%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT251^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:45:18 AM UTC 2026
% Result : Theorem 22.60s 4.69s
% Output : Refutation 22.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT251^1 : TPTP v9.2.1. Released v7.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n015.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 06:12:01 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.48 ---- Original DTF file ---
% 0.31/0.48 thf(spec,logic,$$dhol).
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 % File : DAT251^1 : TPTP v9.2.1. Released v7.0.0.
% 0.31/0.48 % Domain : Data Structures
% 0.31/0.48 % Problem : Infinite streams (sequences/lists) 443
% 0.31/0.48 % Version : [Bla16] axioms : Especial.
% 0.31/0.48 % English :
% 0.31/0.48
% 0.31/0.48 % Refs : [BH+14] Blanchette et al. (2014), Truly Modular (Co)datatypes
% 0.31/0.48 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.31/0.48 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.31/0.48 % Source : [Bla16]
% 0.31/0.48 % Names : stream__443.p [Bla16]
% 0.31/0.48
% 0.31/0.48 % Status : Theorem
% 0.31/0.48 % Rating : 0.33 v9.1.0, 0.00 v7.5.0, 0.33 v7.2.0, 0.25 v7.1.0
% 0.31/0.48 % Syntax : Number of formulae : 326 ( 150 unt; 59 typ; 0 def)
% 0.31/0.48 % Number of atoms : 698 ( 481 equ; 0 cnn)
% 0.31/0.48 % Maximal formula atoms : 12 ( 2 avg)
% 0.31/0.48 % Number of connectives : 4460 ( 140 ~; 30 |; 80 &;3912 @)
% 0.31/0.48 % ( 0 <=>; 298 =>; 0 <=; 0 <~>)
% 0.31/0.48 % Maximal formula depth : 23 ( 7 avg)
% 0.31/0.48 % Number of types : 3 ( 2 usr)
% 0.31/0.48 % Number of type conns : 246 ( 246 >; 0 *; 0 +; 0 <<)
% 0.31/0.48 % Number of symbols : 60 ( 57 usr; 3 con; 0-5 aty)
% 0.31/0.48 % Number of variables : 1171 ( 34 ^;1002 !; 72 ?;1171 :)
% 0.31/0.48 % ( 63 !>; 0 ?*; 0 @-; 0 @+)
% 0.31/0.48 % SPC : TH1_THM_EQU_NAR
% 0.31/0.48
% 0.31/0.48 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.31/0.48 % 2016-07-13 14:42:29.928
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 %----Could-be-implicit typings (6)
% 0.31/0.48 thf(ty_t_Stream__Mirabelle__hbrgyiwlrc_Ostream,type,
% 0.31/0.48 stream170649215stream: $tType > $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_t_List_Olist,type,
% 0.31/0.48 list: $tType > $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_t_Set_Oset,type,
% 0.31/0.48 set: $tType > $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_t_Nat_Onat,type,
% 0.31/0.48 nat: $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_t_itself,type,
% 0.31/0.48 itself: $tType > $tType ).
% 0.31/0.48
% 0.31/0.48 thf(ty_tf_a,type,
% 0.31/0.48 a: $tType ).
% 0.31/0.48
% 0.31/0.48 %----Explicit typings (53)
% 0.31/0.48 thf(sy_cl_HOL_Otype,type,
% 0.31/0.48 type:
% 0.31/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_cl_Orderings_Oord,type,
% 0.31/0.48 ord:
% 0.31/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_cl_Orderings_Oorder,type,
% 0.31/0.48 order:
% 0.31/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_cl_Orderings_Olinorder,type,
% 0.31/0.48 linorder:
% 0.31/0.48 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_BNF__Greatest__Fixpoint_OShift,type,
% 0.31/0.48 bNF_Greatest_Shift:
% 0.31/0.48 !>[A: $tType] : ( ( set @ ( list @ A ) ) > A > ( set @ ( list @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_BNF__Greatest__Fixpoint_OSucc,type,
% 0.31/0.48 bNF_Greatest_Succ:
% 0.31/0.48 !>[A: $tType] : ( ( set @ ( list @ A ) ) > ( list @ A ) > ( set @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_BNF__Greatest__Fixpoint_Oshift,type,
% 0.31/0.48 bNF_Greatest_shift:
% 0.31/0.48 !>[A: $tType,B: $tType] : ( ( ( list @ A ) > B ) > A > ( list @ A ) > B ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_If,type,
% 0.31/0.48 if:
% 0.31/0.48 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Oappend,type,
% 0.31/0.48 append:
% 0.31/0.48 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Obind,type,
% 0.31/0.48 bind:
% 0.31/0.48 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Obutlast,type,
% 0.31/0.48 butlast:
% 0.31/0.48 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Ofold,type,
% 0.31/0.48 fold:
% 0.31/0.48 !>[A: $tType,B: $tType] : ( ( A > B > B ) > ( list @ A ) > B > B ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Oinsert,type,
% 0.31/0.48 insert:
% 0.31/0.48 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olast,type,
% 0.31/0.48 last:
% 0.31/0.48 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_OCons,type,
% 0.31/0.48 cons:
% 0.31/0.48 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_ONil,type,
% 0.31/0.48 nil:
% 0.31/0.48 !>[A: $tType] : ( list @ A ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_Ocase__list,type,
% 0.31/0.48 case_list:
% 0.31/0.48 !>[B: $tType,A: $tType] : ( B > ( A > ( list @ A ) > B ) > ( list @ A ) > B ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_Ohd,type,
% 0.31/0.48 hd:
% 0.31/0.48 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_Omap,type,
% 0.31/0.48 map:
% 0.31/0.48 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( list @ A ) > ( list @ Aa ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist_Otl,type,
% 0.31/0.48 tl:
% 0.31/0.48 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olist__ex1,type,
% 0.31/0.48 list_ex1:
% 0.31/0.48 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Olistrelp,type,
% 0.31/0.48 listrelp:
% 0.31/0.48 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( list @ A ) > ( list @ B ) > $o ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Omap__tailrec,type,
% 0.31/0.48 map_tailrec:
% 0.31/0.48 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Omap__tailrec__rev,type,
% 0.31/0.48 map_tailrec_rev:
% 0.31/0.48 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) > ( list @ B ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Omaps,type,
% 0.31/0.48 maps:
% 0.31/0.48 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Omember,type,
% 0.31/0.48 member:
% 0.31/0.48 !>[A: $tType] : ( ( list @ A ) > A > $o ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Oord_Olexordp__eq,type,
% 0.31/0.48 lexordp_eq:
% 0.31/0.48 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Oord__class_Olexordp,type,
% 0.31/0.48 ord_lexordp:
% 0.31/0.48 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Oord__class_Olexordp__eq,type,
% 0.31/0.48 ord_lexordp_eq:
% 0.31/0.48 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Oproduct__lists,type,
% 0.31/0.48 product_lists:
% 0.31/0.48 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Oremdups__adj,type,
% 0.31/0.48 remdups_adj:
% 0.31/0.48 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Oreplicate,type,
% 0.31/0.48 replicate:
% 0.31/0.48 !>[A: $tType] : ( nat > A > ( list @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Orev,type,
% 0.31/0.48 rev:
% 0.31/0.48 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Orotate1,type,
% 0.31/0.48 rotate1:
% 0.31/0.48 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Osplice,type,
% 0.31/0.48 splice:
% 0.31/0.48 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Osublists,type,
% 0.31/0.48 sublists:
% 0.31/0.48 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_List_Ounion,type,
% 0.31/0.48 union:
% 0.31/0.48 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.31/0.48 ord_less:
% 0.31/0.48 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Pure_Otype,type,
% 0.31/0.48 type2:
% 0.31/0.48 !>[A: $tType] : ( itself @ A ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Set_OCollect,type,
% 0.31/0.48 collect:
% 0.31/0.48 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ocycle,type,
% 0.31/0.48 stream317748790_cycle:
% 0.31/0.48 !>[A: $tType] : ( ( list @ A ) > ( stream170649215stream @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Oflat,type,
% 0.31/0.48 stream942386729e_flat:
% 0.31/0.48 !>[A: $tType] : ( ( stream170649215stream @ ( list @ A ) ) > ( stream170649215stream @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osdrop__while,type,
% 0.31/0.48 stream1195056575_while:
% 0.31/0.48 !>[A: $tType] : ( ( A > $o ) > ( stream170649215stream @ A ) > ( stream170649215stream @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Oshift,type,
% 0.31/0.48 stream1035003186_shift:
% 0.31/0.48 !>[A: $tType] : ( ( list @ A ) > ( stream170649215stream @ A ) > ( stream170649215stream @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osmember,type,
% 0.31/0.48 stream1586597341member:
% 0.31/0.48 !>[A: $tType] : ( A > ( stream170649215stream @ A ) > $o ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_OSCons,type,
% 0.31/0.48 stream641971652_SCons:
% 0.31/0.48 !>[A: $tType] : ( A > ( stream170649215stream @ A ) > ( stream170649215stream @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Ocase__stream,type,
% 0.31/0.48 stream1342653232stream:
% 0.31/0.48 !>[A: $tType,B: $tType] : ( ( A > ( stream170649215stream @ A ) > B ) > ( stream170649215stream @ A ) > B ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Oshd,type,
% 0.31/0.48 stream_Mirabelle_shd:
% 0.31/0.48 !>[A: $tType] : ( ( stream170649215stream @ A ) > A ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Osmap,type,
% 0.31/0.48 stream2128578057e_smap:
% 0.31/0.48 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( stream170649215stream @ A ) > ( stream170649215stream @ Aa ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Ostl,type,
% 0.31/0.48 stream_Mirabelle_stl:
% 0.31/0.48 !>[A: $tType] : ( ( stream170649215stream @ A ) > ( stream170649215stream @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostreams,type,
% 0.31/0.48 stream2015131171treams:
% 0.31/0.48 !>[A: $tType] : ( ( set @ A ) > ( set @ ( stream170649215stream @ A ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_c_member,type,
% 0.31/0.48 member2:
% 0.31/0.48 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.31/0.48
% 0.31/0.48 thf(sy_v_ws,type,
% 0.31/0.48 ws: stream170649215stream @ ( list @ a ) ).
% 0.31/0.48
% 0.31/0.48 %----Relevant facts (255)
% 0.31/0.48 thf(fact_0_shift__left__inj,axiom,
% 0.31/0.48 ! [A: $tType,Xs: list @ A,S1: stream170649215stream @ A,S2: stream170649215stream @ A] :
% 0.31/0.48 ( ( ( stream1035003186_shift @ A @ Xs @ S1 )
% 0.31/0.48 = ( stream1035003186_shift @ A @ Xs @ S2 ) )
% 0.31/0.48 = ( S1 = S2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % shift_left_inj
% 0.31/0.48 thf(fact_1_shift_Osimps_I1_J,axiom,
% 0.31/0.48 ! [A: $tType,S: stream170649215stream @ A] :
% 0.31/0.48 ( ( stream1035003186_shift @ A @ ( nil @ A ) @ S )
% 0.31/0.48 = S ) ).
% 0.31/0.48
% 0.31/0.48 % shift.simps(1)
% 0.31/0.48 thf(fact_2_stream_Oexpand,axiom,
% 0.31/0.48 ! [A: $tType,Stream: stream170649215stream @ A,Stream2: stream170649215stream @ A] :
% 0.31/0.48 ( ( ( ( stream_Mirabelle_shd @ A @ Stream )
% 0.31/0.48 = ( stream_Mirabelle_shd @ A @ Stream2 ) )
% 0.31/0.48 & ( ( stream_Mirabelle_stl @ A @ Stream )
% 0.31/0.48 = ( stream_Mirabelle_stl @ A @ Stream2 ) ) )
% 0.31/0.48 => ( Stream = Stream2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % stream.expand
% 0.31/0.48 thf(fact_3_stream_Ocoinduct,axiom,
% 0.31/0.48 ! [A: $tType,R: ( stream170649215stream @ A ) > ( stream170649215stream @ A ) > $o,Stream: stream170649215stream @ A,Stream2: stream170649215stream @ A] :
% 0.31/0.48 ( ( R @ Stream @ Stream2 )
% 0.31/0.48 => ( ! [Stream3: stream170649215stream @ A,Stream4: stream170649215stream @ A] :
% 0.31/0.48 ( ( R @ Stream3 @ Stream4 )
% 0.31/0.48 => ( ( ( stream_Mirabelle_shd @ A @ Stream3 )
% 0.31/0.48 = ( stream_Mirabelle_shd @ A @ Stream4 ) )
% 0.31/0.48 & ( R @ ( stream_Mirabelle_stl @ A @ Stream3 ) @ ( stream_Mirabelle_stl @ A @ Stream4 ) ) ) )
% 0.31/0.48 => ( Stream = Stream2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % stream.coinduct
% 0.31/0.48 thf(fact_4_stream_Ocoinduct__strong,axiom,
% 0.31/0.48 ! [A: $tType,R: ( stream170649215stream @ A ) > ( stream170649215stream @ A ) > $o,Stream: stream170649215stream @ A,Stream2: stream170649215stream @ A] :
% 0.31/0.48 ( ( R @ Stream @ Stream2 )
% 0.31/0.48 => ( ! [Stream3: stream170649215stream @ A,Stream4: stream170649215stream @ A] :
% 0.31/0.48 ( ( R @ Stream3 @ Stream4 )
% 0.31/0.48 => ( ( ( stream_Mirabelle_shd @ A @ Stream3 )
% 0.31/0.48 = ( stream_Mirabelle_shd @ A @ Stream4 ) )
% 0.31/0.48 & ( ( R @ ( stream_Mirabelle_stl @ A @ Stream3 ) @ ( stream_Mirabelle_stl @ A @ Stream4 ) )
% 0.31/0.48 | ( ( stream_Mirabelle_stl @ A @ Stream3 )
% 0.31/0.48 = ( stream_Mirabelle_stl @ A @ Stream4 ) ) ) ) )
% 0.31/0.48 => ( Stream = Stream2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % stream.coinduct_strong
% 0.31/0.48 thf(fact_5_flat__Stream,axiom,
% 0.31/0.48 ! [A: $tType,Xs: list @ A,Ws: stream170649215stream @ ( list @ A )] :
% 0.31/0.48 ( ( Xs
% 0.31/0.48 != ( nil @ A ) )
% 0.31/0.48 => ( ( stream942386729e_flat @ A @ ( stream641971652_SCons @ ( list @ A ) @ Xs @ Ws ) )
% 0.31/0.48 = ( stream1035003186_shift @ A @ Xs @ ( stream942386729e_flat @ A @ Ws ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % flat_Stream
% 0.31/0.48 thf(fact_6_shift__simps_I1_J,axiom,
% 0.31/0.48 ! [A: $tType,Xs: list @ A,S: stream170649215stream @ A] :
% 0.31/0.48 ( ( ( Xs
% 0.31/0.48 = ( nil @ A ) )
% 0.31/0.48 => ( ( stream_Mirabelle_shd @ A @ ( stream1035003186_shift @ A @ Xs @ S ) )
% 0.31/0.48 = ( stream_Mirabelle_shd @ A @ S ) ) )
% 0.31/0.48 & ( ( Xs
% 0.31/0.48 != ( nil @ A ) )
% 0.31/0.48 => ( ( stream_Mirabelle_shd @ A @ ( stream1035003186_shift @ A @ Xs @ S ) )
% 0.31/0.48 = ( hd @ A @ Xs ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % shift_simps(1)
% 0.31/0.48 thf(fact_7_flat_Osimps_I1_J,axiom,
% 0.31/0.48 ! [A: $tType,Ws: stream170649215stream @ ( list @ A )] :
% 0.31/0.48 ( ( stream_Mirabelle_shd @ A @ ( stream942386729e_flat @ A @ Ws ) )
% 0.31/0.48 = ( hd @ A @ ( stream_Mirabelle_shd @ ( list @ A ) @ Ws ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % flat.simps(1)
% 0.31/0.48 thf(fact_8_stream_Ocase__eq__if,axiom,
% 0.31/0.48 ! [B: $tType,A: $tType] :
% 0.31/0.48 ( ( stream1342653232stream @ A @ B )
% 0.31/0.48 = ( ^ [F: A > ( stream170649215stream @ A ) > B,Stream5: stream170649215stream @ A] : ( F @ ( stream_Mirabelle_shd @ A @ Stream5 ) @ ( stream_Mirabelle_stl @ A @ Stream5 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % stream.case_eq_if
% 0.31/0.48 thf(fact_9_shift__simps_I2_J,axiom,
% 0.31/0.48 ! [A: $tType,Xs: list @ A,S: stream170649215stream @ A] :
% 0.31/0.48 ( ( ( Xs
% 0.31/0.48 = ( nil @ A ) )
% 0.31/0.48 => ( ( stream_Mirabelle_stl @ A @ ( stream1035003186_shift @ A @ Xs @ S ) )
% 0.31/0.48 = ( stream_Mirabelle_stl @ A @ S ) ) )
% 0.31/0.48 & ( ( Xs
% 0.31/0.48 != ( nil @ A ) )
% 0.31/0.48 => ( ( stream_Mirabelle_stl @ A @ ( stream1035003186_shift @ A @ Xs @ S ) )
% 0.31/0.48 = ( stream1035003186_shift @ A @ ( tl @ A @ Xs ) @ S ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % shift_simps(2)
% 0.31/0.48 thf(fact_10_sdrop__while_Osimps,axiom,
% 0.31/0.48 ! [A: $tType] :
% 0.31/0.48 ( ( stream1195056575_while @ A )
% 0.31/0.48 = ( ^ [P: A > $o,S3: stream170649215stream @ A] : ( if @ ( stream170649215stream @ A ) @ ( P @ ( stream_Mirabelle_shd @ A @ S3 ) ) @ ( stream1195056575_while @ A @ P @ ( stream_Mirabelle_stl @ A @ S3 ) ) @ S3 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % sdrop_while.simps
% 0.31/0.48 thf(fact_11_flat_Osimps_I2_J,axiom,
% 0.31/0.48 ! [A: $tType,Ws: stream170649215stream @ ( list @ A )] :
% 0.31/0.48 ( ( stream_Mirabelle_stl @ A @ ( stream942386729e_flat @ A @ Ws ) )
% 0.31/0.48 = ( stream942386729e_flat @ A
% 0.31/0.48 @ ( if @ ( stream170649215stream @ ( list @ A ) )
% 0.31/0.48 @ ( ( tl @ A @ ( stream_Mirabelle_shd @ ( list @ A ) @ Ws ) )
% 0.31/0.48 = ( nil @ A ) )
% 0.31/0.48 @ ( stream_Mirabelle_stl @ ( list @ A ) @ Ws )
% 0.31/0.48 @ ( stream641971652_SCons @ ( list @ A ) @ ( tl @ A @ ( stream_Mirabelle_shd @ ( list @ A ) @ Ws ) ) @ ( stream_Mirabelle_stl @ ( list @ A ) @ Ws ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % flat.simps(2)
% 0.31/0.48 thf(fact_12_cycle__decomp,axiom,
% 0.31/0.48 ! [A: $tType,U: list @ A] :
% 0.31/0.48 ( ( U
% 0.31/0.48 != ( nil @ A ) )
% 0.31/0.48 => ( ( stream317748790_cycle @ A @ U )
% 0.31/0.48 = ( stream1035003186_shift @ A @ U @ ( stream317748790_cycle @ A @ U ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % cycle_decomp
% 0.31/0.48 thf(fact_13_stream_Ocollapse,axiom,
% 0.31/0.48 ! [A: $tType,Stream: stream170649215stream @ A] :
% 0.31/0.48 ( ( stream641971652_SCons @ A @ ( stream_Mirabelle_shd @ A @ Stream ) @ ( stream_Mirabelle_stl @ A @ Stream ) )
% 0.31/0.48 = Stream ) ).
% 0.31/0.48
% 0.31/0.48 % stream.collapse
% 0.31/0.48 thf(fact_14_streamsE,axiom,
% 0.31/0.48 ! [A: $tType,S: stream170649215stream @ A,A2: set @ A] :
% 0.31/0.48 ( ( member2 @ ( stream170649215stream @ A ) @ S @ ( stream2015131171treams @ A @ A2 ) )
% 0.31/0.48 => ~ ( ( member2 @ A @ ( stream_Mirabelle_shd @ A @ S ) @ A2 )
% 0.31/0.48 => ~ ( member2 @ ( stream170649215stream @ A ) @ ( stream_Mirabelle_stl @ A @ S ) @ ( stream2015131171treams @ A @ A2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % streamsE
% 0.31/0.48 thf(fact_15_in__streams,axiom,
% 0.31/0.48 ! [A: $tType,S: stream170649215stream @ A,S4: set @ A] :
% 0.31/0.48 ( ( member2 @ ( stream170649215stream @ A ) @ ( stream_Mirabelle_stl @ A @ S ) @ ( stream2015131171treams @ A @ S4 ) )
% 0.31/0.48 => ( ( member2 @ A @ ( stream_Mirabelle_shd @ A @ S ) @ S4 )
% 0.31/0.48 => ( member2 @ ( stream170649215stream @ A ) @ S @ ( stream2015131171treams @ A @ S4 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % in_streams
% 0.31/0.48 thf(fact_16_stream_Oinject,axiom,
% 0.31/0.48 ! [A: $tType,X1: A,X2: stream170649215stream @ A,Y1: A,Y2: stream170649215stream @ A] :
% 0.31/0.48 ( ( ( stream641971652_SCons @ A @ X1 @ X2 )
% 0.31/0.48 = ( stream641971652_SCons @ A @ Y1 @ Y2 ) )
% 0.31/0.48 = ( ( X1 = Y1 )
% 0.31/0.48 & ( X2 = Y2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % stream.inject
% 0.31/0.48 thf(fact_17_list_Oexpand,axiom,
% 0.31/0.48 ! [A: $tType,List: list @ A,List2: list @ A] :
% 0.31/0.48 ( ( ( List
% 0.31/0.48 = ( nil @ A ) )
% 0.31/0.48 = ( List2
% 0.31/0.48 = ( nil @ A ) ) )
% 0.31/0.48 => ( ( ( List
% 0.31/0.48 != ( nil @ A ) )
% 0.31/0.48 => ( ( List2
% 0.31/0.48 != ( nil @ A ) )
% 0.31/0.48 => ( ( ( hd @ A @ List )
% 0.31/0.48 = ( hd @ A @ List2 ) )
% 0.31/0.48 & ( ( tl @ A @ List )
% 0.31/0.48 = ( tl @ A @ List2 ) ) ) ) )
% 0.31/0.48 => ( List = List2 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % list.expand
% 0.31/0.48 thf(fact_18_stream_Ocase,axiom,
% 0.31/0.48 ! [B: $tType,A: $tType,F2: A > ( stream170649215stream @ A ) > B,X1: A,X2: stream170649215stream @ A] :
% 0.31/0.48 ( ( stream1342653232stream @ A @ B @ F2 @ ( stream641971652_SCons @ A @ X1 @ X2 ) )
% 0.31/0.48 = ( F2 @ X1 @ X2 ) ) ).
% 0.31/0.48
% 0.31/0.48 % stream.case
% 0.31/0.48 thf(fact_19_streams_Ocases,axiom,
% 0.31/0.48 ! [A: $tType,A3: stream170649215stream @ A,A2: set @ A] :
% 0.31/0.48 ( ( member2 @ ( stream170649215stream @ A ) @ A3 @ ( stream2015131171treams @ A @ A2 ) )
% 0.31/0.48 => ~ ! [A4: A,S5: stream170649215stream @ A] :
% 0.31/0.48 ( ( A3
% 0.31/0.48 = ( stream641971652_SCons @ A @ A4 @ S5 ) )
% 0.31/0.48 => ( ( member2 @ A @ A4 @ A2 )
% 0.31/0.48 => ~ ( member2 @ ( stream170649215stream @ A ) @ S5 @ ( stream2015131171treams @ A @ A2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % streams.cases
% 0.31/0.48 thf(fact_20_streams_Osimps,axiom,
% 0.31/0.48 ! [A: $tType,A3: stream170649215stream @ A,A2: set @ A] :
% 0.31/0.48 ( ( member2 @ ( stream170649215stream @ A ) @ A3 @ ( stream2015131171treams @ A @ A2 ) )
% 0.31/0.48 = ( ? [A5: A,S3: stream170649215stream @ A] :
% 0.31/0.48 ( ( A3
% 0.31/0.48 = ( stream641971652_SCons @ A @ A5 @ S3 ) )
% 0.31/0.48 & ( member2 @ A @ A5 @ A2 )
% 0.31/0.48 & ( member2 @ ( stream170649215stream @ A ) @ S3 @ ( stream2015131171treams @ A @ A2 ) ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % streams.simps
% 0.31/0.48 thf(fact_21_stream_Oexhaust,axiom,
% 0.31/0.48 ! [A: $tType,Y: stream170649215stream @ A] :
% 0.31/0.48 ~ ! [X12: A,X22: stream170649215stream @ A] :
% 0.31/0.48 ( Y
% 0.31/0.48 != ( stream641971652_SCons @ A @ X12 @ X22 ) ) ).
% 0.31/0.48
% 0.31/0.48 % stream.exhaust
% 0.31/0.48 thf(fact_22_streams__Stream,axiom,
% 0.31/0.48 ! [A: $tType,X: A,S: stream170649215stream @ A,A2: set @ A] :
% 0.31/0.48 ( ( member2 @ ( stream170649215stream @ A ) @ ( stream641971652_SCons @ A @ X @ S ) @ ( stream2015131171treams @ A @ A2 ) )
% 0.31/0.48 = ( ( member2 @ A @ X @ A2 )
% 0.31/0.48 & ( member2 @ ( stream170649215stream @ A ) @ S @ ( stream2015131171treams @ A @ A2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % streams_Stream
% 0.31/0.48 thf(fact_23_streams_Ocoinduct,axiom,
% 0.31/0.48 ! [A: $tType,X3: ( stream170649215stream @ A ) > $o,X: stream170649215stream @ A,A2: set @ A] :
% 0.31/0.48 ( ( X3 @ X )
% 0.31/0.48 => ( ! [X4: stream170649215stream @ A] :
% 0.31/0.48 ( ( X3 @ X4 )
% 0.31/0.48 => ? [A6: A,S6: stream170649215stream @ A] :
% 0.31/0.48 ( ( X4
% 0.31/0.48 = ( stream641971652_SCons @ A @ A6 @ S6 ) )
% 0.31/0.48 & ( member2 @ A @ A6 @ A2 )
% 0.31/0.48 & ( ( X3 @ S6 )
% 0.31/0.48 | ( member2 @ ( stream170649215stream @ A ) @ S6 @ ( stream2015131171treams @ A @ A2 ) ) ) ) )
% 0.31/0.48 => ( member2 @ ( stream170649215stream @ A ) @ X @ ( stream2015131171treams @ A @ A2 ) ) ) ) ).
% 0.31/0.48
% 0.31/0.48 % streams.coinduct
% 0.31/0.48 thf(fact_24_sdrop__while__SCons,axiom,
% 0.31/0.48 ! [A: $tType,P2: A > $o,A3: A,S: stream170649215stream @ A] :
% 0.31/0.48 ( ( ( P2 @ A3 )
% 0.31/0.49 => ( ( stream1195056575_while @ A @ P2 @ ( stream641971652_SCons @ A @ A3 @ S ) )
% 0.31/0.49 = ( stream1195056575_while @ A @ P2 @ S ) ) )
% 0.31/0.49 & ( ~ ( P2 @ A3 )
% 0.31/0.49 => ( ( stream1195056575_while @ A @ P2 @ ( stream641971652_SCons @ A @ A3 @ S ) )
% 0.31/0.49 = ( stream641971652_SCons @ A @ A3 @ S ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sdrop_while_SCons
% 0.31/0.49 thf(fact_25_list_Osel_I2_J,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( tl @ A @ ( nil @ A ) )
% 0.31/0.49 = ( nil @ A ) ) ).
% 0.31/0.49
% 0.31/0.49 % list.sel(2)
% 0.31/0.49 thf(fact_26_cycle_Osimps_I1_J,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( stream_Mirabelle_shd @ A @ ( stream317748790_cycle @ A @ Xs ) )
% 0.31/0.49 = ( hd @ A @ Xs ) ) ).
% 0.31/0.49
% 0.31/0.49 % cycle.simps(1)
% 0.31/0.49 thf(fact_27_flat_Ocode,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( stream942386729e_flat @ A )
% 0.31/0.49 = ( ^ [Ws2: stream170649215stream @ ( list @ A )] :
% 0.31/0.49 ( stream641971652_SCons @ A @ ( hd @ A @ ( stream_Mirabelle_shd @ ( list @ A ) @ Ws2 ) )
% 0.31/0.49 @ ( stream942386729e_flat @ A
% 0.31/0.49 @ ( if @ ( stream170649215stream @ ( list @ A ) )
% 0.31/0.49 @ ( ( tl @ A @ ( stream_Mirabelle_shd @ ( list @ A ) @ Ws2 ) )
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 @ ( stream_Mirabelle_stl @ ( list @ A ) @ Ws2 )
% 0.31/0.49 @ ( stream641971652_SCons @ ( list @ A ) @ ( tl @ A @ ( stream_Mirabelle_shd @ ( list @ A ) @ Ws2 ) ) @ ( stream_Mirabelle_stl @ ( list @ A ) @ Ws2 ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % flat.code
% 0.31/0.49 thf(fact_28_stream_Osel_I2_J,axiom,
% 0.31/0.49 ! [A: $tType,X1: A,X2: stream170649215stream @ A] :
% 0.31/0.49 ( ( stream_Mirabelle_stl @ A @ ( stream641971652_SCons @ A @ X1 @ X2 ) )
% 0.31/0.49 = X2 ) ).
% 0.31/0.49
% 0.31/0.49 % stream.sel(2)
% 0.31/0.49 thf(fact_29_stream_Osel_I1_J,axiom,
% 0.31/0.49 ! [A: $tType,X1: A,X2: stream170649215stream @ A] :
% 0.31/0.49 ( ( stream_Mirabelle_shd @ A @ ( stream641971652_SCons @ A @ X1 @ X2 ) )
% 0.31/0.49 = X1 ) ).
% 0.31/0.49
% 0.31/0.49 % stream.sel(1)
% 0.31/0.49 thf(fact_30_stream_Osplit__sel__asm,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,P2: B > $o,F2: A > ( stream170649215stream @ A ) > B,Stream: stream170649215stream @ A] :
% 0.31/0.49 ( ( P2 @ ( stream1342653232stream @ A @ B @ F2 @ Stream ) )
% 0.31/0.49 = ( ~ ( ( Stream
% 0.31/0.49 = ( stream641971652_SCons @ A @ ( stream_Mirabelle_shd @ A @ Stream ) @ ( stream_Mirabelle_stl @ A @ Stream ) ) )
% 0.31/0.49 & ~ ( P2 @ ( F2 @ ( stream_Mirabelle_shd @ A @ Stream ) @ ( stream_Mirabelle_stl @ A @ Stream ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % stream.split_sel_asm
% 0.31/0.49 thf(fact_31_stream_Osplit__sel,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,P2: B > $o,F2: A > ( stream170649215stream @ A ) > B,Stream: stream170649215stream @ A] :
% 0.31/0.49 ( ( P2 @ ( stream1342653232stream @ A @ B @ F2 @ Stream ) )
% 0.31/0.49 = ( ( Stream
% 0.31/0.49 = ( stream641971652_SCons @ A @ ( stream_Mirabelle_shd @ A @ Stream ) @ ( stream_Mirabelle_stl @ A @ Stream ) ) )
% 0.31/0.49 => ( P2 @ ( F2 @ ( stream_Mirabelle_shd @ A @ Stream ) @ ( stream_Mirabelle_stl @ A @ Stream ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % stream.split_sel
% 0.31/0.49 thf(fact_32_streams__stl,axiom,
% 0.31/0.49 ! [A: $tType,S: stream170649215stream @ A,A2: set @ A] :
% 0.31/0.49 ( ( member2 @ ( stream170649215stream @ A ) @ S @ ( stream2015131171treams @ A @ A2 ) )
% 0.31/0.49 => ( member2 @ ( stream170649215stream @ A ) @ ( stream_Mirabelle_stl @ A @ S ) @ ( stream2015131171treams @ A @ A2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % streams_stl
% 0.31/0.49 thf(fact_33_streams__shd,axiom,
% 0.31/0.49 ! [A: $tType,S: stream170649215stream @ A,A2: set @ A] :
% 0.31/0.49 ( ( member2 @ ( stream170649215stream @ A ) @ S @ ( stream2015131171treams @ A @ A2 ) )
% 0.31/0.49 => ( member2 @ A @ ( stream_Mirabelle_shd @ A @ S ) @ A2 ) ) ).
% 0.31/0.49
% 0.31/0.49 % streams_shd
% 0.31/0.49 thf(fact_34_stream_Oexhaust__sel,axiom,
% 0.31/0.49 ! [A: $tType,Stream: stream170649215stream @ A] :
% 0.31/0.49 ( Stream
% 0.31/0.49 = ( stream641971652_SCons @ A @ ( stream_Mirabelle_shd @ A @ Stream ) @ ( stream_Mirabelle_stl @ A @ Stream ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % stream.exhaust_sel
% 0.31/0.49 thf(fact_35_smember__code,axiom,
% 0.31/0.49 ! [A: $tType,X: A,Y: A,S: stream170649215stream @ A] :
% 0.31/0.49 ( ( stream1586597341member @ A @ X @ ( stream641971652_SCons @ A @ Y @ S ) )
% 0.31/0.49 = ( ( X != Y )
% 0.31/0.49 => ( stream1586597341member @ A @ X @ S ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % smember_code
% 0.31/0.49 thf(fact_36_flat__Cons,axiom,
% 0.31/0.49 ! [A: $tType,X: A,Xs: list @ A,Ws: stream170649215stream @ ( list @ A )] :
% 0.31/0.49 ( ( stream942386729e_flat @ A @ ( stream641971652_SCons @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ Ws ) )
% 0.31/0.49 = ( stream641971652_SCons @ A @ X
% 0.31/0.49 @ ( stream942386729e_flat @ A
% 0.31/0.49 @ ( if @ ( stream170649215stream @ ( list @ A ) )
% 0.31/0.49 @ ( Xs
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 @ Ws
% 0.31/0.49 @ ( stream641971652_SCons @ ( list @ A ) @ Xs @ Ws ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % flat_Cons
% 0.31/0.49 thf(fact_37_list_Ocase__eq__if,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType] :
% 0.31/0.49 ( ( case_list @ B @ A )
% 0.31/0.49 = ( ^ [F1: B,F22: A > ( list @ A ) > B,List3: list @ A] :
% 0.31/0.49 ( if @ B
% 0.31/0.49 @ ( List3
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 @ F1
% 0.31/0.49 @ ( F22 @ ( hd @ A @ List3 ) @ ( tl @ A @ List3 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % list.case_eq_if
% 0.31/0.49 thf(fact_38_list__ex1__simps_I1_J,axiom,
% 0.31/0.49 ! [A: $tType,P2: A > $o] :
% 0.31/0.49 ~ ( list_ex1 @ A @ P2 @ ( nil @ A ) ) ).
% 0.31/0.49
% 0.31/0.49 % list_ex1_simps(1)
% 0.31/0.49 thf(fact_39_hd__Cons__tl,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( cons @ A @ ( hd @ A @ Xs ) @ ( tl @ A @ Xs ) )
% 0.31/0.49 = Xs ) ) ).
% 0.31/0.49
% 0.31/0.49 % hd_Cons_tl
% 0.31/0.49 thf(fact_40_list_Ocollapse,axiom,
% 0.31/0.49 ! [A: $tType,List: list @ A] :
% 0.31/0.49 ( ( List
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) )
% 0.31/0.49 = List ) ) ).
% 0.31/0.49
% 0.31/0.49 % list.collapse
% 0.31/0.49 thf(fact_41_smap__ctr,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,F2: B > A,S: stream170649215stream @ B,X: A,S7: stream170649215stream @ A] :
% 0.31/0.49 ( ( ( stream2128578057e_smap @ B @ A @ F2 @ S )
% 0.31/0.49 = ( stream641971652_SCons @ A @ X @ S7 ) )
% 0.31/0.49 = ( ( ( F2 @ ( stream_Mirabelle_shd @ B @ S ) )
% 0.31/0.49 = X )
% 0.31/0.49 & ( ( stream2128578057e_smap @ B @ A @ F2 @ ( stream_Mirabelle_stl @ B @ S ) )
% 0.31/0.49 = S7 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % smap_ctr
% 0.31/0.49 thf(fact_42_bind__simps_I1_J,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,F2: B > ( list @ A )] :
% 0.31/0.49 ( ( bind @ B @ A @ ( nil @ B ) @ F2 )
% 0.31/0.49 = ( nil @ A ) ) ).
% 0.31/0.49
% 0.31/0.49 % bind_simps(1)
% 0.31/0.49 thf(fact_43_list_Oexhaust__sel,axiom,
% 0.31/0.49 ! [A: $tType,List: list @ A] :
% 0.31/0.49 ( ( List
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( List
% 0.31/0.49 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % list.exhaust_sel
% 0.31/0.49 thf(fact_44_mem__Collect__eq,axiom,
% 0.31/0.49 ! [A: $tType,A3: A,P2: A > $o] :
% 0.31/0.49 ( ( member2 @ A @ A3 @ ( collect @ A @ P2 ) )
% 0.31/0.49 = ( P2 @ A3 ) ) ).
% 0.31/0.49
% 0.31/0.49 % mem_Collect_eq
% 0.31/0.49 thf(fact_45_Collect__mem__eq,axiom,
% 0.31/0.49 ! [A: $tType,A2: set @ A] :
% 0.31/0.49 ( ( collect @ A
% 0.31/0.49 @ ^ [X5: A] : ( member2 @ A @ X5 @ A2 ) )
% 0.31/0.49 = A2 ) ).
% 0.31/0.49
% 0.31/0.49 % Collect_mem_eq
% 0.31/0.49 thf(fact_46_Collect__cong,axiom,
% 0.31/0.49 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 0.31/0.49 ( ! [X4: A] :
% 0.31/0.49 ( ( P2 @ X4 )
% 0.31/0.49 = ( Q @ X4 ) )
% 0.31/0.49 => ( ( collect @ A @ P2 )
% 0.31/0.49 = ( collect @ A @ Q ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Collect_cong
% 0.31/0.49 thf(fact_47_ext,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,F2: A > B,G: A > B] :
% 0.31/0.49 ( ! [X4: A] :
% 0.31/0.49 ( ( F2 @ X4 )
% 0.31/0.49 = ( G @ X4 ) )
% 0.31/0.49 => ( F2 = G ) ) ).
% 0.31/0.49
% 0.31/0.49 % ext
% 0.31/0.49 thf(fact_48_member__rec_I2_J,axiom,
% 0.31/0.49 ! [A: $tType,Y: A] :
% 0.31/0.49 ~ ( member @ A @ ( nil @ A ) @ Y ) ).
% 0.31/0.49
% 0.31/0.49 % member_rec(2)
% 0.31/0.49 thf(fact_49_list_Oinject,axiom,
% 0.31/0.49 ! [A: $tType,X21: A,X222: list @ A,Y21: A,Y22: list @ A] :
% 0.31/0.49 ( ( ( cons @ A @ X21 @ X222 )
% 0.31/0.49 = ( cons @ A @ Y21 @ Y22 ) )
% 0.31/0.49 = ( ( X21 = Y21 )
% 0.31/0.49 & ( X222 = Y22 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % list.inject
% 0.31/0.49 thf(fact_50_stream_Omap__sel_I2_J,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,F2: A > B,A3: stream170649215stream @ A] :
% 0.31/0.49 ( ( stream_Mirabelle_stl @ B @ ( stream2128578057e_smap @ A @ B @ F2 @ A3 ) )
% 0.31/0.49 = ( stream2128578057e_smap @ A @ B @ F2 @ ( stream_Mirabelle_stl @ A @ A3 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % stream.map_sel(2)
% 0.31/0.49 thf(fact_51_stream_Omap__sel_I1_J,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,F2: A > B,A3: stream170649215stream @ A] :
% 0.31/0.49 ( ( stream_Mirabelle_shd @ B @ ( stream2128578057e_smap @ A @ B @ F2 @ A3 ) )
% 0.31/0.49 = ( F2 @ ( stream_Mirabelle_shd @ A @ A3 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % stream.map_sel(1)
% 0.31/0.49 thf(fact_52_list_Osimps_I5_J,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,F12: B,F23: A > ( list @ A ) > B,X21: A,X222: list @ A] :
% 0.31/0.49 ( ( case_list @ B @ A @ F12 @ F23 @ ( cons @ A @ X21 @ X222 ) )
% 0.31/0.49 = ( F23 @ X21 @ X222 ) ) ).
% 0.31/0.49
% 0.31/0.49 % list.simps(5)
% 0.31/0.49 thf(fact_53_member__rec_I1_J,axiom,
% 0.31/0.49 ! [A: $tType,X: A,Xs: list @ A,Y: A] :
% 0.31/0.49 ( ( member @ A @ ( cons @ A @ X @ Xs ) @ Y )
% 0.31/0.49 = ( ( X = Y )
% 0.31/0.49 | ( member @ A @ Xs @ Y ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % member_rec(1)
% 0.31/0.49 thf(fact_54_not__Cons__self2,axiom,
% 0.31/0.49 ! [A: $tType,X: A,Xs: list @ A] :
% 0.31/0.49 ( ( cons @ A @ X @ Xs )
% 0.31/0.49 != Xs ) ).
% 0.31/0.49
% 0.31/0.49 % not_Cons_self2
% 0.31/0.49 thf(fact_55_transpose_Ocases,axiom,
% 0.31/0.49 ! [A: $tType,X: list @ ( list @ A )] :
% 0.31/0.49 ( ( X
% 0.31/0.49 != ( nil @ ( list @ A ) ) )
% 0.31/0.49 => ( ! [Xss: list @ ( list @ A )] :
% 0.31/0.49 ( X
% 0.31/0.49 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.31/0.49 => ~ ! [X4: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.31/0.49 ( X
% 0.31/0.49 != ( cons @ ( list @ A ) @ ( cons @ A @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % transpose.cases
% 0.31/0.49 thf(fact_56_list_Odistinct_I1_J,axiom,
% 0.31/0.49 ! [A: $tType,X21: A,X222: list @ A] :
% 0.31/0.49 ( ( nil @ A )
% 0.31/0.49 != ( cons @ A @ X21 @ X222 ) ) ).
% 0.31/0.49
% 0.31/0.49 % list.distinct(1)
% 0.31/0.49 thf(fact_57_list_OdiscI,axiom,
% 0.31/0.49 ! [A: $tType,List: list @ A,X21: A,X222: list @ A] :
% 0.31/0.49 ( ( List
% 0.31/0.49 = ( cons @ A @ X21 @ X222 ) )
% 0.31/0.49 => ( List
% 0.31/0.49 != ( nil @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % list.discI
% 0.31/0.49 thf(fact_58_list_Oexhaust,axiom,
% 0.31/0.49 ! [A: $tType,Y: list @ A] :
% 0.31/0.49 ( ( Y
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ~ ! [X212: A,X223: list @ A] :
% 0.31/0.49 ( Y
% 0.31/0.49 != ( cons @ A @ X212 @ X223 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % list.exhaust
% 0.31/0.49 thf(fact_59_list_Oinducts,axiom,
% 0.31/0.49 ! [A: $tType,P2: ( list @ A ) > $o,List: list @ A] :
% 0.31/0.49 ( ( P2 @ ( nil @ A ) )
% 0.31/0.49 => ( ! [X12: A,X22: list @ A] :
% 0.31/0.49 ( ( P2 @ X22 )
% 0.31/0.49 => ( P2 @ ( cons @ A @ X12 @ X22 ) ) )
% 0.31/0.49 => ( P2 @ List ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % list.inducts
% 0.31/0.49 thf(fact_60_neq__Nil__conv,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 = ( ? [Y3: A,Ys: list @ A] :
% 0.31/0.49 ( Xs
% 0.31/0.49 = ( cons @ A @ Y3 @ Ys ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % neq_Nil_conv
% 0.31/0.49 thf(fact_61_list__induct2_H,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,P2: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys2: list @ B] :
% 0.31/0.49 ( ( P2 @ ( nil @ A ) @ ( nil @ B ) )
% 0.31/0.49 => ( ! [X4: A,Xs2: list @ A] : ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( nil @ B ) )
% 0.31/0.49 => ( ! [Y4: B,Ys3: list @ B] : ( P2 @ ( nil @ A ) @ ( cons @ B @ Y4 @ Ys3 ) )
% 0.31/0.49 => ( ! [X4: A,Xs2: list @ A,Y4: B,Ys3: list @ B] :
% 0.31/0.49 ( ( P2 @ Xs2 @ Ys3 )
% 0.31/0.49 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y4 @ Ys3 ) ) )
% 0.31/0.49 => ( P2 @ Xs @ Ys2 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % list_induct2'
% 0.31/0.49 thf(fact_62_splice_Oinduct,axiom,
% 0.31/0.49 ! [A: $tType,P2: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.31/0.49 ( ! [X12: list @ A] : ( P2 @ ( nil @ A ) @ X12 )
% 0.31/0.49 => ( ! [V: A,Va: list @ A] : ( P2 @ ( cons @ A @ V @ Va ) @ ( nil @ A ) )
% 0.31/0.49 => ( ! [X4: A,Xs2: list @ A,Y4: A,Ys3: list @ A] :
% 0.31/0.49 ( ( P2 @ Xs2 @ Ys3 )
% 0.31/0.49 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 0.31/0.49 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % splice.induct
% 0.31/0.49 thf(fact_63_remdups__adj_Ocases,axiom,
% 0.31/0.49 ! [A: $tType,X: list @ A] :
% 0.31/0.49 ( ( X
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ! [X4: A] :
% 0.31/0.49 ( X
% 0.31/0.49 != ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.31/0.49 => ~ ! [X4: A,Y4: A,Xs2: list @ A] :
% 0.31/0.49 ( X
% 0.31/0.49 != ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % remdups_adj.cases
% 0.31/0.49 thf(fact_64_remdups__adj_Oinduct,axiom,
% 0.31/0.49 ! [A: $tType,P2: ( list @ A ) > $o,A0: list @ A] :
% 0.31/0.49 ( ( P2 @ ( nil @ A ) )
% 0.31/0.49 => ( ! [X4: A] : ( P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.31/0.49 => ( ! [X4: A,Y4: A,Xs2: list @ A] :
% 0.31/0.49 ( ( ( X4 = Y4 )
% 0.31/0.49 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) ) )
% 0.31/0.49 => ( ( ( X4 != Y4 )
% 0.31/0.49 => ( P2 @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 0.31/0.49 => ( P2 @ ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) )
% 0.31/0.49 => ( P2 @ A0 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % remdups_adj.induct
% 0.31/0.49 thf(fact_65_list__nonempty__induct,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,P2: ( list @ A ) > $o] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ! [X4: A] : ( P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.31/0.49 => ( ! [X4: A,Xs2: list @ A] :
% 0.31/0.49 ( ( Xs2
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( P2 @ Xs2 )
% 0.31/0.49 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) ) ) )
% 0.31/0.49 => ( P2 @ Xs ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % list_nonempty_induct
% 0.31/0.49 thf(fact_66_map__tailrec__rev_Oinduct,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,P2: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.31/0.49 ( ! [F3: A > B,X12: list @ B] : ( P2 @ F3 @ ( nil @ A ) @ X12 )
% 0.31/0.49 => ( ! [F3: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 0.31/0.49 ( ( P2 @ F3 @ As @ ( cons @ B @ ( F3 @ A4 ) @ Bs ) )
% 0.31/0.49 => ( P2 @ F3 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 0.31/0.49 => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % map_tailrec_rev.induct
% 0.31/0.49 thf(fact_67_list_Osel_I3_J,axiom,
% 0.31/0.49 ! [A: $tType,X21: A,X222: list @ A] :
% 0.31/0.49 ( ( tl @ A @ ( cons @ A @ X21 @ X222 ) )
% 0.31/0.49 = X222 ) ).
% 0.31/0.49
% 0.31/0.49 % list.sel(3)
% 0.31/0.49 thf(fact_68_list_Osel_I1_J,axiom,
% 0.31/0.49 ! [A: $tType,X21: A,X222: list @ A] :
% 0.31/0.49 ( ( hd @ A @ ( cons @ A @ X21 @ X222 ) )
% 0.31/0.49 = X21 ) ).
% 0.31/0.49
% 0.31/0.49 % list.sel(1)
% 0.31/0.49 thf(fact_69_stream_Omap,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,F2: A > B,X1: A,X2: stream170649215stream @ A] :
% 0.31/0.49 ( ( stream2128578057e_smap @ A @ B @ F2 @ ( stream641971652_SCons @ A @ X1 @ X2 ) )
% 0.31/0.49 = ( stream641971652_SCons @ B @ ( F2 @ X1 ) @ ( stream2128578057e_smap @ A @ B @ F2 @ X2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % stream.map
% 0.31/0.49 thf(fact_70_smap__streams,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,S: stream170649215stream @ A,A2: set @ A,F2: A > B,B2: set @ B] :
% 0.31/0.49 ( ( member2 @ ( stream170649215stream @ A ) @ S @ ( stream2015131171treams @ A @ A2 ) )
% 0.31/0.49 => ( ! [X4: A] :
% 0.31/0.49 ( ( member2 @ A @ X4 @ A2 )
% 0.31/0.49 => ( member2 @ B @ ( F2 @ X4 ) @ B2 ) )
% 0.31/0.49 => ( member2 @ ( stream170649215stream @ B ) @ ( stream2128578057e_smap @ A @ B @ F2 @ S ) @ ( stream2015131171treams @ B @ B2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % smap_streams
% 0.31/0.49 thf(fact_71_list_Osimps_I4_J,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,F12: B,F23: A > ( list @ A ) > B] :
% 0.31/0.49 ( ( case_list @ B @ A @ F12 @ F23 @ ( nil @ A ) )
% 0.31/0.49 = F12 ) ).
% 0.31/0.49
% 0.31/0.49 % list.simps(4)
% 0.31/0.49 thf(fact_72_list_Osplit__sel__asm,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,P2: B > $o,F12: B,F23: A > ( list @ A ) > B,List: list @ A] :
% 0.31/0.49 ( ( P2 @ ( case_list @ B @ A @ F12 @ F23 @ List ) )
% 0.31/0.49 = ( ~ ( ( ( List
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 & ~ ( P2 @ F12 ) )
% 0.31/0.49 | ( ( List
% 0.31/0.49 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) )
% 0.31/0.49 & ~ ( P2 @ ( F23 @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % list.split_sel_asm
% 0.31/0.49 thf(fact_73_list_Osplit__sel,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,P2: B > $o,F12: B,F23: A > ( list @ A ) > B,List: list @ A] :
% 0.31/0.49 ( ( P2 @ ( case_list @ B @ A @ F12 @ F23 @ List ) )
% 0.31/0.49 = ( ( ( List
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 => ( P2 @ F12 ) )
% 0.31/0.49 & ( ( List
% 0.31/0.49 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) )
% 0.31/0.49 => ( P2 @ ( F23 @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % list.split_sel
% 0.31/0.49 thf(fact_74_tl__Nil,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( ( tl @ A @ Xs )
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 = ( ( Xs
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 | ? [X5: A] :
% 0.31/0.49 ( Xs
% 0.31/0.49 = ( cons @ A @ X5 @ ( nil @ A ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % tl_Nil
% 0.31/0.49 thf(fact_75_Nil__tl,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( ( nil @ A )
% 0.31/0.49 = ( tl @ A @ Xs ) )
% 0.31/0.49 = ( ( Xs
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 | ? [X5: A] :
% 0.31/0.49 ( Xs
% 0.31/0.49 = ( cons @ A @ X5 @ ( nil @ A ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Nil_tl
% 0.31/0.49 thf(fact_76_shift_Osimps_I2_J,axiom,
% 0.31/0.49 ! [A: $tType,X: A,Xs: list @ A,S: stream170649215stream @ A] :
% 0.31/0.49 ( ( stream1035003186_shift @ A @ ( cons @ A @ X @ Xs ) @ S )
% 0.31/0.49 = ( stream641971652_SCons @ A @ X @ ( stream1035003186_shift @ A @ Xs @ S ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % shift.simps(2)
% 0.31/0.49 thf(fact_77_cycle__rotated,axiom,
% 0.31/0.49 ! [A: $tType,V2: list @ A,U: list @ A,S: stream170649215stream @ A] :
% 0.31/0.49 ( ( V2
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( ( stream317748790_cycle @ A @ U )
% 0.31/0.49 = ( stream1035003186_shift @ A @ V2 @ S ) )
% 0.31/0.49 => ( ( stream317748790_cycle @ A @ ( append @ A @ ( tl @ A @ U ) @ ( cons @ A @ ( hd @ A @ U ) @ ( nil @ A ) ) ) )
% 0.31/0.49 = ( stream1035003186_shift @ A @ ( tl @ A @ V2 ) @ S ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % cycle_rotated
% 0.31/0.49 thf(fact_78_cycle_Osimps_I2_J,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( stream_Mirabelle_stl @ A @ ( stream317748790_cycle @ A @ Xs ) )
% 0.31/0.49 = ( stream317748790_cycle @ A @ ( append @ A @ ( tl @ A @ Xs ) @ ( cons @ A @ ( hd @ A @ Xs ) @ ( nil @ A ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % cycle.simps(2)
% 0.31/0.49 thf(fact_79_cycle_Ocode,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( stream317748790_cycle @ A )
% 0.31/0.49 = ( ^ [Xs3: list @ A] : ( stream641971652_SCons @ A @ ( hd @ A @ Xs3 ) @ ( stream317748790_cycle @ A @ ( append @ A @ ( tl @ A @ Xs3 ) @ ( cons @ A @ ( hd @ A @ Xs3 ) @ ( nil @ A ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % cycle.code
% 0.31/0.49 thf(fact_80_insert__Nil,axiom,
% 0.31/0.49 ! [A: $tType,X: A] :
% 0.31/0.49 ( ( insert @ A @ X @ ( nil @ A ) )
% 0.31/0.49 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % insert_Nil
% 0.31/0.49 thf(fact_81_cycle__Cons,axiom,
% 0.31/0.49 ! [A: $tType,X: A,Xs: list @ A] :
% 0.31/0.49 ( ( stream317748790_cycle @ A @ ( cons @ A @ X @ Xs ) )
% 0.31/0.49 = ( stream641971652_SCons @ A @ X @ ( stream317748790_cycle @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % cycle_Cons
% 0.31/0.49 thf(fact_82_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.31/0.49 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A] :
% 0.31/0.49 ~ ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( nil @ A ) ) ).
% 0.31/0.49
% 0.31/0.49 % ord.lexordp_eq_simps(3)
% 0.31/0.49 thf(fact_83_map__tailrec__rev_Oelims,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,X: A > B,Xa: list @ A,Xb: list @ B,Y: list @ B] :
% 0.31/0.49 ( ( ( map_tailrec_rev @ A @ B @ X @ Xa @ Xb )
% 0.31/0.49 = Y )
% 0.31/0.49 => ( ( ( Xa
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 => ( Y != Xb ) )
% 0.31/0.49 => ~ ! [A4: A,As: list @ A] :
% 0.31/0.49 ( ( Xa
% 0.31/0.49 = ( cons @ A @ A4 @ As ) )
% 0.31/0.49 => ( Y
% 0.31/0.49 != ( map_tailrec_rev @ A @ B @ X @ As @ ( cons @ B @ ( X @ A4 ) @ Xb ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % map_tailrec_rev.elims
% 0.31/0.49 thf(fact_84_splice_Oelims,axiom,
% 0.31/0.49 ! [A: $tType,X: list @ A,Xa: list @ A,Y: list @ A] :
% 0.31/0.49 ( ( ( splice @ A @ X @ Xa )
% 0.31/0.49 = Y )
% 0.31/0.49 => ( ( ( X
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 => ( Y != Xa ) )
% 0.31/0.49 => ( ! [V: A,Va: list @ A] :
% 0.31/0.49 ( ( X
% 0.31/0.49 = ( cons @ A @ V @ Va ) )
% 0.31/0.49 => ( ( Xa
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 => ( Y
% 0.31/0.49 != ( cons @ A @ V @ Va ) ) ) )
% 0.31/0.49 => ~ ! [X4: A,Xs2: list @ A] :
% 0.31/0.49 ( ( X
% 0.31/0.49 = ( cons @ A @ X4 @ Xs2 ) )
% 0.31/0.49 => ! [Y4: A,Ys3: list @ A] :
% 0.31/0.49 ( ( Xa
% 0.31/0.49 = ( cons @ A @ Y4 @ Ys3 ) )
% 0.31/0.49 => ( Y
% 0.31/0.49 != ( cons @ A @ X4 @ ( cons @ A @ Y4 @ ( splice @ A @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % splice.elims
% 0.31/0.49 thf(fact_85_same__append__eq,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs: list @ A] :
% 0.31/0.49 ( ( ( append @ A @ Xs @ Ys2 )
% 0.31/0.49 = ( append @ A @ Xs @ Zs ) )
% 0.31/0.49 = ( Ys2 = Zs ) ) ).
% 0.31/0.49
% 0.31/0.49 % same_append_eq
% 0.31/0.49 thf(fact_86_append__same__eq,axiom,
% 0.31/0.49 ! [A: $tType,Ys2: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.31/0.49 ( ( ( append @ A @ Ys2 @ Xs )
% 0.31/0.49 = ( append @ A @ Zs @ Xs ) )
% 0.31/0.49 = ( Ys2 = Zs ) ) ).
% 0.31/0.49
% 0.31/0.49 % append_same_eq
% 0.31/0.49 thf(fact_87_append__assoc,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs: list @ A] :
% 0.31/0.49 ( ( append @ A @ ( append @ A @ Xs @ Ys2 ) @ Zs )
% 0.31/0.49 = ( append @ A @ Xs @ ( append @ A @ Ys2 @ Zs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % append_assoc
% 0.31/0.49 thf(fact_88_append__is__Nil__conv,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( ( append @ A @ Xs @ Ys2 )
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 = ( ( Xs
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 & ( Ys2
% 0.31/0.49 = ( nil @ A ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % append_is_Nil_conv
% 0.31/0.49 thf(fact_89_Nil__is__append__conv,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( ( nil @ A )
% 0.31/0.49 = ( append @ A @ Xs @ Ys2 ) )
% 0.31/0.49 = ( ( Xs
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 & ( Ys2
% 0.31/0.49 = ( nil @ A ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Nil_is_append_conv
% 0.31/0.49 thf(fact_90_self__append__conv2,axiom,
% 0.31/0.49 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 0.31/0.49 ( ( Ys2
% 0.31/0.49 = ( append @ A @ Xs @ Ys2 ) )
% 0.31/0.49 = ( Xs
% 0.31/0.49 = ( nil @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % self_append_conv2
% 0.31/0.49 thf(fact_91_append__self__conv2,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( ( append @ A @ Xs @ Ys2 )
% 0.31/0.49 = Ys2 )
% 0.31/0.49 = ( Xs
% 0.31/0.49 = ( nil @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % append_self_conv2
% 0.31/0.49 thf(fact_92_self__append__conv,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 = ( append @ A @ Xs @ Ys2 ) )
% 0.31/0.49 = ( Ys2
% 0.31/0.49 = ( nil @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % self_append_conv
% 0.31/0.49 thf(fact_93_append__self__conv,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( ( append @ A @ Xs @ Ys2 )
% 0.31/0.49 = Xs )
% 0.31/0.49 = ( Ys2
% 0.31/0.49 = ( nil @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % append_self_conv
% 0.31/0.49 thf(fact_94_append__Nil2,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( append @ A @ Xs @ ( nil @ A ) )
% 0.31/0.49 = Xs ) ).
% 0.31/0.49
% 0.31/0.49 % append_Nil2
% 0.31/0.49 thf(fact_95_shift__append,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A,S: stream170649215stream @ A] :
% 0.31/0.49 ( ( stream1035003186_shift @ A @ ( append @ A @ Xs @ Ys2 ) @ S )
% 0.31/0.49 = ( stream1035003186_shift @ A @ Xs @ ( stream1035003186_shift @ A @ Ys2 @ S ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % shift_append
% 0.31/0.49 thf(fact_96_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.31/0.49 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A,Y: A,Ys2: list @ A] :
% 0.31/0.49 ( ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) )
% 0.31/0.49 = ( ( Less @ X @ Y )
% 0.31/0.49 | ( ~ ( Less @ Y @ X )
% 0.31/0.49 & ( lexordp_eq @ A @ Less @ Xs @ Ys2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % ord.lexordp_eq_simps(4)
% 0.31/0.49 thf(fact_97_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.31/0.49 ! [A: $tType,Less: A > A > $o,Ys2: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys2 ) ).
% 0.31/0.49
% 0.31/0.49 % ord.lexordp_eq_simps(1)
% 0.31/0.49 thf(fact_98_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.31/0.49 ! [A: $tType,Less: A > A > $o,Xs: list @ A] :
% 0.31/0.49 ( ( lexordp_eq @ A @ Less @ Xs @ ( nil @ A ) )
% 0.31/0.49 = ( Xs
% 0.31/0.49 = ( nil @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % ord.lexordp_eq_simps(2)
% 0.31/0.49 thf(fact_99_splice__Nil2,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( splice @ A @ Xs @ ( nil @ A ) )
% 0.31/0.49 = Xs ) ).
% 0.31/0.49
% 0.31/0.49 % splice_Nil2
% 0.31/0.49 thf(fact_100_append1__eq__conv,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,X: A,Ys2: list @ A,Y: A] :
% 0.31/0.49 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.31/0.49 = ( append @ A @ Ys2 @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.31/0.49 = ( ( Xs = Ys2 )
% 0.31/0.49 & ( X = Y ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % append1_eq_conv
% 0.31/0.49 thf(fact_101_tl__append2,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( tl @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.31/0.49 = ( append @ A @ ( tl @ A @ Xs ) @ Ys2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % tl_append2
% 0.31/0.49 thf(fact_102_hd__append2,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.31/0.49 = ( hd @ A @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % hd_append2
% 0.31/0.49 thf(fact_103_bind__simps_I2_J,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,X: B,Xs: list @ B,F2: B > ( list @ A )] :
% 0.31/0.49 ( ( bind @ B @ A @ ( cons @ B @ X @ Xs ) @ F2 )
% 0.31/0.49 = ( append @ A @ ( F2 @ X ) @ ( bind @ B @ A @ Xs @ F2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % bind_simps(2)
% 0.31/0.49 thf(fact_104_append__eq__append__conv2,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs: list @ A,Ts: list @ A] :
% 0.31/0.49 ( ( ( append @ A @ Xs @ Ys2 )
% 0.31/0.49 = ( append @ A @ Zs @ Ts ) )
% 0.31/0.49 = ( ? [Us: list @ A] :
% 0.31/0.49 ( ( ( Xs
% 0.31/0.49 = ( append @ A @ Zs @ Us ) )
% 0.31/0.49 & ( ( append @ A @ Us @ Ys2 )
% 0.31/0.49 = Ts ) )
% 0.31/0.49 | ( ( ( append @ A @ Xs @ Us )
% 0.31/0.49 = Zs )
% 0.31/0.49 & ( Ys2
% 0.31/0.49 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % append_eq_append_conv2
% 0.31/0.49 thf(fact_105_ord_Olexordp__eq__refl,axiom,
% 0.31/0.49 ! [A: $tType,Less: A > A > $o,Xs: list @ A] : ( lexordp_eq @ A @ Less @ Xs @ Xs ) ).
% 0.31/0.49
% 0.31/0.49 % ord.lexordp_eq_refl
% 0.31/0.49 thf(fact_106_append__eq__appendI,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs: list @ A,Ys2: list @ A,Us2: list @ A] :
% 0.31/0.49 ( ( ( append @ A @ Xs @ Xs1 )
% 0.31/0.49 = Zs )
% 0.31/0.49 => ( ( Ys2
% 0.31/0.49 = ( append @ A @ Xs1 @ Us2 ) )
% 0.31/0.49 => ( ( append @ A @ Xs @ Ys2 )
% 0.31/0.49 = ( append @ A @ Zs @ Us2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % append_eq_appendI
% 0.31/0.49 thf(fact_107_append__Cons,axiom,
% 0.31/0.49 ! [A: $tType,X: A,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys2 )
% 0.31/0.49 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % append_Cons
% 0.31/0.49 thf(fact_108_Cons__eq__appendI,axiom,
% 0.31/0.49 ! [A: $tType,X: A,Xs1: list @ A,Ys2: list @ A,Xs: list @ A,Zs: list @ A] :
% 0.31/0.49 ( ( ( cons @ A @ X @ Xs1 )
% 0.31/0.49 = Ys2 )
% 0.31/0.49 => ( ( Xs
% 0.31/0.49 = ( append @ A @ Xs1 @ Zs ) )
% 0.31/0.49 => ( ( cons @ A @ X @ Xs )
% 0.31/0.49 = ( append @ A @ Ys2 @ Zs ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Cons_eq_appendI
% 0.31/0.49 thf(fact_109_append__Nil,axiom,
% 0.31/0.49 ! [A: $tType,Ys2: list @ A] :
% 0.31/0.49 ( ( append @ A @ ( nil @ A ) @ Ys2 )
% 0.31/0.49 = Ys2 ) ).
% 0.31/0.49
% 0.31/0.49 % append_Nil
% 0.31/0.49 thf(fact_110_eq__Nil__appendI,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( Xs = Ys2 )
% 0.31/0.49 => ( Xs
% 0.31/0.49 = ( append @ A @ ( nil @ A ) @ Ys2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % eq_Nil_appendI
% 0.31/0.49 thf(fact_111_ord_Olexordp__eq_OCons__eq,axiom,
% 0.31/0.49 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ~ ( Less @ X @ Y )
% 0.31/0.49 => ( ~ ( Less @ Y @ X )
% 0.31/0.49 => ( ( lexordp_eq @ A @ Less @ Xs @ Ys2 )
% 0.31/0.49 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % ord.lexordp_eq.Cons_eq
% 0.31/0.49 thf(fact_112_ord_Olexordp__eq_OCons,axiom,
% 0.31/0.49 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( Less @ X @ Y )
% 0.31/0.49 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % ord.lexordp_eq.Cons
% 0.31/0.49 thf(fact_113_ord_Olexordp__eq_ONil,axiom,
% 0.31/0.49 ! [A: $tType,Less: A > A > $o,Ys2: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys2 ) ).
% 0.31/0.49
% 0.31/0.49 % ord.lexordp_eq.Nil
% 0.31/0.49 thf(fact_114_splice_Osimps_I3_J,axiom,
% 0.31/0.49 ! [A: $tType,X: A,Xs: list @ A,Y: A,Ys2: list @ A] :
% 0.31/0.49 ( ( splice @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) )
% 0.31/0.49 = ( cons @ A @ X @ ( cons @ A @ Y @ ( splice @ A @ Xs @ Ys2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % splice.simps(3)
% 0.31/0.49 thf(fact_115_splice_Osimps_I1_J,axiom,
% 0.31/0.49 ! [A: $tType,Ys2: list @ A] :
% 0.31/0.49 ( ( splice @ A @ ( nil @ A ) @ Ys2 )
% 0.31/0.49 = Ys2 ) ).
% 0.31/0.49
% 0.31/0.49 % splice.simps(1)
% 0.31/0.49 thf(fact_116_rev__nonempty__induct,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,P2: ( list @ A ) > $o] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ! [X4: A] : ( P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.31/0.49 => ( ! [X4: A,Xs2: list @ A] :
% 0.31/0.49 ( ( Xs2
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( P2 @ Xs2 )
% 0.31/0.49 => ( P2 @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) )
% 0.31/0.49 => ( P2 @ Xs ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % rev_nonempty_induct
% 0.31/0.49 thf(fact_117_append__eq__Cons__conv,axiom,
% 0.31/0.49 ! [A: $tType,Ys2: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 0.31/0.49 ( ( ( append @ A @ Ys2 @ Zs )
% 0.31/0.49 = ( cons @ A @ X @ Xs ) )
% 0.31/0.49 = ( ( ( Ys2
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 & ( Zs
% 0.31/0.49 = ( cons @ A @ X @ Xs ) ) )
% 0.31/0.49 | ? [Ys4: list @ A] :
% 0.31/0.49 ( ( Ys2
% 0.31/0.49 = ( cons @ A @ X @ Ys4 ) )
% 0.31/0.49 & ( ( append @ A @ Ys4 @ Zs )
% 0.31/0.49 = Xs ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % append_eq_Cons_conv
% 0.31/0.49 thf(fact_118_Cons__eq__append__conv,axiom,
% 0.31/0.49 ! [A: $tType,X: A,Xs: list @ A,Ys2: list @ A,Zs: list @ A] :
% 0.31/0.49 ( ( ( cons @ A @ X @ Xs )
% 0.31/0.49 = ( append @ A @ Ys2 @ Zs ) )
% 0.31/0.49 = ( ( ( Ys2
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 & ( ( cons @ A @ X @ Xs )
% 0.31/0.49 = Zs ) )
% 0.31/0.49 | ? [Ys4: list @ A] :
% 0.31/0.49 ( ( ( cons @ A @ X @ Ys4 )
% 0.31/0.49 = Ys2 )
% 0.31/0.49 & ( Xs
% 0.31/0.49 = ( append @ A @ Ys4 @ Zs ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Cons_eq_append_conv
% 0.31/0.49 thf(fact_119_rev__exhaust,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ~ ! [Ys3: list @ A,Y4: A] :
% 0.31/0.49 ( Xs
% 0.31/0.49 != ( append @ A @ Ys3 @ ( cons @ A @ Y4 @ ( nil @ A ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % rev_exhaust
% 0.31/0.49 thf(fact_120_rev__induct,axiom,
% 0.31/0.49 ! [A: $tType,P2: ( list @ A ) > $o,Xs: list @ A] :
% 0.31/0.49 ( ( P2 @ ( nil @ A ) )
% 0.31/0.49 => ( ! [X4: A,Xs2: list @ A] :
% 0.31/0.49 ( ( P2 @ Xs2 )
% 0.31/0.49 => ( P2 @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) )
% 0.31/0.49 => ( P2 @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % rev_induct
% 0.31/0.49 thf(fact_121_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,F2: A > B,A3: A,As2: list @ A,Bs2: list @ B] :
% 0.31/0.49 ( ( map_tailrec_rev @ A @ B @ F2 @ ( cons @ A @ A3 @ As2 ) @ Bs2 )
% 0.31/0.49 = ( map_tailrec_rev @ A @ B @ F2 @ As2 @ ( cons @ B @ ( F2 @ A3 ) @ Bs2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % map_tailrec_rev.simps(2)
% 0.31/0.49 thf(fact_122_map__tailrec__rev_Osimps_I1_J,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,F2: A > B,Bs2: list @ B] :
% 0.31/0.49 ( ( map_tailrec_rev @ A @ B @ F2 @ ( nil @ A ) @ Bs2 )
% 0.31/0.49 = Bs2 ) ).
% 0.31/0.49
% 0.31/0.49 % map_tailrec_rev.simps(1)
% 0.31/0.49 thf(fact_123_hd__append,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( ( Xs
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.31/0.49 = ( hd @ A @ Ys2 ) ) )
% 0.31/0.49 & ( ( Xs
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.31/0.49 = ( hd @ A @ Xs ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % hd_append
% 0.31/0.49 thf(fact_124_longest__common__prefix,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ? [Ps: list @ A,Xs4: list @ A,Ys5: list @ A] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 = ( append @ A @ Ps @ Xs4 ) )
% 0.31/0.49 & ( Ys2
% 0.31/0.49 = ( append @ A @ Ps @ Ys5 ) )
% 0.31/0.49 & ( ( Xs4
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 | ( Ys5
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 | ( ( hd @ A @ Xs4 )
% 0.31/0.49 != ( hd @ A @ Ys5 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % longest_common_prefix
% 0.31/0.49 thf(fact_125_ord_Olexordp__eq_Ocases,axiom,
% 0.31/0.49 ! [A: $tType,Less: A > A > $o,A1: list @ A,A22: list @ A] :
% 0.31/0.49 ( ( lexordp_eq @ A @ Less @ A1 @ A22 )
% 0.31/0.49 => ( ( ( A1
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 => ! [Ys3: list @ A] : ( A22 != Ys3 ) )
% 0.31/0.49 => ( ! [X4: A] :
% 0.31/0.49 ( ? [Xs2: list @ A] :
% 0.31/0.49 ( A1
% 0.31/0.49 = ( cons @ A @ X4 @ Xs2 ) )
% 0.31/0.49 => ! [Y4: A] :
% 0.31/0.49 ( ? [Ys3: list @ A] :
% 0.31/0.49 ( A22
% 0.31/0.49 = ( cons @ A @ Y4 @ Ys3 ) )
% 0.31/0.49 => ~ ( Less @ X4 @ Y4 ) ) )
% 0.31/0.49 => ~ ! [X4: A,Y4: A,Xs2: list @ A] :
% 0.31/0.49 ( ( A1
% 0.31/0.49 = ( cons @ A @ X4 @ Xs2 ) )
% 0.31/0.49 => ! [Ys3: list @ A] :
% 0.31/0.49 ( ( A22
% 0.31/0.49 = ( cons @ A @ Y4 @ Ys3 ) )
% 0.31/0.49 => ( ~ ( Less @ X4 @ Y4 )
% 0.31/0.49 => ( ~ ( Less @ Y4 @ X4 )
% 0.31/0.49 => ~ ( lexordp_eq @ A @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % ord.lexordp_eq.cases
% 0.31/0.49 thf(fact_126_ord_Olexordp__eq_Osimps,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( lexordp_eq @ A )
% 0.31/0.49 = ( ^ [Less2: A > A > $o,A12: list @ A,A23: list @ A] :
% 0.31/0.49 ( ? [Ys: list @ A] :
% 0.31/0.49 ( ( A12
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 & ( A23 = Ys ) )
% 0.31/0.49 | ? [X5: A,Y3: A,Xs3: list @ A,Ys: list @ A] :
% 0.31/0.49 ( ( A12
% 0.31/0.49 = ( cons @ A @ X5 @ Xs3 ) )
% 0.31/0.49 & ( A23
% 0.31/0.49 = ( cons @ A @ Y3 @ Ys ) )
% 0.31/0.49 & ( Less2 @ X5 @ Y3 ) )
% 0.31/0.49 | ? [X5: A,Y3: A,Xs3: list @ A,Ys: list @ A] :
% 0.31/0.49 ( ( A12
% 0.31/0.49 = ( cons @ A @ X5 @ Xs3 ) )
% 0.31/0.49 & ( A23
% 0.31/0.49 = ( cons @ A @ Y3 @ Ys ) )
% 0.31/0.49 & ~ ( Less2 @ X5 @ Y3 )
% 0.31/0.49 & ~ ( Less2 @ Y3 @ X5 )
% 0.31/0.49 & ( lexordp_eq @ A @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % ord.lexordp_eq.simps
% 0.31/0.49 thf(fact_127_ord_Olexordp__eq_Oinducts,axiom,
% 0.31/0.49 ! [A: $tType,Less: A > A > $o,X1: list @ A,X2: list @ A,P2: ( list @ A ) > ( list @ A ) > $o] :
% 0.31/0.49 ( ( lexordp_eq @ A @ Less @ X1 @ X2 )
% 0.31/0.49 => ( ! [X12: list @ A] : ( P2 @ ( nil @ A ) @ X12 )
% 0.31/0.49 => ( ! [X4: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 0.31/0.49 ( ( Less @ X4 @ Y4 )
% 0.31/0.49 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 0.31/0.49 => ( ! [X4: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 0.31/0.49 ( ~ ( Less @ X4 @ Y4 )
% 0.31/0.49 => ( ~ ( Less @ Y4 @ X4 )
% 0.31/0.49 => ( ( lexordp_eq @ A @ Less @ Xs2 @ Ys3 )
% 0.31/0.49 => ( ( P2 @ Xs2 @ Ys3 )
% 0.31/0.49 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) ) ) ) )
% 0.31/0.49 => ( P2 @ X1 @ X2 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % ord.lexordp_eq.inducts
% 0.31/0.49 thf(fact_128_splice_Osimps_I2_J,axiom,
% 0.31/0.49 ! [A: $tType,V2: A,Va2: list @ A] :
% 0.31/0.49 ( ( splice @ A @ ( cons @ A @ V2 @ Va2 ) @ ( nil @ A ) )
% 0.31/0.49 = ( cons @ A @ V2 @ Va2 ) ) ).
% 0.31/0.49
% 0.31/0.49 % splice.simps(2)
% 0.31/0.49 thf(fact_129_rotate1__hd__tl,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( rotate1 @ A @ Xs )
% 0.31/0.49 = ( append @ A @ ( tl @ A @ Xs ) @ ( cons @ A @ ( hd @ A @ Xs ) @ ( nil @ A ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % rotate1_hd_tl
% 0.31/0.49 thf(fact_130_sublists_Osimps_I1_J,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( sublists @ A @ ( nil @ A ) )
% 0.31/0.49 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % sublists.simps(1)
% 0.31/0.49 thf(fact_131_product__lists_Osimps_I1_J,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.31/0.49 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % product_lists.simps(1)
% 0.31/0.49 thf(fact_132_maps__simps_I1_J,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,F2: B > ( list @ A ),X: B,Xs: list @ B] :
% 0.31/0.49 ( ( maps @ B @ A @ F2 @ ( cons @ B @ X @ Xs ) )
% 0.31/0.49 = ( append @ A @ ( F2 @ X ) @ ( maps @ B @ A @ F2 @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % maps_simps(1)
% 0.31/0.49 thf(fact_133_rotate1_Osimps_I2_J,axiom,
% 0.31/0.49 ! [A: $tType,X: A,Xs: list @ A] :
% 0.31/0.49 ( ( rotate1 @ A @ ( cons @ A @ X @ Xs ) )
% 0.31/0.49 = ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % rotate1.simps(2)
% 0.31/0.49 thf(fact_134_remdups__adj__append,axiom,
% 0.31/0.49 ! [A: $tType,Xs_1: list @ A,X: A,Xs_2: list @ A] :
% 0.31/0.49 ( ( remdups_adj @ A @ ( append @ A @ Xs_1 @ ( cons @ A @ X @ Xs_2 ) ) )
% 0.31/0.49 = ( append @ A @ ( remdups_adj @ A @ ( append @ A @ Xs_1 @ ( cons @ A @ X @ ( nil @ A ) ) ) ) @ ( tl @ A @ ( remdups_adj @ A @ ( cons @ A @ X @ Xs_2 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % remdups_adj_append
% 0.31/0.49 thf(fact_135_remdups__adj__Nil__iff,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( ( remdups_adj @ A @ Xs )
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 = ( Xs
% 0.31/0.49 = ( nil @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % remdups_adj_Nil_iff
% 0.31/0.49 thf(fact_136_hd__remdups__adj,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( hd @ A @ ( remdups_adj @ A @ Xs ) )
% 0.31/0.49 = ( hd @ A @ Xs ) ) ).
% 0.31/0.49
% 0.31/0.49 % hd_remdups_adj
% 0.31/0.49 thf(fact_137_rotate1__is__Nil__conv,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( ( rotate1 @ A @ Xs )
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 = ( Xs
% 0.31/0.49 = ( nil @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % rotate1_is_Nil_conv
% 0.31/0.49 thf(fact_138_remdups__adj__Cons__alt,axiom,
% 0.31/0.49 ! [A: $tType,X: A,Xs: list @ A] :
% 0.31/0.49 ( ( cons @ A @ X @ ( tl @ A @ ( remdups_adj @ A @ ( cons @ A @ X @ Xs ) ) ) )
% 0.31/0.49 = ( remdups_adj @ A @ ( cons @ A @ X @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % remdups_adj_Cons_alt
% 0.31/0.49 thf(fact_139_remdups__adj_Osimps_I3_J,axiom,
% 0.31/0.49 ! [A: $tType,X: A,Y: A,Xs: list @ A] :
% 0.31/0.49 ( ( ( X = Y )
% 0.31/0.49 => ( ( remdups_adj @ A @ ( cons @ A @ X @ ( cons @ A @ Y @ Xs ) ) )
% 0.31/0.49 = ( remdups_adj @ A @ ( cons @ A @ X @ Xs ) ) ) )
% 0.31/0.49 & ( ( X != Y )
% 0.31/0.49 => ( ( remdups_adj @ A @ ( cons @ A @ X @ ( cons @ A @ Y @ Xs ) ) )
% 0.31/0.49 = ( cons @ A @ X @ ( remdups_adj @ A @ ( cons @ A @ Y @ Xs ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % remdups_adj.simps(3)
% 0.31/0.49 thf(fact_140_remdups__adj_Osimps_I1_J,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( remdups_adj @ A @ ( nil @ A ) )
% 0.31/0.49 = ( nil @ A ) ) ).
% 0.31/0.49
% 0.31/0.49 % remdups_adj.simps(1)
% 0.31/0.49 thf(fact_141_rotate1_Osimps_I1_J,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( rotate1 @ A @ ( nil @ A ) )
% 0.31/0.49 = ( nil @ A ) ) ).
% 0.31/0.49
% 0.31/0.49 % rotate1.simps(1)
% 0.31/0.49 thf(fact_142_remdups__adj_Oelims,axiom,
% 0.31/0.49 ! [A: $tType,X: list @ A,Y: list @ A] :
% 0.31/0.49 ( ( ( remdups_adj @ A @ X )
% 0.31/0.49 = Y )
% 0.31/0.49 => ( ( ( X
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 => ( Y
% 0.31/0.49 != ( nil @ A ) ) )
% 0.31/0.49 => ( ! [X4: A] :
% 0.31/0.49 ( ( X
% 0.31/0.49 = ( cons @ A @ X4 @ ( nil @ A ) ) )
% 0.31/0.49 => ( Y
% 0.31/0.49 != ( cons @ A @ X4 @ ( nil @ A ) ) ) )
% 0.31/0.49 => ~ ! [X4: A,Y4: A,Xs2: list @ A] :
% 0.31/0.49 ( ( X
% 0.31/0.49 = ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 0.31/0.49 => ~ ( ( ( X4 = Y4 )
% 0.31/0.49 => ( Y
% 0.31/0.49 = ( remdups_adj @ A @ ( cons @ A @ X4 @ Xs2 ) ) ) )
% 0.31/0.49 & ( ( X4 != Y4 )
% 0.31/0.49 => ( Y
% 0.31/0.49 = ( cons @ A @ X4 @ ( remdups_adj @ A @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % remdups_adj.elims
% 0.31/0.49 thf(fact_143_remdups__adj_Osimps_I2_J,axiom,
% 0.31/0.49 ! [A: $tType,X: A] :
% 0.31/0.49 ( ( remdups_adj @ A @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.31/0.49 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % remdups_adj.simps(2)
% 0.31/0.49 thf(fact_144_maps__simps_I2_J,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,F2: B > ( list @ A )] :
% 0.31/0.49 ( ( maps @ B @ A @ F2 @ ( nil @ B ) )
% 0.31/0.49 = ( nil @ A ) ) ).
% 0.31/0.49
% 0.31/0.49 % maps_simps(2)
% 0.31/0.49 thf(fact_145_remdups__adj__append__two,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,X: A,Y: A] :
% 0.31/0.49 ( ( remdups_adj @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) )
% 0.31/0.49 = ( append @ A @ ( remdups_adj @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) ) @ ( if @ ( list @ A ) @ ( X = Y ) @ ( nil @ A ) @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % remdups_adj_append_two
% 0.31/0.49 thf(fact_146_last__snoc,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,X: A] :
% 0.31/0.49 ( ( last @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.31/0.49 = X ) ).
% 0.31/0.49
% 0.31/0.49 % last_snoc
% 0.31/0.49 thf(fact_147_butlast__snoc,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,X: A] :
% 0.31/0.49 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.31/0.49 = Xs ) ).
% 0.31/0.49
% 0.31/0.49 % butlast_snoc
% 0.31/0.49 thf(fact_148_SuccD,axiom,
% 0.31/0.49 ! [A: $tType,K: A,Kl: set @ ( list @ A ),Kl2: list @ A] :
% 0.31/0.49 ( ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl @ Kl2 ) )
% 0.31/0.49 => ( member2 @ ( list @ A ) @ ( append @ A @ Kl2 @ ( cons @ A @ K @ ( nil @ A ) ) ) @ Kl ) ) ).
% 0.31/0.49
% 0.31/0.49 % SuccD
% 0.31/0.49 thf(fact_149_SuccI,axiom,
% 0.31/0.49 ! [A: $tType,Kl2: list @ A,K: A,Kl: set @ ( list @ A )] :
% 0.31/0.49 ( ( member2 @ ( list @ A ) @ ( append @ A @ Kl2 @ ( cons @ A @ K @ ( nil @ A ) ) ) @ Kl )
% 0.31/0.49 => ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl @ Kl2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % SuccI
% 0.31/0.49 thf(fact_150_last__appendR,axiom,
% 0.31/0.49 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 0.31/0.49 ( ( Ys2
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.31/0.49 = ( last @ A @ Ys2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % last_appendR
% 0.31/0.49 thf(fact_151_last__appendL,axiom,
% 0.31/0.49 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 0.31/0.49 ( ( Ys2
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.31/0.49 = ( last @ A @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % last_appendL
% 0.31/0.49 thf(fact_152_append__butlast__last__id,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( append @ A @ ( butlast @ A @ Xs ) @ ( cons @ A @ ( last @ A @ Xs ) @ ( nil @ A ) ) )
% 0.31/0.49 = Xs ) ) ).
% 0.31/0.49
% 0.31/0.49 % append_butlast_last_id
% 0.31/0.49 thf(fact_153_butlast_Osimps_I1_J,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( butlast @ A @ ( nil @ A ) )
% 0.31/0.49 = ( nil @ A ) ) ).
% 0.31/0.49
% 0.31/0.49 % butlast.simps(1)
% 0.31/0.49 thf(fact_154_butlast__tl,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( butlast @ A @ ( tl @ A @ Xs ) )
% 0.31/0.49 = ( tl @ A @ ( butlast @ A @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % butlast_tl
% 0.31/0.49 thf(fact_155_snoc__eq__iff__butlast,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,X: A,Ys2: list @ A] :
% 0.31/0.49 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.31/0.49 = Ys2 )
% 0.31/0.49 = ( ( Ys2
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 & ( ( butlast @ A @ Ys2 )
% 0.31/0.49 = Xs )
% 0.31/0.49 & ( ( last @ A @ Ys2 )
% 0.31/0.49 = X ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % snoc_eq_iff_butlast
% 0.31/0.49 thf(fact_156_butlast_Osimps_I2_J,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,X: A] :
% 0.31/0.49 ( ( ( Xs
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 0.31/0.49 = ( nil @ A ) ) )
% 0.31/0.49 & ( ( Xs
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 0.31/0.49 = ( cons @ A @ X @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % butlast.simps(2)
% 0.31/0.49 thf(fact_157_last_Osimps,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,X: A] :
% 0.31/0.49 ( ( ( Xs
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 0.31/0.49 = X ) )
% 0.31/0.49 & ( ( Xs
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 0.31/0.49 = ( last @ A @ Xs ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % last.simps
% 0.31/0.49 thf(fact_158_last__ConsL,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,X: A] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 0.31/0.49 = X ) ) ).
% 0.31/0.49
% 0.31/0.49 % last_ConsL
% 0.31/0.49 thf(fact_159_last__ConsR,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,X: A] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 0.31/0.49 = ( last @ A @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % last_ConsR
% 0.31/0.49 thf(fact_160_longest__common__suffix,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ? [Ss: list @ A,Xs4: list @ A,Ys5: list @ A] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 = ( append @ A @ Xs4 @ Ss ) )
% 0.31/0.49 & ( Ys2
% 0.31/0.49 = ( append @ A @ Ys5 @ Ss ) )
% 0.31/0.49 & ( ( Xs4
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 | ( Ys5
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 | ( ( last @ A @ Xs4 )
% 0.31/0.49 != ( last @ A @ Ys5 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % longest_common_suffix
% 0.31/0.49 thf(fact_161_butlast__append,axiom,
% 0.31/0.49 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 0.31/0.49 ( ( ( Ys2
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.31/0.49 = ( butlast @ A @ Xs ) ) )
% 0.31/0.49 & ( ( Ys2
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.31/0.49 = ( append @ A @ Xs @ ( butlast @ A @ Ys2 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % butlast_append
% 0.31/0.49 thf(fact_162_last__append,axiom,
% 0.31/0.49 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 0.31/0.49 ( ( ( Ys2
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.31/0.49 = ( last @ A @ Xs ) ) )
% 0.31/0.49 & ( ( Ys2
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.31/0.49 = ( last @ A @ Ys2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % last_append
% 0.31/0.49 thf(fact_163_last__tl,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( ( Xs
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 | ( ( tl @ A @ Xs )
% 0.31/0.49 != ( nil @ A ) ) )
% 0.31/0.49 => ( ( last @ A @ ( tl @ A @ Xs ) )
% 0.31/0.49 = ( last @ A @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % last_tl
% 0.31/0.49 thf(fact_164_BNF__Greatest__Fixpoint_Oshift__def,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType] :
% 0.31/0.49 ( ( bNF_Greatest_shift @ A @ B )
% 0.31/0.49 = ( ^ [Lab: ( list @ A ) > B,K2: A,Kl3: list @ A] : ( Lab @ ( cons @ A @ K2 @ Kl3 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % BNF_Greatest_Fixpoint.shift_def
% 0.31/0.49 thf(fact_165_empty__Shift,axiom,
% 0.31/0.49 ! [A: $tType,Kl: set @ ( list @ A ),K: A] :
% 0.31/0.49 ( ( member2 @ ( list @ A ) @ ( nil @ A ) @ Kl )
% 0.31/0.49 => ( ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl @ ( nil @ A ) ) )
% 0.31/0.49 => ( member2 @ ( list @ A ) @ ( nil @ A ) @ ( bNF_Greatest_Shift @ A @ Kl @ K ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % empty_Shift
% 0.31/0.49 thf(fact_166_Succ__Shift,axiom,
% 0.31/0.49 ! [A: $tType,Kl: set @ ( list @ A ),K: A,Kl2: list @ A] :
% 0.31/0.49 ( ( bNF_Greatest_Succ @ A @ ( bNF_Greatest_Shift @ A @ Kl @ K ) @ Kl2 )
% 0.31/0.49 = ( bNF_Greatest_Succ @ A @ Kl @ ( cons @ A @ K @ Kl2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Succ_Shift
% 0.31/0.49 thf(fact_167_ShiftD,axiom,
% 0.31/0.49 ! [A: $tType,Kl2: list @ A,Kl: set @ ( list @ A ),K: A] :
% 0.31/0.49 ( ( member2 @ ( list @ A ) @ Kl2 @ ( bNF_Greatest_Shift @ A @ Kl @ K ) )
% 0.31/0.49 => ( member2 @ ( list @ A ) @ ( cons @ A @ K @ Kl2 ) @ Kl ) ) ).
% 0.31/0.49
% 0.31/0.49 % ShiftD
% 0.31/0.49 thf(fact_168_rev__eq__Cons__iff,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Y: A,Ys2: list @ A] :
% 0.31/0.49 ( ( ( rev @ A @ Xs )
% 0.31/0.49 = ( cons @ A @ Y @ Ys2 ) )
% 0.31/0.49 = ( Xs
% 0.31/0.49 = ( append @ A @ ( rev @ A @ Ys2 ) @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % rev_eq_Cons_iff
% 0.31/0.49 thf(fact_169_listrelp_Oinducts,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,R2: A > B > $o,X1: list @ A,X2: list @ B,P2: ( list @ A ) > ( list @ B ) > $o] :
% 0.31/0.49 ( ( listrelp @ A @ B @ R2 @ X1 @ X2 )
% 0.31/0.49 => ( ( P2 @ ( nil @ A ) @ ( nil @ B ) )
% 0.31/0.49 => ( ! [X4: A,Y4: B,Xs2: list @ A,Ys3: list @ B] :
% 0.31/0.49 ( ( R2 @ X4 @ Y4 )
% 0.31/0.49 => ( ( listrelp @ A @ B @ R2 @ Xs2 @ Ys3 )
% 0.31/0.49 => ( ( P2 @ Xs2 @ Ys3 )
% 0.31/0.49 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y4 @ Ys3 ) ) ) ) )
% 0.31/0.49 => ( P2 @ X1 @ X2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % listrelp.inducts
% 0.31/0.49 thf(fact_170_listrelp_Osimps,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType] :
% 0.31/0.49 ( ( listrelp @ A @ B )
% 0.31/0.49 = ( ^ [R3: A > B > $o,A12: list @ A,A23: list @ B] :
% 0.31/0.49 ( ( ( A12
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 & ( A23
% 0.31/0.49 = ( nil @ B ) ) )
% 0.31/0.49 | ? [X5: A,Y3: B,Xs3: list @ A,Ys: list @ B] :
% 0.31/0.49 ( ( A12
% 0.31/0.49 = ( cons @ A @ X5 @ Xs3 ) )
% 0.31/0.49 & ( A23
% 0.31/0.49 = ( cons @ B @ Y3 @ Ys ) )
% 0.31/0.49 & ( R3 @ X5 @ Y3 )
% 0.31/0.49 & ( listrelp @ A @ B @ R3 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % listrelp.simps
% 0.31/0.49 thf(fact_171_rev__is__rev__conv,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( ( rev @ A @ Xs )
% 0.31/0.49 = ( rev @ A @ Ys2 ) )
% 0.31/0.49 = ( Xs = Ys2 ) ) ).
% 0.31/0.49
% 0.31/0.49 % rev_is_rev_conv
% 0.31/0.49 thf(fact_172_rev__rev__ident,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( rev @ A @ ( rev @ A @ Xs ) )
% 0.31/0.49 = Xs ) ).
% 0.31/0.49
% 0.31/0.49 % rev_rev_ident
% 0.31/0.49 thf(fact_173_Nil__is__rev__conv,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( ( nil @ A )
% 0.31/0.49 = ( rev @ A @ Xs ) )
% 0.31/0.49 = ( Xs
% 0.31/0.49 = ( nil @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Nil_is_rev_conv
% 0.31/0.49 thf(fact_174_rev__is__Nil__conv,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( ( rev @ A @ Xs )
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 = ( Xs
% 0.31/0.49 = ( nil @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % rev_is_Nil_conv
% 0.31/0.49 thf(fact_175_rev__append,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( rev @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.31/0.49 = ( append @ A @ ( rev @ A @ Ys2 ) @ ( rev @ A @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % rev_append
% 0.31/0.49 thf(fact_176_remdups__adj__rev,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( remdups_adj @ A @ ( rev @ A @ Xs ) )
% 0.31/0.49 = ( rev @ A @ ( remdups_adj @ A @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % remdups_adj_rev
% 0.31/0.49 thf(fact_177_rev__singleton__conv,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,X: A] :
% 0.31/0.49 ( ( ( rev @ A @ Xs )
% 0.31/0.49 = ( cons @ A @ X @ ( nil @ A ) ) )
% 0.31/0.49 = ( Xs
% 0.31/0.49 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % rev_singleton_conv
% 0.31/0.49 thf(fact_178_singleton__rev__conv,axiom,
% 0.31/0.49 ! [A: $tType,X: A,Xs: list @ A] :
% 0.31/0.49 ( ( ( cons @ A @ X @ ( nil @ A ) )
% 0.31/0.49 = ( rev @ A @ Xs ) )
% 0.31/0.49 = ( Xs
% 0.31/0.49 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % singleton_rev_conv
% 0.31/0.49 thf(fact_179_rev_Osimps_I1_J,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( rev @ A @ ( nil @ A ) )
% 0.31/0.49 = ( nil @ A ) ) ).
% 0.31/0.49
% 0.31/0.49 % rev.simps(1)
% 0.31/0.49 thf(fact_180_rev__swap,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( ( rev @ A @ Xs )
% 0.31/0.49 = Ys2 )
% 0.31/0.49 = ( Xs
% 0.31/0.49 = ( rev @ A @ Ys2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % rev_swap
% 0.31/0.49 thf(fact_181_listrelp_OCons,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,R2: A > B > $o,X: A,Y: B,Xs: list @ A,Ys2: list @ B] :
% 0.31/0.49 ( ( R2 @ X @ Y )
% 0.31/0.49 => ( ( listrelp @ A @ B @ R2 @ Xs @ Ys2 )
% 0.31/0.49 => ( listrelp @ A @ B @ R2 @ ( cons @ A @ X @ Xs ) @ ( cons @ B @ Y @ Ys2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % listrelp.Cons
% 0.31/0.49 thf(fact_182_listrelp_ONil,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,R2: A > B > $o] : ( listrelp @ A @ B @ R2 @ ( nil @ A ) @ ( nil @ B ) ) ).
% 0.31/0.49
% 0.31/0.49 % listrelp.Nil
% 0.31/0.49 thf(fact_183_rev_Osimps_I2_J,axiom,
% 0.31/0.49 ! [A: $tType,X: A,Xs: list @ A] :
% 0.31/0.49 ( ( rev @ A @ ( cons @ A @ X @ Xs ) )
% 0.31/0.49 = ( append @ A @ ( rev @ A @ Xs ) @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % rev.simps(2)
% 0.31/0.49 thf(fact_184_last__rev,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( last @ A @ ( rev @ A @ Xs ) )
% 0.31/0.49 = ( hd @ A @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % last_rev
% 0.31/0.49 thf(fact_185_hd__rev,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( hd @ A @ ( rev @ A @ Xs ) )
% 0.31/0.49 = ( last @ A @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % hd_rev
% 0.31/0.49 thf(fact_186_listrelp_Ocases,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,R2: A > B > $o,A1: list @ A,A22: list @ B] :
% 0.31/0.49 ( ( listrelp @ A @ B @ R2 @ A1 @ A22 )
% 0.31/0.49 => ( ( ( A1
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 => ( A22
% 0.31/0.49 != ( nil @ B ) ) )
% 0.31/0.49 => ~ ! [X4: A,Y4: B,Xs2: list @ A] :
% 0.31/0.49 ( ( A1
% 0.31/0.49 = ( cons @ A @ X4 @ Xs2 ) )
% 0.31/0.49 => ! [Ys3: list @ B] :
% 0.31/0.49 ( ( A22
% 0.31/0.49 = ( cons @ B @ Y4 @ Ys3 ) )
% 0.31/0.49 => ( ( R2 @ X4 @ Y4 )
% 0.31/0.49 => ~ ( listrelp @ A @ B @ R2 @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % listrelp.cases
% 0.31/0.49 thf(fact_187_map__tailrec__def,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType] :
% 0.31/0.49 ( ( map_tailrec @ A @ B )
% 0.31/0.49 = ( ^ [F: A > B,As3: list @ A] : ( rev @ B @ ( map_tailrec_rev @ A @ B @ F @ As3 @ ( nil @ B ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % map_tailrec_def
% 0.31/0.49 thf(fact_188_lexordp__eq__simps_I3_J,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [X: A,Xs: list @ A] :
% 0.31/0.49 ~ ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( nil @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq_simps(3)
% 0.31/0.49 thf(fact_189_fold__Cons__rev,axiom,
% 0.31/0.49 ! [A: $tType,Xs: list @ A] :
% 0.31/0.49 ( ( fold @ A @ ( list @ A ) @ ( cons @ A ) @ Xs )
% 0.31/0.49 = ( append @ A @ ( rev @ A @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % fold_Cons_rev
% 0.31/0.49 thf(fact_190_lexordp__eq__simps_I1_J,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Ys2: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys2 ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq_simps(1)
% 0.31/0.49 thf(fact_191_lexordp__eq__simps_I2_J,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Xs: list @ A] :
% 0.31/0.49 ( ( ord_lexordp_eq @ A @ Xs @ ( nil @ A ) )
% 0.31/0.49 = ( Xs
% 0.31/0.49 = ( nil @ A ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq_simps(2)
% 0.31/0.49 thf(fact_192_lexordp__eq__refl,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Xs: list @ A] : ( ord_lexordp_eq @ A @ Xs @ Xs ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq_refl
% 0.31/0.49 thf(fact_193_lexordp__eq__trans,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Xs: list @ A,Ys2: list @ A,Zs: list @ A] :
% 0.31/0.49 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 0.31/0.49 => ( ( ord_lexordp_eq @ A @ Ys2 @ Zs )
% 0.31/0.49 => ( ord_lexordp_eq @ A @ Xs @ Zs ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq_trans
% 0.31/0.49 thf(fact_194_lexordp__eq__linear,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 0.31/0.49 | ( ord_lexordp_eq @ A @ Ys2 @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq_linear
% 0.31/0.49 thf(fact_195_lexordp__eq__antisym,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 0.31/0.49 => ( ( ord_lexordp_eq @ A @ Ys2 @ Xs )
% 0.31/0.49 => ( Xs = Ys2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq_antisym
% 0.31/0.49 thf(fact_196_lexordp__eq_ONil,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Ys2: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys2 ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.Nil
% 0.31/0.49 thf(fact_197_fold__simps_I1_J,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,F2: B > A > A,S: A] :
% 0.31/0.49 ( ( fold @ B @ A @ F2 @ ( nil @ B ) @ S )
% 0.31/0.49 = S ) ).
% 0.31/0.49
% 0.31/0.49 % fold_simps(1)
% 0.31/0.49 thf(fact_198_fold__simps_I2_J,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,F2: B > A > A,X: B,Xs: list @ B,S: A] :
% 0.31/0.49 ( ( fold @ B @ A @ F2 @ ( cons @ B @ X @ Xs ) @ S )
% 0.31/0.49 = ( fold @ B @ A @ F2 @ Xs @ ( F2 @ X @ S ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % fold_simps(2)
% 0.31/0.49 thf(fact_199_rev__conv__fold,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( rev @ A )
% 0.31/0.49 = ( ^ [Xs3: list @ A] : ( fold @ A @ ( list @ A ) @ ( cons @ A ) @ Xs3 @ ( nil @ A ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % rev_conv_fold
% 0.31/0.49 thf(fact_200_List_Ounion__def,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( union @ A )
% 0.31/0.49 = ( fold @ A @ ( list @ A ) @ ( insert @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % List.union_def
% 0.31/0.49 thf(fact_201_lexordp__eq_Oinducts,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [X1: list @ A,X2: list @ A,P2: ( list @ A ) > ( list @ A ) > $o] :
% 0.31/0.49 ( ( ord_lexordp_eq @ A @ X1 @ X2 )
% 0.31/0.49 => ( ! [X12: list @ A] : ( P2 @ ( nil @ A ) @ X12 )
% 0.31/0.49 => ( ! [X4: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 0.31/0.49 ( ( ord_less @ A @ X4 @ Y4 )
% 0.31/0.49 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 0.31/0.49 => ( ! [X4: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 0.31/0.49 ( ~ ( ord_less @ A @ X4 @ Y4 )
% 0.31/0.49 => ( ~ ( ord_less @ A @ Y4 @ X4 )
% 0.31/0.49 => ( ( ord_lexordp_eq @ A @ Xs2 @ Ys3 )
% 0.31/0.49 => ( ( P2 @ Xs2 @ Ys3 )
% 0.31/0.49 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) ) ) ) )
% 0.31/0.49 => ( P2 @ X1 @ X2 ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.inducts
% 0.31/0.49 thf(fact_202_lexordp__eq__simps_I4_J,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [X: A,Xs: list @ A,Y: A,Ys2: list @ A] :
% 0.31/0.49 ( ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) )
% 0.31/0.49 = ( ( ord_less @ A @ X @ Y )
% 0.31/0.49 | ( ~ ( ord_less @ A @ Y @ X )
% 0.31/0.49 & ( ord_lexordp_eq @ A @ Xs @ Ys2 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq_simps(4)
% 0.31/0.49 thf(fact_203_lexordp__eq_OCons__eq,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [X: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ~ ( ord_less @ A @ X @ Y )
% 0.31/0.49 => ( ~ ( ord_less @ A @ Y @ X )
% 0.31/0.49 => ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 0.31/0.49 => ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.Cons_eq
% 0.31/0.49 thf(fact_204_lexordp__eq_OCons,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [X: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( ord_less @ A @ X @ Y )
% 0.31/0.49 => ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.Cons
% 0.31/0.49 thf(fact_205_lexordp__eq_Ocases,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [A1: list @ A,A22: list @ A] :
% 0.31/0.49 ( ( ord_lexordp_eq @ A @ A1 @ A22 )
% 0.31/0.49 => ( ( ( A1
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 => ! [Ys3: list @ A] : ( A22 != Ys3 ) )
% 0.31/0.49 => ( ! [X4: A] :
% 0.31/0.49 ( ? [Xs2: list @ A] :
% 0.31/0.49 ( A1
% 0.31/0.49 = ( cons @ A @ X4 @ Xs2 ) )
% 0.31/0.49 => ! [Y4: A] :
% 0.31/0.49 ( ? [Ys3: list @ A] :
% 0.31/0.49 ( A22
% 0.31/0.49 = ( cons @ A @ Y4 @ Ys3 ) )
% 0.31/0.49 => ~ ( ord_less @ A @ X4 @ Y4 ) ) )
% 0.31/0.49 => ~ ! [X4: A,Y4: A,Xs2: list @ A] :
% 0.31/0.49 ( ( A1
% 0.31/0.49 = ( cons @ A @ X4 @ Xs2 ) )
% 0.31/0.49 => ! [Ys3: list @ A] :
% 0.31/0.49 ( ( A22
% 0.31/0.49 = ( cons @ A @ Y4 @ Ys3 ) )
% 0.31/0.49 => ( ~ ( ord_less @ A @ X4 @ Y4 )
% 0.31/0.49 => ( ~ ( ord_less @ A @ Y4 @ X4 )
% 0.31/0.49 => ~ ( ord_lexordp_eq @ A @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.cases
% 0.31/0.49 thf(fact_206_lexordp__eq_Osimps,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ( ( ord_lexordp_eq @ A )
% 0.31/0.49 = ( ^ [A12: list @ A,A23: list @ A] :
% 0.31/0.49 ( ? [Ys: list @ A] :
% 0.31/0.49 ( ( A12
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 & ( A23 = Ys ) )
% 0.31/0.49 | ? [X5: A,Y3: A,Xs3: list @ A,Ys: list @ A] :
% 0.31/0.49 ( ( A12
% 0.31/0.49 = ( cons @ A @ X5 @ Xs3 ) )
% 0.31/0.49 & ( A23
% 0.31/0.49 = ( cons @ A @ Y3 @ Ys ) )
% 0.31/0.49 & ( ord_less @ A @ X5 @ Y3 ) )
% 0.31/0.49 | ? [X5: A,Y3: A,Xs3: list @ A,Ys: list @ A] :
% 0.31/0.49 ( ( A12
% 0.31/0.49 = ( cons @ A @ X5 @ Xs3 ) )
% 0.31/0.49 & ( A23
% 0.31/0.49 = ( cons @ A @ Y3 @ Ys ) )
% 0.31/0.49 & ~ ( ord_less @ A @ X5 @ Y3 )
% 0.31/0.49 & ~ ( ord_less @ A @ Y3 @ X5 )
% 0.31/0.49 & ( ord_lexordp_eq @ A @ Xs3 @ Ys ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq.simps
% 0.31/0.49 thf(fact_207_lexordp__append__left__rightI,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [X: A,Y: A,Us2: list @ A,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( ord_less @ A @ X @ Y )
% 0.31/0.49 => ( ord_lexordp @ A @ ( append @ A @ Us2 @ ( cons @ A @ X @ Xs ) ) @ ( append @ A @ Us2 @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_append_left_rightI
% 0.31/0.49 thf(fact_208_lexordp__iff,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.31/0.49 => ( ( ord_lexordp @ A )
% 0.31/0.49 = ( ^ [Xs3: list @ A,Ys: list @ A] :
% 0.31/0.49 ( ? [X5: A,Vs: list @ A] :
% 0.31/0.49 ( Ys
% 0.31/0.49 = ( append @ A @ Xs3 @ ( cons @ A @ X5 @ Vs ) ) )
% 0.31/0.49 | ? [Us: list @ A,A5: A,B3: A,Vs: list @ A,Ws2: list @ A] :
% 0.31/0.49 ( ( ord_less @ A @ A5 @ B3 )
% 0.31/0.49 & ( Xs3
% 0.31/0.49 = ( append @ A @ Us @ ( cons @ A @ A5 @ Vs ) ) )
% 0.31/0.49 & ( Ys
% 0.31/0.49 = ( append @ A @ Us @ ( cons @ A @ B3 @ Ws2 ) ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_iff
% 0.31/0.49 thf(fact_209_lexordp__simps_I1_J,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Ys2: list @ A] :
% 0.31/0.49 ( ( ord_lexordp @ A @ ( nil @ A ) @ Ys2 )
% 0.31/0.49 = ( Ys2
% 0.31/0.49 != ( nil @ A ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_simps(1)
% 0.31/0.49 thf(fact_210_lexordp__simps_I2_J,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Xs: list @ A] :
% 0.31/0.49 ~ ( ord_lexordp @ A @ Xs @ ( nil @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_simps(2)
% 0.31/0.49 thf(fact_211_lexordp__simps_I3_J,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [X: A,Xs: list @ A,Y: A,Ys2: list @ A] :
% 0.31/0.49 ( ( ord_lexordp @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) )
% 0.31/0.49 = ( ( ord_less @ A @ X @ Y )
% 0.31/0.49 | ( ~ ( ord_less @ A @ Y @ X )
% 0.31/0.49 & ( ord_lexordp @ A @ Xs @ Ys2 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_simps(3)
% 0.31/0.49 thf(fact_212_lexordp__irreflexive,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Xs: list @ A] :
% 0.31/0.49 ( ! [X4: A] :
% 0.31/0.49 ~ ( ord_less @ A @ X4 @ X4 )
% 0.31/0.49 => ~ ( ord_lexordp @ A @ Xs @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_irreflexive
% 0.31/0.49 thf(fact_213_lexordp__append__leftD,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Xs: list @ A,Us2: list @ A,Vs2: list @ A] :
% 0.31/0.49 ( ( ord_lexordp @ A @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Xs @ Vs2 ) )
% 0.31/0.49 => ( ! [A4: A] :
% 0.31/0.49 ~ ( ord_less @ A @ A4 @ A4 )
% 0.31/0.49 => ( ord_lexordp @ A @ Us2 @ Vs2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_append_leftD
% 0.31/0.49 thf(fact_214_lexordp_OCons__eq,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [X: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ~ ( ord_less @ A @ X @ Y )
% 0.31/0.49 => ( ~ ( ord_less @ A @ Y @ X )
% 0.31/0.49 => ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 0.31/0.49 => ( ord_lexordp @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp.Cons_eq
% 0.31/0.49 thf(fact_215_lexordp_OCons,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [X: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( ord_less @ A @ X @ Y )
% 0.31/0.49 => ( ord_lexordp @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp.Cons
% 0.31/0.49 thf(fact_216_lexordp_ONil,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Y: A,Ys2: list @ A] : ( ord_lexordp @ A @ ( nil @ A ) @ ( cons @ A @ Y @ Ys2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp.Nil
% 0.31/0.49 thf(fact_217_lexordp__append__rightI,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Ys2: list @ A,Xs: list @ A] :
% 0.31/0.49 ( ( Ys2
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ord_lexordp @ A @ Xs @ ( append @ A @ Xs @ Ys2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_append_rightI
% 0.31/0.49 thf(fact_218_lexordp__antisym,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( order @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 0.31/0.49 => ~ ( ord_lexordp @ A @ Ys2 @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_antisym
% 0.31/0.49 thf(fact_219_lexordp__trans,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Xs: list @ A,Ys2: list @ A,Zs: list @ A] :
% 0.31/0.49 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 0.31/0.49 => ( ( ord_lexordp @ A @ Ys2 @ Zs )
% 0.31/0.49 => ( ord_lexordp @ A @ Xs @ Zs ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_trans
% 0.31/0.49 thf(fact_220_lexordp__linear,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 0.31/0.49 | ( Xs = Ys2 )
% 0.31/0.49 | ( ord_lexordp @ A @ Ys2 @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_linear
% 0.31/0.49 thf(fact_221_lexordp__irreflexive_H,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( order @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Xs: list @ A] :
% 0.31/0.49 ~ ( ord_lexordp @ A @ Xs @ Xs ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_irreflexive'
% 0.31/0.49 thf(fact_222_lexordp__append__leftI,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Us2: list @ A,Vs2: list @ A,Xs: list @ A] :
% 0.31/0.49 ( ( ord_lexordp @ A @ Us2 @ Vs2 )
% 0.31/0.49 => ( ord_lexordp @ A @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Xs @ Vs2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_append_leftI
% 0.31/0.49 thf(fact_223_lexordp__conv__lexordp__eq,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.31/0.49 => ( ( ord_lexordp @ A )
% 0.31/0.49 = ( ^ [Xs3: list @ A,Ys: list @ A] :
% 0.31/0.49 ( ( ord_lexordp_eq @ A @ Xs3 @ Ys )
% 0.31/0.49 & ~ ( ord_lexordp_eq @ A @ Ys @ Xs3 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_conv_lexordp_eq
% 0.31/0.49 thf(fact_224_lexordp__eq__conv__lexord,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.31/0.49 => ( ( ord_lexordp_eq @ A )
% 0.31/0.49 = ( ^ [Xs3: list @ A,Ys: list @ A] :
% 0.31/0.49 ( ( Xs3 = Ys )
% 0.31/0.49 | ( ord_lexordp @ A @ Xs3 @ Ys ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_eq_conv_lexord
% 0.31/0.49 thf(fact_225_lexordp__into__lexordp__eq,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 0.31/0.49 => ( ord_lexordp_eq @ A @ Xs @ Ys2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_into_lexordp_eq
% 0.31/0.49 thf(fact_226_lexordp__induct,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Xs: list @ A,Ys2: list @ A,P2: ( list @ A ) > ( list @ A ) > $o] :
% 0.31/0.49 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 0.31/0.49 => ( ! [Y4: A,Ys3: list @ A] : ( P2 @ ( nil @ A ) @ ( cons @ A @ Y4 @ Ys3 ) )
% 0.31/0.49 => ( ! [X4: A,Xs2: list @ A,Y4: A,Ys3: list @ A] :
% 0.31/0.49 ( ( ord_less @ A @ X4 @ Y4 )
% 0.31/0.49 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 0.31/0.49 => ( ! [X4: A,Xs2: list @ A,Ys3: list @ A] :
% 0.31/0.49 ( ( ord_lexordp @ A @ Xs2 @ Ys3 )
% 0.31/0.49 => ( ( P2 @ Xs2 @ Ys3 )
% 0.31/0.49 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ X4 @ Ys3 ) ) ) )
% 0.31/0.49 => ( P2 @ Xs @ Ys2 ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_induct
% 0.31/0.49 thf(fact_227_lexordp__cases,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( linorder @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [Xs: list @ A,Ys2: list @ A] :
% 0.31/0.49 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 0.31/0.49 => ( ( ( Xs
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 => ! [Y4: A,Ys5: list @ A] :
% 0.31/0.49 ( Ys2
% 0.31/0.49 != ( cons @ A @ Y4 @ Ys5 ) ) )
% 0.31/0.49 => ( ! [X4: A] :
% 0.31/0.49 ( ? [Xs4: list @ A] :
% 0.31/0.49 ( Xs
% 0.31/0.49 = ( cons @ A @ X4 @ Xs4 ) )
% 0.31/0.49 => ! [Y4: A] :
% 0.31/0.49 ( ? [Ys5: list @ A] :
% 0.31/0.49 ( Ys2
% 0.31/0.49 = ( cons @ A @ Y4 @ Ys5 ) )
% 0.31/0.49 => ~ ( ord_less @ A @ X4 @ Y4 ) ) )
% 0.31/0.49 => ~ ! [X4: A,Xs4: list @ A] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 = ( cons @ A @ X4 @ Xs4 ) )
% 0.31/0.49 => ! [Ys5: list @ A] :
% 0.31/0.49 ( ( Ys2
% 0.31/0.49 = ( cons @ A @ X4 @ Ys5 ) )
% 0.31/0.49 => ~ ( ord_lexordp @ A @ Xs4 @ Ys5 ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp_cases
% 0.31/0.49 thf(fact_228_lexordp_Oinducts,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [X1: list @ A,X2: list @ A,P2: ( list @ A ) > ( list @ A ) > $o] :
% 0.31/0.49 ( ( ord_lexordp @ A @ X1 @ X2 )
% 0.31/0.49 => ( ! [Y4: A,Ys3: list @ A] : ( P2 @ ( nil @ A ) @ ( cons @ A @ Y4 @ Ys3 ) )
% 0.31/0.49 => ( ! [X4: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 0.31/0.49 ( ( ord_less @ A @ X4 @ Y4 )
% 0.31/0.49 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 0.31/0.49 => ( ! [X4: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 0.31/0.49 ( ~ ( ord_less @ A @ X4 @ Y4 )
% 0.31/0.49 => ( ~ ( ord_less @ A @ Y4 @ X4 )
% 0.31/0.49 => ( ( ord_lexordp @ A @ Xs2 @ Ys3 )
% 0.31/0.49 => ( ( P2 @ Xs2 @ Ys3 )
% 0.31/0.49 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) ) ) ) )
% 0.31/0.49 => ( P2 @ X1 @ X2 ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp.inducts
% 0.31/0.49 thf(fact_229_lexordp_Osimps,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ( ( ord_lexordp @ A )
% 0.31/0.49 = ( ^ [A12: list @ A,A23: list @ A] :
% 0.31/0.49 ( ? [Y3: A,Ys: list @ A] :
% 0.31/0.49 ( ( A12
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 & ( A23
% 0.31/0.49 = ( cons @ A @ Y3 @ Ys ) ) )
% 0.31/0.49 | ? [X5: A,Y3: A,Xs3: list @ A,Ys: list @ A] :
% 0.31/0.49 ( ( A12
% 0.31/0.49 = ( cons @ A @ X5 @ Xs3 ) )
% 0.31/0.49 & ( A23
% 0.31/0.49 = ( cons @ A @ Y3 @ Ys ) )
% 0.31/0.49 & ( ord_less @ A @ X5 @ Y3 ) )
% 0.31/0.49 | ? [X5: A,Y3: A,Xs3: list @ A,Ys: list @ A] :
% 0.31/0.49 ( ( A12
% 0.31/0.49 = ( cons @ A @ X5 @ Xs3 ) )
% 0.31/0.49 & ( A23
% 0.31/0.49 = ( cons @ A @ Y3 @ Ys ) )
% 0.31/0.49 & ~ ( ord_less @ A @ X5 @ Y3 )
% 0.31/0.49 & ~ ( ord_less @ A @ Y3 @ X5 )
% 0.31/0.49 & ( ord_lexordp @ A @ Xs3 @ Ys ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp.simps
% 0.31/0.49 thf(fact_230_lexordp_Ocases,axiom,
% 0.31/0.49 ! [A: $tType] :
% 0.31/0.49 ( ( ord @ A @ ( type2 @ A ) )
% 0.31/0.49 => ! [A1: list @ A,A22: list @ A] :
% 0.31/0.49 ( ( ord_lexordp @ A @ A1 @ A22 )
% 0.31/0.49 => ( ( ( A1
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 => ! [Y4: A,Ys3: list @ A] :
% 0.31/0.49 ( A22
% 0.31/0.49 != ( cons @ A @ Y4 @ Ys3 ) ) )
% 0.31/0.49 => ( ! [X4: A] :
% 0.31/0.49 ( ? [Xs2: list @ A] :
% 0.31/0.49 ( A1
% 0.31/0.49 = ( cons @ A @ X4 @ Xs2 ) )
% 0.31/0.49 => ! [Y4: A] :
% 0.31/0.49 ( ? [Ys3: list @ A] :
% 0.31/0.49 ( A22
% 0.31/0.49 = ( cons @ A @ Y4 @ Ys3 ) )
% 0.31/0.49 => ~ ( ord_less @ A @ X4 @ Y4 ) ) )
% 0.31/0.49 => ~ ! [X4: A,Y4: A,Xs2: list @ A] :
% 0.31/0.49 ( ( A1
% 0.31/0.49 = ( cons @ A @ X4 @ Xs2 ) )
% 0.31/0.49 => ! [Ys3: list @ A] :
% 0.31/0.49 ( ( A22
% 0.31/0.49 = ( cons @ A @ Y4 @ Ys3 ) )
% 0.31/0.49 => ( ~ ( ord_less @ A @ X4 @ Y4 )
% 0.31/0.49 => ( ~ ( ord_less @ A @ Y4 @ X4 )
% 0.31/0.49 => ~ ( ord_lexordp @ A @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % lexordp.cases
% 0.31/0.49 thf(fact_231_map__tailrec__rev,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType] :
% 0.31/0.49 ( ( map_tailrec_rev @ B @ A )
% 0.31/0.49 = ( ^ [F: B > A,As3: list @ B] : ( append @ A @ ( rev @ A @ ( map @ B @ A @ F @ As3 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % map_tailrec_rev
% 0.31/0.49 thf(fact_232_replicate__append__same,axiom,
% 0.31/0.49 ! [A: $tType,I: nat,X: A] :
% 0.31/0.49 ( ( append @ A @ ( replicate @ A @ I @ X ) @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.31/0.49 = ( cons @ A @ X @ ( replicate @ A @ I @ X ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % replicate_append_same
% 0.31/0.49 thf(fact_233_Nil__is__map__conv,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B] :
% 0.31/0.49 ( ( ( nil @ A )
% 0.31/0.49 = ( map @ B @ A @ F2 @ Xs ) )
% 0.31/0.49 = ( Xs
% 0.31/0.49 = ( nil @ B ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Nil_is_map_conv
% 0.31/0.49 thf(fact_234_map__is__Nil__conv,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B] :
% 0.31/0.49 ( ( ( map @ B @ A @ F2 @ Xs )
% 0.31/0.49 = ( nil @ A ) )
% 0.31/0.49 = ( Xs
% 0.31/0.49 = ( nil @ B ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % map_is_Nil_conv
% 0.31/0.49 thf(fact_235_list_Omap__disc__iff,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,F2: A > B,A3: list @ A] :
% 0.31/0.49 ( ( ( map @ A @ B @ F2 @ A3 )
% 0.31/0.49 = ( nil @ B ) )
% 0.31/0.49 = ( A3
% 0.31/0.49 = ( nil @ A ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % list.map_disc_iff
% 0.31/0.49 thf(fact_236_map__append,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B,Ys2: list @ B] :
% 0.31/0.49 ( ( map @ B @ A @ F2 @ ( append @ B @ Xs @ Ys2 ) )
% 0.31/0.49 = ( append @ A @ ( map @ B @ A @ F2 @ Xs ) @ ( map @ B @ A @ F2 @ Ys2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % map_append
% 0.31/0.49 thf(fact_237_map__replicate,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,F2: B > A,N: nat,X: B] :
% 0.31/0.49 ( ( map @ B @ A @ F2 @ ( replicate @ B @ N @ X ) )
% 0.31/0.49 = ( replicate @ A @ N @ ( F2 @ X ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % map_replicate
% 0.31/0.49 thf(fact_238_rev__replicate,axiom,
% 0.31/0.49 ! [A: $tType,N: nat,X: A] :
% 0.31/0.49 ( ( rev @ A @ ( replicate @ A @ N @ X ) )
% 0.31/0.49 = ( replicate @ A @ N @ X ) ) ).
% 0.31/0.49
% 0.31/0.49 % rev_replicate
% 0.31/0.49 thf(fact_239_smap__shift,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B,S: stream170649215stream @ B] :
% 0.31/0.49 ( ( stream2128578057e_smap @ B @ A @ F2 @ ( stream1035003186_shift @ B @ Xs @ S ) )
% 0.31/0.49 = ( stream1035003186_shift @ A @ ( map @ B @ A @ F2 @ Xs ) @ ( stream2128578057e_smap @ B @ A @ F2 @ S ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % smap_shift
% 0.31/0.49 thf(fact_240_map__eq__map__tailrec,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType] :
% 0.31/0.49 ( ( map @ A @ B )
% 0.31/0.49 = ( map_tailrec @ A @ B ) ) ).
% 0.31/0.49
% 0.31/0.49 % map_eq_map_tailrec
% 0.31/0.49 thf(fact_241_list_Omap__sel_I2_J,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,A3: list @ A,F2: A > B] :
% 0.31/0.49 ( ( A3
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( tl @ B @ ( map @ A @ B @ F2 @ A3 ) )
% 0.31/0.49 = ( map @ A @ B @ F2 @ ( tl @ A @ A3 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % list.map_sel(2)
% 0.31/0.49 thf(fact_242_hd__map,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,Xs: list @ A,F2: A > B] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( hd @ B @ ( map @ A @ B @ F2 @ Xs ) )
% 0.31/0.49 = ( F2 @ ( hd @ A @ Xs ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % hd_map
% 0.31/0.49 thf(fact_243_list_Omap__sel_I1_J,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,A3: list @ A,F2: A > B] :
% 0.31/0.49 ( ( A3
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( hd @ B @ ( map @ A @ B @ F2 @ A3 ) )
% 0.31/0.49 = ( F2 @ ( hd @ A @ A3 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % list.map_sel(1)
% 0.31/0.49 thf(fact_244_last__map,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,Xs: list @ A,F2: A > B] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 != ( nil @ A ) )
% 0.31/0.49 => ( ( last @ B @ ( map @ A @ B @ F2 @ Xs ) )
% 0.31/0.49 = ( F2 @ ( last @ A @ Xs ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % last_map
% 0.31/0.49 thf(fact_245_replicate__app__Cons__same,axiom,
% 0.31/0.49 ! [A: $tType,N: nat,X: A,Xs: list @ A] :
% 0.31/0.49 ( ( append @ A @ ( replicate @ A @ N @ X ) @ ( cons @ A @ X @ Xs ) )
% 0.31/0.49 = ( cons @ A @ X @ ( append @ A @ ( replicate @ A @ N @ X ) @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % replicate_app_Cons_same
% 0.31/0.49 thf(fact_246_list_Osimps_I9_J,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,F2: A > B,X21: A,X222: list @ A] :
% 0.31/0.49 ( ( map @ A @ B @ F2 @ ( cons @ A @ X21 @ X222 ) )
% 0.31/0.49 = ( cons @ B @ ( F2 @ X21 ) @ ( map @ A @ B @ F2 @ X222 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % list.simps(9)
% 0.31/0.49 thf(fact_247_Cons__eq__map__D,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,X: A,Xs: list @ A,F2: B > A,Ys2: list @ B] :
% 0.31/0.49 ( ( ( cons @ A @ X @ Xs )
% 0.31/0.49 = ( map @ B @ A @ F2 @ Ys2 ) )
% 0.31/0.49 => ? [Z: B,Zs2: list @ B] :
% 0.31/0.49 ( ( Ys2
% 0.31/0.49 = ( cons @ B @ Z @ Zs2 ) )
% 0.31/0.49 & ( X
% 0.31/0.49 = ( F2 @ Z ) )
% 0.31/0.49 & ( Xs
% 0.31/0.49 = ( map @ B @ A @ F2 @ Zs2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Cons_eq_map_D
% 0.31/0.49 thf(fact_248_map__eq__Cons__D,axiom,
% 0.31/0.49 ! [B: $tType,A: $tType,F2: B > A,Xs: list @ B,Y: A,Ys2: list @ A] :
% 0.31/0.49 ( ( ( map @ B @ A @ F2 @ Xs )
% 0.31/0.49 = ( cons @ A @ Y @ Ys2 ) )
% 0.31/0.49 => ? [Z: B,Zs2: list @ B] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 = ( cons @ B @ Z @ Zs2 ) )
% 0.31/0.49 & ( ( F2 @ Z )
% 0.31/0.49 = Y )
% 0.31/0.49 & ( ( map @ B @ A @ F2 @ Zs2 )
% 0.31/0.49 = Ys2 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % map_eq_Cons_D
% 0.31/0.49 thf(fact_249_Cons__eq__map__conv,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,X: A,Xs: list @ A,F2: B > A,Ys2: list @ B] :
% 0.31/0.49 ( ( ( cons @ A @ X @ Xs )
% 0.31/0.49 = ( map @ B @ A @ F2 @ Ys2 ) )
% 0.31/0.49 = ( ? [Z2: B,Zs3: list @ B] :
% 0.31/0.49 ( ( Ys2
% 0.31/0.49 = ( cons @ B @ Z2 @ Zs3 ) )
% 0.31/0.49 & ( X
% 0.31/0.49 = ( F2 @ Z2 ) )
% 0.31/0.49 & ( Xs
% 0.31/0.49 = ( map @ B @ A @ F2 @ Zs3 ) ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % Cons_eq_map_conv
% 0.31/0.49 thf(fact_250_map__eq__Cons__conv,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B,Y: A,Ys2: list @ A] :
% 0.31/0.49 ( ( ( map @ B @ A @ F2 @ Xs )
% 0.31/0.49 = ( cons @ A @ Y @ Ys2 ) )
% 0.31/0.49 = ( ? [Z2: B,Zs3: list @ B] :
% 0.31/0.49 ( ( Xs
% 0.31/0.49 = ( cons @ B @ Z2 @ Zs3 ) )
% 0.31/0.49 & ( ( F2 @ Z2 )
% 0.31/0.49 = Y )
% 0.31/0.49 & ( ( map @ B @ A @ F2 @ Zs3 )
% 0.31/0.49 = Ys2 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % map_eq_Cons_conv
% 0.31/0.49 thf(fact_251_list_Osimps_I8_J,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,F2: A > B] :
% 0.31/0.49 ( ( map @ A @ B @ F2 @ ( nil @ A ) )
% 0.31/0.49 = ( nil @ B ) ) ).
% 0.31/0.49
% 0.31/0.49 % list.simps(8)
% 0.31/0.49 thf(fact_252_map__tl,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B] :
% 0.31/0.49 ( ( map @ B @ A @ F2 @ ( tl @ B @ Xs ) )
% 0.31/0.49 = ( tl @ A @ ( map @ B @ A @ F2 @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % map_tl
% 0.31/0.49 thf(fact_253_append__replicate__commute,axiom,
% 0.31/0.49 ! [A: $tType,N: nat,X: A,K: nat] :
% 0.31/0.49 ( ( append @ A @ ( replicate @ A @ N @ X ) @ ( replicate @ A @ K @ X ) )
% 0.31/0.49 = ( append @ A @ ( replicate @ A @ K @ X ) @ ( replicate @ A @ N @ X ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % append_replicate_commute
% 0.31/0.49 thf(fact_254_map__butlast,axiom,
% 0.31/0.49 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B] :
% 0.31/0.49 ( ( map @ B @ A @ F2 @ ( butlast @ B @ Xs ) )
% 0.31/0.49 = ( butlast @ A @ ( map @ B @ A @ F2 @ Xs ) ) ) ).
% 0.31/0.49
% 0.31/0.49 % map_butlast
% 0.31/0.49
% 0.31/0.49 %----Type constructors (7)
% 0.31/0.49 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.31/0.49 ! [A7: $tType,A8: $tType] :
% 0.31/0.49 ( ( order @ A8 @ ( type2 @ A8 ) )
% 0.31/0.49 => ( order @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 thf(tcon_fun___Orderings_Oord,axiom,
% 0.31/0.49 ! [A7: $tType,A8: $tType] :
% 0.31/0.49 ( ( ord @ A8 @ ( type2 @ A8 ) )
% 0.31/0.49 => ( ord @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 thf(tcon_Set_Oset___Orderings_Oorder_1,axiom,
% 0.31/0.49 ! [A7: $tType] : ( order @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 0.31/0.49 ! [A7: $tType] : ( ord @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 0.31/0.49
% 0.31/0.49 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.31/0.49 linorder @ $o @ ( type2 @ $o ) ).
% 0.31/0.49
% 0.31/0.49 thf(tcon_HOL_Obool___Orderings_Oorder_3,axiom,
% 0.31/0.49 order @ $o @ ( type2 @ $o ) ).
% 0.31/0.49
% 0.31/0.49 thf(tcon_HOL_Obool___Orderings_Oord_4,axiom,
% 0.31/0.49 ord @ $o @ ( type2 @ $o ) ).
% 0.31/0.49
% 0.31/0.49 %----Helper facts (3)
% 0.31/0.49 thf(help_If_3_1_T,axiom,
% 0.31/0.49 ! [P2: $o] :
% 0.31/0.49 ( ( P2 = $true )
% 0.31/0.49 | ( P2 = $false ) ) ).
% 0.31/0.49
% 0.31/0.49 thf(help_If_2_1_T,axiom,
% 0.31/0.49 ! [A: $tType,X: A,Y: A] :
% 0.31/0.49 ( ( if @ A @ $false @ X @ Y )
% 0.31/0.49 = Y ) ).
% 0.31/0.49
% 0.31/0.49 thf(help_If_1_1_T,axiom,
% 0.31/0.49 ! [A: $tType,X: A,Y: A] :
% 0.31/0.49 ( ( if @ A @ $true @ X @ Y )
% 0.31/0.49 = X ) ).
% 0.31/0.49
% 0.31/0.49 %----Conjectures (2)
% 0.31/0.49 thf(conj_0,hypothesis,
% 0.31/0.49 ( ( stream_Mirabelle_shd @ ( list @ a ) @ ws )
% 0.31/0.49 != ( nil @ a ) ) ).
% 0.31/0.49
% 0.31/0.49 thf(conj_1,conjecture,
% 0.31/0.49 ( ( stream942386729e_flat @ a @ ws )
% 0.31/0.49 = ( stream1035003186_shift @ a @ ( stream_Mirabelle_shd @ ( list @ a ) @ ws ) @ ( stream942386729e_flat @ a @ ( stream_Mirabelle_stl @ ( list @ a ) @ ws ) ) ) ) ).
% 0.31/0.49
% 0.31/0.49 %------------------------------------------------------------------------------
% 0.31/0.49 ------------------------
% 2.71/1.52 ---- Embedded in THF ---
% 2.71/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.71/1.52 %%% Generated on Tue Feb 24 06:12:02 EST 2026
% 2.71/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 2.71/1.52 %%% Logic specification used:
% 2.71/1.52 %%% thf(spec, logic, $$dhol).
% 2.71/1.52
% 2.71/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.wxvlm3pJrl/DTF2DTF3154.p
% 2.71/1.52 thf(ty_t_Stream__Mirabelle__hbrgyiwlrc_Ostream, type, stream170649215stream: ($tType > $tType)).
% 2.71/1.52 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.71/1.52 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.71/1.52 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.71/1.52 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.71/1.52 thf(ty_tf_a, type, a: $tType).
% 2.71/1.52 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.71/1.52 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.71/1.52 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.71/1.52 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.71/1.52 thf(sy_c_BNF__Greatest__Fixpoint_OShift, type, bNF_Greatest_Shift: (!> [A:$tType]: (((set @ (list @ A)) > (A > (set @ (list @ A))))))).
% 2.71/1.52 thf(sy_c_BNF__Greatest__Fixpoint_OSucc, type, bNF_Greatest_Succ: (!> [A:$tType]: (((set @ (list @ A)) > ((list @ A) > (set @ A)))))).
% 2.71/1.52 thf(sy_c_BNF__Greatest__Fixpoint_Oshift, type, bNF_Greatest_shift: (!> [A:$tType,B:$tType]: ((((list @ A) > B) > (A > ((list @ A) > B)))))).
% 2.71/1.52 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.71/1.52 thf(sy_c_List_Oappend, type, append: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.71/1.52 thf(sy_c_List_Obind, type, bind: (!> [A:$tType,B:$tType]: (((list @ A) > ((A > (list @ B)) > (list @ B)))))).
% 2.71/1.52 thf(sy_c_List_Obutlast, type, butlast: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.71/1.52 thf(sy_c_List_Ofold, type, fold: (!> [A:$tType,B:$tType]: (((A > (B > B)) > ((list @ A) > (B > B)))))).
% 2.71/1.52 thf(sy_c_List_Oinsert, type, insert: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.71/1.52 thf(sy_c_List_Olast, type, last: (!> [A:$tType]: (((list @ A) > A)))).
% 2.71/1.52 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.71/1.52 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.71/1.52 thf(sy_c_List_Olist_Ocase__list, type, case_list: (!> [B:$tType,A:$tType]: ((B > ((A > ((list @ A) > B)) > ((list @ A) > B)))))).
% 2.71/1.52 thf(sy_c_List_Olist_Ohd, type, hd: (!> [A:$tType]: (((list @ A) > A)))).
% 2.71/1.52 thf(sy_c_List_Olist_Omap, type, map: (!> [A:$tType,Aa:$tType]: (((A > Aa) > ((list @ A) > (list @ Aa)))))).
% 2.71/1.52 thf(sy_c_List_Olist_Otl, type, tl: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.71/1.52 thf(sy_c_List_Olist__ex1, type, list_ex1: (!> [A:$tType]: (((A > $o) > ((list @ A) > $o))))).
% 2.71/1.52 thf(sy_c_List_Olistrelp, type, listrelp: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((list @ A) > ((list @ B) > $o)))))).
% 2.71/1.52 thf(sy_c_List_Omap__tailrec, type, map_tailrec: (!> [A:$tType,B:$tType]: (((A > B) > ((list @ A) > (list @ B)))))).
% 2.71/1.52 thf(sy_c_List_Omap__tailrec__rev, type, map_tailrec_rev: (!> [A:$tType,B:$tType]: (((A > B) > ((list @ A) > ((list @ B) > (list @ B))))))).
% 2.71/1.52 thf(sy_c_List_Omaps, type, maps: (!> [A:$tType,B:$tType]: (((A > (list @ B)) > ((list @ A) > (list @ B)))))).
% 2.71/1.52 thf(sy_c_List_Omember, type, member: (!> [A:$tType]: (((list @ A) > (A > $o))))).
% 2.71/1.52 thf(sy_c_List_Oord_Olexordp__eq, type, lexordp_eq: (!> [A:$tType]: (((A > (A > $o)) > ((list @ A) > ((list @ A) > $o)))))).
% 2.71/1.52 thf(sy_c_List_Oord__class_Olexordp, type, ord_lexordp: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.71/1.52 thf(sy_c_List_Oord__class_Olexordp__eq, type, ord_lexordp_eq: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.71/1.52 thf(sy_c_List_Oproduct__lists, type, product_lists: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 2.71/1.52 thf(sy_c_List_Oremdups__adj, type, remdups_adj: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.71/1.52 thf(sy_c_List_Oreplicate, type, replicate: (!> [A:$tType]: ((nat > (A > (list @ A)))))).
% 2.71/1.52 thf(sy_c_List_Orev, type, rev: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.71/1.52 thf(sy_c_List_Orotate1, type, rotate1: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.71/1.52 thf(sy_c_List_Osplice, type, splice: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.71/1.52 thf(sy_c_List_Osublists, type, sublists: (!> [A:$tType]: (((list @ A) > (list @ (list @ A)))))).
% 2.71/1.52 thf(sy_c_List_Ounion, type, union: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.71/1.52 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.71/1.52 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.71/1.52 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.71/1.52 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ocycle, type, stream317748790_cycle: (!> [A:$tType]: (((list @ A) > (stream170649215stream @ A))))).
% 2.71/1.52 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Oflat, type, stream942386729e_flat: (!> [A:$tType]: (((stream170649215stream @ (list @ A)) > (stream170649215stream @ A))))).
% 2.71/1.52 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osdrop__while, type, stream1195056575_while: (!> [A:$tType]: (((A > $o) > ((stream170649215stream @ A) > (stream170649215stream @ A)))))).
% 2.71/1.52 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Oshift, type, stream1035003186_shift: (!> [A:$tType]: (((list @ A) > ((stream170649215stream @ A) > (stream170649215stream @ A)))))).
% 2.71/1.52 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osmember, type, stream1586597341member: (!> [A:$tType]: ((A > ((stream170649215stream @ A) > $o))))).
% 2.71/1.52 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_OSCons, type, stream641971652_SCons: (!> [A:$tType]: ((A > ((stream170649215stream @ A) > (stream170649215stream @ A)))))).
% 2.71/1.52 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Ocase__stream, type, stream1342653232stream: (!> [A:$tType,B:$tType]: (((A > ((stream170649215stream @ A) > B)) > ((stream170649215stream @ A) > B))))).
% 2.71/1.52 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Oshd, type, stream_Mirabelle_shd: (!> [A:$tType]: (((stream170649215stream @ A) > A)))).
% 2.71/1.52 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Osmap, type, stream2128578057e_smap: (!> [A:$tType,Aa:$tType]: (((A > Aa) > ((stream170649215stream @ A) > (stream170649215stream @ Aa)))))).
% 2.71/1.52 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Ostl, type, stream_Mirabelle_stl: (!> [A:$tType]: (((stream170649215stream @ A) > (stream170649215stream @ A))))).
% 2.71/1.52 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostreams, type, stream2015131171treams: (!> [A:$tType]: (((set @ A) > (set @ (stream170649215stream @ A)))))).
% 2.71/1.52 thf(sy_c_member, type, member2: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.71/1.52 thf(sy_v_ws, type, ws: (stream170649215stream @ (list @ a))).
% 2.71/1.52 thf(fact_0_shift__left__inj, axiom, (! [A:$tType,Xs:(list @ A),S1:(stream170649215stream @ A),S2:(stream170649215stream @ A)]: ((((((stream1035003186_shift @ A) @ Xs) @ S1) = (((stream1035003186_shift @ A) @ Xs) @ S2)) = (S1 = S2))))).
% 2.71/1.52 thf(fact_1_shift_Osimps_I1_J, axiom, (! [A:$tType,S:(stream170649215stream @ A)]: (((((stream1035003186_shift @ A) @ (nil @ A)) @ S) = S)))).
% 2.71/1.52 thf(fact_2_stream_Oexpand, axiom, (! [A:$tType,Stream:(stream170649215stream @ A),Stream2:(stream170649215stream @ A)]: ((((((stream_Mirabelle_shd @ A) @ Stream) = ((stream_Mirabelle_shd @ A) @ Stream2)) & (((stream_Mirabelle_stl @ A) @ Stream) = ((stream_Mirabelle_stl @ A) @ Stream2))) => (Stream = Stream2))))).
% 2.71/1.52 thf(fact_3_stream_Ocoinduct, axiom, (! [A:$tType,R:((stream170649215stream @ A) > ((stream170649215stream @ A) > $o)),Stream:(stream170649215stream @ A),Stream2:(stream170649215stream @ A)]: ((((R @ Stream) @ Stream2) => ((! [Stream3:(stream170649215stream @ A),Stream4:(stream170649215stream @ A)]: ((((R @ Stream3) @ Stream4) => ((((stream_Mirabelle_shd @ A) @ Stream3) = ((stream_Mirabelle_shd @ A) @ Stream4)) & ((R @ ((stream_Mirabelle_stl @ A) @ Stream3)) @ ((stream_Mirabelle_stl @ A) @ Stream4)))))) => (Stream = Stream2)))))).
% 2.71/1.52 thf(fact_4_stream_Ocoinduct__strong, axiom, (! [A:$tType,R:((stream170649215stream @ A) > ((stream170649215stream @ A) > $o)),Stream:(stream170649215stream @ A),Stream2:(stream170649215stream @ A)]: ((((R @ Stream) @ Stream2) => ((! [Stream3:(stream170649215stream @ A),Stream4:(stream170649215stream @ A)]: ((((R @ Stream3) @ Stream4) => ((((stream_Mirabelle_shd @ A) @ Stream3) = ((stream_Mirabelle_shd @ A) @ Stream4)) & (((R @ ((stream_Mirabelle_stl @ A) @ Stream3)) @ ((stream_Mirabelle_stl @ A) @ Stream4)) | (((stream_Mirabelle_stl @ A) @ Stream3) = ((stream_Mirabelle_stl @ A) @ Stream4))))))) => (Stream = Stream2)))))).
% 2.71/1.52 thf(fact_5_flat__Stream, axiom, (! [A:$tType,Xs:(list @ A),Ws:(stream170649215stream @ (list @ A))]: (((Xs != (nil @ A)) => (((stream942386729e_flat @ A) @ (((stream641971652_SCons @ (list @ A)) @ Xs) @ Ws)) = (((stream1035003186_shift @ A) @ Xs) @ ((stream942386729e_flat @ A) @ Ws))))))).
% 2.71/1.52 thf(fact_6_shift__simps_I1_J, axiom, (! [A:$tType,Xs:(list @ A),S:(stream170649215stream @ A)]: ((((Xs = (nil @ A)) => (((stream_Mirabelle_shd @ A) @ (((stream1035003186_shift @ A) @ Xs) @ S)) = ((stream_Mirabelle_shd @ A) @ S))) & ((Xs != (nil @ A)) => (((stream_Mirabelle_shd @ A) @ (((stream1035003186_shift @ A) @ Xs) @ S)) = ((hd @ A) @ Xs))))))).
% 2.71/1.52 thf(fact_7_flat_Osimps_I1_J, axiom, (! [A:$tType,Ws:(stream170649215stream @ (list @ A))]: ((((stream_Mirabelle_shd @ A) @ ((stream942386729e_flat @ A) @ Ws)) = ((hd @ A) @ ((stream_Mirabelle_shd @ (list @ A)) @ Ws)))))).
% 2.71/1.52 thf(fact_8_stream_Ocase__eq__if, axiom, (! [B:$tType,A:$tType]: ((((stream1342653232stream @ A) @ B) = (^ [F:(A > ((stream170649215stream @ A) > B)),Stream5:(stream170649215stream @ A)]: (((F @ ((stream_Mirabelle_shd @ A) @ Stream5)) @ ((stream_Mirabelle_stl @ A) @ Stream5)))))))).
% 2.71/1.52 thf(fact_9_shift__simps_I2_J, axiom, (! [A:$tType,Xs:(list @ A),S:(stream170649215stream @ A)]: ((((Xs = (nil @ A)) => (((stream_Mirabelle_stl @ A) @ (((stream1035003186_shift @ A) @ Xs) @ S)) = ((stream_Mirabelle_stl @ A) @ S))) & ((Xs != (nil @ A)) => (((stream_Mirabelle_stl @ A) @ (((stream1035003186_shift @ A) @ Xs) @ S)) = (((stream1035003186_shift @ A) @ ((tl @ A) @ Xs)) @ S))))))).
% 2.71/1.52 thf(fact_10_sdrop__while_Osimps, axiom, (! [A:$tType]: (((stream1195056575_while @ A) = (^ [P:(A > $o),S3:(stream170649215stream @ A)]: (((((if @ (stream170649215stream @ A)) @ (P @ ((stream_Mirabelle_shd @ A) @ S3))) @ (((stream1195056575_while @ A) @ P) @ ((stream_Mirabelle_stl @ A) @ S3))) @ S3))))))).
% 2.71/1.52 thf(fact_11_flat_Osimps_I2_J, axiom, (! [A:$tType,Ws:(stream170649215stream @ (list @ A))]: ((((stream_Mirabelle_stl @ A) @ ((stream942386729e_flat @ A) @ Ws)) = ((stream942386729e_flat @ A) @ ((((if @ (stream170649215stream @ (list @ A))) @ (((tl @ A) @ ((stream_Mirabelle_shd @ (list @ A)) @ Ws)) = (nil @ A))) @ ((stream_Mirabelle_stl @ (list @ A)) @ Ws)) @ (((stream641971652_SCons @ (list @ A)) @ ((tl @ A) @ ((stream_Mirabelle_shd @ (list @ A)) @ Ws))) @ ((stream_Mirabelle_stl @ (list @ A)) @ Ws)))))))).
% 2.71/1.52 thf(fact_12_cycle__decomp, axiom, (! [A:$tType,U:(list @ A)]: (((U != (nil @ A)) => (((stream317748790_cycle @ A) @ U) = (((stream1035003186_shift @ A) @ U) @ ((stream317748790_cycle @ A) @ U))))))).
% 2.71/1.52 thf(fact_13_stream_Ocollapse, axiom, (! [A:$tType,Stream:(stream170649215stream @ A)]: (((((stream641971652_SCons @ A) @ ((stream_Mirabelle_shd @ A) @ Stream)) @ ((stream_Mirabelle_stl @ A) @ Stream)) = Stream)))).
% 2.71/1.52 thf(fact_14_streamsE, axiom, (! [A:$tType,S:(stream170649215stream @ A),A2:(set @ A)]: (((((member2 @ (stream170649215stream @ A)) @ S) @ ((stream2015131171treams @ A) @ A2)) => (~ (((((member2 @ A) @ ((stream_Mirabelle_shd @ A) @ S)) @ A2) => (~ ((((member2 @ (stream170649215stream @ A)) @ ((stream_Mirabelle_stl @ A) @ S)) @ ((stream2015131171treams @ A) @ A2))))))))))).
% 2.71/1.52 thf(fact_15_in__streams, axiom, (! [A:$tType,S:(stream170649215stream @ A),S4:(set @ A)]: (((((member2 @ (stream170649215stream @ A)) @ ((stream_Mirabelle_stl @ A) @ S)) @ ((stream2015131171treams @ A) @ S4)) => ((((member2 @ A) @ ((stream_Mirabelle_shd @ A) @ S)) @ S4) => (((member2 @ (stream170649215stream @ A)) @ S) @ ((stream2015131171treams @ A) @ S4))))))).
% 2.71/1.52 thf(fact_16_stream_Oinject, axiom, (! [A:$tType,X1:A,X2:(stream170649215stream @ A),Y1:A,Y2:(stream170649215stream @ A)]: ((((((stream641971652_SCons @ A) @ X1) @ X2) = (((stream641971652_SCons @ A) @ Y1) @ Y2)) = ((X1 = Y1) & (X2 = Y2)))))).
% 2.71/1.52 thf(fact_17_list_Oexpand, axiom, (! [A:$tType,List:(list @ A),List2:(list @ A)]: ((((List = (nil @ A)) = (List2 = (nil @ A))) => (((List != (nil @ A)) => ((List2 != (nil @ A)) => ((((hd @ A) @ List) = ((hd @ A) @ List2)) & (((tl @ A) @ List) = ((tl @ A) @ List2))))) => (List = List2)))))).
% 2.71/1.52 thf(fact_18_stream_Ocase, axiom, (! [B:$tType,A:$tType,F2:(A > ((stream170649215stream @ A) > B)),X1:A,X2:(stream170649215stream @ A)]: ((((((stream1342653232stream @ A) @ B) @ F2) @ (((stream641971652_SCons @ A) @ X1) @ X2)) = ((F2 @ X1) @ X2))))).
% 2.71/1.52 thf(fact_19_streams_Ocases, axiom, (! [A:$tType,A3:(stream170649215stream @ A),A2:(set @ A)]: (((((member2 @ (stream170649215stream @ A)) @ A3) @ ((stream2015131171treams @ A) @ A2)) => (~ ((! [A4:A,S5:(stream170649215stream @ A)]: (((A3 = (((stream641971652_SCons @ A) @ A4) @ S5)) => ((((member2 @ A) @ A4) @ A2) => (~ ((((member2 @ (stream170649215stream @ A)) @ S5) @ ((stream2015131171treams @ A) @ A2)))))))))))))).
% 2.71/1.52 thf(fact_20_streams_Osimps, axiom, (! [A:$tType,A3:(stream170649215stream @ A),A2:(set @ A)]: (((((member2 @ (stream170649215stream @ A)) @ A3) @ ((stream2015131171treams @ A) @ A2)) = (? [A5:A,S3:(stream170649215stream @ A)]: (((A3 = (((stream641971652_SCons @ A) @ A5) @ S3)) & ((((member2 @ A) @ A5) @ A2) & (((member2 @ (stream170649215stream @ A)) @ S3) @ ((stream2015131171treams @ A) @ A2)))))))))).
% 2.71/1.52 thf(fact_21_stream_Oexhaust, axiom, (! [A:$tType,Y:(stream170649215stream @ A)]: ((~ ((! [X12:A,X22:(stream170649215stream @ A)]: ((Y != (((stream641971652_SCons @ A) @ X12) @ X22))))))))).
% 2.71/1.52 thf(fact_22_streams__Stream, axiom, (! [A:$tType,X:A,S:(stream170649215stream @ A),A2:(set @ A)]: (((((member2 @ (stream170649215stream @ A)) @ (((stream641971652_SCons @ A) @ X) @ S)) @ ((stream2015131171treams @ A) @ A2)) = ((((member2 @ A) @ X) @ A2) & (((member2 @ (stream170649215stream @ A)) @ S) @ ((stream2015131171treams @ A) @ A2))))))).
% 2.71/1.52 thf(fact_23_streams_Ocoinduct, axiom, (! [A:$tType,X3:((stream170649215stream @ A) > $o),X:(stream170649215stream @ A),A2:(set @ A)]: (((X3 @ X) => ((! [X4:(stream170649215stream @ A)]: (((X3 @ X4) => (? [A6:A,S6:(stream170649215stream @ A)]: (((X4 = (((stream641971652_SCons @ A) @ A6) @ S6)) & ((((member2 @ A) @ A6) @ A2) & ((X3 @ S6) | (((member2 @ (stream170649215stream @ A)) @ S6) @ ((stream2015131171treams @ A) @ A2)))))))))) => (((member2 @ (stream170649215stream @ A)) @ X) @ ((stream2015131171treams @ A) @ A2))))))).
% 2.71/1.52 thf(fact_24_sdrop__while__SCons, axiom, (! [A:$tType,P2:(A > $o),A3:A,S:(stream170649215stream @ A)]: ((((P2 @ A3) => ((((stream1195056575_while @ A) @ P2) @ (((stream641971652_SCons @ A) @ A3) @ S)) = (((stream1195056575_while @ A) @ P2) @ S))) & ((~ ((P2 @ A3))) => ((((stream1195056575_while @ A) @ P2) @ (((stream641971652_SCons @ A) @ A3) @ S)) = (((stream641971652_SCons @ A) @ A3) @ S))))))).
% 2.71/1.52 thf(fact_25_list_Osel_I2_J, axiom, (! [A:$tType]: ((((tl @ A) @ (nil @ A)) = (nil @ A))))).
% 2.71/1.52 thf(fact_26_cycle_Osimps_I1_J, axiom, (! [A:$tType,Xs:(list @ A)]: ((((stream_Mirabelle_shd @ A) @ ((stream317748790_cycle @ A) @ Xs)) = ((hd @ A) @ Xs))))).
% 2.71/1.52 thf(fact_27_flat_Ocode, axiom, (! [A:$tType]: (((stream942386729e_flat @ A) = (^ [Ws2:(stream170649215stream @ (list @ A))]: ((((stream641971652_SCons @ A) @ ((hd @ A) @ ((stream_Mirabelle_shd @ (list @ A)) @ Ws2))) @ ((stream942386729e_flat @ A) @ ((((if @ (stream170649215stream @ (list @ A))) @ (((tl @ A) @ ((stream_Mirabelle_shd @ (list @ A)) @ Ws2)) = (nil @ A))) @ ((stream_Mirabelle_stl @ (list @ A)) @ Ws2)) @ (((stream641971652_SCons @ (list @ A)) @ ((tl @ A) @ ((stream_Mirabelle_shd @ (list @ A)) @ Ws2))) @ ((stream_Mirabelle_stl @ (list @ A)) @ Ws2))))))))))).
% 2.71/1.52 thf(fact_28_stream_Osel_I2_J, axiom, (! [A:$tType,X1:A,X2:(stream170649215stream @ A)]: ((((stream_Mirabelle_stl @ A) @ (((stream641971652_SCons @ A) @ X1) @ X2)) = X2)))).
% 2.71/1.52 thf(fact_29_stream_Osel_I1_J, axiom, (! [A:$tType,X1:A,X2:(stream170649215stream @ A)]: ((((stream_Mirabelle_shd @ A) @ (((stream641971652_SCons @ A) @ X1) @ X2)) = X1)))).
% 2.71/1.52 thf(fact_30_stream_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P2:(B > $o),F2:(A > ((stream170649215stream @ A) > B)),Stream:(stream170649215stream @ A)]: (((P2 @ ((((stream1342653232stream @ A) @ B) @ F2) @ Stream)) = (~ (((Stream = (((stream641971652_SCons @ A) @ ((stream_Mirabelle_shd @ A) @ Stream)) @ ((stream_Mirabelle_stl @ A) @ Stream))) & (~ ((P2 @ ((F2 @ ((stream_Mirabelle_shd @ A) @ Stream)) @ ((stream_Mirabelle_stl @ A) @ Stream)))))))))))).
% 2.71/1.52 thf(fact_31_stream_Osplit__sel, axiom, (! [B:$tType,A:$tType,P2:(B > $o),F2:(A > ((stream170649215stream @ A) > B)),Stream:(stream170649215stream @ A)]: (((P2 @ ((((stream1342653232stream @ A) @ B) @ F2) @ Stream)) = ((Stream = (((stream641971652_SCons @ A) @ ((stream_Mirabelle_shd @ A) @ Stream)) @ ((stream_Mirabelle_stl @ A) @ Stream))) => (P2 @ ((F2 @ ((stream_Mirabelle_shd @ A) @ Stream)) @ ((stream_Mirabelle_stl @ A) @ Stream)))))))).
% 2.71/1.52 thf(fact_32_streams__stl, axiom, (! [A:$tType,S:(stream170649215stream @ A),A2:(set @ A)]: (((((member2 @ (stream170649215stream @ A)) @ S) @ ((stream2015131171treams @ A) @ A2)) => (((member2 @ (stream170649215stream @ A)) @ ((stream_Mirabelle_stl @ A) @ S)) @ ((stream2015131171treams @ A) @ A2)))))).
% 2.71/1.52 thf(fact_33_streams__shd, axiom, (! [A:$tType,S:(stream170649215stream @ A),A2:(set @ A)]: (((((member2 @ (stream170649215stream @ A)) @ S) @ ((stream2015131171treams @ A) @ A2)) => (((member2 @ A) @ ((stream_Mirabelle_shd @ A) @ S)) @ A2))))).
% 2.71/1.52 thf(fact_34_stream_Oexhaust__sel, axiom, (! [A:$tType,Stream:(stream170649215stream @ A)]: ((Stream = (((stream641971652_SCons @ A) @ ((stream_Mirabelle_shd @ A) @ Stream)) @ ((stream_Mirabelle_stl @ A) @ Stream)))))).
% 2.71/1.52 thf(fact_35_smember__code, axiom, (! [A:$tType,X:A,Y:A,S:(stream170649215stream @ A)]: (((((stream1586597341member @ A) @ X) @ (((stream641971652_SCons @ A) @ Y) @ S)) = ((X != Y) => (((stream1586597341member @ A) @ X) @ S)))))).
% 2.71/1.52 thf(fact_36_flat__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ws:(stream170649215stream @ (list @ A))]: ((((stream942386729e_flat @ A) @ (((stream641971652_SCons @ (list @ A)) @ (((cons @ A) @ X) @ Xs)) @ Ws)) = (((stream641971652_SCons @ A) @ X) @ ((stream942386729e_flat @ A) @ ((((if @ (stream170649215stream @ (list @ A))) @ (Xs = (nil @ A))) @ Ws) @ (((stream641971652_SCons @ (list @ A)) @ Xs) @ Ws)))))))).
% 2.71/1.52 thf(fact_37_list_Ocase__eq__if, axiom, (! [A:$tType,B:$tType]: ((((case_list @ B) @ A) = (^ [F1:B,F22:(A > ((list @ A) > B)),List3:(list @ A)]: (((((if @ B) @ (List3 = (nil @ A))) @ F1) @ ((F22 @ ((hd @ A) @ List3)) @ ((tl @ A) @ List3))))))))).
% 2.71/1.52 thf(fact_38_list__ex1__simps_I1_J, axiom, (! [A:$tType,P2:(A > $o)]: ((~ ((((list_ex1 @ A) @ P2) @ (nil @ A))))))).
% 2.71/1.52 thf(fact_39_hd__Cons__tl, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((((cons @ A) @ ((hd @ A) @ Xs)) @ ((tl @ A) @ Xs)) = Xs))))).
% 2.71/1.52 thf(fact_40_list_Ocollapse, axiom, (! [A:$tType,List:(list @ A)]: (((List != (nil @ A)) => ((((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List)) = List))))).
% 2.71/1.52 thf(fact_41_smap__ctr, axiom, (! [B:$tType,A:$tType,F2:(B > A),S:(stream170649215stream @ B),X:A,S7:(stream170649215stream @ A)]: (((((((stream2128578057e_smap @ B) @ A) @ F2) @ S) = (((stream641971652_SCons @ A) @ X) @ S7)) = (((F2 @ ((stream_Mirabelle_shd @ B) @ S)) = X) & (((((stream2128578057e_smap @ B) @ A) @ F2) @ ((stream_Mirabelle_stl @ B) @ S)) = S7)))))).
% 2.71/1.52 thf(fact_42_bind__simps_I1_J, axiom, (! [B:$tType,A:$tType,F2:(B > (list @ A))]: ((((((bind @ B) @ A) @ (nil @ B)) @ F2) = (nil @ A))))).
% 2.71/1.52 thf(fact_43_list_Oexhaust__sel, axiom, (! [A:$tType,List:(list @ A)]: (((List != (nil @ A)) => (List = (((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List))))))).
% 2.71/1.52 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P2:(A > $o)]: (((((member2 @ A) @ A3) @ ((collect @ A) @ P2)) = (P2 @ A3))))).
% 2.71/1.52 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X5:A]: ((((member2 @ A) @ X5) @ A2)))) = A2)))).
% 2.71/1.52 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P2:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P2 @ X4) = (Q @ X4)))) => (((collect @ A) @ P2) = ((collect @ A) @ Q)))))).
% 2.71/1.52 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F2:(A > B),G:(A > B)]: (((! [X4:A]: (((F2 @ X4) = (G @ X4)))) => (F2 = G))))).
% 2.71/1.52 thf(fact_48_member__rec_I2_J, axiom, (! [A:$tType,Y:A]: ((~ ((((member @ A) @ (nil @ A)) @ Y)))))).
% 2.71/1.52 thf(fact_49_list_Oinject, axiom, (! [A:$tType,X21:A,X222:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X222) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X222 = Y22)))))).
% 2.71/1.52 thf(fact_50_stream_Omap__sel_I2_J, axiom, (! [B:$tType,A:$tType,F2:(A > B),A3:(stream170649215stream @ A)]: ((((stream_Mirabelle_stl @ B) @ ((((stream2128578057e_smap @ A) @ B) @ F2) @ A3)) = ((((stream2128578057e_smap @ A) @ B) @ F2) @ ((stream_Mirabelle_stl @ A) @ A3)))))).
% 2.71/1.52 thf(fact_51_stream_Omap__sel_I1_J, axiom, (! [B:$tType,A:$tType,F2:(A > B),A3:(stream170649215stream @ A)]: ((((stream_Mirabelle_shd @ B) @ ((((stream2128578057e_smap @ A) @ B) @ F2) @ A3)) = (F2 @ ((stream_Mirabelle_shd @ A) @ A3)))))).
% 2.71/1.52 thf(fact_52_list_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F12:B,F23:(A > ((list @ A) > B)),X21:A,X222:(list @ A)]: (((((((case_list @ B) @ A) @ F12) @ F23) @ (((cons @ A) @ X21) @ X222)) = ((F23 @ X21) @ X222))))).
% 2.71/1.52 thf(fact_53_member__rec_I1_J, axiom, (! [A:$tType,X:A,Xs:(list @ A),Y:A]: (((((member @ A) @ (((cons @ A) @ X) @ Xs)) @ Y) = ((X = Y) | (((member @ A) @ Xs) @ Y)))))).
% 2.71/1.52 thf(fact_54_not__Cons__self2, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((cons @ A) @ X) @ Xs) != Xs)))).
% 2.71/1.52 thf(fact_55_transpose_Ocases, axiom, (! [A:$tType,X:(list @ (list @ A))]: (((X != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X4:A,Xs2:(list @ A),Xss:(list @ (list @ A))]: ((X != (((cons @ (list @ A)) @ (((cons @ A) @ X4) @ Xs2)) @ Xss))))))))))).
% 2.71/1.52 thf(fact_56_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X222:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X222))))).
% 2.71/1.52 thf(fact_57_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X222:(list @ A)]: (((List = (((cons @ A) @ X21) @ X222)) => (List != (nil @ A)))))).
% 2.71/1.52 thf(fact_58_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X212:A,X223:(list @ A)]: ((Y != (((cons @ A) @ X212) @ X223)))))))))).
% 2.71/1.52 thf(fact_59_list_Oinducts, axiom, (! [A:$tType,P2:((list @ A) > $o),List:(list @ A)]: (((P2 @ (nil @ A)) => ((! [X12:A,X22:(list @ A)]: (((P2 @ X22) => (P2 @ (((cons @ A) @ X12) @ X22))))) => (P2 @ List)))))).
% 2.71/1.52 thf(fact_60_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y3:A,Ys:(list @ A)]: ((Xs = (((cons @ A) @ Y3) @ Ys)))))))).
% 2.71/1.52 thf(fact_61_list__induct2_H, axiom, (! [A:$tType,B:$tType,P2:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys2:(list @ B)]: ((((P2 @ (nil @ A)) @ (nil @ B)) => ((! [X4:A,Xs2:(list @ A)]: (((P2 @ (((cons @ A) @ X4) @ Xs2)) @ (nil @ B)))) => ((! [Y4:B,Ys3:(list @ B)]: (((P2 @ (nil @ A)) @ (((cons @ B) @ Y4) @ Ys3)))) => ((! [X4:A,Xs2:(list @ A),Y4:B,Ys3:(list @ B)]: ((((P2 @ Xs2) @ Ys3) => ((P2 @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ B) @ Y4) @ Ys3))))) => ((P2 @ Xs) @ Ys2)))))))).
% 2.71/1.52 thf(fact_62_splice_Oinduct, axiom, (! [A:$tType,P2:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X12:(list @ A)]: (((P2 @ (nil @ A)) @ X12))) => ((! [V:A,Va:(list @ A)]: (((P2 @ (((cons @ A) @ V) @ Va)) @ (nil @ A)))) => ((! [X4:A,Xs2:(list @ A),Y4:A,Ys3:(list @ A)]: ((((P2 @ Xs2) @ Ys3) => ((P2 @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys3))))) => ((P2 @ A0) @ A1))))))).
% 2.71/1.52 thf(fact_63_remdups__adj_Ocases, axiom, (! [A:$tType,X:(list @ A)]: (((X != (nil @ A)) => ((! [X4:A]: ((X != (((cons @ A) @ X4) @ (nil @ A))))) => (~ ((! [X4:A,Y4:A,Xs2:(list @ A)]: ((X != (((cons @ A) @ X4) @ (((cons @ A) @ Y4) @ Xs2)))))))))))).
% 2.71/1.52 thf(fact_64_remdups__adj_Oinduct, axiom, (! [A:$tType,P2:((list @ A) > $o),A0:(list @ A)]: (((P2 @ (nil @ A)) => ((! [X4:A]: ((P2 @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Y4:A,Xs2:(list @ A)]: ((((X4 = Y4) => (P2 @ (((cons @ A) @ X4) @ Xs2))) => (((X4 != Y4) => (P2 @ (((cons @ A) @ Y4) @ Xs2))) => (P2 @ (((cons @ A) @ X4) @ (((cons @ A) @ Y4) @ Xs2))))))) => (P2 @ A0))))))).
% 2.71/1.52 thf(fact_65_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P2:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X4:A]: ((P2 @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P2 @ Xs2) => (P2 @ (((cons @ A) @ X4) @ Xs2)))))) => (P2 @ Xs))))))).
% 2.71/1.52 thf(fact_66_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P2:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F3:(A > B),X12:(list @ B)]: ((((P2 @ F3) @ (nil @ A)) @ X12))) => ((! [F3:(A > B),A4:A,As:(list @ A),Bs:(list @ B)]: (((((P2 @ F3) @ As) @ (((cons @ B) @ (F3 @ A4)) @ Bs)) => (((P2 @ F3) @ (((cons @ A) @ A4) @ As)) @ Bs)))) => (((P2 @ A0) @ A1) @ A22)))))).
% 2.71/1.52 thf(fact_67_list_Osel_I3_J, axiom, (! [A:$tType,X21:A,X222:(list @ A)]: ((((tl @ A) @ (((cons @ A) @ X21) @ X222)) = X222)))).
% 2.71/1.52 thf(fact_68_list_Osel_I1_J, axiom, (! [A:$tType,X21:A,X222:(list @ A)]: ((((hd @ A) @ (((cons @ A) @ X21) @ X222)) = X21)))).
% 2.71/1.52 thf(fact_69_stream_Omap, axiom, (! [B:$tType,A:$tType,F2:(A > B),X1:A,X2:(stream170649215stream @ A)]: ((((((stream2128578057e_smap @ A) @ B) @ F2) @ (((stream641971652_SCons @ A) @ X1) @ X2)) = (((stream641971652_SCons @ B) @ (F2 @ X1)) @ ((((stream2128578057e_smap @ A) @ B) @ F2) @ X2)))))).
% 2.71/1.52 thf(fact_70_smap__streams, axiom, (! [A:$tType,B:$tType,S:(stream170649215stream @ A),A2:(set @ A),F2:(A > B),B2:(set @ B)]: (((((member2 @ (stream170649215stream @ A)) @ S) @ ((stream2015131171treams @ A) @ A2)) => ((! [X4:A]: (((((member2 @ A) @ X4) @ A2) => (((member2 @ B) @ (F2 @ X4)) @ B2)))) => (((member2 @ (stream170649215stream @ B)) @ ((((stream2128578057e_smap @ A) @ B) @ F2) @ S)) @ ((stream2015131171treams @ B) @ B2))))))).
% 2.71/1.52 thf(fact_71_list_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F12:B,F23:(A > ((list @ A) > B))]: (((((((case_list @ B) @ A) @ F12) @ F23) @ (nil @ A)) = F12)))).
% 2.71/1.52 thf(fact_72_list_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P2:(B > $o),F12:B,F23:(A > ((list @ A) > B)),List:(list @ A)]: (((P2 @ (((((case_list @ B) @ A) @ F12) @ F23) @ List)) = (~ ((((List = (nil @ A)) & (~ ((P2 @ F12)))) | ((List = (((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List))) & (~ ((P2 @ ((F23 @ ((hd @ A) @ List)) @ ((tl @ A) @ List))))))))))))).
% 2.71/1.52 thf(fact_73_list_Osplit__sel, axiom, (! [B:$tType,A:$tType,P2:(B > $o),F12:B,F23:(A > ((list @ A) > B)),List:(list @ A)]: (((P2 @ (((((case_list @ B) @ A) @ F12) @ F23) @ List)) = (((List = (nil @ A)) => (P2 @ F12)) & ((List = (((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List))) => (P2 @ ((F23 @ ((hd @ A) @ List)) @ ((tl @ A) @ List))))))))).
% 2.71/1.52 thf(fact_74_tl__Nil, axiom, (! [A:$tType,Xs:(list @ A)]: (((((tl @ A) @ Xs) = (nil @ A)) = ((Xs = (nil @ A)) | (? [X5:A]: ((Xs = (((cons @ A) @ X5) @ (nil @ A)))))))))).
% 2.71/1.52 thf(fact_75_Nil__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((nil @ A) = ((tl @ A) @ Xs)) = ((Xs = (nil @ A)) | (? [X5:A]: ((Xs = (((cons @ A) @ X5) @ (nil @ A)))))))))).
% 2.71/1.52 thf(fact_76_shift_Osimps_I2_J, axiom, (! [A:$tType,X:A,Xs:(list @ A),S:(stream170649215stream @ A)]: (((((stream1035003186_shift @ A) @ (((cons @ A) @ X) @ Xs)) @ S) = (((stream641971652_SCons @ A) @ X) @ (((stream1035003186_shift @ A) @ Xs) @ S)))))).
% 2.71/1.52 thf(fact_77_cycle__rotated, axiom, (! [A:$tType,V2:(list @ A),U:(list @ A),S:(stream170649215stream @ A)]: (((V2 != (nil @ A)) => ((((stream317748790_cycle @ A) @ U) = (((stream1035003186_shift @ A) @ V2) @ S)) => (((stream317748790_cycle @ A) @ (((append @ A) @ ((tl @ A) @ U)) @ (((cons @ A) @ ((hd @ A) @ U)) @ (nil @ A)))) = (((stream1035003186_shift @ A) @ ((tl @ A) @ V2)) @ S))))))).
% 2.71/1.52 thf(fact_78_cycle_Osimps_I2_J, axiom, (! [A:$tType,Xs:(list @ A)]: ((((stream_Mirabelle_stl @ A) @ ((stream317748790_cycle @ A) @ Xs)) = ((stream317748790_cycle @ A) @ (((append @ A) @ ((tl @ A) @ Xs)) @ (((cons @ A) @ ((hd @ A) @ Xs)) @ (nil @ A)))))))).
% 2.71/1.52 thf(fact_79_cycle_Ocode, axiom, (! [A:$tType]: (((stream317748790_cycle @ A) = (^ [Xs3:(list @ A)]: ((((stream641971652_SCons @ A) @ ((hd @ A) @ Xs3)) @ ((stream317748790_cycle @ A) @ (((append @ A) @ ((tl @ A) @ Xs3)) @ (((cons @ A) @ ((hd @ A) @ Xs3)) @ (nil @ A))))))))))).
% 2.71/1.52 thf(fact_80_insert__Nil, axiom, (! [A:$tType,X:A]: (((((insert @ A) @ X) @ (nil @ A)) = (((cons @ A) @ X) @ (nil @ A)))))).
% 2.71/1.52 thf(fact_81_cycle__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((stream317748790_cycle @ A) @ (((cons @ A) @ X) @ Xs)) = (((stream641971652_SCons @ A) @ X) @ ((stream317748790_cycle @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))))))))).
% 2.71/1.52 thf(fact_82_ord_Olexordp__eq__simps_I3_J, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Xs:(list @ A)]: ((~ (((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (nil @ A))))))).
% 2.71/1.52 thf(fact_83_map__tailrec__rev_Oelims, axiom, (! [A:$tType,B:$tType,X:(A > B),Xa:(list @ A),Xb:(list @ B),Y:(list @ B)]: ((((((((map_tailrec_rev @ A) @ B) @ X) @ Xa) @ Xb) = Y) => (((Xa = (nil @ A)) => (Y != Xb)) => (~ ((! [A4:A,As:(list @ A)]: (((Xa = (((cons @ A) @ A4) @ As)) => (Y != (((((map_tailrec_rev @ A) @ B) @ X) @ As) @ (((cons @ B) @ (X @ A4)) @ Xb))))))))))))).
% 2.71/1.52 thf(fact_84_splice_Oelims, axiom, (! [A:$tType,X:(list @ A),Xa:(list @ A),Y:(list @ A)]: ((((((splice @ A) @ X) @ Xa) = Y) => (((X = (nil @ A)) => (Y != Xa)) => ((! [V:A,Va:(list @ A)]: (((X = (((cons @ A) @ V) @ Va)) => ((Xa = (nil @ A)) => (Y != (((cons @ A) @ V) @ Va)))))) => (~ ((! [X4:A,Xs2:(list @ A)]: (((X = (((cons @ A) @ X4) @ Xs2)) => (! [Y4:A,Ys3:(list @ A)]: (((Xa = (((cons @ A) @ Y4) @ Ys3)) => (Y != (((cons @ A) @ X4) @ (((cons @ A) @ Y4) @ (((splice @ A) @ Xs2) @ Ys3)))))))))))))))))).
% 2.71/1.52 thf(fact_85_same__append__eq, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = (((append @ A) @ Xs) @ Zs)) = (Ys2 = Zs))))).
% 2.71/1.52 thf(fact_86_append__same__eq, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A),Zs:(list @ A)]: ((((((append @ A) @ Ys2) @ Xs) = (((append @ A) @ Zs) @ Xs)) = (Ys2 = Zs))))).
% 2.71/1.52 thf(fact_87_append__assoc, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),Zs:(list @ A)]: (((((append @ A) @ (((append @ A) @ Xs) @ Ys2)) @ Zs) = (((append @ A) @ Xs) @ (((append @ A) @ Ys2) @ Zs)))))).
% 2.71/1.52 thf(fact_88_append__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys2 = (nil @ A))))))).
% 2.71/1.52 thf(fact_89_Nil__is__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((nil @ A) = (((append @ A) @ Xs) @ Ys2)) = ((Xs = (nil @ A)) & (Ys2 = (nil @ A))))))).
% 2.71/1.52 thf(fact_90_self__append__conv2, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A)]: (((Ys2 = (((append @ A) @ Xs) @ Ys2)) = (Xs = (nil @ A)))))).
% 2.71/1.52 thf(fact_91_append__self__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = Ys2) = (Xs = (nil @ A)))))).
% 2.71/1.52 thf(fact_92_self__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((Xs = (((append @ A) @ Xs) @ Ys2)) = (Ys2 = (nil @ A)))))).
% 2.71/1.52 thf(fact_93_append__self__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = Xs) = (Ys2 = (nil @ A)))))).
% 2.71/1.52 thf(fact_94_append__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((append @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.71/1.52 thf(fact_95_shift__append, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),S:(stream170649215stream @ A)]: (((((stream1035003186_shift @ A) @ (((append @ A) @ Xs) @ Ys2)) @ S) = (((stream1035003186_shift @ A) @ Xs) @ (((stream1035003186_shift @ A) @ Ys2) @ S)))))).
% 2.71/1.52 thf(fact_96_ord_Olexordp__eq__simps_I4_J, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Xs:(list @ A),Y:A,Ys2:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys2)) = (((Less @ X) @ Y) | ((~ (((Less @ Y) @ X))) & ((((lexordp_eq @ A) @ Less) @ Xs) @ Ys2))))))).
% 2.71/1.52 thf(fact_97_ord_Olexordp__eq__simps_I1_J, axiom, (! [A:$tType,Less:(A > (A > $o)),Ys2:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ (nil @ A)) @ Ys2)))).
% 2.71/1.52 thf(fact_98_ord_Olexordp__eq__simps_I2_J, axiom, (! [A:$tType,Less:(A > (A > $o)),Xs:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ Xs) @ (nil @ A)) = (Xs = (nil @ A)))))).
% 2.71/1.52 thf(fact_99_splice__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((splice @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.71/1.52 thf(fact_100_append1__eq__conv, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys2:(list @ A),Y:A]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))) = (((append @ A) @ Ys2) @ (((cons @ A) @ Y) @ (nil @ A)))) = ((Xs = Ys2) & (X = Y)))))).
% 2.71/1.52 thf(fact_101_tl__append2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((Xs != (nil @ A)) => (((tl @ A) @ (((append @ A) @ Xs) @ Ys2)) = (((append @ A) @ ((tl @ A) @ Xs)) @ Ys2)))))).
% 2.71/1.52 thf(fact_102_hd__append2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((Xs != (nil @ A)) => (((hd @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((hd @ A) @ Xs)))))).
% 2.71/1.52 thf(fact_103_bind__simps_I2_J, axiom, (! [A:$tType,B:$tType,X:B,Xs:(list @ B),F2:(B > (list @ A))]: ((((((bind @ B) @ A) @ (((cons @ B) @ X) @ Xs)) @ F2) = (((append @ A) @ (F2 @ X)) @ ((((bind @ B) @ A) @ Xs) @ F2)))))).
% 2.71/1.52 thf(fact_104_append__eq__append__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),Zs:(list @ A),Ts:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = (((append @ A) @ Zs) @ Ts)) = (? [Us:(list @ A)]: ((((Xs = (((append @ A) @ Zs) @ Us)) & ((((append @ A) @ Us) @ Ys2) = Ts)) | (((((append @ A) @ Xs) @ Us) = Zs) & (Ys2 = (((append @ A) @ Us) @ Ts)))))))))).
% 2.71/1.52 thf(fact_105_ord_Olexordp__eq__refl, axiom, (! [A:$tType,Less:(A > (A > $o)),Xs:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ Xs) @ Xs)))).
% 2.71/1.52 thf(fact_106_append__eq__appendI, axiom, (! [A:$tType,Xs:(list @ A),Xs1:(list @ A),Zs:(list @ A),Ys2:(list @ A),Us2:(list @ A)]: ((((((append @ A) @ Xs) @ Xs1) = Zs) => ((Ys2 = (((append @ A) @ Xs1) @ Us2)) => ((((append @ A) @ Xs) @ Ys2) = (((append @ A) @ Zs) @ Us2))))))).
% 2.71/1.52 thf(fact_107_append__Cons, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys2:(list @ A)]: (((((append @ A) @ (((cons @ A) @ X) @ Xs)) @ Ys2) = (((cons @ A) @ X) @ (((append @ A) @ Xs) @ Ys2)))))).
% 2.71/1.52 thf(fact_108_Cons__eq__appendI, axiom, (! [A:$tType,X:A,Xs1:(list @ A),Ys2:(list @ A),Xs:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X) @ Xs1) = Ys2) => ((Xs = (((append @ A) @ Xs1) @ Zs)) => ((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys2) @ Zs))))))).
% 2.71/1.52 thf(fact_109_append__Nil, axiom, (! [A:$tType,Ys2:(list @ A)]: (((((append @ A) @ (nil @ A)) @ Ys2) = Ys2)))).
% 2.71/1.52 thf(fact_110_eq__Nil__appendI, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((Xs = Ys2) => (Xs = (((append @ A) @ (nil @ A)) @ Ys2)))))).
% 2.71/1.52 thf(fact_111_ord_Olexordp__eq_OCons__eq, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Y:A,Xs:(list @ A),Ys2:(list @ A)]: (((~ (((Less @ X) @ Y))) => ((~ (((Less @ Y) @ X))) => (((((lexordp_eq @ A) @ Less) @ Xs) @ Ys2) => ((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys2)))))))).
% 2.71/1.52 thf(fact_112_ord_Olexordp__eq_OCons, axiom, (! [A:$tType,Less:(A > (A > $o)),X:A,Y:A,Xs:(list @ A),Ys2:(list @ A)]: ((((Less @ X) @ Y) => ((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys2)))))).
% 2.71/1.52 thf(fact_113_ord_Olexordp__eq_ONil, axiom, (! [A:$tType,Less:(A > (A > $o)),Ys2:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ (nil @ A)) @ Ys2)))).
% 2.71/1.52 thf(fact_114_splice_Osimps_I3_J, axiom, (! [A:$tType,X:A,Xs:(list @ A),Y:A,Ys2:(list @ A)]: (((((splice @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys2)) = (((cons @ A) @ X) @ (((cons @ A) @ Y) @ (((splice @ A) @ Xs) @ Ys2))))))).
% 2.71/1.52 thf(fact_115_splice_Osimps_I1_J, axiom, (! [A:$tType,Ys2:(list @ A)]: (((((splice @ A) @ (nil @ A)) @ Ys2) = Ys2)))).
% 2.71/1.52 thf(fact_116_rev__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P2:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X4:A]: ((P2 @ (((cons @ A) @ X4) @ (nil @ A))))) => ((! [X4:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P2 @ Xs2) => (P2 @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A)))))))) => (P2 @ Xs))))))).
% 2.71/1.52 thf(fact_117_append__eq__Cons__conv, axiom, (! [A:$tType,Ys2:(list @ A),Zs:(list @ A),X:A,Xs:(list @ A)]: ((((((append @ A) @ Ys2) @ Zs) = (((cons @ A) @ X) @ Xs)) = (((Ys2 = (nil @ A)) & (Zs = (((cons @ A) @ X) @ Xs))) | (? [Ys4:(list @ A)]: (((Ys2 = (((cons @ A) @ X) @ Ys4)) & ((((append @ A) @ Ys4) @ Zs) = Xs))))))))).
% 2.71/1.52 thf(fact_118_Cons__eq__append__conv, axiom, (! [A:$tType,X:A,Xs:(list @ A),Ys2:(list @ A),Zs:(list @ A)]: ((((((cons @ A) @ X) @ Xs) = (((append @ A) @ Ys2) @ Zs)) = (((Ys2 = (nil @ A)) & ((((cons @ A) @ X) @ Xs) = Zs)) | (? [Ys4:(list @ A)]: ((((((cons @ A) @ X) @ Ys4) = Ys2) & (Xs = (((append @ A) @ Ys4) @ Zs)))))))))).
% 2.71/1.52 thf(fact_119_rev__exhaust, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (~ ((! [Ys3:(list @ A),Y4:A]: ((Xs != (((append @ A) @ Ys3) @ (((cons @ A) @ Y4) @ (nil @ A)))))))))))).
% 2.71/1.52 thf(fact_120_rev__induct, axiom, (! [A:$tType,P2:((list @ A) > $o),Xs:(list @ A)]: (((P2 @ (nil @ A)) => ((! [X4:A,Xs2:(list @ A)]: (((P2 @ Xs2) => (P2 @ (((append @ A) @ Xs2) @ (((cons @ A) @ X4) @ (nil @ A))))))) => (P2 @ Xs)))))).
% 2.71/1.52 thf(fact_121_map__tailrec__rev_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,F2:(A > B),A3:A,As2:(list @ A),Bs2:(list @ B)]: (((((((map_tailrec_rev @ A) @ B) @ F2) @ (((cons @ A) @ A3) @ As2)) @ Bs2) = (((((map_tailrec_rev @ A) @ B) @ F2) @ As2) @ (((cons @ B) @ (F2 @ A3)) @ Bs2)))))).
% 2.71/1.52 thf(fact_122_map__tailrec__rev_Osimps_I1_J, axiom, (! [A:$tType,B:$tType,F2:(A > B),Bs2:(list @ B)]: (((((((map_tailrec_rev @ A) @ B) @ F2) @ (nil @ A)) @ Bs2) = Bs2)))).
% 2.71/1.52 thf(fact_123_hd__append, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((Xs = (nil @ A)) => (((hd @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((hd @ A) @ Ys2))) & ((Xs != (nil @ A)) => (((hd @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((hd @ A) @ Xs))))))).
% 2.71/1.52 thf(fact_124_longest__common__prefix, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((? [Ps:(list @ A),Xs4:(list @ A),Ys5:(list @ A)]: (((Xs = (((append @ A) @ Ps) @ Xs4)) & ((Ys2 = (((append @ A) @ Ps) @ Ys5)) & ((Xs4 = (nil @ A)) | ((Ys5 = (nil @ A)) | (((hd @ A) @ Xs4) != ((hd @ A) @ Ys5))))))))))).
% 2.71/1.52 thf(fact_125_ord_Olexordp__eq_Ocases, axiom, (! [A:$tType,Less:(A > (A > $o)),A1:(list @ A),A22:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ A1) @ A22) => (((A1 = (nil @ A)) => (! [Ys3:(list @ A)]: ((A22 != Ys3)))) => ((! [X4:A]: (((? [Xs2:(list @ A)]: ((A1 = (((cons @ A) @ X4) @ Xs2)))) => (! [Y4:A]: (((? [Ys3:(list @ A)]: ((A22 = (((cons @ A) @ Y4) @ Ys3)))) => (~ (((Less @ X4) @ Y4))))))))) => (~ ((! [X4:A,Y4:A,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X4) @ Xs2)) => (! [Ys3:(list @ A)]: (((A22 = (((cons @ A) @ Y4) @ Ys3)) => ((~ (((Less @ X4) @ Y4))) => ((~ (((Less @ Y4) @ X4))) => (~ (((((lexordp_eq @ A) @ Less) @ Xs2) @ Ys3))))))))))))))))))).
% 2.71/1.52 thf(fact_126_ord_Olexordp__eq_Osimps, axiom, (! [A:$tType]: (((lexordp_eq @ A) = (^ [Less2:(A > (A > $o)),A12:(list @ A),A23:(list @ A)]: (((? [Ys:(list @ A)]: (((A12 = (nil @ A)) & (A23 = Ys)))) | ((? [X5:A,Y3:A,Xs3:(list @ A),Ys:(list @ A)]: (((A12 = (((cons @ A) @ X5) @ Xs3)) & ((A23 = (((cons @ A) @ Y3) @ Ys)) & ((Less2 @ X5) @ Y3))))) | (? [X5:A,Y3:A,Xs3:(list @ A),Ys:(list @ A)]: (((A12 = (((cons @ A) @ X5) @ Xs3)) & ((A23 = (((cons @ A) @ Y3) @ Ys)) & ((~ (((Less2 @ X5) @ Y3))) & ((~ (((Less2 @ Y3) @ X5))) & ((((lexordp_eq @ A) @ Less2) @ Xs3) @ Ys))))))))))))))).
% 2.71/1.52 thf(fact_127_ord_Olexordp__eq_Oinducts, axiom, (! [A:$tType,Less:(A > (A > $o)),X1:(list @ A),X2:(list @ A),P2:((list @ A) > ((list @ A) > $o))]: ((((((lexordp_eq @ A) @ Less) @ X1) @ X2) => ((! [X12:(list @ A)]: (((P2 @ (nil @ A)) @ X12))) => ((! [X4:A,Y4:A,Xs2:(list @ A),Ys3:(list @ A)]: ((((Less @ X4) @ Y4) => ((P2 @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys3))))) => ((! [X4:A,Y4:A,Xs2:(list @ A),Ys3:(list @ A)]: (((~ (((Less @ X4) @ Y4))) => ((~ (((Less @ Y4) @ X4))) => (((((lexordp_eq @ A) @ Less) @ Xs2) @ Ys3) => (((P2 @ Xs2) @ Ys3) => ((P2 @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys3)))))))) => ((P2 @ X1) @ X2)))))))).
% 2.71/1.52 thf(fact_128_splice_Osimps_I2_J, axiom, (! [A:$tType,V2:A,Va2:(list @ A)]: (((((splice @ A) @ (((cons @ A) @ V2) @ Va2)) @ (nil @ A)) = (((cons @ A) @ V2) @ Va2))))).
% 2.71/1.52 thf(fact_129_rotate1__hd__tl, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((rotate1 @ A) @ Xs) = (((append @ A) @ ((tl @ A) @ Xs)) @ (((cons @ A) @ ((hd @ A) @ Xs)) @ (nil @ A)))))))).
% 2.71/1.52 thf(fact_130_sublists_Osimps_I1_J, axiom, (! [A:$tType]: ((((sublists @ A) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.71/1.52 thf(fact_131_product__lists_Osimps_I1_J, axiom, (! [A:$tType]: ((((product_lists @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.71/1.52 thf(fact_132_maps__simps_I1_J, axiom, (! [A:$tType,B:$tType,F2:(B > (list @ A)),X:B,Xs:(list @ B)]: ((((((maps @ B) @ A) @ F2) @ (((cons @ B) @ X) @ Xs)) = (((append @ A) @ (F2 @ X)) @ ((((maps @ B) @ A) @ F2) @ Xs)))))).
% 2.71/1.52 thf(fact_133_rotate1_Osimps_I2_J, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((rotate1 @ A) @ (((cons @ A) @ X) @ Xs)) = (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))))))).
% 2.71/1.52 thf(fact_134_remdups__adj__append, axiom, (! [A:$tType,Xs_1:(list @ A),X:A,Xs_2:(list @ A)]: ((((remdups_adj @ A) @ (((append @ A) @ Xs_1) @ (((cons @ A) @ X) @ Xs_2))) = (((append @ A) @ ((remdups_adj @ A) @ (((append @ A) @ Xs_1) @ (((cons @ A) @ X) @ (nil @ A))))) @ ((tl @ A) @ ((remdups_adj @ A) @ (((cons @ A) @ X) @ Xs_2)))))))).
% 2.71/1.52 thf(fact_135_remdups__adj__Nil__iff, axiom, (! [A:$tType,Xs:(list @ A)]: (((((remdups_adj @ A) @ Xs) = (nil @ A)) = (Xs = (nil @ A)))))).
% 2.71/1.52 thf(fact_136_hd__remdups__adj, axiom, (! [A:$tType,Xs:(list @ A)]: ((((hd @ A) @ ((remdups_adj @ A) @ Xs)) = ((hd @ A) @ Xs))))).
% 2.71/1.52 thf(fact_137_rotate1__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((rotate1 @ A) @ Xs) = (nil @ A)) = (Xs = (nil @ A)))))).
% 2.71/1.52 thf(fact_138_remdups__adj__Cons__alt, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: (((((cons @ A) @ X) @ ((tl @ A) @ ((remdups_adj @ A) @ (((cons @ A) @ X) @ Xs)))) = ((remdups_adj @ A) @ (((cons @ A) @ X) @ Xs)))))).
% 2.71/1.52 thf(fact_139_remdups__adj_Osimps_I3_J, axiom, (! [A:$tType,X:A,Y:A,Xs:(list @ A)]: ((((X = Y) => (((remdups_adj @ A) @ (((cons @ A) @ X) @ (((cons @ A) @ Y) @ Xs))) = ((remdups_adj @ A) @ (((cons @ A) @ X) @ Xs)))) & ((X != Y) => (((remdups_adj @ A) @ (((cons @ A) @ X) @ (((cons @ A) @ Y) @ Xs))) = (((cons @ A) @ X) @ ((remdups_adj @ A) @ (((cons @ A) @ Y) @ Xs))))))))).
% 2.71/1.52 thf(fact_140_remdups__adj_Osimps_I1_J, axiom, (! [A:$tType]: ((((remdups_adj @ A) @ (nil @ A)) = (nil @ A))))).
% 2.71/1.52 thf(fact_141_rotate1_Osimps_I1_J, axiom, (! [A:$tType]: ((((rotate1 @ A) @ (nil @ A)) = (nil @ A))))).
% 2.71/1.52 thf(fact_142_remdups__adj_Oelims, axiom, (! [A:$tType,X:(list @ A),Y:(list @ A)]: (((((remdups_adj @ A) @ X) = Y) => (((X = (nil @ A)) => (Y != (nil @ A))) => ((! [X4:A]: (((X = (((cons @ A) @ X4) @ (nil @ A))) => (Y != (((cons @ A) @ X4) @ (nil @ A)))))) => (~ ((! [X4:A,Y4:A,Xs2:(list @ A)]: (((X = (((cons @ A) @ X4) @ (((cons @ A) @ Y4) @ Xs2))) => (~ ((((X4 = Y4) => (Y = ((remdups_adj @ A) @ (((cons @ A) @ X4) @ Xs2)))) & ((X4 != Y4) => (Y = (((cons @ A) @ X4) @ ((remdups_adj @ A) @ (((cons @ A) @ Y4) @ Xs2))))))))))))))))))).
% 2.71/1.52 thf(fact_143_remdups__adj_Osimps_I2_J, axiom, (! [A:$tType,X:A]: ((((remdups_adj @ A) @ (((cons @ A) @ X) @ (nil @ A))) = (((cons @ A) @ X) @ (nil @ A)))))).
% 2.71/1.52 thf(fact_144_maps__simps_I2_J, axiom, (! [B:$tType,A:$tType,F2:(B > (list @ A))]: ((((((maps @ B) @ A) @ F2) @ (nil @ B)) = (nil @ A))))).
% 2.71/1.52 thf(fact_145_remdups__adj__append__two, axiom, (! [A:$tType,Xs:(list @ A),X:A,Y:A]: ((((remdups_adj @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (((cons @ A) @ Y) @ (nil @ A))))) = (((append @ A) @ ((remdups_adj @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))))) @ ((((if @ (list @ A)) @ (X = Y)) @ (nil @ A)) @ (((cons @ A) @ Y) @ (nil @ A)))))))).
% 2.71/1.52 thf(fact_146_last__snoc, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((last @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) = X)))).
% 2.71/1.52 thf(fact_147_butlast__snoc, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((butlast @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A)))) = Xs)))).
% 2.71/1.52 thf(fact_148_SuccD, axiom, (! [A:$tType,K:A,Kl:(set @ (list @ A)),Kl2:(list @ A)]: (((((member2 @ A) @ K) @ (((bNF_Greatest_Succ @ A) @ Kl) @ Kl2)) => (((member2 @ (list @ A)) @ (((append @ A) @ Kl2) @ (((cons @ A) @ K) @ (nil @ A)))) @ Kl))))).
% 2.71/1.52 thf(fact_149_SuccI, axiom, (! [A:$tType,Kl2:(list @ A),K:A,Kl:(set @ (list @ A))]: (((((member2 @ (list @ A)) @ (((append @ A) @ Kl2) @ (((cons @ A) @ K) @ (nil @ A)))) @ Kl) => (((member2 @ A) @ K) @ (((bNF_Greatest_Succ @ A) @ Kl) @ Kl2)))))).
% 2.71/1.52 thf(fact_150_last__appendR, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A)]: (((Ys2 != (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((last @ A) @ Ys2)))))).
% 2.71/1.52 thf(fact_151_last__appendL, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A)]: (((Ys2 = (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((last @ A) @ Xs)))))).
% 2.71/1.52 thf(fact_152_append__butlast__last__id, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((((append @ A) @ ((butlast @ A) @ Xs)) @ (((cons @ A) @ ((last @ A) @ Xs)) @ (nil @ A))) = Xs))))).
% 2.71/1.52 thf(fact_153_butlast_Osimps_I1_J, axiom, (! [A:$tType]: ((((butlast @ A) @ (nil @ A)) = (nil @ A))))).
% 2.71/1.52 thf(fact_154_butlast__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((butlast @ A) @ ((tl @ A) @ Xs)) = ((tl @ A) @ ((butlast @ A) @ Xs)))))).
% 2.71/1.52 thf(fact_155_snoc__eq__iff__butlast, axiom, (! [A:$tType,Xs:(list @ A),X:A,Ys2:(list @ A)]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X) @ (nil @ A))) = Ys2) = ((Ys2 != (nil @ A)) & ((((butlast @ A) @ Ys2) = Xs) & (((last @ A) @ Ys2) = X))))))).
% 2.71/1.52 thf(fact_156_butlast_Osimps_I2_J, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((Xs = (nil @ A)) => (((butlast @ A) @ (((cons @ A) @ X) @ Xs)) = (nil @ A))) & ((Xs != (nil @ A)) => (((butlast @ A) @ (((cons @ A) @ X) @ Xs)) = (((cons @ A) @ X) @ ((butlast @ A) @ Xs)))))))).
% 2.71/1.52 thf(fact_157_last_Osimps, axiom, (! [A:$tType,Xs:(list @ A),X:A]: ((((Xs = (nil @ A)) => (((last @ A) @ (((cons @ A) @ X) @ Xs)) = X)) & ((Xs != (nil @ A)) => (((last @ A) @ (((cons @ A) @ X) @ Xs)) = ((last @ A) @ Xs))))))).
% 2.71/1.52 thf(fact_158_last__ConsL, axiom, (! [A:$tType,Xs:(list @ A),X:A]: (((Xs = (nil @ A)) => (((last @ A) @ (((cons @ A) @ X) @ Xs)) = X))))).
% 2.71/1.52 thf(fact_159_last__ConsR, axiom, (! [A:$tType,Xs:(list @ A),X:A]: (((Xs != (nil @ A)) => (((last @ A) @ (((cons @ A) @ X) @ Xs)) = ((last @ A) @ Xs)))))).
% 2.71/1.52 thf(fact_160_longest__common__suffix, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((? [Ss:(list @ A),Xs4:(list @ A),Ys5:(list @ A)]: (((Xs = (((append @ A) @ Xs4) @ Ss)) & ((Ys2 = (((append @ A) @ Ys5) @ Ss)) & ((Xs4 = (nil @ A)) | ((Ys5 = (nil @ A)) | (((last @ A) @ Xs4) != ((last @ A) @ Ys5))))))))))).
% 2.71/1.52 thf(fact_161_butlast__append, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A)]: ((((Ys2 = (nil @ A)) => (((butlast @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((butlast @ A) @ Xs))) & ((Ys2 != (nil @ A)) => (((butlast @ A) @ (((append @ A) @ Xs) @ Ys2)) = (((append @ A) @ Xs) @ ((butlast @ A) @ Ys2)))))))).
% 2.71/1.52 thf(fact_162_last__append, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A)]: ((((Ys2 = (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((last @ A) @ Xs))) & ((Ys2 != (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((last @ A) @ Ys2))))))).
% 2.71/1.52 thf(fact_163_last__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((Xs = (nil @ A)) | (((tl @ A) @ Xs) != (nil @ A))) => (((last @ A) @ ((tl @ A) @ Xs)) = ((last @ A) @ Xs)))))).
% 2.71/1.52 thf(fact_164_BNF__Greatest__Fixpoint_Oshift__def, axiom, (! [B:$tType,A:$tType]: ((((bNF_Greatest_shift @ A) @ B) = (^ [Lab:((list @ A) > B),K2:A,Kl3:(list @ A)]: ((Lab @ (((cons @ A) @ K2) @ Kl3)))))))).
% 2.71/1.52 thf(fact_165_empty__Shift, axiom, (! [A:$tType,Kl:(set @ (list @ A)),K:A]: (((((member2 @ (list @ A)) @ (nil @ A)) @ Kl) => ((((member2 @ A) @ K) @ (((bNF_Greatest_Succ @ A) @ Kl) @ (nil @ A))) => (((member2 @ (list @ A)) @ (nil @ A)) @ (((bNF_Greatest_Shift @ A) @ Kl) @ K))))))).
% 2.71/1.52 thf(fact_166_Succ__Shift, axiom, (! [A:$tType,Kl:(set @ (list @ A)),K:A,Kl2:(list @ A)]: (((((bNF_Greatest_Succ @ A) @ (((bNF_Greatest_Shift @ A) @ Kl) @ K)) @ Kl2) = (((bNF_Greatest_Succ @ A) @ Kl) @ (((cons @ A) @ K) @ Kl2)))))).
% 2.71/1.52 thf(fact_167_ShiftD, axiom, (! [A:$tType,Kl2:(list @ A),Kl:(set @ (list @ A)),K:A]: (((((member2 @ (list @ A)) @ Kl2) @ (((bNF_Greatest_Shift @ A) @ Kl) @ K)) => (((member2 @ (list @ A)) @ (((cons @ A) @ K) @ Kl2)) @ Kl))))).
% 2.71/1.52 thf(fact_168_rev__eq__Cons__iff, axiom, (! [A:$tType,Xs:(list @ A),Y:A,Ys2:(list @ A)]: (((((rev @ A) @ Xs) = (((cons @ A) @ Y) @ Ys2)) = (Xs = (((append @ A) @ ((rev @ A) @ Ys2)) @ (((cons @ A) @ Y) @ (nil @ A)))))))).
% 2.71/1.52 thf(fact_169_listrelp_Oinducts, axiom, (! [A:$tType,B:$tType,R2:(A > (B > $o)),X1:(list @ A),X2:(list @ B),P2:((list @ A) > ((list @ B) > $o))]: (((((((listrelp @ A) @ B) @ R2) @ X1) @ X2) => (((P2 @ (nil @ A)) @ (nil @ B)) => ((! [X4:A,Y4:B,Xs2:(list @ A),Ys3:(list @ B)]: ((((R2 @ X4) @ Y4) => ((((((listrelp @ A) @ B) @ R2) @ Xs2) @ Ys3) => (((P2 @ Xs2) @ Ys3) => ((P2 @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ B) @ Y4) @ Ys3))))))) => ((P2 @ X1) @ X2))))))).
% 2.71/1.52 thf(fact_170_listrelp_Osimps, axiom, (! [B:$tType,A:$tType]: ((((listrelp @ A) @ B) = (^ [R3:(A > (B > $o)),A12:(list @ A),A23:(list @ B)]: ((((A12 = (nil @ A)) & (A23 = (nil @ B))) | (? [X5:A,Y3:B,Xs3:(list @ A),Ys:(list @ B)]: (((A12 = (((cons @ A) @ X5) @ Xs3)) & ((A23 = (((cons @ B) @ Y3) @ Ys)) & (((R3 @ X5) @ Y3) & (((((listrelp @ A) @ B) @ R3) @ Xs3) @ Ys))))))))))))).
% 2.71/1.52 thf(fact_171_rev__is__rev__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((((rev @ A) @ Xs) = ((rev @ A) @ Ys2)) = (Xs = Ys2))))).
% 2.71/1.52 thf(fact_172_rev__rev__ident, axiom, (! [A:$tType,Xs:(list @ A)]: ((((rev @ A) @ ((rev @ A) @ Xs)) = Xs)))).
% 2.71/1.52 thf(fact_173_Nil__is__rev__conv, axiom, (! [A:$tType,Xs:(list @ A)]: ((((nil @ A) = ((rev @ A) @ Xs)) = (Xs = (nil @ A)))))).
% 2.71/1.52 thf(fact_174_rev__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((rev @ A) @ Xs) = (nil @ A)) = (Xs = (nil @ A)))))).
% 2.71/1.52 thf(fact_175_rev__append, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((rev @ A) @ (((append @ A) @ Xs) @ Ys2)) = (((append @ A) @ ((rev @ A) @ Ys2)) @ ((rev @ A) @ Xs)))))).
% 2.71/1.52 thf(fact_176_remdups__adj__rev, axiom, (! [A:$tType,Xs:(list @ A)]: ((((remdups_adj @ A) @ ((rev @ A) @ Xs)) = ((rev @ A) @ ((remdups_adj @ A) @ Xs)))))).
% 2.71/1.52 thf(fact_177_rev__singleton__conv, axiom, (! [A:$tType,Xs:(list @ A),X:A]: (((((rev @ A) @ Xs) = (((cons @ A) @ X) @ (nil @ A))) = (Xs = (((cons @ A) @ X) @ (nil @ A))))))).
% 2.71/1.52 thf(fact_178_singleton__rev__conv, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((((cons @ A) @ X) @ (nil @ A)) = ((rev @ A) @ Xs)) = (Xs = (((cons @ A) @ X) @ (nil @ A))))))).
% 2.71/1.52 thf(fact_179_rev_Osimps_I1_J, axiom, (! [A:$tType]: ((((rev @ A) @ (nil @ A)) = (nil @ A))))).
% 2.71/1.52 thf(fact_180_rev__swap, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((((rev @ A) @ Xs) = Ys2) = (Xs = ((rev @ A) @ Ys2)))))).
% 2.71/1.52 thf(fact_181_listrelp_OCons, axiom, (! [A:$tType,B:$tType,R2:(A > (B > $o)),X:A,Y:B,Xs:(list @ A),Ys2:(list @ B)]: ((((R2 @ X) @ Y) => ((((((listrelp @ A) @ B) @ R2) @ Xs) @ Ys2) => (((((listrelp @ A) @ B) @ R2) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ B) @ Y) @ Ys2))))))).
% 2.71/1.52 thf(fact_182_listrelp_ONil, axiom, (! [A:$tType,B:$tType,R2:(A > (B > $o))]: ((((((listrelp @ A) @ B) @ R2) @ (nil @ A)) @ (nil @ B))))).
% 2.71/1.52 thf(fact_183_rev_Osimps_I2_J, axiom, (! [A:$tType,X:A,Xs:(list @ A)]: ((((rev @ A) @ (((cons @ A) @ X) @ Xs)) = (((append @ A) @ ((rev @ A) @ Xs)) @ (((cons @ A) @ X) @ (nil @ A))))))).
% 2.71/1.52 thf(fact_184_last__rev, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((last @ A) @ ((rev @ A) @ Xs)) = ((hd @ A) @ Xs)))))).
% 2.71/1.52 thf(fact_185_hd__rev, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((hd @ A) @ ((rev @ A) @ Xs)) = ((last @ A) @ Xs)))))).
% 2.71/1.52 thf(fact_186_listrelp_Ocases, axiom, (! [A:$tType,B:$tType,R2:(A > (B > $o)),A1:(list @ A),A22:(list @ B)]: (((((((listrelp @ A) @ B) @ R2) @ A1) @ A22) => (((A1 = (nil @ A)) => (A22 != (nil @ B))) => (~ ((! [X4:A,Y4:B,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X4) @ Xs2)) => (! [Ys3:(list @ B)]: (((A22 = (((cons @ B) @ Y4) @ Ys3)) => (((R2 @ X4) @ Y4) => (~ ((((((listrelp @ A) @ B) @ R2) @ Xs2) @ Ys3))))))))))))))))).
% 2.71/1.52 thf(fact_187_map__tailrec__def, axiom, (! [B:$tType,A:$tType]: ((((map_tailrec @ A) @ B) = (^ [F:(A > B),As3:(list @ A)]: (((rev @ B) @ (((((map_tailrec_rev @ A) @ B) @ F) @ As3) @ (nil @ B))))))))).
% 2.71/1.52 thf(fact_188_lexordp__eq__simps_I3_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Xs:(list @ A)]: ((~ ((((ord_lexordp_eq @ A) @ (((cons @ A) @ X) @ Xs)) @ (nil @ A)))))))))).
% 2.71/1.52 thf(fact_189_fold__Cons__rev, axiom, (! [A:$tType,Xs:(list @ A)]: ((((((fold @ A) @ (list @ A)) @ (cons @ A)) @ Xs) = ((append @ A) @ ((rev @ A) @ Xs)))))).
% 2.71/1.52 thf(fact_190_lexordp__eq__simps_I1_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Ys2:(list @ A)]: ((((ord_lexordp_eq @ A) @ (nil @ A)) @ Ys2))))))).
% 2.71/1.52 thf(fact_191_lexordp__eq__simps_I2_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Xs:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ (nil @ A)) = (Xs = (nil @ A))))))))).
% 2.71/1.52 thf(fact_192_lexordp__eq__refl, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Xs:(list @ A)]: ((((ord_lexordp_eq @ A) @ Xs) @ Xs))))))).
% 2.71/1.52 thf(fact_193_lexordp__eq__trans, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Xs:(list @ A),Ys2:(list @ A),Zs:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys2) => ((((ord_lexordp_eq @ A) @ Ys2) @ Zs) => (((ord_lexordp_eq @ A) @ Xs) @ Zs))))))))).
% 2.71/1.52 thf(fact_194_lexordp__eq__linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Xs:(list @ A),Ys2:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys2) | (((ord_lexordp_eq @ A) @ Ys2) @ Xs)))))))).
% 2.71/1.52 thf(fact_195_lexordp__eq__antisym, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Xs:(list @ A),Ys2:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys2) => ((((ord_lexordp_eq @ A) @ Ys2) @ Xs) => (Xs = Ys2))))))))).
% 2.71/1.52 thf(fact_196_lexordp__eq_ONil, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Ys2:(list @ A)]: ((((ord_lexordp_eq @ A) @ (nil @ A)) @ Ys2))))))).
% 2.71/1.52 thf(fact_197_fold__simps_I1_J, axiom, (! [B:$tType,A:$tType,F2:(B > (A > A)),S:A]: (((((((fold @ B) @ A) @ F2) @ (nil @ B)) @ S) = S)))).
% 2.71/1.52 thf(fact_198_fold__simps_I2_J, axiom, (! [B:$tType,A:$tType,F2:(B > (A > A)),X:B,Xs:(list @ B),S:A]: (((((((fold @ B) @ A) @ F2) @ (((cons @ B) @ X) @ Xs)) @ S) = (((((fold @ B) @ A) @ F2) @ Xs) @ ((F2 @ X) @ S)))))).
% 2.71/1.52 thf(fact_199_rev__conv__fold, axiom, (! [A:$tType]: (((rev @ A) = (^ [Xs3:(list @ A)]: ((((((fold @ A) @ (list @ A)) @ (cons @ A)) @ Xs3) @ (nil @ A)))))))).
% 2.71/1.52 thf(fact_200_List_Ounion__def, axiom, (! [A:$tType]: (((union @ A) = (((fold @ A) @ (list @ A)) @ (insert @ A)))))).
% 2.71/1.52 thf(fact_201_lexordp__eq_Oinducts, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X1:(list @ A),X2:(list @ A),P2:((list @ A) > ((list @ A) > $o))]: (((((ord_lexordp_eq @ A) @ X1) @ X2) => ((! [X12:(list @ A)]: (((P2 @ (nil @ A)) @ X12))) => ((! [X4:A,Y4:A,Xs2:(list @ A),Ys3:(list @ A)]: (((((ord_less @ A) @ X4) @ Y4) => ((P2 @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys3))))) => ((! [X4:A,Y4:A,Xs2:(list @ A),Ys3:(list @ A)]: (((~ ((((ord_less @ A) @ X4) @ Y4))) => ((~ ((((ord_less @ A) @ Y4) @ X4))) => ((((ord_lexordp_eq @ A) @ Xs2) @ Ys3) => (((P2 @ Xs2) @ Ys3) => ((P2 @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys3)))))))) => ((P2 @ X1) @ X2))))))))))).
% 2.71/1.52 thf(fact_202_lexordp__eq__simps_I4_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Xs:(list @ A),Y:A,Ys2:(list @ A)]: (((((ord_lexordp_eq @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys2)) = ((((ord_less @ A) @ X) @ Y) | ((~ ((((ord_less @ A) @ Y) @ X))) & (((ord_lexordp_eq @ A) @ Xs) @ Ys2)))))))))).
% 2.71/1.52 thf(fact_203_lexordp__eq_OCons__eq, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Y:A,Xs:(list @ A),Ys2:(list @ A)]: (((~ ((((ord_less @ A) @ X) @ Y))) => ((~ ((((ord_less @ A) @ Y) @ X))) => ((((ord_lexordp_eq @ A) @ Xs) @ Ys2) => (((ord_lexordp_eq @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys2))))))))))).
% 2.71/1.52 thf(fact_204_lexordp__eq_OCons, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Y:A,Xs:(list @ A),Ys2:(list @ A)]: (((((ord_less @ A) @ X) @ Y) => (((ord_lexordp_eq @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys2))))))))).
% 2.71/1.52 thf(fact_205_lexordp__eq_Ocases, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A1:(list @ A),A22:(list @ A)]: (((((ord_lexordp_eq @ A) @ A1) @ A22) => (((A1 = (nil @ A)) => (! [Ys3:(list @ A)]: ((A22 != Ys3)))) => ((! [X4:A]: (((? [Xs2:(list @ A)]: ((A1 = (((cons @ A) @ X4) @ Xs2)))) => (! [Y4:A]: (((? [Ys3:(list @ A)]: ((A22 = (((cons @ A) @ Y4) @ Ys3)))) => (~ ((((ord_less @ A) @ X4) @ Y4))))))))) => (~ ((! [X4:A,Y4:A,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X4) @ Xs2)) => (! [Ys3:(list @ A)]: (((A22 = (((cons @ A) @ Y4) @ Ys3)) => ((~ ((((ord_less @ A) @ X4) @ Y4))) => ((~ ((((ord_less @ A) @ Y4) @ X4))) => (~ ((((ord_lexordp_eq @ A) @ Xs2) @ Ys3)))))))))))))))))))))).
% 2.71/1.52 thf(fact_206_lexordp__eq_Osimps, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => ((ord_lexordp_eq @ A) = (^ [A12:(list @ A),A23:(list @ A)]: (((? [Ys:(list @ A)]: (((A12 = (nil @ A)) & (A23 = Ys)))) | ((? [X5:A,Y3:A,Xs3:(list @ A),Ys:(list @ A)]: (((A12 = (((cons @ A) @ X5) @ Xs3)) & ((A23 = (((cons @ A) @ Y3) @ Ys)) & (((ord_less @ A) @ X5) @ Y3))))) | (? [X5:A,Y3:A,Xs3:(list @ A),Ys:(list @ A)]: (((A12 = (((cons @ A) @ X5) @ Xs3)) & ((A23 = (((cons @ A) @ Y3) @ Ys)) & ((~ ((((ord_less @ A) @ X5) @ Y3))) & ((~ ((((ord_less @ A) @ Y3) @ X5))) & (((ord_lexordp_eq @ A) @ Xs3) @ Ys)))))))))))))))).
% 2.71/1.52 thf(fact_207_lexordp__append__left__rightI, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Y:A,Us2:(list @ A),Xs:(list @ A),Ys2:(list @ A)]: (((((ord_less @ A) @ X) @ Y) => (((ord_lexordp @ A) @ (((append @ A) @ Us2) @ (((cons @ A) @ X) @ Xs))) @ (((append @ A) @ Us2) @ (((cons @ A) @ Y) @ Ys2)))))))))).
% 2.71/1.52 thf(fact_208_lexordp__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((ord_lexordp @ A) = (^ [Xs3:(list @ A),Ys:(list @ A)]: (((? [X5:A,Vs:(list @ A)]: ((Ys = (((append @ A) @ Xs3) @ (((cons @ A) @ X5) @ Vs))))) | (? [Us:(list @ A),A5:A,B3:A,Vs:(list @ A),Ws2:(list @ A)]: (((((ord_less @ A) @ A5) @ B3) & ((Xs3 = (((append @ A) @ Us) @ (((cons @ A) @ A5) @ Vs))) & (Ys = (((append @ A) @ Us) @ (((cons @ A) @ B3) @ Ws2))))))))))))))).
% 2.71/1.52 thf(fact_209_lexordp__simps_I1_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Ys2:(list @ A)]: (((((ord_lexordp @ A) @ (nil @ A)) @ Ys2) = (Ys2 != (nil @ A))))))))).
% 2.71/1.52 thf(fact_210_lexordp__simps_I2_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Xs:(list @ A)]: ((~ ((((ord_lexordp @ A) @ Xs) @ (nil @ A)))))))))).
% 2.71/1.52 thf(fact_211_lexordp__simps_I3_J, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Xs:(list @ A),Y:A,Ys2:(list @ A)]: (((((ord_lexordp @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys2)) = ((((ord_less @ A) @ X) @ Y) | ((~ ((((ord_less @ A) @ Y) @ X))) & (((ord_lexordp @ A) @ Xs) @ Ys2)))))))))).
% 2.71/1.52 thf(fact_212_lexordp__irreflexive, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Xs:(list @ A)]: (((! [X4:A]: ((~ ((((ord_less @ A) @ X4) @ X4))))) => (~ ((((ord_lexordp @ A) @ Xs) @ Xs)))))))))).
% 2.71/1.52 thf(fact_213_lexordp__append__leftD, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Xs:(list @ A),Us2:(list @ A),Vs2:(list @ A)]: (((((ord_lexordp @ A) @ (((append @ A) @ Xs) @ Us2)) @ (((append @ A) @ Xs) @ Vs2)) => ((! [A4:A]: ((~ ((((ord_less @ A) @ A4) @ A4))))) => (((ord_lexordp @ A) @ Us2) @ Vs2))))))))).
% 2.71/1.52 thf(fact_214_lexordp_OCons__eq, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Y:A,Xs:(list @ A),Ys2:(list @ A)]: (((~ ((((ord_less @ A) @ X) @ Y))) => ((~ ((((ord_less @ A) @ Y) @ X))) => ((((ord_lexordp @ A) @ Xs) @ Ys2) => (((ord_lexordp @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys2))))))))))).
% 2.71/1.52 thf(fact_215_lexordp_OCons, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X:A,Y:A,Xs:(list @ A),Ys2:(list @ A)]: (((((ord_less @ A) @ X) @ Y) => (((ord_lexordp @ A) @ (((cons @ A) @ X) @ Xs)) @ (((cons @ A) @ Y) @ Ys2))))))))).
% 2.71/1.52 thf(fact_216_lexordp_ONil, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Y:A,Ys2:(list @ A)]: ((((ord_lexordp @ A) @ (nil @ A)) @ (((cons @ A) @ Y) @ Ys2)))))))).
% 2.71/1.52 thf(fact_217_lexordp__append__rightI, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Ys2:(list @ A),Xs:(list @ A)]: (((Ys2 != (nil @ A)) => (((ord_lexordp @ A) @ Xs) @ (((append @ A) @ Xs) @ Ys2))))))))).
% 2.71/1.52 thf(fact_218_lexordp__antisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [Xs:(list @ A),Ys2:(list @ A)]: (((((ord_lexordp @ A) @ Xs) @ Ys2) => (~ ((((ord_lexordp @ A) @ Ys2) @ Xs)))))))))).
% 2.71/1.52 thf(fact_219_lexordp__trans, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Xs:(list @ A),Ys2:(list @ A),Zs:(list @ A)]: (((((ord_lexordp @ A) @ Xs) @ Ys2) => ((((ord_lexordp @ A) @ Ys2) @ Zs) => (((ord_lexordp @ A) @ Xs) @ Zs))))))))).
% 2.71/1.52 thf(fact_220_lexordp__linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Xs:(list @ A),Ys2:(list @ A)]: (((((ord_lexordp @ A) @ Xs) @ Ys2) | ((Xs = Ys2) | (((ord_lexordp @ A) @ Ys2) @ Xs))))))))).
% 2.71/1.52 thf(fact_221_lexordp__irreflexive_H, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [Xs:(list @ A)]: ((~ ((((ord_lexordp @ A) @ Xs) @ Xs))))))))).
% 2.71/1.52 thf(fact_222_lexordp__append__leftI, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Us2:(list @ A),Vs2:(list @ A),Xs:(list @ A)]: (((((ord_lexordp @ A) @ Us2) @ Vs2) => (((ord_lexordp @ A) @ (((append @ A) @ Xs) @ Us2)) @ (((append @ A) @ Xs) @ Vs2))))))))).
% 2.71/1.52 thf(fact_223_lexordp__conv__lexordp__eq, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((ord_lexordp @ A) = (^ [Xs3:(list @ A),Ys:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs3) @ Ys) & (~ ((((ord_lexordp_eq @ A) @ Ys) @ Xs3))))))))))).
% 2.71/1.52 thf(fact_224_lexordp__eq__conv__lexord, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => ((ord_lexordp_eq @ A) = (^ [Xs3:(list @ A),Ys:(list @ A)]: (((Xs3 = Ys) | (((ord_lexordp @ A) @ Xs3) @ Ys))))))))).
% 2.71/1.52 thf(fact_225_lexordp__into__lexordp__eq, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Xs:(list @ A),Ys2:(list @ A)]: (((((ord_lexordp @ A) @ Xs) @ Ys2) => (((ord_lexordp_eq @ A) @ Xs) @ Ys2)))))))).
% 2.71/1.52 thf(fact_226_lexordp__induct, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Xs:(list @ A),Ys2:(list @ A),P2:((list @ A) > ((list @ A) > $o))]: (((((ord_lexordp @ A) @ Xs) @ Ys2) => ((! [Y4:A,Ys3:(list @ A)]: (((P2 @ (nil @ A)) @ (((cons @ A) @ Y4) @ Ys3)))) => ((! [X4:A,Xs2:(list @ A),Y4:A,Ys3:(list @ A)]: (((((ord_less @ A) @ X4) @ Y4) => ((P2 @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys3))))) => ((! [X4:A,Xs2:(list @ A),Ys3:(list @ A)]: (((((ord_lexordp @ A) @ Xs2) @ Ys3) => (((P2 @ Xs2) @ Ys3) => ((P2 @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ A) @ X4) @ Ys3)))))) => ((P2 @ Xs) @ Ys2))))))))))).
% 2.71/1.52 thf(fact_227_lexordp__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Xs:(list @ A),Ys2:(list @ A)]: (((((ord_lexordp @ A) @ Xs) @ Ys2) => (((Xs = (nil @ A)) => (! [Y4:A,Ys5:(list @ A)]: ((Ys2 != (((cons @ A) @ Y4) @ Ys5))))) => ((! [X4:A]: (((? [Xs4:(list @ A)]: ((Xs = (((cons @ A) @ X4) @ Xs4)))) => (! [Y4:A]: (((? [Ys5:(list @ A)]: ((Ys2 = (((cons @ A) @ Y4) @ Ys5)))) => (~ ((((ord_less @ A) @ X4) @ Y4))))))))) => (~ ((! [X4:A,Xs4:(list @ A)]: (((Xs = (((cons @ A) @ X4) @ Xs4)) => (! [Ys5:(list @ A)]: (((Ys2 = (((cons @ A) @ X4) @ Ys5)) => (~ ((((ord_lexordp @ A) @ Xs4) @ Ys5)))))))))))))))))))).
% 2.71/1.52 thf(fact_228_lexordp_Oinducts, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [X1:(list @ A),X2:(list @ A),P2:((list @ A) > ((list @ A) > $o))]: (((((ord_lexordp @ A) @ X1) @ X2) => ((! [Y4:A,Ys3:(list @ A)]: (((P2 @ (nil @ A)) @ (((cons @ A) @ Y4) @ Ys3)))) => ((! [X4:A,Y4:A,Xs2:(list @ A),Ys3:(list @ A)]: (((((ord_less @ A) @ X4) @ Y4) => ((P2 @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys3))))) => ((! [X4:A,Y4:A,Xs2:(list @ A),Ys3:(list @ A)]: (((~ ((((ord_less @ A) @ X4) @ Y4))) => ((~ ((((ord_less @ A) @ Y4) @ X4))) => ((((ord_lexordp @ A) @ Xs2) @ Ys3) => (((P2 @ Xs2) @ Ys3) => ((P2 @ (((cons @ A) @ X4) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys3)))))))) => ((P2 @ X1) @ X2))))))))))).
% 2.71/1.52 thf(fact_229_lexordp_Osimps, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => ((ord_lexordp @ A) = (^ [A12:(list @ A),A23:(list @ A)]: (((? [Y3:A,Ys:(list @ A)]: (((A12 = (nil @ A)) & (A23 = (((cons @ A) @ Y3) @ Ys))))) | ((? [X5:A,Y3:A,Xs3:(list @ A),Ys:(list @ A)]: (((A12 = (((cons @ A) @ X5) @ Xs3)) & ((A23 = (((cons @ A) @ Y3) @ Ys)) & (((ord_less @ A) @ X5) @ Y3))))) | (? [X5:A,Y3:A,Xs3:(list @ A),Ys:(list @ A)]: (((A12 = (((cons @ A) @ X5) @ Xs3)) & ((A23 = (((cons @ A) @ Y3) @ Ys)) & ((~ ((((ord_less @ A) @ X5) @ Y3))) & ((~ ((((ord_less @ A) @ Y3) @ X5))) & (((ord_lexordp @ A) @ Xs3) @ Ys)))))))))))))))).
% 2.71/1.52 thf(fact_230_lexordp_Ocases, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A1:(list @ A),A22:(list @ A)]: (((((ord_lexordp @ A) @ A1) @ A22) => (((A1 = (nil @ A)) => (! [Y4:A,Ys3:(list @ A)]: ((A22 != (((cons @ A) @ Y4) @ Ys3))))) => ((! [X4:A]: (((? [Xs2:(list @ A)]: ((A1 = (((cons @ A) @ X4) @ Xs2)))) => (! [Y4:A]: (((? [Ys3:(list @ A)]: ((A22 = (((cons @ A) @ Y4) @ Ys3)))) => (~ ((((ord_less @ A) @ X4) @ Y4))))))))) => (~ ((! [X4:A,Y4:A,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X4) @ Xs2)) => (! [Ys3:(list @ A)]: (((A22 = (((cons @ A) @ Y4) @ Ys3)) => ((~ ((((ord_less @ A) @ X4) @ Y4))) => ((~ ((((ord_less @ A) @ Y4) @ X4))) => (~ ((((ord_lexordp @ A) @ Xs2) @ Ys3)))))))))))))))))))))).
% 2.71/1.52 thf(fact_231_map__tailrec__rev, axiom, (! [A:$tType,B:$tType]: ((((map_tailrec_rev @ B) @ A) = (^ [F:(B > A),As3:(list @ B)]: (((append @ A) @ ((rev @ A) @ ((((map @ B) @ A) @ F) @ As3))))))))).
% 2.71/1.52 thf(fact_232_replicate__append__same, axiom, (! [A:$tType,I:nat,X:A]: (((((append @ A) @ (((replicate @ A) @ I) @ X)) @ (((cons @ A) @ X) @ (nil @ A))) = (((cons @ A) @ X) @ (((replicate @ A) @ I) @ X)))))).
% 2.71/1.52 thf(fact_233_Nil__is__map__conv, axiom, (! [A:$tType,B:$tType,F2:(B > A),Xs:(list @ B)]: ((((nil @ A) = ((((map @ B) @ A) @ F2) @ Xs)) = (Xs = (nil @ B)))))).
% 2.71/1.52 thf(fact_234_map__is__Nil__conv, axiom, (! [A:$tType,B:$tType,F2:(B > A),Xs:(list @ B)]: (((((((map @ B) @ A) @ F2) @ Xs) = (nil @ A)) = (Xs = (nil @ B)))))).
% 2.71/1.52 thf(fact_235_list_Omap__disc__iff, axiom, (! [B:$tType,A:$tType,F2:(A > B),A3:(list @ A)]: (((((((map @ A) @ B) @ F2) @ A3) = (nil @ B)) = (A3 = (nil @ A)))))).
% 2.71/1.52 thf(fact_236_map__append, axiom, (! [A:$tType,B:$tType,F2:(B > A),Xs:(list @ B),Ys2:(list @ B)]: ((((((map @ B) @ A) @ F2) @ (((append @ B) @ Xs) @ Ys2)) = (((append @ A) @ ((((map @ B) @ A) @ F2) @ Xs)) @ ((((map @ B) @ A) @ F2) @ Ys2)))))).
% 2.71/1.52 thf(fact_237_map__replicate, axiom, (! [A:$tType,B:$tType,F2:(B > A),N:nat,X:B]: ((((((map @ B) @ A) @ F2) @ (((replicate @ B) @ N) @ X)) = (((replicate @ A) @ N) @ (F2 @ X)))))).
% 2.71/1.52 thf(fact_238_rev__replicate, axiom, (! [A:$tType,N:nat,X:A]: ((((rev @ A) @ (((replicate @ A) @ N) @ X)) = (((replicate @ A) @ N) @ X))))).
% 2.71/1.52 thf(fact_239_smap__shift, axiom, (! [A:$tType,B:$tType,F2:(B > A),Xs:(list @ B),S:(stream170649215stream @ B)]: ((((((stream2128578057e_smap @ B) @ A) @ F2) @ (((stream1035003186_shift @ B) @ Xs) @ S)) = (((stream1035003186_shift @ A) @ ((((map @ B) @ A) @ F2) @ Xs)) @ ((((stream2128578057e_smap @ B) @ A) @ F2) @ S)))))).
% 2.71/1.52 thf(fact_240_map__eq__map__tailrec, axiom, (! [B:$tType,A:$tType]: ((((map @ A) @ B) = ((map_tailrec @ A) @ B))))).
% 2.71/1.52 thf(fact_241_list_Omap__sel_I2_J, axiom, (! [B:$tType,A:$tType,A3:(list @ A),F2:(A > B)]: (((A3 != (nil @ A)) => (((tl @ B) @ ((((map @ A) @ B) @ F2) @ A3)) = ((((map @ A) @ B) @ F2) @ ((tl @ A) @ A3))))))).
% 2.71/1.52 thf(fact_242_hd__map, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),F2:(A > B)]: (((Xs != (nil @ A)) => (((hd @ B) @ ((((map @ A) @ B) @ F2) @ Xs)) = (F2 @ ((hd @ A) @ Xs))))))).
% 2.71/1.52 thf(fact_243_list_Omap__sel_I1_J, axiom, (! [B:$tType,A:$tType,A3:(list @ A),F2:(A > B)]: (((A3 != (nil @ A)) => (((hd @ B) @ ((((map @ A) @ B) @ F2) @ A3)) = (F2 @ ((hd @ A) @ A3))))))).
% 2.71/1.52 thf(fact_244_last__map, axiom, (! [B:$tType,A:$tType,Xs:(list @ A),F2:(A > B)]: (((Xs != (nil @ A)) => (((last @ B) @ ((((map @ A) @ B) @ F2) @ Xs)) = (F2 @ ((last @ A) @ Xs))))))).
% 2.71/1.52 thf(fact_245_replicate__app__Cons__same, axiom, (! [A:$tType,N:nat,X:A,Xs:(list @ A)]: (((((append @ A) @ (((replicate @ A) @ N) @ X)) @ (((cons @ A) @ X) @ Xs)) = (((cons @ A) @ X) @ (((append @ A) @ (((replicate @ A) @ N) @ X)) @ Xs)))))).
% 2.71/1.52 thf(fact_246_list_Osimps_I9_J, axiom, (! [B:$tType,A:$tType,F2:(A > B),X21:A,X222:(list @ A)]: ((((((map @ A) @ B) @ F2) @ (((cons @ A) @ X21) @ X222)) = (((cons @ B) @ (F2 @ X21)) @ ((((map @ A) @ B) @ F2) @ X222)))))).
% 2.71/1.52 thf(fact_247_Cons__eq__map__D, axiom, (! [A:$tType,B:$tType,X:A,Xs:(list @ A),F2:(B > A),Ys2:(list @ B)]: ((((((cons @ A) @ X) @ Xs) = ((((map @ B) @ A) @ F2) @ Ys2)) => (? [Z:B,Zs2:(list @ B)]: (((Ys2 = (((cons @ B) @ Z) @ Zs2)) & ((X = (F2 @ Z)) & (Xs = ((((map @ B) @ A) @ F2) @ Zs2)))))))))).
% 2.71/1.52 thf(fact_248_map__eq__Cons__D, axiom, (! [B:$tType,A:$tType,F2:(B > A),Xs:(list @ B),Y:A,Ys2:(list @ A)]: (((((((map @ B) @ A) @ F2) @ Xs) = (((cons @ A) @ Y) @ Ys2)) => (? [Z:B,Zs2:(list @ B)]: (((Xs = (((cons @ B) @ Z) @ Zs2)) & (((F2 @ Z) = Y) & (((((map @ B) @ A) @ F2) @ Zs2) = Ys2))))))))).
% 2.71/1.52 thf(fact_249_Cons__eq__map__conv, axiom, (! [A:$tType,B:$tType,X:A,Xs:(list @ A),F2:(B > A),Ys2:(list @ B)]: ((((((cons @ A) @ X) @ Xs) = ((((map @ B) @ A) @ F2) @ Ys2)) = (? [Z2:B,Zs3:(list @ B)]: (((Ys2 = (((cons @ B) @ Z2) @ Zs3)) & ((X = (F2 @ Z2)) & (Xs = ((((map @ B) @ A) @ F2) @ Zs3)))))))))).
% 2.71/1.52 thf(fact_250_map__eq__Cons__conv, axiom, (! [A:$tType,B:$tType,F2:(B > A),Xs:(list @ B),Y:A,Ys2:(list @ A)]: (((((((map @ B) @ A) @ F2) @ Xs) = (((cons @ A) @ Y) @ Ys2)) = (? [Z2:B,Zs3:(list @ B)]: (((Xs = (((cons @ B) @ Z2) @ Zs3)) & (((F2 @ Z2) = Y) & (((((map @ B) @ A) @ F2) @ Zs3) = Ys2))))))))).
% 2.71/1.52 thf(fact_251_list_Osimps_I8_J, axiom, (! [A:$tType,B:$tType,F2:(A > B)]: ((((((map @ A) @ B) @ F2) @ (nil @ A)) = (nil @ B))))).
% 2.71/1.52 thf(fact_252_map__tl, axiom, (! [A:$tType,B:$tType,F2:(B > A),Xs:(list @ B)]: ((((((map @ B) @ A) @ F2) @ ((tl @ B) @ Xs)) = ((tl @ A) @ ((((map @ B) @ A) @ F2) @ Xs)))))).
% 2.71/1.52 thf(fact_253_append__replicate__commute, axiom, (! [A:$tType,N:nat,X:A,K:nat]: (((((append @ A) @ (((replicate @ A) @ N) @ X)) @ (((replicate @ A) @ K) @ X)) = (((append @ A) @ (((replicate @ A) @ K) @ X)) @ (((replicate @ A) @ N) @ X)))))).
% 2.71/1.52 thf(fact_254_map__butlast, axiom, (! [A:$tType,B:$tType,F2:(B > A),Xs:(list @ B)]: ((((((map @ B) @ A) @ F2) @ ((butlast @ B) @ Xs)) = ((butlast @ A) @ ((((map @ B) @ A) @ F2) @ Xs)))))).
% 2.71/1.52 thf(tcon_fun___Orderings_Oorder, axiom, (! [A7:$tType,A8:$tType]: ((((order @ A8) @ (type2 @ A8)) => ((order @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.71/1.52 thf(tcon_fun___Orderings_Oord, axiom, (! [A7:$tType,A8:$tType]: ((((ord @ A8) @ (type2 @ A8)) => ((ord @ (A7 > A8)) @ (type2 @ (A7 > A8))))))).
% 2.71/1.52 thf(tcon_Set_Oset___Orderings_Oorder_1, axiom, (! [A7:$tType]: (((order @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.71/1.52 thf(tcon_Set_Oset___Orderings_Oord_2, axiom, (! [A7:$tType]: (((ord @ (set @ A7)) @ (type2 @ (set @ A7)))))).
% 2.71/1.52 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 2.71/1.52 thf(tcon_HOL_Obool___Orderings_Oorder_3, axiom, ((order @ $o) @ (type2 @ $o))).
% 2.71/1.52 thf(tcon_HOL_Obool___Orderings_Oord_4, axiom, ((ord @ $o) @ (type2 @ $o))).
% 2.71/1.52 thf(help_If_3_1_T, axiom, (! [P2:$o]: (((P2 = $true) | (P2 = $false))))).
% 2.71/1.52 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.71/1.52 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.71/1.52 thf(conj_0, hypothesis, (((stream_Mirabelle_shd @ (list @ a)) @ ws) != (nil @ a))).
% 2.71/1.52 thf(conj_1, conjecture, (((stream942386729e_flat @ a) @ ws) = (((stream1035003186_shift @ a) @ ((stream_Mirabelle_shd @ (list @ a)) @ ws)) @ ((stream942386729e_flat @ a) @ ((stream_Mirabelle_stl @ (list @ a)) @ ws))))).
% 2.71/1.52 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.wxvlm3pJrl/DTF2DTF3154.p
% 2.71/1.52 ------------------------
% 2.71/1.55 ---- Cleaned THF ---
% 2.71/1.55 thf(ty_t_Stream__Mirabelle__hbrgyiwlrc_Ostream,type,
% 2.71/1.55 stream170649215stream: $tType > $tType ).
% 2.71/1.55
% 2.71/1.55 thf(ty_t_List_Olist,type,
% 2.71/1.55 list: $tType > $tType ).
% 2.71/1.55
% 2.71/1.55 thf(ty_t_Set_Oset,type,
% 2.71/1.55 set: $tType > $tType ).
% 2.71/1.55
% 2.71/1.55 thf(ty_t_Nat_Onat,type,
% 2.71/1.55 nat: $tType ).
% 2.71/1.55
% 2.71/1.55 thf(ty_t_itself,type,
% 2.71/1.55 itself: $tType > $tType ).
% 2.71/1.55
% 2.71/1.55 thf(ty_tf_a,type,
% 2.71/1.55 a: $tType ).
% 2.71/1.55
% 2.71/1.55 thf(sy_cl_HOL_Otype,type,
% 2.71/1.55 type:
% 2.71/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_cl_Orderings_Oord,type,
% 2.71/1.55 ord:
% 2.71/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_cl_Orderings_Oorder,type,
% 2.71/1.55 order:
% 2.71/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_cl_Orderings_Olinorder,type,
% 2.71/1.55 linorder:
% 2.71/1.55 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_BNF__Greatest__Fixpoint_OShift,type,
% 2.71/1.55 bNF_Greatest_Shift:
% 2.71/1.55 !>[A: $tType] : ( ( set @ ( list @ A ) ) > A > ( set @ ( list @ A ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_BNF__Greatest__Fixpoint_OSucc,type,
% 2.71/1.55 bNF_Greatest_Succ:
% 2.71/1.55 !>[A: $tType] : ( ( set @ ( list @ A ) ) > ( list @ A ) > ( set @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_BNF__Greatest__Fixpoint_Oshift,type,
% 2.71/1.55 bNF_Greatest_shift:
% 2.71/1.55 !>[A: $tType,B: $tType] : ( ( ( list @ A ) > B ) > A > ( list @ A ) > B ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_If,type,
% 2.71/1.55 if:
% 2.71/1.55 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Oappend,type,
% 2.71/1.55 append:
% 2.71/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Obind,type,
% 2.71/1.55 bind:
% 2.71/1.55 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Obutlast,type,
% 2.71/1.55 butlast:
% 2.71/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Ofold,type,
% 2.71/1.55 fold:
% 2.71/1.55 !>[A: $tType,B: $tType] : ( ( A > B > B ) > ( list @ A ) > B > B ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Oinsert,type,
% 2.71/1.55 insert:
% 2.71/1.55 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Olast,type,
% 2.71/1.55 last:
% 2.71/1.55 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Olist_OCons,type,
% 2.71/1.55 cons:
% 2.71/1.55 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Olist_ONil,type,
% 2.71/1.55 nil:
% 2.71/1.55 !>[A: $tType] : ( list @ A ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Olist_Ocase__list,type,
% 2.71/1.55 case_list:
% 2.71/1.55 !>[B: $tType,A: $tType] : ( B > ( A > ( list @ A ) > B ) > ( list @ A ) > B ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Olist_Ohd,type,
% 2.71/1.55 hd:
% 2.71/1.55 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Olist_Omap,type,
% 2.71/1.55 map:
% 2.71/1.55 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( list @ A ) > ( list @ Aa ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Olist_Otl,type,
% 2.71/1.55 tl:
% 2.71/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Olist__ex1,type,
% 2.71/1.55 list_ex1:
% 2.71/1.55 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Olistrelp,type,
% 2.71/1.55 listrelp:
% 2.71/1.55 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( list @ A ) > ( list @ B ) > $o ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Omap__tailrec,type,
% 2.71/1.55 map_tailrec:
% 2.71/1.55 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Omap__tailrec__rev,type,
% 2.71/1.55 map_tailrec_rev:
% 2.71/1.55 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) > ( list @ B ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Omaps,type,
% 2.71/1.55 maps:
% 2.71/1.55 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Omember,type,
% 2.71/1.55 member:
% 2.71/1.55 !>[A: $tType] : ( ( list @ A ) > A > $o ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Oord_Olexordp__eq,type,
% 2.71/1.55 lexordp_eq:
% 2.71/1.55 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Oord__class_Olexordp,type,
% 2.71/1.55 ord_lexordp:
% 2.71/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Oord__class_Olexordp__eq,type,
% 2.71/1.55 ord_lexordp_eq:
% 2.71/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Oproduct__lists,type,
% 2.71/1.55 product_lists:
% 2.71/1.55 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Oremdups__adj,type,
% 2.71/1.55 remdups_adj:
% 2.71/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Oreplicate,type,
% 2.71/1.55 replicate:
% 2.71/1.55 !>[A: $tType] : ( nat > A > ( list @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Orev,type,
% 2.71/1.55 rev:
% 2.71/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Orotate1,type,
% 2.71/1.55 rotate1:
% 2.71/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Osplice,type,
% 2.71/1.55 splice:
% 2.71/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Osublists,type,
% 2.71/1.55 sublists:
% 2.71/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_List_Ounion,type,
% 2.71/1.55 union:
% 2.71/1.55 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.71/1.55 ord_less:
% 2.71/1.55 !>[A: $tType] : ( A > A > $o ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_Pure_Otype,type,
% 2.71/1.55 type2:
% 2.71/1.55 !>[A: $tType] : ( itself @ A ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_Set_OCollect,type,
% 2.71/1.55 collect:
% 2.71/1.55 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ocycle,type,
% 2.71/1.55 stream317748790_cycle:
% 2.71/1.55 !>[A: $tType] : ( ( list @ A ) > ( stream170649215stream @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Oflat,type,
% 2.71/1.55 stream942386729e_flat:
% 2.71/1.55 !>[A: $tType] : ( ( stream170649215stream @ ( list @ A ) ) > ( stream170649215stream @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osdrop__while,type,
% 2.71/1.55 stream1195056575_while:
% 2.71/1.55 !>[A: $tType] : ( ( A > $o ) > ( stream170649215stream @ A ) > ( stream170649215stream @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Oshift,type,
% 2.71/1.55 stream1035003186_shift:
% 2.71/1.55 !>[A: $tType] : ( ( list @ A ) > ( stream170649215stream @ A ) > ( stream170649215stream @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osmember,type,
% 2.71/1.55 stream1586597341member:
% 2.71/1.55 !>[A: $tType] : ( A > ( stream170649215stream @ A ) > $o ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_OSCons,type,
% 2.71/1.55 stream641971652_SCons:
% 2.71/1.55 !>[A: $tType] : ( A > ( stream170649215stream @ A ) > ( stream170649215stream @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Ocase__stream,type,
% 2.71/1.55 stream1342653232stream:
% 2.71/1.55 !>[A: $tType,B: $tType] : ( ( A > ( stream170649215stream @ A ) > B ) > ( stream170649215stream @ A ) > B ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Oshd,type,
% 2.71/1.55 stream_Mirabelle_shd:
% 2.71/1.55 !>[A: $tType] : ( ( stream170649215stream @ A ) > A ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Osmap,type,
% 2.71/1.55 stream2128578057e_smap:
% 2.71/1.55 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( stream170649215stream @ A ) > ( stream170649215stream @ Aa ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Ostl,type,
% 2.71/1.55 stream_Mirabelle_stl:
% 2.71/1.55 !>[A: $tType] : ( ( stream170649215stream @ A ) > ( stream170649215stream @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostreams,type,
% 2.71/1.55 stream2015131171treams:
% 2.71/1.55 !>[A: $tType] : ( ( set @ A ) > ( set @ ( stream170649215stream @ A ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_c_member,type,
% 2.71/1.55 member2:
% 2.71/1.55 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.71/1.55
% 2.71/1.55 thf(sy_v_ws,type,
% 2.71/1.55 ws: stream170649215stream @ ( list @ a ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_0_shift__left__inj,axiom,
% 2.71/1.55 ! [A: $tType,Xs: list @ A,S1: stream170649215stream @ A,S2: stream170649215stream @ A] :
% 2.71/1.55 ( ( ( stream1035003186_shift @ A @ Xs @ S1 )
% 2.71/1.55 = ( stream1035003186_shift @ A @ Xs @ S2 ) )
% 2.71/1.55 = ( S1 = S2 ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_1_shift_Osimps_I1_J,axiom,
% 2.71/1.55 ! [A: $tType,S: stream170649215stream @ A] :
% 2.71/1.55 ( ( stream1035003186_shift @ A @ ( nil @ A ) @ S )
% 2.71/1.55 = S ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_2_stream_Oexpand,axiom,
% 2.71/1.55 ! [A: $tType,Stream: stream170649215stream @ A,Stream2: stream170649215stream @ A] :
% 2.71/1.55 ( ( ( ( stream_Mirabelle_shd @ A @ Stream )
% 2.71/1.55 = ( stream_Mirabelle_shd @ A @ Stream2 ) )
% 2.71/1.55 & ( ( stream_Mirabelle_stl @ A @ Stream )
% 2.71/1.55 = ( stream_Mirabelle_stl @ A @ Stream2 ) ) )
% 2.71/1.55 => ( Stream = Stream2 ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_3_stream_Ocoinduct,axiom,
% 2.71/1.55 ! [A: $tType,R: ( stream170649215stream @ A ) > ( stream170649215stream @ A ) > $o,Stream: stream170649215stream @ A,Stream2: stream170649215stream @ A] :
% 2.71/1.55 ( ( R @ Stream @ Stream2 )
% 2.71/1.55 => ( ! [Stream3: stream170649215stream @ A,Stream4: stream170649215stream @ A] :
% 2.71/1.55 ( ( R @ Stream3 @ Stream4 )
% 2.71/1.55 => ( ( ( stream_Mirabelle_shd @ A @ Stream3 )
% 2.71/1.55 = ( stream_Mirabelle_shd @ A @ Stream4 ) )
% 2.71/1.55 & ( R @ ( stream_Mirabelle_stl @ A @ Stream3 ) @ ( stream_Mirabelle_stl @ A @ Stream4 ) ) ) )
% 2.71/1.55 => ( Stream = Stream2 ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_4_stream_Ocoinduct__strong,axiom,
% 2.71/1.55 ! [A: $tType,R: ( stream170649215stream @ A ) > ( stream170649215stream @ A ) > $o,Stream: stream170649215stream @ A,Stream2: stream170649215stream @ A] :
% 2.71/1.55 ( ( R @ Stream @ Stream2 )
% 2.71/1.55 => ( ! [Stream3: stream170649215stream @ A,Stream4: stream170649215stream @ A] :
% 2.71/1.55 ( ( R @ Stream3 @ Stream4 )
% 2.71/1.55 => ( ( ( stream_Mirabelle_shd @ A @ Stream3 )
% 2.71/1.55 = ( stream_Mirabelle_shd @ A @ Stream4 ) )
% 2.71/1.55 & ( ( R @ ( stream_Mirabelle_stl @ A @ Stream3 ) @ ( stream_Mirabelle_stl @ A @ Stream4 ) )
% 2.71/1.55 | ( ( stream_Mirabelle_stl @ A @ Stream3 )
% 2.71/1.55 = ( stream_Mirabelle_stl @ A @ Stream4 ) ) ) ) )
% 2.71/1.55 => ( Stream = Stream2 ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_5_flat__Stream,axiom,
% 2.71/1.55 ! [A: $tType,Xs: list @ A,Ws: stream170649215stream @ ( list @ A )] :
% 2.71/1.55 ( ( Xs
% 2.71/1.55 != ( nil @ A ) )
% 2.71/1.55 => ( ( stream942386729e_flat @ A @ ( stream641971652_SCons @ ( list @ A ) @ Xs @ Ws ) )
% 2.71/1.55 = ( stream1035003186_shift @ A @ Xs @ ( stream942386729e_flat @ A @ Ws ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_6_shift__simps_I1_J,axiom,
% 2.71/1.55 ! [A: $tType,Xs: list @ A,S: stream170649215stream @ A] :
% 2.71/1.55 ( ( ( Xs
% 2.71/1.55 = ( nil @ A ) )
% 2.71/1.55 => ( ( stream_Mirabelle_shd @ A @ ( stream1035003186_shift @ A @ Xs @ S ) )
% 2.71/1.55 = ( stream_Mirabelle_shd @ A @ S ) ) )
% 2.71/1.55 & ( ( Xs
% 2.71/1.55 != ( nil @ A ) )
% 2.71/1.55 => ( ( stream_Mirabelle_shd @ A @ ( stream1035003186_shift @ A @ Xs @ S ) )
% 2.71/1.55 = ( hd @ A @ Xs ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_7_flat_Osimps_I1_J,axiom,
% 2.71/1.55 ! [A: $tType,Ws: stream170649215stream @ ( list @ A )] :
% 2.71/1.55 ( ( stream_Mirabelle_shd @ A @ ( stream942386729e_flat @ A @ Ws ) )
% 2.71/1.55 = ( hd @ A @ ( stream_Mirabelle_shd @ ( list @ A ) @ Ws ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_8_stream_Ocase__eq__if,axiom,
% 2.71/1.55 ! [B: $tType,A: $tType] :
% 2.71/1.55 ( ( stream1342653232stream @ A @ B )
% 2.71/1.55 = ( ^ [F: A > ( stream170649215stream @ A ) > B,Stream5: stream170649215stream @ A] : ( F @ ( stream_Mirabelle_shd @ A @ Stream5 ) @ ( stream_Mirabelle_stl @ A @ Stream5 ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_9_shift__simps_I2_J,axiom,
% 2.71/1.55 ! [A: $tType,Xs: list @ A,S: stream170649215stream @ A] :
% 2.71/1.55 ( ( ( Xs
% 2.71/1.55 = ( nil @ A ) )
% 2.71/1.55 => ( ( stream_Mirabelle_stl @ A @ ( stream1035003186_shift @ A @ Xs @ S ) )
% 2.71/1.55 = ( stream_Mirabelle_stl @ A @ S ) ) )
% 2.71/1.55 & ( ( Xs
% 2.71/1.55 != ( nil @ A ) )
% 2.71/1.55 => ( ( stream_Mirabelle_stl @ A @ ( stream1035003186_shift @ A @ Xs @ S ) )
% 2.71/1.55 = ( stream1035003186_shift @ A @ ( tl @ A @ Xs ) @ S ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_10_sdrop__while_Osimps,axiom,
% 2.71/1.55 ! [A: $tType] :
% 2.71/1.55 ( ( stream1195056575_while @ A )
% 2.71/1.55 = ( ^ [P: A > $o,S3: stream170649215stream @ A] : ( if @ ( stream170649215stream @ A ) @ ( P @ ( stream_Mirabelle_shd @ A @ S3 ) ) @ ( stream1195056575_while @ A @ P @ ( stream_Mirabelle_stl @ A @ S3 ) ) @ S3 ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_11_flat_Osimps_I2_J,axiom,
% 2.71/1.55 ! [A: $tType,Ws: stream170649215stream @ ( list @ A )] :
% 2.71/1.55 ( ( stream_Mirabelle_stl @ A @ ( stream942386729e_flat @ A @ Ws ) )
% 2.71/1.55 = ( stream942386729e_flat @ A
% 2.71/1.55 @ ( if @ ( stream170649215stream @ ( list @ A ) )
% 2.71/1.55 @ ( ( tl @ A @ ( stream_Mirabelle_shd @ ( list @ A ) @ Ws ) )
% 2.71/1.55 = ( nil @ A ) )
% 2.71/1.55 @ ( stream_Mirabelle_stl @ ( list @ A ) @ Ws )
% 2.71/1.55 @ ( stream641971652_SCons @ ( list @ A ) @ ( tl @ A @ ( stream_Mirabelle_shd @ ( list @ A ) @ Ws ) ) @ ( stream_Mirabelle_stl @ ( list @ A ) @ Ws ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_12_cycle__decomp,axiom,
% 2.71/1.55 ! [A: $tType,U: list @ A] :
% 2.71/1.55 ( ( U
% 2.71/1.55 != ( nil @ A ) )
% 2.71/1.55 => ( ( stream317748790_cycle @ A @ U )
% 2.71/1.55 = ( stream1035003186_shift @ A @ U @ ( stream317748790_cycle @ A @ U ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_13_stream_Ocollapse,axiom,
% 2.71/1.55 ! [A: $tType,Stream: stream170649215stream @ A] :
% 2.71/1.55 ( ( stream641971652_SCons @ A @ ( stream_Mirabelle_shd @ A @ Stream ) @ ( stream_Mirabelle_stl @ A @ Stream ) )
% 2.71/1.55 = Stream ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_14_streamsE,axiom,
% 2.71/1.55 ! [A: $tType,S: stream170649215stream @ A,A2: set @ A] :
% 2.71/1.55 ( ( member2 @ ( stream170649215stream @ A ) @ S @ ( stream2015131171treams @ A @ A2 ) )
% 2.71/1.55 => ~ ( ( member2 @ A @ ( stream_Mirabelle_shd @ A @ S ) @ A2 )
% 2.71/1.55 => ~ ( member2 @ ( stream170649215stream @ A ) @ ( stream_Mirabelle_stl @ A @ S ) @ ( stream2015131171treams @ A @ A2 ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_15_in__streams,axiom,
% 2.71/1.55 ! [A: $tType,S: stream170649215stream @ A,S4: set @ A] :
% 2.71/1.55 ( ( member2 @ ( stream170649215stream @ A ) @ ( stream_Mirabelle_stl @ A @ S ) @ ( stream2015131171treams @ A @ S4 ) )
% 2.71/1.55 => ( ( member2 @ A @ ( stream_Mirabelle_shd @ A @ S ) @ S4 )
% 2.71/1.55 => ( member2 @ ( stream170649215stream @ A ) @ S @ ( stream2015131171treams @ A @ S4 ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_16_stream_Oinject,axiom,
% 2.71/1.55 ! [A: $tType,X1: A,X2: stream170649215stream @ A,Y1: A,Y2: stream170649215stream @ A] :
% 2.71/1.55 ( ( ( stream641971652_SCons @ A @ X1 @ X2 )
% 2.71/1.55 = ( stream641971652_SCons @ A @ Y1 @ Y2 ) )
% 2.71/1.55 = ( ( X1 = Y1 )
% 2.71/1.55 & ( X2 = Y2 ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_17_list_Oexpand,axiom,
% 2.71/1.55 ! [A: $tType,List: list @ A,List2: list @ A] :
% 2.71/1.55 ( ( ( List
% 2.71/1.55 = ( nil @ A ) )
% 2.71/1.55 = ( List2
% 2.71/1.55 = ( nil @ A ) ) )
% 2.71/1.55 => ( ( ( List
% 2.71/1.55 != ( nil @ A ) )
% 2.71/1.55 => ( ( List2
% 2.71/1.55 != ( nil @ A ) )
% 2.71/1.55 => ( ( ( hd @ A @ List )
% 2.71/1.55 = ( hd @ A @ List2 ) )
% 2.71/1.55 & ( ( tl @ A @ List )
% 2.71/1.55 = ( tl @ A @ List2 ) ) ) ) )
% 2.71/1.55 => ( List = List2 ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_18_stream_Ocase,axiom,
% 2.71/1.55 ! [B: $tType,A: $tType,F2: A > ( stream170649215stream @ A ) > B,X1: A,X2: stream170649215stream @ A] :
% 2.71/1.55 ( ( stream1342653232stream @ A @ B @ F2 @ ( stream641971652_SCons @ A @ X1 @ X2 ) )
% 2.71/1.55 = ( F2 @ X1 @ X2 ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_19_streams_Ocases,axiom,
% 2.71/1.55 ! [A: $tType,A3: stream170649215stream @ A,A2: set @ A] :
% 2.71/1.55 ( ( member2 @ ( stream170649215stream @ A ) @ A3 @ ( stream2015131171treams @ A @ A2 ) )
% 2.71/1.55 => ~ ! [A4: A,S5: stream170649215stream @ A] :
% 2.71/1.55 ( ( A3
% 2.71/1.55 = ( stream641971652_SCons @ A @ A4 @ S5 ) )
% 2.71/1.55 => ( ( member2 @ A @ A4 @ A2 )
% 2.71/1.55 => ~ ( member2 @ ( stream170649215stream @ A ) @ S5 @ ( stream2015131171treams @ A @ A2 ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_20_streams_Osimps,axiom,
% 2.71/1.55 ! [A: $tType,A3: stream170649215stream @ A,A2: set @ A] :
% 2.71/1.55 ( ( member2 @ ( stream170649215stream @ A ) @ A3 @ ( stream2015131171treams @ A @ A2 ) )
% 2.71/1.55 = ( ? [A5: A,S3: stream170649215stream @ A] :
% 2.71/1.55 ( ( A3
% 2.71/1.55 = ( stream641971652_SCons @ A @ A5 @ S3 ) )
% 2.71/1.55 & ( member2 @ A @ A5 @ A2 )
% 2.71/1.55 & ( member2 @ ( stream170649215stream @ A ) @ S3 @ ( stream2015131171treams @ A @ A2 ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_21_stream_Oexhaust,axiom,
% 2.71/1.55 ! [A: $tType,Y: stream170649215stream @ A] :
% 2.71/1.55 ~ ! [X12: A,X22: stream170649215stream @ A] :
% 2.71/1.55 ( Y
% 2.71/1.55 != ( stream641971652_SCons @ A @ X12 @ X22 ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_22_streams__Stream,axiom,
% 2.71/1.55 ! [A: $tType,X: A,S: stream170649215stream @ A,A2: set @ A] :
% 2.71/1.55 ( ( member2 @ ( stream170649215stream @ A ) @ ( stream641971652_SCons @ A @ X @ S ) @ ( stream2015131171treams @ A @ A2 ) )
% 2.71/1.55 = ( ( member2 @ A @ X @ A2 )
% 2.71/1.55 & ( member2 @ ( stream170649215stream @ A ) @ S @ ( stream2015131171treams @ A @ A2 ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_23_streams_Ocoinduct,axiom,
% 2.71/1.55 ! [A: $tType,X3: ( stream170649215stream @ A ) > $o,X: stream170649215stream @ A,A2: set @ A] :
% 2.71/1.55 ( ( X3 @ X )
% 2.71/1.55 => ( ! [X4: stream170649215stream @ A] :
% 2.71/1.55 ( ( X3 @ X4 )
% 2.71/1.55 => ? [A6: A,S6: stream170649215stream @ A] :
% 2.71/1.55 ( ( X4
% 2.71/1.55 = ( stream641971652_SCons @ A @ A6 @ S6 ) )
% 2.71/1.55 & ( member2 @ A @ A6 @ A2 )
% 2.71/1.55 & ( ( X3 @ S6 )
% 2.71/1.55 | ( member2 @ ( stream170649215stream @ A ) @ S6 @ ( stream2015131171treams @ A @ A2 ) ) ) ) )
% 2.71/1.55 => ( member2 @ ( stream170649215stream @ A ) @ X @ ( stream2015131171treams @ A @ A2 ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_24_sdrop__while__SCons,axiom,
% 2.71/1.55 ! [A: $tType,P2: A > $o,A3: A,S: stream170649215stream @ A] :
% 2.71/1.55 ( ( ( P2 @ A3 )
% 2.71/1.55 => ( ( stream1195056575_while @ A @ P2 @ ( stream641971652_SCons @ A @ A3 @ S ) )
% 2.71/1.55 = ( stream1195056575_while @ A @ P2 @ S ) ) )
% 2.71/1.55 & ( ~ ( P2 @ A3 )
% 2.71/1.55 => ( ( stream1195056575_while @ A @ P2 @ ( stream641971652_SCons @ A @ A3 @ S ) )
% 2.71/1.55 = ( stream641971652_SCons @ A @ A3 @ S ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_25_list_Osel_I2_J,axiom,
% 2.71/1.55 ! [A: $tType] :
% 2.71/1.55 ( ( tl @ A @ ( nil @ A ) )
% 2.71/1.55 = ( nil @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_26_cycle_Osimps_I1_J,axiom,
% 2.71/1.55 ! [A: $tType,Xs: list @ A] :
% 2.71/1.55 ( ( stream_Mirabelle_shd @ A @ ( stream317748790_cycle @ A @ Xs ) )
% 2.71/1.55 = ( hd @ A @ Xs ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_27_flat_Ocode,axiom,
% 2.71/1.55 ! [A: $tType] :
% 2.71/1.55 ( ( stream942386729e_flat @ A )
% 2.71/1.55 = ( ^ [Ws2: stream170649215stream @ ( list @ A )] :
% 2.71/1.55 ( stream641971652_SCons @ A @ ( hd @ A @ ( stream_Mirabelle_shd @ ( list @ A ) @ Ws2 ) )
% 2.71/1.55 @ ( stream942386729e_flat @ A
% 2.71/1.55 @ ( if @ ( stream170649215stream @ ( list @ A ) )
% 2.71/1.55 @ ( ( tl @ A @ ( stream_Mirabelle_shd @ ( list @ A ) @ Ws2 ) )
% 2.71/1.55 = ( nil @ A ) )
% 2.71/1.55 @ ( stream_Mirabelle_stl @ ( list @ A ) @ Ws2 )
% 2.71/1.55 @ ( stream641971652_SCons @ ( list @ A ) @ ( tl @ A @ ( stream_Mirabelle_shd @ ( list @ A ) @ Ws2 ) ) @ ( stream_Mirabelle_stl @ ( list @ A ) @ Ws2 ) ) ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_28_stream_Osel_I2_J,axiom,
% 2.71/1.55 ! [A: $tType,X1: A,X2: stream170649215stream @ A] :
% 2.71/1.55 ( ( stream_Mirabelle_stl @ A @ ( stream641971652_SCons @ A @ X1 @ X2 ) )
% 2.71/1.55 = X2 ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_29_stream_Osel_I1_J,axiom,
% 2.71/1.55 ! [A: $tType,X1: A,X2: stream170649215stream @ A] :
% 2.71/1.55 ( ( stream_Mirabelle_shd @ A @ ( stream641971652_SCons @ A @ X1 @ X2 ) )
% 2.71/1.55 = X1 ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_30_stream_Osplit__sel__asm,axiom,
% 2.71/1.55 ! [B: $tType,A: $tType,P2: B > $o,F2: A > ( stream170649215stream @ A ) > B,Stream: stream170649215stream @ A] :
% 2.71/1.55 ( ( P2 @ ( stream1342653232stream @ A @ B @ F2 @ Stream ) )
% 2.71/1.55 = ( ~ ( ( Stream
% 2.71/1.55 = ( stream641971652_SCons @ A @ ( stream_Mirabelle_shd @ A @ Stream ) @ ( stream_Mirabelle_stl @ A @ Stream ) ) )
% 2.71/1.55 & ~ ( P2 @ ( F2 @ ( stream_Mirabelle_shd @ A @ Stream ) @ ( stream_Mirabelle_stl @ A @ Stream ) ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_31_stream_Osplit__sel,axiom,
% 2.71/1.55 ! [B: $tType,A: $tType,P2: B > $o,F2: A > ( stream170649215stream @ A ) > B,Stream: stream170649215stream @ A] :
% 2.71/1.55 ( ( P2 @ ( stream1342653232stream @ A @ B @ F2 @ Stream ) )
% 2.71/1.55 = ( ( Stream
% 2.71/1.55 = ( stream641971652_SCons @ A @ ( stream_Mirabelle_shd @ A @ Stream ) @ ( stream_Mirabelle_stl @ A @ Stream ) ) )
% 2.71/1.55 => ( P2 @ ( F2 @ ( stream_Mirabelle_shd @ A @ Stream ) @ ( stream_Mirabelle_stl @ A @ Stream ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_32_streams__stl,axiom,
% 2.71/1.55 ! [A: $tType,S: stream170649215stream @ A,A2: set @ A] :
% 2.71/1.55 ( ( member2 @ ( stream170649215stream @ A ) @ S @ ( stream2015131171treams @ A @ A2 ) )
% 2.71/1.55 => ( member2 @ ( stream170649215stream @ A ) @ ( stream_Mirabelle_stl @ A @ S ) @ ( stream2015131171treams @ A @ A2 ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_33_streams__shd,axiom,
% 2.71/1.55 ! [A: $tType,S: stream170649215stream @ A,A2: set @ A] :
% 2.71/1.55 ( ( member2 @ ( stream170649215stream @ A ) @ S @ ( stream2015131171treams @ A @ A2 ) )
% 2.71/1.55 => ( member2 @ A @ ( stream_Mirabelle_shd @ A @ S ) @ A2 ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_34_stream_Oexhaust__sel,axiom,
% 2.71/1.55 ! [A: $tType,Stream: stream170649215stream @ A] :
% 2.71/1.55 ( Stream
% 2.71/1.55 = ( stream641971652_SCons @ A @ ( stream_Mirabelle_shd @ A @ Stream ) @ ( stream_Mirabelle_stl @ A @ Stream ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_35_smember__code,axiom,
% 2.71/1.55 ! [A: $tType,X: A,Y: A,S: stream170649215stream @ A] :
% 2.71/1.55 ( ( stream1586597341member @ A @ X @ ( stream641971652_SCons @ A @ Y @ S ) )
% 2.71/1.55 = ( ( X != Y )
% 2.71/1.55 => ( stream1586597341member @ A @ X @ S ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_36_flat__Cons,axiom,
% 2.71/1.55 ! [A: $tType,X: A,Xs: list @ A,Ws: stream170649215stream @ ( list @ A )] :
% 2.71/1.55 ( ( stream942386729e_flat @ A @ ( stream641971652_SCons @ ( list @ A ) @ ( cons @ A @ X @ Xs ) @ Ws ) )
% 2.71/1.55 = ( stream641971652_SCons @ A @ X
% 2.71/1.55 @ ( stream942386729e_flat @ A
% 2.71/1.55 @ ( if @ ( stream170649215stream @ ( list @ A ) )
% 2.71/1.55 @ ( Xs
% 2.71/1.55 = ( nil @ A ) )
% 2.71/1.55 @ Ws
% 2.71/1.55 @ ( stream641971652_SCons @ ( list @ A ) @ Xs @ Ws ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_37_list_Ocase__eq__if,axiom,
% 2.71/1.55 ! [A: $tType,B: $tType] :
% 2.71/1.55 ( ( case_list @ B @ A )
% 2.71/1.55 = ( ^ [F1: B,F22: A > ( list @ A ) > B,List3: list @ A] :
% 2.71/1.55 ( if @ B
% 2.71/1.55 @ ( List3
% 2.71/1.55 = ( nil @ A ) )
% 2.71/1.55 @ F1
% 2.71/1.55 @ ( F22 @ ( hd @ A @ List3 ) @ ( tl @ A @ List3 ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_38_list__ex1__simps_I1_J,axiom,
% 2.71/1.55 ! [A: $tType,P2: A > $o] :
% 2.71/1.55 ~ ( list_ex1 @ A @ P2 @ ( nil @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_39_hd__Cons__tl,axiom,
% 2.71/1.55 ! [A: $tType,Xs: list @ A] :
% 2.71/1.55 ( ( Xs
% 2.71/1.55 != ( nil @ A ) )
% 2.71/1.55 => ( ( cons @ A @ ( hd @ A @ Xs ) @ ( tl @ A @ Xs ) )
% 2.71/1.55 = Xs ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_40_list_Ocollapse,axiom,
% 2.71/1.55 ! [A: $tType,List: list @ A] :
% 2.71/1.55 ( ( List
% 2.71/1.55 != ( nil @ A ) )
% 2.71/1.55 => ( ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) )
% 2.71/1.55 = List ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_41_smap__ctr,axiom,
% 2.71/1.55 ! [B: $tType,A: $tType,F2: B > A,S: stream170649215stream @ B,X: A,S7: stream170649215stream @ A] :
% 2.71/1.55 ( ( ( stream2128578057e_smap @ B @ A @ F2 @ S )
% 2.71/1.55 = ( stream641971652_SCons @ A @ X @ S7 ) )
% 2.71/1.55 = ( ( ( F2 @ ( stream_Mirabelle_shd @ B @ S ) )
% 2.71/1.55 = X )
% 2.71/1.55 & ( ( stream2128578057e_smap @ B @ A @ F2 @ ( stream_Mirabelle_stl @ B @ S ) )
% 2.71/1.55 = S7 ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_42_bind__simps_I1_J,axiom,
% 2.71/1.55 ! [B: $tType,A: $tType,F2: B > ( list @ A )] :
% 2.71/1.55 ( ( bind @ B @ A @ ( nil @ B ) @ F2 )
% 2.71/1.55 = ( nil @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_43_list_Oexhaust__sel,axiom,
% 2.71/1.55 ! [A: $tType,List: list @ A] :
% 2.71/1.55 ( ( List
% 2.71/1.55 != ( nil @ A ) )
% 2.71/1.55 => ( List
% 2.71/1.55 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_44_mem__Collect__eq,axiom,
% 2.71/1.55 ! [A: $tType,A3: A,P2: A > $o] :
% 2.71/1.55 ( ( member2 @ A @ A3 @ ( collect @ A @ P2 ) )
% 2.71/1.55 = ( P2 @ A3 ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_45_Collect__mem__eq,axiom,
% 2.71/1.55 ! [A: $tType,A2: set @ A] :
% 2.71/1.55 ( ( collect @ A
% 2.71/1.55 @ ^ [X5: A] : ( member2 @ A @ X5 @ A2 ) )
% 2.71/1.55 = A2 ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_46_Collect__cong,axiom,
% 2.71/1.55 ! [A: $tType,P2: A > $o,Q: A > $o] :
% 2.71/1.55 ( ! [X4: A] :
% 2.71/1.55 ( ( P2 @ X4 )
% 2.71/1.55 = ( Q @ X4 ) )
% 2.71/1.55 => ( ( collect @ A @ P2 )
% 2.71/1.55 = ( collect @ A @ Q ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_47_ext,axiom,
% 2.71/1.55 ! [B: $tType,A: $tType,F2: A > B,G: A > B] :
% 2.71/1.55 ( ! [X4: A] :
% 2.71/1.55 ( ( F2 @ X4 )
% 2.71/1.55 = ( G @ X4 ) )
% 2.71/1.55 => ( F2 = G ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_48_member__rec_I2_J,axiom,
% 2.71/1.55 ! [A: $tType,Y: A] :
% 2.71/1.55 ~ ( member @ A @ ( nil @ A ) @ Y ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_49_list_Oinject,axiom,
% 2.71/1.55 ! [A: $tType,X21: A,X222: list @ A,Y21: A,Y22: list @ A] :
% 2.71/1.55 ( ( ( cons @ A @ X21 @ X222 )
% 2.71/1.55 = ( cons @ A @ Y21 @ Y22 ) )
% 2.71/1.55 = ( ( X21 = Y21 )
% 2.71/1.55 & ( X222 = Y22 ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_50_stream_Omap__sel_I2_J,axiom,
% 2.71/1.55 ! [B: $tType,A: $tType,F2: A > B,A3: stream170649215stream @ A] :
% 2.71/1.55 ( ( stream_Mirabelle_stl @ B @ ( stream2128578057e_smap @ A @ B @ F2 @ A3 ) )
% 2.71/1.55 = ( stream2128578057e_smap @ A @ B @ F2 @ ( stream_Mirabelle_stl @ A @ A3 ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_51_stream_Omap__sel_I1_J,axiom,
% 2.71/1.55 ! [B: $tType,A: $tType,F2: A > B,A3: stream170649215stream @ A] :
% 2.71/1.55 ( ( stream_Mirabelle_shd @ B @ ( stream2128578057e_smap @ A @ B @ F2 @ A3 ) )
% 2.71/1.55 = ( F2 @ ( stream_Mirabelle_shd @ A @ A3 ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_52_list_Osimps_I5_J,axiom,
% 2.71/1.55 ! [B: $tType,A: $tType,F12: B,F23: A > ( list @ A ) > B,X21: A,X222: list @ A] :
% 2.71/1.55 ( ( case_list @ B @ A @ F12 @ F23 @ ( cons @ A @ X21 @ X222 ) )
% 2.71/1.55 = ( F23 @ X21 @ X222 ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_53_member__rec_I1_J,axiom,
% 2.71/1.55 ! [A: $tType,X: A,Xs: list @ A,Y: A] :
% 2.71/1.55 ( ( member @ A @ ( cons @ A @ X @ Xs ) @ Y )
% 2.71/1.55 = ( ( X = Y )
% 2.71/1.55 | ( member @ A @ Xs @ Y ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_54_not__Cons__self2,axiom,
% 2.71/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.71/1.55 ( ( cons @ A @ X @ Xs )
% 2.71/1.55 != Xs ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_55_transpose_Ocases,axiom,
% 2.71/1.55 ! [A: $tType,X: list @ ( list @ A )] :
% 2.71/1.55 ( ( X
% 2.71/1.55 != ( nil @ ( list @ A ) ) )
% 2.71/1.55 => ( ! [Xss: list @ ( list @ A )] :
% 2.71/1.55 ( X
% 2.71/1.55 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 2.71/1.55 => ~ ! [X4: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 2.71/1.55 ( X
% 2.71/1.55 != ( cons @ ( list @ A ) @ ( cons @ A @ X4 @ Xs2 ) @ Xss ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_56_list_Odistinct_I1_J,axiom,
% 2.71/1.55 ! [A: $tType,X21: A,X222: list @ A] :
% 2.71/1.55 ( ( nil @ A )
% 2.71/1.55 != ( cons @ A @ X21 @ X222 ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_57_list_OdiscI,axiom,
% 2.71/1.55 ! [A: $tType,List: list @ A,X21: A,X222: list @ A] :
% 2.71/1.55 ( ( List
% 2.71/1.55 = ( cons @ A @ X21 @ X222 ) )
% 2.71/1.55 => ( List
% 2.71/1.55 != ( nil @ A ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_58_list_Oexhaust,axiom,
% 2.71/1.55 ! [A: $tType,Y: list @ A] :
% 2.71/1.55 ( ( Y
% 2.71/1.55 != ( nil @ A ) )
% 2.71/1.55 => ~ ! [X212: A,X223: list @ A] :
% 2.71/1.55 ( Y
% 2.71/1.55 != ( cons @ A @ X212 @ X223 ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_59_list_Oinducts,axiom,
% 2.71/1.55 ! [A: $tType,P2: ( list @ A ) > $o,List: list @ A] :
% 2.71/1.55 ( ( P2 @ ( nil @ A ) )
% 2.71/1.55 => ( ! [X12: A,X22: list @ A] :
% 2.71/1.55 ( ( P2 @ X22 )
% 2.71/1.55 => ( P2 @ ( cons @ A @ X12 @ X22 ) ) )
% 2.71/1.55 => ( P2 @ List ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_60_neq__Nil__conv,axiom,
% 2.71/1.55 ! [A: $tType,Xs: list @ A] :
% 2.71/1.55 ( ( Xs
% 2.71/1.55 != ( nil @ A ) )
% 2.71/1.55 = ( ? [Y3: A,Ys: list @ A] :
% 2.71/1.55 ( Xs
% 2.71/1.55 = ( cons @ A @ Y3 @ Ys ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_61_list__induct2_H,axiom,
% 2.71/1.55 ! [A: $tType,B: $tType,P2: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys2: list @ B] :
% 2.71/1.55 ( ( P2 @ ( nil @ A ) @ ( nil @ B ) )
% 2.71/1.55 => ( ! [X4: A,Xs2: list @ A] : ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( nil @ B ) )
% 2.71/1.55 => ( ! [Y4: B,Ys3: list @ B] : ( P2 @ ( nil @ A ) @ ( cons @ B @ Y4 @ Ys3 ) )
% 2.71/1.55 => ( ! [X4: A,Xs2: list @ A,Y4: B,Ys3: list @ B] :
% 2.71/1.55 ( ( P2 @ Xs2 @ Ys3 )
% 2.71/1.55 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y4 @ Ys3 ) ) )
% 2.71/1.55 => ( P2 @ Xs @ Ys2 ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_62_splice_Oinduct,axiom,
% 2.71/1.55 ! [A: $tType,P2: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.71/1.55 ( ! [X12: list @ A] : ( P2 @ ( nil @ A ) @ X12 )
% 2.71/1.55 => ( ! [V: A,Va: list @ A] : ( P2 @ ( cons @ A @ V @ Va ) @ ( nil @ A ) )
% 2.71/1.55 => ( ! [X4: A,Xs2: list @ A,Y4: A,Ys3: list @ A] :
% 2.71/1.55 ( ( P2 @ Xs2 @ Ys3 )
% 2.71/1.55 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 2.71/1.55 => ( P2 @ A0 @ A1 ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_63_remdups__adj_Ocases,axiom,
% 2.71/1.55 ! [A: $tType,X: list @ A] :
% 2.71/1.55 ( ( X
% 2.71/1.55 != ( nil @ A ) )
% 2.71/1.55 => ( ! [X4: A] :
% 2.71/1.55 ( X
% 2.71/1.55 != ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.71/1.55 => ~ ! [X4: A,Y4: A,Xs2: list @ A] :
% 2.71/1.55 ( X
% 2.71/1.55 != ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_64_remdups__adj_Oinduct,axiom,
% 2.71/1.55 ! [A: $tType,P2: ( list @ A ) > $o,A0: list @ A] :
% 2.71/1.55 ( ( P2 @ ( nil @ A ) )
% 2.71/1.55 => ( ! [X4: A] : ( P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.71/1.55 => ( ! [X4: A,Y4: A,Xs2: list @ A] :
% 2.71/1.55 ( ( ( X4 = Y4 )
% 2.71/1.55 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) ) )
% 2.71/1.55 => ( ( ( X4 != Y4 )
% 2.71/1.55 => ( P2 @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 2.71/1.55 => ( P2 @ ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) )
% 2.71/1.55 => ( P2 @ A0 ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_65_list__nonempty__induct,axiom,
% 2.71/1.55 ! [A: $tType,Xs: list @ A,P2: ( list @ A ) > $o] :
% 2.71/1.55 ( ( Xs
% 2.71/1.55 != ( nil @ A ) )
% 2.71/1.55 => ( ! [X4: A] : ( P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.71/1.55 => ( ! [X4: A,Xs2: list @ A] :
% 2.71/1.55 ( ( Xs2
% 2.71/1.55 != ( nil @ A ) )
% 2.71/1.55 => ( ( P2 @ Xs2 )
% 2.71/1.55 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) ) ) )
% 2.71/1.55 => ( P2 @ Xs ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_66_map__tailrec__rev_Oinduct,axiom,
% 2.71/1.55 ! [A: $tType,B: $tType,P2: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 2.71/1.55 ( ! [F3: A > B,X12: list @ B] : ( P2 @ F3 @ ( nil @ A ) @ X12 )
% 2.71/1.55 => ( ! [F3: A > B,A4: A,As: list @ A,Bs: list @ B] :
% 2.71/1.55 ( ( P2 @ F3 @ As @ ( cons @ B @ ( F3 @ A4 ) @ Bs ) )
% 2.71/1.55 => ( P2 @ F3 @ ( cons @ A @ A4 @ As ) @ Bs ) )
% 2.71/1.55 => ( P2 @ A0 @ A1 @ A22 ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_67_list_Osel_I3_J,axiom,
% 2.71/1.55 ! [A: $tType,X21: A,X222: list @ A] :
% 2.71/1.55 ( ( tl @ A @ ( cons @ A @ X21 @ X222 ) )
% 2.71/1.55 = X222 ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_68_list_Osel_I1_J,axiom,
% 2.71/1.55 ! [A: $tType,X21: A,X222: list @ A] :
% 2.71/1.55 ( ( hd @ A @ ( cons @ A @ X21 @ X222 ) )
% 2.71/1.55 = X21 ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_69_stream_Omap,axiom,
% 2.71/1.55 ! [B: $tType,A: $tType,F2: A > B,X1: A,X2: stream170649215stream @ A] :
% 2.71/1.55 ( ( stream2128578057e_smap @ A @ B @ F2 @ ( stream641971652_SCons @ A @ X1 @ X2 ) )
% 2.71/1.55 = ( stream641971652_SCons @ B @ ( F2 @ X1 ) @ ( stream2128578057e_smap @ A @ B @ F2 @ X2 ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_70_smap__streams,axiom,
% 2.71/1.55 ! [A: $tType,B: $tType,S: stream170649215stream @ A,A2: set @ A,F2: A > B,B2: set @ B] :
% 2.71/1.55 ( ( member2 @ ( stream170649215stream @ A ) @ S @ ( stream2015131171treams @ A @ A2 ) )
% 2.71/1.55 => ( ! [X4: A] :
% 2.71/1.55 ( ( member2 @ A @ X4 @ A2 )
% 2.71/1.55 => ( member2 @ B @ ( F2 @ X4 ) @ B2 ) )
% 2.71/1.55 => ( member2 @ ( stream170649215stream @ B ) @ ( stream2128578057e_smap @ A @ B @ F2 @ S ) @ ( stream2015131171treams @ B @ B2 ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_71_list_Osimps_I4_J,axiom,
% 2.71/1.55 ! [A: $tType,B: $tType,F12: B,F23: A > ( list @ A ) > B] :
% 2.71/1.55 ( ( case_list @ B @ A @ F12 @ F23 @ ( nil @ A ) )
% 2.71/1.55 = F12 ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_72_list_Osplit__sel__asm,axiom,
% 2.71/1.55 ! [B: $tType,A: $tType,P2: B > $o,F12: B,F23: A > ( list @ A ) > B,List: list @ A] :
% 2.71/1.55 ( ( P2 @ ( case_list @ B @ A @ F12 @ F23 @ List ) )
% 2.71/1.55 = ( ~ ( ( ( List
% 2.71/1.55 = ( nil @ A ) )
% 2.71/1.55 & ~ ( P2 @ F12 ) )
% 2.71/1.55 | ( ( List
% 2.71/1.55 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) )
% 2.71/1.55 & ~ ( P2 @ ( F23 @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_73_list_Osplit__sel,axiom,
% 2.71/1.55 ! [B: $tType,A: $tType,P2: B > $o,F12: B,F23: A > ( list @ A ) > B,List: list @ A] :
% 2.71/1.55 ( ( P2 @ ( case_list @ B @ A @ F12 @ F23 @ List ) )
% 2.71/1.55 = ( ( ( List
% 2.71/1.55 = ( nil @ A ) )
% 2.71/1.55 => ( P2 @ F12 ) )
% 2.71/1.55 & ( ( List
% 2.71/1.55 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) )
% 2.71/1.55 => ( P2 @ ( F23 @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_74_tl__Nil,axiom,
% 2.71/1.55 ! [A: $tType,Xs: list @ A] :
% 2.71/1.55 ( ( ( tl @ A @ Xs )
% 2.71/1.55 = ( nil @ A ) )
% 2.71/1.55 = ( ( Xs
% 2.71/1.55 = ( nil @ A ) )
% 2.71/1.55 | ? [X5: A] :
% 2.71/1.55 ( Xs
% 2.71/1.55 = ( cons @ A @ X5 @ ( nil @ A ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_75_Nil__tl,axiom,
% 2.71/1.55 ! [A: $tType,Xs: list @ A] :
% 2.71/1.55 ( ( ( nil @ A )
% 2.71/1.55 = ( tl @ A @ Xs ) )
% 2.71/1.55 = ( ( Xs
% 2.71/1.55 = ( nil @ A ) )
% 2.71/1.55 | ? [X5: A] :
% 2.71/1.55 ( Xs
% 2.71/1.55 = ( cons @ A @ X5 @ ( nil @ A ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_76_shift_Osimps_I2_J,axiom,
% 2.71/1.55 ! [A: $tType,X: A,Xs: list @ A,S: stream170649215stream @ A] :
% 2.71/1.55 ( ( stream1035003186_shift @ A @ ( cons @ A @ X @ Xs ) @ S )
% 2.71/1.55 = ( stream641971652_SCons @ A @ X @ ( stream1035003186_shift @ A @ Xs @ S ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_77_cycle__rotated,axiom,
% 2.71/1.55 ! [A: $tType,V2: list @ A,U: list @ A,S: stream170649215stream @ A] :
% 2.71/1.55 ( ( V2
% 2.71/1.55 != ( nil @ A ) )
% 2.71/1.55 => ( ( ( stream317748790_cycle @ A @ U )
% 2.71/1.55 = ( stream1035003186_shift @ A @ V2 @ S ) )
% 2.71/1.55 => ( ( stream317748790_cycle @ A @ ( append @ A @ ( tl @ A @ U ) @ ( cons @ A @ ( hd @ A @ U ) @ ( nil @ A ) ) ) )
% 2.71/1.55 = ( stream1035003186_shift @ A @ ( tl @ A @ V2 ) @ S ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_78_cycle_Osimps_I2_J,axiom,
% 2.71/1.55 ! [A: $tType,Xs: list @ A] :
% 2.71/1.55 ( ( stream_Mirabelle_stl @ A @ ( stream317748790_cycle @ A @ Xs ) )
% 2.71/1.55 = ( stream317748790_cycle @ A @ ( append @ A @ ( tl @ A @ Xs ) @ ( cons @ A @ ( hd @ A @ Xs ) @ ( nil @ A ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_79_cycle_Ocode,axiom,
% 2.71/1.55 ! [A: $tType] :
% 2.71/1.55 ( ( stream317748790_cycle @ A )
% 2.71/1.55 = ( ^ [Xs3: list @ A] : ( stream641971652_SCons @ A @ ( hd @ A @ Xs3 ) @ ( stream317748790_cycle @ A @ ( append @ A @ ( tl @ A @ Xs3 ) @ ( cons @ A @ ( hd @ A @ Xs3 ) @ ( nil @ A ) ) ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_80_insert__Nil,axiom,
% 2.71/1.55 ! [A: $tType,X: A] :
% 2.71/1.55 ( ( insert @ A @ X @ ( nil @ A ) )
% 2.71/1.55 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_81_cycle__Cons,axiom,
% 2.71/1.55 ! [A: $tType,X: A,Xs: list @ A] :
% 2.71/1.55 ( ( stream317748790_cycle @ A @ ( cons @ A @ X @ Xs ) )
% 2.71/1.55 = ( stream641971652_SCons @ A @ X @ ( stream317748790_cycle @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_82_ord_Olexordp__eq__simps_I3_J,axiom,
% 2.71/1.55 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A] :
% 2.71/1.55 ~ ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( nil @ A ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_83_map__tailrec__rev_Oelims,axiom,
% 2.71/1.55 ! [A: $tType,B: $tType,X: A > B,Xa: list @ A,Xb: list @ B,Y: list @ B] :
% 2.71/1.55 ( ( ( map_tailrec_rev @ A @ B @ X @ Xa @ Xb )
% 2.71/1.55 = Y )
% 2.71/1.55 => ( ( ( Xa
% 2.71/1.55 = ( nil @ A ) )
% 2.71/1.55 => ( Y != Xb ) )
% 2.71/1.55 => ~ ! [A4: A,As: list @ A] :
% 2.71/1.55 ( ( Xa
% 2.71/1.55 = ( cons @ A @ A4 @ As ) )
% 2.71/1.55 => ( Y
% 2.71/1.55 != ( map_tailrec_rev @ A @ B @ X @ As @ ( cons @ B @ ( X @ A4 ) @ Xb ) ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_84_splice_Oelims,axiom,
% 2.71/1.55 ! [A: $tType,X: list @ A,Xa: list @ A,Y: list @ A] :
% 2.71/1.55 ( ( ( splice @ A @ X @ Xa )
% 2.71/1.55 = Y )
% 2.71/1.55 => ( ( ( X
% 2.71/1.55 = ( nil @ A ) )
% 2.71/1.55 => ( Y != Xa ) )
% 2.71/1.55 => ( ! [V: A,Va: list @ A] :
% 2.71/1.55 ( ( X
% 2.71/1.55 = ( cons @ A @ V @ Va ) )
% 2.71/1.55 => ( ( Xa
% 2.71/1.55 = ( nil @ A ) )
% 2.71/1.55 => ( Y
% 2.71/1.55 != ( cons @ A @ V @ Va ) ) ) )
% 2.71/1.55 => ~ ! [X4: A,Xs2: list @ A] :
% 2.71/1.55 ( ( X
% 2.71/1.55 = ( cons @ A @ X4 @ Xs2 ) )
% 2.71/1.55 => ! [Y4: A,Ys3: list @ A] :
% 2.71/1.55 ( ( Xa
% 2.71/1.55 = ( cons @ A @ Y4 @ Ys3 ) )
% 2.71/1.55 => ( Y
% 2.71/1.55 != ( cons @ A @ X4 @ ( cons @ A @ Y4 @ ( splice @ A @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_85_same__append__eq,axiom,
% 2.71/1.55 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs: list @ A] :
% 2.71/1.55 ( ( ( append @ A @ Xs @ Ys2 )
% 2.71/1.55 = ( append @ A @ Xs @ Zs ) )
% 2.71/1.55 = ( Ys2 = Zs ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_86_append__same__eq,axiom,
% 2.71/1.55 ! [A: $tType,Ys2: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.71/1.55 ( ( ( append @ A @ Ys2 @ Xs )
% 2.71/1.55 = ( append @ A @ Zs @ Xs ) )
% 2.71/1.55 = ( Ys2 = Zs ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_87_append__assoc,axiom,
% 2.71/1.55 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs: list @ A] :
% 2.71/1.55 ( ( append @ A @ ( append @ A @ Xs @ Ys2 ) @ Zs )
% 2.71/1.55 = ( append @ A @ Xs @ ( append @ A @ Ys2 @ Zs ) ) ) ).
% 2.71/1.55
% 2.71/1.55 thf(fact_88_append__is__Nil__conv,axiom,
% 2.71/1.55 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.55 ( ( ( append @ A @ Xs @ Ys2 )
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 = ( ( Xs
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 & ( Ys2
% 2.71/1.56 = ( nil @ A ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_89_Nil__is__append__conv,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( ( nil @ A )
% 2.71/1.56 = ( append @ A @ Xs @ Ys2 ) )
% 2.71/1.56 = ( ( Xs
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 & ( Ys2
% 2.71/1.56 = ( nil @ A ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_90_self__append__conv2,axiom,
% 2.71/1.56 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 2.71/1.56 ( ( Ys2
% 2.71/1.56 = ( append @ A @ Xs @ Ys2 ) )
% 2.71/1.56 = ( Xs
% 2.71/1.56 = ( nil @ A ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_91_append__self__conv2,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( ( append @ A @ Xs @ Ys2 )
% 2.71/1.56 = Ys2 )
% 2.71/1.56 = ( Xs
% 2.71/1.56 = ( nil @ A ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_92_self__append__conv,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 = ( append @ A @ Xs @ Ys2 ) )
% 2.71/1.56 = ( Ys2
% 2.71/1.56 = ( nil @ A ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_93_append__self__conv,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( ( append @ A @ Xs @ Ys2 )
% 2.71/1.56 = Xs )
% 2.71/1.56 = ( Ys2
% 2.71/1.56 = ( nil @ A ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_94_append__Nil2,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A] :
% 2.71/1.56 ( ( append @ A @ Xs @ ( nil @ A ) )
% 2.71/1.56 = Xs ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_95_shift__append,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A,S: stream170649215stream @ A] :
% 2.71/1.56 ( ( stream1035003186_shift @ A @ ( append @ A @ Xs @ Ys2 ) @ S )
% 2.71/1.56 = ( stream1035003186_shift @ A @ Xs @ ( stream1035003186_shift @ A @ Ys2 @ S ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_96_ord_Olexordp__eq__simps_I4_J,axiom,
% 2.71/1.56 ! [A: $tType,Less: A > A > $o,X: A,Xs: list @ A,Y: A,Ys2: list @ A] :
% 2.71/1.56 ( ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) )
% 2.71/1.56 = ( ( Less @ X @ Y )
% 2.71/1.56 | ( ~ ( Less @ Y @ X )
% 2.71/1.56 & ( lexordp_eq @ A @ Less @ Xs @ Ys2 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_97_ord_Olexordp__eq__simps_I1_J,axiom,
% 2.71/1.56 ! [A: $tType,Less: A > A > $o,Ys2: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys2 ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_98_ord_Olexordp__eq__simps_I2_J,axiom,
% 2.71/1.56 ! [A: $tType,Less: A > A > $o,Xs: list @ A] :
% 2.71/1.56 ( ( lexordp_eq @ A @ Less @ Xs @ ( nil @ A ) )
% 2.71/1.56 = ( Xs
% 2.71/1.56 = ( nil @ A ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_99_splice__Nil2,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A] :
% 2.71/1.56 ( ( splice @ A @ Xs @ ( nil @ A ) )
% 2.71/1.56 = Xs ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_100_append1__eq__conv,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,X: A,Ys2: list @ A,Y: A] :
% 2.71/1.56 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.71/1.56 = ( append @ A @ Ys2 @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.71/1.56 = ( ( Xs = Ys2 )
% 2.71/1.56 & ( X = Y ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_101_tl__append2,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( tl @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.71/1.56 = ( append @ A @ ( tl @ A @ Xs ) @ Ys2 ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_102_hd__append2,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.71/1.56 = ( hd @ A @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_103_bind__simps_I2_J,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,X: B,Xs: list @ B,F2: B > ( list @ A )] :
% 2.71/1.56 ( ( bind @ B @ A @ ( cons @ B @ X @ Xs ) @ F2 )
% 2.71/1.56 = ( append @ A @ ( F2 @ X ) @ ( bind @ B @ A @ Xs @ F2 ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_104_append__eq__append__conv2,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs: list @ A,Ts: list @ A] :
% 2.71/1.56 ( ( ( append @ A @ Xs @ Ys2 )
% 2.71/1.56 = ( append @ A @ Zs @ Ts ) )
% 2.71/1.56 = ( ? [Us: list @ A] :
% 2.71/1.56 ( ( ( Xs
% 2.71/1.56 = ( append @ A @ Zs @ Us ) )
% 2.71/1.56 & ( ( append @ A @ Us @ Ys2 )
% 2.71/1.56 = Ts ) )
% 2.71/1.56 | ( ( ( append @ A @ Xs @ Us )
% 2.71/1.56 = Zs )
% 2.71/1.56 & ( Ys2
% 2.71/1.56 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_105_ord_Olexordp__eq__refl,axiom,
% 2.71/1.56 ! [A: $tType,Less: A > A > $o,Xs: list @ A] : ( lexordp_eq @ A @ Less @ Xs @ Xs ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_106_append__eq__appendI,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs: list @ A,Ys2: list @ A,Us2: list @ A] :
% 2.71/1.56 ( ( ( append @ A @ Xs @ Xs1 )
% 2.71/1.56 = Zs )
% 2.71/1.56 => ( ( Ys2
% 2.71/1.56 = ( append @ A @ Xs1 @ Us2 ) )
% 2.71/1.56 => ( ( append @ A @ Xs @ Ys2 )
% 2.71/1.56 = ( append @ A @ Zs @ Us2 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_107_append__Cons,axiom,
% 2.71/1.56 ! [A: $tType,X: A,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( append @ A @ ( cons @ A @ X @ Xs ) @ Ys2 )
% 2.71/1.56 = ( cons @ A @ X @ ( append @ A @ Xs @ Ys2 ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_108_Cons__eq__appendI,axiom,
% 2.71/1.56 ! [A: $tType,X: A,Xs1: list @ A,Ys2: list @ A,Xs: list @ A,Zs: list @ A] :
% 2.71/1.56 ( ( ( cons @ A @ X @ Xs1 )
% 2.71/1.56 = Ys2 )
% 2.71/1.56 => ( ( Xs
% 2.71/1.56 = ( append @ A @ Xs1 @ Zs ) )
% 2.71/1.56 => ( ( cons @ A @ X @ Xs )
% 2.71/1.56 = ( append @ A @ Ys2 @ Zs ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_109_append__Nil,axiom,
% 2.71/1.56 ! [A: $tType,Ys2: list @ A] :
% 2.71/1.56 ( ( append @ A @ ( nil @ A ) @ Ys2 )
% 2.71/1.56 = Ys2 ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_110_eq__Nil__appendI,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( Xs = Ys2 )
% 2.71/1.56 => ( Xs
% 2.71/1.56 = ( append @ A @ ( nil @ A ) @ Ys2 ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_111_ord_Olexordp__eq_OCons__eq,axiom,
% 2.71/1.56 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ~ ( Less @ X @ Y )
% 2.71/1.56 => ( ~ ( Less @ Y @ X )
% 2.71/1.56 => ( ( lexordp_eq @ A @ Less @ Xs @ Ys2 )
% 2.71/1.56 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_112_ord_Olexordp__eq_OCons,axiom,
% 2.71/1.56 ! [A: $tType,Less: A > A > $o,X: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( Less @ X @ Y )
% 2.71/1.56 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_113_ord_Olexordp__eq_ONil,axiom,
% 2.71/1.56 ! [A: $tType,Less: A > A > $o,Ys2: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys2 ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_114_splice_Osimps_I3_J,axiom,
% 2.71/1.56 ! [A: $tType,X: A,Xs: list @ A,Y: A,Ys2: list @ A] :
% 2.71/1.56 ( ( splice @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) )
% 2.71/1.56 = ( cons @ A @ X @ ( cons @ A @ Y @ ( splice @ A @ Xs @ Ys2 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_115_splice_Osimps_I1_J,axiom,
% 2.71/1.56 ! [A: $tType,Ys2: list @ A] :
% 2.71/1.56 ( ( splice @ A @ ( nil @ A ) @ Ys2 )
% 2.71/1.56 = Ys2 ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_116_rev__nonempty__induct,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,P2: ( list @ A ) > $o] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ! [X4: A] : ( P2 @ ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.71/1.56 => ( ! [X4: A,Xs2: list @ A] :
% 2.71/1.56 ( ( Xs2
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( P2 @ Xs2 )
% 2.71/1.56 => ( P2 @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) )
% 2.71/1.56 => ( P2 @ Xs ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_117_append__eq__Cons__conv,axiom,
% 2.71/1.56 ! [A: $tType,Ys2: list @ A,Zs: list @ A,X: A,Xs: list @ A] :
% 2.71/1.56 ( ( ( append @ A @ Ys2 @ Zs )
% 2.71/1.56 = ( cons @ A @ X @ Xs ) )
% 2.71/1.56 = ( ( ( Ys2
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 & ( Zs
% 2.71/1.56 = ( cons @ A @ X @ Xs ) ) )
% 2.71/1.56 | ? [Ys4: list @ A] :
% 2.71/1.56 ( ( Ys2
% 2.71/1.56 = ( cons @ A @ X @ Ys4 ) )
% 2.71/1.56 & ( ( append @ A @ Ys4 @ Zs )
% 2.71/1.56 = Xs ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_118_Cons__eq__append__conv,axiom,
% 2.71/1.56 ! [A: $tType,X: A,Xs: list @ A,Ys2: list @ A,Zs: list @ A] :
% 2.71/1.56 ( ( ( cons @ A @ X @ Xs )
% 2.71/1.56 = ( append @ A @ Ys2 @ Zs ) )
% 2.71/1.56 = ( ( ( Ys2
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 & ( ( cons @ A @ X @ Xs )
% 2.71/1.56 = Zs ) )
% 2.71/1.56 | ? [Ys4: list @ A] :
% 2.71/1.56 ( ( ( cons @ A @ X @ Ys4 )
% 2.71/1.56 = Ys2 )
% 2.71/1.56 & ( Xs
% 2.71/1.56 = ( append @ A @ Ys4 @ Zs ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_119_rev__exhaust,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ~ ! [Ys3: list @ A,Y4: A] :
% 2.71/1.56 ( Xs
% 2.71/1.56 != ( append @ A @ Ys3 @ ( cons @ A @ Y4 @ ( nil @ A ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_120_rev__induct,axiom,
% 2.71/1.56 ! [A: $tType,P2: ( list @ A ) > $o,Xs: list @ A] :
% 2.71/1.56 ( ( P2 @ ( nil @ A ) )
% 2.71/1.56 => ( ! [X4: A,Xs2: list @ A] :
% 2.71/1.56 ( ( P2 @ Xs2 )
% 2.71/1.56 => ( P2 @ ( append @ A @ Xs2 @ ( cons @ A @ X4 @ ( nil @ A ) ) ) ) )
% 2.71/1.56 => ( P2 @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_121_map__tailrec__rev_Osimps_I2_J,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,F2: A > B,A3: A,As2: list @ A,Bs2: list @ B] :
% 2.71/1.56 ( ( map_tailrec_rev @ A @ B @ F2 @ ( cons @ A @ A3 @ As2 ) @ Bs2 )
% 2.71/1.56 = ( map_tailrec_rev @ A @ B @ F2 @ As2 @ ( cons @ B @ ( F2 @ A3 ) @ Bs2 ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_122_map__tailrec__rev_Osimps_I1_J,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,F2: A > B,Bs2: list @ B] :
% 2.71/1.56 ( ( map_tailrec_rev @ A @ B @ F2 @ ( nil @ A ) @ Bs2 )
% 2.71/1.56 = Bs2 ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_123_hd__append,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( ( Xs
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.71/1.56 = ( hd @ A @ Ys2 ) ) )
% 2.71/1.56 & ( ( Xs
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.71/1.56 = ( hd @ A @ Xs ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_124_longest__common__prefix,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ? [Ps: list @ A,Xs4: list @ A,Ys5: list @ A] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 = ( append @ A @ Ps @ Xs4 ) )
% 2.71/1.56 & ( Ys2
% 2.71/1.56 = ( append @ A @ Ps @ Ys5 ) )
% 2.71/1.56 & ( ( Xs4
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 | ( Ys5
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 | ( ( hd @ A @ Xs4 )
% 2.71/1.56 != ( hd @ A @ Ys5 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_125_ord_Olexordp__eq_Ocases,axiom,
% 2.71/1.56 ! [A: $tType,Less: A > A > $o,A1: list @ A,A22: list @ A] :
% 2.71/1.56 ( ( lexordp_eq @ A @ Less @ A1 @ A22 )
% 2.71/1.56 => ( ( ( A1
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 => ! [Ys3: list @ A] : ( A22 != Ys3 ) )
% 2.71/1.56 => ( ! [X4: A] :
% 2.71/1.56 ( ? [Xs2: list @ A] :
% 2.71/1.56 ( A1
% 2.71/1.56 = ( cons @ A @ X4 @ Xs2 ) )
% 2.71/1.56 => ! [Y4: A] :
% 2.71/1.56 ( ? [Ys3: list @ A] :
% 2.71/1.56 ( A22
% 2.71/1.56 = ( cons @ A @ Y4 @ Ys3 ) )
% 2.71/1.56 => ~ ( Less @ X4 @ Y4 ) ) )
% 2.71/1.56 => ~ ! [X4: A,Y4: A,Xs2: list @ A] :
% 2.71/1.56 ( ( A1
% 2.71/1.56 = ( cons @ A @ X4 @ Xs2 ) )
% 2.71/1.56 => ! [Ys3: list @ A] :
% 2.71/1.56 ( ( A22
% 2.71/1.56 = ( cons @ A @ Y4 @ Ys3 ) )
% 2.71/1.56 => ( ~ ( Less @ X4 @ Y4 )
% 2.71/1.56 => ( ~ ( Less @ Y4 @ X4 )
% 2.71/1.56 => ~ ( lexordp_eq @ A @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_126_ord_Olexordp__eq_Osimps,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( lexordp_eq @ A )
% 2.71/1.56 = ( ^ [Less2: A > A > $o,A12: list @ A,A23: list @ A] :
% 2.71/1.56 ( ? [Ys: list @ A] :
% 2.71/1.56 ( ( A12
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 & ( A23 = Ys ) )
% 2.71/1.56 | ? [X5: A,Y3: A,Xs3: list @ A,Ys: list @ A] :
% 2.71/1.56 ( ( A12
% 2.71/1.56 = ( cons @ A @ X5 @ Xs3 ) )
% 2.71/1.56 & ( A23
% 2.71/1.56 = ( cons @ A @ Y3 @ Ys ) )
% 2.71/1.56 & ( Less2 @ X5 @ Y3 ) )
% 2.71/1.56 | ? [X5: A,Y3: A,Xs3: list @ A,Ys: list @ A] :
% 2.71/1.56 ( ( A12
% 2.71/1.56 = ( cons @ A @ X5 @ Xs3 ) )
% 2.71/1.56 & ( A23
% 2.71/1.56 = ( cons @ A @ Y3 @ Ys ) )
% 2.71/1.56 & ~ ( Less2 @ X5 @ Y3 )
% 2.71/1.56 & ~ ( Less2 @ Y3 @ X5 )
% 2.71/1.56 & ( lexordp_eq @ A @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_127_ord_Olexordp__eq_Oinducts,axiom,
% 2.71/1.56 ! [A: $tType,Less: A > A > $o,X1: list @ A,X2: list @ A,P2: ( list @ A ) > ( list @ A ) > $o] :
% 2.71/1.56 ( ( lexordp_eq @ A @ Less @ X1 @ X2 )
% 2.71/1.56 => ( ! [X12: list @ A] : ( P2 @ ( nil @ A ) @ X12 )
% 2.71/1.56 => ( ! [X4: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 2.71/1.56 ( ( Less @ X4 @ Y4 )
% 2.71/1.56 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 2.71/1.56 => ( ! [X4: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 2.71/1.56 ( ~ ( Less @ X4 @ Y4 )
% 2.71/1.56 => ( ~ ( Less @ Y4 @ X4 )
% 2.71/1.56 => ( ( lexordp_eq @ A @ Less @ Xs2 @ Ys3 )
% 2.71/1.56 => ( ( P2 @ Xs2 @ Ys3 )
% 2.71/1.56 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) ) ) ) )
% 2.71/1.56 => ( P2 @ X1 @ X2 ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_128_splice_Osimps_I2_J,axiom,
% 2.71/1.56 ! [A: $tType,V2: A,Va2: list @ A] :
% 2.71/1.56 ( ( splice @ A @ ( cons @ A @ V2 @ Va2 ) @ ( nil @ A ) )
% 2.71/1.56 = ( cons @ A @ V2 @ Va2 ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_129_rotate1__hd__tl,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( rotate1 @ A @ Xs )
% 2.71/1.56 = ( append @ A @ ( tl @ A @ Xs ) @ ( cons @ A @ ( hd @ A @ Xs ) @ ( nil @ A ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_130_sublists_Osimps_I1_J,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( sublists @ A @ ( nil @ A ) )
% 2.71/1.56 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_131_product__lists_Osimps_I1_J,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 2.71/1.56 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_132_maps__simps_I1_J,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,F2: B > ( list @ A ),X: B,Xs: list @ B] :
% 2.71/1.56 ( ( maps @ B @ A @ F2 @ ( cons @ B @ X @ Xs ) )
% 2.71/1.56 = ( append @ A @ ( F2 @ X ) @ ( maps @ B @ A @ F2 @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_133_rotate1_Osimps_I2_J,axiom,
% 2.71/1.56 ! [A: $tType,X: A,Xs: list @ A] :
% 2.71/1.56 ( ( rotate1 @ A @ ( cons @ A @ X @ Xs ) )
% 2.71/1.56 = ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_134_remdups__adj__append,axiom,
% 2.71/1.56 ! [A: $tType,Xs_1: list @ A,X: A,Xs_2: list @ A] :
% 2.71/1.56 ( ( remdups_adj @ A @ ( append @ A @ Xs_1 @ ( cons @ A @ X @ Xs_2 ) ) )
% 2.71/1.56 = ( append @ A @ ( remdups_adj @ A @ ( append @ A @ Xs_1 @ ( cons @ A @ X @ ( nil @ A ) ) ) ) @ ( tl @ A @ ( remdups_adj @ A @ ( cons @ A @ X @ Xs_2 ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_135_remdups__adj__Nil__iff,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A] :
% 2.71/1.56 ( ( ( remdups_adj @ A @ Xs )
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 = ( Xs
% 2.71/1.56 = ( nil @ A ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_136_hd__remdups__adj,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A] :
% 2.71/1.56 ( ( hd @ A @ ( remdups_adj @ A @ Xs ) )
% 2.71/1.56 = ( hd @ A @ Xs ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_137_rotate1__is__Nil__conv,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A] :
% 2.71/1.56 ( ( ( rotate1 @ A @ Xs )
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 = ( Xs
% 2.71/1.56 = ( nil @ A ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_138_remdups__adj__Cons__alt,axiom,
% 2.71/1.56 ! [A: $tType,X: A,Xs: list @ A] :
% 2.71/1.56 ( ( cons @ A @ X @ ( tl @ A @ ( remdups_adj @ A @ ( cons @ A @ X @ Xs ) ) ) )
% 2.71/1.56 = ( remdups_adj @ A @ ( cons @ A @ X @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_139_remdups__adj_Osimps_I3_J,axiom,
% 2.71/1.56 ! [A: $tType,X: A,Y: A,Xs: list @ A] :
% 2.71/1.56 ( ( ( X = Y )
% 2.71/1.56 => ( ( remdups_adj @ A @ ( cons @ A @ X @ ( cons @ A @ Y @ Xs ) ) )
% 2.71/1.56 = ( remdups_adj @ A @ ( cons @ A @ X @ Xs ) ) ) )
% 2.71/1.56 & ( ( X != Y )
% 2.71/1.56 => ( ( remdups_adj @ A @ ( cons @ A @ X @ ( cons @ A @ Y @ Xs ) ) )
% 2.71/1.56 = ( cons @ A @ X @ ( remdups_adj @ A @ ( cons @ A @ Y @ Xs ) ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_140_remdups__adj_Osimps_I1_J,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( remdups_adj @ A @ ( nil @ A ) )
% 2.71/1.56 = ( nil @ A ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_141_rotate1_Osimps_I1_J,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( rotate1 @ A @ ( nil @ A ) )
% 2.71/1.56 = ( nil @ A ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_142_remdups__adj_Oelims,axiom,
% 2.71/1.56 ! [A: $tType,X: list @ A,Y: list @ A] :
% 2.71/1.56 ( ( ( remdups_adj @ A @ X )
% 2.71/1.56 = Y )
% 2.71/1.56 => ( ( ( X
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 => ( Y
% 2.71/1.56 != ( nil @ A ) ) )
% 2.71/1.56 => ( ! [X4: A] :
% 2.71/1.56 ( ( X
% 2.71/1.56 = ( cons @ A @ X4 @ ( nil @ A ) ) )
% 2.71/1.56 => ( Y
% 2.71/1.56 != ( cons @ A @ X4 @ ( nil @ A ) ) ) )
% 2.71/1.56 => ~ ! [X4: A,Y4: A,Xs2: list @ A] :
% 2.71/1.56 ( ( X
% 2.71/1.56 = ( cons @ A @ X4 @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 2.71/1.56 => ~ ( ( ( X4 = Y4 )
% 2.71/1.56 => ( Y
% 2.71/1.56 = ( remdups_adj @ A @ ( cons @ A @ X4 @ Xs2 ) ) ) )
% 2.71/1.56 & ( ( X4 != Y4 )
% 2.71/1.56 => ( Y
% 2.71/1.56 = ( cons @ A @ X4 @ ( remdups_adj @ A @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_143_remdups__adj_Osimps_I2_J,axiom,
% 2.71/1.56 ! [A: $tType,X: A] :
% 2.71/1.56 ( ( remdups_adj @ A @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.71/1.56 = ( cons @ A @ X @ ( nil @ A ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_144_maps__simps_I2_J,axiom,
% 2.71/1.56 ! [B: $tType,A: $tType,F2: B > ( list @ A )] :
% 2.71/1.56 ( ( maps @ B @ A @ F2 @ ( nil @ B ) )
% 2.71/1.56 = ( nil @ A ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_145_remdups__adj__append__two,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,X: A,Y: A] :
% 2.71/1.56 ( ( remdups_adj @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) )
% 2.71/1.56 = ( append @ A @ ( remdups_adj @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) ) @ ( if @ ( list @ A ) @ ( X = Y ) @ ( nil @ A ) @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_146_last__snoc,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,X: A] :
% 2.71/1.56 ( ( last @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.71/1.56 = X ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_147_butlast__snoc,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,X: A] :
% 2.71/1.56 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.71/1.56 = Xs ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_148_SuccD,axiom,
% 2.71/1.56 ! [A: $tType,K: A,Kl: set @ ( list @ A ),Kl2: list @ A] :
% 2.71/1.56 ( ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl @ Kl2 ) )
% 2.71/1.56 => ( member2 @ ( list @ A ) @ ( append @ A @ Kl2 @ ( cons @ A @ K @ ( nil @ A ) ) ) @ Kl ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_149_SuccI,axiom,
% 2.71/1.56 ! [A: $tType,Kl2: list @ A,K: A,Kl: set @ ( list @ A )] :
% 2.71/1.56 ( ( member2 @ ( list @ A ) @ ( append @ A @ Kl2 @ ( cons @ A @ K @ ( nil @ A ) ) ) @ Kl )
% 2.71/1.56 => ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl @ Kl2 ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_150_last__appendR,axiom,
% 2.71/1.56 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 2.71/1.56 ( ( Ys2
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.71/1.56 = ( last @ A @ Ys2 ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_151_last__appendL,axiom,
% 2.71/1.56 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 2.71/1.56 ( ( Ys2
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.71/1.56 = ( last @ A @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_152_append__butlast__last__id,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( append @ A @ ( butlast @ A @ Xs ) @ ( cons @ A @ ( last @ A @ Xs ) @ ( nil @ A ) ) )
% 2.71/1.56 = Xs ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_153_butlast_Osimps_I1_J,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( butlast @ A @ ( nil @ A ) )
% 2.71/1.56 = ( nil @ A ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_154_butlast__tl,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A] :
% 2.71/1.56 ( ( butlast @ A @ ( tl @ A @ Xs ) )
% 2.71/1.56 = ( tl @ A @ ( butlast @ A @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_155_snoc__eq__iff__butlast,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,X: A,Ys2: list @ A] :
% 2.71/1.56 ( ( ( append @ A @ Xs @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.71/1.56 = Ys2 )
% 2.71/1.56 = ( ( Ys2
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 & ( ( butlast @ A @ Ys2 )
% 2.71/1.56 = Xs )
% 2.71/1.56 & ( ( last @ A @ Ys2 )
% 2.71/1.56 = X ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_156_butlast_Osimps_I2_J,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,X: A] :
% 2.71/1.56 ( ( ( Xs
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 2.71/1.56 = ( nil @ A ) ) )
% 2.71/1.56 & ( ( Xs
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( butlast @ A @ ( cons @ A @ X @ Xs ) )
% 2.71/1.56 = ( cons @ A @ X @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_157_last_Osimps,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,X: A] :
% 2.71/1.56 ( ( ( Xs
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 2.71/1.56 = X ) )
% 2.71/1.56 & ( ( Xs
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 2.71/1.56 = ( last @ A @ Xs ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_158_last__ConsL,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,X: A] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 2.71/1.56 = X ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_159_last__ConsR,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,X: A] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( last @ A @ ( cons @ A @ X @ Xs ) )
% 2.71/1.56 = ( last @ A @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_160_longest__common__suffix,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ? [Ss: list @ A,Xs4: list @ A,Ys5: list @ A] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 = ( append @ A @ Xs4 @ Ss ) )
% 2.71/1.56 & ( Ys2
% 2.71/1.56 = ( append @ A @ Ys5 @ Ss ) )
% 2.71/1.56 & ( ( Xs4
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 | ( Ys5
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 | ( ( last @ A @ Xs4 )
% 2.71/1.56 != ( last @ A @ Ys5 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_161_butlast__append,axiom,
% 2.71/1.56 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 2.71/1.56 ( ( ( Ys2
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.71/1.56 = ( butlast @ A @ Xs ) ) )
% 2.71/1.56 & ( ( Ys2
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.71/1.56 = ( append @ A @ Xs @ ( butlast @ A @ Ys2 ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_162_last__append,axiom,
% 2.71/1.56 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 2.71/1.56 ( ( ( Ys2
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.71/1.56 = ( last @ A @ Xs ) ) )
% 2.71/1.56 & ( ( Ys2
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.71/1.56 = ( last @ A @ Ys2 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_163_last__tl,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A] :
% 2.71/1.56 ( ( ( Xs
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 | ( ( tl @ A @ Xs )
% 2.71/1.56 != ( nil @ A ) ) )
% 2.71/1.56 => ( ( last @ A @ ( tl @ A @ Xs ) )
% 2.71/1.56 = ( last @ A @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_164_BNF__Greatest__Fixpoint_Oshift__def,axiom,
% 2.71/1.56 ! [B: $tType,A: $tType] :
% 2.71/1.56 ( ( bNF_Greatest_shift @ A @ B )
% 2.71/1.56 = ( ^ [Lab: ( list @ A ) > B,K2: A,Kl3: list @ A] : ( Lab @ ( cons @ A @ K2 @ Kl3 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_165_empty__Shift,axiom,
% 2.71/1.56 ! [A: $tType,Kl: set @ ( list @ A ),K: A] :
% 2.71/1.56 ( ( member2 @ ( list @ A ) @ ( nil @ A ) @ Kl )
% 2.71/1.56 => ( ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl @ ( nil @ A ) ) )
% 2.71/1.56 => ( member2 @ ( list @ A ) @ ( nil @ A ) @ ( bNF_Greatest_Shift @ A @ Kl @ K ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_166_Succ__Shift,axiom,
% 2.71/1.56 ! [A: $tType,Kl: set @ ( list @ A ),K: A,Kl2: list @ A] :
% 2.71/1.56 ( ( bNF_Greatest_Succ @ A @ ( bNF_Greatest_Shift @ A @ Kl @ K ) @ Kl2 )
% 2.71/1.56 = ( bNF_Greatest_Succ @ A @ Kl @ ( cons @ A @ K @ Kl2 ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_167_ShiftD,axiom,
% 2.71/1.56 ! [A: $tType,Kl2: list @ A,Kl: set @ ( list @ A ),K: A] :
% 2.71/1.56 ( ( member2 @ ( list @ A ) @ Kl2 @ ( bNF_Greatest_Shift @ A @ Kl @ K ) )
% 2.71/1.56 => ( member2 @ ( list @ A ) @ ( cons @ A @ K @ Kl2 ) @ Kl ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_168_rev__eq__Cons__iff,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,Y: A,Ys2: list @ A] :
% 2.71/1.56 ( ( ( rev @ A @ Xs )
% 2.71/1.56 = ( cons @ A @ Y @ Ys2 ) )
% 2.71/1.56 = ( Xs
% 2.71/1.56 = ( append @ A @ ( rev @ A @ Ys2 ) @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_169_listrelp_Oinducts,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,R2: A > B > $o,X1: list @ A,X2: list @ B,P2: ( list @ A ) > ( list @ B ) > $o] :
% 2.71/1.56 ( ( listrelp @ A @ B @ R2 @ X1 @ X2 )
% 2.71/1.56 => ( ( P2 @ ( nil @ A ) @ ( nil @ B ) )
% 2.71/1.56 => ( ! [X4: A,Y4: B,Xs2: list @ A,Ys3: list @ B] :
% 2.71/1.56 ( ( R2 @ X4 @ Y4 )
% 2.71/1.56 => ( ( listrelp @ A @ B @ R2 @ Xs2 @ Ys3 )
% 2.71/1.56 => ( ( P2 @ Xs2 @ Ys3 )
% 2.71/1.56 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ B @ Y4 @ Ys3 ) ) ) ) )
% 2.71/1.56 => ( P2 @ X1 @ X2 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_170_listrelp_Osimps,axiom,
% 2.71/1.56 ! [B: $tType,A: $tType] :
% 2.71/1.56 ( ( listrelp @ A @ B )
% 2.71/1.56 = ( ^ [R3: A > B > $o,A12: list @ A,A23: list @ B] :
% 2.71/1.56 ( ( ( A12
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 & ( A23
% 2.71/1.56 = ( nil @ B ) ) )
% 2.71/1.56 | ? [X5: A,Y3: B,Xs3: list @ A,Ys: list @ B] :
% 2.71/1.56 ( ( A12
% 2.71/1.56 = ( cons @ A @ X5 @ Xs3 ) )
% 2.71/1.56 & ( A23
% 2.71/1.56 = ( cons @ B @ Y3 @ Ys ) )
% 2.71/1.56 & ( R3 @ X5 @ Y3 )
% 2.71/1.56 & ( listrelp @ A @ B @ R3 @ Xs3 @ Ys ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_171_rev__is__rev__conv,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( ( rev @ A @ Xs )
% 2.71/1.56 = ( rev @ A @ Ys2 ) )
% 2.71/1.56 = ( Xs = Ys2 ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_172_rev__rev__ident,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A] :
% 2.71/1.56 ( ( rev @ A @ ( rev @ A @ Xs ) )
% 2.71/1.56 = Xs ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_173_Nil__is__rev__conv,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A] :
% 2.71/1.56 ( ( ( nil @ A )
% 2.71/1.56 = ( rev @ A @ Xs ) )
% 2.71/1.56 = ( Xs
% 2.71/1.56 = ( nil @ A ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_174_rev__is__Nil__conv,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A] :
% 2.71/1.56 ( ( ( rev @ A @ Xs )
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 = ( Xs
% 2.71/1.56 = ( nil @ A ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_175_rev__append,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( rev @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.71/1.56 = ( append @ A @ ( rev @ A @ Ys2 ) @ ( rev @ A @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_176_remdups__adj__rev,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A] :
% 2.71/1.56 ( ( remdups_adj @ A @ ( rev @ A @ Xs ) )
% 2.71/1.56 = ( rev @ A @ ( remdups_adj @ A @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_177_rev__singleton__conv,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,X: A] :
% 2.71/1.56 ( ( ( rev @ A @ Xs )
% 2.71/1.56 = ( cons @ A @ X @ ( nil @ A ) ) )
% 2.71/1.56 = ( Xs
% 2.71/1.56 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_178_singleton__rev__conv,axiom,
% 2.71/1.56 ! [A: $tType,X: A,Xs: list @ A] :
% 2.71/1.56 ( ( ( cons @ A @ X @ ( nil @ A ) )
% 2.71/1.56 = ( rev @ A @ Xs ) )
% 2.71/1.56 = ( Xs
% 2.71/1.56 = ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_179_rev_Osimps_I1_J,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( rev @ A @ ( nil @ A ) )
% 2.71/1.56 = ( nil @ A ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_180_rev__swap,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( ( rev @ A @ Xs )
% 2.71/1.56 = Ys2 )
% 2.71/1.56 = ( Xs
% 2.71/1.56 = ( rev @ A @ Ys2 ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_181_listrelp_OCons,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,R2: A > B > $o,X: A,Y: B,Xs: list @ A,Ys2: list @ B] :
% 2.71/1.56 ( ( R2 @ X @ Y )
% 2.71/1.56 => ( ( listrelp @ A @ B @ R2 @ Xs @ Ys2 )
% 2.71/1.56 => ( listrelp @ A @ B @ R2 @ ( cons @ A @ X @ Xs ) @ ( cons @ B @ Y @ Ys2 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_182_listrelp_ONil,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,R2: A > B > $o] : ( listrelp @ A @ B @ R2 @ ( nil @ A ) @ ( nil @ B ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_183_rev_Osimps_I2_J,axiom,
% 2.71/1.56 ! [A: $tType,X: A,Xs: list @ A] :
% 2.71/1.56 ( ( rev @ A @ ( cons @ A @ X @ Xs ) )
% 2.71/1.56 = ( append @ A @ ( rev @ A @ Xs ) @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_184_last__rev,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( last @ A @ ( rev @ A @ Xs ) )
% 2.71/1.56 = ( hd @ A @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_185_hd__rev,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( hd @ A @ ( rev @ A @ Xs ) )
% 2.71/1.56 = ( last @ A @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_186_listrelp_Ocases,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,R2: A > B > $o,A1: list @ A,A22: list @ B] :
% 2.71/1.56 ( ( listrelp @ A @ B @ R2 @ A1 @ A22 )
% 2.71/1.56 => ( ( ( A1
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 => ( A22
% 2.71/1.56 != ( nil @ B ) ) )
% 2.71/1.56 => ~ ! [X4: A,Y4: B,Xs2: list @ A] :
% 2.71/1.56 ( ( A1
% 2.71/1.56 = ( cons @ A @ X4 @ Xs2 ) )
% 2.71/1.56 => ! [Ys3: list @ B] :
% 2.71/1.56 ( ( A22
% 2.71/1.56 = ( cons @ B @ Y4 @ Ys3 ) )
% 2.71/1.56 => ( ( R2 @ X4 @ Y4 )
% 2.71/1.56 => ~ ( listrelp @ A @ B @ R2 @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_187_map__tailrec__def,axiom,
% 2.71/1.56 ! [B: $tType,A: $tType] :
% 2.71/1.56 ( ( map_tailrec @ A @ B )
% 2.71/1.56 = ( ^ [F: A > B,As3: list @ A] : ( rev @ B @ ( map_tailrec_rev @ A @ B @ F @ As3 @ ( nil @ B ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_188_lexordp__eq__simps_I3_J,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [X: A,Xs: list @ A] :
% 2.71/1.56 ~ ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( nil @ A ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_189_fold__Cons__rev,axiom,
% 2.71/1.56 ! [A: $tType,Xs: list @ A] :
% 2.71/1.56 ( ( fold @ A @ ( list @ A ) @ ( cons @ A ) @ Xs )
% 2.71/1.56 = ( append @ A @ ( rev @ A @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_190_lexordp__eq__simps_I1_J,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Ys2: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys2 ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_191_lexordp__eq__simps_I2_J,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Xs: list @ A] :
% 2.71/1.56 ( ( ord_lexordp_eq @ A @ Xs @ ( nil @ A ) )
% 2.71/1.56 = ( Xs
% 2.71/1.56 = ( nil @ A ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_192_lexordp__eq__refl,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Xs: list @ A] : ( ord_lexordp_eq @ A @ Xs @ Xs ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_193_lexordp__eq__trans,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Xs: list @ A,Ys2: list @ A,Zs: list @ A] :
% 2.71/1.56 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 2.71/1.56 => ( ( ord_lexordp_eq @ A @ Ys2 @ Zs )
% 2.71/1.56 => ( ord_lexordp_eq @ A @ Xs @ Zs ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_194_lexordp__eq__linear,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 2.71/1.56 | ( ord_lexordp_eq @ A @ Ys2 @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_195_lexordp__eq__antisym,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 2.71/1.56 => ( ( ord_lexordp_eq @ A @ Ys2 @ Xs )
% 2.71/1.56 => ( Xs = Ys2 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_196_lexordp__eq_ONil,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Ys2: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys2 ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_197_fold__simps_I1_J,axiom,
% 2.71/1.56 ! [B: $tType,A: $tType,F2: B > A > A,S: A] :
% 2.71/1.56 ( ( fold @ B @ A @ F2 @ ( nil @ B ) @ S )
% 2.71/1.56 = S ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_198_fold__simps_I2_J,axiom,
% 2.71/1.56 ! [B: $tType,A: $tType,F2: B > A > A,X: B,Xs: list @ B,S: A] :
% 2.71/1.56 ( ( fold @ B @ A @ F2 @ ( cons @ B @ X @ Xs ) @ S )
% 2.71/1.56 = ( fold @ B @ A @ F2 @ Xs @ ( F2 @ X @ S ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_199_rev__conv__fold,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( rev @ A )
% 2.71/1.56 = ( ^ [Xs3: list @ A] : ( fold @ A @ ( list @ A ) @ ( cons @ A ) @ Xs3 @ ( nil @ A ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_200_List_Ounion__def,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( union @ A )
% 2.71/1.56 = ( fold @ A @ ( list @ A ) @ ( insert @ A ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_201_lexordp__eq_Oinducts,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [X1: list @ A,X2: list @ A,P2: ( list @ A ) > ( list @ A ) > $o] :
% 2.71/1.56 ( ( ord_lexordp_eq @ A @ X1 @ X2 )
% 2.71/1.56 => ( ! [X12: list @ A] : ( P2 @ ( nil @ A ) @ X12 )
% 2.71/1.56 => ( ! [X4: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 2.71/1.56 ( ( ord_less @ A @ X4 @ Y4 )
% 2.71/1.56 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 2.71/1.56 => ( ! [X4: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 2.71/1.56 ( ~ ( ord_less @ A @ X4 @ Y4 )
% 2.71/1.56 => ( ~ ( ord_less @ A @ Y4 @ X4 )
% 2.71/1.56 => ( ( ord_lexordp_eq @ A @ Xs2 @ Ys3 )
% 2.71/1.56 => ( ( P2 @ Xs2 @ Ys3 )
% 2.71/1.56 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) ) ) ) )
% 2.71/1.56 => ( P2 @ X1 @ X2 ) ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_202_lexordp__eq__simps_I4_J,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [X: A,Xs: list @ A,Y: A,Ys2: list @ A] :
% 2.71/1.56 ( ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) )
% 2.71/1.56 = ( ( ord_less @ A @ X @ Y )
% 2.71/1.56 | ( ~ ( ord_less @ A @ Y @ X )
% 2.71/1.56 & ( ord_lexordp_eq @ A @ Xs @ Ys2 ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_203_lexordp__eq_OCons__eq,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [X: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ~ ( ord_less @ A @ X @ Y )
% 2.71/1.56 => ( ~ ( ord_less @ A @ Y @ X )
% 2.71/1.56 => ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 2.71/1.56 => ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_204_lexordp__eq_OCons,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [X: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( ord_less @ A @ X @ Y )
% 2.71/1.56 => ( ord_lexordp_eq @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_205_lexordp__eq_Ocases,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [A1: list @ A,A22: list @ A] :
% 2.71/1.56 ( ( ord_lexordp_eq @ A @ A1 @ A22 )
% 2.71/1.56 => ( ( ( A1
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 => ! [Ys3: list @ A] : ( A22 != Ys3 ) )
% 2.71/1.56 => ( ! [X4: A] :
% 2.71/1.56 ( ? [Xs2: list @ A] :
% 2.71/1.56 ( A1
% 2.71/1.56 = ( cons @ A @ X4 @ Xs2 ) )
% 2.71/1.56 => ! [Y4: A] :
% 2.71/1.56 ( ? [Ys3: list @ A] :
% 2.71/1.56 ( A22
% 2.71/1.56 = ( cons @ A @ Y4 @ Ys3 ) )
% 2.71/1.56 => ~ ( ord_less @ A @ X4 @ Y4 ) ) )
% 2.71/1.56 => ~ ! [X4: A,Y4: A,Xs2: list @ A] :
% 2.71/1.56 ( ( A1
% 2.71/1.56 = ( cons @ A @ X4 @ Xs2 ) )
% 2.71/1.56 => ! [Ys3: list @ A] :
% 2.71/1.56 ( ( A22
% 2.71/1.56 = ( cons @ A @ Y4 @ Ys3 ) )
% 2.71/1.56 => ( ~ ( ord_less @ A @ X4 @ Y4 )
% 2.71/1.56 => ( ~ ( ord_less @ A @ Y4 @ X4 )
% 2.71/1.56 => ~ ( ord_lexordp_eq @ A @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_206_lexordp__eq_Osimps,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ( ( ord_lexordp_eq @ A )
% 2.71/1.56 = ( ^ [A12: list @ A,A23: list @ A] :
% 2.71/1.56 ( ? [Ys: list @ A] :
% 2.71/1.56 ( ( A12
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 & ( A23 = Ys ) )
% 2.71/1.56 | ? [X5: A,Y3: A,Xs3: list @ A,Ys: list @ A] :
% 2.71/1.56 ( ( A12
% 2.71/1.56 = ( cons @ A @ X5 @ Xs3 ) )
% 2.71/1.56 & ( A23
% 2.71/1.56 = ( cons @ A @ Y3 @ Ys ) )
% 2.71/1.56 & ( ord_less @ A @ X5 @ Y3 ) )
% 2.71/1.56 | ? [X5: A,Y3: A,Xs3: list @ A,Ys: list @ A] :
% 2.71/1.56 ( ( A12
% 2.71/1.56 = ( cons @ A @ X5 @ Xs3 ) )
% 2.71/1.56 & ( A23
% 2.71/1.56 = ( cons @ A @ Y3 @ Ys ) )
% 2.71/1.56 & ~ ( ord_less @ A @ X5 @ Y3 )
% 2.71/1.56 & ~ ( ord_less @ A @ Y3 @ X5 )
% 2.71/1.56 & ( ord_lexordp_eq @ A @ Xs3 @ Ys ) ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_207_lexordp__append__left__rightI,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [X: A,Y: A,Us2: list @ A,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( ord_less @ A @ X @ Y )
% 2.71/1.56 => ( ord_lexordp @ A @ ( append @ A @ Us2 @ ( cons @ A @ X @ Xs ) ) @ ( append @ A @ Us2 @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_208_lexordp__iff,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.71/1.56 => ( ( ord_lexordp @ A )
% 2.71/1.56 = ( ^ [Xs3: list @ A,Ys: list @ A] :
% 2.71/1.56 ( ? [X5: A,Vs: list @ A] :
% 2.71/1.56 ( Ys
% 2.71/1.56 = ( append @ A @ Xs3 @ ( cons @ A @ X5 @ Vs ) ) )
% 2.71/1.56 | ? [Us: list @ A,A5: A,B3: A,Vs: list @ A,Ws2: list @ A] :
% 2.71/1.56 ( ( ord_less @ A @ A5 @ B3 )
% 2.71/1.56 & ( Xs3
% 2.71/1.56 = ( append @ A @ Us @ ( cons @ A @ A5 @ Vs ) ) )
% 2.71/1.56 & ( Ys
% 2.71/1.56 = ( append @ A @ Us @ ( cons @ A @ B3 @ Ws2 ) ) ) ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_209_lexordp__simps_I1_J,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Ys2: list @ A] :
% 2.71/1.56 ( ( ord_lexordp @ A @ ( nil @ A ) @ Ys2 )
% 2.71/1.56 = ( Ys2
% 2.71/1.56 != ( nil @ A ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_210_lexordp__simps_I2_J,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Xs: list @ A] :
% 2.71/1.56 ~ ( ord_lexordp @ A @ Xs @ ( nil @ A ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_211_lexordp__simps_I3_J,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [X: A,Xs: list @ A,Y: A,Ys2: list @ A] :
% 2.71/1.56 ( ( ord_lexordp @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) )
% 2.71/1.56 = ( ( ord_less @ A @ X @ Y )
% 2.71/1.56 | ( ~ ( ord_less @ A @ Y @ X )
% 2.71/1.56 & ( ord_lexordp @ A @ Xs @ Ys2 ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_212_lexordp__irreflexive,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Xs: list @ A] :
% 2.71/1.56 ( ! [X4: A] :
% 2.71/1.56 ~ ( ord_less @ A @ X4 @ X4 )
% 2.71/1.56 => ~ ( ord_lexordp @ A @ Xs @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_213_lexordp__append__leftD,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Xs: list @ A,Us2: list @ A,Vs2: list @ A] :
% 2.71/1.56 ( ( ord_lexordp @ A @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Xs @ Vs2 ) )
% 2.71/1.56 => ( ! [A4: A] :
% 2.71/1.56 ~ ( ord_less @ A @ A4 @ A4 )
% 2.71/1.56 => ( ord_lexordp @ A @ Us2 @ Vs2 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_214_lexordp_OCons__eq,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [X: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ~ ( ord_less @ A @ X @ Y )
% 2.71/1.56 => ( ~ ( ord_less @ A @ Y @ X )
% 2.71/1.56 => ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 2.71/1.56 => ( ord_lexordp @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_215_lexordp_OCons,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [X: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( ord_less @ A @ X @ Y )
% 2.71/1.56 => ( ord_lexordp @ A @ ( cons @ A @ X @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_216_lexordp_ONil,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Y: A,Ys2: list @ A] : ( ord_lexordp @ A @ ( nil @ A ) @ ( cons @ A @ Y @ Ys2 ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_217_lexordp__append__rightI,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Ys2: list @ A,Xs: list @ A] :
% 2.71/1.56 ( ( Ys2
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ord_lexordp @ A @ Xs @ ( append @ A @ Xs @ Ys2 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_218_lexordp__antisym,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( order @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 2.71/1.56 => ~ ( ord_lexordp @ A @ Ys2 @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_219_lexordp__trans,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Xs: list @ A,Ys2: list @ A,Zs: list @ A] :
% 2.71/1.56 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 2.71/1.56 => ( ( ord_lexordp @ A @ Ys2 @ Zs )
% 2.71/1.56 => ( ord_lexordp @ A @ Xs @ Zs ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_220_lexordp__linear,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 2.71/1.56 | ( Xs = Ys2 )
% 2.71/1.56 | ( ord_lexordp @ A @ Ys2 @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_221_lexordp__irreflexive_H,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( order @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Xs: list @ A] :
% 2.71/1.56 ~ ( ord_lexordp @ A @ Xs @ Xs ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_222_lexordp__append__leftI,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Us2: list @ A,Vs2: list @ A,Xs: list @ A] :
% 2.71/1.56 ( ( ord_lexordp @ A @ Us2 @ Vs2 )
% 2.71/1.56 => ( ord_lexordp @ A @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Xs @ Vs2 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_223_lexordp__conv__lexordp__eq,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.71/1.56 => ( ( ord_lexordp @ A )
% 2.71/1.56 = ( ^ [Xs3: list @ A,Ys: list @ A] :
% 2.71/1.56 ( ( ord_lexordp_eq @ A @ Xs3 @ Ys )
% 2.71/1.56 & ~ ( ord_lexordp_eq @ A @ Ys @ Xs3 ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_224_lexordp__eq__conv__lexord,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.71/1.56 => ( ( ord_lexordp_eq @ A )
% 2.71/1.56 = ( ^ [Xs3: list @ A,Ys: list @ A] :
% 2.71/1.56 ( ( Xs3 = Ys )
% 2.71/1.56 | ( ord_lexordp @ A @ Xs3 @ Ys ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_225_lexordp__into__lexordp__eq,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 2.71/1.56 => ( ord_lexordp_eq @ A @ Xs @ Ys2 ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_226_lexordp__induct,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Xs: list @ A,Ys2: list @ A,P2: ( list @ A ) > ( list @ A ) > $o] :
% 2.71/1.56 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 2.71/1.56 => ( ! [Y4: A,Ys3: list @ A] : ( P2 @ ( nil @ A ) @ ( cons @ A @ Y4 @ Ys3 ) )
% 2.71/1.56 => ( ! [X4: A,Xs2: list @ A,Y4: A,Ys3: list @ A] :
% 2.71/1.56 ( ( ord_less @ A @ X4 @ Y4 )
% 2.71/1.56 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 2.71/1.56 => ( ! [X4: A,Xs2: list @ A,Ys3: list @ A] :
% 2.71/1.56 ( ( ord_lexordp @ A @ Xs2 @ Ys3 )
% 2.71/1.56 => ( ( P2 @ Xs2 @ Ys3 )
% 2.71/1.56 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ X4 @ Ys3 ) ) ) )
% 2.71/1.56 => ( P2 @ Xs @ Ys2 ) ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_227_lexordp__cases,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( linorder @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [Xs: list @ A,Ys2: list @ A] :
% 2.71/1.56 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 2.71/1.56 => ( ( ( Xs
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 => ! [Y4: A,Ys5: list @ A] :
% 2.71/1.56 ( Ys2
% 2.71/1.56 != ( cons @ A @ Y4 @ Ys5 ) ) )
% 2.71/1.56 => ( ! [X4: A] :
% 2.71/1.56 ( ? [Xs4: list @ A] :
% 2.71/1.56 ( Xs
% 2.71/1.56 = ( cons @ A @ X4 @ Xs4 ) )
% 2.71/1.56 => ! [Y4: A] :
% 2.71/1.56 ( ? [Ys5: list @ A] :
% 2.71/1.56 ( Ys2
% 2.71/1.56 = ( cons @ A @ Y4 @ Ys5 ) )
% 2.71/1.56 => ~ ( ord_less @ A @ X4 @ Y4 ) ) )
% 2.71/1.56 => ~ ! [X4: A,Xs4: list @ A] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 = ( cons @ A @ X4 @ Xs4 ) )
% 2.71/1.56 => ! [Ys5: list @ A] :
% 2.71/1.56 ( ( Ys2
% 2.71/1.56 = ( cons @ A @ X4 @ Ys5 ) )
% 2.71/1.56 => ~ ( ord_lexordp @ A @ Xs4 @ Ys5 ) ) ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_228_lexordp_Oinducts,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [X1: list @ A,X2: list @ A,P2: ( list @ A ) > ( list @ A ) > $o] :
% 2.71/1.56 ( ( ord_lexordp @ A @ X1 @ X2 )
% 2.71/1.56 => ( ! [Y4: A,Ys3: list @ A] : ( P2 @ ( nil @ A ) @ ( cons @ A @ Y4 @ Ys3 ) )
% 2.71/1.56 => ( ! [X4: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 2.71/1.56 ( ( ord_less @ A @ X4 @ Y4 )
% 2.71/1.56 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 2.71/1.56 => ( ! [X4: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 2.71/1.56 ( ~ ( ord_less @ A @ X4 @ Y4 )
% 2.71/1.56 => ( ~ ( ord_less @ A @ Y4 @ X4 )
% 2.71/1.56 => ( ( ord_lexordp @ A @ Xs2 @ Ys3 )
% 2.71/1.56 => ( ( P2 @ Xs2 @ Ys3 )
% 2.71/1.56 => ( P2 @ ( cons @ A @ X4 @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) ) ) ) )
% 2.71/1.56 => ( P2 @ X1 @ X2 ) ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_229_lexordp_Osimps,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ( ( ord_lexordp @ A )
% 2.71/1.56 = ( ^ [A12: list @ A,A23: list @ A] :
% 2.71/1.56 ( ? [Y3: A,Ys: list @ A] :
% 2.71/1.56 ( ( A12
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 & ( A23
% 2.71/1.56 = ( cons @ A @ Y3 @ Ys ) ) )
% 2.71/1.56 | ? [X5: A,Y3: A,Xs3: list @ A,Ys: list @ A] :
% 2.71/1.56 ( ( A12
% 2.71/1.56 = ( cons @ A @ X5 @ Xs3 ) )
% 2.71/1.56 & ( A23
% 2.71/1.56 = ( cons @ A @ Y3 @ Ys ) )
% 2.71/1.56 & ( ord_less @ A @ X5 @ Y3 ) )
% 2.71/1.56 | ? [X5: A,Y3: A,Xs3: list @ A,Ys: list @ A] :
% 2.71/1.56 ( ( A12
% 2.71/1.56 = ( cons @ A @ X5 @ Xs3 ) )
% 2.71/1.56 & ( A23
% 2.71/1.56 = ( cons @ A @ Y3 @ Ys ) )
% 2.71/1.56 & ~ ( ord_less @ A @ X5 @ Y3 )
% 2.71/1.56 & ~ ( ord_less @ A @ Y3 @ X5 )
% 2.71/1.56 & ( ord_lexordp @ A @ Xs3 @ Ys ) ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_230_lexordp_Ocases,axiom,
% 2.71/1.56 ! [A: $tType] :
% 2.71/1.56 ( ( ord @ A @ ( type2 @ A ) )
% 2.71/1.56 => ! [A1: list @ A,A22: list @ A] :
% 2.71/1.56 ( ( ord_lexordp @ A @ A1 @ A22 )
% 2.71/1.56 => ( ( ( A1
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 => ! [Y4: A,Ys3: list @ A] :
% 2.71/1.56 ( A22
% 2.71/1.56 != ( cons @ A @ Y4 @ Ys3 ) ) )
% 2.71/1.56 => ( ! [X4: A] :
% 2.71/1.56 ( ? [Xs2: list @ A] :
% 2.71/1.56 ( A1
% 2.71/1.56 = ( cons @ A @ X4 @ Xs2 ) )
% 2.71/1.56 => ! [Y4: A] :
% 2.71/1.56 ( ? [Ys3: list @ A] :
% 2.71/1.56 ( A22
% 2.71/1.56 = ( cons @ A @ Y4 @ Ys3 ) )
% 2.71/1.56 => ~ ( ord_less @ A @ X4 @ Y4 ) ) )
% 2.71/1.56 => ~ ! [X4: A,Y4: A,Xs2: list @ A] :
% 2.71/1.56 ( ( A1
% 2.71/1.56 = ( cons @ A @ X4 @ Xs2 ) )
% 2.71/1.56 => ! [Ys3: list @ A] :
% 2.71/1.56 ( ( A22
% 2.71/1.56 = ( cons @ A @ Y4 @ Ys3 ) )
% 2.71/1.56 => ( ~ ( ord_less @ A @ X4 @ Y4 )
% 2.71/1.56 => ( ~ ( ord_less @ A @ Y4 @ X4 )
% 2.71/1.56 => ~ ( ord_lexordp @ A @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_231_map__tailrec__rev,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType] :
% 2.71/1.56 ( ( map_tailrec_rev @ B @ A )
% 2.71/1.56 = ( ^ [F: B > A,As3: list @ B] : ( append @ A @ ( rev @ A @ ( map @ B @ A @ F @ As3 ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_232_replicate__append__same,axiom,
% 2.71/1.56 ! [A: $tType,I: nat,X: A] :
% 2.71/1.56 ( ( append @ A @ ( replicate @ A @ I @ X ) @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.71/1.56 = ( cons @ A @ X @ ( replicate @ A @ I @ X ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_233_Nil__is__map__conv,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B] :
% 2.71/1.56 ( ( ( nil @ A )
% 2.71/1.56 = ( map @ B @ A @ F2 @ Xs ) )
% 2.71/1.56 = ( Xs
% 2.71/1.56 = ( nil @ B ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_234_map__is__Nil__conv,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B] :
% 2.71/1.56 ( ( ( map @ B @ A @ F2 @ Xs )
% 2.71/1.56 = ( nil @ A ) )
% 2.71/1.56 = ( Xs
% 2.71/1.56 = ( nil @ B ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_235_list_Omap__disc__iff,axiom,
% 2.71/1.56 ! [B: $tType,A: $tType,F2: A > B,A3: list @ A] :
% 2.71/1.56 ( ( ( map @ A @ B @ F2 @ A3 )
% 2.71/1.56 = ( nil @ B ) )
% 2.71/1.56 = ( A3
% 2.71/1.56 = ( nil @ A ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_236_map__append,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B,Ys2: list @ B] :
% 2.71/1.56 ( ( map @ B @ A @ F2 @ ( append @ B @ Xs @ Ys2 ) )
% 2.71/1.56 = ( append @ A @ ( map @ B @ A @ F2 @ Xs ) @ ( map @ B @ A @ F2 @ Ys2 ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_237_map__replicate,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,F2: B > A,N: nat,X: B] :
% 2.71/1.56 ( ( map @ B @ A @ F2 @ ( replicate @ B @ N @ X ) )
% 2.71/1.56 = ( replicate @ A @ N @ ( F2 @ X ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_238_rev__replicate,axiom,
% 2.71/1.56 ! [A: $tType,N: nat,X: A] :
% 2.71/1.56 ( ( rev @ A @ ( replicate @ A @ N @ X ) )
% 2.71/1.56 = ( replicate @ A @ N @ X ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_239_smap__shift,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B,S: stream170649215stream @ B] :
% 2.71/1.56 ( ( stream2128578057e_smap @ B @ A @ F2 @ ( stream1035003186_shift @ B @ Xs @ S ) )
% 2.71/1.56 = ( stream1035003186_shift @ A @ ( map @ B @ A @ F2 @ Xs ) @ ( stream2128578057e_smap @ B @ A @ F2 @ S ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_240_map__eq__map__tailrec,axiom,
% 2.71/1.56 ! [B: $tType,A: $tType] :
% 2.71/1.56 ( ( map @ A @ B )
% 2.71/1.56 = ( map_tailrec @ A @ B ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_241_list_Omap__sel_I2_J,axiom,
% 2.71/1.56 ! [B: $tType,A: $tType,A3: list @ A,F2: A > B] :
% 2.71/1.56 ( ( A3
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( tl @ B @ ( map @ A @ B @ F2 @ A3 ) )
% 2.71/1.56 = ( map @ A @ B @ F2 @ ( tl @ A @ A3 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_242_hd__map,axiom,
% 2.71/1.56 ! [B: $tType,A: $tType,Xs: list @ A,F2: A > B] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( hd @ B @ ( map @ A @ B @ F2 @ Xs ) )
% 2.71/1.56 = ( F2 @ ( hd @ A @ Xs ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_243_list_Omap__sel_I1_J,axiom,
% 2.71/1.56 ! [B: $tType,A: $tType,A3: list @ A,F2: A > B] :
% 2.71/1.56 ( ( A3
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( hd @ B @ ( map @ A @ B @ F2 @ A3 ) )
% 2.71/1.56 = ( F2 @ ( hd @ A @ A3 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_244_last__map,axiom,
% 2.71/1.56 ! [B: $tType,A: $tType,Xs: list @ A,F2: A > B] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 != ( nil @ A ) )
% 2.71/1.56 => ( ( last @ B @ ( map @ A @ B @ F2 @ Xs ) )
% 2.71/1.56 = ( F2 @ ( last @ A @ Xs ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_245_replicate__app__Cons__same,axiom,
% 2.71/1.56 ! [A: $tType,N: nat,X: A,Xs: list @ A] :
% 2.71/1.56 ( ( append @ A @ ( replicate @ A @ N @ X ) @ ( cons @ A @ X @ Xs ) )
% 2.71/1.56 = ( cons @ A @ X @ ( append @ A @ ( replicate @ A @ N @ X ) @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_246_list_Osimps_I9_J,axiom,
% 2.71/1.56 ! [B: $tType,A: $tType,F2: A > B,X21: A,X222: list @ A] :
% 2.71/1.56 ( ( map @ A @ B @ F2 @ ( cons @ A @ X21 @ X222 ) )
% 2.71/1.56 = ( cons @ B @ ( F2 @ X21 ) @ ( map @ A @ B @ F2 @ X222 ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_247_Cons__eq__map__D,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,X: A,Xs: list @ A,F2: B > A,Ys2: list @ B] :
% 2.71/1.56 ( ( ( cons @ A @ X @ Xs )
% 2.71/1.56 = ( map @ B @ A @ F2 @ Ys2 ) )
% 2.71/1.56 => ? [Z: B,Zs2: list @ B] :
% 2.71/1.56 ( ( Ys2
% 2.71/1.56 = ( cons @ B @ Z @ Zs2 ) )
% 2.71/1.56 & ( X
% 2.71/1.56 = ( F2 @ Z ) )
% 2.71/1.56 & ( Xs
% 2.71/1.56 = ( map @ B @ A @ F2 @ Zs2 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_248_map__eq__Cons__D,axiom,
% 2.71/1.56 ! [B: $tType,A: $tType,F2: B > A,Xs: list @ B,Y: A,Ys2: list @ A] :
% 2.71/1.56 ( ( ( map @ B @ A @ F2 @ Xs )
% 2.71/1.56 = ( cons @ A @ Y @ Ys2 ) )
% 2.71/1.56 => ? [Z: B,Zs2: list @ B] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 = ( cons @ B @ Z @ Zs2 ) )
% 2.71/1.56 & ( ( F2 @ Z )
% 2.71/1.56 = Y )
% 2.71/1.56 & ( ( map @ B @ A @ F2 @ Zs2 )
% 2.71/1.56 = Ys2 ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_249_Cons__eq__map__conv,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,X: A,Xs: list @ A,F2: B > A,Ys2: list @ B] :
% 2.71/1.56 ( ( ( cons @ A @ X @ Xs )
% 2.71/1.56 = ( map @ B @ A @ F2 @ Ys2 ) )
% 2.71/1.56 = ( ? [Z2: B,Zs3: list @ B] :
% 2.71/1.56 ( ( Ys2
% 2.71/1.56 = ( cons @ B @ Z2 @ Zs3 ) )
% 2.71/1.56 & ( X
% 2.71/1.56 = ( F2 @ Z2 ) )
% 2.71/1.56 & ( Xs
% 2.71/1.56 = ( map @ B @ A @ F2 @ Zs3 ) ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_250_map__eq__Cons__conv,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B,Y: A,Ys2: list @ A] :
% 2.71/1.56 ( ( ( map @ B @ A @ F2 @ Xs )
% 2.71/1.56 = ( cons @ A @ Y @ Ys2 ) )
% 2.71/1.56 = ( ? [Z2: B,Zs3: list @ B] :
% 2.71/1.56 ( ( Xs
% 2.71/1.56 = ( cons @ B @ Z2 @ Zs3 ) )
% 2.71/1.56 & ( ( F2 @ Z2 )
% 2.71/1.56 = Y )
% 2.71/1.56 & ( ( map @ B @ A @ F2 @ Zs3 )
% 2.71/1.56 = Ys2 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_251_list_Osimps_I8_J,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,F2: A > B] :
% 2.71/1.56 ( ( map @ A @ B @ F2 @ ( nil @ A ) )
% 2.71/1.56 = ( nil @ B ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_252_map__tl,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B] :
% 2.71/1.56 ( ( map @ B @ A @ F2 @ ( tl @ B @ Xs ) )
% 2.71/1.56 = ( tl @ A @ ( map @ B @ A @ F2 @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_253_append__replicate__commute,axiom,
% 2.71/1.56 ! [A: $tType,N: nat,X: A,K: nat] :
% 2.71/1.56 ( ( append @ A @ ( replicate @ A @ N @ X ) @ ( replicate @ A @ K @ X ) )
% 2.71/1.56 = ( append @ A @ ( replicate @ A @ K @ X ) @ ( replicate @ A @ N @ X ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(fact_254_map__butlast,axiom,
% 2.71/1.56 ! [A: $tType,B: $tType,F2: B > A,Xs: list @ B] :
% 2.71/1.56 ( ( map @ B @ A @ F2 @ ( butlast @ B @ Xs ) )
% 2.71/1.56 = ( butlast @ A @ ( map @ B @ A @ F2 @ Xs ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.71/1.56 ! [A7: $tType,A8: $tType] :
% 2.71/1.56 ( ( order @ A8 @ ( type2 @ A8 ) )
% 2.71/1.56 => ( order @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(tcon_fun___Orderings_Oord,axiom,
% 2.71/1.56 ! [A7: $tType,A8: $tType] :
% 2.71/1.56 ( ( ord @ A8 @ ( type2 @ A8 ) )
% 2.71/1.56 => ( ord @ ( A7 > A8 ) @ ( type2 @ ( A7 > A8 ) ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(tcon_Set_Oset___Orderings_Oorder_1,axiom,
% 2.71/1.56 ! [A7: $tType] : ( order @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 2.71/1.56 ! [A7: $tType] : ( ord @ ( set @ A7 ) @ ( type2 @ ( set @ A7 ) ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.71/1.56 linorder @ $o @ ( type2 @ $o ) ).
% 2.71/1.56
% 2.71/1.56 thf(tcon_HOL_Obool___Orderings_Oorder_3,axiom,
% 2.71/1.56 order @ $o @ ( type2 @ $o ) ).
% 2.71/1.56
% 2.71/1.56 thf(tcon_HOL_Obool___Orderings_Oord_4,axiom,
% 2.71/1.56 ord @ $o @ ( type2 @ $o ) ).
% 2.71/1.56
% 2.71/1.56 thf(help_If_3_1_T,axiom,
% 2.71/1.56 ! [P2: $o] :
% 2.71/1.56 ( ( P2 = $true )
% 2.71/1.56 | ( P2 = $false ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(help_If_2_1_T,axiom,
% 2.71/1.56 ! [A: $tType,X: A,Y: A] :
% 2.71/1.56 ( ( if @ A @ $false @ X @ Y )
% 2.71/1.56 = Y ) ).
% 2.71/1.56
% 2.71/1.56 thf(help_If_1_1_T,axiom,
% 2.71/1.56 ! [A: $tType,X: A,Y: A] :
% 2.71/1.56 ( ( if @ A @ $true @ X @ Y )
% 2.71/1.56 = X ) ).
% 2.71/1.56
% 2.71/1.56 thf(conj_0,hypothesis,
% 2.71/1.56 ( ( stream_Mirabelle_shd @ ( list @ a ) @ ws )
% 2.71/1.56 != ( nil @ a ) ) ).
% 2.71/1.56
% 2.71/1.56 thf(conj_1,conjecture,
% 2.71/1.56 ( ( stream942386729e_flat @ a @ ws )
% 2.71/1.56 = ( stream1035003186_shift @ a @ ( stream_Mirabelle_shd @ ( list @ a ) @ ws ) @ ( stream942386729e_flat @ a @ ( stream_Mirabelle_stl @ ( list @ a ) @ ws ) ) ) ) ).
% 2.71/1.56 ------------------------
% 2.71/1.59 % (3547)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3154 for (2999ds/183Mi)
% 2.71/1.59 % (3548)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_3154 for (2999ds/4Mi)
% 2.71/1.59 % (3548)Instruction limit reached!
% 2.71/1.59 % (3548)------------------------------
% 2.71/1.59 % (3548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.71/1.59 % (3548)Termination reason: Unknown
% 2.71/1.59 % (3548)Termination phase: shuffling
% 2.71/1.59
% 2.71/1.59 % (3548)Memory used [KB]: 1407
% 2.71/1.59 % (3548)Time elapsed: 0.003 s
% 2.71/1.59 % (3548)Instructions burned: 5 (million)
% 2.71/1.59 % (3548)------------------------------
% 2.71/1.59 % (3548)------------------------------
% 2.78/1.60 % (3550)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3154 for (2999ds/2Mi)
% 2.78/1.60 % (3551)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_3154 for (2999ds/2Mi)
% 2.78/1.60 % (3553)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3154 for (2999ds/18Mi)
% 2.78/1.60 % (3552)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_3154 for (2999ds/275Mi)
% 2.78/1.60 % (3549)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_3154 for (2999ds/27Mi)
% 2.78/1.60 % (3550)Instruction limit reached!
% 2.78/1.60 % (3550)------------------------------
% 2.78/1.60 % (3550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.60 % (3550)Termination reason: Unknown
% 2.78/1.60 % (3550)Termination phase: shuffling
% 2.78/1.60
% 2.78/1.60 % (3550)Memory used [KB]: 1407
% 2.78/1.60 % (3550)Time elapsed: 0.004 s
% 2.78/1.60 % (3550)Instructions burned: 3 (million)
% 2.78/1.60 % (3550)------------------------------
% 2.78/1.60 % (3550)------------------------------
% 2.78/1.60 % (3551)Instruction limit reached!
% 2.78/1.60 % (3551)------------------------------
% 2.78/1.60 % (3551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.60 % (3551)Termination reason: Unknown
% 2.78/1.60 % (3551)Termination phase: shuffling
% 2.78/1.60
% 2.78/1.60 % (3551)Memory used [KB]: 1407
% 2.78/1.60 % (3551)Time elapsed: 0.004 s
% 2.78/1.60 % (3551)Instructions burned: 3 (million)
% 2.78/1.60 % (3551)------------------------------
% 2.78/1.60 % (3551)------------------------------
% 2.78/1.60 % (3554)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3154 for (2999ds/3Mi)
% 2.78/1.60 % (3554)Instruction limit reached!
% 2.78/1.60 % (3554)------------------------------
% 2.78/1.60 % (3554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.60 % (3554)Termination reason: Unknown
% 2.78/1.60 % (3554)Termination phase: shuffling
% 2.78/1.60
% 2.78/1.60 % (3554)Memory used [KB]: 1407
% 2.78/1.60 % (3554)Time elapsed: 0.002 s
% 2.78/1.60 % (3554)Instructions burned: 3 (million)
% 2.78/1.60 % (3554)------------------------------
% 2.78/1.60 % (3554)------------------------------
% 2.78/1.61 % (3553)Instruction limit reached!
% 2.78/1.61 % (3553)------------------------------
% 2.78/1.61 % (3553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.61 % (3553)Termination reason: Unknown
% 2.78/1.61 % (3553)Termination phase: shuffling
% 2.78/1.61
% 2.78/1.61 % (3553)Memory used [KB]: 1791
% 2.78/1.61 % (3553)Time elapsed: 0.014 s
% 2.78/1.61 % (3553)Instructions burned: 18 (million)
% 2.78/1.61 % (3553)------------------------------
% 2.78/1.61 % (3553)------------------------------
% 2.78/1.61 % (3557)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_3154 for (2999ds/3Mi)
% 2.78/1.61 % (3557)Instruction limit reached!
% 2.78/1.61 % (3557)------------------------------
% 2.78/1.61 % (3557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.61 % (3557)Termination reason: Unknown
% 2.78/1.61 % (3557)Termination phase: shuffling
% 2.78/1.61
% 2.78/1.61 % (3557)Memory used [KB]: 1407
% 2.78/1.61 % (3557)Time elapsed: 0.002 s
% 2.78/1.61 % (3557)Instructions burned: 3 (million)
% 2.78/1.61 % (3557)------------------------------
% 2.78/1.61 % (3557)------------------------------
% 2.78/1.61 % (3549)Instruction limit reached!
% 2.78/1.61 % (3549)------------------------------
% 2.78/1.61 % (3549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.61 % (3549)Termination reason: Unknown
% 2.78/1.61 % (3549)Termination phase: Property scanning
% 2.78/1.61
% 2.78/1.61 % (3549)Memory used [KB]: 1791
% 2.78/1.61 % (3549)Time elapsed: 0.019 s
% 2.78/1.61 % (3549)Instructions burned: 28 (million)
% 2.78/1.61 % (3549)------------------------------
% 2.78/1.61 % (3549)------------------------------
% 2.78/1.62 % (3555)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_3154 for (2999ds/37Mi)
% 2.78/1.62 % (3556)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_3154 for (2999ds/15Mi)
% 2.78/1.62 % (3559)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3154 for (2999ds/7Mi)
% 2.78/1.62 % (3559)Instruction limit reached!
% 2.78/1.62 % (3559)------------------------------
% 2.78/1.62 % (3559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.62 % (3559)Termination reason: Unknown
% 2.78/1.62 % (3559)Termination phase: shuffling
% 2.78/1.62
% 2.78/1.62 % (3559)Memory used [KB]: 1535
% 2.78/1.62 % (3559)Time elapsed: 0.004 s
% 2.78/1.62 % (3559)Instructions burned: 9 (million)
% 2.78/1.62 % (3559)------------------------------
% 2.78/1.62 % (3559)------------------------------
% 2.78/1.63 % (3558)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_3154 for (2999ds/1041Mi)
% 2.78/1.63 % (3556)Instruction limit reached!
% 2.78/1.63 % (3556)------------------------------
% 2.78/1.63 % (3556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.63 % (3556)Termination reason: Unknown
% 2.78/1.63 % (3556)Termination phase: shuffling
% 2.78/1.63
% 2.78/1.63 % (3556)Memory used [KB]: 1663
% 2.78/1.63 % (3556)Time elapsed: 0.012 s
% 2.78/1.63 % (3556)Instructions burned: 16 (million)
% 2.78/1.63 % (3556)------------------------------
% 2.78/1.63 % (3556)------------------------------
% 2.78/1.63 % (3560)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3154 for (2999ds/16Mi)
% 2.78/1.63 % (3561)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_3154 for (2999ds/3Mi)
% 2.78/1.63 % (3561)Instruction limit reached!
% 2.78/1.63 % (3561)------------------------------
% 2.78/1.63 % (3561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.63 % (3561)Termination reason: Unknown
% 2.78/1.63 % (3561)Termination phase: shuffling
% 2.78/1.63
% 2.78/1.63 % (3561)Memory used [KB]: 1407
% 2.78/1.63 % (3561)Time elapsed: 0.003 s
% 2.78/1.63 % (3561)Instructions burned: 5 (million)
% 2.78/1.63 % (3561)------------------------------
% 2.78/1.63 % (3561)------------------------------
% 2.78/1.63 % (3555)Instruction limit reached!
% 2.78/1.63 % (3555)------------------------------
% 2.78/1.63 % (3555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.63 % (3555)Termination reason: Unknown
% 2.78/1.63 % (3555)Termination phase: shuffling
% 2.78/1.63
% 2.78/1.63 % (3555)Memory used [KB]: 2046
% 2.78/1.63 % (3555)Time elapsed: 0.021 s
% 2.78/1.63 % (3555)Instructions burned: 37 (million)
% 2.78/1.63 % (3555)------------------------------
% 2.78/1.63 % (3555)------------------------------
% 2.78/1.64 % (3552)Refutation not found, incomplete strategy
% 2.78/1.64 % (3552)------------------------------
% 2.78/1.64 % (3552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.64 % (3552)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.64
% 2.78/1.64
% 2.78/1.64 % (3552)Memory used [KB]: 6652
% 2.78/1.64 % (3552)Time elapsed: 0.044 s
% 2.78/1.64 % (3552)Instructions burned: 71 (million)
% 2.78/1.64 % (3552)------------------------------
% 2.78/1.64 % (3552)------------------------------
% 2.78/1.64 % (3560)Instruction limit reached!
% 2.78/1.64 % (3560)------------------------------
% 2.78/1.64 % (3560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.64 % (3560)Termination reason: Unknown
% 2.78/1.64 % (3560)Termination phase: shuffling
% 2.78/1.64
% 2.78/1.64 % (3560)Memory used [KB]: 1791
% 2.78/1.64 % (3560)Time elapsed: 0.012 s
% 2.78/1.64 % (3560)Instructions burned: 17 (million)
% 2.78/1.64 % (3560)------------------------------
% 2.78/1.64 % (3560)------------------------------
% 2.78/1.64 % (3547)Instruction limit reached!
% 2.78/1.64 % (3547)------------------------------
% 2.78/1.64 % (3547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.64 % (3547)Termination reason: Unknown
% 2.78/1.64 % (3547)Termination phase: Saturation
% 2.78/1.64
% 2.78/1.64 % (3547)Memory used [KB]: 7291
% 2.78/1.64 % (3547)Time elapsed: 0.055 s
% 2.78/1.64 % (3547)Instructions burned: 183 (million)
% 2.78/1.64 % (3547)------------------------------
% 2.78/1.64 % (3547)------------------------------
% 2.78/1.64 % (3562)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_3154 for (2999ds/3Mi)
% 2.78/1.64 % (3563)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3154 for (2999ds/7Mi)
% 2.78/1.64 % (3562)Instruction limit reached!
% 2.78/1.64 % (3562)------------------------------
% 2.78/1.64 % (3562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.64 % (3562)Termination reason: Unknown
% 2.78/1.64 % (3562)Termination phase: shuffling
% 2.78/1.64
% 2.78/1.64 % (3562)Memory used [KB]: 1407
% 2.78/1.64 % (3562)Time elapsed: 0.003 s
% 2.78/1.64 % (3562)Instructions burned: 3 (million)
% 2.78/1.64 % (3562)------------------------------
% 2.78/1.64 % (3562)------------------------------
% 2.78/1.65 % (3563)Instruction limit reached!
% 2.78/1.65 % (3563)------------------------------
% 2.78/1.65 % (3563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.65 % (3563)Termination reason: Unknown
% 2.78/1.65 % (3563)Termination phase: shuffling
% 2.78/1.65
% 2.78/1.65 % (3563)Memory used [KB]: 1535
% 2.78/1.65 % (3563)Time elapsed: 0.004 s
% 2.78/1.65 % (3563)Instructions burned: 9 (million)
% 2.78/1.65 % (3563)------------------------------
% 2.78/1.65 % (3563)------------------------------
% 2.78/1.65 % (3567)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3154 for (2999ds/710Mi)
% 2.78/1.65 % (3564)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3154 for (2999ds/3Mi)
% 2.78/1.65 % (3564)Instruction limit reached!
% 2.78/1.65 % (3564)------------------------------
% 2.78/1.65 % (3564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.65 % (3564)Termination reason: Unknown
% 2.78/1.65 % (3564)Termination phase: shuffling
% 2.78/1.65
% 2.78/1.65 % (3564)Memory used [KB]: 1407
% 2.78/1.65 % (3564)Time elapsed: 0.004 s
% 2.78/1.65 % (3564)Instructions burned: 4 (million)
% 2.78/1.65 % (3564)------------------------------
% 2.78/1.65 % (3564)------------------------------
% 2.78/1.66 % (3569)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_3154 for (2999ds/902Mi)
% 2.78/1.66 % (3565)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3154 for (2999ds/4Mi)
% 2.78/1.66 % (3566)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3154 for (2999ds/18Mi)
% 2.78/1.66 % (3568)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3154 for (2999ds/6Mi)
% 2.78/1.66 % (3565)Instruction limit reached!
% 2.78/1.66 % (3565)------------------------------
% 2.78/1.66 % (3565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.66 % (3565)Termination reason: Unknown
% 2.78/1.66 % (3565)Termination phase: shuffling
% 2.78/1.66
% 2.78/1.66 % (3565)Memory used [KB]: 1407
% 2.78/1.66 % (3565)Time elapsed: 0.005 s
% 2.78/1.66 % (3565)Instructions burned: 5 (million)
% 2.78/1.66 % (3565)------------------------------
% 2.78/1.66 % (3565)------------------------------
% 2.78/1.66 % (3568)Instruction limit reached!
% 2.78/1.66 % (3568)------------------------------
% 2.78/1.66 % (3568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.66 % (3568)Termination reason: Unknown
% 2.78/1.66 % (3568)Termination phase: shuffling
% 2.78/1.66
% 2.78/1.66 % (3568)Memory used [KB]: 1535
% 2.78/1.66 % (3568)Time elapsed: 0.004 s
% 2.78/1.66 % (3568)Instructions burned: 7 (million)
% 2.78/1.66 % (3568)------------------------------
% 2.78/1.66 % (3568)------------------------------
% 2.78/1.67 % (3566)Instruction limit reached!
% 2.78/1.67 % (3566)------------------------------
% 2.78/1.67 % (3566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.67 % (3566)Termination reason: Unknown
% 2.78/1.67 % (3566)Termination phase: shuffling
% 2.78/1.67
% 2.78/1.67 % (3566)Memory used [KB]: 1791
% 2.78/1.67 % (3566)Time elapsed: 0.012 s
% 2.78/1.67 % (3566)Instructions burned: 20 (million)
% 2.78/1.67 % (3566)------------------------------
% 2.78/1.67 % (3566)------------------------------
% 2.78/1.67 % (3571)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3154 for (2999ds/5Mi)
% 2.78/1.67 % (3570)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_3154 for (2999ds/21Mi)
% 2.78/1.67 % (3571)Instruction limit reached!
% 2.78/1.67 % (3571)------------------------------
% 2.78/1.67 % (3571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.67 % (3571)Termination reason: Unknown
% 2.78/1.67 % (3571)Termination phase: shuffling
% 2.78/1.67
% 2.78/1.67 % (3571)Memory used [KB]: 1535
% 2.78/1.67 % (3571)Time elapsed: 0.003 s
% 2.78/1.67 % (3571)Instructions burned: 8 (million)
% 2.78/1.67 % (3571)------------------------------
% 2.78/1.67 % (3571)------------------------------
% 2.78/1.68 % (3572)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_3154 for (2999ds/6Mi)
% 2.78/1.68 % (3573)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3154 for (2999ds/377Mi)
% 2.78/1.68 % (3572)Instruction limit reached!
% 2.78/1.68 % (3572)------------------------------
% 2.78/1.68 % (3572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.68 % (3572)Termination reason: Unknown
% 2.78/1.68 % (3572)Termination phase: shuffling
% 2.78/1.68
% 2.78/1.68 % (3572)Memory used [KB]: 1407
% 2.78/1.68 % (3572)Time elapsed: 0.005 s
% 2.78/1.68 % (3572)Instructions burned: 6 (million)
% 2.78/1.68 % (3572)------------------------------
% 2.78/1.68 % (3572)------------------------------
% 2.78/1.68 % (3574)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_3154 for (2998ds/779Mi)
% 2.78/1.68 % (3570)Instruction limit reached!
% 2.78/1.68 % (3570)------------------------------
% 2.78/1.68 % (3570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.68 % (3570)Termination reason: Unknown
% 2.78/1.68 % (3570)Termination phase: shuffling
% 2.78/1.68
% 2.78/1.68 % (3570)Memory used [KB]: 1791
% 2.78/1.68 % (3570)Time elapsed: 0.013 s
% 2.78/1.68 % (3570)Instructions burned: 22 (million)
% 2.78/1.68 % (3570)------------------------------
% 2.78/1.68 % (3570)------------------------------
% 2.78/1.69 % (3576)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3154 for (2998ds/879Mi)
% 2.78/1.70 % (3575)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_3154 for (2998ds/19Mi)
% 2.78/1.70 % (3569)Refutation not found, incomplete strategy
% 2.78/1.70 % (3569)------------------------------
% 2.78/1.70 % (3569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.70 % (3569)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.70
% 2.78/1.70
% 2.78/1.70 % (3569)Memory used [KB]: 7547
% 2.78/1.70 % (3569)Time elapsed: 0.049 s
% 2.78/1.70 % (3569)Instructions burned: 161 (million)
% 2.78/1.70 % (3569)------------------------------
% 2.78/1.70 % (3569)------------------------------
% 2.78/1.71 % (3575)Instruction limit reached!
% 2.78/1.71 % (3575)------------------------------
% 2.78/1.71 % (3575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.71 % (3575)Termination reason: Unknown
% 2.78/1.71 % (3575)Termination phase: shuffling
% 2.78/1.71
% 2.78/1.71 % (3575)Memory used [KB]: 1791
% 2.78/1.71 % (3575)Time elapsed: 0.012 s
% 2.78/1.71 % (3575)Instructions burned: 20 (million)
% 2.78/1.71 % (3575)------------------------------
% 2.78/1.71 % (3575)------------------------------
% 2.78/1.71 % (3577)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3154 for (2998ds/17Mi)
% 2.78/1.72 % (3577)Instruction limit reached!
% 2.78/1.72 % (3577)------------------------------
% 2.78/1.72 % (3577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.72 % (3577)Termination reason: Unknown
% 2.78/1.72 % (3577)Termination phase: shuffling
% 2.78/1.72
% 2.78/1.72 % (3577)Memory used [KB]: 1791
% 2.78/1.72 % (3577)Time elapsed: 0.007 s
% 2.78/1.72 % (3577)Instructions burned: 18 (million)
% 2.78/1.72 % (3577)------------------------------
% 2.78/1.72 % (3577)------------------------------
% 2.78/1.72 % (3578)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3154 for (2998ds/3Mi)
% 2.78/1.72 % (3578)Instruction limit reached!
% 2.78/1.72 % (3578)------------------------------
% 2.78/1.72 % (3578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.72 % (3578)Termination reason: Unknown
% 2.78/1.72 % (3578)Termination phase: shuffling
% 2.78/1.72
% 2.78/1.72 % (3578)Memory used [KB]: 1407
% 2.78/1.72 % (3578)Time elapsed: 0.003 s
% 2.78/1.72 % (3578)Instructions burned: 4 (million)
% 2.78/1.72 % (3578)------------------------------
% 2.78/1.72 % (3578)------------------------------
% 2.78/1.73 % (3579)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3154 for (2998ds/30Mi)
% 2.78/1.73 % (3580)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3154 for (2998ds/127Mi)
% 2.78/1.74 % (3579)Instruction limit reached!
% 2.78/1.74 % (3579)------------------------------
% 2.78/1.74 % (3579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.74 % (3579)Termination reason: Unknown
% 2.78/1.74 % (3579)Termination phase: shuffling
% 2.78/1.74
% 2.78/1.74 % (3579)Memory used [KB]: 1918
% 2.78/1.74 % (3579)Time elapsed: 0.011 s
% 2.78/1.74 % (3579)Instructions burned: 31 (million)
% 2.78/1.74 % (3579)------------------------------
% 2.78/1.74 % (3579)------------------------------
% 2.78/1.75 % (3581)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3154 for (2998ds/100Mi)
% 2.78/1.77 % (3580)Instruction limit reached!
% 2.78/1.77 % (3580)------------------------------
% 2.78/1.77 % (3580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.77 % (3580)Termination reason: Unknown
% 2.78/1.77 % (3580)Termination phase: Saturation
% 2.78/1.77
% 2.78/1.77 % (3580)Memory used [KB]: 7036
% 2.78/1.77 % (3580)Time elapsed: 0.041 s
% 2.78/1.77 % (3580)Instructions burned: 128 (million)
% 2.78/1.77 % (3580)------------------------------
% 2.78/1.77 % (3580)------------------------------
% 2.78/1.78 % (3581)Instruction limit reached!
% 2.78/1.78 % (3581)------------------------------
% 2.78/1.78 % (3581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.78 % (3581)Termination reason: Unknown
% 2.78/1.78 % (3581)Termination phase: Preprocessing 3
% 2.78/1.78
% 2.78/1.78 % (3581)Memory used [KB]: 2430
% 2.78/1.78 % (3581)Time elapsed: 0.028 s
% 2.78/1.78 % (3581)Instructions burned: 100 (million)
% 2.78/1.78 % (3581)------------------------------
% 2.78/1.78 % (3581)------------------------------
% 2.78/1.78 % (3582)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_3154 for (2998ds/3Mi)
% 2.78/1.78 % (3582)Instruction limit reached!
% 2.78/1.78 % (3582)------------------------------
% 2.78/1.78 % (3582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.78 % (3582)Termination reason: Unknown
% 2.78/1.78 % (3582)Termination phase: shuffling
% 2.78/1.78
% 2.78/1.78 % (3582)Memory used [KB]: 1407
% 2.78/1.78 % (3582)Time elapsed: 0.003 s
% 2.78/1.78 % (3582)Instructions burned: 4 (million)
% 2.78/1.78 % (3582)------------------------------
% 2.78/1.78 % (3582)------------------------------
% 2.78/1.79 % (3583)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_3154 for (2997ds/20Mi)
% 2.78/1.79 % (3583)Instruction limit reached!
% 2.78/1.79 % (3583)------------------------------
% 2.78/1.79 % (3583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.79 % (3583)Termination reason: Unknown
% 2.78/1.79 % (3583)Termination phase: shuffling
% 2.78/1.79
% 2.78/1.79 % (3583)Memory used [KB]: 1791
% 2.78/1.79 % (3583)Time elapsed: 0.008 s
% 2.78/1.79 % (3583)Instructions burned: 20 (million)
% 2.78/1.79 % (3583)------------------------------
% 2.78/1.79 % (3583)------------------------------
% 2.78/1.79 % (3584)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_3154 for (2997ds/86Mi)
% 2.78/1.80 % (3573)Instruction limit reached!
% 2.78/1.80 % (3573)------------------------------
% 2.78/1.80 % (3573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.80 % (3573)Termination reason: Unknown
% 2.78/1.80 % (3573)Termination phase: Saturation
% 2.78/1.80
% 2.78/1.80 % (3573)Memory used [KB]: 8187
% 2.78/1.80 % (3573)Time elapsed: 0.125 s
% 2.78/1.80 % (3573)Instructions burned: 378 (million)
% 2.78/1.80 % (3573)------------------------------
% 2.78/1.80 % (3573)------------------------------
% 2.78/1.80 % (3585)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_3154 for (2997ds/107Mi)
% 2.78/1.81 % (3586)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_3154 for (2997ds/39Mi)
% 2.78/1.82 % (3584)Instruction limit reached!
% 2.78/1.82 % (3584)------------------------------
% 2.78/1.82 % (3584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.82 % (3584)Termination reason: Unknown
% 2.78/1.82 % (3584)Termination phase: Property scanning
% 2.78/1.82
% 2.78/1.82 % (3584)Memory used [KB]: 2430
% 2.78/1.82 % (3584)Time elapsed: 0.029 s
% 2.78/1.82 % (3584)Instructions burned: 87 (million)
% 2.78/1.82 % (3584)------------------------------
% 2.78/1.82 % (3584)------------------------------
% 2.78/1.82 % (3586)Instruction limit reached!
% 2.78/1.82 % (3586)------------------------------
% 2.78/1.82 % (3586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.82 % (3586)Termination reason: Unknown
% 2.78/1.82 % (3586)Termination phase: shuffling
% 2.78/1.82
% 2.78/1.82 % (3586)Memory used [KB]: 2174
% 2.78/1.82 % (3586)Time elapsed: 0.014 s
% 2.78/1.82 % (3586)Instructions burned: 41 (million)
% 2.78/1.82 % (3586)------------------------------
% 2.78/1.82 % (3586)------------------------------
% 2.78/1.83 % (3587)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_3154 for (2997ds/448Mi)
% 2.78/1.83 % (3585)Instruction limit reached!
% 2.78/1.83 % (3585)------------------------------
% 2.78/1.83 % (3585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.83 % (3585)Termination reason: Unknown
% 2.78/1.83 % (3585)Termination phase: Saturation
% 2.78/1.83
% 2.78/1.83 % (3585)Memory used [KB]: 6908
% 2.78/1.83 % (3585)Time elapsed: 0.032 s
% 2.78/1.83 % (3585)Instructions burned: 108 (million)
% 2.78/1.83 % (3585)------------------------------
% 2.78/1.83 % (3585)------------------------------
% 2.78/1.83 % (3588)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_3154 for (2997ds/46Mi)
% 2.78/1.84 % (3589)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_3154 for (2997ds/98Mi)
% 2.78/1.85 % (3588)Instruction limit reached!
% 2.78/1.85 % (3588)------------------------------
% 2.78/1.85 % (3588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.85 % (3588)Termination reason: Unknown
% 2.78/1.85 % (3588)Termination phase: Preprocessing 1
% 2.78/1.85
% 2.78/1.85 % (3588)Memory used [KB]: 1918
% 2.78/1.85 % (3588)Time elapsed: 0.017 s
% 2.78/1.85 % (3588)Instructions burned: 48 (million)
% 2.78/1.85 % (3588)------------------------------
% 2.78/1.85 % (3588)------------------------------
% 2.78/1.86 % (3590)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_3154 for (2997ds/507Mi)
% 2.78/1.86 % (3567)Instruction limit reached!
% 2.78/1.86 % (3567)------------------------------
% 2.78/1.86 % (3567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.86 % (3567)Termination reason: Unknown
% 2.78/1.86 % (3567)Termination phase: Saturation
% 2.78/1.86
% 2.78/1.86 % (3567)Memory used [KB]: 7931
% 2.78/1.86 % (3567)Time elapsed: 0.214 s
% 2.78/1.86 % (3567)Instructions burned: 711 (million)
% 2.78/1.86 % (3567)------------------------------
% 2.78/1.86 % (3567)------------------------------
% 2.78/1.87 % (3589)Instruction limit reached!
% 2.78/1.87 % (3589)------------------------------
% 2.78/1.87 % (3589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.87 % (3589)Termination reason: Unknown
% 2.78/1.87 % (3589)Termination phase: Preprocessing 3
% 2.78/1.87
% 2.78/1.87 % (3589)Memory used [KB]: 2430
% 2.78/1.87 % (3589)Time elapsed: 0.028 s
% 2.78/1.87 % (3589)Instructions burned: 100 (million)
% 2.78/1.87 % (3589)------------------------------
% 2.78/1.87 % (3589)------------------------------
% 2.78/1.87 % (3591)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_3154 for (2996ds/149Mi)
% 2.78/1.88 % (3592)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_3154 for (2996ds/39Mi)
% 2.78/1.89 % (3592)Instruction limit reached!
% 2.78/1.89 % (3592)------------------------------
% 2.78/1.89 % (3592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.89 % (3592)Termination reason: Unknown
% 2.78/1.89 % (3592)Termination phase: Preprocessing 1
% 2.78/1.89
% 2.78/1.89 % (3592)Memory used [KB]: 1918
% 2.78/1.89 % (3592)Time elapsed: 0.013 s
% 2.78/1.89 % (3592)Instructions burned: 39 (million)
% 2.78/1.89 % (3592)------------------------------
% 2.78/1.89 % (3592)------------------------------
% 2.78/1.90 % (3593)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_3154 for (2996ds/6Mi)
% 2.78/1.90 % (3593)Instruction limit reached!
% 2.78/1.90 % (3593)------------------------------
% 2.78/1.90 % (3593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.90 % (3593)Termination reason: Unknown
% 2.78/1.90 % (3593)Termination phase: shuffling
% 2.78/1.90
% 2.78/1.90 % (3593)Memory used [KB]: 1535
% 2.78/1.90 % (3593)Time elapsed: 0.003 s
% 2.78/1.90 % (3593)Instructions burned: 8 (million)
% 2.78/1.90 % (3593)------------------------------
% 2.78/1.90 % (3593)------------------------------
% 2.78/1.91 % (3594)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_3154 for (2996ds/1087Mi)
% 2.78/1.92 % (3591)Instruction limit reached!
% 2.78/1.92 % (3591)------------------------------
% 2.78/1.92 % (3591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.92 % (3591)Termination reason: Unknown
% 2.78/1.92 % (3591)Termination phase: Saturation
% 2.78/1.92
% 2.78/1.92 % (3591)Memory used [KB]: 7036
% 2.78/1.92 % (3591)Time elapsed: 0.042 s
% 2.78/1.92 % (3591)Instructions burned: 150 (million)
% 2.78/1.92 % (3591)------------------------------
% 2.78/1.92 % (3591)------------------------------
% 2.78/1.92 % (3574)Instruction limit reached!
% 2.78/1.92 % (3574)------------------------------
% 2.78/1.92 % (3574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.92 % (3574)Termination reason: Unknown
% 2.78/1.92 % (3574)Termination phase: Saturation
% 2.78/1.92
% 2.78/1.92 % (3574)Memory used [KB]: 8699
% 2.78/1.92 % (3574)Time elapsed: 0.236 s
% 2.78/1.92 % (3574)Instructions burned: 781 (million)
% 2.78/1.92 % (3574)------------------------------
% 2.78/1.92 % (3574)------------------------------
% 2.78/1.92 % (3590)Refutation not found, incomplete strategy
% 2.78/1.92 % (3590)------------------------------
% 2.78/1.92 % (3590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.92 % (3590)Termination reason: Refutation not found, incomplete strategy
% 2.78/1.92
% 2.78/1.92
% 2.78/1.92 % (3590)Memory used [KB]: 7931
% 2.78/1.92 % (3590)Time elapsed: 0.062 s
% 2.78/1.92 % (3590)Instructions burned: 186 (million)
% 2.78/1.92 % (3590)------------------------------
% 2.78/1.92 % (3590)------------------------------
% 2.78/1.92 % (3595)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_3154 for (2996ds/47Mi)
% 2.78/1.93 % (3596)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_3154 for (2996ds/44Mi)
% 2.78/1.93 % (3597)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_3154 for (2996ds/432Mi)
% 2.78/1.94 % (3596)Instruction limit reached!
% 2.78/1.94 % (3596)------------------------------
% 2.78/1.94 % (3596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.94 % (3596)Termination reason: Unknown
% 2.78/1.94 % (3596)Termination phase: shuffling
% 2.78/1.94
% 2.78/1.94 % (3596)Memory used [KB]: 2302
% 2.78/1.94 % (3596)Time elapsed: 0.014 s
% 2.78/1.94 % (3596)Instructions burned: 46 (million)
% 2.78/1.94 % (3596)------------------------------
% 2.78/1.94 % (3596)------------------------------
% 2.78/1.94 % (3595)Instruction limit reached!
% 2.78/1.94 % (3595)------------------------------
% 2.78/1.94 % (3595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.94 % (3595)Termination reason: Unknown
% 2.78/1.94 % (3595)Termination phase: Preprocessing 3
% 2.78/1.94
% 2.78/1.94 % (3595)Memory used [KB]: 2046
% 2.78/1.94 % (3595)Time elapsed: 0.016 s
% 2.78/1.94 % (3595)Instructions burned: 48 (million)
% 2.78/1.94 % (3595)------------------------------
% 2.78/1.94 % (3595)------------------------------
% 2.78/1.95 % (3599)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_3154 for (2996ds/31Mi)
% 2.78/1.96 % (3598)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_3154 for (2996ds/62Mi)
% 2.78/1.96 % (3599)Instruction limit reached!
% 2.78/1.96 % (3599)------------------------------
% 2.78/1.96 % (3599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.96 % (3599)Termination reason: Unknown
% 2.78/1.96 % (3599)Termination phase: Property scanning
% 2.78/1.96
% 2.78/1.96 % (3599)Memory used [KB]: 1791
% 2.78/1.96 % (3599)Time elapsed: 0.010 s
% 2.78/1.96 % (3599)Instructions burned: 31 (million)
% 2.78/1.96 % (3599)------------------------------
% 2.78/1.96 % (3599)------------------------------
% 2.78/1.97 % (3600)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_3154 for (2996ds/96Mi)
% 2.78/1.97 % (3558)Instruction limit reached!
% 2.78/1.97 % (3558)------------------------------
% 2.78/1.97 % (3558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.97 % (3558)Termination reason: Unknown
% 2.78/1.97 % (3558)Termination phase: Saturation
% 2.78/1.97
% 2.78/1.97 % (3558)Memory used [KB]: 9594
% 2.78/1.97 % (3558)Time elapsed: 0.346 s
% 2.78/1.97 % (3558)Instructions burned: 1042 (million)
% 2.78/1.97 % (3558)------------------------------
% 2.78/1.97 % (3558)------------------------------
% 2.78/1.97 % (3587)Instruction limit reached!
% 2.78/1.97 % (3587)------------------------------
% 2.78/1.97 % (3587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.97 % (3587)Termination reason: Unknown
% 2.78/1.97 % (3587)Termination phase: Saturation
% 2.78/1.97
% 2.78/1.97 % (3587)Memory used [KB]: 8571
% 2.78/1.97 % (3587)Time elapsed: 0.141 s
% 2.78/1.97 % (3587)Instructions burned: 450 (million)
% 2.78/1.97 % (3587)------------------------------
% 2.78/1.97 % (3587)------------------------------
% 2.78/1.98 % (3601)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_3154 for (2995ds/453Mi)
% 2.78/1.98 % (3602)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_3154 for (2995ds/71Mi)
% 2.78/1.99 % (3576)Instruction limit reached!
% 2.78/1.99 % (3576)------------------------------
% 2.78/1.99 % (3576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.99 % (3576)Termination reason: Unknown
% 2.78/1.99 % (3576)Termination phase: Saturation
% 2.78/1.99
% 2.78/1.99 % (3576)Memory used [KB]: 7547
% 2.78/1.99 % (3576)Time elapsed: 0.295 s
% 2.78/1.99 % (3576)Instructions burned: 880 (million)
% 2.78/1.99 % (3576)------------------------------
% 2.78/1.99 % (3576)------------------------------
% 2.78/1.99 % (3598)Instruction limit reached!
% 2.78/1.99 % (3598)------------------------------
% 2.78/1.99 % (3598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.99 % (3598)Termination reason: Unknown
% 2.78/1.99 % (3598)Termination phase: Property scanning
% 2.78/1.99
% 2.78/1.99 % (3598)Memory used [KB]: 2302
% 2.78/1.99 % (3598)Time elapsed: 0.034 s
% 2.78/1.99 % (3598)Instructions burned: 62 (million)
% 2.78/1.99 % (3598)------------------------------
% 2.78/1.99 % (3598)------------------------------
% 2.78/2.00 % (3600)Instruction limit reached!
% 2.78/2.00 % (3600)------------------------------
% 2.78/2.00 % (3600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/2.00 % (3600)Termination reason: Unknown
% 2.78/2.00 % (3600)Termination phase: Property scanning
% 2.78/2.00
% 2.78/2.00 % (3600)Memory used [KB]: 2430
% 2.78/2.00 % (3600)Time elapsed: 0.029 s
% 2.78/2.00 % (3600)Instructions burned: 96 (million)
% 2.78/2.00 % (3600)------------------------------
% 2.78/2.00 % (3600)------------------------------
% 2.78/2.00 % (3603)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_3154 for (2995ds/83Mi)
% 2.78/2.00 % (3602)Instruction limit reached!
% 2.78/2.00 % (3602)------------------------------
% 2.78/2.00 % (3602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/2.00 % (3605)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_3154 for (2995ds/41Mi)
% 2.78/2.00 % (3602)Termination reason: Unknown
% 2.78/2.00 % (3602)Termination phase: Property scanning
% 2.78/2.00
% 2.78/2.00 % (3602)Memory used [KB]: 2558
% 2.78/2.00 % (3602)Time elapsed: 0.026 s
% 2.78/2.00 % (3602)Instructions burned: 74 (million)
% 2.78/2.00 % (3602)------------------------------
% 2.78/2.00 % (3602)------------------------------
% 2.78/2.01 % (3604)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_3154 for (2995ds/11Mi)
% 5.74/2.01 % (3604)Instruction limit reached!
% 5.74/2.01 % (3604)------------------------------
% 5.74/2.01 % (3604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.01 % (3604)Termination reason: Unknown
% 5.74/2.01 % (3604)Termination phase: shuffling
% 5.74/2.01
% 5.74/2.01 % (3604)Memory used [KB]: 1663
% 5.74/2.01 % (3604)Time elapsed: 0.008 s
% 5.74/2.01 % (3604)Instructions burned: 12 (million)
% 5.74/2.01 % (3604)------------------------------
% 5.74/2.01 % (3604)------------------------------
% 5.74/2.02 % (3606)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3154 for (2995ds/6Mi)
% 5.74/2.02 % (3605)Instruction limit reached!
% 5.74/2.02 % (3605)------------------------------
% 5.74/2.02 % (3605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.02 % (3605)Termination reason: Unknown
% 5.74/2.02 % (3605)Termination phase: shuffling
% 5.74/2.02
% 5.74/2.02 % (3605)Memory used [KB]: 2174
% 5.74/2.02 % (3605)Time elapsed: 0.012 s
% 5.74/2.02 % (3605)Instructions burned: 41 (million)
% 5.74/2.02 % (3605)------------------------------
% 5.74/2.02 % (3605)------------------------------
% 5.74/2.02 % (3606)Instruction limit reached!
% 5.74/2.02 % (3606)------------------------------
% 5.74/2.02 % (3606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.02 % (3606)Termination reason: Unknown
% 5.74/2.02 % (3606)Termination phase: shuffling
% 5.74/2.02
% 5.74/2.02 % (3606)Memory used [KB]: 1535
% 5.74/2.02 % (3606)Time elapsed: 0.004 s
% 5.74/2.02 % (3606)Instructions burned: 7 (million)
% 5.74/2.02 % (3606)------------------------------
% 5.74/2.02 % (3606)------------------------------
% 5.74/2.02 % (3603)Instruction limit reached!
% 5.74/2.02 % (3603)------------------------------
% 5.74/2.02 % (3603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.02 % (3603)Termination reason: Unknown
% 5.74/2.02 % (3603)Termination phase: Saturation
% 5.74/2.02
% 5.74/2.02 % (3603)Memory used [KB]: 6524
% 5.74/2.02 % (3603)Time elapsed: 0.028 s
% 5.74/2.02 % (3603)Instructions burned: 83 (million)
% 5.74/2.02 % (3603)------------------------------
% 5.74/2.02 % (3603)------------------------------
% 5.74/2.03 % (3608)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_3154 for (2995ds/343Mi)
% 5.74/2.03 % (3609)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_3154 for (2995ds/109Mi)
% 5.74/2.03 % (3607)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_3154 for (2995ds/150Mi)
% 5.74/2.03 % (3610)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_3154 for (2995ds/253Mi)
% 5.74/2.06 % (3609)Instruction limit reached!
% 5.74/2.06 % (3609)------------------------------
% 5.74/2.06 % (3609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.06 % (3609)Termination reason: Unknown
% 5.74/2.06 % (3609)Termination phase: Property scanning
% 5.74/2.06
% 5.74/2.06 % (3609)Memory used [KB]: 2430
% 5.74/2.06 % (3609)Time elapsed: 0.035 s
% 5.74/2.06 % (3609)Instructions burned: 109 (million)
% 5.74/2.06 % (3609)------------------------------
% 5.74/2.06 % (3609)------------------------------
% 5.74/2.06 % (3610)Refutation not found, incomplete strategy
% 5.74/2.06 % (3610)------------------------------
% 5.74/2.06 % (3610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.06 % (3610)Termination reason: Refutation not found, incomplete strategy
% 5.74/2.06
% 5.74/2.06
% 5.74/2.06 % (3610)Memory used [KB]: 6908
% 5.74/2.06 % (3610)Time elapsed: 0.030 s
% 5.74/2.06 % (3610)Instructions burned: 97 (million)
% 5.74/2.06 % (3610)------------------------------
% 5.74/2.06 % (3610)------------------------------
% 5.74/2.07 % (3597)Instruction limit reached!
% 5.74/2.07 % (3597)------------------------------
% 5.74/2.07 % (3597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.07 % (3597)Termination reason: Unknown
% 5.74/2.07 % (3597)Termination phase: Saturation
% 5.74/2.07
% 5.74/2.07 % (3597)Memory used [KB]: 3582
% 5.74/2.07 % (3597)Time elapsed: 0.138 s
% 5.74/2.07 % (3597)Instructions burned: 432 (million)
% 5.74/2.07 % (3597)------------------------------
% 5.74/2.07 % (3597)------------------------------
% 5.74/2.07 % (3611)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_3154 for (2995ds/140Mi)
% 5.74/2.07 % (3612)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_3154 for (2995ds/614Mi)
% 5.74/2.08 % (3613)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_3154 for (2995ds/202Mi)
% 5.74/2.08 % (3607)Instruction limit reached!
% 5.74/2.08 % (3607)------------------------------
% 5.74/2.08 % (3607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.08 % (3607)Termination reason: Unknown
% 5.74/2.08 % (3607)Termination phase: Saturation
% 5.74/2.08
% 5.74/2.08 % (3607)Memory used [KB]: 7164
% 5.74/2.08 % (3607)Time elapsed: 0.056 s
% 5.74/2.08 % (3607)Instructions burned: 151 (million)
% 5.74/2.08 % (3607)------------------------------
% 5.74/2.08 % (3607)------------------------------
% 5.74/2.09 % (3614)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_3154 for (2994ds/339Mi)
% 5.74/2.10 % (3613)Refutation not found, incomplete strategy
% 5.74/2.10 % (3613)------------------------------
% 5.74/2.10 % (3613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.10 % (3613)Termination reason: Refutation not found, incomplete strategy
% 5.74/2.10
% 5.74/2.10
% 5.74/2.10 % (3613)Memory used [KB]: 6652
% 5.74/2.10 % (3613)Time elapsed: 0.020 s
% 5.74/2.10 % (3613)Instructions burned: 63 (million)
% 5.74/2.10 % (3613)------------------------------
% 5.74/2.10 % (3613)------------------------------
% 5.74/2.11 % (3601)Instruction limit reached!
% 5.74/2.11 % (3601)------------------------------
% 5.74/2.11 % (3601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.74/2.11 % (3601)Termination reason: Unknown
% 5.74/2.11 % (3601)Termination phase: Saturation
% 5.74/2.11
% 5.74/2.11 % (3601)Memory used [KB]: 8443
% 5.74/2.11 % (3601)Time elapsed: 0.127 s
% 5.74/2.11 % (3601)Instructions burned: 453 (million)
% 5.74/2.11 % (3601)------------------------------
% 5.74/2.11 % (3601)------------------------------
% 5.74/2.11 % (3615)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_3154 for (2994ds/283Mi)
% 6.28/2.11 % (3611)Instruction limit reached!
% 6.28/2.11 % (3611)------------------------------
% 6.28/2.11 % (3611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.11 % (3611)Termination reason: Unknown
% 6.28/2.11 % (3611)Termination phase: Saturation
% 6.28/2.11
% 6.28/2.11 % (3611)Memory used [KB]: 7036
% 6.28/2.11 % (3611)Time elapsed: 0.045 s
% 6.28/2.11 % (3611)Instructions burned: 140 (million)
% 6.28/2.11 % (3611)------------------------------
% 6.28/2.11 % (3611)------------------------------
% 6.28/2.12 % (3616)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_3154 for (2994ds/134Mi)
% 6.28/2.12 % (3617)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_3154 for (2994ds/298Mi)
% 6.28/2.13 % (3608)Instruction limit reached!
% 6.28/2.13 % (3608)------------------------------
% 6.28/2.13 % (3608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.13 % (3608)Termination reason: Unknown
% 6.28/2.13 % (3608)Termination phase: Saturation
% 6.28/2.13
% 6.28/2.13 % (3608)Memory used [KB]: 7675
% 6.28/2.13 % (3608)Time elapsed: 0.107 s
% 6.28/2.13 % (3608)Instructions burned: 345 (million)
% 6.28/2.13 % (3608)------------------------------
% 6.28/2.13 % (3608)------------------------------
% 6.28/2.14 % (3618)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_3154 for (2994ds/192Mi)
% 6.28/2.16 % (3616)Instruction limit reached!
% 6.28/2.16 % (3616)------------------------------
% 6.28/2.16 % (3616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.16 % (3616)Termination reason: Unknown
% 6.28/2.16 % (3616)Termination phase: Saturation
% 6.28/2.16
% 6.28/2.16 % (3616)Memory used [KB]: 7036
% 6.28/2.16 % (3616)Time elapsed: 0.041 s
% 6.28/2.16 % (3616)Instructions burned: 137 (million)
% 6.28/2.16 % (3616)------------------------------
% 6.28/2.16 % (3616)------------------------------
% 6.28/2.16 % (3619)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_3154 for (2993ds/258Mi)
% 6.28/2.19 % (3615)Instruction limit reached!
% 6.28/2.19 % (3615)------------------------------
% 6.28/2.19 % (3615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.19 % (3615)Termination reason: Unknown
% 6.28/2.19 % (3615)Termination phase: Saturation
% 6.28/2.19
% 6.28/2.19 % (3615)Memory used [KB]: 7547
% 6.28/2.19 % (3615)Time elapsed: 0.106 s
% 6.28/2.19 % (3615)Instructions burned: 285 (million)
% 6.28/2.19 % (3615)------------------------------
% 6.28/2.19 % (3615)------------------------------
% 6.68/2.20 % (3618)Instruction limit reached!
% 6.68/2.20 % (3618)------------------------------
% 6.68/2.20 % (3618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.20 % (3618)Termination reason: Unknown
% 6.68/2.20 % (3618)Termination phase: Saturation
% 6.68/2.20
% 6.68/2.20 % (3618)Memory used [KB]: 3582
% 6.68/2.20 % (3618)Time elapsed: 0.058 s
% 6.68/2.20 % (3618)Instructions burned: 195 (million)
% 6.68/2.20 % (3618)------------------------------
% 6.68/2.20 % (3618)------------------------------
% 6.68/2.20 % (3614)Instruction limit reached!
% 6.68/2.20 % (3614)------------------------------
% 6.68/2.20 % (3614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.20 % (3614)Termination reason: Unknown
% 6.68/2.20 % (3614)Termination phase: Saturation
% 6.68/2.20
% 6.68/2.20 % (3614)Memory used [KB]: 7547
% 6.68/2.20 % (3614)Time elapsed: 0.107 s
% 6.68/2.20 % (3614)Instructions burned: 340 (million)
% 6.68/2.20 % (3614)------------------------------
% 6.68/2.20 % (3614)------------------------------
% 6.68/2.20 % (3620)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_3154 for (2993ds/90Mi)
% 6.68/2.21 % (3617)Instruction limit reached!
% 6.68/2.21 % (3617)------------------------------
% 6.68/2.21 % (3617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.21 % (3617)Termination reason: Unknown
% 6.68/2.21 % (3617)Termination phase: Saturation
% 6.68/2.21
% 6.68/2.21 % (3617)Memory used [KB]: 7803
% 6.68/2.21 % (3617)Time elapsed: 0.084 s
% 6.68/2.21 % (3617)Instructions burned: 301 (million)
% 6.68/2.21 % (3617)------------------------------
% 6.68/2.21 % (3617)------------------------------
% 6.68/2.21 % (3621)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_3154 for (2993ds/231Mi)
% 6.68/2.21 % (3622)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_3154 for (2993ds/458Mi)
% 6.68/2.22 % (3623)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_3154 for (2993ds/31Mi)
% 6.68/2.23 % (3623)Instruction limit reached!
% 6.68/2.23 % (3623)------------------------------
% 6.68/2.23 % (3623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.23 % (3623)Termination reason: Unknown
% 6.68/2.23 % (3623)Termination phase: Property scanning
% 6.68/2.23
% 6.68/2.23 % (3623)Memory used [KB]: 1791
% 6.68/2.23 % (3623)Time elapsed: 0.010 s
% 6.68/2.23 % (3623)Instructions burned: 31 (million)
% 6.68/2.23 % (3623)------------------------------
% 6.68/2.23 % (3623)------------------------------
% 6.68/2.23 % (3620)Instruction limit reached!
% 6.68/2.23 % (3620)------------------------------
% 6.68/2.23 % (3620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.23 % (3620)Termination reason: Unknown
% 6.68/2.23 % (3620)Termination phase: Property scanning
% 6.68/2.23
% 6.68/2.23 % (3620)Memory used [KB]: 2430
% 6.68/2.23 % (3620)Time elapsed: 0.027 s
% 6.68/2.23 % (3620)Instructions burned: 91 (million)
% 6.68/2.23 % (3620)------------------------------
% 6.68/2.23 % (3620)------------------------------
% 6.68/2.23 % (3624)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_3154 for (2993ds/297Mi)
% 6.68/2.24 % (3625)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_3154 for (2993ds/987Mi)
% 6.68/2.24 % (3619)Instruction limit reached!
% 6.68/2.24 % (3619)------------------------------
% 6.68/2.24 % (3619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.24 % (3619)Termination reason: Unknown
% 6.68/2.24 % (3619)Termination phase: Saturation
% 6.68/2.24
% 6.68/2.24 % (3619)Memory used [KB]: 7803
% 6.68/2.24 % (3619)Time elapsed: 0.080 s
% 6.68/2.24 % (3619)Instructions burned: 260 (million)
% 6.68/2.24 % (3619)------------------------------
% 6.68/2.24 % (3619)------------------------------
% 6.68/2.25 % (3594)Instruction limit reached!
% 6.68/2.25 % (3594)------------------------------
% 6.68/2.25 % (3594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.25 % (3594)Termination reason: Unknown
% 6.68/2.25 % (3594)Termination phase: Saturation
% 6.68/2.25
% 6.68/2.25 % (3594)Memory used [KB]: 8315
% 6.68/2.25 % (3594)Time elapsed: 0.337 s
% 6.68/2.25 % (3594)Instructions burned: 1087 (million)
% 6.68/2.25 % (3594)------------------------------
% 6.68/2.25 % (3594)------------------------------
% 6.68/2.25 % (3626)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_3154 for (2993ds/182Mi)
% 6.68/2.26 % (3627)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_3154 for (2993ds/182Mi)
% 6.68/2.27 % (3612)Instruction limit reached!
% 6.68/2.27 % (3612)------------------------------
% 6.68/2.27 % (3612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.27 % (3612)Termination reason: Unknown
% 6.68/2.27 % (3612)Termination phase: Saturation
% 6.68/2.27
% 6.68/2.27 % (3612)Memory used [KB]: 8187
% 6.68/2.27 % (3612)Time elapsed: 0.192 s
% 6.68/2.27 % (3612)Instructions burned: 616 (million)
% 6.68/2.27 % (3612)------------------------------
% 6.68/2.27 % (3612)------------------------------
% 6.68/2.27 % (3621)Instruction limit reached!
% 6.68/2.27 % (3621)------------------------------
% 6.68/2.27 % (3621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.68/2.27 % (3621)Termination reason: Unknown
% 6.68/2.27 % (3621)Termination phase: Saturation
% 6.68/2.27
% 6.68/2.27 % (3621)Memory used [KB]: 7036
% 6.68/2.27 % (3621)Time elapsed: 0.061 s
% 6.68/2.27 % (3621)Instructions burned: 231 (million)
% 6.68/2.27 % (3621)------------------------------
% 6.68/2.27 % (3621)------------------------------
% 6.68/2.28 % (3628)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_3154 for (2992ds/154Mi)
% 6.68/2.28 % (3629)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_3154 for (2992ds/79Mi)
% 7.42/2.30 % (3629)Instruction limit reached!
% 7.42/2.30 % (3629)------------------------------
% 7.42/2.30 % (3629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.30 % (3629)Termination reason: Unknown
% 7.42/2.30 % (3629)Termination phase: Property scanning
% 7.42/2.30
% 7.42/2.30 % (3629)Memory used [KB]: 2430
% 7.42/2.30 % (3629)Time elapsed: 0.025 s
% 7.42/2.30 % (3629)Instructions burned: 80 (million)
% 7.42/2.30 % (3629)------------------------------
% 7.42/2.30 % (3629)------------------------------
% 7.42/2.31 % (3626)Instruction limit reached!
% 7.42/2.31 % (3626)------------------------------
% 7.42/2.31 % (3626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.31 % (3626)Termination reason: Unknown
% 7.42/2.31 % (3626)Termination phase: Saturation
% 7.42/2.31
% 7.42/2.31 % (3626)Memory used [KB]: 7164
% 7.42/2.31 % (3626)Time elapsed: 0.053 s
% 7.42/2.31 % (3626)Instructions burned: 184 (million)
% 7.42/2.31 % (3626)------------------------------
% 7.42/2.31 % (3626)------------------------------
% 7.42/2.31 % (3630)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_3154 for (2992ds/216Mi)
% 7.42/2.31 % (3627)Instruction limit reached!
% 7.42/2.31 % (3627)------------------------------
% 7.42/2.31 % (3627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.31 % (3627)Termination reason: Unknown
% 7.42/2.31 % (3627)Termination phase: Saturation
% 7.42/2.31
% 7.42/2.31 % (3627)Memory used [KB]: 7291
% 7.42/2.31 % (3627)Time elapsed: 0.056 s
% 7.42/2.31 % (3627)Instructions burned: 183 (million)
% 7.42/2.31 % (3627)------------------------------
% 7.42/2.31 % (3627)------------------------------
% 7.42/2.32 % (3631)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_3154 for (2992ds/114Mi)
% 7.42/2.32 % (3628)Instruction limit reached!
% 7.42/2.32 % (3628)------------------------------
% 7.42/2.32 % (3628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.32 % (3628)Termination reason: Unknown
% 7.42/2.32 % (3628)Termination phase: Saturation
% 7.42/2.32
% 7.42/2.32 % (3628)Memory used [KB]: 2814
% 7.42/2.32 % (3628)Time elapsed: 0.044 s
% 7.42/2.32 % (3628)Instructions burned: 156 (million)
% 7.42/2.32 % (3628)------------------------------
% 7.42/2.32 % (3628)------------------------------
% 7.42/2.32 % (3632)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_3154 for (2992ds/922Mi)
% 7.42/2.32 % (3624)Instruction limit reached!
% 7.42/2.32 % (3624)------------------------------
% 7.42/2.32 % (3624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.32 % (3624)Termination reason: Unknown
% 7.42/2.32 % (3624)Termination phase: Saturation
% 7.42/2.32
% 7.42/2.32 % (3624)Memory used [KB]: 7547
% 7.42/2.32 % (3624)Time elapsed: 0.089 s
% 7.42/2.32 % (3624)Instructions burned: 299 (million)
% 7.42/2.32 % (3624)------------------------------
% 7.42/2.32 % (3624)------------------------------
% 7.42/2.33 % (3633)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_3154 for (2992ds/182Mi)
% 7.42/2.33 % (3634)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_3154 for (2992ds/164Mi)
% 7.42/2.35 % (3631)Instruction limit reached!
% 7.42/2.35 % (3631)------------------------------
% 7.42/2.35 % (3631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.35 % (3631)Termination reason: Unknown
% 7.42/2.35 % (3631)Termination phase: Saturation
% 7.42/2.35
% 7.42/2.35 % (3631)Memory used [KB]: 6908
% 7.42/2.35 % (3631)Time elapsed: 0.033 s
% 7.42/2.35 % (3631)Instructions burned: 114 (million)
% 7.42/2.35 % (3631)------------------------------
% 7.42/2.35 % (3631)------------------------------
% 7.42/2.36 % (3635)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_3154 for (2992ds/50Mi)
% 7.42/2.36 % (3622)Instruction limit reached!
% 7.42/2.36 % (3622)------------------------------
% 7.42/2.36 % (3622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.36 % (3622)Termination reason: Unknown
% 7.42/2.36 % (3622)Termination phase: Saturation
% 7.42/2.36
% 7.42/2.36 % (3622)Memory used [KB]: 8187
% 7.42/2.36 % (3622)Time elapsed: 0.153 s
% 7.42/2.36 % (3622)Instructions burned: 459 (million)
% 7.42/2.36 % (3622)------------------------------
% 7.42/2.36 % (3622)------------------------------
% 7.42/2.37 % (3630)Instruction limit reached!
% 7.42/2.37 % (3630)------------------------------
% 7.42/2.37 % (3630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.37 % (3630)Termination reason: Unknown
% 7.42/2.37 % (3630)Termination phase: Saturation
% 7.42/2.37
% 7.42/2.37 % (3630)Memory used [KB]: 7419
% 7.42/2.37 % (3630)Time elapsed: 0.060 s
% 7.42/2.37 % (3630)Instructions burned: 217 (million)
% 7.42/2.37 % (3630)------------------------------
% 7.42/2.37 % (3630)------------------------------
% 7.42/2.37 % (3635)Instruction limit reached!
% 7.42/2.37 % (3635)------------------------------
% 7.42/2.37 % (3635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.37 % (3635)Termination reason: Unknown
% 7.42/2.37 % (3635)Termination phase: Property scanning
% 7.42/2.37
% 7.42/2.37 % (3635)Memory used [KB]: 2302
% 7.42/2.37 % (3635)Time elapsed: 0.015 s
% 7.42/2.37 % (3635)Instructions burned: 51 (million)
% 7.42/2.37 % (3635)------------------------------
% 7.42/2.37 % (3635)------------------------------
% 7.42/2.37 % (3636)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_3154 for (2992ds/368Mi)
% 7.42/2.38 % (3633)Instruction limit reached!
% 7.42/2.38 % (3633)------------------------------
% 7.42/2.38 % (3633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.38 % (3633)Termination reason: Unknown
% 7.42/2.38 % (3633)Termination phase: Saturation
% 7.42/2.38
% 7.42/2.38 % (3633)Memory used [KB]: 7291
% 7.42/2.38 % (3633)Time elapsed: 0.051 s
% 7.42/2.38 % (3633)Instructions burned: 184 (million)
% 7.42/2.38 % (3633)------------------------------
% 7.42/2.38 % (3633)------------------------------
% 7.42/2.38 % (3634)Instruction limit reached!
% 7.42/2.38 % (3634)------------------------------
% 7.42/2.38 % (3634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.38 % (3634)Termination reason: Unknown
% 7.42/2.38 % (3634)Termination phase: Saturation
% 7.42/2.38
% 7.42/2.38 % (3634)Memory used [KB]: 2686
% 7.42/2.38 % (3634)Time elapsed: 0.047 s
% 7.42/2.38 % (3634)Instructions burned: 166 (million)
% 7.42/2.38 % (3634)------------------------------
% 7.42/2.38 % (3634)------------------------------
% 7.42/2.38 % (3637)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_3154 for (2991ds/1021Mi)
% 7.42/2.38 % (3638)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_3154 for (2991ds/267Mi)
% 7.42/2.39 % (3639)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_3154 for (2991ds/204Mi)
% 7.42/2.39 % (3640)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_3154 for (2991ds/26Mi)
% 7.42/2.40 % (3640)Instruction limit reached!
% 7.42/2.40 % (3640)------------------------------
% 7.42/2.40 % (3640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.42/2.40 % (3640)Termination reason: Unknown
% 7.42/2.40 % (3640)Termination phase: shuffling
% 7.42/2.40
% 7.42/2.40 % (3640)Memory used [KB]: 1918
% 7.42/2.40 % (3640)Time elapsed: 0.009 s
% 7.42/2.40 % (3640)Instructions burned: 27 (million)
% 7.42/2.40 % (3640)------------------------------
% 7.42/2.40 % (3640)------------------------------
% 8.15/2.40 % (3641)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_3154 for (2991ds/53Mi)
% 8.15/2.42 % (3641)Instruction limit reached!
% 8.15/2.42 % (3641)------------------------------
% 8.15/2.42 % (3641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.42 % (3641)Termination reason: Unknown
% 8.15/2.42 % (3641)Termination phase: Property scanning
% 8.15/2.42
% 8.15/2.42 % (3641)Memory used [KB]: 2302
% 8.15/2.42 % (3641)Time elapsed: 0.016 s
% 8.15/2.42 % (3641)Instructions burned: 56 (million)
% 8.15/2.42 % (3641)------------------------------
% 8.15/2.42 % (3641)------------------------------
% 8.15/2.43 % (3642)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_3154 for (2991ds/4436Mi)
% 8.15/2.45 % (3639)Instruction limit reached!
% 8.15/2.45 % (3639)------------------------------
% 8.15/2.45 % (3639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.45 % (3639)Termination reason: Unknown
% 8.15/2.45 % (3639)Termination phase: Saturation
% 8.15/2.45
% 8.15/2.45 % (3639)Memory used [KB]: 7291
% 8.15/2.45 % (3639)Time elapsed: 0.062 s
% 8.15/2.45 % (3639)Instructions burned: 206 (million)
% 8.15/2.45 % (3639)------------------------------
% 8.15/2.45 % (3639)------------------------------
% 8.15/2.46 % (3643)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_3154 for (2991ds/1539Mi)
% 8.15/2.46 % (3638)Instruction limit reached!
% 8.15/2.46 % (3638)------------------------------
% 8.15/2.46 % (3638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.46 % (3638)Termination reason: Unknown
% 8.15/2.46 % (3638)Termination phase: Saturation
% 8.15/2.46
% 8.15/2.46 % (3638)Memory used [KB]: 7547
% 8.15/2.46 % (3638)Time elapsed: 0.080 s
% 8.15/2.46 % (3638)Instructions burned: 268 (million)
% 8.15/2.46 % (3638)------------------------------
% 8.15/2.46 % (3638)------------------------------
% 8.15/2.47 % (3644)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_3154 for (2991ds/408Mi)
% 8.15/2.49 % (3636)Instruction limit reached!
% 8.15/2.49 % (3636)------------------------------
% 8.15/2.49 % (3636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.49 % (3636)Termination reason: Unknown
% 8.15/2.49 % (3636)Termination phase: Saturation
% 8.15/2.49
% 8.15/2.49 % (3636)Memory used [KB]: 8059
% 8.15/2.49 % (3636)Time elapsed: 0.118 s
% 8.15/2.49 % (3636)Instructions burned: 368 (million)
% 8.15/2.49 % (3636)------------------------------
% 8.15/2.49 % (3636)------------------------------
% 8.47/2.50 % (3645)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_3154 for (2990ds/5205Mi)
% 8.47/2.52 % (3644)Refutation not found, incomplete strategy
% 8.47/2.52 % (3644)------------------------------
% 8.47/2.52 % (3644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.47/2.52 % (3644)Termination reason: Refutation not found, incomplete strategy
% 8.47/2.52
% 8.47/2.52
% 8.47/2.52 % (3644)Memory used [KB]: 7931
% 8.47/2.52 % (3644)Time elapsed: 0.057 s
% 8.47/2.52 % (3644)Instructions burned: 188 (million)
% 8.47/2.52 % (3644)------------------------------
% 8.47/2.52 % (3644)------------------------------
% 8.47/2.53 % (3625)Instruction limit reached!
% 8.47/2.53 % (3625)------------------------------
% 8.47/2.53 % (3625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.47/2.53 % (3625)Termination reason: Unknown
% 8.47/2.53 % (3625)Termination phase: Saturation
% 8.47/2.53
% 8.47/2.53 % (3625)Memory used [KB]: 8571
% 8.47/2.53 % (3625)Time elapsed: 0.295 s
% 8.47/2.53 % (3625)Instructions burned: 987 (million)
% 8.47/2.53 % (3625)------------------------------
% 8.47/2.53 % (3625)------------------------------
% 8.47/2.53 % (3646)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_3154 for (2990ds/1913Mi)
% 8.47/2.54 % (3647)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_3154 for (2990ds/4350Mi)
% 8.47/2.56 % (3647)Refutation not found, incomplete strategy
% 8.47/2.56 % (3647)------------------------------
% 8.47/2.56 % (3647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.47/2.56 % (3647)Termination reason: Refutation not found, incomplete strategy
% 8.47/2.56
% 8.47/2.56
% 8.47/2.56 % (3647)Memory used [KB]: 6524
% 8.47/2.56 % (3647)Time elapsed: 0.017 s
% 8.47/2.56 % (3647)Instructions burned: 53 (million)
% 8.47/2.56 % (3647)------------------------------
% 8.47/2.56 % (3647)------------------------------
% 8.47/2.57 % (3648)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_3154 for (2990ds/68Mi)
% 8.47/2.59 % (3648)Instruction limit reached!
% 8.47/2.59 % (3648)------------------------------
% 8.47/2.59 % (3648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.47/2.59 % (3648)Termination reason: Unknown
% 8.47/2.59 % (3648)Termination phase: Property scanning
% 8.47/2.59
% 8.47/2.59 % (3648)Memory used [KB]: 2430
% 8.47/2.59 % (3648)Time elapsed: 0.023 s
% 8.47/2.59 % (3648)Instructions burned: 70 (million)
% 8.47/2.59 % (3648)------------------------------
% 8.47/2.59 % (3648)------------------------------
% 8.90/2.60 % (3649)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_3154 for (2989ds/358Mi)
% 8.90/2.60 % (3632)Instruction limit reached!
% 8.90/2.60 % (3632)------------------------------
% 8.90/2.60 % (3632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.60 % (3632)Termination reason: Unknown
% 8.90/2.60 % (3632)Termination phase: Saturation
% 8.90/2.60
% 8.90/2.60 % (3632)Memory used [KB]: 7419
% 8.90/2.60 % (3632)Time elapsed: 0.279 s
% 8.90/2.60 % (3632)Instructions burned: 922 (million)
% 8.90/2.60 % (3632)------------------------------
% 8.90/2.60 % (3632)------------------------------
% 8.90/2.61 % (3650)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_3154 for (2989ds/31Mi)
% 8.90/2.62 % (3650)Instruction limit reached!
% 8.90/2.62 % (3650)------------------------------
% 8.90/2.62 % (3650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.62 % (3650)Termination reason: Unknown
% 8.90/2.62 % (3650)Termination phase: Property scanning
% 8.90/2.62
% 8.90/2.62 % (3650)Memory used [KB]: 1791
% 8.90/2.62 % (3650)Time elapsed: 0.011 s
% 8.90/2.62 % (3650)Instructions burned: 34 (million)
% 8.90/2.62 % (3650)------------------------------
% 8.90/2.62 % (3650)------------------------------
% 8.90/2.63 % (3651)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_3154 for (2989ds/279Mi)
% 8.90/2.67 % (3651)Refutation not found, incomplete strategy
% 8.90/2.67 % (3651)------------------------------
% 8.90/2.67 % (3651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.67 % (3651)Termination reason: Refutation not found, incomplete strategy
% 8.90/2.67
% 8.90/2.67
% 8.90/2.67 % (3651)Memory used [KB]: 7164
% 8.90/2.67 % (3651)Time elapsed: 0.040 s
% 8.90/2.67 % (3651)Instructions burned: 140 (million)
% 8.90/2.67 % (3651)------------------------------
% 8.90/2.67 % (3651)------------------------------
% 8.90/2.68 % (3652)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_3154 for (2989ds/258Mi)
% 8.90/2.69 % (3637)Instruction limit reached!
% 8.90/2.69 % (3637)------------------------------
% 8.90/2.69 % (3637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.69 % (3637)Termination reason: Unknown
% 8.90/2.69 % (3637)Termination phase: Saturation
% 8.90/2.69
% 8.90/2.69 % (3637)Memory used [KB]: 8443
% 8.90/2.69 % (3637)Time elapsed: 0.314 s
% 8.90/2.69 % (3637)Instructions burned: 1023 (million)
% 8.90/2.69 % (3637)------------------------------
% 8.90/2.69 % (3637)------------------------------
% 9.58/2.71 % (3649)Instruction limit reached!
% 9.58/2.71 % (3649)------------------------------
% 9.58/2.71 % (3649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.58/2.71 % (3649)Termination reason: Unknown
% 9.58/2.71 % (3649)Termination phase: Saturation
% 9.58/2.71
% 9.58/2.71 % (3649)Memory used [KB]: 7291
% 9.58/2.71 % (3649)Time elapsed: 0.111 s
% 9.58/2.71 % (3649)Instructions burned: 358 (million)
% 9.58/2.71 % (3649)------------------------------
% 9.58/2.71 % (3649)------------------------------
% 9.58/2.71 % (3653)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_3154 for (2988ds/26Mi)
% 9.58/2.72 % (3654)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_3154 for (2988ds/995Mi)
% 9.58/2.72 % (3653)Instruction limit reached!
% 9.58/2.72 % (3653)------------------------------
% 9.58/2.72 % (3653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.58/2.72 % (3653)Termination reason: Unknown
% 9.58/2.72 % (3653)Termination phase: shuffling
% 9.58/2.72
% 9.58/2.72 % (3653)Memory used [KB]: 1918
% 9.58/2.72 % (3653)Time elapsed: 0.015 s
% 9.58/2.72 % (3653)Instructions burned: 26 (million)
% 9.58/2.72 % (3653)------------------------------
% 9.58/2.72 % (3653)------------------------------
% 9.58/2.74 % (3655)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_3154 for (2988ds/373Mi)
% 9.58/2.76 % (3652)Instruction limit reached!
% 9.58/2.76 % (3652)------------------------------
% 9.58/2.76 % (3652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.58/2.76 % (3652)Termination reason: Unknown
% 9.58/2.76 % (3652)Termination phase: Saturation
% 9.58/2.76
% 9.58/2.76 % (3652)Memory used [KB]: 7675
% 9.58/2.76 % (3652)Time elapsed: 0.079 s
% 9.58/2.76 % (3652)Instructions burned: 258 (million)
% 9.58/2.76 % (3652)------------------------------
% 9.58/2.76 % (3652)------------------------------
% 9.58/2.76 % (3656)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_3154 for (2987ds/253Mi)
% 9.82/2.83 % (3656)Instruction limit reached!
% 9.82/2.83 % (3656)------------------------------
% 9.82/2.83 % (3656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.82/2.83 % (3656)Termination reason: Unknown
% 9.82/2.83 % (3656)Termination phase: Saturation
% 9.82/2.83
% 9.82/2.83 % (3656)Memory used [KB]: 7547
% 9.82/2.83 % (3656)Time elapsed: 0.070 s
% 9.82/2.83 % (3656)Instructions burned: 253 (million)
% 9.82/2.83 % (3656)------------------------------
% 9.82/2.83 % (3656)------------------------------
% 9.82/2.84 % (3657)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_3154 for (2987ds/832Mi)
% 9.82/2.88 % (3655)Instruction limit reached!
% 9.82/2.88 % (3655)------------------------------
% 9.82/2.88 % (3655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.82/2.88 % (3655)Termination reason: Unknown
% 9.82/2.88 % (3655)Termination phase: Saturation
% 9.82/2.88
% 9.82/2.88 % (3655)Memory used [KB]: 8059
% 9.82/2.88 % (3655)Time elapsed: 0.143 s
% 9.82/2.88 % (3655)Instructions burned: 373 (million)
% 9.82/2.88 % (3655)------------------------------
% 9.82/2.88 % (3655)------------------------------
% 9.82/2.89 % (3658)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_3154 for (2986ds/668Mi)
% 10.05/2.90 % (3657)Refutation not found, incomplete strategy
% 10.05/2.90 % (3657)------------------------------
% 10.05/2.90 % (3657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.05/2.90 % (3657)Termination reason: Refutation not found, incomplete strategy
% 10.05/2.90
% 10.05/2.90
% 10.05/2.90 % (3657)Memory used [KB]: 7931
% 10.05/2.90 % (3657)Time elapsed: 0.057 s
% 10.05/2.90 % (3657)Instructions burned: 183 (million)
% 10.05/2.90 % (3657)------------------------------
% 10.05/2.90 % (3657)------------------------------
% 10.05/2.91 % (3659)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_3154 for (2986ds/40Mi)
% 10.05/2.92 % (3659)Instruction limit reached!
% 10.05/2.92 % (3659)------------------------------
% 10.05/2.92 % (3659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.05/2.92 % (3659)Termination reason: Unknown
% 10.05/2.92 % (3659)Termination phase: shuffling
% 10.05/2.92
% 10.05/2.92 % (3659)Memory used [KB]: 2174
% 10.05/2.92 % (3659)Time elapsed: 0.012 s
% 10.05/2.92 % (3659)Instructions burned: 40 (million)
% 10.05/2.92 % (3659)------------------------------
% 10.05/2.92 % (3659)------------------------------
% 10.05/2.92 % (3643)Instruction limit reached!
% 10.05/2.92 % (3643)------------------------------
% 10.05/2.92 % (3643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.05/2.92 % (3643)Termination reason: Unknown
% 10.05/2.92 % (3643)Termination phase: Saturation
% 10.05/2.92
% 10.05/2.92 % (3643)Memory used [KB]: 9850
% 10.05/2.92 % (3643)Time elapsed: 0.465 s
% 10.05/2.92 % (3643)Instructions burned: 1541 (million)
% 10.05/2.92 % (3643)------------------------------
% 10.05/2.92 % (3643)------------------------------
% 10.05/2.93 % (3660)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_3154 for (2986ds/294Mi)
% 10.05/2.93 % (3661)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_3154 for (2986ds/187Mi)
% 10.05/2.96 % (3660)Refutation not found, incomplete strategy
% 10.05/2.96 % (3660)------------------------------
% 10.05/2.96 % (3660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.05/2.96 % (3660)Termination reason: Refutation not found, incomplete strategy
% 10.05/2.96
% 10.05/2.96
% 10.05/2.96 % (3660)Memory used [KB]: 6908
% 10.05/2.96 % (3660)Time elapsed: 0.030 s
% 10.05/2.96 % (3660)Instructions burned: 108 (million)
% 10.05/2.96 % (3660)------------------------------
% 10.05/2.96 % (3660)------------------------------
% 10.05/2.97 % (3662)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_3154 for (2985ds/371Mi)
% 10.05/2.99 % (3661)Instruction limit reached!
% 10.05/2.99 % (3661)------------------------------
% 10.05/2.99 % (3661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.05/2.99 % (3661)Termination reason: Unknown
% 10.05/2.99 % (3661)Termination phase: Saturation
% 10.05/2.99
% 10.05/2.99 % (3661)Memory used [KB]: 7419
% 10.05/2.99 % (3661)Time elapsed: 0.056 s
% 10.05/2.99 % (3661)Instructions burned: 190 (million)
% 10.05/2.99 % (3661)------------------------------
% 10.05/2.99 % (3661)------------------------------
% 10.05/3.00 % (3663)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_3154 for (2985ds/1827Mi)
% 10.05/3.00 % (3654)Instruction limit reached!
% 10.05/3.00 % (3654)------------------------------
% 10.05/3.00 % (3654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.05/3.00 % (3654)Termination reason: Unknown
% 10.05/3.00 % (3654)Termination phase: Saturation
% 10.05/3.00
% 10.05/3.00 % (3654)Memory used [KB]: 8955
% 10.05/3.00 % (3654)Time elapsed: 0.289 s
% 10.05/3.00 % (3654)Instructions burned: 995 (million)
% 10.05/3.00 % (3654)------------------------------
% 10.05/3.00 % (3654)------------------------------
% 12.77/3.01 % (3664)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_3154 for (2985ds/70Mi)
% 12.77/3.03 % (3664)Instruction limit reached!
% 12.77/3.03 % (3664)------------------------------
% 12.77/3.03 % (3664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.77/3.03 % (3664)Termination reason: Unknown
% 12.77/3.03 % (3664)Termination phase: Property scanning
% 12.77/3.03
% 12.77/3.03 % (3664)Memory used [KB]: 2302
% 12.77/3.03 % (3664)Time elapsed: 0.020 s
% 12.77/3.03 % (3664)Instructions burned: 72 (million)
% 12.77/3.03 % (3664)------------------------------
% 12.77/3.03 % (3664)------------------------------
% 12.77/3.04 % (3665)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_3154 for (2985ds/316Mi)
% 12.77/3.09 % (3662)Instruction limit reached!
% 12.77/3.09 % (3662)------------------------------
% 12.77/3.09 % (3662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.77/3.09 % (3662)Termination reason: Unknown
% 12.77/3.09 % (3662)Termination phase: Saturation
% 12.77/3.09
% 12.77/3.09 % (3662)Memory used [KB]: 7419
% 12.77/3.09 % (3662)Time elapsed: 0.119 s
% 12.77/3.09 % (3662)Instructions burned: 373 (million)
% 12.77/3.09 % (3662)------------------------------
% 12.77/3.09 % (3662)------------------------------
% 12.77/3.10 % (3666)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_3154 for (2984ds/932Mi)
% 12.77/3.11 % (3665)Refutation not found, incomplete strategy
% 12.77/3.11 % (3665)------------------------------
% 12.77/3.11 % (3665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.77/3.11 % (3665)Termination reason: Refutation not found, incomplete strategy
% 12.77/3.11
% 12.77/3.11
% 12.77/3.11 % (3665)Memory used [KB]: 7675
% 12.77/3.11 % (3665)Time elapsed: 0.069 s
% 12.77/3.11 % (3665)Instructions burned: 246 (million)
% 12.77/3.11 % (3665)------------------------------
% 12.77/3.11 % (3665)------------------------------
% 13.48/3.12 % (3667)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_3154 for (2984ds/4714Mi)
% 13.48/3.14 % (3658)Instruction limit reached!
% 13.48/3.14 % (3658)------------------------------
% 13.48/3.14 % (3658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.48/3.14 % (3658)Termination reason: Unknown
% 13.48/3.14 % (3658)Termination phase: Saturation
% 13.48/3.14
% 13.48/3.14 % (3658)Memory used [KB]: 13688
% 13.48/3.14 % (3658)Time elapsed: 0.240 s
% 13.48/3.14 % (3658)Instructions burned: 668 (million)
% 13.48/3.14 % (3658)------------------------------
% 13.48/3.14 % (3658)------------------------------
% 13.48/3.14 % (3646)Instruction limit reached!
% 13.48/3.14 % (3646)------------------------------
% 13.48/3.14 % (3646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.48/3.14 % (3646)Termination reason: Unknown
% 13.48/3.14 % (3646)Termination phase: Saturation
% 13.48/3.14
% 13.48/3.14 % (3646)Memory used [KB]: 3965
% 13.48/3.14 % (3646)Time elapsed: 0.605 s
% 13.48/3.14 % (3646)Instructions burned: 1915 (million)
% 13.48/3.14 % (3646)------------------------------
% 13.48/3.14 % (3646)------------------------------
% 13.48/3.15 % (3668)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_3154 for (2984ds/8250Mi)
% 13.48/3.15 % (3669)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_3154 for (2984ds/770Mi)
% 13.48/3.17 % (3669)Refutation not found, incomplete strategy
% 13.48/3.17 % (3669)------------------------------
% 13.48/3.17 % (3669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.48/3.17 % (3669)Termination reason: Refutation not found, incomplete strategy
% 13.48/3.17
% 13.48/3.17
% 13.48/3.17 % (3669)Memory used [KB]: 6652
% 13.48/3.17 % (3669)Time elapsed: 0.019 s
% 13.48/3.17 % (3669)Instructions burned: 59 (million)
% 13.48/3.17 % (3669)------------------------------
% 13.48/3.17 % (3669)------------------------------
% 13.48/3.18 % (3670)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_3154 for (2983ds/794Mi)
% 13.48/3.19 % (3667)Refutation not found, incomplete strategy
% 13.48/3.19 % (3667)------------------------------
% 13.48/3.19 % (3667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.48/3.19 % (3667)Termination reason: Refutation not found, incomplete strategy
% 13.48/3.19
% 13.48/3.19
% 13.48/3.19 % (3667)Memory used [KB]: 7803
% 13.48/3.19 % (3667)Time elapsed: 0.070 s
% 13.48/3.19 % (3667)Instructions burned: 249 (million)
% 13.48/3.19 % (3667)------------------------------
% 13.48/3.19 % (3667)------------------------------
% 13.90/3.20 % (3671)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_3154 for (2983ds/464Mi)
% 14.20/3.34 % (3671)Instruction limit reached!
% 14.20/3.34 % (3671)------------------------------
% 14.20/3.34 % (3671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.20/3.34 % (3671)Termination reason: Unknown
% 14.20/3.34 % (3671)Termination phase: Saturation
% 14.20/3.34
% 14.20/3.34 % (3671)Memory used [KB]: 7675
% 14.20/3.34 % (3671)Time elapsed: 0.143 s
% 14.20/3.34 % (3671)Instructions burned: 464 (million)
% 14.20/3.34 % (3671)------------------------------
% 14.20/3.34 % (3671)------------------------------
% 14.20/3.35 % (3672)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_3154 for (2982ds/1376Mi)
% 14.20/3.37 % (3666)Instruction limit reached!
% 14.20/3.37 % (3666)------------------------------
% 14.20/3.37 % (3666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.20/3.37 % (3666)Termination reason: Unknown
% 14.20/3.37 % (3666)Termination phase: Saturation
% 14.20/3.37
% 14.20/3.37 % (3666)Memory used [KB]: 9722
% 14.20/3.37 % (3666)Time elapsed: 0.273 s
% 14.20/3.37 % (3666)Instructions burned: 933 (million)
% 14.20/3.37 % (3666)------------------------------
% 14.20/3.37 % (3666)------------------------------
% 14.20/3.38 % (3673)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_3154 for (2981ds/906Mi)
% 14.94/3.42 % (3670)Instruction limit reached!
% 14.94/3.42 % (3670)------------------------------
% 14.94/3.42 % (3670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.94/3.42 % (3670)Termination reason: Unknown
% 14.94/3.42 % (3670)Termination phase: Saturation
% 14.94/3.42
% 14.94/3.42 % (3670)Memory used [KB]: 5117
% 14.94/3.42 % (3670)Time elapsed: 0.249 s
% 14.94/3.42 % (3670)Instructions burned: 794 (million)
% 14.94/3.42 % (3670)------------------------------
% 14.94/3.42 % (3670)------------------------------
% 14.94/3.43 % (3674)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_3154 for (2981ds/434Mi)
% 14.94/3.46 % (3674)Refutation not found, incomplete strategy
% 14.94/3.46 % (3674)------------------------------
% 14.94/3.46 % (3674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.94/3.46 % (3674)Termination reason: Refutation not found, incomplete strategy
% 14.94/3.46
% 14.94/3.46
% 14.94/3.46 % (3674)Memory used [KB]: 6780
% 14.94/3.46 % (3674)Time elapsed: 0.025 s
% 14.94/3.46 % (3674)Instructions burned: 81 (million)
% 14.94/3.46 % (3674)------------------------------
% 14.94/3.46 % (3674)------------------------------
% 14.94/3.47 % (3663)Instruction limit reached!
% 14.94/3.47 % (3663)------------------------------
% 14.94/3.47 % (3663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.94/3.47 % (3663)Termination reason: Unknown
% 14.94/3.47 % (3663)Termination phase: Saturation
% 14.94/3.47
% 14.94/3.47 % (3663)Memory used [KB]: 8315
% 14.94/3.47 % (3663)Time elapsed: 0.473 s
% 14.94/3.47 % (3663)Instructions burned: 1831 (million)
% 14.94/3.47 % (3663)------------------------------
% 14.94/3.47 % (3663)------------------------------
% 14.94/3.47 % (3675)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_3154 for (2981ds/865Mi)
% 14.94/3.48 % (3676)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_3154 for (2980ds/593Mi)
% 15.71/3.65 % (3676)Instruction limit reached!
% 15.71/3.65 % (3676)------------------------------
% 15.71/3.65 % (3676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.71/3.65 % (3676)Termination reason: Unknown
% 15.71/3.65 % (3676)Termination phase: Saturation
% 15.71/3.65
% 15.71/3.65 % (3676)Memory used [KB]: 9466
% 15.71/3.65 % (3676)Time elapsed: 0.169 s
% 15.71/3.65 % (3676)Instructions burned: 594 (million)
% 15.71/3.65 % (3676)------------------------------
% 15.71/3.65 % (3676)------------------------------
% 15.71/3.66 % (3677)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_3154 for (2979ds/443Mi)
% 15.71/3.68 % (3673)Instruction limit reached!
% 15.71/3.68 % (3673)------------------------------
% 15.71/3.68 % (3673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.71/3.68 % (3673)Termination reason: Unknown
% 15.71/3.68 % (3673)Termination phase: Saturation
% 15.71/3.68
% 15.71/3.68 % (3673)Memory used [KB]: 12281
% 15.71/3.68 % (3673)Time elapsed: 0.302 s
% 15.71/3.68 % (3673)Instructions burned: 906 (million)
% 15.71/3.68 % (3673)------------------------------
% 15.71/3.68 % (3673)------------------------------
% 15.71/3.69 % (3678)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_3154 for (2978ds/594Mi)
% 16.40/3.72 % (3675)Instruction limit reached!
% 16.40/3.72 % (3675)------------------------------
% 16.40/3.72 % (3675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.40/3.72 % (3675)Termination reason: Unknown
% 16.40/3.72 % (3675)Termination phase: Saturation
% 16.40/3.72
% 16.40/3.72 % (3675)Memory used [KB]: 8315
% 16.40/3.72 % (3675)Time elapsed: 0.256 s
% 16.40/3.72 % (3675)Instructions burned: 865 (million)
% 16.40/3.72 % (3675)------------------------------
% 16.40/3.72 % (3675)------------------------------
% 16.40/3.73 % (3679)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_3154 for (2978ds/327Mi)
% 16.40/3.77 % (3672)Instruction limit reached!
% 16.40/3.77 % (3672)------------------------------
% 16.40/3.77 % (3672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.40/3.77 % (3672)Termination reason: Unknown
% 16.40/3.77 % (3672)Termination phase: Saturation
% 16.40/3.77
% 16.40/3.77 % (3672)Memory used [KB]: 11001
% 16.40/3.77 % (3672)Time elapsed: 0.419 s
% 16.40/3.77 % (3672)Instructions burned: 1378 (million)
% 16.40/3.77 % (3672)------------------------------
% 16.40/3.77 % (3672)------------------------------
% 16.40/3.78 % (3680)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_3154 for (2977ds/5411Mi)
% 16.40/3.78 % (3642)Instruction limit reached!
% 16.40/3.78 % (3642)------------------------------
% 16.40/3.78 % (3642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.40/3.78 % (3642)Termination reason: Unknown
% 16.40/3.78 % (3642)Termination phase: Saturation
% 16.40/3.78
% 16.40/3.78 % (3642)Memory used [KB]: 11001
% 16.40/3.78 % (3642)Time elapsed: 1.354 s
% 16.40/3.78 % (3642)Instructions burned: 4438 (million)
% 16.40/3.78 % (3642)------------------------------
% 16.40/3.78 % (3642)------------------------------
% 16.40/3.79 % (3677)Instruction limit reached!
% 16.40/3.79 % (3677)------------------------------
% 16.40/3.79 % (3677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.40/3.79 % (3677)Termination reason: Unknown
% 16.40/3.79 % (3677)Termination phase: Saturation
% 16.40/3.79
% 16.40/3.79 % (3677)Memory used [KB]: 7803
% 16.40/3.79 % (3677)Time elapsed: 0.138 s
% 16.40/3.79 % (3677)Instructions burned: 445 (million)
% 16.40/3.79 % (3677)------------------------------
% 16.40/3.79 % (3677)------------------------------
% 16.40/3.79 % (3681)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_3154 for (2977ds/1762Mi)
% 17.44/3.80 % (3682)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_3154 for (2977ds/96Mi)
% 17.44/3.80 % (3680)Refutation not found, incomplete strategy
% 17.44/3.80 % (3680)------------------------------
% 17.44/3.80 % (3680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.80 % (3680)Termination reason: Refutation not found, incomplete strategy
% 17.44/3.80
% 17.44/3.80
% 17.44/3.80 % (3680)Memory used [KB]: 6652
% 17.44/3.80 % (3680)Time elapsed: 0.023 s
% 17.44/3.80 % (3680)Instructions burned: 72 (million)
% 17.44/3.80 % (3680)------------------------------
% 17.44/3.80 % (3680)------------------------------
% 17.44/3.81 % (3683)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_3154 for (2977ds/503Mi)
% 17.44/3.83 % (3682)Instruction limit reached!
% 17.44/3.83 % (3682)------------------------------
% 17.44/3.83 % (3682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.83 % (3682)Termination reason: Unknown
% 17.44/3.83 % (3682)Termination phase: Preprocessing 3
% 17.44/3.83
% 17.44/3.83 % (3682)Memory used [KB]: 2430
% 17.44/3.83 % (3682)Time elapsed: 0.028 s
% 17.44/3.83 % (3682)Instructions burned: 99 (million)
% 17.44/3.83 % (3682)------------------------------
% 17.44/3.83 % (3682)------------------------------
% 17.44/3.83 % (3679)Instruction limit reached!
% 17.44/3.83 % (3679)------------------------------
% 17.44/3.83 % (3679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.83 % (3679)Termination reason: Unknown
% 17.44/3.83 % (3679)Termination phase: Saturation
% 17.44/3.83
% 17.44/3.83 % (3679)Memory used [KB]: 7931
% 17.44/3.83 % (3679)Time elapsed: 0.101 s
% 17.44/3.83 % (3679)Instructions burned: 328 (million)
% 17.44/3.83 % (3679)------------------------------
% 17.44/3.83 % (3679)------------------------------
% 17.44/3.84 % (3684)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_3154 for (2977ds/90Mi)
% 17.44/3.84 % (3683)Refutation not found, incomplete strategy
% 17.44/3.84 % (3683)------------------------------
% 17.44/3.84 % (3683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.84 % (3683)Termination reason: Refutation not found, incomplete strategy
% 17.44/3.84
% 17.44/3.84
% 17.44/3.84 % (3683)Memory used [KB]: 6908
% 17.44/3.84 % (3683)Time elapsed: 0.029 s
% 17.44/3.84 % (3683)Instructions burned: 93 (million)
% 17.44/3.84 % (3683)------------------------------
% 17.44/3.84 % (3683)------------------------------
% 17.44/3.84 % (3685)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_3154 for (2977ds/593Mi)
% 17.44/3.85 % (3686)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_3154 for (2977ds/1512Mi)
% 17.44/3.86 % (3684)Instruction limit reached!
% 17.44/3.86 % (3684)------------------------------
% 17.44/3.86 % (3684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.86 % (3684)Termination reason: Unknown
% 17.44/3.86 % (3684)Termination phase: Property scanning
% 17.44/3.86
% 17.44/3.86 % (3684)Memory used [KB]: 2430
% 17.44/3.86 % (3684)Time elapsed: 0.027 s
% 17.44/3.86 % (3684)Instructions burned: 91 (million)
% 17.44/3.86 % (3684)------------------------------
% 17.44/3.86 % (3684)------------------------------
% 17.44/3.87 % (3687)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_3154 for (2977ds/569Mi)
% 17.44/3.87 % (3678)Instruction limit reached!
% 17.44/3.87 % (3678)------------------------------
% 17.44/3.87 % (3678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.87 % (3678)Termination reason: Unknown
% 17.44/3.87 % (3678)Termination phase: Saturation
% 17.44/3.87
% 17.44/3.87 % (3678)Memory used [KB]: 7419
% 17.44/3.87 % (3678)Time elapsed: 0.185 s
% 17.44/3.87 % (3678)Instructions burned: 596 (million)
% 17.44/3.87 % (3678)------------------------------
% 17.44/3.87 % (3678)------------------------------
% 17.44/3.88 % (3688)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_3154 for (2976ds/501Mi)
% 17.99/3.91 % (3686)Refutation not found, incomplete strategy
% 17.99/3.91 % (3686)------------------------------
% 17.99/3.91 % (3686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.99/3.91 % (3686)Termination reason: Refutation not found, incomplete strategy
% 17.99/3.91
% 17.99/3.91
% 17.99/3.91 % (3686)Memory used [KB]: 8059
% 17.99/3.91 % (3686)Time elapsed: 0.058 s
% 17.99/3.91 % (3686)Instructions burned: 194 (million)
% 17.99/3.91 % (3686)------------------------------
% 17.99/3.91 % (3686)------------------------------
% 17.99/3.92 % (3689)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_3154 for (2976ds/562Mi)
% 19.85/4.03 % (3685)Instruction limit reached!
% 19.85/4.03 % (3685)------------------------------
% 19.85/4.03 % (3685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.85/4.03 % (3685)Termination reason: Unknown
% 19.85/4.03 % (3685)Termination phase: Saturation
% 19.85/4.03
% 19.85/4.03 % (3685)Memory used [KB]: 8443
% 19.85/4.03 % (3685)Time elapsed: 0.184 s
% 19.85/4.03 % (3685)Instructions burned: 595 (million)
% 19.85/4.03 % (3685)------------------------------
% 19.85/4.03 % (3685)------------------------------
% 19.85/4.03 % (3688)Instruction limit reached!
% 19.85/4.03 % (3688)------------------------------
% 19.85/4.03 % (3688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.85/4.03 % (3688)Termination reason: Unknown
% 19.85/4.03 % (3688)Termination phase: Saturation
% 19.85/4.03
% 19.85/4.03 % (3688)Memory used [KB]: 9083
% 19.85/4.03 % (3688)Time elapsed: 0.151 s
% 19.85/4.03 % (3688)Instructions burned: 502 (million)
% 19.85/4.03 % (3688)------------------------------
% 19.85/4.03 % (3688)------------------------------
% 19.85/4.04 % (3690)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_3154 for (2975ds/406Mi)
% 19.85/4.04 % (3687)Instruction limit reached!
% 19.85/4.04 % (3687)------------------------------
% 19.85/4.04 % (3687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.85/4.04 % (3687)Termination reason: Unknown
% 19.85/4.04 % (3687)Termination phase: Saturation
% 19.85/4.04
% 19.85/4.04 % (3687)Memory used [KB]: 8571
% 19.85/4.04 % (3687)Time elapsed: 0.163 s
% 19.85/4.04 % (3687)Instructions burned: 570 (million)
% 19.85/4.04 % (3687)------------------------------
% 19.85/4.04 % (3687)------------------------------
% 19.85/4.04 % (3691)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_3154 for (2975ds/582Mi)
% 19.85/4.04 % (3692)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_3154 for (2975ds/456Mi)
% 19.85/4.06 % (3645)Instruction limit reached!
% 19.85/4.06 % (3645)------------------------------
% 19.85/4.06 % (3645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.85/4.06 % (3645)Termination reason: Unknown
% 19.85/4.06 % (3645)Termination phase: Saturation
% 19.85/4.06
% 19.85/4.06 % (3645)Memory used [KB]: 13304
% 19.85/4.06 % (3645)Time elapsed: 1.562 s
% 19.85/4.06 % (3645)Instructions burned: 5205 (million)
% 19.85/4.06 % (3645)------------------------------
% 19.85/4.06 % (3645)------------------------------
% 19.85/4.07 % (3693)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_3154 for (2974ds/393Mi)
% 19.85/4.08 % (3689)Instruction limit reached!
% 19.85/4.08 % (3689)------------------------------
% 19.85/4.08 % (3689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.85/4.08 % (3689)Termination reason: Unknown
% 19.85/4.08 % (3689)Termination phase: Saturation
% 19.85/4.08
% 19.85/4.08 % (3689)Memory used [KB]: 7931
% 19.85/4.08 % (3689)Time elapsed: 0.164 s
% 19.85/4.08 % (3689)Instructions burned: 562 (million)
% 19.85/4.08 % (3689)------------------------------
% 19.85/4.08 % (3689)------------------------------
% 19.85/4.08 % (3692)Refutation not found, incomplete strategy
% 19.85/4.08 % (3692)------------------------------
% 19.85/4.08 % (3692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.85/4.08 % (3692)Termination reason: Refutation not found, incomplete strategy
% 19.85/4.08
% 19.85/4.08
% 19.85/4.08 % (3692)Memory used [KB]: 7419
% 19.85/4.08 % (3692)Time elapsed: 0.039 s
% 19.85/4.08 % (3692)Instructions burned: 128 (million)
% 19.85/4.08 % (3692)------------------------------
% 19.85/4.08 % (3692)------------------------------
% 19.85/4.09 % (3694)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_3154 for (2974ds/1335Mi)
% 19.85/4.09 % (3695)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_3154 for (2974ds/3373Mi)
% 20.28/4.16 % (3690)Instruction limit reached!
% 20.28/4.16 % (3690)------------------------------
% 20.28/4.16 % (3690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.28/4.16 % (3690)Termination reason: Unknown
% 20.28/4.16 % (3690)Termination phase: Saturation
% 20.28/4.16
% 20.28/4.16 % (3690)Memory used [KB]: 8187
% 20.28/4.16 % (3690)Time elapsed: 0.127 s
% 20.28/4.16 % (3690)Instructions burned: 408 (million)
% 20.28/4.16 % (3690)------------------------------
% 20.28/4.16 % (3690)------------------------------
% 20.28/4.17 % (3696)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_3154 for (2973ds/474Mi)
% 20.28/4.18 % (3693)Instruction limit reached!
% 20.28/4.18 % (3693)------------------------------
% 20.28/4.18 % (3693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.28/4.18 % (3693)Termination reason: Unknown
% 20.28/4.18 % (3693)Termination phase: Saturation
% 20.28/4.18
% 20.28/4.18 % (3693)Memory used [KB]: 7291
% 20.28/4.18 % (3693)Time elapsed: 0.111 s
% 20.28/4.18 % (3693)Instructions burned: 394 (million)
% 20.28/4.18 % (3693)------------------------------
% 20.28/4.18 % (3693)------------------------------
% 20.28/4.19 % (3697)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_3154 for (2973ds/157Mi)
% 20.70/4.22 % (3691)Instruction limit reached!
% 20.70/4.22 % (3691)------------------------------
% 20.70/4.22 % (3691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.70/4.22 % (3691)Termination reason: Unknown
% 20.70/4.22 % (3691)Termination phase: Saturation
% 20.70/4.22
% 20.70/4.22 % (3691)Memory used [KB]: 8059
% 20.70/4.22 % (3691)Time elapsed: 0.182 s
% 20.70/4.22 % (3691)Instructions burned: 583 (million)
% 20.70/4.22 % (3691)------------------------------
% 20.70/4.22 % (3691)------------------------------
% 20.70/4.23 % (3697)Instruction limit reached!
% 20.70/4.23 % (3697)------------------------------
% 20.70/4.23 % (3697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.70/4.23 % (3697)Termination reason: Unknown
% 20.70/4.23 % (3697)Termination phase: Saturation
% 20.70/4.23
% 20.70/4.23 % (3697)Memory used [KB]: 6908
% 20.70/4.23 % (3697)Time elapsed: 0.044 s
% 20.70/4.23 % (3697)Instructions burned: 159 (million)
% 20.70/4.23 % (3697)------------------------------
% 20.70/4.23 % (3697)------------------------------
% 20.70/4.23 % (3698)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_3154 for (2973ds/590Mi)
% 20.70/4.24 % (3699)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_3154 for (2973ds/104Mi)
% 20.70/4.27 % (3699)Instruction limit reached!
% 20.70/4.27 % (3699)------------------------------
% 20.70/4.27 % (3699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.70/4.27 % (3699)Termination reason: Unknown
% 20.70/4.27 % (3699)Termination phase: Property scanning
% 20.70/4.27
% 20.70/4.27 % (3699)Memory used [KB]: 2430
% 20.70/4.27 % (3699)Time elapsed: 0.030 s
% 20.70/4.27 % (3699)Instructions burned: 104 (million)
% 20.70/4.27 % (3699)------------------------------
% 20.70/4.27 % (3699)------------------------------
% 20.70/4.28 % (3700)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_3154 for (2972ds/414Mi)
% 21.18/4.31 % (3681)Instruction limit reached!
% 21.18/4.31 % (3681)------------------------------
% 21.18/4.31 % (3681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.18/4.31 % (3681)Termination reason: Unknown
% 21.18/4.31 % (3681)Termination phase: Saturation
% 21.18/4.31
% 21.18/4.31 % (3681)Memory used [KB]: 9978
% 21.18/4.31 % (3681)Time elapsed: 0.520 s
% 21.18/4.31 % (3681)Instructions burned: 1764 (million)
% 21.18/4.31 % (3681)------------------------------
% 21.18/4.31 % (3681)------------------------------
% 21.18/4.31 % (3696)Instruction limit reached!
% 21.18/4.31 % (3696)------------------------------
% 21.18/4.31 % (3696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.18/4.31 % (3696)Termination reason: Unknown
% 21.18/4.31 % (3696)Termination phase: Saturation
% 21.18/4.31
% 21.18/4.31 % (3696)Memory used [KB]: 7931
% 21.18/4.31 % (3696)Time elapsed: 0.145 s
% 21.18/4.31 % (3696)Instructions burned: 477 (million)
% 21.18/4.31 % (3696)------------------------------
% 21.18/4.31 % (3696)------------------------------
% 21.18/4.32 % (3701)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_3154 for (2972ds/715Mi)
% 21.18/4.32 % (3702)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_3154 for (2972ds/961Mi)
% 21.18/4.40 % (3700)Instruction limit reached!
% 21.18/4.40 % (3700)------------------------------
% 21.18/4.40 % (3700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.18/4.40 % (3700)Termination reason: Unknown
% 21.18/4.40 % (3700)Termination phase: Saturation
% 21.18/4.40
% 21.18/4.40 % (3700)Memory used [KB]: 8443
% 21.18/4.40 % (3700)Time elapsed: 0.118 s
% 21.18/4.40 % (3700)Instructions burned: 416 (million)
% 21.18/4.40 % (3700)------------------------------
% 21.18/4.40 % (3700)------------------------------
% 21.58/4.40 % (3698)Instruction limit reached!
% 21.58/4.40 % (3698)------------------------------
% 21.58/4.40 % (3698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.58/4.40 % (3698)Termination reason: Unknown
% 21.58/4.40 % (3698)Termination phase: Saturation
% 21.58/4.40
% 21.58/4.40 % (3698)Memory used [KB]: 7803
% 21.58/4.40 % (3698)Time elapsed: 0.171 s
% 21.58/4.40 % (3698)Instructions burned: 591 (million)
% 21.58/4.40 % (3698)------------------------------
% 21.58/4.40 % (3698)------------------------------
% 21.58/4.41 % (3703)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_3154 for (2971ds/1213Mi)
% 21.58/4.41 % (3704)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_3154 for (2971ds/1979Mi)
% 21.58/4.48 % (3694)Instruction limit reached!
% 21.58/4.48 % (3694)------------------------------
% 21.58/4.48 % (3694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.58/4.48 % (3694)Termination reason: Unknown
% 21.58/4.48 % (3694)Termination phase: Saturation
% 21.58/4.48
% 21.58/4.48 % (3694)Memory used [KB]: 9083
% 21.58/4.48 % (3694)Time elapsed: 0.394 s
% 21.58/4.48 % (3694)Instructions burned: 1335 (million)
% 21.58/4.48 % (3694)------------------------------
% 21.58/4.48 % (3694)------------------------------
% 21.58/4.49 % (3705)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_3154 for (2970ds/481Mi)
% 22.26/4.54 % (3701)Instruction limit reached!
% 22.26/4.54 % (3701)------------------------------
% 22.26/4.54 % (3701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.26/4.54 % (3701)Termination reason: Unknown
% 22.26/4.54 % (3701)Termination phase: Saturation
% 22.26/4.54
% 22.26/4.54 % (3701)Memory used [KB]: 3965
% 22.26/4.54 % (3701)Time elapsed: 0.217 s
% 22.26/4.54 % (3701)Instructions burned: 716 (million)
% 22.26/4.54 % (3701)------------------------------
% 22.26/4.54 % (3701)------------------------------
% 22.26/4.55 % (3706)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_3154 for (2970ds/783Mi)
% 22.60/4.62 % (3702)Instruction limit reached!
% 22.60/4.62 % (3702)------------------------------
% 22.60/4.62 % (3702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.60/4.62 % (3702)Termination reason: Unknown
% 22.60/4.62 % (3702)Termination phase: Saturation
% 22.60/4.62
% 22.60/4.62 % (3702)Memory used [KB]: 8443
% 22.60/4.62 % (3702)Time elapsed: 0.297 s
% 22.60/4.62 % (3702)Instructions burned: 964 (million)
% 22.60/4.62 % (3702)------------------------------
% 22.60/4.62 % (3702)------------------------------
% 22.60/4.63 % (3707)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_3154 for (2969ds/432Mi)
% 22.60/4.64 % (3705)Instruction limit reached!
% 22.60/4.64 % (3705)------------------------------
% 22.60/4.64 % (3705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.60/4.64 % (3705)Termination reason: Unknown
% 22.60/4.64 % (3705)Termination phase: Saturation
% 22.60/4.64
% 22.60/4.64 % (3705)Memory used [KB]: 7675
% 22.60/4.64 % (3705)Time elapsed: 0.148 s
% 22.60/4.64 % (3705)Instructions burned: 482 (million)
% 22.60/4.64 % (3705)------------------------------
% 22.60/4.64 % (3705)------------------------------
% 22.60/4.65 % (3708)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_3154 for (2969ds/1670Mi)
% 22.60/4.68 % (3668)First to succeed.
% 22.60/4.69 % (3668)Refutation found. Thanks to Tanya!
% 22.60/4.69 % SZS status Theorem for DTF2THF_3154
% 22.60/4.69 % SZS output start Proof for DTF2THF_3154
% 22.60/4.69 thf(type_def_5, type, itself: ($tType) > $tType).
% 22.60/4.69 thf(type_def_7, type, list: ($tType) > $tType).
% 22.60/4.69 thf(type_def_8, type, set: ($tType) > $tType).
% 22.60/4.69 thf(type_def_9, type, nat: $tType).
% 22.60/4.69 thf(type_def_10, type, stream170649215stream: ($tType) > $tType).
% 22.60/4.69 thf(type_def_11, type, a: $tType).
% 22.60/4.69 thf(func_def_0, type, stream170649215stream: ($tType) > $tType).
% 22.60/4.69 thf(func_def_1, type, list: ($tType) > $tType).
% 22.60/4.69 thf(func_def_2, type, set: ($tType) > $tType).
% 22.60/4.69 thf(func_def_3, type, nat: $tType).
% 22.60/4.69 thf(func_def_4, type, itself: ($tType) > $tType).
% 22.60/4.69 thf(func_def_5, type, a: $tType).
% 22.60/4.69 thf(func_def_6, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 22.60/4.69 thf(func_def_7, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 22.60/4.69 thf(func_def_8, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 22.60/4.69 thf(func_def_9, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 22.60/4.69 thf(func_def_10, type, bNF_Greatest_Shift: !>[X0: $tType]:(set @ list @ X0 > X0 > set @ list @ X0)).
% 22.60/4.69 thf(func_def_11, type, bNF_Greatest_Succ: !>[X0: $tType]:(set @ list @ X0 > list @ X0 > set @ X0)).
% 22.60/4.69 thf(func_def_12, type, bNF_Greatest_shift: !>[X0: $tType, X1: $tType]:((list @ X0 > X1) > X0 > list @ X0 > X1)).
% 22.60/4.69 thf(func_def_13, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 22.60/4.69 thf(func_def_14, type, append: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_15, type, bind: !>[X0: $tType, X1: $tType]:(list @ X0 > (X0 > list @ X1) > list @ X1)).
% 22.60/4.69 thf(func_def_16, type, butlast: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_17, type, fold: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > list @ X0 > X1 > X1)).
% 22.60/4.69 thf(func_def_18, type, insert: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_19, type, last: !>[X0: $tType]:(list @ X0 > X0)).
% 22.60/4.69 thf(func_def_20, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_21, type, nil: !>[X0: $tType]:(list @ X0)).
% 22.60/4.69 thf(func_def_22, type, case_list: !>[X0: $tType, X1: $tType]:(X0 > (X1 > list @ X1 > X0) > list @ X1 > X0)).
% 22.60/4.69 thf(func_def_23, type, hd: !>[X0: $tType]:(list @ X0 > X0)).
% 22.60/4.69 thf(func_def_24, type, map: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > list @ X1)).
% 22.60/4.69 thf(func_def_25, type, tl: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_26, type, list_ex1: !>[X0: $tType]:((X0 > $o) > list @ X0 > $o)).
% 22.60/4.69 thf(func_def_27, type, listrelp: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > list @ X0 > list @ X1 > $o)).
% 22.60/4.69 thf(func_def_28, type, map_tailrec: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > list @ X1)).
% 22.60/4.69 thf(func_def_29, type, map_tailrec_rev: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > list @ X1 > list @ X1)).
% 22.60/4.69 thf(func_def_30, type, maps: !>[X0: $tType, X1: $tType]:((X0 > list @ X1) > list @ X0 > list @ X1)).
% 22.60/4.69 thf(func_def_31, type, member: !>[X0: $tType]:(list @ X0 > X0 > $o)).
% 22.60/4.69 thf(func_def_32, type, lexordp_eq: !>[X0: $tType]:((X0 > X0 > $o) > list @ X0 > list @ X0 > $o)).
% 22.60/4.69 thf(func_def_33, type, ord_lexordp: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 22.60/4.69 thf(func_def_34, type, ord_lexordp_eq: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 22.60/4.69 thf(func_def_35, type, product_lists: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 22.60/4.69 thf(func_def_36, type, remdups_adj: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_37, type, replicate: !>[X0: $tType]:(nat > X0 > list @ X0)).
% 22.60/4.69 thf(func_def_38, type, rev: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_39, type, rotate1: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_40, type, splice: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_41, type, sublists: !>[X0: $tType]:(list @ X0 > list @ list @ X0)).
% 22.60/4.69 thf(func_def_42, type, union: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_43, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 22.60/4.69 thf(func_def_44, type, type2: !>[X0: $tType]:(itself @ X0)).
% 22.60/4.69 thf(func_def_45, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 22.60/4.69 thf(func_def_46, type, stream317748790_cycle: !>[X0: $tType]:(list @ X0 > stream170649215stream @ X0)).
% 22.60/4.69 thf(func_def_47, type, stream942386729e_flat: !>[X0: $tType]:(stream170649215stream @ list @ X0 > stream170649215stream @ X0)).
% 22.60/4.69 thf(func_def_48, type, stream1195056575_while: !>[X0: $tType]:((X0 > $o) > stream170649215stream @ X0 > stream170649215stream @ X0)).
% 22.60/4.69 thf(func_def_49, type, stream1035003186_shift: !>[X0: $tType]:(list @ X0 > stream170649215stream @ X0 > stream170649215stream @ X0)).
% 22.60/4.69 thf(func_def_50, type, stream1586597341member: !>[X0: $tType]:(X0 > stream170649215stream @ X0 > $o)).
% 22.60/4.69 thf(func_def_51, type, stream641971652_SCons: !>[X0: $tType]:(X0 > stream170649215stream @ X0 > stream170649215stream @ X0)).
% 22.60/4.69 thf(func_def_52, type, stream1342653232stream: !>[X0: $tType, X1: $tType]:((X0 > stream170649215stream @ X0 > X1) > stream170649215stream @ X0 > X1)).
% 22.60/4.69 thf(func_def_53, type, stream_Mirabelle_shd: !>[X0: $tType]:(stream170649215stream @ X0 > X0)).
% 22.60/4.69 thf(func_def_54, type, stream2128578057e_smap: !>[X0: $tType, X1: $tType]:((X0 > X1) > stream170649215stream @ X0 > stream170649215stream @ X1)).
% 22.60/4.69 thf(func_def_55, type, stream_Mirabelle_stl: !>[X0: $tType]:(stream170649215stream @ X0 > stream170649215stream @ X0)).
% 22.60/4.69 thf(func_def_56, type, stream2015131171treams: !>[X0: $tType]:(set @ X0 > set @ stream170649215stream @ X0)).
% 22.60/4.69 thf(func_def_57, type, member2: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 22.60/4.69 thf(func_def_58, type, ws: stream170649215stream @ list @ a).
% 22.60/4.69 thf(func_def_75, type, sP0: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 22.60/4.69 thf(func_def_76, type, sP1: !>[X0: $tType]:((X0 > X0 > $o) > list @ X0 > list @ X0 > $o)).
% 22.60/4.69 thf(func_def_77, type, sP2: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 22.60/4.69 thf(func_def_78, type, sP3: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 22.60/4.69 thf(func_def_79, type, sP4: !>[X0: $tType]:((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > $o)).
% 22.60/4.69 thf(func_def_80, type, sP5: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > $o)).
% 22.60/4.69 thf(func_def_81, type, sP6: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > $o)).
% 22.60/4.69 thf(func_def_82, type, sP7: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > $o)).
% 22.60/4.69 thf(func_def_83, type, sP8: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 22.60/4.69 thf(func_def_84, type, sK9: !>[X0: $tType]:(list @ X0 > X0 > list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_85, type, sK10: !>[X0: $tType]:(stream170649215stream @ X0 > X0)).
% 22.60/4.69 thf(func_def_86, type, sK11: !>[X0: $tType]:(stream170649215stream @ X0 > stream170649215stream @ X0)).
% 22.60/4.69 thf(func_def_87, type, sK12: !>[X0: $tType]:(X0)).
% 22.60/4.69 thf(func_def_88, type, sK13: !>[X0: $tType]:(set @ X0 > (stream170649215stream @ X0 > $o) > stream170649215stream @ X0)).
% 22.60/4.69 thf(func_def_89, type, sK14: !>[X0: $tType, X1: $tType]:(list @ X1 > list @ X0 > (X0 > X1 > $o) > X0)).
% 22.60/4.69 thf(func_def_90, type, sK15: !>[X0: $tType, X1: $tType]:(list @ X1 > list @ X0 > (X0 > X1 > $o) > X1)).
% 22.60/4.69 thf(func_def_91, type, sK16: !>[X0: $tType, X1: $tType]:(list @ X1 > list @ X0 > (X0 > X1 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_92, type, sK17: !>[X0: $tType, X1: $tType]:(list @ X1 > list @ X0 > (X0 > X1 > $o) > list @ X1)).
% 22.60/4.69 thf(func_def_93, type, sK18: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > (X0 > X1 > $o) > X0)).
% 22.60/4.69 thf(func_def_94, type, sK19: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > (X0 > X1 > $o) > X1)).
% 22.60/4.69 thf(func_def_95, type, sK20: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > (X0 > X1 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_96, type, sK21: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > (X0 > X1 > $o) > list @ X1)).
% 22.60/4.69 thf(func_def_97, type, sK22: !>[X0: $tType]:(list @ X0 > X0)).
% 22.60/4.69 thf(func_def_98, type, sK23: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_99, type, sK24: !>[X0: $tType, X1: $tType]:(list @ X1 > list @ X1 > list @ X0 > (X0 > X1) > X0)).
% 22.60/4.69 thf(func_def_100, type, sK25: !>[X0: $tType, X1: $tType]:(list @ X1 > list @ X1 > list @ X0 > (X0 > X1) > list @ X0)).
% 22.60/4.69 thf(func_def_101, type, sK26: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 22.60/4.69 thf(func_def_102, type, sK27: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0)).
% 22.60/4.69 thf(func_def_103, type, sK28: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_104, type, sK29: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 22.60/4.69 thf(func_def_105, type, sK30: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 22.60/4.69 thf(func_def_106, type, sK31: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 22.60/4.69 thf(func_def_107, type, sK32: !>[X0: $tType]:(list @ X0 > X0)).
% 22.60/4.69 thf(func_def_108, type, sK33: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_109, type, sK34: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_110, type, sK35: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_111, type, sK36: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_112, type, sK37: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_113, type, sK38: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_114, type, sK39: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_115, type, sK40: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_116, type, sK41: !>[X0: $tType]:(list @ X0 > X0)).
% 22.60/4.69 thf(func_def_117, type, sK42: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_118, type, sK43: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_119, type, sK44: !>[X0: $tType]:(list @ X0 > X0)).
% 22.60/4.69 thf(func_def_120, type, sK45: !>[X0: $tType]:(X0)).
% 22.60/4.69 thf(func_def_121, type, sK46: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_122, type, sK47: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_123, type, sK48: !>[X0: $tType]:((X0 > X0 > $o) > list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_124, type, sK49: !>[X0: $tType]:((X0 > X0 > $o) > list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_125, type, sK50: !>[X0: $tType]:((X0 > X0 > $o) > list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_126, type, sK51: !>[X0: $tType]:((X0 > X0 > $o) > list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_127, type, sK52: !>[X0: $tType]:(list @ X0 > list @ X0 > (X0 > X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_128, type, sK53: !>[X0: $tType]:(list @ X0 > list @ X0 > (X0 > X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_129, type, sK54: !>[X0: $tType]:(list @ X0 > list @ X0 > (X0 > X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_130, type, sK55: !>[X0: $tType]:(list @ X0 > list @ X0 > (X0 > X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_131, type, sK56: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_132, type, sK57: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_133, type, sK58: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_134, type, sK59: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_135, type, sK60: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_136, type, sK61: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_137, type, sK62: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_138, type, sK63: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_139, type, sK64: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_140, type, sK65: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_141, type, sK66: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_142, type, sK67: !>[X0: $tType]:(list @ X0 > X0)).
% 22.60/4.69 thf(func_def_143, type, sK68: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_144, type, sK69: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_145, type, sK70: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_146, type, sK71: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_147, type, sK72: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_148, type, sK73: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_149, type, sK74: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_150, type, sK75: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_151, type, sK76: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_152, type, sK77: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_153, type, sK78: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_154, type, sK79: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 22.60/4.69 thf(func_def_155, type, sK80: !>[X0: $tType]:(list @ X0 > X0)).
% 22.60/4.69 thf(func_def_156, type, sK81: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_157, type, sK82: !>[X0: $tType]:(list @ X0 > X0)).
% 22.60/4.69 thf(func_def_158, type, sK83: !>[X0: $tType]:(list @ X0 > X0)).
% 22.60/4.69 thf(func_def_159, type, sK84: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_160, type, sK85: !>[X0: $tType]:(list @ X0 > X0)).
% 22.60/4.69 thf(func_def_161, type, sK86: !>[X0: $tType]:(set @ X0 > stream170649215stream @ X0 > X0)).
% 22.60/4.69 thf(func_def_162, type, sK87: !>[X0: $tType]:(set @ X0 > stream170649215stream @ X0 > stream170649215stream @ X0)).
% 22.60/4.69 thf(func_def_163, type, sK88: !>[X0: $tType]:(list @ list @ X0 > X0)).
% 22.60/4.69 thf(func_def_164, type, sK89: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_165, type, sK90: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 22.60/4.69 thf(func_def_166, type, sK91: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 22.60/4.69 thf(func_def_167, type, sK92: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 22.60/4.69 thf(func_def_168, type, sK93: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_169, type, sK94: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 22.60/4.69 thf(func_def_170, type, sK95: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 22.60/4.69 thf(func_def_171, type, sK96: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 22.60/4.69 thf(func_def_172, type, sK97: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_173, type, sK98: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 22.60/4.69 thf(func_def_174, type, sK99: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 22.60/4.69 thf(func_def_175, type, sK100: !>[X0: $tType]:((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_176, type, sK101: !>[X0: $tType]:((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_177, type, sK102: !>[X0: $tType]:((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_178, type, sK103: !>[X0: $tType]:((X0 > X0 > $o) > (list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_179, type, sK104: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_180, type, sK105: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_181, type, sK106: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_182, type, sK107: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > (X0 > X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_183, type, sK108: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_184, type, sK109: !>[X0: $tType, X1: $tType]:(set @ X1 > (X0 > X1) > set @ X0 > X0)).
% 22.60/4.69 thf(func_def_185, type, sK110: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_186, type, sK111: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_187, type, sK112: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_188, type, sK113: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_189, type, sK114: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_190, type, sK115: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_191, type, sK116: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_192, type, sK117: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_193, type, sK118: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_194, type, sK119: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_195, type, sK120: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_196, type, sK121: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_197, type, sK122: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_198, type, sK123: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_199, type, sK124: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_200, type, sK125: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_201, type, sK126: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_202, type, sK127: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_203, type, sK128: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_204, type, sK129: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_205, type, sK130: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_206, type, sK131: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_207, type, sK132: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_208, type, sK133: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_209, type, sK134: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_210, type, sK135: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_211, type, sK136: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_212, type, sK137: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_213, type, sK138: !>[X0: $tType]:((stream170649215stream @ X0 > stream170649215stream @ X0 > $o) > stream170649215stream @ X0)).
% 22.60/4.69 thf(func_def_214, type, sK139: !>[X0: $tType]:((stream170649215stream @ X0 > stream170649215stream @ X0 > $o) > stream170649215stream @ X0)).
% 22.60/4.69 thf(func_def_215, type, sK140: !>[X0: $tType]:(list @ X0 > X0)).
% 22.60/4.69 thf(func_def_216, type, sK141: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_217, type, sK142: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_218, type, sK143: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_219, type, sK144: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_220, type, sK145: !>[X0: $tType]:(set @ X0 > stream170649215stream @ X0 > X0)).
% 22.60/4.69 thf(func_def_221, type, sK146: !>[X0: $tType]:(set @ X0 > stream170649215stream @ X0 > stream170649215stream @ X0)).
% 22.60/4.69 thf(func_def_222, type, sK147: !>[X0: $tType]:((stream170649215stream @ X0 > stream170649215stream @ X0 > $o) > stream170649215stream @ X0)).
% 22.60/4.69 thf(func_def_223, type, sK148: !>[X0: $tType]:((stream170649215stream @ X0 > stream170649215stream @ X0 > $o) > stream170649215stream @ X0)).
% 22.60/4.69 thf(func_def_224, type, sK149: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_225, type, sK150: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_226, type, sK151: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_227, type, sK152: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_228, type, sK153: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_229, type, sK154: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_230, type, sK155: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_231, type, sK156: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_232, type, sK157: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_233, type, sK158: !>[X0: $tType, X1: $tType]:(list @ X1 > (X1 > X0) > list @ X0 > X0 > X1)).
% 22.60/4.69 thf(func_def_234, type, sK159: !>[X0: $tType, X1: $tType]:(list @ X1 > (X1 > X0) > list @ X0 > X0 > list @ X1)).
% 22.60/4.69 thf(func_def_235, type, sK160: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_236, type, sK161: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_237, type, sK162: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_238, type, sK163: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_239, type, sK164: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_240, type, sK165: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_241, type, sK166: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_242, type, sK167: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_243, type, sK168: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 22.60/4.69 thf(func_def_244, type, sK169: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 22.60/4.69 thf(func_def_245, type, sK170: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_246, type, sK171: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_247, type, sK172: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_248, type, sK173: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_249, type, sK174: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_250, type, sK175: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_251, type, sK176: !>[X0: $tType, X1: $tType]:(list @ X0 > X0 > list @ X1 > (X1 > X0) > X1)).
% 22.60/4.69 thf(func_def_252, type, sK177: !>[X0: $tType, X1: $tType]:(list @ X0 > X0 > list @ X1 > (X1 > X0) > list @ X1)).
% 22.60/4.69 thf(func_def_253, type, sK178: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0 > X0 > list @ X0)).
% 22.60/4.69 thf(func_def_254, type, sK179: !>[X0: $tType, X1: $tType]:(list @ X1 > X1 > list @ X0 > (X0 > X1) > X0)).
% 22.60/4.69 thf(func_def_255, type, sK180: !>[X0: $tType, X1: $tType]:(list @ X1 > X1 > list @ X0 > (X0 > X1) > list @ X0)).
% 22.60/4.69 thf(func_def_256, type, sK181: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_257, type, sK182: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_258, type, sK183: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 22.60/4.69 thf(func_def_259, type, sK184: !>[X0: $tType]:(list @ X0 > list @ X0 > X0)).
% 22.60/4.69 thf(func_def_260, type, sK185: !>[X0: $tType, X1: $tType]:(list @ X1 > (X1 > X0) > list @ X0 > X0 > X1)).
% 22.60/4.69 thf(func_def_261, type, sK186: !>[X0: $tType, X1: $tType]:(list @ X1 > (X1 > X0) > list @ X0 > X0 > list @ X1)).
% 22.60/4.69 thf(func_def_263, type, ph188: !>[X0: $tType]:(X0)).
% 22.60/4.69 thf(f6111,plain,(
% 22.60/4.69 $false),
% 22.60/4.69 inference(subsumption_resolution,[status(thm)],[f6074,f1580])).
% 22.60/4.69 thf(f1580,plain,(
% 22.60/4.69 ((stream_Mirabelle_shd @ list @ a @ ws) != nil @ a)),
% 22.60/4.69 inference(cnf_transformation,[status(thm)],[f266])).
% 22.60/4.69 thf(f266,axiom,(
% 22.60/4.69 ((stream_Mirabelle_shd @ list @ a @ ws) != nil @ a)),
% 22.60/4.69 file('/export/starexec/sandbox/tmp/tmp.wxvlm3pJrl/DTF2THF_3154.p',conj_0)).
% 22.60/4.69 thf(f6074,plain,(
% 22.60/4.69 ((stream_Mirabelle_shd @ list @ a @ ws) = nil @ a)),
% 22.60/4.69 inference(trivial_inequality_removal,[status(thm)],[f6051])).
% 22.60/4.69 thf(f6051,plain,(
% 22.60/4.69 ((stream942386729e_flat @ a @ ws) != (stream942386729e_flat @ a @ ws)) | ((stream_Mirabelle_shd @ list @ a @ ws) = nil @ a)),
% 22.60/4.69 inference(superposition,[status(thm)],[f1554,f1885])).
% 22.60/4.69 thf(f1885,plain,(
% 22.60/4.69 ( ! [X0 : $tType,X1 : stream170649215stream @ list @ X0] : (((stream942386729e_flat @ X0 @ X1) = (stream1035003186_shift @ X0 @ (stream_Mirabelle_shd @ list @ X0 @ X1) @ (stream942386729e_flat @ X0 @ (stream_Mirabelle_stl @ list @ X0 @ X1)))) | (nil @ X0 = (stream_Mirabelle_shd @ list @ X0 @ X1))) )),
% 22.60/4.69 inference(superposition,[status(thm)],[f1474,f1582])).
% 22.60/4.69 thf(f1582,plain,(
% 22.60/4.69 ( ! [X0 : $tType,X1 : stream170649215stream @ X0] : (((stream641971652_SCons @ X0 @ (stream_Mirabelle_shd @ X0 @ X1) @ (stream_Mirabelle_stl @ X0 @ X1)) = X1)) )),
% 22.60/4.69 inference(cnf_transformation,[status(thm)],[f686])).
% 22.60/4.69 thf(f686,plain,(
% 22.60/4.69 ! [X0 : $tType,X1 : stream170649215stream @ X0] : ((stream641971652_SCons @ X0 @ (stream_Mirabelle_shd @ X0 @ X1) @ (stream_Mirabelle_stl @ X0 @ X1)) = X1)),
% 22.60/4.69 inference(rectify,[status(thm)],[f14])).
% 22.60/4.69 thf(f14,axiom,(
% 22.60/4.69 ! [X0 : $tType,X7 : stream170649215stream @ X0] : ((stream641971652_SCons @ X0 @ (stream_Mirabelle_shd @ X0 @ X7) @ (stream_Mirabelle_stl @ X0 @ X7)) = X7)),
% 22.60/4.69 file('/export/starexec/sandbox/tmp/tmp.wxvlm3pJrl/DTF2THF_3154.p',fact_13_stream_Ocollapse)).
% 22.60/4.69 thf(f1474,plain,(
% 22.60/4.69 ( ! [X0 : $tType,X2 : stream170649215stream @ list @ X0,X1 : list @ X0] : (((stream1035003186_shift @ X0 @ X1 @ (stream942386729e_flat @ X0 @ X2)) = (stream942386729e_flat @ X0 @ (stream641971652_SCons @ list @ X0 @ X1 @ X2))) | (nil @ X0 = X1)) )),
% 22.60/4.69 inference(cnf_transformation,[status(thm)],[f850])).
% 22.60/4.69 thf(f850,plain,(
% 22.60/4.69 ! [X0 : $tType,X1 : list @ X0,X2 : stream170649215stream @ list @ X0] : ((nil @ X0 = X1) | ((stream1035003186_shift @ X0 @ X1 @ (stream942386729e_flat @ X0 @ X2)) = (stream942386729e_flat @ X0 @ (stream641971652_SCons @ list @ X0 @ X1 @ X2))))),
% 22.60/4.69 inference(ennf_transformation,[status(thm)],[f664])).
% 22.60/4.69 thf(f664,plain,(
% 22.60/4.69 ! [X0 : $tType,X1 : list @ X0,X2 : stream170649215stream @ list @ X0] : ((nil @ X0 != X1) => ((stream1035003186_shift @ X0 @ X1 @ (stream942386729e_flat @ X0 @ X2)) = (stream942386729e_flat @ X0 @ (stream641971652_SCons @ list @ X0 @ X1 @ X2))))),
% 22.60/4.69 inference(rectify,[status(thm)],[f6])).
% 22.60/4.69 thf(f6,axiom,(
% 22.60/4.69 ! [X0 : $tType,X3 : list @ X0,X12 : stream170649215stream @ list @ X0] : ((nil @ X0 != X3) => ((stream942386729e_flat @ X0 @ (stream641971652_SCons @ list @ X0 @ X3 @ X12)) = (stream1035003186_shift @ X0 @ X3 @ (stream942386729e_flat @ X0 @ X12))))),
% 22.60/4.69 file('/export/starexec/sandbox/tmp/tmp.wxvlm3pJrl/DTF2THF_3154.p',fact_5_flat__Stream)).
% 22.60/4.69 thf(f1554,plain,(
% 22.60/4.69 ((stream942386729e_flat @ a @ ws) != (stream1035003186_shift @ a @ (stream_Mirabelle_shd @ list @ a @ ws) @ (stream942386729e_flat @ a @ (stream_Mirabelle_stl @ list @ a @ ws))))),
% 22.60/4.69 inference(cnf_transformation,[status(thm)],[f575])).
% 22.60/4.69 thf(f575,plain,(
% 22.60/4.69 ((stream942386729e_flat @ a @ ws) != (stream1035003186_shift @ a @ (stream_Mirabelle_shd @ list @ a @ ws) @ (stream942386729e_flat @ a @ (stream_Mirabelle_stl @ list @ a @ ws))))),
% 22.60/4.69 inference(flattening,[status(thm)],[f268])).
% 22.60/4.69 thf(f268,negated_conjecture,(
% 22.60/4.69 ~((stream942386729e_flat @ a @ ws) = (stream1035003186_shift @ a @ (stream_Mirabelle_shd @ list @ a @ ws) @ (stream942386729e_flat @ a @ (stream_Mirabelle_stl @ list @ a @ ws))))),
% 22.60/4.69 inference(negated_conjecture,[status(cth)],[f267])).
% 22.60/4.69 thf(f267,conjecture,(
% 22.60/4.69 ((stream942386729e_flat @ a @ ws) = (stream1035003186_shift @ a @ (stream_Mirabelle_shd @ list @ a @ ws) @ (stream942386729e_flat @ a @ (stream_Mirabelle_stl @ list @ a @ ws))))),
% 22.60/4.69 file('/export/starexec/sandbox/tmp/tmp.wxvlm3pJrl/DTF2THF_3154.p',conj_1)).
% 22.60/4.69 % SZS output end Proof for DTF2THF_3154
% 22.60/4.69 % (3668)------------------------------
% 22.60/4.69 % (3668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.60/4.69 % (3668)Termination reason: Refutation
% 22.60/4.69
% 22.60/4.69 % (3668)Memory used [KB]: 10874
% 22.60/4.69 % (3668)Time elapsed: 1.537 s
% 22.60/4.69 % (3668)Instructions burned: 5145 (million)
% 22.60/4.69 % (3668)------------------------------
% 22.60/4.69 % (3668)------------------------------
% 22.60/4.69 % (3546)Success in time 3.119 s
%------------------------------------------------------------------------------