%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : COM197^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 08:41:55 AM UTC 2026
% Result : Theorem 10.39s 2.97s
% Output : Refutation 10.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM197^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n014.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 04:17:27 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.48 ---- Original DTF file ---
% 0.20/0.48 thf(spec,logic,$$dhol).
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : COM197^1 : TPTP v9.2.1. Released v7.0.0.
% 0.20/0.48 % Domain : Computing Theory
% 0.20/0.48 % Problem : Koenig's lemma (about infinite trees) 51
% 0.20/0.48 % Version : [Bla16] axioms : Especial.
% 0.20/0.48 % English :
% 0.20/0.48
% 0.20/0.48 % Refs : [BH+14] Blanchette et al. (2014), Truly Modular (Co)datatypes
% 0.20/0.48 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.20/0.48 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.20/0.48 % Source : [Bla16]
% 0.20/0.48 % Names : koenig__51.p [Bla16]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % Rating : 0.67 v8.1.0, 0.75 v7.5.0, 1.00 v7.1.0
% 0.20/0.48 % Syntax : Number of formulae : 337 ( 144 unt; 73 typ; 0 def)
% 0.20/0.48 % Number of atoms : 638 ( 344 equ; 4 cnn)
% 0.20/0.48 % Maximal formula atoms : 7 ( 2 avg)
% 0.20/0.48 % Number of connectives : 4751 ( 73 ~; 9 |; 66 &;4318 @)
% 0.20/0.48 % ( 0 <=>; 285 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 22 ( 8 avg)
% 0.20/0.48 % Number of types : 3 ( 2 usr)
% 0.20/0.48 % Number of type conns : 417 ( 417 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 75 ( 71 usr; 5 con; 0-7 aty)
% 0.20/0.48 % Number of variables : 1311 ( 50 ^;1125 !; 59 ?;1311 :)
% 0.20/0.48 % ( 77 !>; 0 ?*; 0 @-; 0 @+)
% 0.20/0.48 % SPC : TH1_THM_EQU_NAR
% 0.20/0.48
% 0.20/0.48 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.20/0.48 % 2016-07-13 14:38:41.216
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 %----Could-be-implicit typings (7)
% 0.20/0.48 thf(ty_t_TreeFI_OtreeFI,type,
% 0.20/0.48 treeFI: $tType > $tType ).
% 0.20/0.48
% 0.20/0.48 thf(ty_t_Stream_Ostream,type,
% 0.20/0.48 stream: $tType > $tType ).
% 0.20/0.48
% 0.20/0.48 thf(ty_t_List_Olist,type,
% 0.20/0.48 list: $tType > $tType ).
% 0.20/0.48
% 0.20/0.48 thf(ty_t_Set_Oset,type,
% 0.20/0.48 set: $tType > $tType ).
% 0.20/0.48
% 0.20/0.48 thf(ty_t_Nat_Onat,type,
% 0.20/0.48 nat: $tType ).
% 0.20/0.48
% 0.20/0.48 thf(ty_t_itself,type,
% 0.20/0.48 itself: $tType > $tType ).
% 0.20/0.48
% 0.20/0.48 thf(ty_tf_a,type,
% 0.20/0.48 a: $tType ).
% 0.20/0.48
% 0.20/0.48 %----Explicit typings (66)
% 0.20/0.48 thf(sy_cl_HOL_Otype,type,
% 0.20/0.48 type:
% 0.20/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_cl_Orderings_Olinorder,type,
% 0.20/0.48 linorder:
% 0.20/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.20/0.48 semilattice_sup:
% 0.20/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Fun_Ocomp,type,
% 0.20/0.48 comp:
% 0.20/0.48 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Fun_Ofun__upd,type,
% 0.20/0.48 fun_upd:
% 0.20/0.48 !>[A: $tType,B: $tType] : ( ( A > B ) > A > B > A > B ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_If,type,
% 0.20/0.48 if:
% 0.20/0.48 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Koenig__Mirabelle__gyfieiccqy_OinfiniteTr,type,
% 0.20/0.48 koenig488553731niteTr:
% 0.20/0.48 !>[A: $tType] : ( ( treeFI @ A ) > $o ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Koenig__Mirabelle__gyfieiccqy_OkonigPath,type,
% 0.20/0.48 koenig1103336060igPath:
% 0.20/0.48 !>[A: $tType] : ( ( treeFI @ A ) > ( stream @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Koenig__Mirabelle__gyfieiccqy_OproperPath,type,
% 0.20/0.48 koenig1755522246erPath:
% 0.20/0.48 !>[A: $tType] : ( ( stream @ A ) > ( treeFI @ A ) > $o ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.20/0.48 sup_sup:
% 0.20/0.48 !>[A: $tType] : ( A > A > A ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Lattices__Big_Osemilattice__sup__class_OSup__fin,type,
% 0.20/0.48 lattic477160up_fin:
% 0.20/0.48 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Oappend,type,
% 0.20/0.48 append:
% 0.20/0.48 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Ocoset,type,
% 0.20/0.48 coset:
% 0.20/0.48 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Ofold,type,
% 0.20/0.48 fold:
% 0.20/0.48 !>[A: $tType,B: $tType] : ( ( A > B > B ) > ( list @ A ) > B > B ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Ofoldr,type,
% 0.20/0.48 foldr:
% 0.20/0.48 !>[A: $tType,B: $tType] : ( ( A > B > B ) > ( list @ A ) > B > B ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Oinsert,type,
% 0.20/0.48 insert:
% 0.20/0.48 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Olinorder__class_Oinsort__key,type,
% 0.20/0.48 linorder_insort_key:
% 0.20/0.48 !>[B: $tType,A: $tType] : ( ( B > A ) > B > ( list @ B ) > ( list @ B ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Olinorder__class_Osorted,type,
% 0.20/0.48 linorder_sorted:
% 0.20/0.48 !>[A: $tType] : ( ( list @ A ) > $o ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Olist_OCons,type,
% 0.20/0.48 cons:
% 0.20/0.48 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Olist_ONil,type,
% 0.20/0.48 nil:
% 0.20/0.48 !>[A: $tType] : ( list @ A ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Olist_Ohd,type,
% 0.20/0.48 hd:
% 0.20/0.48 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Olist_Olist__all,type,
% 0.20/0.48 list_all:
% 0.20/0.48 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Olist_Omap,type,
% 0.20/0.48 map:
% 0.20/0.48 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( list @ A ) > ( list @ Aa ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Olist_Oset,type,
% 0.20/0.48 set2:
% 0.20/0.48 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Olist_Otl,type,
% 0.20/0.48 tl:
% 0.20/0.48 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Olist__update,type,
% 0.20/0.48 list_update:
% 0.20/0.48 !>[A: $tType] : ( ( list @ A ) > nat > A > ( list @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Omember,type,
% 0.20/0.48 member:
% 0.20/0.48 !>[A: $tType] : ( ( list @ A ) > A > $o ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Oremove1,type,
% 0.20/0.48 remove1:
% 0.20/0.48 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Orev,type,
% 0.20/0.48 rev:
% 0.20/0.48 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_List_Ounion,type,
% 0.20/0.48 union:
% 0.20/0.48 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.20/0.48 ord_less_eq:
% 0.20/0.48 !>[A: $tType] : ( A > A > $o ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Pure_Otype,type,
% 0.20/0.48 type2:
% 0.20/0.48 !>[A: $tType] : ( itself @ A ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Set_OCollect,type,
% 0.20/0.48 collect:
% 0.20/0.48 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Set_Oinsert,type,
% 0.20/0.48 insert2:
% 0.20/0.48 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Set_Othe__elem,type,
% 0.20/0.48 the_elem:
% 0.20/0.48 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Ocycle,type,
% 0.20/0.48 cycle:
% 0.20/0.48 !>[A: $tType] : ( ( list @ A ) > ( stream @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Oflat,type,
% 0.20/0.48 flat:
% 0.20/0.48 !>[A: $tType] : ( ( stream @ ( list @ A ) ) > ( stream @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Osdrop__while,type,
% 0.20/0.48 sdrop_while:
% 0.20/0.48 !>[A: $tType] : ( ( A > $o ) > ( stream @ A ) > ( stream @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Osfilter,type,
% 0.20/0.48 sfilter:
% 0.20/0.48 !>[A: $tType] : ( ( A > $o ) > ( stream @ A ) > ( stream @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Oshift,type,
% 0.20/0.48 shift:
% 0.20/0.48 !>[A: $tType] : ( ( list @ A ) > ( stream @ A ) > ( stream @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Osinterleave,type,
% 0.20/0.48 sinterleave:
% 0.20/0.48 !>[A: $tType] : ( ( stream @ A ) > ( stream @ A ) > ( stream @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Osmap2,type,
% 0.20/0.48 smap2:
% 0.20/0.48 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( stream @ A ) > ( stream @ B ) > ( stream @ C ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Osmember,type,
% 0.20/0.48 smember:
% 0.20/0.48 !>[A: $tType] : ( A > ( stream @ A ) > $o ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Ostake,type,
% 0.20/0.48 stake:
% 0.20/0.48 !>[A: $tType] : ( nat > ( stream @ A ) > ( list @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Ostream_OSCons,type,
% 0.20/0.48 sCons:
% 0.20/0.48 !>[A: $tType] : ( A > ( stream @ A ) > ( stream @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Ostream_Ocase__stream,type,
% 0.20/0.48 case_stream:
% 0.20/0.48 !>[A: $tType,B: $tType] : ( ( A > ( stream @ A ) > B ) > ( stream @ A ) > B ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Ostream_Ocorec__stream,type,
% 0.20/0.48 corec_stream:
% 0.20/0.48 !>[C: $tType,A: $tType] : ( ( C > A ) > ( C > $o ) > ( C > ( stream @ A ) ) > ( C > C ) > C > ( stream @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Ostream_Opred__stream,type,
% 0.20/0.48 pred_stream:
% 0.20/0.48 !>[A: $tType] : ( ( A > $o ) > ( stream @ A ) > $o ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Ostream_Oshd,type,
% 0.20/0.48 shd:
% 0.20/0.48 !>[A: $tType] : ( ( stream @ A ) > A ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Ostream_Osmap,type,
% 0.20/0.48 smap:
% 0.20/0.48 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( stream @ A ) > ( stream @ Aa ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Ostream_Osset,type,
% 0.20/0.48 sset:
% 0.20/0.48 !>[A: $tType] : ( ( stream @ A ) > ( set @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Ostream_Ostl,type,
% 0.20/0.48 stl:
% 0.20/0.48 !>[A: $tType] : ( ( stream @ A ) > ( stream @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Ostream__all,type,
% 0.20/0.48 stream_all:
% 0.20/0.48 !>[A: $tType] : ( ( A > $o ) > ( stream @ A ) > $o ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_Stream_Ostreams,type,
% 0.20/0.48 streams:
% 0.20/0.48 !>[A: $tType] : ( ( set @ A ) > ( set @ ( stream @ A ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_TreeFI_OtreeFI_OTree,type,
% 0.20/0.48 tree:
% 0.20/0.48 !>[A: $tType] : ( A > ( list @ ( treeFI @ A ) ) > ( treeFI @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_TreeFI_OtreeFI_Ocase__treeFI,type,
% 0.20/0.48 case_treeFI:
% 0.20/0.48 !>[A: $tType,B: $tType] : ( ( A > ( list @ ( treeFI @ A ) ) > B ) > ( treeFI @ A ) > B ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_TreeFI_OtreeFI_Olab,type,
% 0.20/0.48 lab:
% 0.20/0.48 !>[A: $tType] : ( ( treeFI @ A ) > A ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_TreeFI_OtreeFI_Omap__treeFI,type,
% 0.20/0.48 map_treeFI:
% 0.20/0.48 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( treeFI @ A ) > ( treeFI @ Aa ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_TreeFI_OtreeFI_Opred__treeFI,type,
% 0.20/0.48 pred_treeFI:
% 0.20/0.48 !>[A: $tType] : ( ( A > $o ) > ( treeFI @ A ) > $o ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_TreeFI_OtreeFI_Oset__treeFI,type,
% 0.20/0.48 set_treeFI:
% 0.20/0.48 !>[A: $tType] : ( ( treeFI @ A ) > ( set @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_TreeFI_OtreeFI_Osub,type,
% 0.20/0.48 sub:
% 0.20/0.48 !>[A: $tType] : ( ( treeFI @ A ) > ( list @ ( treeFI @ A ) ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_TreeFI_Otrev,type,
% 0.20/0.48 trev:
% 0.20/0.48 !>[A: $tType] : ( ( treeFI @ A ) > ( treeFI @ A ) ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_c_member,type,
% 0.20/0.48 member2:
% 0.20/0.48 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.20/0.48
% 0.20/0.48 thf(sy_v_as,type,
% 0.20/0.48 as: stream @ a ).
% 0.20/0.48
% 0.20/0.48 thf(sy_v_phi,type,
% 0.20/0.48 phi: ( stream @ a ) > ( treeFI @ a ) > $o ).
% 0.20/0.48
% 0.20/0.48 thf(sy_v_tr,type,
% 0.20/0.48 tr: treeFI @ a ).
% 0.20/0.48
% 0.20/0.48 %----Relevant facts (256)
% 0.20/0.48 thf(fact_0__C_K_K_K_C,axiom,
% 0.20/0.48 ! [As: stream @ a,Tr: treeFI @ a] :
% 0.20/0.48 ( ( phi @ As @ Tr )
% 0.20/0.48 => ? [X: treeFI @ a] :
% 0.20/0.48 ( ( member2 @ ( treeFI @ a ) @ X @ ( set2 @ ( treeFI @ a ) @ ( sub @ a @ Tr ) ) )
% 0.20/0.48 & ( ( phi @ ( stl @ a @ As ) @ X )
% 0.20/0.48 | ( koenig1755522246erPath @ a @ ( stl @ a @ As ) @ X ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % "***"
% 0.20/0.48 thf(fact_1__C_K_C,axiom,
% 0.20/0.48 phi @ as @ tr ).
% 0.20/0.48
% 0.20/0.48 % "*"
% 0.20/0.48 thf(fact_2_properPath_Ocases,axiom,
% 0.20/0.48 ! [A: $tType,A1: stream @ A,A2: treeFI @ A] :
% 0.20/0.48 ( ( koenig1755522246erPath @ A @ A1 @ A2 )
% 0.20/0.48 => ~ ( ( ( shd @ A @ A1 )
% 0.20/0.48 = ( lab @ A @ A2 ) )
% 0.20/0.48 => ! [Tr2: treeFI @ A] :
% 0.20/0.48 ( ( member2 @ ( treeFI @ A ) @ Tr2 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ A2 ) ) )
% 0.20/0.48 => ~ ( koenig1755522246erPath @ A @ ( stl @ A @ A1 ) @ Tr2 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % properPath.cases
% 0.20/0.48 thf(fact_3_properPath_Osimps,axiom,
% 0.20/0.48 ! [A: $tType] :
% 0.20/0.48 ( ( koenig1755522246erPath @ A )
% 0.20/0.48 = ( ^ [A12: stream @ A,A22: treeFI @ A] :
% 0.20/0.48 ? [As2: stream @ A,Tr3: treeFI @ A,Tr4: treeFI @ A] :
% 0.20/0.48 ( ( A12 = As2 )
% 0.20/0.48 & ( A22 = Tr3 )
% 0.20/0.48 & ( ( shd @ A @ As2 )
% 0.20/0.48 = ( lab @ A @ Tr3 ) )
% 0.20/0.48 & ( member2 @ ( treeFI @ A ) @ Tr4 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr3 ) ) )
% 0.20/0.48 & ( koenig1755522246erPath @ A @ ( stl @ A @ As2 ) @ Tr4 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % properPath.simps
% 0.20/0.48 thf(fact_4_properPath_Ointros,axiom,
% 0.20/0.48 ! [A: $tType,As: stream @ A,Tr: treeFI @ A,Tr5: treeFI @ A] :
% 0.20/0.48 ( ( ( shd @ A @ As )
% 0.20/0.48 = ( lab @ A @ Tr ) )
% 0.20/0.48 => ( ( member2 @ ( treeFI @ A ) @ Tr5 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr ) ) )
% 0.20/0.48 => ( ( koenig1755522246erPath @ A @ ( stl @ A @ As ) @ Tr5 )
% 0.20/0.48 => ( koenig1755522246erPath @ A @ As @ Tr ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % properPath.intros
% 0.20/0.48 thf(fact_5_properPath_Ocoinduct,axiom,
% 0.20/0.48 ! [A: $tType,X2: ( stream @ A ) > ( treeFI @ A ) > $o,X3: stream @ A,Xa: treeFI @ A] :
% 0.20/0.48 ( ( X2 @ X3 @ Xa )
% 0.20/0.48 => ( ! [X: stream @ A,Xa2: treeFI @ A] :
% 0.20/0.48 ( ( X2 @ X @ Xa2 )
% 0.20/0.48 => ? [As3: stream @ A,Tr6: treeFI @ A,Tr7: treeFI @ A] :
% 0.20/0.48 ( ( X = As3 )
% 0.20/0.48 & ( Xa2 = Tr6 )
% 0.20/0.48 & ( ( shd @ A @ As3 )
% 0.20/0.48 = ( lab @ A @ Tr6 ) )
% 0.20/0.48 & ( member2 @ ( treeFI @ A ) @ Tr7 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr6 ) ) )
% 0.20/0.48 & ( ( X2 @ ( stl @ A @ As3 ) @ Tr7 )
% 0.20/0.48 | ( koenig1755522246erPath @ A @ ( stl @ A @ As3 ) @ Tr7 ) ) ) )
% 0.20/0.48 => ( koenig1755522246erPath @ A @ X3 @ Xa ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % properPath.coinduct
% 0.20/0.48 thf(fact_6__C_K_K_C,axiom,
% 0.20/0.48 ! [As: stream @ a,Tr: treeFI @ a] :
% 0.20/0.48 ( ( phi @ As @ Tr )
% 0.20/0.48 => ( ( shd @ a @ As )
% 0.20/0.48 = ( lab @ a @ Tr ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % "**"
% 0.20/0.48 thf(fact_7_treeFI_Oexpand,axiom,
% 0.20/0.48 ! [A: $tType,TreeFI: treeFI @ A,TreeFI2: treeFI @ A] :
% 0.20/0.48 ( ( ( ( lab @ A @ TreeFI )
% 0.20/0.48 = ( lab @ A @ TreeFI2 ) )
% 0.20/0.48 & ( ( sub @ A @ TreeFI )
% 0.20/0.48 = ( sub @ A @ TreeFI2 ) ) )
% 0.20/0.48 => ( TreeFI = TreeFI2 ) ) ).
% 0.20/0.48
% 0.20/0.48 % treeFI.expand
% 0.20/0.48 thf(fact_8_stream_Oexpand,axiom,
% 0.20/0.48 ! [A: $tType,Stream: stream @ A,Stream2: stream @ A] :
% 0.20/0.48 ( ( ( ( shd @ A @ Stream )
% 0.20/0.48 = ( shd @ A @ Stream2 ) )
% 0.20/0.48 & ( ( stl @ A @ Stream )
% 0.20/0.48 = ( stl @ A @ Stream2 ) ) )
% 0.20/0.48 => ( Stream = Stream2 ) ) ).
% 0.20/0.48
% 0.20/0.48 % stream.expand
% 0.20/0.48 thf(fact_9_stream_Ocoinduct,axiom,
% 0.20/0.48 ! [A: $tType,R: ( stream @ A ) > ( stream @ A ) > $o,Stream: stream @ A,Stream2: stream @ A] :
% 0.20/0.48 ( ( R @ Stream @ Stream2 )
% 0.20/0.48 => ( ! [Stream3: stream @ A,Stream4: stream @ A] :
% 0.20/0.48 ( ( R @ Stream3 @ Stream4 )
% 0.20/0.48 => ( ( ( shd @ A @ Stream3 )
% 0.20/0.48 = ( shd @ A @ Stream4 ) )
% 0.20/0.48 & ( R @ ( stl @ A @ Stream3 ) @ ( stl @ A @ Stream4 ) ) ) )
% 0.20/0.48 => ( Stream = Stream2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % stream.coinduct
% 0.20/0.48 thf(fact_10_stream_Ocoinduct__strong,axiom,
% 0.20/0.48 ! [A: $tType,R: ( stream @ A ) > ( stream @ A ) > $o,Stream: stream @ A,Stream2: stream @ A] :
% 0.20/0.48 ( ( R @ Stream @ Stream2 )
% 0.20/0.48 => ( ! [Stream3: stream @ A,Stream4: stream @ A] :
% 0.20/0.48 ( ( R @ Stream3 @ Stream4 )
% 0.20/0.48 => ( ( ( shd @ A @ Stream3 )
% 0.20/0.48 = ( shd @ A @ Stream4 ) )
% 0.20/0.48 & ( ( R @ ( stl @ A @ Stream3 ) @ ( stl @ A @ Stream4 ) )
% 0.20/0.48 | ( ( stl @ A @ Stream3 )
% 0.20/0.48 = ( stl @ A @ Stream4 ) ) ) ) )
% 0.20/0.48 => ( Stream = Stream2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % stream.coinduct_strong
% 0.20/0.48 thf(fact_11_konigPath_Osimps_I1_J,axiom,
% 0.20/0.48 ! [A: $tType,T: treeFI @ A] :
% 0.20/0.48 ( ( shd @ A @ ( koenig1103336060igPath @ A @ T ) )
% 0.20/0.48 = ( lab @ A @ T ) ) ).
% 0.20/0.48
% 0.20/0.48 % konigPath.simps(1)
% 0.20/0.48 thf(fact_12_infiniteTr__sub,axiom,
% 0.20/0.48 ! [A: $tType,Tr: treeFI @ A] :
% 0.20/0.48 ( ( koenig488553731niteTr @ A @ Tr )
% 0.20/0.48 => ? [X: treeFI @ A] :
% 0.20/0.48 ( ( member2 @ ( treeFI @ A ) @ X @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr ) ) )
% 0.20/0.48 & ( koenig488553731niteTr @ A @ X ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % infiniteTr_sub
% 0.20/0.48 thf(fact_13_infiniteTr_Ocases,axiom,
% 0.20/0.48 ! [A: $tType,A3: treeFI @ A] :
% 0.20/0.48 ( ( koenig488553731niteTr @ A @ A3 )
% 0.20/0.48 => ~ ! [Tr2: treeFI @ A] :
% 0.20/0.48 ( ( member2 @ ( treeFI @ A ) @ Tr2 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ A3 ) ) )
% 0.20/0.48 => ~ ( koenig488553731niteTr @ A @ Tr2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % infiniteTr.cases
% 0.20/0.48 thf(fact_14_infiniteTr_Osimps,axiom,
% 0.20/0.48 ! [A: $tType] :
% 0.20/0.48 ( ( koenig488553731niteTr @ A )
% 0.20/0.48 = ( ^ [A4: treeFI @ A] :
% 0.20/0.48 ? [Tr4: treeFI @ A,Tr3: treeFI @ A] :
% 0.20/0.48 ( ( A4 = Tr3 )
% 0.20/0.48 & ( member2 @ ( treeFI @ A ) @ Tr4 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr3 ) ) )
% 0.20/0.48 & ( koenig488553731niteTr @ A @ Tr4 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % infiniteTr.simps
% 0.20/0.48 thf(fact_15_infiniteTr__coind,axiom,
% 0.20/0.48 ! [A: $tType,Phi: ( treeFI @ A ) > $o,Tr: treeFI @ A] :
% 0.20/0.48 ( ( Phi @ Tr )
% 0.20/0.48 => ( ! [Tr8: treeFI @ A] :
% 0.20/0.48 ( ( Phi @ Tr8 )
% 0.20/0.48 => ? [X4: treeFI @ A] :
% 0.20/0.48 ( ( member2 @ ( treeFI @ A ) @ X4 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr8 ) ) )
% 0.20/0.48 & ( Phi @ X4 ) ) )
% 0.20/0.48 => ( koenig488553731niteTr @ A @ Tr ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % infiniteTr_coind
% 0.20/0.48 thf(fact_16_infiniteTr_Ointros,axiom,
% 0.20/0.48 ! [A: $tType,Tr5: treeFI @ A,Tr: treeFI @ A] :
% 0.20/0.48 ( ( member2 @ ( treeFI @ A ) @ Tr5 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr ) ) )
% 0.20/0.48 => ( ( koenig488553731niteTr @ A @ Tr5 )
% 0.20/0.48 => ( koenig488553731niteTr @ A @ Tr ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % infiniteTr.intros
% 0.20/0.48 thf(fact_17_infiniteTr_Ocoinduct,axiom,
% 0.20/0.48 ! [A: $tType,X2: ( treeFI @ A ) > $o,X3: treeFI @ A] :
% 0.20/0.48 ( ( X2 @ X3 )
% 0.20/0.48 => ( ! [X: treeFI @ A] :
% 0.20/0.48 ( ( X2 @ X )
% 0.20/0.48 => ? [Tr7: treeFI @ A,Tr6: treeFI @ A] :
% 0.20/0.48 ( ( X = Tr6 )
% 0.20/0.48 & ( member2 @ ( treeFI @ A ) @ Tr7 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr6 ) ) )
% 0.20/0.48 & ( ( X2 @ Tr7 )
% 0.20/0.48 | ( koenig488553731niteTr @ A @ Tr7 ) ) ) )
% 0.20/0.48 => ( koenig488553731niteTr @ A @ X3 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % infiniteTr.coinduct
% 0.20/0.48 thf(fact_18_infiniteTr__strong__coind,axiom,
% 0.20/0.48 ! [A: $tType,Phi: ( treeFI @ A ) > $o,Tr: treeFI @ A] :
% 0.20/0.48 ( ( Phi @ Tr )
% 0.20/0.48 => ( ! [Tr8: treeFI @ A] :
% 0.20/0.48 ( ( Phi @ Tr8 )
% 0.20/0.48 => ? [X4: treeFI @ A] :
% 0.20/0.48 ( ( member2 @ ( treeFI @ A ) @ X4 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr8 ) ) )
% 0.20/0.48 & ( ( Phi @ X4 )
% 0.20/0.48 | ( koenig488553731niteTr @ A @ X4 ) ) ) )
% 0.20/0.48 => ( koenig488553731niteTr @ A @ Tr ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % infiniteTr_strong_coind
% 0.20/0.48 thf(fact_19_treeFI_Ocase__eq__if,axiom,
% 0.20/0.48 ! [B: $tType,A: $tType] :
% 0.20/0.48 ( ( case_treeFI @ A @ B )
% 0.20/0.48 = ( ^ [F: A > ( list @ ( treeFI @ A ) ) > B,TreeFI3: treeFI @ A] : ( F @ ( lab @ A @ TreeFI3 ) @ ( sub @ A @ TreeFI3 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % treeFI.case_eq_if
% 0.20/0.48 thf(fact_20_stream_Ocase__eq__if,axiom,
% 0.20/0.48 ! [B: $tType,A: $tType] :
% 0.20/0.48 ( ( case_stream @ A @ B )
% 0.20/0.48 = ( ^ [F: A > ( stream @ A ) > B,Stream5: stream @ A] : ( F @ ( shd @ A @ Stream5 ) @ ( stl @ A @ Stream5 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % stream.case_eq_if
% 0.20/0.48 thf(fact_21_sdrop__while_Osimps,axiom,
% 0.20/0.48 ! [A: $tType] :
% 0.20/0.48 ( ( sdrop_while @ A )
% 0.20/0.48 = ( ^ [P: A > $o,S: stream @ A] : ( if @ ( stream @ A ) @ ( P @ ( shd @ A @ S ) ) @ ( sdrop_while @ A @ P @ ( stl @ A @ S ) ) @ S ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % sdrop_while.simps
% 0.20/0.48 thf(fact_22_treeFI_Ocollapse,axiom,
% 0.20/0.48 ! [A: $tType,TreeFI: treeFI @ A] :
% 0.20/0.48 ( ( tree @ A @ ( lab @ A @ TreeFI ) @ ( sub @ A @ TreeFI ) )
% 0.20/0.48 = TreeFI ) ).
% 0.20/0.48
% 0.20/0.48 % treeFI.collapse
% 0.20/0.48 thf(fact_23_treeFI_Oset__sel_I2_J,axiom,
% 0.20/0.48 ! [A: $tType,X3: treeFI @ A,A3: treeFI @ A,Xa: A] :
% 0.20/0.48 ( ( member2 @ ( treeFI @ A ) @ X3 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ A3 ) ) )
% 0.20/0.48 => ( ( member2 @ A @ Xa @ ( set_treeFI @ A @ X3 ) )
% 0.20/0.48 => ( member2 @ A @ Xa @ ( set_treeFI @ A @ A3 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % treeFI.set_sel(2)
% 0.20/0.48 thf(fact_24_treeFI_Oexhaust__sel,axiom,
% 0.20/0.48 ! [A: $tType,TreeFI: treeFI @ A] :
% 0.20/0.48 ( TreeFI
% 0.20/0.48 = ( tree @ A @ ( lab @ A @ TreeFI ) @ ( sub @ A @ TreeFI ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % treeFI.exhaust_sel
% 0.20/0.48 thf(fact_25_trev_Osimps_I1_J,axiom,
% 0.20/0.48 ! [A: $tType,T: treeFI @ A] :
% 0.20/0.48 ( ( lab @ A @ ( trev @ A @ T ) )
% 0.20/0.48 = ( lab @ A @ T ) ) ).
% 0.20/0.48
% 0.20/0.48 % trev.simps(1)
% 0.20/0.48 thf(fact_26_stream_Ocollapse,axiom,
% 0.20/0.48 ! [A: $tType,Stream: stream @ A] :
% 0.20/0.48 ( ( sCons @ A @ ( shd @ A @ Stream ) @ ( stl @ A @ Stream ) )
% 0.20/0.48 = Stream ) ).
% 0.20/0.48
% 0.20/0.48 % stream.collapse
% 0.20/0.48 thf(fact_27_in__streams,axiom,
% 0.20/0.48 ! [A: $tType,S2: stream @ A,S3: set @ A] :
% 0.20/0.48 ( ( member2 @ ( stream @ A ) @ ( stl @ A @ S2 ) @ ( streams @ A @ S3 ) )
% 0.20/0.48 => ( ( member2 @ A @ ( shd @ A @ S2 ) @ S3 )
% 0.20/0.48 => ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ S3 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % in_streams
% 0.20/0.48 thf(fact_28_streamsE,axiom,
% 0.20/0.48 ! [A: $tType,S2: stream @ A,A5: set @ A] :
% 0.20/0.48 ( ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) )
% 0.20/0.48 => ~ ( ( member2 @ A @ ( shd @ A @ S2 ) @ A5 )
% 0.20/0.48 => ~ ( member2 @ ( stream @ A ) @ ( stl @ A @ S2 ) @ ( streams @ A @ A5 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % streamsE
% 0.20/0.48 thf(fact_29_stream_Oinject,axiom,
% 0.20/0.48 ! [A: $tType,X1: A,X22: stream @ A,Y1: A,Y2: stream @ A] :
% 0.20/0.48 ( ( ( sCons @ A @ X1 @ X22 )
% 0.20/0.48 = ( sCons @ A @ Y1 @ Y2 ) )
% 0.20/0.48 = ( ( X1 = Y1 )
% 0.20/0.48 & ( X22 = Y2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % stream.inject
% 0.20/0.48 thf(fact_30_treeFI_Oinject,axiom,
% 0.20/0.48 ! [A: $tType,X1: A,X22: list @ ( treeFI @ A ),Y1: A,Y2: list @ ( treeFI @ A )] :
% 0.20/0.48 ( ( ( tree @ A @ X1 @ X22 )
% 0.20/0.48 = ( tree @ A @ Y1 @ Y2 ) )
% 0.20/0.48 = ( ( X1 = Y1 )
% 0.20/0.48 & ( X22 = Y2 ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % treeFI.inject
% 0.20/0.48 thf(fact_31_sdrop__while__SCons,axiom,
% 0.20/0.48 ! [A: $tType,P2: A > $o,A3: A,S2: stream @ A] :
% 0.20/0.48 ( ( ( P2 @ A3 )
% 0.20/0.48 => ( ( sdrop_while @ A @ P2 @ ( sCons @ A @ A3 @ S2 ) )
% 0.20/0.48 = ( sdrop_while @ A @ P2 @ S2 ) ) )
% 0.20/0.48 & ( ~ ( P2 @ A3 )
% 0.20/0.48 => ( ( sdrop_while @ A @ P2 @ ( sCons @ A @ A3 @ S2 ) )
% 0.20/0.48 = ( sCons @ A @ A3 @ S2 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % sdrop_while_SCons
% 0.20/0.48 thf(fact_32_streams_Ocoinduct,axiom,
% 0.20/0.48 ! [A: $tType,X2: ( stream @ A ) > $o,X3: stream @ A,A5: set @ A] :
% 0.20/0.48 ( ( X2 @ X3 )
% 0.20/0.48 => ( ! [X: stream @ A] :
% 0.20/0.48 ( ( X2 @ X )
% 0.20/0.48 => ? [A6: A,S4: stream @ A] :
% 0.20/0.48 ( ( X
% 0.20/0.48 = ( sCons @ A @ A6 @ S4 ) )
% 0.20/0.48 & ( member2 @ A @ A6 @ A5 )
% 0.20/0.48 & ( ( X2 @ S4 )
% 0.20/0.48 | ( member2 @ ( stream @ A ) @ S4 @ ( streams @ A @ A5 ) ) ) ) )
% 0.20/0.48 => ( member2 @ ( stream @ A ) @ X3 @ ( streams @ A @ A5 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % streams.coinduct
% 0.20/0.48 thf(fact_33_treeFI_Oexhaust,axiom,
% 0.20/0.48 ! [A: $tType,Y: treeFI @ A] :
% 0.20/0.48 ~ ! [X12: A,X23: list @ ( treeFI @ A )] :
% 0.20/0.48 ( Y
% 0.20/0.48 != ( tree @ A @ X12 @ X23 ) ) ).
% 0.20/0.48
% 0.20/0.48 % treeFI.exhaust
% 0.20/0.48 thf(fact_34_streams__Stream,axiom,
% 0.20/0.48 ! [A: $tType,X3: A,S2: stream @ A,A5: set @ A] :
% 0.20/0.48 ( ( member2 @ ( stream @ A ) @ ( sCons @ A @ X3 @ S2 ) @ ( streams @ A @ A5 ) )
% 0.20/0.48 = ( ( member2 @ A @ X3 @ A5 )
% 0.20/0.48 & ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % streams_Stream
% 0.20/0.48 thf(fact_35_stream_Oexhaust,axiom,
% 0.20/0.48 ! [A: $tType,Y: stream @ A] :
% 0.20/0.48 ~ ! [X12: A,X23: stream @ A] :
% 0.20/0.48 ( Y
% 0.20/0.48 != ( sCons @ A @ X12 @ X23 ) ) ).
% 0.20/0.48
% 0.20/0.48 % stream.exhaust
% 0.20/0.48 thf(fact_36_streams_Osimps,axiom,
% 0.20/0.48 ! [A: $tType,A3: stream @ A,A5: set @ A] :
% 0.20/0.48 ( ( member2 @ ( stream @ A ) @ A3 @ ( streams @ A @ A5 ) )
% 0.20/0.48 = ( ? [A4: A,S: stream @ A] :
% 0.20/0.48 ( ( A3
% 0.20/0.48 = ( sCons @ A @ A4 @ S ) )
% 0.20/0.48 & ( member2 @ A @ A4 @ A5 )
% 0.20/0.48 & ( member2 @ ( stream @ A ) @ S @ ( streams @ A @ A5 ) ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 % streams.simps
% 0.20/0.48 thf(fact_37_streams_Ocases,axiom,
% 0.33/0.48 ! [A: $tType,A3: stream @ A,A5: set @ A] :
% 0.33/0.48 ( ( member2 @ ( stream @ A ) @ A3 @ ( streams @ A @ A5 ) )
% 0.33/0.48 => ~ ! [A7: A,S5: stream @ A] :
% 0.33/0.48 ( ( A3
% 0.33/0.48 = ( sCons @ A @ A7 @ S5 ) )
% 0.33/0.48 => ( ( member2 @ A @ A7 @ A5 )
% 0.33/0.48 => ~ ( member2 @ ( stream @ A ) @ S5 @ ( streams @ A @ A5 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % streams.cases
% 0.33/0.48 thf(fact_38_treeFI_Ocase,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,F2: A > ( list @ ( treeFI @ A ) ) > B,X1: A,X22: list @ ( treeFI @ A )] :
% 0.33/0.48 ( ( case_treeFI @ A @ B @ F2 @ ( tree @ A @ X1 @ X22 ) )
% 0.33/0.48 = ( F2 @ X1 @ X22 ) ) ).
% 0.33/0.48
% 0.33/0.48 % treeFI.case
% 0.33/0.48 thf(fact_39_stream_Ocase,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,F2: A > ( stream @ A ) > B,X1: A,X22: stream @ A] :
% 0.33/0.48 ( ( case_stream @ A @ B @ F2 @ ( sCons @ A @ X1 @ X22 ) )
% 0.33/0.48 = ( F2 @ X1 @ X22 ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.case
% 0.33/0.48 thf(fact_40_treeFI_Oset__intros_I1_J,axiom,
% 0.33/0.48 ! [A: $tType,A1: A,A2: list @ ( treeFI @ A )] : ( member2 @ A @ A1 @ ( set_treeFI @ A @ ( tree @ A @ A1 @ A2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % treeFI.set_intros(1)
% 0.33/0.48 thf(fact_41_trev__trev,axiom,
% 0.33/0.48 ! [A: $tType,Tr: treeFI @ A] :
% 0.33/0.48 ( ( trev @ A @ ( trev @ A @ Tr ) )
% 0.33/0.48 = Tr ) ).
% 0.33/0.48
% 0.33/0.48 % trev_trev
% 0.33/0.48 thf(fact_42_treeFI_Oset__intros_I2_J,axiom,
% 0.33/0.48 ! [A: $tType,X3: treeFI @ A,A2: list @ ( treeFI @ A ),Xa: A,A1: A] :
% 0.33/0.48 ( ( member2 @ ( treeFI @ A ) @ X3 @ ( set2 @ ( treeFI @ A ) @ A2 ) )
% 0.33/0.48 => ( ( member2 @ A @ Xa @ ( set_treeFI @ A @ X3 ) )
% 0.33/0.48 => ( member2 @ A @ Xa @ ( set_treeFI @ A @ ( tree @ A @ A1 @ A2 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % treeFI.set_intros(2)
% 0.33/0.48 thf(fact_43_treeFI_Oset__cases,axiom,
% 0.33/0.48 ! [A: $tType,E: A,A3: treeFI @ A] :
% 0.33/0.48 ( ( member2 @ A @ E @ ( set_treeFI @ A @ A3 ) )
% 0.33/0.48 => ( ! [Z2: list @ ( treeFI @ A )] :
% 0.33/0.48 ( A3
% 0.33/0.48 != ( tree @ A @ E @ Z2 ) )
% 0.33/0.48 => ~ ! [Z1: A,Z2: list @ ( treeFI @ A )] :
% 0.33/0.48 ( ( A3
% 0.33/0.48 = ( tree @ A @ Z1 @ Z2 ) )
% 0.33/0.48 => ! [X: treeFI @ A] :
% 0.33/0.48 ( ( member2 @ ( treeFI @ A ) @ X @ ( set2 @ ( treeFI @ A ) @ Z2 ) )
% 0.33/0.48 => ~ ( member2 @ A @ E @ ( set_treeFI @ A @ X ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % treeFI.set_cases
% 0.33/0.48 thf(fact_44_treeFI_Oset__induct,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,A3: treeFI @ A,P2: A > ( treeFI @ A ) > $o] :
% 0.33/0.48 ( ( member2 @ A @ X3 @ ( set_treeFI @ A @ A3 ) )
% 0.33/0.48 => ( ! [Z1: A,Z2: list @ ( treeFI @ A )] : ( P2 @ Z1 @ ( tree @ A @ Z1 @ Z2 ) )
% 0.33/0.48 => ( ! [Z1: A,Z2: list @ ( treeFI @ A ),Xa2: treeFI @ A,Xb: A] :
% 0.33/0.48 ( ( member2 @ ( treeFI @ A ) @ Xa2 @ ( set2 @ ( treeFI @ A ) @ Z2 ) )
% 0.33/0.48 => ( ( member2 @ A @ Xb @ ( set_treeFI @ A @ Xa2 ) )
% 0.33/0.48 => ( ( P2 @ Xb @ Xa2 )
% 0.33/0.48 => ( P2 @ Xb @ ( tree @ A @ Z1 @ Z2 ) ) ) ) )
% 0.33/0.48 => ( P2 @ X3 @ A3 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % treeFI.set_induct
% 0.33/0.48 thf(fact_45_mem__Collect__eq,axiom,
% 0.33/0.48 ! [A: $tType,A3: A,P2: A > $o] :
% 0.33/0.48 ( ( member2 @ A @ A3 @ ( collect @ A @ P2 ) )
% 0.33/0.48 = ( P2 @ A3 ) ) ).
% 0.33/0.48
% 0.33/0.48 % mem_Collect_eq
% 0.33/0.48 thf(fact_46_Collect__mem__eq,axiom,
% 0.33/0.48 ! [A: $tType,A5: set @ A] :
% 0.33/0.48 ( ( collect @ A
% 0.33/0.48 @ ^ [X5: A] : ( member2 @ A @ X5 @ A5 ) )
% 0.33/0.48 = A5 ) ).
% 0.33/0.48
% 0.33/0.48 % Collect_mem_eq
% 0.33/0.48 thf(fact_47_Collect__cong,axiom,
% 0.33/0.48 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.33/0.48 ( ! [X: A] :
% 0.33/0.48 ( ( P2 @ X )
% 0.33/0.48 = ( Q @ X ) )
% 0.33/0.48 => ( ( collect @ A @ P2 )
% 0.33/0.48 = ( collect @ A @ Q ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Collect_cong
% 0.33/0.48 thf(fact_48_ext,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,F2: A > B,G: A > B] :
% 0.33/0.48 ( ! [X: A] :
% 0.33/0.48 ( ( F2 @ X )
% 0.33/0.48 = ( G @ X ) )
% 0.33/0.48 => ( F2 = G ) ) ).
% 0.33/0.48
% 0.33/0.48 % ext
% 0.33/0.48 thf(fact_49_stream_Osel_I2_J,axiom,
% 0.33/0.48 ! [A: $tType,X1: A,X22: stream @ A] :
% 0.33/0.48 ( ( stl @ A @ ( sCons @ A @ X1 @ X22 ) )
% 0.33/0.48 = X22 ) ).
% 0.33/0.48
% 0.33/0.48 % stream.sel(2)
% 0.33/0.48 thf(fact_50_stream_Osel_I1_J,axiom,
% 0.33/0.48 ! [A: $tType,X1: A,X22: stream @ A] :
% 0.33/0.48 ( ( shd @ A @ ( sCons @ A @ X1 @ X22 ) )
% 0.33/0.48 = X1 ) ).
% 0.33/0.48
% 0.33/0.48 % stream.sel(1)
% 0.33/0.48 thf(fact_51_stream_Osplit__sel,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,P2: B > $o,F2: A > ( stream @ A ) > B,Stream: stream @ A] :
% 0.33/0.48 ( ( P2 @ ( case_stream @ A @ B @ F2 @ Stream ) )
% 0.33/0.48 = ( ( Stream
% 0.33/0.48 = ( sCons @ A @ ( shd @ A @ Stream ) @ ( stl @ A @ Stream ) ) )
% 0.33/0.48 => ( P2 @ ( F2 @ ( shd @ A @ Stream ) @ ( stl @ A @ Stream ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.split_sel
% 0.33/0.48 thf(fact_52_stream_Osplit__sel__asm,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,P2: B > $o,F2: A > ( stream @ A ) > B,Stream: stream @ A] :
% 0.33/0.48 ( ( P2 @ ( case_stream @ A @ B @ F2 @ Stream ) )
% 0.33/0.48 = ( ~ ( ( Stream
% 0.33/0.48 = ( sCons @ A @ ( shd @ A @ Stream ) @ ( stl @ A @ Stream ) ) )
% 0.33/0.48 & ~ ( P2 @ ( F2 @ ( shd @ A @ Stream ) @ ( stl @ A @ Stream ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.split_sel_asm
% 0.33/0.48 thf(fact_53_streams__stl,axiom,
% 0.33/0.48 ! [A: $tType,S2: stream @ A,A5: set @ A] :
% 0.33/0.48 ( ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) )
% 0.33/0.48 => ( member2 @ ( stream @ A ) @ ( stl @ A @ S2 ) @ ( streams @ A @ A5 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % streams_stl
% 0.33/0.48 thf(fact_54_streams__shd,axiom,
% 0.33/0.48 ! [A: $tType,S2: stream @ A,A5: set @ A] :
% 0.33/0.48 ( ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) )
% 0.33/0.48 => ( member2 @ A @ ( shd @ A @ S2 ) @ A5 ) ) ).
% 0.33/0.48
% 0.33/0.48 % streams_shd
% 0.33/0.48 thf(fact_55_treeFI_Osel_I2_J,axiom,
% 0.33/0.48 ! [A: $tType,X1: A,X22: list @ ( treeFI @ A )] :
% 0.33/0.48 ( ( sub @ A @ ( tree @ A @ X1 @ X22 ) )
% 0.33/0.48 = X22 ) ).
% 0.33/0.48
% 0.33/0.48 % treeFI.sel(2)
% 0.33/0.48 thf(fact_56_treeFI_Osel_I1_J,axiom,
% 0.33/0.48 ! [A: $tType,X1: A,X22: list @ ( treeFI @ A )] :
% 0.33/0.48 ( ( lab @ A @ ( tree @ A @ X1 @ X22 ) )
% 0.33/0.48 = X1 ) ).
% 0.33/0.48
% 0.33/0.48 % treeFI.sel(1)
% 0.33/0.48 thf(fact_57_treeFI_Oset__sel_I1_J,axiom,
% 0.33/0.48 ! [A: $tType,A3: treeFI @ A] : ( member2 @ A @ ( lab @ A @ A3 ) @ ( set_treeFI @ A @ A3 ) ) ).
% 0.33/0.48
% 0.33/0.48 % treeFI.set_sel(1)
% 0.33/0.48 thf(fact_58_treeFI_Osplit__sel,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,P2: B > $o,F2: A > ( list @ ( treeFI @ A ) ) > B,TreeFI: treeFI @ A] :
% 0.33/0.48 ( ( P2 @ ( case_treeFI @ A @ B @ F2 @ TreeFI ) )
% 0.33/0.48 = ( ( TreeFI
% 0.33/0.48 = ( tree @ A @ ( lab @ A @ TreeFI ) @ ( sub @ A @ TreeFI ) ) )
% 0.33/0.48 => ( P2 @ ( F2 @ ( lab @ A @ TreeFI ) @ ( sub @ A @ TreeFI ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % treeFI.split_sel
% 0.33/0.48 thf(fact_59_treeFI_Osplit__sel__asm,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,P2: B > $o,F2: A > ( list @ ( treeFI @ A ) ) > B,TreeFI: treeFI @ A] :
% 0.33/0.48 ( ( P2 @ ( case_treeFI @ A @ B @ F2 @ TreeFI ) )
% 0.33/0.48 = ( ~ ( ( TreeFI
% 0.33/0.48 = ( tree @ A @ ( lab @ A @ TreeFI ) @ ( sub @ A @ TreeFI ) ) )
% 0.33/0.48 & ~ ( P2 @ ( F2 @ ( lab @ A @ TreeFI ) @ ( sub @ A @ TreeFI ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % treeFI.split_sel_asm
% 0.33/0.48 thf(fact_60_stream_Oexhaust__sel,axiom,
% 0.33/0.48 ! [A: $tType,Stream: stream @ A] :
% 0.33/0.48 ( Stream
% 0.33/0.48 = ( sCons @ A @ ( shd @ A @ Stream ) @ ( stl @ A @ Stream ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.exhaust_sel
% 0.33/0.48 thf(fact_61_smember__code,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Y: A,S2: stream @ A] :
% 0.33/0.48 ( ( smember @ A @ X3 @ ( sCons @ A @ Y @ S2 ) )
% 0.33/0.48 = ( ( X3 != Y )
% 0.33/0.48 => ( smember @ A @ X3 @ S2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % smember_code
% 0.33/0.48 thf(fact_62_sinterleave_Ocode,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( sinterleave @ A )
% 0.33/0.48 = ( ^ [S1: stream @ A,S22: stream @ A] : ( sCons @ A @ ( shd @ A @ S1 ) @ ( sinterleave @ A @ S22 @ ( stl @ A @ S1 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % sinterleave.code
% 0.33/0.48 thf(fact_63_smap2_Ocode,axiom,
% 0.33/0.48 ! [C: $tType,B: $tType,A: $tType] :
% 0.33/0.48 ( ( smap2 @ A @ B @ C )
% 0.33/0.48 = ( ^ [F: A > B > C,S1: stream @ A,S22: stream @ B] : ( sCons @ C @ ( F @ ( shd @ A @ S1 ) @ ( shd @ B @ S22 ) ) @ ( smap2 @ A @ B @ C @ F @ ( stl @ A @ S1 ) @ ( stl @ B @ S22 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % smap2.code
% 0.33/0.48 thf(fact_64_smap__ctr,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,F2: B > A,S2: stream @ B,X3: A,S6: stream @ A] :
% 0.33/0.48 ( ( ( smap @ B @ A @ F2 @ S2 )
% 0.33/0.48 = ( sCons @ A @ X3 @ S6 ) )
% 0.33/0.48 = ( ( ( F2 @ ( shd @ B @ S2 ) )
% 0.33/0.48 = X3 )
% 0.33/0.48 & ( ( smap @ B @ A @ F2 @ ( stl @ B @ S2 ) )
% 0.33/0.48 = S6 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % smap_ctr
% 0.33/0.48 thf(fact_65_sfilter_Ocode,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( sfilter @ A )
% 0.33/0.48 = ( ^ [P: A > $o,S: stream @ A] : ( sCons @ A @ ( shd @ A @ ( sdrop_while @ A @ ( comp @ $o @ $o @ A @ (~) @ P ) @ S ) ) @ ( sfilter @ A @ P @ ( stl @ A @ ( sdrop_while @ A @ ( comp @ $o @ $o @ A @ (~) @ P ) @ S ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % sfilter.code
% 0.33/0.48 thf(fact_66_stream__all__Stream,axiom,
% 0.33/0.48 ! [A: $tType,P2: A > $o,X3: A,X2: stream @ A] :
% 0.33/0.48 ( ( stream_all @ A @ P2 @ ( sCons @ A @ X3 @ X2 ) )
% 0.33/0.48 = ( ( P2 @ X3 )
% 0.33/0.48 & ( stream_all @ A @ P2 @ X2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream_all_Stream
% 0.33/0.48 thf(fact_67_stream_Opred__inject,axiom,
% 0.33/0.48 ! [A: $tType,P2: A > $o,A3: A,Aa2: stream @ A] :
% 0.33/0.48 ( ( pred_stream @ A @ P2 @ ( sCons @ A @ A3 @ Aa2 ) )
% 0.33/0.48 = ( ( P2 @ A3 )
% 0.33/0.48 & ( pred_stream @ A @ P2 @ Aa2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.pred_inject
% 0.33/0.48 thf(fact_68_sset__induct,axiom,
% 0.33/0.48 ! [A: $tType,Y: A,S2: stream @ A,P2: A > ( stream @ A ) > $o] :
% 0.33/0.48 ( ( member2 @ A @ Y @ ( sset @ A @ S2 ) )
% 0.33/0.48 => ( ! [S5: stream @ A] : ( P2 @ ( shd @ A @ S5 ) @ S5 )
% 0.33/0.48 => ( ! [S5: stream @ A,Y3: A] :
% 0.33/0.48 ( ( member2 @ A @ Y3 @ ( sset @ A @ ( stl @ A @ S5 ) ) )
% 0.33/0.48 => ( ( P2 @ Y3 @ ( stl @ A @ S5 ) )
% 0.33/0.48 => ( P2 @ Y3 @ S5 ) ) )
% 0.33/0.48 => ( P2 @ Y @ S2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % sset_induct
% 0.33/0.48 thf(fact_69_sfilter__Stream,axiom,
% 0.33/0.48 ! [A: $tType,P2: A > $o,X3: A,S2: stream @ A] :
% 0.33/0.48 ( ( ( P2 @ X3 )
% 0.33/0.48 => ( ( sfilter @ A @ P2 @ ( sCons @ A @ X3 @ S2 ) )
% 0.33/0.48 = ( sCons @ A @ X3 @ ( sfilter @ A @ P2 @ S2 ) ) ) )
% 0.33/0.48 & ( ~ ( P2 @ X3 )
% 0.33/0.48 => ( ( sfilter @ A @ P2 @ ( sCons @ A @ X3 @ S2 ) )
% 0.33/0.48 = ( sfilter @ A @ P2 @ S2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % sfilter_Stream
% 0.33/0.48 thf(fact_70_stream_Omap__sel_I2_J,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,F2: A > B,A3: stream @ A] :
% 0.33/0.48 ( ( stl @ B @ ( smap @ A @ B @ F2 @ A3 ) )
% 0.33/0.48 = ( smap @ A @ B @ F2 @ ( stl @ A @ A3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.map_sel(2)
% 0.33/0.48 thf(fact_71_stream_Omap__sel_I1_J,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,F2: A > B,A3: stream @ A] :
% 0.33/0.48 ( ( shd @ B @ ( smap @ A @ B @ F2 @ A3 ) )
% 0.33/0.48 = ( F2 @ ( shd @ A @ A3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.map_sel(1)
% 0.33/0.48 thf(fact_72_Stream_Osmember__def,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( smember @ A )
% 0.33/0.48 = ( ^ [X5: A,S: stream @ A] : ( member2 @ A @ X5 @ ( sset @ A @ S ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Stream.smember_def
% 0.33/0.48 thf(fact_73_stream_Omap__comp,axiom,
% 0.33/0.48 ! [B: $tType,C: $tType,A: $tType,G: B > C,F2: A > B,V: stream @ A] :
% 0.33/0.48 ( ( smap @ B @ C @ G @ ( smap @ A @ B @ F2 @ V ) )
% 0.33/0.48 = ( smap @ A @ C @ ( comp @ B @ C @ A @ G @ F2 ) @ V ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.map_comp
% 0.33/0.48 thf(fact_74_stream_Omap__cong,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,X3: stream @ A,Ya: stream @ A,F2: A > B,G: A > B] :
% 0.33/0.48 ( ( X3 = Ya )
% 0.33/0.48 => ( ! [Z: A] :
% 0.33/0.48 ( ( member2 @ A @ Z @ ( sset @ A @ Ya ) )
% 0.33/0.48 => ( ( F2 @ Z )
% 0.33/0.48 = ( G @ Z ) ) )
% 0.33/0.48 => ( ( smap @ A @ B @ F2 @ X3 )
% 0.33/0.48 = ( smap @ A @ B @ G @ Ya ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.map_cong
% 0.33/0.48 thf(fact_75_stream_Opred__map,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,Q: B > $o,F2: A > B,X3: stream @ A] :
% 0.33/0.48 ( ( pred_stream @ B @ Q @ ( smap @ A @ B @ F2 @ X3 ) )
% 0.33/0.48 = ( pred_stream @ A @ ( comp @ B @ $o @ A @ Q @ F2 ) @ X3 ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.pred_map
% 0.33/0.48 thf(fact_76_stream_Omap__cong0,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,X3: stream @ A,F2: A > B,G: A > B] :
% 0.33/0.48 ( ! [Z: A] :
% 0.33/0.48 ( ( member2 @ A @ Z @ ( sset @ A @ X3 ) )
% 0.33/0.48 => ( ( F2 @ Z )
% 0.33/0.48 = ( G @ Z ) ) )
% 0.33/0.48 => ( ( smap @ A @ B @ F2 @ X3 )
% 0.33/0.48 = ( smap @ A @ B @ G @ X3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.map_cong0
% 0.33/0.48 thf(fact_77_stream_Opred__cong,axiom,
% 0.33/0.48 ! [A: $tType,X3: stream @ A,Ya: stream @ A,P2: A > $o,Pa: A > $o] :
% 0.33/0.48 ( ( X3 = Ya )
% 0.33/0.48 => ( ! [Z: A] :
% 0.33/0.48 ( ( member2 @ A @ Z @ ( sset @ A @ Ya ) )
% 0.33/0.48 => ( ( P2 @ Z )
% 0.33/0.48 = ( Pa @ Z ) ) )
% 0.33/0.48 => ( ( pred_stream @ A @ P2 @ X3 )
% 0.33/0.48 = ( pred_stream @ A @ Pa @ Ya ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.pred_cong
% 0.33/0.48 thf(fact_78_stream_Oinj__map__strong,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,X3: stream @ A,Xa: stream @ A,F2: A > B,Fa: A > B] :
% 0.33/0.48 ( ! [Z: A,Za: A] :
% 0.33/0.48 ( ( member2 @ A @ Z @ ( sset @ A @ X3 ) )
% 0.33/0.48 => ( ( member2 @ A @ Za @ ( sset @ A @ Xa ) )
% 0.33/0.48 => ( ( ( F2 @ Z )
% 0.33/0.48 = ( Fa @ Za ) )
% 0.33/0.48 => ( Z = Za ) ) ) )
% 0.33/0.48 => ( ( ( smap @ A @ B @ F2 @ X3 )
% 0.33/0.48 = ( smap @ A @ B @ Fa @ Xa ) )
% 0.33/0.48 => ( X3 = Xa ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.inj_map_strong
% 0.33/0.48 thf(fact_79_stream_Opred__mono__strong,axiom,
% 0.33/0.48 ! [A: $tType,P2: A > $o,X3: stream @ A,Pa: A > $o] :
% 0.33/0.48 ( ( pred_stream @ A @ P2 @ X3 )
% 0.33/0.48 => ( ! [Z: A] :
% 0.33/0.48 ( ( member2 @ A @ Z @ ( sset @ A @ X3 ) )
% 0.33/0.48 => ( ( P2 @ Z )
% 0.33/0.48 => ( Pa @ Z ) ) )
% 0.33/0.48 => ( pred_stream @ A @ Pa @ X3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.pred_mono_strong
% 0.33/0.48 thf(fact_80_stream_Omap,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,F2: A > B,X1: A,X22: stream @ A] :
% 0.33/0.48 ( ( smap @ A @ B @ F2 @ ( sCons @ A @ X1 @ X22 ) )
% 0.33/0.48 = ( sCons @ B @ ( F2 @ X1 ) @ ( smap @ A @ B @ F2 @ X22 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.map
% 0.33/0.48 thf(fact_81_stl__sset,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,A3: stream @ A] :
% 0.33/0.48 ( ( member2 @ A @ X3 @ ( sset @ A @ ( stl @ A @ A3 ) ) )
% 0.33/0.48 => ( member2 @ A @ X3 @ ( sset @ A @ A3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stl_sset
% 0.33/0.48 thf(fact_82_shd__sset,axiom,
% 0.33/0.48 ! [A: $tType,A3: stream @ A] : ( member2 @ A @ ( shd @ A @ A3 ) @ ( sset @ A @ A3 ) ) ).
% 0.33/0.48
% 0.33/0.48 % shd_sset
% 0.33/0.48 thf(fact_83_stream_Oset__intros_I2_J,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,A2: stream @ A,A1: A] :
% 0.33/0.48 ( ( member2 @ A @ X3 @ ( sset @ A @ A2 ) )
% 0.33/0.48 => ( member2 @ A @ X3 @ ( sset @ A @ ( sCons @ A @ A1 @ A2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.set_intros(2)
% 0.33/0.48 thf(fact_84_stream_Oset__intros_I1_J,axiom,
% 0.33/0.48 ! [A: $tType,A1: A,A2: stream @ A] : ( member2 @ A @ A1 @ ( sset @ A @ ( sCons @ A @ A1 @ A2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.set_intros(1)
% 0.33/0.48 thf(fact_85_stream_Oset__cases,axiom,
% 0.33/0.48 ! [A: $tType,E: A,A3: stream @ A] :
% 0.33/0.48 ( ( member2 @ A @ E @ ( sset @ A @ A3 ) )
% 0.33/0.48 => ( ! [Z2: stream @ A] :
% 0.33/0.48 ( A3
% 0.33/0.48 != ( sCons @ A @ E @ Z2 ) )
% 0.33/0.48 => ~ ! [Z1: A,Z2: stream @ A] :
% 0.33/0.48 ( ( A3
% 0.33/0.48 = ( sCons @ A @ Z1 @ Z2 ) )
% 0.33/0.48 => ~ ( member2 @ A @ E @ ( sset @ A @ Z2 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.set_cases
% 0.33/0.48 thf(fact_86_stream_Oset__induct,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,A3: stream @ A,P2: A > ( stream @ A ) > $o] :
% 0.33/0.48 ( ( member2 @ A @ X3 @ ( sset @ A @ A3 ) )
% 0.33/0.48 => ( ! [Z1: A,Z2: stream @ A] : ( P2 @ Z1 @ ( sCons @ A @ Z1 @ Z2 ) )
% 0.33/0.48 => ( ! [Z1: A,Z2: stream @ A,Xa2: A] :
% 0.33/0.48 ( ( member2 @ A @ Xa2 @ ( sset @ A @ Z2 ) )
% 0.33/0.48 => ( ( P2 @ Xa2 @ Z2 )
% 0.33/0.48 => ( P2 @ Xa2 @ ( sCons @ A @ Z1 @ Z2 ) ) ) )
% 0.33/0.48 => ( P2 @ X3 @ A3 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.set_induct
% 0.33/0.48 thf(fact_87_smap__streams,axiom,
% 0.33/0.48 ! [A: $tType,B: $tType,S2: stream @ A,A5: set @ A,F2: A > B,B2: set @ B] :
% 0.33/0.48 ( ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) )
% 0.33/0.48 => ( ! [X: A] :
% 0.33/0.48 ( ( member2 @ A @ X @ A5 )
% 0.33/0.48 => ( member2 @ B @ ( F2 @ X ) @ B2 ) )
% 0.33/0.48 => ( member2 @ ( stream @ B ) @ ( smap @ A @ B @ F2 @ S2 ) @ ( streams @ B @ B2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % smap_streams
% 0.33/0.48 thf(fact_88_sfilter_Osimps_I2_J,axiom,
% 0.33/0.48 ! [A: $tType,P2: A > $o,S2: stream @ A] :
% 0.33/0.48 ( ( stl @ A @ ( sfilter @ A @ P2 @ S2 ) )
% 0.33/0.48 = ( sfilter @ A @ P2 @ ( stl @ A @ ( sdrop_while @ A @ ( comp @ $o @ $o @ A @ (~) @ P2 ) @ S2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % sfilter.simps(2)
% 0.33/0.48 thf(fact_89_sfilter_Osimps_I1_J,axiom,
% 0.33/0.48 ! [A: $tType,P2: A > $o,S2: stream @ A] :
% 0.33/0.48 ( ( shd @ A @ ( sfilter @ A @ P2 @ S2 ) )
% 0.33/0.48 = ( shd @ A @ ( sdrop_while @ A @ ( comp @ $o @ $o @ A @ (~) @ P2 ) @ S2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % sfilter.simps(1)
% 0.33/0.48 thf(fact_90_smap2_Osimps_I2_J,axiom,
% 0.33/0.48 ! [A: $tType,C: $tType,B: $tType,F2: A > B > C,S12: stream @ A,S23: stream @ B] :
% 0.33/0.48 ( ( stl @ C @ ( smap2 @ A @ B @ C @ F2 @ S12 @ S23 ) )
% 0.33/0.48 = ( smap2 @ A @ B @ C @ F2 @ ( stl @ A @ S12 ) @ ( stl @ B @ S23 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % smap2.simps(2)
% 0.33/0.48 thf(fact_91_smap2_Osimps_I1_J,axiom,
% 0.33/0.48 ! [A: $tType,C: $tType,B: $tType,F2: A > B > C,S12: stream @ A,S23: stream @ B] :
% 0.33/0.48 ( ( shd @ C @ ( smap2 @ A @ B @ C @ F2 @ S12 @ S23 ) )
% 0.33/0.48 = ( F2 @ ( shd @ A @ S12 ) @ ( shd @ B @ S23 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % smap2.simps(1)
% 0.33/0.48 thf(fact_92_smap2__unfold,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,C: $tType,F2: B > C > A,A3: B,S12: stream @ B,B3: C,S23: stream @ C] :
% 0.33/0.48 ( ( smap2 @ B @ C @ A @ F2 @ ( sCons @ B @ A3 @ S12 ) @ ( sCons @ C @ B3 @ S23 ) )
% 0.33/0.48 = ( sCons @ A @ ( F2 @ A3 @ B3 ) @ ( smap2 @ B @ C @ A @ F2 @ S12 @ S23 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % smap2_unfold
% 0.33/0.48 thf(fact_93_sinterleave_Osimps_I2_J,axiom,
% 0.33/0.48 ! [A: $tType,S12: stream @ A,S23: stream @ A] :
% 0.33/0.48 ( ( stl @ A @ ( sinterleave @ A @ S12 @ S23 ) )
% 0.33/0.48 = ( sinterleave @ A @ S23 @ ( stl @ A @ S12 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % sinterleave.simps(2)
% 0.33/0.48 thf(fact_94_sinterleave_Osimps_I1_J,axiom,
% 0.33/0.48 ! [A: $tType,S12: stream @ A,S23: stream @ A] :
% 0.33/0.48 ( ( shd @ A @ ( sinterleave @ A @ S12 @ S23 ) )
% 0.33/0.48 = ( shd @ A @ S12 ) ) ).
% 0.33/0.48
% 0.33/0.48 % sinterleave.simps(1)
% 0.33/0.48 thf(fact_95_sinterleave__code,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,S12: stream @ A,S23: stream @ A] :
% 0.33/0.48 ( ( sinterleave @ A @ ( sCons @ A @ X3 @ S12 ) @ S23 )
% 0.33/0.48 = ( sCons @ A @ X3 @ ( sinterleave @ A @ S23 @ S12 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % sinterleave_code
% 0.33/0.48 thf(fact_96_comp__apply,axiom,
% 0.33/0.48 ! [C: $tType,A: $tType,B: $tType] :
% 0.33/0.48 ( ( comp @ B @ A @ C )
% 0.33/0.48 = ( ^ [F: B > A,G2: C > B,X5: C] : ( F @ ( G2 @ X5 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % comp_apply
% 0.33/0.48 thf(fact_97_stream_Omap__o__corec,axiom,
% 0.33/0.48 ! [A: $tType,B: $tType,C: $tType,F2: A > B,G: C > A,Ga: C > $o,Gb: C > ( stream @ A ),Gc: C > C] :
% 0.33/0.48 ( ( comp @ ( stream @ A ) @ ( stream @ B ) @ C @ ( smap @ A @ B @ F2 ) @ ( corec_stream @ C @ A @ G @ Ga @ Gb @ Gc ) )
% 0.33/0.48 = ( corec_stream @ C @ B @ ( comp @ A @ B @ C @ F2 @ G ) @ Ga @ ( comp @ ( stream @ A ) @ ( stream @ B ) @ C @ ( smap @ A @ B @ F2 ) @ Gb ) @ Gc ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.map_o_corec
% 0.33/0.48 thf(fact_98_rewriteR__comp__comp2,axiom,
% 0.33/0.48 ! [C: $tType,B: $tType,E2: $tType,D: $tType,A: $tType,G: C > B,H: A > C,R1: D > B,R2: A > D,F2: B > E2,L: D > E2] :
% 0.33/0.48 ( ( ( comp @ C @ B @ A @ G @ H )
% 0.33/0.48 = ( comp @ D @ B @ A @ R1 @ R2 ) )
% 0.33/0.48 => ( ( ( comp @ B @ E2 @ D @ F2 @ R1 )
% 0.33/0.48 = L )
% 0.33/0.48 => ( ( comp @ C @ E2 @ A @ ( comp @ B @ E2 @ C @ F2 @ G ) @ H )
% 0.33/0.48 = ( comp @ D @ E2 @ A @ L @ R2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % rewriteR_comp_comp2
% 0.33/0.48 thf(fact_99_rewriteL__comp__comp2,axiom,
% 0.33/0.48 ! [A: $tType,C: $tType,B: $tType,D: $tType,E2: $tType,F2: C > B,G: A > C,L1: D > B,L2: A > D,H: E2 > A,R3: E2 > D] :
% 0.33/0.48 ( ( ( comp @ C @ B @ A @ F2 @ G )
% 0.33/0.48 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 0.33/0.48 => ( ( ( comp @ A @ D @ E2 @ L2 @ H )
% 0.33/0.48 = R3 )
% 0.33/0.48 => ( ( comp @ C @ B @ E2 @ F2 @ ( comp @ A @ C @ E2 @ G @ H ) )
% 0.33/0.48 = ( comp @ D @ B @ E2 @ L1 @ R3 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % rewriteL_comp_comp2
% 0.33/0.48 thf(fact_100_rewriteR__comp__comp,axiom,
% 0.33/0.48 ! [C: $tType,D: $tType,B: $tType,A: $tType,G: C > B,H: A > C,R3: A > B,F2: B > D] :
% 0.33/0.48 ( ( ( comp @ C @ B @ A @ G @ H )
% 0.33/0.48 = R3 )
% 0.33/0.48 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F2 @ G ) @ H )
% 0.33/0.48 = ( comp @ B @ D @ A @ F2 @ R3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % rewriteR_comp_comp
% 0.33/0.48 thf(fact_101_rewriteL__comp__comp,axiom,
% 0.33/0.48 ! [C: $tType,B: $tType,A: $tType,D: $tType,F2: C > B,G: A > C,L: A > B,H: D > A] :
% 0.33/0.48 ( ( ( comp @ C @ B @ A @ F2 @ G )
% 0.33/0.48 = L )
% 0.33/0.48 => ( ( comp @ C @ B @ D @ F2 @ ( comp @ A @ C @ D @ G @ H ) )
% 0.33/0.48 = ( comp @ A @ B @ D @ L @ H ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % rewriteL_comp_comp
% 0.33/0.48 thf(fact_102_type__copy__map__cong0,axiom,
% 0.33/0.48 ! [B: $tType,D: $tType,E2: $tType,A: $tType,C: $tType,M: B > A,G: C > B,X3: C,N: D > A,H: C > D,F2: A > E2] :
% 0.33/0.48 ( ( ( M @ ( G @ X3 ) )
% 0.33/0.48 = ( N @ ( H @ X3 ) ) )
% 0.33/0.48 => ( ( comp @ B @ E2 @ C @ ( comp @ A @ E2 @ B @ F2 @ M ) @ G @ X3 )
% 0.33/0.48 = ( comp @ D @ E2 @ C @ ( comp @ A @ E2 @ D @ F2 @ N ) @ H @ X3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % type_copy_map_cong0
% 0.33/0.48 thf(fact_103_stream_Ocorec__disc,axiom,
% 0.33/0.48 ! [A: $tType,C: $tType] :
% 0.33/0.48 ( ( corec_stream @ C @ A )
% 0.33/0.48 = ( corec_stream @ C @ A ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.corec_disc
% 0.33/0.48 thf(fact_104_stream_Ocorec__sel_I2_J,axiom,
% 0.33/0.48 ! [A: $tType,C: $tType,Q2: C > $o,A3: C,G1: C > A,G21: C > ( stream @ A ),G22: C > C] :
% 0.33/0.48 ( ( ( Q2 @ A3 )
% 0.33/0.48 => ( ( stl @ A @ ( corec_stream @ C @ A @ G1 @ Q2 @ G21 @ G22 @ A3 ) )
% 0.33/0.48 = ( G21 @ A3 ) ) )
% 0.33/0.48 & ( ~ ( Q2 @ A3 )
% 0.33/0.48 => ( ( stl @ A @ ( corec_stream @ C @ A @ G1 @ Q2 @ G21 @ G22 @ A3 ) )
% 0.33/0.48 = ( corec_stream @ C @ A @ G1 @ Q2 @ G21 @ G22 @ ( G22 @ A3 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.corec_sel(2)
% 0.33/0.48 thf(fact_105_stream_Ocorec__sel_I1_J,axiom,
% 0.33/0.48 ! [A: $tType,C: $tType,G1: C > A,Q2: C > $o,G21: C > ( stream @ A ),G22: C > C,A3: C] :
% 0.33/0.48 ( ( shd @ A @ ( corec_stream @ C @ A @ G1 @ Q2 @ G21 @ G22 @ A3 ) )
% 0.33/0.48 = ( G1 @ A3 ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.corec_sel(1)
% 0.33/0.48 thf(fact_106_stream_Ocorec__code,axiom,
% 0.33/0.48 ! [A: $tType,C: $tType] :
% 0.33/0.48 ( ( corec_stream @ C @ A )
% 0.33/0.48 = ( ^ [G12: C > A,Q22: C > $o,G212: C > ( stream @ A ),G222: C > C,A4: C] : ( sCons @ A @ ( G12 @ A4 ) @ ( if @ ( stream @ A ) @ ( Q22 @ A4 ) @ ( G212 @ A4 ) @ ( corec_stream @ C @ A @ G12 @ Q22 @ G212 @ G222 @ ( G222 @ A4 ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.corec_code
% 0.33/0.48 thf(fact_107_comp__def,axiom,
% 0.33/0.48 ! [A: $tType,C: $tType,B: $tType] :
% 0.33/0.48 ( ( comp @ B @ C @ A )
% 0.33/0.48 = ( ^ [F: B > C,G2: A > B,X5: A] : ( F @ ( G2 @ X5 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % comp_def
% 0.33/0.48 thf(fact_108_comp__assoc,axiom,
% 0.33/0.48 ! [B: $tType,D: $tType,C: $tType,A: $tType,F2: D > B,G: C > D,H: A > C] :
% 0.33/0.48 ( ( comp @ C @ B @ A @ ( comp @ D @ B @ C @ F2 @ G ) @ H )
% 0.33/0.48 = ( comp @ D @ B @ A @ F2 @ ( comp @ C @ D @ A @ G @ H ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % comp_assoc
% 0.33/0.48 thf(fact_109_comp__eq__dest,axiom,
% 0.33/0.48 ! [C: $tType,B: $tType,D: $tType,A: $tType,A3: C > B,B3: A > C,C2: D > B,D2: A > D,V: A] :
% 0.33/0.48 ( ( ( comp @ C @ B @ A @ A3 @ B3 )
% 0.33/0.48 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 0.33/0.48 => ( ( A3 @ ( B3 @ V ) )
% 0.33/0.48 = ( C2 @ ( D2 @ V ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % comp_eq_dest
% 0.33/0.48 thf(fact_110_comp__eq__elim,axiom,
% 0.33/0.48 ! [C: $tType,B: $tType,D: $tType,A: $tType,A3: C > B,B3: A > C,C2: D > B,D2: A > D] :
% 0.33/0.48 ( ( ( comp @ C @ B @ A @ A3 @ B3 )
% 0.33/0.48 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 0.33/0.48 => ! [V2: A] :
% 0.33/0.48 ( ( A3 @ ( B3 @ V2 ) )
% 0.33/0.48 = ( C2 @ ( D2 @ V2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % comp_eq_elim
% 0.33/0.48 thf(fact_111_comp__eq__dest__lhs,axiom,
% 0.33/0.48 ! [C: $tType,B: $tType,A: $tType,A3: C > B,B3: A > C,C2: A > B,V: A] :
% 0.33/0.48 ( ( ( comp @ C @ B @ A @ A3 @ B3 )
% 0.33/0.48 = C2 )
% 0.33/0.48 => ( ( A3 @ ( B3 @ V ) )
% 0.33/0.48 = ( C2 @ V ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % comp_eq_dest_lhs
% 0.33/0.48 thf(fact_112_comp__cong,axiom,
% 0.33/0.48 ! [C: $tType,B: $tType,D: $tType,A: $tType,E2: $tType,F2: B > A,G: C > B,X3: C,F3: D > A,G3: E2 > D,X6: E2] :
% 0.33/0.48 ( ( ( F2 @ ( G @ X3 ) )
% 0.33/0.48 = ( F3 @ ( G3 @ X6 ) ) )
% 0.33/0.48 => ( ( comp @ B @ A @ C @ F2 @ G @ X3 )
% 0.33/0.48 = ( comp @ D @ A @ E2 @ F3 @ G3 @ X6 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % comp_cong
% 0.33/0.48 thf(fact_113_comp__apply__eq,axiom,
% 0.33/0.48 ! [B: $tType,D: $tType,A: $tType,C: $tType,F2: B > A,G: C > B,X3: C,H: D > A,K: C > D] :
% 0.33/0.48 ( ( ( F2 @ ( G @ X3 ) )
% 0.33/0.48 = ( H @ ( K @ X3 ) ) )
% 0.33/0.48 => ( ( comp @ B @ A @ C @ F2 @ G @ X3 )
% 0.33/0.48 = ( comp @ D @ A @ C @ H @ K @ X3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % comp_apply_eq
% 0.33/0.48 thf(fact_114_fun_Omap__comp,axiom,
% 0.33/0.48 ! [B: $tType,C: $tType,A: $tType,D: $tType,G: B > C,F2: A > B,V: D > A] :
% 0.33/0.48 ( ( comp @ B @ C @ D @ G @ ( comp @ A @ B @ D @ F2 @ V ) )
% 0.33/0.48 = ( comp @ A @ C @ D @ ( comp @ B @ C @ A @ G @ F2 ) @ V ) ) ).
% 0.33/0.48
% 0.33/0.48 % fun.map_comp
% 0.33/0.48 thf(fact_115_stream__all__iff,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( stream_all @ A )
% 0.33/0.48 = ( ^ [P: A > $o,S: stream @ A] :
% 0.33/0.48 ! [X5: A] :
% 0.33/0.48 ( ( member2 @ A @ X5 @ ( sset @ A @ S ) )
% 0.33/0.48 => ( P @ X5 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream_all_iff
% 0.33/0.48 thf(fact_116_stream_Oset,axiom,
% 0.33/0.48 ! [A: $tType,X1: A,X22: stream @ A] :
% 0.33/0.48 ( ( sset @ A @ ( sCons @ A @ X1 @ X22 ) )
% 0.33/0.48 = ( insert2 @ A @ X1 @ ( sset @ A @ X22 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.set
% 0.33/0.48 thf(fact_117_stream_Opred__set,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( pred_stream @ A )
% 0.33/0.48 = ( ^ [P: A > $o,X5: stream @ A] :
% 0.33/0.48 ! [Y4: A] :
% 0.33/0.48 ( ( member2 @ A @ Y4 @ ( sset @ A @ X5 ) )
% 0.33/0.48 => ( P @ Y4 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream.pred_set
% 0.33/0.48 thf(fact_118_treeFI_Opred__set,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( pred_treeFI @ A )
% 0.33/0.48 = ( ^ [P: A > $o,X5: treeFI @ A] :
% 0.33/0.48 ! [Y4: A] :
% 0.33/0.48 ( ( member2 @ A @ Y4 @ ( set_treeFI @ A @ X5 ) )
% 0.33/0.48 => ( P @ Y4 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % treeFI.pred_set
% 0.33/0.48 thf(fact_119_sset__sinterleave,axiom,
% 0.33/0.48 ! [A: $tType,S12: stream @ A,S23: stream @ A] :
% 0.33/0.48 ( ( sset @ A @ ( sinterleave @ A @ S12 @ S23 ) )
% 0.33/0.48 = ( sup_sup @ ( set @ A ) @ ( sset @ A @ S12 ) @ ( sset @ A @ S23 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % sset_sinterleave
% 0.33/0.48 thf(fact_120_sset__streams,axiom,
% 0.33/0.48 ! [A: $tType,S2: stream @ A,A5: set @ A] :
% 0.33/0.48 ( ( ord_less_eq @ ( set @ A ) @ ( sset @ A @ S2 ) @ A5 )
% 0.33/0.48 => ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % sset_streams
% 0.33/0.48 thf(fact_121_streams__sset,axiom,
% 0.33/0.48 ! [A: $tType,S2: stream @ A,A5: set @ A] :
% 0.33/0.48 ( ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) )
% 0.33/0.48 => ( ord_less_eq @ ( set @ A ) @ ( sset @ A @ S2 ) @ A5 ) ) ).
% 0.33/0.48
% 0.33/0.48 % streams_sset
% 0.33/0.48 thf(fact_122_streams__mono2,axiom,
% 0.33/0.48 ! [A: $tType,S3: set @ A,T2: set @ A] :
% 0.33/0.48 ( ( ord_less_eq @ ( set @ A ) @ S3 @ T2 )
% 0.33/0.48 => ( ord_less_eq @ ( set @ ( stream @ A ) ) @ ( streams @ A @ S3 ) @ ( streams @ A @ T2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % streams_mono2
% 0.33/0.48 thf(fact_123_streams__mono,axiom,
% 0.33/0.48 ! [A: $tType,S2: stream @ A,A5: set @ A,B2: set @ A] :
% 0.33/0.48 ( ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) )
% 0.33/0.48 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ B2 )
% 0.33/0.48 => ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ B2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % streams_mono
% 0.33/0.48 thf(fact_124_treeFI_Opred__mono__strong,axiom,
% 0.33/0.48 ! [A: $tType,P2: A > $o,X3: treeFI @ A,Pa: A > $o] :
% 0.33/0.48 ( ( pred_treeFI @ A @ P2 @ X3 )
% 0.33/0.48 => ( ! [Z: A] :
% 0.33/0.48 ( ( member2 @ A @ Z @ ( set_treeFI @ A @ X3 ) )
% 0.33/0.48 => ( ( P2 @ Z )
% 0.33/0.48 => ( Pa @ Z ) ) )
% 0.33/0.48 => ( pred_treeFI @ A @ Pa @ X3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % treeFI.pred_mono_strong
% 0.33/0.48 thf(fact_125_treeFI_Opred__cong,axiom,
% 0.33/0.48 ! [A: $tType,X3: treeFI @ A,Ya: treeFI @ A,P2: A > $o,Pa: A > $o] :
% 0.33/0.48 ( ( X3 = Ya )
% 0.33/0.48 => ( ! [Z: A] :
% 0.33/0.48 ( ( member2 @ A @ Z @ ( set_treeFI @ A @ Ya ) )
% 0.33/0.48 => ( ( P2 @ Z )
% 0.33/0.48 = ( Pa @ Z ) ) )
% 0.33/0.48 => ( ( pred_treeFI @ A @ P2 @ X3 )
% 0.33/0.48 = ( pred_treeFI @ A @ Pa @ Ya ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % treeFI.pred_cong
% 0.33/0.48 thf(fact_126_streams__iff__sset,axiom,
% 0.33/0.48 ! [A: $tType,S2: stream @ A,A5: set @ A] :
% 0.33/0.48 ( ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) )
% 0.33/0.48 = ( ord_less_eq @ ( set @ A ) @ ( sset @ A @ S2 ) @ A5 ) ) ).
% 0.33/0.48
% 0.33/0.48 % streams_iff_sset
% 0.33/0.48 thf(fact_127_subset__code_I1_J,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,B2: set @ A] :
% 0.33/0.48 ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ B2 )
% 0.33/0.48 = ( ! [X5: A] :
% 0.33/0.48 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ( member2 @ A @ X5 @ B2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % subset_code(1)
% 0.33/0.48 thf(fact_128_sset__shift,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,S2: stream @ A] :
% 0.33/0.48 ( ( sset @ A @ ( shift @ A @ Xs @ S2 ) )
% 0.33/0.48 = ( sup_sup @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( sset @ A @ S2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % sset_shift
% 0.33/0.48 thf(fact_129_set__union,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.33/0.48 ( ( set2 @ A @ ( union @ A @ Xs @ Ys ) )
% 0.33/0.48 = ( sup_sup @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( set2 @ A @ Ys ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % set_union
% 0.33/0.48 thf(fact_130_treeFI_Opred__inject,axiom,
% 0.33/0.48 ! [A: $tType,P2: A > $o,A3: A,Aa2: list @ ( treeFI @ A )] :
% 0.33/0.48 ( ( pred_treeFI @ A @ P2 @ ( tree @ A @ A3 @ Aa2 ) )
% 0.33/0.48 = ( ( P2 @ A3 )
% 0.33/0.48 & ( list_all @ ( treeFI @ A ) @ ( pred_treeFI @ A @ P2 ) @ Aa2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % treeFI.pred_inject
% 0.33/0.48 thf(fact_131_shift__left__inj,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,S12: stream @ A,S23: stream @ A] :
% 0.33/0.48 ( ( ( shift @ A @ Xs @ S12 )
% 0.33/0.48 = ( shift @ A @ Xs @ S23 ) )
% 0.33/0.48 = ( S12 = S23 ) ) ).
% 0.33/0.48
% 0.33/0.48 % shift_left_inj
% 0.33/0.48 thf(fact_132_stream__all__shift,axiom,
% 0.33/0.48 ! [A: $tType,P2: A > $o,Xs: list @ A,S2: stream @ A] :
% 0.33/0.48 ( ( stream_all @ A @ P2 @ ( shift @ A @ Xs @ S2 ) )
% 0.33/0.48 = ( ( list_all @ A @ P2 @ Xs )
% 0.33/0.48 & ( stream_all @ A @ P2 @ S2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % stream_all_shift
% 0.33/0.48 thf(fact_133_list_Opred__cong,axiom,
% 0.33/0.48 ! [A: $tType,X3: list @ A,Ya: list @ A,P2: A > $o,Pa: A > $o] :
% 0.33/0.48 ( ( X3 = Ya )
% 0.33/0.48 => ( ! [Z: A] :
% 0.33/0.48 ( ( member2 @ A @ Z @ ( set2 @ A @ Ya ) )
% 0.33/0.48 => ( ( P2 @ Z )
% 0.33/0.48 = ( Pa @ Z ) ) )
% 0.33/0.48 => ( ( list_all @ A @ P2 @ X3 )
% 0.33/0.48 = ( list_all @ A @ Pa @ Ya ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % list.pred_cong
% 0.33/0.48 thf(fact_134_list_Opred__mono__strong,axiom,
% 0.33/0.48 ! [A: $tType,P2: A > $o,X3: list @ A,Pa: A > $o] :
% 0.33/0.48 ( ( list_all @ A @ P2 @ X3 )
% 0.33/0.48 => ( ! [Z: A] :
% 0.33/0.48 ( ( member2 @ A @ Z @ ( set2 @ A @ X3 ) )
% 0.33/0.48 => ( ( P2 @ Z )
% 0.33/0.48 => ( Pa @ Z ) ) )
% 0.33/0.48 => ( list_all @ A @ Pa @ X3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % list.pred_mono_strong
% 0.33/0.48 thf(fact_135_list__all__iff,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( list_all @ A )
% 0.33/0.48 = ( ^ [P: A > $o,X5: list @ A] :
% 0.33/0.48 ! [Y4: A] :
% 0.33/0.48 ( ( member2 @ A @ Y4 @ ( set2 @ A @ X5 ) )
% 0.33/0.48 => ( P @ Y4 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % list_all_iff
% 0.33/0.48 thf(fact_136_Ball__set__list__all,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 0.33/0.48 ( ( ! [X5: A] :
% 0.33/0.48 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ( P2 @ X5 ) ) )
% 0.33/0.48 = ( list_all @ A @ P2 @ Xs ) ) ).
% 0.33/0.48
% 0.33/0.48 % Ball_set_list_all
% 0.33/0.48 thf(fact_137_list_Opred__set,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( list_all @ A )
% 0.33/0.48 = ( ^ [P: A > $o,X5: list @ A] :
% 0.33/0.48 ! [Y4: A] :
% 0.33/0.48 ( ( member2 @ A @ Y4 @ ( set2 @ A @ X5 ) )
% 0.33/0.48 => ( P @ Y4 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % list.pred_set
% 0.33/0.48 thf(fact_138_List_Oset__insert,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.33/0.48 ( ( set2 @ A @ ( insert @ A @ X3 @ Xs ) )
% 0.33/0.48 = ( insert2 @ A @ X3 @ ( set2 @ A @ Xs ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % List.set_insert
% 0.33/0.48 thf(fact_139_subset__code_I2_J,axiom,
% 0.33/0.48 ! [B: $tType,A5: set @ B,Ys: list @ B] :
% 0.33/0.48 ( ( ord_less_eq @ ( set @ B ) @ A5 @ ( coset @ B @ Ys ) )
% 0.33/0.48 = ( ! [X5: B] :
% 0.33/0.48 ( ( member2 @ B @ X5 @ ( set2 @ B @ Ys ) )
% 0.33/0.48 => ~ ( member2 @ B @ X5 @ A5 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % subset_code(2)
% 0.33/0.48 thf(fact_140_in__set__member,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.33/0.48 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 = ( member @ A @ Xs @ X3 ) ) ).
% 0.33/0.48
% 0.33/0.48 % in_set_member
% 0.33/0.48 thf(fact_141_union__set__fold,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,A5: set @ A] :
% 0.33/0.48 ( ( sup_sup @ ( set @ A ) @ ( set2 @ A @ Xs ) @ A5 )
% 0.33/0.48 = ( fold @ A @ ( set @ A ) @ ( insert2 @ A ) @ Xs @ A5 ) ) ).
% 0.33/0.48
% 0.33/0.48 % union_set_fold
% 0.33/0.48 thf(fact_142_in__set__insert,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.33/0.48 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ( ( insert @ A @ X3 @ Xs )
% 0.33/0.48 = Xs ) ) ).
% 0.33/0.48
% 0.33/0.48 % in_set_insert
% 0.33/0.48 thf(fact_143_List_Ofold__cong,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,A3: A,B3: A,Xs: list @ B,Ys: list @ B,F2: B > A > A,G: B > A > A] :
% 0.33/0.48 ( ( A3 = B3 )
% 0.33/0.48 => ( ( Xs = Ys )
% 0.33/0.48 => ( ! [X: B] :
% 0.33/0.48 ( ( member2 @ B @ X @ ( set2 @ B @ Xs ) )
% 0.33/0.48 => ( ( F2 @ X )
% 0.33/0.48 = ( G @ X ) ) )
% 0.33/0.48 => ( ( fold @ B @ A @ F2 @ Xs @ A3 )
% 0.33/0.48 = ( fold @ B @ A @ G @ Ys @ B3 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % List.fold_cong
% 0.33/0.48 thf(fact_144_fold__invariant,axiom,
% 0.33/0.48 ! [A: $tType,B: $tType,Xs: list @ A,Q: A > $o,P2: B > $o,S2: B,F2: A > B > B] :
% 0.33/0.48 ( ! [X: A] :
% 0.33/0.48 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ( Q @ X ) )
% 0.33/0.48 => ( ( P2 @ S2 )
% 0.33/0.48 => ( ! [X: A,S5: B] :
% 0.33/0.48 ( ( Q @ X )
% 0.33/0.48 => ( ( P2 @ S5 )
% 0.33/0.48 => ( P2 @ ( F2 @ X @ S5 ) ) ) )
% 0.33/0.48 => ( P2 @ ( fold @ A @ B @ F2 @ Xs @ S2 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % fold_invariant
% 0.33/0.48 thf(fact_145_fold__commute__apply,axiom,
% 0.33/0.48 ! [A: $tType,C: $tType,B: $tType,Xs: list @ A,H: B > C,G: A > B > B,F2: A > C > C,S2: B] :
% 0.33/0.48 ( ! [X: A] :
% 0.33/0.48 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ( ( comp @ B @ C @ B @ H @ ( G @ X ) )
% 0.33/0.48 = ( comp @ C @ C @ B @ ( F2 @ X ) @ H ) ) )
% 0.33/0.48 => ( ( H @ ( fold @ A @ B @ G @ Xs @ S2 ) )
% 0.33/0.48 = ( fold @ A @ C @ F2 @ Xs @ ( H @ S2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % fold_commute_apply
% 0.33/0.48 thf(fact_146_fold__commute,axiom,
% 0.33/0.48 ! [A: $tType,C: $tType,B: $tType,Xs: list @ A,H: B > C,G: A > B > B,F2: A > C > C] :
% 0.33/0.48 ( ! [X: A] :
% 0.33/0.48 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ( ( comp @ B @ C @ B @ H @ ( G @ X ) )
% 0.33/0.48 = ( comp @ C @ C @ B @ ( F2 @ X ) @ H ) ) )
% 0.33/0.48 => ( ( comp @ B @ C @ B @ H @ ( fold @ A @ B @ G @ Xs ) )
% 0.33/0.48 = ( comp @ C @ C @ B @ ( fold @ A @ C @ F2 @ Xs ) @ H ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % fold_commute
% 0.33/0.48 thf(fact_147_foldr__fold,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,Xs: list @ A,F2: A > B > B] :
% 0.33/0.48 ( ! [X: A,Y3: A] :
% 0.33/0.48 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ( ( member2 @ A @ Y3 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ( ( comp @ B @ B @ B @ ( F2 @ Y3 ) @ ( F2 @ X ) )
% 0.33/0.48 = ( comp @ B @ B @ B @ ( F2 @ X ) @ ( F2 @ Y3 ) ) ) ) )
% 0.33/0.48 => ( ( foldr @ A @ B @ F2 @ Xs )
% 0.33/0.48 = ( fold @ A @ B @ F2 @ Xs ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % foldr_fold
% 0.33/0.48 thf(fact_148_fold__remove1__split,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,Xs: list @ A,F2: A > B > B,X3: A] :
% 0.33/0.48 ( ! [X: A,Y3: A] :
% 0.33/0.48 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ( ( member2 @ A @ Y3 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ( ( comp @ B @ B @ B @ ( F2 @ X ) @ ( F2 @ Y3 ) )
% 0.33/0.48 = ( comp @ B @ B @ B @ ( F2 @ Y3 ) @ ( F2 @ X ) ) ) ) )
% 0.33/0.48 => ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ( ( fold @ A @ B @ F2 @ Xs )
% 0.33/0.48 = ( comp @ B @ B @ B @ ( fold @ A @ B @ F2 @ ( remove1 @ A @ X3 @ Xs ) ) @ ( F2 @ X3 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % fold_remove1_split
% 0.33/0.48 thf(fact_149_subset__code_I3_J,axiom,
% 0.33/0.48 ! [C: $tType] :
% 0.33/0.48 ~ ( ord_less_eq @ ( set @ C ) @ ( coset @ C @ ( nil @ C ) ) @ ( set2 @ C @ ( nil @ C ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % subset_code(3)
% 0.33/0.48 thf(fact_150_set__update__subset__insert,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,I: nat,X3: A] : ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ ( list_update @ A @ Xs @ I @ X3 ) ) @ ( insert2 @ A @ X3 @ ( set2 @ A @ Xs ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % set_update_subset_insert
% 0.33/0.48 thf(fact_151_in__set__remove1,axiom,
% 0.33/0.48 ! [A: $tType,A3: A,B3: A,Xs: list @ A] :
% 0.33/0.48 ( ( A3 != B3 )
% 0.33/0.48 => ( ( member2 @ A @ A3 @ ( set2 @ A @ ( remove1 @ A @ B3 @ Xs ) ) )
% 0.33/0.48 = ( member2 @ A @ A3 @ ( set2 @ A @ Xs ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % in_set_remove1
% 0.33/0.48 thf(fact_152_foldr__cong,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,A3: A,B3: A,L: list @ B,K: list @ B,F2: B > A > A,G: B > A > A] :
% 0.33/0.48 ( ( A3 = B3 )
% 0.33/0.48 => ( ( L = K )
% 0.33/0.48 => ( ! [A7: A,X: B] :
% 0.33/0.48 ( ( member2 @ B @ X @ ( set2 @ B @ L ) )
% 0.33/0.48 => ( ( F2 @ X @ A7 )
% 0.33/0.48 = ( G @ X @ A7 ) ) )
% 0.33/0.48 => ( ( foldr @ B @ A @ F2 @ L @ A3 )
% 0.33/0.48 = ( foldr @ B @ A @ G @ K @ B3 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % foldr_cong
% 0.33/0.48 thf(fact_153_notin__set__remove1,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Xs: list @ A,Y: A] :
% 0.33/0.48 ( ~ ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ~ ( member2 @ A @ X3 @ ( set2 @ A @ ( remove1 @ A @ Y @ Xs ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % notin_set_remove1
% 0.33/0.48 thf(fact_154_remove1__idem,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.33/0.48 ( ~ ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ( ( remove1 @ A @ X3 @ Xs )
% 0.33/0.48 = Xs ) ) ).
% 0.33/0.48
% 0.33/0.48 % remove1_idem
% 0.33/0.48 thf(fact_155_shift_Osimps_I1_J,axiom,
% 0.33/0.48 ! [A: $tType,S2: stream @ A] :
% 0.33/0.48 ( ( shift @ A @ ( nil @ A ) @ S2 )
% 0.33/0.48 = S2 ) ).
% 0.33/0.48
% 0.33/0.48 % shift.simps(1)
% 0.33/0.48 thf(fact_156_set__update__subsetI,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,A5: set @ A,X3: A,I: nat] :
% 0.33/0.48 ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ A5 )
% 0.33/0.48 => ( ( member2 @ A @ X3 @ A5 )
% 0.33/0.48 => ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ ( list_update @ A @ Xs @ I @ X3 ) ) @ A5 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % set_update_subsetI
% 0.33/0.48 thf(fact_157_set__remove1__subset,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Xs: list @ A] : ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ ( remove1 @ A @ X3 @ Xs ) ) @ ( set2 @ A @ Xs ) ) ).
% 0.33/0.48
% 0.33/0.48 % set_remove1_subset
% 0.33/0.48 thf(fact_158_sset__cycle,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A] :
% 0.33/0.48 ( ( Xs
% 0.33/0.48 != ( nil @ A ) )
% 0.33/0.48 => ( ( sset @ A @ ( cycle @ A @ Xs ) )
% 0.33/0.48 = ( set2 @ A @ Xs ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % sset_cycle
% 0.33/0.48 thf(fact_159_flat__Stream,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,Ws: stream @ ( list @ A )] :
% 0.33/0.48 ( ( Xs
% 0.33/0.48 != ( nil @ A ) )
% 0.33/0.48 => ( ( flat @ A @ ( sCons @ ( list @ A ) @ Xs @ Ws ) )
% 0.33/0.48 = ( shift @ A @ Xs @ ( flat @ A @ Ws ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % flat_Stream
% 0.33/0.48 thf(fact_160_shift__simps_I1_J,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,S2: stream @ A] :
% 0.33/0.48 ( ( ( Xs
% 0.33/0.48 = ( nil @ A ) )
% 0.33/0.48 => ( ( shd @ A @ ( shift @ A @ Xs @ S2 ) )
% 0.33/0.48 = ( shd @ A @ S2 ) ) )
% 0.33/0.48 & ( ( Xs
% 0.33/0.48 != ( nil @ A ) )
% 0.33/0.48 => ( ( shd @ A @ ( shift @ A @ Xs @ S2 ) )
% 0.33/0.48 = ( hd @ A @ Xs ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % shift_simps(1)
% 0.33/0.48 thf(fact_161_cycle_Osimps_I1_J,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A] :
% 0.33/0.48 ( ( shd @ A @ ( cycle @ A @ Xs ) )
% 0.33/0.48 = ( hd @ A @ Xs ) ) ).
% 0.33/0.48
% 0.33/0.48 % cycle.simps(1)
% 0.33/0.48 thf(fact_162_flat_Osimps_I1_J,axiom,
% 0.33/0.48 ! [A: $tType,Ws: stream @ ( list @ A )] :
% 0.33/0.48 ( ( shd @ A @ ( flat @ A @ Ws ) )
% 0.33/0.48 = ( hd @ A @ ( shd @ ( list @ A ) @ Ws ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % flat.simps(1)
% 0.33/0.48 thf(fact_163_list_Oset__sel_I1_J,axiom,
% 0.33/0.48 ! [A: $tType,A3: list @ A] :
% 0.33/0.48 ( ( A3
% 0.33/0.48 != ( nil @ A ) )
% 0.33/0.48 => ( member2 @ A @ ( hd @ A @ A3 ) @ ( set2 @ A @ A3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % list.set_sel(1)
% 0.33/0.48 thf(fact_164_hd__in__set,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A] :
% 0.33/0.48 ( ( Xs
% 0.33/0.48 != ( nil @ A ) )
% 0.33/0.48 => ( member2 @ A @ ( hd @ A @ Xs ) @ ( set2 @ A @ Xs ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % hd_in_set
% 0.33/0.48 thf(fact_165_cycle__decomp,axiom,
% 0.33/0.48 ! [A: $tType,U: list @ A] :
% 0.33/0.48 ( ( U
% 0.33/0.48 != ( nil @ A ) )
% 0.33/0.48 => ( ( cycle @ A @ U )
% 0.33/0.48 = ( shift @ A @ U @ ( cycle @ A @ U ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % cycle_decomp
% 0.33/0.48 thf(fact_166_flat__unfold,axiom,
% 0.33/0.48 ! [A: $tType,Ws: stream @ ( list @ A )] :
% 0.33/0.48 ( ( ( shd @ ( list @ A ) @ Ws )
% 0.33/0.48 != ( nil @ A ) )
% 0.33/0.48 => ( ( flat @ A @ Ws )
% 0.33/0.48 = ( shift @ A @ ( shd @ ( list @ A ) @ Ws ) @ ( flat @ A @ ( stl @ ( list @ A ) @ Ws ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % flat_unfold
% 0.33/0.48 thf(fact_167_flat_Ocode,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( flat @ A )
% 0.33/0.48 = ( ^ [Ws2: stream @ ( list @ A )] :
% 0.33/0.48 ( sCons @ A @ ( hd @ A @ ( shd @ ( list @ A ) @ Ws2 ) )
% 0.33/0.48 @ ( flat @ A
% 0.33/0.48 @ ( if @ ( stream @ ( list @ A ) )
% 0.33/0.48 @ ( ( tl @ A @ ( shd @ ( list @ A ) @ Ws2 ) )
% 0.33/0.48 = ( nil @ A ) )
% 0.33/0.48 @ ( stl @ ( list @ A ) @ Ws2 )
% 0.33/0.48 @ ( sCons @ ( list @ A ) @ ( tl @ A @ ( shd @ ( list @ A ) @ Ws2 ) ) @ ( stl @ ( list @ A ) @ Ws2 ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % flat.code
% 0.33/0.48 thf(fact_168_flat__Cons,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Xs: list @ A,Ws: stream @ ( list @ A )] :
% 0.33/0.48 ( ( flat @ A @ ( sCons @ ( list @ A ) @ ( cons @ A @ X3 @ Xs ) @ Ws ) )
% 0.33/0.48 = ( sCons @ A @ X3
% 0.33/0.48 @ ( flat @ A
% 0.33/0.48 @ ( if @ ( stream @ ( list @ A ) )
% 0.33/0.48 @ ( Xs
% 0.33/0.48 = ( nil @ A ) )
% 0.33/0.48 @ Ws
% 0.33/0.48 @ ( sCons @ ( list @ A ) @ Xs @ Ws ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % flat_Cons
% 0.33/0.48 thf(fact_169_flat_Osimps_I2_J,axiom,
% 0.33/0.48 ! [A: $tType,Ws: stream @ ( list @ A )] :
% 0.33/0.48 ( ( stl @ A @ ( flat @ A @ Ws ) )
% 0.33/0.48 = ( flat @ A
% 0.33/0.48 @ ( if @ ( stream @ ( list @ A ) )
% 0.33/0.48 @ ( ( tl @ A @ ( shd @ ( list @ A ) @ Ws ) )
% 0.33/0.48 = ( nil @ A ) )
% 0.33/0.48 @ ( stl @ ( list @ A ) @ Ws )
% 0.33/0.48 @ ( sCons @ ( list @ A ) @ ( tl @ A @ ( shd @ ( list @ A ) @ Ws ) ) @ ( stl @ ( list @ A ) @ Ws ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % flat.simps(2)
% 0.33/0.48 thf(fact_170_list_Osimps_I15_J,axiom,
% 0.33/0.48 ! [A: $tType,X21: A,X222: list @ A] :
% 0.33/0.48 ( ( set2 @ A @ ( cons @ A @ X21 @ X222 ) )
% 0.33/0.48 = ( insert2 @ A @ X21 @ ( set2 @ A @ X222 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % list.simps(15)
% 0.33/0.48 thf(fact_171_not__in__set__insert,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.33/0.48 ( ~ ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ( ( insert @ A @ X3 @ Xs )
% 0.33/0.48 = ( cons @ A @ X3 @ Xs ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % not_in_set_insert
% 0.33/0.48 thf(fact_172_shift__simps_I2_J,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,S2: stream @ A] :
% 0.33/0.48 ( ( ( Xs
% 0.33/0.48 = ( nil @ A ) )
% 0.33/0.48 => ( ( stl @ A @ ( shift @ A @ Xs @ S2 ) )
% 0.33/0.48 = ( stl @ A @ S2 ) ) )
% 0.33/0.48 & ( ( Xs
% 0.33/0.48 != ( nil @ A ) )
% 0.33/0.48 => ( ( stl @ A @ ( shift @ A @ Xs @ S2 ) )
% 0.33/0.48 = ( shift @ A @ ( tl @ A @ Xs ) @ S2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % shift_simps(2)
% 0.33/0.48 thf(fact_173_list_Oset__cases,axiom,
% 0.33/0.48 ! [A: $tType,E: A,A3: list @ A] :
% 0.33/0.48 ( ( member2 @ A @ E @ ( set2 @ A @ A3 ) )
% 0.33/0.48 => ( ! [Z2: list @ A] :
% 0.33/0.48 ( A3
% 0.33/0.48 != ( cons @ A @ E @ Z2 ) )
% 0.33/0.48 => ~ ! [Z1: A,Z2: list @ A] :
% 0.33/0.48 ( ( A3
% 0.33/0.48 = ( cons @ A @ Z1 @ Z2 ) )
% 0.33/0.48 => ~ ( member2 @ A @ E @ ( set2 @ A @ Z2 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % list.set_cases
% 0.33/0.48 thf(fact_174_set__ConsD,axiom,
% 0.33/0.48 ! [A: $tType,Y: A,X3: A,Xs: list @ A] :
% 0.33/0.48 ( ( member2 @ A @ Y @ ( set2 @ A @ ( cons @ A @ X3 @ Xs ) ) )
% 0.33/0.48 => ( ( Y = X3 )
% 0.33/0.48 | ( member2 @ A @ Y @ ( set2 @ A @ Xs ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % set_ConsD
% 0.33/0.48 thf(fact_175_list_Oset__intros_I1_J,axiom,
% 0.33/0.48 ! [A: $tType,A1: A,A2: list @ A] : ( member2 @ A @ A1 @ ( set2 @ A @ ( cons @ A @ A1 @ A2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % list.set_intros(1)
% 0.33/0.48 thf(fact_176_list_Oset__intros_I2_J,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,A2: list @ A,A1: A] :
% 0.33/0.48 ( ( member2 @ A @ X3 @ ( set2 @ A @ A2 ) )
% 0.33/0.48 => ( member2 @ A @ X3 @ ( set2 @ A @ ( cons @ A @ A1 @ A2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % list.set_intros(2)
% 0.33/0.48 thf(fact_177_set__subset__Cons,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,X3: A] : ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( set2 @ A @ ( cons @ A @ X3 @ Xs ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % set_subset_Cons
% 0.33/0.48 thf(fact_178_list_Oset__sel_I2_J,axiom,
% 0.33/0.48 ! [A: $tType,A3: list @ A,X3: A] :
% 0.33/0.48 ( ( A3
% 0.33/0.48 != ( nil @ A ) )
% 0.33/0.48 => ( ( member2 @ A @ X3 @ ( set2 @ A @ ( tl @ A @ A3 ) ) )
% 0.33/0.48 => ( member2 @ A @ X3 @ ( set2 @ A @ A3 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % list.set_sel(2)
% 0.33/0.48 thf(fact_179_fold__Cons,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,F2: A > B > B,X3: A,Xs: list @ A] :
% 0.33/0.48 ( ( fold @ A @ B @ F2 @ ( cons @ A @ X3 @ Xs ) )
% 0.33/0.48 = ( comp @ B @ B @ B @ ( fold @ A @ B @ F2 @ Xs ) @ ( F2 @ X3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % fold_Cons
% 0.33/0.48 thf(fact_180_foldr__Cons,axiom,
% 0.33/0.48 ! [B: $tType,A: $tType,F2: A > B > B,X3: A,Xs: list @ A] :
% 0.33/0.48 ( ( foldr @ A @ B @ F2 @ ( cons @ A @ X3 @ Xs ) )
% 0.33/0.48 = ( comp @ B @ B @ B @ ( F2 @ X3 ) @ ( foldr @ A @ B @ F2 @ Xs ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % foldr_Cons
% 0.33/0.48 thf(fact_181_shift_Osimps_I2_J,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Xs: list @ A,S2: stream @ A] :
% 0.33/0.48 ( ( shift @ A @ ( cons @ A @ X3 @ Xs ) @ S2 )
% 0.33/0.48 = ( sCons @ A @ X3 @ ( shift @ A @ Xs @ S2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % shift.simps(2)
% 0.33/0.48 thf(fact_182_List_Oinsert__def,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( insert @ A )
% 0.33/0.48 = ( ^ [X5: A,Xs2: list @ A] : ( if @ ( list @ A ) @ ( member2 @ A @ X5 @ ( set2 @ A @ Xs2 ) ) @ Xs2 @ ( cons @ A @ X5 @ Xs2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % List.insert_def
% 0.33/0.48 thf(fact_183_the__elem__set,axiom,
% 0.33/0.48 ! [A: $tType,X3: A] :
% 0.33/0.48 ( ( the_elem @ A @ ( set2 @ A @ ( cons @ A @ X3 @ ( nil @ A ) ) ) )
% 0.33/0.48 = X3 ) ).
% 0.33/0.48
% 0.33/0.48 % the_elem_set
% 0.33/0.48 thf(fact_184_cycle__rotated,axiom,
% 0.33/0.48 ! [A: $tType,V: list @ A,U: list @ A,S2: stream @ A] :
% 0.33/0.48 ( ( V
% 0.33/0.48 != ( nil @ A ) )
% 0.33/0.48 => ( ( ( cycle @ A @ U )
% 0.33/0.48 = ( shift @ A @ V @ S2 ) )
% 0.33/0.48 => ( ( cycle @ A @ ( append @ A @ ( tl @ A @ U ) @ ( cons @ A @ ( hd @ A @ U ) @ ( nil @ A ) ) ) )
% 0.33/0.48 = ( shift @ A @ ( tl @ A @ V ) @ S2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % cycle_rotated
% 0.33/0.48 thf(fact_185_cycle_Ocode,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( cycle @ A )
% 0.33/0.48 = ( ^ [Xs2: list @ A] : ( sCons @ A @ ( hd @ A @ Xs2 ) @ ( cycle @ A @ ( append @ A @ ( tl @ A @ Xs2 ) @ ( cons @ A @ ( hd @ A @ Xs2 ) @ ( nil @ A ) ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % cycle.code
% 0.33/0.48 thf(fact_186_shift__append,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,Ys: list @ A,S2: stream @ A] :
% 0.33/0.48 ( ( shift @ A @ ( append @ A @ Xs @ Ys ) @ S2 )
% 0.33/0.48 = ( shift @ A @ Xs @ ( shift @ A @ Ys @ S2 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % shift_append
% 0.33/0.48 thf(fact_187_set__append,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 0.33/0.48 ( ( set2 @ A @ ( append @ A @ Xs @ Ys ) )
% 0.33/0.48 = ( sup_sup @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( set2 @ A @ Ys ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % set_append
% 0.33/0.48 thf(fact_188_fold__append,axiom,
% 0.33/0.48 ! [A: $tType,B: $tType,F2: B > A > A,Xs: list @ B,Ys: list @ B] :
% 0.33/0.48 ( ( fold @ B @ A @ F2 @ ( append @ B @ Xs @ Ys ) )
% 0.33/0.48 = ( comp @ A @ A @ A @ ( fold @ B @ A @ F2 @ Ys ) @ ( fold @ B @ A @ F2 @ Xs ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % fold_append
% 0.33/0.48 thf(fact_189_split__list,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.33/0.48 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ? [Ys2: list @ A,Zs: list @ A] :
% 0.33/0.48 ( Xs
% 0.33/0.48 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % split_list
% 0.33/0.48 thf(fact_190_split__list__last,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.33/0.48 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ? [Ys2: list @ A,Zs: list @ A] :
% 0.33/0.48 ( ( Xs
% 0.33/0.48 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs ) ) )
% 0.33/0.48 & ~ ( member2 @ A @ X3 @ ( set2 @ A @ Zs ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % split_list_last
% 0.33/0.48 thf(fact_191_split__list__prop,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 0.33/0.48 ( ? [X4: A] :
% 0.33/0.48 ( ( member2 @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 & ( P2 @ X4 ) )
% 0.33/0.48 => ? [Ys2: list @ A,X: A] :
% 0.33/0.48 ( ? [Zs: list @ A] :
% 0.33/0.48 ( Xs
% 0.33/0.48 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.33/0.48 & ( P2 @ X ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % split_list_prop
% 0.33/0.48 thf(fact_192_split__list__first,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.33/0.48 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ? [Ys2: list @ A,Zs: list @ A] :
% 0.33/0.48 ( ( Xs
% 0.33/0.48 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs ) ) )
% 0.33/0.48 & ~ ( member2 @ A @ X3 @ ( set2 @ A @ Ys2 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % split_list_first
% 0.33/0.48 thf(fact_193_split__list__propE,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 0.33/0.48 ( ? [X4: A] :
% 0.33/0.48 ( ( member2 @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 & ( P2 @ X4 ) )
% 0.33/0.48 => ~ ! [Ys2: list @ A,X: A] :
% 0.33/0.48 ( ? [Zs: list @ A] :
% 0.33/0.48 ( Xs
% 0.33/0.48 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.33/0.48 => ~ ( P2 @ X ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % split_list_propE
% 0.33/0.48 thf(fact_194_in__set__conv__decomp,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.33/0.48 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 0.33/0.48 ( Xs
% 0.33/0.48 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs2 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % in_set_conv_decomp
% 0.33/0.48 thf(fact_195_split__list__last__prop,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 0.33/0.48 ( ? [X4: A] :
% 0.33/0.48 ( ( member2 @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 & ( P2 @ X4 ) )
% 0.33/0.48 => ? [Ys2: list @ A,X: A,Zs: list @ A] :
% 0.33/0.48 ( ( Xs
% 0.33/0.48 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.33/0.48 & ( P2 @ X )
% 0.33/0.48 & ! [Xa3: A] :
% 0.33/0.48 ( ( member2 @ A @ Xa3 @ ( set2 @ A @ Zs ) )
% 0.33/0.48 => ~ ( P2 @ Xa3 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % split_list_last_prop
% 0.33/0.48 thf(fact_196_split__list__first__prop,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 0.33/0.48 ( ? [X4: A] :
% 0.33/0.48 ( ( member2 @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 & ( P2 @ X4 ) )
% 0.33/0.48 => ? [Ys2: list @ A,X: A] :
% 0.33/0.48 ( ? [Zs: list @ A] :
% 0.33/0.48 ( Xs
% 0.33/0.48 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.33/0.48 & ( P2 @ X )
% 0.33/0.48 & ! [Xa3: A] :
% 0.33/0.48 ( ( member2 @ A @ Xa3 @ ( set2 @ A @ Ys2 ) )
% 0.33/0.48 => ~ ( P2 @ Xa3 ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % split_list_first_prop
% 0.33/0.48 thf(fact_197_split__list__last__propE,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 0.33/0.48 ( ? [X4: A] :
% 0.33/0.48 ( ( member2 @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 & ( P2 @ X4 ) )
% 0.33/0.48 => ~ ! [Ys2: list @ A,X: A,Zs: list @ A] :
% 0.33/0.48 ( ( Xs
% 0.33/0.48 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.33/0.48 => ( ( P2 @ X )
% 0.33/0.48 => ~ ! [Xa3: A] :
% 0.33/0.48 ( ( member2 @ A @ Xa3 @ ( set2 @ A @ Zs ) )
% 0.33/0.48 => ~ ( P2 @ Xa3 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % split_list_last_propE
% 0.33/0.48 thf(fact_198_split__list__first__propE,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 0.33/0.48 ( ? [X4: A] :
% 0.33/0.48 ( ( member2 @ A @ X4 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 & ( P2 @ X4 ) )
% 0.33/0.48 => ~ ! [Ys2: list @ A,X: A] :
% 0.33/0.48 ( ? [Zs: list @ A] :
% 0.33/0.48 ( Xs
% 0.33/0.48 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 0.33/0.48 => ( ( P2 @ X )
% 0.33/0.48 => ~ ! [Xa3: A] :
% 0.33/0.48 ( ( member2 @ A @ Xa3 @ ( set2 @ A @ Ys2 ) )
% 0.33/0.48 => ~ ( P2 @ Xa3 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % split_list_first_propE
% 0.33/0.48 thf(fact_199_in__set__conv__decomp__last,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.33/0.48 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 0.33/0.48 ( ( Xs
% 0.33/0.48 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs2 ) ) )
% 0.33/0.48 & ~ ( member2 @ A @ X3 @ ( set2 @ A @ Zs2 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % in_set_conv_decomp_last
% 0.33/0.48 thf(fact_200_in__set__conv__decomp__first,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.33/0.48 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 0.33/0.48 ( ( Xs
% 0.33/0.48 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs2 ) ) )
% 0.33/0.48 & ~ ( member2 @ A @ X3 @ ( set2 @ A @ Ys3 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % in_set_conv_decomp_first
% 0.33/0.48 thf(fact_201_split__list__last__prop__iff,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 0.33/0.48 ( ( ? [X5: A] :
% 0.33/0.48 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 & ( P2 @ X5 ) ) )
% 0.33/0.48 = ( ? [Ys3: list @ A,X5: A,Zs2: list @ A] :
% 0.33/0.48 ( ( Xs
% 0.33/0.48 = ( append @ A @ Ys3 @ ( cons @ A @ X5 @ Zs2 ) ) )
% 0.33/0.48 & ( P2 @ X5 )
% 0.33/0.48 & ! [Y4: A] :
% 0.33/0.48 ( ( member2 @ A @ Y4 @ ( set2 @ A @ Zs2 ) )
% 0.33/0.48 => ~ ( P2 @ Y4 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % split_list_last_prop_iff
% 0.33/0.48 thf(fact_202_split__list__first__prop__iff,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 0.33/0.48 ( ( ? [X5: A] :
% 0.33/0.48 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 & ( P2 @ X5 ) ) )
% 0.33/0.48 = ( ? [Ys3: list @ A,X5: A] :
% 0.33/0.48 ( ? [Zs2: list @ A] :
% 0.33/0.48 ( Xs
% 0.33/0.48 = ( append @ A @ Ys3 @ ( cons @ A @ X5 @ Zs2 ) ) )
% 0.33/0.48 & ( P2 @ X5 )
% 0.33/0.48 & ! [Y4: A] :
% 0.33/0.48 ( ( member2 @ A @ Y4 @ ( set2 @ A @ Ys3 ) )
% 0.33/0.48 => ~ ( P2 @ Y4 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % split_list_first_prop_iff
% 0.33/0.48 thf(fact_203_remove1__append,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Xs: list @ A,Ys: list @ A] :
% 0.33/0.48 ( ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ( ( remove1 @ A @ X3 @ ( append @ A @ Xs @ Ys ) )
% 0.33/0.48 = ( append @ A @ ( remove1 @ A @ X3 @ Xs ) @ Ys ) ) )
% 0.33/0.48 & ( ~ ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ( ( remove1 @ A @ X3 @ ( append @ A @ Xs @ Ys ) )
% 0.33/0.48 = ( append @ A @ Xs @ ( remove1 @ A @ X3 @ Ys ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % remove1_append
% 0.33/0.48 thf(fact_204_cycle__Cons,axiom,
% 0.33/0.48 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.33/0.48 ( ( cycle @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.33/0.48 = ( sCons @ A @ X3 @ ( cycle @ A @ ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % cycle_Cons
% 0.33/0.48 thf(fact_205_cycle_Osimps_I2_J,axiom,
% 0.33/0.48 ! [A: $tType,Xs: list @ A] :
% 0.33/0.48 ( ( stl @ A @ ( cycle @ A @ Xs ) )
% 0.33/0.48 = ( cycle @ A @ ( append @ A @ ( tl @ A @ Xs ) @ ( cons @ A @ ( hd @ A @ Xs ) @ ( nil @ A ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % cycle.simps(2)
% 0.33/0.48 thf(fact_206_Sup__fin_Oset__eq__fold,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.33/0.48 => ! [X3: A,Xs: list @ A] :
% 0.33/0.48 ( ( lattic477160up_fin @ A @ ( set2 @ A @ ( cons @ A @ X3 @ Xs ) ) )
% 0.33/0.48 = ( fold @ A @ A @ ( sup_sup @ A ) @ Xs @ X3 ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % Sup_fin.set_eq_fold
% 0.33/0.48 thf(fact_207_sorted_Ocases,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.48 => ! [A3: list @ A] :
% 0.33/0.48 ( ( linorder_sorted @ A @ A3 )
% 0.33/0.48 => ( ( A3
% 0.33/0.48 != ( nil @ A ) )
% 0.33/0.48 => ~ ! [Xs3: list @ A,X: A] :
% 0.33/0.48 ( ( A3
% 0.33/0.48 = ( cons @ A @ X @ Xs3 ) )
% 0.33/0.48 => ( ! [Xa3: A] :
% 0.33/0.48 ( ( member2 @ A @ Xa3 @ ( set2 @ A @ Xs3 ) )
% 0.33/0.48 => ( ord_less_eq @ A @ X @ Xa3 ) )
% 0.33/0.48 => ~ ( linorder_sorted @ A @ Xs3 ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % sorted.cases
% 0.33/0.48 thf(fact_208_sorted_Osimps,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.48 => ( ( linorder_sorted @ A )
% 0.33/0.48 = ( ^ [A4: list @ A] :
% 0.33/0.48 ( ( A4
% 0.33/0.48 = ( nil @ A ) )
% 0.33/0.48 | ? [Xs2: list @ A,X5: A] :
% 0.33/0.48 ( ( A4
% 0.33/0.48 = ( cons @ A @ X5 @ Xs2 ) )
% 0.33/0.48 & ! [Y4: A] :
% 0.33/0.48 ( ( member2 @ A @ Y4 @ ( set2 @ A @ Xs2 ) )
% 0.33/0.48 => ( ord_less_eq @ A @ X5 @ Y4 ) )
% 0.33/0.48 & ( linorder_sorted @ A @ Xs2 ) ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % sorted.simps
% 0.33/0.48 thf(fact_209_sorted_OCons,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.48 => ! [Xs: list @ A,X3: A] :
% 0.33/0.48 ( ! [X: A] :
% 0.33/0.48 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ( ord_less_eq @ A @ X3 @ X ) )
% 0.33/0.48 => ( ( linorder_sorted @ A @ Xs )
% 0.33/0.48 => ( linorder_sorted @ A @ ( cons @ A @ X3 @ Xs ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % sorted.Cons
% 0.33/0.48 thf(fact_210_sorted__Cons,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.48 => ! [X3: A,Xs: list @ A] :
% 0.33/0.48 ( ( linorder_sorted @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.33/0.48 = ( ( linorder_sorted @ A @ Xs )
% 0.33/0.48 & ! [X5: A] :
% 0.33/0.48 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs ) )
% 0.33/0.48 => ( ord_less_eq @ A @ X3 @ X5 ) ) ) ) ) ).
% 0.33/0.48
% 0.33/0.48 % sorted_Cons
% 0.33/0.48 thf(fact_211_sorted__append,axiom,
% 0.33/0.48 ! [A: $tType] :
% 0.33/0.48 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.48 => ! [Xs: list @ A,Ys: list @ A] :
% 0.33/0.48 ( ( linorder_sorted @ A @ ( append @ A @ Xs @ Ys ) )
% 0.33/0.48 = ( ( linorder_sorted @ A @ Xs )
% 0.33/0.48 & ( linorder_sorted @ A @ Ys )
% 0.33/0.48 & ! [X5: A] :
% 0.33/0.48 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs ) )
% 0.33/0.49 => ! [Y4: A] :
% 0.33/0.49 ( ( member2 @ A @ Y4 @ ( set2 @ A @ Ys ) )
% 0.33/0.49 => ( ord_less_eq @ A @ X5 @ Y4 ) ) ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % sorted_append
% 0.33/0.49 thf(fact_212_sorted_Oinducts,axiom,
% 0.33/0.49 ! [A: $tType] :
% 0.33/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.49 => ! [X3: list @ A,P2: ( list @ A ) > $o] :
% 0.33/0.49 ( ( linorder_sorted @ A @ X3 )
% 0.33/0.49 => ( ( P2 @ ( nil @ A ) )
% 0.33/0.49 => ( ! [Xs3: list @ A,X: A] :
% 0.33/0.49 ( ! [Xa3: A] :
% 0.33/0.49 ( ( member2 @ A @ Xa3 @ ( set2 @ A @ Xs3 ) )
% 0.33/0.49 => ( ord_less_eq @ A @ X @ Xa3 ) )
% 0.33/0.49 => ( ( linorder_sorted @ A @ Xs3 )
% 0.33/0.49 => ( ( P2 @ Xs3 )
% 0.33/0.49 => ( P2 @ ( cons @ A @ X @ Xs3 ) ) ) ) )
% 0.33/0.49 => ( P2 @ X3 ) ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % sorted.inducts
% 0.33/0.49 thf(fact_213_insort__is__Cons,axiom,
% 0.33/0.49 ! [A: $tType,B: $tType] :
% 0.33/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.49 => ! [Xs: list @ B,F2: B > A,A3: B] :
% 0.33/0.49 ( ! [X: B] :
% 0.33/0.49 ( ( member2 @ B @ X @ ( set2 @ B @ Xs ) )
% 0.33/0.49 => ( ord_less_eq @ A @ ( F2 @ A3 ) @ ( F2 @ X ) ) )
% 0.33/0.49 => ( ( linorder_insort_key @ B @ A @ F2 @ A3 @ Xs )
% 0.33/0.49 = ( cons @ B @ A3 @ Xs ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % insort_is_Cons
% 0.33/0.49 thf(fact_214_fold__rev,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,Xs: list @ A,F2: A > B > B] :
% 0.33/0.49 ( ! [X: A,Y3: A] :
% 0.33/0.49 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 0.33/0.49 => ( ( member2 @ A @ Y3 @ ( set2 @ A @ Xs ) )
% 0.33/0.49 => ( ( comp @ B @ B @ B @ ( F2 @ Y3 ) @ ( F2 @ X ) )
% 0.33/0.49 = ( comp @ B @ B @ B @ ( F2 @ X ) @ ( F2 @ Y3 ) ) ) ) )
% 0.33/0.49 => ( ( fold @ A @ B @ F2 @ ( rev @ A @ Xs ) )
% 0.33/0.49 = ( fold @ A @ B @ F2 @ Xs ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % fold_rev
% 0.33/0.49 thf(fact_215_set__rev,axiom,
% 0.33/0.49 ! [A: $tType,Xs: list @ A] :
% 0.33/0.49 ( ( set2 @ A @ ( rev @ A @ Xs ) )
% 0.33/0.49 = ( set2 @ A @ Xs ) ) ).
% 0.33/0.49
% 0.33/0.49 % set_rev
% 0.33/0.49 thf(fact_216_set__insort__key,axiom,
% 0.33/0.49 ! [A: $tType,B: $tType] :
% 0.33/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.33/0.49 => ! [F2: B > A,X3: B,Xs: list @ B] :
% 0.33/0.49 ( ( set2 @ B @ ( linorder_insort_key @ B @ A @ F2 @ X3 @ Xs ) )
% 0.33/0.49 = ( insert2 @ B @ X3 @ ( set2 @ B @ Xs ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % set_insort_key
% 0.33/0.49 thf(fact_217_trev_Ocode,axiom,
% 0.33/0.49 ! [A: $tType] :
% 0.33/0.49 ( ( trev @ A )
% 0.33/0.49 = ( ^ [T3: treeFI @ A] : ( tree @ A @ ( lab @ A @ T3 ) @ ( map @ ( treeFI @ A ) @ ( treeFI @ A ) @ ( trev @ A ) @ ( rev @ ( treeFI @ A ) @ ( sub @ A @ T3 ) ) ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % trev.code
% 0.33/0.49 thf(fact_218_treeFI_Opred__map,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,Q: B > $o,F2: A > B,X3: treeFI @ A] :
% 0.33/0.49 ( ( pred_treeFI @ B @ Q @ ( map_treeFI @ A @ B @ F2 @ X3 ) )
% 0.33/0.49 = ( pred_treeFI @ A @ ( comp @ B @ $o @ A @ Q @ F2 ) @ X3 ) ) ).
% 0.33/0.49
% 0.33/0.49 % treeFI.pred_map
% 0.33/0.49 thf(fact_219_map__map,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,C: $tType,F2: B > A,G: C > B,Xs: list @ C] :
% 0.33/0.49 ( ( map @ B @ A @ F2 @ ( map @ C @ B @ G @ Xs ) )
% 0.33/0.49 = ( map @ C @ A @ ( comp @ B @ A @ C @ F2 @ G ) @ Xs ) ) ).
% 0.33/0.49
% 0.33/0.49 % map_map
% 0.33/0.49 thf(fact_220_List_Omap_Ocomp,axiom,
% 0.33/0.49 ! [C: $tType,B: $tType,A: $tType,F2: B > C,G: A > B] :
% 0.33/0.49 ( ( comp @ ( list @ B ) @ ( list @ C ) @ ( list @ A ) @ ( map @ B @ C @ F2 ) @ ( map @ A @ B @ G ) )
% 0.33/0.49 = ( map @ A @ C @ ( comp @ B @ C @ A @ F2 @ G ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % List.map.comp
% 0.33/0.49 thf(fact_221_map__comp__map,axiom,
% 0.33/0.49 ! [B: $tType,C: $tType,A: $tType,F2: C > B,G: A > C] :
% 0.33/0.49 ( ( comp @ ( list @ C ) @ ( list @ B ) @ ( list @ A ) @ ( map @ C @ B @ F2 ) @ ( map @ A @ C @ G ) )
% 0.33/0.49 = ( map @ A @ B @ ( comp @ C @ B @ A @ F2 @ G ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % map_comp_map
% 0.33/0.49 thf(fact_222_list_Omap__comp,axiom,
% 0.33/0.49 ! [B: $tType,C: $tType,A: $tType,G: B > C,F2: A > B,V: list @ A] :
% 0.33/0.49 ( ( map @ B @ C @ G @ ( map @ A @ B @ F2 @ V ) )
% 0.33/0.49 = ( map @ A @ C @ ( comp @ B @ C @ A @ G @ F2 ) @ V ) ) ).
% 0.33/0.49
% 0.33/0.49 % list.map_comp
% 0.33/0.49 thf(fact_223_List_Omap_Ocompositionality,axiom,
% 0.33/0.49 ! [B: $tType,C: $tType,A: $tType,F2: B > C,G: A > B,List: list @ A] :
% 0.33/0.49 ( ( map @ B @ C @ F2 @ ( map @ A @ B @ G @ List ) )
% 0.33/0.49 = ( map @ A @ C @ ( comp @ B @ C @ A @ F2 @ G ) @ List ) ) ).
% 0.33/0.49
% 0.33/0.49 % List.map.compositionality
% 0.33/0.49 thf(fact_224_map__eq__conv,axiom,
% 0.33/0.49 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B,G: B > A] :
% 0.33/0.49 ( ( ( map @ B @ A @ F2 @ Xs )
% 0.33/0.49 = ( map @ B @ A @ G @ Xs ) )
% 0.33/0.49 = ( ! [X5: B] :
% 0.33/0.49 ( ( member2 @ B @ X5 @ ( set2 @ B @ Xs ) )
% 0.33/0.49 => ( ( F2 @ X5 )
% 0.33/0.49 = ( G @ X5 ) ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % map_eq_conv
% 0.33/0.49 thf(fact_225_smap__shift,axiom,
% 0.33/0.49 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B,S2: stream @ B] :
% 0.33/0.49 ( ( smap @ B @ A @ F2 @ ( shift @ B @ Xs @ S2 ) )
% 0.33/0.49 = ( shift @ A @ ( map @ B @ A @ F2 @ Xs ) @ ( smap @ B @ A @ F2 @ S2 ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % smap_shift
% 0.33/0.49 thf(fact_226_trev_Osimps_I2_J,axiom,
% 0.33/0.49 ! [A: $tType,T: treeFI @ A] :
% 0.33/0.49 ( ( sub @ A @ ( trev @ A @ T ) )
% 0.33/0.49 = ( map @ ( treeFI @ A ) @ ( treeFI @ A ) @ ( trev @ A ) @ ( rev @ ( treeFI @ A ) @ ( sub @ A @ T ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % trev.simps(2)
% 0.33/0.49 thf(fact_227_treeFI_Omap__sel_I1_J,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,F2: A > B,A3: treeFI @ A] :
% 0.33/0.49 ( ( lab @ B @ ( map_treeFI @ A @ B @ F2 @ A3 ) )
% 0.33/0.49 = ( F2 @ ( lab @ A @ A3 ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % treeFI.map_sel(1)
% 0.33/0.49 thf(fact_228_treeFI_Oinj__map__strong,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,X3: treeFI @ A,Xa: treeFI @ A,F2: A > B,Fa: A > B] :
% 0.33/0.49 ( ! [Z: A,Za: A] :
% 0.33/0.49 ( ( member2 @ A @ Z @ ( set_treeFI @ A @ X3 ) )
% 0.33/0.49 => ( ( member2 @ A @ Za @ ( set_treeFI @ A @ Xa ) )
% 0.33/0.49 => ( ( ( F2 @ Z )
% 0.33/0.49 = ( Fa @ Za ) )
% 0.33/0.49 => ( Z = Za ) ) ) )
% 0.33/0.49 => ( ( ( map_treeFI @ A @ B @ F2 @ X3 )
% 0.33/0.49 = ( map_treeFI @ A @ B @ Fa @ Xa ) )
% 0.33/0.49 => ( X3 = Xa ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % treeFI.inj_map_strong
% 0.33/0.49 thf(fact_229_treeFI_Omap__cong0,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,X3: treeFI @ A,F2: A > B,G: A > B] :
% 0.33/0.49 ( ! [Z: A] :
% 0.33/0.49 ( ( member2 @ A @ Z @ ( set_treeFI @ A @ X3 ) )
% 0.33/0.49 => ( ( F2 @ Z )
% 0.33/0.49 = ( G @ Z ) ) )
% 0.33/0.49 => ( ( map_treeFI @ A @ B @ F2 @ X3 )
% 0.33/0.49 = ( map_treeFI @ A @ B @ G @ X3 ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % treeFI.map_cong0
% 0.33/0.49 thf(fact_230_treeFI_Omap__cong,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,X3: treeFI @ A,Ya: treeFI @ A,F2: A > B,G: A > B] :
% 0.33/0.49 ( ( X3 = Ya )
% 0.33/0.49 => ( ! [Z: A] :
% 0.33/0.49 ( ( member2 @ A @ Z @ ( set_treeFI @ A @ Ya ) )
% 0.33/0.49 => ( ( F2 @ Z )
% 0.33/0.49 = ( G @ Z ) ) )
% 0.33/0.49 => ( ( map_treeFI @ A @ B @ F2 @ X3 )
% 0.33/0.49 = ( map_treeFI @ A @ B @ G @ Ya ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % treeFI.map_cong
% 0.33/0.49 thf(fact_231_treeFI_Omap__comp,axiom,
% 0.33/0.49 ! [B: $tType,C: $tType,A: $tType,G: B > C,F2: A > B,V: treeFI @ A] :
% 0.33/0.49 ( ( map_treeFI @ B @ C @ G @ ( map_treeFI @ A @ B @ F2 @ V ) )
% 0.33/0.49 = ( map_treeFI @ A @ C @ ( comp @ B @ C @ A @ G @ F2 ) @ V ) ) ).
% 0.33/0.49
% 0.33/0.49 % treeFI.map_comp
% 0.33/0.49 thf(fact_232_treeFI_Omap,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,F2: A > B,X1: A,X22: list @ ( treeFI @ A )] :
% 0.33/0.49 ( ( map_treeFI @ A @ B @ F2 @ ( tree @ A @ X1 @ X22 ) )
% 0.33/0.49 = ( tree @ B @ ( F2 @ X1 ) @ ( map @ ( treeFI @ A ) @ ( treeFI @ B ) @ ( map_treeFI @ A @ B @ F2 ) @ X22 ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % treeFI.map
% 0.33/0.49 thf(fact_233_treeFI_Omap__sel_I2_J,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,F2: A > B,A3: treeFI @ A] :
% 0.33/0.49 ( ( sub @ B @ ( map_treeFI @ A @ B @ F2 @ A3 ) )
% 0.33/0.49 = ( map @ ( treeFI @ A ) @ ( treeFI @ B ) @ ( map_treeFI @ A @ B @ F2 ) @ ( sub @ A @ A3 ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % treeFI.map_sel(2)
% 0.33/0.49 thf(fact_234_list_Oinj__map__strong,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,X3: list @ A,Xa: list @ A,F2: A > B,Fa: A > B] :
% 0.33/0.49 ( ! [Z: A,Za: A] :
% 0.33/0.49 ( ( member2 @ A @ Z @ ( set2 @ A @ X3 ) )
% 0.33/0.49 => ( ( member2 @ A @ Za @ ( set2 @ A @ Xa ) )
% 0.33/0.49 => ( ( ( F2 @ Z )
% 0.33/0.49 = ( Fa @ Za ) )
% 0.33/0.49 => ( Z = Za ) ) ) )
% 0.33/0.49 => ( ( ( map @ A @ B @ F2 @ X3 )
% 0.33/0.49 = ( map @ A @ B @ Fa @ Xa ) )
% 0.33/0.49 => ( X3 = Xa ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % list.inj_map_strong
% 0.33/0.49 thf(fact_235_list_Omap__cong0,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,X3: list @ A,F2: A > B,G: A > B] :
% 0.33/0.49 ( ! [Z: A] :
% 0.33/0.49 ( ( member2 @ A @ Z @ ( set2 @ A @ X3 ) )
% 0.33/0.49 => ( ( F2 @ Z )
% 0.33/0.49 = ( G @ Z ) ) )
% 0.33/0.49 => ( ( map @ A @ B @ F2 @ X3 )
% 0.33/0.49 = ( map @ A @ B @ G @ X3 ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % list.map_cong0
% 0.33/0.49 thf(fact_236_list_Omap__cong,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,X3: list @ A,Ya: list @ A,F2: A > B,G: A > B] :
% 0.33/0.49 ( ( X3 = Ya )
% 0.33/0.49 => ( ! [Z: A] :
% 0.33/0.49 ( ( member2 @ A @ Z @ ( set2 @ A @ Ya ) )
% 0.33/0.49 => ( ( F2 @ Z )
% 0.33/0.49 = ( G @ Z ) ) )
% 0.33/0.49 => ( ( map @ A @ B @ F2 @ X3 )
% 0.33/0.49 = ( map @ A @ B @ G @ Ya ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % list.map_cong
% 0.33/0.49 thf(fact_237_ex__map__conv,axiom,
% 0.33/0.49 ! [A: $tType,B: $tType,Ys: list @ B,F2: A > B] :
% 0.33/0.49 ( ( ? [Xs2: list @ A] :
% 0.33/0.49 ( Ys
% 0.33/0.49 = ( map @ A @ B @ F2 @ Xs2 ) ) )
% 0.33/0.49 = ( ! [X5: B] :
% 0.33/0.49 ( ( member2 @ B @ X5 @ ( set2 @ B @ Ys ) )
% 0.33/0.49 => ? [Y4: A] :
% 0.33/0.49 ( X5
% 0.33/0.49 = ( F2 @ Y4 ) ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % ex_map_conv
% 0.33/0.49 thf(fact_238_map__cong,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,Xs: list @ A,Ys: list @ A,F2: A > B,G: A > B] :
% 0.33/0.49 ( ( Xs = Ys )
% 0.33/0.49 => ( ! [X: A] :
% 0.33/0.49 ( ( member2 @ A @ X @ ( set2 @ A @ Ys ) )
% 0.33/0.49 => ( ( F2 @ X )
% 0.33/0.49 = ( G @ X ) ) )
% 0.33/0.49 => ( ( map @ A @ B @ F2 @ Xs )
% 0.33/0.49 = ( map @ A @ B @ G @ Ys ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % map_cong
% 0.33/0.49 thf(fact_239_map__idI,axiom,
% 0.33/0.49 ! [A: $tType,Xs: list @ A,F2: A > A] :
% 0.33/0.49 ( ! [X: A] :
% 0.33/0.49 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 0.33/0.49 => ( ( F2 @ X )
% 0.33/0.49 = X ) )
% 0.33/0.49 => ( ( map @ A @ A @ F2 @ Xs )
% 0.33/0.49 = Xs ) ) ).
% 0.33/0.49
% 0.33/0.49 % map_idI
% 0.33/0.49 thf(fact_240_map__ext,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,Xs: list @ A,F2: A > B,G: A > B] :
% 0.33/0.49 ( ! [X: A] :
% 0.33/0.49 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 0.33/0.49 => ( ( F2 @ X )
% 0.33/0.49 = ( G @ X ) ) )
% 0.33/0.49 => ( ( map @ A @ B @ F2 @ Xs )
% 0.33/0.49 = ( map @ A @ B @ G @ Xs ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % map_ext
% 0.33/0.49 thf(fact_241_foldr__map,axiom,
% 0.33/0.49 ! [C: $tType,B: $tType,A: $tType,G: B > A > A,F2: C > B,Xs: list @ C,A3: A] :
% 0.33/0.49 ( ( foldr @ B @ A @ G @ ( map @ C @ B @ F2 @ Xs ) @ A3 )
% 0.33/0.49 = ( foldr @ C @ A @ ( comp @ B @ ( A > A ) @ C @ G @ F2 ) @ Xs @ A3 ) ) ).
% 0.33/0.49
% 0.33/0.49 % foldr_map
% 0.33/0.49 thf(fact_242_fold__map,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,C: $tType,G: B > A > A,F2: C > B,Xs: list @ C] :
% 0.33/0.49 ( ( fold @ B @ A @ G @ ( map @ C @ B @ F2 @ Xs ) )
% 0.33/0.49 = ( fold @ C @ A @ ( comp @ B @ ( A > A ) @ C @ G @ F2 ) @ Xs ) ) ).
% 0.33/0.49
% 0.33/0.49 % fold_map
% 0.33/0.49 thf(fact_243_list_Opred__map,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,Q: B > $o,F2: A > B,X3: list @ A] :
% 0.33/0.49 ( ( list_all @ B @ Q @ ( map @ A @ B @ F2 @ X3 ) )
% 0.33/0.49 = ( list_all @ A @ ( comp @ B @ $o @ A @ Q @ F2 ) @ X3 ) ) ).
% 0.33/0.49
% 0.33/0.49 % list.pred_map
% 0.33/0.49 thf(fact_244_stake__smap,axiom,
% 0.33/0.49 ! [A: $tType,B: $tType,N2: nat,F2: B > A,S2: stream @ B] :
% 0.33/0.49 ( ( stake @ A @ N2 @ ( smap @ B @ A @ F2 @ S2 ) )
% 0.33/0.49 = ( map @ B @ A @ F2 @ ( stake @ B @ N2 @ S2 ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % stake_smap
% 0.33/0.49 thf(fact_245_map__fun__upd,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,Y: A,Xs: list @ A,F2: A > B,V: B] :
% 0.33/0.49 ( ~ ( member2 @ A @ Y @ ( set2 @ A @ Xs ) )
% 0.33/0.49 => ( ( map @ A @ B @ ( fun_upd @ A @ B @ F2 @ Y @ V ) @ Xs )
% 0.33/0.49 = ( map @ A @ B @ F2 @ Xs ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % map_fun_upd
% 0.33/0.49 thf(fact_246_fun__upd__apply,axiom,
% 0.33/0.49 ! [A: $tType,B: $tType] :
% 0.33/0.49 ( ( fun_upd @ B @ A )
% 0.33/0.49 = ( ^ [F: B > A,X5: B,Y4: A,Z3: B] : ( if @ A @ ( Z3 = X5 ) @ Y4 @ ( F @ Z3 ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % fun_upd_apply
% 0.33/0.49 thf(fact_247_fun__upd__triv,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,F2: A > B,X3: A] :
% 0.33/0.49 ( ( fun_upd @ A @ B @ F2 @ X3 @ ( F2 @ X3 ) )
% 0.33/0.49 = F2 ) ).
% 0.33/0.49
% 0.33/0.49 % fun_upd_triv
% 0.33/0.49 thf(fact_248_fun__upd__upd,axiom,
% 0.33/0.49 ! [A: $tType,B: $tType,F2: A > B,X3: A,Y: B,Z4: B] :
% 0.33/0.49 ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ F2 @ X3 @ Y ) @ X3 @ Z4 )
% 0.33/0.49 = ( fun_upd @ A @ B @ F2 @ X3 @ Z4 ) ) ).
% 0.33/0.49
% 0.33/0.49 % fun_upd_upd
% 0.33/0.49 thf(fact_249_fun__upd__comp,axiom,
% 0.33/0.49 ! [A: $tType,B: $tType,C: $tType,F2: C > B,G: A > C,X3: A,Y: C] :
% 0.33/0.49 ( ( comp @ C @ B @ A @ F2 @ ( fun_upd @ A @ C @ G @ X3 @ Y ) )
% 0.33/0.49 = ( fun_upd @ A @ B @ ( comp @ C @ B @ A @ F2 @ G ) @ X3 @ ( F2 @ Y ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % fun_upd_comp
% 0.33/0.49 thf(fact_250_fun__upd__idem__iff,axiom,
% 0.33/0.49 ! [A: $tType,B: $tType,F2: A > B,X3: A,Y: B] :
% 0.33/0.49 ( ( ( fun_upd @ A @ B @ F2 @ X3 @ Y )
% 0.33/0.49 = F2 )
% 0.33/0.49 = ( ( F2 @ X3 )
% 0.33/0.49 = Y ) ) ).
% 0.33/0.49
% 0.33/0.49 % fun_upd_idem_iff
% 0.33/0.49 thf(fact_251_fun__upd__twist,axiom,
% 0.33/0.49 ! [A: $tType,B: $tType,A3: A,C2: A,M2: A > B,B3: B,D2: B] :
% 0.33/0.49 ( ( A3 != C2 )
% 0.33/0.49 => ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M2 @ A3 @ B3 ) @ C2 @ D2 )
% 0.33/0.49 = ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M2 @ C2 @ D2 ) @ A3 @ B3 ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % fun_upd_twist
% 0.33/0.49 thf(fact_252_fun__upd__other,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,Z4: A,X3: A,F2: A > B,Y: B] :
% 0.33/0.49 ( ( Z4 != X3 )
% 0.33/0.49 => ( ( fun_upd @ A @ B @ F2 @ X3 @ Y @ Z4 )
% 0.33/0.49 = ( F2 @ Z4 ) ) ) ).
% 0.33/0.49
% 0.33/0.49 % fun_upd_other
% 0.33/0.49 thf(fact_253_fun__upd__same,axiom,
% 0.33/0.49 ! [B: $tType,A: $tType,F2: B > A,X3: B,Y: A] :
% 0.33/0.49 ( ( fun_upd @ B @ A @ F2 @ X3 @ Y @ X3 )
% 0.33/0.49 = Y ) ).
% 0.33/0.49
% 0.33/0.49 % fun_upd_same
% 0.33/0.49 thf(fact_254_fun__upd__idem,axiom,
% 0.33/0.49 ! [A: $tType,B: $tType,F2: B > A,X3: B,Y: A] :
% 0.33/0.49 ( ( ( F2 @ X3 )
% 0.33/0.49 = Y )
% 0.33/0.49 => ( ( fun_upd @ B @ A @ F2 @ X3 @ Y )
% 0.33/0.49 = F2 ) ) ).
% 0.33/0.49
% 0.33/0.49 % fun_upd_idem
% 0.33/0.49 thf(fact_255_fun__upd__eqD,axiom,
% 0.33/0.49 ! [A: $tType,B: $tType,F2: A > B,X3: A,Y: B,G: A > B,Z4: B] :
% 0.33/0.49 ( ( ( fun_upd @ A @ B @ F2 @ X3 @ Y )
% 0.33/0.49 = ( fun_upd @ A @ B @ G @ X3 @ Z4 ) )
% 0.33/0.49 => ( Y = Z4 ) ) ).
% 0.33/0.49
% 0.33/0.49 % fun_upd_eqD
% 0.33/0.49
% 0.33/0.49 %----Type constructors (4)
% 0.33/0.49 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.33/0.49 ! [A8: $tType,A9: $tType] :
% 0.33/0.49 ( ( semilattice_sup @ A9 @ ( type2 @ A9 ) )
% 0.33/0.49 => ( semilattice_sup @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_1,axiom,
% 0.33/0.49 ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_2,axiom,
% 0.33/0.49 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 0.33/0.49
% 0.33/0.49 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.33/0.49 linorder @ $o @ ( type2 @ $o ) ).
% 0.33/0.49
% 0.33/0.49 %----Helper facts (3)
% 0.33/0.49 thf(help_If_3_1_T,axiom,
% 0.33/0.49 ! [P2: $o] :
% 0.33/0.49 ( ( P2 = $true )
% 0.33/0.49 | ( P2 = $false ) ) ).
% 0.33/0.49
% 0.33/0.49 thf(help_If_2_1_T,axiom,
% 0.33/0.49 ! [A: $tType,X3: A,Y: A] :
% 0.33/0.49 ( ( if @ A @ $false @ X3 @ Y )
% 0.33/0.49 = Y ) ).
% 0.33/0.49
% 0.33/0.49 thf(help_If_1_1_T,axiom,
% 0.33/0.49 ! [A: $tType,X3: A,Y: A] :
% 0.33/0.49 ( ( if @ A @ $true @ X3 @ Y )
% 0.33/0.49 = X3 ) ).
% 0.33/0.49
% 0.33/0.49 %----Conjectures (1)
% 0.33/0.49 thf(conj_0,conjecture,
% 0.33/0.49 koenig1755522246erPath @ a @ as @ tr ).
% 0.33/0.49
% 0.33/0.49 %------------------------------------------------------------------------------
% 0.33/0.49 ------------------------
% 3.20/1.77 ---- Embedded in THF ---
% 3.20/1.77 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.20/1.77 %%% Generated on Tue Feb 24 04:17:28 EST 2026
% 3.20/1.77 %%% using '$$dhol' embedding, version 1.3.0.
% 3.20/1.77 %%% Logic specification used:
% 3.20/1.77 %%% thf(spec, logic, $$dhol).
% 3.20/1.77
% 3.20/1.77 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.BDekGnPrVg/DTF2DTF27722.p
% 3.20/1.77 thf(ty_t_TreeFI_OtreeFI, type, treeFI: ($tType > $tType)).
% 3.20/1.77 thf(ty_t_Stream_Ostream, type, stream: ($tType > $tType)).
% 3.20/1.77 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 3.20/1.77 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.20/1.77 thf(ty_t_Nat_Onat, type, nat: $tType).
% 3.20/1.77 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 3.20/1.77 thf(ty_tf_a, type, a: $tType).
% 3.20/1.77 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.77 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.77 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: (((itself @ A) > $o)))).
% 3.20/1.77 thf(sy_c_Fun_Ocomp, type, comp: (!> [B:$tType,C:$tType,A:$tType]: (((B > C) > ((A > B) > (A > C)))))).
% 3.20/1.77 thf(sy_c_Fun_Ofun__upd, type, fun_upd: (!> [A:$tType,B:$tType]: (((A > B) > (A > (B > (A > B))))))).
% 3.20/1.77 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 3.20/1.77 thf(sy_c_Koenig__Mirabelle__gyfieiccqy_OinfiniteTr, type, koenig488553731niteTr: (!> [A:$tType]: (((treeFI @ A) > $o)))).
% 3.20/1.77 thf(sy_c_Koenig__Mirabelle__gyfieiccqy_OkonigPath, type, koenig1103336060igPath: (!> [A:$tType]: (((treeFI @ A) > (stream @ A))))).
% 3.20/1.77 thf(sy_c_Koenig__Mirabelle__gyfieiccqy_OproperPath, type, koenig1755522246erPath: (!> [A:$tType]: (((stream @ A) > ((treeFI @ A) > $o))))).
% 3.20/1.77 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 3.20/1.77 thf(sy_c_Lattices__Big_Osemilattice__sup__class_OSup__fin, type, lattic477160up_fin: (!> [A:$tType]: (((set @ A) > A)))).
% 3.20/1.77 thf(sy_c_List_Oappend, type, append: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 3.20/1.77 thf(sy_c_List_Ocoset, type, coset: (!> [A:$tType]: (((list @ A) > (set @ A))))).
% 3.20/1.77 thf(sy_c_List_Ofold, type, fold: (!> [A:$tType,B:$tType]: (((A > (B > B)) > ((list @ A) > (B > B)))))).
% 3.20/1.77 thf(sy_c_List_Ofoldr, type, foldr: (!> [A:$tType,B:$tType]: (((A > (B > B)) > ((list @ A) > (B > B)))))).
% 3.20/1.77 thf(sy_c_List_Oinsert, type, insert: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 3.20/1.77 thf(sy_c_List_Olinorder__class_Oinsort__key, type, linorder_insort_key: (!> [B:$tType,A:$tType]: (((B > A) > (B > ((list @ B) > (list @ B))))))).
% 3.20/1.77 thf(sy_c_List_Olinorder__class_Osorted, type, linorder_sorted: (!> [A:$tType]: (((list @ A) > $o)))).
% 3.20/1.77 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 3.20/1.77 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 3.20/1.77 thf(sy_c_List_Olist_Ohd, type, hd: (!> [A:$tType]: (((list @ A) > A)))).
% 3.20/1.77 thf(sy_c_List_Olist_Olist__all, type, list_all: (!> [A:$tType]: (((A > $o) > ((list @ A) > $o))))).
% 3.20/1.77 thf(sy_c_List_Olist_Omap, type, map: (!> [A:$tType,Aa:$tType]: (((A > Aa) > ((list @ A) > (list @ Aa)))))).
% 3.20/1.77 thf(sy_c_List_Olist_Oset, type, set2: (!> [A:$tType]: (((list @ A) > (set @ A))))).
% 3.20/1.77 thf(sy_c_List_Olist_Otl, type, tl: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 3.20/1.77 thf(sy_c_List_Olist__update, type, list_update: (!> [A:$tType]: (((list @ A) > (nat > (A > (list @ A))))))).
% 3.20/1.77 thf(sy_c_List_Omember, type, member: (!> [A:$tType]: (((list @ A) > (A > $o))))).
% 3.20/1.77 thf(sy_c_List_Oremove1, type, remove1: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 3.20/1.77 thf(sy_c_List_Orev, type, rev: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 3.20/1.77 thf(sy_c_List_Ounion, type, union: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 3.20/1.77 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 3.20/1.77 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 3.20/1.77 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.20/1.77 thf(sy_c_Set_Oinsert, type, insert2: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 3.20/1.77 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 3.20/1.77 thf(sy_c_Stream_Ocycle, type, cycle: (!> [A:$tType]: (((list @ A) > (stream @ A))))).
% 3.20/1.77 thf(sy_c_Stream_Oflat, type, flat: (!> [A:$tType]: (((stream @ (list @ A)) > (stream @ A))))).
% 3.20/1.77 thf(sy_c_Stream_Osdrop__while, type, sdrop_while: (!> [A:$tType]: (((A > $o) > ((stream @ A) > (stream @ A)))))).
% 3.20/1.77 thf(sy_c_Stream_Osfilter, type, sfilter: (!> [A:$tType]: (((A > $o) > ((stream @ A) > (stream @ A)))))).
% 3.20/1.77 thf(sy_c_Stream_Oshift, type, shift: (!> [A:$tType]: (((list @ A) > ((stream @ A) > (stream @ A)))))).
% 3.20/1.77 thf(sy_c_Stream_Osinterleave, type, sinterleave: (!> [A:$tType]: (((stream @ A) > ((stream @ A) > (stream @ A)))))).
% 3.20/1.77 thf(sy_c_Stream_Osmap2, type, smap2: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > ((stream @ A) > ((stream @ B) > (stream @ C))))))).
% 3.20/1.77 thf(sy_c_Stream_Osmember, type, smember: (!> [A:$tType]: ((A > ((stream @ A) > $o))))).
% 3.20/1.77 thf(sy_c_Stream_Ostake, type, stake: (!> [A:$tType]: ((nat > ((stream @ A) > (list @ A)))))).
% 3.20/1.77 thf(sy_c_Stream_Ostream_OSCons, type, sCons: (!> [A:$tType]: ((A > ((stream @ A) > (stream @ A)))))).
% 3.20/1.77 thf(sy_c_Stream_Ostream_Ocase__stream, type, case_stream: (!> [A:$tType,B:$tType]: (((A > ((stream @ A) > B)) > ((stream @ A) > B))))).
% 3.20/1.77 thf(sy_c_Stream_Ostream_Ocorec__stream, type, corec_stream: (!> [C:$tType,A:$tType]: (((C > A) > ((C > $o) > ((C > (stream @ A)) > ((C > C) > (C > (stream @ A))))))))).
% 3.20/1.77 thf(sy_c_Stream_Ostream_Opred__stream, type, pred_stream: (!> [A:$tType]: (((A > $o) > ((stream @ A) > $o))))).
% 3.20/1.77 thf(sy_c_Stream_Ostream_Oshd, type, shd: (!> [A:$tType]: (((stream @ A) > A)))).
% 3.20/1.77 thf(sy_c_Stream_Ostream_Osmap, type, smap: (!> [A:$tType,Aa:$tType]: (((A > Aa) > ((stream @ A) > (stream @ Aa)))))).
% 3.20/1.77 thf(sy_c_Stream_Ostream_Osset, type, sset: (!> [A:$tType]: (((stream @ A) > (set @ A))))).
% 3.20/1.77 thf(sy_c_Stream_Ostream_Ostl, type, stl: (!> [A:$tType]: (((stream @ A) > (stream @ A))))).
% 3.20/1.77 thf(sy_c_Stream_Ostream__all, type, stream_all: (!> [A:$tType]: (((A > $o) > ((stream @ A) > $o))))).
% 3.20/1.77 thf(sy_c_Stream_Ostreams, type, streams: (!> [A:$tType]: (((set @ A) > (set @ (stream @ A)))))).
% 3.20/1.77 thf(sy_c_TreeFI_OtreeFI_OTree, type, tree: (!> [A:$tType]: ((A > ((list @ (treeFI @ A)) > (treeFI @ A)))))).
% 3.20/1.77 thf(sy_c_TreeFI_OtreeFI_Ocase__treeFI, type, case_treeFI: (!> [A:$tType,B:$tType]: (((A > ((list @ (treeFI @ A)) > B)) > ((treeFI @ A) > B))))).
% 3.20/1.77 thf(sy_c_TreeFI_OtreeFI_Olab, type, lab: (!> [A:$tType]: (((treeFI @ A) > A)))).
% 3.20/1.77 thf(sy_c_TreeFI_OtreeFI_Omap__treeFI, type, map_treeFI: (!> [A:$tType,Aa:$tType]: (((A > Aa) > ((treeFI @ A) > (treeFI @ Aa)))))).
% 3.20/1.77 thf(sy_c_TreeFI_OtreeFI_Opred__treeFI, type, pred_treeFI: (!> [A:$tType]: (((A > $o) > ((treeFI @ A) > $o))))).
% 3.20/1.77 thf(sy_c_TreeFI_OtreeFI_Oset__treeFI, type, set_treeFI: (!> [A:$tType]: (((treeFI @ A) > (set @ A))))).
% 3.20/1.77 thf(sy_c_TreeFI_OtreeFI_Osub, type, sub: (!> [A:$tType]: (((treeFI @ A) > (list @ (treeFI @ A)))))).
% 3.20/1.77 thf(sy_c_TreeFI_Otrev, type, trev: (!> [A:$tType]: (((treeFI @ A) > (treeFI @ A))))).
% 3.20/1.77 thf(sy_c_member, type, member2: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.20/1.77 thf(sy_v_as, type, as: (stream @ a)).
% 3.20/1.77 thf(sy_v_phi, type, phi: ((stream @ a) > ((treeFI @ a) > $o))).
% 3.20/1.77 thf(sy_v_tr, type, tr: (treeFI @ a)).
% 3.20/1.77 thf(fact_0__C_K_K_K_C, axiom, (! [As:(stream @ a),Tr:(treeFI @ a)]: ((((phi @ As) @ Tr) => (? [X:(treeFI @ a)]: (((((member2 @ (treeFI @ a)) @ X) @ ((set2 @ (treeFI @ a)) @ ((sub @ a) @ Tr))) & (((phi @ ((stl @ a) @ As)) @ X) | (((koenig1755522246erPath @ a) @ ((stl @ a) @ As)) @ X))))))))).
% 3.20/1.77 thf(fact_1__C_K_C, axiom, ((phi @ as) @ tr)).
% 3.20/1.77 thf(fact_2_properPath_Ocases, axiom, (! [A:$tType,A1:(stream @ A),A2:(treeFI @ A)]: (((((koenig1755522246erPath @ A) @ A1) @ A2) => (~ (((((shd @ A) @ A1) = ((lab @ A) @ A2)) => (! [Tr2:(treeFI @ A)]: (((((member2 @ (treeFI @ A)) @ Tr2) @ ((set2 @ (treeFI @ A)) @ ((sub @ A) @ A2))) => (~ ((((koenig1755522246erPath @ A) @ ((stl @ A) @ A1)) @ Tr2))))))))))))).
% 3.20/1.77 thf(fact_3_properPath_Osimps, axiom, (! [A:$tType]: (((koenig1755522246erPath @ A) = (^ [A12:(stream @ A),A22:(treeFI @ A)]: ((? [As2:(stream @ A),Tr3:(treeFI @ A),Tr4:(treeFI @ A)]: (((A12 = As2) & ((A22 = Tr3) & ((((shd @ A) @ As2) = ((lab @ A) @ Tr3)) & ((((member2 @ (treeFI @ A)) @ Tr4) @ ((set2 @ (treeFI @ A)) @ ((sub @ A) @ Tr3))) & (((koenig1755522246erPath @ A) @ ((stl @ A) @ As2)) @ Tr4))))))))))))).
% 3.20/1.77 thf(fact_4_properPath_Ointros, axiom, (! [A:$tType,As:(stream @ A),Tr:(treeFI @ A),Tr5:(treeFI @ A)]: (((((shd @ A) @ As) = ((lab @ A) @ Tr)) => ((((member2 @ (treeFI @ A)) @ Tr5) @ ((set2 @ (treeFI @ A)) @ ((sub @ A) @ Tr))) => ((((koenig1755522246erPath @ A) @ ((stl @ A) @ As)) @ Tr5) => (((koenig1755522246erPath @ A) @ As) @ Tr))))))).
% 3.20/1.77 thf(fact_5_properPath_Ocoinduct, axiom, (! [A:$tType,X2:((stream @ A) > ((treeFI @ A) > $o)),X3:(stream @ A),Xa:(treeFI @ A)]: ((((X2 @ X3) @ Xa) => ((! [X:(stream @ A),Xa2:(treeFI @ A)]: ((((X2 @ X) @ Xa2) => (? [As3:(stream @ A),Tr6:(treeFI @ A),Tr7:(treeFI @ A)]: (((X = As3) & ((Xa2 = Tr6) & ((((shd @ A) @ As3) = ((lab @ A) @ Tr6)) & ((((member2 @ (treeFI @ A)) @ Tr7) @ ((set2 @ (treeFI @ A)) @ ((sub @ A) @ Tr6))) & (((X2 @ ((stl @ A) @ As3)) @ Tr7) | (((koenig1755522246erPath @ A) @ ((stl @ A) @ As3)) @ Tr7))))))))))) => (((koenig1755522246erPath @ A) @ X3) @ Xa)))))).
% 3.20/1.77 thf(fact_6__C_K_K_C, axiom, (! [As:(stream @ a),Tr:(treeFI @ a)]: ((((phi @ As) @ Tr) => (((shd @ a) @ As) = ((lab @ a) @ Tr)))))).
% 3.20/1.77 thf(fact_7_treeFI_Oexpand, axiom, (! [A:$tType,TreeFI:(treeFI @ A),TreeFI2:(treeFI @ A)]: ((((((lab @ A) @ TreeFI) = ((lab @ A) @ TreeFI2)) & (((sub @ A) @ TreeFI) = ((sub @ A) @ TreeFI2))) => (TreeFI = TreeFI2))))).
% 3.20/1.77 thf(fact_8_stream_Oexpand, axiom, (! [A:$tType,Stream:(stream @ A),Stream2:(stream @ A)]: ((((((shd @ A) @ Stream) = ((shd @ A) @ Stream2)) & (((stl @ A) @ Stream) = ((stl @ A) @ Stream2))) => (Stream = Stream2))))).
% 3.20/1.77 thf(fact_9_stream_Ocoinduct, axiom, (! [A:$tType,R:((stream @ A) > ((stream @ A) > $o)),Stream:(stream @ A),Stream2:(stream @ A)]: ((((R @ Stream) @ Stream2) => ((! [Stream3:(stream @ A),Stream4:(stream @ A)]: ((((R @ Stream3) @ Stream4) => ((((shd @ A) @ Stream3) = ((shd @ A) @ Stream4)) & ((R @ ((stl @ A) @ Stream3)) @ ((stl @ A) @ Stream4)))))) => (Stream = Stream2)))))).
% 3.20/1.77 thf(fact_10_stream_Ocoinduct__strong, axiom, (! [A:$tType,R:((stream @ A) > ((stream @ A) > $o)),Stream:(stream @ A),Stream2:(stream @ A)]: ((((R @ Stream) @ Stream2) => ((! [Stream3:(stream @ A),Stream4:(stream @ A)]: ((((R @ Stream3) @ Stream4) => ((((shd @ A) @ Stream3) = ((shd @ A) @ Stream4)) & (((R @ ((stl @ A) @ Stream3)) @ ((stl @ A) @ Stream4)) | (((stl @ A) @ Stream3) = ((stl @ A) @ Stream4))))))) => (Stream = Stream2)))))).
% 3.20/1.77 thf(fact_11_konigPath_Osimps_I1_J, axiom, (! [A:$tType,T:(treeFI @ A)]: ((((shd @ A) @ ((koenig1103336060igPath @ A) @ T)) = ((lab @ A) @ T))))).
% 3.20/1.77 thf(fact_12_infiniteTr__sub, axiom, (! [A:$tType,Tr:(treeFI @ A)]: ((((koenig488553731niteTr @ A) @ Tr) => (? [X:(treeFI @ A)]: (((((member2 @ (treeFI @ A)) @ X) @ ((set2 @ (treeFI @ A)) @ ((sub @ A) @ Tr))) & ((koenig488553731niteTr @ A) @ X)))))))).
% 3.20/1.77 thf(fact_13_infiniteTr_Ocases, axiom, (! [A:$tType,A3:(treeFI @ A)]: ((((koenig488553731niteTr @ A) @ A3) => (~ ((! [Tr2:(treeFI @ A)]: (((((member2 @ (treeFI @ A)) @ Tr2) @ ((set2 @ (treeFI @ A)) @ ((sub @ A) @ A3))) => (~ (((koenig488553731niteTr @ A) @ Tr2)))))))))))).
% 3.20/1.77 thf(fact_14_infiniteTr_Osimps, axiom, (! [A:$tType]: (((koenig488553731niteTr @ A) = (^ [A4:(treeFI @ A)]: ((? [Tr4:(treeFI @ A),Tr3:(treeFI @ A)]: (((A4 = Tr3) & ((((member2 @ (treeFI @ A)) @ Tr4) @ ((set2 @ (treeFI @ A)) @ ((sub @ A) @ Tr3))) & ((koenig488553731niteTr @ A) @ Tr4))))))))))).
% 3.20/1.77 thf(fact_15_infiniteTr__coind, axiom, (! [A:$tType,Phi:((treeFI @ A) > $o),Tr:(treeFI @ A)]: (((Phi @ Tr) => ((! [Tr8:(treeFI @ A)]: (((Phi @ Tr8) => (? [X4:(treeFI @ A)]: (((((member2 @ (treeFI @ A)) @ X4) @ ((set2 @ (treeFI @ A)) @ ((sub @ A) @ Tr8))) & (Phi @ X4))))))) => ((koenig488553731niteTr @ A) @ Tr)))))).
% 3.20/1.77 thf(fact_16_infiniteTr_Ointros, axiom, (! [A:$tType,Tr5:(treeFI @ A),Tr:(treeFI @ A)]: (((((member2 @ (treeFI @ A)) @ Tr5) @ ((set2 @ (treeFI @ A)) @ ((sub @ A) @ Tr))) => (((koenig488553731niteTr @ A) @ Tr5) => ((koenig488553731niteTr @ A) @ Tr)))))).
% 3.20/1.77 thf(fact_17_infiniteTr_Ocoinduct, axiom, (! [A:$tType,X2:((treeFI @ A) > $o),X3:(treeFI @ A)]: (((X2 @ X3) => ((! [X:(treeFI @ A)]: (((X2 @ X) => (? [Tr7:(treeFI @ A),Tr6:(treeFI @ A)]: (((X = Tr6) & ((((member2 @ (treeFI @ A)) @ Tr7) @ ((set2 @ (treeFI @ A)) @ ((sub @ A) @ Tr6))) & ((X2 @ Tr7) | ((koenig488553731niteTr @ A) @ Tr7))))))))) => ((koenig488553731niteTr @ A) @ X3)))))).
% 3.20/1.77 thf(fact_18_infiniteTr__strong__coind, axiom, (! [A:$tType,Phi:((treeFI @ A) > $o),Tr:(treeFI @ A)]: (((Phi @ Tr) => ((! [Tr8:(treeFI @ A)]: (((Phi @ Tr8) => (? [X4:(treeFI @ A)]: (((((member2 @ (treeFI @ A)) @ X4) @ ((set2 @ (treeFI @ A)) @ ((sub @ A) @ Tr8))) & ((Phi @ X4) | ((koenig488553731niteTr @ A) @ X4)))))))) => ((koenig488553731niteTr @ A) @ Tr)))))).
% 3.20/1.77 thf(fact_19_treeFI_Ocase__eq__if, axiom, (! [B:$tType,A:$tType]: ((((case_treeFI @ A) @ B) = (^ [F:(A > ((list @ (treeFI @ A)) > B)),TreeFI3:(treeFI @ A)]: (((F @ ((lab @ A) @ TreeFI3)) @ ((sub @ A) @ TreeFI3)))))))).
% 3.20/1.77 thf(fact_20_stream_Ocase__eq__if, axiom, (! [B:$tType,A:$tType]: ((((case_stream @ A) @ B) = (^ [F:(A > ((stream @ A) > B)),Stream5:(stream @ A)]: (((F @ ((shd @ A) @ Stream5)) @ ((stl @ A) @ Stream5)))))))).
% 3.20/1.77 thf(fact_21_sdrop__while_Osimps, axiom, (! [A:$tType]: (((sdrop_while @ A) = (^ [P:(A > $o),S:(stream @ A)]: (((((if @ (stream @ A)) @ (P @ ((shd @ A) @ S))) @ (((sdrop_while @ A) @ P) @ ((stl @ A) @ S))) @ S))))))).
% 3.20/1.77 thf(fact_22_treeFI_Ocollapse, axiom, (! [A:$tType,TreeFI:(treeFI @ A)]: (((((tree @ A) @ ((lab @ A) @ TreeFI)) @ ((sub @ A) @ TreeFI)) = TreeFI)))).
% 3.20/1.77 thf(fact_23_treeFI_Oset__sel_I2_J, axiom, (! [A:$tType,X3:(treeFI @ A),A3:(treeFI @ A),Xa:A]: (((((member2 @ (treeFI @ A)) @ X3) @ ((set2 @ (treeFI @ A)) @ ((sub @ A) @ A3))) => ((((member2 @ A) @ Xa) @ ((set_treeFI @ A) @ X3)) => (((member2 @ A) @ Xa) @ ((set_treeFI @ A) @ A3))))))).
% 3.20/1.77 thf(fact_24_treeFI_Oexhaust__sel, axiom, (! [A:$tType,TreeFI:(treeFI @ A)]: ((TreeFI = (((tree @ A) @ ((lab @ A) @ TreeFI)) @ ((sub @ A) @ TreeFI)))))).
% 3.20/1.77 thf(fact_25_trev_Osimps_I1_J, axiom, (! [A:$tType,T:(treeFI @ A)]: ((((lab @ A) @ ((trev @ A) @ T)) = ((lab @ A) @ T))))).
% 3.20/1.77 thf(fact_26_stream_Ocollapse, axiom, (! [A:$tType,Stream:(stream @ A)]: (((((sCons @ A) @ ((shd @ A) @ Stream)) @ ((stl @ A) @ Stream)) = Stream)))).
% 3.20/1.77 thf(fact_27_in__streams, axiom, (! [A:$tType,S2:(stream @ A),S3:(set @ A)]: (((((member2 @ (stream @ A)) @ ((stl @ A) @ S2)) @ ((streams @ A) @ S3)) => ((((member2 @ A) @ ((shd @ A) @ S2)) @ S3) => (((member2 @ (stream @ A)) @ S2) @ ((streams @ A) @ S3))))))).
% 3.20/1.77 thf(fact_28_streamsE, axiom, (! [A:$tType,S2:(stream @ A),A5:(set @ A)]: (((((member2 @ (stream @ A)) @ S2) @ ((streams @ A) @ A5)) => (~ (((((member2 @ A) @ ((shd @ A) @ S2)) @ A5) => (~ ((((member2 @ (stream @ A)) @ ((stl @ A) @ S2)) @ ((streams @ A) @ A5))))))))))).
% 3.20/1.77 thf(fact_29_stream_Oinject, axiom, (! [A:$tType,X1:A,X22:(stream @ A),Y1:A,Y2:(stream @ A)]: ((((((sCons @ A) @ X1) @ X22) = (((sCons @ A) @ Y1) @ Y2)) = ((X1 = Y1) & (X22 = Y2)))))).
% 3.20/1.77 thf(fact_30_treeFI_Oinject, axiom, (! [A:$tType,X1:A,X22:(list @ (treeFI @ A)),Y1:A,Y2:(list @ (treeFI @ A))]: ((((((tree @ A) @ X1) @ X22) = (((tree @ A) @ Y1) @ Y2)) = ((X1 = Y1) & (X22 = Y2)))))).
% 3.20/1.77 thf(fact_31_sdrop__while__SCons, axiom, (! [A:$tType,P2:(A > $o),A3:A,S2:(stream @ A)]: ((((P2 @ A3) => ((((sdrop_while @ A) @ P2) @ (((sCons @ A) @ A3) @ S2)) = (((sdrop_while @ A) @ P2) @ S2))) & ((~ ((P2 @ A3))) => ((((sdrop_while @ A) @ P2) @ (((sCons @ A) @ A3) @ S2)) = (((sCons @ A) @ A3) @ S2))))))).
% 3.20/1.77 thf(fact_32_streams_Ocoinduct, axiom, (! [A:$tType,X2:((stream @ A) > $o),X3:(stream @ A),A5:(set @ A)]: (((X2 @ X3) => ((! [X:(stream @ A)]: (((X2 @ X) => (? [A6:A,S4:(stream @ A)]: (((X = (((sCons @ A) @ A6) @ S4)) & ((((member2 @ A) @ A6) @ A5) & ((X2 @ S4) | (((member2 @ (stream @ A)) @ S4) @ ((streams @ A) @ A5)))))))))) => (((member2 @ (stream @ A)) @ X3) @ ((streams @ A) @ A5))))))).
% 3.20/1.77 thf(fact_33_treeFI_Oexhaust, axiom, (! [A:$tType,Y:(treeFI @ A)]: ((~ ((! [X12:A,X23:(list @ (treeFI @ A))]: ((Y != (((tree @ A) @ X12) @ X23))))))))).
% 3.20/1.77 thf(fact_34_streams__Stream, axiom, (! [A:$tType,X3:A,S2:(stream @ A),A5:(set @ A)]: (((((member2 @ (stream @ A)) @ (((sCons @ A) @ X3) @ S2)) @ ((streams @ A) @ A5)) = ((((member2 @ A) @ X3) @ A5) & (((member2 @ (stream @ A)) @ S2) @ ((streams @ A) @ A5))))))).
% 3.20/1.77 thf(fact_35_stream_Oexhaust, axiom, (! [A:$tType,Y:(stream @ A)]: ((~ ((! [X12:A,X23:(stream @ A)]: ((Y != (((sCons @ A) @ X12) @ X23))))))))).
% 3.20/1.77 thf(fact_36_streams_Osimps, axiom, (! [A:$tType,A3:(stream @ A),A5:(set @ A)]: (((((member2 @ (stream @ A)) @ A3) @ ((streams @ A) @ A5)) = (? [A4:A,S:(stream @ A)]: (((A3 = (((sCons @ A) @ A4) @ S)) & ((((member2 @ A) @ A4) @ A5) & (((member2 @ (stream @ A)) @ S) @ ((streams @ A) @ A5)))))))))).
% 3.20/1.77 thf(fact_37_streams_Ocases, axiom, (! [A:$tType,A3:(stream @ A),A5:(set @ A)]: (((((member2 @ (stream @ A)) @ A3) @ ((streams @ A) @ A5)) => (~ ((! [A7:A,S5:(stream @ A)]: (((A3 = (((sCons @ A) @ A7) @ S5)) => ((((member2 @ A) @ A7) @ A5) => (~ ((((member2 @ (stream @ A)) @ S5) @ ((streams @ A) @ A5)))))))))))))).
% 3.20/1.77 thf(fact_38_treeFI_Ocase, axiom, (! [B:$tType,A:$tType,F2:(A > ((list @ (treeFI @ A)) > B)),X1:A,X22:(list @ (treeFI @ A))]: ((((((case_treeFI @ A) @ B) @ F2) @ (((tree @ A) @ X1) @ X22)) = ((F2 @ X1) @ X22))))).
% 3.20/1.77 thf(fact_39_stream_Ocase, axiom, (! [B:$tType,A:$tType,F2:(A > ((stream @ A) > B)),X1:A,X22:(stream @ A)]: ((((((case_stream @ A) @ B) @ F2) @ (((sCons @ A) @ X1) @ X22)) = ((F2 @ X1) @ X22))))).
% 3.20/1.77 thf(fact_40_treeFI_Oset__intros_I1_J, axiom, (! [A:$tType,A1:A,A2:(list @ (treeFI @ A))]: ((((member2 @ A) @ A1) @ ((set_treeFI @ A) @ (((tree @ A) @ A1) @ A2)))))).
% 3.20/1.77 thf(fact_41_trev__trev, axiom, (! [A:$tType,Tr:(treeFI @ A)]: ((((trev @ A) @ ((trev @ A) @ Tr)) = Tr)))).
% 3.20/1.77 thf(fact_42_treeFI_Oset__intros_I2_J, axiom, (! [A:$tType,X3:(treeFI @ A),A2:(list @ (treeFI @ A)),Xa:A,A1:A]: (((((member2 @ (treeFI @ A)) @ X3) @ ((set2 @ (treeFI @ A)) @ A2)) => ((((member2 @ A) @ Xa) @ ((set_treeFI @ A) @ X3)) => (((member2 @ A) @ Xa) @ ((set_treeFI @ A) @ (((tree @ A) @ A1) @ A2)))))))).
% 3.20/1.77 thf(fact_43_treeFI_Oset__cases, axiom, (! [A:$tType,E:A,A3:(treeFI @ A)]: (((((member2 @ A) @ E) @ ((set_treeFI @ A) @ A3)) => ((! [Z2:(list @ (treeFI @ A))]: ((A3 != (((tree @ A) @ E) @ Z2)))) => (~ ((! [Z1:A,Z2:(list @ (treeFI @ A))]: (((A3 = (((tree @ A) @ Z1) @ Z2)) => (! [X:(treeFI @ A)]: (((((member2 @ (treeFI @ A)) @ X) @ ((set2 @ (treeFI @ A)) @ Z2)) => (~ ((((member2 @ A) @ E) @ ((set_treeFI @ A) @ X))))))))))))))))).
% 3.20/1.77 thf(fact_44_treeFI_Oset__induct, axiom, (! [A:$tType,X3:A,A3:(treeFI @ A),P2:(A > ((treeFI @ A) > $o))]: (((((member2 @ A) @ X3) @ ((set_treeFI @ A) @ A3)) => ((! [Z1:A,Z2:(list @ (treeFI @ A))]: (((P2 @ Z1) @ (((tree @ A) @ Z1) @ Z2)))) => ((! [Z1:A,Z2:(list @ (treeFI @ A)),Xa2:(treeFI @ A),Xb:A]: (((((member2 @ (treeFI @ A)) @ Xa2) @ ((set2 @ (treeFI @ A)) @ Z2)) => ((((member2 @ A) @ Xb) @ ((set_treeFI @ A) @ Xa2)) => (((P2 @ Xb) @ Xa2) => ((P2 @ Xb) @ (((tree @ A) @ Z1) @ Z2))))))) => ((P2 @ X3) @ A3))))))).
% 3.20/1.77 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P2:(A > $o)]: (((((member2 @ A) @ A3) @ ((collect @ A) @ P2)) = (P2 @ A3))))).
% 3.20/1.77 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A5:(set @ A)]: ((((collect @ A) @ (^ [X5:A]: ((((member2 @ A) @ X5) @ A5)))) = A5)))).
% 3.20/1.77 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X:A]: (((P2 @ X) = (Q @ X)))) => (((collect @ A) @ P2) = ((collect @ A) @ Q)))))).
% 3.20/1.77 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F2:(A > B),G:(A > B)]: (((! [X:A]: (((F2 @ X) = (G @ X)))) => (F2 = G))))).
% 3.20/1.77 thf(fact_49_stream_Osel_I2_J, axiom, (! [A:$tType,X1:A,X22:(stream @ A)]: ((((stl @ A) @ (((sCons @ A) @ X1) @ X22)) = X22)))).
% 3.20/1.77 thf(fact_50_stream_Osel_I1_J, axiom, (! [A:$tType,X1:A,X22:(stream @ A)]: ((((shd @ A) @ (((sCons @ A) @ X1) @ X22)) = X1)))).
% 3.20/1.77 thf(fact_51_stream_Osplit__sel, axiom, (! [B:$tType,A:$tType,P2:(B > $o),F2:(A > ((stream @ A) > B)),Stream:(stream @ A)]: (((P2 @ ((((case_stream @ A) @ B) @ F2) @ Stream)) = ((Stream = (((sCons @ A) @ ((shd @ A) @ Stream)) @ ((stl @ A) @ Stream))) => (P2 @ ((F2 @ ((shd @ A) @ Stream)) @ ((stl @ A) @ Stream)))))))).
% 3.20/1.77 thf(fact_52_stream_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P2:(B > $o),F2:(A > ((stream @ A) > B)),Stream:(stream @ A)]: (((P2 @ ((((case_stream @ A) @ B) @ F2) @ Stream)) = (~ (((Stream = (((sCons @ A) @ ((shd @ A) @ Stream)) @ ((stl @ A) @ Stream))) & (~ ((P2 @ ((F2 @ ((shd @ A) @ Stream)) @ ((stl @ A) @ Stream)))))))))))).
% 3.20/1.77 thf(fact_53_streams__stl, axiom, (! [A:$tType,S2:(stream @ A),A5:(set @ A)]: (((((member2 @ (stream @ A)) @ S2) @ ((streams @ A) @ A5)) => (((member2 @ (stream @ A)) @ ((stl @ A) @ S2)) @ ((streams @ A) @ A5)))))).
% 3.20/1.77 thf(fact_54_streams__shd, axiom, (! [A:$tType,S2:(stream @ A),A5:(set @ A)]: (((((member2 @ (stream @ A)) @ S2) @ ((streams @ A) @ A5)) => (((member2 @ A) @ ((shd @ A) @ S2)) @ A5))))).
% 3.20/1.77 thf(fact_55_treeFI_Osel_I2_J, axiom, (! [A:$tType,X1:A,X22:(list @ (treeFI @ A))]: ((((sub @ A) @ (((tree @ A) @ X1) @ X22)) = X22)))).
% 3.20/1.77 thf(fact_56_treeFI_Osel_I1_J, axiom, (! [A:$tType,X1:A,X22:(list @ (treeFI @ A))]: ((((lab @ A) @ (((tree @ A) @ X1) @ X22)) = X1)))).
% 3.20/1.77 thf(fact_57_treeFI_Oset__sel_I1_J, axiom, (! [A:$tType,A3:(treeFI @ A)]: ((((member2 @ A) @ ((lab @ A) @ A3)) @ ((set_treeFI @ A) @ A3))))).
% 3.20/1.77 thf(fact_58_treeFI_Osplit__sel, axiom, (! [B:$tType,A:$tType,P2:(B > $o),F2:(A > ((list @ (treeFI @ A)) > B)),TreeFI:(treeFI @ A)]: (((P2 @ ((((case_treeFI @ A) @ B) @ F2) @ TreeFI)) = ((TreeFI = (((tree @ A) @ ((lab @ A) @ TreeFI)) @ ((sub @ A) @ TreeFI))) => (P2 @ ((F2 @ ((lab @ A) @ TreeFI)) @ ((sub @ A) @ TreeFI)))))))).
% 3.20/1.77 thf(fact_59_treeFI_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P2:(B > $o),F2:(A > ((list @ (treeFI @ A)) > B)),TreeFI:(treeFI @ A)]: (((P2 @ ((((case_treeFI @ A) @ B) @ F2) @ TreeFI)) = (~ (((TreeFI = (((tree @ A) @ ((lab @ A) @ TreeFI)) @ ((sub @ A) @ TreeFI))) & (~ ((P2 @ ((F2 @ ((lab @ A) @ TreeFI)) @ ((sub @ A) @ TreeFI)))))))))))).
% 3.20/1.77 thf(fact_60_stream_Oexhaust__sel, axiom, (! [A:$tType,Stream:(stream @ A)]: ((Stream = (((sCons @ A) @ ((shd @ A) @ Stream)) @ ((stl @ A) @ Stream)))))).
% 3.20/1.77 thf(fact_61_smember__code, axiom, (! [A:$tType,X3:A,Y:A,S2:(stream @ A)]: (((((smember @ A) @ X3) @ (((sCons @ A) @ Y) @ S2)) = ((X3 != Y) => (((smember @ A) @ X3) @ S2)))))).
% 3.20/1.77 thf(fact_62_sinterleave_Ocode, axiom, (! [A:$tType]: (((sinterleave @ A) = (^ [S1:(stream @ A),S22:(stream @ A)]: ((((sCons @ A) @ ((shd @ A) @ S1)) @ (((sinterleave @ A) @ S22) @ ((stl @ A) @ S1))))))))).
% 3.20/1.77 thf(fact_63_smap2_Ocode, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((smap2 @ A) @ B) @ C) = (^ [F:(A > (B > C)),S1:(stream @ A),S22:(stream @ B)]: ((((sCons @ C) @ ((F @ ((shd @ A) @ S1)) @ ((shd @ B) @ S22))) @ ((((((smap2 @ A) @ B) @ C) @ F) @ ((stl @ A) @ S1)) @ ((stl @ B) @ S22))))))))).
% 3.20/1.77 thf(fact_64_smap__ctr, axiom, (! [B:$tType,A:$tType,F2:(B > A),S2:(stream @ B),X3:A,S6:(stream @ A)]: (((((((smap @ B) @ A) @ F2) @ S2) = (((sCons @ A) @ X3) @ S6)) = (((F2 @ ((shd @ B) @ S2)) = X3) & (((((smap @ B) @ A) @ F2) @ ((stl @ B) @ S2)) = S6)))))).
% 3.20/1.77 thf(fact_65_sfilter_Ocode, axiom, (! [A:$tType]: (((sfilter @ A) = (^ [P:(A > $o),S:(stream @ A)]: ((((sCons @ A) @ ((shd @ A) @ (((sdrop_while @ A) @ (((((comp @ $o) @ $o) @ A) @ (~)) @ P)) @ S))) @ (((sfilter @ A) @ P) @ ((stl @ A) @ (((sdrop_while @ A) @ (((((comp @ $o) @ $o) @ A) @ (~)) @ P)) @ S)))))))))).
% 3.20/1.77 thf(fact_66_stream__all__Stream, axiom, (! [A:$tType,P2:(A > $o),X3:A,X2:(stream @ A)]: (((((stream_all @ A) @ P2) @ (((sCons @ A) @ X3) @ X2)) = ((P2 @ X3) & (((stream_all @ A) @ P2) @ X2)))))).
% 3.20/1.77 thf(fact_67_stream_Opred__inject, axiom, (! [A:$tType,P2:(A > $o),A3:A,Aa2:(stream @ A)]: (((((pred_stream @ A) @ P2) @ (((sCons @ A) @ A3) @ Aa2)) = ((P2 @ A3) & (((pred_stream @ A) @ P2) @ Aa2)))))).
% 3.20/1.77 thf(fact_68_sset__induct, axiom, (! [A:$tType,Y:A,S2:(stream @ A),P2:(A > ((stream @ A) > $o))]: (((((member2 @ A) @ Y) @ ((sset @ A) @ S2)) => ((! [S5:(stream @ A)]: (((P2 @ ((shd @ A) @ S5)) @ S5))) => ((! [S5:(stream @ A),Y3:A]: (((((member2 @ A) @ Y3) @ ((sset @ A) @ ((stl @ A) @ S5))) => (((P2 @ Y3) @ ((stl @ A) @ S5)) => ((P2 @ Y3) @ S5))))) => ((P2 @ Y) @ S2))))))).
% 3.20/1.77 thf(fact_69_sfilter__Stream, axiom, (! [A:$tType,P2:(A > $o),X3:A,S2:(stream @ A)]: ((((P2 @ X3) => ((((sfilter @ A) @ P2) @ (((sCons @ A) @ X3) @ S2)) = (((sCons @ A) @ X3) @ (((sfilter @ A) @ P2) @ S2)))) & ((~ ((P2 @ X3))) => ((((sfilter @ A) @ P2) @ (((sCons @ A) @ X3) @ S2)) = (((sfilter @ A) @ P2) @ S2))))))).
% 3.20/1.77 thf(fact_70_stream_Omap__sel_I2_J, axiom, (! [B:$tType,A:$tType,F2:(A > B),A3:(stream @ A)]: ((((stl @ B) @ ((((smap @ A) @ B) @ F2) @ A3)) = ((((smap @ A) @ B) @ F2) @ ((stl @ A) @ A3)))))).
% 3.20/1.77 thf(fact_71_stream_Omap__sel_I1_J, axiom, (! [B:$tType,A:$tType,F2:(A > B),A3:(stream @ A)]: ((((shd @ B) @ ((((smap @ A) @ B) @ F2) @ A3)) = (F2 @ ((shd @ A) @ A3)))))).
% 3.20/1.77 thf(fact_72_Stream_Osmember__def, axiom, (! [A:$tType]: (((smember @ A) = (^ [X5:A,S:(stream @ A)]: ((((member2 @ A) @ X5) @ ((sset @ A) @ S)))))))).
% 3.20/1.77 thf(fact_73_stream_Omap__comp, axiom, (! [B:$tType,C:$tType,A:$tType,G:(B > C),F2:(A > B),V:(stream @ A)]: ((((((smap @ B) @ C) @ G) @ ((((smap @ A) @ B) @ F2) @ V)) = ((((smap @ A) @ C) @ (((((comp @ B) @ C) @ A) @ G) @ F2)) @ V))))).
% 3.20/1.77 thf(fact_74_stream_Omap__cong, axiom, (! [B:$tType,A:$tType,X3:(stream @ A),Ya:(stream @ A),F2:(A > B),G:(A > B)]: (((X3 = Ya) => ((! [Z:A]: (((((member2 @ A) @ Z) @ ((sset @ A) @ Ya)) => ((F2 @ Z) = (G @ Z))))) => (((((smap @ A) @ B) @ F2) @ X3) = ((((smap @ A) @ B) @ G) @ Ya))))))).
% 3.20/1.77 thf(fact_75_stream_Opred__map, axiom, (! [B:$tType,A:$tType,Q:(B > $o),F2:(A > B),X3:(stream @ A)]: (((((pred_stream @ B) @ Q) @ ((((smap @ A) @ B) @ F2) @ X3)) = (((pred_stream @ A) @ (((((comp @ B) @ $o) @ A) @ Q) @ F2)) @ X3))))).
% 3.20/1.77 thf(fact_76_stream_Omap__cong0, axiom, (! [B:$tType,A:$tType,X3:(stream @ A),F2:(A > B),G:(A > B)]: (((! [Z:A]: (((((member2 @ A) @ Z) @ ((sset @ A) @ X3)) => ((F2 @ Z) = (G @ Z))))) => (((((smap @ A) @ B) @ F2) @ X3) = ((((smap @ A) @ B) @ G) @ X3)))))).
% 3.20/1.77 thf(fact_77_stream_Opred__cong, axiom, (! [A:$tType,X3:(stream @ A),Ya:(stream @ A),P2:(A > $o),Pa:(A > $o)]: (((X3 = Ya) => ((! [Z:A]: (((((member2 @ A) @ Z) @ ((sset @ A) @ Ya)) => ((P2 @ Z) = (Pa @ Z))))) => ((((pred_stream @ A) @ P2) @ X3) = (((pred_stream @ A) @ Pa) @ Ya))))))).
% 3.20/1.77 thf(fact_78_stream_Oinj__map__strong, axiom, (! [B:$tType,A:$tType,X3:(stream @ A),Xa:(stream @ A),F2:(A > B),Fa:(A > B)]: (((! [Z:A,Za:A]: (((((member2 @ A) @ Z) @ ((sset @ A) @ X3)) => ((((member2 @ A) @ Za) @ ((sset @ A) @ Xa)) => (((F2 @ Z) = (Fa @ Za)) => (Z = Za)))))) => ((((((smap @ A) @ B) @ F2) @ X3) = ((((smap @ A) @ B) @ Fa) @ Xa)) => (X3 = Xa)))))).
% 3.20/1.77 thf(fact_79_stream_Opred__mono__strong, axiom, (! [A:$tType,P2:(A > $o),X3:(stream @ A),Pa:(A > $o)]: (((((pred_stream @ A) @ P2) @ X3) => ((! [Z:A]: (((((member2 @ A) @ Z) @ ((sset @ A) @ X3)) => ((P2 @ Z) => (Pa @ Z))))) => (((pred_stream @ A) @ Pa) @ X3)))))).
% 3.20/1.77 thf(fact_80_stream_Omap, axiom, (! [B:$tType,A:$tType,F2:(A > B),X1:A,X22:(stream @ A)]: ((((((smap @ A) @ B) @ F2) @ (((sCons @ A) @ X1) @ X22)) = (((sCons @ B) @ (F2 @ X1)) @ ((((smap @ A) @ B) @ F2) @ X22)))))).
% 3.20/1.77 thf(fact_81_stl__sset, axiom, (! [A:$tType,X3:A,A3:(stream @ A)]: (((((member2 @ A) @ X3) @ ((sset @ A) @ ((stl @ A) @ A3))) => (((member2 @ A) @ X3) @ ((sset @ A) @ A3)))))).
% 3.20/1.77 thf(fact_82_shd__sset, axiom, (! [A:$tType,A3:(stream @ A)]: ((((member2 @ A) @ ((shd @ A) @ A3)) @ ((sset @ A) @ A3))))).
% 3.20/1.77 thf(fact_83_stream_Oset__intros_I2_J, axiom, (! [A:$tType,X3:A,A2:(stream @ A),A1:A]: (((((member2 @ A) @ X3) @ ((sset @ A) @ A2)) => (((member2 @ A) @ X3) @ ((sset @ A) @ (((sCons @ A) @ A1) @ A2))))))).
% 3.20/1.77 thf(fact_84_stream_Oset__intros_I1_J, axiom, (! [A:$tType,A1:A,A2:(stream @ A)]: ((((member2 @ A) @ A1) @ ((sset @ A) @ (((sCons @ A) @ A1) @ A2)))))).
% 3.20/1.77 thf(fact_85_stream_Oset__cases, axiom, (! [A:$tType,E:A,A3:(stream @ A)]: (((((member2 @ A) @ E) @ ((sset @ A) @ A3)) => ((! [Z2:(stream @ A)]: ((A3 != (((sCons @ A) @ E) @ Z2)))) => (~ ((! [Z1:A,Z2:(stream @ A)]: (((A3 = (((sCons @ A) @ Z1) @ Z2)) => (~ ((((member2 @ A) @ E) @ ((sset @ A) @ Z2)))))))))))))).
% 3.20/1.77 thf(fact_86_stream_Oset__induct, axiom, (! [A:$tType,X3:A,A3:(stream @ A),P2:(A > ((stream @ A) > $o))]: (((((member2 @ A) @ X3) @ ((sset @ A) @ A3)) => ((! [Z1:A,Z2:(stream @ A)]: (((P2 @ Z1) @ (((sCons @ A) @ Z1) @ Z2)))) => ((! [Z1:A,Z2:(stream @ A),Xa2:A]: (((((member2 @ A) @ Xa2) @ ((sset @ A) @ Z2)) => (((P2 @ Xa2) @ Z2) => ((P2 @ Xa2) @ (((sCons @ A) @ Z1) @ Z2)))))) => ((P2 @ X3) @ A3))))))).
% 3.20/1.77 thf(fact_87_smap__streams, axiom, (! [A:$tType,B:$tType,S2:(stream @ A),A5:(set @ A),F2:(A > B),B2:(set @ B)]: (((((member2 @ (stream @ A)) @ S2) @ ((streams @ A) @ A5)) => ((! [X:A]: (((((member2 @ A) @ X) @ A5) => (((member2 @ B) @ (F2 @ X)) @ B2)))) => (((member2 @ (stream @ B)) @ ((((smap @ A) @ B) @ F2) @ S2)) @ ((streams @ B) @ B2))))))).
% 3.20/1.77 thf(fact_88_sfilter_Osimps_I2_J, axiom, (! [A:$tType,P2:(A > $o),S2:(stream @ A)]: ((((stl @ A) @ (((sfilter @ A) @ P2) @ S2)) = (((sfilter @ A) @ P2) @ ((stl @ A) @ (((sdrop_while @ A) @ (((((comp @ $o) @ $o) @ A) @ (~)) @ P2)) @ S2))))))).
% 3.20/1.77 thf(fact_89_sfilter_Osimps_I1_J, axiom, (! [A:$tType,P2:(A > $o),S2:(stream @ A)]: ((((shd @ A) @ (((sfilter @ A) @ P2) @ S2)) = ((shd @ A) @ (((sdrop_while @ A) @ (((((comp @ $o) @ $o) @ A) @ (~)) @ P2)) @ S2)))))).
% 3.20/1.77 thf(fact_90_smap2_Osimps_I2_J, axiom, (! [A:$tType,C:$tType,B:$tType,F2:(A > (B > C)),S12:(stream @ A),S23:(stream @ B)]: ((((stl @ C) @ ((((((smap2 @ A) @ B) @ C) @ F2) @ S12) @ S23)) = ((((((smap2 @ A) @ B) @ C) @ F2) @ ((stl @ A) @ S12)) @ ((stl @ B) @ S23)))))).
% 3.20/1.77 thf(fact_91_smap2_Osimps_I1_J, axiom, (! [A:$tType,C:$tType,B:$tType,F2:(A > (B > C)),S12:(stream @ A),S23:(stream @ B)]: ((((shd @ C) @ ((((((smap2 @ A) @ B) @ C) @ F2) @ S12) @ S23)) = ((F2 @ ((shd @ A) @ S12)) @ ((shd @ B) @ S23)))))).
% 3.20/1.77 thf(fact_92_smap2__unfold, axiom, (! [B:$tType,A:$tType,C:$tType,F2:(B > (C > A)),A3:B,S12:(stream @ B),B3:C,S23:(stream @ C)]: ((((((((smap2 @ B) @ C) @ A) @ F2) @ (((sCons @ B) @ A3) @ S12)) @ (((sCons @ C) @ B3) @ S23)) = (((sCons @ A) @ ((F2 @ A3) @ B3)) @ ((((((smap2 @ B) @ C) @ A) @ F2) @ S12) @ S23)))))).
% 3.20/1.77 thf(fact_93_sinterleave_Osimps_I2_J, axiom, (! [A:$tType,S12:(stream @ A),S23:(stream @ A)]: ((((stl @ A) @ (((sinterleave @ A) @ S12) @ S23)) = (((sinterleave @ A) @ S23) @ ((stl @ A) @ S12)))))).
% 3.20/1.77 thf(fact_94_sinterleave_Osimps_I1_J, axiom, (! [A:$tType,S12:(stream @ A),S23:(stream @ A)]: ((((shd @ A) @ (((sinterleave @ A) @ S12) @ S23)) = ((shd @ A) @ S12))))).
% 3.20/1.77 thf(fact_95_sinterleave__code, axiom, (! [A:$tType,X3:A,S12:(stream @ A),S23:(stream @ A)]: (((((sinterleave @ A) @ (((sCons @ A) @ X3) @ S12)) @ S23) = (((sCons @ A) @ X3) @ (((sinterleave @ A) @ S23) @ S12)))))).
% 3.20/1.77 thf(fact_96_comp__apply, axiom, (! [C:$tType,A:$tType,B:$tType]: (((((comp @ B) @ A) @ C) = (^ [F:(B > A),G2:(C > B),X5:C]: ((F @ (G2 @ X5)))))))).
% 3.20/1.77 thf(fact_97_stream_Omap__o__corec, axiom, (! [A:$tType,B:$tType,C:$tType,F2:(A > B),G:(C > A),Ga:(C > $o),Gb:(C > (stream @ A)),Gc:(C > C)]: (((((((comp @ (stream @ A)) @ (stream @ B)) @ C) @ (((smap @ A) @ B) @ F2)) @ ((((((corec_stream @ C) @ A) @ G) @ Ga) @ Gb) @ Gc)) = ((((((corec_stream @ C) @ B) @ (((((comp @ A) @ B) @ C) @ F2) @ G)) @ Ga) @ (((((comp @ (stream @ A)) @ (stream @ B)) @ C) @ (((smap @ A) @ B) @ F2)) @ Gb)) @ Gc))))).
% 3.20/1.77 thf(fact_98_rewriteR__comp__comp2, axiom, (! [C:$tType,B:$tType,E2:$tType,D:$tType,A:$tType,G:(C > B),H:(A > C),R1:(D > B),R2:(A > D),F2:(B > E2),L:(D > E2)]: ((((((((comp @ C) @ B) @ A) @ G) @ H) = (((((comp @ D) @ B) @ A) @ R1) @ R2)) => (((((((comp @ B) @ E2) @ D) @ F2) @ R1) = L) => ((((((comp @ C) @ E2) @ A) @ (((((comp @ B) @ E2) @ C) @ F2) @ G)) @ H) = (((((comp @ D) @ E2) @ A) @ L) @ R2))))))).
% 3.20/1.77 thf(fact_99_rewriteL__comp__comp2, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,E2:$tType,F2:(C > B),G:(A > C),L1:(D > B),L2:(A > D),H:(E2 > A),R3:(E2 > D)]: ((((((((comp @ C) @ B) @ A) @ F2) @ G) = (((((comp @ D) @ B) @ A) @ L1) @ L2)) => (((((((comp @ A) @ D) @ E2) @ L2) @ H) = R3) => ((((((comp @ C) @ B) @ E2) @ F2) @ (((((comp @ A) @ C) @ E2) @ G) @ H)) = (((((comp @ D) @ B) @ E2) @ L1) @ R3))))))).
% 3.20/1.77 thf(fact_100_rewriteR__comp__comp, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,G:(C > B),H:(A > C),R3:(A > B),F2:(B > D)]: ((((((((comp @ C) @ B) @ A) @ G) @ H) = R3) => ((((((comp @ C) @ D) @ A) @ (((((comp @ B) @ D) @ C) @ F2) @ G)) @ H) = (((((comp @ B) @ D) @ A) @ F2) @ R3)))))).
% 3.20/1.77 thf(fact_101_rewriteL__comp__comp, axiom, (! [C:$tType,B:$tType,A:$tType,D:$tType,F2:(C > B),G:(A > C),L:(A > B),H:(D > A)]: ((((((((comp @ C) @ B) @ A) @ F2) @ G) = L) => ((((((comp @ C) @ B) @ D) @ F2) @ (((((comp @ A) @ C) @ D) @ G) @ H)) = (((((comp @ A) @ B) @ D) @ L) @ H)))))).
% 3.20/1.77 thf(fact_102_type__copy__map__cong0, axiom, (! [B:$tType,D:$tType,E2:$tType,A:$tType,C:$tType,M:(B > A),G:(C > B),X3:C,N:(D > A),H:(C > D),F2:(A > E2)]: ((((M @ (G @ X3)) = (N @ (H @ X3))) => (((((((comp @ B) @ E2) @ C) @ (((((comp @ A) @ E2) @ B) @ F2) @ M)) @ G) @ X3) = ((((((comp @ D) @ E2) @ C) @ (((((comp @ A) @ E2) @ D) @ F2) @ N)) @ H) @ X3)))))).
% 3.20/1.77 thf(fact_103_stream_Ocorec__disc, axiom, (! [A:$tType,C:$tType]: ((((corec_stream @ C) @ A) = ((corec_stream @ C) @ A))))).
% 3.20/1.77 thf(fact_104_stream_Ocorec__sel_I2_J, axiom, (! [A:$tType,C:$tType,Q2:(C > $o),A3:C,G1:(C > A),G21:(C > (stream @ A)),G22:(C > C)]: ((((Q2 @ A3) => (((stl @ A) @ (((((((corec_stream @ C) @ A) @ G1) @ Q2) @ G21) @ G22) @ A3)) = (G21 @ A3))) & ((~ ((Q2 @ A3))) => (((stl @ A) @ (((((((corec_stream @ C) @ A) @ G1) @ Q2) @ G21) @ G22) @ A3)) = (((((((corec_stream @ C) @ A) @ G1) @ Q2) @ G21) @ G22) @ (G22 @ A3)))))))).
% 3.20/1.77 thf(fact_105_stream_Ocorec__sel_I1_J, axiom, (! [A:$tType,C:$tType,G1:(C > A),Q2:(C > $o),G21:(C > (stream @ A)),G22:(C > C),A3:C]: ((((shd @ A) @ (((((((corec_stream @ C) @ A) @ G1) @ Q2) @ G21) @ G22) @ A3)) = (G1 @ A3))))).
% 3.20/1.77 thf(fact_106_stream_Ocorec__code, axiom, (! [A:$tType,C:$tType]: ((((corec_stream @ C) @ A) = (^ [G12:(C > A),Q22:(C > $o),G212:(C > (stream @ A)),G222:(C > C),A4:C]: ((((sCons @ A) @ (G12 @ A4)) @ ((((if @ (stream @ A)) @ (Q22 @ A4)) @ (G212 @ A4)) @ (((((((corec_stream @ C) @ A) @ G12) @ Q22) @ G212) @ G222) @ (G222 @ A4)))))))))).
% 3.20/1.77 thf(fact_107_comp__def, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((comp @ B) @ C) @ A) = (^ [F:(B > C),G2:(A > B),X5:A]: ((F @ (G2 @ X5)))))))).
% 3.20/1.77 thf(fact_108_comp__assoc, axiom, (! [B:$tType,D:$tType,C:$tType,A:$tType,F2:(D > B),G:(C > D),H:(A > C)]: (((((((comp @ C) @ B) @ A) @ (((((comp @ D) @ B) @ C) @ F2) @ G)) @ H) = (((((comp @ D) @ B) @ A) @ F2) @ (((((comp @ C) @ D) @ A) @ G) @ H)))))).
% 3.20/1.77 thf(fact_109_comp__eq__dest, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A3:(C > B),B3:(A > C),C2:(D > B),D2:(A > D),V:A]: ((((((((comp @ C) @ B) @ A) @ A3) @ B3) = (((((comp @ D) @ B) @ A) @ C2) @ D2)) => ((A3 @ (B3 @ V)) = (C2 @ (D2 @ V))))))).
% 3.20/1.77 thf(fact_110_comp__eq__elim, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,A3:(C > B),B3:(A > C),C2:(D > B),D2:(A > D)]: ((((((((comp @ C) @ B) @ A) @ A3) @ B3) = (((((comp @ D) @ B) @ A) @ C2) @ D2)) => (! [V2:A]: (((A3 @ (B3 @ V2)) = (C2 @ (D2 @ V2))))))))).
% 3.20/1.77 thf(fact_111_comp__eq__dest__lhs, axiom, (! [C:$tType,B:$tType,A:$tType,A3:(C > B),B3:(A > C),C2:(A > B),V:A]: ((((((((comp @ C) @ B) @ A) @ A3) @ B3) = C2) => ((A3 @ (B3 @ V)) = (C2 @ V)))))).
% 3.20/1.77 thf(fact_112_comp__cong, axiom, (! [C:$tType,B:$tType,D:$tType,A:$tType,E2:$tType,F2:(B > A),G:(C > B),X3:C,F3:(D > A),G3:(E2 > D),X6:E2]: ((((F2 @ (G @ X3)) = (F3 @ (G3 @ X6))) => (((((((comp @ B) @ A) @ C) @ F2) @ G) @ X3) = ((((((comp @ D) @ A) @ E2) @ F3) @ G3) @ X6)))))).
% 3.20/1.77 thf(fact_113_comp__apply__eq, axiom, (! [B:$tType,D:$tType,A:$tType,C:$tType,F2:(B > A),G:(C > B),X3:C,H:(D > A),K:(C > D)]: ((((F2 @ (G @ X3)) = (H @ (K @ X3))) => (((((((comp @ B) @ A) @ C) @ F2) @ G) @ X3) = ((((((comp @ D) @ A) @ C) @ H) @ K) @ X3)))))).
% 3.20/1.77 thf(fact_114_fun_Omap__comp, axiom, (! [B:$tType,C:$tType,A:$tType,D:$tType,G:(B > C),F2:(A > B),V:(D > A)]: (((((((comp @ B) @ C) @ D) @ G) @ (((((comp @ A) @ B) @ D) @ F2) @ V)) = (((((comp @ A) @ C) @ D) @ (((((comp @ B) @ C) @ A) @ G) @ F2)) @ V))))).
% 3.20/1.77 thf(fact_115_stream__all__iff, axiom, (! [A:$tType]: (((stream_all @ A) = (^ [P:(A > $o),S:(stream @ A)]: ((! [X5:A]: (((((member2 @ A) @ X5) @ ((sset @ A) @ S)) => (P @ X5)))))))))).
% 3.20/1.77 thf(fact_116_stream_Oset, axiom, (! [A:$tType,X1:A,X22:(stream @ A)]: ((((sset @ A) @ (((sCons @ A) @ X1) @ X22)) = (((insert2 @ A) @ X1) @ ((sset @ A) @ X22)))))).
% 3.20/1.77 thf(fact_117_stream_Opred__set, axiom, (! [A:$tType]: (((pred_stream @ A) = (^ [P:(A > $o),X5:(stream @ A)]: ((! [Y4:A]: (((((member2 @ A) @ Y4) @ ((sset @ A) @ X5)) => (P @ Y4)))))))))).
% 3.20/1.77 thf(fact_118_treeFI_Opred__set, axiom, (! [A:$tType]: (((pred_treeFI @ A) = (^ [P:(A > $o),X5:(treeFI @ A)]: ((! [Y4:A]: (((((member2 @ A) @ Y4) @ ((set_treeFI @ A) @ X5)) => (P @ Y4)))))))))).
% 3.20/1.77 thf(fact_119_sset__sinterleave, axiom, (! [A:$tType,S12:(stream @ A),S23:(stream @ A)]: ((((sset @ A) @ (((sinterleave @ A) @ S12) @ S23)) = (((sup_sup @ (set @ A)) @ ((sset @ A) @ S12)) @ ((sset @ A) @ S23)))))).
% 3.20/1.77 thf(fact_120_sset__streams, axiom, (! [A:$tType,S2:(stream @ A),A5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ ((sset @ A) @ S2)) @ A5) => (((member2 @ (stream @ A)) @ S2) @ ((streams @ A) @ A5)))))).
% 3.20/1.77 thf(fact_121_streams__sset, axiom, (! [A:$tType,S2:(stream @ A),A5:(set @ A)]: (((((member2 @ (stream @ A)) @ S2) @ ((streams @ A) @ A5)) => (((ord_less_eq @ (set @ A)) @ ((sset @ A) @ S2)) @ A5))))).
% 3.20/1.77 thf(fact_122_streams__mono2, axiom, (! [A:$tType,S3:(set @ A),T2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ S3) @ T2) => (((ord_less_eq @ (set @ (stream @ A))) @ ((streams @ A) @ S3)) @ ((streams @ A) @ T2)))))).
% 3.20/1.77 thf(fact_123_streams__mono, axiom, (! [A:$tType,S2:(stream @ A),A5:(set @ A),B2:(set @ A)]: (((((member2 @ (stream @ A)) @ S2) @ ((streams @ A) @ A5)) => ((((ord_less_eq @ (set @ A)) @ A5) @ B2) => (((member2 @ (stream @ A)) @ S2) @ ((streams @ A) @ B2))))))).
% 3.20/1.77 thf(fact_124_treeFI_Opred__mono__strong, axiom, (! [A:$tType,P2:(A > $o),X3:(treeFI @ A),Pa:(A > $o)]: (((((pred_treeFI @ A) @ P2) @ X3) => ((! [Z:A]: (((((member2 @ A) @ Z) @ ((set_treeFI @ A) @ X3)) => ((P2 @ Z) => (Pa @ Z))))) => (((pred_treeFI @ A) @ Pa) @ X3)))))).
% 3.20/1.77 thf(fact_125_treeFI_Opred__cong, axiom, (! [A:$tType,X3:(treeFI @ A),Ya:(treeFI @ A),P2:(A > $o),Pa:(A > $o)]: (((X3 = Ya) => ((! [Z:A]: (((((member2 @ A) @ Z) @ ((set_treeFI @ A) @ Ya)) => ((P2 @ Z) = (Pa @ Z))))) => ((((pred_treeFI @ A) @ P2) @ X3) = (((pred_treeFI @ A) @ Pa) @ Ya))))))).
% 3.20/1.77 thf(fact_126_streams__iff__sset, axiom, (! [A:$tType,S2:(stream @ A),A5:(set @ A)]: (((((member2 @ (stream @ A)) @ S2) @ ((streams @ A) @ A5)) = (((ord_less_eq @ (set @ A)) @ ((sset @ A) @ S2)) @ A5))))).
% 3.20/1.77 thf(fact_127_subset__code_I1_J, axiom, (! [A:$tType,Xs:(list @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ Xs)) @ B2) = (! [X5:A]: (((((member2 @ A) @ X5) @ ((set2 @ A) @ Xs)) => (((member2 @ A) @ X5) @ B2)))))))).
% 3.20/1.77 thf(fact_128_sset__shift, axiom, (! [A:$tType,Xs:(list @ A),S2:(stream @ A)]: ((((sset @ A) @ (((shift @ A) @ Xs) @ S2)) = (((sup_sup @ (set @ A)) @ ((set2 @ A) @ Xs)) @ ((sset @ A) @ S2)))))).
% 3.20/1.77 thf(fact_129_set__union, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((set2 @ A) @ (((union @ A) @ Xs) @ Ys)) = (((sup_sup @ (set @ A)) @ ((set2 @ A) @ Xs)) @ ((set2 @ A) @ Ys)))))).
% 3.20/1.77 thf(fact_130_treeFI_Opred__inject, axiom, (! [A:$tType,P2:(A > $o),A3:A,Aa2:(list @ (treeFI @ A))]: (((((pred_treeFI @ A) @ P2) @ (((tree @ A) @ A3) @ Aa2)) = ((P2 @ A3) & (((list_all @ (treeFI @ A)) @ ((pred_treeFI @ A) @ P2)) @ Aa2)))))).
% 3.20/1.77 thf(fact_131_shift__left__inj, axiom, (! [A:$tType,Xs:(list @ A),S12:(stream @ A),S23:(stream @ A)]: ((((((shift @ A) @ Xs) @ S12) = (((shift @ A) @ Xs) @ S23)) = (S12 = S23))))).
% 3.20/1.77 thf(fact_132_stream__all__shift, axiom, (! [A:$tType,P2:(A > $o),Xs:(list @ A),S2:(stream @ A)]: (((((stream_all @ A) @ P2) @ (((shift @ A) @ Xs) @ S2)) = ((((list_all @ A) @ P2) @ Xs) & (((stream_all @ A) @ P2) @ S2)))))).
% 3.20/1.77 thf(fact_133_list_Opred__cong, axiom, (! [A:$tType,X3:(list @ A),Ya:(list @ A),P2:(A > $o),Pa:(A > $o)]: (((X3 = Ya) => ((! [Z:A]: (((((member2 @ A) @ Z) @ ((set2 @ A) @ Ya)) => ((P2 @ Z) = (Pa @ Z))))) => ((((list_all @ A) @ P2) @ X3) = (((list_all @ A) @ Pa) @ Ya))))))).
% 3.20/1.77 thf(fact_134_list_Opred__mono__strong, axiom, (! [A:$tType,P2:(A > $o),X3:(list @ A),Pa:(A > $o)]: (((((list_all @ A) @ P2) @ X3) => ((! [Z:A]: (((((member2 @ A) @ Z) @ ((set2 @ A) @ X3)) => ((P2 @ Z) => (Pa @ Z))))) => (((list_all @ A) @ Pa) @ X3)))))).
% 3.20/1.77 thf(fact_135_list__all__iff, axiom, (! [A:$tType]: (((list_all @ A) = (^ [P:(A > $o),X5:(list @ A)]: ((! [Y4:A]: (((((member2 @ A) @ Y4) @ ((set2 @ A) @ X5)) => (P @ Y4)))))))))).
% 3.20/1.77 thf(fact_136_Ball__set__list__all, axiom, (! [A:$tType,Xs:(list @ A),P2:(A > $o)]: (((! [X5:A]: (((((member2 @ A) @ X5) @ ((set2 @ A) @ Xs)) => (P2 @ X5)))) = (((list_all @ A) @ P2) @ Xs))))).
% 3.20/1.77 thf(fact_137_list_Opred__set, axiom, (! [A:$tType]: (((list_all @ A) = (^ [P:(A > $o),X5:(list @ A)]: ((! [Y4:A]: (((((member2 @ A) @ Y4) @ ((set2 @ A) @ X5)) => (P @ Y4)))))))))).
% 3.20/1.77 thf(fact_138_List_Oset__insert, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: ((((set2 @ A) @ (((insert @ A) @ X3) @ Xs)) = (((insert2 @ A) @ X3) @ ((set2 @ A) @ Xs)))))).
% 3.20/1.77 thf(fact_139_subset__code_I2_J, axiom, (! [B:$tType,A5:(set @ B),Ys:(list @ B)]: (((((ord_less_eq @ (set @ B)) @ A5) @ ((coset @ B) @ Ys)) = (! [X5:B]: (((((member2 @ B) @ X5) @ ((set2 @ B) @ Ys)) => (~ ((((member2 @ B) @ X5) @ A5)))))))))).
% 3.20/1.77 thf(fact_140_in__set__member, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: (((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs)) = (((member @ A) @ Xs) @ X3))))).
% 3.20/1.77 thf(fact_141_union__set__fold, axiom, (! [A:$tType,Xs:(list @ A),A5:(set @ A)]: (((((sup_sup @ (set @ A)) @ ((set2 @ A) @ Xs)) @ A5) = (((((fold @ A) @ (set @ A)) @ (insert2 @ A)) @ Xs) @ A5))))).
% 3.20/1.77 thf(fact_142_in__set__insert, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: (((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs)) => ((((insert @ A) @ X3) @ Xs) = Xs))))).
% 3.20/1.77 thf(fact_143_List_Ofold__cong, axiom, (! [B:$tType,A:$tType,A3:A,B3:A,Xs:(list @ B),Ys:(list @ B),F2:(B > (A > A)),G:(B > (A > A))]: (((A3 = B3) => ((Xs = Ys) => ((! [X:B]: (((((member2 @ B) @ X) @ ((set2 @ B) @ Xs)) => ((F2 @ X) = (G @ X))))) => ((((((fold @ B) @ A) @ F2) @ Xs) @ A3) = (((((fold @ B) @ A) @ G) @ Ys) @ B3)))))))).
% 3.20/1.77 thf(fact_144_fold__invariant, axiom, (! [A:$tType,B:$tType,Xs:(list @ A),Q:(A > $o),P2:(B > $o),S2:B,F2:(A > (B > B))]: (((! [X:A]: (((((member2 @ A) @ X) @ ((set2 @ A) @ Xs)) => (Q @ X)))) => ((P2 @ S2) => ((! [X:A,S5:B]: (((Q @ X) => ((P2 @ S5) => (P2 @ ((F2 @ X) @ S5)))))) => (P2 @ (((((fold @ A) @ B) @ F2) @ Xs) @ S2)))))))).
% 3.20/1.77 thf(fact_145_fold__commute__apply, axiom, (! [A:$tType,C:$tType,B:$tType,Xs:(list @ A),H:(B > C),G:(A > (B > B)),F2:(A > (C > C)),S2:B]: (((! [X:A]: (((((member2 @ A) @ X) @ ((set2 @ A) @ Xs)) => ((((((comp @ B) @ C) @ B) @ H) @ (G @ X)) = (((((comp @ C) @ C) @ B) @ (F2 @ X)) @ H))))) => ((H @ (((((fold @ A) @ B) @ G) @ Xs) @ S2)) = (((((fold @ A) @ C) @ F2) @ Xs) @ (H @ S2))))))).
% 3.20/1.77 thf(fact_146_fold__commute, axiom, (! [A:$tType,C:$tType,B:$tType,Xs:(list @ A),H:(B > C),G:(A > (B > B)),F2:(A > (C > C))]: (((! [X:A]: (((((member2 @ A) @ X) @ ((set2 @ A) @ Xs)) => ((((((comp @ B) @ C) @ B) @ H) @ (G @ X)) = (((((comp @ C) @ C) @ B) @ (F2 @ X)) @ H))))) => ((((((comp @ B) @ C) @ B) @ H) @ ((((fold @ A) @ B) @ G) @ Xs)) = (((((comp @ C) @ C) @ B) @ ((((fold @ A) @ C) @ F2) @ Xs)) @ H)))))).
% 3.20/1.77 thf(fact_147_foldr__fold, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),F2:(A > (B > B))]: (((! [X:A,Y3:A]: (((((member2 @ A) @ X) @ ((set2 @ A) @ Xs)) => ((((member2 @ A) @ Y3) @ ((set2 @ A) @ Xs)) => ((((((comp @ B) @ B) @ B) @ (F2 @ Y3)) @ (F2 @ X)) = (((((comp @ B) @ B) @ B) @ (F2 @ X)) @ (F2 @ Y3))))))) => (((((foldr @ A) @ B) @ F2) @ Xs) = ((((fold @ A) @ B) @ F2) @ Xs)))))).
% 3.20/1.77 thf(fact_148_fold__remove1__split, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),F2:(A > (B > B)),X3:A]: (((! [X:A,Y3:A]: (((((member2 @ A) @ X) @ ((set2 @ A) @ Xs)) => ((((member2 @ A) @ Y3) @ ((set2 @ A) @ Xs)) => ((((((comp @ B) @ B) @ B) @ (F2 @ X)) @ (F2 @ Y3)) = (((((comp @ B) @ B) @ B) @ (F2 @ Y3)) @ (F2 @ X))))))) => ((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs)) => (((((fold @ A) @ B) @ F2) @ Xs) = (((((comp @ B) @ B) @ B) @ ((((fold @ A) @ B) @ F2) @ (((remove1 @ A) @ X3) @ Xs))) @ (F2 @ X3)))))))).
% 3.20/1.77 thf(fact_149_subset__code_I3_J, axiom, (! [C:$tType]: ((~ ((((ord_less_eq @ (set @ C)) @ ((coset @ C) @ (nil @ C))) @ ((set2 @ C) @ (nil @ C)))))))).
% 3.20/1.77 thf(fact_150_set__update__subset__insert, axiom, (! [A:$tType,Xs:(list @ A),I:nat,X3:A]: ((((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ ((((list_update @ A) @ Xs) @ I) @ X3))) @ (((insert2 @ A) @ X3) @ ((set2 @ A) @ Xs)))))).
% 3.20/1.77 thf(fact_151_in__set__remove1, axiom, (! [A:$tType,A3:A,B3:A,Xs:(list @ A)]: (((A3 != B3) => ((((member2 @ A) @ A3) @ ((set2 @ A) @ (((remove1 @ A) @ B3) @ Xs))) = (((member2 @ A) @ A3) @ ((set2 @ A) @ Xs))))))).
% 3.20/1.77 thf(fact_152_foldr__cong, axiom, (! [B:$tType,A:$tType,A3:A,B3:A,L:(list @ B),K:(list @ B),F2:(B > (A > A)),G:(B > (A > A))]: (((A3 = B3) => ((L = K) => ((! [A7:A,X:B]: (((((member2 @ B) @ X) @ ((set2 @ B) @ L)) => (((F2 @ X) @ A7) = ((G @ X) @ A7))))) => ((((((foldr @ B) @ A) @ F2) @ L) @ A3) = (((((foldr @ B) @ A) @ G) @ K) @ B3)))))))).
% 3.20/1.77 thf(fact_153_notin__set__remove1, axiom, (! [A:$tType,X3:A,Xs:(list @ A),Y:A]: (((~ ((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs)))) => (~ ((((member2 @ A) @ X3) @ ((set2 @ A) @ (((remove1 @ A) @ Y) @ Xs))))))))).
% 3.20/1.77 thf(fact_154_remove1__idem, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: (((~ ((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs)))) => ((((remove1 @ A) @ X3) @ Xs) = Xs))))).
% 3.20/1.77 thf(fact_155_shift_Osimps_I1_J, axiom, (! [A:$tType,S2:(stream @ A)]: (((((shift @ A) @ (nil @ A)) @ S2) = S2)))).
% 3.20/1.77 thf(fact_156_set__update__subsetI, axiom, (! [A:$tType,Xs:(list @ A),A5:(set @ A),X3:A,I:nat]: (((((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ Xs)) @ A5) => ((((member2 @ A) @ X3) @ A5) => (((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ ((((list_update @ A) @ Xs) @ I) @ X3))) @ A5)))))).
% 3.20/1.77 thf(fact_157_set__remove1__subset, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: ((((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ (((remove1 @ A) @ X3) @ Xs))) @ ((set2 @ A) @ Xs))))).
% 3.20/1.77 thf(fact_158_sset__cycle, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((sset @ A) @ ((cycle @ A) @ Xs)) = ((set2 @ A) @ Xs)))))).
% 3.20/1.77 thf(fact_159_flat__Stream, axiom, (! [A:$tType,Xs:(list @ A),Ws:(stream @ (list @ A))]: (((Xs != (nil @ A)) => (((flat @ A) @ (((sCons @ (list @ A)) @ Xs) @ Ws)) = (((shift @ A) @ Xs) @ ((flat @ A) @ Ws))))))).
% 3.20/1.77 thf(fact_160_shift__simps_I1_J, axiom, (! [A:$tType,Xs:(list @ A),S2:(stream @ A)]: ((((Xs = (nil @ A)) => (((shd @ A) @ (((shift @ A) @ Xs) @ S2)) = ((shd @ A) @ S2))) & ((Xs != (nil @ A)) => (((shd @ A) @ (((shift @ A) @ Xs) @ S2)) = ((hd @ A) @ Xs))))))).
% 3.20/1.77 thf(fact_161_cycle_Osimps_I1_J, axiom, (! [A:$tType,Xs:(list @ A)]: ((((shd @ A) @ ((cycle @ A) @ Xs)) = ((hd @ A) @ Xs))))).
% 3.20/1.77 thf(fact_162_flat_Osimps_I1_J, axiom, (! [A:$tType,Ws:(stream @ (list @ A))]: ((((shd @ A) @ ((flat @ A) @ Ws)) = ((hd @ A) @ ((shd @ (list @ A)) @ Ws)))))).
% 3.20/1.77 thf(fact_163_list_Oset__sel_I1_J, axiom, (! [A:$tType,A3:(list @ A)]: (((A3 != (nil @ A)) => (((member2 @ A) @ ((hd @ A) @ A3)) @ ((set2 @ A) @ A3)))))).
% 3.20/1.77 thf(fact_164_hd__in__set, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((member2 @ A) @ ((hd @ A) @ Xs)) @ ((set2 @ A) @ Xs)))))).
% 3.20/1.77 thf(fact_165_cycle__decomp, axiom, (! [A:$tType,U:(list @ A)]: (((U != (nil @ A)) => (((cycle @ A) @ U) = (((shift @ A) @ U) @ ((cycle @ A) @ U))))))).
% 3.20/1.77 thf(fact_166_flat__unfold, axiom, (! [A:$tType,Ws:(stream @ (list @ A))]: (((((shd @ (list @ A)) @ Ws) != (nil @ A)) => (((flat @ A) @ Ws) = (((shift @ A) @ ((shd @ (list @ A)) @ Ws)) @ ((flat @ A) @ ((stl @ (list @ A)) @ Ws)))))))).
% 3.20/1.77 thf(fact_167_flat_Ocode, axiom, (! [A:$tType]: (((flat @ A) = (^ [Ws2:(stream @ (list @ A))]: ((((sCons @ A) @ ((hd @ A) @ ((shd @ (list @ A)) @ Ws2))) @ ((flat @ A) @ ((((if @ (stream @ (list @ A))) @ (((tl @ A) @ ((shd @ (list @ A)) @ Ws2)) = (nil @ A))) @ ((stl @ (list @ A)) @ Ws2)) @ (((sCons @ (list @ A)) @ ((tl @ A) @ ((shd @ (list @ A)) @ Ws2))) @ ((stl @ (list @ A)) @ Ws2))))))))))).
% 3.20/1.77 thf(fact_168_flat__Cons, axiom, (! [A:$tType,X3:A,Xs:(list @ A),Ws:(stream @ (list @ A))]: ((((flat @ A) @ (((sCons @ (list @ A)) @ (((cons @ A) @ X3) @ Xs)) @ Ws)) = (((sCons @ A) @ X3) @ ((flat @ A) @ ((((if @ (stream @ (list @ A))) @ (Xs = (nil @ A))) @ Ws) @ (((sCons @ (list @ A)) @ Xs) @ Ws)))))))).
% 3.20/1.77 thf(fact_169_flat_Osimps_I2_J, axiom, (! [A:$tType,Ws:(stream @ (list @ A))]: ((((stl @ A) @ ((flat @ A) @ Ws)) = ((flat @ A) @ ((((if @ (stream @ (list @ A))) @ (((tl @ A) @ ((shd @ (list @ A)) @ Ws)) = (nil @ A))) @ ((stl @ (list @ A)) @ Ws)) @ (((sCons @ (list @ A)) @ ((tl @ A) @ ((shd @ (list @ A)) @ Ws))) @ ((stl @ (list @ A)) @ Ws)))))))).
% 3.20/1.77 thf(fact_170_list_Osimps_I15_J, axiom, (! [A:$tType,X21:A,X222:(list @ A)]: ((((set2 @ A) @ (((cons @ A) @ X21) @ X222)) = (((insert2 @ A) @ X21) @ ((set2 @ A) @ X222)))))).
% 3.20/1.77 thf(fact_171_not__in__set__insert, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: (((~ ((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs)))) => ((((insert @ A) @ X3) @ Xs) = (((cons @ A) @ X3) @ Xs)))))).
% 3.20/1.77 thf(fact_172_shift__simps_I2_J, axiom, (! [A:$tType,Xs:(list @ A),S2:(stream @ A)]: ((((Xs = (nil @ A)) => (((stl @ A) @ (((shift @ A) @ Xs) @ S2)) = ((stl @ A) @ S2))) & ((Xs != (nil @ A)) => (((stl @ A) @ (((shift @ A) @ Xs) @ S2)) = (((shift @ A) @ ((tl @ A) @ Xs)) @ S2))))))).
% 3.20/1.77 thf(fact_173_list_Oset__cases, axiom, (! [A:$tType,E:A,A3:(list @ A)]: (((((member2 @ A) @ E) @ ((set2 @ A) @ A3)) => ((! [Z2:(list @ A)]: ((A3 != (((cons @ A) @ E) @ Z2)))) => (~ ((! [Z1:A,Z2:(list @ A)]: (((A3 = (((cons @ A) @ Z1) @ Z2)) => (~ ((((member2 @ A) @ E) @ ((set2 @ A) @ Z2)))))))))))))).
% 3.20/1.77 thf(fact_174_set__ConsD, axiom, (! [A:$tType,Y:A,X3:A,Xs:(list @ A)]: (((((member2 @ A) @ Y) @ ((set2 @ A) @ (((cons @ A) @ X3) @ Xs))) => ((Y = X3) | (((member2 @ A) @ Y) @ ((set2 @ A) @ Xs))))))).
% 3.20/1.77 thf(fact_175_list_Oset__intros_I1_J, axiom, (! [A:$tType,A1:A,A2:(list @ A)]: ((((member2 @ A) @ A1) @ ((set2 @ A) @ (((cons @ A) @ A1) @ A2)))))).
% 3.20/1.77 thf(fact_176_list_Oset__intros_I2_J, axiom, (! [A:$tType,X3:A,A2:(list @ A),A1:A]: (((((member2 @ A) @ X3) @ ((set2 @ A) @ A2)) => (((member2 @ A) @ X3) @ ((set2 @ A) @ (((cons @ A) @ A1) @ A2))))))).
% 3.20/1.77 thf(fact_177_set__subset__Cons, axiom, (! [A:$tType,Xs:(list @ A),X3:A]: ((((ord_less_eq @ (set @ A)) @ ((set2 @ A) @ Xs)) @ ((set2 @ A) @ (((cons @ A) @ X3) @ Xs)))))).
% 3.20/1.77 thf(fact_178_list_Oset__sel_I2_J, axiom, (! [A:$tType,A3:(list @ A),X3:A]: (((A3 != (nil @ A)) => ((((member2 @ A) @ X3) @ ((set2 @ A) @ ((tl @ A) @ A3))) => (((member2 @ A) @ X3) @ ((set2 @ A) @ A3))))))).
% 3.20/1.77 thf(fact_179_fold__Cons, axiom, (! [B:$tType,A:$tType,F2:(A > (B > B)),X3:A,Xs:(list @ A)]: ((((((fold @ A) @ B) @ F2) @ (((cons @ A) @ X3) @ Xs)) = (((((comp @ B) @ B) @ B) @ ((((fold @ A) @ B) @ F2) @ Xs)) @ (F2 @ X3)))))).
% 3.20/1.77 thf(fact_180_foldr__Cons, axiom, (! [B:$tType,A:$tType,F2:(A > (B > B)),X3:A,Xs:(list @ A)]: ((((((foldr @ A) @ B) @ F2) @ (((cons @ A) @ X3) @ Xs)) = (((((comp @ B) @ B) @ B) @ (F2 @ X3)) @ ((((foldr @ A) @ B) @ F2) @ Xs)))))).
% 3.20/1.77 thf(fact_181_shift_Osimps_I2_J, axiom, (! [A:$tType,X3:A,Xs:(list @ A),S2:(stream @ A)]: (((((shift @ A) @ (((cons @ A) @ X3) @ Xs)) @ S2) = (((sCons @ A) @ X3) @ (((shift @ A) @ Xs) @ S2)))))).
% 3.20/1.77 thf(fact_182_List_Oinsert__def, axiom, (! [A:$tType]: (((insert @ A) = (^ [X5:A,Xs2:(list @ A)]: (((((if @ (list @ A)) @ (((member2 @ A) @ X5) @ ((set2 @ A) @ Xs2))) @ Xs2) @ (((cons @ A) @ X5) @ Xs2)))))))).
% 3.20/1.77 thf(fact_183_the__elem__set, axiom, (! [A:$tType,X3:A]: ((((the_elem @ A) @ ((set2 @ A) @ (((cons @ A) @ X3) @ (nil @ A)))) = X3)))).
% 3.20/1.77 thf(fact_184_cycle__rotated, axiom, (! [A:$tType,V:(list @ A),U:(list @ A),S2:(stream @ A)]: (((V != (nil @ A)) => ((((cycle @ A) @ U) = (((shift @ A) @ V) @ S2)) => (((cycle @ A) @ (((append @ A) @ ((tl @ A) @ U)) @ (((cons @ A) @ ((hd @ A) @ U)) @ (nil @ A)))) = (((shift @ A) @ ((tl @ A) @ V)) @ S2))))))).
% 3.20/1.77 thf(fact_185_cycle_Ocode, axiom, (! [A:$tType]: (((cycle @ A) = (^ [Xs2:(list @ A)]: ((((sCons @ A) @ ((hd @ A) @ Xs2)) @ ((cycle @ A) @ (((append @ A) @ ((tl @ A) @ Xs2)) @ (((cons @ A) @ ((hd @ A) @ Xs2)) @ (nil @ A))))))))))).
% 3.20/1.77 thf(fact_186_shift__append, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A),S2:(stream @ A)]: (((((shift @ A) @ (((append @ A) @ Xs) @ Ys)) @ S2) = (((shift @ A) @ Xs) @ (((shift @ A) @ Ys) @ S2)))))).
% 3.20/1.77 thf(fact_187_set__append, axiom, (! [A:$tType,Xs:(list @ A),Ys:(list @ A)]: ((((set2 @ A) @ (((append @ A) @ Xs) @ Ys)) = (((sup_sup @ (set @ A)) @ ((set2 @ A) @ Xs)) @ ((set2 @ A) @ Ys)))))).
% 3.20/1.77 thf(fact_188_fold__append, axiom, (! [A:$tType,B:$tType,F2:(B > (A > A)),Xs:(list @ B),Ys:(list @ B)]: ((((((fold @ B) @ A) @ F2) @ (((append @ B) @ Xs) @ Ys)) = (((((comp @ A) @ A) @ A) @ ((((fold @ B) @ A) @ F2) @ Ys)) @ ((((fold @ B) @ A) @ F2) @ Xs)))))).
% 3.20/1.77 thf(fact_189_split__list, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: (((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs))))))))).
% 3.20/1.77 thf(fact_190_split__list__last, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: (((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs))) & (~ ((((member2 @ A) @ X3) @ ((set2 @ A) @ Zs))))))))))).
% 3.20/1.77 thf(fact_191_split__list__prop, axiom, (! [A:$tType,Xs:(list @ A),P2:(A > $o)]: (((? [X4:A]: (((((member2 @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P2 @ X4)))) => (? [Ys2:(list @ A),X:A]: (((? [Zs:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs))))) & (P2 @ X)))))))).
% 3.20/1.77 thf(fact_192_split__list__first, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: (((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs)) => (? [Ys2:(list @ A),Zs:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X3) @ Zs))) & (~ ((((member2 @ A) @ X3) @ ((set2 @ A) @ Ys2))))))))))).
% 3.20/1.77 thf(fact_193_split__list__propE, axiom, (! [A:$tType,Xs:(list @ A),P2:(A > $o)]: (((? [X4:A]: (((((member2 @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P2 @ X4)))) => (~ ((! [Ys2:(list @ A),X:A]: (((? [Zs:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs))))) => (~ ((P2 @ X)))))))))))).
% 3.20/1.77 thf(fact_194_in__set__conv__decomp, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: (((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X3) @ Zs2))))))))).
% 3.20/1.77 thf(fact_195_split__list__last__prop, axiom, (! [A:$tType,Xs:(list @ A),P2:(A > $o)]: (((? [X4:A]: (((((member2 @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P2 @ X4)))) => (? [Ys2:(list @ A),X:A,Zs:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs))) & ((P2 @ X) & (! [Xa3:A]: (((((member2 @ A) @ Xa3) @ ((set2 @ A) @ Zs)) => (~ ((P2 @ Xa3)))))))))))))).
% 3.20/1.77 thf(fact_196_split__list__first__prop, axiom, (! [A:$tType,Xs:(list @ A),P2:(A > $o)]: (((? [X4:A]: (((((member2 @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P2 @ X4)))) => (? [Ys2:(list @ A),X:A]: (((? [Zs:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs))))) & ((P2 @ X) & (! [Xa3:A]: (((((member2 @ A) @ Xa3) @ ((set2 @ A) @ Ys2)) => (~ ((P2 @ Xa3)))))))))))))).
% 3.20/1.77 thf(fact_197_split__list__last__propE, axiom, (! [A:$tType,Xs:(list @ A),P2:(A > $o)]: (((? [X4:A]: (((((member2 @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P2 @ X4)))) => (~ ((! [Ys2:(list @ A),X:A,Zs:(list @ A)]: (((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs))) => ((P2 @ X) => (~ ((! [Xa3:A]: (((((member2 @ A) @ Xa3) @ ((set2 @ A) @ Zs)) => (~ ((P2 @ Xa3)))))))))))))))))).
% 3.20/1.77 thf(fact_198_split__list__first__propE, axiom, (! [A:$tType,Xs:(list @ A),P2:(A > $o)]: (((? [X4:A]: (((((member2 @ A) @ X4) @ ((set2 @ A) @ Xs)) & (P2 @ X4)))) => (~ ((! [Ys2:(list @ A),X:A]: (((? [Zs:(list @ A)]: ((Xs = (((append @ A) @ Ys2) @ (((cons @ A) @ X) @ Zs))))) => ((P2 @ X) => (~ ((! [Xa3:A]: (((((member2 @ A) @ Xa3) @ ((set2 @ A) @ Ys2)) => (~ ((P2 @ Xa3)))))))))))))))))).
% 3.20/1.77 thf(fact_199_in__set__conv__decomp__last, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: (((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X3) @ Zs2))) & (~ ((((member2 @ A) @ X3) @ ((set2 @ A) @ Zs2))))))))))).
% 3.20/1.77 thf(fact_200_in__set__conv__decomp__first, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: (((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs)) = (? [Ys3:(list @ A),Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X3) @ Zs2))) & (~ ((((member2 @ A) @ X3) @ ((set2 @ A) @ Ys3))))))))))).
% 3.20/1.77 thf(fact_201_split__list__last__prop__iff, axiom, (! [A:$tType,Xs:(list @ A),P2:(A > $o)]: (((? [X5:A]: (((((member2 @ A) @ X5) @ ((set2 @ A) @ Xs)) & (P2 @ X5)))) = (? [Ys3:(list @ A),X5:A,Zs2:(list @ A)]: (((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X5) @ Zs2))) & ((P2 @ X5) & (! [Y4:A]: (((((member2 @ A) @ Y4) @ ((set2 @ A) @ Zs2)) => (~ ((P2 @ Y4)))))))))))))).
% 3.20/1.77 thf(fact_202_split__list__first__prop__iff, axiom, (! [A:$tType,Xs:(list @ A),P2:(A > $o)]: (((? [X5:A]: (((((member2 @ A) @ X5) @ ((set2 @ A) @ Xs)) & (P2 @ X5)))) = (? [Ys3:(list @ A),X5:A]: (((? [Zs2:(list @ A)]: ((Xs = (((append @ A) @ Ys3) @ (((cons @ A) @ X5) @ Zs2))))) & ((P2 @ X5) & (! [Y4:A]: (((((member2 @ A) @ Y4) @ ((set2 @ A) @ Ys3)) => (~ ((P2 @ Y4)))))))))))))).
% 3.20/1.77 thf(fact_203_remove1__append, axiom, (! [A:$tType,X3:A,Xs:(list @ A),Ys:(list @ A)]: ((((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs)) => ((((remove1 @ A) @ X3) @ (((append @ A) @ Xs) @ Ys)) = (((append @ A) @ (((remove1 @ A) @ X3) @ Xs)) @ Ys))) & ((~ ((((member2 @ A) @ X3) @ ((set2 @ A) @ Xs)))) => ((((remove1 @ A) @ X3) @ (((append @ A) @ Xs) @ Ys)) = (((append @ A) @ Xs) @ (((remove1 @ A) @ X3) @ Ys)))))))).
% 3.20/1.77 thf(fact_204_cycle__Cons, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: ((((cycle @ A) @ (((cons @ A) @ X3) @ Xs)) = (((sCons @ A) @ X3) @ ((cycle @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X3) @ (nil @ A))))))))).
% 3.20/1.77 thf(fact_205_cycle_Osimps_I2_J, axiom, (! [A:$tType,Xs:(list @ A)]: ((((stl @ A) @ ((cycle @ A) @ Xs)) = ((cycle @ A) @ (((append @ A) @ ((tl @ A) @ Xs)) @ (((cons @ A) @ ((hd @ A) @ Xs)) @ (nil @ A)))))))).
% 3.20/1.77 thf(fact_206_Sup__fin_Oset__eq__fold, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X3:A,Xs:(list @ A)]: ((((lattic477160up_fin @ A) @ ((set2 @ A) @ (((cons @ A) @ X3) @ Xs))) = (((((fold @ A) @ A) @ (sup_sup @ A)) @ Xs) @ X3)))))))).
% 3.20/1.77 thf(fact_207_sorted_Ocases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [A3:(list @ A)]: ((((linorder_sorted @ A) @ A3) => ((A3 != (nil @ A)) => (~ ((! [Xs3:(list @ A),X:A]: (((A3 = (((cons @ A) @ X) @ Xs3)) => ((! [Xa3:A]: (((((member2 @ A) @ Xa3) @ ((set2 @ A) @ Xs3)) => (((ord_less_eq @ A) @ X) @ Xa3)))) => (~ (((linorder_sorted @ A) @ Xs3))))))))))))))))).
% 3.20/1.77 thf(fact_208_sorted_Osimps, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((linorder_sorted @ A) = (^ [A4:(list @ A)]: (((A4 = (nil @ A)) | (? [Xs2:(list @ A),X5:A]: (((A4 = (((cons @ A) @ X5) @ Xs2)) & ((! [Y4:A]: (((((member2 @ A) @ Y4) @ ((set2 @ A) @ Xs2)) => (((ord_less_eq @ A) @ X5) @ Y4)))) & ((linorder_sorted @ A) @ Xs2))))))))))))).
% 3.20/1.77 thf(fact_209_sorted_OCons, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Xs:(list @ A),X3:A]: (((! [X:A]: (((((member2 @ A) @ X) @ ((set2 @ A) @ Xs)) => (((ord_less_eq @ A) @ X3) @ X)))) => (((linorder_sorted @ A) @ Xs) => ((linorder_sorted @ A) @ (((cons @ A) @ X3) @ Xs)))))))))).
% 3.20/1.77 thf(fact_210_sorted__Cons, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:A,Xs:(list @ A)]: ((((linorder_sorted @ A) @ (((cons @ A) @ X3) @ Xs)) = (((linorder_sorted @ A) @ Xs) & (! [X5:A]: (((((member2 @ A) @ X5) @ ((set2 @ A) @ Xs)) => (((ord_less_eq @ A) @ X3) @ X5)))))))))))).
% 3.20/1.77 thf(fact_211_sorted__append, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Xs:(list @ A),Ys:(list @ A)]: ((((linorder_sorted @ A) @ (((append @ A) @ Xs) @ Ys)) = (((linorder_sorted @ A) @ Xs) & (((linorder_sorted @ A) @ Ys) & (! [X5:A]: (((((member2 @ A) @ X5) @ ((set2 @ A) @ Xs)) => (! [Y4:A]: (((((member2 @ A) @ Y4) @ ((set2 @ A) @ Ys)) => (((ord_less_eq @ A) @ X5) @ Y4)))))))))))))))).
% 3.20/1.77 thf(fact_212_sorted_Oinducts, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X3:(list @ A),P2:((list @ A) > $o)]: ((((linorder_sorted @ A) @ X3) => ((P2 @ (nil @ A)) => ((! [Xs3:(list @ A),X:A]: (((! [Xa3:A]: (((((member2 @ A) @ Xa3) @ ((set2 @ A) @ Xs3)) => (((ord_less_eq @ A) @ X) @ Xa3)))) => (((linorder_sorted @ A) @ Xs3) => ((P2 @ Xs3) => (P2 @ (((cons @ A) @ X) @ Xs3))))))) => (P2 @ X3)))))))))).
% 3.20/1.77 thf(fact_213_insort__is__Cons, axiom, (! [A:$tType,B:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Xs:(list @ B),F2:(B > A),A3:B]: (((! [X:B]: (((((member2 @ B) @ X) @ ((set2 @ B) @ Xs)) => (((ord_less_eq @ A) @ (F2 @ A3)) @ (F2 @ X))))) => ((((((linorder_insort_key @ B) @ A) @ F2) @ A3) @ Xs) = (((cons @ B) @ A3) @ Xs))))))))).
% 3.20/1.77 thf(fact_214_fold__rev, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),F2:(A > (B > B))]: (((! [X:A,Y3:A]: (((((member2 @ A) @ X) @ ((set2 @ A) @ Xs)) => ((((member2 @ A) @ Y3) @ ((set2 @ A) @ Xs)) => ((((((comp @ B) @ B) @ B) @ (F2 @ Y3)) @ (F2 @ X)) = (((((comp @ B) @ B) @ B) @ (F2 @ X)) @ (F2 @ Y3))))))) => (((((fold @ A) @ B) @ F2) @ ((rev @ A) @ Xs)) = ((((fold @ A) @ B) @ F2) @ Xs)))))).
% 3.20/1.77 thf(fact_215_set__rev, axiom, (! [A:$tType,Xs:(list @ A)]: ((((set2 @ A) @ ((rev @ A) @ Xs)) = ((set2 @ A) @ Xs))))).
% 3.20/1.77 thf(fact_216_set__insort__key, axiom, (! [A:$tType,B:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [F2:(B > A),X3:B,Xs:(list @ B)]: ((((set2 @ B) @ (((((linorder_insort_key @ B) @ A) @ F2) @ X3) @ Xs)) = (((insert2 @ B) @ X3) @ ((set2 @ B) @ Xs))))))))).
% 3.20/1.77 thf(fact_217_trev_Ocode, axiom, (! [A:$tType]: (((trev @ A) = (^ [T3:(treeFI @ A)]: ((((tree @ A) @ ((lab @ A) @ T3)) @ ((((map @ (treeFI @ A)) @ (treeFI @ A)) @ (trev @ A)) @ ((rev @ (treeFI @ A)) @ ((sub @ A) @ T3)))))))))).
% 3.20/1.77 thf(fact_218_treeFI_Opred__map, axiom, (! [B:$tType,A:$tType,Q:(B > $o),F2:(A > B),X3:(treeFI @ A)]: (((((pred_treeFI @ B) @ Q) @ ((((map_treeFI @ A) @ B) @ F2) @ X3)) = (((pred_treeFI @ A) @ (((((comp @ B) @ $o) @ A) @ Q) @ F2)) @ X3))))).
% 3.20/1.77 thf(fact_219_map__map, axiom, (! [B:$tType,A:$tType,C:$tType,F2:(B > A),G:(C > B),Xs:(list @ C)]: ((((((map @ B) @ A) @ F2) @ ((((map @ C) @ B) @ G) @ Xs)) = ((((map @ C) @ A) @ (((((comp @ B) @ A) @ C) @ F2) @ G)) @ Xs))))).
% 3.20/1.77 thf(fact_220_List_Omap_Ocomp, axiom, (! [C:$tType,B:$tType,A:$tType,F2:(B > C),G:(A > B)]: (((((((comp @ (list @ B)) @ (list @ C)) @ (list @ A)) @ (((map @ B) @ C) @ F2)) @ (((map @ A) @ B) @ G)) = (((map @ A) @ C) @ (((((comp @ B) @ C) @ A) @ F2) @ G)))))).
% 3.20/1.77 thf(fact_221_map__comp__map, axiom, (! [B:$tType,C:$tType,A:$tType,F2:(C > B),G:(A > C)]: (((((((comp @ (list @ C)) @ (list @ B)) @ (list @ A)) @ (((map @ C) @ B) @ F2)) @ (((map @ A) @ C) @ G)) = (((map @ A) @ B) @ (((((comp @ C) @ B) @ A) @ F2) @ G)))))).
% 3.20/1.77 thf(fact_222_list_Omap__comp, axiom, (! [B:$tType,C:$tType,A:$tType,G:(B > C),F2:(A > B),V:(list @ A)]: ((((((map @ B) @ C) @ G) @ ((((map @ A) @ B) @ F2) @ V)) = ((((map @ A) @ C) @ (((((comp @ B) @ C) @ A) @ G) @ F2)) @ V))))).
% 3.20/1.77 thf(fact_223_List_Omap_Ocompositionality, axiom, (! [B:$tType,C:$tType,A:$tType,F2:(B > C),G:(A > B),List:(list @ A)]: ((((((map @ B) @ C) @ F2) @ ((((map @ A) @ B) @ G) @ List)) = ((((map @ A) @ C) @ (((((comp @ B) @ C) @ A) @ F2) @ G)) @ List))))).
% 3.20/1.77 thf(fact_224_map__eq__conv, axiom, (! [A:$tType,B:$tType,F2:(B > A),Xs:(list @ B),G:(B > A)]: (((((((map @ B) @ A) @ F2) @ Xs) = ((((map @ B) @ A) @ G) @ Xs)) = (! [X5:B]: (((((member2 @ B) @ X5) @ ((set2 @ B) @ Xs)) => ((F2 @ X5) = (G @ X5))))))))).
% 3.20/1.77 thf(fact_225_smap__shift, axiom, (! [A:$tType,B:$tType,F2:(B > A),Xs:(list @ B),S2:(stream @ B)]: ((((((smap @ B) @ A) @ F2) @ (((shift @ B) @ Xs) @ S2)) = (((shift @ A) @ ((((map @ B) @ A) @ F2) @ Xs)) @ ((((smap @ B) @ A) @ F2) @ S2)))))).
% 3.20/1.77 thf(fact_226_trev_Osimps_I2_J, axiom, (! [A:$tType,T:(treeFI @ A)]: ((((sub @ A) @ ((trev @ A) @ T)) = ((((map @ (treeFI @ A)) @ (treeFI @ A)) @ (trev @ A)) @ ((rev @ (treeFI @ A)) @ ((sub @ A) @ T))))))).
% 3.20/1.77 thf(fact_227_treeFI_Omap__sel_I1_J, axiom, (! [B:$tType,A:$tType,F2:(A > B),A3:(treeFI @ A)]: ((((lab @ B) @ ((((map_treeFI @ A) @ B) @ F2) @ A3)) = (F2 @ ((lab @ A) @ A3)))))).
% 3.20/1.77 thf(fact_228_treeFI_Oinj__map__strong, axiom, (! [B:$tType,A:$tType,X3:(treeFI @ A),Xa:(treeFI @ A),F2:(A > B),Fa:(A > B)]: (((! [Z:A,Za:A]: (((((member2 @ A) @ Z) @ ((set_treeFI @ A) @ X3)) => ((((member2 @ A) @ Za) @ ((set_treeFI @ A) @ Xa)) => (((F2 @ Z) = (Fa @ Za)) => (Z = Za)))))) => ((((((map_treeFI @ A) @ B) @ F2) @ X3) = ((((map_treeFI @ A) @ B) @ Fa) @ Xa)) => (X3 = Xa)))))).
% 3.20/1.77 thf(fact_229_treeFI_Omap__cong0, axiom, (! [B:$tType,A:$tType,X3:(treeFI @ A),F2:(A > B),G:(A > B)]: (((! [Z:A]: (((((member2 @ A) @ Z) @ ((set_treeFI @ A) @ X3)) => ((F2 @ Z) = (G @ Z))))) => (((((map_treeFI @ A) @ B) @ F2) @ X3) = ((((map_treeFI @ A) @ B) @ G) @ X3)))))).
% 3.20/1.77 thf(fact_230_treeFI_Omap__cong, axiom, (! [B:$tType,A:$tType,X3:(treeFI @ A),Ya:(treeFI @ A),F2:(A > B),G:(A > B)]: (((X3 = Ya) => ((! [Z:A]: (((((member2 @ A) @ Z) @ ((set_treeFI @ A) @ Ya)) => ((F2 @ Z) = (G @ Z))))) => (((((map_treeFI @ A) @ B) @ F2) @ X3) = ((((map_treeFI @ A) @ B) @ G) @ Ya))))))).
% 3.20/1.77 thf(fact_231_treeFI_Omap__comp, axiom, (! [B:$tType,C:$tType,A:$tType,G:(B > C),F2:(A > B),V:(treeFI @ A)]: ((((((map_treeFI @ B) @ C) @ G) @ ((((map_treeFI @ A) @ B) @ F2) @ V)) = ((((map_treeFI @ A) @ C) @ (((((comp @ B) @ C) @ A) @ G) @ F2)) @ V))))).
% 3.20/1.77 thf(fact_232_treeFI_Omap, axiom, (! [B:$tType,A:$tType,F2:(A > B),X1:A,X22:(list @ (treeFI @ A))]: ((((((map_treeFI @ A) @ B) @ F2) @ (((tree @ A) @ X1) @ X22)) = (((tree @ B) @ (F2 @ X1)) @ ((((map @ (treeFI @ A)) @ (treeFI @ B)) @ (((map_treeFI @ A) @ B) @ F2)) @ X22)))))).
% 3.20/1.77 thf(fact_233_treeFI_Omap__sel_I2_J, axiom, (! [B:$tType,A:$tType,F2:(A > B),A3:(treeFI @ A)]: ((((sub @ B) @ ((((map_treeFI @ A) @ B) @ F2) @ A3)) = ((((map @ (treeFI @ A)) @ (treeFI @ B)) @ (((map_treeFI @ A) @ B) @ F2)) @ ((sub @ A) @ A3)))))).
% 3.20/1.77 thf(fact_234_list_Oinj__map__strong, axiom, (! [B:$tType,A:$tType,X3:(list @ A),Xa:(list @ A),F2:(A > B),Fa:(A > B)]: (((! [Z:A,Za:A]: (((((member2 @ A) @ Z) @ ((set2 @ A) @ X3)) => ((((member2 @ A) @ Za) @ ((set2 @ A) @ Xa)) => (((F2 @ Z) = (Fa @ Za)) => (Z = Za)))))) => ((((((map @ A) @ B) @ F2) @ X3) = ((((map @ A) @ B) @ Fa) @ Xa)) => (X3 = Xa)))))).
% 3.20/1.77 thf(fact_235_list_Omap__cong0, axiom, (! [B:$tType,A:$tType,X3:(list @ A),F2:(A > B),G:(A > B)]: (((! [Z:A]: (((((member2 @ A) @ Z) @ ((set2 @ A) @ X3)) => ((F2 @ Z) = (G @ Z))))) => (((((map @ A) @ B) @ F2) @ X3) = ((((map @ A) @ B) @ G) @ X3)))))).
% 3.20/1.77 thf(fact_236_list_Omap__cong, axiom, (! [B:$tType,A:$tType,X3:(list @ A),Ya:(list @ A),F2:(A > B),G:(A > B)]: (((X3 = Ya) => ((! [Z:A]: (((((member2 @ A) @ Z) @ ((set2 @ A) @ Ya)) => ((F2 @ Z) = (G @ Z))))) => (((((map @ A) @ B) @ F2) @ X3) = ((((map @ A) @ B) @ G) @ Ya))))))).
% 3.20/1.77 thf(fact_237_ex__map__conv, axiom, (! [A:$tType,B:$tType,Ys:(list @ B),F2:(A > B)]: (((? [Xs2:(list @ A)]: ((Ys = ((((map @ A) @ B) @ F2) @ Xs2)))) = (! [X5:B]: (((((member2 @ B) @ X5) @ ((set2 @ B) @ Ys)) => (? [Y4:A]: ((X5 = (F2 @ Y4))))))))))).
% 3.20/1.77 thf(fact_238_map__cong, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),Ys:(list @ A),F2:(A > B),G:(A > B)]: (((Xs = Ys) => ((! [X:A]: (((((member2 @ A) @ X) @ ((set2 @ A) @ Ys)) => ((F2 @ X) = (G @ X))))) => (((((map @ A) @ B) @ F2) @ Xs) = ((((map @ A) @ B) @ G) @ Ys))))))).
% 3.20/1.77 thf(fact_239_map__idI, axiom, (! [A:$tType,Xs:(list @ A),F2:(A > A)]: (((! [X:A]: (((((member2 @ A) @ X) @ ((set2 @ A) @ Xs)) => ((F2 @ X) = X)))) => (((((map @ A) @ A) @ F2) @ Xs) = Xs))))).
% 3.20/1.77 thf(fact_240_map__ext, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),F2:(A > B),G:(A > B)]: (((! [X:A]: (((((member2 @ A) @ X) @ ((set2 @ A) @ Xs)) => ((F2 @ X) = (G @ X))))) => (((((map @ A) @ B) @ F2) @ Xs) = ((((map @ A) @ B) @ G) @ Xs)))))).
% 3.20/1.77 thf(fact_241_foldr__map, axiom, (! [C:$tType,B:$tType,A:$tType,G:(B > (A > A)),F2:(C > B),Xs:(list @ C),A3:A]: (((((((foldr @ B) @ A) @ G) @ ((((map @ C) @ B) @ F2) @ Xs)) @ A3) = (((((foldr @ C) @ A) @ (((((comp @ B) @ (A > A)) @ C) @ G) @ F2)) @ Xs) @ A3))))).
% 3.20/1.77 thf(fact_242_fold__map, axiom, (! [B:$tType,A:$tType,C:$tType,G:(B > (A > A)),F2:(C > B),Xs:(list @ C)]: ((((((fold @ B) @ A) @ G) @ ((((map @ C) @ B) @ F2) @ Xs)) = ((((fold @ C) @ A) @ (((((comp @ B) @ (A > A)) @ C) @ G) @ F2)) @ Xs))))).
% 3.20/1.77 thf(fact_243_list_Opred__map, axiom, (! [B:$tType,A:$tType,Q:(B > $o),F2:(A > B),X3:(list @ A)]: (((((list_all @ B) @ Q) @ ((((map @ A) @ B) @ F2) @ X3)) = (((list_all @ A) @ (((((comp @ B) @ $o) @ A) @ Q) @ F2)) @ X3))))).
% 3.20/1.77 thf(fact_244_stake__smap, axiom, (! [A:$tType,B:$tType,N2:nat,F2:(B > A),S2:(stream @ B)]: (((((stake @ A) @ N2) @ ((((smap @ B) @ A) @ F2) @ S2)) = ((((map @ B) @ A) @ F2) @ (((stake @ B) @ N2) @ S2)))))).
% 3.20/1.77 thf(fact_245_map__fun__upd, axiom, (! [B:$tType,A:$tType,Y:A,Xs:(list @ A),F2:(A > B),V:B]: (((~ ((((member2 @ A) @ Y) @ ((set2 @ A) @ Xs)))) => (((((map @ A) @ B) @ (((((fun_upd @ A) @ B) @ F2) @ Y) @ V)) @ Xs) = ((((map @ A) @ B) @ F2) @ Xs)))))).
% 3.20/1.77 thf(fact_246_fun__upd__apply, axiom, (! [A:$tType,B:$tType]: ((((fun_upd @ B) @ A) = (^ [F:(B > A),X5:B,Y4:A,Z3:B]: (((((if @ A) @ (Z3 = X5)) @ Y4) @ (F @ Z3)))))))).
% 3.20/1.77 thf(fact_247_fun__upd__triv, axiom, (! [B:$tType,A:$tType,F2:(A > B),X3:A]: (((((((fun_upd @ A) @ B) @ F2) @ X3) @ (F2 @ X3)) = F2)))).
% 3.20/1.77 thf(fact_248_fun__upd__upd, axiom, (! [A:$tType,B:$tType,F2:(A > B),X3:A,Y:B,Z4:B]: (((((((fun_upd @ A) @ B) @ (((((fun_upd @ A) @ B) @ F2) @ X3) @ Y)) @ X3) @ Z4) = (((((fun_upd @ A) @ B) @ F2) @ X3) @ Z4))))).
% 3.20/1.77 thf(fact_249_fun__upd__comp, axiom, (! [A:$tType,B:$tType,C:$tType,F2:(C > B),G:(A > C),X3:A,Y:C]: (((((((comp @ C) @ B) @ A) @ F2) @ (((((fun_upd @ A) @ C) @ G) @ X3) @ Y)) = (((((fun_upd @ A) @ B) @ (((((comp @ C) @ B) @ A) @ F2) @ G)) @ X3) @ (F2 @ Y)))))).
% 3.20/1.77 thf(fact_250_fun__upd__idem__iff, axiom, (! [A:$tType,B:$tType,F2:(A > B),X3:A,Y:B]: ((((((((fun_upd @ A) @ B) @ F2) @ X3) @ Y) = F2) = ((F2 @ X3) = Y))))).
% 3.20/1.77 thf(fact_251_fun__upd__twist, axiom, (! [A:$tType,B:$tType,A3:A,C2:A,M2:(A > B),B3:B,D2:B]: (((A3 != C2) => ((((((fun_upd @ A) @ B) @ (((((fun_upd @ A) @ B) @ M2) @ A3) @ B3)) @ C2) @ D2) = (((((fun_upd @ A) @ B) @ (((((fun_upd @ A) @ B) @ M2) @ C2) @ D2)) @ A3) @ B3)))))).
% 3.20/1.77 thf(fact_252_fun__upd__other, axiom, (! [B:$tType,A:$tType,Z4:A,X3:A,F2:(A > B),Y:B]: (((Z4 != X3) => (((((((fun_upd @ A) @ B) @ F2) @ X3) @ Y) @ Z4) = (F2 @ Z4)))))).
% 3.20/1.77 thf(fact_253_fun__upd__same, axiom, (! [B:$tType,A:$tType,F2:(B > A),X3:B,Y:A]: ((((((((fun_upd @ B) @ A) @ F2) @ X3) @ Y) @ X3) = Y)))).
% 3.20/1.77 thf(fact_254_fun__upd__idem, axiom, (! [A:$tType,B:$tType,F2:(B > A),X3:B,Y:A]: ((((F2 @ X3) = Y) => ((((((fun_upd @ B) @ A) @ F2) @ X3) @ Y) = F2))))).
% 3.20/1.77 thf(fact_255_fun__upd__eqD, axiom, (! [A:$tType,B:$tType,F2:(A > B),X3:A,Y:B,G:(A > B),Z4:B]: ((((((((fun_upd @ A) @ B) @ F2) @ X3) @ Y) = (((((fun_upd @ A) @ B) @ G) @ X3) @ Z4)) => (Y = Z4))))).
% 3.20/1.77 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A8:$tType,A9:$tType]: ((((semilattice_sup @ A9) @ (type2 @ A9)) => ((semilattice_sup @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 3.20/1.77 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_1, axiom, (! [A8:$tType]: (((semilattice_sup @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 3.20/1.77 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_2, axiom, ((semilattice_sup @ $o) @ (type2 @ $o))).
% 3.20/1.77 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 3.20/1.77 thf(help_If_3_1_T, axiom, (! [P2:$o]: (((P2 = $true) | (P2 = $false))))).
% 3.20/1.77 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $false) @ X3) @ Y) = Y)))).
% 3.20/1.77 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $true) @ X3) @ Y) = X3)))).
% 3.20/1.77 thf(conj_0, conjecture, (((koenig1755522246erPath @ a) @ as) @ tr)).
% 3.20/1.77 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.BDekGnPrVg/DTF2DTF27722.p
% 3.20/1.77 ------------------------
% 3.39/1.83 ---- Cleaned THF ---
% 3.39/1.83 thf(ty_t_TreeFI_OtreeFI,type,
% 3.39/1.83 treeFI: $tType > $tType ).
% 3.39/1.83
% 3.39/1.83 thf(ty_t_Stream_Ostream,type,
% 3.39/1.83 stream: $tType > $tType ).
% 3.39/1.83
% 3.39/1.83 thf(ty_t_List_Olist,type,
% 3.39/1.83 list: $tType > $tType ).
% 3.39/1.83
% 3.39/1.83 thf(ty_t_Set_Oset,type,
% 3.39/1.83 set: $tType > $tType ).
% 3.39/1.83
% 3.39/1.83 thf(ty_t_Nat_Onat,type,
% 3.39/1.83 nat: $tType ).
% 3.39/1.83
% 3.39/1.83 thf(ty_t_itself,type,
% 3.39/1.83 itself: $tType > $tType ).
% 3.39/1.83
% 3.39/1.83 thf(ty_tf_a,type,
% 3.39/1.83 a: $tType ).
% 3.39/1.83
% 3.39/1.83 thf(sy_cl_HOL_Otype,type,
% 3.39/1.83 type:
% 3.39/1.83 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_cl_Orderings_Olinorder,type,
% 3.39/1.83 linorder:
% 3.39/1.83 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 3.39/1.83 semilattice_sup:
% 3.39/1.83 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Fun_Ocomp,type,
% 3.39/1.83 comp:
% 3.39/1.83 !>[B: $tType,C: $tType,A: $tType] : ( ( B > C ) > ( A > B ) > A > C ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Fun_Ofun__upd,type,
% 3.39/1.83 fun_upd:
% 3.39/1.83 !>[A: $tType,B: $tType] : ( ( A > B ) > A > B > A > B ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_If,type,
% 3.39/1.83 if:
% 3.39/1.83 !>[A: $tType] : ( $o > A > A > A ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Koenig__Mirabelle__gyfieiccqy_OinfiniteTr,type,
% 3.39/1.83 koenig488553731niteTr:
% 3.39/1.83 !>[A: $tType] : ( ( treeFI @ A ) > $o ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Koenig__Mirabelle__gyfieiccqy_OkonigPath,type,
% 3.39/1.83 koenig1103336060igPath:
% 3.39/1.83 !>[A: $tType] : ( ( treeFI @ A ) > ( stream @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Koenig__Mirabelle__gyfieiccqy_OproperPath,type,
% 3.39/1.83 koenig1755522246erPath:
% 3.39/1.83 !>[A: $tType] : ( ( stream @ A ) > ( treeFI @ A ) > $o ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Lattices_Osup__class_Osup,type,
% 3.39/1.83 sup_sup:
% 3.39/1.83 !>[A: $tType] : ( A > A > A ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Lattices__Big_Osemilattice__sup__class_OSup__fin,type,
% 3.39/1.83 lattic477160up_fin:
% 3.39/1.83 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Oappend,type,
% 3.39/1.83 append:
% 3.39/1.83 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Ocoset,type,
% 3.39/1.83 coset:
% 3.39/1.83 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Ofold,type,
% 3.39/1.83 fold:
% 3.39/1.83 !>[A: $tType,B: $tType] : ( ( A > B > B ) > ( list @ A ) > B > B ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Ofoldr,type,
% 3.39/1.83 foldr:
% 3.39/1.83 !>[A: $tType,B: $tType] : ( ( A > B > B ) > ( list @ A ) > B > B ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Oinsert,type,
% 3.39/1.83 insert:
% 3.39/1.83 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Olinorder__class_Oinsort__key,type,
% 3.39/1.83 linorder_insort_key:
% 3.39/1.83 !>[B: $tType,A: $tType] : ( ( B > A ) > B > ( list @ B ) > ( list @ B ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Olinorder__class_Osorted,type,
% 3.39/1.83 linorder_sorted:
% 3.39/1.83 !>[A: $tType] : ( ( list @ A ) > $o ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Olist_OCons,type,
% 3.39/1.83 cons:
% 3.39/1.83 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Olist_ONil,type,
% 3.39/1.83 nil:
% 3.39/1.83 !>[A: $tType] : ( list @ A ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Olist_Ohd,type,
% 3.39/1.83 hd:
% 3.39/1.83 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Olist_Olist__all,type,
% 3.39/1.83 list_all:
% 3.39/1.83 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Olist_Omap,type,
% 3.39/1.83 map:
% 3.39/1.83 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( list @ A ) > ( list @ Aa ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Olist_Oset,type,
% 3.39/1.83 set2:
% 3.39/1.83 !>[A: $tType] : ( ( list @ A ) > ( set @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Olist_Otl,type,
% 3.39/1.83 tl:
% 3.39/1.83 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Olist__update,type,
% 3.39/1.83 list_update:
% 3.39/1.83 !>[A: $tType] : ( ( list @ A ) > nat > A > ( list @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Omember,type,
% 3.39/1.83 member:
% 3.39/1.83 !>[A: $tType] : ( ( list @ A ) > A > $o ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Oremove1,type,
% 3.39/1.83 remove1:
% 3.39/1.83 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Orev,type,
% 3.39/1.83 rev:
% 3.39/1.83 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_List_Ounion,type,
% 3.39/1.83 union:
% 3.39/1.83 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 3.39/1.83 ord_less_eq:
% 3.39/1.83 !>[A: $tType] : ( A > A > $o ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Pure_Otype,type,
% 3.39/1.83 type2:
% 3.39/1.83 !>[A: $tType] : ( itself @ A ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Set_OCollect,type,
% 3.39/1.83 collect:
% 3.39/1.83 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Set_Oinsert,type,
% 3.39/1.83 insert2:
% 3.39/1.83 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Set_Othe__elem,type,
% 3.39/1.83 the_elem:
% 3.39/1.83 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Ocycle,type,
% 3.39/1.83 cycle:
% 3.39/1.83 !>[A: $tType] : ( ( list @ A ) > ( stream @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Oflat,type,
% 3.39/1.83 flat:
% 3.39/1.83 !>[A: $tType] : ( ( stream @ ( list @ A ) ) > ( stream @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Osdrop__while,type,
% 3.39/1.83 sdrop_while:
% 3.39/1.83 !>[A: $tType] : ( ( A > $o ) > ( stream @ A ) > ( stream @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Osfilter,type,
% 3.39/1.83 sfilter:
% 3.39/1.83 !>[A: $tType] : ( ( A > $o ) > ( stream @ A ) > ( stream @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Oshift,type,
% 3.39/1.83 shift:
% 3.39/1.83 !>[A: $tType] : ( ( list @ A ) > ( stream @ A ) > ( stream @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Osinterleave,type,
% 3.39/1.83 sinterleave:
% 3.39/1.83 !>[A: $tType] : ( ( stream @ A ) > ( stream @ A ) > ( stream @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Osmap2,type,
% 3.39/1.83 smap2:
% 3.39/1.83 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( stream @ A ) > ( stream @ B ) > ( stream @ C ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Osmember,type,
% 3.39/1.83 smember:
% 3.39/1.83 !>[A: $tType] : ( A > ( stream @ A ) > $o ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Ostake,type,
% 3.39/1.83 stake:
% 3.39/1.83 !>[A: $tType] : ( nat > ( stream @ A ) > ( list @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Ostream_OSCons,type,
% 3.39/1.83 sCons:
% 3.39/1.83 !>[A: $tType] : ( A > ( stream @ A ) > ( stream @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Ostream_Ocase__stream,type,
% 3.39/1.83 case_stream:
% 3.39/1.83 !>[A: $tType,B: $tType] : ( ( A > ( stream @ A ) > B ) > ( stream @ A ) > B ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Ostream_Ocorec__stream,type,
% 3.39/1.83 corec_stream:
% 3.39/1.83 !>[C: $tType,A: $tType] : ( ( C > A ) > ( C > $o ) > ( C > ( stream @ A ) ) > ( C > C ) > C > ( stream @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Ostream_Opred__stream,type,
% 3.39/1.83 pred_stream:
% 3.39/1.83 !>[A: $tType] : ( ( A > $o ) > ( stream @ A ) > $o ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Ostream_Oshd,type,
% 3.39/1.83 shd:
% 3.39/1.83 !>[A: $tType] : ( ( stream @ A ) > A ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Ostream_Osmap,type,
% 3.39/1.83 smap:
% 3.39/1.83 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( stream @ A ) > ( stream @ Aa ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Ostream_Osset,type,
% 3.39/1.83 sset:
% 3.39/1.83 !>[A: $tType] : ( ( stream @ A ) > ( set @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Ostream_Ostl,type,
% 3.39/1.83 stl:
% 3.39/1.83 !>[A: $tType] : ( ( stream @ A ) > ( stream @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Ostream__all,type,
% 3.39/1.83 stream_all:
% 3.39/1.83 !>[A: $tType] : ( ( A > $o ) > ( stream @ A ) > $o ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_Stream_Ostreams,type,
% 3.39/1.83 streams:
% 3.39/1.83 !>[A: $tType] : ( ( set @ A ) > ( set @ ( stream @ A ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_TreeFI_OtreeFI_OTree,type,
% 3.39/1.83 tree:
% 3.39/1.83 !>[A: $tType] : ( A > ( list @ ( treeFI @ A ) ) > ( treeFI @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_TreeFI_OtreeFI_Ocase__treeFI,type,
% 3.39/1.83 case_treeFI:
% 3.39/1.83 !>[A: $tType,B: $tType] : ( ( A > ( list @ ( treeFI @ A ) ) > B ) > ( treeFI @ A ) > B ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_TreeFI_OtreeFI_Olab,type,
% 3.39/1.83 lab:
% 3.39/1.83 !>[A: $tType] : ( ( treeFI @ A ) > A ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_TreeFI_OtreeFI_Omap__treeFI,type,
% 3.39/1.83 map_treeFI:
% 3.39/1.83 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( treeFI @ A ) > ( treeFI @ Aa ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_TreeFI_OtreeFI_Opred__treeFI,type,
% 3.39/1.83 pred_treeFI:
% 3.39/1.83 !>[A: $tType] : ( ( A > $o ) > ( treeFI @ A ) > $o ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_TreeFI_OtreeFI_Oset__treeFI,type,
% 3.39/1.83 set_treeFI:
% 3.39/1.83 !>[A: $tType] : ( ( treeFI @ A ) > ( set @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_TreeFI_OtreeFI_Osub,type,
% 3.39/1.83 sub:
% 3.39/1.83 !>[A: $tType] : ( ( treeFI @ A ) > ( list @ ( treeFI @ A ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_TreeFI_Otrev,type,
% 3.39/1.83 trev:
% 3.39/1.83 !>[A: $tType] : ( ( treeFI @ A ) > ( treeFI @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_c_member,type,
% 3.39/1.83 member2:
% 3.39/1.83 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.39/1.83
% 3.39/1.83 thf(sy_v_as,type,
% 3.39/1.83 as: stream @ a ).
% 3.39/1.83
% 3.39/1.83 thf(sy_v_phi,type,
% 3.39/1.83 phi: ( stream @ a ) > ( treeFI @ a ) > $o ).
% 3.39/1.83
% 3.39/1.83 thf(sy_v_tr,type,
% 3.39/1.83 tr: treeFI @ a ).
% 3.39/1.83
% 3.39/1.83 thf(fact_0__C_K_K_K_C,axiom,
% 3.39/1.83 ! [As: stream @ a,Tr: treeFI @ a] :
% 3.39/1.83 ( ( phi @ As @ Tr )
% 3.39/1.83 => ? [X: treeFI @ a] :
% 3.39/1.83 ( ( member2 @ ( treeFI @ a ) @ X @ ( set2 @ ( treeFI @ a ) @ ( sub @ a @ Tr ) ) )
% 3.39/1.83 & ( ( phi @ ( stl @ a @ As ) @ X )
% 3.39/1.83 | ( koenig1755522246erPath @ a @ ( stl @ a @ As ) @ X ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_1__C_K_C,axiom,
% 3.39/1.83 phi @ as @ tr ).
% 3.39/1.83
% 3.39/1.83 thf(fact_2_properPath_Ocases,axiom,
% 3.39/1.83 ! [A: $tType,A1: stream @ A,A2: treeFI @ A] :
% 3.39/1.83 ( ( koenig1755522246erPath @ A @ A1 @ A2 )
% 3.39/1.83 => ~ ( ( ( shd @ A @ A1 )
% 3.39/1.83 = ( lab @ A @ A2 ) )
% 3.39/1.83 => ! [Tr2: treeFI @ A] :
% 3.39/1.83 ( ( member2 @ ( treeFI @ A ) @ Tr2 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ A2 ) ) )
% 3.39/1.83 => ~ ( koenig1755522246erPath @ A @ ( stl @ A @ A1 ) @ Tr2 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_3_properPath_Osimps,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( koenig1755522246erPath @ A )
% 3.39/1.83 = ( ^ [A12: stream @ A,A22: treeFI @ A] :
% 3.39/1.83 ? [As2: stream @ A,Tr3: treeFI @ A,Tr4: treeFI @ A] :
% 3.39/1.83 ( ( A12 = As2 )
% 3.39/1.83 & ( A22 = Tr3 )
% 3.39/1.83 & ( ( shd @ A @ As2 )
% 3.39/1.83 = ( lab @ A @ Tr3 ) )
% 3.39/1.83 & ( member2 @ ( treeFI @ A ) @ Tr4 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr3 ) ) )
% 3.39/1.83 & ( koenig1755522246erPath @ A @ ( stl @ A @ As2 ) @ Tr4 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_4_properPath_Ointros,axiom,
% 3.39/1.83 ! [A: $tType,As: stream @ A,Tr: treeFI @ A,Tr5: treeFI @ A] :
% 3.39/1.83 ( ( ( shd @ A @ As )
% 3.39/1.83 = ( lab @ A @ Tr ) )
% 3.39/1.83 => ( ( member2 @ ( treeFI @ A ) @ Tr5 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr ) ) )
% 3.39/1.83 => ( ( koenig1755522246erPath @ A @ ( stl @ A @ As ) @ Tr5 )
% 3.39/1.83 => ( koenig1755522246erPath @ A @ As @ Tr ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_5_properPath_Ocoinduct,axiom,
% 3.39/1.83 ! [A: $tType,X2: ( stream @ A ) > ( treeFI @ A ) > $o,X3: stream @ A,Xa: treeFI @ A] :
% 3.39/1.83 ( ( X2 @ X3 @ Xa )
% 3.39/1.83 => ( ! [X: stream @ A,Xa2: treeFI @ A] :
% 3.39/1.83 ( ( X2 @ X @ Xa2 )
% 3.39/1.83 => ? [As3: stream @ A,Tr6: treeFI @ A,Tr7: treeFI @ A] :
% 3.39/1.83 ( ( X = As3 )
% 3.39/1.83 & ( Xa2 = Tr6 )
% 3.39/1.83 & ( ( shd @ A @ As3 )
% 3.39/1.83 = ( lab @ A @ Tr6 ) )
% 3.39/1.83 & ( member2 @ ( treeFI @ A ) @ Tr7 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr6 ) ) )
% 3.39/1.83 & ( ( X2 @ ( stl @ A @ As3 ) @ Tr7 )
% 3.39/1.83 | ( koenig1755522246erPath @ A @ ( stl @ A @ As3 ) @ Tr7 ) ) ) )
% 3.39/1.83 => ( koenig1755522246erPath @ A @ X3 @ Xa ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_6__C_K_K_C,axiom,
% 3.39/1.83 ! [As: stream @ a,Tr: treeFI @ a] :
% 3.39/1.83 ( ( phi @ As @ Tr )
% 3.39/1.83 => ( ( shd @ a @ As )
% 3.39/1.83 = ( lab @ a @ Tr ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_7_treeFI_Oexpand,axiom,
% 3.39/1.83 ! [A: $tType,TreeFI: treeFI @ A,TreeFI2: treeFI @ A] :
% 3.39/1.83 ( ( ( ( lab @ A @ TreeFI )
% 3.39/1.83 = ( lab @ A @ TreeFI2 ) )
% 3.39/1.83 & ( ( sub @ A @ TreeFI )
% 3.39/1.83 = ( sub @ A @ TreeFI2 ) ) )
% 3.39/1.83 => ( TreeFI = TreeFI2 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_8_stream_Oexpand,axiom,
% 3.39/1.83 ! [A: $tType,Stream: stream @ A,Stream2: stream @ A] :
% 3.39/1.83 ( ( ( ( shd @ A @ Stream )
% 3.39/1.83 = ( shd @ A @ Stream2 ) )
% 3.39/1.83 & ( ( stl @ A @ Stream )
% 3.39/1.83 = ( stl @ A @ Stream2 ) ) )
% 3.39/1.83 => ( Stream = Stream2 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_9_stream_Ocoinduct,axiom,
% 3.39/1.83 ! [A: $tType,R: ( stream @ A ) > ( stream @ A ) > $o,Stream: stream @ A,Stream2: stream @ A] :
% 3.39/1.83 ( ( R @ Stream @ Stream2 )
% 3.39/1.83 => ( ! [Stream3: stream @ A,Stream4: stream @ A] :
% 3.39/1.83 ( ( R @ Stream3 @ Stream4 )
% 3.39/1.83 => ( ( ( shd @ A @ Stream3 )
% 3.39/1.83 = ( shd @ A @ Stream4 ) )
% 3.39/1.83 & ( R @ ( stl @ A @ Stream3 ) @ ( stl @ A @ Stream4 ) ) ) )
% 3.39/1.83 => ( Stream = Stream2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_10_stream_Ocoinduct__strong,axiom,
% 3.39/1.83 ! [A: $tType,R: ( stream @ A ) > ( stream @ A ) > $o,Stream: stream @ A,Stream2: stream @ A] :
% 3.39/1.83 ( ( R @ Stream @ Stream2 )
% 3.39/1.83 => ( ! [Stream3: stream @ A,Stream4: stream @ A] :
% 3.39/1.83 ( ( R @ Stream3 @ Stream4 )
% 3.39/1.83 => ( ( ( shd @ A @ Stream3 )
% 3.39/1.83 = ( shd @ A @ Stream4 ) )
% 3.39/1.83 & ( ( R @ ( stl @ A @ Stream3 ) @ ( stl @ A @ Stream4 ) )
% 3.39/1.83 | ( ( stl @ A @ Stream3 )
% 3.39/1.83 = ( stl @ A @ Stream4 ) ) ) ) )
% 3.39/1.83 => ( Stream = Stream2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_11_konigPath_Osimps_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,T: treeFI @ A] :
% 3.39/1.83 ( ( shd @ A @ ( koenig1103336060igPath @ A @ T ) )
% 3.39/1.83 = ( lab @ A @ T ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_12_infiniteTr__sub,axiom,
% 3.39/1.83 ! [A: $tType,Tr: treeFI @ A] :
% 3.39/1.83 ( ( koenig488553731niteTr @ A @ Tr )
% 3.39/1.83 => ? [X: treeFI @ A] :
% 3.39/1.83 ( ( member2 @ ( treeFI @ A ) @ X @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr ) ) )
% 3.39/1.83 & ( koenig488553731niteTr @ A @ X ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_13_infiniteTr_Ocases,axiom,
% 3.39/1.83 ! [A: $tType,A3: treeFI @ A] :
% 3.39/1.83 ( ( koenig488553731niteTr @ A @ A3 )
% 3.39/1.83 => ~ ! [Tr2: treeFI @ A] :
% 3.39/1.83 ( ( member2 @ ( treeFI @ A ) @ Tr2 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ A3 ) ) )
% 3.39/1.83 => ~ ( koenig488553731niteTr @ A @ Tr2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_14_infiniteTr_Osimps,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( koenig488553731niteTr @ A )
% 3.39/1.83 = ( ^ [A4: treeFI @ A] :
% 3.39/1.83 ? [Tr4: treeFI @ A,Tr3: treeFI @ A] :
% 3.39/1.83 ( ( A4 = Tr3 )
% 3.39/1.83 & ( member2 @ ( treeFI @ A ) @ Tr4 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr3 ) ) )
% 3.39/1.83 & ( koenig488553731niteTr @ A @ Tr4 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_15_infiniteTr__coind,axiom,
% 3.39/1.83 ! [A: $tType,Phi: ( treeFI @ A ) > $o,Tr: treeFI @ A] :
% 3.39/1.83 ( ( Phi @ Tr )
% 3.39/1.83 => ( ! [Tr8: treeFI @ A] :
% 3.39/1.83 ( ( Phi @ Tr8 )
% 3.39/1.83 => ? [X4: treeFI @ A] :
% 3.39/1.83 ( ( member2 @ ( treeFI @ A ) @ X4 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr8 ) ) )
% 3.39/1.83 & ( Phi @ X4 ) ) )
% 3.39/1.83 => ( koenig488553731niteTr @ A @ Tr ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_16_infiniteTr_Ointros,axiom,
% 3.39/1.83 ! [A: $tType,Tr5: treeFI @ A,Tr: treeFI @ A] :
% 3.39/1.83 ( ( member2 @ ( treeFI @ A ) @ Tr5 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr ) ) )
% 3.39/1.83 => ( ( koenig488553731niteTr @ A @ Tr5 )
% 3.39/1.83 => ( koenig488553731niteTr @ A @ Tr ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_17_infiniteTr_Ocoinduct,axiom,
% 3.39/1.83 ! [A: $tType,X2: ( treeFI @ A ) > $o,X3: treeFI @ A] :
% 3.39/1.83 ( ( X2 @ X3 )
% 3.39/1.83 => ( ! [X: treeFI @ A] :
% 3.39/1.83 ( ( X2 @ X )
% 3.39/1.83 => ? [Tr7: treeFI @ A,Tr6: treeFI @ A] :
% 3.39/1.83 ( ( X = Tr6 )
% 3.39/1.83 & ( member2 @ ( treeFI @ A ) @ Tr7 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr6 ) ) )
% 3.39/1.83 & ( ( X2 @ Tr7 )
% 3.39/1.83 | ( koenig488553731niteTr @ A @ Tr7 ) ) ) )
% 3.39/1.83 => ( koenig488553731niteTr @ A @ X3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_18_infiniteTr__strong__coind,axiom,
% 3.39/1.83 ! [A: $tType,Phi: ( treeFI @ A ) > $o,Tr: treeFI @ A] :
% 3.39/1.83 ( ( Phi @ Tr )
% 3.39/1.83 => ( ! [Tr8: treeFI @ A] :
% 3.39/1.83 ( ( Phi @ Tr8 )
% 3.39/1.83 => ? [X4: treeFI @ A] :
% 3.39/1.83 ( ( member2 @ ( treeFI @ A ) @ X4 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ Tr8 ) ) )
% 3.39/1.83 & ( ( Phi @ X4 )
% 3.39/1.83 | ( koenig488553731niteTr @ A @ X4 ) ) ) )
% 3.39/1.83 => ( koenig488553731niteTr @ A @ Tr ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_19_treeFI_Ocase__eq__if,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType] :
% 3.39/1.83 ( ( case_treeFI @ A @ B )
% 3.39/1.83 = ( ^ [F: A > ( list @ ( treeFI @ A ) ) > B,TreeFI3: treeFI @ A] : ( F @ ( lab @ A @ TreeFI3 ) @ ( sub @ A @ TreeFI3 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_20_stream_Ocase__eq__if,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType] :
% 3.39/1.83 ( ( case_stream @ A @ B )
% 3.39/1.83 = ( ^ [F: A > ( stream @ A ) > B,Stream5: stream @ A] : ( F @ ( shd @ A @ Stream5 ) @ ( stl @ A @ Stream5 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_21_sdrop__while_Osimps,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( sdrop_while @ A )
% 3.39/1.83 = ( ^ [P: A > $o,S: stream @ A] : ( if @ ( stream @ A ) @ ( P @ ( shd @ A @ S ) ) @ ( sdrop_while @ A @ P @ ( stl @ A @ S ) ) @ S ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_22_treeFI_Ocollapse,axiom,
% 3.39/1.83 ! [A: $tType,TreeFI: treeFI @ A] :
% 3.39/1.83 ( ( tree @ A @ ( lab @ A @ TreeFI ) @ ( sub @ A @ TreeFI ) )
% 3.39/1.83 = TreeFI ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_23_treeFI_Oset__sel_I2_J,axiom,
% 3.39/1.83 ! [A: $tType,X3: treeFI @ A,A3: treeFI @ A,Xa: A] :
% 3.39/1.83 ( ( member2 @ ( treeFI @ A ) @ X3 @ ( set2 @ ( treeFI @ A ) @ ( sub @ A @ A3 ) ) )
% 3.39/1.83 => ( ( member2 @ A @ Xa @ ( set_treeFI @ A @ X3 ) )
% 3.39/1.83 => ( member2 @ A @ Xa @ ( set_treeFI @ A @ A3 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_24_treeFI_Oexhaust__sel,axiom,
% 3.39/1.83 ! [A: $tType,TreeFI: treeFI @ A] :
% 3.39/1.83 ( TreeFI
% 3.39/1.83 = ( tree @ A @ ( lab @ A @ TreeFI ) @ ( sub @ A @ TreeFI ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_25_trev_Osimps_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,T: treeFI @ A] :
% 3.39/1.83 ( ( lab @ A @ ( trev @ A @ T ) )
% 3.39/1.83 = ( lab @ A @ T ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_26_stream_Ocollapse,axiom,
% 3.39/1.83 ! [A: $tType,Stream: stream @ A] :
% 3.39/1.83 ( ( sCons @ A @ ( shd @ A @ Stream ) @ ( stl @ A @ Stream ) )
% 3.39/1.83 = Stream ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_27_in__streams,axiom,
% 3.39/1.83 ! [A: $tType,S2: stream @ A,S3: set @ A] :
% 3.39/1.83 ( ( member2 @ ( stream @ A ) @ ( stl @ A @ S2 ) @ ( streams @ A @ S3 ) )
% 3.39/1.83 => ( ( member2 @ A @ ( shd @ A @ S2 ) @ S3 )
% 3.39/1.83 => ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ S3 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_28_streamsE,axiom,
% 3.39/1.83 ! [A: $tType,S2: stream @ A,A5: set @ A] :
% 3.39/1.83 ( ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) )
% 3.39/1.83 => ~ ( ( member2 @ A @ ( shd @ A @ S2 ) @ A5 )
% 3.39/1.83 => ~ ( member2 @ ( stream @ A ) @ ( stl @ A @ S2 ) @ ( streams @ A @ A5 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_29_stream_Oinject,axiom,
% 3.39/1.83 ! [A: $tType,X1: A,X22: stream @ A,Y1: A,Y2: stream @ A] :
% 3.39/1.83 ( ( ( sCons @ A @ X1 @ X22 )
% 3.39/1.83 = ( sCons @ A @ Y1 @ Y2 ) )
% 3.39/1.83 = ( ( X1 = Y1 )
% 3.39/1.83 & ( X22 = Y2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_30_treeFI_Oinject,axiom,
% 3.39/1.83 ! [A: $tType,X1: A,X22: list @ ( treeFI @ A ),Y1: A,Y2: list @ ( treeFI @ A )] :
% 3.39/1.83 ( ( ( tree @ A @ X1 @ X22 )
% 3.39/1.83 = ( tree @ A @ Y1 @ Y2 ) )
% 3.39/1.83 = ( ( X1 = Y1 )
% 3.39/1.83 & ( X22 = Y2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_31_sdrop__while__SCons,axiom,
% 3.39/1.83 ! [A: $tType,P2: A > $o,A3: A,S2: stream @ A] :
% 3.39/1.83 ( ( ( P2 @ A3 )
% 3.39/1.83 => ( ( sdrop_while @ A @ P2 @ ( sCons @ A @ A3 @ S2 ) )
% 3.39/1.83 = ( sdrop_while @ A @ P2 @ S2 ) ) )
% 3.39/1.83 & ( ~ ( P2 @ A3 )
% 3.39/1.83 => ( ( sdrop_while @ A @ P2 @ ( sCons @ A @ A3 @ S2 ) )
% 3.39/1.83 = ( sCons @ A @ A3 @ S2 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_32_streams_Ocoinduct,axiom,
% 3.39/1.83 ! [A: $tType,X2: ( stream @ A ) > $o,X3: stream @ A,A5: set @ A] :
% 3.39/1.83 ( ( X2 @ X3 )
% 3.39/1.83 => ( ! [X: stream @ A] :
% 3.39/1.83 ( ( X2 @ X )
% 3.39/1.83 => ? [A6: A,S4: stream @ A] :
% 3.39/1.83 ( ( X
% 3.39/1.83 = ( sCons @ A @ A6 @ S4 ) )
% 3.39/1.83 & ( member2 @ A @ A6 @ A5 )
% 3.39/1.83 & ( ( X2 @ S4 )
% 3.39/1.83 | ( member2 @ ( stream @ A ) @ S4 @ ( streams @ A @ A5 ) ) ) ) )
% 3.39/1.83 => ( member2 @ ( stream @ A ) @ X3 @ ( streams @ A @ A5 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_33_treeFI_Oexhaust,axiom,
% 3.39/1.83 ! [A: $tType,Y: treeFI @ A] :
% 3.39/1.83 ~ ! [X12: A,X23: list @ ( treeFI @ A )] :
% 3.39/1.83 ( Y
% 3.39/1.83 != ( tree @ A @ X12 @ X23 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_34_streams__Stream,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,S2: stream @ A,A5: set @ A] :
% 3.39/1.83 ( ( member2 @ ( stream @ A ) @ ( sCons @ A @ X3 @ S2 ) @ ( streams @ A @ A5 ) )
% 3.39/1.83 = ( ( member2 @ A @ X3 @ A5 )
% 3.39/1.83 & ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_35_stream_Oexhaust,axiom,
% 3.39/1.83 ! [A: $tType,Y: stream @ A] :
% 3.39/1.83 ~ ! [X12: A,X23: stream @ A] :
% 3.39/1.83 ( Y
% 3.39/1.83 != ( sCons @ A @ X12 @ X23 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_36_streams_Osimps,axiom,
% 3.39/1.83 ! [A: $tType,A3: stream @ A,A5: set @ A] :
% 3.39/1.83 ( ( member2 @ ( stream @ A ) @ A3 @ ( streams @ A @ A5 ) )
% 3.39/1.83 = ( ? [A4: A,S: stream @ A] :
% 3.39/1.83 ( ( A3
% 3.39/1.83 = ( sCons @ A @ A4 @ S ) )
% 3.39/1.83 & ( member2 @ A @ A4 @ A5 )
% 3.39/1.83 & ( member2 @ ( stream @ A ) @ S @ ( streams @ A @ A5 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_37_streams_Ocases,axiom,
% 3.39/1.83 ! [A: $tType,A3: stream @ A,A5: set @ A] :
% 3.39/1.83 ( ( member2 @ ( stream @ A ) @ A3 @ ( streams @ A @ A5 ) )
% 3.39/1.83 => ~ ! [A7: A,S5: stream @ A] :
% 3.39/1.83 ( ( A3
% 3.39/1.83 = ( sCons @ A @ A7 @ S5 ) )
% 3.39/1.83 => ( ( member2 @ A @ A7 @ A5 )
% 3.39/1.83 => ~ ( member2 @ ( stream @ A ) @ S5 @ ( streams @ A @ A5 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_38_treeFI_Ocase,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,F2: A > ( list @ ( treeFI @ A ) ) > B,X1: A,X22: list @ ( treeFI @ A )] :
% 3.39/1.83 ( ( case_treeFI @ A @ B @ F2 @ ( tree @ A @ X1 @ X22 ) )
% 3.39/1.83 = ( F2 @ X1 @ X22 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_39_stream_Ocase,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,F2: A > ( stream @ A ) > B,X1: A,X22: stream @ A] :
% 3.39/1.83 ( ( case_stream @ A @ B @ F2 @ ( sCons @ A @ X1 @ X22 ) )
% 3.39/1.83 = ( F2 @ X1 @ X22 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_40_treeFI_Oset__intros_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,A1: A,A2: list @ ( treeFI @ A )] : ( member2 @ A @ A1 @ ( set_treeFI @ A @ ( tree @ A @ A1 @ A2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_41_trev__trev,axiom,
% 3.39/1.83 ! [A: $tType,Tr: treeFI @ A] :
% 3.39/1.83 ( ( trev @ A @ ( trev @ A @ Tr ) )
% 3.39/1.83 = Tr ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_42_treeFI_Oset__intros_I2_J,axiom,
% 3.39/1.83 ! [A: $tType,X3: treeFI @ A,A2: list @ ( treeFI @ A ),Xa: A,A1: A] :
% 3.39/1.83 ( ( member2 @ ( treeFI @ A ) @ X3 @ ( set2 @ ( treeFI @ A ) @ A2 ) )
% 3.39/1.83 => ( ( member2 @ A @ Xa @ ( set_treeFI @ A @ X3 ) )
% 3.39/1.83 => ( member2 @ A @ Xa @ ( set_treeFI @ A @ ( tree @ A @ A1 @ A2 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_43_treeFI_Oset__cases,axiom,
% 3.39/1.83 ! [A: $tType,E: A,A3: treeFI @ A] :
% 3.39/1.83 ( ( member2 @ A @ E @ ( set_treeFI @ A @ A3 ) )
% 3.39/1.83 => ( ! [Z2: list @ ( treeFI @ A )] :
% 3.39/1.83 ( A3
% 3.39/1.83 != ( tree @ A @ E @ Z2 ) )
% 3.39/1.83 => ~ ! [Z1: A,Z2: list @ ( treeFI @ A )] :
% 3.39/1.83 ( ( A3
% 3.39/1.83 = ( tree @ A @ Z1 @ Z2 ) )
% 3.39/1.83 => ! [X: treeFI @ A] :
% 3.39/1.83 ( ( member2 @ ( treeFI @ A ) @ X @ ( set2 @ ( treeFI @ A ) @ Z2 ) )
% 3.39/1.83 => ~ ( member2 @ A @ E @ ( set_treeFI @ A @ X ) ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_44_treeFI_Oset__induct,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,A3: treeFI @ A,P2: A > ( treeFI @ A ) > $o] :
% 3.39/1.83 ( ( member2 @ A @ X3 @ ( set_treeFI @ A @ A3 ) )
% 3.39/1.83 => ( ! [Z1: A,Z2: list @ ( treeFI @ A )] : ( P2 @ Z1 @ ( tree @ A @ Z1 @ Z2 ) )
% 3.39/1.83 => ( ! [Z1: A,Z2: list @ ( treeFI @ A ),Xa2: treeFI @ A,Xb: A] :
% 3.39/1.83 ( ( member2 @ ( treeFI @ A ) @ Xa2 @ ( set2 @ ( treeFI @ A ) @ Z2 ) )
% 3.39/1.83 => ( ( member2 @ A @ Xb @ ( set_treeFI @ A @ Xa2 ) )
% 3.39/1.83 => ( ( P2 @ Xb @ Xa2 )
% 3.39/1.83 => ( P2 @ Xb @ ( tree @ A @ Z1 @ Z2 ) ) ) ) )
% 3.39/1.83 => ( P2 @ X3 @ A3 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_45_mem__Collect__eq,axiom,
% 3.39/1.83 ! [A: $tType,A3: A,P2: A > $o] :
% 3.39/1.83 ( ( member2 @ A @ A3 @ ( collect @ A @ P2 ) )
% 3.39/1.83 = ( P2 @ A3 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_46_Collect__mem__eq,axiom,
% 3.39/1.83 ! [A: $tType,A5: set @ A] :
% 3.39/1.83 ( ( collect @ A
% 3.39/1.83 @ ^ [X5: A] : ( member2 @ A @ X5 @ A5 ) )
% 3.39/1.83 = A5 ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_47_Collect__cong,axiom,
% 3.39/1.83 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 3.39/1.83 ( ! [X: A] :
% 3.39/1.83 ( ( P2 @ X )
% 3.39/1.83 = ( Q @ X ) )
% 3.39/1.83 => ( ( collect @ A @ P2 )
% 3.39/1.83 = ( collect @ A @ Q ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_48_ext,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,F2: A > B,G: A > B] :
% 3.39/1.83 ( ! [X: A] :
% 3.39/1.83 ( ( F2 @ X )
% 3.39/1.83 = ( G @ X ) )
% 3.39/1.83 => ( F2 = G ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_49_stream_Osel_I2_J,axiom,
% 3.39/1.83 ! [A: $tType,X1: A,X22: stream @ A] :
% 3.39/1.83 ( ( stl @ A @ ( sCons @ A @ X1 @ X22 ) )
% 3.39/1.83 = X22 ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_50_stream_Osel_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,X1: A,X22: stream @ A] :
% 3.39/1.83 ( ( shd @ A @ ( sCons @ A @ X1 @ X22 ) )
% 3.39/1.83 = X1 ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_51_stream_Osplit__sel,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,P2: B > $o,F2: A > ( stream @ A ) > B,Stream: stream @ A] :
% 3.39/1.83 ( ( P2 @ ( case_stream @ A @ B @ F2 @ Stream ) )
% 3.39/1.83 = ( ( Stream
% 3.39/1.83 = ( sCons @ A @ ( shd @ A @ Stream ) @ ( stl @ A @ Stream ) ) )
% 3.39/1.83 => ( P2 @ ( F2 @ ( shd @ A @ Stream ) @ ( stl @ A @ Stream ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_52_stream_Osplit__sel__asm,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,P2: B > $o,F2: A > ( stream @ A ) > B,Stream: stream @ A] :
% 3.39/1.83 ( ( P2 @ ( case_stream @ A @ B @ F2 @ Stream ) )
% 3.39/1.83 = ( ~ ( ( Stream
% 3.39/1.83 = ( sCons @ A @ ( shd @ A @ Stream ) @ ( stl @ A @ Stream ) ) )
% 3.39/1.83 & ~ ( P2 @ ( F2 @ ( shd @ A @ Stream ) @ ( stl @ A @ Stream ) ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_53_streams__stl,axiom,
% 3.39/1.83 ! [A: $tType,S2: stream @ A,A5: set @ A] :
% 3.39/1.83 ( ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) )
% 3.39/1.83 => ( member2 @ ( stream @ A ) @ ( stl @ A @ S2 ) @ ( streams @ A @ A5 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_54_streams__shd,axiom,
% 3.39/1.83 ! [A: $tType,S2: stream @ A,A5: set @ A] :
% 3.39/1.83 ( ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) )
% 3.39/1.83 => ( member2 @ A @ ( shd @ A @ S2 ) @ A5 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_55_treeFI_Osel_I2_J,axiom,
% 3.39/1.83 ! [A: $tType,X1: A,X22: list @ ( treeFI @ A )] :
% 3.39/1.83 ( ( sub @ A @ ( tree @ A @ X1 @ X22 ) )
% 3.39/1.83 = X22 ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_56_treeFI_Osel_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,X1: A,X22: list @ ( treeFI @ A )] :
% 3.39/1.83 ( ( lab @ A @ ( tree @ A @ X1 @ X22 ) )
% 3.39/1.83 = X1 ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_57_treeFI_Oset__sel_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,A3: treeFI @ A] : ( member2 @ A @ ( lab @ A @ A3 ) @ ( set_treeFI @ A @ A3 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_58_treeFI_Osplit__sel,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,P2: B > $o,F2: A > ( list @ ( treeFI @ A ) ) > B,TreeFI: treeFI @ A] :
% 3.39/1.83 ( ( P2 @ ( case_treeFI @ A @ B @ F2 @ TreeFI ) )
% 3.39/1.83 = ( ( TreeFI
% 3.39/1.83 = ( tree @ A @ ( lab @ A @ TreeFI ) @ ( sub @ A @ TreeFI ) ) )
% 3.39/1.83 => ( P2 @ ( F2 @ ( lab @ A @ TreeFI ) @ ( sub @ A @ TreeFI ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_59_treeFI_Osplit__sel__asm,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,P2: B > $o,F2: A > ( list @ ( treeFI @ A ) ) > B,TreeFI: treeFI @ A] :
% 3.39/1.83 ( ( P2 @ ( case_treeFI @ A @ B @ F2 @ TreeFI ) )
% 3.39/1.83 = ( ~ ( ( TreeFI
% 3.39/1.83 = ( tree @ A @ ( lab @ A @ TreeFI ) @ ( sub @ A @ TreeFI ) ) )
% 3.39/1.83 & ~ ( P2 @ ( F2 @ ( lab @ A @ TreeFI ) @ ( sub @ A @ TreeFI ) ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_60_stream_Oexhaust__sel,axiom,
% 3.39/1.83 ! [A: $tType,Stream: stream @ A] :
% 3.39/1.83 ( Stream
% 3.39/1.83 = ( sCons @ A @ ( shd @ A @ Stream ) @ ( stl @ A @ Stream ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_61_smember__code,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Y: A,S2: stream @ A] :
% 3.39/1.83 ( ( smember @ A @ X3 @ ( sCons @ A @ Y @ S2 ) )
% 3.39/1.83 = ( ( X3 != Y )
% 3.39/1.83 => ( smember @ A @ X3 @ S2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_62_sinterleave_Ocode,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( sinterleave @ A )
% 3.39/1.83 = ( ^ [S1: stream @ A,S22: stream @ A] : ( sCons @ A @ ( shd @ A @ S1 ) @ ( sinterleave @ A @ S22 @ ( stl @ A @ S1 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_63_smap2_Ocode,axiom,
% 3.39/1.83 ! [C: $tType,B: $tType,A: $tType] :
% 3.39/1.83 ( ( smap2 @ A @ B @ C )
% 3.39/1.83 = ( ^ [F: A > B > C,S1: stream @ A,S22: stream @ B] : ( sCons @ C @ ( F @ ( shd @ A @ S1 ) @ ( shd @ B @ S22 ) ) @ ( smap2 @ A @ B @ C @ F @ ( stl @ A @ S1 ) @ ( stl @ B @ S22 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_64_smap__ctr,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,F2: B > A,S2: stream @ B,X3: A,S6: stream @ A] :
% 3.39/1.83 ( ( ( smap @ B @ A @ F2 @ S2 )
% 3.39/1.83 = ( sCons @ A @ X3 @ S6 ) )
% 3.39/1.83 = ( ( ( F2 @ ( shd @ B @ S2 ) )
% 3.39/1.83 = X3 )
% 3.39/1.83 & ( ( smap @ B @ A @ F2 @ ( stl @ B @ S2 ) )
% 3.39/1.83 = S6 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_65_sfilter_Ocode,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( sfilter @ A )
% 3.39/1.83 = ( ^ [P: A > $o,S: stream @ A] : ( sCons @ A @ ( shd @ A @ ( sdrop_while @ A @ ( comp @ $o @ $o @ A @ (~) @ P ) @ S ) ) @ ( sfilter @ A @ P @ ( stl @ A @ ( sdrop_while @ A @ ( comp @ $o @ $o @ A @ (~) @ P ) @ S ) ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_66_stream__all__Stream,axiom,
% 3.39/1.83 ! [A: $tType,P2: A > $o,X3: A,X2: stream @ A] :
% 3.39/1.83 ( ( stream_all @ A @ P2 @ ( sCons @ A @ X3 @ X2 ) )
% 3.39/1.83 = ( ( P2 @ X3 )
% 3.39/1.83 & ( stream_all @ A @ P2 @ X2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_67_stream_Opred__inject,axiom,
% 3.39/1.83 ! [A: $tType,P2: A > $o,A3: A,Aa2: stream @ A] :
% 3.39/1.83 ( ( pred_stream @ A @ P2 @ ( sCons @ A @ A3 @ Aa2 ) )
% 3.39/1.83 = ( ( P2 @ A3 )
% 3.39/1.83 & ( pred_stream @ A @ P2 @ Aa2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_68_sset__induct,axiom,
% 3.39/1.83 ! [A: $tType,Y: A,S2: stream @ A,P2: A > ( stream @ A ) > $o] :
% 3.39/1.83 ( ( member2 @ A @ Y @ ( sset @ A @ S2 ) )
% 3.39/1.83 => ( ! [S5: stream @ A] : ( P2 @ ( shd @ A @ S5 ) @ S5 )
% 3.39/1.83 => ( ! [S5: stream @ A,Y3: A] :
% 3.39/1.83 ( ( member2 @ A @ Y3 @ ( sset @ A @ ( stl @ A @ S5 ) ) )
% 3.39/1.83 => ( ( P2 @ Y3 @ ( stl @ A @ S5 ) )
% 3.39/1.83 => ( P2 @ Y3 @ S5 ) ) )
% 3.39/1.83 => ( P2 @ Y @ S2 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_69_sfilter__Stream,axiom,
% 3.39/1.83 ! [A: $tType,P2: A > $o,X3: A,S2: stream @ A] :
% 3.39/1.83 ( ( ( P2 @ X3 )
% 3.39/1.83 => ( ( sfilter @ A @ P2 @ ( sCons @ A @ X3 @ S2 ) )
% 3.39/1.83 = ( sCons @ A @ X3 @ ( sfilter @ A @ P2 @ S2 ) ) ) )
% 3.39/1.83 & ( ~ ( P2 @ X3 )
% 3.39/1.83 => ( ( sfilter @ A @ P2 @ ( sCons @ A @ X3 @ S2 ) )
% 3.39/1.83 = ( sfilter @ A @ P2 @ S2 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_70_stream_Omap__sel_I2_J,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,F2: A > B,A3: stream @ A] :
% 3.39/1.83 ( ( stl @ B @ ( smap @ A @ B @ F2 @ A3 ) )
% 3.39/1.83 = ( smap @ A @ B @ F2 @ ( stl @ A @ A3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_71_stream_Omap__sel_I1_J,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,F2: A > B,A3: stream @ A] :
% 3.39/1.83 ( ( shd @ B @ ( smap @ A @ B @ F2 @ A3 ) )
% 3.39/1.83 = ( F2 @ ( shd @ A @ A3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_72_Stream_Osmember__def,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( smember @ A )
% 3.39/1.83 = ( ^ [X5: A,S: stream @ A] : ( member2 @ A @ X5 @ ( sset @ A @ S ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_73_stream_Omap__comp,axiom,
% 3.39/1.83 ! [B: $tType,C: $tType,A: $tType,G: B > C,F2: A > B,V: stream @ A] :
% 3.39/1.83 ( ( smap @ B @ C @ G @ ( smap @ A @ B @ F2 @ V ) )
% 3.39/1.83 = ( smap @ A @ C @ ( comp @ B @ C @ A @ G @ F2 ) @ V ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_74_stream_Omap__cong,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,X3: stream @ A,Ya: stream @ A,F2: A > B,G: A > B] :
% 3.39/1.83 ( ( X3 = Ya )
% 3.39/1.83 => ( ! [Z: A] :
% 3.39/1.83 ( ( member2 @ A @ Z @ ( sset @ A @ Ya ) )
% 3.39/1.83 => ( ( F2 @ Z )
% 3.39/1.83 = ( G @ Z ) ) )
% 3.39/1.83 => ( ( smap @ A @ B @ F2 @ X3 )
% 3.39/1.83 = ( smap @ A @ B @ G @ Ya ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_75_stream_Opred__map,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,Q: B > $o,F2: A > B,X3: stream @ A] :
% 3.39/1.83 ( ( pred_stream @ B @ Q @ ( smap @ A @ B @ F2 @ X3 ) )
% 3.39/1.83 = ( pred_stream @ A @ ( comp @ B @ $o @ A @ Q @ F2 ) @ X3 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_76_stream_Omap__cong0,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,X3: stream @ A,F2: A > B,G: A > B] :
% 3.39/1.83 ( ! [Z: A] :
% 3.39/1.83 ( ( member2 @ A @ Z @ ( sset @ A @ X3 ) )
% 3.39/1.83 => ( ( F2 @ Z )
% 3.39/1.83 = ( G @ Z ) ) )
% 3.39/1.83 => ( ( smap @ A @ B @ F2 @ X3 )
% 3.39/1.83 = ( smap @ A @ B @ G @ X3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_77_stream_Opred__cong,axiom,
% 3.39/1.83 ! [A: $tType,X3: stream @ A,Ya: stream @ A,P2: A > $o,Pa: A > $o] :
% 3.39/1.83 ( ( X3 = Ya )
% 3.39/1.83 => ( ! [Z: A] :
% 3.39/1.83 ( ( member2 @ A @ Z @ ( sset @ A @ Ya ) )
% 3.39/1.83 => ( ( P2 @ Z )
% 3.39/1.83 = ( Pa @ Z ) ) )
% 3.39/1.83 => ( ( pred_stream @ A @ P2 @ X3 )
% 3.39/1.83 = ( pred_stream @ A @ Pa @ Ya ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_78_stream_Oinj__map__strong,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,X3: stream @ A,Xa: stream @ A,F2: A > B,Fa: A > B] :
% 3.39/1.83 ( ! [Z: A,Za: A] :
% 3.39/1.83 ( ( member2 @ A @ Z @ ( sset @ A @ X3 ) )
% 3.39/1.83 => ( ( member2 @ A @ Za @ ( sset @ A @ Xa ) )
% 3.39/1.83 => ( ( ( F2 @ Z )
% 3.39/1.83 = ( Fa @ Za ) )
% 3.39/1.83 => ( Z = Za ) ) ) )
% 3.39/1.83 => ( ( ( smap @ A @ B @ F2 @ X3 )
% 3.39/1.83 = ( smap @ A @ B @ Fa @ Xa ) )
% 3.39/1.83 => ( X3 = Xa ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_79_stream_Opred__mono__strong,axiom,
% 3.39/1.83 ! [A: $tType,P2: A > $o,X3: stream @ A,Pa: A > $o] :
% 3.39/1.83 ( ( pred_stream @ A @ P2 @ X3 )
% 3.39/1.83 => ( ! [Z: A] :
% 3.39/1.83 ( ( member2 @ A @ Z @ ( sset @ A @ X3 ) )
% 3.39/1.83 => ( ( P2 @ Z )
% 3.39/1.83 => ( Pa @ Z ) ) )
% 3.39/1.83 => ( pred_stream @ A @ Pa @ X3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_80_stream_Omap,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,F2: A > B,X1: A,X22: stream @ A] :
% 3.39/1.83 ( ( smap @ A @ B @ F2 @ ( sCons @ A @ X1 @ X22 ) )
% 3.39/1.83 = ( sCons @ B @ ( F2 @ X1 ) @ ( smap @ A @ B @ F2 @ X22 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_81_stl__sset,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,A3: stream @ A] :
% 3.39/1.83 ( ( member2 @ A @ X3 @ ( sset @ A @ ( stl @ A @ A3 ) ) )
% 3.39/1.83 => ( member2 @ A @ X3 @ ( sset @ A @ A3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_82_shd__sset,axiom,
% 3.39/1.83 ! [A: $tType,A3: stream @ A] : ( member2 @ A @ ( shd @ A @ A3 ) @ ( sset @ A @ A3 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_83_stream_Oset__intros_I2_J,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,A2: stream @ A,A1: A] :
% 3.39/1.83 ( ( member2 @ A @ X3 @ ( sset @ A @ A2 ) )
% 3.39/1.83 => ( member2 @ A @ X3 @ ( sset @ A @ ( sCons @ A @ A1 @ A2 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_84_stream_Oset__intros_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,A1: A,A2: stream @ A] : ( member2 @ A @ A1 @ ( sset @ A @ ( sCons @ A @ A1 @ A2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_85_stream_Oset__cases,axiom,
% 3.39/1.83 ! [A: $tType,E: A,A3: stream @ A] :
% 3.39/1.83 ( ( member2 @ A @ E @ ( sset @ A @ A3 ) )
% 3.39/1.83 => ( ! [Z2: stream @ A] :
% 3.39/1.83 ( A3
% 3.39/1.83 != ( sCons @ A @ E @ Z2 ) )
% 3.39/1.83 => ~ ! [Z1: A,Z2: stream @ A] :
% 3.39/1.83 ( ( A3
% 3.39/1.83 = ( sCons @ A @ Z1 @ Z2 ) )
% 3.39/1.83 => ~ ( member2 @ A @ E @ ( sset @ A @ Z2 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_86_stream_Oset__induct,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,A3: stream @ A,P2: A > ( stream @ A ) > $o] :
% 3.39/1.83 ( ( member2 @ A @ X3 @ ( sset @ A @ A3 ) )
% 3.39/1.83 => ( ! [Z1: A,Z2: stream @ A] : ( P2 @ Z1 @ ( sCons @ A @ Z1 @ Z2 ) )
% 3.39/1.83 => ( ! [Z1: A,Z2: stream @ A,Xa2: A] :
% 3.39/1.83 ( ( member2 @ A @ Xa2 @ ( sset @ A @ Z2 ) )
% 3.39/1.83 => ( ( P2 @ Xa2 @ Z2 )
% 3.39/1.83 => ( P2 @ Xa2 @ ( sCons @ A @ Z1 @ Z2 ) ) ) )
% 3.39/1.83 => ( P2 @ X3 @ A3 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_87_smap__streams,axiom,
% 3.39/1.83 ! [A: $tType,B: $tType,S2: stream @ A,A5: set @ A,F2: A > B,B2: set @ B] :
% 3.39/1.83 ( ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) )
% 3.39/1.83 => ( ! [X: A] :
% 3.39/1.83 ( ( member2 @ A @ X @ A5 )
% 3.39/1.83 => ( member2 @ B @ ( F2 @ X ) @ B2 ) )
% 3.39/1.83 => ( member2 @ ( stream @ B ) @ ( smap @ A @ B @ F2 @ S2 ) @ ( streams @ B @ B2 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_88_sfilter_Osimps_I2_J,axiom,
% 3.39/1.83 ! [A: $tType,P2: A > $o,S2: stream @ A] :
% 3.39/1.83 ( ( stl @ A @ ( sfilter @ A @ P2 @ S2 ) )
% 3.39/1.83 = ( sfilter @ A @ P2 @ ( stl @ A @ ( sdrop_while @ A @ ( comp @ $o @ $o @ A @ (~) @ P2 ) @ S2 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_89_sfilter_Osimps_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,P2: A > $o,S2: stream @ A] :
% 3.39/1.83 ( ( shd @ A @ ( sfilter @ A @ P2 @ S2 ) )
% 3.39/1.83 = ( shd @ A @ ( sdrop_while @ A @ ( comp @ $o @ $o @ A @ (~) @ P2 ) @ S2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_90_smap2_Osimps_I2_J,axiom,
% 3.39/1.83 ! [A: $tType,C: $tType,B: $tType,F2: A > B > C,S12: stream @ A,S23: stream @ B] :
% 3.39/1.83 ( ( stl @ C @ ( smap2 @ A @ B @ C @ F2 @ S12 @ S23 ) )
% 3.39/1.83 = ( smap2 @ A @ B @ C @ F2 @ ( stl @ A @ S12 ) @ ( stl @ B @ S23 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_91_smap2_Osimps_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,C: $tType,B: $tType,F2: A > B > C,S12: stream @ A,S23: stream @ B] :
% 3.39/1.83 ( ( shd @ C @ ( smap2 @ A @ B @ C @ F2 @ S12 @ S23 ) )
% 3.39/1.83 = ( F2 @ ( shd @ A @ S12 ) @ ( shd @ B @ S23 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_92_smap2__unfold,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,C: $tType,F2: B > C > A,A3: B,S12: stream @ B,B3: C,S23: stream @ C] :
% 3.39/1.83 ( ( smap2 @ B @ C @ A @ F2 @ ( sCons @ B @ A3 @ S12 ) @ ( sCons @ C @ B3 @ S23 ) )
% 3.39/1.83 = ( sCons @ A @ ( F2 @ A3 @ B3 ) @ ( smap2 @ B @ C @ A @ F2 @ S12 @ S23 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_93_sinterleave_Osimps_I2_J,axiom,
% 3.39/1.83 ! [A: $tType,S12: stream @ A,S23: stream @ A] :
% 3.39/1.83 ( ( stl @ A @ ( sinterleave @ A @ S12 @ S23 ) )
% 3.39/1.83 = ( sinterleave @ A @ S23 @ ( stl @ A @ S12 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_94_sinterleave_Osimps_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,S12: stream @ A,S23: stream @ A] :
% 3.39/1.83 ( ( shd @ A @ ( sinterleave @ A @ S12 @ S23 ) )
% 3.39/1.83 = ( shd @ A @ S12 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_95_sinterleave__code,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,S12: stream @ A,S23: stream @ A] :
% 3.39/1.83 ( ( sinterleave @ A @ ( sCons @ A @ X3 @ S12 ) @ S23 )
% 3.39/1.83 = ( sCons @ A @ X3 @ ( sinterleave @ A @ S23 @ S12 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_96_comp__apply,axiom,
% 3.39/1.83 ! [C: $tType,A: $tType,B: $tType] :
% 3.39/1.83 ( ( comp @ B @ A @ C )
% 3.39/1.83 = ( ^ [F: B > A,G2: C > B,X5: C] : ( F @ ( G2 @ X5 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_97_stream_Omap__o__corec,axiom,
% 3.39/1.83 ! [A: $tType,B: $tType,C: $tType,F2: A > B,G: C > A,Ga: C > $o,Gb: C > ( stream @ A ),Gc: C > C] :
% 3.39/1.83 ( ( comp @ ( stream @ A ) @ ( stream @ B ) @ C @ ( smap @ A @ B @ F2 ) @ ( corec_stream @ C @ A @ G @ Ga @ Gb @ Gc ) )
% 3.39/1.83 = ( corec_stream @ C @ B @ ( comp @ A @ B @ C @ F2 @ G ) @ Ga @ ( comp @ ( stream @ A ) @ ( stream @ B ) @ C @ ( smap @ A @ B @ F2 ) @ Gb ) @ Gc ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_98_rewriteR__comp__comp2,axiom,
% 3.39/1.83 ! [C: $tType,B: $tType,E2: $tType,D: $tType,A: $tType,G: C > B,H: A > C,R1: D > B,R2: A > D,F2: B > E2,L: D > E2] :
% 3.39/1.83 ( ( ( comp @ C @ B @ A @ G @ H )
% 3.39/1.83 = ( comp @ D @ B @ A @ R1 @ R2 ) )
% 3.39/1.83 => ( ( ( comp @ B @ E2 @ D @ F2 @ R1 )
% 3.39/1.83 = L )
% 3.39/1.83 => ( ( comp @ C @ E2 @ A @ ( comp @ B @ E2 @ C @ F2 @ G ) @ H )
% 3.39/1.83 = ( comp @ D @ E2 @ A @ L @ R2 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_99_rewriteL__comp__comp2,axiom,
% 3.39/1.83 ! [A: $tType,C: $tType,B: $tType,D: $tType,E2: $tType,F2: C > B,G: A > C,L1: D > B,L2: A > D,H: E2 > A,R3: E2 > D] :
% 3.39/1.83 ( ( ( comp @ C @ B @ A @ F2 @ G )
% 3.39/1.83 = ( comp @ D @ B @ A @ L1 @ L2 ) )
% 3.39/1.83 => ( ( ( comp @ A @ D @ E2 @ L2 @ H )
% 3.39/1.83 = R3 )
% 3.39/1.83 => ( ( comp @ C @ B @ E2 @ F2 @ ( comp @ A @ C @ E2 @ G @ H ) )
% 3.39/1.83 = ( comp @ D @ B @ E2 @ L1 @ R3 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_100_rewriteR__comp__comp,axiom,
% 3.39/1.83 ! [C: $tType,D: $tType,B: $tType,A: $tType,G: C > B,H: A > C,R3: A > B,F2: B > D] :
% 3.39/1.83 ( ( ( comp @ C @ B @ A @ G @ H )
% 3.39/1.83 = R3 )
% 3.39/1.83 => ( ( comp @ C @ D @ A @ ( comp @ B @ D @ C @ F2 @ G ) @ H )
% 3.39/1.83 = ( comp @ B @ D @ A @ F2 @ R3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_101_rewriteL__comp__comp,axiom,
% 3.39/1.83 ! [C: $tType,B: $tType,A: $tType,D: $tType,F2: C > B,G: A > C,L: A > B,H: D > A] :
% 3.39/1.83 ( ( ( comp @ C @ B @ A @ F2 @ G )
% 3.39/1.83 = L )
% 3.39/1.83 => ( ( comp @ C @ B @ D @ F2 @ ( comp @ A @ C @ D @ G @ H ) )
% 3.39/1.83 = ( comp @ A @ B @ D @ L @ H ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_102_type__copy__map__cong0,axiom,
% 3.39/1.83 ! [B: $tType,D: $tType,E2: $tType,A: $tType,C: $tType,M: B > A,G: C > B,X3: C,N: D > A,H: C > D,F2: A > E2] :
% 3.39/1.83 ( ( ( M @ ( G @ X3 ) )
% 3.39/1.83 = ( N @ ( H @ X3 ) ) )
% 3.39/1.83 => ( ( comp @ B @ E2 @ C @ ( comp @ A @ E2 @ B @ F2 @ M ) @ G @ X3 )
% 3.39/1.83 = ( comp @ D @ E2 @ C @ ( comp @ A @ E2 @ D @ F2 @ N ) @ H @ X3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_103_stream_Ocorec__disc,axiom,
% 3.39/1.83 ! [A: $tType,C: $tType] :
% 3.39/1.83 ( ( corec_stream @ C @ A )
% 3.39/1.83 = ( corec_stream @ C @ A ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_104_stream_Ocorec__sel_I2_J,axiom,
% 3.39/1.83 ! [A: $tType,C: $tType,Q2: C > $o,A3: C,G1: C > A,G21: C > ( stream @ A ),G22: C > C] :
% 3.39/1.83 ( ( ( Q2 @ A3 )
% 3.39/1.83 => ( ( stl @ A @ ( corec_stream @ C @ A @ G1 @ Q2 @ G21 @ G22 @ A3 ) )
% 3.39/1.83 = ( G21 @ A3 ) ) )
% 3.39/1.83 & ( ~ ( Q2 @ A3 )
% 3.39/1.83 => ( ( stl @ A @ ( corec_stream @ C @ A @ G1 @ Q2 @ G21 @ G22 @ A3 ) )
% 3.39/1.83 = ( corec_stream @ C @ A @ G1 @ Q2 @ G21 @ G22 @ ( G22 @ A3 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_105_stream_Ocorec__sel_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,C: $tType,G1: C > A,Q2: C > $o,G21: C > ( stream @ A ),G22: C > C,A3: C] :
% 3.39/1.83 ( ( shd @ A @ ( corec_stream @ C @ A @ G1 @ Q2 @ G21 @ G22 @ A3 ) )
% 3.39/1.83 = ( G1 @ A3 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_106_stream_Ocorec__code,axiom,
% 3.39/1.83 ! [A: $tType,C: $tType] :
% 3.39/1.83 ( ( corec_stream @ C @ A )
% 3.39/1.83 = ( ^ [G12: C > A,Q22: C > $o,G212: C > ( stream @ A ),G222: C > C,A4: C] : ( sCons @ A @ ( G12 @ A4 ) @ ( if @ ( stream @ A ) @ ( Q22 @ A4 ) @ ( G212 @ A4 ) @ ( corec_stream @ C @ A @ G12 @ Q22 @ G212 @ G222 @ ( G222 @ A4 ) ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_107_comp__def,axiom,
% 3.39/1.83 ! [A: $tType,C: $tType,B: $tType] :
% 3.39/1.83 ( ( comp @ B @ C @ A )
% 3.39/1.83 = ( ^ [F: B > C,G2: A > B,X5: A] : ( F @ ( G2 @ X5 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_108_comp__assoc,axiom,
% 3.39/1.83 ! [B: $tType,D: $tType,C: $tType,A: $tType,F2: D > B,G: C > D,H: A > C] :
% 3.39/1.83 ( ( comp @ C @ B @ A @ ( comp @ D @ B @ C @ F2 @ G ) @ H )
% 3.39/1.83 = ( comp @ D @ B @ A @ F2 @ ( comp @ C @ D @ A @ G @ H ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_109_comp__eq__dest,axiom,
% 3.39/1.83 ! [C: $tType,B: $tType,D: $tType,A: $tType,A3: C > B,B3: A > C,C2: D > B,D2: A > D,V: A] :
% 3.39/1.83 ( ( ( comp @ C @ B @ A @ A3 @ B3 )
% 3.39/1.83 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 3.39/1.83 => ( ( A3 @ ( B3 @ V ) )
% 3.39/1.83 = ( C2 @ ( D2 @ V ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_110_comp__eq__elim,axiom,
% 3.39/1.83 ! [C: $tType,B: $tType,D: $tType,A: $tType,A3: C > B,B3: A > C,C2: D > B,D2: A > D] :
% 3.39/1.83 ( ( ( comp @ C @ B @ A @ A3 @ B3 )
% 3.39/1.83 = ( comp @ D @ B @ A @ C2 @ D2 ) )
% 3.39/1.83 => ! [V2: A] :
% 3.39/1.83 ( ( A3 @ ( B3 @ V2 ) )
% 3.39/1.83 = ( C2 @ ( D2 @ V2 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_111_comp__eq__dest__lhs,axiom,
% 3.39/1.83 ! [C: $tType,B: $tType,A: $tType,A3: C > B,B3: A > C,C2: A > B,V: A] :
% 3.39/1.83 ( ( ( comp @ C @ B @ A @ A3 @ B3 )
% 3.39/1.83 = C2 )
% 3.39/1.83 => ( ( A3 @ ( B3 @ V ) )
% 3.39/1.83 = ( C2 @ V ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_112_comp__cong,axiom,
% 3.39/1.83 ! [C: $tType,B: $tType,D: $tType,A: $tType,E2: $tType,F2: B > A,G: C > B,X3: C,F3: D > A,G3: E2 > D,X6: E2] :
% 3.39/1.83 ( ( ( F2 @ ( G @ X3 ) )
% 3.39/1.83 = ( F3 @ ( G3 @ X6 ) ) )
% 3.39/1.83 => ( ( comp @ B @ A @ C @ F2 @ G @ X3 )
% 3.39/1.83 = ( comp @ D @ A @ E2 @ F3 @ G3 @ X6 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_113_comp__apply__eq,axiom,
% 3.39/1.83 ! [B: $tType,D: $tType,A: $tType,C: $tType,F2: B > A,G: C > B,X3: C,H: D > A,K: C > D] :
% 3.39/1.83 ( ( ( F2 @ ( G @ X3 ) )
% 3.39/1.83 = ( H @ ( K @ X3 ) ) )
% 3.39/1.83 => ( ( comp @ B @ A @ C @ F2 @ G @ X3 )
% 3.39/1.83 = ( comp @ D @ A @ C @ H @ K @ X3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_114_fun_Omap__comp,axiom,
% 3.39/1.83 ! [B: $tType,C: $tType,A: $tType,D: $tType,G: B > C,F2: A > B,V: D > A] :
% 3.39/1.83 ( ( comp @ B @ C @ D @ G @ ( comp @ A @ B @ D @ F2 @ V ) )
% 3.39/1.83 = ( comp @ A @ C @ D @ ( comp @ B @ C @ A @ G @ F2 ) @ V ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_115_stream__all__iff,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( stream_all @ A )
% 3.39/1.83 = ( ^ [P: A > $o,S: stream @ A] :
% 3.39/1.83 ! [X5: A] :
% 3.39/1.83 ( ( member2 @ A @ X5 @ ( sset @ A @ S ) )
% 3.39/1.83 => ( P @ X5 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_116_stream_Oset,axiom,
% 3.39/1.83 ! [A: $tType,X1: A,X22: stream @ A] :
% 3.39/1.83 ( ( sset @ A @ ( sCons @ A @ X1 @ X22 ) )
% 3.39/1.83 = ( insert2 @ A @ X1 @ ( sset @ A @ X22 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_117_stream_Opred__set,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( pred_stream @ A )
% 3.39/1.83 = ( ^ [P: A > $o,X5: stream @ A] :
% 3.39/1.83 ! [Y4: A] :
% 3.39/1.83 ( ( member2 @ A @ Y4 @ ( sset @ A @ X5 ) )
% 3.39/1.83 => ( P @ Y4 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_118_treeFI_Opred__set,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( pred_treeFI @ A )
% 3.39/1.83 = ( ^ [P: A > $o,X5: treeFI @ A] :
% 3.39/1.83 ! [Y4: A] :
% 3.39/1.83 ( ( member2 @ A @ Y4 @ ( set_treeFI @ A @ X5 ) )
% 3.39/1.83 => ( P @ Y4 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_119_sset__sinterleave,axiom,
% 3.39/1.83 ! [A: $tType,S12: stream @ A,S23: stream @ A] :
% 3.39/1.83 ( ( sset @ A @ ( sinterleave @ A @ S12 @ S23 ) )
% 3.39/1.83 = ( sup_sup @ ( set @ A ) @ ( sset @ A @ S12 ) @ ( sset @ A @ S23 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_120_sset__streams,axiom,
% 3.39/1.83 ! [A: $tType,S2: stream @ A,A5: set @ A] :
% 3.39/1.83 ( ( ord_less_eq @ ( set @ A ) @ ( sset @ A @ S2 ) @ A5 )
% 3.39/1.83 => ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_121_streams__sset,axiom,
% 3.39/1.83 ! [A: $tType,S2: stream @ A,A5: set @ A] :
% 3.39/1.83 ( ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) )
% 3.39/1.83 => ( ord_less_eq @ ( set @ A ) @ ( sset @ A @ S2 ) @ A5 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_122_streams__mono2,axiom,
% 3.39/1.83 ! [A: $tType,S3: set @ A,T2: set @ A] :
% 3.39/1.83 ( ( ord_less_eq @ ( set @ A ) @ S3 @ T2 )
% 3.39/1.83 => ( ord_less_eq @ ( set @ ( stream @ A ) ) @ ( streams @ A @ S3 ) @ ( streams @ A @ T2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_123_streams__mono,axiom,
% 3.39/1.83 ! [A: $tType,S2: stream @ A,A5: set @ A,B2: set @ A] :
% 3.39/1.83 ( ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) )
% 3.39/1.83 => ( ( ord_less_eq @ ( set @ A ) @ A5 @ B2 )
% 3.39/1.83 => ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ B2 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_124_treeFI_Opred__mono__strong,axiom,
% 3.39/1.83 ! [A: $tType,P2: A > $o,X3: treeFI @ A,Pa: A > $o] :
% 3.39/1.83 ( ( pred_treeFI @ A @ P2 @ X3 )
% 3.39/1.83 => ( ! [Z: A] :
% 3.39/1.83 ( ( member2 @ A @ Z @ ( set_treeFI @ A @ X3 ) )
% 3.39/1.83 => ( ( P2 @ Z )
% 3.39/1.83 => ( Pa @ Z ) ) )
% 3.39/1.83 => ( pred_treeFI @ A @ Pa @ X3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_125_treeFI_Opred__cong,axiom,
% 3.39/1.83 ! [A: $tType,X3: treeFI @ A,Ya: treeFI @ A,P2: A > $o,Pa: A > $o] :
% 3.39/1.83 ( ( X3 = Ya )
% 3.39/1.83 => ( ! [Z: A] :
% 3.39/1.83 ( ( member2 @ A @ Z @ ( set_treeFI @ A @ Ya ) )
% 3.39/1.83 => ( ( P2 @ Z )
% 3.39/1.83 = ( Pa @ Z ) ) )
% 3.39/1.83 => ( ( pred_treeFI @ A @ P2 @ X3 )
% 3.39/1.83 = ( pred_treeFI @ A @ Pa @ Ya ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_126_streams__iff__sset,axiom,
% 3.39/1.83 ! [A: $tType,S2: stream @ A,A5: set @ A] :
% 3.39/1.83 ( ( member2 @ ( stream @ A ) @ S2 @ ( streams @ A @ A5 ) )
% 3.39/1.83 = ( ord_less_eq @ ( set @ A ) @ ( sset @ A @ S2 ) @ A5 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_127_subset__code_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,B2: set @ A] :
% 3.39/1.83 ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ B2 )
% 3.39/1.83 = ( ! [X5: A] :
% 3.39/1.83 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( member2 @ A @ X5 @ B2 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_128_sset__shift,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,S2: stream @ A] :
% 3.39/1.83 ( ( sset @ A @ ( shift @ A @ Xs @ S2 ) )
% 3.39/1.83 = ( sup_sup @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( sset @ A @ S2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_129_set__union,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 3.39/1.83 ( ( set2 @ A @ ( union @ A @ Xs @ Ys ) )
% 3.39/1.83 = ( sup_sup @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( set2 @ A @ Ys ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_130_treeFI_Opred__inject,axiom,
% 3.39/1.83 ! [A: $tType,P2: A > $o,A3: A,Aa2: list @ ( treeFI @ A )] :
% 3.39/1.83 ( ( pred_treeFI @ A @ P2 @ ( tree @ A @ A3 @ Aa2 ) )
% 3.39/1.83 = ( ( P2 @ A3 )
% 3.39/1.83 & ( list_all @ ( treeFI @ A ) @ ( pred_treeFI @ A @ P2 ) @ Aa2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_131_shift__left__inj,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,S12: stream @ A,S23: stream @ A] :
% 3.39/1.83 ( ( ( shift @ A @ Xs @ S12 )
% 3.39/1.83 = ( shift @ A @ Xs @ S23 ) )
% 3.39/1.83 = ( S12 = S23 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_132_stream__all__shift,axiom,
% 3.39/1.83 ! [A: $tType,P2: A > $o,Xs: list @ A,S2: stream @ A] :
% 3.39/1.83 ( ( stream_all @ A @ P2 @ ( shift @ A @ Xs @ S2 ) )
% 3.39/1.83 = ( ( list_all @ A @ P2 @ Xs )
% 3.39/1.83 & ( stream_all @ A @ P2 @ S2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_133_list_Opred__cong,axiom,
% 3.39/1.83 ! [A: $tType,X3: list @ A,Ya: list @ A,P2: A > $o,Pa: A > $o] :
% 3.39/1.83 ( ( X3 = Ya )
% 3.39/1.83 => ( ! [Z: A] :
% 3.39/1.83 ( ( member2 @ A @ Z @ ( set2 @ A @ Ya ) )
% 3.39/1.83 => ( ( P2 @ Z )
% 3.39/1.83 = ( Pa @ Z ) ) )
% 3.39/1.83 => ( ( list_all @ A @ P2 @ X3 )
% 3.39/1.83 = ( list_all @ A @ Pa @ Ya ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_134_list_Opred__mono__strong,axiom,
% 3.39/1.83 ! [A: $tType,P2: A > $o,X3: list @ A,Pa: A > $o] :
% 3.39/1.83 ( ( list_all @ A @ P2 @ X3 )
% 3.39/1.83 => ( ! [Z: A] :
% 3.39/1.83 ( ( member2 @ A @ Z @ ( set2 @ A @ X3 ) )
% 3.39/1.83 => ( ( P2 @ Z )
% 3.39/1.83 => ( Pa @ Z ) ) )
% 3.39/1.83 => ( list_all @ A @ Pa @ X3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_135_list__all__iff,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( list_all @ A )
% 3.39/1.83 = ( ^ [P: A > $o,X5: list @ A] :
% 3.39/1.83 ! [Y4: A] :
% 3.39/1.83 ( ( member2 @ A @ Y4 @ ( set2 @ A @ X5 ) )
% 3.39/1.83 => ( P @ Y4 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_136_Ball__set__list__all,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 3.39/1.83 ( ( ! [X5: A] :
% 3.39/1.83 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( P2 @ X5 ) ) )
% 3.39/1.83 = ( list_all @ A @ P2 @ Xs ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_137_list_Opred__set,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( list_all @ A )
% 3.39/1.83 = ( ^ [P: A > $o,X5: list @ A] :
% 3.39/1.83 ! [Y4: A] :
% 3.39/1.83 ( ( member2 @ A @ Y4 @ ( set2 @ A @ X5 ) )
% 3.39/1.83 => ( P @ Y4 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_138_List_Oset__insert,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.39/1.83 ( ( set2 @ A @ ( insert @ A @ X3 @ Xs ) )
% 3.39/1.83 = ( insert2 @ A @ X3 @ ( set2 @ A @ Xs ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_139_subset__code_I2_J,axiom,
% 3.39/1.83 ! [B: $tType,A5: set @ B,Ys: list @ B] :
% 3.39/1.83 ( ( ord_less_eq @ ( set @ B ) @ A5 @ ( coset @ B @ Ys ) )
% 3.39/1.83 = ( ! [X5: B] :
% 3.39/1.83 ( ( member2 @ B @ X5 @ ( set2 @ B @ Ys ) )
% 3.39/1.83 => ~ ( member2 @ B @ X5 @ A5 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_140_in__set__member,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.39/1.83 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 = ( member @ A @ Xs @ X3 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_141_union__set__fold,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,A5: set @ A] :
% 3.39/1.83 ( ( sup_sup @ ( set @ A ) @ ( set2 @ A @ Xs ) @ A5 )
% 3.39/1.83 = ( fold @ A @ ( set @ A ) @ ( insert2 @ A ) @ Xs @ A5 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_142_in__set__insert,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.39/1.83 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ( insert @ A @ X3 @ Xs )
% 3.39/1.83 = Xs ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_143_List_Ofold__cong,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,A3: A,B3: A,Xs: list @ B,Ys: list @ B,F2: B > A > A,G: B > A > A] :
% 3.39/1.83 ( ( A3 = B3 )
% 3.39/1.83 => ( ( Xs = Ys )
% 3.39/1.83 => ( ! [X: B] :
% 3.39/1.83 ( ( member2 @ B @ X @ ( set2 @ B @ Xs ) )
% 3.39/1.83 => ( ( F2 @ X )
% 3.39/1.83 = ( G @ X ) ) )
% 3.39/1.83 => ( ( fold @ B @ A @ F2 @ Xs @ A3 )
% 3.39/1.83 = ( fold @ B @ A @ G @ Ys @ B3 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_144_fold__invariant,axiom,
% 3.39/1.83 ! [A: $tType,B: $tType,Xs: list @ A,Q: A > $o,P2: B > $o,S2: B,F2: A > B > B] :
% 3.39/1.83 ( ! [X: A] :
% 3.39/1.83 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( Q @ X ) )
% 3.39/1.83 => ( ( P2 @ S2 )
% 3.39/1.83 => ( ! [X: A,S5: B] :
% 3.39/1.83 ( ( Q @ X )
% 3.39/1.83 => ( ( P2 @ S5 )
% 3.39/1.83 => ( P2 @ ( F2 @ X @ S5 ) ) ) )
% 3.39/1.83 => ( P2 @ ( fold @ A @ B @ F2 @ Xs @ S2 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_145_fold__commute__apply,axiom,
% 3.39/1.83 ! [A: $tType,C: $tType,B: $tType,Xs: list @ A,H: B > C,G: A > B > B,F2: A > C > C,S2: B] :
% 3.39/1.83 ( ! [X: A] :
% 3.39/1.83 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ( comp @ B @ C @ B @ H @ ( G @ X ) )
% 3.39/1.83 = ( comp @ C @ C @ B @ ( F2 @ X ) @ H ) ) )
% 3.39/1.83 => ( ( H @ ( fold @ A @ B @ G @ Xs @ S2 ) )
% 3.39/1.83 = ( fold @ A @ C @ F2 @ Xs @ ( H @ S2 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_146_fold__commute,axiom,
% 3.39/1.83 ! [A: $tType,C: $tType,B: $tType,Xs: list @ A,H: B > C,G: A > B > B,F2: A > C > C] :
% 3.39/1.83 ( ! [X: A] :
% 3.39/1.83 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ( comp @ B @ C @ B @ H @ ( G @ X ) )
% 3.39/1.83 = ( comp @ C @ C @ B @ ( F2 @ X ) @ H ) ) )
% 3.39/1.83 => ( ( comp @ B @ C @ B @ H @ ( fold @ A @ B @ G @ Xs ) )
% 3.39/1.83 = ( comp @ C @ C @ B @ ( fold @ A @ C @ F2 @ Xs ) @ H ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_147_foldr__fold,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,Xs: list @ A,F2: A > B > B] :
% 3.39/1.83 ( ! [X: A,Y3: A] :
% 3.39/1.83 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ( member2 @ A @ Y3 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ( comp @ B @ B @ B @ ( F2 @ Y3 ) @ ( F2 @ X ) )
% 3.39/1.83 = ( comp @ B @ B @ B @ ( F2 @ X ) @ ( F2 @ Y3 ) ) ) ) )
% 3.39/1.83 => ( ( foldr @ A @ B @ F2 @ Xs )
% 3.39/1.83 = ( fold @ A @ B @ F2 @ Xs ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_148_fold__remove1__split,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,Xs: list @ A,F2: A > B > B,X3: A] :
% 3.39/1.83 ( ! [X: A,Y3: A] :
% 3.39/1.83 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ( member2 @ A @ Y3 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ( comp @ B @ B @ B @ ( F2 @ X ) @ ( F2 @ Y3 ) )
% 3.39/1.83 = ( comp @ B @ B @ B @ ( F2 @ Y3 ) @ ( F2 @ X ) ) ) ) )
% 3.39/1.83 => ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ( fold @ A @ B @ F2 @ Xs )
% 3.39/1.83 = ( comp @ B @ B @ B @ ( fold @ A @ B @ F2 @ ( remove1 @ A @ X3 @ Xs ) ) @ ( F2 @ X3 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_149_subset__code_I3_J,axiom,
% 3.39/1.83 ! [C: $tType] :
% 3.39/1.83 ~ ( ord_less_eq @ ( set @ C ) @ ( coset @ C @ ( nil @ C ) ) @ ( set2 @ C @ ( nil @ C ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_150_set__update__subset__insert,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,I: nat,X3: A] : ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ ( list_update @ A @ Xs @ I @ X3 ) ) @ ( insert2 @ A @ X3 @ ( set2 @ A @ Xs ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_151_in__set__remove1,axiom,
% 3.39/1.83 ! [A: $tType,A3: A,B3: A,Xs: list @ A] :
% 3.39/1.83 ( ( A3 != B3 )
% 3.39/1.83 => ( ( member2 @ A @ A3 @ ( set2 @ A @ ( remove1 @ A @ B3 @ Xs ) ) )
% 3.39/1.83 = ( member2 @ A @ A3 @ ( set2 @ A @ Xs ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_152_foldr__cong,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,A3: A,B3: A,L: list @ B,K: list @ B,F2: B > A > A,G: B > A > A] :
% 3.39/1.83 ( ( A3 = B3 )
% 3.39/1.83 => ( ( L = K )
% 3.39/1.83 => ( ! [A7: A,X: B] :
% 3.39/1.83 ( ( member2 @ B @ X @ ( set2 @ B @ L ) )
% 3.39/1.83 => ( ( F2 @ X @ A7 )
% 3.39/1.83 = ( G @ X @ A7 ) ) )
% 3.39/1.83 => ( ( foldr @ B @ A @ F2 @ L @ A3 )
% 3.39/1.83 = ( foldr @ B @ A @ G @ K @ B3 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_153_notin__set__remove1,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Xs: list @ A,Y: A] :
% 3.39/1.83 ( ~ ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ~ ( member2 @ A @ X3 @ ( set2 @ A @ ( remove1 @ A @ Y @ Xs ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_154_remove1__idem,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.39/1.83 ( ~ ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ( remove1 @ A @ X3 @ Xs )
% 3.39/1.83 = Xs ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_155_shift_Osimps_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,S2: stream @ A] :
% 3.39/1.83 ( ( shift @ A @ ( nil @ A ) @ S2 )
% 3.39/1.83 = S2 ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_156_set__update__subsetI,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,A5: set @ A,X3: A,I: nat] :
% 3.39/1.83 ( ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ A5 )
% 3.39/1.83 => ( ( member2 @ A @ X3 @ A5 )
% 3.39/1.83 => ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ ( list_update @ A @ Xs @ I @ X3 ) ) @ A5 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_157_set__remove1__subset,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Xs: list @ A] : ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ ( remove1 @ A @ X3 @ Xs ) ) @ ( set2 @ A @ Xs ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_158_sset__cycle,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A] :
% 3.39/1.83 ( ( Xs
% 3.39/1.83 != ( nil @ A ) )
% 3.39/1.83 => ( ( sset @ A @ ( cycle @ A @ Xs ) )
% 3.39/1.83 = ( set2 @ A @ Xs ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_159_flat__Stream,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,Ws: stream @ ( list @ A )] :
% 3.39/1.83 ( ( Xs
% 3.39/1.83 != ( nil @ A ) )
% 3.39/1.83 => ( ( flat @ A @ ( sCons @ ( list @ A ) @ Xs @ Ws ) )
% 3.39/1.83 = ( shift @ A @ Xs @ ( flat @ A @ Ws ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_160_shift__simps_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,S2: stream @ A] :
% 3.39/1.83 ( ( ( Xs
% 3.39/1.83 = ( nil @ A ) )
% 3.39/1.83 => ( ( shd @ A @ ( shift @ A @ Xs @ S2 ) )
% 3.39/1.83 = ( shd @ A @ S2 ) ) )
% 3.39/1.83 & ( ( Xs
% 3.39/1.83 != ( nil @ A ) )
% 3.39/1.83 => ( ( shd @ A @ ( shift @ A @ Xs @ S2 ) )
% 3.39/1.83 = ( hd @ A @ Xs ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_161_cycle_Osimps_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A] :
% 3.39/1.83 ( ( shd @ A @ ( cycle @ A @ Xs ) )
% 3.39/1.83 = ( hd @ A @ Xs ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_162_flat_Osimps_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,Ws: stream @ ( list @ A )] :
% 3.39/1.83 ( ( shd @ A @ ( flat @ A @ Ws ) )
% 3.39/1.83 = ( hd @ A @ ( shd @ ( list @ A ) @ Ws ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_163_list_Oset__sel_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,A3: list @ A] :
% 3.39/1.83 ( ( A3
% 3.39/1.83 != ( nil @ A ) )
% 3.39/1.83 => ( member2 @ A @ ( hd @ A @ A3 ) @ ( set2 @ A @ A3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_164_hd__in__set,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A] :
% 3.39/1.83 ( ( Xs
% 3.39/1.83 != ( nil @ A ) )
% 3.39/1.83 => ( member2 @ A @ ( hd @ A @ Xs ) @ ( set2 @ A @ Xs ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_165_cycle__decomp,axiom,
% 3.39/1.83 ! [A: $tType,U: list @ A] :
% 3.39/1.83 ( ( U
% 3.39/1.83 != ( nil @ A ) )
% 3.39/1.83 => ( ( cycle @ A @ U )
% 3.39/1.83 = ( shift @ A @ U @ ( cycle @ A @ U ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_166_flat__unfold,axiom,
% 3.39/1.83 ! [A: $tType,Ws: stream @ ( list @ A )] :
% 3.39/1.83 ( ( ( shd @ ( list @ A ) @ Ws )
% 3.39/1.83 != ( nil @ A ) )
% 3.39/1.83 => ( ( flat @ A @ Ws )
% 3.39/1.83 = ( shift @ A @ ( shd @ ( list @ A ) @ Ws ) @ ( flat @ A @ ( stl @ ( list @ A ) @ Ws ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_167_flat_Ocode,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( flat @ A )
% 3.39/1.83 = ( ^ [Ws2: stream @ ( list @ A )] :
% 3.39/1.83 ( sCons @ A @ ( hd @ A @ ( shd @ ( list @ A ) @ Ws2 ) )
% 3.39/1.83 @ ( flat @ A
% 3.39/1.83 @ ( if @ ( stream @ ( list @ A ) )
% 3.39/1.83 @ ( ( tl @ A @ ( shd @ ( list @ A ) @ Ws2 ) )
% 3.39/1.83 = ( nil @ A ) )
% 3.39/1.83 @ ( stl @ ( list @ A ) @ Ws2 )
% 3.39/1.83 @ ( sCons @ ( list @ A ) @ ( tl @ A @ ( shd @ ( list @ A ) @ Ws2 ) ) @ ( stl @ ( list @ A ) @ Ws2 ) ) ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_168_flat__Cons,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Xs: list @ A,Ws: stream @ ( list @ A )] :
% 3.39/1.83 ( ( flat @ A @ ( sCons @ ( list @ A ) @ ( cons @ A @ X3 @ Xs ) @ Ws ) )
% 3.39/1.83 = ( sCons @ A @ X3
% 3.39/1.83 @ ( flat @ A
% 3.39/1.83 @ ( if @ ( stream @ ( list @ A ) )
% 3.39/1.83 @ ( Xs
% 3.39/1.83 = ( nil @ A ) )
% 3.39/1.83 @ Ws
% 3.39/1.83 @ ( sCons @ ( list @ A ) @ Xs @ Ws ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_169_flat_Osimps_I2_J,axiom,
% 3.39/1.83 ! [A: $tType,Ws: stream @ ( list @ A )] :
% 3.39/1.83 ( ( stl @ A @ ( flat @ A @ Ws ) )
% 3.39/1.83 = ( flat @ A
% 3.39/1.83 @ ( if @ ( stream @ ( list @ A ) )
% 3.39/1.83 @ ( ( tl @ A @ ( shd @ ( list @ A ) @ Ws ) )
% 3.39/1.83 = ( nil @ A ) )
% 3.39/1.83 @ ( stl @ ( list @ A ) @ Ws )
% 3.39/1.83 @ ( sCons @ ( list @ A ) @ ( tl @ A @ ( shd @ ( list @ A ) @ Ws ) ) @ ( stl @ ( list @ A ) @ Ws ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_170_list_Osimps_I15_J,axiom,
% 3.39/1.83 ! [A: $tType,X21: A,X222: list @ A] :
% 3.39/1.83 ( ( set2 @ A @ ( cons @ A @ X21 @ X222 ) )
% 3.39/1.83 = ( insert2 @ A @ X21 @ ( set2 @ A @ X222 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_171_not__in__set__insert,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.39/1.83 ( ~ ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ( insert @ A @ X3 @ Xs )
% 3.39/1.83 = ( cons @ A @ X3 @ Xs ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_172_shift__simps_I2_J,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,S2: stream @ A] :
% 3.39/1.83 ( ( ( Xs
% 3.39/1.83 = ( nil @ A ) )
% 3.39/1.83 => ( ( stl @ A @ ( shift @ A @ Xs @ S2 ) )
% 3.39/1.83 = ( stl @ A @ S2 ) ) )
% 3.39/1.83 & ( ( Xs
% 3.39/1.83 != ( nil @ A ) )
% 3.39/1.83 => ( ( stl @ A @ ( shift @ A @ Xs @ S2 ) )
% 3.39/1.83 = ( shift @ A @ ( tl @ A @ Xs ) @ S2 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_173_list_Oset__cases,axiom,
% 3.39/1.83 ! [A: $tType,E: A,A3: list @ A] :
% 3.39/1.83 ( ( member2 @ A @ E @ ( set2 @ A @ A3 ) )
% 3.39/1.83 => ( ! [Z2: list @ A] :
% 3.39/1.83 ( A3
% 3.39/1.83 != ( cons @ A @ E @ Z2 ) )
% 3.39/1.83 => ~ ! [Z1: A,Z2: list @ A] :
% 3.39/1.83 ( ( A3
% 3.39/1.83 = ( cons @ A @ Z1 @ Z2 ) )
% 3.39/1.83 => ~ ( member2 @ A @ E @ ( set2 @ A @ Z2 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_174_set__ConsD,axiom,
% 3.39/1.83 ! [A: $tType,Y: A,X3: A,Xs: list @ A] :
% 3.39/1.83 ( ( member2 @ A @ Y @ ( set2 @ A @ ( cons @ A @ X3 @ Xs ) ) )
% 3.39/1.83 => ( ( Y = X3 )
% 3.39/1.83 | ( member2 @ A @ Y @ ( set2 @ A @ Xs ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_175_list_Oset__intros_I1_J,axiom,
% 3.39/1.83 ! [A: $tType,A1: A,A2: list @ A] : ( member2 @ A @ A1 @ ( set2 @ A @ ( cons @ A @ A1 @ A2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_176_list_Oset__intros_I2_J,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,A2: list @ A,A1: A] :
% 3.39/1.83 ( ( member2 @ A @ X3 @ ( set2 @ A @ A2 ) )
% 3.39/1.83 => ( member2 @ A @ X3 @ ( set2 @ A @ ( cons @ A @ A1 @ A2 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_177_set__subset__Cons,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,X3: A] : ( ord_less_eq @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( set2 @ A @ ( cons @ A @ X3 @ Xs ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_178_list_Oset__sel_I2_J,axiom,
% 3.39/1.83 ! [A: $tType,A3: list @ A,X3: A] :
% 3.39/1.83 ( ( A3
% 3.39/1.83 != ( nil @ A ) )
% 3.39/1.83 => ( ( member2 @ A @ X3 @ ( set2 @ A @ ( tl @ A @ A3 ) ) )
% 3.39/1.83 => ( member2 @ A @ X3 @ ( set2 @ A @ A3 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_179_fold__Cons,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,F2: A > B > B,X3: A,Xs: list @ A] :
% 3.39/1.83 ( ( fold @ A @ B @ F2 @ ( cons @ A @ X3 @ Xs ) )
% 3.39/1.83 = ( comp @ B @ B @ B @ ( fold @ A @ B @ F2 @ Xs ) @ ( F2 @ X3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_180_foldr__Cons,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,F2: A > B > B,X3: A,Xs: list @ A] :
% 3.39/1.83 ( ( foldr @ A @ B @ F2 @ ( cons @ A @ X3 @ Xs ) )
% 3.39/1.83 = ( comp @ B @ B @ B @ ( F2 @ X3 ) @ ( foldr @ A @ B @ F2 @ Xs ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_181_shift_Osimps_I2_J,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Xs: list @ A,S2: stream @ A] :
% 3.39/1.83 ( ( shift @ A @ ( cons @ A @ X3 @ Xs ) @ S2 )
% 3.39/1.83 = ( sCons @ A @ X3 @ ( shift @ A @ Xs @ S2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_182_List_Oinsert__def,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( insert @ A )
% 3.39/1.83 = ( ^ [X5: A,Xs2: list @ A] : ( if @ ( list @ A ) @ ( member2 @ A @ X5 @ ( set2 @ A @ Xs2 ) ) @ Xs2 @ ( cons @ A @ X5 @ Xs2 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_183_the__elem__set,axiom,
% 3.39/1.83 ! [A: $tType,X3: A] :
% 3.39/1.83 ( ( the_elem @ A @ ( set2 @ A @ ( cons @ A @ X3 @ ( nil @ A ) ) ) )
% 3.39/1.83 = X3 ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_184_cycle__rotated,axiom,
% 3.39/1.83 ! [A: $tType,V: list @ A,U: list @ A,S2: stream @ A] :
% 3.39/1.83 ( ( V
% 3.39/1.83 != ( nil @ A ) )
% 3.39/1.83 => ( ( ( cycle @ A @ U )
% 3.39/1.83 = ( shift @ A @ V @ S2 ) )
% 3.39/1.83 => ( ( cycle @ A @ ( append @ A @ ( tl @ A @ U ) @ ( cons @ A @ ( hd @ A @ U ) @ ( nil @ A ) ) ) )
% 3.39/1.83 = ( shift @ A @ ( tl @ A @ V ) @ S2 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_185_cycle_Ocode,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( cycle @ A )
% 3.39/1.83 = ( ^ [Xs2: list @ A] : ( sCons @ A @ ( hd @ A @ Xs2 ) @ ( cycle @ A @ ( append @ A @ ( tl @ A @ Xs2 ) @ ( cons @ A @ ( hd @ A @ Xs2 ) @ ( nil @ A ) ) ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_186_shift__append,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,Ys: list @ A,S2: stream @ A] :
% 3.39/1.83 ( ( shift @ A @ ( append @ A @ Xs @ Ys ) @ S2 )
% 3.39/1.83 = ( shift @ A @ Xs @ ( shift @ A @ Ys @ S2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_187_set__append,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,Ys: list @ A] :
% 3.39/1.83 ( ( set2 @ A @ ( append @ A @ Xs @ Ys ) )
% 3.39/1.83 = ( sup_sup @ ( set @ A ) @ ( set2 @ A @ Xs ) @ ( set2 @ A @ Ys ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_188_fold__append,axiom,
% 3.39/1.83 ! [A: $tType,B: $tType,F2: B > A > A,Xs: list @ B,Ys: list @ B] :
% 3.39/1.83 ( ( fold @ B @ A @ F2 @ ( append @ B @ Xs @ Ys ) )
% 3.39/1.83 = ( comp @ A @ A @ A @ ( fold @ B @ A @ F2 @ Ys ) @ ( fold @ B @ A @ F2 @ Xs ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_189_split__list,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.39/1.83 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ? [Ys2: list @ A,Zs: list @ A] :
% 3.39/1.83 ( Xs
% 3.39/1.83 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_190_split__list__last,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.39/1.83 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ? [Ys2: list @ A,Zs: list @ A] :
% 3.39/1.83 ( ( Xs
% 3.39/1.83 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs ) ) )
% 3.39/1.83 & ~ ( member2 @ A @ X3 @ ( set2 @ A @ Zs ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_191_split__list__prop,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 3.39/1.83 ( ? [X4: A] :
% 3.39/1.83 ( ( member2 @ A @ X4 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 & ( P2 @ X4 ) )
% 3.39/1.83 => ? [Ys2: list @ A,X: A] :
% 3.39/1.83 ( ? [Zs: list @ A] :
% 3.39/1.83 ( Xs
% 3.39/1.83 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 3.39/1.83 & ( P2 @ X ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_192_split__list__first,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.39/1.83 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ? [Ys2: list @ A,Zs: list @ A] :
% 3.39/1.83 ( ( Xs
% 3.39/1.83 = ( append @ A @ Ys2 @ ( cons @ A @ X3 @ Zs ) ) )
% 3.39/1.83 & ~ ( member2 @ A @ X3 @ ( set2 @ A @ Ys2 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_193_split__list__propE,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 3.39/1.83 ( ? [X4: A] :
% 3.39/1.83 ( ( member2 @ A @ X4 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 & ( P2 @ X4 ) )
% 3.39/1.83 => ~ ! [Ys2: list @ A,X: A] :
% 3.39/1.83 ( ? [Zs: list @ A] :
% 3.39/1.83 ( Xs
% 3.39/1.83 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 3.39/1.83 => ~ ( P2 @ X ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_194_in__set__conv__decomp,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.39/1.83 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 3.39/1.83 ( Xs
% 3.39/1.83 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs2 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_195_split__list__last__prop,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 3.39/1.83 ( ? [X4: A] :
% 3.39/1.83 ( ( member2 @ A @ X4 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 & ( P2 @ X4 ) )
% 3.39/1.83 => ? [Ys2: list @ A,X: A,Zs: list @ A] :
% 3.39/1.83 ( ( Xs
% 3.39/1.83 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 3.39/1.83 & ( P2 @ X )
% 3.39/1.83 & ! [Xa3: A] :
% 3.39/1.83 ( ( member2 @ A @ Xa3 @ ( set2 @ A @ Zs ) )
% 3.39/1.83 => ~ ( P2 @ Xa3 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_196_split__list__first__prop,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 3.39/1.83 ( ? [X4: A] :
% 3.39/1.83 ( ( member2 @ A @ X4 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 & ( P2 @ X4 ) )
% 3.39/1.83 => ? [Ys2: list @ A,X: A] :
% 3.39/1.83 ( ? [Zs: list @ A] :
% 3.39/1.83 ( Xs
% 3.39/1.83 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 3.39/1.83 & ( P2 @ X )
% 3.39/1.83 & ! [Xa3: A] :
% 3.39/1.83 ( ( member2 @ A @ Xa3 @ ( set2 @ A @ Ys2 ) )
% 3.39/1.83 => ~ ( P2 @ Xa3 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_197_split__list__last__propE,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 3.39/1.83 ( ? [X4: A] :
% 3.39/1.83 ( ( member2 @ A @ X4 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 & ( P2 @ X4 ) )
% 3.39/1.83 => ~ ! [Ys2: list @ A,X: A,Zs: list @ A] :
% 3.39/1.83 ( ( Xs
% 3.39/1.83 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 3.39/1.83 => ( ( P2 @ X )
% 3.39/1.83 => ~ ! [Xa3: A] :
% 3.39/1.83 ( ( member2 @ A @ Xa3 @ ( set2 @ A @ Zs ) )
% 3.39/1.83 => ~ ( P2 @ Xa3 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_198_split__list__first__propE,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 3.39/1.83 ( ? [X4: A] :
% 3.39/1.83 ( ( member2 @ A @ X4 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 & ( P2 @ X4 ) )
% 3.39/1.83 => ~ ! [Ys2: list @ A,X: A] :
% 3.39/1.83 ( ? [Zs: list @ A] :
% 3.39/1.83 ( Xs
% 3.39/1.83 = ( append @ A @ Ys2 @ ( cons @ A @ X @ Zs ) ) )
% 3.39/1.83 => ( ( P2 @ X )
% 3.39/1.83 => ~ ! [Xa3: A] :
% 3.39/1.83 ( ( member2 @ A @ Xa3 @ ( set2 @ A @ Ys2 ) )
% 3.39/1.83 => ~ ( P2 @ Xa3 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_199_in__set__conv__decomp__last,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.39/1.83 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 3.39/1.83 ( ( Xs
% 3.39/1.83 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs2 ) ) )
% 3.39/1.83 & ~ ( member2 @ A @ X3 @ ( set2 @ A @ Zs2 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_200_in__set__conv__decomp__first,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.39/1.83 ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 = ( ? [Ys3: list @ A,Zs2: list @ A] :
% 3.39/1.83 ( ( Xs
% 3.39/1.83 = ( append @ A @ Ys3 @ ( cons @ A @ X3 @ Zs2 ) ) )
% 3.39/1.83 & ~ ( member2 @ A @ X3 @ ( set2 @ A @ Ys3 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_201_split__list__last__prop__iff,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 3.39/1.83 ( ( ? [X5: A] :
% 3.39/1.83 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 & ( P2 @ X5 ) ) )
% 3.39/1.83 = ( ? [Ys3: list @ A,X5: A,Zs2: list @ A] :
% 3.39/1.83 ( ( Xs
% 3.39/1.83 = ( append @ A @ Ys3 @ ( cons @ A @ X5 @ Zs2 ) ) )
% 3.39/1.83 & ( P2 @ X5 )
% 3.39/1.83 & ! [Y4: A] :
% 3.39/1.83 ( ( member2 @ A @ Y4 @ ( set2 @ A @ Zs2 ) )
% 3.39/1.83 => ~ ( P2 @ Y4 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_202_split__list__first__prop__iff,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,P2: A > $o] :
% 3.39/1.83 ( ( ? [X5: A] :
% 3.39/1.83 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 & ( P2 @ X5 ) ) )
% 3.39/1.83 = ( ? [Ys3: list @ A,X5: A] :
% 3.39/1.83 ( ? [Zs2: list @ A] :
% 3.39/1.83 ( Xs
% 3.39/1.83 = ( append @ A @ Ys3 @ ( cons @ A @ X5 @ Zs2 ) ) )
% 3.39/1.83 & ( P2 @ X5 )
% 3.39/1.83 & ! [Y4: A] :
% 3.39/1.83 ( ( member2 @ A @ Y4 @ ( set2 @ A @ Ys3 ) )
% 3.39/1.83 => ~ ( P2 @ Y4 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_203_remove1__append,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Xs: list @ A,Ys: list @ A] :
% 3.39/1.83 ( ( ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ( remove1 @ A @ X3 @ ( append @ A @ Xs @ Ys ) )
% 3.39/1.83 = ( append @ A @ ( remove1 @ A @ X3 @ Xs ) @ Ys ) ) )
% 3.39/1.83 & ( ~ ( member2 @ A @ X3 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ( remove1 @ A @ X3 @ ( append @ A @ Xs @ Ys ) )
% 3.39/1.83 = ( append @ A @ Xs @ ( remove1 @ A @ X3 @ Ys ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_204_cycle__Cons,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.39/1.83 ( ( cycle @ A @ ( cons @ A @ X3 @ Xs ) )
% 3.39/1.83 = ( sCons @ A @ X3 @ ( cycle @ A @ ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_205_cycle_Osimps_I2_J,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A] :
% 3.39/1.83 ( ( stl @ A @ ( cycle @ A @ Xs ) )
% 3.39/1.83 = ( cycle @ A @ ( append @ A @ ( tl @ A @ Xs ) @ ( cons @ A @ ( hd @ A @ Xs ) @ ( nil @ A ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_206_Sup__fin_Oset__eq__fold,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 3.39/1.83 => ! [X3: A,Xs: list @ A] :
% 3.39/1.83 ( ( lattic477160up_fin @ A @ ( set2 @ A @ ( cons @ A @ X3 @ Xs ) ) )
% 3.39/1.83 = ( fold @ A @ A @ ( sup_sup @ A ) @ Xs @ X3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_207_sorted_Ocases,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.83 => ! [A3: list @ A] :
% 3.39/1.83 ( ( linorder_sorted @ A @ A3 )
% 3.39/1.83 => ( ( A3
% 3.39/1.83 != ( nil @ A ) )
% 3.39/1.83 => ~ ! [Xs3: list @ A,X: A] :
% 3.39/1.83 ( ( A3
% 3.39/1.83 = ( cons @ A @ X @ Xs3 ) )
% 3.39/1.83 => ( ! [Xa3: A] :
% 3.39/1.83 ( ( member2 @ A @ Xa3 @ ( set2 @ A @ Xs3 ) )
% 3.39/1.83 => ( ord_less_eq @ A @ X @ Xa3 ) )
% 3.39/1.83 => ~ ( linorder_sorted @ A @ Xs3 ) ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_208_sorted_Osimps,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.83 => ( ( linorder_sorted @ A )
% 3.39/1.83 = ( ^ [A4: list @ A] :
% 3.39/1.83 ( ( A4
% 3.39/1.83 = ( nil @ A ) )
% 3.39/1.83 | ? [Xs2: list @ A,X5: A] :
% 3.39/1.83 ( ( A4
% 3.39/1.83 = ( cons @ A @ X5 @ Xs2 ) )
% 3.39/1.83 & ! [Y4: A] :
% 3.39/1.83 ( ( member2 @ A @ Y4 @ ( set2 @ A @ Xs2 ) )
% 3.39/1.83 => ( ord_less_eq @ A @ X5 @ Y4 ) )
% 3.39/1.83 & ( linorder_sorted @ A @ Xs2 ) ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_209_sorted_OCons,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.83 => ! [Xs: list @ A,X3: A] :
% 3.39/1.83 ( ! [X: A] :
% 3.39/1.83 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ord_less_eq @ A @ X3 @ X ) )
% 3.39/1.83 => ( ( linorder_sorted @ A @ Xs )
% 3.39/1.83 => ( linorder_sorted @ A @ ( cons @ A @ X3 @ Xs ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_210_sorted__Cons,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.83 => ! [X3: A,Xs: list @ A] :
% 3.39/1.83 ( ( linorder_sorted @ A @ ( cons @ A @ X3 @ Xs ) )
% 3.39/1.83 = ( ( linorder_sorted @ A @ Xs )
% 3.39/1.83 & ! [X5: A] :
% 3.39/1.83 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ord_less_eq @ A @ X3 @ X5 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_211_sorted__append,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.83 => ! [Xs: list @ A,Ys: list @ A] :
% 3.39/1.83 ( ( linorder_sorted @ A @ ( append @ A @ Xs @ Ys ) )
% 3.39/1.83 = ( ( linorder_sorted @ A @ Xs )
% 3.39/1.83 & ( linorder_sorted @ A @ Ys )
% 3.39/1.83 & ! [X5: A] :
% 3.39/1.83 ( ( member2 @ A @ X5 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ! [Y4: A] :
% 3.39/1.83 ( ( member2 @ A @ Y4 @ ( set2 @ A @ Ys ) )
% 3.39/1.83 => ( ord_less_eq @ A @ X5 @ Y4 ) ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_212_sorted_Oinducts,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.83 => ! [X3: list @ A,P2: ( list @ A ) > $o] :
% 3.39/1.83 ( ( linorder_sorted @ A @ X3 )
% 3.39/1.83 => ( ( P2 @ ( nil @ A ) )
% 3.39/1.83 => ( ! [Xs3: list @ A,X: A] :
% 3.39/1.83 ( ! [Xa3: A] :
% 3.39/1.83 ( ( member2 @ A @ Xa3 @ ( set2 @ A @ Xs3 ) )
% 3.39/1.83 => ( ord_less_eq @ A @ X @ Xa3 ) )
% 3.39/1.83 => ( ( linorder_sorted @ A @ Xs3 )
% 3.39/1.83 => ( ( P2 @ Xs3 )
% 3.39/1.83 => ( P2 @ ( cons @ A @ X @ Xs3 ) ) ) ) )
% 3.39/1.83 => ( P2 @ X3 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_213_insort__is__Cons,axiom,
% 3.39/1.83 ! [A: $tType,B: $tType] :
% 3.39/1.83 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.83 => ! [Xs: list @ B,F2: B > A,A3: B] :
% 3.39/1.83 ( ! [X: B] :
% 3.39/1.83 ( ( member2 @ B @ X @ ( set2 @ B @ Xs ) )
% 3.39/1.83 => ( ord_less_eq @ A @ ( F2 @ A3 ) @ ( F2 @ X ) ) )
% 3.39/1.83 => ( ( linorder_insort_key @ B @ A @ F2 @ A3 @ Xs )
% 3.39/1.83 = ( cons @ B @ A3 @ Xs ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_214_fold__rev,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,Xs: list @ A,F2: A > B > B] :
% 3.39/1.83 ( ! [X: A,Y3: A] :
% 3.39/1.83 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ( member2 @ A @ Y3 @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ( comp @ B @ B @ B @ ( F2 @ Y3 ) @ ( F2 @ X ) )
% 3.39/1.83 = ( comp @ B @ B @ B @ ( F2 @ X ) @ ( F2 @ Y3 ) ) ) ) )
% 3.39/1.83 => ( ( fold @ A @ B @ F2 @ ( rev @ A @ Xs ) )
% 3.39/1.83 = ( fold @ A @ B @ F2 @ Xs ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_215_set__rev,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A] :
% 3.39/1.83 ( ( set2 @ A @ ( rev @ A @ Xs ) )
% 3.39/1.83 = ( set2 @ A @ Xs ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_216_set__insort__key,axiom,
% 3.39/1.83 ! [A: $tType,B: $tType] :
% 3.39/1.83 ( ( linorder @ A @ ( type2 @ A ) )
% 3.39/1.83 => ! [F2: B > A,X3: B,Xs: list @ B] :
% 3.39/1.83 ( ( set2 @ B @ ( linorder_insort_key @ B @ A @ F2 @ X3 @ Xs ) )
% 3.39/1.83 = ( insert2 @ B @ X3 @ ( set2 @ B @ Xs ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_217_trev_Ocode,axiom,
% 3.39/1.83 ! [A: $tType] :
% 3.39/1.83 ( ( trev @ A )
% 3.39/1.83 = ( ^ [T3: treeFI @ A] : ( tree @ A @ ( lab @ A @ T3 ) @ ( map @ ( treeFI @ A ) @ ( treeFI @ A ) @ ( trev @ A ) @ ( rev @ ( treeFI @ A ) @ ( sub @ A @ T3 ) ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_218_treeFI_Opred__map,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,Q: B > $o,F2: A > B,X3: treeFI @ A] :
% 3.39/1.83 ( ( pred_treeFI @ B @ Q @ ( map_treeFI @ A @ B @ F2 @ X3 ) )
% 3.39/1.83 = ( pred_treeFI @ A @ ( comp @ B @ $o @ A @ Q @ F2 ) @ X3 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_219_map__map,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,C: $tType,F2: B > A,G: C > B,Xs: list @ C] :
% 3.39/1.83 ( ( map @ B @ A @ F2 @ ( map @ C @ B @ G @ Xs ) )
% 3.39/1.83 = ( map @ C @ A @ ( comp @ B @ A @ C @ F2 @ G ) @ Xs ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_220_List_Omap_Ocomp,axiom,
% 3.39/1.83 ! [C: $tType,B: $tType,A: $tType,F2: B > C,G: A > B] :
% 3.39/1.83 ( ( comp @ ( list @ B ) @ ( list @ C ) @ ( list @ A ) @ ( map @ B @ C @ F2 ) @ ( map @ A @ B @ G ) )
% 3.39/1.83 = ( map @ A @ C @ ( comp @ B @ C @ A @ F2 @ G ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_221_map__comp__map,axiom,
% 3.39/1.83 ! [B: $tType,C: $tType,A: $tType,F2: C > B,G: A > C] :
% 3.39/1.83 ( ( comp @ ( list @ C ) @ ( list @ B ) @ ( list @ A ) @ ( map @ C @ B @ F2 ) @ ( map @ A @ C @ G ) )
% 3.39/1.83 = ( map @ A @ B @ ( comp @ C @ B @ A @ F2 @ G ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_222_list_Omap__comp,axiom,
% 3.39/1.83 ! [B: $tType,C: $tType,A: $tType,G: B > C,F2: A > B,V: list @ A] :
% 3.39/1.83 ( ( map @ B @ C @ G @ ( map @ A @ B @ F2 @ V ) )
% 3.39/1.83 = ( map @ A @ C @ ( comp @ B @ C @ A @ G @ F2 ) @ V ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_223_List_Omap_Ocompositionality,axiom,
% 3.39/1.83 ! [B: $tType,C: $tType,A: $tType,F2: B > C,G: A > B,List: list @ A] :
% 3.39/1.83 ( ( map @ B @ C @ F2 @ ( map @ A @ B @ G @ List ) )
% 3.39/1.83 = ( map @ A @ C @ ( comp @ B @ C @ A @ F2 @ G ) @ List ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_224_map__eq__conv,axiom,
% 3.39/1.83 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B,G: B > A] :
% 3.39/1.83 ( ( ( map @ B @ A @ F2 @ Xs )
% 3.39/1.83 = ( map @ B @ A @ G @ Xs ) )
% 3.39/1.83 = ( ! [X5: B] :
% 3.39/1.83 ( ( member2 @ B @ X5 @ ( set2 @ B @ Xs ) )
% 3.39/1.83 => ( ( F2 @ X5 )
% 3.39/1.83 = ( G @ X5 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_225_smap__shift,axiom,
% 3.39/1.83 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B,S2: stream @ B] :
% 3.39/1.83 ( ( smap @ B @ A @ F2 @ ( shift @ B @ Xs @ S2 ) )
% 3.39/1.83 = ( shift @ A @ ( map @ B @ A @ F2 @ Xs ) @ ( smap @ B @ A @ F2 @ S2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_226_trev_Osimps_I2_J,axiom,
% 3.39/1.83 ! [A: $tType,T: treeFI @ A] :
% 3.39/1.83 ( ( sub @ A @ ( trev @ A @ T ) )
% 3.39/1.83 = ( map @ ( treeFI @ A ) @ ( treeFI @ A ) @ ( trev @ A ) @ ( rev @ ( treeFI @ A ) @ ( sub @ A @ T ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_227_treeFI_Omap__sel_I1_J,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,F2: A > B,A3: treeFI @ A] :
% 3.39/1.83 ( ( lab @ B @ ( map_treeFI @ A @ B @ F2 @ A3 ) )
% 3.39/1.83 = ( F2 @ ( lab @ A @ A3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_228_treeFI_Oinj__map__strong,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,X3: treeFI @ A,Xa: treeFI @ A,F2: A > B,Fa: A > B] :
% 3.39/1.83 ( ! [Z: A,Za: A] :
% 3.39/1.83 ( ( member2 @ A @ Z @ ( set_treeFI @ A @ X3 ) )
% 3.39/1.83 => ( ( member2 @ A @ Za @ ( set_treeFI @ A @ Xa ) )
% 3.39/1.83 => ( ( ( F2 @ Z )
% 3.39/1.83 = ( Fa @ Za ) )
% 3.39/1.83 => ( Z = Za ) ) ) )
% 3.39/1.83 => ( ( ( map_treeFI @ A @ B @ F2 @ X3 )
% 3.39/1.83 = ( map_treeFI @ A @ B @ Fa @ Xa ) )
% 3.39/1.83 => ( X3 = Xa ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_229_treeFI_Omap__cong0,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,X3: treeFI @ A,F2: A > B,G: A > B] :
% 3.39/1.83 ( ! [Z: A] :
% 3.39/1.83 ( ( member2 @ A @ Z @ ( set_treeFI @ A @ X3 ) )
% 3.39/1.83 => ( ( F2 @ Z )
% 3.39/1.83 = ( G @ Z ) ) )
% 3.39/1.83 => ( ( map_treeFI @ A @ B @ F2 @ X3 )
% 3.39/1.83 = ( map_treeFI @ A @ B @ G @ X3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_230_treeFI_Omap__cong,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,X3: treeFI @ A,Ya: treeFI @ A,F2: A > B,G: A > B] :
% 3.39/1.83 ( ( X3 = Ya )
% 3.39/1.83 => ( ! [Z: A] :
% 3.39/1.83 ( ( member2 @ A @ Z @ ( set_treeFI @ A @ Ya ) )
% 3.39/1.83 => ( ( F2 @ Z )
% 3.39/1.83 = ( G @ Z ) ) )
% 3.39/1.83 => ( ( map_treeFI @ A @ B @ F2 @ X3 )
% 3.39/1.83 = ( map_treeFI @ A @ B @ G @ Ya ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_231_treeFI_Omap__comp,axiom,
% 3.39/1.83 ! [B: $tType,C: $tType,A: $tType,G: B > C,F2: A > B,V: treeFI @ A] :
% 3.39/1.83 ( ( map_treeFI @ B @ C @ G @ ( map_treeFI @ A @ B @ F2 @ V ) )
% 3.39/1.83 = ( map_treeFI @ A @ C @ ( comp @ B @ C @ A @ G @ F2 ) @ V ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_232_treeFI_Omap,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,F2: A > B,X1: A,X22: list @ ( treeFI @ A )] :
% 3.39/1.83 ( ( map_treeFI @ A @ B @ F2 @ ( tree @ A @ X1 @ X22 ) )
% 3.39/1.83 = ( tree @ B @ ( F2 @ X1 ) @ ( map @ ( treeFI @ A ) @ ( treeFI @ B ) @ ( map_treeFI @ A @ B @ F2 ) @ X22 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_233_treeFI_Omap__sel_I2_J,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,F2: A > B,A3: treeFI @ A] :
% 3.39/1.83 ( ( sub @ B @ ( map_treeFI @ A @ B @ F2 @ A3 ) )
% 3.39/1.83 = ( map @ ( treeFI @ A ) @ ( treeFI @ B ) @ ( map_treeFI @ A @ B @ F2 ) @ ( sub @ A @ A3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_234_list_Oinj__map__strong,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,X3: list @ A,Xa: list @ A,F2: A > B,Fa: A > B] :
% 3.39/1.83 ( ! [Z: A,Za: A] :
% 3.39/1.83 ( ( member2 @ A @ Z @ ( set2 @ A @ X3 ) )
% 3.39/1.83 => ( ( member2 @ A @ Za @ ( set2 @ A @ Xa ) )
% 3.39/1.83 => ( ( ( F2 @ Z )
% 3.39/1.83 = ( Fa @ Za ) )
% 3.39/1.83 => ( Z = Za ) ) ) )
% 3.39/1.83 => ( ( ( map @ A @ B @ F2 @ X3 )
% 3.39/1.83 = ( map @ A @ B @ Fa @ Xa ) )
% 3.39/1.83 => ( X3 = Xa ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_235_list_Omap__cong0,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,X3: list @ A,F2: A > B,G: A > B] :
% 3.39/1.83 ( ! [Z: A] :
% 3.39/1.83 ( ( member2 @ A @ Z @ ( set2 @ A @ X3 ) )
% 3.39/1.83 => ( ( F2 @ Z )
% 3.39/1.83 = ( G @ Z ) ) )
% 3.39/1.83 => ( ( map @ A @ B @ F2 @ X3 )
% 3.39/1.83 = ( map @ A @ B @ G @ X3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_236_list_Omap__cong,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,X3: list @ A,Ya: list @ A,F2: A > B,G: A > B] :
% 3.39/1.83 ( ( X3 = Ya )
% 3.39/1.83 => ( ! [Z: A] :
% 3.39/1.83 ( ( member2 @ A @ Z @ ( set2 @ A @ Ya ) )
% 3.39/1.83 => ( ( F2 @ Z )
% 3.39/1.83 = ( G @ Z ) ) )
% 3.39/1.83 => ( ( map @ A @ B @ F2 @ X3 )
% 3.39/1.83 = ( map @ A @ B @ G @ Ya ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_237_ex__map__conv,axiom,
% 3.39/1.83 ! [A: $tType,B: $tType,Ys: list @ B,F2: A > B] :
% 3.39/1.83 ( ( ? [Xs2: list @ A] :
% 3.39/1.83 ( Ys
% 3.39/1.83 = ( map @ A @ B @ F2 @ Xs2 ) ) )
% 3.39/1.83 = ( ! [X5: B] :
% 3.39/1.83 ( ( member2 @ B @ X5 @ ( set2 @ B @ Ys ) )
% 3.39/1.83 => ? [Y4: A] :
% 3.39/1.83 ( X5
% 3.39/1.83 = ( F2 @ Y4 ) ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_238_map__cong,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,Xs: list @ A,Ys: list @ A,F2: A > B,G: A > B] :
% 3.39/1.83 ( ( Xs = Ys )
% 3.39/1.83 => ( ! [X: A] :
% 3.39/1.83 ( ( member2 @ A @ X @ ( set2 @ A @ Ys ) )
% 3.39/1.83 => ( ( F2 @ X )
% 3.39/1.83 = ( G @ X ) ) )
% 3.39/1.83 => ( ( map @ A @ B @ F2 @ Xs )
% 3.39/1.83 = ( map @ A @ B @ G @ Ys ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_239_map__idI,axiom,
% 3.39/1.83 ! [A: $tType,Xs: list @ A,F2: A > A] :
% 3.39/1.83 ( ! [X: A] :
% 3.39/1.83 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ( F2 @ X )
% 3.39/1.83 = X ) )
% 3.39/1.83 => ( ( map @ A @ A @ F2 @ Xs )
% 3.39/1.83 = Xs ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_240_map__ext,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,Xs: list @ A,F2: A > B,G: A > B] :
% 3.39/1.83 ( ! [X: A] :
% 3.39/1.83 ( ( member2 @ A @ X @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ( F2 @ X )
% 3.39/1.83 = ( G @ X ) ) )
% 3.39/1.83 => ( ( map @ A @ B @ F2 @ Xs )
% 3.39/1.83 = ( map @ A @ B @ G @ Xs ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_241_foldr__map,axiom,
% 3.39/1.83 ! [C: $tType,B: $tType,A: $tType,G: B > A > A,F2: C > B,Xs: list @ C,A3: A] :
% 3.39/1.83 ( ( foldr @ B @ A @ G @ ( map @ C @ B @ F2 @ Xs ) @ A3 )
% 3.39/1.83 = ( foldr @ C @ A @ ( comp @ B @ ( A > A ) @ C @ G @ F2 ) @ Xs @ A3 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_242_fold__map,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,C: $tType,G: B > A > A,F2: C > B,Xs: list @ C] :
% 3.39/1.83 ( ( fold @ B @ A @ G @ ( map @ C @ B @ F2 @ Xs ) )
% 3.39/1.83 = ( fold @ C @ A @ ( comp @ B @ ( A > A ) @ C @ G @ F2 ) @ Xs ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_243_list_Opred__map,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,Q: B > $o,F2: A > B,X3: list @ A] :
% 3.39/1.83 ( ( list_all @ B @ Q @ ( map @ A @ B @ F2 @ X3 ) )
% 3.39/1.83 = ( list_all @ A @ ( comp @ B @ $o @ A @ Q @ F2 ) @ X3 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_244_stake__smap,axiom,
% 3.39/1.83 ! [A: $tType,B: $tType,N2: nat,F2: B > A,S2: stream @ B] :
% 3.39/1.83 ( ( stake @ A @ N2 @ ( smap @ B @ A @ F2 @ S2 ) )
% 3.39/1.83 = ( map @ B @ A @ F2 @ ( stake @ B @ N2 @ S2 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_245_map__fun__upd,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,Y: A,Xs: list @ A,F2: A > B,V: B] :
% 3.39/1.83 ( ~ ( member2 @ A @ Y @ ( set2 @ A @ Xs ) )
% 3.39/1.83 => ( ( map @ A @ B @ ( fun_upd @ A @ B @ F2 @ Y @ V ) @ Xs )
% 3.39/1.83 = ( map @ A @ B @ F2 @ Xs ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_246_fun__upd__apply,axiom,
% 3.39/1.83 ! [A: $tType,B: $tType] :
% 3.39/1.83 ( ( fun_upd @ B @ A )
% 3.39/1.83 = ( ^ [F: B > A,X5: B,Y4: A,Z3: B] : ( if @ A @ ( Z3 = X5 ) @ Y4 @ ( F @ Z3 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_247_fun__upd__triv,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,F2: A > B,X3: A] :
% 3.39/1.83 ( ( fun_upd @ A @ B @ F2 @ X3 @ ( F2 @ X3 ) )
% 3.39/1.83 = F2 ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_248_fun__upd__upd,axiom,
% 3.39/1.83 ! [A: $tType,B: $tType,F2: A > B,X3: A,Y: B,Z4: B] :
% 3.39/1.83 ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ F2 @ X3 @ Y ) @ X3 @ Z4 )
% 3.39/1.83 = ( fun_upd @ A @ B @ F2 @ X3 @ Z4 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_249_fun__upd__comp,axiom,
% 3.39/1.83 ! [A: $tType,B: $tType,C: $tType,F2: C > B,G: A > C,X3: A,Y: C] :
% 3.39/1.83 ( ( comp @ C @ B @ A @ F2 @ ( fun_upd @ A @ C @ G @ X3 @ Y ) )
% 3.39/1.83 = ( fun_upd @ A @ B @ ( comp @ C @ B @ A @ F2 @ G ) @ X3 @ ( F2 @ Y ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_250_fun__upd__idem__iff,axiom,
% 3.39/1.83 ! [A: $tType,B: $tType,F2: A > B,X3: A,Y: B] :
% 3.39/1.83 ( ( ( fun_upd @ A @ B @ F2 @ X3 @ Y )
% 3.39/1.83 = F2 )
% 3.39/1.83 = ( ( F2 @ X3 )
% 3.39/1.83 = Y ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_251_fun__upd__twist,axiom,
% 3.39/1.83 ! [A: $tType,B: $tType,A3: A,C2: A,M2: A > B,B3: B,D2: B] :
% 3.39/1.83 ( ( A3 != C2 )
% 3.39/1.83 => ( ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M2 @ A3 @ B3 ) @ C2 @ D2 )
% 3.39/1.83 = ( fun_upd @ A @ B @ ( fun_upd @ A @ B @ M2 @ C2 @ D2 ) @ A3 @ B3 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_252_fun__upd__other,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,Z4: A,X3: A,F2: A > B,Y: B] :
% 3.39/1.83 ( ( Z4 != X3 )
% 3.39/1.83 => ( ( fun_upd @ A @ B @ F2 @ X3 @ Y @ Z4 )
% 3.39/1.83 = ( F2 @ Z4 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_253_fun__upd__same,axiom,
% 3.39/1.83 ! [B: $tType,A: $tType,F2: B > A,X3: B,Y: A] :
% 3.39/1.83 ( ( fun_upd @ B @ A @ F2 @ X3 @ Y @ X3 )
% 3.39/1.83 = Y ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_254_fun__upd__idem,axiom,
% 3.39/1.83 ! [A: $tType,B: $tType,F2: B > A,X3: B,Y: A] :
% 3.39/1.83 ( ( ( F2 @ X3 )
% 3.39/1.83 = Y )
% 3.39/1.83 => ( ( fun_upd @ B @ A @ F2 @ X3 @ Y )
% 3.39/1.83 = F2 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(fact_255_fun__upd__eqD,axiom,
% 3.39/1.83 ! [A: $tType,B: $tType,F2: A > B,X3: A,Y: B,G: A > B,Z4: B] :
% 3.39/1.83 ( ( ( fun_upd @ A @ B @ F2 @ X3 @ Y )
% 3.39/1.83 = ( fun_upd @ A @ B @ G @ X3 @ Z4 ) )
% 3.39/1.83 => ( Y = Z4 ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 3.39/1.83 ! [A8: $tType,A9: $tType] :
% 3.39/1.83 ( ( semilattice_sup @ A9 @ ( type2 @ A9 ) )
% 3.39/1.83 => ( semilattice_sup @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_1,axiom,
% 3.39/1.83 ! [A8: $tType] : ( semilattice_sup @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_2,axiom,
% 3.39/1.83 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 3.39/1.83
% 3.39/1.83 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 3.39/1.83 linorder @ $o @ ( type2 @ $o ) ).
% 3.39/1.83
% 3.39/1.83 thf(help_If_3_1_T,axiom,
% 3.39/1.83 ! [P2: $o] :
% 3.39/1.83 ( ( P2 = $true )
% 3.39/1.83 | ( P2 = $false ) ) ).
% 3.39/1.83
% 3.39/1.83 thf(help_If_2_1_T,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Y: A] :
% 3.39/1.83 ( ( if @ A @ $false @ X3 @ Y )
% 3.39/1.83 = Y ) ).
% 3.39/1.83
% 3.39/1.83 thf(help_If_1_1_T,axiom,
% 3.39/1.83 ! [A: $tType,X3: A,Y: A] :
% 3.39/1.83 ( ( if @ A @ $true @ X3 @ Y )
% 3.39/1.83 = X3 ) ).
% 3.39/1.83
% 3.39/1.83 thf(conj_0,conjecture,
% 3.39/1.83 koenig1755522246erPath @ a @ as @ tr ).
% 3.39/1.83 ------------------------
% 3.39/1.87 % (27840)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_27722 for (2999ds/2Mi)
% 3.39/1.87 % (27839)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27722 for (2999ds/2Mi)
% 3.39/1.87 % (27837)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_27722 for (2999ds/4Mi)
% 3.39/1.87 % (27841)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_27722 for (2999ds/275Mi)
% 3.39/1.87 % (27838)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_27722 for (2999ds/27Mi)
% 3.39/1.87 % (27842)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27722 for (2999ds/18Mi)
% 3.39/1.87 % (27836)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27722 for (2999ds/183Mi)
% 3.39/1.87 % (27839)Instruction limit reached!
% 3.39/1.87 % (27839)------------------------------
% 3.39/1.87 % (27839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.87 % (27839)Termination reason: Unknown
% 3.39/1.87 % (27839)Termination phase: shuffling
% 3.39/1.87
% 3.39/1.87 % (27839)Memory used [KB]: 1407
% 3.39/1.87 % (27839)Time elapsed: 0.003 s
% 3.39/1.87 % (27839)Instructions burned: 2 (million)
% 3.39/1.87 % (27839)------------------------------
% 3.39/1.87 % (27839)------------------------------
% 3.39/1.87 % (27840)Instruction limit reached!
% 3.39/1.87 % (27840)------------------------------
% 3.39/1.87 % (27840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.87 % (27840)Termination reason: Unknown
% 3.39/1.87 % (27840)Termination phase: shuffling
% 3.39/1.87
% 3.39/1.87 % (27840)Memory used [KB]: 1407
% 3.39/1.87 % (27840)Time elapsed: 0.003 s
% 3.39/1.87 % (27840)Instructions burned: 2 (million)
% 3.39/1.87 % (27840)------------------------------
% 3.39/1.87 % (27840)------------------------------
% 3.39/1.87 % (27837)Instruction limit reached!
% 3.39/1.87 % (27837)------------------------------
% 3.39/1.87 % (27837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.87 % (27837)Termination reason: Unknown
% 3.39/1.87 % (27837)Termination phase: shuffling
% 3.39/1.87
% 3.39/1.87 % (27837)Memory used [KB]: 1535
% 3.39/1.87 % (27837)Time elapsed: 0.004 s
% 3.39/1.87 % (27837)Instructions burned: 4 (million)
% 3.39/1.87 % (27837)------------------------------
% 3.39/1.87 % (27837)------------------------------
% 3.39/1.88 % (27842)Instruction limit reached!
% 3.39/1.88 % (27842)------------------------------
% 3.39/1.88 % (27842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.88 % (27842)Termination reason: Unknown
% 3.39/1.88 % (27842)Termination phase: shuffling
% 3.39/1.88
% 3.39/1.88 % (27842)Memory used [KB]: 1791
% 3.39/1.88 % (27842)Time elapsed: 0.011 s
% 3.39/1.88 % (27842)Instructions burned: 18 (million)
% 3.39/1.88 % (27842)------------------------------
% 3.39/1.88 % (27842)------------------------------
% 3.39/1.89 % (27838)Instruction limit reached!
% 3.39/1.89 % (27838)------------------------------
% 3.39/1.89 % (27838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.89 % (27838)Termination reason: Unknown
% 3.39/1.89 % (27838)Termination phase: Property scanning
% 3.39/1.89
% 3.39/1.89 % (27838)Memory used [KB]: 1918
% 3.39/1.89 % (27838)Time elapsed: 0.016 s
% 3.39/1.89 % (27838)Instructions burned: 28 (million)
% 3.39/1.89 % (27838)------------------------------
% 3.39/1.89 % (27838)------------------------------
% 3.39/1.89 % (27843)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27722 for (2999ds/3Mi)
% 3.39/1.89 % (27844)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_27722 for (2999ds/37Mi)
% 3.39/1.89 % (27845)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_27722 for (2999ds/15Mi)
% 3.39/1.89 % (27843)Instruction limit reached!
% 3.39/1.89 % (27843)------------------------------
% 3.39/1.89 % (27843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.89 % (27843)Termination reason: Unknown
% 3.39/1.89 % (27843)Termination phase: shuffling
% 3.39/1.89
% 3.39/1.89 % (27843)Memory used [KB]: 1407
% 3.39/1.89 % (27843)Time elapsed: 0.003 s
% 3.39/1.89 % (27843)Instructions burned: 3 (million)
% 3.39/1.89 % (27843)------------------------------
% 3.39/1.89 % (27843)------------------------------
% 3.39/1.90 % (27841)Refutation not found, incomplete strategy
% 3.39/1.90 % (27841)------------------------------
% 3.39/1.90 % (27841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.39/1.90 % (27841)Termination reason: Refutation not found, incomplete strategy
% 3.39/1.90
% 3.39/1.90
% 3.39/1.90 % (27841)Memory used [KB]: 6524
% 3.39/1.90 % (27841)Time elapsed: 0.025 s
% 3.39/1.90 % (27841)Instructions burned: 47 (million)
% 3.39/1.90 % (27841)------------------------------
% 3.39/1.90 % (27841)------------------------------
% 3.45/1.90 % (27846)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_27722 for (2999ds/3Mi)
% 3.45/1.90 % (27845)Instruction limit reached!
% 3.45/1.90 % (27845)------------------------------
% 3.45/1.90 % (27845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.90 % (27845)Termination reason: Unknown
% 3.45/1.90 % (27845)Termination phase: shuffling
% 3.45/1.90
% 3.45/1.90 % (27845)Memory used [KB]: 1791
% 3.45/1.90 % (27845)Time elapsed: 0.010 s
% 3.45/1.90 % (27845)Instructions burned: 16 (million)
% 3.45/1.90 % (27845)------------------------------
% 3.45/1.90 % (27845)------------------------------
% 3.45/1.90 % (27846)Instruction limit reached!
% 3.45/1.90 % (27846)------------------------------
% 3.45/1.90 % (27846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.90 % (27846)Termination reason: Unknown
% 3.45/1.90 % (27846)Termination phase: shuffling
% 3.45/1.90
% 3.45/1.90 % (27846)Memory used [KB]: 1407
% 3.45/1.90 % (27846)Time elapsed: 0.003 s
% 3.45/1.90 % (27846)Instructions burned: 3 (million)
% 3.45/1.90 % (27846)------------------------------
% 3.45/1.90 % (27846)------------------------------
% 3.45/1.90 % (27847)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_27722 for (2999ds/1041Mi)
% 3.45/1.91 % (27848)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27722 for (2999ds/7Mi)
% 3.45/1.91 % (27844)Instruction limit reached!
% 3.45/1.91 % (27844)------------------------------
% 3.45/1.91 % (27844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.91 % (27844)Termination reason: Unknown
% 3.45/1.91 % (27844)Termination phase: shuffling
% 3.45/1.91
% 3.45/1.91 % (27844)Memory used [KB]: 2174
% 3.45/1.91 % (27844)Time elapsed: 0.019 s
% 3.45/1.91 % (27844)Instructions burned: 38 (million)
% 3.45/1.91 % (27844)------------------------------
% 3.45/1.91 % (27844)------------------------------
% 3.45/1.91 % (27848)Instruction limit reached!
% 3.45/1.91 % (27848)------------------------------
% 3.45/1.91 % (27848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.91 % (27848)Termination reason: Unknown
% 3.45/1.91 % (27848)Termination phase: shuffling
% 3.45/1.91
% 3.45/1.91 % (27848)Memory used [KB]: 1535
% 3.45/1.91 % (27848)Time elapsed: 0.005 s
% 3.45/1.91 % (27848)Instructions burned: 7 (million)
% 3.45/1.91 % (27848)------------------------------
% 3.45/1.91 % (27848)------------------------------
% 3.45/1.91 % (27849)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27722 for (2999ds/16Mi)
% 3.45/1.91 % (27850)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_27722 for (2999ds/3Mi)
% 3.45/1.91 % (27851)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_27722 for (2999ds/3Mi)
% 3.45/1.92 % (27850)Instruction limit reached!
% 3.45/1.92 % (27850)------------------------------
% 3.45/1.92 % (27850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.92 % (27850)Termination reason: Unknown
% 3.45/1.92 % (27850)Termination phase: shuffling
% 3.45/1.92
% 3.45/1.92 % (27850)Memory used [KB]: 1407
% 3.45/1.92 % (27850)Time elapsed: 0.003 s
% 3.45/1.92 % (27850)Instructions burned: 3 (million)
% 3.45/1.92 % (27850)------------------------------
% 3.45/1.92 % (27850)------------------------------
% 3.45/1.92 % (27851)Instruction limit reached!
% 3.45/1.92 % (27851)------------------------------
% 3.45/1.92 % (27851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.92 % (27851)Termination reason: Unknown
% 3.45/1.92 % (27851)Termination phase: shuffling
% 3.45/1.92
% 3.45/1.92 % (27851)Memory used [KB]: 1407
% 3.45/1.92 % (27851)Time elapsed: 0.003 s
% 3.45/1.92 % (27851)Instructions burned: 3 (million)
% 3.45/1.92 % (27851)------------------------------
% 3.45/1.92 % (27851)------------------------------
% 3.45/1.92 % (27849)Instruction limit reached!
% 3.45/1.92 % (27849)------------------------------
% 3.45/1.92 % (27849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.92 % (27849)Termination reason: Unknown
% 3.45/1.92 % (27849)Termination phase: shuffling
% 3.45/1.92
% 3.45/1.92 % (27849)Memory used [KB]: 1791
% 3.45/1.92 % (27849)Time elapsed: 0.010 s
% 3.45/1.92 % (27849)Instructions burned: 17 (million)
% 3.45/1.92 % (27849)------------------------------
% 3.45/1.92 % (27849)------------------------------
% 3.45/1.92 % (27853)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27722 for (2999ds/7Mi)
% 3.45/1.93 % (27854)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_27722 for (2999ds/3Mi)
% 3.45/1.93 % (27853)Instruction limit reached!
% 3.45/1.93 % (27853)------------------------------
% 3.45/1.93 % (27853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.93 % (27853)Termination reason: Unknown
% 3.45/1.93 % (27853)Termination phase: shuffling
% 3.45/1.93
% 3.45/1.93 % (27853)Memory used [KB]: 1535
% 3.45/1.93 % (27853)Time elapsed: 0.005 s
% 3.45/1.93 % (27853)Instructions burned: 7 (million)
% 3.45/1.93 % (27853)------------------------------
% 3.45/1.93 % (27853)------------------------------
% 3.45/1.93 % (27854)Instruction limit reached!
% 3.45/1.93 % (27854)------------------------------
% 3.45/1.93 % (27854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.93 % (27854)Termination reason: Unknown
% 3.45/1.93 % (27854)Termination phase: shuffling
% 3.45/1.93
% 3.45/1.93 % (27854)Memory used [KB]: 1535
% 3.45/1.93 % (27854)Time elapsed: 0.003 s
% 3.45/1.93 % (27854)Instructions burned: 3 (million)
% 3.45/1.93 % (27854)------------------------------
% 3.45/1.93 % (27854)------------------------------
% 3.45/1.93 % (27855)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_27722 for (2999ds/4Mi)
% 3.45/1.93 % (27856)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_27722 for (2999ds/18Mi)
% 3.45/1.93 % (27855)Instruction limit reached!
% 3.45/1.93 % (27855)------------------------------
% 3.45/1.93 % (27855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.93 % (27855)Termination reason: Unknown
% 3.45/1.93 % (27855)Termination phase: shuffling
% 3.45/1.93
% 3.45/1.93 % (27855)Memory used [KB]: 1535
% 3.45/1.93 % (27855)Time elapsed: 0.004 s
% 3.45/1.93 % (27855)Instructions burned: 5 (million)
% 3.45/1.93 % (27855)------------------------------
% 3.45/1.93 % (27855)------------------------------
% 3.45/1.94 % (27857)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_27722 for (2999ds/710Mi)
% 3.45/1.94 % (27856)Instruction limit reached!
% 3.45/1.94 % (27856)------------------------------
% 3.45/1.94 % (27856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.94 % (27856)Termination reason: Unknown
% 3.45/1.94 % (27856)Termination phase: shuffling
% 3.45/1.94
% 3.45/1.94 % (27856)Memory used [KB]: 1791
% 3.45/1.94 % (27856)Time elapsed: 0.011 s
% 3.45/1.94 % (27856)Instructions burned: 19 (million)
% 3.45/1.94 % (27856)------------------------------
% 3.45/1.94 % (27856)------------------------------
% 3.45/1.94 % (27858)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27722 for (2999ds/6Mi)
% 3.45/1.94 % (27859)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_27722 for (2999ds/902Mi)
% 3.45/1.95 % (27858)Instruction limit reached!
% 3.45/1.95 % (27858)------------------------------
% 3.45/1.95 % (27858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.95 % (27858)Termination reason: Unknown
% 3.45/1.95 % (27858)Termination phase: shuffling
% 3.45/1.95
% 3.45/1.95 % (27858)Memory used [KB]: 1535
% 3.45/1.95 % (27858)Time elapsed: 0.005 s
% 3.45/1.95 % (27858)Instructions burned: 7 (million)
% 3.45/1.95 % (27858)------------------------------
% 3.45/1.95 % (27858)------------------------------
% 3.45/1.95 % (27860)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_27722 for (2999ds/21Mi)
% 3.45/1.96 % (27861)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_27722 for (2999ds/5Mi)
% 3.45/1.96 % (27836)Instruction limit reached!
% 3.45/1.96 % (27836)------------------------------
% 3.45/1.96 % (27836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.96 % (27836)Termination reason: Unknown
% 3.45/1.96 % (27836)Termination phase: Saturation
% 3.45/1.96
% 3.45/1.96 % (27836)Memory used [KB]: 7547
% 3.45/1.96 % (27836)Time elapsed: 0.089 s
% 3.45/1.96 % (27836)Instructions burned: 183 (million)
% 3.45/1.96 % (27836)------------------------------
% 3.45/1.96 % (27836)------------------------------
% 3.45/1.96 % (27861)Instruction limit reached!
% 3.45/1.96 % (27861)------------------------------
% 3.45/1.96 % (27861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.96 % (27861)Termination reason: Unknown
% 3.45/1.96 % (27861)Termination phase: shuffling
% 3.45/1.96
% 3.45/1.96 % (27861)Memory used [KB]: 1535
% 3.45/1.96 % (27861)Time elapsed: 0.004 s
% 3.45/1.96 % (27861)Instructions burned: 5 (million)
% 3.45/1.96 % (27861)------------------------------
% 3.45/1.96 % (27861)------------------------------
% 3.45/1.96 % (27860)Instruction limit reached!
% 3.45/1.96 % (27860)------------------------------
% 3.45/1.96 % (27860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.96 % (27860)Termination reason: Unknown
% 3.45/1.96 % (27860)Termination phase: shuffling
% 3.45/1.96
% 3.45/1.96 % (27860)Memory used [KB]: 1918
% 3.45/1.96 % (27860)Time elapsed: 0.013 s
% 3.45/1.96 % (27860)Instructions burned: 22 (million)
% 3.45/1.96 % (27860)------------------------------
% 3.45/1.96 % (27860)------------------------------
% 3.45/1.96 % (27862)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_27722 for (2998ds/6Mi)
% 3.45/1.97 % (27862)Instruction limit reached!
% 3.45/1.97 % (27862)------------------------------
% 3.45/1.97 % (27862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.97 % (27862)Termination reason: Unknown
% 3.45/1.97 % (27862)Termination phase: shuffling
% 3.45/1.97
% 3.45/1.97 % (27862)Memory used [KB]: 1663
% 3.45/1.97 % (27862)Time elapsed: 0.005 s
% 3.45/1.97 % (27862)Instructions burned: 7 (million)
% 3.45/1.97 % (27862)------------------------------
% 3.45/1.97 % (27862)------------------------------
% 3.45/1.98 % (27864)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_27722 for (2998ds/779Mi)
% 3.45/1.98 % (27863)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_27722 for (2998ds/377Mi)
% 3.45/1.98 % (27865)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_27722 for (2998ds/19Mi)
% 3.45/1.98 % (27866)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_27722 for (2998ds/879Mi)
% 3.45/1.99 % (27865)Instruction limit reached!
% 3.45/1.99 % (27865)------------------------------
% 3.45/1.99 % (27865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/1.99 % (27865)Termination reason: Unknown
% 3.45/1.99 % (27865)Termination phase: shuffling
% 3.45/1.99
% 3.45/1.99 % (27865)Memory used [KB]: 1918
% 3.45/1.99 % (27865)Time elapsed: 0.011 s
% 3.45/1.99 % (27865)Instructions burned: 20 (million)
% 3.45/1.99 % (27865)------------------------------
% 3.45/1.99 % (27865)------------------------------
% 3.45/2.00 % (27867)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_27722 for (2998ds/17Mi)
% 3.45/2.01 % (27867)Instruction limit reached!
% 3.45/2.01 % (27867)------------------------------
% 3.45/2.01 % (27867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/2.01 % (27867)Termination reason: Unknown
% 3.45/2.01 % (27867)Termination phase: shuffling
% 3.45/2.01
% 3.45/2.01 % (27867)Memory used [KB]: 1791
% 3.45/2.01 % (27867)Time elapsed: 0.010 s
% 3.45/2.01 % (27867)Instructions burned: 17 (million)
% 3.45/2.01 % (27867)------------------------------
% 3.45/2.01 % (27867)------------------------------
% 3.45/2.02 % (27859)Refutation not found, incomplete strategy
% 3.45/2.02 % (27859)------------------------------
% 3.45/2.02 % (27859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.45/2.02 % (27859)Termination reason: Refutation not found, incomplete strategy
% 3.45/2.02
% 3.45/2.02
% 3.45/2.02 % (27859)Memory used [KB]: 7547
% 3.45/2.02 % (27859)Time elapsed: 0.078 s
% 3.45/2.02 % (27859)Instructions burned: 155 (million)
% 3.45/2.02 % (27859)------------------------------
% 3.45/2.02 % (27859)------------------------------
% 4.60/2.03 % (27868)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_27722 for (2998ds/3Mi)
% 4.60/2.03 % (27868)Instruction limit reached!
% 4.60/2.03 % (27868)------------------------------
% 4.60/2.03 % (27868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.60/2.03 % (27868)Termination reason: Unknown
% 4.60/2.03 % (27868)Termination phase: shuffling
% 4.60/2.03
% 4.60/2.03 % (27868)Memory used [KB]: 1535
% 4.60/2.03 % (27868)Time elapsed: 0.004 s
% 4.60/2.03 % (27868)Instructions burned: 4 (million)
% 4.60/2.03 % (27868)------------------------------
% 4.60/2.03 % (27868)------------------------------
% 4.60/2.04 % (27869)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_27722 for (2998ds/30Mi)
% 4.60/2.05 % (27870)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_27722 for (2998ds/127Mi)
% 4.60/2.05 % (27869)Instruction limit reached!
% 4.60/2.05 % (27869)------------------------------
% 4.60/2.05 % (27869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.60/2.05 % (27869)Termination reason: Unknown
% 4.60/2.05 % (27869)Termination phase: shuffling
% 4.60/2.05
% 4.60/2.05 % (27869)Memory used [KB]: 2046
% 4.60/2.05 % (27869)Time elapsed: 0.018 s
% 4.60/2.05 % (27869)Instructions burned: 31 (million)
% 4.60/2.05 % (27869)------------------------------
% 4.60/2.05 % (27869)------------------------------
% 4.60/2.07 % (27871)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_27722 for (2997ds/100Mi)
% 4.60/2.11 % (27870)Instruction limit reached!
% 4.60/2.11 % (27870)------------------------------
% 4.60/2.11 % (27870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.60/2.11 % (27870)Termination reason: Unknown
% 4.60/2.11 % (27870)Termination phase: Saturation
% 4.60/2.11
% 4.60/2.11 % (27870)Memory used [KB]: 7036
% 4.60/2.11 % (27870)Time elapsed: 0.062 s
% 4.60/2.11 % (27870)Instructions burned: 127 (million)
% 4.60/2.11 % (27870)------------------------------
% 4.60/2.11 % (27870)------------------------------
% 4.60/2.12 % (27871)Instruction limit reached!
% 4.60/2.12 % (27871)------------------------------
% 4.60/2.12 % (27871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.60/2.12 % (27871)Termination reason: Unknown
% 4.60/2.12 % (27871)Termination phase: Preprocessing 3
% 4.60/2.12
% 4.60/2.12 % (27871)Memory used [KB]: 2686
% 4.60/2.12 % (27871)Time elapsed: 0.048 s
% 4.60/2.12 % (27871)Instructions burned: 101 (million)
% 4.60/2.12 % (27871)------------------------------
% 4.60/2.12 % (27871)------------------------------
% 4.60/2.12 % (27872)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_27722 for (2997ds/3Mi)
% 5.28/2.13 % (27872)Instruction limit reached!
% 5.28/2.13 % (27872)------------------------------
% 5.28/2.13 % (27872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.28/2.13 % (27872)Termination reason: Unknown
% 5.28/2.13 % (27872)Termination phase: shuffling
% 5.28/2.13
% 5.28/2.13 % (27872)Memory used [KB]: 1535
% 5.28/2.13 % (27872)Time elapsed: 0.004 s
% 5.28/2.13 % (27872)Instructions burned: 4 (million)
% 5.28/2.13 % (27872)------------------------------
% 5.28/2.13 % (27872)------------------------------
% 5.28/2.13 % (27873)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_27722 for (2997ds/20Mi)
% 5.28/2.14 % (27874)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_27722 for (2997ds/86Mi)
% 5.28/2.14 % (27873)Instruction limit reached!
% 5.28/2.14 % (27873)------------------------------
% 5.28/2.14 % (27873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.28/2.14 % (27873)Termination reason: Unknown
% 5.28/2.14 % (27873)Termination phase: shuffling
% 5.28/2.14
% 5.28/2.14 % (27873)Memory used [KB]: 1791
% 5.28/2.14 % (27873)Time elapsed: 0.012 s
% 5.28/2.14 % (27873)Instructions burned: 20 (million)
% 5.28/2.14 % (27873)------------------------------
% 5.28/2.14 % (27873)------------------------------
% 5.28/2.16 % (27875)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_27722 for (2996ds/107Mi)
% 5.28/2.16 % (27863)Instruction limit reached!
% 5.28/2.16 % (27863)------------------------------
% 5.28/2.16 % (27863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.28/2.16 % (27863)Termination reason: Unknown
% 5.28/2.16 % (27863)Termination phase: Saturation
% 5.28/2.16
% 5.28/2.16 % (27863)Memory used [KB]: 8443
% 5.28/2.16 % (27863)Time elapsed: 0.189 s
% 5.28/2.16 % (27863)Instructions burned: 377 (million)
% 5.28/2.16 % (27863)------------------------------
% 5.28/2.16 % (27863)------------------------------
% 5.28/2.18 % (27876)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_27722 for (2996ds/39Mi)
% 5.28/2.19 % (27874)Instruction limit reached!
% 5.28/2.19 % (27874)------------------------------
% 5.28/2.19 % (27874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.28/2.19 % (27874)Termination reason: Unknown
% 5.28/2.19 % (27874)Termination phase: Function definition elimination
% 5.28/2.19
% 5.28/2.19 % (27874)Memory used [KB]: 2430
% 5.28/2.19 % (27874)Time elapsed: 0.044 s
% 5.28/2.19 % (27874)Instructions burned: 87 (million)
% 5.28/2.19 % (27874)------------------------------
% 5.28/2.19 % (27874)------------------------------
% 5.71/2.20 % (27876)Instruction limit reached!
% 5.71/2.20 % (27876)------------------------------
% 5.71/2.20 % (27876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.71/2.20 % (27876)Termination reason: Unknown
% 5.71/2.20 % (27876)Termination phase: shuffling
% 5.71/2.20
% 5.71/2.20 % (27876)Memory used [KB]: 2174
% 5.71/2.20 % (27876)Time elapsed: 0.020 s
% 5.71/2.20 % (27876)Instructions burned: 39 (million)
% 5.71/2.20 % (27876)------------------------------
% 5.71/2.20 % (27876)------------------------------
% 5.71/2.20 % (27877)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_27722 for (2996ds/448Mi)
% 5.71/2.21 % (27875)Instruction limit reached!
% 5.71/2.21 % (27875)------------------------------
% 5.71/2.21 % (27875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.71/2.21 % (27875)Termination reason: Unknown
% 5.71/2.21 % (27875)Termination phase: Saturation
% 5.71/2.21
% 5.71/2.21 % (27875)Memory used [KB]: 6908
% 5.71/2.21 % (27875)Time elapsed: 0.053 s
% 5.71/2.21 % (27875)Instructions burned: 107 (million)
% 5.71/2.21 % (27875)------------------------------
% 5.71/2.21 % (27875)------------------------------
% 5.71/2.21 % (27878)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_27722 for (2996ds/46Mi)
% 5.71/2.23 % (27879)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_27722 for (2996ds/98Mi)
% 5.71/2.24 % (27878)Instruction limit reached!
% 5.71/2.24 % (27878)------------------------------
% 5.71/2.24 % (27878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.71/2.24 % (27878)Termination reason: Unknown
% 5.71/2.24 % (27878)Termination phase: Preprocessing 1
% 5.71/2.24
% 5.71/2.24 % (27878)Memory used [KB]: 1918
% 5.71/2.24 % (27878)Time elapsed: 0.024 s
% 5.71/2.24 % (27878)Instructions burned: 46 (million)
% 5.71/2.24 % (27878)------------------------------
% 5.71/2.24 % (27878)------------------------------
% 5.71/2.25 % (27880)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_27722 for (2995ds/507Mi)
% 5.71/2.27 % (27879)Instruction limit reached!
% 5.71/2.27 % (27879)------------------------------
% 5.71/2.27 % (27879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.71/2.27 % (27879)Termination reason: Unknown
% 5.71/2.27 % (27879)Termination phase: Preprocessing 3
% 5.71/2.27
% 5.71/2.27 % (27879)Memory used [KB]: 2686
% 5.71/2.27 % (27879)Time elapsed: 0.047 s
% 5.71/2.27 % (27879)Instructions burned: 98 (million)
% 5.71/2.27 % (27879)------------------------------
% 5.71/2.27 % (27879)------------------------------
% 5.71/2.28 % (27857)Instruction limit reached!
% 5.71/2.28 % (27857)------------------------------
% 5.71/2.28 % (27857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.71/2.28 % (27857)Termination reason: Unknown
% 5.71/2.28 % (27857)Termination phase: Saturation
% 5.71/2.28
% 5.71/2.28 % (27857)Memory used [KB]: 7931
% 5.71/2.28 % (27857)Time elapsed: 0.344 s
% 5.71/2.28 % (27857)Instructions burned: 710 (million)
% 5.71/2.28 % (27857)------------------------------
% 5.71/2.28 % (27857)------------------------------
% 5.71/2.29 % (27881)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_27722 for (2995ds/149Mi)
% 5.71/2.30 % (27882)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_27722 for (2995ds/39Mi)
% 6.29/2.32 % (27882)Instruction limit reached!
% 6.29/2.32 % (27882)------------------------------
% 6.29/2.32 % (27882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.32 % (27882)Termination reason: Unknown
% 6.29/2.32 % (27882)Termination phase: Preprocessing 1
% 6.29/2.32
% 6.29/2.32 % (27882)Memory used [KB]: 1918
% 6.29/2.32 % (27882)Time elapsed: 0.021 s
% 6.29/2.32 % (27882)Instructions burned: 40 (million)
% 6.29/2.32 % (27882)------------------------------
% 6.29/2.32 % (27882)------------------------------
% 6.29/2.32 % (27866)Refutation not found, non-redundant clauses discarded% (27866)------------------------------
% 6.29/2.32 % (27866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.32 % (27866)Termination reason: Refutation not found, non-redundant clauses discarded
% 6.29/2.32
% 6.29/2.32 % (27866)Memory used [KB]: 8315
% 6.29/2.32 % (27866)Time elapsed: 0.339 s
% 6.29/2.32 % (27866)Instructions burned: 678 (million)
% 6.29/2.32 % (27866)------------------------------
% 6.29/2.32 % (27866)------------------------------
% 6.29/2.33 % (27883)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_27722 for (2995ds/6Mi)
% 6.29/2.33 % (27883)Instruction limit reached!
% 6.29/2.33 % (27883)------------------------------
% 6.29/2.33 % (27883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.33 % (27883)Termination reason: Unknown
% 6.29/2.33 % (27883)Termination phase: shuffling
% 6.29/2.33
% 6.29/2.33 % (27883)Memory used [KB]: 1663
% 6.29/2.33 % (27883)Time elapsed: 0.005 s
% 6.29/2.33 % (27883)Instructions burned: 7 (million)
% 6.29/2.33 % (27883)------------------------------
% 6.29/2.33 % (27883)------------------------------
% 6.29/2.34 % (27884)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_27722 for (2995ds/1087Mi)
% 6.29/2.35 % (27885)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_27722 for (2995ds/47Mi)
% 6.29/2.36 % (27864)Instruction limit reached!
% 6.29/2.36 % (27864)------------------------------
% 6.29/2.36 % (27864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.36 % (27864)Termination reason: Unknown
% 6.29/2.36 % (27864)Termination phase: Saturation
% 6.29/2.36
% 6.29/2.36 % (27864)Memory used [KB]: 9594
% 6.29/2.36 % (27864)Time elapsed: 0.381 s
% 6.29/2.36 % (27864)Instructions burned: 780 (million)
% 6.29/2.36 % (27864)------------------------------
% 6.29/2.36 % (27864)------------------------------
% 6.29/2.36 % (27881)Instruction limit reached!
% 6.29/2.36 % (27881)------------------------------
% 6.29/2.36 % (27881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.36 % (27881)Termination reason: Unknown
% 6.29/2.36 % (27881)Termination phase: Saturation
% 6.29/2.36
% 6.29/2.36 % (27881)Memory used [KB]: 7291
% 6.29/2.36 % (27881)Time elapsed: 0.073 s
% 6.29/2.36 % (27881)Instructions burned: 150 (million)
% 6.29/2.36 % (27881)------------------------------
% 6.29/2.36 % (27881)------------------------------
% 6.29/2.37 % (27886)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_27722 for (2994ds/44Mi)
% 6.29/2.37 % (27885)Instruction limit reached!
% 6.29/2.37 % (27885)------------------------------
% 6.29/2.37 % (27885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.37 % (27885)Termination reason: Unknown
% 6.29/2.37 % (27885)Termination phase: Preprocessing 3
% 6.29/2.37
% 6.29/2.37 % (27885)Memory used [KB]: 2174
% 6.29/2.37 % (27885)Time elapsed: 0.025 s
% 6.29/2.37 % (27885)Instructions burned: 48 (million)
% 6.29/2.37 % (27885)------------------------------
% 6.29/2.37 % (27885)------------------------------
% 6.29/2.38 % (27887)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_27722 for (2994ds/432Mi)
% 6.29/2.39 % (27888)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_27722 for (2994ds/62Mi)
% 6.29/2.39 % (27886)Instruction limit reached!
% 6.29/2.39 % (27886)------------------------------
% 6.29/2.39 % (27886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.29/2.39 % (27886)Termination reason: Unknown
% 6.29/2.39 % (27886)Termination phase: shuffling
% 6.29/2.39
% 6.29/2.39 % (27886)Memory used [KB]: 2302
% 6.29/2.39 % (27886)Time elapsed: 0.022 s
% 6.29/2.39 % (27886)Instructions burned: 44 (million)
% 6.29/2.39 % (27886)------------------------------
% 6.29/2.39 % (27886)------------------------------
% 6.72/2.41 % (27847)Instruction limit reached!
% 6.72/2.41 % (27847)------------------------------
% 6.72/2.41 % (27847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.41 % (27847)Termination reason: Unknown
% 6.72/2.41 % (27847)Termination phase: Saturation
% 6.72/2.41
% 6.72/2.41 % (27847)Memory used [KB]: 9850
% 6.72/2.41 % (27847)Time elapsed: 0.505 s
% 6.72/2.41 % (27847)Instructions burned: 1042 (million)
% 6.72/2.41 % (27847)------------------------------
% 6.72/2.41 % (27847)------------------------------
% 6.72/2.41 % (27889)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_27722 for (2994ds/31Mi)
% 6.72/2.41 % (27877)Instruction limit reached!
% 6.72/2.41 % (27877)------------------------------
% 6.72/2.41 % (27877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.41 % (27877)Termination reason: Unknown
% 6.72/2.41 % (27877)Termination phase: Saturation
% 6.72/2.41
% 6.72/2.41 % (27877)Memory used [KB]: 9083
% 6.72/2.41 % (27877)Time elapsed: 0.214 s
% 6.72/2.41 % (27877)Instructions burned: 449 (million)
% 6.72/2.41 % (27877)------------------------------
% 6.72/2.41 % (27877)------------------------------
% 6.72/2.42 % (27888)Instruction limit reached!
% 6.72/2.42 % (27888)------------------------------
% 6.72/2.42 % (27888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.42 % (27888)Termination reason: Unknown
% 6.72/2.42 % (27888)Termination phase: Property scanning
% 6.72/2.42
% 6.72/2.42 % (27888)Memory used [KB]: 2430
% 6.72/2.42 % (27888)Time elapsed: 0.031 s
% 6.72/2.42 % (27888)Instructions burned: 63 (million)
% 6.72/2.42 % (27888)------------------------------
% 6.72/2.42 % (27888)------------------------------
% 6.72/2.42 % (27890)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_27722 for (2994ds/96Mi)
% 6.72/2.42 % (27889)Instruction limit reached!
% 6.72/2.42 % (27889)------------------------------
% 6.72/2.42 % (27889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.42 % (27889)Termination reason: Unknown
% 6.72/2.42 % (27889)Termination phase: Property scanning
% 6.72/2.42
% 6.72/2.42 % (27889)Memory used [KB]: 1918
% 6.72/2.42 % (27889)Time elapsed: 0.017 s
% 6.72/2.42 % (27889)Instructions burned: 31 (million)
% 6.72/2.42 % (27889)------------------------------
% 6.72/2.42 % (27889)------------------------------
% 6.72/2.43 % (27891)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_27722 for (2994ds/453Mi)
% 6.72/2.44 % (27892)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_27722 for (2994ds/71Mi)
% 6.72/2.44 % (27893)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_27722 for (2994ds/83Mi)
% 6.72/2.47 % (27890)Instruction limit reached!
% 6.72/2.47 % (27890)------------------------------
% 6.72/2.47 % (27890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.47 % (27890)Termination reason: Unknown
% 6.72/2.47 % (27890)Termination phase: Property scanning
% 6.72/2.47
% 6.72/2.47 % (27890)Memory used [KB]: 2430
% 6.72/2.47 % (27890)Time elapsed: 0.047 s
% 6.72/2.47 % (27890)Instructions burned: 96 (million)
% 6.72/2.47 % (27890)------------------------------
% 6.72/2.47 % (27890)------------------------------
% 6.72/2.47 % (27892)Instruction limit reached!
% 6.72/2.47 % (27892)------------------------------
% 6.72/2.47 % (27892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.47 % (27892)Termination reason: Unknown
% 6.72/2.47 % (27892)Termination phase: Property scanning
% 6.72/2.47
% 6.72/2.47 % (27892)Memory used [KB]: 2558
% 6.72/2.47 % (27892)Time elapsed: 0.036 s
% 6.72/2.47 % (27892)Instructions burned: 71 (million)
% 6.72/2.47 % (27892)------------------------------
% 6.72/2.47 % (27892)------------------------------
% 6.72/2.48 % (27893)Instruction limit reached!
% 6.72/2.48 % (27893)------------------------------
% 6.72/2.48 % (27893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.48 % (27893)Termination reason: Unknown
% 6.72/2.48 % (27893)Termination phase: Saturation
% 6.72/2.48
% 6.72/2.48 % (27893)Memory used [KB]: 6780
% 6.72/2.48 % (27893)Time elapsed: 0.043 s
% 6.72/2.48 % (27893)Instructions burned: 84 (million)
% 6.72/2.48 % (27893)------------------------------
% 6.72/2.48 % (27893)------------------------------
% 6.72/2.48 % (27894)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_27722 for (2993ds/11Mi)
% 6.72/2.49 % (27895)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_27722 for (2993ds/41Mi)
% 6.72/2.49 % (27894)Instruction limit reached!
% 6.72/2.49 % (27894)------------------------------
% 6.72/2.49 % (27894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.49 % (27894)Termination reason: Unknown
% 6.72/2.49 % (27894)Termination phase: shuffling
% 6.72/2.49
% 6.72/2.49 % (27894)Memory used [KB]: 1663
% 6.72/2.49 % (27894)Time elapsed: 0.007 s
% 6.72/2.49 % (27894)Instructions burned: 11 (million)
% 6.72/2.49 % (27894)------------------------------
% 6.72/2.49 % (27894)------------------------------
% 6.72/2.50 % (27880)Instruction limit reached!
% 6.72/2.50 % (27880)------------------------------
% 6.72/2.50 % (27880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.72/2.50 % (27880)Termination reason: Unknown
% 6.72/2.50 % (27880)Termination phase: Saturation
% 6.72/2.50
% 6.72/2.50 % (27880)Memory used [KB]: 9850
% 6.72/2.50 % (27880)Time elapsed: 0.244 s
% 6.72/2.50 % (27880)Instructions burned: 508 (million)
% 6.72/2.50 % (27880)------------------------------
% 6.72/2.50 % (27880)------------------------------
% 7.24/2.50 % (27896)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27722 for (2993ds/6Mi)
% 7.24/2.50 % (27896)Instruction limit reached!
% 7.24/2.50 % (27896)------------------------------
% 7.24/2.50 % (27896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.50 % (27896)Termination reason: Unknown
% 7.24/2.50 % (27896)Termination phase: shuffling
% 7.24/2.50
% 7.24/2.50 % (27896)Memory used [KB]: 1535
% 7.24/2.50 % (27896)Time elapsed: 0.005 s
% 7.24/2.50 % (27896)Instructions burned: 7 (million)
% 7.24/2.50 % (27896)------------------------------
% 7.24/2.50 % (27896)------------------------------
% 7.24/2.51 % (27897)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_27722 for (2993ds/150Mi)
% 7.24/2.51 % (27895)Instruction limit reached!
% 7.24/2.51 % (27895)------------------------------
% 7.24/2.51 % (27895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.51 % (27895)Termination reason: Unknown
% 7.24/2.51 % (27895)Termination phase: shuffling
% 7.24/2.51
% 7.24/2.51 % (27895)Memory used [KB]: 2302
% 7.24/2.51 % (27895)Time elapsed: 0.021 s
% 7.24/2.51 % (27895)Instructions burned: 42 (million)
% 7.24/2.51 % (27895)------------------------------
% 7.24/2.51 % (27895)------------------------------
% 7.24/2.51 % (27898)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_27722 for (2993ds/343Mi)
% 7.24/2.52 % (27899)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_27722 for (2993ds/109Mi)
% 7.24/2.52 % (27900)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_27722 for (2993ds/253Mi)
% 7.24/2.57 % (27899)Instruction limit reached!
% 7.24/2.57 % (27899)------------------------------
% 7.24/2.57 % (27899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.57 % (27899)Termination reason: Unknown
% 7.24/2.57 % (27899)Termination phase: Property scanning
% 7.24/2.57
% 7.24/2.57 % (27899)Memory used [KB]: 2430
% 7.24/2.57 % (27899)Time elapsed: 0.053 s
% 7.24/2.57 % (27899)Instructions burned: 109 (million)
% 7.24/2.57 % (27899)------------------------------
% 7.24/2.57 % (27899)------------------------------
% 7.24/2.58 % (27897)Instruction limit reached!
% 7.24/2.58 % (27897)------------------------------
% 7.24/2.58 % (27897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.58 % (27897)Termination reason: Unknown
% 7.24/2.58 % (27897)Termination phase: Saturation
% 7.24/2.58
% 7.24/2.58 % (27897)Memory used [KB]: 7291
% 7.24/2.58 % (27897)Time elapsed: 0.073 s
% 7.24/2.58 % (27897)Instructions burned: 151 (million)
% 7.24/2.58 % (27897)------------------------------
% 7.24/2.58 % (27897)------------------------------
% 7.24/2.59 % (27901)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_27722 for (2992ds/140Mi)
% 7.24/2.59 % (27887)Instruction limit reached!
% 7.24/2.59 % (27887)------------------------------
% 7.24/2.59 % (27887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.59 % (27887)Termination reason: Unknown
% 7.24/2.59 % (27887)Termination phase: Saturation
% 7.24/2.59
% 7.24/2.59 % (27887)Memory used [KB]: 4349
% 7.24/2.59 % (27887)Time elapsed: 0.213 s
% 7.24/2.59 % (27887)Instructions burned: 432 (million)
% 7.24/2.59 % (27887)------------------------------
% 7.24/2.59 % (27887)------------------------------
% 7.24/2.59 % (27902)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_27722 for (2992ds/614Mi)
% 7.94/2.60 % (27903)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_27722 for (2992ds/202Mi)
% 7.94/2.63 % (27903)Refutation not found, incomplete strategy
% 7.94/2.63 % (27903)------------------------------
% 7.94/2.63 % (27903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.94/2.63 % (27903)Termination reason: Refutation not found, incomplete strategy
% 7.94/2.63
% 7.94/2.63
% 7.94/2.63 % (27903)Memory used [KB]: 6524
% 7.94/2.63 % (27903)Time elapsed: 0.025 s
% 7.94/2.63 % (27903)Instructions burned: 46 (million)
% 7.94/2.63 % (27903)------------------------------
% 7.94/2.63 % (27903)------------------------------
% 7.94/2.64 % (27891)Instruction limit reached!
% 7.94/2.64 % (27891)------------------------------
% 7.94/2.64 % (27891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.94/2.64 % (27891)Termination reason: Unknown
% 7.94/2.64 % (27891)Termination phase: Saturation
% 7.94/2.64
% 7.94/2.64 % (27891)Memory used [KB]: 8827
% 7.94/2.64 % (27891)Time elapsed: 0.211 s
% 7.94/2.64 % (27891)Instructions burned: 453 (million)
% 7.94/2.64 % (27891)------------------------------
% 7.94/2.64 % (27891)------------------------------
% 7.94/2.64 % (27904)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_27722 for (2992ds/339Mi)
% 7.94/2.65 % (27900)Instruction limit reached!
% 7.94/2.65 % (27900)------------------------------
% 7.94/2.65 % (27900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.94/2.65 % (27900)Termination reason: Unknown
% 7.94/2.65 % (27900)Termination phase: Saturation
% 7.94/2.65
% 7.94/2.65 % (27900)Memory used [KB]: 7036
% 7.94/2.65 % (27900)Time elapsed: 0.129 s
% 7.94/2.65 % (27900)Instructions burned: 253 (million)
% 7.94/2.65 % (27900)------------------------------
% 7.94/2.65 % (27900)------------------------------
% 7.94/2.66 % (27901)Instruction limit reached!
% 7.94/2.66 % (27901)------------------------------
% 7.94/2.66 % (27901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.94/2.66 % (27901)Termination reason: Unknown
% 7.94/2.66 % (27901)Termination phase: Saturation
% 7.94/2.66
% 7.94/2.66 % (27901)Memory used [KB]: 7164
% 7.94/2.66 % (27901)Time elapsed: 0.072 s
% 7.94/2.66 % (27901)Instructions burned: 141 (million)
% 7.94/2.66 % (27901)------------------------------
% 7.94/2.66 % (27901)------------------------------
% 7.94/2.66 % (27905)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_27722 for (2992ds/283Mi)
% 7.94/2.67 % (27906)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_27722 for (2991ds/134Mi)
% 7.94/2.67 % (27907)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_27722 for (2991ds/298Mi)
% 7.94/2.68 % (27898)Instruction limit reached!
% 7.94/2.68 % (27898)------------------------------
% 7.94/2.68 % (27898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.94/2.68 % (27898)Termination reason: Unknown
% 7.94/2.68 % (27898)Termination phase: Saturation
% 7.94/2.68
% 7.94/2.68 % (27898)Memory used [KB]: 8059
% 7.94/2.68 % (27898)Time elapsed: 0.171 s
% 7.94/2.68 % (27898)Instructions burned: 343 (million)
% 7.94/2.68 % (27898)------------------------------
% 7.94/2.68 % (27898)------------------------------
% 8.62/2.70 % (27908)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_27722 for (2991ds/192Mi)
% 8.62/2.73 % (27906)Instruction limit reached!
% 8.62/2.73 % (27906)------------------------------
% 8.62/2.73 % (27906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.73 % (27906)Termination reason: Unknown
% 8.62/2.73 % (27906)Termination phase: Saturation
% 8.62/2.73
% 8.62/2.73 % (27906)Memory used [KB]: 7164
% 8.62/2.73 % (27906)Time elapsed: 0.065 s
% 8.62/2.73 % (27906)Instructions burned: 134 (million)
% 8.62/2.73 % (27906)------------------------------
% 8.62/2.73 % (27906)------------------------------
% 8.62/2.75 % (27909)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_27722 for (2991ds/258Mi)
% 8.62/2.79 % (27908)Instruction limit reached!
% 8.62/2.79 % (27908)------------------------------
% 8.62/2.79 % (27908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.79 % (27908)Termination reason: Unknown
% 8.62/2.79 % (27908)Termination phase: Saturation
% 8.62/2.79
% 8.62/2.79 % (27908)Memory used [KB]: 3709
% 8.62/2.79 % (27908)Time elapsed: 0.096 s
% 8.62/2.79 % (27908)Instructions burned: 192 (million)
% 8.62/2.79 % (27908)------------------------------
% 8.62/2.79 % (27908)------------------------------
% 8.62/2.79 % (27905)Instruction limit reached!
% 8.62/2.79 % (27905)------------------------------
% 8.62/2.79 % (27905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.79 % (27905)Termination reason: Unknown
% 8.62/2.79 % (27905)Termination phase: Saturation
% 8.62/2.79
% 8.62/2.79 % (27905)Memory used [KB]: 7803
% 8.62/2.79 % (27905)Time elapsed: 0.139 s
% 8.62/2.79 % (27905)Instructions burned: 284 (million)
% 8.62/2.79 % (27905)------------------------------
% 8.62/2.79 % (27905)------------------------------
% 8.96/2.81 % (27904)Instruction limit reached!
% 8.96/2.81 % (27904)------------------------------
% 8.96/2.81 % (27904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.81 % (27904)Termination reason: Unknown
% 8.96/2.81 % (27904)Termination phase: Saturation
% 8.96/2.81
% 8.96/2.81 % (27904)Memory used [KB]: 8315
% 8.96/2.81 % (27904)Time elapsed: 0.163 s
% 8.96/2.81 % (27904)Instructions burned: 339 (million)
% 8.96/2.81 % (27904)------------------------------
% 8.96/2.81 % (27904)------------------------------
% 8.96/2.81 % (27910)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_27722 for (2990ds/90Mi)
% 8.96/2.81 % (27911)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_27722 for (2990ds/231Mi)
% 8.96/2.81 % (27907)Instruction limit reached!
% 8.96/2.81 % (27907)------------------------------
% 8.96/2.81 % (27907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.81 % (27907)Termination reason: Unknown
% 8.96/2.81 % (27907)Termination phase: Saturation
% 8.96/2.81
% 8.96/2.81 % (27907)Memory used [KB]: 8827
% 8.96/2.81 % (27907)Time elapsed: 0.141 s
% 8.96/2.81 % (27907)Instructions burned: 298 (million)
% 8.96/2.81 % (27907)------------------------------
% 8.96/2.81 % (27907)------------------------------
% 8.96/2.82 % (27912)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_27722 for (2990ds/458Mi)
% 8.96/2.83 % (27913)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_27722 for (2990ds/31Mi)
% 8.96/2.84 % (27913)Instruction limit reached!
% 8.96/2.84 % (27913)------------------------------
% 8.96/2.84 % (27913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.84 % (27913)Termination reason: Unknown
% 8.96/2.84 % (27913)Termination phase: Property scanning
% 8.96/2.84
% 8.96/2.84 % (27913)Memory used [KB]: 1918
% 8.96/2.84 % (27913)Time elapsed: 0.017 s
% 8.96/2.84 % (27913)Instructions burned: 31 (million)
% 8.96/2.84 % (27913)------------------------------
% 8.96/2.84 % (27913)------------------------------
% 8.96/2.85 % (27910)Instruction limit reached!
% 8.96/2.85 % (27910)------------------------------
% 8.96/2.85 % (27910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.85 % (27910)Termination reason: Unknown
% 8.96/2.85 % (27910)Termination phase: Property scanning
% 8.96/2.85
% 8.96/2.85 % (27910)Memory used [KB]: 2430
% 8.96/2.85 % (27910)Time elapsed: 0.045 s
% 8.96/2.85 % (27910)Instructions burned: 90 (million)
% 8.96/2.85 % (27910)------------------------------
% 8.96/2.85 % (27910)------------------------------
% 8.96/2.86 % (27914)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_27722 for (2989ds/297Mi)
% 8.96/2.86 % (27884)Instruction limit reached!
% 8.96/2.86 % (27884)------------------------------
% 8.96/2.86 % (27884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.86 % (27884)Termination reason: Unknown
% 8.96/2.86 % (27884)Termination phase: Saturation
% 8.96/2.86
% 8.96/2.86 % (27884)Memory used [KB]: 7803
% 8.96/2.86 % (27884)Time elapsed: 0.528 s
% 8.96/2.86 % (27884)Instructions burned: 1088 (million)
% 8.96/2.86 % (27884)------------------------------
% 8.96/2.86 % (27884)------------------------------
% 8.96/2.87 % (27915)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_27722 for (2989ds/987Mi)
% 8.96/2.87 % (27909)Instruction limit reached!
% 8.96/2.87 % (27909)------------------------------
% 8.96/2.87 % (27909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.87 % (27909)Termination reason: Unknown
% 8.96/2.87 % (27909)Termination phase: Saturation
% 8.96/2.87
% 8.96/2.87 % (27909)Memory used [KB]: 7291
% 8.96/2.87 % (27909)Time elapsed: 0.152 s
% 8.96/2.87 % (27909)Instructions burned: 258 (million)
% 8.96/2.87 % (27909)------------------------------
% 8.96/2.87 % (27909)------------------------------
% 8.96/2.88 % (27916)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_27722 for (2989ds/182Mi)
% 8.96/2.89 % (27917)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_27722 for (2989ds/182Mi)
% 8.96/2.89 % (27902)Instruction limit reached!
% 8.96/2.89 % (27902)------------------------------
% 8.96/2.89 % (27902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.89 % (27902)Termination reason: Unknown
% 8.96/2.89 % (27902)Termination phase: Saturation
% 8.96/2.89
% 8.96/2.89 % (27902)Memory used [KB]: 8571
% 8.96/2.89 % (27902)Time elapsed: 0.301 s
% 8.96/2.89 % (27902)Instructions burned: 615 (million)
% 8.96/2.89 % (27902)------------------------------
% 8.96/2.89 % (27902)------------------------------
% 10.39/2.91 % (27918)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_27722 for (2989ds/154Mi)
% 10.39/2.92 % (27911)Instruction limit reached!
% 10.39/2.92 % (27911)------------------------------
% 10.39/2.92 % (27911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/2.92 % (27911)Termination reason: Unknown
% 10.39/2.92 % (27911)Termination phase: Saturation
% 10.39/2.92
% 10.39/2.92 % (27911)Memory used [KB]: 7419
% 10.39/2.92 % (27911)Time elapsed: 0.107 s
% 10.39/2.92 % (27911)Instructions burned: 232 (million)
% 10.39/2.92 % (27911)------------------------------
% 10.39/2.92 % (27911)------------------------------
% 10.39/2.93 % (27919)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_27722 for (2989ds/79Mi)
% 10.39/2.97 % (27916)Instruction limit reached!
% 10.39/2.97 % (27916)------------------------------
% 10.39/2.97 % (27916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/2.97 % (27916)Termination reason: Unknown
% 10.39/2.97 % (27916)Termination phase: Saturation
% 10.39/2.97
% 10.39/2.97 % (27916)Memory used [KB]: 7547
% 10.39/2.97 % (27916)Time elapsed: 0.089 s
% 10.39/2.97 % (27916)Instructions burned: 182 (million)
% 10.39/2.97 % (27916)------------------------------
% 10.39/2.97 % (27916)------------------------------
% 10.39/2.97 % (27917)First to succeed.
% 10.39/2.97 % (27919)Instruction limit reached!
% 10.39/2.97 % (27919)------------------------------
% 10.39/2.97 % (27919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/2.97 % (27919)Termination reason: Unknown
% 10.39/2.97 % (27919)Termination phase: Function definition elimination
% 10.39/2.97
% 10.39/2.97 % (27919)Memory used [KB]: 2430
% 10.39/2.97 % (27919)Time elapsed: 0.040 s
% 10.39/2.97 % (27919)Instructions burned: 80 (million)
% 10.39/2.97 % (27919)------------------------------
% 10.39/2.97 % (27919)------------------------------
% 10.39/2.97 % (27917)Refutation found. Thanks to Tanya!
% 10.39/2.97 % SZS status Theorem for DTF2THF_27722
% 10.39/2.97 % SZS output start Proof for DTF2THF_27722
% 10.39/2.97 thf(type_def_5, type, itself: ($tType) > $tType).
% 10.39/2.97 thf(type_def_7, type, treeFI: ($tType) > $tType).
% 10.39/2.97 thf(type_def_8, type, stream: ($tType) > $tType).
% 10.39/2.97 thf(type_def_9, type, set: ($tType) > $tType).
% 10.39/2.97 thf(type_def_10, type, list: ($tType) > $tType).
% 10.39/2.97 thf(type_def_11, type, nat: $tType).
% 10.39/2.97 thf(type_def_12, type, a: $tType).
% 10.39/2.97 thf(func_def_0, type, treeFI: ($tType) > $tType).
% 10.39/2.97 thf(func_def_1, type, stream: ($tType) > $tType).
% 10.39/2.97 thf(func_def_2, type, list: ($tType) > $tType).
% 10.39/2.97 thf(func_def_3, type, set: ($tType) > $tType).
% 10.39/2.97 thf(func_def_4, type, nat: $tType).
% 10.39/2.97 thf(func_def_5, type, itself: ($tType) > $tType).
% 10.39/2.97 thf(func_def_6, type, a: $tType).
% 10.39/2.97 thf(func_def_7, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.39/2.97 thf(func_def_8, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.39/2.97 thf(func_def_9, type, semilattice_sup: !>[X0: $tType]:(itself @ X0 > $o)).
% 10.39/2.97 thf(func_def_10, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > (X2 > X0) > X2 > X1)).
% 10.39/2.97 thf(func_def_11, type, fun_upd: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0 > X1 > X0 > X1)).
% 10.39/2.97 thf(func_def_12, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 10.39/2.97 thf(func_def_13, type, koenig488553731niteTr: !>[X0: $tType]:(treeFI @ X0 > $o)).
% 10.39/2.97 thf(func_def_14, type, koenig1103336060igPath: !>[X0: $tType]:(treeFI @ X0 > stream @ X0)).
% 10.39/2.97 thf(func_def_15, type, koenig1755522246erPath: !>[X0: $tType]:(stream @ X0 > treeFI @ X0 > $o)).
% 10.39/2.97 thf(func_def_16, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 10.39/2.97 thf(func_def_17, type, lattic477160up_fin: !>[X0: $tType]:(set @ X0 > X0)).
% 10.39/2.97 thf(func_def_18, type, append: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_19, type, coset: !>[X0: $tType]:(list @ X0 > set @ X0)).
% 10.39/2.97 thf(func_def_20, type, fold: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > list @ X0 > X1 > X1)).
% 10.39/2.97 thf(func_def_21, type, foldr: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > list @ X0 > X1 > X1)).
% 10.39/2.97 thf(func_def_22, type, insert: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_23, type, linorder_insort_key: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0 > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_24, type, linorder_sorted: !>[X0: $tType]:(list @ X0 > $o)).
% 10.39/2.97 thf(func_def_25, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_26, type, nil: !>[X0: $tType]:(list @ X0)).
% 10.39/2.97 thf(func_def_27, type, hd: !>[X0: $tType]:(list @ X0 > X0)).
% 10.39/2.97 thf(func_def_28, type, list_all: !>[X0: $tType]:((X0 > $o) > list @ X0 > $o)).
% 10.39/2.97 thf(func_def_29, type, map: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > list @ X1)).
% 10.39/2.97 thf(func_def_30, type, set2: !>[X0: $tType]:(list @ X0 > set @ X0)).
% 10.39/2.97 thf(func_def_31, type, tl: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_32, type, list_update: !>[X0: $tType]:(list @ X0 > nat > X0 > list @ X0)).
% 10.39/2.97 thf(func_def_33, type, member: !>[X0: $tType]:(list @ X0 > X0 > $o)).
% 10.39/2.97 thf(func_def_34, type, remove1: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_35, type, rev: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_36, type, union: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_37, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 10.39/2.97 thf(func_def_38, type, type2: !>[X0: $tType]:(itself @ X0)).
% 10.39/2.97 thf(func_def_39, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 10.39/2.97 thf(func_def_40, type, insert2: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 10.39/2.97 thf(func_def_41, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 10.39/2.97 thf(func_def_42, type, cycle: !>[X0: $tType]:(list @ X0 > stream @ X0)).
% 10.39/2.97 thf(func_def_43, type, flat: !>[X0: $tType]:(stream @ list @ X0 > stream @ X0)).
% 10.39/2.97 thf(func_def_44, type, sdrop_while: !>[X0: $tType]:((X0 > $o) > stream @ X0 > stream @ X0)).
% 10.39/2.97 thf(func_def_45, type, sfilter: !>[X0: $tType]:((X0 > $o) > stream @ X0 > stream @ X0)).
% 10.39/2.97 thf(func_def_46, type, shift: !>[X0: $tType]:(list @ X0 > stream @ X0 > stream @ X0)).
% 10.39/2.97 thf(func_def_47, type, sinterleave: !>[X0: $tType]:(stream @ X0 > stream @ X0 > stream @ X0)).
% 10.39/2.97 thf(func_def_48, type, smap2: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > stream @ X0 > stream @ X1 > stream @ X2)).
% 10.39/2.97 thf(func_def_49, type, smember: !>[X0: $tType]:(X0 > stream @ X0 > $o)).
% 10.39/2.97 thf(func_def_50, type, stake: !>[X0: $tType]:(nat > stream @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_51, type, sCons: !>[X0: $tType]:(X0 > stream @ X0 > stream @ X0)).
% 10.39/2.97 thf(func_def_52, type, case_stream: !>[X0: $tType, X1: $tType]:((X0 > stream @ X0 > X1) > stream @ X0 > X1)).
% 10.39/2.97 thf(func_def_53, type, corec_stream: !>[X0: $tType, X1: $tType]:((X0 > X1) > (X0 > $o) > (X0 > stream @ X1) > (X0 > X0) > X0 > stream @ X1)).
% 10.39/2.97 thf(func_def_54, type, pred_stream: !>[X0: $tType]:((X0 > $o) > stream @ X0 > $o)).
% 10.39/2.97 thf(func_def_55, type, shd: !>[X0: $tType]:(stream @ X0 > X0)).
% 10.39/2.97 thf(func_def_56, type, smap: !>[X0: $tType, X1: $tType]:((X0 > X1) > stream @ X0 > stream @ X1)).
% 10.39/2.97 thf(func_def_57, type, sset: !>[X0: $tType]:(stream @ X0 > set @ X0)).
% 10.39/2.97 thf(func_def_58, type, stl: !>[X0: $tType]:(stream @ X0 > stream @ X0)).
% 10.39/2.97 thf(func_def_59, type, stream_all: !>[X0: $tType]:((X0 > $o) > stream @ X0 > $o)).
% 10.39/2.97 thf(func_def_60, type, streams: !>[X0: $tType]:(set @ X0 > set @ stream @ X0)).
% 10.39/2.97 thf(func_def_61, type, tree: !>[X0: $tType]:(X0 > list @ treeFI @ X0 > treeFI @ X0)).
% 10.39/2.97 thf(func_def_62, type, case_treeFI: !>[X0: $tType, X1: $tType]:((X0 > list @ treeFI @ X0 > X1) > treeFI @ X0 > X1)).
% 10.39/2.97 thf(func_def_63, type, lab: !>[X0: $tType]:(treeFI @ X0 > X0)).
% 10.39/2.97 thf(func_def_64, type, map_treeFI: !>[X0: $tType, X1: $tType]:((X0 > X1) > treeFI @ X0 > treeFI @ X1)).
% 10.39/2.97 thf(func_def_65, type, pred_treeFI: !>[X0: $tType]:((X0 > $o) > treeFI @ X0 > $o)).
% 10.39/2.97 thf(func_def_66, type, set_treeFI: !>[X0: $tType]:(treeFI @ X0 > set @ X0)).
% 10.39/2.97 thf(func_def_67, type, sub: !>[X0: $tType]:(treeFI @ X0 > list @ treeFI @ X0)).
% 10.39/2.97 thf(func_def_68, type, trev: !>[X0: $tType]:(treeFI @ X0 > treeFI @ X0)).
% 10.39/2.97 thf(func_def_69, type, member2: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 10.39/2.97 thf(func_def_70, type, as: stream @ a).
% 10.39/2.97 thf(func_def_71, type, phi: stream @ a > treeFI @ a > $o).
% 10.39/2.97 thf(func_def_72, type, tr: treeFI @ a).
% 10.39/2.97 thf(func_def_89, type, sK0: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X1) > (X0 > X2 > X2) > (X2 > X1) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_90, type, sK1: !>[X0: $tType]:(treeFI @ X0 > stream @ X0 > treeFI @ X0)).
% 10.39/2.97 thf(func_def_91, type, sK2: !>[X0: $tType]:((stream @ X0 > stream @ X0 > $o) > stream @ X0)).
% 10.39/2.97 thf(func_def_92, type, sK3: !>[X0: $tType]:((stream @ X0 > stream @ X0 > $o) > stream @ X0)).
% 10.39/2.97 thf(func_def_93, type, sK4: !>[X0: $tType]:((stream @ X0 > treeFI @ X0 > $o) > stream @ X0)).
% 10.39/2.97 thf(func_def_94, type, sK5: !>[X0: $tType]:((stream @ X0 > treeFI @ X0 > $o) > treeFI @ X0)).
% 10.39/2.97 thf(func_def_95, type, sK6: !>[X0: $tType, X1: $tType]:((X1 > X0 > X0) > list @ X1 > X1)).
% 10.39/2.97 thf(func_def_96, type, sK7: !>[X0: $tType, X1: $tType]:((X1 > X0 > X0) > list @ X1 > X1)).
% 10.39/2.97 thf(func_def_97, type, sK8: !>[X0: $tType]:((X0 > $o) > list @ X0 > (X0 > $o) > X0)).
% 10.39/2.97 thf(func_def_98, type, sK9: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_99, type, sK10: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_100, type, sK11: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_101, type, sK12: !>[X0: $tType]:(stream @ X0 > X0 > X0)).
% 10.39/2.97 thf(func_def_102, type, sK13: !>[X0: $tType]:(stream @ X0 > X0 > stream @ X0)).
% 10.39/2.97 thf(func_def_103, type, sK14: !>[X0: $tType]:(stream @ X0 > X0 > stream @ X0)).
% 10.39/2.97 thf(func_def_104, type, sK15: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_105, type, sK16: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_106, type, sK17: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_107, type, sK18: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > (X1 > $o) > (X0 > $o) > X0)).
% 10.39/2.97 thf(func_def_108, type, sK19: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > (X1 > $o) > (X0 > $o) > X1)).
% 10.39/2.97 thf(func_def_109, type, sK20: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_110, type, sK21: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_111, type, sK22: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_112, type, sK23: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_113, type, sK24: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > stream @ X1 > X1)).
% 10.39/2.97 thf(func_def_114, type, sK25: !>[X0: $tType]:(set @ X0 > stream @ X0 > X0)).
% 10.39/2.97 thf(func_def_115, type, sK26: !>[X0: $tType]:(set @ X0 > stream @ X0 > stream @ X0)).
% 10.39/2.97 thf(func_def_116, type, sK27: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > list @ X1 > X1)).
% 10.39/2.97 thf(func_def_117, type, sK28: !>[X0: $tType]:((treeFI @ X0 > $o) > treeFI @ X0)).
% 10.39/2.97 thf(func_def_118, type, sK29: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 10.39/2.97 thf(func_def_119, type, sK30: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 10.39/2.97 thf(func_def_120, type, sK31: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > treeFI @ X1 > X1)).
% 10.39/2.97 thf(func_def_121, type, sK32: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > X1) > set @ X0 > X0)).
% 10.39/2.97 thf(func_def_122, type, sK33: !>[X0: $tType]:(X0 > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_123, type, sK34: !>[X0: $tType]:(set @ X0 > (stream @ X0 > $o) > stream @ X0)).
% 10.39/2.97 thf(func_def_124, type, sK35: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 10.39/2.97 thf(func_def_125, type, sK36: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 10.39/2.97 thf(func_def_126, type, sK37: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_127, type, sK38: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_128, type, sK39: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_129, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X1) > (X0 > X2 > X2) > (X2 > X1) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_130, type, sK41: !>[X0: $tType]:((X0 > $o) > treeFI @ X0 > (X0 > $o) > X0)).
% 10.39/2.97 thf(func_def_131, type, sK42: !>[X0: $tType, X1: $tType]:(X1 > (X1 > X0) > list @ X1 > X1)).
% 10.39/2.97 thf(func_def_132, type, sK43: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_133, type, sK44: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_134, type, sK45: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_135, type, sK46: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > (X0 > X1 > X1) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_136, type, sK47: !>[X0: $tType]:(treeFI @ X0 > X0 > X0)).
% 10.39/2.97 thf(func_def_137, type, sK48: !>[X0: $tType]:(treeFI @ X0 > X0 > list @ treeFI @ X0)).
% 10.39/2.97 thf(func_def_138, type, sK49: !>[X0: $tType]:(treeFI @ X0 > X0 > treeFI @ X0)).
% 10.39/2.97 thf(func_def_139, type, sK50: !>[X0: $tType]:(treeFI @ X0 > X0 > list @ treeFI @ X0)).
% 10.39/2.97 thf(func_def_140, type, sK51: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 10.39/2.97 thf(func_def_141, type, sK52: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 10.39/2.97 thf(func_def_142, type, sK53: !>[X0: $tType]:(stream @ X0 > X0)).
% 10.39/2.97 thf(func_def_143, type, sK54: !>[X0: $tType]:(stream @ X0 > stream @ X0)).
% 10.39/2.97 thf(func_def_144, type, sK55: !>[X0: $tType]:(list @ X0 > set @ X0 > X0)).
% 10.39/2.97 thf(func_def_145, type, sK56: !>[X0: $tType]:((X0 > $o) > stream @ X0 > (X0 > $o) > X0)).
% 10.39/2.97 thf(func_def_146, type, sK57: !>[X0: $tType]:((treeFI @ X0 > $o) > treeFI @ X0)).
% 10.39/2.97 thf(func_def_147, type, sK58: !>[X0: $tType, X1: $tType]:((X1 > X0 > X0) > list @ X1 > X1)).
% 10.39/2.97 thf(func_def_148, type, sK59: !>[X0: $tType, X1: $tType]:((X1 > X0 > X0) > list @ X1 > X1)).
% 10.39/2.97 thf(func_def_149, type, sK60: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X1 > list @ X0)).
% 10.39/2.97 thf(func_def_150, type, sK61: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X1 > X1)).
% 10.39/2.97 thf(func_def_151, type, sK62: !>[X0: $tType, X1: $tType]:(X1 > (X0 > X1) > X0)).
% 10.39/2.97 thf(func_def_152, type, sK63: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 10.39/2.97 thf(func_def_153, type, sK64: !>[X0: $tType]:(list @ X0 > X0 > X0)).
% 10.39/2.97 thf(func_def_154, type, sK65: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 10.39/2.97 thf(func_def_155, type, sK66: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > treeFI @ X0 > X0)).
% 10.39/2.97 thf(func_def_156, type, sK67: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > stream @ X0 > X0)).
% 10.39/2.97 thf(func_def_157, type, sK68: !>[X0: $tType]:((stream @ X0 > stream @ X0 > $o) > stream @ X0)).
% 10.39/2.97 thf(func_def_158, type, sK69: !>[X0: $tType]:((stream @ X0 > stream @ X0 > $o) > stream @ X0)).
% 10.39/2.97 thf(func_def_159, type, sK70: treeFI @ a > stream @ a > treeFI @ a).
% 10.39/2.97 thf(func_def_160, type, sK71: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_161, type, sK72: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 10.39/2.97 thf(func_def_162, type, sK73: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_163, type, sK74: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_164, type, sK75: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_165, type, sK76: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 10.39/2.97 thf(func_def_166, type, sK77: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 10.39/2.97 thf(func_def_167, type, sK78: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_168, type, sK79: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_169, type, sK80: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_170, type, sK81: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_171, type, sK82: !>[X0: $tType]:(list @ X0 > (X0 > $o) > X0)).
% 10.39/2.97 thf(func_def_172, type, sK83: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > list @ X1 > list @ X1 > X1)).
% 10.39/2.97 thf(func_def_173, type, sK84: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > list @ X1 > list @ X1 > X1)).
% 10.39/2.97 thf(func_def_174, type, sK85: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > stream @ X1 > stream @ X1 > X1)).
% 10.39/2.97 thf(func_def_175, type, sK86: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > stream @ X1 > stream @ X1 > X1)).
% 10.39/2.97 thf(func_def_176, type, sK87: !>[X0: $tType]:(set @ X0 > stream @ X0 > X0)).
% 10.39/2.97 thf(func_def_177, type, sK88: !>[X0: $tType]:(set @ X0 > stream @ X0 > stream @ X0)).
% 10.39/2.97 thf(func_def_178, type, sK89: !>[X0: $tType]:((X0 > stream @ X0 > $o) > stream @ X0)).
% 10.39/2.97 thf(func_def_179, type, sK90: !>[X0: $tType]:((X0 > stream @ X0 > $o) > stream @ X0)).
% 10.39/2.97 thf(func_def_180, type, sK91: !>[X0: $tType]:((X0 > stream @ X0 > $o) > X0)).
% 10.39/2.97 thf(func_def_181, type, sK92: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_182, type, sK93: !>[X0: $tType]:((X0 > stream @ X0 > $o) > X0)).
% 10.39/2.97 thf(func_def_183, type, sK94: !>[X0: $tType]:((X0 > stream @ X0 > $o) > stream @ X0)).
% 10.39/2.97 thf(func_def_184, type, sK95: !>[X0: $tType]:((X0 > stream @ X0 > $o) > X0)).
% 10.39/2.97 thf(func_def_185, type, sK96: !>[X0: $tType]:((X0 > stream @ X0 > $o) > X0)).
% 10.39/2.97 thf(func_def_186, type, sK97: !>[X0: $tType]:((X0 > stream @ X0 > $o) > stream @ X0)).
% 10.39/2.97 thf(func_def_187, type, sK98: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_188, type, sK99: !>[X0: $tType]:(list @ X0 > X0)).
% 10.39/2.97 thf(func_def_189, type, sK100: !>[X0: $tType]:((X0 > treeFI @ X0 > $o) > X0)).
% 10.39/2.97 thf(func_def_190, type, sK101: !>[X0: $tType]:((X0 > treeFI @ X0 > $o) > list @ treeFI @ X0)).
% 10.39/2.97 thf(func_def_191, type, sK102: !>[X0: $tType]:((X0 > treeFI @ X0 > $o) > X0)).
% 10.39/2.97 thf(func_def_192, type, sK103: !>[X0: $tType]:((X0 > treeFI @ X0 > $o) > list @ treeFI @ X0)).
% 10.39/2.97 thf(func_def_193, type, sK104: !>[X0: $tType]:((X0 > treeFI @ X0 > $o) > treeFI @ X0)).
% 10.39/2.97 thf(func_def_194, type, sK105: !>[X0: $tType]:((X0 > treeFI @ X0 > $o) > X0)).
% 10.39/2.97 thf(func_def_195, type, sK106: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > list @ X1 > X1)).
% 10.39/2.97 thf(func_def_196, type, sK107: !>[X0: $tType]:((X0 > X0) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_197, type, sK108: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > treeFI @ X1 > X1)).
% 10.39/2.97 thf(func_def_198, type, sK109: !>[X0: $tType]:(treeFI @ X0 > treeFI @ X0)).
% 10.39/2.97 thf(func_def_199, type, sK110: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_200, type, sK111: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_201, type, sK112: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_202, type, sK113: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 10.39/2.97 thf(func_def_203, type, sK114: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 10.39/2.97 thf(func_def_204, type, sK115: !>[X0: $tType, X1: $tType]:((X1 > X0 > X0) > list @ X1 > X1)).
% 10.39/2.97 thf(func_def_205, type, sK116: !>[X0: $tType, X1: $tType]:((X1 > X0 > X0) > list @ X1 > X1)).
% 10.39/2.97 thf(func_def_206, type, sK117: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 10.39/2.97 thf(func_def_207, type, sK118: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 10.39/2.97 thf(func_def_208, type, sK119: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 10.39/2.97 thf(func_def_209, type, sK120: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 10.39/2.97 thf(func_def_210, type, sK121: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_211, type, sK122: !>[X0: $tType]:((X0 > $o) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_212, type, sK123: !>[X0: $tType]:((X0 > $o) > list @ X0 > list @ X0)).
% 10.39/2.97 thf(func_def_213, type, sK124: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > stream @ X1 > X1)).
% 10.39/2.97 thf(func_def_214, type, sK125: !>[X0: $tType]:(set @ X0 > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_215, type, sK126: !>[X0: $tType]:((treeFI @ X0 > $o) > treeFI @ X0)).
% 10.39/2.97 thf(func_def_216, type, sK127: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > list @ X1 > X1)).
% 10.39/2.97 thf(func_def_217, type, sK128: !>[X0: $tType]:(treeFI @ X0 > treeFI @ X0)).
% 10.39/2.97 thf(func_def_218, type, sK129: !>[X0: $tType]:(treeFI @ X0 > X0)).
% 10.39/2.97 thf(func_def_219, type, sK130: !>[X0: $tType]:(treeFI @ X0 > list @ treeFI @ X0)).
% 10.39/2.97 thf(func_def_220, type, sK131: !>[X0: $tType, X1: $tType]:((X1 > X0) > list @ X1 > (X1 > X0) > X1)).
% 10.39/2.97 thf(func_def_221, type, sK132: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 10.39/2.97 thf(func_def_222, type, sK133: !>[X0: $tType]:(list @ X0 > X0 > list @ X0)).
% 10.39/2.97 thf(func_def_223, type, sK134: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > (X0 > X1 > X1) > list @ X0 > X1)).
% 10.39/2.97 thf(func_def_224, type, sK135: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > (X0 > X1 > X1) > list @ X0 > X0)).
% 10.39/2.97 thf(func_def_225, type, sK136: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > treeFI @ X1 > treeFI @ X1 > X1)).
% 10.39/2.97 thf(func_def_226, type, sK137: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > treeFI @ X1 > treeFI @ X1 > X1)).
% 10.39/2.97 thf(func_def_227, type, sK138: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > list @ X1 > X1)).
% 10.39/2.97 thf(func_def_228, type, sK139: !>[X0: $tType]:(list @ X0 > X0 > X0)).
% 10.39/2.97 thf(func_def_230, type, ph141: !>[X0: $tType]:(X0)).
% 10.39/2.97 thf(f1745,plain,(
% 10.39/2.97 $false),
% 10.39/2.97 inference(avatar_sat_refutation,[status(thm)],[f1707,f1734,f1737,f1744])).
% 10.39/2.97 thf(f1744,plain,(
% 10.39/2.97 ~spl140_5),
% 10.39/2.97 inference(avatar_contradiction_clause,[status(thm)],[f1743])).
% 10.39/2.97 thf(f1743,plain,(
% 10.39/2.97 $false | ~spl140_5),
% 10.39/2.97 inference(subsumption_resolution,[status(thm)],[f1742,f1391])).
% 10.39/2.97 thf(f1391,plain,(
% 10.39/2.97 ((koenig1755522246erPath @ a @ as @ tr) != $true)),
% 10.39/2.97 inference(cnf_transformation,[status(thm)],[f651])).
% 10.39/2.97 thf(f651,plain,(
% 10.39/2.97 ((koenig1755522246erPath @ a @ as @ tr) != $true)),
% 10.39/2.97 inference(flattening,[status(thm)],[f404])).
% 10.39/2.97 thf(f404,plain,(
% 10.39/2.97 ~((koenig1755522246erPath @ a @ as @ tr) = $true)),
% 10.39/2.97 inference(fool_elimination,[status(thm)],[f403])).
% 10.39/2.97 thf(f403,plain,(
% 10.39/2.97 ~(koenig1755522246erPath @ a @ as @ tr)),
% 10.39/2.97 inference(rectify,[status(thm)],[f265])).
% 10.39/2.97 thf(f265,negated_conjecture,(
% 10.39/2.97 ~(koenig1755522246erPath @ a @ as @ tr)),
% 10.39/2.97 inference(negated_conjecture,[status(cth)],[f264])).
% 10.39/2.97 thf(f264,conjecture,(
% 10.39/2.97 (koenig1755522246erPath @ a @ as @ tr)),
% 10.39/2.97 file('/export/starexec/sandbox/tmp/tmp.BDekGnPrVg/DTF2THF_27722.p',conj_0)).
% 10.39/2.97 thf(f1742,plain,(
% 10.39/2.97 ((koenig1755522246erPath @ a @ as @ tr) = $true) | ~spl140_5),
% 10.39/2.97 inference(trivial_inequality_removal,[status(thm)],[f1739])).
% 10.39/2.97 thf(f1739,plain,(
% 10.39/2.97 ((koenig1755522246erPath @ a @ as @ tr) = $true) | ($true != $true) | ~spl140_5),
% 10.39/2.97 inference(superposition,[status(thm)],[f1733,f1258])).
% 10.39/2.97 thf(f1258,plain,(
% 10.39/2.97 ((phi @ as @ tr) = $true)),
% 10.39/2.97 inference(cnf_transformation,[status(thm)],[f340])).
% 10.39/2.97 thf(f340,plain,(
% 10.39/2.97 ((phi @ as @ tr) = $true)),
% 10.39/2.97 inference(fool_elimination,[status(thm)],[f339])).
% 10.39/2.97 thf(f339,plain,(
% 10.39/2.97 (phi @ as @ tr)),
% 10.39/2.97 inference(rectify,[status(thm)],[f2])).
% 10.39/2.97 thf(f2,axiom,(
% 10.39/2.97 (phi @ as @ tr)),
% 10.39/2.97 file('/export/starexec/sandbox/tmp/tmp.BDekGnPrVg/DTF2THF_27722.p',fact_1__C_K_C)).
% 10.39/2.97 thf(f1733,plain,(
% 10.39/2.97 ( ! [X0 : stream @ a,X1 : treeFI @ a] : (($true != (phi @ X0 @ X1)) | ($true = (koenig1755522246erPath @ a @ X0 @ X1))) ) | ~spl140_5),
% 10.39/2.97 inference(avatar_component_clause,[status(thm)],[f1732])).
% 10.39/2.97 thf(f1732,definition,(
% 10.39/2.97 spl140_5 <=> ! [X0 : stream @ a,X1 : treeFI @ a] : (($true = (koenig1755522246erPath @ a @ X0 @ X1)) | ($true != (phi @ X0 @ X1)))),
% 10.39/2.97 introduced(definition,[new_symbols(naming,[spl140_5])],[avatar_definition])).
% 10.39/2.97 thf(f1737,plain,(
% 10.39/2.97 spl140_5 | ~spl140_2),
% 10.39/2.97 inference(avatar_split_clause,[status(thm)],[f1736,f1704,f1732])).
% 10.39/2.97 thf(f1704,definition,(
% 10.39/2.97 spl140_2 <=> ($true = (koenig1755522246erPath @ a @ (stl @ a @ (sK4 @ a @ phi)) @ (sK70 @ (sK5 @ a @ phi) @ (sK4 @ a @ phi))))),
% 10.39/2.97 introduced(definition,[new_symbols(naming,[spl140_2])],[avatar_definition])).
% 10.39/2.97 thf(f1736,plain,(
% 10.39/2.97 ( ! [X0 : stream @ a,X1 : treeFI @ a] : (($true != (phi @ X0 @ X1)) | ($true = (koenig1755522246erPath @ a @ X0 @ X1))) ) | ~spl140_2),
% 10.39/2.97 inference(subsumption_resolution,[status(thm)],[f1735,f1693])).
% 10.39/2.97 thf(f1693,plain,(
% 10.39/2.97 ((shd @ a @ (sK4 @ a @ phi)) = (lab @ a @ (sK5 @ a @ phi)))),
% 10.39/2.97 inference(trivial_inequality_removal,[status(thm)],[f1691])).
% 10.39/2.97 thf(f1691,plain,(
% 10.39/2.97 ((shd @ a @ (sK4 @ a @ phi)) = (lab @ a @ (sK5 @ a @ phi))) | ($true != $true)),
% 10.39/2.97 inference(superposition,[status(thm)],[f1476,f1689])).
% 10.39/2.97 thf(f1689,plain,(
% 10.39/2.97 ($true = (phi @ (sK4 @ a @ phi) @ (sK5 @ a @ phi)))),
% 10.39/2.97 inference(subsumption_resolution,[status(thm)],[f1687,f1391])).
% 10.39/2.97 thf(f1687,plain,(
% 10.39/2.97 ($true = (phi @ (sK4 @ a @ phi) @ (sK5 @ a @ phi))) | ((koenig1755522246erPath @ a @ as @ tr) = $true)),
% 10.39/2.97 inference(trivial_inequality_removal,[status(thm)],[f1682])).
% 10.39/2.97 thf(f1682,plain,(
% 10.39/2.97 ($true = (phi @ (sK4 @ a @ phi) @ (sK5 @ a @ phi))) | ($true != $true) | ((koenig1755522246erPath @ a @ as @ tr) = $true)),
% 10.39/2.97 inference(superposition,[status(thm)],[f1162,f1258])).
% 10.39/2.97 thf(f1162,plain,(
% 10.39/2.97 ( ! [X0 : $tType,X2 : stream @ X0,X3 : treeFI @ X0,X1 : stream @ X0 > treeFI @ X0 > $o] : (($true != (X1 @ X2 @ X3)) | ($true = (koenig1755522246erPath @ X0 @ X2 @ X3)) | ($true = (X1 @ (sK4 @ X0 @ X1) @ (sK5 @ X0 @ X1)))) )),
% 10.39/2.97 inference(cnf_transformation,[status(thm)],[f923])).
% 10.39/2.97 thf(f923,plain,(
% 10.39/2.97 ! [X0 : $tType,X1 : stream @ X0 > treeFI @ X0 > $o,X2 : stream @ X0,X3 : treeFI @ X0] : ((($true = (X1 @ (sK4 @ X0 @ X1) @ (sK5 @ X0 @ X1))) & ! [X6 : stream @ X0,X7 : treeFI @ X0,X8 : treeFI @ X0] : ((($true != (koenig1755522246erPath @ X0 @ (stl @ X0 @ X6) @ X8)) & ($true != (X1 @ (stl @ X0 @ X6) @ X8))) | ((shd @ X0 @ X6) != (lab @ X0 @ X7)) | ((sK4 @ X0 @ X1) != X6) | ($true != (member2 @ treeFI @ X0 @ X8 @ (set2 @ treeFI @ X0 @ (sub @ X0 @ X7)))) | ((sK5 @ X0 @ X1) != X7))) | ($true = (koenig1755522246erPath @ X0 @ X2 @ X3)) | ($true != (X1 @ X2 @ X3)))),
% 10.39/2.97 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f733,f922])).
% 10.39/2.97 thf(f922,plain,(
% 10.39/2.97 ! [X0 : $tType,X1 : stream @ X0 > treeFI @ X0 > $o] : (? [X4 : stream @ X0,X5 : treeFI @ X0] : (($true = (X1 @ X4 @ X5)) & ! [X6 : stream @ X0,X7 : treeFI @ X0,X8 : treeFI @ X0] : ((($true != (koenig1755522246erPath @ X0 @ (stl @ X0 @ X6) @ X8)) & ($true != (X1 @ (stl @ X0 @ X6) @ X8))) | ((shd @ X0 @ X6) != (lab @ X0 @ X7)) | (X4 != X6) | ($true != (member2 @ treeFI @ X0 @ X8 @ (set2 @ treeFI @ X0 @ (sub @ X0 @ X7)))) | (X5 != X7))) => (($true = (X1 @ (sK4 @ X0 @ X1) @ (sK5 @ X0 @ X1))) & ! [X8 : treeFI @ X0,X7 : treeFI @ X0,X6 : stream @ X0] : ((($true != (koenig1755522246erPath @ X0 @ (stl @ X0 @ X6) @ X8)) & ($true != (X1 @ (stl @ X0 @ X6) @ X8))) | ((shd @ X0 @ X6) != (lab @ X0 @ X7)) | ((sK4 @ X0 @ X1) != X6) | ($true != (member2 @ treeFI @ X0 @ X8 @ (set2 @ treeFI @ X0 @ (sub @ X0 @ X7)))) | ((sK5 @ X0 @ X1) != X7))))),
% 10.39/2.97 introduced(definition,[],[choice_axiom])).
% 10.39/2.97 thf(f733,plain,(
% 10.39/2.97 ! [X0 : $tType,X1 : stream @ X0 > treeFI @ X0 > $o,X2 : stream @ X0,X3 : treeFI @ X0] : (? [X4 : stream @ X0,X5 : treeFI @ X0] : (($true = (X1 @ X4 @ X5)) & ! [X6 : stream @ X0,X7 : treeFI @ X0,X8 : treeFI @ X0] : ((($true != (koenig1755522246erPath @ X0 @ (stl @ X0 @ X6) @ X8)) & ($true != (X1 @ (stl @ X0 @ X6) @ X8))) | ((shd @ X0 @ X6) != (lab @ X0 @ X7)) | (X4 != X6) | ($true != (member2 @ treeFI @ X0 @ X8 @ (set2 @ treeFI @ X0 @ (sub @ X0 @ X7)))) | (X5 != X7))) | ($true = (koenig1755522246erPath @ X0 @ X2 @ X3)) | ($true != (X1 @ X2 @ X3)))),
% 10.39/2.97 inference(flattening,[status(thm)],[f732])).
% 10.39/2.97 thf(f732,plain,(
% 10.39/2.97 ! [X0 : $tType,X1 : stream @ X0 > treeFI @ X0 > $o,X2 : stream @ X0,X3 : treeFI @ X0] : ((($true = (koenig1755522246erPath @ X0 @ X2 @ X3)) | ? [X4 : stream @ X0,X5 : treeFI @ X0] : (($true = (X1 @ X4 @ X5)) & ! [X6 : stream @ X0,X7 : treeFI @ X0,X8 : treeFI @ X0] : ((($true != (koenig1755522246erPath @ X0 @ (stl @ X0 @ X6) @ X8)) & ($true != (X1 @ (stl @ X0 @ X6) @ X8))) | ((shd @ X0 @ X6) != (lab @ X0 @ X7)) | (X4 != X6) | ($true != (member2 @ treeFI @ X0 @ X8 @ (set2 @ treeFI @ X0 @ (sub @ X0 @ X7)))) | (X5 != X7)))) | ($true != (X1 @ X2 @ X3)))),
% 10.39/2.97 inference(ennf_transformation,[status(thm)],[f276])).
% 10.39/2.97 thf(f276,plain,(
% 10.39/2.97 ! [X0 : $tType,X1 : stream @ X0 > treeFI @ X0 > $o,X2 : stream @ X0,X3 : treeFI @ X0] : (($true = (X1 @ X2 @ X3)) => (! [X4 : stream @ X0,X5 : treeFI @ X0] : (($true = (X1 @ X4 @ X5)) => ? [X6 : stream @ X0,X7 : treeFI @ X0,X8 : treeFI @ X0] : ((($true = (koenig1755522246erPath @ X0 @ (stl @ X0 @ X6) @ X8)) | ($true = (X1 @ (stl @ X0 @ X6) @ X8))) & ((shd @ X0 @ X6) = (lab @ X0 @ X7)) & (X4 = X6) & ($true = (member2 @ treeFI @ X0 @ X8 @ (set2 @ treeFI @ X0 @ (sub @ X0 @ X7)))) & (X5 = X7))) => ($true = (koenig1755522246erPath @ X0 @ X2 @ X3))))),
% 10.39/2.97 inference(fool_elimination,[status(thm)],[f275])).
% 10.39/2.97 thf(f275,plain,(
% 10.39/2.97 ! [X0 : $tType,X1 : stream @ X0 > treeFI @ X0 > $o,X2 : stream @ X0,X3 : treeFI @ X0] : ((X1 @ X2 @ X3) => (! [X4 : stream @ X0,X5 : treeFI @ X0] : ((X1 @ X4 @ X5) => ? [X6 : stream @ X0,X7 : treeFI @ X0,X8 : treeFI @ X0] : ((member2 @ treeFI @ X0 @ X8 @ (set2 @ treeFI @ X0 @ (sub @ X0 @ X7))) & (X5 = X7) & (X4 = X6) & ((X1 @ (stl @ X0 @ X6) @ X8) | (koenig1755522246erPath @ X0 @ (stl @ X0 @ X6) @ X8)) & ((shd @ X0 @ X6) = (lab @ X0 @ X7)))) => (koenig1755522246erPath @ X0 @ X2 @ X3)))),
% 10.39/2.97 inference(rectify,[status(thm)],[f6])).
% 10.39/2.97 thf(f6,axiom,(
% 10.39/2.97 ! [X0 : $tType,X16 : stream @ X0 > treeFI @ X0 > $o,X17 : stream @ X0,X18 : treeFI @ X0] : ((X16 @ X17 @ X18) => (! [X6 : stream @ X0,X19 : treeFI @ X0] : ((X16 @ X6 @ X19) => ? [X20 : stream @ X0,X21 : treeFI @ X0,X22 : treeFI @ X0] : ((member2 @ treeFI @ X0 @ X22 @ (set2 @ treeFI @ X0 @ (sub @ X0 @ X21))) & (X19 = X21) & (X6 = X20) & ((X16 @ (stl @ X0 @ X20) @ X22) | (koenig1755522246erPath @ X0 @ (stl @ X0 @ X20) @ X22)) & ((shd @ X0 @ X20) = (lab @ X0 @ X21)))) => (koenig1755522246erPath @ X0 @ X17 @ X18)))),
% 10.39/2.97 file('/export/starexec/sandbox/tmp/tmp.BDekGnPrVg/DTF2THF_27722.p',fact_5_properPath_Ocoinduct)).
% 10.39/2.97 thf(f1476,plain,(
% 10.39/2.97 ( ! [X0 : stream @ a,X1 : treeFI @ a] : (($true != (phi @ X0 @ X1)) | ((shd @ a @ X0) = (lab @ a @ X1))) )),
% 10.39/2.97 inference(cnf_transformation,[status(thm)],[f891])).
% 10.39/2.97 thf(f891,plain,(
% 10.39/2.97 ! [X0 : stream @ a,X1 : treeFI @ a] : (($true != (phi @ X0 @ X1)) | ((shd @ a @ X0) = (lab @ a @ X1)))),
% 10.39/2.97 inference(ennf_transformation,[status(thm)],[f532])).
% 10.39/2.97 thf(f532,plain,(
% 10.39/2.97 ! [X0 : stream @ a,X1 : treeFI @ a] : (($true = (phi @ X0 @ X1)) => ((shd @ a @ X0) = (lab @ a @ X1)))),
% 10.39/2.97 inference(fool_elimination,[status(thm)],[f531])).
% 10.39/2.97 thf(f531,plain,(
% 10.39/2.97 ! [X0 : stream @ a,X1 : treeFI @ a] : ((phi @ X0 @ X1) => ((shd @ a @ X0) = (lab @ a @ X1)))),
% 10.39/2.97 inference(rectify,[status(thm)],[f7])).
% 10.39/2.97 thf(f7,axiom,(
% 10.39/2.97 ! [X4 : stream @ a,X5 : treeFI @ a] : ((phi @ X4 @ X5) => ((shd @ a @ X4) = (lab @ a @ X5)))),
% 10.39/2.97 file('/export/starexec/sandbox/tmp/tmp.BDekGnPrVg/DTF2THF_27722.p',fact_6__C_K_K_C)).
% 10.39/2.97 thf(f1735,plain,(
% 10.39/2.97 ( ! [X0 : stream @ a,X1 : treeFI @ a] : (((shd @ a @ (sK4 @ a @ phi)) != (lab @ a @ (sK5 @ a @ phi))) | ($true = (koenig1755522246erPath @ a @ X0 @ X1)) | ($true != (phi @ X0 @ X1))) ) | ~spl140_2),
% 10.39/2.97 inference(subsumption_resolution,[status(thm)],[f1727,f1706])).
% 10.39/2.97 thf(f1706,plain,(
% 10.39/2.97 ($true = (koenig1755522246erPath @ a @ (stl @ a @ (sK4 @ a @ phi)) @ (sK70 @ (sK5 @ a @ phi) @ (sK4 @ a @ phi)))) | ~spl140_2),
% 10.39/2.97 inference(avatar_component_clause,[status(thm)],[f1704])).
% 10.39/2.97 thf(f1727,plain,(
% 10.39/2.97 ( ! [X0 : stream @ a,X1 : treeFI @ a] : (($true != (phi @ X0 @ X1)) | ($true != (koenig1755522246erPath @ a @ (stl @ a @ (sK4 @ a @ phi)) @ (sK70 @ (sK5 @ a @ phi) @ (sK4 @ a @ phi)))) | ((shd @ a @ (sK4 @ a @ phi)) != (lab @ a @ (sK5 @ a @ phi))) | ($true = (koenig1755522246erPath @ a @ X0 @ X1))) )),
% 10.39/2.97 inference(trivial_inequality_removal,[status(thm)],[f1724])).
% 10.39/2.97 thf(f1724,plain,(
% 10.39/2.97 ( ! [X0 : stream @ a,X1 : treeFI @ a] : (($true != (koenig1755522246erPath @ a @ (stl @ a @ (sK4 @ a @ phi)) @ (sK70 @ (sK5 @ a @ phi) @ (sK4 @ a @ phi)))) | ((shd @ a @ (sK4 @ a @ phi)) != (lab @ a @ (sK5 @ a @ phi))) | ($true != (phi @ X0 @ X1)) | ($true = (koenig1755522246erPath @ a @ X0 @ X1)) | ($true != $true)) )),
% 10.39/2.97 inference(superposition,[status(thm)],[f1576,f1694])).
% 10.39/2.97 thf(f1694,plain,(
% 10.39/2.97 ((member2 @ treeFI @ a @ (sK70 @ (sK5 @ a @ phi) @ (sK4 @ a @ phi)) @ (set2 @ treeFI @ a @ (sub @ a @ (sK5 @ a @ phi)))) = $true)),
% 10.39/2.97 inference(trivial_inequality_removal,[status(thm)],[f1690])).
% 10.39/2.97 thf(f1690,plain,(
% 10.39/2.97 ((member2 @ treeFI @ a @ (sK70 @ (sK5 @ a @ phi) @ (sK4 @ a @ phi)) @ (set2 @ treeFI @ a @ (sub @ a @ (sK5 @ a @ phi)))) = $true) | ($true != $true)),
% 10.39/2.97 inference(superposition,[status(thm)],[f1359,f1689])).
% 10.39/2.97 thf(f1359,plain,(
% 10.39/2.97 ( ! [X0 : stream @ a,X1 : treeFI @ a] : (($true != (phi @ X0 @ X1)) | ($true = (member2 @ treeFI @ a @ (sK70 @ X1 @ X0) @ (set2 @ treeFI @ a @ (sub @ a @ X1))))) )),
% 10.39/2.97 inference(cnf_transformation,[status(thm)],[f1037])).
% 10.39/2.97 thf(f1037,plain,(
% 10.39/2.97 ! [X0 : stream @ a,X1 : treeFI @ a] : ((($true = (member2 @ treeFI @ a @ (sK70 @ X1 @ X0) @ (set2 @ treeFI @ a @ (sub @ a @ X1)))) & (($true = (koenig1755522246erPath @ a @ (stl @ a @ X0) @ (sK70 @ X1 @ X0))) | ($true = (phi @ (stl @ a @ X0) @ (sK70 @ X1 @ X0))))) | ($true != (phi @ X0 @ X1)))),
% 10.39/2.97 inference(skolemisation,[status(esa),new_symbols(skolem,[sK70])],[f778,f1036])).
% 10.39/2.97 thf(f1036,plain,(
% 10.39/2.97 ! [X0 : stream @ a,X1 : treeFI @ a] : (? [X2 : treeFI @ a] : (($true = (member2 @ treeFI @ a @ X2 @ (set2 @ treeFI @ a @ (sub @ a @ X1)))) & (($true = (koenig1755522246erPath @ a @ (stl @ a @ X0) @ X2)) | ($true = (phi @ (stl @ a @ X0) @ X2)))) => (($true = (member2 @ treeFI @ a @ (sK70 @ X1 @ X0) @ (set2 @ treeFI @ a @ (sub @ a @ X1)))) & (($true = (koenig1755522246erPath @ a @ (stl @ a @ X0) @ (sK70 @ X1 @ X0))) | ($true = (phi @ (stl @ a @ X0) @ (sK70 @ X1 @ X0))))))),
% 10.39/2.97 introduced(definition,[],[choice_axiom])).
% 10.39/2.97 thf(f778,plain,(
% 10.39/2.97 ! [X0 : stream @ a,X1 : treeFI @ a] : (? [X2 : treeFI @ a] : (($true = (member2 @ treeFI @ a @ X2 @ (set2 @ treeFI @ a @ (sub @ a @ X1)))) & (($true = (koenig1755522246erPath @ a @ (stl @ a @ X0) @ X2)) | ($true = (phi @ (stl @ a @ X0) @ X2)))) | ($true != (phi @ X0 @ X1)))),
% 10.39/2.97 inference(ennf_transformation,[status(thm)],[f306])).
% 10.39/2.97 thf(f306,plain,(
% 10.39/2.97 ! [X0 : stream @ a,X1 : treeFI @ a] : (($true = (phi @ X0 @ X1)) => ? [X2 : treeFI @ a] : (($true = (member2 @ treeFI @ a @ X2 @ (set2 @ treeFI @ a @ (sub @ a @ X1)))) & (($true = (koenig1755522246erPath @ a @ (stl @ a @ X0) @ X2)) | ($true = (phi @ (stl @ a @ X0) @ X2)))))),
% 10.39/2.97 inference(fool_elimination,[status(thm)],[f305])).
% 10.39/2.97 thf(f305,plain,(
% 10.39/2.97 ! [X0 : stream @ a,X1 : treeFI @ a] : ((phi @ X0 @ X1) => ? [X2 : treeFI @ a] : ((member2 @ treeFI @ a @ X2 @ (set2 @ treeFI @ a @ (sub @ a @ X1))) & ((koenig1755522246erPath @ a @ (stl @ a @ X0) @ X2) | (phi @ (stl @ a @ X0) @ X2))))),
% 10.39/2.97 inference(rectify,[status(thm)],[f1])).
% 10.39/2.97 thf(f1,axiom,(
% 10.39/2.97 ! [X4 : stream @ a,X5 : treeFI @ a] : ((phi @ X4 @ X5) => ? [X6 : treeFI @ a] : ((member2 @ treeFI @ a @ X6 @ (set2 @ treeFI @ a @ (sub @ a @ X5))) & ((koenig1755522246erPath @ a @ (stl @ a @ X4) @ X6) | (phi @ (stl @ a @ X4) @ X6))))),
% 10.39/2.97 file('/export/starexec/sandbox/tmp/tmp.BDekGnPrVg/DTF2THF_27722.p',fact_0__C_K_K_K_C)).
% 10.39/2.97 thf(f1576,plain,(
% 10.39/2.97 ( ! [X0 : $tType,X2 : stream @ X0,X3 : treeFI @ X0,X1 : stream @ X0 > treeFI @ X0 > $o,X8 : treeFI @ X0] : (($true != (member2 @ treeFI @ X0 @ X8 @ (set2 @ treeFI @ X0 @ (sub @ X0 @ (sK5 @ X0 @ X1))))) | ($true = (koenig1755522246erPath @ X0 @ X2 @ X3)) | ($true != (X1 @ X2 @ X3)) | ((shd @ X0 @ (sK4 @ X0 @ X1)) != (lab @ X0 @ (sK5 @ X0 @ X1))) | ((koenig1755522246erPath @ X0 @ (stl @ X0 @ (sK4 @ X0 @ X1)) @ X8) != $true)) )),
% 10.39/2.97 inference(equality_resolution,[status(thm)],[f1575])).
% 10.39/2.97 thf(f1575,plain,(
% 10.39/2.97 ( ! [X0 : $tType,X2 : stream @ X0,X3 : treeFI @ X0,X1 : stream @ X0 > treeFI @ X0 > $o,X8 : treeFI @ X0,X7 : treeFI @ X0] : (((koenig1755522246erPath @ X0 @ (stl @ X0 @ (sK4 @ X0 @ X1)) @ X8) != $true) | ((shd @ X0 @ (sK4 @ X0 @ X1)) != (lab @ X0 @ X7)) | ($true != (member2 @ treeFI @ X0 @ X8 @ (set2 @ treeFI @ X0 @ (sub @ X0 @ X7)))) | ((sK5 @ X0 @ X1) != X7) | ($true = (koenig1755522246erPath @ X0 @ X2 @ X3)) | ($true != (X1 @ X2 @ X3))) )),
% 10.39/2.97 inference(equality_resolution,[status(thm)],[f1161])).
% 10.39/2.97 thf(f1161,plain,(
% 10.39/2.97 ( ! [X0 : $tType,X2 : stream @ X0,X3 : treeFI @ X0,X1 : stream @ X0 > treeFI @ X0 > $o,X8 : treeFI @ X0,X6 : stream @ X0,X7 : treeFI @ X0] : (($true != (koenig1755522246erPath @ X0 @ (stl @ X0 @ X6) @ X8)) | ((shd @ X0 @ X6) != (lab @ X0 @ X7)) | ((sK4 @ X0 @ X1) != X6) | ($true != (member2 @ treeFI @ X0 @ X8 @ (set2 @ treeFI @ X0 @ (sub @ X0 @ X7)))) | ((sK5 @ X0 @ X1) != X7) | ($true = (koenig1755522246erPath @ X0 @ X2 @ X3)) | ($true != (X1 @ X2 @ X3))) )),
% 10.39/2.97 inference(cnf_transformation,[status(thm)],[f923])).
% 10.39/2.97 thf(f1734,plain,(
% 10.39/2.97 ~spl140_1 | spl140_5),
% 10.39/2.97 inference(avatar_split_clause,[status(thm)],[f1730,f1732,f1700])).
% 10.39/2.97 thf(f1700,definition,(
% 10.39/2.97 spl140_1 <=> ($true = (phi @ (stl @ a @ (sK4 @ a @ phi)) @ (sK70 @ (sK5 @ a @ phi) @ (sK4 @ a @ phi))))),
% 10.39/2.97 introduced(definition,[new_symbols(naming,[spl140_1])],[avatar_definition])).
% 10.39/2.97 thf(f1730,plain,(
% 10.39/2.97 ( ! [X0 : stream @ a,X1 : treeFI @ a] : (($true = (koenig1755522246erPath @ a @ X0 @ X1)) | ($true != (phi @ (stl @ a @ (sK4 @ a @ phi)) @ (sK70 @ (sK5 @ a @ phi) @ (sK4 @ a @ phi)))) | ($true != (phi @ X0 @ X1))) )),
% 10.39/2.97 inference(subsumption_resolution,[status(thm)],[f1728,f1693])).
% 10.39/2.97 thf(f1728,plain,(
% 10.39/2.97 ( ! [X0 : stream @ a,X1 : treeFI @ a] : (($true != (phi @ (stl @ a @ (sK4 @ a @ phi)) @ (sK70 @ (sK5 @ a @ phi) @ (sK4 @ a @ phi)))) | ($true = (koenig1755522246erPath @ a @ X0 @ X1)) | ((shd @ a @ (sK4 @ a @ phi)) != (lab @ a @ (sK5 @ a @ phi))) | ($true != (phi @ X0 @ X1))) )),
% 10.39/2.97 inference(trivial_inequality_removal,[status(thm)],[f1725])).
% 10.39/2.97 thf(f1725,plain,(
% 10.39/2.97 ( ! [X0 : stream @ a,X1 : treeFI @ a] : (($true != (phi @ (stl @ a @ (sK4 @ a @ phi)) @ (sK70 @ (sK5 @ a @ phi) @ (sK4 @ a @ phi)))) | ($true != $true) | ($true = (koenig1755522246erPath @ a @ X0 @ X1)) | ($true != (phi @ X0 @ X1)) | ((shd @ a @ (sK4 @ a @ phi)) != (lab @ a @ (sK5 @ a @ phi)))) )),
% 10.39/2.97 inference(superposition,[status(thm)],[f1578,f1694])).
% 10.39/2.97 thf(f1578,plain,(
% 10.39/2.97 ( ! [X0 : $tType,X2 : stream @ X0,X3 : treeFI @ X0,X1 : stream @ X0 > treeFI @ X0 > $o,X8 : treeFI @ X0] : (($true != (member2 @ treeFI @ X0 @ X8 @ (set2 @ treeFI @ X0 @ (sub @ X0 @ (sK5 @ X0 @ X1))))) | ($true != (X1 @ X2 @ X3)) | ($true = (koenig1755522246erPath @ X0 @ X2 @ X3)) | ($true != (X1 @ (stl @ X0 @ (sK4 @ X0 @ X1)) @ X8)) | ((shd @ X0 @ (sK4 @ X0 @ X1)) != (lab @ X0 @ (sK5 @ X0 @ X1)))) )),
% 10.39/2.97 inference(equality_resolution,[status(thm)],[f1577])).
% 10.39/2.97 thf(f1577,plain,(
% 10.39/2.97 ( ! [X0 : $tType,X2 : stream @ X0,X3 : treeFI @ X0,X1 : stream @ X0 > treeFI @ X0 > $o,X8 : treeFI @ X0,X7 : treeFI @ X0] : (($true != (X1 @ (stl @ X0 @ (sK4 @ X0 @ X1)) @ X8)) | ((shd @ X0 @ (sK4 @ X0 @ X1)) != (lab @ X0 @ X7)) | ($true != (member2 @ treeFI @ X0 @ X8 @ (set2 @ treeFI @ X0 @ (sub @ X0 @ X7)))) | ((sK5 @ X0 @ X1) != X7) | ($true = (koenig1755522246erPath @ X0 @ X2 @ X3)) | ($true != (X1 @ X2 @ X3))) )),
% 10.39/2.97 inference(equality_resolution,[status(thm)],[f1160])).
% 10.39/2.97 thf(f1160,plain,(
% 10.39/2.97 ( ! [X0 : $tType,X2 : stream @ X0,X3 : treeFI @ X0,X1 : stream @ X0 > treeFI @ X0 > $o,X8 : treeFI @ X0,X6 : stream @ X0,X7 : treeFI @ X0] : (($true != (X1 @ (stl @ X0 @ X6) @ X8)) | ((shd @ X0 @ X6) != (lab @ X0 @ X7)) | ((sK4 @ X0 @ X1) != X6) | ($true != (member2 @ treeFI @ X0 @ X8 @ (set2 @ treeFI @ X0 @ (sub @ X0 @ X7)))) | ((sK5 @ X0 @ X1) != X7) | ($true = (koenig1755522246erPath @ X0 @ X2 @ X3)) | ($true != (X1 @ X2 @ X3))) )),
% 10.39/2.97 inference(cnf_transformation,[status(thm)],[f923])).
% 10.39/2.97 thf(f1707,plain,(
% 10.39/2.97 spl140_1 | spl140_2),
% 10.39/2.97 inference(avatar_split_clause,[status(thm)],[f1698,f1704,f1700])).
% 10.39/2.97 thf(f1698,plain,(
% 10.39/2.97 ($true = (koenig1755522246erPath @ a @ (stl @ a @ (sK4 @ a @ phi)) @ (sK70 @ (sK5 @ a @ phi) @ (sK4 @ a @ phi)))) | ($true = (phi @ (stl @ a @ (sK4 @ a @ phi)) @ (sK70 @ (sK5 @ a @ phi) @ (sK4 @ a @ phi))))),
% 10.39/2.97 inference(trivial_inequality_removal,[status(thm)],[f1696])).
% 10.39/2.97 thf(f1696,plain,(
% 10.39/2.97 ($true != $true) | ($true = (phi @ (stl @ a @ (sK4 @ a @ phi)) @ (sK70 @ (sK5 @ a @ phi) @ (sK4 @ a @ phi)))) | ($true = (koenig1755522246erPath @ a @ (stl @ a @ (sK4 @ a @ phi)) @ (sK70 @ (sK5 @ a @ phi) @ (sK4 @ a @ phi))))),
% 10.39/2.97 inference(superposition,[status(thm)],[f1358,f1689])).
% 10.39/2.97 thf(f1358,plain,(
% 10.39/2.97 ( ! [X0 : stream @ a,X1 : treeFI @ a] : (($true != (phi @ X0 @ X1)) | ($true = (koenig1755522246erPath @ a @ (stl @ a @ X0) @ (sK70 @ X1 @ X0))) | ($true = (phi @ (stl @ a @ X0) @ (sK70 @ X1 @ X0)))) )),
% 10.39/2.97 inference(cnf_transformation,[status(thm)],[f1037])).
% 10.39/2.97 % SZS output end Proof for DTF2THF_27722
% 10.39/2.97 % (27917)------------------------------
% 10.39/2.97 % (27917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.39/2.97 % (27917)Termination reason: Refutation
% 10.39/2.97
% 10.39/2.97 % (27917)Memory used [KB]: 7291
% 10.39/2.97 % (27917)Time elapsed: 0.081 s
% 10.39/2.97 % (27917)Instructions burned: 156 (million)
% 10.39/2.97 % (27917)------------------------------
% 10.39/2.97 % (27917)------------------------------
% 10.39/2.97 % (27835)Success in time 1.135 s
%------------------------------------------------------------------------------