/0.46 => ( ( Ys
% 0.30/0.46 = ( append @ A @ Xs1 @ Us2 ) )
% 0.30/0.46 => ( ( append @ A @ Xs @ Ys )
% 0.30/0.46 = ( append @ A @ Zs2 @ Us2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_eq_appendI
% 0.30/0.46 thf(fact_86_list_Oset__cases,axiom,
% 0.30/0.46 ! [A: $tType,E: A,A2: list @ A] :
% 0.30/0.46 ( ( member @ A @ E @ ( set2 @ A @ A2 ) )
% 0.30/0.46 => ( ! [Z2: list @ A] :
% 0.30/0.46 ( A2
% 0.30/0.46 != ( cons @ A @ E @ Z2 ) )
% 0.30/0.46 => ~ ! [Z1: A,Z2: list @ A] :
% 0.30/0.46 ( ( A2
% 0.30/0.46 = ( cons @ A @ Z1 @ Z2 ) )
% 0.30/0.46 => ~ ( member @ A @ E @ ( set2 @ A @ Z2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.set_cases
% 0.30/0.46 thf(fact_87_set__ConsD,axiom,
% 0.30/0.46 ! [A: $tType,Y: A,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X @ Xs ) ) )
% 0.30/0.46 => ( ( Y = X )
% 0.30/0.46 | ( member @ A @ Y @ ( set2 @ A @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % set_ConsD
% 0.30/0.46 thf(fact_88_list_Oset__intros_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,A1: A,A22: list @ A] : ( member @ A @ A1 @ ( set2 @ A @ ( cons @ A @ A1 @ A22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.set_intros(1)
% 0.30/0.46 thf(fact_89_list_Oset__intros_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,X: A,A22: list @ A,A1: A] :
% 0.30/0.46 ( ( member @ A @ X @ ( set2 @ A @ A22 ) )
% 0.30/0.46 => ( member @ A @ X @ ( set2 @ A @ ( cons @ A @ A1 @ A22 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.set_intros(2)
% 0.30/0.46 thf(fact_90_append__Cons,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 0.30/0.46 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_Cons
% 0.30/0.46 thf(fact_91_Cons__eq__appendI,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs1: list @ A,Ys: list @ A,Xs: list @ A,Zs2: list @ A] :
% 0.30/0.46 ( ( ( cons @ A @ X @ Xs1 )
% 0.30/0.46 = Ys )
% 0.30/0.46 => ( ( Xs
% 0.30/0.46 = ( append @ A @ Xs1 @ Zs2 ) )
% 0.30/0.46 => ( ( cons @ A @ X @ Xs )
% 0.30/0.46 = ( append @ A @ Ys @ Zs2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Cons_eq_appendI
% 0.30/0.46 thf(fact_92_split__list__first__prop__iff,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.30/0.46 ( ( ? [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.30/0.46 & ( P @ X3 ) ) )
% 0.30/0.46 = ( ? [Ys3: list @ A,X3: A] :
% 0.30/0.46 ( ? [Zs3: list @ A] :
% 0.30/0.46 ( Xs
% 0.30/0.46 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.30/0.46 & ( P @ X3 )
% 0.30/0.46 & ! [Y3: A] :
% 0.30/0.46 ( ( member @ A @ Y3 @ ( set2 @ A @ Ys3 ) )
% 0.30/0.46 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_list_first_prop_iff
% 0.30/0.46 thf(fact_93_split__list__last__prop__iff,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.30/0.46 ( ( ? [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.30/0.46 & ( P @ X3 ) ) )
% 0.30/0.46 = ( ? [Ys3: list @ A,X3: A,Zs3: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 0.30/0.46 & ( P @ X3 )
% 0.30/0.46 & ! [Y3: A] :
% 0.30/0.46 ( ( member @ A @ Y3 @ ( set2 @ A @ Zs3 ) )
% 0.30/0.46 => ~ ( P @ Y3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_list_last_prop_iff
% 0.30/0.46 thf(fact_94_in__set__conv__decomp__first,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.30/0.46 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) )
% 0.30/0.46 & ~ ( member @ A @ X @ ( set2 @ A @ Ys3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_set_conv_decomp_first
% 0.30/0.46 thf(fact_95_in__set__conv__decomp__last,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.30/0.46 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) )
% 0.30/0.46 & ~ ( member @ A @ X @ ( set2 @ A @ Zs3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_set_conv_decomp_last
% 0.30/0.46 thf(fact_96_split__list__first__propE,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 0.30/0.46 ( ? [X7: A] :
% 0.30/0.46 ( ( member @ A @ X7 @ ( set2 @ A @ Xs ) )
% 0.30/0.46 & ( P @ X7 ) )
% 0.30/0.46 => ~ ! [Ys2: list @ A,X2: A] :
% 0.30/0.46 ( ? [Zs: list @ A] :
% 0.30/0.46 ( Xs
% 0.30/0.46 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) )
% 0.30/0.46 => ( ( P @ X2 )
% 0.30/0.46 => ~ ! [Xa: A] :
% 0.30/0.46 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 0.30/0.46 => ~ ( P @ Xa ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % split_list_first_propE
% 0.30/0.46 thf(fact_97_bind__simps_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X: B,Xs: list @ B,F: B > ( list @ A )] :
% 0.30/0.46 ( ( bind @ B @ A @ ( cons @ B @ X @ Xs ) @ F )
% 0.30/0.46 = ( append @ A @ ( F @ X ) @ ( bind @ B @ A @ Xs @ F ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % bind_simps(2)
% 0.30/0.46 thf(fact_98_llast__lappend__LCons,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.30/0.46 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) )
% 0.30/0.46 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llast_lappend_LCons
% 0.30/0.46 thf(fact_99_lappend__llist__of__LCons,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lappend @ A @ ( coinductive_llist_of @ A @ Xs ) @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.30/0.46 = ( coinductive_lappend @ A @ ( coinductive_llist_of @ A @ ( append @ A @ Xs @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) @ Ys ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_llist_of_LCons
% 0.30/0.46 thf(fact_100_list__of__aux__code_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( coindu1384447384of_aux @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.30/0.46 = ( coindu1384447384of_aux @ A @ ( cons @ A @ Y @ Xs ) @ Ys ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_of_aux_code(2)
% 0.30/0.46 thf(fact_101_llimit__induct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 0.30/0.46 ( ( P @ ( coinductive_LNil @ A ) )
% 0.30/0.46 => ( ! [X2: A,Xs2: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lfinite @ A @ Xs2 )
% 0.30/0.46 => ( ( P @ Xs2 )
% 0.30/0.46 => ( P @ ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) )
% 0.30/0.46 => ( ( ! [Ys4: coinductive_llist @ A] :
% 0.30/0.46 ( ( coindu1478340336prefix @ A @ Ys4 @ Xs )
% 0.30/0.46 => ( P @ Ys4 ) )
% 0.30/0.46 => ( P @ Xs ) )
% 0.30/0.46 => ( P @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llimit_induct
% 0.30/0.46 thf(fact_102_set__list__of,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.30/0.46 => ( ( set2 @ A @ ( coinductive_list_of @ A @ Xs ) )
% 0.30/0.46 = ( coinductive_lset @ A @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % set_list_of
% 0.30/0.46 thf(fact_103_append__Nil2,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( append @ A @ Xs @ ( nil @ A ) )
% 0.30/0.46 = Xs ) ).
% 0.30/0.46
% 0.30/0.46 % append_Nil2
% 0.30/0.46 thf(fact_104_append__self__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ( ( ( append @ A @ Xs @ Ys )
% 0.30/0.46 = Xs )
% 0.30/0.46 = ( Ys
% 0.30/0.46 = ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_self_conv
% 0.30/0.46 thf(fact_105_self__append__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( Ys
% 0.30/0.46 = ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % self_append_conv
% 0.30/0.46 thf(fact_106_append__self__conv2,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ( ( ( append @ A @ Xs @ Ys )
% 0.30/0.46 = Ys )
% 0.30/0.46 = ( Xs
% 0.30/0.46 = ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_self_conv2
% 0.30/0.46 thf(fact_107_self__append__conv2,axiom,
% 0.30/0.46 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.30/0.46 ( ( Ys
% 0.30/0.46 = ( append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( Xs
% 0.30/0.46 = ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % self_append_conv2
% 0.30/0.46 thf(fact_108_Nil__is__append__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ( ( ( nil @ A )
% 0.30/0.46 = ( append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( ( Xs
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 & ( Ys
% 0.30/0.46 = ( nil @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Nil_is_append_conv
% 0.30/0.46 thf(fact_109_append__is__Nil__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ( ( ( append @ A @ Xs @ Ys )
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 = ( ( Xs
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 & ( Ys
% 0.30/0.46 = ( nil @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_is_Nil_conv
% 0.30/0.46 thf(fact_110_llast__LCons2,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A,Xs: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs ) ) )
% 0.30/0.46 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llast_LCons2
% 0.30/0.46 thf(fact_111_list__of__llist__of,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( coinductive_list_of @ A @ ( coinductive_llist_of @ A @ Xs ) )
% 0.30/0.46 = Xs ) ).
% 0.30/0.46
% 0.30/0.46 % list_of_llist_of
% 0.30/0.46 thf(fact_112_lstrict__prefix__code_I4_J,axiom,
% 0.30/0.46 ! [B: $tType,X: B,Xs: coinductive_llist @ B,Y: B,Ys: coinductive_llist @ B] :
% 0.30/0.46 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 0.30/0.46 = ( ( X = Y )
% 0.30/0.46 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lstrict_prefix_code(4)
% 0.30/0.46 thf(fact_113_lstrict__prefix__code_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % lstrict_prefix_code(1)
% 0.30/0.46 thf(fact_114_bind__simps_I1_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 0.30/0.46 ( ( bind @ B @ A @ ( nil @ B ) @ F )
% 0.30/0.46 = ( nil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % bind_simps(1)
% 0.30/0.46 thf(fact_115_append1__eq__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 0.30/0.46 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.30/0.46 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.30/0.46 = ( ( Xs = Ys )
% 0.30/0.46 & ( X = Y ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append1_eq_conv
% 0.30/0.46 thf(fact_116_list__of__LNil,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( coinductive_list_of @ A @ ( coinductive_LNil @ A ) )
% 0.30/0.46 = ( nil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_of_LNil
% 0.30/0.46 thf(fact_117_llast__singleton,axiom,
% 0.30/0.46 ! [A: $tType,X: A] :
% 0.30/0.46 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % llast_singleton
% 0.30/0.46 thf(fact_118_lstrict__prefix__code_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,Y: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y @ Ys ) ) ).
% 0.30/0.46
% 0.30/0.46 % lstrict_prefix_code(2)
% 0.30/0.46 thf(fact_119_lstrict__prefix__code_I3_J,axiom,
% 0.30/0.46 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 0.30/0.46 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % lstrict_prefix_code(3)
% 0.30/0.46 thf(fact_120_llist__of__list__of,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.30/0.46 => ( ( coinductive_llist_of @ A @ ( coinductive_list_of @ A @ Xs ) )
% 0.30/0.46 = Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist_of_list_of
% 0.30/0.46 thf(fact_121_list__of__LCons,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 0.30/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.30/0.46 => ( ( coinductive_list_of @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.30/0.46 = ( cons @ A @ X @ ( coinductive_list_of @ A @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_of_LCons
% 0.30/0.46 thf(fact_122_transpose_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,X: list @ ( list @ A )] :
% 0.30/0.46 ( ( X
% 0.30/0.46 != ( nil @ ( list @ A ) ) )
% 0.30/0.46 => ( ! [Xss: list @ ( list @ A )] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.30/0.46 => ~ ! [X2: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( cons @ ( list @ A ) @ ( cons @ A @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % transpose.cases
% 0.30/0.46 thf(fact_123_llist__less__induct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 0.30/0.46 ( ! [Xs2: coinductive_llist @ A] :
% 0.30/0.46 ( ! [Ys4: coinductive_llist @ A] :
% 0.30/0.46 ( ( coindu1478340336prefix @ A @ Ys4 @ Xs2 )
% 0.30/0.46 => ( P @ Ys4 ) )
% 0.30/0.46 => ( P @ Xs2 ) )
% 0.30/0.46 => ( P @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist_less_induct
% 0.30/0.46 thf(fact_124_list__of__code,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( coinductive_list_of @ A )
% 0.30/0.46 = ( coindu1384447384of_aux @ A @ ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_of_code
% 0.30/0.46 thf(fact_125_list_Odistinct_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,X21: A,X22: list @ A] :
% 0.30/0.46 ( ( nil @ A )
% 0.30/0.46 != ( cons @ A @ X21 @ X22 ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.distinct(1)
% 0.30/0.46 thf(fact_126_list_OdiscI,axiom,
% 0.30/0.46 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 0.30/0.46 ( ( List
% 0.30/0.46 = ( cons @ A @ X21 @ X22 ) )
% 0.30/0.46 => ( List
% 0.30/0.46 != ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.discI
% 0.30/0.46 thf(fact_127_list_Oexhaust,axiom,
% 0.30/0.46 ! [A: $tType,Y: list @ A] :
% 0.30/0.46 ( ( Y
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ~ ! [X212: A,X222: list @ A] :
% 0.30/0.46 ( Y
% 0.30/0.46 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.exhaust
% 0.30/0.46 thf(fact_128_list_Oinducts,axiom,
% 0.30/0.46 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.30/0.46 ( ( P @ ( nil @ A ) )
% 0.30/0.46 => ( ! [X1: A,X23: list @ A] :
% 0.30/0.46 ( ( P @ X23 )
% 0.30/0.46 => ( P @ ( cons @ A @ X1 @ X23 ) ) )
% 0.30/0.46 => ( P @ List ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.inducts
% 0.30/0.46 thf(fact_129_neq__Nil__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 = ( ? [Y3: A,Ys3: list @ A] :
% 0.30/0.46 ( Xs
% 0.30/0.46 = ( cons @ A @ Y3 @ Ys3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % neq_Nil_conv
% 0.30/0.46 thf(fact_130_list__induct2_H,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 0.30/0.46 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.30/0.46 => ( ! [X2: A,Xs2: list @ A] : ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( nil @ B ) )
% 0.30/0.46 => ( ! [Y2: B,Ys2: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y2 @ Ys2 ) )
% 0.30/0.46 => ( ! [X2: A,Xs2: list @ A,Y2: B,Ys2: list @ B] :
% 0.30/0.46 ( ( P @ Xs2 @ Ys2 )
% 0.30/0.46 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) )
% 0.30/0.46 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_induct2'
% 0.30/0.46 thf(fact_131_splice_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.30/0.46 ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 0.30/0.46 => ( ! [V: A,Va: list @ A] : ( P @ ( cons @ A @ V @ Va ) @ ( nil @ A ) )
% 0.30/0.46 => ( ! [X2: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 0.30/0.46 ( ( P @ Xs2 @ Ys2 )
% 0.30/0.46 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 0.30/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % splice.induct
% 0.30/0.46 thf(fact_132_remdups__adj_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,X: list @ A] :
% 0.30/0.46 ( ( X
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ! [X2: A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.30/0.46 => ~ ! [X2: A,Y2: A,Xs2: list @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % remdups_adj.cases
% 0.30/0.46 thf(fact_133_remdups__adj_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.30/0.46 ( ( P @ ( nil @ A ) )
% 0.30/0.46 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.30/0.46 => ( ! [X2: A,Y2: A,Xs2: list @ A] :
% 0.30/0.46 ( ( ( X2 = Y2 )
% 0.30/0.46 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) )
% 0.30/0.46 => ( ( ( X2 != Y2 )
% 0.30/0.46 => ( P @ ( cons @ A @ Y2 @ Xs2 ) ) )
% 0.30/0.46 => ( P @ ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) )
% 0.30/0.46 => ( P @ A0 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % remdups_adj.induct
% 0.30/0.46 thf(fact_134_list__nonempty__induct,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.30/0.46 => ( ! [X2: A,Xs2: list @ A] :
% 0.30/0.46 ( ( Xs2
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ( P @ Xs2 )
% 0.30/0.46 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) ) )
% 0.30/0.46 => ( P @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_nonempty_induct
% 0.30/0.46 thf(fact_135_map__tailrec__rev_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.30/0.46 ( ! [F2: A > B,X1: list @ B] : ( P @ F2 @ ( nil @ A ) @ X1 )
% 0.30/0.46 => ( ! [F2: A > B,A5: A,As: list @ A,Bs: list @ B] :
% 0.30/0.46 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A5 ) @ Bs ) )
% 0.30/0.46 => ( P @ F2 @ ( cons @ A @ A5 @ As ) @ Bs ) )
% 0.30/0.46 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_tailrec_rev.induct
% 0.30/0.46 thf(fact_136_eq__Nil__appendI,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ( ( Xs = Ys )
% 0.30/0.46 => ( Xs
% 0.30/0.46 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % eq_Nil_appendI
% 0.30/0.46 thf(fact_137_append__Nil,axiom,
% 0.30/0.46 ! [A: $tType,Ys: list @ A] :
% 0.30/0.46 ( ( append @ A @ ( nil @ A ) @ Ys )
% 0.30/0.46 = Ys ) ).
% 0.30/0.46
% 0.30/0.46 % append_Nil
% 0.30/0.46 thf(fact_138_lstrict__prefix__lfinite1,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( coindu1478340336prefix @ A @ Xs @ Ys )
% 0.30/0.46 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % lstrict_prefix_lfinite1
% 0.30/0.46 thf(fact_139_rev__induct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.30/0.46 ( ( P @ ( nil @ A ) )
% 0.30/0.46 => ( ! [X2: A,Xs2: list @ A] :
% 0.30/0.46 ( ( P @ Xs2 )
% 0.30/0.46 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) )
% 0.30/0.46 => ( P @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_induct
% 0.30/0.46 thf(fact_140_rev__exhaust,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ~ ! [Ys2: list @ A,Y2: A] :
% 0.30/0.46 ( Xs
% 0.30/0.46 != ( append @ A @ Ys2 @ ( cons @ A @ Y2 @ ( nil @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_exhaust
% 0.30/0.46 thf(fact_141_Cons__eq__append__conv,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.30/0.46 ( ( ( cons @ A @ X @ Xs )
% 0.30/0.46 = ( append @ A @ Ys @ Zs2 ) )
% 0.30/0.46 = ( ( ( Ys
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 & ( ( cons @ A @ X @ Xs )
% 0.30/0.46 = Zs2 ) )
% 0.30/0.46 | ? [Ys5: list @ A] :
% 0.30/0.46 ( ( ( cons @ A @ X @ Ys5 )
% 0.30/0.46 = Ys )
% 0.30/0.46 & ( Xs
% 0.30/0.46 = ( append @ A @ Ys5 @ Zs2 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Cons_eq_append_conv
% 0.30/0.46 thf(fact_142_append__eq__Cons__conv,axiom,
% 0.30/0.46 ! [A: $tType,Ys: list @ A,Zs2: list @ A,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( ( append @ A @ Ys @ Zs2 )
% 0.30/0.46 = ( cons @ A @ X @ Xs ) )
% 0.30/0.46 = ( ( ( Ys
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 & ( Zs2
% 0.30/0.46 = ( cons @ A @ X @ Xs ) ) )
% 0.30/0.46 | ? [Ys5: list @ A] :
% 0.30/0.46 ( ( Ys
% 0.30/0.46 = ( cons @ A @ X @ Ys5 ) )
% 0.30/0.46 & ( ( append @ A @ Ys5 @ Zs2 )
% 0.30/0.46 = Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_eq_Cons_conv
% 0.30/0.46 thf(fact_143_rev__nonempty__induct,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 0.30/0.46 => ( ! [X2: A,Xs2: list @ A] :
% 0.30/0.46 ( ( Xs2
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ( P @ Xs2 )
% 0.30/0.46 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) ) )
% 0.30/0.46 => ( P @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_nonempty_induct
% 0.30/0.46 thf(fact_144_llist__of__eq__LNil__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( ( coinductive_llist_of @ A @ Xs )
% 0.30/0.46 = ( coinductive_LNil @ A ) )
% 0.30/0.46 = ( Xs
% 0.30/0.46 = ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist_of_eq_LNil_conv
% 0.30/0.46 thf(fact_145_llist__of_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( coinductive_llist_of @ A @ ( nil @ A ) )
% 0.30/0.46 = ( coinductive_LNil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % llist_of.simps(1)
% 0.30/0.46 thf(fact_146_list__bind__cong,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,Xs: list @ A,Ys: list @ A,F: A > ( list @ B ),G: A > ( list @ B )] :
% 0.30/0.46 ( ( Xs = Ys )
% 0.30/0.46 => ( ! [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.30/0.46 => ( ( F @ X2 )
% 0.30/0.46 = ( G @ X2 ) ) )
% 0.30/0.46 => ( ( bind @ A @ B @ Xs @ F )
% 0.30/0.46 = ( bind @ A @ B @ Ys @ G ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_bind_cong
% 0.30/0.46 thf(fact_147_list__of__lappend,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.30/0.46 => ( ( coinductive_lfinite @ A @ Ys )
% 0.30/0.46 => ( ( coinductive_list_of @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( append @ A @ ( coinductive_list_of @ A @ Xs ) @ ( coinductive_list_of @ A @ Ys ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_of_lappend
% 0.30/0.46 thf(fact_148_Koenigslemma__Mirabelle__aepjeeakgn_Oconnected__def,axiom,
% 0.30/0.46 ! [Node: $tType] :
% 0.30/0.46 ( ( koenig793108494nected @ Node )
% 0.30/0.46 = ( ^ [Graph2: Node > Node > $o] :
% 0.30/0.46 ! [N: Node,N2: Node] :
% 0.30/0.46 ? [Xs3: list @ Node] : ( member @ ( coinductive_llist @ Node ) @ ( coinductive_llist_of @ Node @ ( cons @ Node @ N @ ( append @ Node @ Xs3 @ ( cons @ Node @ N2 @ ( nil @ Node ) ) ) ) ) @ ( koenig916195507_paths @ Node @ Graph2 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Koenigslemma_Mirabelle_aepjeeakgn.connected_def
% 0.30/0.46 thf(fact_149_Koenigslemma__Mirabelle__aepjeeakgn_OconnectedD,axiom,
% 0.30/0.46 ! [A: $tType,Graph: A > A > $o,N3: A,N4: A] :
% 0.30/0.46 ( ( koenig793108494nected @ A @ Graph )
% 0.30/0.46 => ? [Xs2: list @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_llist_of @ A @ ( cons @ A @ N3 @ ( append @ A @ Xs2 @ ( cons @ A @ N4 @ ( nil @ A ) ) ) ) ) @ ( koenig916195507_paths @ A @ Graph ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Koenigslemma_Mirabelle_aepjeeakgn.connectedD
% 0.30/0.46 thf(fact_150_the__elem__set,axiom,
% 0.30/0.46 ! [A: $tType,X: A] :
% 0.30/0.46 ( ( the_elem @ A @ ( set2 @ A @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % the_elem_set
% 0.30/0.46 thf(fact_151_longest__common__prefix_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.30/0.46 ( ! [X2: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 0.30/0.46 ( ( ( X2 = Y2 )
% 0.30/0.46 => ( P @ Xs2 @ Ys2 ) )
% 0.30/0.46 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 0.30/0.46 => ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 0.30/0.46 => ( ! [Uu: list @ A] : ( P @ Uu @ ( nil @ A ) )
% 0.30/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % longest_common_prefix.induct
% 0.30/0.46 thf(fact_152_prefixes_Oinduct,axiom,
% 0.30/0.46 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.30/0.46 ( ( P @ ( nil @ A ) )
% 0.30/0.46 => ( ! [X2: A,Xs2: list @ A] :
% 0.30/0.46 ( ( P @ Xs2 )
% 0.30/0.46 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) )
% 0.30/0.46 => ( P @ A0 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prefixes.induct
% 0.30/0.46 thf(fact_153_prefixes_Ocases,axiom,
% 0.30/0.46 ! [A: $tType,X: list @ A] :
% 0.30/0.46 ( ( X
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ~ ! [X2: A,Xs2: list @ A] :
% 0.30/0.46 ( X
% 0.30/0.46 != ( cons @ A @ X2 @ Xs2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prefixes.cases
% 0.30/0.46 thf(fact_154_prefixes__snoc,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,X: A] :
% 0.30/0.46 ( ( prefixes @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.30/0.46 = ( append @ ( list @ A ) @ ( prefixes @ A @ Xs ) @ ( cons @ ( list @ A ) @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) @ ( nil @ ( list @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prefixes_snoc
% 0.30/0.46 thf(fact_155_prefixes__eq__Snoc,axiom,
% 0.30/0.46 ! [A: $tType,Ys: list @ A,Xs: list @ ( list @ A ),X: list @ A] :
% 0.30/0.46 ( ( ( prefixes @ A @ Ys )
% 0.30/0.46 = ( append @ ( list @ A ) @ Xs @ ( cons @ ( list @ A ) @ X @ ( nil @ ( list @ A ) ) ) ) )
% 0.30/0.46 = ( ( ( ( Ys
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 & ( Xs
% 0.30/0.46 = ( nil @ ( list @ A ) ) ) )
% 0.30/0.46 | ? [Z: A,Zs3: list @ A] :
% 0.30/0.46 ( ( Ys
% 0.30/0.46 = ( append @ A @ Zs3 @ ( cons @ A @ Z @ ( nil @ A ) ) ) )
% 0.30/0.46 & ( Xs
% 0.30/0.46 = ( prefixes @ A @ Zs3 ) ) ) )
% 0.30/0.46 & ( X = Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prefixes_eq_Snoc
% 0.30/0.46 thf(fact_156_sublists_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( sublists @ A @ ( nil @ A ) )
% 0.30/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % sublists.simps(1)
% 0.30/0.46 thf(fact_157_prefixes_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( prefixes @ A @ ( nil @ A ) )
% 0.30/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prefixes.simps(1)
% 0.30/0.46 thf(fact_158_product__lists_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.30/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % product_lists.simps(1)
% 0.30/0.46 thf(fact_159_prefixes_Oelims,axiom,
% 0.30/0.46 ! [A: $tType,X: list @ A,Y: list @ ( list @ A )] :
% 0.30/0.46 ( ( ( prefixes @ A @ X )
% 0.30/0.46 = Y )
% 0.30/0.46 => ( ( ( X
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 => ( Y
% 0.30/0.46 != ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) )
% 0.30/0.46 => ~ ! [X2: A,Xs2: list @ A] :
% 0.30/0.46 ( ( X
% 0.30/0.46 = ( cons @ A @ X2 @ Xs2 ) )
% 0.30/0.46 => ( Y
% 0.30/0.46 != ( cons @ ( list @ A ) @ ( nil @ A ) @ ( map @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 ) @ ( prefixes @ A @ Xs2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prefixes.elims
% 0.30/0.46 thf(fact_160_maps__simps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F: B > ( list @ A ),X: B,Xs: list @ B] :
% 0.30/0.46 ( ( maps @ B @ A @ F @ ( cons @ B @ X @ Xs ) )
% 0.30/0.46 = ( append @ A @ ( F @ X ) @ ( maps @ B @ A @ F @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % maps_simps(1)
% 0.30/0.46 thf(fact_161_list_Omap__disc__iff,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: A > B,A2: list @ A] :
% 0.30/0.46 ( ( ( map @ A @ B @ F @ A2 )
% 0.30/0.46 = ( nil @ B ) )
% 0.30/0.46 = ( A2
% 0.30/0.46 = ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.map_disc_iff
% 0.30/0.46 thf(fact_162_map__is__Nil__conv,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 0.30/0.46 ( ( ( map @ B @ A @ F @ Xs )
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 = ( Xs
% 0.30/0.46 = ( nil @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_is_Nil_conv
% 0.30/0.46 thf(fact_163_Nil__is__map__conv,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 0.30/0.46 ( ( ( nil @ A )
% 0.30/0.46 = ( map @ B @ A @ F @ Xs ) )
% 0.30/0.46 = ( Xs
% 0.30/0.46 = ( nil @ B ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Nil_is_map_conv
% 0.30/0.46 thf(fact_164_map__eq__conv,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B,G: B > A] :
% 0.30/0.46 ( ( ( map @ B @ A @ F @ Xs )
% 0.30/0.46 = ( map @ B @ A @ G @ Xs ) )
% 0.30/0.46 = ( ! [X3: B] :
% 0.30/0.46 ( ( member @ B @ X3 @ ( set2 @ B @ Xs ) )
% 0.30/0.46 => ( ( F @ X3 )
% 0.30/0.46 = ( G @ X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_eq_conv
% 0.30/0.46 thf(fact_165_map__append,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B,Ys: list @ B] :
% 0.30/0.46 ( ( map @ B @ A @ F @ ( append @ B @ Xs @ Ys ) )
% 0.30/0.46 = ( append @ A @ ( map @ B @ A @ F @ Xs ) @ ( map @ B @ A @ F @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_append
% 0.30/0.46 thf(fact_166_list_Oinj__map__strong,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X: list @ A,Xa2: list @ A,F: A > B,Fa: A > B] :
% 0.30/0.46 ( ! [Z3: A,Za: A] :
% 0.30/0.46 ( ( member @ A @ Z3 @ ( set2 @ A @ X ) )
% 0.30/0.46 => ( ( member @ A @ Za @ ( set2 @ A @ Xa2 ) )
% 0.30/0.46 => ( ( ( F @ Z3 )
% 0.30/0.46 = ( Fa @ Za ) )
% 0.30/0.46 => ( Z3 = Za ) ) ) )
% 0.30/0.46 => ( ( ( map @ A @ B @ F @ X )
% 0.30/0.46 = ( map @ A @ B @ Fa @ Xa2 ) )
% 0.30/0.46 => ( X = Xa2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.inj_map_strong
% 0.30/0.46 thf(fact_167_list_Omap__cong0,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X: list @ A,F: A > B,G: A > B] :
% 0.30/0.46 ( ! [Z3: A] :
% 0.30/0.46 ( ( member @ A @ Z3 @ ( set2 @ A @ X ) )
% 0.30/0.46 => ( ( F @ Z3 )
% 0.30/0.46 = ( G @ Z3 ) ) )
% 0.30/0.46 => ( ( map @ A @ B @ F @ X )
% 0.30/0.46 = ( map @ A @ B @ G @ X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.map_cong0
% 0.30/0.46 thf(fact_168_list_Omap__cong,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,X: list @ A,Ya: list @ A,F: A > B,G: A > B] :
% 0.30/0.46 ( ( X = Ya )
% 0.30/0.46 => ( ! [Z3: A] :
% 0.30/0.46 ( ( member @ A @ Z3 @ ( set2 @ A @ Ya ) )
% 0.30/0.46 => ( ( F @ Z3 )
% 0.30/0.46 = ( G @ Z3 ) ) )
% 0.30/0.46 => ( ( map @ A @ B @ F @ X )
% 0.30/0.46 = ( map @ A @ B @ G @ Ya ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.map_cong
% 0.30/0.46 thf(fact_169_ex__map__conv,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,Ys: list @ B,F: A > B] :
% 0.30/0.46 ( ( ? [Xs3: list @ A] :
% 0.30/0.46 ( Ys
% 0.30/0.46 = ( map @ A @ B @ F @ Xs3 ) ) )
% 0.30/0.46 = ( ! [X3: B] :
% 0.30/0.46 ( ( member @ B @ X3 @ ( set2 @ B @ Ys ) )
% 0.30/0.46 => ? [Y3: A] :
% 0.30/0.46 ( X3
% 0.30/0.46 = ( F @ Y3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % ex_map_conv
% 0.30/0.46 thf(fact_170_map__cong,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,Xs: list @ A,Ys: list @ A,F: A > B,G: A > B] :
% 0.30/0.46 ( ( Xs = Ys )
% 0.30/0.46 => ( ! [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ ( set2 @ A @ Ys ) )
% 0.30/0.46 => ( ( F @ X2 )
% 0.30/0.46 = ( G @ X2 ) ) )
% 0.30/0.46 => ( ( map @ A @ B @ F @ Xs )
% 0.30/0.46 = ( map @ A @ B @ G @ Ys ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_cong
% 0.30/0.46 thf(fact_171_map__idI,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,F: A > A] :
% 0.30/0.46 ( ! [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.30/0.46 => ( ( F @ X2 )
% 0.30/0.46 = X2 ) )
% 0.30/0.46 => ( ( map @ A @ A @ F @ Xs )
% 0.30/0.46 = Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_idI
% 0.30/0.46 thf(fact_172_map__ext,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,Xs: list @ A,F: A > B,G: A > B] :
% 0.30/0.46 ( ! [X2: A] :
% 0.30/0.46 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 0.30/0.46 => ( ( F @ X2 )
% 0.30/0.46 = ( G @ X2 ) ) )
% 0.30/0.46 => ( ( map @ A @ B @ F @ Xs )
% 0.30/0.46 = ( map @ A @ B @ G @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_ext
% 0.30/0.46 thf(fact_173_list_Osimps_I9_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: A > B,X21: A,X22: list @ A] :
% 0.30/0.46 ( ( map @ A @ B @ F @ ( cons @ A @ X21 @ X22 ) )
% 0.30/0.46 = ( cons @ B @ ( F @ X21 ) @ ( map @ A @ B @ F @ X22 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.simps(9)
% 0.30/0.46 thf(fact_174_Cons__eq__map__D,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X: A,Xs: list @ A,F: B > A,Ys: list @ B] :
% 0.30/0.46 ( ( ( cons @ A @ X @ Xs )
% 0.30/0.46 = ( map @ B @ A @ F @ Ys ) )
% 0.30/0.46 => ? [Z3: B,Zs: list @ B] :
% 0.30/0.46 ( ( Ys
% 0.30/0.46 = ( cons @ B @ Z3 @ Zs ) )
% 0.30/0.46 & ( X
% 0.30/0.46 = ( F @ Z3 ) )
% 0.30/0.46 & ( Xs
% 0.30/0.46 = ( map @ B @ A @ F @ Zs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Cons_eq_map_D
% 0.30/0.46 thf(fact_175_map__eq__Cons__D,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: B > A,Xs: list @ B,Y: A,Ys: list @ A] :
% 0.30/0.46 ( ( ( map @ B @ A @ F @ Xs )
% 0.30/0.46 = ( cons @ A @ Y @ Ys ) )
% 0.30/0.46 => ? [Z3: B,Zs: list @ B] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( cons @ B @ Z3 @ Zs ) )
% 0.30/0.46 & ( ( F @ Z3 )
% 0.30/0.46 = Y )
% 0.30/0.46 & ( ( map @ B @ A @ F @ Zs )
% 0.30/0.46 = Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_eq_Cons_D
% 0.30/0.46 thf(fact_176_Cons__eq__map__conv,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X: A,Xs: list @ A,F: B > A,Ys: list @ B] :
% 0.30/0.46 ( ( ( cons @ A @ X @ Xs )
% 0.30/0.46 = ( map @ B @ A @ F @ Ys ) )
% 0.30/0.46 = ( ? [Z: B,Zs3: list @ B] :
% 0.30/0.46 ( ( Ys
% 0.30/0.46 = ( cons @ B @ Z @ Zs3 ) )
% 0.30/0.46 & ( X
% 0.30/0.46 = ( F @ Z ) )
% 0.30/0.46 & ( Xs
% 0.30/0.46 = ( map @ B @ A @ F @ Zs3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Cons_eq_map_conv
% 0.30/0.46 thf(fact_177_map__eq__Cons__conv,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B,Y: A,Ys: list @ A] :
% 0.30/0.46 ( ( ( map @ B @ A @ F @ Xs )
% 0.30/0.46 = ( cons @ A @ Y @ Ys ) )
% 0.30/0.46 = ( ? [Z: B,Zs3: list @ B] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( cons @ B @ Z @ Zs3 ) )
% 0.30/0.46 & ( ( F @ Z )
% 0.30/0.46 = Y )
% 0.30/0.46 & ( ( map @ B @ A @ F @ Zs3 )
% 0.30/0.46 = Ys ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_eq_Cons_conv
% 0.30/0.46 thf(fact_178_list_Osimps_I8_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F: A > B] :
% 0.30/0.46 ( ( map @ A @ B @ F @ ( nil @ A ) )
% 0.30/0.46 = ( nil @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % list.simps(8)
% 0.30/0.46 thf(fact_179_maps__simps_I2_J,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 0.30/0.46 ( ( maps @ B @ A @ F @ ( nil @ B ) )
% 0.30/0.46 = ( nil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % maps_simps(2)
% 0.30/0.46 thf(fact_180_prefixes_Osimps_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( prefixes @ A @ ( cons @ A @ X @ Xs ) )
% 0.30/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( map @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X ) @ ( prefixes @ A @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prefixes.simps(2)
% 0.30/0.46 thf(fact_181_prefixes_Opelims,axiom,
% 0.30/0.46 ! [A: $tType,X: list @ A,Y: list @ ( list @ A )] :
% 0.30/0.46 ( ( ( prefixes @ A @ X )
% 0.30/0.46 = Y )
% 0.30/0.46 => ( ( accp @ ( list @ A ) @ ( prefixes_rel @ A ) @ X )
% 0.30/0.46 => ( ( ( X
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 => ( ( Y
% 0.30/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) )
% 0.30/0.46 => ~ ( accp @ ( list @ A ) @ ( prefixes_rel @ A ) @ ( nil @ A ) ) ) )
% 0.30/0.46 => ~ ! [X2: A,Xs2: list @ A] :
% 0.30/0.46 ( ( X
% 0.30/0.46 = ( cons @ A @ X2 @ Xs2 ) )
% 0.30/0.46 => ( ( Y
% 0.30/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( map @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 ) @ ( prefixes @ A @ Xs2 ) ) ) )
% 0.30/0.46 => ~ ( accp @ ( list @ A ) @ ( prefixes_rel @ A ) @ ( cons @ A @ X2 @ Xs2 ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % prefixes.pelims
% 0.30/0.46 thf(fact_182_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.30/0.46 = ( ( Xs
% 0.30/0.46 = ( coinductive_LNil @ A ) )
% 0.30/0.46 | ? [Xs7: coinductive_llist @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( coinductive_LCons @ A @ Y @ Xs7 ) )
% 0.30/0.46 & ( coindu328551480prefix @ A @ Xs7 @ Ys ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Coinductive_List.finite_lprefix_nitpick_simps(3)
% 0.30/0.46 thf(fact_183_not__in__set__insert,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.30/0.46 ( ~ ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.30/0.46 => ( ( insert @ A @ X @ Xs )
% 0.30/0.46 = ( cons @ A @ X @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % not_in_set_insert
% 0.30/0.46 thf(fact_184_in__set__insert,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 0.30/0.46 => ( ( insert @ A @ X @ Xs )
% 0.30/0.46 = Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_set_insert
% 0.30/0.46 thf(fact_185_insert__Nil,axiom,
% 0.30/0.46 ! [A: $tType,X: A] :
% 0.30/0.46 ( ( insert @ A @ X @ ( nil @ A ) )
% 0.30/0.46 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % insert_Nil
% 0.30/0.46 thf(fact_186_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.30/0.46 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.30/0.46 = ( Xs
% 0.30/0.46 = ( coinductive_LNil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Coinductive_List.finite_lprefix_nitpick_simps(1)
% 0.30/0.46 thf(fact_187_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 0.30/0.46
% 0.30/0.46 % Coinductive_List.finite_lprefix_nitpick_simps(2)
% 0.30/0.46 thf(fact_188_List_Oinsert__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( insert @ A )
% 0.30/0.46 = ( ^ [X3: A,Xs3: list @ A] : ( if @ ( list @ A ) @ ( member @ A @ X3 @ ( set2 @ A @ Xs3 ) ) @ Xs3 @ ( cons @ A @ X3 @ Xs3 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % List.insert_def
% 0.30/0.46 thf(fact_189_rotate1_Osimps_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( rotate1 @ A @ ( cons @ A @ X @ Xs ) )
% 0.30/0.46 = ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rotate1.simps(2)
% 0.30/0.46 thf(fact_190_map__eq__map__tailrec,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( map @ A @ B )
% 0.30/0.46 = ( map_tailrec @ A @ B ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_eq_map_tailrec
% 0.30/0.46 thf(fact_191_last__snoc,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,X: A] :
% 0.30/0.46 ( ( last @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 % last_snoc
% 0.30/0.46 thf(fact_192_rotate1__is__Nil__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( ( rotate1 @ A @ Xs )
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 = ( Xs
% 0.30/0.46 = ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rotate1_is_Nil_conv
% 0.30/0.46 thf(fact_193_set__rotate1,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( set2 @ A @ ( rotate1 @ A @ Xs ) )
% 0.30/0.46 = ( set2 @ A @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % set_rotate1
% 0.30/0.46 thf(fact_194_last__appendR,axiom,
% 0.30/0.46 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.30/0.46 ( ( Ys
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( last @ A @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % last_appendR
% 0.30/0.46 thf(fact_195_last__appendL,axiom,
% 0.30/0.46 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.30/0.46 ( ( Ys
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( last @ A @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % last_appendL
% 0.30/0.46 thf(fact_196_llast__llist__of,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( coinductive_llast @ A @ ( coinductive_llist_of @ A @ Xs ) )
% 0.30/0.46 = ( last @ A @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % llast_llist_of
% 0.30/0.46 thf(fact_197_rotate1_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( rotate1 @ A @ ( nil @ A ) )
% 0.30/0.46 = ( nil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % rotate1.simps(1)
% 0.30/0.46 thf(fact_198_last__ConsR,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,X: A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 0.30/0.46 = ( last @ A @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % last_ConsR
% 0.30/0.46 thf(fact_199_last__ConsL,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,X: A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 0.30/0.46 = X ) ) ).
% 0.30/0.46
% 0.30/0.46 % last_ConsL
% 0.30/0.46 thf(fact_200_last_Osimps,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,X: A] :
% 0.30/0.46 ( ( ( Xs
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 0.30/0.46 = X ) )
% 0.30/0.46 & ( ( Xs
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 0.30/0.46 = ( last @ A @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % last.simps
% 0.30/0.46 thf(fact_201_last__in__set,axiom,
% 0.30/0.46 ! [A: $tType,As2: list @ A] :
% 0.30/0.46 ( ( As2
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( member @ A @ ( last @ A @ As2 ) @ ( set2 @ A @ As2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % last_in_set
% 0.30/0.46 thf(fact_202_last__map,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType,Xs: list @ A,F: A > B] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ( last @ B @ ( map @ A @ B @ F @ Xs ) )
% 0.30/0.46 = ( F @ ( last @ A @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % last_map
% 0.30/0.46 thf(fact_203_longest__common__suffix,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ? [Ss: list @ A,Xs5: list @ A,Ys6: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 = ( append @ A @ Xs5 @ Ss ) )
% 0.30/0.46 & ( Ys
% 0.30/0.46 = ( append @ A @ Ys6 @ Ss ) )
% 0.30/0.46 & ( ( Xs5
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 | ( Ys6
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 | ( ( last @ A @ Xs5 )
% 0.30/0.46 != ( last @ A @ Ys6 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % longest_common_suffix
% 0.30/0.46 thf(fact_204_last__append,axiom,
% 0.30/0.46 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.30/0.46 ( ( ( Ys
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( last @ A @ Xs ) ) )
% 0.30/0.46 & ( ( Ys
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( last @ A @ Ys ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % last_append
% 0.30/0.46 thf(fact_205_append__butlast__last__id,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( Xs
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ( append @ A @ ( butlast @ A @ Xs ) @ ( cons @ A @ ( last @ A @ Xs ) @ ( nil @ A ) ) )
% 0.30/0.46 = Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % append_butlast_last_id
% 0.30/0.46 thf(fact_206_snoc__eq__iff__butlast,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A] :
% 0.30/0.46 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.30/0.46 = Ys )
% 0.30/0.46 = ( ( Ys
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 & ( ( butlast @ A @ Ys )
% 0.30/0.46 = Xs )
% 0.30/0.46 & ( ( last @ A @ Ys )
% 0.30/0.46 = X ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % snoc_eq_iff_butlast
% 0.30/0.46 thf(fact_207_butlast__snoc,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,X: A] :
% 0.30/0.46 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.30/0.46 = Xs ) ).
% 0.30/0.46
% 0.30/0.46 % butlast_snoc
% 0.30/0.46 thf(fact_208_butlast_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( butlast @ A @ ( nil @ A ) )
% 0.30/0.46 = ( nil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % butlast.simps(1)
% 0.30/0.46 thf(fact_209_in__set__butlastD,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 0.30/0.46 => ( member @ A @ X @ ( set2 @ A @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_set_butlastD
% 0.30/0.46 thf(fact_210_map__butlast,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 0.30/0.46 ( ( map @ B @ A @ F @ ( butlast @ B @ Xs ) )
% 0.30/0.46 = ( butlast @ A @ ( map @ B @ A @ F @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_butlast
% 0.30/0.46 thf(fact_211_butlast_Osimps_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,X: A] :
% 0.30/0.46 ( ( ( Xs
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 0.30/0.46 = ( nil @ A ) ) )
% 0.30/0.46 & ( ( Xs
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 0.30/0.46 = ( cons @ A @ X @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % butlast.simps(2)
% 0.30/0.46 thf(fact_212_butlast__append,axiom,
% 0.30/0.46 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 0.30/0.46 ( ( ( Ys
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( butlast @ A @ Xs ) ) )
% 0.30/0.46 & ( ( Ys
% 0.30/0.46 != ( nil @ A ) )
% 0.30/0.46 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( append @ A @ Xs @ ( butlast @ A @ Ys ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % butlast_append
% 0.30/0.46 thf(fact_213_in__set__butlast__appendI,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ( ( ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 0.30/0.46 | ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Ys ) ) ) )
% 0.30/0.46 => ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ ( append @ A @ Xs @ Ys ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % in_set_butlast_appendI
% 0.30/0.46 thf(fact_214_list__ex1__simps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o] :
% 0.30/0.46 ~ ( list_ex1 @ A @ P @ ( nil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_ex1_simps(1)
% 0.30/0.46 thf(fact_215_list__of__LCons__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 0.30/0.46 ( ( ( coinductive_lfinite @ A @ Xs )
% 0.30/0.46 => ( ( coinductive_list_of @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.30/0.46 = ( cons @ A @ X @ ( coinductive_list_of @ A @ Xs ) ) ) )
% 0.30/0.46 & ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.30/0.46 => ( ( coinductive_list_of @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.30/0.46 = ( undefined @ ( list @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_of_LCons_conv
% 0.30/0.46 thf(fact_216_llast__LNil,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( coinductive_llast @ A @ ( coinductive_LNil @ A ) )
% 0.30/0.46 = ( undefined @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % llast_LNil
% 0.30/0.46 thf(fact_217_llast__linfinite,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.30/0.46 ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.30/0.46 => ( ( coinductive_llast @ A @ Xs )
% 0.30/0.46 = ( undefined @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llast_linfinite
% 0.30/0.46 thf(fact_218_list__ex1__iff,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( list_ex1 @ A )
% 0.30/0.46 = ( ^ [P2: A > $o,Xs3: list @ A] :
% 0.30/0.46 ? [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ ( set2 @ A @ Xs3 ) )
% 0.30/0.46 & ( P2 @ X3 )
% 0.30/0.46 & ! [Y3: A] :
% 0.30/0.46 ( ( ( member @ A @ Y3 @ ( set2 @ A @ Xs3 ) )
% 0.30/0.46 & ( P2 @ Y3 ) )
% 0.30/0.46 => ( Y3 = X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_ex1_iff
% 0.30/0.46 thf(fact_219_can__select__set__list__ex1,axiom,
% 0.30/0.46 ! [A: $tType,P: A > $o,A3: list @ A] :
% 0.30/0.46 ( ( can_select @ A @ P @ ( set2 @ A @ A3 ) )
% 0.30/0.46 = ( list_ex1 @ A @ P @ A3 ) ) ).
% 0.30/0.46
% 0.30/0.46 % can_select_set_list_ex1
% 0.30/0.46 thf(fact_220_list__of__aux__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( coindu1384447384of_aux @ A )
% 0.30/0.46 = ( ^ [Xs3: list @ A,Ys3: coinductive_llist @ A] : ( if @ ( list @ A ) @ ( coinductive_lfinite @ A @ Ys3 ) @ ( append @ A @ ( rev @ A @ Xs3 ) @ ( coinductive_list_of @ A @ Ys3 ) ) @ ( undefined @ ( list @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_of_aux_def
% 0.30/0.46 thf(fact_221_rev__is__rev__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ( ( ( rev @ A @ Xs )
% 0.30/0.46 = ( rev @ A @ Ys ) )
% 0.30/0.46 = ( Xs = Ys ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_is_rev_conv
% 0.30/0.46 thf(fact_222_rev__rev__ident,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( rev @ A @ ( rev @ A @ Xs ) )
% 0.30/0.46 = Xs ) ).
% 0.30/0.46
% 0.30/0.46 % rev_rev_ident
% 0.30/0.46 thf(fact_223_Nil__is__rev__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( ( nil @ A )
% 0.30/0.46 = ( rev @ A @ Xs ) )
% 0.30/0.46 = ( Xs
% 0.30/0.46 = ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % Nil_is_rev_conv
% 0.30/0.46 thf(fact_224_rev__is__Nil__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( ( rev @ A @ Xs )
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 = ( Xs
% 0.30/0.46 = ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_is_Nil_conv
% 0.30/0.46 thf(fact_225_set__rev,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( set2 @ A @ ( rev @ A @ Xs ) )
% 0.30/0.46 = ( set2 @ A @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % set_rev
% 0.30/0.46 thf(fact_226_rev__append,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ( ( rev @ A @ ( append @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( append @ A @ ( rev @ A @ Ys ) @ ( rev @ A @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_append
% 0.30/0.46 thf(fact_227_singleton__rev__conv,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( ( cons @ A @ X @ ( nil @ A ) )
% 0.30/0.46 = ( rev @ A @ Xs ) )
% 0.30/0.46 = ( Xs
% 0.30/0.46 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % singleton_rev_conv
% 0.30/0.46 thf(fact_228_rev__singleton__conv,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,X: A] :
% 0.30/0.46 ( ( ( rev @ A @ Xs )
% 0.30/0.46 = ( cons @ A @ X @ ( nil @ A ) ) )
% 0.30/0.46 = ( Xs
% 0.30/0.46 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_singleton_conv
% 0.30/0.46 thf(fact_229_rev__eq__Cons__iff,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Y: A,Ys: list @ A] :
% 0.30/0.46 ( ( ( rev @ A @ Xs )
% 0.30/0.46 = ( cons @ A @ Y @ Ys ) )
% 0.30/0.46 = ( Xs
% 0.30/0.46 = ( append @ A @ ( rev @ A @ Ys ) @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_eq_Cons_iff
% 0.30/0.46 thf(fact_230_list__of__aux__code_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( coindu1384447384of_aux @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.30/0.46 = ( rev @ A @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % list_of_aux_code(1)
% 0.30/0.46 thf(fact_231_rev_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( rev @ A @ ( nil @ A ) )
% 0.30/0.46 = ( nil @ A ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev.simps(1)
% 0.30/0.46 thf(fact_232_rev__swap,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.30/0.46 ( ( ( rev @ A @ Xs )
% 0.30/0.46 = Ys )
% 0.30/0.46 = ( Xs
% 0.30/0.46 = ( rev @ A @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_swap
% 0.30/0.46 thf(fact_233_can__select__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( can_select @ A )
% 0.30/0.46 = ( ^ [P2: A > $o,A6: set @ A] :
% 0.30/0.46 ? [X3: A] :
% 0.30/0.46 ( ( member @ A @ X3 @ A6 )
% 0.30/0.46 & ( P2 @ X3 )
% 0.30/0.46 & ! [Y3: A] :
% 0.30/0.46 ( ( ( member @ A @ Y3 @ A6 )
% 0.30/0.46 & ( P2 @ Y3 ) )
% 0.30/0.46 => ( Y3 = X3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % can_select_def
% 0.30/0.46 thf(fact_234_rev__map,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 0.30/0.46 ( ( rev @ A @ ( map @ B @ A @ F @ Xs ) )
% 0.30/0.46 = ( map @ B @ A @ F @ ( rev @ B @ Xs ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev_map
% 0.30/0.46 thf(fact_235_rev_Osimps_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Xs: list @ A] :
% 0.30/0.46 ( ( rev @ A @ ( cons @ A @ X @ Xs ) )
% 0.30/0.46 = ( append @ A @ ( rev @ A @ Xs ) @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % rev.simps(2)
% 0.30/0.46 thf(fact_236_map__tailrec__def,axiom,
% 0.30/0.46 ! [B: $tType,A: $tType] :
% 0.30/0.46 ( ( map_tailrec @ A @ B )
% 0.30/0.46 = ( ^ [F3: A > B,As3: list @ A] : ( rev @ B @ ( map_tailrec_rev @ A @ B @ F3 @ As3 @ ( nil @ B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_tailrec_def
% 0.30/0.46 thf(fact_237_map__tailrec__rev,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType] :
% 0.30/0.46 ( ( map_tailrec_rev @ B @ A )
% 0.30/0.46 = ( ^ [F3: B > A,As3: list @ B] : ( append @ A @ ( rev @ A @ ( map @ B @ A @ F3 @ As3 ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_tailrec_rev
% 0.30/0.46 thf(fact_238_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F: A > B,A2: A,As2: list @ A,Bs2: list @ B] :
% 0.30/0.46 ( ( map_tailrec_rev @ A @ B @ F @ ( cons @ A @ A2 @ As2 ) @ Bs2 )
% 0.30/0.46 = ( map_tailrec_rev @ A @ B @ F @ As2 @ ( cons @ B @ ( F @ A2 ) @ Bs2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_tailrec_rev.simps(2)
% 0.30/0.46 thf(fact_239_map__tailrec__rev_Osimps_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,F: A > B,Bs2: list @ B] :
% 0.30/0.46 ( ( map_tailrec_rev @ A @ B @ F @ ( nil @ A ) @ Bs2 )
% 0.30/0.46 = Bs2 ) ).
% 0.30/0.46
% 0.30/0.46 % map_tailrec_rev.simps(1)
% 0.30/0.46 thf(fact_240_map__tailrec__rev_Oelims,axiom,
% 0.30/0.46 ! [A: $tType,B: $tType,X: A > B,Xa2: list @ A,Xb: list @ B,Y: list @ B] :
% 0.30/0.46 ( ( ( map_tailrec_rev @ A @ B @ X @ Xa2 @ Xb )
% 0.30/0.46 = Y )
% 0.30/0.46 => ( ( ( Xa2
% 0.30/0.46 = ( nil @ A ) )
% 0.30/0.46 => ( Y != Xb ) )
% 0.30/0.46 => ~ ! [A5: A,As: list @ A] :
% 0.30/0.46 ( ( Xa2
% 0.30/0.46 = ( cons @ A @ A5 @ As ) )
% 0.30/0.46 => ( Y
% 0.30/0.46 != ( map_tailrec_rev @ A @ B @ X @ As @ ( cons @ B @ ( X @ A5 ) @ Xb ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % map_tailrec_rev.elims
% 0.30/0.46 thf(fact_241_llast__lappend,axiom,
% 0.30/0.46 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 0.30/0.46 ( ( ( coinductive_lnull @ A @ Ys )
% 0.30/0.46 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( coinductive_llast @ A @ Xs ) ) )
% 0.30/0.46 & ( ~ ( coinductive_lnull @ A @ Ys )
% 0.30/0.46 => ( ( ( coinductive_lfinite @ A @ Xs )
% 0.30/0.46 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( coinductive_llast @ A @ Ys ) ) )
% 0.30/0.46 & ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.30/0.46 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( undefined @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llast_lappend
% 0.30/0.46 thf(fact_242_strict__suffix__def,axiom,
% 0.30/0.46 ! [A: $tType] :
% 0.30/0.46 ( ( strict_suffix @ A )
% 0.30/0.46 = ( ^ [Xs3: list @ A,Ys3: list @ A] :
% 0.30/0.46 ? [Us: list @ A] :
% 0.30/0.46 ( ( Ys3
% 0.30/0.46 = ( append @ A @ Us @ Xs3 ) )
% 0.30/0.46 & ( Us
% 0.30/0.46 != ( nil @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % strict_suffix_def
% 0.30/0.46 thf(fact_243_lappend_Odisc__iff_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) )
% 0.30/0.46 = ( ~ ( coinductive_lnull @ A @ Xs )
% 0.30/0.46 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend.disc_iff(2)
% 0.30/0.46 thf(fact_244_lnull__lappend,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.30/0.46 = ( ( coinductive_lnull @ A @ Xs )
% 0.30/0.46 & ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lnull_lappend
% 0.30/0.46 thf(fact_245_lnull__llist__of,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A] :
% 0.30/0.46 ( ( coinductive_lnull @ A @ ( coinductive_llist_of @ A @ Xs ) )
% 0.30/0.46 = ( Xs
% 0.30/0.46 = ( nil @ A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lnull_llist_of
% 0.30/0.46 thf(fact_246_llast__LCons,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 0.30/0.46 ( ( ( coinductive_lnull @ A @ Xs )
% 0.30/0.46 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.30/0.46 = X ) )
% 0.30/0.46 & ( ~ ( coinductive_lnull @ A @ Xs )
% 0.30/0.46 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.30/0.46 = ( coinductive_llast @ A @ Xs ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % llast_LCons
% 0.30/0.46 thf(fact_247_strict__suffix__trans,axiom,
% 0.30/0.46 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 0.30/0.46 ( ( strict_suffix @ A @ Xs @ Ys )
% 0.30/0.46 => ( ( strict_suffix @ A @ Ys @ Zs2 )
% 0.30/0.46 => ( strict_suffix @ A @ Xs @ Zs2 ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % strict_suffix_trans
% 0.30/0.46 thf(fact_248_lappend_Odisc_I2_J,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 0.30/0.46 | ~ ( coinductive_lnull @ A @ Ys ) )
% 0.30/0.46 => ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend.disc(2)
% 0.30/0.46 thf(fact_249_lappend_Odisc_I1_J,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lnull @ A @ Xs )
% 0.30/0.46 => ( ( coinductive_lnull @ A @ Ys )
% 0.30/0.46 => ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend.disc(1)
% 0.30/0.46 thf(fact_250_lappend__lnull1,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lnull @ A @ Xs )
% 0.30/0.46 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.30/0.46 = Ys ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_lnull1
% 0.30/0.46 thf(fact_251_lappend__lnull2,axiom,
% 0.30/0.46 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lnull @ A @ Ys )
% 0.30/0.46 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.30/0.46 = Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend_lnull2
% 0.30/0.46 thf(fact_252_lnull__imp__lfinite,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.30/0.46 ( ( coinductive_lnull @ A @ Xs )
% 0.30/0.46 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.30/0.46
% 0.30/0.46 % lnull_imp_lfinite
% 0.30/0.46 thf(fact_253_lappend_Oexhaust,axiom,
% 0.30/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.30/0.46 ( ( ( coinductive_lnull @ A @ Xs )
% 0.30/0.46 => ~ ( coinductive_lnull @ A @ Ys ) )
% 0.30/0.46 => ( ~ ( coinductive_lnull @ A @ Xs )
% 0.30/0.46 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.30/0.46
% 0.30/0.46 % lappend.exhaust
% 0.30/0.46
% 0.30/0.46 %----Helper facts (3)
% 0.30/0.46 thf(help_If_3_1_T,axiom,
% 0.30/0.46 ! [P: $o] :
% 0.30/0.46 ( ( P = $true )
% 0.30/0.46 | ( P = $false ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(help_If_2_1_T,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A] :
% 0.30/0.46 ( ( if @ A @ $false @ X @ Y )
% 0.30/0.46 = Y ) ).
% 0.30/0.46
% 0.30/0.46 thf(help_If_1_1_T,axiom,
% 0.30/0.46 ! [A: $tType,X: A,Y: A] :
% 0.30/0.46 ( ( if @ A @ $true @ X @ Y )
% 0.30/0.46 = X ) ).
% 0.30/0.46
% 0.30/0.46 %----Conjectures (1)
% 0.30/0.46 thf(conj_0,conjecture,
% 0.30/0.46 member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ ( coinductive_LCons @ a @ n @ ( coinductive_llist_of @ a @ ys ) ) @ ( coinductive_lappend @ a @ ( coinductive_LCons @ a @ n @ ( coinductive_lappend @ a @ ( coinductive_llist_of @ a @ zs ) @ ( coinductive_LCons @ a @ x @ ( coinductive_LNil @ a ) ) ) ) @ xs3 ) ) @ ( koenig916195507_paths @ a @ graph ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 2.67/1.51 ---- Embedded in THF ---
% 2.67/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.67/1.51 %%% Generated on Tue Feb 24 04:16:15 EST 2026
% 2.67/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 2.67/1.51 %%% Logic specification used:
% 2.67/1.51 %%% thf(spec, logic, $$dhol).
% 2.67/1.51
% 2.67/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.fWo8BEA7MH/DTF2DTF22272.p
% 2.67/1.51 thf(ty_t_Coinductive__List_Ollist, type, coinductive_llist: ($tType > $tType)).
% 2.67/1.51 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.67/1.51 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.67/1.51 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.67/1.51 thf(ty_tf_a, type, a: $tType).
% 2.67/1.51 thf(sy_c_Coinductive__List_Ofinite__lprefix, type, coindu328551480prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.67/1.51 thf(sy_c_Coinductive__List_Olappend, type, coinductive_lappend: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.67/1.51 thf(sy_c_Coinductive__List_Olfinite, type, coinductive_lfinite: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 2.67/1.51 thf(sy_c_Coinductive__List_Olist__of, type, coinductive_list_of: (!> [A:$tType]: (((coinductive_llist @ A) > (list @ A))))).
% 2.67/1.51 thf(sy_c_Coinductive__List_Olist__of__aux, type, coindu1384447384of_aux: (!> [A:$tType]: (((list @ A) > ((coinductive_llist @ A) > (list @ A)))))).
% 2.67/1.51 thf(sy_c_Coinductive__List_Ollast, type, coinductive_llast: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 2.67/1.51 thf(sy_c_Coinductive__List_Ollist_OLCons, type, coinductive_LCons: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.67/1.51 thf(sy_c_Coinductive__List_Ollist_OLNil, type, coinductive_LNil: (!> [A:$tType]: ((coinductive_llist @ A)))).
% 2.67/1.51 thf(sy_c_Coinductive__List_Ollist_Olnull, type, coinductive_lnull: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 2.67/1.51 thf(sy_c_Coinductive__List_Ollist_Olset, type, coinductive_lset: (!> [A:$tType]: (((coinductive_llist @ A) > (set @ A))))).
% 2.67/1.51 thf(sy_c_Coinductive__List_Ollist__of, type, coinductive_llist_of: (!> [A:$tType]: (((list @ A) > (coinductive_llist @ A))))).
% 2.67/1.51 thf(sy_c_Coinductive__List_Olstrict__prefix, type, coindu1478340336prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.67/1.51 thf(sy_c_HOL_Oundefined, type, undefined: (!> [A:$tType]: (A))).
% 2.67/1.51 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.67/1.51 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Oconnected, type, koenig793108494nected: (!> [Node:$tType]: (((Node > (Node > $o)) > $o)))).
% 2.67/1.51 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Opaths, type, koenig916195507_paths: (!> [Node:$tType]: (((Node > (Node > $o)) > (set @ (coinductive_llist @ Node)))))).
% 2.67/1.51 thf(sy_c_List_Oappend, type, append: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.67/1.51 thf(sy_c_List_Obind, type, bind: (!> [A:$tType,B:$tType]: (((list @ A) > ((A > (list @ B)) > (list @ B)))))).
% 2.67/1.51 thf(sy_c_List_Obutlast, type, butlast: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.67/1.51 thf(sy_c_List_Ocan__select, type, can_select: (!> [A:$tType]: (((A > $o) > ((set @ A) > $o))))).
% 2.67/1.51 thf(sy_c_List_Oinsert, type, insert: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.67/1.51 thf(sy_c_List_Olast, type, last: (!> [A:$tType]: (((list @ A) > A)))).
% 2.67/1.51 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.67/1.51 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.67/1.51 thf(sy_c_List_Olist_Omap, type, map: (!> [A:$tType,Aa:$tType]: (((A > Aa) > ((list @ A) > (list @ Aa)))))).
% 2.67/1.51 thf(sy_c_List_Olist_Oset, type, set2: (!> [A:$tType]: (((list @ A) > (set @ A))))).
% 2.67/1.51 thf(sy_c_List_Olist__ex1, type, list_ex1: (!> [A:$tType]: (((A > $o) > ((list @ A) > $o))))).
% 2.67/1.51 thf(sy_c_List_Omap__tailrec, type, map_tailrec: (!> [A:$tType,B:$tType]: (((A > B) > ((list @ A) > (list @ B)))))).
% 2.67/1.51 thf(sy_c_List_Omap__tailrec__rev, type, map_tailrec_rev: (!> [A:$tType,B:$tType]: (((A > B) > ((list @ A) > ((list @ B) > (list @ B))))))).
% 2.67/1.51 thf(sy_c_List_Omaps, type, maps: (!> [A:$tType,B:$tType]: (((A > (list @ B)) > ((list @ A) > (list @ B)))))).
% 2.67/1.51 thf(sy_c_List_Oproduct__lists, type, product_lists: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 2.67/1.51 thf(sy_c_List_Orev, type, rev: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.67/1.51 thf(sy_c_List_Orotate1, type, rotate1: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.67/1.51 thf(sy_c_List_Osublists, type, sublists: (!> [A:$tType]: (((list @ A) > (list @ (list @ A)))))).
% 2.67/1.51 thf(sy_c_Pure_Otype, type, type: (!> [A:$tType]: ((itself @ A)))).
% 2.67/1.51 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.67/1.51 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 2.67/1.51 thf(sy_c_Sublist_Oprefixes, type, prefixes: (!> [A:$tType]: (((list @ A) > (list @ (list @ A)))))).
% 2.67/1.51 thf(sy_c_Sublist_Oprefixes__rel, type, prefixes_rel: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.67/1.51 thf(sy_c_Sublist_Ostrict__suffix, type, strict_suffix: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.67/1.51 thf(sy_c_Wellfounded_Oaccp, type, accp: (!> [A:$tType]: (((A > (A > $o)) > (A > $o))))).
% 2.67/1.51 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.67/1.51 thf(sy_v_XS_H____, type, xs: (list @ a)).
% 2.67/1.51 thf(sy_v_graph, type, graph: (a > (a > $o))).
% 2.67/1.51 thf(sy_v_n, type, n: a).
% 2.67/1.51 thf(sy_v_x, type, x: a).
% 2.67/1.51 thf(sy_v_xs, type, xs2: (coinductive_llist @ a)).
% 2.67/1.51 thf(sy_v_xs_H_H____, type, xs3: (coinductive_llist @ a)).
% 2.67/1.51 thf(sy_v_xs_H____, type, xs4: (coinductive_llist @ a)).
% 2.67/1.51 thf(sy_v_ys____, type, ys: (list @ a)).
% 2.67/1.51 thf(sy_v_zs____, type, zs: (list @ a)).
% 2.67/1.51 thf(fact_0_xs_H, axiom, (xs4 = ((coinductive_llist_of @ a) @ xs))).
% 2.67/1.51 thf(fact_1_n__neq__x, axiom, (n != x)).
% 2.67/1.51 thf(fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062XS_H_O_Axs_H_A_061_Allist__of_AXS_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [XS:(list @ a)]: ((xs4 != ((coinductive_llist_of @ a) @ XS))))))).
% 2.67/1.51 thf(fact_3_path, axiom, (((member @ (coinductive_llist @ a)) @ (((coinductive_LCons @ a) @ n) @ xs2)) @ ((koenig916195507_paths @ a) @ graph))).
% 2.67/1.51 thf(fact_4_xs, axiom, (xs2 = (((coinductive_lappend @ a) @ xs4) @ (((coinductive_LCons @ a) @ x) @ xs3)))).
% 2.67/1.51 thf(fact_5_XS_H, axiom, (xs = (((append @ a) @ ys) @ (((cons @ a) @ n) @ zs)))).
% 2.67/1.51 thf(fact_6__092_060open_062n_A_092_060notin_062_Aset_Azs_092_060close_062, axiom, (~ ((((member @ a) @ n) @ ((set2 @ a) @ zs))))).
% 2.67/1.51 thf(fact_7_paths_OEmpty, axiom, (! [Node:$tType,Graph:(Node > (Node > $o))]: ((((member @ (coinductive_llist @ Node)) @ (coinductive_LNil @ Node)) @ ((koenig916195507_paths @ Node) @ Graph))))).
% 2.67/1.51 thf(fact_8_paths_OLCons, axiom, (! [Node:$tType,Graph:(Node > (Node > $o)),X:Node,Y:Node,Xs:(coinductive_llist @ Node)]: ((((Graph @ X) @ Y) => ((((member @ (coinductive_llist @ Node)) @ (((coinductive_LCons @ Node) @ Y) @ Xs)) @ ((koenig916195507_paths @ Node) @ Graph)) => (((member @ (coinductive_llist @ Node)) @ (((coinductive_LCons @ Node) @ X) @ (((coinductive_LCons @ Node) @ Y) @ Xs))) @ ((koenig916195507_paths @ Node) @ Graph))))))).
% 2.67/1.51 thf(fact_9_paths_Ocases, axiom, (! [Node:$tType,A2:(coinductive_llist @ Node),Graph:(Node > (Node > $o))]: (((((member @ (coinductive_llist @ Node)) @ A2) @ ((koenig916195507_paths @ Node) @ Graph)) => ((A2 != (coinductive_LNil @ Node)) => ((! [X2:Node]: ((A2 != (((coinductive_LCons @ Node) @ X2) @ (coinductive_LNil @ Node))))) => (~ ((! [X2:Node,Y2:Node,Xs2:(coinductive_llist @ Node)]: (((A2 = (((coinductive_LCons @ Node) @ X2) @ (((coinductive_LCons @ Node) @ Y2) @ Xs2))) => (((Graph @ X2) @ Y2) => (~ ((((member @ (coinductive_llist @ Node)) @ (((coinductive_LCons @ Node) @ Y2) @ Xs2)) @ ((koenig916195507_paths @ Node) @ Graph)))))))))))))))).
% 2.67/1.51 thf(fact_10_paths_Osimps, axiom, (! [Node:$tType,A2:(coinductive_llist @ Node),Graph:(Node > (Node > $o))]: (((((member @ (coinductive_llist @ Node)) @ A2) @ ((koenig916195507_paths @ Node) @ Graph)) = ((A2 = (coinductive_LNil @ Node)) | ((? [X3:Node]: ((A2 = (((coinductive_LCons @ Node) @ X3) @ (coinductive_LNil @ Node))))) | (? [X3:Node,Y3:Node,Xs3:(coinductive_llist @ Node)]: (((A2 = (((coinductive_LCons @ Node) @ X3) @ (((coinductive_LCons @ Node) @ Y3) @ Xs3))) & (((Graph @ X3) @ Y3) & (((member @ (coinductive_llist @ Node)) @ (((coinductive_LCons @ Node) @ Y3) @ Xs3)) @ ((koenig916195507_paths @ Node) @ Graph)))))))))))).
% 2.67/1.51 thf(fact_11_paths_OSingle, axiom, (! [Node:$tType,X:Node,Graph:(Node > (Node > $o))]: ((((member @ (coinductive_llist @ Node)) @ (((coinductive_LCons @ Node) @ X) @ (coinductive_LNil @ Node))) @ ((koenig916195507_paths @ Node) @ Graph))))).
% 2.67/1.51 thf(fact_12_paths__LConsD, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),Graph:(A > (A > $o))]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ ((koenig916195507_paths @ A) @ Graph)) => (((member @ (coinductive_llist @ A)) @ Xs) @ ((koenig916195507_paths @ A) @ Graph)))))).
% 2.67/1.51 thf(fact_13_paths_Ocoinduct, axiom, (! [Node:$tType,X4:((coinductive_llist @ Node) > $o),X:(coinductive_llist @ Node),Graph:(Node > (Node > $o))]: (((X4 @ X) => ((! [X2:(coinductive_llist @ Node)]: (((X4 @ X2) => ((X2 = (coinductive_LNil @ Node)) | ((? [Xa:Node]: ((X2 = (((coinductive_LCons @ Node) @ Xa) @ (coinductive_LNil @ Node))))) | (? [Xa:Node,Y4:Node,Xs4:(coinductive_llist @ Node)]: (((X2 = (((coinductive_LCons @ Node) @ Xa) @ (((coinductive_LCons @ Node) @ Y4) @ Xs4))) & (((Graph @ Xa) @ Y4) & ((X4 @ (((coinductive_LCons @ Node) @ Y4) @ Xs4)) | (((member @ (coinductive_llist @ Node)) @ (((coinductive_LCons @ Node) @ Y4) @ Xs4)) @ ((koenig916195507_paths @ Node) @ Graph)))))))))))) => (((member @ (coinductive_llist @ Node)) @ X) @ ((koenig916195507_paths @ Node) @ Graph))))))).
% 2.67/1.51 thf(fact_14_paths__lappendD1, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Graph:(A > (A > $o))]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) @ ((koenig916195507_paths @ A) @ Graph)) => (((member @ (coinductive_llist @ A)) @ Xs) @ ((koenig916195507_paths @ A) @ Graph)))))).
% 2.67/1.51 thf(fact_15_set, axiom, (((member @ a) @ x) @ ((coinductive_lset @ a) @ xs2))).
% 2.67/1.51 thf(fact_16__092_060open_062x_A_092_060notin_062_Alset_Axs_H_092_060close_062, axiom, (~ ((((member @ a) @ x) @ ((coinductive_lset @ a) @ xs4))))).
% 2.67/1.51 thf(fact_17_True, axiom, (((member @ a) @ n) @ ((coinductive_lset @ a) @ xs4))).
% 2.67/1.51 thf(fact_18_calculation, axiom, ((coinductive_lfinite @ a) @ (((coinductive_LCons @ a) @ n) @ ((coinductive_llist_of @ a) @ ys)))).
% 2.67/1.51 thf(fact_19_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ Ys) = Ys)))).
% 2.67/1.51 thf(fact_20_lappend__LNil2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ Xs) @ (coinductive_LNil @ A)) = Xs)))).
% 2.67/1.51 thf(fact_21_lappend__code_I2_J, axiom, (! [A:$tType,Xa2:A,X:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_LCons @ A) @ Xa2) @ X)) @ Ys) = (((coinductive_LCons @ A) @ Xa2) @ (((coinductive_lappend @ A) @ X) @ Ys)))))).
% 2.67/1.51 thf(fact_22_lappend__snocL1__conv__LCons2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ (coinductive_LNil @ A)))) @ Ys) = (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys)))))).
% 2.67/1.51 thf(fact_23_llist__of__inject, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((coinductive_llist_of @ A) @ Xs) = ((coinductive_llist_of @ A) @ Ys)) = (Xs = Ys))))).
% 2.67/1.51 thf(fact_24_llist_Oinject, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A),Y21:A,Y22:(coinductive_llist @ A)]: ((((((coinductive_LCons @ A) @ X21) @ X22) = (((coinductive_LCons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.67/1.51 thf(fact_25_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.67/1.51 thf(fact_26_LNil__eq__lappend__iff, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_LNil @ A) = (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((Xs = (coinductive_LNil @ A)) & (Ys = (coinductive_LNil @ A))))))).
% 2.67/1.51 thf(fact_27__092_060open_062lfinite_Axs_H_092_060close_062, axiom, ((coinductive_lfinite @ a) @ xs4)).
% 2.67/1.51 thf(fact_28__092_060open_062n_A_092_060in_062_Aset_AXS_H_092_060close_062, axiom, (((member @ a) @ n) @ ((set2 @ a) @ xs))).
% 2.67/1.51 thf(fact_29_lfinite__LCons, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = ((coinductive_lfinite @ A) @ Xs))))).
% 2.67/1.51 thf(fact_30_lfinite__code_I2_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B)]: ((((coinductive_lfinite @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) = ((coinductive_lfinite @ B) @ Xs))))).
% 2.67/1.51 thf(fact_31_lfinite__code_I1_J, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) @ (coinductive_LNil @ A))))).
% 2.67/1.51 thf(fact_32_lfinite__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lfinite @ A) @ Xs) & ((coinductive_lfinite @ A) @ Ys)))))).
% 2.67/1.51 thf(fact_33__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ys_Azs_O_A_092_060lbrakk_062XS_H_A_061_Ays_A_064_An_A_D_Azs_059_An_A_092_060notin_062_Aset_Azs_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [Ys2:(list @ a),Zs:(list @ a)]: (((xs = (((append @ a) @ Ys2) @ (((cons @ a) @ n) @ Zs))) => (((member @ a) @ n) @ ((set2 @ a) @ Zs)))))))).
% 2.67/1.51 thf(fact_34__092_060open_062_092_060exists_062ys_Azs_O_AXS_H_A_061_Ays_A_064_An_A_D_Azs_A_092_060and_062_An_A_092_060notin_062_Aset_Azs_092_060close_062, axiom, (? [Ys2:(list @ a),Zs:(list @ a)]: (((xs = (((append @ a) @ Ys2) @ (((cons @ a) @ n) @ Zs))) & (~ ((((member @ a) @ n) @ ((set2 @ a) @ Zs)))))))).
% 2.67/1.51 thf(fact_35__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_H_Axs_H_H_O_A_092_060lbrakk_062lfinite_Axs_H_059_Axs_A_061_Alappend_Axs_H_A_ILCons_Ax_Axs_H_H_J_059_Ax_A_092_060notin_062_Alset_Axs_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [Xs5:(coinductive_llist @ a)]: ((((coinductive_lfinite @ a) @ Xs5) => ((? [Xs6:(coinductive_llist @ a)]: ((xs2 = (((coinductive_lappend @ a) @ Xs5) @ (((coinductive_LCons @ a) @ x) @ Xs6))))) => (((member @ a) @ x) @ ((coinductive_lset @ a) @ Xs5))))))))).
% 2.67/1.51 thf(fact_36_lset__llist__of, axiom, (! [A:$tType,Xs:(list @ A)]: ((((coinductive_lset @ A) @ ((coinductive_llist_of @ A) @ Xs)) = ((set2 @ A) @ Xs))))).
% 2.67/1.51 thf(fact_37_in__lset__lappend__iff, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys))) = ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) | (((coinductive_lfinite @ A) @ Xs) & (((member @ A) @ X) @ ((coinductive_lset @ A) @ Ys)))))))).
% 2.67/1.51 thf(fact_38_lfinite__LConsI, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),X:A]: ((((coinductive_lfinite @ A) @ Xs) => ((coinductive_lfinite @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)))))).
% 2.67/1.51 thf(fact_39_lfinite__LNil, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) @ (coinductive_LNil @ A))))).
% 2.67/1.51 thf(fact_40_llist_Oset__induct, axiom, (! [A:$tType,X:A,A2:(coinductive_llist @ A),P:(A > ((coinductive_llist @ A) > $o))]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ A2)) => ((! [Z1:A,Z2:(coinductive_llist @ A)]: (((P @ Z1) @ (((coinductive_LCons @ A) @ Z1) @ Z2)))) => ((! [Z1:A,Z2:(coinductive_llist @ A),Xa3:A]: (((((member @ A) @ Xa3) @ ((coinductive_lset @ A) @ Z2)) => (((P @ Xa3) @ Z2) => ((P @ Xa3) @ (((coinductive_LCons @ A) @ Z1) @ Z2)))))) => ((P @ X) @ A2))))))).
% 2.67/1.51 thf(fact_41_llist_Oset__cases, axiom, (! [A:$tType,E:A,A2:(coinductive_llist @ A)]: (((((member @ A) @ E) @ ((coinductive_lset @ A) @ A2)) => ((! [Z2:(coinductive_llist @ A)]: ((A2 != (((coinductive_LCons @ A) @ E) @ Z2)))) => (~ ((! [Z1:A,Z2:(coinductive_llist @ A)]: (((A2 = (((coinductive_LCons @ A) @ Z1) @ Z2)) => (~ ((((member @ A) @ E) @ ((coinductive_lset @ A) @ Z2)))))))))))))).
% 2.67/1.51 thf(fact_42_lset__induct_H, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => ((! [Xs2:(coinductive_llist @ A)]: ((P @ (((coinductive_LCons @ A) @ X) @ Xs2)))) => ((! [X5:A,Xs2:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs2)) => ((P @ Xs2) => (P @ (((coinductive_LCons @ A) @ X5) @ Xs2)))))) => (P @ Xs))))))).
% 2.67/1.51 thf(fact_43_lset__induct, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => ((! [Xs2:(coinductive_llist @ A)]: ((P @ (((coinductive_LCons @ A) @ X) @ Xs2)))) => ((! [X5:A,Xs2:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs2)) => ((X != X5) => ((P @ Xs2) => (P @ (((coinductive_LCons @ A) @ X5) @ Xs2))))))) => (P @ Xs))))))).
% 2.67/1.51 thf(fact_44_lset__cases, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => ((! [Xs5:(coinductive_llist @ A)]: ((Xs != (((coinductive_LCons @ A) @ X) @ Xs5)))) => (~ ((! [X5:A,Xs5:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ X5) @ Xs5)) => (~ ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs5)))))))))))))).
% 2.67/1.51 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 2.67/1.51 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A3)))) = A3)))).
% 2.67/1.51 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X2:A]: (((P @ X2) = (Q @ X2)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.67/1.51 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X2:A]: (((F @ X2) = (G @ X2)))) => (F = G))))).
% 2.67/1.51 thf(fact_49_llist_Oset__intros_I1_J, axiom, (! [A:$tType,A1:A,A22:(coinductive_llist @ A)]: ((((member @ A) @ A1) @ ((coinductive_lset @ A) @ (((coinductive_LCons @ A) @ A1) @ A22)))))).
% 2.67/1.51 thf(fact_50_llist_Oset__intros_I2_J, axiom, (! [A:$tType,X:A,A22:(coinductive_llist @ A),A1:A]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ A22)) => (((member @ A) @ X) @ ((coinductive_lset @ A) @ (((coinductive_LCons @ A) @ A1) @ A22))))))).
% 2.67/1.51 thf(fact_51_lset__intros_I1_J, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: ((((member @ A) @ X) @ ((coinductive_lset @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)))))).
% 2.67/1.51 thf(fact_52_lset__intros_I2_J, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),X6:A]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => (((member @ A) @ X) @ ((coinductive_lset @ A) @ (((coinductive_LCons @ A) @ X6) @ Xs))))))).
% 2.67/1.51 thf(fact_53_lappend__inf, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((~ (((coinductive_lfinite @ A) @ Xs))) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = Xs))))).
% 2.67/1.51 thf(fact_54_lfinite__llist__of, axiom, (! [A:$tType,Xs:(list @ A)]: (((coinductive_lfinite @ A) @ ((coinductive_llist_of @ A) @ Xs))))).
% 2.67/1.51 thf(fact_55_split__llist__first, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => (? [Ys2:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: (((Xs = (((coinductive_lappend @ A) @ Ys2) @ (((coinductive_LCons @ A) @ X) @ Zs))) & (((coinductive_lfinite @ A) @ Ys2) & (~ ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Ys2)))))))))))).
% 2.67/1.51 thf(fact_56_split__llist, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => (? [Ys2:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: (((Xs = (((coinductive_lappend @ A) @ Ys2) @ (((coinductive_LCons @ A) @ X) @ Zs))) & ((coinductive_lfinite @ A) @ Ys2)))))))).
% 2.67/1.51 thf(fact_57_lfinite_Oinducts, axiom, (! [A:$tType,X:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: ((((coinductive_lfinite @ A) @ X) => ((P @ (coinductive_LNil @ A)) => ((! [Xs2:(coinductive_llist @ A),X2:A]: ((((coinductive_lfinite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coinductive_LCons @ A) @ X2) @ Xs2)))))) => (P @ X))))))).
% 2.67/1.51 thf(fact_58_lfinite_Osimps, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) = (^ [A4:(coinductive_llist @ A)]: (((A4 = (coinductive_LNil @ A)) | (? [Xs3:(coinductive_llist @ A),X3:A]: (((A4 = (((coinductive_LCons @ A) @ X3) @ Xs3)) & ((coinductive_lfinite @ A) @ Xs3))))))))))).
% 2.67/1.51 thf(fact_59_lfinite_Ocases, axiom, (! [A:$tType,A2:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ A2) => ((A2 != (coinductive_LNil @ A)) => (~ ((! [Xs2:(coinductive_llist @ A)]: (((? [X2:A]: ((A2 = (((coinductive_LCons @ A) @ X2) @ Xs2)))) => (~ (((coinductive_lfinite @ A) @ Xs2))))))))))))).
% 2.67/1.51 thf(fact_60_lfinite__rev__induct, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: ((((coinductive_lfinite @ A) @ Xs) => ((P @ (coinductive_LNil @ A)) => ((! [X2:A,Xs2:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coinductive_lappend @ A) @ Xs2) @ (((coinductive_LCons @ A) @ X2) @ (coinductive_LNil @ A)))))))) => (P @ Xs))))))).
% 2.67/1.51 thf(fact_61_paths__lappendD2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Graph:(A > (A > $o))]: ((((coinductive_lfinite @ A) @ Xs) => ((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) @ ((koenig916195507_paths @ A) @ Graph)) => (((member @ (coinductive_llist @ A)) @ Ys) @ ((koenig916195507_paths @ A) @ Graph))))))).
% 2.67/1.51 thf(fact_62_lappend__assoc, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs2:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) @ Zs2) = (((coinductive_lappend @ A) @ Xs) @ (((coinductive_lappend @ A) @ Ys) @ Zs2)))))).
% 2.67/1.51 thf(fact_63_llist__of__eq__LCons__conv, axiom, (! [A:$tType,Xs:(list @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coinductive_llist_of @ A) @ Xs) = (((coinductive_LCons @ A) @ Y) @ Ys)) = (? [Xs7:(list @ A)]: (((Xs = (((cons @ A) @ Y) @ Xs7)) & (Ys = ((coinductive_llist_of @ A) @ Xs7))))))))).
% 2.67/1.51 thf(fact_64_llist__of_Osimps_I2_J, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((coinductive_llist_of @ A) @ (((cons @ A) @ X) @ Xs)) = (((coinductive_LCons @ A) @ X) @ ((coinductive_llist_of @ A) @ Xs)))))).
% 2.67/1.51 thf(fact_65_lappend__llist__of__llist__of, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((coinductive_lappend @ A) @ ((coinductive_llist_of @ A) @ Xs)) @ ((coinductive_llist_of @ A) @ Ys)) = ((coinductive_llist_of @ A) @ (((append @ A) @ Xs) @ Ys)))))).
% 2.67/1.51 thf(fact_66_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((Xs != (coinductive_LNil @ A)) = (? [X3:A,Xs7:(coinductive_llist @ A)]: ((Xs = (((coinductive_LCons @ A) @ X3) @ Xs7)))))))).
% 2.67/1.51 thf(fact_67_llist_Oexhaust, axiom, (! [A:$tType,Y:(coinductive_llist @ A)]: (((Y != (coinductive_LNil @ A)) => (~ ((! [X212:A,X222:(coinductive_llist @ A)]: ((Y != (((coinductive_LCons @ A) @ X212) @ X222)))))))))).
% 2.67/1.51 thf(fact_68_llist_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A)]: (((coinductive_LNil @ A) != (((coinductive_LCons @ A) @ X21) @ X22))))).
% 2.67/1.51 thf(fact_69_lappend__eq__LNil__iff, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((((coinductive_lappend @ A) @ Xs) @ Ys) = (coinductive_LNil @ A)) = ((Xs = (coinductive_LNil @ A)) & (Ys = (coinductive_LNil @ A))))))).
% 2.67/1.51 thf(fact_70_split__list, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs))))))))).
% 2.67/1.51 thf(fact_71_split__list__last, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Zs))))))))))).
% 2.67/1.51 thf(fact_72_split__list__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X7:A]: (((((member @ A) @ X7) @ ((set2 @ A) @ Xs)) & (P @ X7)))) => (? [Ys2:(list @ A),X2:A]: (((? [Zs:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X2) @ Zs))))) & (P @ X2)))))))).
% 2.67/1.51 thf(fact_73_split__list__first, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Ys2))))))))))).
% 2.67/1.51 thf(fact_74_split__list__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X7:A]: (((((member @ A) @ X7) @ ((set2 @ A) @ Xs)) & (P @ X7)))) => (~ ((! [Ys2:(list @ A),X2:A]: (((? [Zs:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X2) @ Zs))))) => (~ ((P @ X2)))))))))))).
% 2.67/1.51 thf(fact_75_in__set__conv__decomp, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs3))))))))).
% 2.67/1.51 thf(fact_76_split__list__last__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X7:A]: (((((member @ A) @ X7) @ ((set2 @ A) @ Xs)) & (P @ X7)))) => (? [Ys2:(list @ A),X2:A,Zs:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X2) @ Zs))) & ((P @ X2) & (! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Zs)) => (~ ((P @ Xa)))))))))))))).
% 2.67/1.51 thf(fact_77_split__list__first__prop, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X7:A]: (((((member @ A) @ X7) @ ((set2 @ A) @ Xs)) & (P @ X7)))) => (? [Ys2:(list @ A),X2:A]: (((? [Zs:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X2) @ Zs))))) & ((P @ X2) & (! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Ys2)) => (~ ((P @ Xa)))))))))))))).
% 2.67/1.51 thf(fact_78_split__list__last__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X7:A]: (((((member @ A) @ X7) @ ((set2 @ A) @ Xs)) & (P @ X7)))) => (~ ((! [Ys2:(list @ A),X2:A,Zs:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X2) @ Zs))) => ((P @ X2) => (~ ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Zs)) => (~ ((P @ Xa)))))))))))))))))).
% 2.67/1.51 thf(fact_79_list_Oinject, axiom, (! [A:$tType,X21:A,X22:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X22) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.67/1.51 thf(fact_80_same__append__eq, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Xs) @ Zs2)) = (Ys = Zs2))))).
% 2.67/1.51 thf(fact_81_append__same__eq, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A),Zs2:(list @ A)]: ((((((append @ A) @ Ys) @ Xs) = (((append @ A) @ Zs2) @ Xs)) = (Ys = Zs2))))).
% 2.67/1.51 thf(fact_82_append__assoc, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A)]: (((((append @ A) @ (((append @ A) @ Xs) @ Ys)) @ Zs2) = (((append @ A) @ Xs) @ (((append @ A) @ Ys) @ Zs2)))))).
% 2.67/1.51 thf(fact_83_not__Cons__self2, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((cons @ A) @ X) @ Xs) != Xs)))).
% 2.67/1.51 thf(fact_84_append__eq__append__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A),Ts:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Zs2) @ Ts)) = (? [Us:(list @ A)]: ((((Xs = (((append @ A) @ Zs2) @ Us)) & ((((append @ A) @ Us) @ Ys) = Ts)) | (((((append @ A) @ Xs) @ Us) = Zs2) & (Ys = (((append @ A) @ Us) @ Ts)))))))))).
% 2.67/1.51 thf(fact_85_append__eq__appendI, axiom, (! [A:$tType,Xs:(list @ A),Xs1:(list @ A),Zs2:(list @ A),Ys:(list @ A),Us2:(list @ A)]: ((((((append @ A) @ Xs) @ Xs1) = Zs2) => ((Ys = (((append @ A) @ Xs1) @ Us2)) => ((((append @ A) @ Xs) @ Ys) = (((append @ A) @ Zs2) @ Us2))))))).
% 2.67/1.51 thf(fact_86_list_Oset__cases, axiom, (! [A:$tType,E:A,A2:(list @ A)]: (((((member @ A) @ E) @ ((set2 @ A) @ A2)) => ((! [Z2:(list @ A)]: ((A2 != (((cons @ A) @ E) @ Z2)))) => (~ ((! [Z1:A,Z2:(list @ A)]: (((A2 = (((cons @ A) @ Z1) @ Z2)) => (~ ((((member @ A) @ E) @ ((set2 @ A) @ Z2)))))))))))))).
% 2.67/1.51 thf(fact_87_set__ConsD, axiom, (! [A:$tType,Y:A,X:A,Xs:(list @ A)]: (((((member @ A) @ Y) @ ((set2 @ A) @ (((cons @ A) @ X) @ Xs))) => ((Y = X) | (((member @ A) @ Y) @ ((set2 @ A) @ Xs))))))).
% 2.67/1.51 thf(fact_88_list_Oset__intros_I1_J, axiom, (! [A:$tType,A1:A,A22:(list @ A)]: ((((member @ A) @ A1) @ ((set2 @ A) @ (((cons @ A) @ A1) @ A22)))))).
% 2.67/1.51 thf(fact_89_list_Oset__intros_I2_J, axiom, (! [A:$tType,X:A,A22:(list @ A),A1:A]: (((((member @ A) @ X) @ ((set2 @ A) @ A22)) => (((member @ A) @ X) @ ((set2 @ A) @ (((cons @ A) @ A1) @ A22))))))).
% 2.67/1.51 thf(fact_90_append__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A)]: (((((append @ A) @ (((cons @ A) @ X) @ Xs)) @ Ys) = (((cons @ A) @ X) @ (((append @ A) @ Xs) @ Ys)))))).
% 2.67/1.51 thf(fact_91_Cons__eq__appendI, axiom, (! [A:$tType,X:A,Xs1:(list @ A),Ys:(list @ A),Xs:(list @ A),Zs2:(list @ A)]: ((((((cons @ A) @ X) @ Xs1) = Ys) => ((Xs = (((append @ A) @ Xs1) @ Zs2)) => ((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys) @ Zs2))))))).
% 2.67/1.51 thf(fact_92_split__list__first__prop__iff, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs)) & (P @ X3)))) = (? [Ys3:(list @ A),X3:A]: (((? [Zs3:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X3) @ Zs3))))) & ((P @ X3) & (! [Y3:A]: (((((member @ A) @ Y3) @ ((set2 @ A) @ Ys3)) => (~ ((P @ Y3)))))))))))))).
% 2.67/1.51 thf(fact_93_split__list__last__prop__iff, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs)) & (P @ X3)))) = (? [Ys3:(list @ A),X3:A,Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X3) @ Zs3))) & ((P @ X3) & (! [Y3:A]: (((((member @ A) @ Y3) @ ((set2 @ A) @ Zs3)) => (~ ((P @ Y3)))))))))))))).
% 2.67/1.51 thf(fact_94_in__set__conv__decomp__first, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs3))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Ys3))))))))))).
% 2.67/1.51 thf(fact_95_in__set__conv__decomp__last, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs3:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X) @ Zs3))) & (~ ((((member @ A) @ X) @ ((set2 @ A) @ Zs3))))))))))).
% 2.67/1.51 thf(fact_96_split__list__first__propE, axiom, (! [A:$tType,Xs:(list @ A),P:(A > $o)]: (((? [X7:A]: (((((member @ A) @ X7) @ ((set2 @ A) @ Xs)) & (P @ X7)))) => (~ ((! [Ys2:(list @ A),X2:A]: (((? [Zs:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X2) @ Zs))))) => ((P @ X2) => (~ ((! [Xa:A]: (((((member @ A) @ Xa) @ ((set2 @ A) @ Ys2)) => (~ ((P @ Xa)))))))))))))))))).
% 2.67/1.51 thf(fact_97_bind__simps_I2_J, axiom, (! [A:$tType,B:$tType,X:B,Xs:(list @ B),F:(B > (list @ A))]: ((((((bind @ B) @ A) @ (((cons @ B) @ X) @ Xs)) @ F) = (((append @ A) @ (F @ X)) @ ((((bind @ B) @ A) @ Xs) @ F)))))).
% 2.67/1.51 thf(fact_98_llast__lappend__LCons, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys))) = ((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ Y) @ Ys))))))).
% 2.67/1.51 thf(fact_99_lappend__llist__of__LCons, axiom, (! [A:$tType,Xs:(list @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ ((coinductive_llist_of @ A) @ Xs)) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = (((coinductive_lappend @ A) @ ((coinductive_llist_of @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ Y) @ (nil @ A))))) @ Ys))))).
% 2.67/1.51 thf(fact_100_list__of__aux__code_I2_J, axiom, (! [A:$tType,Xs:(list @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coindu1384447384of_aux @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = (((coindu1384447384of_aux @ A) @ (((cons @ A) @ Y) @ Xs)) @ Ys))))).
% 2.67/1.51 thf(fact_101_llimit__induct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > $o),Xs:(coinductive_llist @ A)]: (((P @ (coinductive_LNil @ A)) => ((! [X2:A,Xs2:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coinductive_LCons @ A) @ X2) @ Xs2)))))) => (((! [Ys4:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys4) @ Xs) => (P @ Ys4)))) => (P @ Xs)) => (P @ Xs))))))).
% 2.67/1.51 thf(fact_102_set__list__of, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => (((set2 @ A) @ ((coinductive_list_of @ A) @ Xs)) = ((coinductive_lset @ A) @ Xs)))))).
% 2.67/1.51 thf(fact_103_append__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((append @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.67/1.51 thf(fact_104_append__self__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Xs) = (Ys = (nil @ A)))))).
% 2.67/1.51 thf(fact_105_self__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = (((append @ A) @ Xs) @ Ys)) = (Ys = (nil @ A)))))).
% 2.67/1.51 thf(fact_106_append__self__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = Ys) = (Xs = (nil @ A)))))).
% 2.67/1.51 thf(fact_107_self__append__conv2, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys = (((append @ A) @ Xs) @ Ys)) = (Xs = (nil @ A)))))).
% 2.67/1.51 thf(fact_108_Nil__is__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((nil @ A) = (((append @ A) @ Xs) @ Ys)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.67/1.51 thf(fact_109_append__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((((append @ A) @ Xs) @ Ys) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys = (nil @ A))))))).
% 2.67/1.51 thf(fact_110_llast__LCons2, axiom, (! [A:$tType,X:A,Y:A,Xs:(coinductive_llist @ A)]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ (((coinductive_LCons @ A) @ Y) @ Xs))) = ((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ Y) @ Xs)))))).
% 2.67/1.51 thf(fact_111_list__of__llist__of, axiom, (! [A:$tType,Xs:(list @ A)]: ((((coinductive_list_of @ A) @ ((coinductive_llist_of @ A) @ Xs)) = Xs)))).
% 2.67/1.51 thf(fact_112_lstrict__prefix__code_I4_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B),Y:B,Ys:(coinductive_llist @ B)]: (((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) @ (((coinductive_LCons @ B) @ Y) @ Ys)) = ((X = Y) & (((coindu1478340336prefix @ B) @ Xs) @ Ys)))))).
% 2.67/1.51 thf(fact_113_lstrict__prefix__code_I1_J, axiom, (! [A:$tType]: ((~ ((((coindu1478340336prefix @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A))))))).
% 2.67/1.51 thf(fact_114_bind__simps_I1_J, axiom, (! [B:$tType,A:$tType,F:(B > (list @ A))]: ((((((bind @ B) @ A) @ (nil @ B)) @ F) = (nil @ A))))).
% 2.67/1.51 thf(fact_115_append1__eq__conv, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys:(list @ A),Y:A]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))) = (((append @ A) @ Ys) @ (((cons @ A) @ Y) @ (nil @ A)))) = ((Xs = Ys) & (X = Y)))))).
% 2.67/1.51 thf(fact_116_list__of__LNil, axiom, (! [A:$tType]: ((((coinductive_list_of @ A) @ (coinductive_LNil @ A)) = (nil @ A))))).
% 2.67/1.51 thf(fact_117_llast__singleton, axiom, (! [A:$tType,X:A]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A))) = X)))).
% 2.67/1.51 thf(fact_118_lstrict__prefix__code_I2_J, axiom, (! [B:$tType,Y:B,Ys:(coinductive_llist @ B)]: ((((coindu1478340336prefix @ B) @ (coinductive_LNil @ B)) @ (((coinductive_LCons @ B) @ Y) @ Ys))))).
% 2.67/1.51 thf(fact_119_lstrict__prefix__code_I3_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B)]: ((~ ((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) @ (coinductive_LNil @ B))))))).
% 2.67/1.51 thf(fact_120_llist__of__list__of, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_llist_of @ A) @ ((coinductive_list_of @ A) @ Xs)) = Xs))))).
% 2.67/1.51 thf(fact_121_list__of__LCons, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),X:A]: ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_list_of @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = (((cons @ A) @ X) @ ((coinductive_list_of @ A) @ Xs))))))).
% 2.67/1.51 thf(fact_122_transpose_Ocases, axiom, (! [A:$tType,X:(list @ (list @ A))]: (((X != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X2:A,Xs2:(list @ A),Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (((cons @ A) @ X2) @ Xs2)) @ Xss))))))))))).
% 2.67/1.51 thf(fact_123_llist__less__induct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > $o),Xs:(coinductive_llist @ A)]: (((! [Xs2:(coinductive_llist @ A)]: (((! [Ys4:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys4) @ Xs2) => (P @ Ys4)))) => (P @ Xs2)))) => (P @ Xs))))).
% 2.67/1.51 thf(fact_124_list__of__code, axiom, (! [A:$tType]: (((coinductive_list_of @ A) = ((coindu1384447384of_aux @ A) @ (nil @ A)))))).
% 2.67/1.51 thf(fact_125_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X22))))).
% 2.67/1.51 thf(fact_126_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X22:(list @ A)]: (((List = (((cons @ A) @ X21) @ X22)) => (List != (nil @ A)))))).
% 2.67/1.51 thf(fact_127_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X212:A,X222:(list @ A)]: ((Y != (((cons @ A) @ X212) @ X222)))))))))).
% 2.67/1.51 thf(fact_128_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X1:A,X23:(list @ A)]: (((P @ X23) => (P @ (((cons @ A) @ X1) @ X23))))) => (P @ List)))))).
% 2.67/1.51 thf(fact_129_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y3:A,Ys3:(list @ A)]: ((Xs = (((cons @ A) @ Y3) @ Ys3)))))))).
% 2.67/1.51 thf(fact_130_list__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X2:A,Xs2:(list @ A)]: (((P @ (((cons @ A) @ X2) @ Xs2)) @ (nil @ B)))) => ((! [Y2:B,Ys2:(list @ B)]: (((P @ (nil @ A)) @ (((cons @ B) @ Y2) @ Ys2)))) => ((! [X2:A,Xs2:(list @ A),Y2:B,Ys2:(list @ B)]: ((((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ B) @ Y2) @ Ys2))))) => ((P @ Xs) @ Ys)))))))).
% 2.67/1.51 thf(fact_131_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X1:(list @ A)]: (((P @ (nil @ A)) @ X1))) => ((! [V:A,Va:(list @ A)]: (((P @ (((cons @ A) @ V) @ Va)) @ (nil @ A)))) => ((! [X2:A,Xs2:(list @ A),Y2:A,Ys2:(list @ A)]: ((((P @ Xs2) @ Ys2) => ((P @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys2))))) => ((P @ A0) @ A1))))))).
% 2.67/1.51 thf(fact_132_remdups__adj_Ocases, axiom, (! [A:$tType,X:(list @ A)]: (((X != (nil @ A)) => ((! [X2:A]: ((X != (((cons @ A) @ X2) @ (nil @ A))))) => (~ ((! [X2:A,Y2:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X2) @ (((cons @ A) @ Y2) @ Xs2)))))))))))).
% 2.67/1.51 thf(fact_133_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X2:A]: ((P @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X2:A,Y2:A,Xs2:(list @ A)]: ((((X2 = Y2) => (P @ (((cons @ A) @ X2) @ Xs2))) => (((X2 != Y2) => (P @ (((cons @ A) @ Y2) @ Xs2))) => (P @ (((cons @ A) @ X2) @ (((cons @ A) @ Y2) @ Xs2))))))) => (P @ A0))))))).
% 2.67/1.51 thf(fact_134_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X2:A]: ((P @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X2:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((cons @ A) @ X2) @ Xs2)))))) => (P @ Xs))))))).
% 2.67/1.51 thf(fact_135_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F2:(A > B),X1:(list @ B)]: ((((P @ F2) @ (nil @ A)) @ X1))) => ((! [F2:(A > B),A5:A,As:(list @ A),Bs:(list @ B)]: (((((P @ F2) @ As) @ (((cons @ B) @ (F2 @ A5)) @ Bs)) => (((P @ F2) @ (((cons @ A) @ A5) @ As)) @ Bs)))) => (((P @ A0) @ A1) @ A22)))))).
% 2.67/1.51 thf(fact_136_eq__Nil__appendI, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((Xs = Ys) => (Xs = (((append @ A) @ (nil @ A)) @ Ys)))))).
% 2.67/1.51 thf(fact_137_append__Nil, axiom, (! [A:$tType,Ys:(list @ A)]: (((((append @ A) @ (nil @ A)) @ Ys) = Ys)))).
% 2.67/1.51 thf(fact_138_lstrict__prefix__lfinite1, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Xs) @ Ys) => ((coinductive_lfinite @ A) @ Xs))))).
% 2.67/1.51 thf(fact_139_rev__induct, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X2:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X2) @ (nil @ A))))))) => (P @ Xs)))))).
% 2.67/1.51 thf(fact_140_rev__exhaust, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (~ ((! [Ys2:(list @ A),Y2:A]: ((Xs != (((append @ A) @ Ys2) @ (((cons @ A) @ Y2) @ (nil @ A)))))))))))).
% 2.67/1.51 thf(fact_141_Cons__eq__append__conv, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A)]: ((((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys) @ Zs2)) = (((Ys = (nil @ A)) & ((((cons @ A) @ X) @ Xs) = Zs2)) | (? [Ys5:(list @ A)]: ((((((cons @ A) @ X) @ Ys5) = Ys) & (Xs = (((append @ A) @ Ys5) @ Zs2)))))))))).
% 2.67/1.51 thf(fact_142_append__eq__Cons__conv, axiom, (! [A:$tType,Ys:(list @ A),Zs2:(list @ A),X:A,Xs:(list @ A)]: ((((((append @ A) @ Ys) @ Zs2) = (((cons @ A) @ X) @ Xs)) = (((Ys = (nil @ A)) & (Zs2 = (((cons @ A) @ X) @ Xs))) | (? [Ys5:(list @ A)]: (((Ys = (((cons @ A) @ X) @ Ys5)) & ((((append @ A) @ Ys5) @ Zs2) = Xs))))))))).
% 2.67/1.51 thf(fact_143_rev__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X2:A]: ((P @ (((cons @ A) @ X2) @ (nil @ A))))) => ((! [X2:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X2) @ (nil @ A)))))))) => (P @ Xs))))))).
% 2.67/1.51 thf(fact_144_llist__of__eq__LNil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((coinductive_llist_of @ A) @ Xs) = (coinductive_LNil @ A)) = (Xs = (nil @ A)))))).
% 2.67/1.51 thf(fact_145_llist__of_Osimps_I1_J, axiom, (! [A:$tType]: ((((coinductive_llist_of @ A) @ (nil @ A)) = (coinductive_LNil @ A))))).
% 2.67/1.51 thf(fact_146_list__bind__cong, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),Ys:(list @ A),F:(A > (list @ B)),G:(A > (list @ B))]: (((Xs = Ys) => ((! [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) => ((F @ X2) = (G @ X2))))) => (((((bind @ A) @ B) @ Xs) @ F) = ((((bind @ A) @ B) @ Ys) @ G))))))).
% 2.67/1.51 thf(fact_147_list__of__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_lfinite @ A) @ Ys) => (((coinductive_list_of @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((append @ A) @ ((coinductive_list_of @ A) @ Xs)) @ ((coinductive_list_of @ A) @ Ys)))))))).
% 2.67/1.51 thf(fact_148_Koenigslemma__Mirabelle__aepjeeakgn_Oconnected__def, axiom, (! [Node:$tType]: (((koenig793108494nected @ Node) = (^ [Graph2:(Node > (Node > $o))]: ((! [N:Node,N2:Node]: ((? [Xs3:(list @ Node)]: ((((member @ (coinductive_llist @ Node)) @ ((coinductive_llist_of @ Node) @ (((cons @ Node) @ N) @ (((append @ Node) @ Xs3) @ (((cons @ Node) @ N2) @ (nil @ Node)))))) @ ((koenig916195507_paths @ Node) @ Graph2)))))))))))).
% 2.67/1.51 thf(fact_149_Koenigslemma__Mirabelle__aepjeeakgn_OconnectedD, axiom, (! [A:$tType,Graph:(A > (A > $o)),N3:A,N4:A]: ((((koenig793108494nected @ A) @ Graph) => (? [Xs2:(list @ A)]: ((((member @ (coinductive_llist @ A)) @ ((coinductive_llist_of @ A) @ (((cons @ A) @ N3) @ (((append @ A) @ Xs2) @ (((cons @ A) @ N4) @ (nil @ A)))))) @ ((koenig916195507_paths @ A) @ Graph)))))))).
% 2.67/1.51 thf(fact_150_the__elem__set, axiom, (! [A:$tType,X:A]: ((((the_elem @ A) @ ((set2 @ A) @ (((cons @ A) @ X) @ (nil @ A)))) = X)))).
% 2.67/1.51 thf(fact_151_longest__common__prefix_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X2:A,Xs2:(list @ A),Y2:A,Ys2:(list @ A)]: ((((X2 = Y2) => ((P @ Xs2) @ Ys2)) => ((P @ (((cons @ A) @ X2) @ Xs2)) @ (((cons @ A) @ Y2) @ Ys2))))) => ((! [X1:(list @ A)]: (((P @ (nil @ A)) @ X1))) => ((! [Uu:(list @ A)]: (((P @ Uu) @ (nil @ A)))) => ((P @ A0) @ A1))))))).
% 2.67/1.51 thf(fact_152_prefixes_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X2:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((cons @ A) @ X2) @ Xs2))))) => (P @ A0)))))).
% 2.67/1.51 thf(fact_153_prefixes_Ocases, axiom, (! [A:$tType,X:(list @ A)]: (((X != (nil @ A)) => (~ ((! [X2:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X2) @ Xs2)))))))))).
% 2.67/1.51 thf(fact_154_prefixes__snoc, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((prefixes @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) = (((append @ (list @ A)) @ ((prefixes @ A) @ Xs)) @ (((cons @ (list @ A)) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) @ (nil @ (list @ A)))))))).
% 2.67/1.51 thf(fact_155_prefixes__eq__Snoc, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ (list @ A)),X:(list @ A)]: (((((prefixes @ A) @ Ys) = (((append @ (list @ A)) @ Xs) @ (((cons @ (list @ A)) @ X) @ (nil @ (list @ A))))) = ((((Ys = (nil @ A)) & (Xs = (nil @ (list @ A)))) | (? [Z:A,Zs3:(list @ A)]: (((Ys = (((append @ A) @ Zs3) @ (((cons @ A) @ Z) @ (nil @ A)))) & (Xs = ((prefixes @ A) @ Zs3)))))) & (X = Ys)))))).
% 2.67/1.51 thf(fact_156_sublists_Osimps_I1_J, axiom, (! [A:$tType]: ((((sublists @ A) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.67/1.51 thf(fact_157_prefixes_Osimps_I1_J, axiom, (! [A:$tType]: ((((prefixes @ A) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.67/1.51 thf(fact_158_product__lists_Osimps_I1_J, axiom, (! [A:$tType]: ((((product_lists @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.67/1.51 thf(fact_159_prefixes_Oelims, axiom, (! [A:$tType,X:(list @ A),Y:(list @ (list @ A))]: (((((prefixes @ A) @ X) = Y) => (((X = (nil @ A)) => (Y != (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))) => (~ ((! [X2:A,Xs2:(list @ A)]: (((X = (((cons @ A) @ X2) @ Xs2)) => (Y != (((cons @ (list @ A)) @ (nil @ A)) @ ((((map @ (list @ A)) @ (list @ A)) @ ((cons @ A) @ X2)) @ ((prefixes @ A) @ Xs2)))))))))))))).
% 2.67/1.51 thf(fact_160_maps__simps_I1_J, axiom, (! [A:$tType,B:$tType,F:(B > (list @ A)),X:B,Xs:(list @ B)]: ((((((maps @ B) @ A) @ F) @ (((cons @ B) @ X) @ Xs)) = (((append @ A) @ (F @ X)) @ ((((maps @ B) @ A) @ F) @ Xs)))))).
% 2.67/1.51 thf(fact_161_list_Omap__disc__iff, axiom, (! [B:$tType,A:$tType,F:(A > B),A2:(list @ A)]: (((((((map @ A) @ B) @ F) @ A2) = (nil @ B)) = (A2 = (nil @ A)))))).
% 2.67/1.51 thf(fact_162_map__is__Nil__conv, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(list @ B)]: (((((((map @ B) @ A) @ F) @ Xs) = (nil @ A)) = (Xs = (nil @ B)))))).
% 2.67/1.51 thf(fact_163_Nil__is__map__conv, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(list @ B)]: ((((nil @ A) = ((((map @ B) @ A) @ F) @ Xs)) = (Xs = (nil @ B)))))).
% 2.67/1.51 thf(fact_164_map__eq__conv, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(list @ B),G:(B > A)]: (((((((map @ B) @ A) @ F) @ Xs) = ((((map @ B) @ A) @ G) @ Xs)) = (! [X3:B]: (((((member @ B) @ X3) @ ((set2 @ B) @ Xs)) => ((F @ X3) = (G @ X3))))))))).
% 2.67/1.51 thf(fact_165_map__append, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(list @ B),Ys:(list @ B)]: ((((((map @ B) @ A) @ F) @ (((append @ B) @ Xs) @ Ys)) = (((append @ A) @ ((((map @ B) @ A) @ F) @ Xs)) @ ((((map @ B) @ A) @ F) @ Ys)))))).
% 2.67/1.51 thf(fact_166_list_Oinj__map__strong, axiom, (! [B:$tType,A:$tType,X:(list @ A),Xa2:(list @ A),F:(A > B),Fa:(A > B)]: (((! [Z3:A,Za:A]: (((((member @ A) @ Z3) @ ((set2 @ A) @ X)) => ((((member @ A) @ Za) @ ((set2 @ A) @ Xa2)) => (((F @ Z3) = (Fa @ Za)) => (Z3 = Za)))))) => ((((((map @ A) @ B) @ F) @ X) = ((((map @ A) @ B) @ Fa) @ Xa2)) => (X = Xa2)))))).
% 2.67/1.51 thf(fact_167_list_Omap__cong0, axiom, (! [B:$tType,A:$tType,X:(list @ A),F:(A > B),G:(A > B)]: (((! [Z3:A]: (((((member @ A) @ Z3) @ ((set2 @ A) @ X)) => ((F @ Z3) = (G @ Z3))))) => (((((map @ A) @ B) @ F) @ X) = ((((map @ A) @ B) @ G) @ X)))))).
% 2.67/1.51 thf(fact_168_list_Omap__cong, axiom, (! [B:$tType,A:$tType,X:(list @ A),Ya:(list @ A),F:(A > B),G:(A > B)]: (((X = Ya) => ((! [Z3:A]: (((((member @ A) @ Z3) @ ((set2 @ A) @ Ya)) => ((F @ Z3) = (G @ Z3))))) => (((((map @ A) @ B) @ F) @ X) = ((((map @ A) @ B) @ G) @ Ya))))))).
% 2.67/1.51 thf(fact_169_ex__map__conv, axiom, (! [A:$tType,B:$tType,Ys:(list @ B),F:(A > B)]: (((? [Xs3:(list @ A)]: ((Ys = ((((map @ A) @ B) @ F) @ Xs3)))) = (! [X3:B]: (((((member @ B) @ X3) @ ((set2 @ B) @ Ys)) => (? [Y3:A]: ((X3 = (F @ Y3))))))))))).
% 2.67/1.51 thf(fact_170_map__cong, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),Ys:(list @ A),F:(A > B),G:(A > B)]: (((Xs = Ys) => ((! [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Ys)) => ((F @ X2) = (G @ X2))))) => (((((map @ A) @ B) @ F) @ Xs) = ((((map @ A) @ B) @ G) @ Ys))))))).
% 2.67/1.51 thf(fact_171_map__idI, axiom, (! [A:$tType,Xs:(list @ A),F:(A > A)]: (((! [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) => ((F @ X2) = X2)))) => (((((map @ A) @ A) @ F) @ Xs) = Xs))))).
% 2.67/1.51 thf(fact_172_map__ext, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),F:(A > B),G:(A > B)]: (((! [X2:A]: (((((member @ A) @ X2) @ ((set2 @ A) @ Xs)) => ((F @ X2) = (G @ X2))))) => (((((map @ A) @ B) @ F) @ Xs) = ((((map @ A) @ B) @ G) @ Xs)))))).
% 2.67/1.51 thf(fact_173_list_Osimps_I9_J, axiom, (! [B:$tType,A:$tType,F:(A > B),X21:A,X22:(list @ A)]: ((((((map @ A) @ B) @ F) @ (((cons @ A) @ X21) @ X22)) = (((cons @ B) @ (F @ X21)) @ ((((map @ A) @ B) @ F) @ X22)))))).
% 2.67/1.51 thf(fact_174_Cons__eq__map__D, axiom, (! [A:$tType,B:$tType,X:A,Xs:(list @ A),F:(B > A),Ys:(list @ B)]: ((((((cons @ A) @ X) @ Xs) = ((((map @ B) @ A) @ F) @ Ys)) => (? [Z3:B,Zs:(list @ B)]: (((Ys = (((cons @ B) @ Z3) @ Zs)) & ((X = (F @ Z3)) & (Xs = ((((map @ B) @ A) @ F) @ Zs)))))))))).
% 2.67/1.51 thf(fact_175_map__eq__Cons__D, axiom, (! [B:$tType,A:$tType,F:(B > A),Xs:(list @ B),Y:A,Ys:(list @ A)]: (((((((map @ B) @ A) @ F) @ Xs) = (((cons @ A) @ Y) @ Ys)) => (? [Z3:B,Zs:(list @ B)]: (((Xs = (((cons @ B) @ Z3) @ Zs)) & (((F @ Z3) = Y) & (((((map @ B) @ A) @ F) @ Zs) = Ys))))))))).
% 2.67/1.51 thf(fact_176_Cons__eq__map__conv, axiom, (! [A:$tType,B:$tType,X:A,Xs:(list @ A),F:(B > A),Ys:(list @ B)]: ((((((cons @ A) @ X) @ Xs) = ((((map @ B) @ A) @ F) @ Ys)) = (? [Z:B,Zs3:(list @ B)]: (((Ys = (((cons @ B) @ Z) @ Zs3)) & ((X = (F @ Z)) & (Xs = ((((map @ B) @ A) @ F) @ Zs3)))))))))).
% 2.67/1.51 thf(fact_177_map__eq__Cons__conv, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(list @ B),Y:A,Ys:(list @ A)]: (((((((map @ B) @ A) @ F) @ Xs) = (((cons @ A) @ Y) @ Ys)) = (? [Z:B,Zs3:(list @ B)]: (((Xs = (((cons @ B) @ Z) @ Zs3)) & (((F @ Z) = Y) & (((((map @ B) @ A) @ F) @ Zs3) = Ys))))))))).
% 2.67/1.51 thf(fact_178_list_Osimps_I8_J, axiom, (! [A:$tType,B:$tType,F:(A > B)]: ((((((map @ A) @ B) @ F) @ (nil @ A)) = (nil @ B))))).
% 2.67/1.51 thf(fact_179_maps__simps_I2_J, axiom, (! [B:$tType,A:$tType,F:(B > (list @ A))]: ((((((maps @ B) @ A) @ F) @ (nil @ B)) = (nil @ A))))).
% 2.67/1.51 thf(fact_180_prefixes_Osimps_I2_J, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((prefixes @ A) @ (((cons @ A) @ X) @ Xs)) = (((cons @ (list @ A)) @ (nil @ A)) @ ((((map @ (list @ A)) @ (list @ A)) @ ((cons @ A) @ X)) @ ((prefixes @ A) @ Xs))))))).
% 2.67/1.51 thf(fact_181_prefixes_Opelims, axiom, (! [A:$tType,X:(list @ A),Y:(list @ (list @ A))]: (((((prefixes @ A) @ X) = Y) => ((((accp @ (list @ A)) @ (prefixes_rel @ A)) @ X) => (((X = (nil @ A)) => ((Y = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A)))) => (~ ((((accp @ (list @ A)) @ (prefixes_rel @ A)) @ (nil @ A)))))) => (~ ((! [X2:A,Xs2:(list @ A)]: (((X = (((cons @ A) @ X2) @ Xs2)) => ((Y = (((cons @ (list @ A)) @ (nil @ A)) @ ((((map @ (list @ A)) @ (list @ A)) @ ((cons @ A) @ X2)) @ ((prefixes @ A) @ Xs2)))) => (~ ((((accp @ (list @ A)) @ (prefixes_rel @ A)) @ (((cons @ A) @ X2) @ Xs2)))))))))))))))).
% 2.67/1.51 thf(fact_182_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = ((Xs = (coinductive_LNil @ A)) | (? [Xs7:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ Y) @ Xs7)) & (((coindu328551480prefix @ A) @ Xs7) @ Ys))))))))).
% 2.67/1.51 thf(fact_183_not__in__set__insert, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((~ ((((member @ A) @ X) @ ((set2 @ A) @ Xs)))) => ((((insert @ A) @ X) @ Xs) = (((cons @ A) @ X) @ Xs)))))).
% 2.67/1.51 thf(fact_184_in__set__insert, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ Xs)) => ((((insert @ A) @ X) @ Xs) = Xs))))).
% 2.67/1.51 thf(fact_185_insert__Nil, axiom, (! [A:$tType,X:A]: (((((insert @ A) @ X) @ (nil @ A)) = (((cons @ A) @ X) @ (nil @ A)))))).
% 2.67/1.51 thf(fact_186_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (coinductive_LNil @ A)) = (Xs = (coinductive_LNil @ A)))))).
% 2.67/1.51 thf(fact_187_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coindu328551480prefix @ A) @ (coinductive_LNil @ A)) @ Xs)))).
% 2.67/1.51 thf(fact_188_List_Oinsert__def, axiom, (! [A:$tType]: (((insert @ A) = (^ [X3:A,Xs3:(list @ A)]: (((((if @ (list @ A)) @ (((member @ A) @ X3) @ ((set2 @ A) @ Xs3))) @ Xs3) @ (((cons @ A) @ X3) @ Xs3)))))))).
% 2.67/1.51 thf(fact_189_rotate1_Osimps_I2_J, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((rotate1 @ A) @ (((cons @ A) @ X) @ Xs)) = (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))))))).
% 2.67/1.51 thf(fact_190_map__eq__map__tailrec, axiom, (! [B:$tType,A:$tType]: ((((map @ A) @ B) = ((map_tailrec @ A) @ B))))).
% 2.67/1.51 thf(fact_191_last__snoc, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((last @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) = X)))).
% 2.67/1.51 thf(fact_192_rotate1__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((rotate1 @ A) @ Xs) = (nil @ A)) = (Xs = (nil @ A)))))).
% 2.67/1.51 thf(fact_193_set__rotate1, axiom, (! [A:$tType,Xs:(list @ A)]: ((((set2 @ A) @ ((rotate1 @ A) @ Xs)) = ((set2 @ A) @ Xs))))).
% 2.67/1.51 thf(fact_194_last__appendR, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys != (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys)) = ((last @ A) @ Ys)))))).
% 2.67/1.51 thf(fact_195_last__appendL, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: (((Ys = (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys)) = ((last @ A) @ Xs)))))).
% 2.67/1.51 thf(fact_196_llast__llist__of, axiom, (! [A:$tType,Xs:(list @ A)]: ((((coinductive_llast @ A) @ ((coinductive_llist_of @ A) @ Xs)) = ((last @ A) @ Xs))))).
% 2.67/1.51 thf(fact_197_rotate1_Osimps_I1_J, axiom, (! [A:$tType]: ((((rotate1 @ A) @ (nil @ A)) = (nil @ A))))).
% 2.67/1.51 thf(fact_198_last__ConsR, axiom, (! [A:$tType,Xs:(list @ A),X:A]: (((Xs != (nil @ A)) => (((last @ A) @ (((cons @ A) @ X) @ Xs)) = ((last @ A) @ Xs)))))).
% 2.67/1.51 thf(fact_199_last__ConsL, axiom, (! [A:$tType,Xs:(list @ A),X:A]: (((Xs = (nil @ A)) => (((last @ A) @ (((cons @ A) @ X) @ Xs)) = X))))).
% 2.67/1.51 thf(fact_200_last_Osimps, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((Xs = (nil @ A)) => (((last @ A) @ (((cons @ A) @ X) @ Xs)) = X)) & ((Xs != (nil @ A)) => (((last @ A) @ (((cons @ A) @ X) @ Xs)) = ((last @ A) @ Xs))))))).
% 2.67/1.51 thf(fact_201_last__in__set, axiom, (! [A:$tType,As2:(list @ A)]: (((As2 != (nil @ A)) => (((member @ A) @ ((last @ A) @ As2)) @ ((set2 @ A) @ As2)))))).
% 2.67/1.51 thf(fact_202_last__map, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),F:(A > B)]: (((Xs != (nil @ A)) => (((last @ B) @ ((((map @ A) @ B) @ F) @ Xs)) = (F @ ((last @ A) @ Xs))))))).
% 2.67/1.51 thf(fact_203_longest__common__suffix, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((? [Ss:(list @ A),Xs5:(list @ A),Ys6:(list @ A)]: (((Xs = (((append @ A) @ Xs5) @ Ss)) & ((Ys = (((append @ A) @ Ys6) @ Ss)) & ((Xs5 = (nil @ A)) | ((Ys6 = (nil @ A)) | (((last @ A) @ Xs5) != ((last @ A) @ Ys6))))))))))).
% 2.67/1.51 thf(fact_204_last__append, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: ((((Ys = (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys)) = ((last @ A) @ Xs))) & ((Ys != (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys)) = ((last @ A) @ Ys))))))).
% 2.67/1.51 thf(fact_205_append__butlast__last__id, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((((append @ A) @ ((butlast @ A) @ Xs)) @ (((cons @ A) @ ((last @ A) @ Xs)) @ (nil @ A))) = Xs))))).
% 2.67/1.51 thf(fact_206_snoc__eq__iff__butlast, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys:(list @ A)]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))) = Ys) = ((Ys != (nil @ A)) & ((((butlast @ A) @ Ys) = Xs) & (((last @ A) @ Ys) = X))))))).
% 2.67/1.51 thf(fact_207_butlast__snoc, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((butlast @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) = Xs)))).
% 2.67/1.51 thf(fact_208_butlast_Osimps_I1_J, axiom, (! [A:$tType]: ((((butlast @ A) @ (nil @ A)) = (nil @ A))))).
% 2.67/1.51 thf(fact_209_in__set__butlastD, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((member @ A) @ X) @ ((set2 @ A) @ ((butlast @ A) @ Xs))) => (((member @ A) @ X) @ ((set2 @ A) @ Xs)))))).
% 2.67/1.51 thf(fact_210_map__butlast, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(list @ B)]: ((((((map @ B) @ A) @ F) @ ((butlast @ B) @ Xs)) = ((butlast @ A) @ ((((map @ B) @ A) @ F) @ Xs)))))).
% 2.67/1.51 thf(fact_211_butlast_Osimps_I2_J, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((Xs = (nil @ A)) => (((butlast @ A) @ (((cons @ A) @ X) @ Xs)) = (nil @ A))) & ((Xs != (nil @ A)) => (((butlast @ A) @ (((cons @ A) @ X) @ Xs)) = (((cons @ A) @ X) @ ((butlast @ A) @ Xs)))))))).
% 2.67/1.51 thf(fact_212_butlast__append, axiom, (! [A:$tType,Ys:(list @ A),Xs:(list @ A)]: ((((Ys = (nil @ A)) => (((butlast @ A) @ (((append @ A) @ Xs) @ Ys)) = ((butlast @ A) @ Xs))) & ((Ys != (nil @ A)) => (((butlast @ A) @ (((append @ A) @ Xs) @ Ys)) = (((append @ A) @ Xs) @ ((butlast @ A) @ Ys)))))))).
% 2.67/1.51 thf(fact_213_in__set__butlast__appendI, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys:(list @ A)]: ((((((member @ A) @ X) @ ((set2 @ A) @ ((butlast @ A) @ Xs))) | (((member @ A) @ X) @ ((set2 @ A) @ ((butlast @ A) @ Ys)))) => (((member @ A) @ X) @ ((set2 @ A) @ ((butlast @ A) @ (((append @ A) @ Xs) @ Ys)))))))).
% 2.67/1.51 thf(fact_214_list__ex1__simps_I1_J, axiom, (! [A:$tType,P:(A > $o)]: ((~ ((((list_ex1 @ A) @ P) @ (nil @ A))))))).
% 2.67/1.51 thf(fact_215_list__of__LCons__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),X:A]: (((((coinductive_lfinite @ A) @ Xs) => (((coinductive_list_of @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = (((cons @ A) @ X) @ ((coinductive_list_of @ A) @ Xs)))) & ((~ (((coinductive_lfinite @ A) @ Xs))) => (((coinductive_list_of @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = (undefined @ (list @ A)))))))).
% 2.67/1.51 thf(fact_216_llast__LNil, axiom, (! [A:$tType]: ((((coinductive_llast @ A) @ (coinductive_LNil @ A)) = (undefined @ A))))).
% 2.67/1.51 thf(fact_217_llast__linfinite, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((~ (((coinductive_lfinite @ A) @ Xs))) => (((coinductive_llast @ A) @ Xs) = (undefined @ A)))))).
% 2.67/1.51 thf(fact_218_list__ex1__iff, axiom, (! [A:$tType]: (((list_ex1 @ A) = (^ [P2:(A > $o),Xs3:(list @ A)]: ((? [X3:A]: (((((member @ A) @ X3) @ ((set2 @ A) @ Xs3)) & ((P2 @ X3) & (! [Y3:A]: ((((((member @ A) @ Y3) @ ((set2 @ A) @ Xs3)) & (P2 @ Y3)) => (Y3 = X3)))))))))))))).
% 2.67/1.51 thf(fact_219_can__select__set__list__ex1, axiom, (! [A:$tType,P:(A > $o),A3:(list @ A)]: (((((can_select @ A) @ P) @ ((set2 @ A) @ A3)) = (((list_ex1 @ A) @ P) @ A3))))).
% 2.67/1.51 thf(fact_220_list__of__aux__def, axiom, (! [A:$tType]: (((coindu1384447384of_aux @ A) = (^ [Xs3:(list @ A),Ys3:(coinductive_llist @ A)]: (((((if @ (list @ A)) @ ((coinductive_lfinite @ A) @ Ys3)) @ (((append @ A) @ ((rev @ A) @ Xs3)) @ ((coinductive_list_of @ A) @ Ys3))) @ (undefined @ (list @ A))))))))).
% 2.67/1.51 thf(fact_221_rev__is__rev__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((rev @ A) @ Xs) = ((rev @ A) @ Ys)) = (Xs = Ys))))).
% 2.67/1.51 thf(fact_222_rev__rev__ident, axiom, (! [A:$tType,Xs:(list @ A)]: ((((rev @ A) @ ((rev @ A) @ Xs)) = Xs)))).
% 2.67/1.51 thf(fact_223_Nil__is__rev__conv, axiom, (! [A:$tType,Xs:(list @ A)]: ((((nil @ A) = ((rev @ A) @ Xs)) = (Xs = (nil @ A)))))).
% 2.67/1.51 thf(fact_224_rev__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((rev @ A) @ Xs) = (nil @ A)) = (Xs = (nil @ A)))))).
% 2.67/1.51 thf(fact_225_set__rev, axiom, (! [A:$tType,Xs:(list @ A)]: ((((set2 @ A) @ ((rev @ A) @ Xs)) = ((set2 @ A) @ Xs))))).
% 2.67/1.51 thf(fact_226_rev__append, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((rev @ A) @ (((append @ A) @ Xs) @ Ys)) = (((append @ A) @ ((rev @ A) @ Ys)) @ ((rev @ A) @ Xs)))))).
% 2.67/1.51 thf(fact_227_singleton__rev__conv, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((((cons @ A) @ X) @ (nil @ A)) = ((rev @ A) @ Xs)) = (Xs = (((cons @ A) @ X) @ (nil @ A))))))).
% 2.67/1.51 thf(fact_228_rev__singleton__conv, axiom, (! [A:$tType,Xs:(list @ A),X:A]: (((((rev @ A) @ Xs) = (((cons @ A) @ X) @ (nil @ A))) = (Xs = (((cons @ A) @ X) @ (nil @ A))))))).
% 2.67/1.51 thf(fact_229_rev__eq__Cons__iff, axiom, (! [A:$tType,Xs:(list @ A),Y:A,Ys:(list @ A)]: (((((rev @ A) @ Xs) = (((cons @ A) @ Y) @ Ys)) = (Xs = (((append @ A) @ ((rev @ A) @ Ys)) @ (((cons @ A) @ Y) @ (nil @ A)))))))).
% 2.67/1.51 thf(fact_230_list__of__aux__code_I1_J, axiom, (! [A:$tType,Xs:(list @ A)]: (((((coindu1384447384of_aux @ A) @ Xs) @ (coinductive_LNil @ A)) = ((rev @ A) @ Xs))))).
% 2.67/1.51 thf(fact_231_rev_Osimps_I1_J, axiom, (! [A:$tType]: ((((rev @ A) @ (nil @ A)) = (nil @ A))))).
% 2.67/1.51 thf(fact_232_rev__swap, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: (((((rev @ A) @ Xs) = Ys) = (Xs = ((rev @ A) @ Ys)))))).
% 2.67/1.51 thf(fact_233_can__select__def, axiom, (! [A:$tType]: (((can_select @ A) = (^ [P2:(A > $o),A6:(set @ A)]: ((? [X3:A]: (((((member @ A) @ X3) @ A6) & ((P2 @ X3) & (! [Y3:A]: ((((((member @ A) @ Y3) @ A6) & (P2 @ Y3)) => (Y3 = X3)))))))))))))).
% 2.67/1.51 thf(fact_234_rev__map, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(list @ B)]: ((((rev @ A) @ ((((map @ B) @ A) @ F) @ Xs)) = ((((map @ B) @ A) @ F) @ ((rev @ B) @ Xs)))))).
% 2.67/1.51 thf(fact_235_rev_Osimps_I2_J, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((rev @ A) @ (((cons @ A) @ X) @ Xs)) = (((append @ A) @ ((rev @ A) @ Xs)) @ (((cons @ A) @ X) @ (nil @ A))))))).
% 2.67/1.51 thf(fact_236_map__tailrec__def, axiom, (! [B:$tType,A:$tType]: ((((map_tailrec @ A) @ B) = (^ [F3:(A > B),As3:(list @ A)]: (((rev @ B) @ (((((map_tailrec_rev @ A) @ B) @ F3) @ As3) @ (nil @ B))))))))).
% 2.67/1.51 thf(fact_237_map__tailrec__rev, axiom, (! [A:$tType,B:$tType]: ((((map_tailrec_rev @ B) @ A) = (^ [F3:(B > A),As3:(list @ B)]: (((append @ A) @ ((rev @ A) @ ((((map @ B) @ A) @ F3) @ As3))))))))).
% 2.67/1.51 thf(fact_238_map__tailrec__rev_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,F:(A > B),A2:A,As2:(list @ A),Bs2:(list @ B)]: (((((((map_tailrec_rev @ A) @ B) @ F) @ (((cons @ A) @ A2) @ As2)) @ Bs2) = (((((map_tailrec_rev @ A) @ B) @ F) @ As2) @ (((cons @ B) @ (F @ A2)) @ Bs2)))))).
% 2.67/1.51 thf(fact_239_map__tailrec__rev_Osimps_I1_J, axiom, (! [A:$tType,B:$tType,F:(A > B),Bs2:(list @ B)]: (((((((map_tailrec_rev @ A) @ B) @ F) @ (nil @ A)) @ Bs2) = Bs2)))).
% 2.67/1.51 thf(fact_240_map__tailrec__rev_Oelims, axiom, (! [A:$tType,B:$tType,X:(A > B),Xa2:(list @ A),Xb:(list @ B),Y:(list @ B)]: ((((((((map_tailrec_rev @ A) @ B) @ X) @ Xa2) @ Xb) = Y) => (((Xa2 = (nil @ A)) => (Y != Xb)) => (~ ((! [A5:A,As:(list @ A)]: (((Xa2 = (((cons @ A) @ A5) @ As)) => (Y != (((((map_tailrec_rev @ A) @ B) @ X) @ As) @ (((cons @ B) @ (X @ A5)) @ Xb))))))))))))).
% 2.67/1.51 thf(fact_241_llast__lappend, axiom, (! [A:$tType,Ys:(coinductive_llist @ A),Xs:(coinductive_llist @ A)]: (((((coinductive_lnull @ A) @ Ys) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((coinductive_llast @ A) @ Xs))) & ((~ (((coinductive_lnull @ A) @ Ys))) => ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((coinductive_llast @ A) @ Ys))) & ((~ (((coinductive_lfinite @ A) @ Xs))) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (undefined @ A))))))))).
% 2.67/1.51 thf(fact_242_strict__suffix__def, axiom, (! [A:$tType]: (((strict_suffix @ A) = (^ [Xs3:(list @ A),Ys3:(list @ A)]: ((? [Us:(list @ A)]: (((Ys3 = (((append @ A) @ Us) @ Xs3)) & (Us != (nil @ A))))))))))).
% 2.67/1.51 thf(fact_243_lappend_Odisc__iff_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((~ (((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)))) = ((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))))))).
% 2.67/1.51 thf(fact_244_lnull__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lnull @ A) @ Xs) & ((coinductive_lnull @ A) @ Ys)))))).
% 2.67/1.51 thf(fact_245_lnull__llist__of, axiom, (! [A:$tType,Xs:(list @ A)]: ((((coinductive_lnull @ A) @ ((coinductive_llist_of @ A) @ Xs)) = (Xs = (nil @ A)))))).
% 2.67/1.51 thf(fact_246_llast__LCons, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),X:A]: (((((coinductive_lnull @ A) @ Xs) => (((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = X)) & ((~ (((coinductive_lnull @ A) @ Xs))) => (((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = ((coinductive_llast @ A) @ Xs))))))).
% 2.67/1.51 thf(fact_247_strict__suffix__trans, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),Zs2:(list @ A)]: (((((strict_suffix @ A) @ Xs) @ Ys) => ((((strict_suffix @ A) @ Ys) @ Zs2) => (((strict_suffix @ A) @ Xs) @ Zs2)))))).
% 2.67/1.51 thf(fact_248_lappend_Odisc_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))) => (~ (((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)))))))).
% 2.67/1.51 thf(fact_249_lappend_Odisc_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => (((coinductive_lnull @ A) @ Ys) => ((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys))))))).
% 2.67/1.51 thf(fact_250_lappend__lnull1, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = Ys))))).
% 2.67/1.51 thf(fact_251_lappend__lnull2, axiom, (! [A:$tType,Ys:(coinductive_llist @ A),Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Ys) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = Xs))))).
% 2.67/1.51 thf(fact_252_lnull__imp__lfinite, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => ((coinductive_lfinite @ A) @ Xs))))).
% 2.67/1.51 thf(fact_253_lappend_Oexhaust, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lnull @ A) @ Xs) => (~ (((coinductive_lnull @ A) @ Ys)))) => ((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))))))).
% 2.67/1.51 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.67/1.51 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.67/1.51 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.67/1.51 thf(conj_0, conjecture, (((member @ (coinductive_llist @ a)) @ (((coinductive_lappend @ a) @ (((coinductive_LCons @ a) @ n) @ ((coinductive_llist_of @ a) @ ys))) @ (((coinductive_lappend @ a) @ (((coinductive_LCons @ a) @ n) @ (((coinductive_lappend @ a) @ ((coinductive_llist_of @ a) @ zs)) @ (((coinductive_LCons @ a) @ x) @ (coinductive_LNil @ a))))) @ xs3))) @ ((koenig916195507_paths @ a) @ graph))).
% 2.67/1.51 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.fWo8BEA7MH/DTF2DTF22272.p
% 2.67/1.51 ------------------------
% 2.67/1.55 ---- Cleaned THF ---
% 2.67/1.55 thf(ty_t_Coinductive__List_Ollist,type,
% 2.67/1.55 coinductive_llist: $tType > $tType ).
% 2.67/1.55
% 2.67/1.55 thf(ty_t_List_Olist,type,
% 2.67/1.55 list: $tType > $tType ).
% 2.67/1.55
% 2.67/1.55 thf(ty_t_Set_Oset,type,
% 2.67/1.55 set: $tType > $tType ).
% 2.67/1.55
% 2.67/1.55 thf(ty_t_itself,type,
% 2.67/1.55 itself: $tType > $tType ).
% 2.67/1.55
% 2.67/1.55 thf(ty_tf_a,type,
% 2.67/1.55 a: $tType ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 2.67/1.55 coindu328551480prefix:
% 2.67/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Coinductive__List_Olappend,type,
% 2.67/1.55 coinductive_lappend:
% 2.67/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Coinductive__List_Olfinite,type,
% 2.67/1.55 coinductive_lfinite:
% 2.67/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Coinductive__List_Olist__of,type,
% 2.67/1.55 coinductive_list_of:
% 2.67/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( list @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Coinductive__List_Olist__of__aux,type,
% 2.67/1.55 coindu1384447384of_aux:
% 2.67/1.55 !>[A: $tType] : ( ( list @ A ) > ( coinductive_llist @ A ) > ( list @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Coinductive__List_Ollast,type,
% 2.67/1.55 coinductive_llast:
% 2.67/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 2.67/1.55 coinductive_LCons:
% 2.67/1.55 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 2.67/1.55 coinductive_LNil:
% 2.67/1.55 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Coinductive__List_Ollist_Olnull,type,
% 2.67/1.55 coinductive_lnull:
% 2.67/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Coinductive__List_Ollist_Olset,type,
% 2.67/1.55 coinductive_lset:
% 2.67/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Coinductive__List_Ollist__of,type,
% 2.67/1.55 coinductive_llist_of:
% 2.67/1.55 !>[A: $tType] : ( ( list @ A ) > ( coinductive_llist @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 2.67/1.55 coindu1478340336prefix:
% 2.67/1.55 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_HOL_Oundefined,type,
% 2.67/1.55 undefined:
% 2.67/1.55 !>[A: $tType] : A ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_If,type,
% 2.67/1.55 if:
% 2.67/1.55 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Oconnected,type,
% 2.67/1.55 koenig793108494nected:
% 2.67/1.55 !>[Node: $tType] : ( ( Node > Node > $o ) > $o ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Koenigslemma__Mirabelle__aepjeeakgn_Opaths,type,
% 2.67/1.55 koenig916195507_paths:
% 2.67/1.55 !>[Node: $tType] : ( ( Node > Node > $o ) > ( set @ ( coinductive_llist @ Node ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Oappend,type,
% 2.67/1.55 append:
% 2.67/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Obind,type,
% 2.67/1.55 bind:
% 2.67/1.55 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Obutlast,type,
% 2.67/1.55 butlast:
% 2.67/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Ocan__select,type,
% 2.67/1.55 can_select:
% 2.67/1.55 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) > $o ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Oinsert,type,
% 2.67/1.55 insert:
% 2.67/1.55 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Olast,type,
% 2.67/1.55 last:
% 2.67/1.55 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Olist_OCons,type,
% 2.67/1.55 cons:
% 2.67/1.55 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Olist_ONil,type,
% 2.67/1.55 nil:
% 2.67/1.55 !>[A: $tType] : ( list @ A ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Olist_Omap,type,
% 2.67/1.55 map:
% 2.67/1.55 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( list @ A ) > ( list @ Aa ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Olist_Oset,type,
% 2.67/1.55 set2:
% 2.67/1.55 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Olist__ex1,type,
% 2.67/1.55 list_ex1:
% 2.67/1.55 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Omap__tailrec,type,
% 2.67/1.55 map_tailrec:
% 2.67/1.55 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Omap__tailrec__rev,type,
% 2.67/1.55 map_tailrec_rev:
% 2.67/1.55 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) > ( list @ B ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Omaps,type,
% 2.67/1.55 maps:
% 2.67/1.55 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Oproduct__lists,type,
% 2.67/1.55 product_lists:
% 2.67/1.55 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Orev,type,
% 2.67/1.55 rev:
% 2.67/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Orotate1,type,
% 2.67/1.55 rotate1:
% 2.67/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_List_Osublists,type,
% 2.67/1.55 sublists:
% 2.67/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Pure_Otype,type,
% 2.67/1.55 type:
% 2.67/1.55 !>[A: $tType] : ( itself @ A ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Set_OCollect,type,
% 2.67/1.55 collect:
% 2.67/1.55 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Set_Othe__elem,type,
% 2.67/1.55 the_elem:
% 2.67/1.55 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Sublist_Oprefixes,type,
% 2.67/1.55 prefixes:
% 2.67/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Sublist_Oprefixes__rel,type,
% 2.67/1.55 prefixes_rel:
% 2.67/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Sublist_Ostrict__suffix,type,
% 2.67/1.55 strict_suffix:
% 2.67/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_Wellfounded_Oaccp,type,
% 2.67/1.55 accp:
% 2.67/1.55 !>[A: $tType] : ( ( A > A > $o ) > A > $o ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_c_member,type,
% 2.67/1.55 member:
% 2.67/1.55 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.67/1.55
% 2.67/1.55 thf(sy_v_XS_H____,type,
% 2.67/1.55 xs: list @ a ).
% 2.67/1.55
% 2.67/1.55 thf(sy_v_graph,type,
% 2.67/1.55 graph: a > a > $o ).
% 2.67/1.55
% 2.67/1.55 thf(sy_v_n,type,
% 2.67/1.55 n: a ).
% 2.67/1.55
% 2.67/1.55 thf(sy_v_x,type,
% 2.67/1.55 x: a ).
% 2.67/1.55
% 2.67/1.55 thf(sy_v_xs,type,
% 2.67/1.55 xs2: coinductive_llist @ a ).
% 2.67/1.55
% 2.67/1.55 thf(sy_v_xs_H_H____,type,
% 2.67/1.55 xs3: coinductive_llist @ a ).
% 2.67/1.55
% 2.67/1.55 thf(sy_v_xs_H____,type,
% 2.67/1.55 xs4: coinductive_llist @ a ).
% 2.67/1.55
% 2.67/1.55 thf(sy_v_ys____,type,
% 2.67/1.55 ys: list @ a ).
% 2.67/1.55
% 2.67/1.55 thf(sy_v_zs____,type,
% 2.67/1.55 zs: list @ a ).
% 2.67/1.55
% 2.67/1.55 thf(fact_0_xs_H,axiom,
% 2.67/1.55 ( xs4
% 2.67/1.55 = ( coinductive_llist_of @ a @ xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_1_n__neq__x,axiom,
% 2.67/1.55 n != x ).
% 2.67/1.55
% 2.67/1.55 thf(fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062XS_H_O_Axs_H_A_061_Allist__of_AXS_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.67/1.55 ~ ! [XS: list @ a] :
% 2.67/1.55 ( xs4
% 2.67/1.55 != ( coinductive_llist_of @ a @ XS ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_3_path,axiom,
% 2.67/1.55 member @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ n @ xs2 ) @ ( koenig916195507_paths @ a @ graph ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_4_xs,axiom,
% 2.67/1.55 ( xs2
% 2.67/1.55 = ( coinductive_lappend @ a @ xs4 @ ( coinductive_LCons @ a @ x @ xs3 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_5_XS_H,axiom,
% 2.67/1.55 ( xs
% 2.67/1.55 = ( append @ a @ ys @ ( cons @ a @ n @ zs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_6__092_060open_062n_A_092_060notin_062_Aset_Azs_092_060close_062,axiom,
% 2.67/1.55 ~ ( member @ a @ n @ ( set2 @ a @ zs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_7_paths_OEmpty,axiom,
% 2.67/1.55 ! [Node: $tType,Graph: Node > Node > $o] : ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LNil @ Node ) @ ( koenig916195507_paths @ Node @ Graph ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_8_paths_OLCons,axiom,
% 2.67/1.55 ! [Node: $tType,Graph: Node > Node > $o,X: Node,Y: Node,Xs: coinductive_llist @ Node] :
% 2.67/1.55 ( ( Graph @ X @ Y )
% 2.67/1.55 => ( ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ Y @ Xs ) @ ( koenig916195507_paths @ Node @ Graph ) )
% 2.67/1.55 => ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ X @ ( coinductive_LCons @ Node @ Y @ Xs ) ) @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_9_paths_Ocases,axiom,
% 2.67/1.55 ! [Node: $tType,A2: coinductive_llist @ Node,Graph: Node > Node > $o] :
% 2.67/1.55 ( ( member @ ( coinductive_llist @ Node ) @ A2 @ ( koenig916195507_paths @ Node @ Graph ) )
% 2.67/1.55 => ( ( A2
% 2.67/1.55 != ( coinductive_LNil @ Node ) )
% 2.67/1.55 => ( ! [X2: Node] :
% 2.67/1.55 ( A2
% 2.67/1.55 != ( coinductive_LCons @ Node @ X2 @ ( coinductive_LNil @ Node ) ) )
% 2.67/1.55 => ~ ! [X2: Node,Y2: Node,Xs2: coinductive_llist @ Node] :
% 2.67/1.55 ( ( A2
% 2.67/1.55 = ( coinductive_LCons @ Node @ X2 @ ( coinductive_LCons @ Node @ Y2 @ Xs2 ) ) )
% 2.67/1.55 => ( ( Graph @ X2 @ Y2 )
% 2.67/1.55 => ~ ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ Y2 @ Xs2 ) @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_10_paths_Osimps,axiom,
% 2.67/1.55 ! [Node: $tType,A2: coinductive_llist @ Node,Graph: Node > Node > $o] :
% 2.67/1.55 ( ( member @ ( coinductive_llist @ Node ) @ A2 @ ( koenig916195507_paths @ Node @ Graph ) )
% 2.67/1.55 = ( ( A2
% 2.67/1.55 = ( coinductive_LNil @ Node ) )
% 2.67/1.55 | ? [X3: Node] :
% 2.67/1.55 ( A2
% 2.67/1.55 = ( coinductive_LCons @ Node @ X3 @ ( coinductive_LNil @ Node ) ) )
% 2.67/1.55 | ? [X3: Node,Y3: Node,Xs3: coinductive_llist @ Node] :
% 2.67/1.55 ( ( A2
% 2.67/1.55 = ( coinductive_LCons @ Node @ X3 @ ( coinductive_LCons @ Node @ Y3 @ Xs3 ) ) )
% 2.67/1.55 & ( Graph @ X3 @ Y3 )
% 2.67/1.55 & ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ Y3 @ Xs3 ) @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_11_paths_OSingle,axiom,
% 2.67/1.55 ! [Node: $tType,X: Node,Graph: Node > Node > $o] : ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ X @ ( coinductive_LNil @ Node ) ) @ ( koenig916195507_paths @ Node @ Graph ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_12_paths__LConsD,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Graph: A > A > $o] :
% 2.67/1.55 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X @ Xs ) @ ( koenig916195507_paths @ A @ Graph ) )
% 2.67/1.55 => ( member @ ( coinductive_llist @ A ) @ Xs @ ( koenig916195507_paths @ A @ Graph ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_13_paths_Ocoinduct,axiom,
% 2.67/1.55 ! [Node: $tType,X4: ( coinductive_llist @ Node ) > $o,X: coinductive_llist @ Node,Graph: Node > Node > $o] :
% 2.67/1.55 ( ( X4 @ X )
% 2.67/1.55 => ( ! [X2: coinductive_llist @ Node] :
% 2.67/1.55 ( ( X4 @ X2 )
% 2.67/1.55 => ( ( X2
% 2.67/1.55 = ( coinductive_LNil @ Node ) )
% 2.67/1.55 | ? [Xa: Node] :
% 2.67/1.55 ( X2
% 2.67/1.55 = ( coinductive_LCons @ Node @ Xa @ ( coinductive_LNil @ Node ) ) )
% 2.67/1.55 | ? [Xa: Node,Y4: Node,Xs4: coinductive_llist @ Node] :
% 2.67/1.55 ( ( X2
% 2.67/1.55 = ( coinductive_LCons @ Node @ Xa @ ( coinductive_LCons @ Node @ Y4 @ Xs4 ) ) )
% 2.67/1.55 & ( Graph @ Xa @ Y4 )
% 2.67/1.55 & ( ( X4 @ ( coinductive_LCons @ Node @ Y4 @ Xs4 ) )
% 2.67/1.55 | ( member @ ( coinductive_llist @ Node ) @ ( coinductive_LCons @ Node @ Y4 @ Xs4 ) @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ) )
% 2.67/1.55 => ( member @ ( coinductive_llist @ Node ) @ X @ ( koenig916195507_paths @ Node @ Graph ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_14_paths__lappendD1,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Graph: A > A > $o] :
% 2.67/1.55 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( koenig916195507_paths @ A @ Graph ) )
% 2.67/1.55 => ( member @ ( coinductive_llist @ A ) @ Xs @ ( koenig916195507_paths @ A @ Graph ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_15_set,axiom,
% 2.67/1.55 member @ a @ x @ ( coinductive_lset @ a @ xs2 ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_16__092_060open_062x_A_092_060notin_062_Alset_Axs_H_092_060close_062,axiom,
% 2.67/1.55 ~ ( member @ a @ x @ ( coinductive_lset @ a @ xs4 ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_17_True,axiom,
% 2.67/1.55 member @ a @ n @ ( coinductive_lset @ a @ xs4 ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_18_calculation,axiom,
% 2.67/1.55 coinductive_lfinite @ a @ ( coinductive_LCons @ a @ n @ ( coinductive_llist_of @ a @ ys ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_19_lappend__code_I1_J,axiom,
% 2.67/1.55 ! [A: $tType,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 2.67/1.55 = Ys ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_20_lappend__LNil2,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.67/1.55 = Xs ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_21_lappend__code_I2_J,axiom,
% 2.67/1.55 ! [A: $tType,Xa2: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa2 @ X ) @ Ys )
% 2.67/1.55 = ( coinductive_LCons @ A @ Xa2 @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_22_lappend__snocL1__conv__LCons2,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 2.67/1.55 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_23_llist__of__inject,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.67/1.55 ( ( ( coinductive_llist_of @ A @ Xs )
% 2.67/1.55 = ( coinductive_llist_of @ A @ Ys ) )
% 2.67/1.55 = ( Xs = Ys ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_24_llist_Oinject,axiom,
% 2.67/1.55 ! [A: $tType,X21: A,X22: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 2.67/1.55 ( ( ( coinductive_LCons @ A @ X21 @ X22 )
% 2.67/1.55 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 2.67/1.55 = ( ( X21 = Y21 )
% 2.67/1.55 & ( X22 = Y22 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_25_lappend__LNil__LNil,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 2.67/1.55 = ( coinductive_LNil @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_26_LNil__eq__lappend__iff,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( ( coinductive_LNil @ A )
% 2.67/1.55 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.67/1.55 = ( ( Xs
% 2.67/1.55 = ( coinductive_LNil @ A ) )
% 2.67/1.55 & ( Ys
% 2.67/1.55 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_27__092_060open_062lfinite_Axs_H_092_060close_062,axiom,
% 2.67/1.55 coinductive_lfinite @ a @ xs4 ).
% 2.67/1.55
% 2.67/1.55 thf(fact_28__092_060open_062n_A_092_060in_062_Aset_AXS_H_092_060close_062,axiom,
% 2.67/1.55 member @ a @ n @ ( set2 @ a @ xs ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_29_lfinite__LCons,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.67/1.55 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_30_lfinite__code_I2_J,axiom,
% 2.67/1.55 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 2.67/1.55 ( ( coinductive_lfinite @ B @ ( coinductive_LCons @ B @ X @ Xs ) )
% 2.67/1.55 = ( coinductive_lfinite @ B @ Xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_31_lfinite__code_I1_J,axiom,
% 2.67/1.55 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_32_lfinite__lappend,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lfinite @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.67/1.55 = ( ( coinductive_lfinite @ A @ Xs )
% 2.67/1.55 & ( coinductive_lfinite @ A @ Ys ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_33__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ys_Azs_O_A_092_060lbrakk_062XS_H_A_061_Ays_A_064_An_A_D_Azs_059_An_A_092_060notin_062_Aset_Azs_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.67/1.55 ~ ! [Ys2: list @ a,Zs: list @ a] :
% 2.67/1.55 ( ( xs
% 2.67/1.55 = ( append @ a @ Ys2 @ ( cons @ a @ n @ Zs ) ) )
% 2.67/1.55 => ( member @ a @ n @ ( set2 @ a @ Zs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_34__092_060open_062_092_060exists_062ys_Azs_O_AXS_H_A_061_Ays_A_064_An_A_D_Azs_A_092_060and_062_An_A_092_060notin_062_Aset_Azs_092_060close_062,axiom,
% 2.67/1.55 ? [Ys2: list @ a,Zs: list @ a] :
% 2.67/1.55 ( ( xs
% 2.67/1.55 = ( append @ a @ Ys2 @ ( cons @ a @ n @ Zs ) ) )
% 2.67/1.55 & ~ ( member @ a @ n @ ( set2 @ a @ Zs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_35__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_H_Axs_H_H_O_A_092_060lbrakk_062lfinite_Axs_H_059_Axs_A_061_Alappend_Axs_H_A_ILCons_Ax_Axs_H_H_J_059_Ax_A_092_060notin_062_Alset_Axs_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.67/1.55 ~ ! [Xs5: coinductive_llist @ a] :
% 2.67/1.55 ( ( coinductive_lfinite @ a @ Xs5 )
% 2.67/1.55 => ( ? [Xs6: coinductive_llist @ a] :
% 2.67/1.55 ( xs2
% 2.67/1.55 = ( coinductive_lappend @ a @ Xs5 @ ( coinductive_LCons @ a @ x @ Xs6 ) ) )
% 2.67/1.55 => ( member @ a @ x @ ( coinductive_lset @ a @ Xs5 ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_36_lset__llist__of,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A] :
% 2.67/1.55 ( ( coinductive_lset @ A @ ( coinductive_llist_of @ A @ Xs ) )
% 2.67/1.55 = ( set2 @ A @ Xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_37_in__lset__lappend__iff,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) )
% 2.67/1.55 = ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.67/1.55 | ( ( coinductive_lfinite @ A @ Xs )
% 2.67/1.55 & ( member @ A @ X @ ( coinductive_lset @ A @ Ys ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_38_lfinite__LConsI,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 2.67/1.55 ( ( coinductive_lfinite @ A @ Xs )
% 2.67/1.55 => ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_39_lfinite__LNil,axiom,
% 2.67/1.55 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_40_llist_Oset__induct,axiom,
% 2.67/1.55 ! [A: $tType,X: A,A2: coinductive_llist @ A,P: A > ( coinductive_llist @ A ) > $o] :
% 2.67/1.55 ( ( member @ A @ X @ ( coinductive_lset @ A @ A2 ) )
% 2.67/1.55 => ( ! [Z1: A,Z2: coinductive_llist @ A] : ( P @ Z1 @ ( coinductive_LCons @ A @ Z1 @ Z2 ) )
% 2.67/1.55 => ( ! [Z1: A,Z2: coinductive_llist @ A,Xa3: A] :
% 2.67/1.55 ( ( member @ A @ Xa3 @ ( coinductive_lset @ A @ Z2 ) )
% 2.67/1.55 => ( ( P @ Xa3 @ Z2 )
% 2.67/1.55 => ( P @ Xa3 @ ( coinductive_LCons @ A @ Z1 @ Z2 ) ) ) )
% 2.67/1.55 => ( P @ X @ A2 ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_41_llist_Oset__cases,axiom,
% 2.67/1.55 ! [A: $tType,E: A,A2: coinductive_llist @ A] :
% 2.67/1.55 ( ( member @ A @ E @ ( coinductive_lset @ A @ A2 ) )
% 2.67/1.55 => ( ! [Z2: coinductive_llist @ A] :
% 2.67/1.55 ( A2
% 2.67/1.55 != ( coinductive_LCons @ A @ E @ Z2 ) )
% 2.67/1.55 => ~ ! [Z1: A,Z2: coinductive_llist @ A] :
% 2.67/1.55 ( ( A2
% 2.67/1.55 = ( coinductive_LCons @ A @ Z1 @ Z2 ) )
% 2.67/1.55 => ~ ( member @ A @ E @ ( coinductive_lset @ A @ Z2 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_42_lset__induct_H,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.67/1.55 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.67/1.55 => ( ! [Xs2: coinductive_llist @ A] : ( P @ ( coinductive_LCons @ A @ X @ Xs2 ) )
% 2.67/1.55 => ( ! [X5: A,Xs2: coinductive_llist @ A] :
% 2.67/1.55 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs2 ) )
% 2.67/1.55 => ( ( P @ Xs2 )
% 2.67/1.55 => ( P @ ( coinductive_LCons @ A @ X5 @ Xs2 ) ) ) )
% 2.67/1.55 => ( P @ Xs ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_43_lset__induct,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.67/1.55 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.67/1.55 => ( ! [Xs2: coinductive_llist @ A] : ( P @ ( coinductive_LCons @ A @ X @ Xs2 ) )
% 2.67/1.55 => ( ! [X5: A,Xs2: coinductive_llist @ A] :
% 2.67/1.55 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs2 ) )
% 2.67/1.55 => ( ( X != X5 )
% 2.67/1.55 => ( ( P @ Xs2 )
% 2.67/1.55 => ( P @ ( coinductive_LCons @ A @ X5 @ Xs2 ) ) ) ) )
% 2.67/1.55 => ( P @ Xs ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_44_lset__cases,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 2.67/1.55 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.67/1.55 => ( ! [Xs5: coinductive_llist @ A] :
% 2.67/1.55 ( Xs
% 2.67/1.55 != ( coinductive_LCons @ A @ X @ Xs5 ) )
% 2.67/1.55 => ~ ! [X5: A,Xs5: coinductive_llist @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 = ( coinductive_LCons @ A @ X5 @ Xs5 ) )
% 2.67/1.55 => ~ ( member @ A @ X @ ( coinductive_lset @ A @ Xs5 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_45_mem__Collect__eq,axiom,
% 2.67/1.55 ! [A: $tType,A2: A,P: A > $o] :
% 2.67/1.55 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 2.67/1.55 = ( P @ A2 ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_46_Collect__mem__eq,axiom,
% 2.67/1.55 ! [A: $tType,A3: set @ A] :
% 2.67/1.55 ( ( collect @ A
% 2.67/1.55 @ ^ [X3: A] : ( member @ A @ X3 @ A3 ) )
% 2.67/1.55 = A3 ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_47_Collect__cong,axiom,
% 2.67/1.55 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.67/1.55 ( ! [X2: A] :
% 2.67/1.55 ( ( P @ X2 )
% 2.67/1.55 = ( Q @ X2 ) )
% 2.67/1.55 => ( ( collect @ A @ P )
% 2.67/1.55 = ( collect @ A @ Q ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_48_ext,axiom,
% 2.67/1.55 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.67/1.55 ( ! [X2: A] :
% 2.67/1.55 ( ( F @ X2 )
% 2.67/1.55 = ( G @ X2 ) )
% 2.67/1.55 => ( F = G ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_49_llist_Oset__intros_I1_J,axiom,
% 2.67/1.55 ! [A: $tType,A1: A,A22: coinductive_llist @ A] : ( member @ A @ A1 @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ A1 @ A22 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_50_llist_Oset__intros_I2_J,axiom,
% 2.67/1.55 ! [A: $tType,X: A,A22: coinductive_llist @ A,A1: A] :
% 2.67/1.55 ( ( member @ A @ X @ ( coinductive_lset @ A @ A22 ) )
% 2.67/1.55 => ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ A1 @ A22 ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_51_lset__intros_I1_J,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: coinductive_llist @ A] : ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_52_lset__intros_I2_J,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: coinductive_llist @ A,X6: A] :
% 2.67/1.55 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.67/1.55 => ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ X6 @ Xs ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_53_lappend__inf,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ~ ( coinductive_lfinite @ A @ Xs )
% 2.67/1.55 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.67/1.55 = Xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_54_lfinite__llist__of,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A] : ( coinductive_lfinite @ A @ ( coinductive_llist_of @ A @ Xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_55_split__llist__first,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 2.67/1.55 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.67/1.55 => ? [Ys2: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 = ( coinductive_lappend @ A @ Ys2 @ ( coinductive_LCons @ A @ X @ Zs ) ) )
% 2.67/1.55 & ( coinductive_lfinite @ A @ Ys2 )
% 2.67/1.55 & ~ ( member @ A @ X @ ( coinductive_lset @ A @ Ys2 ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_56_split__llist,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 2.67/1.55 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.67/1.55 => ? [Ys2: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 = ( coinductive_lappend @ A @ Ys2 @ ( coinductive_LCons @ A @ X @ Zs ) ) )
% 2.67/1.55 & ( coinductive_lfinite @ A @ Ys2 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_57_lfinite_Oinducts,axiom,
% 2.67/1.55 ! [A: $tType,X: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.67/1.55 ( ( coinductive_lfinite @ A @ X )
% 2.67/1.55 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.67/1.55 => ( ! [Xs2: coinductive_llist @ A,X2: A] :
% 2.67/1.55 ( ( coinductive_lfinite @ A @ Xs2 )
% 2.67/1.55 => ( ( P @ Xs2 )
% 2.67/1.55 => ( P @ ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) )
% 2.67/1.55 => ( P @ X ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_58_lfinite_Osimps,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ( ( coinductive_lfinite @ A )
% 2.67/1.55 = ( ^ [A4: coinductive_llist @ A] :
% 2.67/1.55 ( ( A4
% 2.67/1.55 = ( coinductive_LNil @ A ) )
% 2.67/1.55 | ? [Xs3: coinductive_llist @ A,X3: A] :
% 2.67/1.55 ( ( A4
% 2.67/1.55 = ( coinductive_LCons @ A @ X3 @ Xs3 ) )
% 2.67/1.55 & ( coinductive_lfinite @ A @ Xs3 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_59_lfinite_Ocases,axiom,
% 2.67/1.55 ! [A: $tType,A2: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lfinite @ A @ A2 )
% 2.67/1.55 => ( ( A2
% 2.67/1.55 != ( coinductive_LNil @ A ) )
% 2.67/1.55 => ~ ! [Xs2: coinductive_llist @ A] :
% 2.67/1.55 ( ? [X2: A] :
% 2.67/1.55 ( A2
% 2.67/1.55 = ( coinductive_LCons @ A @ X2 @ Xs2 ) )
% 2.67/1.55 => ~ ( coinductive_lfinite @ A @ Xs2 ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_60_lfinite__rev__induct,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.67/1.55 ( ( coinductive_lfinite @ A @ Xs )
% 2.67/1.55 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.67/1.55 => ( ! [X2: A,Xs2: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lfinite @ A @ Xs2 )
% 2.67/1.55 => ( ( P @ Xs2 )
% 2.67/1.55 => ( P @ ( coinductive_lappend @ A @ Xs2 @ ( coinductive_LCons @ A @ X2 @ ( coinductive_LNil @ A ) ) ) ) ) )
% 2.67/1.55 => ( P @ Xs ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_61_paths__lappendD2,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Graph: A > A > $o] :
% 2.67/1.55 ( ( coinductive_lfinite @ A @ Xs )
% 2.67/1.55 => ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( koenig916195507_paths @ A @ Graph ) )
% 2.67/1.55 => ( member @ ( coinductive_llist @ A ) @ Ys @ ( koenig916195507_paths @ A @ Graph ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_62_lappend__assoc,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs2: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs2 )
% 2.67/1.55 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs2 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_63_llist__of__eq__LCons__conv,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( ( coinductive_llist_of @ A @ Xs )
% 2.67/1.55 = ( coinductive_LCons @ A @ Y @ Ys ) )
% 2.67/1.55 = ( ? [Xs7: list @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 = ( cons @ A @ Y @ Xs7 ) )
% 2.67/1.55 & ( Ys
% 2.67/1.55 = ( coinductive_llist_of @ A @ Xs7 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_64_llist__of_Osimps_I2_J,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.67/1.55 ( ( coinductive_llist_of @ A @ ( cons @ A @ X @ Xs ) )
% 2.67/1.55 = ( coinductive_LCons @ A @ X @ ( coinductive_llist_of @ A @ Xs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_65_lappend__llist__of__llist__of,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.67/1.55 ( ( coinductive_lappend @ A @ ( coinductive_llist_of @ A @ Xs ) @ ( coinductive_llist_of @ A @ Ys ) )
% 2.67/1.55 = ( coinductive_llist_of @ A @ ( append @ A @ Xs @ Ys ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_66_neq__LNil__conv,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 != ( coinductive_LNil @ A ) )
% 2.67/1.55 = ( ? [X3: A,Xs7: coinductive_llist @ A] :
% 2.67/1.55 ( Xs
% 2.67/1.55 = ( coinductive_LCons @ A @ X3 @ Xs7 ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_67_llist_Oexhaust,axiom,
% 2.67/1.55 ! [A: $tType,Y: coinductive_llist @ A] :
% 2.67/1.55 ( ( Y
% 2.67/1.55 != ( coinductive_LNil @ A ) )
% 2.67/1.55 => ~ ! [X212: A,X222: coinductive_llist @ A] :
% 2.67/1.55 ( Y
% 2.67/1.55 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_68_llist_Odistinct_I1_J,axiom,
% 2.67/1.55 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_LNil @ A )
% 2.67/1.55 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_69_lappend__eq__LNil__iff,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.67/1.55 = ( coinductive_LNil @ A ) )
% 2.67/1.55 = ( ( Xs
% 2.67/1.55 = ( coinductive_LNil @ A ) )
% 2.67/1.55 & ( Ys
% 2.67/1.55 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_70_split__list,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.67/1.55 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.67/1.55 => ? [Ys2: list @ A,Zs: list @ A] :
% 2.67/1.55 ( Xs
% 2.67/1.55 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_71_split__list__last,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.67/1.55 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.67/1.55 => ? [Ys2: list @ A,Zs: list @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 2.67/1.55 & ~ ( member @ A @ X @ ( set2 @ A @ Zs ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_72_split__list__prop,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.67/1.55 ( ? [X7: A] :
% 2.67/1.55 ( ( member @ A @ X7 @ ( set2 @ A @ Xs ) )
% 2.67/1.55 & ( P @ X7 ) )
% 2.67/1.55 => ? [Ys2: list @ A,X2: A] :
% 2.67/1.55 ( ? [Zs: list @ A] :
% 2.67/1.55 ( Xs
% 2.67/1.55 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) )
% 2.67/1.55 & ( P @ X2 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_73_split__list__first,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.67/1.55 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.67/1.55 => ? [Ys2: list @ A,Zs: list @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 2.67/1.55 & ~ ( member @ A @ X @ ( set2 @ A @ Ys2 ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_74_split__list__propE,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.67/1.55 ( ? [X7: A] :
% 2.67/1.55 ( ( member @ A @ X7 @ ( set2 @ A @ Xs ) )
% 2.67/1.55 & ( P @ X7 ) )
% 2.67/1.55 => ~ ! [Ys2: list @ A,X2: A] :
% 2.67/1.55 ( ? [Zs: list @ A] :
% 2.67/1.55 ( Xs
% 2.67/1.55 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) )
% 2.67/1.55 => ~ ( P @ X2 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_75_in__set__conv__decomp,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.67/1.55 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.67/1.55 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 2.67/1.55 ( Xs
% 2.67/1.55 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_76_split__list__last__prop,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.67/1.55 ( ? [X7: A] :
% 2.67/1.55 ( ( member @ A @ X7 @ ( set2 @ A @ Xs ) )
% 2.67/1.55 & ( P @ X7 ) )
% 2.67/1.55 => ? [Ys2: list @ A,X2: A,Zs: list @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) )
% 2.67/1.55 & ( P @ X2 )
% 2.67/1.55 & ! [Xa: A] :
% 2.67/1.55 ( ( member @ A @ Xa @ ( set2 @ A @ Zs ) )
% 2.67/1.55 => ~ ( P @ Xa ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_77_split__list__first__prop,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.67/1.55 ( ? [X7: A] :
% 2.67/1.55 ( ( member @ A @ X7 @ ( set2 @ A @ Xs ) )
% 2.67/1.55 & ( P @ X7 ) )
% 2.67/1.55 => ? [Ys2: list @ A,X2: A] :
% 2.67/1.55 ( ? [Zs: list @ A] :
% 2.67/1.55 ( Xs
% 2.67/1.55 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) )
% 2.67/1.55 & ( P @ X2 )
% 2.67/1.55 & ! [Xa: A] :
% 2.67/1.55 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 2.67/1.55 => ~ ( P @ Xa ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_78_split__list__last__propE,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.67/1.55 ( ? [X7: A] :
% 2.67/1.55 ( ( member @ A @ X7 @ ( set2 @ A @ Xs ) )
% 2.67/1.55 & ( P @ X7 ) )
% 2.67/1.55 => ~ ! [Ys2: list @ A,X2: A,Zs: list @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) )
% 2.67/1.55 => ( ( P @ X2 )
% 2.67/1.55 => ~ ! [Xa: A] :
% 2.67/1.55 ( ( member @ A @ Xa @ ( set2 @ A @ Zs ) )
% 2.67/1.55 => ~ ( P @ Xa ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_79_list_Oinject,axiom,
% 2.67/1.55 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 2.67/1.55 ( ( ( cons @ A @ X21 @ X22 )
% 2.67/1.55 = ( cons @ A @ Y21 @ Y22 ) )
% 2.67/1.55 = ( ( X21 = Y21 )
% 2.67/1.55 & ( X22 = Y22 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_80_same__append__eq,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 2.67/1.55 ( ( ( append @ A @ Xs @ Ys )
% 2.67/1.55 = ( append @ A @ Xs @ Zs2 ) )
% 2.67/1.55 = ( Ys = Zs2 ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_81_append__same__eq,axiom,
% 2.67/1.55 ! [A: $tType,Ys: list @ A,Xs: list @ A,Zs2: list @ A] :
% 2.67/1.55 ( ( ( append @ A @ Ys @ Xs )
% 2.67/1.55 = ( append @ A @ Zs2 @ Xs ) )
% 2.67/1.55 = ( Ys = Zs2 ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_82_append__assoc,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 2.67/1.55 ( ( append @ A @ ( append @ A @ Xs @ Ys ) @ Zs2 )
% 2.67/1.55 = ( append @ A @ Xs @ ( append @ A @ Ys @ Zs2 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_83_not__Cons__self2,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.67/1.55 ( ( cons @ A @ X @ Xs )
% 2.67/1.55 != Xs ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_84_append__eq__append__conv2,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A,Ts: list @ A] :
% 2.67/1.55 ( ( ( append @ A @ Xs @ Ys )
% 2.67/1.55 = ( append @ A @ Zs2 @ Ts ) )
% 2.67/1.55 = ( ? [Us: list @ A] :
% 2.67/1.55 ( ( ( Xs
% 2.67/1.55 = ( append @ A @ Zs2 @ Us ) )
% 2.67/1.55 & ( ( append @ A @ Us @ Ys )
% 2.67/1.55 = Ts ) )
% 2.67/1.55 | ( ( ( append @ A @ Xs @ Us )
% 2.67/1.55 = Zs2 )
% 2.67/1.55 & ( Ys
% 2.67/1.55 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_85_append__eq__appendI,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs2: list @ A,Ys: list @ A,Us2: list @ A] :
% 2.67/1.55 ( ( ( append @ A @ Xs @ Xs1 )
% 2.67/1.55 = Zs2 )
% 2.67/1.55 => ( ( Ys
% 2.67/1.55 = ( append @ A @ Xs1 @ Us2 ) )
% 2.67/1.55 => ( ( append @ A @ Xs @ Ys )
% 2.67/1.55 = ( append @ A @ Zs2 @ Us2 ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_86_list_Oset__cases,axiom,
% 2.67/1.55 ! [A: $tType,E: A,A2: list @ A] :
% 2.67/1.55 ( ( member @ A @ E @ ( set2 @ A @ A2 ) )
% 2.67/1.55 => ( ! [Z2: list @ A] :
% 2.67/1.55 ( A2
% 2.67/1.55 != ( cons @ A @ E @ Z2 ) )
% 2.67/1.55 => ~ ! [Z1: A,Z2: list @ A] :
% 2.67/1.55 ( ( A2
% 2.67/1.55 = ( cons @ A @ Z1 @ Z2 ) )
% 2.67/1.55 => ~ ( member @ A @ E @ ( set2 @ A @ Z2 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_87_set__ConsD,axiom,
% 2.67/1.55 ! [A: $tType,Y: A,X: A,Xs: list @ A] :
% 2.67/1.55 ( ( member @ A @ Y @ ( set2 @ A @ ( cons @ A @ X @ Xs ) ) )
% 2.67/1.55 => ( ( Y = X )
% 2.67/1.55 | ( member @ A @ Y @ ( set2 @ A @ Xs ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_88_list_Oset__intros_I1_J,axiom,
% 2.67/1.55 ! [A: $tType,A1: A,A22: list @ A] : ( member @ A @ A1 @ ( set2 @ A @ ( cons @ A @ A1 @ A22 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_89_list_Oset__intros_I2_J,axiom,
% 2.67/1.55 ! [A: $tType,X: A,A22: list @ A,A1: A] :
% 2.67/1.55 ( ( member @ A @ X @ ( set2 @ A @ A22 ) )
% 2.67/1.55 => ( member @ A @ X @ ( set2 @ A @ ( cons @ A @ A1 @ A22 ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_90_append__Cons,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 2.67/1.55 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys )
% 2.67/1.55 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_91_Cons__eq__appendI,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs1: list @ A,Ys: list @ A,Xs: list @ A,Zs2: list @ A] :
% 2.67/1.55 ( ( ( cons @ A @ X @ Xs1 )
% 2.67/1.55 = Ys )
% 2.67/1.55 => ( ( Xs
% 2.67/1.55 = ( append @ A @ Xs1 @ Zs2 ) )
% 2.67/1.55 => ( ( cons @ A @ X @ Xs )
% 2.67/1.55 = ( append @ A @ Ys @ Zs2 ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_92_split__list__first__prop__iff,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.67/1.55 ( ( ? [X3: A] :
% 2.67/1.55 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 2.67/1.55 & ( P @ X3 ) ) )
% 2.67/1.55 = ( ? [Ys3: list @ A,X3: A] :
% 2.67/1.55 ( ? [Zs3: list @ A] :
% 2.67/1.55 ( Xs
% 2.67/1.55 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.67/1.55 & ( P @ X3 )
% 2.67/1.55 & ! [Y3: A] :
% 2.67/1.55 ( ( member @ A @ Y3 @ ( set2 @ A @ Ys3 ) )
% 2.67/1.55 => ~ ( P @ Y3 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_93_split__list__last__prop__iff,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.67/1.55 ( ( ? [X3: A] :
% 2.67/1.55 ( ( member @ A @ X3 @ ( set2 @ A @ Xs ) )
% 2.67/1.55 & ( P @ X3 ) ) )
% 2.67/1.55 = ( ? [Ys3: list @ A,X3: A,Zs3: list @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs3 ) ) )
% 2.67/1.55 & ( P @ X3 )
% 2.67/1.55 & ! [Y3: A] :
% 2.67/1.55 ( ( member @ A @ Y3 @ ( set2 @ A @ Zs3 ) )
% 2.67/1.55 => ~ ( P @ Y3 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_94_in__set__conv__decomp__first,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.67/1.55 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.67/1.55 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) )
% 2.67/1.55 & ~ ( member @ A @ X @ ( set2 @ A @ Ys3 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_95_in__set__conv__decomp__last,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.67/1.55 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.67/1.55 = ( ? [Ys3: list @ A,Zs3: list @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 = ( append @ A @ Ys3 @ ( cons @ A @ X @ Zs3 ) ) )
% 2.67/1.55 & ~ ( member @ A @ X @ ( set2 @ A @ Zs3 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_96_split__list__first__propE,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,P: A > $o] :
% 2.67/1.55 ( ? [X7: A] :
% 2.67/1.55 ( ( member @ A @ X7 @ ( set2 @ A @ Xs ) )
% 2.67/1.55 & ( P @ X7 ) )
% 2.67/1.55 => ~ ! [Ys2: list @ A,X2: A] :
% 2.67/1.55 ( ? [Zs: list @ A] :
% 2.67/1.55 ( Xs
% 2.67/1.55 = ( append @ A @ Ys2 @ ( cons @ A @ X2 @ Zs ) ) )
% 2.67/1.55 => ( ( P @ X2 )
% 2.67/1.55 => ~ ! [Xa: A] :
% 2.67/1.55 ( ( member @ A @ Xa @ ( set2 @ A @ Ys2 ) )
% 2.67/1.55 => ~ ( P @ Xa ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_97_bind__simps_I2_J,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,X: B,Xs: list @ B,F: B > ( list @ A )] :
% 2.67/1.55 ( ( bind @ B @ A @ ( cons @ B @ X @ Xs ) @ F )
% 2.67/1.55 = ( append @ A @ ( F @ X ) @ ( bind @ B @ A @ Xs @ F ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_98_llast__lappend__LCons,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lfinite @ A @ Xs )
% 2.67/1.55 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) )
% 2.67/1.55 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_99_lappend__llist__of__LCons,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lappend @ A @ ( coinductive_llist_of @ A @ Xs ) @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 2.67/1.55 = ( coinductive_lappend @ A @ ( coinductive_llist_of @ A @ ( append @ A @ Xs @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) @ Ys ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_100_list__of__aux__code_I2_J,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( coindu1384447384of_aux @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 2.67/1.55 = ( coindu1384447384of_aux @ A @ ( cons @ A @ Y @ Xs ) @ Ys ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_101_llimit__induct,axiom,
% 2.67/1.55 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 2.67/1.55 ( ( P @ ( coinductive_LNil @ A ) )
% 2.67/1.55 => ( ! [X2: A,Xs2: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lfinite @ A @ Xs2 )
% 2.67/1.55 => ( ( P @ Xs2 )
% 2.67/1.55 => ( P @ ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) )
% 2.67/1.55 => ( ( ! [Ys4: coinductive_llist @ A] :
% 2.67/1.55 ( ( coindu1478340336prefix @ A @ Ys4 @ Xs )
% 2.67/1.55 => ( P @ Ys4 ) )
% 2.67/1.55 => ( P @ Xs ) )
% 2.67/1.55 => ( P @ Xs ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_102_set__list__of,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lfinite @ A @ Xs )
% 2.67/1.55 => ( ( set2 @ A @ ( coinductive_list_of @ A @ Xs ) )
% 2.67/1.55 = ( coinductive_lset @ A @ Xs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_103_append__Nil2,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A] :
% 2.67/1.55 ( ( append @ A @ Xs @ ( nil @ A ) )
% 2.67/1.55 = Xs ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_104_append__self__conv,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.67/1.55 ( ( ( append @ A @ Xs @ Ys )
% 2.67/1.55 = Xs )
% 2.67/1.55 = ( Ys
% 2.67/1.55 = ( nil @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_105_self__append__conv,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 = ( append @ A @ Xs @ Ys ) )
% 2.67/1.55 = ( Ys
% 2.67/1.55 = ( nil @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_106_append__self__conv2,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.67/1.55 ( ( ( append @ A @ Xs @ Ys )
% 2.67/1.55 = Ys )
% 2.67/1.55 = ( Xs
% 2.67/1.55 = ( nil @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_107_self__append__conv2,axiom,
% 2.67/1.55 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.67/1.55 ( ( Ys
% 2.67/1.55 = ( append @ A @ Xs @ Ys ) )
% 2.67/1.55 = ( Xs
% 2.67/1.55 = ( nil @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_108_Nil__is__append__conv,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.67/1.55 ( ( ( nil @ A )
% 2.67/1.55 = ( append @ A @ Xs @ Ys ) )
% 2.67/1.55 = ( ( Xs
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 & ( Ys
% 2.67/1.55 = ( nil @ A ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_109_append__is__Nil__conv,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.67/1.55 ( ( ( append @ A @ Xs @ Ys )
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 = ( ( Xs
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 & ( Ys
% 2.67/1.55 = ( nil @ A ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_110_llast__LCons2,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Y: A,Xs: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs ) ) )
% 2.67/1.55 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Xs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_111_list__of__llist__of,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A] :
% 2.67/1.55 ( ( coinductive_list_of @ A @ ( coinductive_llist_of @ A @ Xs ) )
% 2.67/1.55 = Xs ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_112_lstrict__prefix__code_I4_J,axiom,
% 2.67/1.55 ! [B: $tType,X: B,Xs: coinductive_llist @ B,Y: B,Ys: coinductive_llist @ B] :
% 2.67/1.55 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 2.67/1.55 = ( ( X = Y )
% 2.67/1.55 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_113_lstrict__prefix__code_I1_J,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_114_bind__simps_I1_J,axiom,
% 2.67/1.55 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 2.67/1.55 ( ( bind @ B @ A @ ( nil @ B ) @ F )
% 2.67/1.55 = ( nil @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_115_append1__eq__conv,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A,Y: A] :
% 2.67/1.55 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.67/1.55 = ( append @ A @ Ys @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.67/1.55 = ( ( Xs = Ys )
% 2.67/1.55 & ( X = Y ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_116_list__of__LNil,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ( ( coinductive_list_of @ A @ ( coinductive_LNil @ A ) )
% 2.67/1.55 = ( nil @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_117_llast__singleton,axiom,
% 2.67/1.55 ! [A: $tType,X: A] :
% 2.67/1.55 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) )
% 2.67/1.55 = X ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_118_lstrict__prefix__code_I2_J,axiom,
% 2.67/1.55 ! [B: $tType,Y: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y @ Ys ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_119_lstrict__prefix__code_I3_J,axiom,
% 2.67/1.55 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 2.67/1.55 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_120_llist__of__list__of,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lfinite @ A @ Xs )
% 2.67/1.55 => ( ( coinductive_llist_of @ A @ ( coinductive_list_of @ A @ Xs ) )
% 2.67/1.55 = Xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_121_list__of__LCons,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 2.67/1.55 ( ( coinductive_lfinite @ A @ Xs )
% 2.67/1.55 => ( ( coinductive_list_of @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.67/1.55 = ( cons @ A @ X @ ( coinductive_list_of @ A @ Xs ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_122_transpose_Ocases,axiom,
% 2.67/1.55 ! [A: $tType,X: list @ ( list @ A )] :
% 2.67/1.55 ( ( X
% 2.67/1.55 != ( nil @ ( list @ A ) ) )
% 2.67/1.55 => ( ! [Xss: list @ ( list @ A )] :
% 2.67/1.55 ( X
% 2.67/1.55 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 2.67/1.55 => ~ ! [X2: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 2.67/1.55 ( X
% 2.67/1.55 != ( cons @ ( list @ A ) @ ( cons @ A @ X2 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_123_llist__less__induct,axiom,
% 2.67/1.55 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 2.67/1.55 ( ! [Xs2: coinductive_llist @ A] :
% 2.67/1.55 ( ! [Ys4: coinductive_llist @ A] :
% 2.67/1.55 ( ( coindu1478340336prefix @ A @ Ys4 @ Xs2 )
% 2.67/1.55 => ( P @ Ys4 ) )
% 2.67/1.55 => ( P @ Xs2 ) )
% 2.67/1.55 => ( P @ Xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_124_list__of__code,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ( ( coinductive_list_of @ A )
% 2.67/1.55 = ( coindu1384447384of_aux @ A @ ( nil @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_125_list_Odistinct_I1_J,axiom,
% 2.67/1.55 ! [A: $tType,X21: A,X22: list @ A] :
% 2.67/1.55 ( ( nil @ A )
% 2.67/1.55 != ( cons @ A @ X21 @ X22 ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_126_list_OdiscI,axiom,
% 2.67/1.55 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 2.67/1.55 ( ( List
% 2.67/1.55 = ( cons @ A @ X21 @ X22 ) )
% 2.67/1.55 => ( List
% 2.67/1.55 != ( nil @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_127_list_Oexhaust,axiom,
% 2.67/1.55 ! [A: $tType,Y: list @ A] :
% 2.67/1.55 ( ( Y
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 => ~ ! [X212: A,X222: list @ A] :
% 2.67/1.55 ( Y
% 2.67/1.55 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_128_list_Oinducts,axiom,
% 2.67/1.55 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 2.67/1.55 ( ( P @ ( nil @ A ) )
% 2.67/1.55 => ( ! [X1: A,X23: list @ A] :
% 2.67/1.55 ( ( P @ X23 )
% 2.67/1.55 => ( P @ ( cons @ A @ X1 @ X23 ) ) )
% 2.67/1.55 => ( P @ List ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_129_neq__Nil__conv,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 = ( ? [Y3: A,Ys3: list @ A] :
% 2.67/1.55 ( Xs
% 2.67/1.55 = ( cons @ A @ Y3 @ Ys3 ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_130_list__induct2_H,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys: list @ B] :
% 2.67/1.55 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.67/1.55 => ( ! [X2: A,Xs2: list @ A] : ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( nil @ B ) )
% 2.67/1.55 => ( ! [Y2: B,Ys2: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y2 @ Ys2 ) )
% 2.67/1.55 => ( ! [X2: A,Xs2: list @ A,Y2: B,Ys2: list @ B] :
% 2.67/1.55 ( ( P @ Xs2 @ Ys2 )
% 2.67/1.55 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ B @ Y2 @ Ys2 ) ) )
% 2.67/1.55 => ( P @ Xs @ Ys ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_131_splice_Oinduct,axiom,
% 2.67/1.55 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.67/1.55 ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 2.67/1.55 => ( ! [V: A,Va: list @ A] : ( P @ ( cons @ A @ V @ Va ) @ ( nil @ A ) )
% 2.67/1.55 => ( ! [X2: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 2.67/1.55 ( ( P @ Xs2 @ Ys2 )
% 2.67/1.55 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 2.67/1.55 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_132_remdups__adj_Ocases,axiom,
% 2.67/1.55 ! [A: $tType,X: list @ A] :
% 2.67/1.55 ( ( X
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 => ( ! [X2: A] :
% 2.67/1.55 ( X
% 2.67/1.55 != ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.67/1.55 => ~ ! [X2: A,Y2: A,Xs2: list @ A] :
% 2.67/1.55 ( X
% 2.67/1.55 != ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_133_remdups__adj_Oinduct,axiom,
% 2.67/1.55 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 2.67/1.55 ( ( P @ ( nil @ A ) )
% 2.67/1.55 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.67/1.55 => ( ! [X2: A,Y2: A,Xs2: list @ A] :
% 2.67/1.55 ( ( ( X2 = Y2 )
% 2.67/1.55 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) )
% 2.67/1.55 => ( ( ( X2 != Y2 )
% 2.67/1.55 => ( P @ ( cons @ A @ Y2 @ Xs2 ) ) )
% 2.67/1.55 => ( P @ ( cons @ A @ X2 @ ( cons @ A @ Y2 @ Xs2 ) ) ) ) )
% 2.67/1.55 => ( P @ A0 ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_134_list__nonempty__induct,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.67/1.55 => ( ! [X2: A,Xs2: list @ A] :
% 2.67/1.55 ( ( Xs2
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 => ( ( P @ Xs2 )
% 2.67/1.55 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) ) )
% 2.67/1.55 => ( P @ Xs ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_135_map__tailrec__rev_Oinduct,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 2.67/1.55 ( ! [F2: A > B,X1: list @ B] : ( P @ F2 @ ( nil @ A ) @ X1 )
% 2.67/1.55 => ( ! [F2: A > B,A5: A,As: list @ A,Bs: list @ B] :
% 2.67/1.55 ( ( P @ F2 @ As @ ( cons @ B @ ( F2 @ A5 ) @ Bs ) )
% 2.67/1.55 => ( P @ F2 @ ( cons @ A @ A5 @ As ) @ Bs ) )
% 2.67/1.55 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_136_eq__Nil__appendI,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.67/1.55 ( ( Xs = Ys )
% 2.67/1.55 => ( Xs
% 2.67/1.55 = ( append @ A @ ( nil @ A ) @ Ys ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_137_append__Nil,axiom,
% 2.67/1.55 ! [A: $tType,Ys: list @ A] :
% 2.67/1.55 ( ( append @ A @ ( nil @ A ) @ Ys )
% 2.67/1.55 = Ys ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_138_lstrict__prefix__lfinite1,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( coindu1478340336prefix @ A @ Xs @ Ys )
% 2.67/1.55 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_139_rev__induct,axiom,
% 2.67/1.55 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.67/1.55 ( ( P @ ( nil @ A ) )
% 2.67/1.55 => ( ! [X2: A,Xs2: list @ A] :
% 2.67/1.55 ( ( P @ Xs2 )
% 2.67/1.55 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) )
% 2.67/1.55 => ( P @ Xs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_140_rev__exhaust,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 => ~ ! [Ys2: list @ A,Y2: A] :
% 2.67/1.55 ( Xs
% 2.67/1.55 != ( append @ A @ Ys2 @ ( cons @ A @ Y2 @ ( nil @ A ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_141_Cons__eq__append__conv,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 2.67/1.55 ( ( ( cons @ A @ X @ Xs )
% 2.67/1.55 = ( append @ A @ Ys @ Zs2 ) )
% 2.67/1.55 = ( ( ( Ys
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 & ( ( cons @ A @ X @ Xs )
% 2.67/1.55 = Zs2 ) )
% 2.67/1.55 | ? [Ys5: list @ A] :
% 2.67/1.55 ( ( ( cons @ A @ X @ Ys5 )
% 2.67/1.55 = Ys )
% 2.67/1.55 & ( Xs
% 2.67/1.55 = ( append @ A @ Ys5 @ Zs2 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_142_append__eq__Cons__conv,axiom,
% 2.67/1.55 ! [A: $tType,Ys: list @ A,Zs2: list @ A,X: A,Xs: list @ A] :
% 2.67/1.55 ( ( ( append @ A @ Ys @ Zs2 )
% 2.67/1.55 = ( cons @ A @ X @ Xs ) )
% 2.67/1.55 = ( ( ( Ys
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 & ( Zs2
% 2.67/1.55 = ( cons @ A @ X @ Xs ) ) )
% 2.67/1.55 | ? [Ys5: list @ A] :
% 2.67/1.55 ( ( Ys
% 2.67/1.55 = ( cons @ A @ X @ Ys5 ) )
% 2.67/1.55 & ( ( append @ A @ Ys5 @ Zs2 )
% 2.67/1.55 = Xs ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_143_rev__nonempty__induct,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 => ( ! [X2: A] : ( P @ ( cons @ A @ X2 @ ( nil @ A ) ) )
% 2.67/1.55 => ( ! [X2: A,Xs2: list @ A] :
% 2.67/1.55 ( ( Xs2
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 => ( ( P @ Xs2 )
% 2.67/1.55 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X2 @ ( nil @ A ) ) ) ) ) )
% 2.67/1.55 => ( P @ Xs ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_144_llist__of__eq__LNil__conv,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A] :
% 2.67/1.55 ( ( ( coinductive_llist_of @ A @ Xs )
% 2.67/1.55 = ( coinductive_LNil @ A ) )
% 2.67/1.55 = ( Xs
% 2.67/1.55 = ( nil @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_145_llist__of_Osimps_I1_J,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ( ( coinductive_llist_of @ A @ ( nil @ A ) )
% 2.67/1.55 = ( coinductive_LNil @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_146_list__bind__cong,axiom,
% 2.67/1.55 ! [B: $tType,A: $tType,Xs: list @ A,Ys: list @ A,F: A > ( list @ B ),G: A > ( list @ B )] :
% 2.67/1.55 ( ( Xs = Ys )
% 2.67/1.55 => ( ! [X2: A] :
% 2.67/1.55 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.67/1.55 => ( ( F @ X2 )
% 2.67/1.55 = ( G @ X2 ) ) )
% 2.67/1.55 => ( ( bind @ A @ B @ Xs @ F )
% 2.67/1.55 = ( bind @ A @ B @ Ys @ G ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_147_list__of__lappend,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lfinite @ A @ Xs )
% 2.67/1.55 => ( ( coinductive_lfinite @ A @ Ys )
% 2.67/1.55 => ( ( coinductive_list_of @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.67/1.55 = ( append @ A @ ( coinductive_list_of @ A @ Xs ) @ ( coinductive_list_of @ A @ Ys ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_148_Koenigslemma__Mirabelle__aepjeeakgn_Oconnected__def,axiom,
% 2.67/1.55 ! [Node: $tType] :
% 2.67/1.55 ( ( koenig793108494nected @ Node )
% 2.67/1.55 = ( ^ [Graph2: Node > Node > $o] :
% 2.67/1.55 ! [N: Node,N2: Node] :
% 2.67/1.55 ? [Xs3: list @ Node] : ( member @ ( coinductive_llist @ Node ) @ ( coinductive_llist_of @ Node @ ( cons @ Node @ N @ ( append @ Node @ Xs3 @ ( cons @ Node @ N2 @ ( nil @ Node ) ) ) ) ) @ ( koenig916195507_paths @ Node @ Graph2 ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_149_Koenigslemma__Mirabelle__aepjeeakgn_OconnectedD,axiom,
% 2.67/1.55 ! [A: $tType,Graph: A > A > $o,N3: A,N4: A] :
% 2.67/1.55 ( ( koenig793108494nected @ A @ Graph )
% 2.67/1.55 => ? [Xs2: list @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_llist_of @ A @ ( cons @ A @ N3 @ ( append @ A @ Xs2 @ ( cons @ A @ N4 @ ( nil @ A ) ) ) ) ) @ ( koenig916195507_paths @ A @ Graph ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_150_the__elem__set,axiom,
% 2.67/1.55 ! [A: $tType,X: A] :
% 2.67/1.55 ( ( the_elem @ A @ ( set2 @ A @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.67/1.55 = X ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_151_longest__common__prefix_Oinduct,axiom,
% 2.67/1.55 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.67/1.55 ( ! [X2: A,Xs2: list @ A,Y2: A,Ys2: list @ A] :
% 2.67/1.55 ( ( ( X2 = Y2 )
% 2.67/1.55 => ( P @ Xs2 @ Ys2 ) )
% 2.67/1.55 => ( P @ ( cons @ A @ X2 @ Xs2 ) @ ( cons @ A @ Y2 @ Ys2 ) ) )
% 2.67/1.55 => ( ! [X1: list @ A] : ( P @ ( nil @ A ) @ X1 )
% 2.67/1.55 => ( ! [Uu: list @ A] : ( P @ Uu @ ( nil @ A ) )
% 2.67/1.55 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_152_prefixes_Oinduct,axiom,
% 2.67/1.55 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 2.67/1.55 ( ( P @ ( nil @ A ) )
% 2.67/1.55 => ( ! [X2: A,Xs2: list @ A] :
% 2.67/1.55 ( ( P @ Xs2 )
% 2.67/1.55 => ( P @ ( cons @ A @ X2 @ Xs2 ) ) )
% 2.67/1.55 => ( P @ A0 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_153_prefixes_Ocases,axiom,
% 2.67/1.55 ! [A: $tType,X: list @ A] :
% 2.67/1.55 ( ( X
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 => ~ ! [X2: A,Xs2: list @ A] :
% 2.67/1.55 ( X
% 2.67/1.55 != ( cons @ A @ X2 @ Xs2 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_154_prefixes__snoc,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,X: A] :
% 2.67/1.55 ( ( prefixes @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.67/1.55 = ( append @ ( list @ A ) @ ( prefixes @ A @ Xs ) @ ( cons @ ( list @ A ) @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) @ ( nil @ ( list @ A ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_155_prefixes__eq__Snoc,axiom,
% 2.67/1.55 ! [A: $tType,Ys: list @ A,Xs: list @ ( list @ A ),X: list @ A] :
% 2.67/1.55 ( ( ( prefixes @ A @ Ys )
% 2.67/1.55 = ( append @ ( list @ A ) @ Xs @ ( cons @ ( list @ A ) @ X @ ( nil @ ( list @ A ) ) ) ) )
% 2.67/1.55 = ( ( ( ( Ys
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 & ( Xs
% 2.67/1.55 = ( nil @ ( list @ A ) ) ) )
% 2.67/1.55 | ? [Z: A,Zs3: list @ A] :
% 2.67/1.55 ( ( Ys
% 2.67/1.55 = ( append @ A @ Zs3 @ ( cons @ A @ Z @ ( nil @ A ) ) ) )
% 2.67/1.55 & ( Xs
% 2.67/1.55 = ( prefixes @ A @ Zs3 ) ) ) )
% 2.67/1.55 & ( X = Ys ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_156_sublists_Osimps_I1_J,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ( ( sublists @ A @ ( nil @ A ) )
% 2.67/1.55 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_157_prefixes_Osimps_I1_J,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ( ( prefixes @ A @ ( nil @ A ) )
% 2.67/1.55 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_158_product__lists_Osimps_I1_J,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 2.67/1.55 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_159_prefixes_Oelims,axiom,
% 2.67/1.55 ! [A: $tType,X: list @ A,Y: list @ ( list @ A )] :
% 2.67/1.55 ( ( ( prefixes @ A @ X )
% 2.67/1.55 = Y )
% 2.67/1.55 => ( ( ( X
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 => ( Y
% 2.67/1.55 != ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) )
% 2.67/1.55 => ~ ! [X2: A,Xs2: list @ A] :
% 2.67/1.55 ( ( X
% 2.67/1.55 = ( cons @ A @ X2 @ Xs2 ) )
% 2.67/1.55 => ( Y
% 2.67/1.55 != ( cons @ ( list @ A ) @ ( nil @ A ) @ ( map @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 ) @ ( prefixes @ A @ Xs2 ) ) ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_160_maps__simps_I1_J,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,F: B > ( list @ A ),X: B,Xs: list @ B] :
% 2.67/1.55 ( ( maps @ B @ A @ F @ ( cons @ B @ X @ Xs ) )
% 2.67/1.55 = ( append @ A @ ( F @ X ) @ ( maps @ B @ A @ F @ Xs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_161_list_Omap__disc__iff,axiom,
% 2.67/1.55 ! [B: $tType,A: $tType,F: A > B,A2: list @ A] :
% 2.67/1.55 ( ( ( map @ A @ B @ F @ A2 )
% 2.67/1.55 = ( nil @ B ) )
% 2.67/1.55 = ( A2
% 2.67/1.55 = ( nil @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_162_map__is__Nil__conv,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 2.67/1.55 ( ( ( map @ B @ A @ F @ Xs )
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 = ( Xs
% 2.67/1.55 = ( nil @ B ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_163_Nil__is__map__conv,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 2.67/1.55 ( ( ( nil @ A )
% 2.67/1.55 = ( map @ B @ A @ F @ Xs ) )
% 2.67/1.55 = ( Xs
% 2.67/1.55 = ( nil @ B ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_164_map__eq__conv,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B,G: B > A] :
% 2.67/1.55 ( ( ( map @ B @ A @ F @ Xs )
% 2.67/1.55 = ( map @ B @ A @ G @ Xs ) )
% 2.67/1.55 = ( ! [X3: B] :
% 2.67/1.55 ( ( member @ B @ X3 @ ( set2 @ B @ Xs ) )
% 2.67/1.55 => ( ( F @ X3 )
% 2.67/1.55 = ( G @ X3 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_165_map__append,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B,Ys: list @ B] :
% 2.67/1.55 ( ( map @ B @ A @ F @ ( append @ B @ Xs @ Ys ) )
% 2.67/1.55 = ( append @ A @ ( map @ B @ A @ F @ Xs ) @ ( map @ B @ A @ F @ Ys ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_166_list_Oinj__map__strong,axiom,
% 2.67/1.55 ! [B: $tType,A: $tType,X: list @ A,Xa2: list @ A,F: A > B,Fa: A > B] :
% 2.67/1.55 ( ! [Z3: A,Za: A] :
% 2.67/1.55 ( ( member @ A @ Z3 @ ( set2 @ A @ X ) )
% 2.67/1.55 => ( ( member @ A @ Za @ ( set2 @ A @ Xa2 ) )
% 2.67/1.55 => ( ( ( F @ Z3 )
% 2.67/1.55 = ( Fa @ Za ) )
% 2.67/1.55 => ( Z3 = Za ) ) ) )
% 2.67/1.55 => ( ( ( map @ A @ B @ F @ X )
% 2.67/1.55 = ( map @ A @ B @ Fa @ Xa2 ) )
% 2.67/1.55 => ( X = Xa2 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_167_list_Omap__cong0,axiom,
% 2.67/1.55 ! [B: $tType,A: $tType,X: list @ A,F: A > B,G: A > B] :
% 2.67/1.55 ( ! [Z3: A] :
% 2.67/1.55 ( ( member @ A @ Z3 @ ( set2 @ A @ X ) )
% 2.67/1.55 => ( ( F @ Z3 )
% 2.67/1.55 = ( G @ Z3 ) ) )
% 2.67/1.55 => ( ( map @ A @ B @ F @ X )
% 2.67/1.55 = ( map @ A @ B @ G @ X ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_168_list_Omap__cong,axiom,
% 2.67/1.55 ! [B: $tType,A: $tType,X: list @ A,Ya: list @ A,F: A > B,G: A > B] :
% 2.67/1.55 ( ( X = Ya )
% 2.67/1.55 => ( ! [Z3: A] :
% 2.67/1.55 ( ( member @ A @ Z3 @ ( set2 @ A @ Ya ) )
% 2.67/1.55 => ( ( F @ Z3 )
% 2.67/1.55 = ( G @ Z3 ) ) )
% 2.67/1.55 => ( ( map @ A @ B @ F @ X )
% 2.67/1.55 = ( map @ A @ B @ G @ Ya ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_169_ex__map__conv,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,Ys: list @ B,F: A > B] :
% 2.67/1.55 ( ( ? [Xs3: list @ A] :
% 2.67/1.55 ( Ys
% 2.67/1.55 = ( map @ A @ B @ F @ Xs3 ) ) )
% 2.67/1.55 = ( ! [X3: B] :
% 2.67/1.55 ( ( member @ B @ X3 @ ( set2 @ B @ Ys ) )
% 2.67/1.55 => ? [Y3: A] :
% 2.67/1.55 ( X3
% 2.67/1.55 = ( F @ Y3 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_170_map__cong,axiom,
% 2.67/1.55 ! [B: $tType,A: $tType,Xs: list @ A,Ys: list @ A,F: A > B,G: A > B] :
% 2.67/1.55 ( ( Xs = Ys )
% 2.67/1.55 => ( ! [X2: A] :
% 2.67/1.55 ( ( member @ A @ X2 @ ( set2 @ A @ Ys ) )
% 2.67/1.55 => ( ( F @ X2 )
% 2.67/1.55 = ( G @ X2 ) ) )
% 2.67/1.55 => ( ( map @ A @ B @ F @ Xs )
% 2.67/1.55 = ( map @ A @ B @ G @ Ys ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_171_map__idI,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,F: A > A] :
% 2.67/1.55 ( ! [X2: A] :
% 2.67/1.55 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.67/1.55 => ( ( F @ X2 )
% 2.67/1.55 = X2 ) )
% 2.67/1.55 => ( ( map @ A @ A @ F @ Xs )
% 2.67/1.55 = Xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_172_map__ext,axiom,
% 2.67/1.55 ! [B: $tType,A: $tType,Xs: list @ A,F: A > B,G: A > B] :
% 2.67/1.55 ( ! [X2: A] :
% 2.67/1.55 ( ( member @ A @ X2 @ ( set2 @ A @ Xs ) )
% 2.67/1.55 => ( ( F @ X2 )
% 2.67/1.55 = ( G @ X2 ) ) )
% 2.67/1.55 => ( ( map @ A @ B @ F @ Xs )
% 2.67/1.55 = ( map @ A @ B @ G @ Xs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_173_list_Osimps_I9_J,axiom,
% 2.67/1.55 ! [B: $tType,A: $tType,F: A > B,X21: A,X22: list @ A] :
% 2.67/1.55 ( ( map @ A @ B @ F @ ( cons @ A @ X21 @ X22 ) )
% 2.67/1.55 = ( cons @ B @ ( F @ X21 ) @ ( map @ A @ B @ F @ X22 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_174_Cons__eq__map__D,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,X: A,Xs: list @ A,F: B > A,Ys: list @ B] :
% 2.67/1.55 ( ( ( cons @ A @ X @ Xs )
% 2.67/1.55 = ( map @ B @ A @ F @ Ys ) )
% 2.67/1.55 => ? [Z3: B,Zs: list @ B] :
% 2.67/1.55 ( ( Ys
% 2.67/1.55 = ( cons @ B @ Z3 @ Zs ) )
% 2.67/1.55 & ( X
% 2.67/1.55 = ( F @ Z3 ) )
% 2.67/1.55 & ( Xs
% 2.67/1.55 = ( map @ B @ A @ F @ Zs ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_175_map__eq__Cons__D,axiom,
% 2.67/1.55 ! [B: $tType,A: $tType,F: B > A,Xs: list @ B,Y: A,Ys: list @ A] :
% 2.67/1.55 ( ( ( map @ B @ A @ F @ Xs )
% 2.67/1.55 = ( cons @ A @ Y @ Ys ) )
% 2.67/1.55 => ? [Z3: B,Zs: list @ B] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 = ( cons @ B @ Z3 @ Zs ) )
% 2.67/1.55 & ( ( F @ Z3 )
% 2.67/1.55 = Y )
% 2.67/1.55 & ( ( map @ B @ A @ F @ Zs )
% 2.67/1.55 = Ys ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_176_Cons__eq__map__conv,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,X: A,Xs: list @ A,F: B > A,Ys: list @ B] :
% 2.67/1.55 ( ( ( cons @ A @ X @ Xs )
% 2.67/1.55 = ( map @ B @ A @ F @ Ys ) )
% 2.67/1.55 = ( ? [Z: B,Zs3: list @ B] :
% 2.67/1.55 ( ( Ys
% 2.67/1.55 = ( cons @ B @ Z @ Zs3 ) )
% 2.67/1.55 & ( X
% 2.67/1.55 = ( F @ Z ) )
% 2.67/1.55 & ( Xs
% 2.67/1.55 = ( map @ B @ A @ F @ Zs3 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_177_map__eq__Cons__conv,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B,Y: A,Ys: list @ A] :
% 2.67/1.55 ( ( ( map @ B @ A @ F @ Xs )
% 2.67/1.55 = ( cons @ A @ Y @ Ys ) )
% 2.67/1.55 = ( ? [Z: B,Zs3: list @ B] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 = ( cons @ B @ Z @ Zs3 ) )
% 2.67/1.55 & ( ( F @ Z )
% 2.67/1.55 = Y )
% 2.67/1.55 & ( ( map @ B @ A @ F @ Zs3 )
% 2.67/1.55 = Ys ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_178_list_Osimps_I8_J,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,F: A > B] :
% 2.67/1.55 ( ( map @ A @ B @ F @ ( nil @ A ) )
% 2.67/1.55 = ( nil @ B ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_179_maps__simps_I2_J,axiom,
% 2.67/1.55 ! [B: $tType,A: $tType,F: B > ( list @ A )] :
% 2.67/1.55 ( ( maps @ B @ A @ F @ ( nil @ B ) )
% 2.67/1.55 = ( nil @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_180_prefixes_Osimps_I2_J,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.67/1.55 ( ( prefixes @ A @ ( cons @ A @ X @ Xs ) )
% 2.67/1.55 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( map @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X ) @ ( prefixes @ A @ Xs ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_181_prefixes_Opelims,axiom,
% 2.67/1.55 ! [A: $tType,X: list @ A,Y: list @ ( list @ A )] :
% 2.67/1.55 ( ( ( prefixes @ A @ X )
% 2.67/1.55 = Y )
% 2.67/1.55 => ( ( accp @ ( list @ A ) @ ( prefixes_rel @ A ) @ X )
% 2.67/1.55 => ( ( ( X
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 => ( ( Y
% 2.67/1.55 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) )
% 2.67/1.55 => ~ ( accp @ ( list @ A ) @ ( prefixes_rel @ A ) @ ( nil @ A ) ) ) )
% 2.67/1.55 => ~ ! [X2: A,Xs2: list @ A] :
% 2.67/1.55 ( ( X
% 2.67/1.55 = ( cons @ A @ X2 @ Xs2 ) )
% 2.67/1.55 => ( ( Y
% 2.67/1.55 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( map @ ( list @ A ) @ ( list @ A ) @ ( cons @ A @ X2 ) @ ( prefixes @ A @ Xs2 ) ) ) )
% 2.67/1.55 => ~ ( accp @ ( list @ A ) @ ( prefixes_rel @ A ) @ ( cons @ A @ X2 @ Xs2 ) ) ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_182_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 2.67/1.55 = ( ( Xs
% 2.67/1.55 = ( coinductive_LNil @ A ) )
% 2.67/1.55 | ? [Xs7: coinductive_llist @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 = ( coinductive_LCons @ A @ Y @ Xs7 ) )
% 2.67/1.55 & ( coindu328551480prefix @ A @ Xs7 @ Ys ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_183_not__in__set__insert,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.67/1.55 ( ~ ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.67/1.55 => ( ( insert @ A @ X @ Xs )
% 2.67/1.55 = ( cons @ A @ X @ Xs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_184_in__set__insert,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.67/1.55 ( ( member @ A @ X @ ( set2 @ A @ Xs ) )
% 2.67/1.55 => ( ( insert @ A @ X @ Xs )
% 2.67/1.55 = Xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_185_insert__Nil,axiom,
% 2.67/1.55 ! [A: $tType,X: A] :
% 2.67/1.55 ( ( insert @ A @ X @ ( nil @ A ) )
% 2.67/1.55 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_186_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.67/1.55 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.67/1.55 = ( Xs
% 2.67/1.55 = ( coinductive_LNil @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_187_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_188_List_Oinsert__def,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ( ( insert @ A )
% 2.67/1.55 = ( ^ [X3: A,Xs3: list @ A] : ( if @ ( list @ A ) @ ( member @ A @ X3 @ ( set2 @ A @ Xs3 ) ) @ Xs3 @ ( cons @ A @ X3 @ Xs3 ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_189_rotate1_Osimps_I2_J,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.67/1.55 ( ( rotate1 @ A @ ( cons @ A @ X @ Xs ) )
% 2.67/1.55 = ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_190_map__eq__map__tailrec,axiom,
% 2.67/1.55 ! [B: $tType,A: $tType] :
% 2.67/1.55 ( ( map @ A @ B )
% 2.67/1.55 = ( map_tailrec @ A @ B ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_191_last__snoc,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,X: A] :
% 2.67/1.55 ( ( last @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.67/1.55 = X ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_192_rotate1__is__Nil__conv,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A] :
% 2.67/1.55 ( ( ( rotate1 @ A @ Xs )
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 = ( Xs
% 2.67/1.55 = ( nil @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_193_set__rotate1,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A] :
% 2.67/1.55 ( ( set2 @ A @ ( rotate1 @ A @ Xs ) )
% 2.67/1.55 = ( set2 @ A @ Xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_194_last__appendR,axiom,
% 2.67/1.55 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.67/1.55 ( ( Ys
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 2.67/1.55 = ( last @ A @ Ys ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_195_last__appendL,axiom,
% 2.67/1.55 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.67/1.55 ( ( Ys
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 2.67/1.55 = ( last @ A @ Xs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_196_llast__llist__of,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A] :
% 2.67/1.55 ( ( coinductive_llast @ A @ ( coinductive_llist_of @ A @ Xs ) )
% 2.67/1.55 = ( last @ A @ Xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_197_rotate1_Osimps_I1_J,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ( ( rotate1 @ A @ ( nil @ A ) )
% 2.67/1.55 = ( nil @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_198_last__ConsR,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,X: A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 2.67/1.55 = ( last @ A @ Xs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_199_last__ConsL,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,X: A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 2.67/1.55 = X ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_200_last_Osimps,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,X: A] :
% 2.67/1.55 ( ( ( Xs
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 2.67/1.55 = X ) )
% 2.67/1.55 & ( ( Xs
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 2.67/1.55 = ( last @ A @ Xs ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_201_last__in__set,axiom,
% 2.67/1.55 ! [A: $tType,As2: list @ A] :
% 2.67/1.55 ( ( As2
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 => ( member @ A @ ( last @ A @ As2 ) @ ( set2 @ A @ As2 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_202_last__map,axiom,
% 2.67/1.55 ! [B: $tType,A: $tType,Xs: list @ A,F: A > B] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 => ( ( last @ B @ ( map @ A @ B @ F @ Xs ) )
% 2.67/1.55 = ( F @ ( last @ A @ Xs ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_203_longest__common__suffix,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.67/1.55 ? [Ss: list @ A,Xs5: list @ A,Ys6: list @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 = ( append @ A @ Xs5 @ Ss ) )
% 2.67/1.55 & ( Ys
% 2.67/1.55 = ( append @ A @ Ys6 @ Ss ) )
% 2.67/1.55 & ( ( Xs5
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 | ( Ys6
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 | ( ( last @ A @ Xs5 )
% 2.67/1.55 != ( last @ A @ Ys6 ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_204_last__append,axiom,
% 2.67/1.55 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.67/1.55 ( ( ( Ys
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 2.67/1.55 = ( last @ A @ Xs ) ) )
% 2.67/1.55 & ( ( Ys
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 => ( ( last @ A @ ( append @ A @ Xs @ Ys ) )
% 2.67/1.55 = ( last @ A @ Ys ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_205_append__butlast__last__id,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A] :
% 2.67/1.55 ( ( Xs
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 => ( ( append @ A @ ( butlast @ A @ Xs ) @ ( cons @ A @ ( last @ A @ Xs ) @ ( nil @ A ) ) )
% 2.67/1.55 = Xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_206_snoc__eq__iff__butlast,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,X: A,Ys: list @ A] :
% 2.67/1.55 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.67/1.55 = Ys )
% 2.67/1.55 = ( ( Ys
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 & ( ( butlast @ A @ Ys )
% 2.67/1.55 = Xs )
% 2.67/1.55 & ( ( last @ A @ Ys )
% 2.67/1.55 = X ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_207_butlast__snoc,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,X: A] :
% 2.67/1.55 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.67/1.55 = Xs ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_208_butlast_Osimps_I1_J,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ( ( butlast @ A @ ( nil @ A ) )
% 2.67/1.55 = ( nil @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_209_in__set__butlastD,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.67/1.55 ( ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 2.67/1.55 => ( member @ A @ X @ ( set2 @ A @ Xs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_210_map__butlast,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 2.67/1.55 ( ( map @ B @ A @ F @ ( butlast @ B @ Xs ) )
% 2.67/1.55 = ( butlast @ A @ ( map @ B @ A @ F @ Xs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_211_butlast_Osimps_I2_J,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,X: A] :
% 2.67/1.55 ( ( ( Xs
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 2.67/1.55 = ( nil @ A ) ) )
% 2.67/1.55 & ( ( Xs
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 2.67/1.55 = ( cons @ A @ X @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_212_butlast__append,axiom,
% 2.67/1.55 ! [A: $tType,Ys: list @ A,Xs: list @ A] :
% 2.67/1.55 ( ( ( Ys
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 2.67/1.55 = ( butlast @ A @ Xs ) ) )
% 2.67/1.55 & ( ( Ys
% 2.67/1.55 != ( nil @ A ) )
% 2.67/1.55 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys ) )
% 2.67/1.55 = ( append @ A @ Xs @ ( butlast @ A @ Ys ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_213_in__set__butlast__appendI,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A,Ys: list @ A] :
% 2.67/1.55 ( ( ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Xs ) ) )
% 2.67/1.55 | ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ Ys ) ) ) )
% 2.67/1.55 => ( member @ A @ X @ ( set2 @ A @ ( butlast @ A @ ( append @ A @ Xs @ Ys ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_214_list__ex1__simps_I1_J,axiom,
% 2.67/1.55 ! [A: $tType,P: A > $o] :
% 2.67/1.55 ~ ( list_ex1 @ A @ P @ ( nil @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_215_list__of__LCons__conv,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 2.67/1.55 ( ( ( coinductive_lfinite @ A @ Xs )
% 2.67/1.55 => ( ( coinductive_list_of @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.67/1.55 = ( cons @ A @ X @ ( coinductive_list_of @ A @ Xs ) ) ) )
% 2.67/1.55 & ( ~ ( coinductive_lfinite @ A @ Xs )
% 2.67/1.55 => ( ( coinductive_list_of @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.67/1.55 = ( undefined @ ( list @ A ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_216_llast__LNil,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ( ( coinductive_llast @ A @ ( coinductive_LNil @ A ) )
% 2.67/1.55 = ( undefined @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_217_llast__linfinite,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.67/1.55 ( ~ ( coinductive_lfinite @ A @ Xs )
% 2.67/1.55 => ( ( coinductive_llast @ A @ Xs )
% 2.67/1.55 = ( undefined @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_218_list__ex1__iff,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ( ( list_ex1 @ A )
% 2.67/1.55 = ( ^ [P2: A > $o,Xs3: list @ A] :
% 2.67/1.55 ? [X3: A] :
% 2.67/1.55 ( ( member @ A @ X3 @ ( set2 @ A @ Xs3 ) )
% 2.67/1.55 & ( P2 @ X3 )
% 2.67/1.55 & ! [Y3: A] :
% 2.67/1.55 ( ( ( member @ A @ Y3 @ ( set2 @ A @ Xs3 ) )
% 2.67/1.55 & ( P2 @ Y3 ) )
% 2.67/1.55 => ( Y3 = X3 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_219_can__select__set__list__ex1,axiom,
% 2.67/1.55 ! [A: $tType,P: A > $o,A3: list @ A] :
% 2.67/1.55 ( ( can_select @ A @ P @ ( set2 @ A @ A3 ) )
% 2.67/1.55 = ( list_ex1 @ A @ P @ A3 ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_220_list__of__aux__def,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ( ( coindu1384447384of_aux @ A )
% 2.67/1.55 = ( ^ [Xs3: list @ A,Ys3: coinductive_llist @ A] : ( if @ ( list @ A ) @ ( coinductive_lfinite @ A @ Ys3 ) @ ( append @ A @ ( rev @ A @ Xs3 ) @ ( coinductive_list_of @ A @ Ys3 ) ) @ ( undefined @ ( list @ A ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_221_rev__is__rev__conv,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.67/1.55 ( ( ( rev @ A @ Xs )
% 2.67/1.55 = ( rev @ A @ Ys ) )
% 2.67/1.55 = ( Xs = Ys ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_222_rev__rev__ident,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A] :
% 2.67/1.55 ( ( rev @ A @ ( rev @ A @ Xs ) )
% 2.67/1.55 = Xs ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_223_Nil__is__rev__conv,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A] :
% 2.67/1.55 ( ( ( nil @ A )
% 2.67/1.55 = ( rev @ A @ Xs ) )
% 2.67/1.55 = ( Xs
% 2.67/1.55 = ( nil @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_224_rev__is__Nil__conv,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A] :
% 2.67/1.55 ( ( ( rev @ A @ Xs )
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 = ( Xs
% 2.67/1.55 = ( nil @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_225_set__rev,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A] :
% 2.67/1.55 ( ( set2 @ A @ ( rev @ A @ Xs ) )
% 2.67/1.55 = ( set2 @ A @ Xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_226_rev__append,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.67/1.55 ( ( rev @ A @ ( append @ A @ Xs @ Ys ) )
% 2.67/1.55 = ( append @ A @ ( rev @ A @ Ys ) @ ( rev @ A @ Xs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_227_singleton__rev__conv,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.67/1.55 ( ( ( cons @ A @ X @ ( nil @ A ) )
% 2.67/1.55 = ( rev @ A @ Xs ) )
% 2.67/1.55 = ( Xs
% 2.67/1.55 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_228_rev__singleton__conv,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,X: A] :
% 2.67/1.55 ( ( ( rev @ A @ Xs )
% 2.67/1.55 = ( cons @ A @ X @ ( nil @ A ) ) )
% 2.67/1.55 = ( Xs
% 2.67/1.55 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_229_rev__eq__Cons__iff,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Y: A,Ys: list @ A] :
% 2.67/1.55 ( ( ( rev @ A @ Xs )
% 2.67/1.55 = ( cons @ A @ Y @ Ys ) )
% 2.67/1.55 = ( Xs
% 2.67/1.55 = ( append @ A @ ( rev @ A @ Ys ) @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_230_list__of__aux__code_I1_J,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A] :
% 2.67/1.55 ( ( coindu1384447384of_aux @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.67/1.55 = ( rev @ A @ Xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_231_rev_Osimps_I1_J,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ( ( rev @ A @ ( nil @ A ) )
% 2.67/1.55 = ( nil @ A ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_232_rev__swap,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 2.67/1.55 ( ( ( rev @ A @ Xs )
% 2.67/1.55 = Ys )
% 2.67/1.55 = ( Xs
% 2.67/1.55 = ( rev @ A @ Ys ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_233_can__select__def,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ( ( can_select @ A )
% 2.67/1.55 = ( ^ [P2: A > $o,A6: set @ A] :
% 2.67/1.55 ? [X3: A] :
% 2.67/1.55 ( ( member @ A @ X3 @ A6 )
% 2.67/1.55 & ( P2 @ X3 )
% 2.67/1.55 & ! [Y3: A] :
% 2.67/1.55 ( ( ( member @ A @ Y3 @ A6 )
% 2.67/1.55 & ( P2 @ Y3 ) )
% 2.67/1.55 => ( Y3 = X3 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_234_rev__map,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,F: B > A,Xs: list @ B] :
% 2.67/1.55 ( ( rev @ A @ ( map @ B @ A @ F @ Xs ) )
% 2.67/1.55 = ( map @ B @ A @ F @ ( rev @ B @ Xs ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_235_rev_Osimps_I2_J,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.67/1.55 ( ( rev @ A @ ( cons @ A @ X @ Xs ) )
% 2.67/1.55 = ( append @ A @ ( rev @ A @ Xs ) @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_236_map__tailrec__def,axiom,
% 2.67/1.55 ! [B: $tType,A: $tType] :
% 2.67/1.55 ( ( map_tailrec @ A @ B )
% 2.67/1.55 = ( ^ [F3: A > B,As3: list @ A] : ( rev @ B @ ( map_tailrec_rev @ A @ B @ F3 @ As3 @ ( nil @ B ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_237_map__tailrec__rev,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType] :
% 2.67/1.55 ( ( map_tailrec_rev @ B @ A )
% 2.67/1.55 = ( ^ [F3: B > A,As3: list @ B] : ( append @ A @ ( rev @ A @ ( map @ B @ A @ F3 @ As3 ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_238_map__tailrec__rev_Osimps_I2_J,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,F: A > B,A2: A,As2: list @ A,Bs2: list @ B] :
% 2.67/1.55 ( ( map_tailrec_rev @ A @ B @ F @ ( cons @ A @ A2 @ As2 ) @ Bs2 )
% 2.67/1.55 = ( map_tailrec_rev @ A @ B @ F @ As2 @ ( cons @ B @ ( F @ A2 ) @ Bs2 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_239_map__tailrec__rev_Osimps_I1_J,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,F: A > B,Bs2: list @ B] :
% 2.67/1.55 ( ( map_tailrec_rev @ A @ B @ F @ ( nil @ A ) @ Bs2 )
% 2.67/1.55 = Bs2 ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_240_map__tailrec__rev_Oelims,axiom,
% 2.67/1.55 ! [A: $tType,B: $tType,X: A > B,Xa2: list @ A,Xb: list @ B,Y: list @ B] :
% 2.67/1.55 ( ( ( map_tailrec_rev @ A @ B @ X @ Xa2 @ Xb )
% 2.67/1.55 = Y )
% 2.67/1.55 => ( ( ( Xa2
% 2.67/1.55 = ( nil @ A ) )
% 2.67/1.55 => ( Y != Xb ) )
% 2.67/1.55 => ~ ! [A5: A,As: list @ A] :
% 2.67/1.55 ( ( Xa2
% 2.67/1.55 = ( cons @ A @ A5 @ As ) )
% 2.67/1.55 => ( Y
% 2.67/1.55 != ( map_tailrec_rev @ A @ B @ X @ As @ ( cons @ B @ ( X @ A5 ) @ Xb ) ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_241_llast__lappend,axiom,
% 2.67/1.55 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 2.67/1.55 ( ( ( coinductive_lnull @ A @ Ys )
% 2.67/1.55 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.67/1.55 = ( coinductive_llast @ A @ Xs ) ) )
% 2.67/1.55 & ( ~ ( coinductive_lnull @ A @ Ys )
% 2.67/1.55 => ( ( ( coinductive_lfinite @ A @ Xs )
% 2.67/1.55 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.67/1.55 = ( coinductive_llast @ A @ Ys ) ) )
% 2.67/1.55 & ( ~ ( coinductive_lfinite @ A @ Xs )
% 2.67/1.55 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.67/1.55 = ( undefined @ A ) ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_242_strict__suffix__def,axiom,
% 2.67/1.55 ! [A: $tType] :
% 2.67/1.55 ( ( strict_suffix @ A )
% 2.67/1.55 = ( ^ [Xs3: list @ A,Ys3: list @ A] :
% 2.67/1.55 ? [Us: list @ A] :
% 2.67/1.55 ( ( Ys3
% 2.67/1.55 = ( append @ A @ Us @ Xs3 ) )
% 2.67/1.55 & ( Us
% 2.67/1.55 != ( nil @ A ) ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_243_lappend_Odisc__iff_I2_J,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) )
% 2.67/1.55 = ( ~ ( coinductive_lnull @ A @ Xs )
% 2.67/1.55 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_244_lnull__lappend,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.67/1.55 = ( ( coinductive_lnull @ A @ Xs )
% 2.67/1.55 & ( coinductive_lnull @ A @ Ys ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_245_lnull__llist__of,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A] :
% 2.67/1.55 ( ( coinductive_lnull @ A @ ( coinductive_llist_of @ A @ Xs ) )
% 2.67/1.55 = ( Xs
% 2.67/1.55 = ( nil @ A ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_246_llast__LCons,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 2.67/1.55 ( ( ( coinductive_lnull @ A @ Xs )
% 2.67/1.55 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.67/1.55 = X ) )
% 2.67/1.55 & ( ~ ( coinductive_lnull @ A @ Xs )
% 2.67/1.55 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.67/1.55 = ( coinductive_llast @ A @ Xs ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_247_strict__suffix__trans,axiom,
% 2.67/1.55 ! [A: $tType,Xs: list @ A,Ys: list @ A,Zs2: list @ A] :
% 2.67/1.55 ( ( strict_suffix @ A @ Xs @ Ys )
% 2.67/1.55 => ( ( strict_suffix @ A @ Ys @ Zs2 )
% 2.67/1.55 => ( strict_suffix @ A @ Xs @ Zs2 ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_248_lappend_Odisc_I2_J,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 2.67/1.55 | ~ ( coinductive_lnull @ A @ Ys ) )
% 2.67/1.55 => ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_249_lappend_Odisc_I1_J,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lnull @ A @ Xs )
% 2.67/1.55 => ( ( coinductive_lnull @ A @ Ys )
% 2.67/1.55 => ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_250_lappend__lnull1,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lnull @ A @ Xs )
% 2.67/1.55 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.67/1.55 = Ys ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_251_lappend__lnull2,axiom,
% 2.67/1.55 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lnull @ A @ Ys )
% 2.67/1.55 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.67/1.55 = Xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_252_lnull__imp__lfinite,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.67/1.55 ( ( coinductive_lnull @ A @ Xs )
% 2.67/1.55 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(fact_253_lappend_Oexhaust,axiom,
% 2.67/1.55 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.67/1.55 ( ( ( coinductive_lnull @ A @ Xs )
% 2.67/1.55 => ~ ( coinductive_lnull @ A @ Ys ) )
% 2.67/1.55 => ( ~ ( coinductive_lnull @ A @ Xs )
% 2.67/1.55 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(help_If_3_1_T,axiom,
% 2.67/1.55 ! [P: $o] :
% 2.67/1.55 ( ( P = $true )
% 2.67/1.55 | ( P = $false ) ) ).
% 2.67/1.55
% 2.67/1.55 thf(help_If_2_1_T,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Y: A] :
% 2.67/1.55 ( ( if @ A @ $false @ X @ Y )
% 2.67/1.55 = Y ) ).
% 2.67/1.55
% 2.67/1.55 thf(help_If_1_1_T,axiom,
% 2.67/1.55 ! [A: $tType,X: A,Y: A] :
% 2.67/1.55 ( ( if @ A @ $true @ X @ Y )
% 2.67/1.55 = X ) ).
% 2.67/1.55
% 2.67/1.55 thf(conj_0,conjecture,
% 2.67/1.55 member @ ( coinductive_llist @ a ) @ ( coinductive_lappend @ a @ ( coinductive_LCons @ a @ n @ ( coinductive_llist_of @ a @ ys ) ) @ ( coinductive_lappend @ a @ ( coinductive_LCons @ a @ n @ ( coinductive_lappend @ a @ ( coinductive_llist_of @ a @ zs ) @ ( coinductive_LCons @ a @ x @ ( coinductive_LNil @ a ) ) ) ) @ xs3 ) ) @ ( koenig916195507_paths @ a @ graph ) ).
% 2.67/1.55 ------------------------
% 2.67/1.58 % (22487)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_22272 for (2999ds/4Mi)
% 2.67/1.59 % (22487)Instruction limit reached!
% 2.67/1.59 % (22487)------------------------------
% 2.67/1.59 % (22487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.59 % (22487)Termination reason: Unknown
% 2.67/1.59 % (22487)Termination phase: shuffling
% 2.67/1.59
% 2.67/1.59 % (22487)Memory used [KB]: 1407
% 2.67/1.59 % (22487)Time elapsed: 0.003 s
% 2.67/1.59 % (22487)Instructions burned: 6 (million)
% 2.67/1.59 % (22487)------------------------------
% 2.67/1.59 % (22487)------------------------------
% 2.67/1.59 % (22490)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_22272 for (2999ds/2Mi)
% 2.67/1.59 % (22490)Instruction limit reached!
% 2.67/1.59 % (22490)------------------------------
% 2.67/1.59 % (22490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.59 % (22490)Termination reason: Unknown
% 2.67/1.59 % (22490)Termination phase: shuffling
% 2.67/1.59
% 2.67/1.59 % (22490)Memory used [KB]: 1407
% 2.67/1.59 % (22490)Time elapsed: 0.003 s
% 2.67/1.59 % (22490)Instructions burned: 4 (million)
% 2.67/1.59 % (22490)------------------------------
% 2.67/1.59 % (22490)------------------------------
% 2.67/1.59 % (22486)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22272 for (2999ds/183Mi)
% 2.67/1.59 % (22488)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_22272 for (2999ds/27Mi)
% 2.67/1.59 % (22489)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22272 for (2999ds/2Mi)
% 2.67/1.59 % (22491)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_22272 for (2999ds/275Mi)
% 2.67/1.59 % (22492)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22272 for (2999ds/18Mi)
% 2.67/1.59 % (22489)Instruction limit reached!
% 2.67/1.59 % (22489)------------------------------
% 2.67/1.59 % (22489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.67/1.59 % (22489)Termination reason: Unknown
% 2.67/1.59 % (22489)Termination phase: shuffling
% 2.67/1.59
% 2.67/1.59 % (22489)Memory used [KB]: 1407
% 2.67/1.59 % (22489)Time elapsed: 0.004 s
% 2.67/1.59 % (22489)Instructions burned: 3 (million)
% 2.67/1.59 % (22489)------------------------------
% 2.67/1.59 % (22489)------------------------------
% 2.67/1.60 % (22493)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22272 for (2999ds/3Mi)
% 2.74/1.60 % (22493)Instruction limit reached!
% 2.74/1.60 % (22493)------------------------------
% 2.74/1.60 % (22493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.60 % (22493)Termination reason: Unknown
% 2.74/1.60 % (22493)Termination phase: shuffling
% 2.74/1.60
% 2.74/1.60 % (22493)Memory used [KB]: 1407
% 2.74/1.60 % (22493)Time elapsed: 0.003 s
% 2.74/1.60 % (22493)Instructions burned: 3 (million)
% 2.74/1.60 % (22493)------------------------------
% 2.74/1.60 % (22493)------------------------------
% 2.74/1.60 % (22494)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_22272 for (2999ds/37Mi)
% 2.74/1.60 % (22492)Instruction limit reached!
% 2.74/1.60 % (22492)------------------------------
% 2.74/1.60 % (22492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.60 % (22492)Termination reason: Unknown
% 2.74/1.60 % (22492)Termination phase: shuffling
% 2.74/1.60
% 2.74/1.60 % (22492)Memory used [KB]: 1663
% 2.74/1.60 % (22492)Time elapsed: 0.014 s
% 2.74/1.60 % (22492)Instructions burned: 18 (million)
% 2.74/1.60 % (22492)------------------------------
% 2.74/1.60 % (22492)------------------------------
% 2.74/1.61 % (22488)Instruction limit reached!
% 2.74/1.61 % (22488)------------------------------
% 2.74/1.61 % (22488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.61 % (22488)Termination reason: Unknown
% 2.74/1.61 % (22488)Termination phase: Property scanning
% 2.74/1.61
% 2.74/1.61 % (22488)Memory used [KB]: 1791
% 2.74/1.61 % (22488)Time elapsed: 0.018 s
% 2.74/1.61 % (22488)Instructions burned: 27 (million)
% 2.74/1.61 % (22488)------------------------------
% 2.74/1.61 % (22488)------------------------------
% 2.74/1.61 % (22496)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_22272 for (2999ds/3Mi)
% 2.74/1.61 % (22496)Instruction limit reached!
% 2.74/1.61 % (22496)------------------------------
% 2.74/1.61 % (22496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.61 % (22496)Termination reason: Unknown
% 2.74/1.61 % (22496)Termination phase: shuffling
% 2.74/1.61
% 2.74/1.61 % (22496)Memory used [KB]: 1407
% 2.74/1.61 % (22496)Time elapsed: 0.003 s
% 2.74/1.61 % (22496)Instructions burned: 4 (million)
% 2.74/1.61 % (22496)------------------------------
% 2.74/1.61 % (22496)------------------------------
% 2.74/1.61 % (22495)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_22272 for (2999ds/15Mi)
% 2.74/1.61 % (22494)Instruction limit reached!
% 2.74/1.61 % (22494)------------------------------
% 2.74/1.61 % (22494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.61 % (22494)Termination reason: Unknown
% 2.74/1.61 % (22494)Termination phase: shuffling
% 2.74/1.61
% 2.74/1.61 % (22494)Memory used [KB]: 2046
% 2.74/1.61 % (22494)Time elapsed: 0.013 s
% 2.74/1.61 % (22494)Instructions burned: 38 (million)
% 2.74/1.61 % (22494)------------------------------
% 2.74/1.61 % (22494)------------------------------
% 2.74/1.62 % (22499)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22272 for (2999ds/16Mi)
% 2.74/1.62 % (22495)Instruction limit reached!
% 2.74/1.62 % (22495)------------------------------
% 2.74/1.62 % (22495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.62 % (22495)Termination reason: Unknown
% 2.74/1.62 % (22495)Termination phase: shuffling
% 2.74/1.62
% 2.74/1.62 % (22495)Memory used [KB]: 1663
% 2.74/1.62 % (22495)Time elapsed: 0.012 s
% 2.74/1.62 % (22495)Instructions burned: 16 (million)
% 2.74/1.62 % (22495)------------------------------
% 2.74/1.62 % (22495)------------------------------
% 2.74/1.62 % (22497)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_22272 for (2999ds/1041Mi)
% 2.74/1.62 % (22500)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_22272 for (2999ds/3Mi)
% 2.74/1.62 % (22498)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22272 for (2999ds/7Mi)
% 2.74/1.63 % (22500)Instruction limit reached!
% 2.74/1.63 % (22500)------------------------------
% 2.74/1.63 % (22500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.63 % (22500)Termination reason: Unknown
% 2.74/1.63 % (22500)Termination phase: shuffling
% 2.74/1.63
% 2.74/1.63 % (22500)Memory used [KB]: 1407
% 2.74/1.63 % (22500)Time elapsed: 0.003 s
% 2.74/1.63 % (22500)Instructions burned: 6 (million)
% 2.74/1.63 % (22500)------------------------------
% 2.74/1.63 % (22500)------------------------------
% 2.74/1.63 % (22499)Instruction limit reached!
% 2.74/1.63 % (22499)------------------------------
% 2.74/1.63 % (22499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.63 % (22499)Termination reason: Unknown
% 2.74/1.63 % (22499)Termination phase: shuffling
% 2.74/1.63
% 2.74/1.63 % (22499)Memory used [KB]: 1663
% 2.74/1.63 % (22499)Time elapsed: 0.008 s
% 2.74/1.63 % (22499)Instructions burned: 18 (million)
% 2.74/1.63 % (22499)------------------------------
% 2.74/1.63 % (22499)------------------------------
% 2.74/1.63 % (22498)Instruction limit reached!
% 2.74/1.63 % (22498)------------------------------
% 2.74/1.63 % (22498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.63 % (22498)Termination reason: Unknown
% 2.74/1.63 % (22498)Termination phase: shuffling
% 2.74/1.63
% 2.74/1.63 % (22498)Memory used [KB]: 1407
% 2.74/1.63 % (22498)Time elapsed: 0.006 s
% 2.74/1.63 % (22498)Instructions burned: 7 (million)
% 2.74/1.63 % (22498)------------------------------
% 2.74/1.63 % (22498)------------------------------
% 2.74/1.63 % (22502)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22272 for (2999ds/7Mi)
% 2.74/1.64 % (22503)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22272 for (2999ds/3Mi)
% 2.74/1.64 % (22503)Instruction limit reached!
% 2.74/1.64 % (22503)------------------------------
% 2.74/1.64 % (22503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.64 % (22503)Termination reason: Unknown
% 2.74/1.64 % (22503)Termination phase: shuffling
% 2.74/1.64
% 2.74/1.64 % (22503)Memory used [KB]: 1407
% 2.74/1.64 % (22503)Time elapsed: 0.003 s
% 2.74/1.64 % (22503)Instructions burned: 4 (million)
% 2.74/1.64 % (22503)------------------------------
% 2.74/1.64 % (22503)------------------------------
% 2.74/1.64 % (22502)Instruction limit reached!
% 2.74/1.64 % (22502)------------------------------
% 2.74/1.64 % (22502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.64 % (22502)Termination reason: Unknown
% 2.74/1.64 % (22502)Termination phase: shuffling
% 2.74/1.64
% 2.74/1.64 % (22502)Memory used [KB]: 1407
% 2.74/1.64 % (22502)Time elapsed: 0.004 s
% 2.74/1.64 % (22502)Instructions burned: 9 (million)
% 2.74/1.64 % (22502)------------------------------
% 2.74/1.64 % (22502)------------------------------
% 2.74/1.64 % (22501)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_22272 for (2999ds/3Mi)
% 2.74/1.64 % (22501)Instruction limit reached!
% 2.74/1.64 % (22501)------------------------------
% 2.74/1.64 % (22501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.64 % (22501)Termination reason: Unknown
% 2.74/1.64 % (22501)Termination phase: shuffling
% 2.74/1.64
% 2.74/1.64 % (22501)Memory used [KB]: 1407
% 2.74/1.64 % (22501)Time elapsed: 0.004 s
% 2.74/1.64 % (22501)Instructions burned: 3 (million)
% 2.74/1.64 % (22501)------------------------------
% 2.74/1.64 % (22501)------------------------------
% 2.74/1.65 % (22504)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22272 for (2999ds/4Mi)
% 2.74/1.65 % (22505)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22272 for (2999ds/18Mi)
% 2.74/1.65 % (22506)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22272 for (2999ds/710Mi)
% 2.74/1.65 % (22504)Instruction limit reached!
% 2.74/1.65 % (22504)------------------------------
% 2.74/1.65 % (22504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.65 % (22504)Termination reason: Unknown
% 2.74/1.65 % (22504)Termination phase: shuffling
% 2.74/1.65
% 2.74/1.65 % (22504)Memory used [KB]: 1407
% 2.74/1.65 % (22504)Time elapsed: 0.004 s
% 2.74/1.65 % (22504)Instructions burned: 4 (million)
% 2.74/1.65 % (22504)------------------------------
% 2.74/1.65 % (22504)------------------------------
% 2.74/1.65 % (22505)Instruction limit reached!
% 2.74/1.65 % (22505)------------------------------
% 2.74/1.65 % (22505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.65 % (22505)Termination reason: Unknown
% 2.74/1.65 % (22505)Termination phase: shuffling
% 2.74/1.65
% 2.74/1.65 % (22505)Memory used [KB]: 1663
% 2.74/1.65 % (22505)Time elapsed: 0.008 s
% 2.74/1.65 % (22505)Instructions burned: 18 (million)
% 2.74/1.65 % (22505)------------------------------
% 2.74/1.65 % (22505)------------------------------
% 2.74/1.66 % (22507)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22272 for (2999ds/6Mi)
% 2.74/1.66 % (22508)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_22272 for (2999ds/902Mi)
% 2.74/1.66 % (22507)Instruction limit reached!
% 2.74/1.66 % (22507)------------------------------
% 2.74/1.66 % (22507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.66 % (22507)Termination reason: Unknown
% 2.74/1.66 % (22507)Termination phase: shuffling
% 2.74/1.66
% 2.74/1.66 % (22507)Memory used [KB]: 1407
% 2.74/1.66 % (22507)Time elapsed: 0.005 s
% 2.74/1.66 % (22507)Instructions burned: 7 (million)
% 2.74/1.66 % (22507)------------------------------
% 2.74/1.66 % (22507)------------------------------
% 2.74/1.66 % (22509)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_22272 for (2999ds/21Mi)
% 2.74/1.67 % (22509)Instruction limit reached!
% 2.74/1.67 % (22509)------------------------------
% 2.74/1.67 % (22509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.67 % (22509)Termination reason: Unknown
% 2.74/1.67 % (22509)Termination phase: shuffling
% 2.74/1.67
% 2.74/1.67 % (22509)Memory used [KB]: 1791
% 2.74/1.67 % (22509)Time elapsed: 0.009 s
% 2.74/1.67 % (22509)Instructions burned: 21 (million)
% 2.74/1.67 % (22509)------------------------------
% 2.74/1.67 % (22509)------------------------------
% 2.74/1.67 % (22510)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22272 for (2999ds/5Mi)
% 2.74/1.67 % (22510)Instruction limit reached!
% 2.74/1.67 % (22510)------------------------------
% 2.74/1.67 % (22510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.67 % (22510)Termination reason: Unknown
% 2.74/1.67 % (22510)Termination phase: shuffling
% 2.74/1.67
% 2.74/1.67 % (22510)Memory used [KB]: 1407
% 2.74/1.67 % (22510)Time elapsed: 0.003 s
% 2.74/1.67 % (22510)Instructions burned: 6 (million)
% 2.74/1.67 % (22510)------------------------------
% 2.74/1.67 % (22510)------------------------------
% 2.74/1.68 % (22511)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_22272 for (2998ds/6Mi)
% 2.74/1.68 % (22511)Instruction limit reached!
% 2.74/1.68 % (22511)------------------------------
% 2.74/1.68 % (22511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.68 % (22511)Termination reason: Unknown
% 2.74/1.68 % (22511)Termination phase: shuffling
% 2.74/1.68
% 2.74/1.68 % (22511)Memory used [KB]: 1407
% 2.74/1.68 % (22511)Time elapsed: 0.004 s
% 2.74/1.68 % (22511)Instructions burned: 7 (million)
% 2.74/1.68 % (22511)------------------------------
% 2.74/1.68 % (22511)------------------------------
% 2.74/1.68 % (22512)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22272 for (2998ds/377Mi)
% 2.74/1.69 % (22486)Instruction limit reached!
% 2.74/1.69 % (22486)------------------------------
% 2.74/1.69 % (22486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.69 % (22486)Termination reason: Unknown
% 2.74/1.69 % (22486)Termination phase: Saturation
% 2.74/1.69
% 2.74/1.69 % (22486)Memory used [KB]: 7291
% 2.74/1.69 % (22486)Time elapsed: 0.100 s
% 2.74/1.69 % (22486)Instructions burned: 184 (million)
% 2.74/1.69 % (22486)------------------------------
% 2.74/1.69 % (22486)------------------------------
% 2.74/1.69 % (22513)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_22272 for (2998ds/779Mi)
% 2.74/1.69 % (22491)Instruction limit reached!
% 2.74/1.69 % (22491)------------------------------
% 2.74/1.69 % (22491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.69 % (22491)Termination reason: Unknown
% 2.74/1.69 % (22491)Termination phase: Saturation
% 2.74/1.69
% 2.74/1.69 % (22491)Memory used [KB]: 7419
% 2.74/1.69 % (22491)Time elapsed: 0.104 s
% 2.74/1.69 % (22491)Instructions burned: 275 (million)
% 2.74/1.69 % (22491)------------------------------
% 2.74/1.69 % (22491)------------------------------
% 2.74/1.70 % (22514)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_22272 for (2998ds/19Mi)
% 2.74/1.70 % (22515)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_22272 for (2998ds/879Mi)
% 2.74/1.71 % (22514)Instruction limit reached!
% 2.74/1.71 % (22514)------------------------------
% 2.74/1.71 % (22514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.71 % (22514)Termination reason: Unknown
% 2.74/1.71 % (22514)Termination phase: shuffling
% 2.74/1.71
% 2.74/1.71 % (22514)Memory used [KB]: 1791
% 2.74/1.71 % (22514)Time elapsed: 0.008 s
% 2.74/1.71 % (22514)Instructions burned: 22 (million)
% 2.74/1.71 % (22514)------------------------------
% 2.74/1.71 % (22514)------------------------------
% 2.74/1.72 % (22516)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_22272 for (2998ds/17Mi)
% 2.74/1.72 % (22516)Instruction limit reached!
% 2.74/1.72 % (22516)------------------------------
% 2.74/1.72 % (22516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.72 % (22516)Termination reason: Unknown
% 2.74/1.72 % (22516)Termination phase: shuffling
% 2.74/1.72
% 2.74/1.72 % (22516)Memory used [KB]: 1663
% 2.74/1.72 % (22516)Time elapsed: 0.008 s
% 2.74/1.72 % (22516)Instructions burned: 18 (million)
% 2.74/1.72 % (22516)------------------------------
% 2.74/1.72 % (22516)------------------------------
% 2.74/1.73 % (22517)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22272 for (2998ds/3Mi)
% 2.74/1.73 % (22517)Instruction limit reached!
% 2.74/1.73 % (22517)------------------------------
% 2.74/1.73 % (22517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.73 % (22517)Termination reason: Unknown
% 2.74/1.73 % (22517)Termination phase: shuffling
% 2.74/1.73
% 2.74/1.73 % (22517)Memory used [KB]: 1407
% 2.74/1.73 % (22517)Time elapsed: 0.003 s
% 2.74/1.73 % (22517)Instructions burned: 4 (million)
% 2.74/1.73 % (22517)------------------------------
% 2.74/1.73 % (22517)------------------------------
% 2.74/1.74 % (22518)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_22272 for (2998ds/30Mi)
% 2.74/1.75 % (22518)Instruction limit reached!
% 2.74/1.75 % (22518)------------------------------
% 2.74/1.75 % (22518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.75 % (22518)Termination reason: Unknown
% 2.74/1.75 % (22518)Termination phase: Property scanning
% 2.74/1.75
% 2.74/1.75 % (22518)Memory used [KB]: 1791
% 2.74/1.75 % (22518)Time elapsed: 0.012 s
% 2.74/1.75 % (22518)Instructions burned: 30 (million)
% 2.74/1.75 % (22518)------------------------------
% 2.74/1.75 % (22518)------------------------------
% 2.74/1.76 % (22519)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_22272 for (2998ds/127Mi)
% 2.74/1.81 % (22519)Instruction limit reached!
% 2.74/1.81 % (22519)------------------------------
% 2.74/1.81 % (22519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.81 % (22519)Termination reason: Unknown
% 2.74/1.81 % (22519)Termination phase: Saturation
% 2.74/1.81
% 2.74/1.81 % (22519)Memory used [KB]: 7036
% 2.74/1.81 % (22519)Time elapsed: 0.042 s
% 2.74/1.81 % (22519)Instructions burned: 129 (million)
% 2.74/1.81 % (22519)------------------------------
% 2.74/1.81 % (22519)------------------------------
% 2.74/1.81 % (22512)Instruction limit reached!
% 2.74/1.81 % (22512)------------------------------
% 2.74/1.81 % (22512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.81 % (22512)Termination reason: Unknown
% 2.74/1.81 % (22512)Termination phase: Saturation
% 2.74/1.81
% 2.74/1.81 % (22512)Memory used [KB]: 8187
% 2.74/1.81 % (22512)Time elapsed: 0.127 s
% 2.74/1.81 % (22512)Instructions burned: 379 (million)
% 2.74/1.81 % (22512)------------------------------
% 2.74/1.81 % (22512)------------------------------
% 2.74/1.82 % (22520)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_22272 for (2997ds/100Mi)
% 2.74/1.82 % (22521)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_22272 for (2997ds/3Mi)
% 2.74/1.82 % (22521)Instruction limit reached!
% 2.74/1.82 % (22521)------------------------------
% 2.74/1.82 % (22521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.82 % (22521)Termination reason: Unknown
% 2.74/1.82 % (22521)Termination phase: shuffling
% 2.74/1.82
% 2.74/1.82 % (22521)Memory used [KB]: 1407
% 2.74/1.82 % (22521)Time elapsed: 0.003 s
% 2.74/1.82 % (22521)Instructions burned: 4 (million)
% 2.74/1.82 % (22521)------------------------------
% 2.74/1.82 % (22521)------------------------------
% 2.74/1.83 % (22522)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_22272 for (2997ds/20Mi)
% 2.74/1.84 % (22522)Instruction limit reached!
% 2.74/1.84 % (22522)------------------------------
% 2.74/1.84 % (22522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.84 % (22522)Termination reason: Unknown
% 2.74/1.84 % (22522)Termination phase: Property scanning
% 2.74/1.84
% 2.74/1.84 % (22522)Memory used [KB]: 1663
% 2.74/1.84 % (22522)Time elapsed: 0.009 s
% 2.74/1.84 % (22522)Instructions burned: 21 (million)
% 2.74/1.84 % (22522)------------------------------
% 2.74/1.84 % (22522)------------------------------
% 2.74/1.84 % (22520)Instruction limit reached!
% 2.74/1.84 % (22520)------------------------------
% 2.74/1.84 % (22520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.84 % (22520)Termination reason: Unknown
% 2.74/1.84 % (22520)Termination phase: Property scanning
% 2.74/1.84
% 2.74/1.84 % (22520)Memory used [KB]: 2302
% 2.74/1.84 % (22520)Time elapsed: 0.031 s
% 2.74/1.84 % (22520)Instructions burned: 100 (million)
% 2.74/1.84 % (22520)------------------------------
% 2.74/1.84 % (22520)------------------------------
% 2.74/1.85 % (22523)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_22272 for (2997ds/86Mi)
% 2.74/1.85 % (22524)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_22272 for (2997ds/107Mi)
% 2.74/1.87 % (22506)Instruction limit reached!
% 2.74/1.87 % (22506)------------------------------
% 2.74/1.87 % (22506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.87 % (22506)Termination reason: Unknown
% 2.74/1.87 % (22506)Termination phase: Saturation
% 2.74/1.87
% 2.74/1.87 % (22506)Memory used [KB]: 7547
% 2.74/1.87 % (22506)Time elapsed: 0.229 s
% 2.74/1.87 % (22506)Instructions burned: 712 (million)
% 2.74/1.87 % (22506)------------------------------
% 2.74/1.87 % (22506)------------------------------
% 2.74/1.88 % (22523)Instruction limit reached!
% 2.74/1.88 % (22523)------------------------------
% 2.74/1.88 % (22523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.88 % (22523)Termination reason: Unknown
% 2.74/1.88 % (22523)Termination phase: Property scanning
% 2.74/1.88
% 2.74/1.88 % (22523)Memory used [KB]: 2174
% 2.74/1.88 % (22523)Time elapsed: 0.029 s
% 2.74/1.88 % (22523)Instructions burned: 89 (million)
% 2.74/1.88 % (22523)------------------------------
% 2.74/1.88 % (22523)------------------------------
% 2.74/1.88 % (22525)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_22272 for (2996ds/39Mi)
% 2.74/1.89 % (22526)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_22272 for (2996ds/448Mi)
% 2.74/1.89 % (22524)Instruction limit reached!
% 2.74/1.89 % (22524)------------------------------
% 2.74/1.89 % (22524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.89 % (22524)Termination reason: Unknown
% 2.74/1.89 % (22524)Termination phase: Saturation
% 2.74/1.89
% 2.74/1.89 % (22524)Memory used [KB]: 6908
% 2.74/1.89 % (22524)Time elapsed: 0.035 s
% 2.74/1.89 % (22524)Instructions burned: 107 (million)
% 2.74/1.89 % (22524)------------------------------
% 2.74/1.89 % (22524)------------------------------
% 2.74/1.90 % (22525)Instruction limit reached!
% 2.74/1.90 % (22525)------------------------------
% 2.74/1.90 % (22525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.90 % (22525)Termination reason: Unknown
% 2.74/1.90 % (22525)Termination phase: shuffling
% 2.74/1.90
% 2.74/1.90 % (22525)Memory used [KB]: 2174
% 2.74/1.90 % (22525)Time elapsed: 0.012 s
% 2.74/1.90 % (22525)Instructions burned: 40 (million)
% 2.74/1.90 % (22525)------------------------------
% 2.74/1.90 % (22525)------------------------------
% 2.74/1.90 % (22527)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_22272 for (2996ds/46Mi)
% 2.74/1.90 % (22528)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_22272 for (2996ds/98Mi)
% 2.74/1.91 % (22527)Instruction limit reached!
% 2.74/1.91 % (22527)------------------------------
% 2.74/1.91 % (22527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.91 % (22527)Termination reason: Unknown
% 2.74/1.91 % (22527)Termination phase: Preprocessing 3
% 2.74/1.91
% 2.74/1.91 % (22527)Memory used [KB]: 1918
% 2.74/1.91 % (22527)Time elapsed: 0.017 s
% 2.74/1.91 % (22527)Instructions burned: 47 (million)
% 2.74/1.91 % (22527)------------------------------
% 2.74/1.91 % (22527)------------------------------
% 2.74/1.92 % (22529)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_22272 for (2996ds/507Mi)
% 2.74/1.92 % (22508)Instruction limit reached!
% 2.74/1.92 % (22508)------------------------------
% 2.74/1.92 % (22508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.92 % (22508)Termination reason: Unknown
% 2.74/1.92 % (22508)Termination phase: Saturation
% 2.74/1.92
% 2.74/1.92 % (22508)Memory used [KB]: 8059
% 2.74/1.92 % (22508)Time elapsed: 0.264 s
% 2.74/1.92 % (22508)Instructions burned: 904 (million)
% 2.74/1.92 % (22508)------------------------------
% 2.74/1.92 % (22508)------------------------------
% 2.74/1.93 % (22528)Instruction limit reached!
% 2.74/1.93 % (22528)------------------------------
% 2.74/1.93 % (22528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.93 % (22528)Termination reason: Unknown
% 2.74/1.93 % (22528)Termination phase: Property scanning
% 2.74/1.93
% 2.74/1.93 % (22528)Memory used [KB]: 2302
% 2.74/1.93 % (22528)Time elapsed: 0.028 s
% 2.74/1.93 % (22528)Instructions burned: 100 (million)
% 2.74/1.93 % (22528)------------------------------
% 2.74/1.93 % (22528)------------------------------
% 2.74/1.93 % (22530)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_22272 for (2996ds/149Mi)
% 2.74/1.94 % (22531)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_22272 for (2996ds/39Mi)
% 2.74/1.95 % (22513)Instruction limit reached!
% 2.74/1.95 % (22513)------------------------------
% 2.74/1.95 % (22513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.95 % (22513)Termination reason: Unknown
% 2.74/1.95 % (22513)Termination phase: Saturation
% 2.74/1.95
% 2.74/1.95 % (22513)Memory used [KB]: 8955
% 2.74/1.95 % (22513)Time elapsed: 0.260 s
% 2.74/1.95 % (22513)Instructions burned: 780 (million)
% 2.74/1.95 % (22513)------------------------------
% 2.74/1.95 % (22513)------------------------------
% 2.74/1.95 % (22531)Instruction limit reached!
% 2.74/1.95 % (22531)------------------------------
% 2.74/1.95 % (22531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.95 % (22531)Termination reason: Unknown
% 2.74/1.95 % (22531)Termination phase: Preprocessing 3
% 2.74/1.95
% 2.74/1.95 % (22531)Memory used [KB]: 1918
% 2.74/1.95 % (22531)Time elapsed: 0.014 s
% 2.74/1.95 % (22531)Instructions burned: 41 (million)
% 2.74/1.95 % (22531)------------------------------
% 2.74/1.95 % (22531)------------------------------
% 2.74/1.96 % (22532)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_22272 for (2996ds/6Mi)
% 2.74/1.96 % (22532)Instruction limit reached!
% 2.74/1.96 % (22532)------------------------------
% 2.74/1.96 % (22532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.96 % (22532)Termination reason: Unknown
% 2.74/1.96 % (22532)Termination phase: shuffling
% 2.74/1.96
% 2.74/1.96 % (22532)Memory used [KB]: 1407
% 2.74/1.96 % (22532)Time elapsed: 0.003 s
% 2.74/1.96 % (22532)Instructions burned: 6 (million)
% 2.74/1.96 % (22532)------------------------------
% 2.74/1.96 % (22532)------------------------------
% 2.74/1.96 % (22533)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_22272 for (2996ds/1087Mi)
% 2.74/1.97 % (22534)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_22272 for (2995ds/47Mi)
% 2.74/1.98 % (22530)Instruction limit reached!
% 2.74/1.98 % (22530)------------------------------
% 2.74/1.98 % (22530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.98 % (22530)Termination reason: Unknown
% 2.74/1.98 % (22530)Termination phase: Saturation
% 2.74/1.98
% 2.74/1.98 % (22530)Memory used [KB]: 7164
% 2.74/1.98 % (22530)Time elapsed: 0.045 s
% 2.74/1.98 % (22530)Instructions burned: 149 (million)
% 2.74/1.98 % (22530)------------------------------
% 2.74/1.98 % (22530)------------------------------
% 2.74/1.98 % (22497)Instruction limit reached!
% 2.74/1.98 % (22497)------------------------------
% 2.74/1.98 % (22497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.98 % (22497)Termination reason: Unknown
% 2.74/1.98 % (22497)Termination phase: Saturation
% 2.74/1.98
% 2.74/1.98 % (22497)Memory used [KB]: 9210
% 2.74/1.98 % (22497)Time elapsed: 0.365 s
% 2.74/1.98 % (22497)Instructions burned: 1042 (million)
% 2.74/1.98 % (22497)------------------------------
% 2.74/1.98 % (22497)------------------------------
% 2.74/1.99 % (22535)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_22272 for (2995ds/44Mi)
% 2.74/1.99 % (22534)Instruction limit reached!
% 2.74/1.99 % (22534)------------------------------
% 2.74/1.99 % (22534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.99 % (22534)Termination reason: Unknown
% 2.74/1.99 % (22534)Termination phase: Preprocessing 3
% 2.74/1.99
% 2.74/1.99 % (22534)Memory used [KB]: 2046
% 2.74/1.99 % (22534)Time elapsed: 0.016 s
% 2.74/1.99 % (22534)Instructions burned: 48 (million)
% 2.74/1.99 % (22534)------------------------------
% 2.74/1.99 % (22534)------------------------------
% 2.74/1.99 % (22515)Instruction limit reached!
% 2.74/1.99 % (22515)------------------------------
% 2.74/1.99 % (22515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.99 % (22515)Termination reason: Unknown
% 2.74/1.99 % (22515)Termination phase: Saturation
% 2.74/1.99
% 2.74/1.99 % (22515)Memory used [KB]: 7547
% 2.74/1.99 % (22515)Time elapsed: 0.309 s
% 2.74/1.99 % (22515)Instructions burned: 879 (million)
% 2.74/1.99 % (22515)------------------------------
% 2.74/1.99 % (22515)------------------------------
% 2.74/1.99 % (22536)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_22272 for (2995ds/432Mi)
% 2.74/2.00 % (22537)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_22272 for (2995ds/62Mi)
% 2.74/2.00 % (22535)Instruction limit reached!
% 2.74/2.00 % (22535)------------------------------
% 2.74/2.00 % (22535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/2.00 % (22535)Termination reason: Unknown
% 2.74/2.00 % (22535)Termination phase: Property scanning
% 2.74/2.00
% 2.74/2.00 % (22535)Memory used [KB]: 2174
% 2.74/2.00 % (22535)Time elapsed: 0.013 s
% 2.74/2.00 % (22535)Instructions burned: 44 (million)
% 2.74/2.00 % (22535)------------------------------
% 2.74/2.00 % (22535)------------------------------
% 2.74/2.00 % (22538)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_22272 for (2995ds/31Mi)
% 2.74/2.01 % (22539)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_22272 for (2995ds/96Mi)
% 2.74/2.01 % (22538)Instruction limit reached!
% 2.74/2.01 % (22538)------------------------------
% 2.74/2.01 % (22538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/2.01 % (22538)Termination reason: Unknown
% 2.74/2.01 % (22538)Termination phase: Property scanning
% 2.74/2.01
% 2.74/2.01 % (22538)Memory used [KB]: 1791
% 2.74/2.01 % (22538)Time elapsed: 0.010 s
% 2.74/2.01 % (22538)Instructions burned: 31 (million)
% 2.74/2.01 % (22538)------------------------------
% 2.74/2.01 % (22538)------------------------------
% 5.76/2.01 % (22537)Instruction limit reached!
% 5.76/2.01 % (22537)------------------------------
% 5.76/2.01 % (22537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.01 % (22537)Termination reason: Unknown
% 5.76/2.01 % (22537)Termination phase: Property scanning
% 5.76/2.01
% 5.76/2.01 % (22537)Memory used [KB]: 2174
% 5.76/2.01 % (22537)Time elapsed: 0.018 s
% 5.76/2.01 % (22537)Instructions burned: 65 (million)
% 5.76/2.01 % (22537)------------------------------
% 5.76/2.01 % (22537)------------------------------
% 5.76/2.02 % (22540)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_22272 for (2995ds/453Mi)
% 5.76/2.02 % (22541)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_22272 for (2995ds/71Mi)
% 5.76/2.03 % (22526)Instruction limit reached!
% 5.76/2.03 % (22526)------------------------------
% 5.76/2.03 % (22526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.03 % (22526)Termination reason: Unknown
% 5.76/2.03 % (22526)Termination phase: Saturation
% 5.76/2.03
% 5.76/2.03 % (22526)Memory used [KB]: 8699
% 5.76/2.03 % (22526)Time elapsed: 0.145 s
% 5.76/2.03 % (22526)Instructions burned: 449 (million)
% 5.76/2.03 % (22526)------------------------------
% 5.76/2.03 % (22526)------------------------------
% 5.76/2.04 % (22539)Instruction limit reached!
% 5.76/2.04 % (22539)------------------------------
% 5.76/2.04 % (22539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.04 % (22539)Termination reason: Unknown
% 5.76/2.04 % (22539)Termination phase: Saturation
% 5.76/2.04
% 5.76/2.04 % (22539)Memory used [KB]: 6780
% 5.76/2.04 % (22539)Time elapsed: 0.029 s
% 5.76/2.04 % (22539)Instructions burned: 98 (million)
% 5.76/2.04 % (22539)------------------------------
% 5.76/2.04 % (22539)------------------------------
% 5.76/2.04 % (22542)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_22272 for (2995ds/83Mi)
% 5.76/2.04 % (22541)Instruction limit reached!
% 5.76/2.04 % (22541)------------------------------
% 5.76/2.04 % (22541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.04 % (22541)Termination reason: Unknown
% 5.76/2.04 % (22541)Termination phase: Function definition elimination
% 5.76/2.04
% 5.76/2.04 % (22541)Memory used [KB]: 2174
% 5.76/2.04 % (22541)Time elapsed: 0.023 s
% 5.76/2.04 % (22541)Instructions burned: 74 (million)
% 5.76/2.04 % (22541)------------------------------
% 5.76/2.04 % (22541)------------------------------
% 5.76/2.05 % (22543)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_22272 for (2995ds/11Mi)
% 5.76/2.05 % (22543)Instruction limit reached!
% 5.76/2.05 % (22543)------------------------------
% 5.76/2.05 % (22543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.05 % (22543)Termination reason: Unknown
% 5.76/2.05 % (22543)Termination phase: shuffling
% 5.76/2.05
% 5.76/2.05 % (22543)Memory used [KB]: 1535
% 5.76/2.05 % (22543)Time elapsed: 0.004 s
% 5.76/2.05 % (22543)Instructions burned: 11 (million)
% 5.76/2.05 % (22543)------------------------------
% 5.76/2.05 % (22543)------------------------------
% 5.76/2.05 % (22544)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_22272 for (2995ds/41Mi)
% 5.76/2.06 % (22545)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22272 for (2995ds/6Mi)
% 5.76/2.06 % (22545)Instruction limit reached!
% 5.76/2.06 % (22545)------------------------------
% 5.76/2.06 % (22545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.06 % (22545)Termination reason: Unknown
% 5.76/2.06 % (22545)Termination phase: shuffling
% 5.76/2.06
% 5.76/2.06 % (22545)Memory used [KB]: 1407
% 5.76/2.06 % (22545)Time elapsed: 0.004 s
% 5.76/2.06 % (22545)Instructions burned: 8 (million)
% 5.76/2.06 % (22545)------------------------------
% 5.76/2.06 % (22545)------------------------------
% 5.76/2.07 % (22544)Instruction limit reached!
% 5.76/2.07 % (22544)------------------------------
% 5.76/2.07 % (22544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.07 % (22544)Termination reason: Unknown
% 5.76/2.07 % (22544)Termination phase: shuffling
% 5.76/2.07
% 5.76/2.07 % (22544)Memory used [KB]: 2174
% 5.76/2.07 % (22544)Time elapsed: 0.013 s
% 5.76/2.07 % (22544)Instructions burned: 42 (million)
% 5.76/2.07 % (22544)------------------------------
% 5.76/2.07 % (22544)------------------------------
% 5.76/2.07 % (22542)Instruction limit reached!
% 5.76/2.07 % (22542)------------------------------
% 5.76/2.07 % (22542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.07 % (22542)Termination reason: Unknown
% 5.76/2.07 % (22542)Termination phase: Saturation
% 5.76/2.07
% 5.76/2.07 % (22542)Memory used [KB]: 6524
% 5.76/2.07 % (22542)Time elapsed: 0.029 s
% 5.76/2.07 % (22542)Instructions burned: 84 (million)
% 5.76/2.07 % (22542)------------------------------
% 5.76/2.07 % (22542)------------------------------
% 5.76/2.07 % (22546)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_22272 for (2995ds/150Mi)
% 5.76/2.08 % (22547)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_22272 for (2995ds/343Mi)
% 5.76/2.08 % (22548)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_22272 for (2995ds/109Mi)
% 5.76/2.09 % (22529)Instruction limit reached!
% 5.76/2.09 % (22529)------------------------------
% 5.76/2.09 % (22529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.09 % (22529)Termination reason: Unknown
% 5.76/2.09 % (22529)Termination phase: Saturation
% 5.76/2.09
% 5.76/2.09 % (22529)Memory used [KB]: 8187
% 5.76/2.09 % (22529)Time elapsed: 0.164 s
% 5.76/2.09 % (22529)Instructions burned: 509 (million)
% 5.76/2.09 % (22529)------------------------------
% 5.76/2.09 % (22529)------------------------------
% 5.76/2.10 % (22549)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_22272 for (2994ds/253Mi)
% 5.76/2.11 % (22548)Instruction limit reached!
% 5.76/2.11 % (22548)------------------------------
% 5.76/2.11 % (22548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.76/2.11 % (22548)Termination reason: Unknown
% 5.76/2.11 % (22548)Termination phase: Saturation
% 5.76/2.11
% 5.76/2.11 % (22548)Memory used [KB]: 6908
% 5.76/2.11 % (22548)Time elapsed: 0.033 s
% 5.76/2.11 % (22548)Instructions burned: 110 (million)
% 5.76/2.11 % (22548)------------------------------
% 5.76/2.11 % (22548)------------------------------
% 6.28/2.12 % (22546)Instruction limit reached!
% 6.28/2.12 % (22546)------------------------------
% 6.28/2.12 % (22546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.12 % (22546)Termination reason: Unknown
% 6.28/2.12 % (22546)Termination phase: Saturation
% 6.28/2.12
% 6.28/2.12 % (22546)Memory used [KB]: 7164
% 6.28/2.12 % (22546)Time elapsed: 0.046 s
% 6.28/2.12 % (22546)Instructions burned: 152 (million)
% 6.28/2.12 % (22546)------------------------------
% 6.28/2.12 % (22546)------------------------------
% 6.28/2.12 % (22550)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_22272 for (2994ds/140Mi)
% 6.28/2.12 % (22551)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_22272 for (2994ds/614Mi)
% 6.28/2.15 % (22540)Instruction limit reached!
% 6.28/2.15 % (22540)------------------------------
% 6.28/2.15 % (22540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.15 % (22540)Termination reason: Unknown
% 6.28/2.15 % (22540)Termination phase: Saturation
% 6.28/2.15
% 6.28/2.15 % (22540)Memory used [KB]: 7931
% 6.28/2.15 % (22540)Time elapsed: 0.131 s
% 6.28/2.15 % (22540)Instructions burned: 455 (million)
% 6.28/2.15 % (22540)------------------------------
% 6.28/2.15 % (22540)------------------------------
% 6.28/2.16 % (22552)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_22272 for (2994ds/202Mi)
% 6.28/2.16 % (22550)Instruction limit reached!
% 6.28/2.16 % (22550)------------------------------
% 6.28/2.16 % (22550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.16 % (22550)Termination reason: Unknown
% 6.28/2.16 % (22550)Termination phase: Saturation
% 6.28/2.16
% 6.28/2.16 % (22550)Memory used [KB]: 6908
% 6.28/2.16 % (22550)Time elapsed: 0.045 s
% 6.28/2.16 % (22550)Instructions burned: 140 (million)
% 6.28/2.16 % (22550)------------------------------
% 6.28/2.16 % (22550)------------------------------
% 6.28/2.17 % (22553)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_22272 for (2993ds/339Mi)
% 6.28/2.17 % (22549)Instruction limit reached!
% 6.28/2.17 % (22549)------------------------------
% 6.28/2.17 % (22549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.17 % (22549)Termination reason: Unknown
% 6.28/2.17 % (22549)Termination phase: Saturation
% 6.28/2.17
% 6.28/2.17 % (22549)Memory used [KB]: 7803
% 6.28/2.17 % (22549)Time elapsed: 0.077 s
% 6.28/2.17 % (22549)Instructions burned: 253 (million)
% 6.28/2.17 % (22549)------------------------------
% 6.28/2.17 % (22549)------------------------------
% 6.28/2.18 % (22554)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_22272 for (2993ds/283Mi)
% 6.28/2.18 % (22547)Instruction limit reached!
% 6.28/2.18 % (22547)------------------------------
% 6.28/2.18 % (22547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.18 % (22547)Termination reason: Unknown
% 6.28/2.18 % (22547)Termination phase: Saturation
% 6.28/2.18
% 6.28/2.18 % (22547)Memory used [KB]: 7675
% 6.28/2.18 % (22547)Time elapsed: 0.109 s
% 6.28/2.18 % (22547)Instructions burned: 344 (million)
% 6.28/2.18 % (22547)------------------------------
% 6.28/2.18 % (22547)------------------------------
% 6.28/2.19 % (22536)Instruction limit reached!
% 6.28/2.19 % (22536)------------------------------
% 6.28/2.19 % (22536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.19 % (22536)Termination reason: Unknown
% 6.28/2.19 % (22536)Termination phase: Saturation
% 6.28/2.19
% 6.28/2.19 % (22536)Memory used [KB]: 3326
% 6.28/2.19 % (22536)Time elapsed: 0.196 s
% 6.28/2.19 % (22536)Instructions burned: 432 (million)
% 6.28/2.19 % (22536)------------------------------
% 6.28/2.19 % (22536)------------------------------
% 6.28/2.19 % (22555)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_22272 for (2993ds/134Mi)
% 6.89/2.20 % (22556)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_22272 for (2993ds/298Mi)
% 6.89/2.22 % (22552)Instruction limit reached!
% 6.89/2.22 % (22552)------------------------------
% 6.89/2.22 % (22552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.22 % (22552)Termination reason: Unknown
% 6.89/2.22 % (22552)Termination phase: Saturation
% 6.89/2.22
% 6.89/2.22 % (22552)Memory used [KB]: 7419
% 6.89/2.22 % (22552)Time elapsed: 0.062 s
% 6.89/2.22 % (22552)Instructions burned: 203 (million)
% 6.89/2.22 % (22552)------------------------------
% 6.89/2.22 % (22552)------------------------------
% 6.89/2.23 % (22557)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_22272 for (2993ds/192Mi)
% 6.89/2.23 % (22555)Instruction limit reached!
% 6.89/2.23 % (22555)------------------------------
% 6.89/2.23 % (22555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.23 % (22555)Termination reason: Unknown
% 6.89/2.23 % (22555)Termination phase: Saturation
% 6.89/2.23
% 6.89/2.23 % (22555)Memory used [KB]: 7036
% 6.89/2.23 % (22555)Time elapsed: 0.040 s
% 6.89/2.23 % (22555)Instructions burned: 136 (million)
% 6.89/2.23 % (22555)------------------------------
% 6.89/2.23 % (22555)------------------------------
% 6.89/2.24 % (22558)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_22272 for (2993ds/258Mi)
% 6.89/2.26 % (22554)Instruction limit reached!
% 6.89/2.26 % (22554)------------------------------
% 6.89/2.26 % (22554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.26 % (22554)Termination reason: Unknown
% 6.89/2.26 % (22554)Termination phase: Saturation
% 6.89/2.26
% 6.89/2.26 % (22554)Memory used [KB]: 7419
% 6.89/2.26 % (22554)Time elapsed: 0.085 s
% 6.89/2.26 % (22554)Instructions burned: 283 (million)
% 6.89/2.26 % (22554)------------------------------
% 6.89/2.26 % (22554)------------------------------
% 6.89/2.27 % (22553)Instruction limit reached!
% 6.89/2.27 % (22553)------------------------------
% 6.89/2.27 % (22553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.27 % (22553)Termination reason: Unknown
% 6.89/2.27 % (22553)Termination phase: Saturation
% 6.89/2.27
% 6.89/2.27 % (22553)Memory used [KB]: 7675
% 6.89/2.27 % (22553)Time elapsed: 0.099 s
% 6.89/2.27 % (22553)Instructions burned: 339 (million)
% 6.89/2.27 % (22553)------------------------------
% 6.89/2.27 % (22553)------------------------------
% 6.89/2.27 % (22559)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_22272 for (2992ds/90Mi)
% 6.89/2.28 % (22560)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_22272 for (2992ds/231Mi)
% 6.89/2.29 % (22557)Instruction limit reached!
% 6.89/2.29 % (22557)------------------------------
% 6.89/2.29 % (22557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.29 % (22557)Termination reason: Unknown
% 6.89/2.29 % (22557)Termination phase: Saturation
% 6.89/2.29
% 6.89/2.29 % (22557)Memory used [KB]: 8059
% 6.89/2.29 % (22557)Time elapsed: 0.059 s
% 6.89/2.29 % (22557)Instructions burned: 195 (million)
% 6.89/2.29 % (22557)------------------------------
% 6.89/2.29 % (22557)------------------------------
% 6.89/2.29 % (22556)Instruction limit reached!
% 6.89/2.29 % (22556)------------------------------
% 6.89/2.29 % (22556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.29 % (22556)Termination reason: Unknown
% 6.89/2.29 % (22556)Termination phase: Saturation
% 6.89/2.29
% 6.89/2.29 % (22556)Memory used [KB]: 7931
% 6.89/2.29 % (22556)Time elapsed: 0.091 s
% 6.89/2.29 % (22556)Instructions burned: 298 (million)
% 6.89/2.29 % (22556)------------------------------
% 6.89/2.29 % (22556)------------------------------
% 6.89/2.30 % (22561)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_22272 for (2992ds/458Mi)
% 7.49/2.30 % (22562)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_22272 for (2992ds/31Mi)
% 7.49/2.30 % (22559)Instruction limit reached!
% 7.49/2.30 % (22559)------------------------------
% 7.49/2.30 % (22559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.30 % (22559)Termination reason: Unknown
% 7.49/2.30 % (22559)Termination phase: Property scanning
% 7.49/2.30
% 7.49/2.30 % (22559)Memory used [KB]: 2174
% 7.49/2.30 % (22559)Time elapsed: 0.027 s
% 7.49/2.30 % (22559)Instructions burned: 91 (million)
% 7.49/2.30 % (22559)------------------------------
% 7.49/2.30 % (22559)------------------------------
% 7.49/2.31 % (22533)Instruction limit reached!
% 7.49/2.31 % (22533)------------------------------
% 7.49/2.31 % (22533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.31 % (22533)Termination reason: Unknown
% 7.49/2.31 % (22533)Termination phase: Saturation
% 7.49/2.31
% 7.49/2.31 % (22533)Memory used [KB]: 8955
% 7.49/2.31 % (22533)Time elapsed: 0.343 s
% 7.49/2.31 % (22533)Instructions burned: 1088 (million)
% 7.49/2.31 % (22533)------------------------------
% 7.49/2.31 % (22533)------------------------------
% 7.49/2.31 % (22562)Instruction limit reached!
% 7.49/2.31 % (22562)------------------------------
% 7.49/2.31 % (22562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.31 % (22562)Termination reason: Unknown
% 7.49/2.31 % (22562)Termination phase: Property scanning
% 7.49/2.31
% 7.49/2.31 % (22562)Memory used [KB]: 1791
% 7.49/2.31 % (22562)Time elapsed: 0.011 s
% 7.49/2.31 % (22562)Instructions burned: 31 (million)
% 7.49/2.31 % (22562)------------------------------
% 7.49/2.31 % (22562)------------------------------
% 7.49/2.31 % (22563)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_22272 for (2992ds/297Mi)
% 7.49/2.31 % (22551)Instruction limit reached!
% 7.49/2.31 % (22551)------------------------------
% 7.49/2.31 % (22551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.31 % (22551)Termination reason: Unknown
% 7.49/2.31 % (22551)Termination phase: Saturation
% 7.49/2.31
% 7.49/2.31 % (22551)Memory used [KB]: 8827
% 7.49/2.31 % (22551)Time elapsed: 0.188 s
% 7.49/2.31 % (22551)Instructions burned: 614 (million)
% 7.49/2.31 % (22551)------------------------------
% 7.49/2.31 % (22551)------------------------------
% 7.49/2.32 % (22564)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_22272 for (2992ds/987Mi)
% 7.49/2.32 % (22558)Instruction limit reached!
% 7.49/2.32 % (22558)------------------------------
% 7.49/2.32 % (22558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.32 % (22558)Termination reason: Unknown
% 7.49/2.32 % (22558)Termination phase: Saturation
% 7.49/2.32
% 7.49/2.32 % (22558)Memory used [KB]: 7931
% 7.49/2.32 % (22558)Time elapsed: 0.078 s
% 7.49/2.32 % (22558)Instructions burned: 258 (million)
% 7.49/2.32 % (22558)------------------------------
% 7.49/2.32 % (22558)------------------------------
% 7.49/2.32 % (22565)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_22272 for (2992ds/182Mi)
% 7.49/2.32 % (22566)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_22272 for (2992ds/182Mi)
% 7.49/2.33 % (22567)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_22272 for (2992ds/154Mi)
% 7.49/2.35 % (22560)Instruction limit reached!
% 7.49/2.35 % (22560)------------------------------
% 7.49/2.35 % (22560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.35 % (22560)Termination reason: Unknown
% 7.49/2.35 % (22560)Termination phase: Saturation
% 7.49/2.35
% 7.49/2.35 % (22560)Memory used [KB]: 7164
% 7.49/2.35 % (22560)Time elapsed: 0.070 s
% 7.49/2.35 % (22560)Instructions burned: 233 (million)
% 7.49/2.35 % (22560)------------------------------
% 7.49/2.35 % (22560)------------------------------
% 7.49/2.36 % (22568)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_22272 for (2992ds/79Mi)
% 7.49/2.37 % (22567)Instruction limit reached!
% 7.49/2.37 % (22567)------------------------------
% 7.49/2.37 % (22567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.37 % (22567)Termination reason: Unknown
% 7.49/2.37 % (22567)Termination phase: Saturation
% 7.49/2.37
% 7.49/2.37 % (22567)Memory used [KB]: 2430
% 7.49/2.37 % (22567)Time elapsed: 0.043 s
% 7.49/2.37 % (22567)Instructions burned: 155 (million)
% 7.49/2.37 % (22567)------------------------------
% 7.49/2.37 % (22567)------------------------------
% 7.49/2.38 % (22565)Instruction limit reached!
% 7.49/2.38 % (22565)------------------------------
% 7.49/2.38 % (22565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.38 % (22565)Termination reason: Unknown
% 7.49/2.38 % (22565)Termination phase: Saturation
% 7.49/2.38
% 7.49/2.38 % (22565)Memory used [KB]: 7291
% 7.49/2.38 % (22565)Time elapsed: 0.060 s
% 7.49/2.38 % (22565)Instructions burned: 182 (million)
% 7.49/2.38 % (22565)------------------------------
% 7.49/2.38 % (22565)------------------------------
% 7.49/2.38 % (22566)Instruction limit reached!
% 7.49/2.38 % (22566)------------------------------
% 7.49/2.38 % (22566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.38 % (22566)Termination reason: Unknown
% 7.49/2.38 % (22566)Termination phase: Saturation
% 7.49/2.38
% 7.49/2.38 % (22566)Memory used [KB]: 7291
% 7.49/2.38 % (22566)Time elapsed: 0.058 s
% 7.49/2.38 % (22566)Instructions burned: 183 (million)
% 7.49/2.38 % (22566)------------------------------
% 7.49/2.38 % (22566)------------------------------
% 7.49/2.38 % (22569)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_22272 for (2991ds/216Mi)
% 7.49/2.38 % (22568)Instruction limit reached!
% 7.49/2.38 % (22568)------------------------------
% 7.49/2.38 % (22568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.38 % (22568)Termination reason: Unknown
% 7.49/2.38 % (22568)Termination phase: Property scanning
% 7.49/2.38
% 7.49/2.38 % (22568)Memory used [KB]: 2174
% 7.49/2.38 % (22568)Time elapsed: 0.024 s
% 7.49/2.38 % (22568)Instructions burned: 80 (million)
% 7.49/2.38 % (22568)------------------------------
% 7.49/2.38 % (22568)------------------------------
% 7.49/2.39 % (22570)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_22272 for (2991ds/114Mi)
% 7.49/2.39 % (22571)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_22272 for (2991ds/922Mi)
% 7.49/2.39 % (22572)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_22272 for (2991ds/182Mi)
% 7.49/2.39 % (22563)Instruction limit reached!
% 7.49/2.39 % (22563)------------------------------
% 7.49/2.39 % (22563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.49/2.39 % (22563)Termination reason: Unknown
% 7.49/2.39 % (22563)Termination phase: Saturation
% 7.49/2.39
% 7.49/2.39 % (22563)Memory used [KB]: 7419
% 7.49/2.39 % (22563)Time elapsed: 0.086 s
% 7.49/2.39 % (22563)Instructions burned: 297 (million)
% 7.49/2.39 % (22563)------------------------------
% 7.49/2.39 % (22563)------------------------------
% 8.24/2.40 % (22573)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_22272 for (2991ds/164Mi)
% 8.24/2.42 % (22570)Instruction limit reached!
% 8.24/2.42 % (22570)------------------------------
% 8.24/2.42 % (22570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.42 % (22570)Termination reason: Unknown
% 8.24/2.42 % (22570)Termination phase: Saturation
% 8.24/2.42
% 8.24/2.42 % (22570)Memory used [KB]: 6908
% 8.24/2.42 % (22570)Time elapsed: 0.037 s
% 8.24/2.42 % (22570)Instructions burned: 114 (million)
% 8.24/2.42 % (22570)------------------------------
% 8.24/2.42 % (22570)------------------------------
% 8.24/2.43 % (22574)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_22272 for (2991ds/50Mi)
% 8.24/2.44 % (22561)Instruction limit reached!
% 8.24/2.44 % (22561)------------------------------
% 8.24/2.44 % (22561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.44 % (22561)Termination reason: Unknown
% 8.24/2.44 % (22561)Termination phase: Saturation
% 8.24/2.44
% 8.24/2.44 % (22561)Memory used [KB]: 8187
% 8.24/2.44 % (22561)Time elapsed: 0.143 s
% 8.24/2.44 % (22561)Instructions burned: 461 (million)
% 8.24/2.44 % (22561)------------------------------
% 8.24/2.44 % (22561)------------------------------
% 8.24/2.44 % (22569)Instruction limit reached!
% 8.24/2.44 % (22569)------------------------------
% 8.24/2.44 % (22569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.44 % (22569)Termination reason: Unknown
% 8.24/2.44 % (22569)Termination phase: Saturation
% 8.24/2.44
% 8.24/2.44 % (22569)Memory used [KB]: 7291
% 8.24/2.44 % (22569)Time elapsed: 0.060 s
% 8.24/2.44 % (22569)Instructions burned: 218 (million)
% 8.24/2.44 % (22569)------------------------------
% 8.24/2.44 % (22569)------------------------------
% 8.24/2.44 % (22572)Instruction limit reached!
% 8.24/2.44 % (22572)------------------------------
% 8.24/2.44 % (22572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.44 % (22572)Termination reason: Unknown
% 8.24/2.44 % (22572)Termination phase: Saturation
% 8.24/2.44
% 8.24/2.44 % (22572)Memory used [KB]: 6908
% 8.24/2.44 % (22572)Time elapsed: 0.050 s
% 8.24/2.44 % (22572)Instructions burned: 185 (million)
% 8.24/2.44 % (22572)------------------------------
% 8.24/2.44 % (22572)------------------------------
% 8.24/2.45 % (22575)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_22272 for (2991ds/368Mi)
% 8.24/2.45 % (22576)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_22272 for (2991ds/1021Mi)
% 8.24/2.45 % (22577)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_22272 for (2991ds/267Mi)
% 8.24/2.45 % (22574)Instruction limit reached!
% 8.24/2.45 % (22574)------------------------------
% 8.24/2.45 % (22574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.45 % (22574)Termination reason: Unknown
% 8.24/2.45 % (22574)Termination phase: Property scanning
% 8.24/2.45
% 8.24/2.45 % (22574)Memory used [KB]: 2174
% 8.24/2.45 % (22574)Time elapsed: 0.017 s
% 8.24/2.45 % (22574)Instructions burned: 52 (million)
% 8.24/2.45 % (22574)------------------------------
% 8.24/2.45 % (22574)------------------------------
% 8.24/2.45 % (22573)Instruction limit reached!
% 8.24/2.45 % (22573)------------------------------
% 8.24/2.45 % (22573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.45 % (22573)Termination reason: Unknown
% 8.24/2.45 % (22573)Termination phase: Saturation
% 8.24/2.45
% 8.24/2.45 % (22573)Memory used [KB]: 2430
% 8.24/2.45 % (22573)Time elapsed: 0.046 s
% 8.24/2.45 % (22573)Instructions burned: 166 (million)
% 8.24/2.45 % (22573)------------------------------
% 8.24/2.45 % (22573)------------------------------
% 8.24/2.46 % (22578)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_22272 for (2991ds/204Mi)
% 8.24/2.46 % (22579)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_22272 for (2991ds/26Mi)
% 8.24/2.47 % (22579)Instruction limit reached!
% 8.24/2.47 % (22579)------------------------------
% 8.24/2.47 % (22579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.47 % (22579)Termination reason: Unknown
% 8.24/2.47 % (22579)Termination phase: shuffling
% 8.24/2.47
% 8.24/2.47 % (22579)Memory used [KB]: 1918
% 8.24/2.47 % (22579)Time elapsed: 0.009 s
% 8.24/2.47 % (22579)Instructions burned: 27 (million)
% 8.24/2.47 % (22579)------------------------------
% 8.24/2.47 % (22579)------------------------------
% 8.24/2.48 % (22580)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_22272 for (2990ds/53Mi)
% 8.24/2.49 % (22580)Instruction limit reached!
% 8.24/2.49 % (22580)------------------------------
% 8.24/2.49 % (22580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.24/2.49 % (22580)Termination reason: Unknown
% 8.24/2.49 % (22580)Termination phase: Property scanning
% 8.24/2.49
% 8.24/2.49 % (22580)Memory used [KB]: 2174
% 8.24/2.49 % (22580)Time elapsed: 0.016 s
% 8.24/2.49 % (22580)Instructions burned: 57 (million)
% 8.24/2.49 % (22580)------------------------------
% 8.24/2.49 % (22580)------------------------------
% 8.68/2.50 % (22581)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_22272 for (2990ds/4436Mi)
% 8.68/2.52 % (22578)Instruction limit reached!
% 8.68/2.52 % (22578)------------------------------
% 8.68/2.52 % (22578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.68/2.52 % (22578)Termination reason: Unknown
% 8.68/2.52 % (22578)Termination phase: Saturation
% 8.68/2.52
% 8.68/2.52 % (22578)Memory used [KB]: 7291
% 8.68/2.52 % (22578)Time elapsed: 0.064 s
% 8.68/2.52 % (22578)Instructions burned: 204 (million)
% 8.68/2.52 % (22578)------------------------------
% 8.68/2.52 % (22578)------------------------------
% 8.68/2.53 % (22577)Instruction limit reached!
% 8.68/2.53 % (22577)------------------------------
% 8.68/2.53 % (22577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.68/2.53 % (22577)Termination reason: Unknown
% 8.68/2.53 % (22577)Termination phase: Saturation
% 8.68/2.53
% 8.68/2.53 % (22577)Memory used [KB]: 7419
% 8.68/2.53 % (22577)Time elapsed: 0.080 s
% 8.68/2.53 % (22577)Instructions burned: 268 (million)
% 8.68/2.53 % (22577)------------------------------
% 8.68/2.53 % (22577)------------------------------
% 8.68/2.53 % (22582)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_22272 for (2990ds/1539Mi)
% 8.68/2.54 % (22583)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_22272 for (2990ds/408Mi)
% 8.68/2.56 % (22575)Instruction limit reached!
% 8.68/2.56 % (22575)------------------------------
% 8.68/2.56 % (22575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.68/2.56 % (22575)Termination reason: Unknown
% 8.68/2.56 % (22575)Termination phase: Saturation
% 8.68/2.56
% 8.68/2.56 % (22575)Memory used [KB]: 8059
% 8.68/2.56 % (22575)Time elapsed: 0.115 s
% 8.68/2.56 % (22575)Instructions burned: 370 (million)
% 8.68/2.56 % (22575)------------------------------
% 8.68/2.56 % (22575)------------------------------
% 8.68/2.57 % (22584)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_22272 for (2990ds/5205Mi)
% 8.96/2.61 % (22564)Instruction limit reached!
% 8.96/2.61 % (22564)------------------------------
% 8.96/2.61 % (22564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.61 % (22564)Termination reason: Unknown
% 8.96/2.61 % (22564)Termination phase: Saturation
% 8.96/2.61
% 8.96/2.61 % (22564)Memory used [KB]: 8315
% 8.96/2.61 % (22564)Time elapsed: 0.297 s
% 8.96/2.61 % (22564)Instructions burned: 988 (million)
% 8.96/2.61 % (22564)------------------------------
% 8.96/2.61 % (22564)------------------------------
% 8.96/2.62 % (22585)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_22272 for (2989ds/1913Mi)
% 8.96/2.66 % (22583)Instruction limit reached!
% 8.96/2.66 % (22583)------------------------------
% 8.96/2.66 % (22583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.66 % (22583)Termination reason: Unknown
% 8.96/2.66 % (22583)Termination phase: Saturation
% 8.96/2.66
% 8.96/2.66 % (22583)Memory used [KB]: 8315
% 8.96/2.66 % (22583)Time elapsed: 0.125 s
% 8.96/2.66 % (22583)Instructions burned: 409 (million)
% 8.96/2.66 % (22583)------------------------------
% 8.96/2.66 % (22583)------------------------------
% 8.96/2.67 % (22586)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_22272 for (2989ds/4350Mi)
% 8.96/2.68 % (22571)Instruction limit reached!
% 8.96/2.68 % (22571)------------------------------
% 8.96/2.68 % (22571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.68 % (22571)Termination reason: Unknown
% 8.96/2.68 % (22571)Termination phase: Saturation
% 8.96/2.68
% 8.96/2.68 % (22571)Memory used [KB]: 8571
% 8.96/2.68 % (22571)Time elapsed: 0.290 s
% 8.96/2.68 % (22571)Instructions burned: 924 (million)
% 8.96/2.68 % (22571)------------------------------
% 8.96/2.68 % (22571)------------------------------
% 8.96/2.69 % (22587)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_22272 for (2988ds/68Mi)
% 9.70/2.71 % (22587)Instruction limit reached!
% 9.70/2.71 % (22587)------------------------------
% 9.70/2.71 % (22587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.70/2.71 % (22587)Termination reason: Unknown
% 9.70/2.71 % (22587)Termination phase: Property scanning
% 9.70/2.71
% 9.70/2.71 % (22587)Memory used [KB]: 2046
% 9.70/2.71 % (22587)Time elapsed: 0.021 s
% 9.70/2.71 % (22587)Instructions burned: 69 (million)
% 9.70/2.71 % (22587)------------------------------
% 9.70/2.71 % (22587)------------------------------
% 9.70/2.72 % (22588)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_22272 for (2988ds/358Mi)
% 9.70/2.77 % (22576)Instruction limit reached!
% 9.70/2.77 % (22576)------------------------------
% 9.70/2.77 % (22576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.70/2.77 % (22576)Termination reason: Unknown
% 9.70/2.77 % (22576)Termination phase: Saturation
% 9.70/2.77
% 9.70/2.77 % (22576)Memory used [KB]: 8315
% 9.70/2.77 % (22576)Time elapsed: 0.322 s
% 9.70/2.77 % (22576)Instructions burned: 1023 (million)
% 9.70/2.77 % (22576)------------------------------
% 9.70/2.77 % (22576)------------------------------
% 9.70/2.78 % (22589)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_22272 for (2987ds/31Mi)
% 9.70/2.79 % (22589)Instruction limit reached!
% 9.70/2.79 % (22589)------------------------------
% 9.70/2.79 % (22589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.70/2.79 % (22589)Termination reason: Unknown
% 9.70/2.79 % (22589)Termination phase: Preprocessing 1
% 9.70/2.79
% 9.70/2.79 % (22589)Memory used [KB]: 1791
% 9.70/2.79 % (22589)Time elapsed: 0.011 s
% 9.70/2.79 % (22589)Instructions burned: 34 (million)
% 9.70/2.79 % (22589)------------------------------
% 9.70/2.79 % (22589)------------------------------
% 10.09/2.80 % (22590)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_22272 for (2987ds/279Mi)
% 10.09/2.83 % (22588)Instruction limit reached!
% 10.09/2.83 % (22588)------------------------------
% 10.09/2.83 % (22588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.83 % (22588)Termination reason: Unknown
% 10.09/2.83 % (22588)Termination phase: Saturation
% 10.09/2.83
% 10.09/2.83 % (22588)Memory used [KB]: 7547
% 10.09/2.83 % (22588)Time elapsed: 0.135 s
% 10.09/2.83 % (22588)Instructions burned: 358 (million)
% 10.09/2.83 % (22588)------------------------------
% 10.09/2.83 % (22588)------------------------------
% 10.09/2.84 % (22591)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_22272 for (2987ds/258Mi)
% 10.09/2.84 % (22590)Refutation not found, incomplete strategy
% 10.09/2.84 % (22590)------------------------------
% 10.09/2.84 % (22590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.84 % (22590)Termination reason: Refutation not found, incomplete strategy
% 10.09/2.84
% 10.09/2.84
% 10.09/2.84 % (22590)Memory used [KB]: 7036
% 10.09/2.84 % (22590)Time elapsed: 0.045 s
% 10.09/2.84 % (22590)Instructions burned: 160 (million)
% 10.09/2.84 % (22590)------------------------------
% 10.09/2.84 % (22590)------------------------------
% 10.09/2.85 % (22592)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_22272 for (2987ds/26Mi)
% 10.09/2.86 % (22592)Instruction limit reached!
% 10.09/2.86 % (22592)------------------------------
% 10.09/2.86 % (22592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.09/2.86 % (22592)Termination reason: Unknown
% 10.09/2.86 % (22592)Termination phase: shuffling
% 10.09/2.86
% 10.09/2.86 % (22592)Memory used [KB]: 1918
% 10.09/2.86 % (22592)Time elapsed: 0.008 s
% 10.09/2.86 % (22592)Instructions burned: 26 (million)
% 10.09/2.86 % (22592)------------------------------
% 10.09/2.86 % (22592)------------------------------
% 10.09/2.87 % (22593)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_22272 for (2986ds/995Mi)
% 10.29/2.91 % (22591)Instruction limit reached!
% 10.29/2.91 % (22591)------------------------------
% 10.29/2.91 % (22591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.29/2.91 % (22591)Termination reason: Unknown
% 10.29/2.91 % (22591)Termination phase: Saturation
% 10.29/2.91
% 10.29/2.91 % (22591)Memory used [KB]: 7547
% 10.29/2.91 % (22591)Time elapsed: 0.078 s
% 10.29/2.91 % (22591)Instructions burned: 259 (million)
% 10.29/2.91 % (22591)------------------------------
% 10.29/2.91 % (22591)------------------------------
% 10.29/2.92 % (22594)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_22272 for (2986ds/373Mi)
% 10.29/3.02 % (22582)Instruction limit reached!
% 10.29/3.02 % (22582)------------------------------
% 10.29/3.02 % (22582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.29/3.02 % (22582)Termination reason: Unknown
% 10.29/3.02 % (22582)Termination phase: Saturation
% 10.29/3.02
% 10.29/3.02 % (22582)Memory used [KB]: 9466
% 10.29/3.02 % (22582)Time elapsed: 0.491 s
% 10.29/3.02 % (22582)Instructions burned: 1539 (million)
% 10.29/3.02 % (22582)------------------------------
% 10.29/3.02 % (22582)------------------------------
% 12.36/3.04 % (22594)Instruction limit reached!
% 12.36/3.04 % (22594)------------------------------
% 12.36/3.04 % (22594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.36/3.04 % (22594)Termination reason: Unknown
% 12.36/3.04 % (22594)Termination phase: Saturation
% 12.36/3.04
% 12.36/3.04 % (22594)Memory used [KB]: 7931
% 12.36/3.04 % (22594)Time elapsed: 0.116 s
% 12.36/3.04 % (22594)Instructions burned: 373 (million)
% 12.36/3.04 % (22594)------------------------------
% 12.36/3.04 % (22594)------------------------------
% 12.36/3.04 % (22595)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_22272 for (2985ds/253Mi)
% 12.36/3.05 % (22596)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_22272 for (2985ds/832Mi)
% 13.39/3.14 % (22585)Instruction limit reached!
% 13.39/3.14 % (22585)------------------------------
% 13.39/3.14 % (22585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.39/3.14 % (22585)Termination reason: Unknown
% 13.39/3.14 % (22585)Termination phase: Saturation
% 13.39/3.14
% 13.39/3.14 % (22585)Memory used [KB]: 3582
% 13.39/3.14 % (22585)Time elapsed: 0.545 s
% 13.39/3.14 % (22585)Instructions burned: 1915 (million)
% 13.39/3.14 % (22585)------------------------------
% 13.39/3.14 % (22585)------------------------------
% 13.39/3.15 % (22597)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_22272 for (2984ds/668Mi)
% 13.39/3.15 % (22595)Instruction limit reached!
% 13.39/3.15 % (22595)------------------------------
% 13.39/3.15 % (22595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.39/3.15 % (22595)Termination reason: Unknown
% 13.39/3.15 % (22595)Termination phase: Saturation
% 13.39/3.15
% 13.39/3.15 % (22595)Memory used [KB]: 7675
% 13.39/3.15 % (22595)Time elapsed: 0.113 s
% 13.39/3.15 % (22595)Instructions burned: 253 (million)
% 13.39/3.15 % (22595)------------------------------
% 13.39/3.15 % (22595)------------------------------
% 13.39/3.16 % (22593)Instruction limit reached!
% 13.39/3.16 % (22593)------------------------------
% 13.39/3.16 % (22593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.39/3.16 % (22593)Termination reason: Unknown
% 13.39/3.16 % (22593)Termination phase: Saturation
% 13.39/3.16
% 13.39/3.16 % (22593)Memory used [KB]: 9466
% 13.39/3.16 % (22593)Time elapsed: 0.293 s
% 13.39/3.16 % (22593)Instructions burned: 996 (million)
% 13.39/3.16 % (22593)------------------------------
% 13.39/3.16 % (22593)------------------------------
% 13.39/3.17 % (22598)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_22272 for (2984ds/40Mi)
% 13.39/3.17 % (22599)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_22272 for (2983ds/294Mi)
% 13.39/3.18 % (22598)Instruction limit reached!
% 13.39/3.18 % (22598)------------------------------
% 13.39/3.18 % (22598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.39/3.18 % (22598)Termination reason: Unknown
% 13.39/3.18 % (22598)Termination phase: shuffling
% 13.39/3.18
% 13.39/3.18 % (22598)Memory used [KB]: 2174
% 13.39/3.18 % (22598)Time elapsed: 0.014 s
% 13.39/3.18 % (22598)Instructions burned: 41 (million)
% 13.39/3.18 % (22598)------------------------------
% 13.39/3.18 % (22598)------------------------------
% 13.39/3.19 % (22600)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_22272 for (2983ds/187Mi)
% 13.84/3.20 % (22599)Refutation not found, incomplete strategy
% 13.84/3.20 % (22599)------------------------------
% 13.84/3.20 % (22599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.84/3.20 % (22599)Termination reason: Refutation not found, incomplete strategy
% 13.84/3.20
% 13.84/3.20
% 13.84/3.20 % (22599)Memory used [KB]: 6908
% 13.84/3.20 % (22599)Time elapsed: 0.032 s
% 13.84/3.20 % (22599)Instructions burned: 116 (million)
% 13.84/3.20 % (22599)------------------------------
% 13.84/3.20 % (22599)------------------------------
% 13.84/3.21 % (22601)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_22272 for (2983ds/371Mi)
% 13.84/3.25 % (22600)Instruction limit reached!
% 13.84/3.25 % (22600)------------------------------
% 13.84/3.25 % (22600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.84/3.25 % (22600)Termination reason: Unknown
% 13.84/3.25 % (22600)Termination phase: Saturation
% 13.84/3.25
% 13.84/3.25 % (22600)Memory used [KB]: 7419
% 13.84/3.25 % (22600)Time elapsed: 0.063 s
% 13.84/3.25 % (22600)Instructions burned: 189 (million)
% 13.84/3.25 % (22600)------------------------------
% 13.84/3.25 % (22600)------------------------------
% 13.84/3.26 % (22602)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_22272 for (2983ds/1827Mi)
% 13.84/3.30 % (22596)Instruction limit reached!
% 13.84/3.30 % (22596)------------------------------
% 13.84/3.30 % (22596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.84/3.30 % (22596)Termination reason: Unknown
% 13.84/3.30 % (22596)Termination phase: Saturation
% 13.84/3.30
% 13.84/3.30 % (22596)Memory used [KB]: 8443
% 13.84/3.30 % (22596)Time elapsed: 0.248 s
% 13.84/3.30 % (22596)Instructions burned: 833 (million)
% 13.84/3.30 % (22596)------------------------------
% 13.84/3.30 % (22596)------------------------------
% 14.51/3.31 % (22603)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_22272 for (2982ds/70Mi)
% 14.51/3.32 % (22603)Instruction limit reached!
% 14.51/3.32 % (22603)------------------------------
% 14.51/3.32 % (22603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.51/3.32 % (22603)Termination reason: Unknown
% 14.51/3.32 % (22603)Termination phase: Preprocessing 1
% 14.51/3.32
% 14.51/3.32 % (22603)Memory used [KB]: 2174
% 14.51/3.32 % (22603)Time elapsed: 0.020 s
% 14.51/3.32 % (22603)Instructions burned: 70 (million)
% 14.51/3.32 % (22603)------------------------------
% 14.51/3.32 % (22603)------------------------------
% 14.51/3.33 % (22601)Instruction limit reached!
% 14.51/3.33 % (22601)------------------------------
% 14.51/3.33 % (22601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.51/3.33 % (22601)Termination reason: Unknown
% 14.51/3.33 % (22601)Termination phase: Saturation
% 14.51/3.33
% 14.51/3.33 % (22601)Memory used [KB]: 7675
% 14.51/3.33 % (22601)Time elapsed: 0.120 s
% 14.51/3.33 % (22601)Instructions burned: 371 (million)
% 14.51/3.33 % (22601)------------------------------
% 14.51/3.33 % (22601)------------------------------
% 14.51/3.33 % (22604)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_22272 for (2982ds/316Mi)
% 14.51/3.34 % (22605)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_22272 for (2982ds/932Mi)
% 14.51/3.35 % (22597)Instruction limit reached!
% 14.51/3.35 % (22597)------------------------------
% 14.51/3.35 % (22597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.51/3.35 % (22597)Termination reason: Unknown
% 14.51/3.35 % (22597)Termination phase: Saturation
% 14.51/3.35
% 14.51/3.35 % (22597)Memory used [KB]: 13688
% 14.51/3.35 % (22597)Time elapsed: 0.197 s
% 14.51/3.35 % (22597)Instructions burned: 670 (million)
% 14.51/3.35 % (22597)------------------------------
% 14.51/3.35 % (22597)------------------------------
% 14.51/3.36 % (22606)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_22272 for (2982ds/4714Mi)
% 14.51/3.39 % (22604)Refutation not found, incomplete strategy
% 14.51/3.39 % (22604)------------------------------
% 14.51/3.39 % (22604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.51/3.39 % (22604)Termination reason: Refutation not found, incomplete strategy
% 14.51/3.39
% 14.51/3.39
% 14.51/3.39 % (22604)Memory used [KB]: 7547
% 14.51/3.39 % (22604)Time elapsed: 0.059 s
% 14.51/3.39 % (22604)Instructions burned: 212 (million)
% 14.51/3.39 % (22604)------------------------------
% 14.51/3.39 % (22604)------------------------------
% 15.25/3.40 % (22607)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_22272 for (2981ds/8250Mi)
% 15.25/3.43 % (22606)Refutation not found, incomplete strategy
% 15.25/3.43 % (22606)------------------------------
% 15.25/3.43 % (22606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.25/3.43 % (22606)Termination reason: Refutation not found, incomplete strategy
% 15.25/3.43
% 15.25/3.43
% 15.25/3.43 % (22606)Memory used [KB]: 7675
% 15.25/3.43 % (22606)Time elapsed: 0.067 s
% 15.25/3.43 % (22606)Instructions burned: 241 (million)
% 15.25/3.43 % (22606)------------------------------
% 15.25/3.43 % (22606)------------------------------
% 15.25/3.44 % (22608)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_22272 for (2981ds/770Mi)
% 15.92/3.62 % (22605)Instruction limit reached!
% 15.92/3.62 % (22605)------------------------------
% 15.92/3.62 % (22605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.92/3.62 % (22605)Termination reason: Unknown
% 15.92/3.62 % (22605)Termination phase: Saturation
% 15.92/3.62
% 15.92/3.62 % (22605)Memory used [KB]: 9338
% 15.92/3.62 % (22605)Time elapsed: 0.276 s
% 15.92/3.62 % (22605)Instructions burned: 934 (million)
% 15.92/3.62 % (22605)------------------------------
% 15.92/3.62 % (22605)------------------------------
% 15.92/3.63 % (22609)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_22272 for (2979ds/794Mi)
% 15.92/3.67 % (22608)Instruction limit reached!
% 15.92/3.67 % (22608)------------------------------
% 15.92/3.67 % (22608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.92/3.67 % (22608)Termination reason: Unknown
% 15.92/3.67 % (22608)Termination phase: Saturation
% 15.92/3.67
% 15.92/3.67 % (22608)Memory used [KB]: 8059
% 15.92/3.67 % (22608)Time elapsed: 0.236 s
% 15.92/3.67 % (22608)Instructions burned: 773 (million)
% 15.92/3.67 % (22608)------------------------------
% 15.92/3.67 % (22608)------------------------------
% 15.92/3.68 % (22610)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_22272 for (2978ds/464Mi)
% 17.04/3.83 % (22610)Instruction limit reached!
% 17.04/3.83 % (22610)------------------------------
% 17.04/3.83 % (22610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.04/3.83 % (22610)Termination reason: Unknown
% 17.04/3.83 % (22610)Termination phase: Saturation
% 17.04/3.83
% 17.04/3.83 % (22610)Memory used [KB]: 7547
% 17.04/3.83 % (22610)Time elapsed: 0.147 s
% 17.04/3.83 % (22610)Instructions burned: 466 (million)
% 17.04/3.83 % (22610)------------------------------
% 17.04/3.83 % (22610)------------------------------
% 17.04/3.84 % (22611)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_22272 for (2977ds/1376Mi)
% 17.04/3.85 % (22602)Instruction limit reached!
% 17.04/3.85 % (22602)------------------------------
% 17.04/3.85 % (22602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.04/3.85 % (22602)Termination reason: Unknown
% 17.04/3.85 % (22602)Termination phase: Saturation
% 17.04/3.85
% 17.04/3.85 % (22602)Memory used [KB]: 9978
% 17.04/3.85 % (22602)Time elapsed: 0.596 s
% 17.04/3.85 % (22602)Instructions burned: 1829 (million)
% 17.04/3.85 % (22602)------------------------------
% 17.04/3.85 % (22602)------------------------------
% 17.04/3.86 % (22612)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_22272 for (2977ds/906Mi)
% 17.04/3.88 % (22581)Instruction limit reached!
% 17.04/3.88 % (22581)------------------------------
% 17.04/3.88 % (22581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.04/3.88 % (22581)Termination reason: Unknown
% 17.04/3.88 % (22581)Termination phase: Saturation
% 17.04/3.88
% 17.04/3.88 % (22581)Memory used [KB]: 13560
% 17.04/3.88 % (22581)Time elapsed: 1.379 s
% 17.04/3.88 % (22581)Instructions burned: 4437 (million)
% 17.04/3.88 % (22581)------------------------------
% 17.04/3.88 % (22581)------------------------------
% 17.04/3.88 % (22609)Instruction limit reached!
% 17.04/3.88 % (22609)------------------------------
% 17.04/3.88 % (22609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.04/3.88 % (22609)Termination reason: Unknown
% 17.04/3.88 % (22609)Termination phase: Saturation
% 17.04/3.88
% 17.04/3.88 % (22609)Memory used [KB]: 5756
% 17.04/3.88 % (22609)Time elapsed: 0.255 s
% 17.04/3.88 % (22609)Instructions burned: 794 (million)
% 17.04/3.88 % (22609)------------------------------
% 17.04/3.88 % (22609)------------------------------
% 17.04/3.89 % (22613)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_22272 for (2976ds/434Mi)
% 17.04/3.89 % (22614)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_22272 for (2976ds/865Mi)
% 18.36/3.96 % (22586)Instruction limit reached!
% 18.36/3.96 % (22586)------------------------------
% 18.36/3.96 % (22586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.36/3.96 % (22586)Termination reason: Unknown
% 18.36/3.96 % (22586)Termination phase: Saturation
% 18.36/3.96
% 18.36/3.96 % (22586)Memory used [KB]: 12537
% 18.36/3.96 % (22586)Time elapsed: 1.310 s
% 18.36/3.96 % (22586)Instructions burned: 4352 (million)
% 18.36/3.96 % (22586)------------------------------
% 18.36/3.96 % (22586)------------------------------
% 18.36/3.97 % (22615)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_22272 for (2976ds/593Mi)
% 19.80/4.02 % (22613)Instruction limit reached!
% 19.80/4.02 % (22613)------------------------------
% 19.80/4.02 % (22613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.80/4.02 % (22613)Termination reason: Unknown
% 19.80/4.02 % (22613)Termination phase: Saturation
% 19.80/4.02
% 19.80/4.02 % (22613)Memory used [KB]: 7803
% 19.80/4.02 % (22613)Time elapsed: 0.130 s
% 19.80/4.02 % (22613)Instructions burned: 437 (million)
% 19.80/4.02 % (22613)------------------------------
% 19.80/4.02 % (22613)------------------------------
% 19.80/4.03 % (22616)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_22272 for (2975ds/443Mi)
% 20.42/4.14 % (22615)Instruction limit reached!
% 20.42/4.14 % (22615)------------------------------
% 20.42/4.14 % (22615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.42/4.14 % (22615)Termination reason: Unknown
% 20.42/4.14 % (22615)Termination phase: Saturation
% 20.42/4.14
% 20.42/4.14 % (22615)Memory used [KB]: 9210
% 20.42/4.14 % (22615)Time elapsed: 0.195 s
% 20.42/4.14 % (22615)Instructions burned: 594 (million)
% 20.42/4.14 % (22615)------------------------------
% 20.42/4.14 % (22615)------------------------------
% 20.42/4.14 % (22614)Instruction limit reached!
% 20.42/4.14 % (22614)------------------------------
% 20.42/4.14 % (22614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.42/4.14 % (22614)Termination reason: Unknown
% 20.42/4.14 % (22614)Termination phase: Saturation
% 20.42/4.14
% 20.42/4.14 % (22614)Memory used [KB]: 9083
% 20.42/4.14 % (22614)Time elapsed: 0.254 s
% 20.42/4.14 % (22614)Instructions burned: 867 (million)
% 20.42/4.14 % (22614)------------------------------
% 20.42/4.14 % (22614)------------------------------
% 20.42/4.15 % (22584)Instruction limit reached!
% 20.42/4.15 % (22584)------------------------------
% 20.42/4.15 % (22584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.42/4.15 % (22584)Termination reason: Unknown
% 20.42/4.15 % (22584)Termination phase: Saturation
% 20.42/4.15
% 20.42/4.15 % (22584)Memory used [KB]: 13688
% 20.42/4.15 % (22584)Time elapsed: 1.601 s
% 20.42/4.15 % (22584)Instructions burned: 5205 (million)
% 20.42/4.15 % (22584)------------------------------
% 20.42/4.15 % (22584)------------------------------
% 20.42/4.15 % (22617)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_22272 for (2974ds/594Mi)
% 20.42/4.15 % (22618)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_22272 for (2974ds/327Mi)
% 20.42/4.16 % (22619)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_22272 for (2974ds/5411Mi)
% 20.42/4.17 % (22616)Instruction limit reached!
% 20.42/4.17 % (22616)------------------------------
% 20.42/4.17 % (22616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.42/4.17 % (22616)Termination reason: Unknown
% 20.42/4.17 % (22616)Termination phase: Saturation
% 20.42/4.17
% 20.42/4.17 % (22616)Memory used [KB]: 7547
% 20.42/4.17 % (22616)Time elapsed: 0.140 s
% 20.42/4.17 % (22616)Instructions burned: 444 (million)
% 20.42/4.17 % (22616)------------------------------
% 20.42/4.17 % (22616)------------------------------
% 20.42/4.18 % (22620)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_22272 for (2973ds/1762Mi)
% 20.93/4.25 % (22612)Instruction limit reached!
% 20.93/4.25 % (22612)------------------------------
% 20.93/4.25 % (22612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.93/4.25 % (22612)Termination reason: Unknown
% 20.93/4.25 % (22612)Termination phase: Saturation
% 20.93/4.25
% 20.93/4.25 % (22612)Memory used [KB]: 12281
% 20.93/4.25 % (22612)Time elapsed: 0.390 s
% 20.93/4.25 % (22612)Instructions burned: 908 (million)
% 20.93/4.25 % (22612)------------------------------
% 20.93/4.25 % (22612)------------------------------
% 20.93/4.26 % (22618)Instruction limit reached!
% 20.93/4.26 % (22618)------------------------------
% 20.93/4.26 % (22618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.93/4.26 % (22618)Termination reason: Unknown
% 20.93/4.26 % (22618)Termination phase: Saturation
% 20.93/4.26
% 20.93/4.26 % (22618)Memory used [KB]: 7931
% 20.93/4.26 % (22618)Time elapsed: 0.107 s
% 20.93/4.26 % (22618)Instructions burned: 328 (million)
% 20.93/4.26 % (22618)------------------------------
% 20.93/4.26 % (22618)------------------------------
% 20.93/4.26 % (22611)Instruction limit reached!
% 20.93/4.26 % (22611)------------------------------
% 20.93/4.26 % (22611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.93/4.26 % (22611)Termination reason: Unknown
% 20.93/4.26 % (22611)Termination phase: Saturation
% 20.93/4.26
% 20.93/4.26 % (22611)Memory used [KB]: 10362
% 20.93/4.26 % (22611)Time elapsed: 0.428 s
% 20.93/4.26 % (22611)Instructions burned: 1378 (million)
% 20.93/4.26 % (22611)------------------------------
% 20.93/4.26 % (22611)------------------------------
% 20.93/4.26 % (22621)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_22272 for (2973ds/96Mi)
% 20.93/4.27 % (22622)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_22272 for (2972ds/503Mi)
% 20.93/4.27 % (22623)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_22272 for (2972ds/90Mi)
% 20.93/4.29 % (22621)Instruction limit reached!
% 20.93/4.29 % (22621)------------------------------
% 20.93/4.29 % (22621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.93/4.29 % (22621)Termination reason: Unknown
% 20.93/4.29 % (22621)Termination phase: Property scanning
% 20.93/4.29
% 20.93/4.29 % (22621)Memory used [KB]: 2302
% 20.93/4.29 % (22621)Time elapsed: 0.030 s
% 20.93/4.29 % (22621)Instructions burned: 98 (million)
% 20.93/4.29 % (22621)------------------------------
% 20.93/4.29 % (22621)------------------------------
% 21.34/4.30 % (22623)Instruction limit reached!
% 21.34/4.30 % (22623)------------------------------
% 21.34/4.30 % (22623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.34/4.30 % (22623)Termination reason: Unknown
% 21.34/4.30 % (22623)Termination phase: Property scanning
% 21.34/4.30
% 21.34/4.30 % (22623)Memory used [KB]: 2174
% 21.34/4.30 % (22623)Time elapsed: 0.027 s
% 21.34/4.30 % (22623)Instructions burned: 92 (million)
% 21.34/4.30 % (22623)------------------------------
% 21.34/4.30 % (22623)------------------------------
% 21.34/4.30 % (22622)Refutation not found, incomplete strategy
% 21.34/4.30 % (22622)------------------------------
% 21.34/4.30 % (22622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.34/4.30 % (22622)Termination reason: Refutation not found, incomplete strategy
% 21.34/4.30
% 21.34/4.30
% 21.34/4.30 % (22622)Memory used [KB]: 7291
% 21.34/4.30 % (22622)Time elapsed: 0.035 s
% 21.34/4.30 % (22622)Instructions burned: 111 (million)
% 21.34/4.30 % (22622)------------------------------
% 21.34/4.30 % (22622)------------------------------
% 21.34/4.30 % (22624)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_22272 for (2972ds/593Mi)
% 21.34/4.31 % (22625)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_22272 for (2972ds/1512Mi)
% 21.34/4.32 % (22626)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_22272 for (2972ds/569Mi)
% 21.34/4.34 % (22617)Instruction limit reached!
% 21.34/4.34 % (22617)------------------------------
% 21.34/4.34 % (22617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.34/4.34 % (22617)Termination reason: Unknown
% 21.34/4.34 % (22617)Termination phase: Saturation
% 21.34/4.34
% 21.34/4.34 % (22617)Memory used [KB]: 7547
% 21.34/4.34 % (22617)Time elapsed: 0.189 s
% 21.34/4.34 % (22617)Instructions burned: 594 (million)
% 21.34/4.34 % (22617)------------------------------
% 21.34/4.34 % (22617)------------------------------
% 21.34/4.35 % (22627)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_22272 for (2972ds/501Mi)
% 21.80/4.50 % (22627)Instruction limit reached!
% 21.80/4.50 % (22627)------------------------------
% 21.80/4.50 % (22627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.80/4.50 % (22627)Termination reason: Unknown
% 21.80/4.50 % (22627)Termination phase: Saturation
% 21.80/4.50
% 21.80/4.50 % (22627)Memory used [KB]: 8571
% 21.80/4.50 % (22627)Time elapsed: 0.150 s
% 21.80/4.50 % (22627)Instructions burned: 501 (million)
% 21.80/4.50 % (22627)------------------------------
% 21.80/4.50 % (22627)------------------------------
% 21.80/4.50 % (22624)Instruction limit reached!
% 21.80/4.50 % (22624)------------------------------
% 21.80/4.50 % (22624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.80/4.50 % (22624)Termination reason: Unknown
% 21.80/4.50 % (22624)Termination phase: Saturation
% 21.80/4.50
% 21.80/4.50 % (22624)Memory used [KB]: 8443
% 21.80/4.50 % (22624)Time elapsed: 0.204 s
% 21.80/4.50 % (22624)Instructions burned: 595 (million)
% 21.80/4.50 % (22624)------------------------------
% 21.80/4.50 % (22624)------------------------------
% 21.80/4.51 % (22628)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_22272 for (2970ds/562Mi)
% 21.80/4.51 % (22626)Instruction limit reached!
% 21.80/4.51 % (22626)------------------------------
% 21.80/4.51 % (22626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.80/4.51 % (22626)Termination reason: Unknown
% 21.80/4.51 % (22626)Termination phase: Saturation
% 21.80/4.51
% 21.80/4.51 % (22626)Memory used [KB]: 8699
% 21.80/4.51 % (22626)Time elapsed: 0.191 s
% 21.80/4.51 % (22626)Instructions burned: 571 (million)
% 21.80/4.51 % (22626)------------------------------
% 21.80/4.51 % (22626)------------------------------
% 21.80/4.52 % (22629)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_22272 for (2970ds/406Mi)
% 21.80/4.52 % (22630)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_22272 for (2970ds/582Mi)
% 22.47/4.65 % (22629)Instruction limit reached!
% 22.47/4.65 % (22629)------------------------------
% 22.47/4.65 % (22629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.47/4.65 % (22629)Termination reason: Unknown
% 22.47/4.65 % (22629)Termination phase: Saturation
% 22.47/4.65
% 22.47/4.65 % (22629)Memory used [KB]: 8059
% 22.47/4.65 % (22629)Time elapsed: 0.131 s
% 22.47/4.65 % (22629)Instructions burned: 406 (million)
% 22.47/4.65 % (22629)------------------------------
% 22.47/4.65 % (22629)------------------------------
% 22.47/4.65 % (22631)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_22272 for (2969ds/456Mi)
% 22.47/4.68 % (22628)Instruction limit reached!
% 22.47/4.68 % (22628)------------------------------
% 22.47/4.68 % (22628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.47/4.68 % (22628)Termination reason: Unknown
% 22.47/4.68 % (22628)Termination phase: Saturation
% 22.47/4.68
% 22.47/4.68 % (22628)Memory used [KB]: 8059
% 22.47/4.68 % (22628)Time elapsed: 0.170 s
% 22.47/4.68 % (22628)Instructions burned: 563 (million)
% 22.47/4.68 % (22628)------------------------------
% 22.47/4.68 % (22628)------------------------------
% 22.47/4.69 % (22632)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_22272 for (2968ds/393Mi)
% 22.91/4.70 % (22620)Instruction limit reached!
% 22.91/4.70 % (22620)------------------------------
% 22.91/4.70 % (22620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.91/4.70 % (22620)Termination reason: Unknown
% 22.91/4.70 % (22620)Termination phase: Saturation
% 22.91/4.70
% 22.91/4.70 % (22620)Memory used [KB]: 8827
% 22.91/4.70 % (22620)Time elapsed: 0.524 s
% 22.91/4.70 % (22620)Instructions burned: 1762 (million)
% 22.91/4.70 % (22620)------------------------------
% 22.91/4.70 % (22620)------------------------------
% 22.91/4.71 % (22630)Instruction limit reached!
% 22.91/4.71 % (22630)------------------------------
% 22.91/4.71 % (22630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.91/4.71 % (22630)Termination reason: Unknown
% 22.91/4.71 % (22630)Termination phase: Saturation
% 22.91/4.71
% 22.91/4.71 % (22630)Memory used [KB]: 7419
% 22.91/4.71 % (22630)Time elapsed: 0.188 s
% 22.91/4.71 % (22630)Instructions burned: 585 (million)
% 22.91/4.71 % (22630)------------------------------
% 22.91/4.71 % (22630)------------------------------
% 22.91/4.71 % (22633)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_22272 for (2968ds/1335Mi)
% 22.91/4.71 % (22634)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_22272 for (2968ds/3373Mi)
% 22.91/4.77 % (22625)Instruction limit reached!
% 22.91/4.77 % (22625)------------------------------
% 22.91/4.77 % (22625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.91/4.77 % (22625)Termination reason: Unknown
% 22.91/4.77 % (22625)Termination phase: Saturation
% 22.91/4.77
% 22.91/4.77 % (22625)Memory used [KB]: 8827
% 22.91/4.77 % (22625)Time elapsed: 0.463 s
% 22.91/4.77 % (22625)Instructions burned: 1514 (million)
% 22.91/4.77 % (22625)------------------------------
% 22.91/4.77 % (22625)------------------------------
% 22.91/4.78 % (22635)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_22272 for (2967ds/474Mi)
% 24.21/4.80 % (22632)Instruction limit reached!
% 24.21/4.80 % (22632)------------------------------
% 24.21/4.80 % (22632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.21/4.80 % (22632)Termination reason: Unknown
% 24.21/4.80 % (22632)Termination phase: Saturation
% 24.21/4.80
% 24.21/4.80 % (22632)Memory used [KB]: 7547
% 24.21/4.80 % (22632)Time elapsed: 0.113 s
% 24.21/4.80 % (22632)Instructions burned: 395 (million)
% 24.21/4.80 % (22632)------------------------------
% 24.21/4.80 % (22632)------------------------------
% 24.21/4.80 % (22631)Instruction limit reached!
% 24.21/4.80 % (22631)------------------------------
% 24.21/4.80 % (22631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.21/4.80 % (22631)Termination reason: Unknown
% 24.21/4.80 % (22631)Termination phase: Saturation
% 24.21/4.80
% 24.21/4.80 % (22631)Memory used [KB]: 8187
% 24.21/4.80 % (22631)Time elapsed: 0.145 s
% 24.21/4.80 % (22631)Instructions burned: 458 (million)
% 24.21/4.80 % (22631)------------------------------
% 24.21/4.80 % (22631)------------------------------
% 24.21/4.81 % (22636)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_22272 for (2967ds/157Mi)
% 24.21/4.81 % (22637)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_22272 for (2967ds/590Mi)
% 24.21/4.85 % (22636)Instruction limit reached!
% 24.21/4.85 % (22636)------------------------------
% 24.21/4.85 % (22636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.21/4.85 % (22636)Termination reason: Unknown
% 24.21/4.85 % (22636)Termination phase: Saturation
% 24.21/4.85
% 24.21/4.85 % (22636)Memory used [KB]: 6780
% 24.21/4.85 % (22636)Time elapsed: 0.043 s
% 24.21/4.85 % (22636)Instructions burned: 159 (million)
% 24.21/4.85 % (22636)------------------------------
% 24.21/4.85 % (22636)------------------------------
% 24.21/4.86 % (22638)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_22272 for (2967ds/104Mi)
% 24.21/4.89 % (22638)Instruction limit reached!
% 24.21/4.89 % (22638)------------------------------
% 24.21/4.89 % (22638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.21/4.89 % (22638)Termination reason: Unknown
% 24.21/4.89 % (22638)Termination phase: Saturation
% 24.21/4.89
% 24.21/4.89 % (22638)Memory used [KB]: 2558
% 24.21/4.89 % (22638)Time elapsed: 0.033 s
% 24.21/4.89 % (22638)Instructions burned: 106 (million)
% 24.21/4.89 % (22638)------------------------------
% 24.21/4.89 % (22638)------------------------------
% 24.68/4.90 % (22639)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_22272 for (2966ds/414Mi)
% 24.68/4.92 % (22635)Instruction limit reached!
% 24.68/4.92 % (22635)------------------------------
% 24.68/4.92 % (22635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.68/4.92 % (22635)Termination reason: Unknown
% 24.68/4.92 % (22635)Termination phase: Saturation
% 24.68/4.92
% 24.68/4.92 % (22635)Memory used [KB]: 7547
% 24.68/4.92 % (22635)Time elapsed: 0.144 s
% 24.68/4.92 % (22635)Instructions burned: 474 (million)
% 24.68/4.92 % (22635)------------------------------
% 24.68/4.92 % (22635)------------------------------
% 24.68/4.93 % (22640)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_22272 for (2966ds/715Mi)
% 24.68/4.98 % (22637)Instruction limit reached!
% 24.68/4.98 % (22637)------------------------------
% 24.68/4.98 % (22637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.68/4.98 % (22637)Termination reason: Unknown
% 24.68/4.98 % (22637)Termination phase: Saturation
% 24.68/4.98
% 24.68/4.98 % (22637)Memory used [KB]: 8699
% 24.68/4.98 % (22637)Time elapsed: 0.171 s
% 24.68/4.98 % (22637)Instructions burned: 592 (million)
% 24.68/4.98 % (22637)------------------------------
% 24.68/4.98 % (22637)------------------------------
% 24.68/4.99 % (22641)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_22272 for (2965ds/961Mi)
% 24.68/5.02 % (22639)Instruction limit reached!
% 24.68/5.02 % (22639)------------------------------
% 24.68/5.02 % (22639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.68/5.02 % (22639)Termination reason: Unknown
% 24.68/5.02 % (22639)Termination phase: Saturation
% 24.68/5.02
% 24.68/5.02 % (22639)Memory used [KB]: 7803
% 24.68/5.02 % (22639)Time elapsed: 0.120 s
% 24.68/5.02 % (22639)Instructions burned: 414 (million)
% 24.68/5.02 % (22639)------------------------------
% 24.68/5.02 % (22639)------------------------------
% 26.80/5.03 % (22642)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_22272 for (2965ds/1213Mi)
% 26.80/5.11 % (22633)Instruction limit reached!
% 26.80/5.11 % (22633)------------------------------
% 26.80/5.11 % (22633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.80/5.11 % (22633)Termination reason: Unknown
% 26.80/5.11 % (22633)Termination phase: Saturation
% 26.80/5.11
% 26.80/5.11 % (22633)Memory used [KB]: 9594
% 26.80/5.11 % (22633)Time elapsed: 0.402 s
% 26.80/5.11 % (22633)Instructions burned: 1335 (million)
% 26.80/5.11 % (22633)------------------------------
% 26.80/5.11 % (22633)------------------------------
% 26.80/5.12 % (22643)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_22272 for (2964ds/1979Mi)
% 27.46/5.16 % (22640)Instruction limit reached!
% 27.46/5.16 % (22640)------------------------------
% 27.46/5.16 % (22640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.46/5.16 % (22640)Termination reason: Unknown
% 27.46/5.16 % (22640)Termination phase: Saturation
% 27.46/5.16
% 27.46/5.16 % (22640)Memory used [KB]: 3837
% 27.46/5.16 % (22640)Time elapsed: 0.226 s
% 27.46/5.16 % (22640)Instructions burned: 715 (million)
% 27.46/5.16 % (22640)------------------------------
% 27.46/5.16 % (22640)------------------------------
% 27.46/5.17 % (22644)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_22272 for (2963ds/481Mi)
% 27.81/5.24 % (22641)Instruction limit reached!
% 27.81/5.24 % (22641)------------------------------
% 27.81/5.24 % (22641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.81/5.24 % (22641)Termination reason: Unknown
% 27.81/5.24 % (22641)Termination phase: Saturation
% 27.81/5.24
% 27.81/5.24 % (22641)Memory used [KB]: 7547
% 27.81/5.24 % (22641)Time elapsed: 0.252 s
% 27.81/5.24 % (22641)Instructions burned: 962 (million)
% 27.81/5.24 % (22641)------------------------------
% 27.81/5.24 % (22641)------------------------------
% 27.81/5.25 % (22645)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_22272 for (2963ds/783Mi)
% 28.15/5.31 % (22644)Instruction limit reached!
% 28.15/5.31 % (22644)------------------------------
% 28.15/5.31 % (22644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.15/5.31 % (22644)Termination reason: Unknown
% 28.15/5.31 % (22644)Termination phase: Saturation
% 28.15/5.31
% 28.15/5.31 % (22644)Memory used [KB]: 7419
% 28.15/5.31 % (22644)Time elapsed: 0.148 s
% 28.15/5.31 % (22644)Instructions burned: 483 (million)
% 28.15/5.31 % (22644)------------------------------
% 28.15/5.31 % (22644)------------------------------
% 28.15/5.32 % (22646)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_22272 for (2962ds/432Mi)
% 28.62/5.41 % (22642)Instruction limit reached!
% 28.62/5.41 % (22642)------------------------------
% 28.62/5.41 % (22642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.62/5.41 % (22642)Termination reason: Unknown
% 28.62/5.41 % (22642)Termination phase: Saturation
% 28.62/5.41
% 28.62/5.41 % (22642)Memory used [KB]: 8827
% 28.62/5.41 % (22642)Time elapsed: 0.399 s
% 28.62/5.41 % (22642)Instructions burned: 1214 (million)
% 28.62/5.41 % (22642)------------------------------
% 28.62/5.41 % (22642)------------------------------
% 28.62/5.42 % (22647)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_22272 for (2961ds/1670Mi)
% 28.62/5.43 % (22646)Instruction limit reached!
% 28.62/5.43 % (22646)------------------------------
% 28.62/5.43 % (22646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.62/5.43 % (22646)Termination reason: Unknown
% 28.62/5.43 % (22646)Termination phase: Saturation
% 28.62/5.43
% 28.62/5.43 % (22646)Memory used [KB]: 6652
% 28.62/5.43 % (22646)Time elapsed: 0.105 s
% 28.62/5.43 % (22646)Instructions burned: 434 (million)
% 28.62/5.43 % (22646)------------------------------
% 28.62/5.43 % (22646)------------------------------
% 28.62/5.44 % (22648)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_22272 for (2961ds/90Mi)
% 28.62/5.46 % (22648)Instruction limit reached!
% 28.62/5.46 % (22648)------------------------------
% 28.62/5.46 % (22648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.62/5.46 % (22648)Termination reason: Unknown
% 28.62/5.46 % (22648)Termination phase: Property scanning
% 28.62/5.46
% 28.62/5.46 % (22648)Memory used [KB]: 2174
% 28.62/5.46 % (22648)Time elapsed: 0.027 s
% 28.62/5.46 % (22648)Instructions burned: 92 (million)
% 28.62/5.46 % (22648)------------------------------
% 28.62/5.46 % (22648)------------------------------
% 28.62/5.47 % (22649)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_22272 for (2960ds/346Mi)
% 28.62/5.49 % (22645)Instruction limit reached!
% 28.62/5.49 % (22645)------------------------------
% 28.62/5.49 % (22645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.62/5.49 % (22645)Termination reason: Unknown
% 28.62/5.49 % (22645)Termination phase: Saturation
% 28.62/5.49
% 28.62/5.49 % (22645)Memory used [KB]: 8443
% 28.62/5.49 % (22645)Time elapsed: 0.241 s
% 28.62/5.49 % (22645)Instructions burned: 784 (million)
% 28.62/5.49 % (22645)------------------------------
% 28.62/5.49 % (22645)------------------------------
% 29.70/5.50 % (22650)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_22272 for (2960ds/401Mi)
% 29.70/5.58 % (22649)Instruction limit reached!
% 29.70/5.58 % (22649)------------------------------
% 29.70/5.58 % (22649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.70/5.58 % (22649)Termination reason: Unknown
% 29.70/5.58 % (22649)Termination phase: Saturation
% 29.70/5.58
% 29.70/5.58 % (22649)Memory used [KB]: 7419
% 29.70/5.58 % (22649)Time elapsed: 0.104 s
% 29.70/5.58 % (22649)Instructions burned: 348 (million)
% 29.70/5.58 % (22649)------------------------------
% 29.70/5.58 % (22649)------------------------------
% 29.70/5.58 % (22651)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_22272 for (2959ds/6454Mi)
% 30.11/5.61 % (22650)Instruction limit reached!
% 30.11/5.61 % (22650)------------------------------
% 30.11/5.61 % (22650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.11/5.61 % (22650)Termination reason: Unknown
% 30.11/5.61 % (22650)Termination phase: Saturation
% 30.11/5.61
% 30.11/5.61 % (22650)Memory used [KB]: 8955
% 30.11/5.61 % (22650)Time elapsed: 0.115 s
% 30.11/5.61 % (22650)Instructions burned: 402 (million)
% 30.11/5.61 % (22650)------------------------------
% 30.11/5.61 % (22650)------------------------------
% 30.11/5.62 % (22652)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_22272 for (2959ds/283Mi)
% 30.53/5.71 % (22619)Instruction limit reached!
% 30.53/5.71 % (22619)------------------------------
% 30.53/5.71 % (22619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.53/5.71 % (22619)Termination reason: Unknown
% 30.53/5.71 % (22619)Termination phase: Saturation
% 30.53/5.71
% 30.53/5.71 % (22619)Memory used [KB]: 9338
% 30.53/5.71 % (22619)Time elapsed: 1.549 s
% 30.53/5.71 % (22619)Instructions burned: 5414 (million)
% 30.53/5.71 % (22619)------------------------------
% 30.53/5.71 % (22619)------------------------------
% 30.53/5.71 % (22652)Instruction limit reached!
% 30.53/5.71 % (22652)------------------------------
% 30.53/5.71 % (22652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.53/5.71 % (22652)Termination reason: Unknown
% 30.53/5.71 % (22652)Termination phase: Saturation
% 30.53/5.71
% 30.53/5.71 % (22652)Memory used [KB]: 7803
% 30.53/5.71 % (22652)Time elapsed: 0.091 s
% 30.53/5.71 % (22652)Instructions burned: 284 (million)
% 30.53/5.71 % (22652)------------------------------
% 30.53/5.71 % (22652)------------------------------
% 30.53/5.72 % (22653)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_22272 for (2958ds/865Mi)
% 30.53/5.72 % (22654)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_22272 for (2958ds/4528Mi)
% 30.53/5.74 % (22643)Instruction limit reached!
% 30.53/5.74 % (22643)------------------------------
% 30.53/5.74 % (22643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.53/5.74 % (22643)Termination reason: Unknown
% 30.53/5.74 % (22643)Termination phase: Saturation
% 30.53/5.74
% 30.53/5.74 % (22643)Memory used [KB]: 8443
% 30.53/5.74 % (22643)Time elapsed: 0.641 s
% 30.53/5.74 % (22643)Instructions burned: 1979 (million)
% 30.53/5.74 % (22643)------------------------------
% 30.53/5.74 % (22643)------------------------------
% 30.53/5.75 % (22655)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_22272 for (2958ds/1001Mi)
% 30.53/5.78 % (22634)Instruction limit reached!
% 30.53/5.78 % (22634)------------------------------
% 30.53/5.78 % (22634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.53/5.78 % (22634)Termination reason: Unknown
% 30.53/5.78 % (22634)Termination phase: Saturation
% 30.53/5.78
% 30.53/5.78 % (22634)Memory used [KB]: 12409
% 30.53/5.78 % (22634)Time elapsed: 1.070 s
% 30.53/5.78 % (22634)Instructions burned: 3373 (million)
% 30.53/5.78 % (22634)------------------------------
% 30.53/5.78 % (22634)------------------------------
% 30.53/5.79 % (22656)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_22272 for (2957ds/102Mi)
% 31.48/5.81 % (22656)Instruction limit reached!
% 31.48/5.81 % (22656)------------------------------
% 31.48/5.81 % (22656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.48/5.81 % (22656)Termination reason: Unknown
% 31.48/5.81 % (22656)Termination phase: Property scanning
% 31.48/5.81
% 31.48/5.81 % (22656)Memory used [KB]: 2302
% 31.48/5.81 % (22656)Time elapsed: 0.029 s
% 31.48/5.81 % (22656)Instructions burned: 104 (million)
% 31.48/5.81 % (22656)------------------------------
% 31.48/5.81 % (22656)------------------------------
% 31.48/5.82 % (22657)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_22272 for (2957ds/952Mi)
% 31.62/5.92 % (22647)Instruction limit reached!
% 31.62/5.92 % (22647)------------------------------
% 31.62/5.92 % (22647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.62/5.92 % (22647)Termination reason: Unknown
% 31.62/5.92 % (22647)Termination phase: Saturation
% 31.62/5.92
% 31.62/5.92 % (22647)Memory used [KB]: 10234
% 31.62/5.92 % (22647)Time elapsed: 0.506 s
% 31.62/5.92 % (22647)Instructions burned: 1670 (million)
% 31.62/5.92 % (22647)------------------------------
% 31.62/5.92 % (22647)------------------------------
% 31.62/5.93 % (22658)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_22272 for (2956ds/578Mi)
% 31.62/5.97 % (22653)Instruction limit reached!
% 31.62/5.97 % (22653)------------------------------
% 31.62/5.97 % (22653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.62/5.97 % (22653)Termination reason: Unknown
% 31.62/5.97 % (22653)Termination phase: Saturation
% 31.62/5.97
% 31.62/5.97 % (22653)Memory used [KB]: 8955
% 31.62/5.97 % (22653)Time elapsed: 0.254 s
% 31.62/5.97 % (22653)Instructions burned: 865 (million)
% 31.62/5.97 % (22653)------------------------------
% 31.62/5.97 % (22653)------------------------------
% 31.62/5.98 % (22607)Instruction limit reached!
% 31.62/5.98 % (22607)------------------------------
% 31.62/5.98 % (22607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.62/5.98 % (22607)Termination reason: Unknown
% 31.62/5.98 % (22607)Termination phase: Saturation
% 31.62/5.98
% 31.62/5.98 % (22607)Memory used [KB]: 17654
% 31.62/5.98 % (22607)Time elapsed: 2.579 s
% 31.62/5.98 % (22607)Instructions burned: 8251 (million)
% 31.62/5.98 % (22607)------------------------------
% 31.62/5.98 % (22607)------------------------------
% 31.62/5.98 % (22659)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_22272 for (2955ds/643Mi)
% 31.62/5.99 % (22660)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_22272 for (2955ds/865Mi)
% 33.79/6.06 % (22655)Instruction limit reached!
% 33.79/6.06 % (22655)------------------------------
% 33.79/6.06 % (22655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.79/6.06 % (22655)Termination reason: Unknown
% 33.79/6.06 % (22655)Termination phase: Saturation
% 33.79/6.06
% 33.79/6.06 % (22655)Memory used [KB]: 8827
% 33.79/6.06 % (22655)Time elapsed: 0.310 s
% 33.79/6.06 % (22655)Instructions burned: 1001 (million)
% 33.79/6.06 % (22655)------------------------------
% 33.79/6.06 % (22655)------------------------------
% 33.79/6.07 % (22661)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_22272 for (2954ds/1174Mi)
% 33.79/6.10 % (22658)Instruction limit reached!
% 33.79/6.10 % (22658)------------------------------
% 33.79/6.10 % (22658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.79/6.10 % (22658)Termination reason: Unknown
% 33.79/6.10 % (22658)Termination phase: Saturation
% 33.79/6.10
% 33.79/6.10 % (22658)Memory used [KB]: 8059
% 33.79/6.10 % (22658)Time elapsed: 0.167 s
% 33.79/6.10 % (22658)Instructions burned: 579 (million)
% 33.79/6.10 % (22658)------------------------------
% 33.79/6.10 % (22658)------------------------------
% 33.79/6.11 % (22662)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_22272 for (2954ds/644Mi)
% 34.44/6.18 % (22659)Instruction limit reached!
% 34.44/6.18 % (22659)------------------------------
% 34.44/6.18 % (22659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.44/6.18 % (22659)Termination reason: Unknown
% 34.44/6.18 % (22659)Termination phase: Saturation
% 34.44/6.18
% 34.44/6.18 % (22659)Memory used [KB]: 9083
% 34.44/6.18 % (22659)Time elapsed: 0.196 s
% 34.44/6.18 % (22659)Instructions burned: 645 (million)
% 34.44/6.18 % (22659)------------------------------
% 34.44/6.18 % (22659)------------------------------
% 34.44/6.18 % (22657)Instruction limit reached!
% 34.44/6.18 % (22657)------------------------------
% 34.44/6.18 % (22657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.44/6.18 % (22657)Termination reason: Unknown
% 34.44/6.18 % (22657)Termination phase: Saturation
% 34.44/6.18
% 34.44/6.18 % (22657)Memory used [KB]: 8827
% 34.44/6.18 % (22657)Time elapsed: 0.360 s
% 34.44/6.18 % (22657)Instructions burned: 953 (million)
% 34.44/6.18 % (22657)------------------------------
% 34.44/6.18 % (22657)------------------------------
% 34.44/6.19 % (22663)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_22272 for (2953ds/1201Mi)
% 34.44/6.19 % (22664)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_22272 for (2953ds/1046Mi)
% 34.85/6.21 % (22660)Refutation not found, non-redundant clauses discarded% (22660)------------------------------
% 34.85/6.21 % (22660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.85/6.21 % (22660)Termination reason: Refutation not found, non-redundant clauses discarded
% 34.85/6.21
% 34.85/6.21 % (22660)Memory used [KB]: 8571
% 34.85/6.21 % (22660)Time elapsed: 0.217 s
% 34.85/6.21 % (22660)Instructions burned: 690 (million)
% 34.85/6.21 % (22660)------------------------------
% 34.85/6.21 % (22660)------------------------------
% 34.85/6.22 % (22665)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_22272 for (2953ds/222Mi)
% 34.85/6.28 % (22665)Instruction limit reached!
% 34.85/6.28 % (22665)------------------------------
% 34.85/6.28 % (22665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.85/6.28 % (22665)Termination reason: Unknown
% 34.85/6.28 % (22665)Termination phase: Saturation
% 34.85/6.28
% 34.85/6.28 % (22665)Memory used [KB]: 7291
% 34.85/6.28 % (22665)Time elapsed: 0.062 s
% 34.85/6.28 % (22665)Instructions burned: 223 (million)
% 34.85/6.28 % (22665)------------------------------
% 34.85/6.28 % (22665)------------------------------
% 34.85/6.29 % (22666)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_22272 for (2952ds/68Mi)
% 35.14/6.30 % (22662)Instruction limit reached!
% 35.14/6.30 % (22662)------------------------------
% 35.14/6.30 % (22662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.14/6.30 % (22662)Termination reason: Unknown
% 35.14/6.30 % (22662)Termination phase: Saturation
% 35.14/6.30
% 35.14/6.30 % (22662)Memory used [KB]: 9466
% 35.14/6.30 % (22662)Time elapsed: 0.197 s
% 35.14/6.30 % (22662)Instructions burned: 646 (million)
% 35.14/6.30 % (22662)------------------------------
% 35.14/6.30 % (22662)------------------------------
% 35.14/6.31 % (22666)Instruction limit reached!
% 35.14/6.31 % (22666)------------------------------
% 35.14/6.31 % (22666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.14/6.31 % (22666)Termination reason: Unknown
% 35.14/6.31 % (22666)Termination phase: Property scanning
% 35.14/6.31
% 35.14/6.31 % (22666)Memory used [KB]: 2174
% 35.14/6.31 % (22666)Time elapsed: 0.022 s
% 35.14/6.31 % (22666)Instructions burned: 69 (million)
% 35.14/6.31 % (22666)------------------------------
% 35.14/6.31 % (22666)------------------------------
% 35.14/6.31 % (22667)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_22272 for (2952ds/454Mi)
% 35.14/6.32 % (22668)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_22272 for (2952ds/360Mi)
% 35.60/6.42 % (22651)First to succeed.
% 35.60/6.42 % (22668)Instruction limit reached!
% 35.60/6.42 % (22668)------------------------------
% 35.60/6.42 % (22668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.60/6.42 % (22668)Termination reason: Unknown
% 35.60/6.42 % (22668)Termination phase: Saturation
% 35.60/6.42
% 35.60/6.42 % (22668)Memory used [KB]: 8699
% 35.60/6.42 % (22668)Time elapsed: 0.101 s
% 35.60/6.42 % (22668)Instructions burned: 363 (million)
% 35.60/6.42 % (22668)------------------------------
% 35.60/6.42 % (22668)------------------------------
% 35.60/6.42 % (22651)Refutation found. Thanks to Tanya!
% 35.60/6.42 % SZS status Theorem for DTF2THF_22272
% 35.60/6.42 % SZS output start Proof for DTF2THF_22272
% 35.60/6.42 thf(type_def_5, type, coinductive_llist: ($tType) > $tType).
% 35.60/6.42 thf(type_def_7, type, list: ($tType) > $tType).
% 35.60/6.42 thf(type_def_8, type, set: ($tType) > $tType).
% 35.60/6.42 thf(type_def_9, type, itself: ($tType) > $tType).
% 35.60/6.42 thf(type_def_10, type, a: $tType).
% 35.60/6.42 thf(func_def_0, type, coinductive_llist: ($tType) > $tType).
% 35.60/6.42 thf(func_def_1, type, list: ($tType) > $tType).
% 35.60/6.42 thf(func_def_2, type, set: ($tType) > $tType).
% 35.60/6.42 thf(func_def_3, type, itself: ($tType) > $tType).
% 35.60/6.42 thf(func_def_4, type, a: $tType).
% 35.60/6.42 thf(func_def_5, type, coindu328551480prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 35.60/6.42 thf(func_def_6, type, coinductive_lappend: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_7, type, coinductive_lfinite: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 35.60/6.42 thf(func_def_8, type, coinductive_list_of: !>[X0: $tType]:(coinductive_llist @ X0 > list @ X0)).
% 35.60/6.42 thf(func_def_9, type, coindu1384447384of_aux: !>[X0: $tType]:(list @ X0 > coinductive_llist @ X0 > list @ X0)).
% 35.60/6.42 thf(func_def_10, type, coinductive_llast: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 35.60/6.42 thf(func_def_11, type, coinductive_LCons: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_12, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_13, type, coinductive_lnull: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 35.60/6.42 thf(func_def_14, type, coinductive_lset: !>[X0: $tType]:(coinductive_llist @ X0 > set @ X0)).
% 35.60/6.42 thf(func_def_15, type, coinductive_llist_of: !>[X0: $tType]:(list @ X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_16, type, coindu1478340336prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 35.60/6.42 thf(func_def_17, type, undefined: !>[X0: $tType]:(X0)).
% 35.60/6.42 thf(func_def_18, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 35.60/6.42 thf(func_def_19, type, koenig793108494nected: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 35.60/6.42 thf(func_def_20, type, koenig916195507_paths: !>[X0: $tType]:((X0 > X0 > $o) > set @ coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_21, type, append: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 35.60/6.42 thf(func_def_22, type, bind: !>[X0: $tType, X1: $tType]:(list @ X0 > (X0 > list @ X1) > list @ X1)).
% 35.60/6.42 thf(func_def_23, type, butlast: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 35.60/6.42 thf(func_def_24, type, can_select: !>[X0: $tType]:((X0 > $o) > set @ X0 > $o)).
% 35.60/6.42 thf(func_def_25, type, insert: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 35.60/6.42 thf(func_def_26, type, last: !>[X0: $tType]:(list @ X0 > X0)).
% 35.60/6.42 thf(func_def_27, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 35.60/6.42 thf(func_def_28, type, nil: !>[X0: $tType]:(list @ X0)).
% 35.60/6.42 thf(func_def_29, type, map: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > list @ X1)).
% 35.60/6.42 thf(func_def_30, type, set2: !>[X0: $tType]:(list @ X0 > set @ X0)).
% 35.60/6.42 thf(func_def_31, type, list_ex1: !>[X0: $tType]:((X0 > $o) > list @ X0 > $o)).
% 35.60/6.42 thf(func_def_32, type, map_tailrec: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > list @ X1)).
% 35.60/6.42 thf(func_def_33, type, map_tailrec_rev: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > list @ X1 > list @ X1)).
% 35.60/6.42 thf(func_def_34, type, maps: !>[X0: $tType, X1: $tType]:((X0 > list @ X1) > list @ X0 > list @ X1)).
% 35.60/6.42 thf(func_def_35, type, product_lists: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 35.60/6.42 thf(func_def_36, type, rev: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 35.60/6.42 thf(func_def_37, type, rotate1: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 35.60/6.42 thf(func_def_38, type, sublists: !>[X0: $tType]:(list @ X0 > list @ list @ X0)).
% 35.60/6.42 thf(func_def_39, type, type: !>[X0: $tType]:(itself @ X0)).
% 35.60/6.42 thf(func_def_40, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 35.60/6.42 thf(func_def_41, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 35.60/6.42 thf(func_def_42, type, prefixes: !>[X0: $tType]:(list @ X0 > list @ list @ X0)).
% 35.60/6.42 thf(func_def_43, type, prefixes_rel: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 35.60/6.42 thf(func_def_44, type, strict_suffix: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 35.60/6.42 thf(func_def_45, type, accp: !>[X0: $tType]:((X0 > X0 > $o) > X0 > $o)).
% 35.60/6.42 thf(func_def_46, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 35.60/6.42 thf(func_def_47, type, xs: list @ a).
% 35.60/6.42 thf(func_def_48, type, graph: a > a > $o).
% 35.60/6.42 thf(func_def_49, type, n: a).
% 35.60/6.42 thf(func_def_50, type, x: a).
% 35.60/6.42 thf(func_def_51, type, xs2: coinductive_llist @ a).
% 35.60/6.42 thf(func_def_52, type, xs3: coinductive_llist @ a).
% 35.60/6.42 thf(func_def_53, type, xs4: coinductive_llist @ a).
% 35.60/6.42 thf(func_def_54, type, ys: list @ a).
% 35.60/6.42 thf(func_def_55, type, zs: list @ a).
% 35.60/6.42 thf(func_def_71, type, sK0: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 35.60/6.42 thf(func_def_72, type, sK1: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_73, type, sK2: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_74, type, sK3: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 35.60/6.42 thf(func_def_75, type, sK4: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_76, type, sK5: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > X0 > X0)).
% 35.60/6.42 thf(func_def_77, type, sK6: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_78, type, sK7: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 35.60/6.42 thf(func_def_79, type, sK8: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_80, type, sK9: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_81, type, sK10: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > X0)).
% 35.60/6.42 thf(func_def_82, type, sK11: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_83, type, sK12: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_84, type, sK13: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > X0 > X0)).
% 35.60/6.42 thf(func_def_85, type, sK14: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_86, type, sK15: list @ a).
% 35.60/6.42 thf(func_def_87, type, sK16: list @ a).
% 35.60/6.42 thf(func_def_88, type, sK17: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > X0)).
% 35.60/6.42 thf(func_def_89, type, sK18: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_90, type, sK19: !>[X0: $tType]:((X0 > X0 > $o) > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_91, type, sK20: !>[X0: $tType]:(X0 > X0 > (X0 > X0 > $o) > list @ X0)).
% 35.60/6.42 thf(func_def_92, type, sK21: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_93, type, sK22: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_94, type, sK23: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o) > X0)).
% 35.60/6.42 thf(func_def_95, type, sK24: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_96, type, sK25: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o) > X0)).
% 35.60/6.42 thf(func_def_97, type, sK26: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o) > X0)).
% 35.60/6.42 thf(func_def_98, type, sK27: !>[X0: $tType]:((X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_99, type, sK28: coinductive_llist @ a).
% 35.60/6.42 thf(func_def_100, type, sK29: coinductive_llist @ a).
% 35.60/6.42 thf(func_def_101, type, sK30: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 35.60/6.42 thf(func_def_102, type, sK31: !>[X0: $tType]:((X0 > X0 > $o) > coinductive_llist @ X0 > X0)).
% 35.60/6.42 thf(func_def_103, type, sK32: !>[X0: $tType]:((X0 > X0 > $o) > coinductive_llist @ X0 > X0)).
% 35.60/6.42 thf(func_def_104, type, sK33: !>[X0: $tType]:((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_105, type, sK34: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_106, type, sK35: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > X0)).
% 35.60/6.42 thf(func_def_107, type, sK36: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_108, type, sK37: list @ a).
% 35.60/6.42 thf(func_def_109, type, sK38: list @ a).
% 35.60/6.42 thf(func_def_110, type, sK39: list @ a).
% 35.60/6.42 thf(func_def_111, type, sK40: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_112, type, sK41: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > X0)).
% 35.60/6.42 thf(func_def_113, type, sK42: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_114, type, sK43: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > X0)).
% 35.60/6.42 thf(func_def_115, type, sK44: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_117, type, sK46: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 35.60/6.42 thf(func_def_118, type, sK47: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 35.60/6.42 thf(func_def_119, type, sK48: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 35.60/6.42 thf(func_def_120, type, sK49: !>[X0: $tType]:(coinductive_llist @ X0 > (X0 > X0 > $o) > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_121, type, sK50: !>[X0: $tType]:(coinductive_llist @ X0 > (X0 > X0 > $o) > X0)).
% 35.60/6.42 thf(func_def_122, type, sK51: !>[X0: $tType]:(coinductive_llist @ X0 > (X0 > X0 > $o) > X0)).
% 35.60/6.42 thf(func_def_123, type, sK52: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_124, type, sK53: !>[X0: $tType]:(coinductive_llist @ X0 > list @ X0 > X0 > list @ X0)).
% 35.60/6.42 thf(func_def_125, type, sK54: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 35.60/6.42 thf(func_def_126, type, sK55: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 35.60/6.42 thf(func_def_127, type, ph56: !>[X0: $tType]:(X0)).
% 35.60/6.42 thf(f4212,plain,(
% 35.60/6.42 $false),
% 35.60/6.42 inference(subsumption_resolution,[status(thm)],[f4211,f884])).
% 35.60/6.42 thf(f884,plain,(
% 35.60/6.42 ((member @ coinductive_llist @ a @ (coinductive_LCons @ a @ n @ (coinductive_lappend @ a @ sK28 @ (coinductive_LCons @ a @ x @ sK29))) @ (koenig916195507_paths @ a @ graph)) = $true)),
% 35.60/6.42 inference(definition_unfolding,[status(thm)],[f840,f819])).
% 35.60/6.42 thf(f819,plain,(
% 35.60/6.42 (xs2 = (coinductive_lappend @ a @ sK28 @ (coinductive_LCons @ a @ x @ sK29)))),
% 35.60/6.42 inference(cnf_transformation,[status(thm)],[f716])).
% 35.60/6.42 thf(f716,plain,(
% 35.60/6.42 ($true != (member @ a @ x @ (coinductive_lset @ a @ sK28))) & (xs2 = (coinductive_lappend @ a @ sK28 @ (coinductive_LCons @ a @ x @ sK29))) & ((coinductive_lfinite @ a @ sK28) = $true)),
% 35.60/6.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f671,f715,f714])).
% 35.60/6.42 thf(f714,plain,(
% 35.60/6.42 ? [X0 : coinductive_llist @ a] : (((member @ a @ x @ (coinductive_lset @ a @ X0)) != $true) & ? [X1 : coinductive_llist @ a] : (xs2 = (coinductive_lappend @ a @ X0 @ (coinductive_LCons @ a @ x @ X1))) & ($true = (coinductive_lfinite @ a @ X0))) => (($true != (member @ a @ x @ (coinductive_lset @ a @ sK28))) & ? [X1 : coinductive_llist @ a] : (xs2 = (coinductive_lappend @ a @ sK28 @ (coinductive_LCons @ a @ x @ X1))) & ((coinductive_lfinite @ a @ sK28) = $true))),
% 35.60/6.42 introduced(definition,[],[choice_axiom])).
% 35.60/6.42 thf(f715,plain,(
% 35.60/6.42 ? [X1 : coinductive_llist @ a] : (xs2 = (coinductive_lappend @ a @ sK28 @ (coinductive_LCons @ a @ x @ X1))) => (xs2 = (coinductive_lappend @ a @ sK28 @ (coinductive_LCons @ a @ x @ sK29)))),
% 35.60/6.42 introduced(definition,[],[choice_axiom])).
% 35.60/6.42 thf(f671,plain,(
% 35.60/6.42 ? [X0 : coinductive_llist @ a] : (((member @ a @ x @ (coinductive_lset @ a @ X0)) != $true) & ? [X1 : coinductive_llist @ a] : (xs2 = (coinductive_lappend @ a @ X0 @ (coinductive_LCons @ a @ x @ X1))) & ($true = (coinductive_lfinite @ a @ X0)))),
% 35.60/6.42 inference(flattening,[status(thm)],[f670])).
% 35.60/6.42 thf(f670,plain,(
% 35.60/6.42 ? [X0 : coinductive_llist @ a] : ((((member @ a @ x @ (coinductive_lset @ a @ X0)) != $true) & ? [X1 : coinductive_llist @ a] : (xs2 = (coinductive_lappend @ a @ X0 @ (coinductive_LCons @ a @ x @ X1)))) & ($true = (coinductive_lfinite @ a @ X0)))),
% 35.60/6.42 inference(ennf_transformation,[status(thm)],[f298])).
% 35.60/6.42 thf(f298,plain,(
% 35.60/6.42 ~! [X0 : coinductive_llist @ a] : (($true = (coinductive_lfinite @ a @ X0)) => (? [X1 : coinductive_llist @ a] : (xs2 = (coinductive_lappend @ a @ X0 @ (coinductive_LCons @ a @ x @ X1))) => ((member @ a @ x @ (coinductive_lset @ a @ X0)) = $true)))),
% 35.60/6.42 inference(fool_elimination,[status(thm)],[f297])).
% 35.60/6.42 thf(f297,plain,(
% 35.60/6.42 ~! [X0 : coinductive_llist @ a] : ((coinductive_lfinite @ a @ X0) => (? [X1 : coinductive_llist @ a] : (xs2 = (coinductive_lappend @ a @ X0 @ (coinductive_LCons @ a @ x @ X1))) => (member @ a @ x @ (coinductive_lset @ a @ X0))))),
% 35.60/6.42 inference(rectify,[status(thm)],[f36])).
% 35.60/6.42 thf(f36,axiom,(
% 35.60/6.42 ~! [X28 : coinductive_llist @ a] : ((coinductive_lfinite @ a @ X28) => (? [X29 : coinductive_llist @ a] : (xs2 = (coinductive_lappend @ a @ X28 @ (coinductive_LCons @ a @ x @ X29))) => (member @ a @ x @ (coinductive_lset @ a @ X28))))),
% 35.60/6.42 file('/export/starexec/sandbox2/tmp/tmp.fWo8BEA7MH/DTF2THF_22272.p',fact_35__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062xs_H_Axs_H_H_O_A_092_060lbrakk_062lfinite_Axs_H_059_Axs_A_061_Alappend_Axs_H_A_ILCons_Ax_Axs_H_H_J_059_Ax_A_092_060notin_062_Alset_Axs_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)).
% 35.60/6.42 thf(f840,plain,(
% 35.60/6.42 ((member @ coinductive_llist @ a @ (coinductive_LCons @ a @ n @ xs2) @ (koenig916195507_paths @ a @ graph)) = $true)),
% 35.60/6.42 inference(cnf_transformation,[status(thm)],[f264])).
% 35.60/6.42 thf(f264,plain,(
% 35.60/6.42 ((member @ coinductive_llist @ a @ (coinductive_LCons @ a @ n @ xs2) @ (koenig916195507_paths @ a @ graph)) = $true)),
% 35.60/6.42 inference(fool_elimination,[status(thm)],[f263])).
% 35.60/6.42 thf(f263,plain,(
% 35.60/6.42 (member @ coinductive_llist @ a @ (coinductive_LCons @ a @ n @ xs2) @ (koenig916195507_paths @ a @ graph))),
% 35.60/6.42 inference(rectify,[status(thm)],[f4])).
% 35.60/6.42 thf(f4,axiom,(
% 35.60/6.42 (member @ coinductive_llist @ a @ (coinductive_LCons @ a @ n @ xs2) @ (koenig916195507_paths @ a @ graph))),
% 35.60/6.42 file('/export/starexec/sandbox2/tmp/tmp.fWo8BEA7MH/DTF2THF_22272.p',fact_3_path)).
% 35.60/6.42 thf(f4211,plain,(
% 35.60/6.42 ((member @ coinductive_llist @ a @ (coinductive_LCons @ a @ n @ (coinductive_lappend @ a @ sK28 @ (coinductive_LCons @ a @ x @ sK29))) @ (koenig916195507_paths @ a @ graph)) != $true)),
% 35.60/6.42 inference(forward_demodulation,[status(thm)],[f4210,f885])).
% 35.60/6.42 thf(f885,plain,(
% 35.60/6.42 ((coinductive_lappend @ a @ (coinductive_llist_of @ a @ sK37) @ (coinductive_LCons @ a @ x @ xs3)) = (coinductive_lappend @ a @ sK28 @ (coinductive_LCons @ a @ x @ sK29)))),
% 35.60/6.42 inference(definition_unfolding,[status(thm)],[f846,f819,f835])).
% 35.60/6.42 thf(f835,plain,(
% 35.60/6.42 (xs4 = (coinductive_llist_of @ a @ sK37))),
% 35.60/6.42 inference(cnf_transformation,[status(thm)],[f724])).
% 35.60/6.42 thf(f724,plain,(
% 35.60/6.42 (xs4 = (coinductive_llist_of @ a @ sK37))),
% 35.60/6.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f651,f723])).
% 35.60/6.42 thf(f723,plain,(
% 35.60/6.42 ? [X0 : list @ a] : (xs4 = (coinductive_llist_of @ a @ X0)) => (xs4 = (coinductive_llist_of @ a @ sK37))),
% 35.60/6.42 introduced(definition,[],[choice_axiom])).
% 35.60/6.42 thf(f651,plain,(
% 35.60/6.42 ? [X0 : list @ a] : (xs4 = (coinductive_llist_of @ a @ X0))),
% 35.60/6.42 inference(ennf_transformation,[status(thm)],[f604])).
% 35.60/6.42 thf(f604,plain,(
% 35.60/6.42 ~! [X0 : list @ a] : (xs4 != (coinductive_llist_of @ a @ X0))),
% 35.60/6.42 inference(rectify,[status(thm)],[f3])).
% 35.60/6.42 thf(f3,axiom,(
% 35.60/6.42 ~! [X4 : list @ a] : (xs4 != (coinductive_llist_of @ a @ X4))),
% 35.60/6.42 file('/export/starexec/sandbox2/tmp/tmp.fWo8BEA7MH/DTF2THF_22272.p',fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062XS_H_O_Axs_H_A_061_Allist__of_AXS_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)).
% 35.60/6.42 thf(f846,plain,(
% 35.60/6.42 (xs2 = (coinductive_lappend @ a @ xs4 @ (coinductive_LCons @ a @ x @ xs3)))),
% 35.60/6.42 inference(cnf_transformation,[status(thm)],[f5])).
% 35.60/6.42 thf(f5,axiom,(
% 35.60/6.42 (xs2 = (coinductive_lappend @ a @ xs4 @ (coinductive_LCons @ a @ x @ xs3)))),
% 35.60/6.42 file('/export/starexec/sandbox2/tmp/tmp.fWo8BEA7MH/DTF2THF_22272.p',fact_4_xs)).
% 35.60/6.42 thf(f4210,plain,(
% 35.60/6.42 ($true != (member @ coinductive_llist @ a @ (coinductive_LCons @ a @ n @ (coinductive_lappend @ a @ (coinductive_llist_of @ a @ sK37) @ (coinductive_LCons @ a @ x @ xs3))) @ (koenig916195507_paths @ a @ graph)))),
% 35.60/6.42 inference(forward_demodulation,[status(thm)],[f4209,f2676])).
% 35.60/6.42 thf(f2676,plain,(
% 35.60/6.42 ((append @ a @ ys @ (cons @ a @ n @ zs)) = sK37)),
% 35.60/6.42 inference(forward_demodulation,[status(thm)],[f2633,f776])).
% 35.60/6.42 thf(f776,plain,(
% 35.60/6.42 ( ! [X0 : $tType,X1 : list @ X0] : (((coinductive_list_of @ X0 @ (coinductive_llist_of @ X0 @ X1)) = X1)) )),
% 35.60/6.42 inference(cnf_transformation,[status(thm)],[f625])).
% 35.60/6.42 thf(f625,plain,(
% 35.60/6.42 ! [X0 : $tType,X1 : list @ X0] : ((coinductive_list_of @ X0 @ (coinductive_llist_of @ X0 @ X1)) = X1)),
% 35.60/6.42 inference(rectify,[status(thm)],[f112])).
% 35.60/6.42 thf(f112,axiom,(
% 35.60/6.42 ! [X0 : $tType,X8 : list @ X0] : ((coinductive_list_of @ X0 @ (coinductive_llist_of @ X0 @ X8)) = X8)),
% 35.60/6.42 file('/export/starexec/sandbox2/tmp/tmp.fWo8BEA7MH/DTF2THF_22272.p',fact_111_list__of__llist__of)).
% 35.60/6.42 thf(f2633,plain,(
% 35.60/6.42 ((append @ a @ ys @ (cons @ a @ n @ zs)) = (coinductive_list_of @ a @ (coinductive_llist_of @ a @ sK37)))),
% 35.60/6.42 inference(superposition,[status(thm)],[f776,f1076])).
% 35.60/6.42 thf(f1076,plain,(
% 35.60/6.42 ((coinductive_llist_of @ a @ (append @ a @ ys @ (cons @ a @ n @ zs))) = (coinductive_llist_of @ a @ sK37))),
% 35.60/6.42 inference(backward_demodulation,[status(thm)],[f887,f878])).
% 35.60/6.42 thf(f878,plain,(
% 35.60/6.42 ((append @ a @ ys @ (cons @ a @ n @ zs)) = (append @ a @ sK15 @ (cons @ a @ n @ sK16)))),
% 35.60/6.42 inference(definition_unfolding,[status(thm)],[f800,f774])).
% 35.60/6.42 thf(f774,plain,(
% 35.60/6.42 (xs = (append @ a @ sK15 @ (cons @ a @ n @ sK16)))),
% 35.60/6.42 inference(cnf_transformation,[status(thm)],[f700])).
% 35.60/6.42 thf(f700,plain,(
% 35.60/6.42 ((member @ a @ n @ (set2 @ a @ sK16)) != $true) & (xs = (append @ a @ sK15 @ (cons @ a @ n @ sK16)))),
% 35.60/6.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f645,f699])).
% 35.60/6.42 thf(f699,plain,(
% 35.60/6.42 ? [X0 : list @ a,X1 : list @ a] : (($true != (member @ a @ n @ (set2 @ a @ X1))) & (xs = (append @ a @ X0 @ (cons @ a @ n @ X1)))) => (((member @ a @ n @ (set2 @ a @ sK16)) != $true) & (xs = (append @ a @ sK15 @ (cons @ a @ n @ sK16))))),
% 35.60/6.42 introduced(definition,[],[choice_axiom])).
% 35.60/6.42 thf(f645,plain,(
% 35.60/6.42 ? [X0 : list @ a,X1 : list @ a] : (($true != (member @ a @ n @ (set2 @ a @ X1))) & (xs = (append @ a @ X0 @ (cons @ a @ n @ X1))))),
% 35.60/6.42 inference(ennf_transformation,[status(thm)],[f506])).
% 35.60/6.42 thf(f506,plain,(
% 35.60/6.42 ~! [X0 : list @ a,X1 : list @ a] : ((xs = (append @ a @ X0 @ (cons @ a @ n @ X1))) => ($true = (member @ a @ n @ (set2 @ a @ X1))))),
% 35.60/6.42 inference(fool_elimination,[status(thm)],[f505])).
% 35.60/6.42 thf(f505,plain,(
% 35.60/6.42 ~! [X0 : list @ a,X1 : list @ a] : ((xs = (append @ a @ X0 @ (cons @ a @ n @ X1))) => (member @ a @ n @ (set2 @ a @ X1)))),
% 35.60/6.42 inference(rectify,[status(thm)],[f34])).
% 35.60/6.42 thf(f34,axiom,(
% 35.60/6.42 ~! [X26 : list @ a,X27 : list @ a] : ((xs = (append @ a @ X26 @ (cons @ a @ n @ X27))) => (member @ a @ n @ (set2 @ a @ X27)))),
% 35.60/6.42 file('/export/starexec/sandbox2/tmp/tmp.fWo8BEA7MH/DTF2THF_22272.p',fact_33__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062ys_Azs_O_A_092_060lbrakk_062XS_H_A_061_Ays_A_064_An_A_D_Azs_059_An_A_092_060notin_062_Aset_Azs_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062)).
% 35.60/6.42 thf(f800,plain,(
% 35.60/6.42 (xs = (append @ a @ ys @ (cons @ a @ n @ zs)))),
% 35.60/6.42 inference(cnf_transformation,[status(thm)],[f6])).
% 35.60/6.42 thf(f6,axiom,(
% 35.60/6.42 (xs = (append @ a @ ys @ (cons @ a @ n @ zs)))),
% 35.60/6.42 file('/export/starexec/sandbox2/tmp/tmp.fWo8BEA7MH/DTF2THF_22272.p',fact_5_XS_H)).
% 35.60/6.42 thf(f887,plain,(
% 35.60/6.42 ((coinductive_llist_of @ a @ sK37) = (coinductive_llist_of @ a @ (append @ a @ sK15 @ (cons @ a @ n @ sK16))))),
% 35.60/6.42 inference(definition_unfolding,[status(thm)],[f850,f835,f774])).
% 35.60/6.42 thf(f850,plain,(
% 35.60/6.42 (xs4 = (coinductive_llist_of @ a @ xs))),
% 35.60/6.42 inference(cnf_transformation,[status(thm)],[f1])).
% 35.60/6.42 thf(f1,axiom,(
% 35.60/6.42 (xs4 = (coinductive_llist_of @ a @ xs))),
% 35.60/6.42 file('/export/starexec/sandbox2/tmp/tmp.fWo8BEA7MH/DTF2THF_22272.p',fact_0_xs_H)).
% 35.60/6.42 thf(f4209,plain,(
% 35.60/6.42 ((member @ coinductive_llist @ a @ (coinductive_LCons @ a @ n @ (coinductive_lappend @ a @ (coinductive_llist_of @ a @ (append @ a @ ys @ (cons @ a @ n @ zs))) @ (coinductive_LCons @ a @ x @ xs3))) @ (koenig916195507_paths @ a @ graph)) != $true)),
% 35.60/6.42 inference(backward_demodulation,[status(thm)],[f1079,f4206])).
% 35.60/6.42 thf(f4206,plain,(
% 35.60/6.42 ( ! [X0 : $tType,X2 : X0,X3 : list @ X0,X1 : list @ X0,X4 : coinductive_llist @ X0] : (((coinductive_lappend @ X0 @ (coinductive_llist_of @ X0 @ (append @ X0 @ X1 @ (cons @ X0 @ X2 @ X3))) @ X4) = (coinductive_lappend @ X0 @ (coinductive_llist_of @ X0 @ X1) @ (coinductive_LCons @ X0 @ X2 @ (coinductive_lappend @ X0 @ (coinductive_llist_of @ X0 @ X3) @ X4))))) )),
% 35.60/6.42 inference(forward_demodulation,[status(thm)],[f4196,f735])).
% 35.60/6.42 thf(f735,plain,(
% 35.60/6.42 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X3 : coinductive_llist @ X0,X1 : X0] : (((coinductive_lappend @ X0 @ (coinductive_LCons @ X0 @ X1 @ X2) @ X3) = (coinductive_LCons @ X0 @ X1 @ (coinductive_lappend @ X0 @ X2 @ X3)))) )),
% 35.60/6.42 inference(cnf_transformation,[status(thm)],[f597])).
% 35.60/6.42 thf(f597,plain,(
% 35.60/6.42 ! [X0 : $tType,X1 : X0,X2 : coinductive_llist @ X0,X3 : coinductive_llist @ X0] : ((coinductive_lappend @ X0 @ (coinductive_LCons @ X0 @ X1 @ X2) @ X3) = (coinductive_LCons @ X0 @ X1 @ (coinductive_lappend @ X0 @ X2 @ X3)))),
% 35.60/6.42 inference(rectify,[status(thm)],[f22])).
% 35.60/6.42 thf(f22,axiom,(
% 35.60/6.42 ! [X0 : $tType,X21 : X0,X6 : coinductive_llist @ X0,X20 : coinductive_llist @ X0] : ((coinductive_lappend @ X0 @ (coinductive_LCons @ X0 @ X21 @ X6) @ X20) = (coinductive_LCons @ X0 @ X21 @ (coinductive_lappend @ X0 @ X6 @ X20)))),
% 35.60/6.42 file('/export/starexec/sandbox2/tmp/tmp.fWo8BEA7MH/DTF2THF_22272.p',fact_21_lappend__code_I2_J)).
% 35.60/6.42 thf(f4196,plain,(
% 35.60/6.42 ( ! [X0 : $tType,X2 : X0,X3 : list @ X0,X1 : list @ X0,X4 : coinductive_llist @ X0] : (((coinductive_lappend @ X0 @ (coinductive_llist_of @ X0 @ (append @ X0 @ X1 @ (cons @ X0 @ X2 @ X3))) @ X4) = (coinductive_lappend @ X0 @ (coinductive_llist_of @ X0 @ X1) @ (coinductive_lappend @ X0 @ (coinductive_LCons @ X0 @ X2 @ (coinductive_llist_of @ X0 @ X3)) @ X4)))) )),
% 35.60/6.42 inference(superposition,[status(thm)],[f752,f1205])).
% 35.60/6.42 thf(f1205,plain,(
% 35.60/6.42 ( ! [X0 : $tType,X2 : list @ X0,X3 : list @ X0,X1 : X0] : (((coinductive_lappend @ X0 @ (coinductive_llist_of @ X0 @ X3) @ (coinductive_LCons @ X0 @ X1 @ (coinductive_llist_of @ X0 @ X2))) = (coinductive_llist_of @ X0 @ (append @ X0 @ X3 @ (cons @ X0 @ X1 @ X2))))) )),
% 35.60/6.42 inference(superposition,[status(thm)],[f757,f847])).
% 35.60/6.42 thf(f847,plain,(
% 35.60/6.42 ( ! [X0 : $tType,X2 : list @ X0,X1 : X0] : (((coinductive_llist_of @ X0 @ (cons @ X0 @ X1 @ X2)) = (coinductive_LCons @ X0 @ X1 @ (coinductive_llist_of @ X0 @ X2)))) )),
% 35.60/6.42 inference(cnf_transformation,[status(thm)],[f614])).
% 35.60/6.42 thf(f614,plain,(
% 35.60/6.42 ! [X0 : $tType,X1 : X0,X2 : list @ X0] : ((coinductive_llist_of @ X0 @ (cons @ X0 @ X1 @ X2)) = (coinductive_LCons @ X0 @ X1 @ (coinductive_llist_of @ X0 @ X2)))),
% 35.60/6.42 inference(rectify,[status(thm)],[f65])).
% 35.60/6.42 thf(f65,axiom,(
% 35.60/6.42 ! [X0 : $tType,X6 : X0,X8 : list @ X0] : ((coinductive_llist_of @ X0 @ (cons @ X0 @ X6 @ X8)) = (coinductive_LCons @ X0 @ X6 @ (coinductive_llist_of @ X0 @ X8)))),
% 35.60/6.42 file('/export/starexec/sandbox2/tmp/tmp.fWo8BEA7MH/DTF2THF_22272.p',fact_64_llist__of_Osimps_I2_J)).
% 35.60/6.42 thf(f757,plain,(
% 35.60/6.42 ( ! [X0 : $tType,X2 : list @ X0,X1 : list @ X0] : (((coinductive_llist_of @ X0 @ (append @ X0 @ X1 @ X2)) = (coinductive_lappend @ X0 @ (coinductive_llist_of @ X0 @ X1) @ (coinductive_llist_of @ X0 @ X2)))) )),
% 35.60/6.42 inference(cnf_transformation,[status(thm)],[f596])).
% 35.60/6.42 thf(f596,plain,(
% 35.60/6.42 ! [X0 : $tType,X1 : list @ X0,X2 : list @ X0] : ((coinductive_llist_of @ X0 @ (append @ X0 @ X1 @ X2)) = (coinductive_lappend @ X0 @ (coinductive_llist_of @ X0 @ X1) @ (coinductive_llist_of @ X0 @ X2)))),
% 35.60/6.42 inference(rectify,[status(thm)],[f66])).
% 35.60/6.42 thf(f66,axiom,(
% 35.60/6.42 ! [X0 : $tType,X8 : list @ X0,X20 : list @ X0] : ((coinductive_lappend @ X0 @ (coinductive_llist_of @ X0 @ X8) @ (coinductive_llist_of @ X0 @ X20)) = (coinductive_llist_of @ X0 @ (append @ X0 @ X8 @ X20)))),
% 35.60/6.42 file('/export/starexec/sandbox2/tmp/tmp.fWo8BEA7MH/DTF2THF_22272.p',fact_65_lappend__llist__of__llist__of)).
% 35.60/6.42 thf(f752,plain,(
% 35.60/6.42 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X3 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : (((coinductive_lappend @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2) @ X3) = (coinductive_lappend @ X0 @ X1 @ (coinductive_lappend @ X0 @ X2 @ X3)))) )),
% 35.60/6.42 inference(cnf_transformation,[status(thm)],[f598])).
% 35.60/6.42 thf(f598,plain,(
% 35.60/6.42 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0,X3 : coinductive_llist @ X0] : ((coinductive_lappend @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2) @ X3) = (coinductive_lappend @ X0 @ X1 @ (coinductive_lappend @ X0 @ X2 @ X3)))),
% 35.60/6.42 inference(rectify,[status(thm)],[f63])).
% 35.60/6.42 thf(f63,axiom,(
% 35.60/6.42 ! [X0 : $tType,X8 : coinductive_llist @ X0,X20 : coinductive_llist @ X0,X44 : coinductive_llist @ X0] : ((coinductive_lappend @ X0 @ (coinductive_lappend @ X0 @ X8 @ X20) @ X44) = (coinductive_lappend @ X0 @ X8 @ (coinductive_lappend @ X0 @ X20 @ X44)))),
% 35.60/6.42 file('/export/starexec/sandbox2/tmp/tmp.fWo8BEA7MH/DTF2THF_22272.p',fact_62_lappend__assoc)).
% 35.60/6.42 thf(f1079,plain,(
% 35.60/6.42 ((member @ coinductive_llist @ a @ (coinductive_LCons @ a @ n @ (coinductive_lappend @ a @ (coinductive_llist_of @ a @ ys) @ (coinductive_LCons @ a @ n @ (coinductive_lappend @ a @ (coinductive_llist_of @ a @ zs) @ (coinductive_LCons @ a @ x @ xs3))))) @ (koenig916195507_paths @ a @ graph)) != $true)),
% 35.60/6.42 inference(forward_demodulation,[status(thm)],[f1078,f865])).
% 35.60/6.42 thf(f865,plain,(
% 35.60/6.42 ( ! [X0 : $tType,X2 : X0,X3 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : (((coinductive_lappend @ X0 @ X1 @ (coinductive_LCons @ X0 @ X2 @ X3)) = (coinductive_lappend @ X0 @ (coinductive_lappend @ X0 @ X1 @ (coinductive_LCons @ X0 @ X2 @ coinductive_LNil @ X0)) @ X3))) )),
% 35.60/6.42 inference(cnf_transformation,[status(thm)],[f601])).
% 35.60/6.42 thf(f601,plain,(
% 35.60/6.42 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : X0,X3 : coinductive_llist @ X0] : ((coinductive_lappend @ X0 @ X1 @ (coinductive_LCons @ X0 @ X2 @ X3)) = (coinductive_lappend @ X0 @ (coinductive_lappend @ X0 @ X1 @ (coinductive_LCons @ X0 @ X2 @ coinductive_LNil @ X0)) @ X3))),
% 35.60/6.42 inference(rectify,[status(thm)],[f23])).
% 35.60/6.42 thf(f23,axiom,(
% 35.60/6.42 ! [X0 : $tType,X8 : coinductive_llist @ X0,X7 : X0,X20 : coinductive_llist @ X0] : ((coinductive_lappend @ X0 @ (coinductive_lappend @ X0 @ X8 @ (coinductive_LCons @ X0 @ X7 @ coinductive_LNil @ X0)) @ X20) = (coinductive_lappend @ X0 @ X8 @ (coinductive_LCons @ X0 @ X7 @ X20)))),
% 35.60/6.42 file('/export/starexec/sandbox2/tmp/tmp.fWo8BEA7MH/DTF2THF_22272.p',fact_22_lappend__snocL1__conv__LCons2)).
% 35.60/6.42 thf(f1078,plain,(
% 35.60/6.42 ((member @ coinductive_llist @ a @ (coinductive_LCons @ a @ n @ (coinductive_lappend @ a @ (coinductive_llist_of @ a @ ys) @ (coinductive_LCons @ a @ n @ (coinductive_lappend @ a @ (coinductive_lappend @ a @ (coinductive_llist_of @ a @ zs) @ (coinductive_LCons @ a @ x @ coinductive_LNil @ a)) @ xs3)))) @ (koenig916195507_paths @ a @ graph)) != $true)),
% 35.60/6.42 inference(forward_demodulation,[status(thm)],[f1077,f735])).
% 35.60/6.42 thf(f1077,plain,(
% 35.60/6.42 ((member @ coinductive_llist @ a @ (coinductive_lappend @ a @ (coinductive_LCons @ a @ n @ (coinductive_llist_of @ a @ ys)) @ (coinductive_LCons @ a @ n @ (coinductive_lappend @ a @ (coinductive_lappend @ a @ (coinductive_llist_of @ a @ zs) @ (coinductive_LCons @ a @ x @ coinductive_LNil @ a)) @ xs3))) @ (koenig916195507_paths @ a @ graph)) != $true)),
% 35.60/6.42 inference(backward_demodulation,[status(thm)],[f843,f735])).
% 35.60/6.42 thf(f843,plain,(
% 35.60/6.42 ((member @ coinductive_llist @ a @ (coinductive_lappend @ a @ (coinductive_LCons @ a @ n @ (coinductive_llist_of @ a @ ys)) @ (coinductive_lappend @ a @ (coinductive_LCons @ a @ n @ (coinductive_lappend @ a @ (coinductive_llist_of @ a @ zs) @ (coinductive_LCons @ a @ x @ coinductive_LNil @ a))) @ xs3)) @ (koenig916195507_paths @ a @ graph)) != $true)),
% 35.60/6.42 inference(cnf_transformation,[status(thm)],[f591])).
% 35.60/6.42 thf(f591,plain,(
% 35.60/6.42 ((member @ coinductive_llist @ a @ (coinductive_lappend @ a @ (coinductive_LCons @ a @ n @ (coinductive_llist_of @ a @ ys)) @ (coinductive_lappend @ a @ (coinductive_LCons @ a @ n @ (coinductive_lappend @ a @ (coinductive_llist_of @ a @ zs) @ (coinductive_LCons @ a @ x @ coinductive_LNil @ a))) @ xs3)) @ (koenig916195507_paths @ a @ graph)) != $true)),
% 35.60/6.42 inference(flattening,[status(thm)],[f542])).
% 35.60/6.42 thf(f542,plain,(
% 35.60/6.42 ~((member @ coinductive_llist @ a @ (coinductive_lappend @ a @ (coinductive_LCons @ a @ n @ (coinductive_llist_of @ a @ ys)) @ (coinductive_lappend @ a @ (coinductive_LCons @ a @ n @ (coinductive_lappend @ a @ (coinductive_llist_of @ a @ zs) @ (coinductive_LCons @ a @ x @ coinductive_LNil @ a))) @ xs3)) @ (koenig916195507_paths @ a @ graph)) = $true)),
% 35.60/6.42 inference(fool_elimination,[status(thm)],[f541])).
% 35.60/6.42 thf(f541,plain,(
% 35.60/6.42 ~(member @ coinductive_llist @ a @ (coinductive_lappend @ a @ (coinductive_LCons @ a @ n @ (coinductive_llist_of @ a @ ys)) @ (coinductive_lappend @ a @ (coinductive_LCons @ a @ n @ (coinductive_lappend @ a @ (coinductive_llist_of @ a @ zs) @ (coinductive_LCons @ a @ x @ coinductive_LNil @ a))) @ xs3)) @ (koenig916195507_paths @ a @ graph))),
% 35.60/6.42 inference(rectify,[status(thm)],[f259])).
% 35.60/6.42 thf(f259,negated_conjecture,(
% 35.60/6.42 ~(member @ coinductive_llist @ a @ (coinductive_lappend @ a @ (coinductive_LCons @ a @ n @ (coinductive_llist_of @ a @ ys)) @ (coinductive_lappend @ a @ (coinductive_LCons @ a @ n @ (coinductive_lappend @ a @ (coinductive_llist_of @ a @ zs) @ (coinductive_LCons @ a @ x @ coinductive_LNil @ a))) @ xs3)) @ (koenig916195507_paths @ a @ graph))),
% 35.60/6.42 inference(negated_conjecture,[status(cth)],[f258])).
% 35.60/6.42 thf(f258,conjecture,(
% 35.60/6.42 (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ (coinductive_LCons @ a @ n @ (coinductive_llist_of @ a @ ys)) @ (coinductive_lappend @ a @ (coinductive_LCons @ a @ n @ (coinductive_lappend @ a @ (coinductive_llist_of @ a @ zs) @ (coinductive_LCons @ a @ x @ coinductive_LNil @ a))) @ xs3)) @ (koenig916195507_paths @ a @ graph))),
% 35.60/6.42 file('/export/starexec/sandbox2/tmp/tmp.fWo8BEA7MH/DTF2THF_22272.p',conj_0)).
% 35.60/6.42 % SZS output end Proof for DTF2THF_22272
% 35.60/6.42 % (22651)------------------------------
% 35.60/6.42 % (22651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.60/6.42 % (22651)Termination reason: Refutation
% 35.60/6.42
% 35.60/6.42 % (22651)Memory used [KB]: 9210
% 35.60/6.42 % (22651)Time elapsed: 0.833 s
% 35.60/6.42 % (22651)Instructions burned: 2599 (million)
% 35.60/6.42 % (22651)------------------------------
% 35.60/6.42 % (22651)------------------------------
% 35.60/6.42 % (22485)Success in time 4.865 s
%------------------------------------------------------------------------------