%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT190^1 : 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 : n012.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 08:45:05 AM UTC 2026
% Result : Theorem 74.60s 11.67s
% Output : Refutation 74.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : DAT190^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 06:10:30 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.33 ---- Original DTF file ---
% 0.07/0.34 thf(spec,logic,$$dhol).
% 0.07/0.34 %------------------------------------------------------------------------------
% 0.07/0.34 % File : DAT190^1 : TPTP v9.2.1. Released v7.0.0.
% 0.07/0.34 % Domain : Data Structures
% 0.07/0.34 % Problem : Lazy list mirror 44
% 0.07/0.34 % Version : [Bla16] axioms : Especial.
% 0.07/0.34 % English :
% 0.07/0.34
% 0.07/0.34 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.07/0.34 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.07/0.34 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.07/0.34 % Source : [Bla16]
% 0.07/0.34 % Names : lmirror__44.p [Bla16]
% 0.07/0.34
% 0.07/0.34 % Status : Theorem
% 0.07/0.34 % Rating : 1.00 v9.0.0, 0.67 v8.1.0, 0.75 v7.5.0, 1.00 v7.3.0, 0.67 v7.2.0, 0.75 v7.1.0
% 0.07/0.34 % Syntax : Number of formulae : 300 ( 138 unt; 42 typ; 0 def)
% 0.07/0.34 % Number of atoms : 675 ( 294 equ; 0 cnn)
% 0.07/0.34 % Maximal formula atoms : 8 ( 2 avg)
% 0.07/0.34 % Number of connectives : 4198 ( 157 ~; 54 |; 84 &;3641 @)
% 0.07/0.34 % ( 0 <=>; 262 =>; 0 <=; 0 <~>)
% 0.07/0.34 % Maximal formula depth : 28 ( 8 avg)
% 0.07/0.34 % Number of types : 3 ( 2 usr)
% 0.07/0.34 % Number of type conns : 248 ( 248 >; 0 *; 0 +; 0 <<)
% 0.07/0.34 % Number of symbols : 43 ( 40 usr; 6 con; 0-6 aty)
% 0.07/0.34 % Number of variables : 1117 ( 30 ^; 987 !; 60 ?;1117 :)
% 0.07/0.34 % ( 40 !>; 0 ?*; 0 @-; 0 @+)
% 0.07/0.34 % SPC : TH1_THM_EQU_NAR
% 0.07/0.34
% 0.07/0.34 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.07/0.34 % 2016-07-13 14:40:54.235
% 0.07/0.34 %------------------------------------------------------------------------------
% 0.07/0.34 %----Could-be-implicit typings (6)
% 0.07/0.34 thf(ty_t_Coinductive__List_Ollist,type,
% 0.07/0.34 coinductive_llist: $tType > $tType ).
% 0.07/0.34
% 0.07/0.34 thf(ty_t_Product__Type_Oprod,type,
% 0.07/0.34 product_prod: $tType > $tType > $tType ).
% 0.07/0.34
% 0.07/0.34 thf(ty_t_Set_Oset,type,
% 0.07/0.34 set: $tType > $tType ).
% 0.07/0.34
% 0.07/0.34 thf(ty_t_Nat_Onat,type,
% 0.07/0.34 nat: $tType ).
% 0.07/0.34
% 0.07/0.34 thf(ty_t_itself,type,
% 0.07/0.34 itself: $tType > $tType ).
% 0.07/0.34
% 0.07/0.34 thf(ty_tf_a,type,
% 0.07/0.34 a: $tType ).
% 0.07/0.34
% 0.07/0.34 %----Explicit typings (36)
% 0.07/0.34 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 0.07/0.34 coindu328551480prefix:
% 0.07/0.34 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Ogen__lset,type,
% 0.07/0.34 coinductive_gen_lset:
% 0.07/0.34 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Olappend,type,
% 0.07/0.34 coinductive_lappend:
% 0.07/0.34 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Olconcat,type,
% 0.07/0.34 coinductive_lconcat:
% 0.07/0.34 !>[A: $tType] : ( ( coinductive_llist @ ( coinductive_llist @ A ) ) > ( coinductive_llist @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Oldropn,type,
% 0.07/0.34 coinductive_ldropn:
% 0.07/0.34 !>[A: $tType] : ( nat > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Olfinite,type,
% 0.07/0.34 coinductive_lfinite:
% 0.07/0.34 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Ollast,type,
% 0.07/0.34 coinductive_llast:
% 0.07/0.34 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Ollexord,type,
% 0.07/0.34 coinductive_llexord:
% 0.07/0.34 !>[A: $tType] : ( ( A > A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.07/0.34 coinductive_LCons:
% 0.07/0.34 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 0.07/0.34 coinductive_LNil:
% 0.07/0.34 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Ollist_Ocase__llist,type,
% 0.07/0.34 coindu1381640503_llist:
% 0.07/0.34 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B ) > ( coinductive_llist @ A ) > B ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Ollist_Olhd,type,
% 0.07/0.34 coinductive_lhd:
% 0.07/0.34 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Ollist_Olnull,type,
% 0.07/0.34 coinductive_lnull:
% 0.07/0.34 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Ollist_Olset,type,
% 0.07/0.34 coinductive_lset:
% 0.07/0.34 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Ollist_Oltl,type,
% 0.07/0.34 coinductive_ltl:
% 0.07/0.34 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Olmember,type,
% 0.07/0.34 coinductive_lmember:
% 0.07/0.34 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > $o ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Olprefix,type,
% 0.07/0.34 coinductive_lprefix:
% 0.07/0.34 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 0.07/0.34 coindu1478340336prefix:
% 0.07/0.34 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_OltakeWhile,type,
% 0.07/0.34 coindu501562517eWhile:
% 0.07/0.34 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Olzip,type,
% 0.07/0.34 coinductive_lzip:
% 0.07/0.34 !>[A: $tType,B: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ B ) > ( coinductive_llist @ ( product_prod @ A @ B ) ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Oord_Olsorted,type,
% 0.07/0.34 coinductive_lsorted:
% 0.07/0.34 !>[A: $tType] : ( ( A > A > $o ) > ( coinductive_llist @ A ) > $o ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Coinductive__List_Ounfold__llist,type,
% 0.07/0.34 coindu1441602521_llist:
% 0.07/0.34 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > B ) > ( A > A ) > A > ( coinductive_llist @ B ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_HOL_Oundefined,type,
% 0.07/0.34 undefined:
% 0.07/0.34 !>[A: $tType] : A ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_If,type,
% 0.07/0.34 if:
% 0.07/0.34 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_LMirror__Mirabelle__wyovfcktfy_Olmirror,type,
% 0.07/0.34 lMirro427583474mirror:
% 0.07/0.34 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_LMirror__Mirabelle__wyovfcktfy_Olmirror__aux,type,
% 0.07/0.34 lMirro999291890or_aux:
% 0.07/0.34 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Product__Type_OPair,type,
% 0.07/0.34 product_Pair:
% 0.07/0.34 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.07/0.34 produc2004651681e_prod:
% 0.07/0.34 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 0.07/0.34 product_rec_prod:
% 0.07/0.34 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Pure_Otype,type,
% 0.07/0.34 type:
% 0.07/0.34 !>[A: $tType] : ( itself @ A ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_Set_OCollect,type,
% 0.07/0.34 collect:
% 0.07/0.34 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_c_member,type,
% 0.07/0.34 member:
% 0.07/0.34 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.07/0.34
% 0.07/0.34 thf(sy_v_acc,type,
% 0.07/0.34 acc: coinductive_llist @ a ).
% 0.07/0.34
% 0.07/0.34 thf(sy_v_acca____,type,
% 0.07/0.34 acca: coinductive_llist @ a ).
% 0.07/0.34
% 0.07/0.34 thf(sy_v_xs,type,
% 0.07/0.34 xs: coinductive_llist @ a ).
% 0.07/0.34
% 0.07/0.34 thf(sy_v_xsa____,type,
% 0.07/0.34 xsa: coinductive_llist @ a ).
% 0.07/0.34
% 0.07/0.34 %----Relevant facts (254)
% 0.07/0.34 thf(fact_0__092_060open_062lfinite_A_Ilmirror__aux_Aacc_Axs_J_092_060close_062,axiom,
% 0.07/0.34 coinductive_lfinite @ a @ ( lMirro999291890or_aux @ a @ acc @ xs ) ).
% 0.07/0.34
% 0.07/0.34 % \<open>lfinite (lmirror_aux acc xs)\<close>
% 0.07/0.34 thf(fact_1_LCons_Ohyps_I2_J,axiom,
% 0.07/0.34 ~ ( coinductive_lnull @ a @ ( lMirro999291890or_aux @ a @ acca @ xsa ) ) ).
% 0.07/0.34
% 0.07/0.34 % LCons.hyps(2)
% 0.07/0.34 thf(fact_2_LCons_Ohyps_I1_J,axiom,
% 0.07/0.34 coinductive_lfinite @ a @ ( lMirro999291890or_aux @ a @ acca @ xsa ) ).
% 0.07/0.34
% 0.07/0.34 % LCons.hyps(1)
% 0.07/0.34 thf(fact_3_LCons_Ohyps_I3_J,axiom,
% 0.07/0.34 ! [Acc: coinductive_llist @ a,Xs: coinductive_llist @ a] :
% 0.07/0.34 ( ( ( coinductive_ltl @ a @ ( lMirro999291890or_aux @ a @ acca @ xsa ) )
% 0.07/0.34 = ( lMirro999291890or_aux @ a @ Acc @ Xs ) )
% 0.07/0.34 => ( ( coinductive_lfinite @ a @ Xs )
% 0.07/0.34 & ( coinductive_lfinite @ a @ Acc ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % LCons.hyps(3)
% 0.07/0.34 thf(fact_4_lfinite__ltl,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lfinite @ A @ ( coinductive_ltl @ A @ Xs ) )
% 0.07/0.34 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.07/0.34
% 0.07/0.34 % lfinite_ltl
% 0.07/0.34 thf(fact_5_lnull__imp__lfinite,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.07/0.34
% 0.07/0.34 % lnull_imp_lfinite
% 0.07/0.34 thf(fact_6_lmirror__aux_Oexhaust,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Acc: coinductive_llist @ A] :
% 0.07/0.34 ( ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ~ ( coinductive_lnull @ A @ Acc ) )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 | ~ ( coinductive_lnull @ A @ Acc ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lmirror_aux.exhaust
% 0.07/0.34 thf(fact_7_lmirror__aux_Odisc__iff_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,Acc: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( ~ ( coinductive_lnull @ A @ ( lMirro999291890or_aux @ A @ Acc @ Xs ) ) )
% 0.07/0.34 = ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 | ~ ( coinductive_lnull @ A @ Acc ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lmirror_aux.disc_iff(2)
% 0.07/0.34 thf(fact_8_lnull__lmirror__aux,axiom,
% 0.07/0.34 ! [A: $tType,Acc: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ ( lMirro999291890or_aux @ A @ Acc @ Xs ) )
% 0.07/0.34 = ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 & ( coinductive_lnull @ A @ Acc ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lnull_lmirror_aux
% 0.07/0.34 thf(fact_9_lfinite__induct,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.07/0.34 ( ( coinductive_lfinite @ A @ Xs )
% 0.07/0.34 => ( ! [Xs2: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ Xs2 )
% 0.07/0.34 => ( P @ Xs2 ) )
% 0.07/0.34 => ( ! [Xs2: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lfinite @ A @ Xs2 )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ Xs2 )
% 0.07/0.34 => ( ( P @ ( coinductive_ltl @ A @ Xs2 ) )
% 0.07/0.34 => ( P @ Xs2 ) ) ) )
% 0.07/0.34 => ( P @ Xs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lfinite_induct
% 0.07/0.34 thf(fact_10_lstrict__prefix__lfinite1,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coindu1478340336prefix @ A @ Xs @ Ys )
% 0.07/0.34 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.07/0.34
% 0.07/0.34 % lstrict_prefix_lfinite1
% 0.07/0.34 thf(fact_11_lfinite__code_I1_J,axiom,
% 0.07/0.34 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 % lfinite_code(1)
% 0.07/0.34 thf(fact_12_lfinite__ldropn,axiom,
% 0.07/0.34 ! [A: $tType,N: nat,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lfinite @ A @ ( coinductive_ldropn @ A @ N @ Xs ) )
% 0.07/0.34 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.07/0.34
% 0.07/0.34 % lfinite_ldropn
% 0.07/0.34 thf(fact_13_lfinite__lzip,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.07/0.34 ( ( coinductive_lfinite @ ( product_prod @ A @ B ) @ ( coinductive_lzip @ A @ B @ Xs @ Ys ) )
% 0.07/0.34 = ( ( coinductive_lfinite @ A @ Xs )
% 0.07/0.34 | ( coinductive_lfinite @ B @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lfinite_lzip
% 0.07/0.34 thf(fact_14_lfinite__code_I2_J,axiom,
% 0.07/0.34 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 0.07/0.34 ( ( coinductive_lfinite @ B @ ( coinductive_LCons @ B @ X @ Xs ) )
% 0.07/0.34 = ( coinductive_lfinite @ B @ Xs ) ) ).
% 0.07/0.34
% 0.07/0.34 % lfinite_code(2)
% 0.07/0.34 thf(fact_15_lfinite__LCons,axiom,
% 0.07/0.34 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.07/0.34 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.07/0.34
% 0.07/0.34 % lfinite_LCons
% 0.07/0.34 thf(fact_16_llist_Oinject,axiom,
% 0.07/0.34 ! [A: $tType,X21: A,X22: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 0.07/0.34 ( ( ( coinductive_LCons @ A @ X21 @ X22 )
% 0.07/0.34 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 0.07/0.34 = ( ( X21 = Y21 )
% 0.07/0.34 & ( X22 = Y22 ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.inject
% 0.07/0.34 thf(fact_17_lzip_Odisc__iff_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.07/0.34 ( ( ~ ( coinductive_lnull @ ( product_prod @ A @ B ) @ ( coinductive_lzip @ A @ B @ Xs @ Ys ) ) )
% 0.07/0.34 = ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 & ~ ( coinductive_lnull @ B @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lzip.disc_iff(2)
% 0.07/0.34 thf(fact_18_lnull__lzip,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.07/0.34 ( ( coinductive_lnull @ ( product_prod @ A @ B ) @ ( coinductive_lzip @ A @ B @ Xs @ Ys ) )
% 0.07/0.34 = ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 | ( coinductive_lnull @ B @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lnull_lzip
% 0.07/0.34 thf(fact_19_lzip__simps_I2_J,axiom,
% 0.07/0.34 ! [D: $tType,C: $tType,Xs: coinductive_llist @ C] :
% 0.07/0.34 ( ( coinductive_lzip @ C @ D @ Xs @ ( coinductive_LNil @ D ) )
% 0.07/0.34 = ( coinductive_LNil @ ( product_prod @ C @ D ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lzip_simps(2)
% 0.07/0.34 thf(fact_20_lzip__simps_I1_J,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,Ys: coinductive_llist @ B] :
% 0.07/0.34 ( ( coinductive_lzip @ A @ B @ ( coinductive_LNil @ A ) @ Ys )
% 0.07/0.34 = ( coinductive_LNil @ ( product_prod @ A @ B ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lzip_simps(1)
% 0.07/0.34 thf(fact_21_ldropn__LNil,axiom,
% 0.07/0.34 ! [A: $tType,N: nat] :
% 0.07/0.34 ( ( coinductive_ldropn @ A @ N @ ( coinductive_LNil @ A ) )
% 0.07/0.34 = ( coinductive_LNil @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 % ldropn_LNil
% 0.07/0.34 thf(fact_22_ldropn__lzip,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,N: nat,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.07/0.34 ( ( coinductive_ldropn @ ( product_prod @ A @ B ) @ N @ ( coinductive_lzip @ A @ B @ Xs @ Ys ) )
% 0.07/0.34 = ( coinductive_lzip @ A @ B @ ( coinductive_ldropn @ A @ N @ Xs ) @ ( coinductive_ldropn @ B @ N @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ldropn_lzip
% 0.07/0.34 thf(fact_23_lmirror__aux__simps_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,Acc: coinductive_llist @ A,Xa: A,X: coinductive_llist @ A] :
% 0.07/0.34 ( ( lMirro999291890or_aux @ A @ Acc @ ( coinductive_LCons @ A @ Xa @ X ) )
% 0.07/0.34 = ( coinductive_LCons @ A @ Xa @ ( lMirro999291890or_aux @ A @ ( coinductive_LCons @ A @ Xa @ Acc ) @ X ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lmirror_aux_simps(2)
% 0.07/0.34 thf(fact_24_lmirror__aux__simps_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,Acc: coinductive_llist @ A] :
% 0.07/0.34 ( ( lMirro999291890or_aux @ A @ Acc @ ( coinductive_LNil @ A ) )
% 0.07/0.34 = Acc ) ).
% 0.07/0.34
% 0.07/0.34 % lmirror_aux_simps(1)
% 0.07/0.34 thf(fact_25_lstrict__prefix__code_I4_J,axiom,
% 0.07/0.34 ! [B: $tType,X: B,Xs: coinductive_llist @ B,Y: B,Ys: coinductive_llist @ B] :
% 0.07/0.34 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 0.07/0.34 = ( ( X = Y )
% 0.07/0.34 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lstrict_prefix_code(4)
% 0.07/0.34 thf(fact_26_lstrict__prefix__code_I1_J,axiom,
% 0.07/0.34 ! [A: $tType] :
% 0.07/0.34 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 % lstrict_prefix_code(1)
% 0.07/0.34 thf(fact_27_lstrict__prefix__code_I3_J,axiom,
% 0.07/0.34 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 0.07/0.34 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 0.07/0.34
% 0.07/0.34 % lstrict_prefix_code(3)
% 0.07/0.34 thf(fact_28_lstrict__prefix__code_I2_J,axiom,
% 0.07/0.34 ! [B: $tType,Y: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y @ Ys ) ) ).
% 0.07/0.34
% 0.07/0.34 % lstrict_prefix_code(2)
% 0.07/0.34 thf(fact_29_lzip_Octr_I1_J,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.07/0.34 ( ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 | ( coinductive_lnull @ B @ Ys ) )
% 0.07/0.34 => ( ( coinductive_lzip @ A @ B @ Xs @ Ys )
% 0.07/0.34 = ( coinductive_LNil @ ( product_prod @ A @ B ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lzip.ctr(1)
% 0.07/0.34 thf(fact_30_ltl__simps_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_ltl @ A @ ( coinductive_LCons @ A @ X21 @ X22 ) )
% 0.07/0.34 = X22 ) ).
% 0.07/0.34
% 0.07/0.34 % ltl_simps(2)
% 0.07/0.34 thf(fact_31_ltl__simps_I1_J,axiom,
% 0.07/0.34 ! [A: $tType] :
% 0.07/0.34 ( ( coinductive_ltl @ A @ ( coinductive_LNil @ A ) )
% 0.07/0.34 = ( coinductive_LNil @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltl_simps(1)
% 0.07/0.34 thf(fact_32_lzip_Odisc_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.07/0.34 ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ B @ Ys )
% 0.07/0.34 => ~ ( coinductive_lnull @ ( product_prod @ A @ B ) @ ( coinductive_lzip @ A @ B @ Xs @ Ys ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lzip.disc(2)
% 0.07/0.34 thf(fact_33_lzip_Odisc_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.07/0.34 ( ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 | ( coinductive_lnull @ B @ Ys ) )
% 0.07/0.34 => ( coinductive_lnull @ ( product_prod @ A @ B ) @ ( coinductive_lzip @ A @ B @ Xs @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lzip.disc(1)
% 0.07/0.34 thf(fact_34_llist_Odisc_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 0.07/0.34 ~ ( coinductive_lnull @ A @ ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.disc(2)
% 0.07/0.34 thf(fact_35_llist_Odisc_I1_J,axiom,
% 0.07/0.34 ! [A: $tType] : ( coinductive_lnull @ A @ ( coinductive_LNil @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.disc(1)
% 0.07/0.34 thf(fact_36_llist_OdiscI_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,Llist: coinductive_llist @ A,X21: A,X22: coinductive_llist @ A] :
% 0.07/0.34 ( ( Llist
% 0.07/0.34 = ( coinductive_LCons @ A @ X21 @ X22 ) )
% 0.07/0.34 => ~ ( coinductive_lnull @ A @ Llist ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.discI(2)
% 0.07/0.34 thf(fact_37_llist_OdiscI_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,Llist: coinductive_llist @ A] :
% 0.07/0.34 ( ( Llist
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 => ( coinductive_lnull @ A @ Llist ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.discI(1)
% 0.07/0.34 thf(fact_38_llist_Ocollapse_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,Llist: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ Llist )
% 0.07/0.34 => ( Llist
% 0.07/0.34 = ( coinductive_LNil @ A ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.collapse(1)
% 0.07/0.34 thf(fact_39_llist_Odistinct_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_LNil @ A )
% 0.07/0.34 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.distinct(1)
% 0.07/0.34 thf(fact_40_lmirror__aux_Octr_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Acc: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_lnull @ A @ Acc )
% 0.07/0.34 => ( ( lMirro999291890or_aux @ A @ Acc @ Xs )
% 0.07/0.34 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lmirror_aux.ctr(1)
% 0.07/0.34 thf(fact_41_ltl__lzip,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.07/0.34 ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ B @ Ys )
% 0.07/0.34 => ( ( coinductive_ltl @ ( product_prod @ A @ B ) @ ( coinductive_lzip @ A @ B @ Xs @ Ys ) )
% 0.07/0.34 = ( coinductive_lzip @ A @ B @ ( coinductive_ltl @ A @ Xs ) @ ( coinductive_ltl @ B @ Ys ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltl_lzip
% 0.07/0.34 thf(fact_42_lnull__ltlI,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( coinductive_lnull @ A @ ( coinductive_ltl @ A @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lnull_ltlI
% 0.07/0.34 thf(fact_43_ltl__ldropn,axiom,
% 0.07/0.34 ! [A: $tType,N: nat,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_ltl @ A @ ( coinductive_ldropn @ A @ N @ Xs ) )
% 0.07/0.34 = ( coinductive_ldropn @ A @ N @ ( coinductive_ltl @ A @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltl_ldropn
% 0.07/0.34 thf(fact_44_mem__Collect__eq,axiom,
% 0.07/0.34 ! [A: $tType,A2: A,P: A > $o] :
% 0.07/0.34 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 0.07/0.34 = ( P @ A2 ) ) ).
% 0.07/0.34
% 0.07/0.34 % mem_Collect_eq
% 0.07/0.34 thf(fact_45_Collect__mem__eq,axiom,
% 0.07/0.34 ! [A: $tType,A3: set @ A] :
% 0.07/0.34 ( ( collect @ A
% 0.07/0.34 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 0.07/0.34 = A3 ) ).
% 0.07/0.34
% 0.07/0.34 % Collect_mem_eq
% 0.07/0.34 thf(fact_46_Collect__cong,axiom,
% 0.07/0.34 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.07/0.34 ( ! [X3: A] :
% 0.07/0.34 ( ( P @ X3 )
% 0.07/0.34 = ( Q @ X3 ) )
% 0.07/0.34 => ( ( collect @ A @ P )
% 0.07/0.34 = ( collect @ A @ Q ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % Collect_cong
% 0.07/0.34 thf(fact_47_ext,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.07/0.34 ( ! [X3: A] :
% 0.07/0.34 ( ( F @ X3 )
% 0.07/0.34 = ( G @ X3 ) )
% 0.07/0.34 => ( F = G ) ) ).
% 0.07/0.34
% 0.07/0.34 % ext
% 0.07/0.34 thf(fact_48_ldropn__lnull,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,N: nat] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_ldropn @ A @ N @ Xs )
% 0.07/0.34 = ( coinductive_LNil @ A ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ldropn_lnull
% 0.07/0.34 thf(fact_49_lzip_Oexhaust,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.07/0.34 ( ~ ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 | ( coinductive_lnull @ B @ Ys ) )
% 0.07/0.34 => ~ ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( coinductive_lnull @ B @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lzip.exhaust
% 0.07/0.34 thf(fact_50_lfinite_Ocases,axiom,
% 0.07/0.34 ! [A: $tType,A2: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lfinite @ A @ A2 )
% 0.07/0.34 => ( ( A2
% 0.07/0.34 != ( coinductive_LNil @ A ) )
% 0.07/0.34 => ~ ! [Xs2: coinductive_llist @ A] :
% 0.07/0.34 ( ? [X3: A] :
% 0.07/0.34 ( A2
% 0.07/0.34 = ( coinductive_LCons @ A @ X3 @ Xs2 ) )
% 0.07/0.34 => ~ ( coinductive_lfinite @ A @ Xs2 ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lfinite.cases
% 0.07/0.34 thf(fact_51_lfinite_Osimps,axiom,
% 0.07/0.34 ! [A: $tType] :
% 0.07/0.34 ( ( coinductive_lfinite @ A )
% 0.07/0.34 = ( ^ [A4: coinductive_llist @ A] :
% 0.07/0.34 ( ( A4
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 | ? [Xs3: coinductive_llist @ A,X2: A] :
% 0.07/0.34 ( ( A4
% 0.07/0.34 = ( coinductive_LCons @ A @ X2 @ Xs3 ) )
% 0.07/0.34 & ( coinductive_lfinite @ A @ Xs3 ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lfinite.simps
% 0.07/0.34 thf(fact_52_llimit__induct,axiom,
% 0.07/0.34 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( P @ ( coinductive_LNil @ A ) )
% 0.07/0.34 => ( ! [X3: A,Xs2: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lfinite @ A @ Xs2 )
% 0.07/0.34 => ( ( P @ Xs2 )
% 0.07/0.34 => ( P @ ( coinductive_LCons @ A @ X3 @ Xs2 ) ) ) )
% 0.07/0.34 => ( ( ! [Ys2: coinductive_llist @ A] :
% 0.07/0.34 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs )
% 0.07/0.34 => ( P @ Ys2 ) )
% 0.07/0.34 => ( P @ Xs ) )
% 0.07/0.34 => ( P @ Xs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llimit_induct
% 0.07/0.34 thf(fact_53_llist_Oexhaust,axiom,
% 0.07/0.34 ! [A: $tType,Y: coinductive_llist @ A] :
% 0.07/0.34 ( ( Y
% 0.07/0.34 != ( coinductive_LNil @ A ) )
% 0.07/0.34 => ~ ! [X212: A,X222: coinductive_llist @ A] :
% 0.07/0.34 ( Y
% 0.07/0.34 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.exhaust
% 0.07/0.34 thf(fact_54_neq__LNil__conv,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( Xs
% 0.07/0.34 != ( coinductive_LNil @ A ) )
% 0.07/0.34 = ( ? [X2: A,Xs4: coinductive_llist @ A] :
% 0.07/0.34 ( Xs
% 0.07/0.34 = ( coinductive_LCons @ A @ X2 @ Xs4 ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % neq_LNil_conv
% 0.07/0.34 thf(fact_55_not__lnull__conv,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( ~ ( coinductive_lnull @ A @ Xs ) )
% 0.07/0.34 = ( ? [X2: A,Xs4: coinductive_llist @ A] :
% 0.07/0.34 ( Xs
% 0.07/0.34 = ( coinductive_LCons @ A @ X2 @ Xs4 ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % not_lnull_conv
% 0.07/0.34 thf(fact_56_lappend_Oexhaust,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ~ ( coinductive_lnull @ A @ Ys ) )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lappend.exhaust
% 0.07/0.34 thf(fact_57_lfinite_Oinducts,axiom,
% 0.07/0.34 ! [A: $tType,X: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.07/0.34 ( ( coinductive_lfinite @ A @ X )
% 0.07/0.34 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.07/0.34 => ( ! [Xs2: coinductive_llist @ A,X3: A] :
% 0.07/0.34 ( ( coinductive_lfinite @ A @ Xs2 )
% 0.07/0.34 => ( ( P @ Xs2 )
% 0.07/0.34 => ( P @ ( coinductive_LCons @ A @ X3 @ Xs2 ) ) ) )
% 0.07/0.34 => ( P @ X ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lfinite.inducts
% 0.07/0.34 thf(fact_58_lnull__def,axiom,
% 0.07/0.34 ! [A: $tType] :
% 0.07/0.34 ( ( coinductive_lnull @ A )
% 0.07/0.34 = ( ^ [Llist2: coinductive_llist @ A] :
% 0.07/0.34 ( Llist2
% 0.07/0.34 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lnull_def
% 0.07/0.34 thf(fact_59_llist__less__induct,axiom,
% 0.07/0.34 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ! [Xs2: coinductive_llist @ A] :
% 0.07/0.34 ( ! [Ys2: coinductive_llist @ A] :
% 0.07/0.34 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs2 )
% 0.07/0.34 => ( P @ Ys2 ) )
% 0.07/0.34 => ( P @ Xs2 ) )
% 0.07/0.34 => ( P @ Xs ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist_less_induct
% 0.07/0.34 thf(fact_60_lzip__eq__LNil__conv,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.07/0.34 ( ( ( coinductive_lzip @ A @ B @ Xs @ Ys )
% 0.07/0.34 = ( coinductive_LNil @ ( product_prod @ A @ B ) ) )
% 0.07/0.34 = ( ( Xs
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 | ( Ys
% 0.07/0.34 = ( coinductive_LNil @ B ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lzip_eq_LNil_conv
% 0.07/0.34 thf(fact_61_lfinite__LConsI,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 0.07/0.34 ( ( coinductive_lfinite @ A @ Xs )
% 0.07/0.34 => ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lfinite_LConsI
% 0.07/0.34 thf(fact_62_lfinite__LNil,axiom,
% 0.07/0.34 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 % lfinite_LNil
% 0.07/0.34 thf(fact_63_lmirror__aux_Odisc_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Acc: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_lnull @ A @ Acc )
% 0.07/0.34 => ( coinductive_lnull @ A @ ( lMirro999291890or_aux @ A @ Acc @ Xs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lmirror_aux.disc(1)
% 0.07/0.34 thf(fact_64_lmirror__aux_Odisc_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Acc: coinductive_llist @ A] :
% 0.07/0.34 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 | ~ ( coinductive_lnull @ A @ Acc ) )
% 0.07/0.34 => ~ ( coinductive_lnull @ A @ ( lMirro999291890or_aux @ A @ Acc @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lmirror_aux.disc(2)
% 0.07/0.34 thf(fact_65_lmirror__def,axiom,
% 0.07/0.34 ! [A: $tType] :
% 0.07/0.34 ( ( lMirro427583474mirror @ A )
% 0.07/0.34 = ( lMirro999291890or_aux @ A @ ( coinductive_LNil @ A ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lmirror_def
% 0.07/0.34 thf(fact_66_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.07/0.34 = ( ( Xs
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 | ? [Xs4: coinductive_llist @ A] :
% 0.07/0.34 ( ( Xs
% 0.07/0.34 = ( coinductive_LCons @ A @ Y @ Xs4 ) )
% 0.07/0.34 & ( coindu328551480prefix @ A @ Xs4 @ Ys ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % Coinductive_List.finite_lprefix_nitpick_simps(3)
% 0.07/0.34 thf(fact_67_ltl__lmirror__aux,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Acc: coinductive_llist @ A] :
% 0.07/0.34 ( ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_ltl @ A @ ( lMirro999291890or_aux @ A @ Acc @ Xs ) )
% 0.07/0.34 = ( coinductive_ltl @ A @ Acc ) ) )
% 0.07/0.34 & ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_ltl @ A @ ( lMirro999291890or_aux @ A @ Acc @ Xs ) )
% 0.07/0.34 = ( lMirro999291890or_aux @ A @ ( coinductive_LCons @ A @ ( coinductive_lhd @ A @ Xs ) @ Acc ) @ ( coinductive_ltl @ A @ Xs ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltl_lmirror_aux
% 0.07/0.34 thf(fact_68_llast__singleton,axiom,
% 0.07/0.34 ! [A: $tType,X: A] :
% 0.07/0.34 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) )
% 0.07/0.34 = X ) ).
% 0.07/0.34
% 0.07/0.34 % llast_singleton
% 0.07/0.34 thf(fact_69_lhd__LCons__ltl,axiom,
% 0.07/0.34 ! [A: $tType,Llist: coinductive_llist @ A] :
% 0.07/0.34 ( ~ ( coinductive_lnull @ A @ Llist )
% 0.07/0.34 => ( ( coinductive_LCons @ A @ ( coinductive_lhd @ A @ Llist ) @ ( coinductive_ltl @ A @ Llist ) )
% 0.07/0.34 = Llist ) ) ).
% 0.07/0.34
% 0.07/0.34 % lhd_LCons_ltl
% 0.07/0.34 thf(fact_70_lmember__code_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,X: A] :
% 0.07/0.34 ~ ( coinductive_lmember @ A @ X @ ( coinductive_LNil @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 % lmember_code(1)
% 0.07/0.34 thf(fact_71_lmember__code_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,X: A,Y: A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lmember @ A @ X @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.07/0.34 = ( ( X = Y )
% 0.07/0.34 | ( coinductive_lmember @ A @ X @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lmember_code(2)
% 0.07/0.34 thf(fact_72_lstrict__prefix__lappend__conv,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coindu1478340336prefix @ A @ Xs @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.07/0.34 = ( ( coinductive_lfinite @ A @ Xs )
% 0.07/0.34 & ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lstrict_prefix_lappend_conv
% 0.07/0.34 thf(fact_73_gen__lset__code_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,A3: set @ A] :
% 0.07/0.34 ( ( coinductive_gen_lset @ A @ A3 @ ( coinductive_LNil @ A ) )
% 0.07/0.34 = A3 ) ).
% 0.07/0.34
% 0.07/0.34 % gen_lset_code(1)
% 0.07/0.34 thf(fact_74_llast__LCons,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 0.07/0.34 ( ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.07/0.34 = X ) )
% 0.07/0.34 & ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.07/0.34 = ( coinductive_llast @ A @ Xs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llast_LCons
% 0.07/0.34 thf(fact_75_lappend__code_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,Xa: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa @ X ) @ Ys )
% 0.07/0.34 = ( coinductive_LCons @ A @ Xa @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lappend_code(2)
% 0.07/0.34 thf(fact_76_lnull__lappend,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.07/0.34 = ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 & ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lnull_lappend
% 0.07/0.34 thf(fact_77_lappend_Odisc__iff_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) )
% 0.07/0.34 = ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lappend.disc_iff(2)
% 0.07/0.34 thf(fact_78_lappend__LNil2,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.07/0.34 = Xs ) ).
% 0.07/0.34
% 0.07/0.34 % lappend_LNil2
% 0.07/0.34 thf(fact_79_lappend__code_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 0.07/0.34 = Ys ) ).
% 0.07/0.34
% 0.07/0.34 % lappend_code(1)
% 0.07/0.34 thf(fact_80_lfinite__lappend,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lfinite @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.07/0.34 = ( ( coinductive_lfinite @ A @ Xs )
% 0.07/0.34 & ( coinductive_lfinite @ A @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lfinite_lappend
% 0.07/0.34 thf(fact_81_llast__LCons2,axiom,
% 0.07/0.34 ! [A: $tType,X: A,Y: A,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs ) ) )
% 0.07/0.34 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llast_LCons2
% 0.07/0.34 thf(fact_82_ltl__lappend,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_ltl @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.07/0.34 = ( coinductive_ltl @ A @ Ys ) ) )
% 0.07/0.34 & ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_ltl @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.07/0.34 = ( coinductive_lappend @ A @ ( coinductive_ltl @ A @ Xs ) @ Ys ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltl_lappend
% 0.07/0.34 thf(fact_83_lhd__lappend,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_lhd @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.07/0.34 = ( coinductive_lhd @ A @ Ys ) ) )
% 0.07/0.34 & ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_lhd @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.07/0.34 = ( coinductive_lhd @ A @ Xs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lhd_lappend
% 0.07/0.34 thf(fact_84_llast__lappend__LCons,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lfinite @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) )
% 0.07/0.34 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llast_lappend_LCons
% 0.07/0.34 thf(fact_85_lappend__assoc,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 0.07/0.34 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lappend_assoc
% 0.07/0.34 thf(fact_86_lhd__LCons,axiom,
% 0.07/0.34 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lhd @ A @ ( coinductive_LCons @ A @ X21 @ X22 ) )
% 0.07/0.34 = X21 ) ).
% 0.07/0.34
% 0.07/0.34 % lhd_LCons
% 0.07/0.34 thf(fact_87_ltakeWhile_Oexhaust,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 0.07/0.34 ( ~ ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 | ~ ( P @ ( coinductive_lhd @ A @ Xs ) ) )
% 0.07/0.34 => ~ ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ~ ( P @ ( coinductive_lhd @ A @ Xs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltakeWhile.exhaust
% 0.07/0.34 thf(fact_88_lappend__lnull2,axiom,
% 0.07/0.34 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ Ys )
% 0.07/0.34 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.07/0.34 = Xs ) ) ).
% 0.07/0.34
% 0.07/0.34 % lappend_lnull2
% 0.07/0.34 thf(fact_89_lappend__lnull1,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.07/0.34 = Ys ) ) ).
% 0.07/0.34
% 0.07/0.34 % lappend_lnull1
% 0.07/0.34 thf(fact_90_lappend_Odisc_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_lnull @ A @ Ys )
% 0.07/0.34 => ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lappend.disc(1)
% 0.07/0.34 thf(fact_91_lappend_Odisc_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 | ~ ( coinductive_lnull @ A @ Ys ) )
% 0.07/0.34 => ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lappend.disc(2)
% 0.07/0.34 thf(fact_92_lappend__eq__LNil__iff,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 = ( ( Xs
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 & ( Ys
% 0.07/0.34 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lappend_eq_LNil_iff
% 0.07/0.34 thf(fact_93_LNil__eq__lappend__iff,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( ( coinductive_LNil @ A )
% 0.07/0.34 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.07/0.34 = ( ( Xs
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 & ( Ys
% 0.07/0.34 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % LNil_eq_lappend_iff
% 0.07/0.34 thf(fact_94_lappend__LNil__LNil,axiom,
% 0.07/0.34 ! [A: $tType] :
% 0.07/0.34 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 0.07/0.34 = ( coinductive_LNil @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 % lappend_LNil_LNil
% 0.07/0.34 thf(fact_95_lappend__inf,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.07/0.34 = Xs ) ) ).
% 0.07/0.34
% 0.07/0.34 % lappend_inf
% 0.07/0.34 thf(fact_96_lappend__snocL1__conv__LCons2,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 0.07/0.34 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lappend_snocL1_conv_LCons2
% 0.07/0.34 thf(fact_97_lappend_Octr_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_lnull @ A @ Ys )
% 0.07/0.34 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.07/0.34 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lappend.ctr(1)
% 0.07/0.34 thf(fact_98_llist_Ocoinduct__strong,axiom,
% 0.07/0.34 ! [A: $tType,R: ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o,Llist: coinductive_llist @ A,Llist3: coinductive_llist @ A] :
% 0.07/0.34 ( ( R @ Llist @ Llist3 )
% 0.07/0.34 => ( ! [Llist4: coinductive_llist @ A,Llist5: coinductive_llist @ A] :
% 0.07/0.34 ( ( R @ Llist4 @ Llist5 )
% 0.07/0.34 => ( ( ( coinductive_lnull @ A @ Llist4 )
% 0.07/0.34 = ( coinductive_lnull @ A @ Llist5 ) )
% 0.07/0.34 & ( ~ ( coinductive_lnull @ A @ Llist4 )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ Llist5 )
% 0.07/0.34 => ( ( ( coinductive_lhd @ A @ Llist4 )
% 0.07/0.34 = ( coinductive_lhd @ A @ Llist5 ) )
% 0.07/0.34 & ( ( R @ ( coinductive_ltl @ A @ Llist4 ) @ ( coinductive_ltl @ A @ Llist5 ) )
% 0.07/0.34 | ( ( coinductive_ltl @ A @ Llist4 )
% 0.07/0.34 = ( coinductive_ltl @ A @ Llist5 ) ) ) ) ) ) ) )
% 0.07/0.34 => ( Llist = Llist3 ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.coinduct_strong
% 0.07/0.34 thf(fact_99_llist_Ocoinduct,axiom,
% 0.07/0.34 ! [A: $tType,R: ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o,Llist: coinductive_llist @ A,Llist3: coinductive_llist @ A] :
% 0.07/0.34 ( ( R @ Llist @ Llist3 )
% 0.07/0.34 => ( ! [Llist4: coinductive_llist @ A,Llist5: coinductive_llist @ A] :
% 0.07/0.34 ( ( R @ Llist4 @ Llist5 )
% 0.07/0.34 => ( ( ( coinductive_lnull @ A @ Llist4 )
% 0.07/0.34 = ( coinductive_lnull @ A @ Llist5 ) )
% 0.07/0.34 & ( ~ ( coinductive_lnull @ A @ Llist4 )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ Llist5 )
% 0.07/0.34 => ( ( ( coinductive_lhd @ A @ Llist4 )
% 0.07/0.34 = ( coinductive_lhd @ A @ Llist5 ) )
% 0.07/0.34 & ( R @ ( coinductive_ltl @ A @ Llist4 ) @ ( coinductive_ltl @ A @ Llist5 ) ) ) ) ) ) )
% 0.07/0.34 => ( Llist = Llist3 ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.coinduct
% 0.07/0.34 thf(fact_100_llist_Oexpand,axiom,
% 0.07/0.34 ! [A: $tType,Llist: coinductive_llist @ A,Llist3: coinductive_llist @ A] :
% 0.07/0.34 ( ( ( coinductive_lnull @ A @ Llist )
% 0.07/0.34 = ( coinductive_lnull @ A @ Llist3 ) )
% 0.07/0.34 => ( ( ~ ( coinductive_lnull @ A @ Llist )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ Llist3 )
% 0.07/0.34 => ( ( ( coinductive_lhd @ A @ Llist )
% 0.07/0.34 = ( coinductive_lhd @ A @ Llist3 ) )
% 0.07/0.34 & ( ( coinductive_ltl @ A @ Llist )
% 0.07/0.34 = ( coinductive_ltl @ A @ Llist3 ) ) ) ) )
% 0.07/0.34 => ( Llist = Llist3 ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.expand
% 0.07/0.34 thf(fact_101_lappend__ltl,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_lappend @ A @ ( coinductive_ltl @ A @ Xs ) @ Ys )
% 0.07/0.34 = ( coinductive_ltl @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lappend_ltl
% 0.07/0.34 thf(fact_102_lhd__lmirror__aux,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Acc: coinductive_llist @ A] :
% 0.07/0.34 ( ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_lhd @ A @ ( lMirro999291890or_aux @ A @ Acc @ Xs ) )
% 0.07/0.34 = ( coinductive_lhd @ A @ Acc ) ) )
% 0.07/0.34 & ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_lhd @ A @ ( lMirro999291890or_aux @ A @ Acc @ Xs ) )
% 0.07/0.34 = ( coinductive_lhd @ A @ Xs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lhd_lmirror_aux
% 0.07/0.34 thf(fact_103_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.07/0.34 = ( Xs
% 0.07/0.34 = ( coinductive_LNil @ A ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % Coinductive_List.finite_lprefix_nitpick_simps(1)
% 0.07/0.34 thf(fact_104_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 0.07/0.34
% 0.07/0.34 % Coinductive_List.finite_lprefix_nitpick_simps(2)
% 0.07/0.34 thf(fact_105_llist_Oexhaust__sel,axiom,
% 0.07/0.34 ! [A: $tType,Llist: coinductive_llist @ A] :
% 0.07/0.34 ( ( Llist
% 0.07/0.34 != ( coinductive_LNil @ A ) )
% 0.07/0.34 => ( Llist
% 0.07/0.34 = ( coinductive_LCons @ A @ ( coinductive_lhd @ A @ Llist ) @ ( coinductive_ltl @ A @ Llist ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.exhaust_sel
% 0.07/0.34 thf(fact_106_eq__LConsD,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( Xs
% 0.07/0.34 = ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.07/0.34 => ( ( Xs
% 0.07/0.34 != ( coinductive_LNil @ A ) )
% 0.07/0.34 & ( ( coinductive_lhd @ A @ Xs )
% 0.07/0.34 = Y )
% 0.07/0.34 & ( ( coinductive_ltl @ A @ Xs )
% 0.07/0.34 = Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % eq_LConsD
% 0.07/0.34 thf(fact_107_lfinite__rev__induct,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.07/0.34 ( ( coinductive_lfinite @ A @ Xs )
% 0.07/0.34 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.07/0.34 => ( ! [X3: A,Xs2: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lfinite @ A @ Xs2 )
% 0.07/0.34 => ( ( P @ Xs2 )
% 0.07/0.34 => ( P @ ( coinductive_lappend @ A @ Xs2 @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) ) ) ) )
% 0.07/0.34 => ( P @ Xs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lfinite_rev_induct
% 0.07/0.34 thf(fact_108_lzip_Ocode,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType] :
% 0.07/0.34 ( ( coinductive_lzip @ A @ B )
% 0.07/0.34 = ( ^ [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ B] :
% 0.07/0.34 ( if @ ( coinductive_llist @ ( product_prod @ A @ B ) )
% 0.07/0.34 @ ( ( coinductive_lnull @ A @ Xs3 )
% 0.07/0.34 | ( coinductive_lnull @ B @ Ys3 ) )
% 0.07/0.34 @ ( coinductive_LNil @ ( product_prod @ A @ B ) )
% 0.07/0.34 @ ( coinductive_LCons @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ ( coinductive_lhd @ A @ Xs3 ) @ ( coinductive_lhd @ B @ Ys3 ) ) @ ( coinductive_lzip @ A @ B @ ( coinductive_ltl @ A @ Xs3 ) @ ( coinductive_ltl @ B @ Ys3 ) ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lzip.code
% 0.07/0.34 thf(fact_109_llexord__conv,axiom,
% 0.07/0.34 ! [A: $tType] :
% 0.07/0.34 ( ( coinductive_llexord @ A )
% 0.07/0.34 = ( ^ [R2: A > A > $o,Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A] :
% 0.07/0.34 ( ( Xs3 = Ys3 )
% 0.07/0.34 | ? [Zs2: coinductive_llist @ A,Xs4: coinductive_llist @ A,Y2: A,Ys4: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lfinite @ A @ Zs2 )
% 0.07/0.34 & ( Xs3
% 0.07/0.34 = ( coinductive_lappend @ A @ Zs2 @ Xs4 ) )
% 0.07/0.34 & ( Ys3
% 0.07/0.34 = ( coinductive_lappend @ A @ Zs2 @ ( coinductive_LCons @ A @ Y2 @ Ys4 ) ) )
% 0.07/0.34 & ( ( Xs4
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 | ( R2 @ ( coinductive_lhd @ A @ Xs4 ) @ Y2 ) ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_conv
% 0.07/0.34 thf(fact_110_llist_Osplit__sel__asm,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( coinductive_llist @ A ) > B,Llist: coinductive_llist @ A] :
% 0.07/0.34 ( ( P @ ( coindu1381640503_llist @ B @ A @ F1 @ F2 @ Llist ) )
% 0.07/0.34 = ( ~ ( ( ( Llist
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 & ~ ( P @ F1 ) )
% 0.07/0.34 | ( ( Llist
% 0.07/0.34 = ( coinductive_LCons @ A @ ( coinductive_lhd @ A @ Llist ) @ ( coinductive_ltl @ A @ Llist ) ) )
% 0.07/0.34 & ~ ( P @ ( F2 @ ( coinductive_lhd @ A @ Llist ) @ ( coinductive_ltl @ A @ Llist ) ) ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.split_sel_asm
% 0.07/0.34 thf(fact_111_llist_Osplit__sel,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( coinductive_llist @ A ) > B,Llist: coinductive_llist @ A] :
% 0.07/0.34 ( ( P @ ( coindu1381640503_llist @ B @ A @ F1 @ F2 @ Llist ) )
% 0.07/0.34 = ( ( ( Llist
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 => ( P @ F1 ) )
% 0.07/0.34 & ( ( Llist
% 0.07/0.34 = ( coinductive_LCons @ A @ ( coinductive_lhd @ A @ Llist ) @ ( coinductive_ltl @ A @ Llist ) ) )
% 0.07/0.34 => ( P @ ( F2 @ ( coinductive_lhd @ A @ Llist ) @ ( coinductive_ltl @ A @ Llist ) ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.split_sel
% 0.07/0.34 thf(fact_112_unfold__llist__id,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coindu1441602521_llist @ ( coinductive_llist @ A ) @ A @ ( coinductive_lnull @ A ) @ ( coinductive_lhd @ A ) @ ( coinductive_ltl @ A ) @ Xs )
% 0.07/0.34 = Xs ) ).
% 0.07/0.34
% 0.07/0.34 % unfold_llist_id
% 0.07/0.34 thf(fact_113_ltakeWhile_Ocode,axiom,
% 0.07/0.34 ! [A: $tType] :
% 0.07/0.34 ( ( coindu501562517eWhile @ A )
% 0.07/0.34 = ( ^ [P2: A > $o,Xs3: coinductive_llist @ A] :
% 0.07/0.34 ( if @ ( coinductive_llist @ A )
% 0.07/0.34 @ ( ( coinductive_lnull @ A @ Xs3 )
% 0.07/0.34 | ~ ( P2 @ ( coinductive_lhd @ A @ Xs3 ) ) )
% 0.07/0.34 @ ( coinductive_LNil @ A )
% 0.07/0.34 @ ( coinductive_LCons @ A @ ( coinductive_lhd @ A @ Xs3 ) @ ( coindu501562517eWhile @ A @ P2 @ ( coinductive_ltl @ A @ Xs3 ) ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltakeWhile.code
% 0.07/0.34 thf(fact_114_llexord__refl,axiom,
% 0.07/0.34 ! [A: $tType,R3: A > A > $o,Xs: coinductive_llist @ A] : ( coinductive_llexord @ A @ R3 @ Xs @ Xs ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_refl
% 0.07/0.34 thf(fact_115_ltakeWhile__LNil,axiom,
% 0.07/0.34 ! [A: $tType,P: A > $o] :
% 0.07/0.34 ( ( coindu501562517eWhile @ A @ P @ ( coinductive_LNil @ A ) )
% 0.07/0.34 = ( coinductive_LNil @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltakeWhile_LNil
% 0.07/0.34 thf(fact_116_llexord__LCons__LCons,axiom,
% 0.07/0.34 ! [A: $tType,R3: A > A > $o,X: A,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_llexord @ A @ R3 @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.07/0.34 = ( ( ( X = Y )
% 0.07/0.34 & ( coinductive_llexord @ A @ R3 @ Xs @ Ys ) )
% 0.07/0.34 | ( R3 @ X @ Y ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_LCons_LCons
% 0.07/0.34 thf(fact_117_llexord__LNil__right,axiom,
% 0.07/0.34 ! [A: $tType,Ys: coinductive_llist @ A,R3: A > A > $o,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ Ys )
% 0.07/0.34 => ( ( coinductive_llexord @ A @ R3 @ Xs @ Ys )
% 0.07/0.34 = ( coinductive_lnull @ A @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_LNil_right
% 0.07/0.34 thf(fact_118_llexord__code_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,R3: A > A > $o,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R3 @ ( coinductive_LNil @ A ) @ Ys ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_code(1)
% 0.07/0.34 thf(fact_119_unfold__llist__eq__LCons,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B2: B,X: A,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ B2 )
% 0.07/0.34 = ( coinductive_LCons @ A @ X @ Xs ) )
% 0.07/0.34 = ( ~ ( IS_LNIL @ B2 )
% 0.07/0.34 & ( X
% 0.07/0.34 = ( LHD @ B2 ) )
% 0.07/0.34 & ( Xs
% 0.07/0.34 = ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B2 ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % unfold_llist_eq_LCons
% 0.07/0.34 thf(fact_120_unfold__llist_Odisc__iff_I2_J,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,P3: A > $o,G21: A > B,G22: A > A,A2: A] :
% 0.07/0.34 ( ( ~ ( coinductive_lnull @ B @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) ) )
% 0.07/0.34 = ( ~ ( P3 @ A2 ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % unfold_llist.disc_iff(2)
% 0.07/0.34 thf(fact_121_unfold__llist_Odisc__iff_I1_J,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,P3: A > $o,G21: A > B,G22: A > A,A2: A] :
% 0.07/0.34 ( ( coinductive_lnull @ B @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) )
% 0.07/0.34 = ( P3 @ A2 ) ) ).
% 0.07/0.34
% 0.07/0.34 % unfold_llist.disc_iff(1)
% 0.07/0.34 thf(fact_122_ltakeWhile__LCons,axiom,
% 0.07/0.34 ! [A: $tType,P: A > $o,X: A,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( ( P @ X )
% 0.07/0.34 => ( ( coindu501562517eWhile @ A @ P @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.07/0.34 = ( coinductive_LCons @ A @ X @ ( coindu501562517eWhile @ A @ P @ Xs ) ) ) )
% 0.07/0.34 & ( ~ ( P @ X )
% 0.07/0.34 => ( ( coindu501562517eWhile @ A @ P @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.07/0.34 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltakeWhile_LCons
% 0.07/0.34 thf(fact_123_ltakeWhile_Odisc__iff_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( ~ ( coinductive_lnull @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) ) )
% 0.07/0.34 = ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 & ( P @ ( coinductive_lhd @ A @ Xs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltakeWhile.disc_iff(2)
% 0.07/0.34 thf(fact_124_ltakeWhile_Odisc__iff_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) )
% 0.07/0.34 = ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 | ~ ( P @ ( coinductive_lhd @ A @ Xs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltakeWhile.disc_iff(1)
% 0.07/0.34 thf(fact_125_lnull__ltakeWhile,axiom,
% 0.07/0.34 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) )
% 0.07/0.34 = ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ~ ( P @ ( coinductive_lhd @ A @ Xs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lnull_ltakeWhile
% 0.07/0.34 thf(fact_126_lzip__simps_I3_J,axiom,
% 0.07/0.34 ! [C: $tType,B: $tType,X: C,Xs: coinductive_llist @ C,Y: B,Ys: coinductive_llist @ B] :
% 0.07/0.34 ( ( coinductive_lzip @ C @ B @ ( coinductive_LCons @ C @ X @ Xs ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 0.07/0.34 = ( coinductive_LCons @ ( product_prod @ C @ B ) @ ( product_Pair @ C @ B @ X @ Y ) @ ( coinductive_lzip @ C @ B @ Xs @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lzip_simps(3)
% 0.07/0.34 thf(fact_127_llexord__antisym,axiom,
% 0.07/0.34 ! [A: $tType,R3: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_llexord @ A @ R3 @ Xs @ Ys )
% 0.07/0.34 => ( ( coinductive_llexord @ A @ R3 @ Ys @ Xs )
% 0.07/0.34 => ( ! [A5: A,B3: A] :
% 0.07/0.34 ( ( R3 @ A5 @ B3 )
% 0.07/0.34 => ~ ( R3 @ B3 @ A5 ) )
% 0.07/0.34 => ( Xs = Ys ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_antisym
% 0.07/0.34 thf(fact_128_llexord__linear,axiom,
% 0.07/0.34 ! [A: $tType,R3: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ! [X3: A,Y3: A] :
% 0.07/0.34 ( ( R3 @ X3 @ Y3 )
% 0.07/0.34 | ( X3 = Y3 )
% 0.07/0.34 | ( R3 @ Y3 @ X3 ) )
% 0.07/0.34 => ( ( coinductive_llexord @ A @ R3 @ Xs @ Ys )
% 0.07/0.34 | ( coinductive_llexord @ A @ R3 @ Ys @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_linear
% 0.07/0.34 thf(fact_129_llexord__trans,axiom,
% 0.07/0.34 ! [A: $tType,R3: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_llexord @ A @ R3 @ Xs @ Ys )
% 0.07/0.34 => ( ( coinductive_llexord @ A @ R3 @ Ys @ Zs )
% 0.07/0.34 => ( ! [A5: A,B3: A,C2: A] :
% 0.07/0.34 ( ( R3 @ A5 @ B3 )
% 0.07/0.34 => ( ( R3 @ B3 @ C2 )
% 0.07/0.34 => ( R3 @ A5 @ C2 ) ) )
% 0.07/0.34 => ( coinductive_llexord @ A @ R3 @ Xs @ Zs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_trans
% 0.07/0.34 thf(fact_130_llexord__code_I3_J,axiom,
% 0.07/0.34 ! [A: $tType,R3: A > A > $o,X: A,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_llexord @ A @ R3 @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.07/0.34 = ( ( R3 @ X @ Y )
% 0.07/0.34 | ( ( X = Y )
% 0.07/0.34 & ( coinductive_llexord @ A @ R3 @ Xs @ Ys ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_code(3)
% 0.07/0.34 thf(fact_131_llexord__LCons__left,axiom,
% 0.07/0.34 ! [A: $tType,R3: A > A > $o,X: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_llexord @ A @ R3 @ ( coinductive_LCons @ A @ X @ Xs ) @ Ys )
% 0.07/0.34 = ( ? [Y2: A,Ys4: coinductive_llist @ A] :
% 0.07/0.34 ( ( Ys
% 0.07/0.34 = ( coinductive_LCons @ A @ Y2 @ Ys4 ) )
% 0.07/0.34 & ( ( ( X = Y2 )
% 0.07/0.34 & ( coinductive_llexord @ A @ R3 @ Xs @ Ys4 ) )
% 0.07/0.34 | ( R3 @ X @ Y2 ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_LCons_left
% 0.07/0.34 thf(fact_132_llexord__LCons__eq,axiom,
% 0.07/0.34 ! [A: $tType,R3: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,X: A] :
% 0.07/0.34 ( ( coinductive_llexord @ A @ R3 @ Xs @ Ys )
% 0.07/0.34 => ( coinductive_llexord @ A @ R3 @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ X @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_LCons_eq
% 0.07/0.34 thf(fact_133_llexord__LCons__less,axiom,
% 0.07/0.34 ! [A: $tType,R3: A > A > $o,X: A,Y: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( R3 @ X @ Y )
% 0.07/0.34 => ( coinductive_llexord @ A @ R3 @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_LCons_less
% 0.07/0.34 thf(fact_134_lnull__llexord,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,R3: A > A > $o,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( coinductive_llexord @ A @ R3 @ Xs @ Ys ) ) ).
% 0.07/0.34
% 0.07/0.34 % lnull_llexord
% 0.07/0.34 thf(fact_135_llexord__LNil,axiom,
% 0.07/0.34 ! [A: $tType,R3: A > A > $o,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R3 @ ( coinductive_LNil @ A ) @ Ys ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_LNil
% 0.07/0.34 thf(fact_136_llexord__lappend__leftI,axiom,
% 0.07/0.34 ! [A: $tType,R3: A > A > $o,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_llexord @ A @ R3 @ Ys @ Zs )
% 0.07/0.34 => ( coinductive_llexord @ A @ R3 @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( coinductive_lappend @ A @ Xs @ Zs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_lappend_leftI
% 0.07/0.34 thf(fact_137_llexord__append__right,axiom,
% 0.07/0.34 ! [A: $tType,R3: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R3 @ Xs @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_append_right
% 0.07/0.34 thf(fact_138_unfold__llist_Octr_I2_J,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.07/0.34 ( ~ ( P3 @ A2 )
% 0.07/0.34 => ( ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A2 )
% 0.07/0.34 = ( coinductive_LCons @ B @ ( G21 @ A2 ) @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ ( G22 @ A2 ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % unfold_llist.ctr(2)
% 0.07/0.34 thf(fact_139_unfold__llist_Odisc_I2_J,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.07/0.34 ( ~ ( P3 @ A2 )
% 0.07/0.34 => ~ ( coinductive_lnull @ B @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % unfold_llist.disc(2)
% 0.07/0.34 thf(fact_140_unfold__llist_Odisc_I1_J,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.07/0.34 ( ( P3 @ A2 )
% 0.07/0.34 => ( coinductive_lnull @ B @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % unfold_llist.disc(1)
% 0.07/0.34 thf(fact_141_unfold__llist_Octr_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.07/0.34 ( ( P3 @ A2 )
% 0.07/0.34 => ( ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A2 )
% 0.07/0.34 = ( coinductive_LNil @ B ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % unfold_llist.ctr(1)
% 0.07/0.34 thf(fact_142_llist_Osimps_I5_J,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,F1: B,F2: A > ( coinductive_llist @ A ) > B,X21: A,X22: coinductive_llist @ A] :
% 0.07/0.34 ( ( coindu1381640503_llist @ B @ A @ F1 @ F2 @ ( coinductive_LCons @ A @ X21 @ X22 ) )
% 0.07/0.34 = ( F2 @ X21 @ X22 ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.simps(5)
% 0.07/0.34 thf(fact_143_llist_Osimps_I4_J,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,F1: B,F2: A > ( coinductive_llist @ A ) > B] :
% 0.07/0.34 ( ( coindu1381640503_llist @ B @ A @ F1 @ F2 @ ( coinductive_LNil @ A ) )
% 0.07/0.34 = F1 ) ).
% 0.07/0.34
% 0.07/0.34 % llist.simps(4)
% 0.07/0.34 thf(fact_144_unfold__llist_Osimps_I4_J,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.07/0.34 ( ~ ( P3 @ A2 )
% 0.07/0.34 => ( ( coinductive_ltl @ B @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) )
% 0.07/0.34 = ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ ( G22 @ A2 ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % unfold_llist.simps(4)
% 0.07/0.34 thf(fact_145_unfold__llist_Osimps_I3_J,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 0.07/0.34 ( ~ ( P3 @ A2 )
% 0.07/0.34 => ( ( coinductive_lhd @ B @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) )
% 0.07/0.34 = ( G21 @ A2 ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % unfold_llist.simps(3)
% 0.07/0.34 thf(fact_146_lhd__ltakeWhile,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 0.07/0.34 ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( P @ ( coinductive_lhd @ A @ Xs ) )
% 0.07/0.34 => ( ( coinductive_lhd @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) )
% 0.07/0.34 = ( coinductive_lhd @ A @ Xs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lhd_ltakeWhile
% 0.07/0.34 thf(fact_147_ltakeWhile_Odisc_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 0.07/0.34 ( ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 | ~ ( P @ ( coinductive_lhd @ A @ Xs ) ) )
% 0.07/0.34 => ( coinductive_lnull @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltakeWhile.disc(1)
% 0.07/0.34 thf(fact_148_ltakeWhile_Odisc_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 0.07/0.34 ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( P @ ( coinductive_lhd @ A @ Xs ) )
% 0.07/0.34 => ~ ( coinductive_lnull @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltakeWhile.disc(2)
% 0.07/0.34 thf(fact_149_ltakeWhile__eq__LNil__iff,axiom,
% 0.07/0.34 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( ( coindu501562517eWhile @ A @ P @ Xs )
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 = ( ( Xs
% 0.07/0.34 != ( coinductive_LNil @ A ) )
% 0.07/0.34 => ~ ( P @ ( coinductive_lhd @ A @ Xs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltakeWhile_eq_LNil_iff
% 0.07/0.34 thf(fact_150_lzip__eq__LCons__conv,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,Z: product_prod @ A @ B,Zs: coinductive_llist @ ( product_prod @ A @ B )] :
% 0.07/0.34 ( ( ( coinductive_lzip @ A @ B @ Xs @ Ys )
% 0.07/0.34 = ( coinductive_LCons @ ( product_prod @ A @ B ) @ Z @ Zs ) )
% 0.07/0.34 = ( ? [X2: A,Xs4: coinductive_llist @ A,Y2: B,Ys4: coinductive_llist @ B] :
% 0.07/0.34 ( ( Xs
% 0.07/0.34 = ( coinductive_LCons @ A @ X2 @ Xs4 ) )
% 0.07/0.34 & ( Ys
% 0.07/0.34 = ( coinductive_LCons @ B @ Y2 @ Ys4 ) )
% 0.07/0.34 & ( Z
% 0.07/0.34 = ( product_Pair @ A @ B @ X2 @ Y2 ) )
% 0.07/0.34 & ( Zs
% 0.07/0.34 = ( coinductive_lzip @ A @ B @ Xs4 @ Ys4 ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lzip_eq_LCons_conv
% 0.07/0.34 thf(fact_151_llexord__code_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,R3: A > A > $o,X: A,Xs: coinductive_llist @ A] :
% 0.07/0.34 ~ ( coinductive_llexord @ A @ R3 @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LNil @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_code(2)
% 0.07/0.34 thf(fact_152_llexord_Ocases,axiom,
% 0.07/0.34 ! [A: $tType,R3: A > A > $o,A1: coinductive_llist @ A,A22: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_llexord @ A @ R3 @ A1 @ A22 )
% 0.07/0.34 => ( ! [Xs2: coinductive_llist @ A,Ys5: coinductive_llist @ A,X3: A] :
% 0.07/0.34 ( ( A1
% 0.07/0.34 = ( coinductive_LCons @ A @ X3 @ Xs2 ) )
% 0.07/0.34 => ( ( A22
% 0.07/0.34 = ( coinductive_LCons @ A @ X3 @ Ys5 ) )
% 0.07/0.34 => ~ ( coinductive_llexord @ A @ R3 @ Xs2 @ Ys5 ) ) )
% 0.07/0.34 => ( ! [X3: A] :
% 0.07/0.34 ( ? [Xs2: coinductive_llist @ A] :
% 0.07/0.34 ( A1
% 0.07/0.34 = ( coinductive_LCons @ A @ X3 @ Xs2 ) )
% 0.07/0.34 => ! [Y3: A] :
% 0.07/0.34 ( ? [Ys5: coinductive_llist @ A] :
% 0.07/0.34 ( A22
% 0.07/0.34 = ( coinductive_LCons @ A @ Y3 @ Ys5 ) )
% 0.07/0.34 => ~ ( R3 @ X3 @ Y3 ) ) )
% 0.07/0.34 => ~ ( ( A1
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 => ! [Ys5: coinductive_llist @ A] : ( A22 != Ys5 ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord.cases
% 0.07/0.34 thf(fact_153_llexord_Osimps,axiom,
% 0.07/0.34 ! [A: $tType] :
% 0.07/0.34 ( ( coinductive_llexord @ A )
% 0.07/0.34 = ( ^ [R2: A > A > $o,A12: coinductive_llist @ A,A23: coinductive_llist @ A] :
% 0.07/0.34 ( ? [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A,X2: A] :
% 0.07/0.34 ( ( A12
% 0.07/0.34 = ( coinductive_LCons @ A @ X2 @ Xs3 ) )
% 0.07/0.34 & ( A23
% 0.07/0.34 = ( coinductive_LCons @ A @ X2 @ Ys3 ) )
% 0.07/0.34 & ( coinductive_llexord @ A @ R2 @ Xs3 @ Ys3 ) )
% 0.07/0.34 | ? [X2: A,Y2: A,Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A] :
% 0.07/0.34 ( ( A12
% 0.07/0.34 = ( coinductive_LCons @ A @ X2 @ Xs3 ) )
% 0.07/0.34 & ( A23
% 0.07/0.34 = ( coinductive_LCons @ A @ Y2 @ Ys3 ) )
% 0.07/0.34 & ( R2 @ X2 @ Y2 ) )
% 0.07/0.34 | ? [Ys3: coinductive_llist @ A] :
% 0.07/0.34 ( ( A12
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 & ( A23 = Ys3 ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord.simps
% 0.07/0.34 thf(fact_154_llexord_Ocoinduct,axiom,
% 0.07/0.34 ! [A: $tType,X4: ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,Xa: coinductive_llist @ A,R3: A > A > $o] :
% 0.07/0.34 ( ( X4 @ X @ Xa )
% 0.07/0.34 => ( ! [X3: coinductive_llist @ A,Xa2: coinductive_llist @ A] :
% 0.07/0.34 ( ( X4 @ X3 @ Xa2 )
% 0.07/0.34 => ( ? [Xs5: coinductive_llist @ A,Ys2: coinductive_llist @ A,Xb: A] :
% 0.07/0.34 ( ( X3
% 0.07/0.34 = ( coinductive_LCons @ A @ Xb @ Xs5 ) )
% 0.07/0.34 & ( Xa2
% 0.07/0.34 = ( coinductive_LCons @ A @ Xb @ Ys2 ) )
% 0.07/0.34 & ( ( X4 @ Xs5 @ Ys2 )
% 0.07/0.34 | ( coinductive_llexord @ A @ R3 @ Xs5 @ Ys2 ) ) )
% 0.07/0.34 | ? [Xb: A,Y4: A,Xs5: coinductive_llist @ A,Ys2: coinductive_llist @ A] :
% 0.07/0.34 ( ( X3
% 0.07/0.34 = ( coinductive_LCons @ A @ Xb @ Xs5 ) )
% 0.07/0.34 & ( Xa2
% 0.07/0.34 = ( coinductive_LCons @ A @ Y4 @ Ys2 ) )
% 0.07/0.34 & ( R3 @ Xb @ Y4 ) )
% 0.07/0.34 | ? [Ys2: coinductive_llist @ A] :
% 0.07/0.34 ( ( X3
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 & ( Xa2 = Ys2 ) ) ) )
% 0.07/0.34 => ( coinductive_llexord @ A @ R3 @ X @ Xa ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord.coinduct
% 0.07/0.34 thf(fact_155_unfold__llist_Ocode,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType] :
% 0.07/0.34 ( ( coindu1441602521_llist @ A @ B )
% 0.07/0.34 = ( ^ [P4: A > $o,G212: A > B,G222: A > A,A4: A] : ( if @ ( coinductive_llist @ B ) @ ( P4 @ A4 ) @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ ( G212 @ A4 ) @ ( coindu1441602521_llist @ A @ B @ P4 @ G212 @ G222 @ ( G222 @ A4 ) ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % unfold_llist.code
% 0.07/0.34 thf(fact_156_ltl__unfold__llist,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,IS_LNIL: B > $o,A2: B,LHD: B > A,LTL: B > B] :
% 0.07/0.34 ( ( ( IS_LNIL @ A2 )
% 0.07/0.34 => ( ( coinductive_ltl @ A @ ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 0.07/0.34 = ( coinductive_LNil @ A ) ) )
% 0.07/0.34 & ( ~ ( IS_LNIL @ A2 )
% 0.07/0.34 => ( ( coinductive_ltl @ A @ ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 0.07/0.34 = ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ A2 ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltl_unfold_llist
% 0.07/0.34 thf(fact_157_ltakeWhile_Octr_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 0.07/0.34 ( ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 | ~ ( P @ ( coinductive_lhd @ A @ Xs ) ) )
% 0.07/0.34 => ( ( coindu501562517eWhile @ A @ P @ Xs )
% 0.07/0.34 = ( coinductive_LNil @ A ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltakeWhile.ctr(1)
% 0.07/0.34 thf(fact_158_ltakeWhile_Osimps_I4_J,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 0.07/0.34 ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( P @ ( coinductive_lhd @ A @ Xs ) )
% 0.07/0.34 => ( ( coinductive_ltl @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) )
% 0.07/0.34 = ( coindu501562517eWhile @ A @ P @ ( coinductive_ltl @ A @ Xs ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltakeWhile.simps(4)
% 0.07/0.34 thf(fact_159_ltl__ltakeWhile,axiom,
% 0.07/0.34 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( ( P @ ( coinductive_lhd @ A @ Xs ) )
% 0.07/0.34 => ( ( coinductive_ltl @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) )
% 0.07/0.34 = ( coindu501562517eWhile @ A @ P @ ( coinductive_ltl @ A @ Xs ) ) ) )
% 0.07/0.34 & ( ~ ( P @ ( coinductive_lhd @ A @ Xs ) )
% 0.07/0.34 => ( ( coinductive_ltl @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) )
% 0.07/0.34 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltl_ltakeWhile
% 0.07/0.34 thf(fact_160_lhd__lzip,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.07/0.34 ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ B @ Ys )
% 0.07/0.34 => ( ( coinductive_lhd @ ( product_prod @ A @ B ) @ ( coinductive_lzip @ A @ B @ Xs @ Ys ) )
% 0.07/0.34 = ( product_Pair @ A @ B @ ( coinductive_lhd @ A @ Xs ) @ ( coinductive_lhd @ B @ Ys ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lhd_lzip
% 0.07/0.34 thf(fact_161_llexord__coinduct,axiom,
% 0.07/0.34 ! [A: $tType,X4: ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,R3: A > A > $o] :
% 0.07/0.34 ( ( X4 @ Xs @ Ys )
% 0.07/0.34 => ( ! [Xs2: coinductive_llist @ A,Ys5: coinductive_llist @ A] :
% 0.07/0.34 ( ( X4 @ Xs2 @ Ys5 )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ Xs2 )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ Ys5 )
% 0.07/0.34 & ( ~ ( coinductive_lnull @ A @ Ys5 )
% 0.07/0.34 => ( ( R3 @ ( coinductive_lhd @ A @ Xs2 ) @ ( coinductive_lhd @ A @ Ys5 ) )
% 0.07/0.34 | ( ( ( coinductive_lhd @ A @ Xs2 )
% 0.07/0.34 = ( coinductive_lhd @ A @ Ys5 ) )
% 0.07/0.34 & ( ( X4 @ ( coinductive_ltl @ A @ Xs2 ) @ ( coinductive_ltl @ A @ Ys5 ) )
% 0.07/0.34 | ( coinductive_llexord @ A @ R3 @ ( coinductive_ltl @ A @ Xs2 ) @ ( coinductive_ltl @ A @ Ys5 ) ) ) ) ) ) ) ) )
% 0.07/0.34 => ( coinductive_llexord @ A @ R3 @ Xs @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_coinduct
% 0.07/0.34 thf(fact_162_ltakeWhile_Octr_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 0.07/0.34 ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( P @ ( coinductive_lhd @ A @ Xs ) )
% 0.07/0.34 => ( ( coindu501562517eWhile @ A @ P @ Xs )
% 0.07/0.34 = ( coinductive_LCons @ A @ ( coinductive_lhd @ A @ Xs ) @ ( coindu501562517eWhile @ A @ P @ ( coinductive_ltl @ A @ Xs ) ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltakeWhile.ctr(2)
% 0.07/0.34 thf(fact_163_llist_Ocase__eq__if,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType] :
% 0.07/0.34 ( ( coindu1381640503_llist @ B @ A )
% 0.07/0.34 = ( ^ [F12: B,F22: A > ( coinductive_llist @ A ) > B,Llist2: coinductive_llist @ A] : ( if @ B @ ( coinductive_lnull @ A @ Llist2 ) @ F12 @ ( F22 @ ( coinductive_lhd @ A @ Llist2 ) @ ( coinductive_ltl @ A @ Llist2 ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.case_eq_if
% 0.07/0.34 thf(fact_164_lzip_Octr_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.07/0.34 ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ B @ Ys )
% 0.07/0.34 => ( ( coinductive_lzip @ A @ B @ Xs @ Ys )
% 0.07/0.34 = ( coinductive_LCons @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ ( coinductive_lhd @ A @ Xs ) @ ( coinductive_lhd @ B @ Ys ) ) @ ( coinductive_lzip @ A @ B @ ( coinductive_ltl @ A @ Xs ) @ ( coinductive_ltl @ B @ Ys ) ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lzip.ctr(2)
% 0.07/0.34 thf(fact_165_prod_Oinject,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,X1: A,X23: B,Y1: A,Y23: B] :
% 0.07/0.34 ( ( ( product_Pair @ A @ B @ X1 @ X23 )
% 0.07/0.34 = ( product_Pair @ A @ B @ Y1 @ Y23 ) )
% 0.07/0.34 = ( ( X1 = Y1 )
% 0.07/0.34 & ( X23 = Y23 ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % prod.inject
% 0.07/0.34 thf(fact_166_old_Oprod_Oinject,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B4: B] :
% 0.07/0.34 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.07/0.34 = ( product_Pair @ A @ B @ A6 @ B4 ) )
% 0.07/0.34 = ( ( A2 = A6 )
% 0.07/0.34 & ( B2 = B4 ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % old.prod.inject
% 0.07/0.34 thf(fact_167_llast__lappend,axiom,
% 0.07/0.34 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( ( coinductive_lnull @ A @ Ys )
% 0.07/0.34 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.07/0.34 = ( coinductive_llast @ A @ Xs ) ) )
% 0.07/0.34 & ( ~ ( coinductive_lnull @ A @ Ys )
% 0.07/0.34 => ( ( ( coinductive_lfinite @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.07/0.34 = ( coinductive_llast @ A @ Ys ) ) )
% 0.07/0.34 & ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.07/0.34 = ( undefined @ A ) ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llast_lappend
% 0.07/0.34 thf(fact_168_ltl__lconcat,axiom,
% 0.07/0.34 ! [A: $tType,Xss: coinductive_llist @ ( coinductive_llist @ A )] :
% 0.07/0.34 ( ~ ( coinductive_lnull @ ( coinductive_llist @ A ) @ Xss )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ ( coinductive_lhd @ ( coinductive_llist @ A ) @ Xss ) )
% 0.07/0.34 => ( ( coinductive_ltl @ A @ ( coinductive_lconcat @ A @ Xss ) )
% 0.07/0.34 = ( coinductive_lappend @ A @ ( coinductive_ltl @ A @ ( coinductive_lhd @ ( coinductive_llist @ A ) @ Xss ) ) @ ( coinductive_lconcat @ A @ ( coinductive_ltl @ ( coinductive_llist @ A ) @ Xss ) ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ltl_lconcat
% 0.07/0.34 thf(fact_169_lconcat__LNil,axiom,
% 0.07/0.34 ! [A: $tType] :
% 0.07/0.34 ( ( coinductive_lconcat @ A @ ( coinductive_LNil @ ( coinductive_llist @ A ) ) )
% 0.07/0.34 = ( coinductive_LNil @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 % lconcat_LNil
% 0.07/0.34 thf(fact_170_lconcat__LCons,axiom,
% 0.07/0.34 ! [B: $tType,Xs: coinductive_llist @ B,Xss: coinductive_llist @ ( coinductive_llist @ B )] :
% 0.07/0.34 ( ( coinductive_lconcat @ B @ ( coinductive_LCons @ ( coinductive_llist @ B ) @ Xs @ Xss ) )
% 0.07/0.34 = ( coinductive_lappend @ B @ Xs @ ( coinductive_lconcat @ B @ Xss ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lconcat_LCons
% 0.07/0.34 thf(fact_171_lconcat__lappend,axiom,
% 0.07/0.34 ! [A: $tType,Xss: coinductive_llist @ ( coinductive_llist @ A ),Yss: coinductive_llist @ ( coinductive_llist @ A )] :
% 0.07/0.34 ( ( coinductive_lfinite @ ( coinductive_llist @ A ) @ Xss )
% 0.07/0.34 => ( ( coinductive_lconcat @ A @ ( coinductive_lappend @ ( coinductive_llist @ A ) @ Xss @ Yss ) )
% 0.07/0.34 = ( coinductive_lappend @ A @ ( coinductive_lconcat @ A @ Xss ) @ ( coinductive_lconcat @ A @ Yss ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lconcat_lappend
% 0.07/0.34 thf(fact_172_lhd__lconcat,axiom,
% 0.07/0.34 ! [A: $tType,Xss: coinductive_llist @ ( coinductive_llist @ A )] :
% 0.07/0.34 ( ~ ( coinductive_lnull @ ( coinductive_llist @ A ) @ Xss )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ ( coinductive_lhd @ ( coinductive_llist @ A ) @ Xss ) )
% 0.07/0.34 => ( ( coinductive_lhd @ A @ ( coinductive_lconcat @ A @ Xss ) )
% 0.07/0.34 = ( coinductive_lhd @ A @ ( coinductive_lhd @ ( coinductive_llist @ A ) @ Xss ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lhd_lconcat
% 0.07/0.34 thf(fact_173_llast__LNil,axiom,
% 0.07/0.34 ! [A: $tType] :
% 0.07/0.34 ( ( coinductive_llast @ A @ ( coinductive_LNil @ A ) )
% 0.07/0.34 = ( undefined @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 % llast_LNil
% 0.07/0.34 thf(fact_174_llast__linfinite,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_llast @ A @ Xs )
% 0.07/0.34 = ( undefined @ A ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llast_linfinite
% 0.07/0.34 thf(fact_175_old_Oprod_Oinducts,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.07/0.34 ( ! [A5: A,B3: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B3 ) )
% 0.07/0.34 => ( P @ Prod ) ) ).
% 0.07/0.34
% 0.07/0.34 % old.prod.inducts
% 0.07/0.34 thf(fact_176_old_Oprod_Oexhaust,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 0.07/0.34 ~ ! [A5: A,B3: B] :
% 0.07/0.34 ( Y
% 0.07/0.34 != ( product_Pair @ A @ B @ A5 @ B3 ) ) ).
% 0.07/0.34
% 0.07/0.34 % old.prod.exhaust
% 0.07/0.34 thf(fact_177_prod__induct7,axiom,
% 0.07/0.34 ! [G2: $tType,F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) ) )] :
% 0.07/0.34 ( ! [A5: A,B3: B,C2: C,D2: D,E2: E,F4: F3,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) ) @ B3 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F3 @ G2 ) @ E2 @ ( product_Pair @ F3 @ G2 @ F4 @ G3 ) ) ) ) ) ) )
% 0.07/0.34 => ( P @ X ) ) ).
% 0.07/0.34
% 0.07/0.34 % prod_induct7
% 0.07/0.34 thf(fact_178_prod__induct6,axiom,
% 0.07/0.34 ! [F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 0.07/0.34 ( ! [A5: A,B3: B,C2: C,D2: D,E2: E,F4: F3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B3 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D2 @ ( product_Pair @ E @ F3 @ E2 @ F4 ) ) ) ) ) )
% 0.07/0.34 => ( P @ X ) ) ).
% 0.07/0.34
% 0.07/0.34 % prod_induct6
% 0.07/0.34 thf(fact_179_prod__induct5,axiom,
% 0.07/0.34 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.07/0.34 ( ! [A5: A,B3: B,C2: C,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B3 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 0.07/0.34 => ( P @ X ) ) ).
% 0.07/0.34
% 0.07/0.34 % prod_induct5
% 0.07/0.34 thf(fact_180_prod__induct4,axiom,
% 0.07/0.34 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.07/0.34 ( ! [A5: A,B3: B,C2: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B3 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 0.07/0.34 => ( P @ X ) ) ).
% 0.07/0.34
% 0.07/0.34 % prod_induct4
% 0.07/0.34 thf(fact_181_prod__induct3,axiom,
% 0.07/0.34 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.07/0.34 ( ! [A5: A,B3: B,C2: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B3 @ C2 ) ) )
% 0.07/0.34 => ( P @ X ) ) ).
% 0.07/0.34
% 0.07/0.34 % prod_induct3
% 0.07/0.34 thf(fact_182_prod__cases7,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) ) )] :
% 0.07/0.34 ~ ! [A5: A,B3: B,C2: C,D2: D,E2: E,F4: F3,G3: G2] :
% 0.07/0.34 ( Y
% 0.07/0.34 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) ) @ B3 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F3 @ G2 ) @ E2 @ ( product_Pair @ F3 @ G2 @ F4 @ G3 ) ) ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % prod_cases7
% 0.07/0.34 thf(fact_183_prod__cases6,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 0.07/0.34 ~ ! [A5: A,B3: B,C2: C,D2: D,E2: E,F4: F3] :
% 0.07/0.34 ( Y
% 0.07/0.34 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B3 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D2 @ ( product_Pair @ E @ F3 @ E2 @ F4 ) ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % prod_cases6
% 0.07/0.34 thf(fact_184_prod__cases5,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.07/0.34 ~ ! [A5: A,B3: B,C2: C,D2: D,E2: E] :
% 0.07/0.34 ( Y
% 0.07/0.34 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B3 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % prod_cases5
% 0.07/0.34 thf(fact_185_prod__cases4,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.07/0.34 ~ ! [A5: A,B3: B,C2: C,D2: D] :
% 0.07/0.34 ( Y
% 0.07/0.34 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B3 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % prod_cases4
% 0.07/0.34 thf(fact_186_prod__cases3,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.07/0.34 ~ ! [A5: A,B3: B,C2: C] :
% 0.07/0.34 ( Y
% 0.07/0.34 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B3 @ C2 ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % prod_cases3
% 0.07/0.34 thf(fact_187_Pair__inject,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B4: B] :
% 0.07/0.34 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 0.07/0.34 = ( product_Pair @ A @ B @ A6 @ B4 ) )
% 0.07/0.34 => ~ ( ( A2 = A6 )
% 0.07/0.34 => ( B2 != B4 ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % Pair_inject
% 0.07/0.34 thf(fact_188_prod__cases,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 0.07/0.34 ( ! [A5: A,B3: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B3 ) )
% 0.07/0.34 => ( P @ P3 ) ) ).
% 0.07/0.34
% 0.07/0.34 % prod_cases
% 0.07/0.34 thf(fact_189_surj__pair,axiom,
% 0.07/0.34 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 0.07/0.34 ? [X3: A,Y3: B] :
% 0.07/0.34 ( P3
% 0.07/0.34 = ( product_Pair @ A @ B @ X3 @ Y3 ) ) ).
% 0.07/0.34
% 0.07/0.34 % surj_pair
% 0.07/0.34 thf(fact_190_old_Oprod_Orec,axiom,
% 0.07/0.34 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 0.07/0.34 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 0.07/0.34 = ( F1 @ A2 @ B2 ) ) ).
% 0.07/0.34
% 0.07/0.34 % old.prod.rec
% 0.07/0.34 thf(fact_191_internal__case__prod__conv,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 0.07/0.34 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 0.07/0.34 = ( C3 @ A2 @ B2 ) ) ).
% 0.07/0.34
% 0.07/0.34 % internal_case_prod_conv
% 0.07/0.34 thf(fact_192_ord_Olsorted__coinduct_H,axiom,
% 0.07/0.34 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A,Less_eq: A > A > $o] :
% 0.07/0.34 ( ( X4 @ Xs )
% 0.07/0.34 => ( ! [Xs2: coinductive_llist @ A] :
% 0.07/0.34 ( ( X4 @ Xs2 )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ Xs2 )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ ( coinductive_ltl @ A @ Xs2 ) )
% 0.07/0.34 => ( ( Less_eq @ ( coinductive_lhd @ A @ Xs2 ) @ ( coinductive_lhd @ A @ ( coinductive_ltl @ A @ Xs2 ) ) )
% 0.07/0.34 & ( ( X4 @ ( coinductive_ltl @ A @ Xs2 ) )
% 0.07/0.34 | ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_ltl @ A @ Xs2 ) ) ) ) ) ) )
% 0.07/0.34 => ( coinductive_lsorted @ A @ Less_eq @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ord.lsorted_coinduct'
% 0.07/0.34 thf(fact_193_ord_Olsorted__LCons__LCons,axiom,
% 0.07/0.34 ! [A: $tType,Less_eq: A > A > $o,X: A,Y: A,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs ) ) )
% 0.07/0.34 = ( ( Less_eq @ X @ Y )
% 0.07/0.34 & ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ Y @ Xs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ord.lsorted_LCons_LCons
% 0.07/0.34 thf(fact_194_ord_OLCons__LCons,axiom,
% 0.07/0.34 ! [A: $tType,Less_eq: A > A > $o,X: A,Y: A,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( Less_eq @ X @ Y )
% 0.07/0.34 => ( ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ Y @ Xs ) )
% 0.07/0.34 => ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ord.LCons_LCons
% 0.07/0.34 thf(fact_195_ord_OLNil,axiom,
% 0.07/0.34 ! [A: $tType,Less_eq: A > A > $o] : ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LNil @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 % ord.LNil
% 0.07/0.34 thf(fact_196_ord_Olsorted__code_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,Less_eq: A > A > $o] : ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LNil @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 % ord.lsorted_code(1)
% 0.07/0.34 thf(fact_197_ord_Olsorted__ltlI,axiom,
% 0.07/0.34 ! [A: $tType,Less_eq: A > A > $o,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lsorted @ A @ Less_eq @ Xs )
% 0.07/0.34 => ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_ltl @ A @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ord.lsorted_ltlI
% 0.07/0.34 thf(fact_198_ord_Olsorted__ldropn,axiom,
% 0.07/0.34 ! [A: $tType,Less_eq: A > A > $o,Xs: coinductive_llist @ A,N: nat] :
% 0.07/0.34 ( ( coinductive_lsorted @ A @ Less_eq @ Xs )
% 0.07/0.34 => ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_ldropn @ A @ N @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ord.lsorted_ldropn
% 0.07/0.34 thf(fact_199_ord_Olsorted__code_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,Less_eq: A > A > $o,X: A] : ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ord.lsorted_code(2)
% 0.07/0.34 thf(fact_200_ord_Olsorted_Ocases,axiom,
% 0.07/0.34 ! [A: $tType,Less_eq: A > A > $o,A2: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lsorted @ A @ Less_eq @ A2 )
% 0.07/0.34 => ( ( A2
% 0.07/0.34 != ( coinductive_LNil @ A ) )
% 0.07/0.34 => ( ! [X3: A] :
% 0.07/0.34 ( A2
% 0.07/0.34 != ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) )
% 0.07/0.34 => ~ ! [X3: A,Y3: A,Xs2: coinductive_llist @ A] :
% 0.07/0.34 ( ( A2
% 0.07/0.34 = ( coinductive_LCons @ A @ X3 @ ( coinductive_LCons @ A @ Y3 @ Xs2 ) ) )
% 0.07/0.34 => ( ( Less_eq @ X3 @ Y3 )
% 0.07/0.34 => ~ ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ Y3 @ Xs2 ) ) ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ord.lsorted.cases
% 0.07/0.34 thf(fact_201_ord_Olsorted_Osimps,axiom,
% 0.07/0.34 ! [A: $tType] :
% 0.07/0.34 ( ( coinductive_lsorted @ A )
% 0.07/0.34 = ( ^ [Less_eq2: A > A > $o,A4: coinductive_llist @ A] :
% 0.07/0.34 ( ( A4
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 | ? [X2: A] :
% 0.07/0.34 ( A4
% 0.07/0.34 = ( coinductive_LCons @ A @ X2 @ ( coinductive_LNil @ A ) ) )
% 0.07/0.34 | ? [X2: A,Y2: A,Xs3: coinductive_llist @ A] :
% 0.07/0.34 ( ( A4
% 0.07/0.34 = ( coinductive_LCons @ A @ X2 @ ( coinductive_LCons @ A @ Y2 @ Xs3 ) ) )
% 0.07/0.34 & ( Less_eq2 @ X2 @ Y2 )
% 0.07/0.34 & ( coinductive_lsorted @ A @ Less_eq2 @ ( coinductive_LCons @ A @ Y2 @ Xs3 ) ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ord.lsorted.simps
% 0.07/0.34 thf(fact_202_ord_Olsorted_Ocoinduct,axiom,
% 0.07/0.34 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,Less_eq: A > A > $o] :
% 0.07/0.34 ( ( X4 @ X )
% 0.07/0.34 => ( ! [X3: coinductive_llist @ A] :
% 0.07/0.34 ( ( X4 @ X3 )
% 0.07/0.34 => ( ( X3
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 | ? [Xa3: A] :
% 0.07/0.34 ( X3
% 0.07/0.34 = ( coinductive_LCons @ A @ Xa3 @ ( coinductive_LNil @ A ) ) )
% 0.07/0.34 | ? [Xa3: A,Y4: A,Xs5: coinductive_llist @ A] :
% 0.07/0.34 ( ( X3
% 0.07/0.34 = ( coinductive_LCons @ A @ Xa3 @ ( coinductive_LCons @ A @ Y4 @ Xs5 ) ) )
% 0.07/0.34 & ( Less_eq @ Xa3 @ Y4 )
% 0.07/0.34 & ( ( X4 @ ( coinductive_LCons @ A @ Y4 @ Xs5 ) )
% 0.07/0.34 | ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ Y4 @ Xs5 ) ) ) ) ) )
% 0.07/0.34 => ( coinductive_lsorted @ A @ Less_eq @ X ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ord.lsorted.coinduct
% 0.07/0.34 thf(fact_203_ord_OSingleton,axiom,
% 0.07/0.34 ! [A: $tType,Less_eq: A > A > $o,X: A] : ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ord.Singleton
% 0.07/0.34 thf(fact_204_ord_Olsorted__LCons_H,axiom,
% 0.07/0.34 ! [A: $tType,Less_eq: A > A > $o,X: A,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.07/0.34 = ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( Less_eq @ X @ ( coinductive_lhd @ A @ Xs ) )
% 0.07/0.34 & ( coinductive_lsorted @ A @ Less_eq @ Xs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ord.lsorted_LCons'
% 0.07/0.34 thf(fact_205_ord_Olsorted__lhdD,axiom,
% 0.07/0.34 ! [A: $tType,Less_eq: A > A > $o,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lsorted @ A @ Less_eq @ Xs )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ ( coinductive_ltl @ A @ Xs ) )
% 0.07/0.34 => ( Less_eq @ ( coinductive_lhd @ A @ Xs ) @ ( coinductive_lhd @ A @ ( coinductive_ltl @ A @ Xs ) ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ord.lsorted_lhdD
% 0.07/0.34 thf(fact_206_ssubst__Pair__rhs,axiom,
% 0.07/0.34 ! [B: $tType,A: $tType,R3: A,S: B,R: set @ ( product_prod @ A @ B ),S2: B] :
% 0.07/0.34 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S ) @ R )
% 0.07/0.34 => ( ( S2 = S )
% 0.07/0.34 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S2 ) @ R ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ssubst_Pair_rhs
% 0.07/0.34 thf(fact_207_lprefix__expand,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ Ys )
% 0.07/0.34 & ( ( coinductive_lhd @ A @ Xs )
% 0.07/0.34 = ( coinductive_lhd @ A @ Ys ) )
% 0.07/0.34 & ( coinductive_lprefix @ A @ ( coinductive_ltl @ A @ Xs ) @ ( coinductive_ltl @ A @ Ys ) ) ) )
% 0.07/0.34 => ( coinductive_lprefix @ A @ Xs @ Ys ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_expand
% 0.07/0.34 thf(fact_208_lprefix__refl,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A] : ( coinductive_lprefix @ A @ Xs @ Xs ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_refl
% 0.07/0.34 thf(fact_209_llist_Oleq__refl,axiom,
% 0.07/0.34 ! [A: $tType,X: coinductive_llist @ A] : ( coinductive_lprefix @ A @ X @ X ) ).
% 0.07/0.34
% 0.07/0.34 % llist.leq_refl
% 0.07/0.34 thf(fact_210_LCons__lprefix__LCons,axiom,
% 0.07/0.34 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.07/0.34 = ( ( X = Y )
% 0.07/0.34 & ( coinductive_lprefix @ A @ Xs @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % LCons_lprefix_LCons
% 0.07/0.34 thf(fact_211_lprefix__code_I1_J,axiom,
% 0.07/0.34 ! [A: $tType,Ys: coinductive_llist @ A] : ( coinductive_lprefix @ A @ ( coinductive_LNil @ A ) @ Ys ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_code(1)
% 0.07/0.34 thf(fact_212_lprefix__LNil,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.07/0.34 = ( coinductive_lnull @ A @ Xs ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_LNil
% 0.07/0.34 thf(fact_213_lprefix__lappend__same,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( coinductive_lappend @ A @ Xs @ Zs ) )
% 0.07/0.34 = ( ( coinductive_lfinite @ A @ Xs )
% 0.07/0.34 => ( coinductive_lprefix @ A @ Ys @ Zs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_lappend_same
% 0.07/0.34 thf(fact_214_ord_Olsorted__lprefixD,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Less_eq: A > A > $o] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.07/0.34 => ( ( coinductive_lsorted @ A @ Less_eq @ Ys )
% 0.07/0.34 => ( coinductive_lsorted @ A @ Less_eq @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % ord.lsorted_lprefixD
% 0.07/0.34 thf(fact_215_lprefix__lappend,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] : ( coinductive_lprefix @ A @ Xs @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_lappend
% 0.07/0.34 thf(fact_216_lappend__lprefixE,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 0.07/0.34 => ~ ! [Zs3: coinductive_llist @ A] :
% 0.07/0.34 ( Zs
% 0.07/0.34 != ( coinductive_lappend @ A @ Xs @ Zs3 ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lappend_lprefixE
% 0.07/0.34 thf(fact_217_lprefix__lappendD,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) )
% 0.07/0.34 => ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.07/0.34 | ( coinductive_lprefix @ A @ Ys @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_lappendD
% 0.07/0.34 thf(fact_218_lprefix__conv__lappend,axiom,
% 0.07/0.34 ! [A: $tType] :
% 0.07/0.34 ( ( coinductive_lprefix @ A )
% 0.07/0.34 = ( ^ [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A] :
% 0.07/0.34 ? [Zs2: coinductive_llist @ A] :
% 0.07/0.34 ( Ys3
% 0.07/0.34 = ( coinductive_lappend @ A @ Xs3 @ Zs2 ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_conv_lappend
% 0.07/0.34 thf(fact_219_lprefix__lappend__sameI,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.07/0.34 => ( coinductive_lprefix @ A @ ( coinductive_lappend @ A @ Zs @ Xs ) @ ( coinductive_lappend @ A @ Zs @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_lappend_sameI
% 0.07/0.34 thf(fact_220_lprefix__lfiniteD,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.07/0.34 => ( ( coinductive_lfinite @ A @ Ys )
% 0.07/0.34 => ( coinductive_lfinite @ A @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_lfiniteD
% 0.07/0.34 thf(fact_221_not__lfinite__lprefix__conv__eq,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.07/0.34 = ( Xs = Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % not_lfinite_lprefix_conv_eq
% 0.07/0.34 thf(fact_222_LNil__lprefix,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A] : ( coinductive_lprefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 0.07/0.34
% 0.07/0.34 % LNil_lprefix
% 0.07/0.34 thf(fact_223_LCons__lprefix__conv,axiom,
% 0.07/0.34 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ ( coinductive_LCons @ A @ X @ Xs ) @ Ys )
% 0.07/0.34 = ( ? [Ys4: coinductive_llist @ A] :
% 0.07/0.34 ( ( Ys
% 0.07/0.34 = ( coinductive_LCons @ A @ X @ Ys4 ) )
% 0.07/0.34 & ( coinductive_lprefix @ A @ Xs @ Ys4 ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % LCons_lprefix_conv
% 0.07/0.34 thf(fact_224_Le__LCons,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,X: A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.07/0.34 => ( coinductive_lprefix @ A @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ X @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % Le_LCons
% 0.07/0.34 thf(fact_225_lprefixI,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,X4: set @ ( product_prod @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) )] :
% 0.07/0.34 ( ( member @ ( product_prod @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) ) @ ( product_Pair @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) @ Xs @ Ys ) @ X4 )
% 0.07/0.34 => ( ! [Xs2: coinductive_llist @ A,Ys5: coinductive_llist @ A] :
% 0.07/0.34 ( ( member @ ( product_prod @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) ) @ ( product_Pair @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) @ Xs2 @ Ys5 ) @ X4 )
% 0.07/0.34 => ( ( coinductive_lnull @ A @ Xs2 )
% 0.07/0.34 | ? [X5: A,Xs6: coinductive_llist @ A,Ys6: coinductive_llist @ A] :
% 0.07/0.34 ( ( Xs2
% 0.07/0.34 = ( coinductive_LCons @ A @ X5 @ Xs6 ) )
% 0.07/0.34 & ( Ys5
% 0.07/0.34 = ( coinductive_LCons @ A @ X5 @ Ys6 ) )
% 0.07/0.34 & ( ( member @ ( product_prod @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) ) @ ( product_Pair @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) @ Xs6 @ Ys6 ) @ X4 )
% 0.07/0.34 | ( coinductive_lprefix @ A @ Xs6 @ Ys6 ) ) ) ) )
% 0.07/0.34 => ( coinductive_lprefix @ A @ Xs @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefixI
% 0.07/0.34 thf(fact_226_lprefix__code_I2_J,axiom,
% 0.07/0.34 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.07/0.34 ~ ( coinductive_lprefix @ A @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LNil @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_code(2)
% 0.07/0.34 thf(fact_227_lprefix_Ocases,axiom,
% 0.07/0.34 ! [A: $tType,A1: coinductive_llist @ A,A22: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ A1 @ A22 )
% 0.07/0.34 => ( ( ( A1
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 => ! [Xs2: coinductive_llist @ A] : ( A22 != Xs2 ) )
% 0.07/0.34 => ~ ! [Xs2: coinductive_llist @ A,Ys5: coinductive_llist @ A,X3: A] :
% 0.07/0.34 ( ( A1
% 0.07/0.34 = ( coinductive_LCons @ A @ X3 @ Xs2 ) )
% 0.07/0.34 => ( ( A22
% 0.07/0.34 = ( coinductive_LCons @ A @ X3 @ Ys5 ) )
% 0.07/0.34 => ~ ( coinductive_lprefix @ A @ Xs2 @ Ys5 ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix.cases
% 0.07/0.34 thf(fact_228_lprefix_Osimps,axiom,
% 0.07/0.34 ! [A: $tType] :
% 0.07/0.34 ( ( coinductive_lprefix @ A )
% 0.07/0.34 = ( ^ [A12: coinductive_llist @ A,A23: coinductive_llist @ A] :
% 0.07/0.34 ( ? [Xs3: coinductive_llist @ A] :
% 0.07/0.34 ( ( A12
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 & ( A23 = Xs3 ) )
% 0.07/0.34 | ? [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A,X2: A] :
% 0.07/0.34 ( ( A12
% 0.07/0.34 = ( coinductive_LCons @ A @ X2 @ Xs3 ) )
% 0.07/0.34 & ( A23
% 0.07/0.34 = ( coinductive_LCons @ A @ X2 @ Ys3 ) )
% 0.07/0.34 & ( coinductive_lprefix @ A @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix.simps
% 0.07/0.34 thf(fact_229_lprefix_Ocoinduct,axiom,
% 0.07/0.34 ! [A: $tType,X4: ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,Xa: coinductive_llist @ A] :
% 0.07/0.34 ( ( X4 @ X @ Xa )
% 0.07/0.34 => ( ! [X3: coinductive_llist @ A,Xa2: coinductive_llist @ A] :
% 0.07/0.34 ( ( X4 @ X3 @ Xa2 )
% 0.07/0.34 => ( ? [Xs5: coinductive_llist @ A] :
% 0.07/0.34 ( ( X3
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 & ( Xa2 = Xs5 ) )
% 0.07/0.34 | ? [Xs5: coinductive_llist @ A,Ys2: coinductive_llist @ A,Xb: A] :
% 0.07/0.34 ( ( X3
% 0.07/0.34 = ( coinductive_LCons @ A @ Xb @ Xs5 ) )
% 0.07/0.34 & ( Xa2
% 0.07/0.34 = ( coinductive_LCons @ A @ Xb @ Ys2 ) )
% 0.07/0.34 & ( ( X4 @ Xs5 @ Ys2 )
% 0.07/0.34 | ( coinductive_lprefix @ A @ Xs5 @ Ys2 ) ) ) ) )
% 0.07/0.34 => ( coinductive_lprefix @ A @ X @ Xa ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix.coinduct
% 0.07/0.34 thf(fact_230_lprefix__LCons__conv,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.07/0.34 = ( ( Xs
% 0.07/0.34 = ( coinductive_LNil @ A ) )
% 0.07/0.34 | ? [Xs4: coinductive_llist @ A] :
% 0.07/0.34 ( ( Xs
% 0.07/0.34 = ( coinductive_LCons @ A @ Y @ Xs4 ) )
% 0.07/0.34 & ( coinductive_lprefix @ A @ Xs4 @ Ys ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_LCons_conv
% 0.07/0.34 thf(fact_231_lprefix__lhdD,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( ( coinductive_lhd @ A @ Xs )
% 0.07/0.34 = ( coinductive_lhd @ A @ Ys ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_lhdD
% 0.07/0.34 thf(fact_232_lprefix__imp__llexord,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,R3: A > A > $o] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.07/0.34 => ( coinductive_llexord @ A @ R3 @ Xs @ Ys ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_imp_llexord
% 0.07/0.34 thf(fact_233_lprefix__ltakeWhile,axiom,
% 0.07/0.34 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] : ( coinductive_lprefix @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) @ Xs ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_ltakeWhile
% 0.07/0.34 thf(fact_234_lprefix__trans,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.07/0.34 => ( ( coinductive_lprefix @ A @ Ys @ Zs )
% 0.07/0.34 => ( coinductive_lprefix @ A @ Xs @ Zs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_trans
% 0.07/0.34 thf(fact_235_llist_Oleq__trans,axiom,
% 0.07/0.34 ! [A: $tType,X: coinductive_llist @ A,Y: coinductive_llist @ A,Z: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ X @ Y )
% 0.07/0.34 => ( ( coinductive_lprefix @ A @ Y @ Z )
% 0.07/0.34 => ( coinductive_lprefix @ A @ X @ Z ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.leq_trans
% 0.07/0.34 thf(fact_236_lprefix__antisym,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.07/0.34 => ( ( coinductive_lprefix @ A @ Ys @ Xs )
% 0.07/0.34 => ( Xs = Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_antisym
% 0.07/0.34 thf(fact_237_llist_Oleq__antisym,axiom,
% 0.07/0.34 ! [A: $tType,X: coinductive_llist @ A,Y: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ X @ Y )
% 0.07/0.34 => ( ( coinductive_lprefix @ A @ Y @ X )
% 0.07/0.34 => ( X = Y ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llist.leq_antisym
% 0.07/0.34 thf(fact_238_lprefix__down__linear,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Zs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ Xs @ Zs )
% 0.07/0.34 => ( ( coinductive_lprefix @ A @ Ys @ Zs )
% 0.07/0.34 => ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.07/0.34 | ( coinductive_lprefix @ A @ Ys @ Xs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_down_linear
% 0.07/0.34 thf(fact_239_Coinductive__List_Ofinite__lprefix__def,axiom,
% 0.07/0.34 ! [A: $tType] :
% 0.07/0.34 ( ( coindu328551480prefix @ A )
% 0.07/0.34 = ( coinductive_lprefix @ A ) ) ).
% 0.07/0.34
% 0.07/0.34 % Coinductive_List.finite_lprefix_def
% 0.07/0.34 thf(fact_240_lstrict__prefix__def,axiom,
% 0.07/0.34 ! [A: $tType] :
% 0.07/0.34 ( ( coindu1478340336prefix @ A )
% 0.07/0.34 = ( ^ [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ Xs3 @ Ys3 )
% 0.07/0.34 & ( Xs3 != Ys3 ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lstrict_prefix_def
% 0.07/0.34 thf(fact_241_lprefix__lconcatI,axiom,
% 0.07/0.34 ! [A: $tType,Xss: coinductive_llist @ ( coinductive_llist @ A ),Yss: coinductive_llist @ ( coinductive_llist @ A )] :
% 0.07/0.34 ( ( coinductive_lprefix @ ( coinductive_llist @ A ) @ Xss @ Yss )
% 0.07/0.34 => ( coinductive_lprefix @ A @ ( coinductive_lconcat @ A @ Xss ) @ ( coinductive_lconcat @ A @ Yss ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_lconcatI
% 0.07/0.34 thf(fact_242_lprefix__ltlI,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.07/0.34 => ( coinductive_lprefix @ A @ ( coinductive_ltl @ A @ Xs ) @ ( coinductive_ltl @ A @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_ltlI
% 0.07/0.34 thf(fact_243_lprefix__not__lnullD,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_not_lnullD
% 0.07/0.34 thf(fact_244_lprefix__lnullD,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.07/0.34 => ( ( coinductive_lnull @ A @ Ys )
% 0.07/0.34 => ( coinductive_lnull @ A @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_lnullD
% 0.07/0.34 thf(fact_245_lprefix__lnull,axiom,
% 0.07/0.34 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ Ys )
% 0.07/0.34 => ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.07/0.34 = ( coinductive_lnull @ A @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_lnull
% 0.07/0.34 thf(fact_246_lnull__lprefix,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lnull @ A @ Xs )
% 0.07/0.34 => ( coinductive_lprefix @ A @ Xs @ Ys ) ) ).
% 0.07/0.34
% 0.07/0.34 % lnull_lprefix
% 0.07/0.34 thf(fact_247_Coinductive__List_Olprefix__nitpick__simps,axiom,
% 0.07/0.34 ! [A: $tType] :
% 0.07/0.34 ( ( coinductive_lprefix @ A )
% 0.07/0.34 = ( ^ [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A] :
% 0.07/0.34 ( ( ( coinductive_lfinite @ A @ Xs3 )
% 0.07/0.34 => ( coindu328551480prefix @ A @ Xs3 @ Ys3 ) )
% 0.07/0.34 & ( ~ ( coinductive_lfinite @ A @ Xs3 )
% 0.07/0.34 => ( Xs3 = Ys3 ) ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % Coinductive_List.lprefix_nitpick_simps
% 0.07/0.34 thf(fact_248_lprefix__coinduct,axiom,
% 0.07/0.34 ! [A: $tType,P: ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.07/0.34 ( ( P @ Xs @ Ys )
% 0.07/0.34 => ( ! [Xs2: coinductive_llist @ A,Ys5: coinductive_llist @ A] :
% 0.07/0.34 ( ( P @ Xs2 @ Ys5 )
% 0.07/0.34 => ( ( ( coinductive_lnull @ A @ Ys5 )
% 0.07/0.34 => ( coinductive_lnull @ A @ Xs2 ) )
% 0.07/0.34 & ( ~ ( coinductive_lnull @ A @ Xs2 )
% 0.07/0.34 => ( ~ ( coinductive_lnull @ A @ Ys5 )
% 0.07/0.34 => ( ( ( coinductive_lhd @ A @ Xs2 )
% 0.07/0.34 = ( coinductive_lhd @ A @ Ys5 ) )
% 0.07/0.34 & ( ( P @ ( coinductive_ltl @ A @ Xs2 ) @ ( coinductive_ltl @ A @ Ys5 ) )
% 0.07/0.34 | ( coinductive_lprefix @ A @ ( coinductive_ltl @ A @ Xs2 ) @ ( coinductive_ltl @ A @ Ys5 ) ) ) ) ) ) ) )
% 0.07/0.34 => ( coinductive_lprefix @ A @ Xs @ Ys ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % lprefix_coinduct
% 0.07/0.34 thf(fact_249_llexord__lappend__left,axiom,
% 0.07/0.34 ! [A: $tType,Xs: coinductive_llist @ A,R3: A > A > $o,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_lfinite @ A @ Xs )
% 0.07/0.34 => ( ! [X3: A] :
% 0.07/0.34 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 0.07/0.34 => ~ ( R3 @ X3 @ X3 ) )
% 0.07/0.34 => ( ( coinductive_llexord @ A @ R3 @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( coinductive_lappend @ A @ Xs @ Zs ) )
% 0.07/0.34 = ( coinductive_llexord @ A @ R3 @ Ys @ Zs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_lappend_left
% 0.07/0.34 thf(fact_250_llexord__lappend__leftD,axiom,
% 0.07/0.34 ! [A: $tType,R3: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.07/0.34 ( ( coinductive_llexord @ A @ R3 @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( coinductive_lappend @ A @ Xs @ Zs ) )
% 0.07/0.34 => ( ( coinductive_lfinite @ A @ Xs )
% 0.07/0.34 => ( ! [X3: A] :
% 0.07/0.34 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 0.07/0.34 => ~ ( R3 @ X3 @ X3 ) )
% 0.07/0.34 => ( coinductive_llexord @ A @ R3 @ Ys @ Zs ) ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % llexord_lappend_leftD
% 0.07/0.34 thf(fact_251_in__lset__ltlD,axiom,
% 0.07/0.34 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_ltl @ A @ Xs ) ) )
% 0.07/0.34 => ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % in_lset_ltlD
% 0.07/0.34 thf(fact_252_lset__lmember,axiom,
% 0.07/0.34 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.07/0.34 = ( coinductive_lmember @ A @ X @ Xs ) ) ).
% 0.07/0.34
% 0.07/0.34 % lset_lmember
% 0.07/0.34 thf(fact_253_in__lset__ldropnD,axiom,
% 0.07/0.34 ! [A: $tType,X: A,N: nat,Xs: coinductive_llist @ A] :
% 0.07/0.34 ( ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_ldropn @ A @ N @ Xs ) ) )
% 0.07/0.34 => ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) ) ) ).
% 0.07/0.34
% 0.07/0.34 % in_lset_ldropnD
% 0.07/0.34
% 0.07/0.34 %----Helper facts (3)
% 0.07/0.34 thf(help_If_3_1_T,axiom,
% 0.07/0.34 ! [P: $o] :
% 0.07/0.34 ( ( P = $true )
% 0.07/0.34 | ( P = $false ) ) ).
% 0.07/0.34
% 0.07/0.34 thf(help_If_2_1_T,axiom,
% 0.07/0.34 ! [A: $tType,X: A,Y: A] :
% 0.07/0.34 ( ( if @ A @ $false @ X @ Y )
% 0.07/0.34 = Y ) ).
% 0.07/0.34
% 0.07/0.34 thf(help_If_1_1_T,axiom,
% 0.07/0.34 ! [A: $tType,X: A,Y: A] :
% 0.07/0.34 ( ( if @ A @ $true @ X @ Y )
% 0.07/0.34 = X ) ).
% 0.07/0.34
% 0.07/0.34 %----Conjectures (1)
% 0.07/0.34 thf(conj_0,conjecture,
% 0.07/0.34 ( ( coinductive_lfinite @ a @ xsa )
% 0.07/0.34 & ( coinductive_lfinite @ a @ acca ) ) ).
% 0.07/0.34
% 0.07/0.34 %------------------------------------------------------------------------------
% 0.07/0.34 ------------------------
% 1.61/1.08 ---- Embedded in THF ---
% 1.61/1.08 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.61/1.08 %%% Generated on Tue Feb 24 06:10:31 EST 2026
% 1.61/1.08 %%% using '$$dhol' embedding, version 1.3.0.
% 1.61/1.08 %%% Logic specification used:
% 1.61/1.08 %%% thf(spec, logic, $$dhol).
% 1.61/1.08
% 1.61/1.08 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.tZ0Cg1ODeg/DTF2DTF26636.p
% 1.61/1.08 thf(ty_t_Coinductive__List_Ollist, type, coinductive_llist: ($tType > $tType)).
% 1.61/1.08 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 1.61/1.08 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 1.61/1.08 thf(ty_t_Nat_Onat, type, nat: $tType).
% 1.61/1.08 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 1.61/1.08 thf(ty_tf_a, type, a: $tType).
% 1.61/1.08 thf(sy_c_Coinductive__List_Ofinite__lprefix, type, coindu328551480prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Ogen__lset, type, coinductive_gen_lset: (!> [A:$tType]: (((set @ A) > ((coinductive_llist @ A) > (set @ A)))))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Olappend, type, coinductive_lappend: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Olconcat, type, coinductive_lconcat: (!> [A:$tType]: (((coinductive_llist @ (coinductive_llist @ A)) > (coinductive_llist @ A))))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Oldropn, type, coinductive_ldropn: (!> [A:$tType]: ((nat > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Olfinite, type, coinductive_lfinite: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Ollast, type, coinductive_llast: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Ollexord, type, coinductive_llexord: (!> [A:$tType]: (((A > (A > $o)) > ((coinductive_llist @ A) > ((coinductive_llist @ A) > $o)))))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Ollist_OLCons, type, coinductive_LCons: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Ollist_OLNil, type, coinductive_LNil: (!> [A:$tType]: ((coinductive_llist @ A)))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Ollist_Ocase__llist, type, coindu1381640503_llist: (!> [B:$tType,A:$tType]: ((B > ((A > ((coinductive_llist @ A) > B)) > ((coinductive_llist @ A) > B)))))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Ollist_Olhd, type, coinductive_lhd: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Ollist_Olnull, type, coinductive_lnull: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Ollist_Olset, type, coinductive_lset: (!> [A:$tType]: (((coinductive_llist @ A) > (set @ A))))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Ollist_Oltl, type, coinductive_ltl: (!> [A:$tType]: (((coinductive_llist @ A) > (coinductive_llist @ A))))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Olmember, type, coinductive_lmember: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > $o))))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Olprefix, type, coinductive_lprefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Olstrict__prefix, type, coindu1478340336prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 1.61/1.08 thf(sy_c_Coinductive__List_OltakeWhile, type, coindu501562517eWhile: (!> [A:$tType]: (((A > $o) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Olzip, type, coinductive_lzip: (!> [A:$tType,B:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ B) > (coinductive_llist @ ((product_prod @ A) @ B))))))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Oord_Olsorted, type, coinductive_lsorted: (!> [A:$tType]: (((A > (A > $o)) > ((coinductive_llist @ A) > $o))))).
% 1.61/1.08 thf(sy_c_Coinductive__List_Ounfold__llist, type, coindu1441602521_llist: (!> [A:$tType,B:$tType]: (((A > $o) > ((A > B) > ((A > A) > (A > (coinductive_llist @ B)))))))).
% 1.61/1.08 thf(sy_c_HOL_Oundefined, type, undefined: (!> [A:$tType]: (A))).
% 1.61/1.08 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 1.61/1.08 thf(sy_c_LMirror__Mirabelle__wyovfcktfy_Olmirror, type, lMirro427583474mirror: (!> [A:$tType]: (((coinductive_llist @ A) > (coinductive_llist @ A))))).
% 1.61/1.08 thf(sy_c_LMirror__Mirabelle__wyovfcktfy_Olmirror__aux, type, lMirro999291890or_aux: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 1.61/1.08 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 1.61/1.08 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 1.61/1.08 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod, type, product_rec_prod: (!> [A:$tType,B:$tType,T:$tType]: (((A > (B > T)) > (((product_prod @ A) @ B) > T))))).
% 1.61/1.08 thf(sy_c_Pure_Otype, type, type: (!> [A:$tType]: ((itself @ A)))).
% 1.61/1.08 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 1.61/1.08 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 1.61/1.08 thf(sy_v_acc, type, acc: (coinductive_llist @ a)).
% 1.61/1.08 thf(sy_v_acca____, type, acca: (coinductive_llist @ a)).
% 1.61/1.08 thf(sy_v_xs, type, xs: (coinductive_llist @ a)).
% 1.61/1.08 thf(sy_v_xsa____, type, xsa: (coinductive_llist @ a)).
% 1.61/1.08 thf(fact_0__092_060open_062lfinite_A_Ilmirror__aux_Aacc_Axs_J_092_060close_062, axiom, ((coinductive_lfinite @ a) @ (((lMirro999291890or_aux @ a) @ acc) @ xs))).
% 1.61/1.08 thf(fact_1_LCons_Ohyps_I2_J, axiom, (~ (((coinductive_lnull @ a) @ (((lMirro999291890or_aux @ a) @ acca) @ xsa))))).
% 1.61/1.08 thf(fact_2_LCons_Ohyps_I1_J, axiom, ((coinductive_lfinite @ a) @ (((lMirro999291890or_aux @ a) @ acca) @ xsa))).
% 1.61/1.08 thf(fact_3_LCons_Ohyps_I3_J, axiom, (! [Acc:(coinductive_llist @ a),Xs:(coinductive_llist @ a)]: (((((coinductive_ltl @ a) @ (((lMirro999291890or_aux @ a) @ acca) @ xsa)) = (((lMirro999291890or_aux @ a) @ Acc) @ Xs)) => (((coinductive_lfinite @ a) @ Xs) & ((coinductive_lfinite @ a) @ Acc)))))).
% 1.61/1.08 thf(fact_4_lfinite__ltl, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ ((coinductive_ltl @ A) @ Xs)) = ((coinductive_lfinite @ A) @ Xs))))).
% 1.61/1.08 thf(fact_5_lnull__imp__lfinite, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => ((coinductive_lfinite @ A) @ Xs))))).
% 1.61/1.08 thf(fact_6_lmirror__aux_Oexhaust, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Acc:(coinductive_llist @ A)]: (((((coinductive_lnull @ A) @ Xs) => (~ (((coinductive_lnull @ A) @ Acc)))) => ((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Acc)))))))).
% 1.61/1.08 thf(fact_7_lmirror__aux_Odisc__iff_I2_J, axiom, (! [A:$tType,Acc:(coinductive_llist @ A),Xs:(coinductive_llist @ A)]: (((~ (((coinductive_lnull @ A) @ (((lMirro999291890or_aux @ A) @ Acc) @ Xs)))) = ((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Acc)))))))).
% 1.61/1.08 thf(fact_8_lnull__lmirror__aux, axiom, (! [A:$tType,Acc:(coinductive_llist @ A),Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ (((lMirro999291890or_aux @ A) @ Acc) @ Xs)) = (((coinductive_lnull @ A) @ Xs) & ((coinductive_lnull @ A) @ Acc)))))).
% 1.61/1.08 thf(fact_9_lfinite__induct, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: ((((coinductive_lfinite @ A) @ Xs) => ((! [Xs2:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs2) => (P @ Xs2)))) => ((! [Xs2:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs2) => ((~ (((coinductive_lnull @ A) @ Xs2))) => ((P @ ((coinductive_ltl @ A) @ Xs2)) => (P @ Xs2)))))) => (P @ Xs))))))).
% 1.61/1.08 thf(fact_10_lstrict__prefix__lfinite1, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Xs) @ Ys) => ((coinductive_lfinite @ A) @ Xs))))).
% 1.61/1.08 thf(fact_11_lfinite__code_I1_J, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) @ (coinductive_LNil @ A))))).
% 1.61/1.08 thf(fact_12_lfinite__ldropn, axiom, (! [A:$tType,N:nat,Xs:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ (((coinductive_ldropn @ A) @ N) @ Xs)) = ((coinductive_lfinite @ A) @ Xs))))).
% 1.61/1.08 thf(fact_13_lfinite__lzip, axiom, (! [A:$tType,B:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: ((((coinductive_lfinite @ ((product_prod @ A) @ B)) @ ((((coinductive_lzip @ A) @ B) @ Xs) @ Ys)) = (((coinductive_lfinite @ A) @ Xs) | ((coinductive_lfinite @ B) @ Ys)))))).
% 1.61/1.08 thf(fact_14_lfinite__code_I2_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B)]: ((((coinductive_lfinite @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) = ((coinductive_lfinite @ B) @ Xs))))).
% 1.61/1.08 thf(fact_15_lfinite__LCons, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = ((coinductive_lfinite @ A) @ Xs))))).
% 1.61/1.08 thf(fact_16_llist_Oinject, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A),Y21:A,Y22:(coinductive_llist @ A)]: ((((((coinductive_LCons @ A) @ X21) @ X22) = (((coinductive_LCons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 1.61/1.08 thf(fact_17_lzip_Odisc__iff_I2_J, axiom, (! [A:$tType,B:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((~ (((coinductive_lnull @ ((product_prod @ A) @ B)) @ ((((coinductive_lzip @ A) @ B) @ Xs) @ Ys)))) = ((~ (((coinductive_lnull @ A) @ Xs))) & (~ (((coinductive_lnull @ B) @ Ys)))))))).
% 1.61/1.08 thf(fact_18_lnull__lzip, axiom, (! [A:$tType,B:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: ((((coinductive_lnull @ ((product_prod @ A) @ B)) @ ((((coinductive_lzip @ A) @ B) @ Xs) @ Ys)) = (((coinductive_lnull @ A) @ Xs) | ((coinductive_lnull @ B) @ Ys)))))).
% 1.61/1.08 thf(fact_19_lzip__simps_I2_J, axiom, (! [D:$tType,C:$tType,Xs:(coinductive_llist @ C)]: ((((((coinductive_lzip @ C) @ D) @ Xs) @ (coinductive_LNil @ D)) = (coinductive_LNil @ ((product_prod @ C) @ D)))))).
% 1.61/1.08 thf(fact_20_lzip__simps_I1_J, axiom, (! [B:$tType,A:$tType,Ys:(coinductive_llist @ B)]: ((((((coinductive_lzip @ A) @ B) @ (coinductive_LNil @ A)) @ Ys) = (coinductive_LNil @ ((product_prod @ A) @ B)))))).
% 1.61/1.08 thf(fact_21_ldropn__LNil, axiom, (! [A:$tType,N:nat]: (((((coinductive_ldropn @ A) @ N) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 1.61/1.08 thf(fact_22_ldropn__lzip, axiom, (! [A:$tType,B:$tType,N:nat,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((((coinductive_ldropn @ ((product_prod @ A) @ B)) @ N) @ ((((coinductive_lzip @ A) @ B) @ Xs) @ Ys)) = ((((coinductive_lzip @ A) @ B) @ (((coinductive_ldropn @ A) @ N) @ Xs)) @ (((coinductive_ldropn @ B) @ N) @ Ys)))))).
% 1.61/1.08 thf(fact_23_lmirror__aux__simps_I2_J, axiom, (! [A:$tType,Acc:(coinductive_llist @ A),Xa:A,X:(coinductive_llist @ A)]: (((((lMirro999291890or_aux @ A) @ Acc) @ (((coinductive_LCons @ A) @ Xa) @ X)) = (((coinductive_LCons @ A) @ Xa) @ (((lMirro999291890or_aux @ A) @ (((coinductive_LCons @ A) @ Xa) @ Acc)) @ X)))))).
% 1.61/1.08 thf(fact_24_lmirror__aux__simps_I1_J, axiom, (! [A:$tType,Acc:(coinductive_llist @ A)]: (((((lMirro999291890or_aux @ A) @ Acc) @ (coinductive_LNil @ A)) = Acc)))).
% 1.61/1.08 thf(fact_25_lstrict__prefix__code_I4_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B),Y:B,Ys:(coinductive_llist @ B)]: (((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) @ (((coinductive_LCons @ B) @ Y) @ Ys)) = ((X = Y) & (((coindu1478340336prefix @ B) @ Xs) @ Ys)))))).
% 1.61/1.08 thf(fact_26_lstrict__prefix__code_I1_J, axiom, (! [A:$tType]: ((~ ((((coindu1478340336prefix @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A))))))).
% 1.61/1.08 thf(fact_27_lstrict__prefix__code_I3_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B)]: ((~ ((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) @ (coinductive_LNil @ B))))))).
% 1.61/1.08 thf(fact_28_lstrict__prefix__code_I2_J, axiom, (! [B:$tType,Y:B,Ys:(coinductive_llist @ B)]: ((((coindu1478340336prefix @ B) @ (coinductive_LNil @ B)) @ (((coinductive_LCons @ B) @ Y) @ Ys))))).
% 1.61/1.08 thf(fact_29_lzip_Octr_I1_J, axiom, (! [B:$tType,A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((((coinductive_lnull @ A) @ Xs) | ((coinductive_lnull @ B) @ Ys)) => (((((coinductive_lzip @ A) @ B) @ Xs) @ Ys) = (coinductive_LNil @ ((product_prod @ A) @ B))))))).
% 1.61/1.08 thf(fact_30_ltl__simps_I2_J, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A)]: ((((coinductive_ltl @ A) @ (((coinductive_LCons @ A) @ X21) @ X22)) = X22)))).
% 1.61/1.08 thf(fact_31_ltl__simps_I1_J, axiom, (! [A:$tType]: ((((coinductive_ltl @ A) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 1.61/1.08 thf(fact_32_lzip_Odisc_I2_J, axiom, (! [A:$tType,B:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((~ (((coinductive_lnull @ A) @ Xs))) => ((~ (((coinductive_lnull @ B) @ Ys))) => (~ (((coinductive_lnull @ ((product_prod @ A) @ B)) @ ((((coinductive_lzip @ A) @ B) @ Xs) @ Ys))))))))).
% 1.61/1.08 thf(fact_33_lzip_Odisc_I1_J, axiom, (! [A:$tType,B:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((((coinductive_lnull @ A) @ Xs) | ((coinductive_lnull @ B) @ Ys)) => ((coinductive_lnull @ ((product_prod @ A) @ B)) @ ((((coinductive_lzip @ A) @ B) @ Xs) @ Ys)))))).
% 1.61/1.08 thf(fact_34_llist_Odisc_I2_J, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A)]: ((~ (((coinductive_lnull @ A) @ (((coinductive_LCons @ A) @ X21) @ X22))))))).
% 1.61/1.08 thf(fact_35_llist_Odisc_I1_J, axiom, (! [A:$tType]: (((coinductive_lnull @ A) @ (coinductive_LNil @ A))))).
% 1.61/1.08 thf(fact_36_llist_OdiscI_I2_J, axiom, (! [A:$tType,Llist:(coinductive_llist @ A),X21:A,X22:(coinductive_llist @ A)]: (((Llist = (((coinductive_LCons @ A) @ X21) @ X22)) => (~ (((coinductive_lnull @ A) @ Llist))))))).
% 1.61/1.08 thf(fact_37_llist_OdiscI_I1_J, axiom, (! [A:$tType,Llist:(coinductive_llist @ A)]: (((Llist = (coinductive_LNil @ A)) => ((coinductive_lnull @ A) @ Llist))))).
% 1.61/1.08 thf(fact_38_llist_Ocollapse_I1_J, axiom, (! [A:$tType,Llist:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Llist) => (Llist = (coinductive_LNil @ A)))))).
% 1.61/1.08 thf(fact_39_llist_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A)]: (((coinductive_LNil @ A) != (((coinductive_LCons @ A) @ X21) @ X22))))).
% 1.61/1.08 thf(fact_40_lmirror__aux_Octr_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Acc:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => (((coinductive_lnull @ A) @ Acc) => ((((lMirro999291890or_aux @ A) @ Acc) @ Xs) = (coinductive_LNil @ A))))))).
% 1.61/1.08 thf(fact_41_ltl__lzip, axiom, (! [A:$tType,B:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((~ (((coinductive_lnull @ A) @ Xs))) => ((~ (((coinductive_lnull @ B) @ Ys))) => (((coinductive_ltl @ ((product_prod @ A) @ B)) @ ((((coinductive_lzip @ A) @ B) @ Xs) @ Ys)) = ((((coinductive_lzip @ A) @ B) @ ((coinductive_ltl @ A) @ Xs)) @ ((coinductive_ltl @ B) @ Ys)))))))).
% 1.61/1.08 thf(fact_42_lnull__ltlI, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => ((coinductive_lnull @ A) @ ((coinductive_ltl @ A) @ Xs)))))).
% 1.61/1.08 thf(fact_43_ltl__ldropn, axiom, (! [A:$tType,N:nat,Xs:(coinductive_llist @ A)]: ((((coinductive_ltl @ A) @ (((coinductive_ldropn @ A) @ N) @ Xs)) = (((coinductive_ldropn @ A) @ N) @ ((coinductive_ltl @ A) @ Xs)))))).
% 1.61/1.08 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A2:A,P:(A > $o)]: (((((member @ A) @ A2) @ ((collect @ A) @ P)) = (P @ A2))))).
% 1.61/1.08 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A3:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A3)))) = A3)))).
% 1.61/1.08 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 1.61/1.08 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 1.61/1.08 thf(fact_48_ldropn__lnull, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),N:nat]: ((((coinductive_lnull @ A) @ Xs) => ((((coinductive_ldropn @ A) @ N) @ Xs) = (coinductive_LNil @ A)))))).
% 1.61/1.08 thf(fact_49_lzip_Oexhaust, axiom, (! [A:$tType,B:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((~ ((((coinductive_lnull @ A) @ Xs) | ((coinductive_lnull @ B) @ Ys)))) => (~ (((~ (((coinductive_lnull @ A) @ Xs))) => ((coinductive_lnull @ B) @ Ys)))))))).
% 1.61/1.08 thf(fact_50_lfinite_Ocases, axiom, (! [A:$tType,A2:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ A2) => ((A2 != (coinductive_LNil @ A)) => (~ ((! [Xs2:(coinductive_llist @ A)]: (((? [X3:A]: ((A2 = (((coinductive_LCons @ A) @ X3) @ Xs2)))) => (~ (((coinductive_lfinite @ A) @ Xs2))))))))))))).
% 1.61/1.08 thf(fact_51_lfinite_Osimps, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) = (^ [A4:(coinductive_llist @ A)]: (((A4 = (coinductive_LNil @ A)) | (? [Xs3:(coinductive_llist @ A),X2:A]: (((A4 = (((coinductive_LCons @ A) @ X2) @ Xs3)) & ((coinductive_lfinite @ A) @ Xs3))))))))))).
% 1.61/1.08 thf(fact_52_llimit__induct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > $o),Xs:(coinductive_llist @ A)]: (((P @ (coinductive_LNil @ A)) => ((! [X3:A,Xs2:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coinductive_LCons @ A) @ X3) @ Xs2)))))) => (((! [Ys2:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys2) @ Xs) => (P @ Ys2)))) => (P @ Xs)) => (P @ Xs))))))).
% 1.61/1.08 thf(fact_53_llist_Oexhaust, axiom, (! [A:$tType,Y:(coinductive_llist @ A)]: (((Y != (coinductive_LNil @ A)) => (~ ((! [X212:A,X222:(coinductive_llist @ A)]: ((Y != (((coinductive_LCons @ A) @ X212) @ X222)))))))))).
% 1.61/1.08 thf(fact_54_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((Xs != (coinductive_LNil @ A)) = (? [X2:A,Xs4:(coinductive_llist @ A)]: ((Xs = (((coinductive_LCons @ A) @ X2) @ Xs4)))))))).
% 1.61/1.08 thf(fact_55_not__lnull__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((~ (((coinductive_lnull @ A) @ Xs))) = (? [X2:A,Xs4:(coinductive_llist @ A)]: ((Xs = (((coinductive_LCons @ A) @ X2) @ Xs4)))))))).
% 1.61/1.08 thf(fact_56_lappend_Oexhaust, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lnull @ A) @ Xs) => (~ (((coinductive_lnull @ A) @ Ys)))) => ((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))))))).
% 1.61/1.08 thf(fact_57_lfinite_Oinducts, axiom, (! [A:$tType,X:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: ((((coinductive_lfinite @ A) @ X) => ((P @ (coinductive_LNil @ A)) => ((! [Xs2:(coinductive_llist @ A),X3:A]: ((((coinductive_lfinite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coinductive_LCons @ A) @ X3) @ Xs2)))))) => (P @ X))))))).
% 1.61/1.08 thf(fact_58_lnull__def, axiom, (! [A:$tType]: (((coinductive_lnull @ A) = (^ [Llist2:(coinductive_llist @ A)]: ((Llist2 = (coinductive_LNil @ A)))))))).
% 1.61/1.08 thf(fact_59_llist__less__induct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > $o),Xs:(coinductive_llist @ A)]: (((! [Xs2:(coinductive_llist @ A)]: (((! [Ys2:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys2) @ Xs2) => (P @ Ys2)))) => (P @ Xs2)))) => (P @ Xs))))).
% 1.61/1.08 thf(fact_60_lzip__eq__LNil__conv, axiom, (! [A:$tType,B:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((((((coinductive_lzip @ A) @ B) @ Xs) @ Ys) = (coinductive_LNil @ ((product_prod @ A) @ B))) = ((Xs = (coinductive_LNil @ A)) | (Ys = (coinductive_LNil @ B))))))).
% 1.61/1.08 thf(fact_61_lfinite__LConsI, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),X:A]: ((((coinductive_lfinite @ A) @ Xs) => ((coinductive_lfinite @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)))))).
% 1.61/1.08 thf(fact_62_lfinite__LNil, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) @ (coinductive_LNil @ A))))).
% 1.61/1.08 thf(fact_63_lmirror__aux_Odisc_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Acc:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => (((coinductive_lnull @ A) @ Acc) => ((coinductive_lnull @ A) @ (((lMirro999291890or_aux @ A) @ Acc) @ Xs))))))).
% 1.61/1.08 thf(fact_64_lmirror__aux_Odisc_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Acc:(coinductive_llist @ A)]: ((((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Acc)))) => (~ (((coinductive_lnull @ A) @ (((lMirro999291890or_aux @ A) @ Acc) @ Xs)))))))).
% 1.61/1.08 thf(fact_65_lmirror__def, axiom, (! [A:$tType]: (((lMirro427583474mirror @ A) = ((lMirro999291890or_aux @ A) @ (coinductive_LNil @ A)))))).
% 1.61/1.08 thf(fact_66_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = ((Xs = (coinductive_LNil @ A)) | (? [Xs4:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ Y) @ Xs4)) & (((coindu328551480prefix @ A) @ Xs4) @ Ys))))))))).
% 1.61/1.08 thf(fact_67_ltl__lmirror__aux, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Acc:(coinductive_llist @ A)]: (((((coinductive_lnull @ A) @ Xs) => (((coinductive_ltl @ A) @ (((lMirro999291890or_aux @ A) @ Acc) @ Xs)) = ((coinductive_ltl @ A) @ Acc))) & ((~ (((coinductive_lnull @ A) @ Xs))) => (((coinductive_ltl @ A) @ (((lMirro999291890or_aux @ A) @ Acc) @ Xs)) = (((lMirro999291890or_aux @ A) @ (((coinductive_LCons @ A) @ ((coinductive_lhd @ A) @ Xs)) @ Acc)) @ ((coinductive_ltl @ A) @ Xs)))))))).
% 1.61/1.08 thf(fact_68_llast__singleton, axiom, (! [A:$tType,X:A]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A))) = X)))).
% 1.61/1.08 thf(fact_69_lhd__LCons__ltl, axiom, (! [A:$tType,Llist:(coinductive_llist @ A)]: (((~ (((coinductive_lnull @ A) @ Llist))) => ((((coinductive_LCons @ A) @ ((coinductive_lhd @ A) @ Llist)) @ ((coinductive_ltl @ A) @ Llist)) = Llist))))).
% 1.61/1.08 thf(fact_70_lmember__code_I1_J, axiom, (! [A:$tType,X:A]: ((~ ((((coinductive_lmember @ A) @ X) @ (coinductive_LNil @ A))))))).
% 1.61/1.08 thf(fact_71_lmember__code_I2_J, axiom, (! [A:$tType,X:A,Y:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lmember @ A) @ X) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = ((X = Y) | (((coinductive_lmember @ A) @ X) @ Ys)))))).
% 1.61/1.08 thf(fact_72_lstrict__prefix__lappend__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Xs) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lfinite @ A) @ Xs) & (~ (((coinductive_lnull @ A) @ Ys)))))))).
% 1.61/1.08 thf(fact_73_gen__lset__code_I1_J, axiom, (! [A:$tType,A3:(set @ A)]: (((((coinductive_gen_lset @ A) @ A3) @ (coinductive_LNil @ A)) = A3)))).
% 1.61/1.08 thf(fact_74_llast__LCons, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),X:A]: (((((coinductive_lnull @ A) @ Xs) => (((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = X)) & ((~ (((coinductive_lnull @ A) @ Xs))) => (((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = ((coinductive_llast @ A) @ Xs))))))).
% 1.61/1.08 thf(fact_75_lappend__code_I2_J, axiom, (! [A:$tType,Xa:A,X:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_LCons @ A) @ Xa) @ X)) @ Ys) = (((coinductive_LCons @ A) @ Xa) @ (((coinductive_lappend @ A) @ X) @ Ys)))))).
% 1.61/1.08 thf(fact_76_lnull__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lnull @ A) @ Xs) & ((coinductive_lnull @ A) @ Ys)))))).
% 1.61/1.08 thf(fact_77_lappend_Odisc__iff_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((~ (((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)))) = ((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))))))).
% 1.61/1.08 thf(fact_78_lappend__LNil2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ Xs) @ (coinductive_LNil @ A)) = Xs)))).
% 1.61/1.08 thf(fact_79_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ Ys) = Ys)))).
% 1.61/1.08 thf(fact_80_lfinite__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lfinite @ A) @ Xs) & ((coinductive_lfinite @ A) @ Ys)))))).
% 1.61/1.08 thf(fact_81_llast__LCons2, axiom, (! [A:$tType,X:A,Y:A,Xs:(coinductive_llist @ A)]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ (((coinductive_LCons @ A) @ Y) @ Xs))) = ((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ Y) @ Xs)))))).
% 1.61/1.08 thf(fact_82_ltl__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lnull @ A) @ Xs) => (((coinductive_ltl @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((coinductive_ltl @ A) @ Ys))) & ((~ (((coinductive_lnull @ A) @ Xs))) => (((coinductive_ltl @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lappend @ A) @ ((coinductive_ltl @ A) @ Xs)) @ Ys))))))).
% 1.61/1.08 thf(fact_83_lhd__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lnull @ A) @ Xs) => (((coinductive_lhd @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((coinductive_lhd @ A) @ Ys))) & ((~ (((coinductive_lnull @ A) @ Xs))) => (((coinductive_lhd @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((coinductive_lhd @ A) @ Xs))))))).
% 1.61/1.08 thf(fact_84_llast__lappend__LCons, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys))) = ((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ Y) @ Ys))))))).
% 1.61/1.08 thf(fact_85_lappend__assoc, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) @ Zs) = (((coinductive_lappend @ A) @ Xs) @ (((coinductive_lappend @ A) @ Ys) @ Zs)))))).
% 1.61/1.08 thf(fact_86_lhd__LCons, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A)]: ((((coinductive_lhd @ A) @ (((coinductive_LCons @ A) @ X21) @ X22)) = X21)))).
% 1.61/1.08 thf(fact_87_ltakeWhile_Oexhaust, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:(A > $o)]: (((~ ((((coinductive_lnull @ A) @ Xs) | (~ ((P @ ((coinductive_lhd @ A) @ Xs))))))) => (~ (((~ (((coinductive_lnull @ A) @ Xs))) => (~ ((P @ ((coinductive_lhd @ A) @ Xs))))))))))).
% 1.61/1.08 thf(fact_88_lappend__lnull2, axiom, (! [A:$tType,Ys:(coinductive_llist @ A),Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Ys) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = Xs))))).
% 1.61/1.08 thf(fact_89_lappend__lnull1, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = Ys))))).
% 1.61/1.08 thf(fact_90_lappend_Odisc_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => (((coinductive_lnull @ A) @ Ys) => ((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys))))))).
% 1.61/1.08 thf(fact_91_lappend_Odisc_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))) => (~ (((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)))))))).
% 1.61/1.08 thf(fact_92_lappend__eq__LNil__iff, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((((coinductive_lappend @ A) @ Xs) @ Ys) = (coinductive_LNil @ A)) = ((Xs = (coinductive_LNil @ A)) & (Ys = (coinductive_LNil @ A))))))).
% 1.61/1.08 thf(fact_93_LNil__eq__lappend__iff, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_LNil @ A) = (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((Xs = (coinductive_LNil @ A)) & (Ys = (coinductive_LNil @ A))))))).
% 1.61/1.08 thf(fact_94_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 1.61/1.08 thf(fact_95_lappend__inf, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((~ (((coinductive_lfinite @ A) @ Xs))) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = Xs))))).
% 1.61/1.08 thf(fact_96_lappend__snocL1__conv__LCons2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ (coinductive_LNil @ A)))) @ Ys) = (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys)))))).
% 1.61/1.08 thf(fact_97_lappend_Octr_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => (((coinductive_lnull @ A) @ Ys) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = (coinductive_LNil @ A))))))).
% 1.61/1.08 thf(fact_98_llist_Ocoinduct__strong, axiom, (! [A:$tType,R:((coinductive_llist @ A) > ((coinductive_llist @ A) > $o)),Llist:(coinductive_llist @ A),Llist3:(coinductive_llist @ A)]: ((((R @ Llist) @ Llist3) => ((! [Llist4:(coinductive_llist @ A),Llist5:(coinductive_llist @ A)]: ((((R @ Llist4) @ Llist5) => ((((coinductive_lnull @ A) @ Llist4) = ((coinductive_lnull @ A) @ Llist5)) & ((~ (((coinductive_lnull @ A) @ Llist4))) => ((~ (((coinductive_lnull @ A) @ Llist5))) => ((((coinductive_lhd @ A) @ Llist4) = ((coinductive_lhd @ A) @ Llist5)) & (((R @ ((coinductive_ltl @ A) @ Llist4)) @ ((coinductive_ltl @ A) @ Llist5)) | (((coinductive_ltl @ A) @ Llist4) = ((coinductive_ltl @ A) @ Llist5)))))))))) => (Llist = Llist3)))))).
% 1.61/1.08 thf(fact_99_llist_Ocoinduct, axiom, (! [A:$tType,R:((coinductive_llist @ A) > ((coinductive_llist @ A) > $o)),Llist:(coinductive_llist @ A),Llist3:(coinductive_llist @ A)]: ((((R @ Llist) @ Llist3) => ((! [Llist4:(coinductive_llist @ A),Llist5:(coinductive_llist @ A)]: ((((R @ Llist4) @ Llist5) => ((((coinductive_lnull @ A) @ Llist4) = ((coinductive_lnull @ A) @ Llist5)) & ((~ (((coinductive_lnull @ A) @ Llist4))) => ((~ (((coinductive_lnull @ A) @ Llist5))) => ((((coinductive_lhd @ A) @ Llist4) = ((coinductive_lhd @ A) @ Llist5)) & ((R @ ((coinductive_ltl @ A) @ Llist4)) @ ((coinductive_ltl @ A) @ Llist5))))))))) => (Llist = Llist3)))))).
% 1.61/1.08 thf(fact_100_llist_Oexpand, axiom, (! [A:$tType,Llist:(coinductive_llist @ A),Llist3:(coinductive_llist @ A)]: (((((coinductive_lnull @ A) @ Llist) = ((coinductive_lnull @ A) @ Llist3)) => (((~ (((coinductive_lnull @ A) @ Llist))) => ((~ (((coinductive_lnull @ A) @ Llist3))) => ((((coinductive_lhd @ A) @ Llist) = ((coinductive_lhd @ A) @ Llist3)) & (((coinductive_ltl @ A) @ Llist) = ((coinductive_ltl @ A) @ Llist3))))) => (Llist = Llist3)))))).
% 1.61/1.08 thf(fact_101_lappend__ltl, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((~ (((coinductive_lnull @ A) @ Xs))) => ((((coinductive_lappend @ A) @ ((coinductive_ltl @ A) @ Xs)) @ Ys) = ((coinductive_ltl @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys))))))).
% 1.61/1.08 thf(fact_102_lhd__lmirror__aux, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Acc:(coinductive_llist @ A)]: (((((coinductive_lnull @ A) @ Xs) => (((coinductive_lhd @ A) @ (((lMirro999291890or_aux @ A) @ Acc) @ Xs)) = ((coinductive_lhd @ A) @ Acc))) & ((~ (((coinductive_lnull @ A) @ Xs))) => (((coinductive_lhd @ A) @ (((lMirro999291890or_aux @ A) @ Acc) @ Xs)) = ((coinductive_lhd @ A) @ Xs))))))).
% 1.61/1.08 thf(fact_103_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (coinductive_LNil @ A)) = (Xs = (coinductive_LNil @ A)))))).
% 1.61/1.08 thf(fact_104_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coindu328551480prefix @ A) @ (coinductive_LNil @ A)) @ Xs)))).
% 1.61/1.08 thf(fact_105_llist_Oexhaust__sel, axiom, (! [A:$tType,Llist:(coinductive_llist @ A)]: (((Llist != (coinductive_LNil @ A)) => (Llist = (((coinductive_LCons @ A) @ ((coinductive_lhd @ A) @ Llist)) @ ((coinductive_ltl @ A) @ Llist))))))).
% 1.61/1.08 thf(fact_106_eq__LConsD, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ Y) @ Ys)) => ((Xs != (coinductive_LNil @ A)) & ((((coinductive_lhd @ A) @ Xs) = Y) & (((coinductive_ltl @ A) @ Xs) = Ys))))))).
% 1.61/1.08 thf(fact_107_lfinite__rev__induct, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: ((((coinductive_lfinite @ A) @ Xs) => ((P @ (coinductive_LNil @ A)) => ((! [X3:A,Xs2:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs2) => ((P @ Xs2) => (P @ (((coinductive_lappend @ A) @ Xs2) @ (((coinductive_LCons @ A) @ X3) @ (coinductive_LNil @ A)))))))) => (P @ Xs))))))).
% 1.61/1.08 thf(fact_108_lzip_Ocode, axiom, (! [B:$tType,A:$tType]: ((((coinductive_lzip @ A) @ B) = (^ [Xs3:(coinductive_llist @ A),Ys3:(coinductive_llist @ B)]: (((((if @ (coinductive_llist @ ((product_prod @ A) @ B))) @ (((coinductive_lnull @ A) @ Xs3) | ((coinductive_lnull @ B) @ Ys3))) @ (coinductive_LNil @ ((product_prod @ A) @ B))) @ (((coinductive_LCons @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ ((coinductive_lhd @ A) @ Xs3)) @ ((coinductive_lhd @ B) @ Ys3))) @ ((((coinductive_lzip @ A) @ B) @ ((coinductive_ltl @ A) @ Xs3)) @ ((coinductive_ltl @ B) @ Ys3)))))))))).
% 1.61/1.08 thf(fact_109_llexord__conv, axiom, (! [A:$tType]: (((coinductive_llexord @ A) = (^ [R2:(A > (A > $o)),Xs3:(coinductive_llist @ A),Ys3:(coinductive_llist @ A)]: (((Xs3 = Ys3) | (? [Zs2:(coinductive_llist @ A),Xs4:(coinductive_llist @ A),Y2:A,Ys4:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Zs2) & ((Xs3 = (((coinductive_lappend @ A) @ Zs2) @ Xs4)) & ((Ys3 = (((coinductive_lappend @ A) @ Zs2) @ (((coinductive_LCons @ A) @ Y2) @ Ys4))) & ((Xs4 = (coinductive_LNil @ A)) | ((R2 @ ((coinductive_lhd @ A) @ Xs4)) @ Y2)))))))))))))).
% 1.61/1.08 thf(fact_110_llist_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F2:(A > ((coinductive_llist @ A) > B)),Llist:(coinductive_llist @ A)]: (((P @ (((((coindu1381640503_llist @ B) @ A) @ F1) @ F2) @ Llist)) = (~ ((((Llist = (coinductive_LNil @ A)) & (~ ((P @ F1)))) | ((Llist = (((coinductive_LCons @ A) @ ((coinductive_lhd @ A) @ Llist)) @ ((coinductive_ltl @ A) @ Llist))) & (~ ((P @ ((F2 @ ((coinductive_lhd @ A) @ Llist)) @ ((coinductive_ltl @ A) @ Llist))))))))))))).
% 1.61/1.08 thf(fact_111_llist_Osplit__sel, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F2:(A > ((coinductive_llist @ A) > B)),Llist:(coinductive_llist @ A)]: (((P @ (((((coindu1381640503_llist @ B) @ A) @ F1) @ F2) @ Llist)) = (((Llist = (coinductive_LNil @ A)) => (P @ F1)) & ((Llist = (((coinductive_LCons @ A) @ ((coinductive_lhd @ A) @ Llist)) @ ((coinductive_ltl @ A) @ Llist))) => (P @ ((F2 @ ((coinductive_lhd @ A) @ Llist)) @ ((coinductive_ltl @ A) @ Llist))))))))).
% 1.61/1.08 thf(fact_112_unfold__llist__id, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((((((coindu1441602521_llist @ (coinductive_llist @ A)) @ A) @ (coinductive_lnull @ A)) @ (coinductive_lhd @ A)) @ (coinductive_ltl @ A)) @ Xs) = Xs)))).
% 1.61/1.08 thf(fact_113_ltakeWhile_Ocode, axiom, (! [A:$tType]: (((coindu501562517eWhile @ A) = (^ [P2:(A > $o),Xs3:(coinductive_llist @ A)]: (((((if @ (coinductive_llist @ A)) @ (((coinductive_lnull @ A) @ Xs3) | (~ ((P2 @ ((coinductive_lhd @ A) @ Xs3)))))) @ (coinductive_LNil @ A)) @ (((coinductive_LCons @ A) @ ((coinductive_lhd @ A) @ Xs3)) @ (((coindu501562517eWhile @ A) @ P2) @ ((coinductive_ltl @ A) @ Xs3)))))))))).
% 1.61/1.08 thf(fact_114_llexord__refl, axiom, (! [A:$tType,R3:(A > (A > $o)),Xs:(coinductive_llist @ A)]: (((((coinductive_llexord @ A) @ R3) @ Xs) @ Xs)))).
% 1.61/1.08 thf(fact_115_ltakeWhile__LNil, axiom, (! [A:$tType,P:(A > $o)]: (((((coindu501562517eWhile @ A) @ P) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 1.61/1.08 thf(fact_116_llexord__LCons__LCons, axiom, (! [A:$tType,R3:(A > (A > $o)),X:A,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R3) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = (((X = Y) & ((((coinductive_llexord @ A) @ R3) @ Xs) @ Ys)) | ((R3 @ X) @ Y)))))).
% 1.61/1.08 thf(fact_117_llexord__LNil__right, axiom, (! [A:$tType,Ys:(coinductive_llist @ A),R3:(A > (A > $o)),Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Ys) => (((((coinductive_llexord @ A) @ R3) @ Xs) @ Ys) = ((coinductive_lnull @ A) @ Xs)))))).
% 1.61/1.08 thf(fact_118_llexord__code_I1_J, axiom, (! [A:$tType,R3:(A > (A > $o)),Ys:(coinductive_llist @ A)]: (((((coinductive_llexord @ A) @ R3) @ (coinductive_LNil @ A)) @ Ys)))).
% 1.61/1.08 thf(fact_119_unfold__llist__eq__LCons, axiom, (! [A:$tType,B:$tType,IS_LNIL:(B > $o),LHD:(B > A),LTL:(B > B),B2:B,X:A,Xs:(coinductive_llist @ A)]: (((((((((coindu1441602521_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ B2) = (((coinductive_LCons @ A) @ X) @ Xs)) = ((~ ((IS_LNIL @ B2))) & ((X = (LHD @ B2)) & (Xs = ((((((coindu1441602521_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ (LTL @ B2))))))))).
% 1.61/1.08 thf(fact_120_unfold__llist_Odisc__iff_I2_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),G21:(A > B),G22:(A > A),A2:A]: (((~ (((coinductive_lnull @ B) @ ((((((coindu1441602521_llist @ A) @ B) @ P3) @ G21) @ G22) @ A2)))) = (~ ((P3 @ A2))))))).
% 1.61/1.08 thf(fact_121_unfold__llist_Odisc__iff_I1_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),G21:(A > B),G22:(A > A),A2:A]: ((((coinductive_lnull @ B) @ ((((((coindu1441602521_llist @ A) @ B) @ P3) @ G21) @ G22) @ A2)) = (P3 @ A2))))).
% 1.61/1.08 thf(fact_122_ltakeWhile__LCons, axiom, (! [A:$tType,P:(A > $o),X:A,Xs:(coinductive_llist @ A)]: ((((P @ X) => ((((coindu501562517eWhile @ A) @ P) @ (((coinductive_LCons @ A) @ X) @ Xs)) = (((coinductive_LCons @ A) @ X) @ (((coindu501562517eWhile @ A) @ P) @ Xs)))) & ((~ ((P @ X))) => ((((coindu501562517eWhile @ A) @ P) @ (((coinductive_LCons @ A) @ X) @ Xs)) = (coinductive_LNil @ A))))))).
% 1.61/1.08 thf(fact_123_ltakeWhile_Odisc__iff_I2_J, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: (((~ (((coinductive_lnull @ A) @ (((coindu501562517eWhile @ A) @ P) @ Xs)))) = ((~ (((coinductive_lnull @ A) @ Xs))) & (P @ ((coinductive_lhd @ A) @ Xs))))))).
% 1.61/1.08 thf(fact_124_ltakeWhile_Odisc__iff_I1_J, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ (((coindu501562517eWhile @ A) @ P) @ Xs)) = (((coinductive_lnull @ A) @ Xs) | (~ ((P @ ((coinductive_lhd @ A) @ Xs))))))))).
% 1.61/1.08 thf(fact_125_lnull__ltakeWhile, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ (((coindu501562517eWhile @ A) @ P) @ Xs)) = ((~ (((coinductive_lnull @ A) @ Xs))) => (~ ((P @ ((coinductive_lhd @ A) @ Xs))))))))).
% 1.61/1.08 thf(fact_126_lzip__simps_I3_J, axiom, (! [C:$tType,B:$tType,X:C,Xs:(coinductive_llist @ C),Y:B,Ys:(coinductive_llist @ B)]: ((((((coinductive_lzip @ C) @ B) @ (((coinductive_LCons @ C) @ X) @ Xs)) @ (((coinductive_LCons @ B) @ Y) @ Ys)) = (((coinductive_LCons @ ((product_prod @ C) @ B)) @ ((((product_Pair @ C) @ B) @ X) @ Y)) @ ((((coinductive_lzip @ C) @ B) @ Xs) @ Ys)))))).
% 1.61/1.08 thf(fact_127_llexord__antisym, axiom, (! [A:$tType,R3:(A > (A > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R3) @ Xs) @ Ys) => (((((coinductive_llexord @ A) @ R3) @ Ys) @ Xs) => ((! [A5:A,B3:A]: ((((R3 @ A5) @ B3) => (~ (((R3 @ B3) @ A5)))))) => (Xs = Ys))))))).
% 1.61/1.08 thf(fact_128_llexord__linear, axiom, (! [A:$tType,R3:(A > (A > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((! [X3:A,Y3:A]: ((((R3 @ X3) @ Y3) | ((X3 = Y3) | ((R3 @ Y3) @ X3))))) => (((((coinductive_llexord @ A) @ R3) @ Xs) @ Ys) | ((((coinductive_llexord @ A) @ R3) @ Ys) @ Xs)))))).
% 1.61/1.08 thf(fact_129_llexord__trans, axiom, (! [A:$tType,R3:(A > (A > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R3) @ Xs) @ Ys) => (((((coinductive_llexord @ A) @ R3) @ Ys) @ Zs) => ((! [A5:A,B3:A,C2:A]: ((((R3 @ A5) @ B3) => (((R3 @ B3) @ C2) => ((R3 @ A5) @ C2))))) => ((((coinductive_llexord @ A) @ R3) @ Xs) @ Zs))))))).
% 1.61/1.08 thf(fact_130_llexord__code_I3_J, axiom, (! [A:$tType,R3:(A > (A > $o)),X:A,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R3) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = (((R3 @ X) @ Y) | ((X = Y) & ((((coinductive_llexord @ A) @ R3) @ Xs) @ Ys))))))).
% 1.61/1.08 thf(fact_131_llexord__LCons__left, axiom, (! [A:$tType,R3:(A > (A > $o)),X:A,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R3) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ Ys) = (? [Y2:A,Ys4:(coinductive_llist @ A)]: (((Ys = (((coinductive_LCons @ A) @ Y2) @ Ys4)) & (((X = Y2) & ((((coinductive_llexord @ A) @ R3) @ Xs) @ Ys4)) | ((R3 @ X) @ Y2))))))))).
% 1.61/1.08 thf(fact_132_llexord__LCons__eq, axiom, (! [A:$tType,R3:(A > (A > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),X:A]: ((((((coinductive_llexord @ A) @ R3) @ Xs) @ Ys) => ((((coinductive_llexord @ A) @ R3) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ (((coinductive_LCons @ A) @ X) @ Ys)))))).
% 1.61/1.08 thf(fact_133_llexord__LCons__less, axiom, (! [A:$tType,R3:(A > (A > $o)),X:A,Y:A,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((R3 @ X) @ Y) => ((((coinductive_llexord @ A) @ R3) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ (((coinductive_LCons @ A) @ Y) @ Ys)))))).
% 1.61/1.08 thf(fact_134_lnull__llexord, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),R3:(A > (A > $o)),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => ((((coinductive_llexord @ A) @ R3) @ Xs) @ Ys))))).
% 1.61/1.08 thf(fact_135_llexord__LNil, axiom, (! [A:$tType,R3:(A > (A > $o)),Ys:(coinductive_llist @ A)]: (((((coinductive_llexord @ A) @ R3) @ (coinductive_LNil @ A)) @ Ys)))).
% 1.61/1.08 thf(fact_136_llexord__lappend__leftI, axiom, (! [A:$tType,R3:(A > (A > $o)),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A),Xs:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R3) @ Ys) @ Zs) => ((((coinductive_llexord @ A) @ R3) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) @ (((coinductive_lappend @ A) @ Xs) @ Zs)))))).
% 1.61/1.08 thf(fact_137_llexord__append__right, axiom, (! [A:$tType,R3:(A > (A > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_llexord @ A) @ R3) @ Xs) @ (((coinductive_lappend @ A) @ Xs) @ Ys))))).
% 1.61/1.08 thf(fact_138_unfold__llist_Octr_I2_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((~ ((P3 @ A2))) => (((((((coindu1441602521_llist @ A) @ B) @ P3) @ G21) @ G22) @ A2) = (((coinductive_LCons @ B) @ (G21 @ A2)) @ ((((((coindu1441602521_llist @ A) @ B) @ P3) @ G21) @ G22) @ (G22 @ A2)))))))).
% 1.61/1.08 thf(fact_139_unfold__llist_Odisc_I2_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((~ ((P3 @ A2))) => (~ (((coinductive_lnull @ B) @ ((((((coindu1441602521_llist @ A) @ B) @ P3) @ G21) @ G22) @ A2)))))))).
% 1.61/1.08 thf(fact_140_unfold__llist_Odisc_I1_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((P3 @ A2) => ((coinductive_lnull @ B) @ ((((((coindu1441602521_llist @ A) @ B) @ P3) @ G21) @ G22) @ A2)))))).
% 1.61/1.08 thf(fact_141_unfold__llist_Octr_I1_J, axiom, (! [A:$tType,B:$tType,P3:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((P3 @ A2) => (((((((coindu1441602521_llist @ A) @ B) @ P3) @ G21) @ G22) @ A2) = (coinductive_LNil @ B)))))).
% 1.61/1.08 thf(fact_142_llist_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F2:(A > ((coinductive_llist @ A) > B)),X21:A,X22:(coinductive_llist @ A)]: (((((((coindu1381640503_llist @ B) @ A) @ F1) @ F2) @ (((coinductive_LCons @ A) @ X21) @ X22)) = ((F2 @ X21) @ X22))))).
% 1.61/1.08 thf(fact_143_llist_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F2:(A > ((coinductive_llist @ A) > B))]: (((((((coindu1381640503_llist @ B) @ A) @ F1) @ F2) @ (coinductive_LNil @ A)) = F1)))).
% 1.61/1.08 thf(fact_144_unfold__llist_Osimps_I4_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((~ ((P3 @ A2))) => (((coinductive_ltl @ B) @ ((((((coindu1441602521_llist @ A) @ B) @ P3) @ G21) @ G22) @ A2)) = ((((((coindu1441602521_llist @ A) @ B) @ P3) @ G21) @ G22) @ (G22 @ A2))))))).
% 1.61/1.08 thf(fact_145_unfold__llist_Osimps_I3_J, axiom, (! [B:$tType,A:$tType,P3:(A > $o),A2:A,G21:(A > B),G22:(A > A)]: (((~ ((P3 @ A2))) => (((coinductive_lhd @ B) @ ((((((coindu1441602521_llist @ A) @ B) @ P3) @ G21) @ G22) @ A2)) = (G21 @ A2)))))).
% 1.61/1.08 thf(fact_146_lhd__ltakeWhile, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:(A > $o)]: (((~ (((coinductive_lnull @ A) @ Xs))) => ((P @ ((coinductive_lhd @ A) @ Xs)) => (((coinductive_lhd @ A) @ (((coindu501562517eWhile @ A) @ P) @ Xs)) = ((coinductive_lhd @ A) @ Xs))))))).
% 1.61/1.08 thf(fact_147_ltakeWhile_Odisc_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:(A > $o)]: (((((coinductive_lnull @ A) @ Xs) | (~ ((P @ ((coinductive_lhd @ A) @ Xs))))) => ((coinductive_lnull @ A) @ (((coindu501562517eWhile @ A) @ P) @ Xs)))))).
% 1.61/1.08 thf(fact_148_ltakeWhile_Odisc_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:(A > $o)]: (((~ (((coinductive_lnull @ A) @ Xs))) => ((P @ ((coinductive_lhd @ A) @ Xs)) => (~ (((coinductive_lnull @ A) @ (((coindu501562517eWhile @ A) @ P) @ Xs))))))))).
% 1.61/1.08 thf(fact_149_ltakeWhile__eq__LNil__iff, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: ((((((coindu501562517eWhile @ A) @ P) @ Xs) = (coinductive_LNil @ A)) = ((Xs != (coinductive_LNil @ A)) => (~ ((P @ ((coinductive_lhd @ A) @ Xs))))))))).
% 1.61/1.08 thf(fact_150_lzip__eq__LCons__conv, axiom, (! [B:$tType,A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B),Z:((product_prod @ A) @ B),Zs:(coinductive_llist @ ((product_prod @ A) @ B))]: (((((((coinductive_lzip @ A) @ B) @ Xs) @ Ys) = (((coinductive_LCons @ ((product_prod @ A) @ B)) @ Z) @ Zs)) = (? [X2:A,Xs4:(coinductive_llist @ A),Y2:B,Ys4:(coinductive_llist @ B)]: (((Xs = (((coinductive_LCons @ A) @ X2) @ Xs4)) & ((Ys = (((coinductive_LCons @ B) @ Y2) @ Ys4)) & ((Z = ((((product_Pair @ A) @ B) @ X2) @ Y2)) & (Zs = ((((coinductive_lzip @ A) @ B) @ Xs4) @ Ys4))))))))))).
% 1.61/1.08 thf(fact_151_llexord__code_I2_J, axiom, (! [A:$tType,R3:(A > (A > $o)),X:A,Xs:(coinductive_llist @ A)]: ((~ (((((coinductive_llexord @ A) @ R3) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ (coinductive_LNil @ A))))))).
% 1.61/1.08 thf(fact_152_llexord_Ocases, axiom, (! [A:$tType,R3:(A > (A > $o)),A1:(coinductive_llist @ A),A22:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R3) @ A1) @ A22) => ((! [Xs2:(coinductive_llist @ A),Ys5:(coinductive_llist @ A),X3:A]: (((A1 = (((coinductive_LCons @ A) @ X3) @ Xs2)) => ((A22 = (((coinductive_LCons @ A) @ X3) @ Ys5)) => (~ (((((coinductive_llexord @ A) @ R3) @ Xs2) @ Ys5))))))) => ((! [X3:A]: (((? [Xs2:(coinductive_llist @ A)]: ((A1 = (((coinductive_LCons @ A) @ X3) @ Xs2)))) => (! [Y3:A]: (((? [Ys5:(coinductive_llist @ A)]: ((A22 = (((coinductive_LCons @ A) @ Y3) @ Ys5)))) => (~ (((R3 @ X3) @ Y3))))))))) => (~ (((A1 = (coinductive_LNil @ A)) => (! [Ys5:(coinductive_llist @ A)]: ((A22 != Ys5)))))))))))).
% 1.61/1.08 thf(fact_153_llexord_Osimps, axiom, (! [A:$tType]: (((coinductive_llexord @ A) = (^ [R2:(A > (A > $o)),A12:(coinductive_llist @ A),A23:(coinductive_llist @ A)]: (((? [Xs3:(coinductive_llist @ A),Ys3:(coinductive_llist @ A),X2:A]: (((A12 = (((coinductive_LCons @ A) @ X2) @ Xs3)) & ((A23 = (((coinductive_LCons @ A) @ X2) @ Ys3)) & ((((coinductive_llexord @ A) @ R2) @ Xs3) @ Ys3))))) | ((? [X2:A,Y2:A,Xs3:(coinductive_llist @ A),Ys3:(coinductive_llist @ A)]: (((A12 = (((coinductive_LCons @ A) @ X2) @ Xs3)) & ((A23 = (((coinductive_LCons @ A) @ Y2) @ Ys3)) & ((R2 @ X2) @ Y2))))) | (? [Ys3:(coinductive_llist @ A)]: (((A12 = (coinductive_LNil @ A)) & (A23 = Ys3)))))))))))).
% 1.61/1.08 thf(fact_154_llexord_Ocoinduct, axiom, (! [A:$tType,X4:((coinductive_llist @ A) > ((coinductive_llist @ A) > $o)),X:(coinductive_llist @ A),Xa:(coinductive_llist @ A),R3:(A > (A > $o))]: ((((X4 @ X) @ Xa) => ((! [X3:(coinductive_llist @ A),Xa2:(coinductive_llist @ A)]: ((((X4 @ X3) @ Xa2) => ((? [Xs5:(coinductive_llist @ A),Ys2:(coinductive_llist @ A),Xb:A]: (((X3 = (((coinductive_LCons @ A) @ Xb) @ Xs5)) & ((Xa2 = (((coinductive_LCons @ A) @ Xb) @ Ys2)) & (((X4 @ Xs5) @ Ys2) | ((((coinductive_llexord @ A) @ R3) @ Xs5) @ Ys2)))))) | ((? [Xb:A,Y4:A,Xs5:(coinductive_llist @ A),Ys2:(coinductive_llist @ A)]: (((X3 = (((coinductive_LCons @ A) @ Xb) @ Xs5)) & ((Xa2 = (((coinductive_LCons @ A) @ Y4) @ Ys2)) & ((R3 @ Xb) @ Y4))))) | (? [Ys2:(coinductive_llist @ A)]: (((X3 = (coinductive_LNil @ A)) & (Xa2 = Ys2))))))))) => ((((coinductive_llexord @ A) @ R3) @ X) @ Xa)))))).
% 1.61/1.08 thf(fact_155_unfold__llist_Ocode, axiom, (! [B:$tType,A:$tType]: ((((coindu1441602521_llist @ A) @ B) = (^ [P4:(A > $o),G212:(A > B),G222:(A > A),A4:A]: (((((if @ (coinductive_llist @ B)) @ (P4 @ A4)) @ (coinductive_LNil @ B)) @ (((coinductive_LCons @ B) @ (G212 @ A4)) @ ((((((coindu1441602521_llist @ A) @ B) @ P4) @ G212) @ G222) @ (G222 @ A4)))))))))).
% 1.61/1.08 thf(fact_156_ltl__unfold__llist, axiom, (! [A:$tType,B:$tType,IS_LNIL:(B > $o),A2:B,LHD:(B > A),LTL:(B > B)]: ((((IS_LNIL @ A2) => (((coinductive_ltl @ A) @ ((((((coindu1441602521_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ A2)) = (coinductive_LNil @ A))) & ((~ ((IS_LNIL @ A2))) => (((coinductive_ltl @ A) @ ((((((coindu1441602521_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ A2)) = ((((((coindu1441602521_llist @ B) @ A) @ IS_LNIL) @ LHD) @ LTL) @ (LTL @ A2)))))))).
% 1.61/1.08 thf(fact_157_ltakeWhile_Octr_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:(A > $o)]: (((((coinductive_lnull @ A) @ Xs) | (~ ((P @ ((coinductive_lhd @ A) @ Xs))))) => ((((coindu501562517eWhile @ A) @ P) @ Xs) = (coinductive_LNil @ A)))))).
% 1.61/1.08 thf(fact_158_ltakeWhile_Osimps_I4_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:(A > $o)]: (((~ (((coinductive_lnull @ A) @ Xs))) => ((P @ ((coinductive_lhd @ A) @ Xs)) => (((coinductive_ltl @ A) @ (((coindu501562517eWhile @ A) @ P) @ Xs)) = (((coindu501562517eWhile @ A) @ P) @ ((coinductive_ltl @ A) @ Xs)))))))).
% 1.61/1.08 thf(fact_159_ltl__ltakeWhile, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: ((((P @ ((coinductive_lhd @ A) @ Xs)) => (((coinductive_ltl @ A) @ (((coindu501562517eWhile @ A) @ P) @ Xs)) = (((coindu501562517eWhile @ A) @ P) @ ((coinductive_ltl @ A) @ Xs)))) & ((~ ((P @ ((coinductive_lhd @ A) @ Xs)))) => (((coinductive_ltl @ A) @ (((coindu501562517eWhile @ A) @ P) @ Xs)) = (coinductive_LNil @ A))))))).
% 1.61/1.08 thf(fact_160_lhd__lzip, axiom, (! [A:$tType,B:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((~ (((coinductive_lnull @ A) @ Xs))) => ((~ (((coinductive_lnull @ B) @ Ys))) => (((coinductive_lhd @ ((product_prod @ A) @ B)) @ ((((coinductive_lzip @ A) @ B) @ Xs) @ Ys)) = ((((product_Pair @ A) @ B) @ ((coinductive_lhd @ A) @ Xs)) @ ((coinductive_lhd @ B) @ Ys)))))))).
% 1.61/1.08 thf(fact_161_llexord__coinduct, axiom, (! [A:$tType,X4:((coinductive_llist @ A) > ((coinductive_llist @ A) > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),R3:(A > (A > $o))]: ((((X4 @ Xs) @ Ys) => ((! [Xs2:(coinductive_llist @ A),Ys5:(coinductive_llist @ A)]: ((((X4 @ Xs2) @ Ys5) => ((~ (((coinductive_lnull @ A) @ Xs2))) => ((~ (((coinductive_lnull @ A) @ Ys5))) & ((~ (((coinductive_lnull @ A) @ Ys5))) => (((R3 @ ((coinductive_lhd @ A) @ Xs2)) @ ((coinductive_lhd @ A) @ Ys5)) | ((((coinductive_lhd @ A) @ Xs2) = ((coinductive_lhd @ A) @ Ys5)) & (((X4 @ ((coinductive_ltl @ A) @ Xs2)) @ ((coinductive_ltl @ A) @ Ys5)) | ((((coinductive_llexord @ A) @ R3) @ ((coinductive_ltl @ A) @ Xs2)) @ ((coinductive_ltl @ A) @ Ys5))))))))))) => ((((coinductive_llexord @ A) @ R3) @ Xs) @ Ys)))))).
% 1.61/1.08 thf(fact_162_ltakeWhile_Octr_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:(A > $o)]: (((~ (((coinductive_lnull @ A) @ Xs))) => ((P @ ((coinductive_lhd @ A) @ Xs)) => ((((coindu501562517eWhile @ A) @ P) @ Xs) = (((coinductive_LCons @ A) @ ((coinductive_lhd @ A) @ Xs)) @ (((coindu501562517eWhile @ A) @ P) @ ((coinductive_ltl @ A) @ Xs))))))))).
% 1.61/1.08 thf(fact_163_llist_Ocase__eq__if, axiom, (! [A:$tType,B:$tType]: ((((coindu1381640503_llist @ B) @ A) = (^ [F12:B,F22:(A > ((coinductive_llist @ A) > B)),Llist2:(coinductive_llist @ A)]: (((((if @ B) @ ((coinductive_lnull @ A) @ Llist2)) @ F12) @ ((F22 @ ((coinductive_lhd @ A) @ Llist2)) @ ((coinductive_ltl @ A) @ Llist2))))))))).
% 1.61/1.08 thf(fact_164_lzip_Octr_I2_J, axiom, (! [A:$tType,B:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((~ (((coinductive_lnull @ A) @ Xs))) => ((~ (((coinductive_lnull @ B) @ Ys))) => (((((coinductive_lzip @ A) @ B) @ Xs) @ Ys) = (((coinductive_LCons @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ ((coinductive_lhd @ A) @ Xs)) @ ((coinductive_lhd @ B) @ Ys))) @ ((((coinductive_lzip @ A) @ B) @ ((coinductive_ltl @ A) @ Xs)) @ ((coinductive_ltl @ B) @ Ys))))))))).
% 1.61/1.08 thf(fact_165_prod_Oinject, axiom, (! [A:$tType,B:$tType,X1:A,X23:B,Y1:A,Y23:B]: (((((((product_Pair @ A) @ B) @ X1) @ X23) = ((((product_Pair @ A) @ B) @ Y1) @ Y23)) = ((X1 = Y1) & (X23 = Y23)))))).
% 1.61/1.08 thf(fact_166_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A6:A,B4:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A6) @ B4)) = ((A2 = A6) & (B2 = B4)))))).
% 1.61/1.08 thf(fact_167_llast__lappend, axiom, (! [A:$tType,Ys:(coinductive_llist @ A),Xs:(coinductive_llist @ A)]: (((((coinductive_lnull @ A) @ Ys) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((coinductive_llast @ A) @ Xs))) & ((~ (((coinductive_lnull @ A) @ Ys))) => ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((coinductive_llast @ A) @ Ys))) & ((~ (((coinductive_lfinite @ A) @ Xs))) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (undefined @ A))))))))).
% 1.61/1.08 thf(fact_168_ltl__lconcat, axiom, (! [A:$tType,Xss:(coinductive_llist @ (coinductive_llist @ A))]: (((~ (((coinductive_lnull @ (coinductive_llist @ A)) @ Xss))) => ((~ (((coinductive_lnull @ A) @ ((coinductive_lhd @ (coinductive_llist @ A)) @ Xss)))) => (((coinductive_ltl @ A) @ ((coinductive_lconcat @ A) @ Xss)) = (((coinductive_lappend @ A) @ ((coinductive_ltl @ A) @ ((coinductive_lhd @ (coinductive_llist @ A)) @ Xss))) @ ((coinductive_lconcat @ A) @ ((coinductive_ltl @ (coinductive_llist @ A)) @ Xss))))))))).
% 1.61/1.08 thf(fact_169_lconcat__LNil, axiom, (! [A:$tType]: ((((coinductive_lconcat @ A) @ (coinductive_LNil @ (coinductive_llist @ A))) = (coinductive_LNil @ A))))).
% 1.61/1.08 thf(fact_170_lconcat__LCons, axiom, (! [B:$tType,Xs:(coinductive_llist @ B),Xss:(coinductive_llist @ (coinductive_llist @ B))]: ((((coinductive_lconcat @ B) @ (((coinductive_LCons @ (coinductive_llist @ B)) @ Xs) @ Xss)) = (((coinductive_lappend @ B) @ Xs) @ ((coinductive_lconcat @ B) @ Xss)))))).
% 1.61/1.08 thf(fact_171_lconcat__lappend, axiom, (! [A:$tType,Xss:(coinductive_llist @ (coinductive_llist @ A)),Yss:(coinductive_llist @ (coinductive_llist @ A))]: ((((coinductive_lfinite @ (coinductive_llist @ A)) @ Xss) => (((coinductive_lconcat @ A) @ (((coinductive_lappend @ (coinductive_llist @ A)) @ Xss) @ Yss)) = (((coinductive_lappend @ A) @ ((coinductive_lconcat @ A) @ Xss)) @ ((coinductive_lconcat @ A) @ Yss))))))).
% 1.61/1.08 thf(fact_172_lhd__lconcat, axiom, (! [A:$tType,Xss:(coinductive_llist @ (coinductive_llist @ A))]: (((~ (((coinductive_lnull @ (coinductive_llist @ A)) @ Xss))) => ((~ (((coinductive_lnull @ A) @ ((coinductive_lhd @ (coinductive_llist @ A)) @ Xss)))) => (((coinductive_lhd @ A) @ ((coinductive_lconcat @ A) @ Xss)) = ((coinductive_lhd @ A) @ ((coinductive_lhd @ (coinductive_llist @ A)) @ Xss)))))))).
% 1.61/1.08 thf(fact_173_llast__LNil, axiom, (! [A:$tType]: ((((coinductive_llast @ A) @ (coinductive_LNil @ A)) = (undefined @ A))))).
% 1.61/1.08 thf(fact_174_llast__linfinite, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((~ (((coinductive_lfinite @ A) @ Xs))) => (((coinductive_llast @ A) @ Xs) = (undefined @ A)))))).
% 1.61/1.08 thf(fact_175_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A5:A,B3:B]: ((P @ ((((product_Pair @ A) @ B) @ A5) @ B3)))) => (P @ Prod))))).
% 1.61/1.08 thf(fact_176_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y:((product_prod @ A) @ B)]: ((~ ((! [A5:A,B3:B]: ((Y != ((((product_Pair @ A) @ B) @ A5) @ B3))))))))).
% 1.61/1.08 thf(fact_177_prod__induct7, axiom, (! [G2:$tType,F3:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G2)))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G2))))))]: (((! [A5:A,B3:B,C2:C,D2:D,E2:E,F4:F3,G3:G2]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G2)))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G2))))) @ B3) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G2)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G2))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F3) @ G2)) @ E2) @ ((((product_Pair @ F3) @ G2) @ F4) @ G3))))))))) => (P @ X))))).
% 1.61/1.08 thf(fact_178_prod__induct6, axiom, (! [F3:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))))]: (((! [A5:A,B3:B,C2:C,D2:D,E2:E,F4:F3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))) @ B3) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F3)) @ D2) @ ((((product_Pair @ E) @ F3) @ E2) @ F4)))))))) => (P @ X))))).
% 1.61/1.08 thf(fact_179_prod__induct5, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: (((! [A5:A,B3:B,C2:C,D2:D,E2:E]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B3) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C2) @ ((((product_Pair @ D) @ E) @ D2) @ E2))))))) => (P @ X))))).
% 1.61/1.08 thf(fact_180_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A5:A,B3:B,C2:C,D2:D]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B3) @ ((((product_Pair @ C) @ D) @ C2) @ D2)))))) => (P @ X))))).
% 1.61/1.08 thf(fact_181_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A5:A,B3:B,C2:C]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A5) @ ((((product_Pair @ B) @ C) @ B3) @ C2))))) => (P @ X))))).
% 1.61/1.08 thf(fact_182_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F3:$tType,G2:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G2))))))]: ((~ ((! [A5:A,B3:B,C2:C,D2:D,E2:E,F4:F3,G3:G2]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G2)))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G2))))) @ B3) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G2)))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G2))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F3) @ G2)) @ E2) @ ((((product_Pair @ F3) @ G2) @ F4) @ G3)))))))))))))).
% 1.61/1.08 thf(fact_183_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F3:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))))]: ((~ ((! [A5:A,B3:B,C2:C,D2:D,E2:E,F4:F3]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))) @ B3) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))) @ C2) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F3)) @ D2) @ ((((product_Pair @ E) @ F3) @ E2) @ F4))))))))))))).
% 1.61/1.08 thf(fact_184_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: ((~ ((! [A5:A,B3:B,C2:C,D2:D,E2:E]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B3) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C2) @ ((((product_Pair @ D) @ E) @ D2) @ E2)))))))))))).
% 1.61/1.08 thf(fact_185_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A5:A,B3:B,C2:C,D2:D]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A5) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B3) @ ((((product_Pair @ C) @ D) @ C2) @ D2))))))))))).
% 1.61/1.08 thf(fact_186_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A5:A,B3:B,C2:C]: ((Y != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A5) @ ((((product_Pair @ B) @ C) @ B3) @ C2)))))))))).
% 1.61/1.08 thf(fact_187_Pair__inject, axiom, (! [A:$tType,B:$tType,A2:A,B2:B,A6:A,B4:B]: (((((((product_Pair @ A) @ B) @ A2) @ B2) = ((((product_Pair @ A) @ B) @ A6) @ B4)) => (~ (((A2 = A6) => (B2 != B4)))))))).
% 1.61/1.08 thf(fact_188_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P3:((product_prod @ A) @ B)]: (((! [A5:A,B3:B]: ((P @ ((((product_Pair @ A) @ B) @ A5) @ B3)))) => (P @ P3))))).
% 1.61/1.08 thf(fact_189_surj__pair, axiom, (! [A:$tType,B:$tType,P3:((product_prod @ A) @ B)]: ((? [X3:A,Y3:B]: ((P3 = ((((product_Pair @ A) @ B) @ X3) @ Y3))))))).
% 1.61/1.08 thf(fact_190_old_Oprod_Orec, axiom, (! [A:$tType,T:$tType,B:$tType,F1:(A > (B > T)),A2:A,B2:B]: (((((((product_rec_prod @ A) @ B) @ T) @ F1) @ ((((product_Pair @ A) @ B) @ A2) @ B2)) = ((F1 @ A2) @ B2))))).
% 1.61/1.08 thf(fact_191_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C3:(B > (C > A)),A2:B,B2:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C3) @ ((((product_Pair @ B) @ C) @ A2) @ B2)) = ((C3 @ A2) @ B2))))).
% 1.61/1.08 thf(fact_192_ord_Olsorted__coinduct_H, axiom, (! [A:$tType,X4:((coinductive_llist @ A) > $o),Xs:(coinductive_llist @ A),Less_eq:(A > (A > $o))]: (((X4 @ Xs) => ((! [Xs2:(coinductive_llist @ A)]: (((X4 @ Xs2) => ((~ (((coinductive_lnull @ A) @ Xs2))) => ((~ (((coinductive_lnull @ A) @ ((coinductive_ltl @ A) @ Xs2)))) => (((Less_eq @ ((coinductive_lhd @ A) @ Xs2)) @ ((coinductive_lhd @ A) @ ((coinductive_ltl @ A) @ Xs2))) & ((X4 @ ((coinductive_ltl @ A) @ Xs2)) | (((coinductive_lsorted @ A) @ Less_eq) @ ((coinductive_ltl @ A) @ Xs2))))))))) => (((coinductive_lsorted @ A) @ Less_eq) @ Xs)))))).
% 1.61/1.08 thf(fact_193_ord_Olsorted__LCons__LCons, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),X:A,Y:A,Xs:(coinductive_llist @ A)]: (((((coinductive_lsorted @ A) @ Less_eq) @ (((coinductive_LCons @ A) @ X) @ (((coinductive_LCons @ A) @ Y) @ Xs))) = (((Less_eq @ X) @ Y) & (((coinductive_lsorted @ A) @ Less_eq) @ (((coinductive_LCons @ A) @ Y) @ Xs))))))).
% 1.61/1.08 thf(fact_194_ord_OLCons__LCons, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),X:A,Y:A,Xs:(coinductive_llist @ A)]: ((((Less_eq @ X) @ Y) => ((((coinductive_lsorted @ A) @ Less_eq) @ (((coinductive_LCons @ A) @ Y) @ Xs)) => (((coinductive_lsorted @ A) @ Less_eq) @ (((coinductive_LCons @ A) @ X) @ (((coinductive_LCons @ A) @ Y) @ Xs)))))))).
% 1.61/1.08 thf(fact_195_ord_OLNil, axiom, (! [A:$tType,Less_eq:(A > (A > $o))]: ((((coinductive_lsorted @ A) @ Less_eq) @ (coinductive_LNil @ A))))).
% 1.61/1.08 thf(fact_196_ord_Olsorted__code_I1_J, axiom, (! [A:$tType,Less_eq:(A > (A > $o))]: ((((coinductive_lsorted @ A) @ Less_eq) @ (coinductive_LNil @ A))))).
% 1.61/1.08 thf(fact_197_ord_Olsorted__ltlI, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Xs:(coinductive_llist @ A)]: (((((coinductive_lsorted @ A) @ Less_eq) @ Xs) => (((coinductive_lsorted @ A) @ Less_eq) @ ((coinductive_ltl @ A) @ Xs)))))).
% 1.61/1.08 thf(fact_198_ord_Olsorted__ldropn, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Xs:(coinductive_llist @ A),N:nat]: (((((coinductive_lsorted @ A) @ Less_eq) @ Xs) => (((coinductive_lsorted @ A) @ Less_eq) @ (((coinductive_ldropn @ A) @ N) @ Xs)))))).
% 1.61/1.08 thf(fact_199_ord_Olsorted__code_I2_J, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),X:A]: ((((coinductive_lsorted @ A) @ Less_eq) @ (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A)))))).
% 1.61/1.08 thf(fact_200_ord_Olsorted_Ocases, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),A2:(coinductive_llist @ A)]: (((((coinductive_lsorted @ A) @ Less_eq) @ A2) => ((A2 != (coinductive_LNil @ A)) => ((! [X3:A]: ((A2 != (((coinductive_LCons @ A) @ X3) @ (coinductive_LNil @ A))))) => (~ ((! [X3:A,Y3:A,Xs2:(coinductive_llist @ A)]: (((A2 = (((coinductive_LCons @ A) @ X3) @ (((coinductive_LCons @ A) @ Y3) @ Xs2))) => (((Less_eq @ X3) @ Y3) => (~ ((((coinductive_lsorted @ A) @ Less_eq) @ (((coinductive_LCons @ A) @ Y3) @ Xs2)))))))))))))))).
% 1.61/1.08 thf(fact_201_ord_Olsorted_Osimps, axiom, (! [A:$tType]: (((coinductive_lsorted @ A) = (^ [Less_eq2:(A > (A > $o)),A4:(coinductive_llist @ A)]: (((A4 = (coinductive_LNil @ A)) | ((? [X2:A]: ((A4 = (((coinductive_LCons @ A) @ X2) @ (coinductive_LNil @ A))))) | (? [X2:A,Y2:A,Xs3:(coinductive_llist @ A)]: (((A4 = (((coinductive_LCons @ A) @ X2) @ (((coinductive_LCons @ A) @ Y2) @ Xs3))) & (((Less_eq2 @ X2) @ Y2) & (((coinductive_lsorted @ A) @ Less_eq2) @ (((coinductive_LCons @ A) @ Y2) @ Xs3)))))))))))))).
% 1.61/1.08 thf(fact_202_ord_Olsorted_Ocoinduct, axiom, (! [A:$tType,X4:((coinductive_llist @ A) > $o),X:(coinductive_llist @ A),Less_eq:(A > (A > $o))]: (((X4 @ X) => ((! [X3:(coinductive_llist @ A)]: (((X4 @ X3) => ((X3 = (coinductive_LNil @ A)) | ((? [Xa3:A]: ((X3 = (((coinductive_LCons @ A) @ Xa3) @ (coinductive_LNil @ A))))) | (? [Xa3:A,Y4:A,Xs5:(coinductive_llist @ A)]: (((X3 = (((coinductive_LCons @ A) @ Xa3) @ (((coinductive_LCons @ A) @ Y4) @ Xs5))) & (((Less_eq @ Xa3) @ Y4) & ((X4 @ (((coinductive_LCons @ A) @ Y4) @ Xs5)) | (((coinductive_lsorted @ A) @ Less_eq) @ (((coinductive_LCons @ A) @ Y4) @ Xs5)))))))))))) => (((coinductive_lsorted @ A) @ Less_eq) @ X)))))).
% 1.61/1.08 thf(fact_203_ord_OSingleton, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),X:A]: ((((coinductive_lsorted @ A) @ Less_eq) @ (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A)))))).
% 1.61/1.08 thf(fact_204_ord_Olsorted__LCons_H, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),X:A,Xs:(coinductive_llist @ A)]: (((((coinductive_lsorted @ A) @ Less_eq) @ (((coinductive_LCons @ A) @ X) @ Xs)) = ((~ (((coinductive_lnull @ A) @ Xs))) => (((Less_eq @ X) @ ((coinductive_lhd @ A) @ Xs)) & (((coinductive_lsorted @ A) @ Less_eq) @ Xs))))))).
% 1.61/1.08 thf(fact_205_ord_Olsorted__lhdD, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Xs:(coinductive_llist @ A)]: (((((coinductive_lsorted @ A) @ Less_eq) @ Xs) => ((~ (((coinductive_lnull @ A) @ Xs))) => ((~ (((coinductive_lnull @ A) @ ((coinductive_ltl @ A) @ Xs)))) => ((Less_eq @ ((coinductive_lhd @ A) @ Xs)) @ ((coinductive_lhd @ A) @ ((coinductive_ltl @ A) @ Xs))))))))).
% 1.61/1.08 thf(fact_206_ssubst__Pair__rhs, axiom, (! [B:$tType,A:$tType,R3:A,S:B,R:(set @ ((product_prod @ A) @ B)),S2:B]: (((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R3) @ S)) @ R) => ((S2 = S) => (((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ R3) @ S2)) @ R)))))).
% 1.61/1.08 thf(fact_207_lprefix__expand, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((~ (((coinductive_lnull @ A) @ Xs))) => ((~ (((coinductive_lnull @ A) @ Ys))) & ((((coinductive_lhd @ A) @ Xs) = ((coinductive_lhd @ A) @ Ys)) & (((coinductive_lprefix @ A) @ ((coinductive_ltl @ A) @ Xs)) @ ((coinductive_ltl @ A) @ Ys))))) => (((coinductive_lprefix @ A) @ Xs) @ Ys))))).
% 1.61/1.08 thf(fact_208_lprefix__refl, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coinductive_lprefix @ A) @ Xs) @ Xs)))).
% 1.61/1.08 thf(fact_209_llist_Oleq__refl, axiom, (! [A:$tType,X:(coinductive_llist @ A)]: ((((coinductive_lprefix @ A) @ X) @ X)))).
% 1.61/1.08 thf(fact_210_LCons__lprefix__LCons, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = ((X = Y) & (((coinductive_lprefix @ A) @ Xs) @ Ys)))))).
% 1.61/1.08 thf(fact_211_lprefix__code_I1_J, axiom, (! [A:$tType,Ys:(coinductive_llist @ A)]: ((((coinductive_lprefix @ A) @ (coinductive_LNil @ A)) @ Ys)))).
% 1.61/1.08 thf(fact_212_lprefix__LNil, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ (coinductive_LNil @ A)) = ((coinductive_lnull @ A) @ Xs))))).
% 1.61/1.08 thf(fact_213_lprefix__lappend__same, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) @ (((coinductive_lappend @ A) @ Xs) @ Zs)) = (((coinductive_lfinite @ A) @ Xs) => (((coinductive_lprefix @ A) @ Ys) @ Zs)))))).
% 1.61/1.08 thf(fact_214_ord_Olsorted__lprefixD, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Less_eq:(A > (A > $o))]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => ((((coinductive_lsorted @ A) @ Less_eq) @ Ys) => (((coinductive_lsorted @ A) @ Less_eq) @ Xs)))))).
% 1.61/1.08 thf(fact_215_lprefix__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lprefix @ A) @ Xs) @ (((coinductive_lappend @ A) @ Xs) @ Ys))))).
% 1.61/1.08 thf(fact_216_lappend__lprefixE, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) @ Zs) => (~ ((! [Zs3:(coinductive_llist @ A)]: ((Zs != (((coinductive_lappend @ A) @ Xs) @ Zs3)))))))))).
% 1.61/1.08 thf(fact_217_lprefix__lappendD, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ (((coinductive_lappend @ A) @ Ys) @ Zs)) => ((((coinductive_lprefix @ A) @ Xs) @ Ys) | (((coinductive_lprefix @ A) @ Ys) @ Xs)))))).
% 1.61/1.08 thf(fact_218_lprefix__conv__lappend, axiom, (! [A:$tType]: (((coinductive_lprefix @ A) = (^ [Xs3:(coinductive_llist @ A),Ys3:(coinductive_llist @ A)]: ((? [Zs2:(coinductive_llist @ A)]: ((Ys3 = (((coinductive_lappend @ A) @ Xs3) @ Zs2)))))))))).
% 1.61/1.08 thf(fact_219_lprefix__lappend__sameI, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => (((coinductive_lprefix @ A) @ (((coinductive_lappend @ A) @ Zs) @ Xs)) @ (((coinductive_lappend @ A) @ Zs) @ Ys)))))).
% 1.61/1.08 thf(fact_220_lprefix__lfiniteD, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => (((coinductive_lfinite @ A) @ Ys) => ((coinductive_lfinite @ A) @ Xs)))))).
% 1.61/1.08 thf(fact_221_not__lfinite__lprefix__conv__eq, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((~ (((coinductive_lfinite @ A) @ Xs))) => ((((coinductive_lprefix @ A) @ Xs) @ Ys) = (Xs = Ys)))))).
% 1.61/1.08 thf(fact_222_LNil__lprefix, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coinductive_lprefix @ A) @ (coinductive_LNil @ A)) @ Xs)))).
% 1.61/1.08 thf(fact_223_LCons__lprefix__conv, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ Ys) = (? [Ys4:(coinductive_llist @ A)]: (((Ys = (((coinductive_LCons @ A) @ X) @ Ys4)) & (((coinductive_lprefix @ A) @ Xs) @ Ys4)))))))).
% 1.61/1.08 thf(fact_224_Le__LCons, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),X:A]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => (((coinductive_lprefix @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ (((coinductive_LCons @ A) @ X) @ Ys)))))).
% 1.61/1.08 thf(fact_225_lprefixI, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),X4:(set @ ((product_prod @ (coinductive_llist @ A)) @ (coinductive_llist @ A)))]: (((((member @ ((product_prod @ (coinductive_llist @ A)) @ (coinductive_llist @ A))) @ ((((product_Pair @ (coinductive_llist @ A)) @ (coinductive_llist @ A)) @ Xs) @ Ys)) @ X4) => ((! [Xs2:(coinductive_llist @ A),Ys5:(coinductive_llist @ A)]: (((((member @ ((product_prod @ (coinductive_llist @ A)) @ (coinductive_llist @ A))) @ ((((product_Pair @ (coinductive_llist @ A)) @ (coinductive_llist @ A)) @ Xs2) @ Ys5)) @ X4) => (((coinductive_lnull @ A) @ Xs2) | (? [X5:A,Xs6:(coinductive_llist @ A),Ys6:(coinductive_llist @ A)]: (((Xs2 = (((coinductive_LCons @ A) @ X5) @ Xs6)) & ((Ys5 = (((coinductive_LCons @ A) @ X5) @ Ys6)) & ((((member @ ((product_prod @ (coinductive_llist @ A)) @ (coinductive_llist @ A))) @ ((((product_Pair @ (coinductive_llist @ A)) @ (coinductive_llist @ A)) @ Xs6) @ Ys6)) @ X4) | (((coinductive_lprefix @ A) @ Xs6) @ Ys6)))))))))) => (((coinductive_lprefix @ A) @ Xs) @ Ys)))))).
% 1.61/1.08 thf(fact_226_lprefix__code_I2_J, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: ((~ ((((coinductive_lprefix @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ (coinductive_LNil @ A))))))).
% 1.61/1.08 thf(fact_227_lprefix_Ocases, axiom, (! [A:$tType,A1:(coinductive_llist @ A),A22:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ A1) @ A22) => (((A1 = (coinductive_LNil @ A)) => (! [Xs2:(coinductive_llist @ A)]: ((A22 != Xs2)))) => (~ ((! [Xs2:(coinductive_llist @ A),Ys5:(coinductive_llist @ A),X3:A]: (((A1 = (((coinductive_LCons @ A) @ X3) @ Xs2)) => ((A22 = (((coinductive_LCons @ A) @ X3) @ Ys5)) => (~ ((((coinductive_lprefix @ A) @ Xs2) @ Ys5)))))))))))))).
% 1.61/1.08 thf(fact_228_lprefix_Osimps, axiom, (! [A:$tType]: (((coinductive_lprefix @ A) = (^ [A12:(coinductive_llist @ A),A23:(coinductive_llist @ A)]: (((? [Xs3:(coinductive_llist @ A)]: (((A12 = (coinductive_LNil @ A)) & (A23 = Xs3)))) | (? [Xs3:(coinductive_llist @ A),Ys3:(coinductive_llist @ A),X2:A]: (((A12 = (((coinductive_LCons @ A) @ X2) @ Xs3)) & ((A23 = (((coinductive_LCons @ A) @ X2) @ Ys3)) & (((coinductive_lprefix @ A) @ Xs3) @ Ys3)))))))))))).
% 1.61/1.08 thf(fact_229_lprefix_Ocoinduct, axiom, (! [A:$tType,X4:((coinductive_llist @ A) > ((coinductive_llist @ A) > $o)),X:(coinductive_llist @ A),Xa:(coinductive_llist @ A)]: ((((X4 @ X) @ Xa) => ((! [X3:(coinductive_llist @ A),Xa2:(coinductive_llist @ A)]: ((((X4 @ X3) @ Xa2) => ((? [Xs5:(coinductive_llist @ A)]: (((X3 = (coinductive_LNil @ A)) & (Xa2 = Xs5)))) | (? [Xs5:(coinductive_llist @ A),Ys2:(coinductive_llist @ A),Xb:A]: (((X3 = (((coinductive_LCons @ A) @ Xb) @ Xs5)) & ((Xa2 = (((coinductive_LCons @ A) @ Xb) @ Ys2)) & (((X4 @ Xs5) @ Ys2) | (((coinductive_lprefix @ A) @ Xs5) @ Ys2)))))))))) => (((coinductive_lprefix @ A) @ X) @ Xa)))))).
% 1.61/1.08 thf(fact_230_lprefix__LCons__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = ((Xs = (coinductive_LNil @ A)) | (? [Xs4:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ Y) @ Xs4)) & (((coinductive_lprefix @ A) @ Xs4) @ Ys))))))))).
% 1.61/1.08 thf(fact_231_lprefix__lhdD, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => ((~ (((coinductive_lnull @ A) @ Xs))) => (((coinductive_lhd @ A) @ Xs) = ((coinductive_lhd @ A) @ Ys))))))).
% 1.61/1.08 thf(fact_232_lprefix__imp__llexord, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),R3:(A > (A > $o))]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => ((((coinductive_llexord @ A) @ R3) @ Xs) @ Ys))))).
% 1.61/1.08 thf(fact_233_lprefix__ltakeWhile, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: ((((coinductive_lprefix @ A) @ (((coindu501562517eWhile @ A) @ P) @ Xs)) @ Xs)))).
% 1.61/1.08 thf(fact_234_lprefix__trans, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => ((((coinductive_lprefix @ A) @ Ys) @ Zs) => (((coinductive_lprefix @ A) @ Xs) @ Zs)))))).
% 1.61/1.08 thf(fact_235_llist_Oleq__trans, axiom, (! [A:$tType,X:(coinductive_llist @ A),Y:(coinductive_llist @ A),Z:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ X) @ Y) => ((((coinductive_lprefix @ A) @ Y) @ Z) => (((coinductive_lprefix @ A) @ X) @ Z)))))).
% 1.61/1.08 thf(fact_236_lprefix__antisym, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => ((((coinductive_lprefix @ A) @ Ys) @ Xs) => (Xs = Ys)))))).
% 1.61/1.08 thf(fact_237_llist_Oleq__antisym, axiom, (! [A:$tType,X:(coinductive_llist @ A),Y:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ X) @ Y) => ((((coinductive_lprefix @ A) @ Y) @ X) => (X = Y)))))).
% 1.61/1.08 thf(fact_238_lprefix__down__linear, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Zs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ Zs) => ((((coinductive_lprefix @ A) @ Ys) @ Zs) => ((((coinductive_lprefix @ A) @ Xs) @ Ys) | (((coinductive_lprefix @ A) @ Ys) @ Xs))))))).
% 1.61/1.08 thf(fact_239_Coinductive__List_Ofinite__lprefix__def, axiom, (! [A:$tType]: (((coindu328551480prefix @ A) = (coinductive_lprefix @ A))))).
% 1.61/1.08 thf(fact_240_lstrict__prefix__def, axiom, (! [A:$tType]: (((coindu1478340336prefix @ A) = (^ [Xs3:(coinductive_llist @ A),Ys3:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs3) @ Ys3) & (Xs3 != Ys3)))))))).
% 1.61/1.08 thf(fact_241_lprefix__lconcatI, axiom, (! [A:$tType,Xss:(coinductive_llist @ (coinductive_llist @ A)),Yss:(coinductive_llist @ (coinductive_llist @ A))]: (((((coinductive_lprefix @ (coinductive_llist @ A)) @ Xss) @ Yss) => (((coinductive_lprefix @ A) @ ((coinductive_lconcat @ A) @ Xss)) @ ((coinductive_lconcat @ A) @ Yss)))))).
% 1.61/1.08 thf(fact_242_lprefix__ltlI, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => (((coinductive_lprefix @ A) @ ((coinductive_ltl @ A) @ Xs)) @ ((coinductive_ltl @ A) @ Ys)))))).
% 1.61/1.08 thf(fact_243_lprefix__not__lnullD, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => ((~ (((coinductive_lnull @ A) @ Xs))) => (~ (((coinductive_lnull @ A) @ Ys)))))))).
% 1.61/1.08 thf(fact_244_lprefix__lnullD, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => (((coinductive_lnull @ A) @ Ys) => ((coinductive_lnull @ A) @ Xs)))))).
% 1.61/1.08 thf(fact_245_lprefix__lnull, axiom, (! [A:$tType,Ys:(coinductive_llist @ A),Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Ys) => ((((coinductive_lprefix @ A) @ Xs) @ Ys) = ((coinductive_lnull @ A) @ Xs)))))).
% 1.61/1.08 thf(fact_246_lnull__lprefix, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => (((coinductive_lprefix @ A) @ Xs) @ Ys))))).
% 1.61/1.08 thf(fact_247_Coinductive__List_Olprefix__nitpick__simps, axiom, (! [A:$tType]: (((coinductive_lprefix @ A) = (^ [Xs3:(coinductive_llist @ A),Ys3:(coinductive_llist @ A)]: (((((coinductive_lfinite @ A) @ Xs3) => (((coindu328551480prefix @ A) @ Xs3) @ Ys3)) & ((~ (((coinductive_lfinite @ A) @ Xs3))) => (Xs3 = Ys3))))))))).
% 1.61/1.08 thf(fact_248_lprefix__coinduct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > ((coinductive_llist @ A) > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((P @ Xs) @ Ys) => ((! [Xs2:(coinductive_llist @ A),Ys5:(coinductive_llist @ A)]: ((((P @ Xs2) @ Ys5) => ((((coinductive_lnull @ A) @ Ys5) => ((coinductive_lnull @ A) @ Xs2)) & ((~ (((coinductive_lnull @ A) @ Xs2))) => ((~ (((coinductive_lnull @ A) @ Ys5))) => ((((coinductive_lhd @ A) @ Xs2) = ((coinductive_lhd @ A) @ Ys5)) & (((P @ ((coinductive_ltl @ A) @ Xs2)) @ ((coinductive_ltl @ A) @ Ys5)) | (((coinductive_lprefix @ A) @ ((coinductive_ltl @ A) @ Xs2)) @ ((coinductive_ltl @ A) @ Ys5)))))))))) => (((coinductive_lprefix @ A) @ Xs) @ Ys)))))).
% 1.61/1.08 thf(fact_249_llexord__lappend__left, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),R3:(A > (A > $o)),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => ((! [X3:A]: (((((member @ A) @ X3) @ ((coinductive_lset @ A) @ Xs)) => (~ (((R3 @ X3) @ X3)))))) => (((((coinductive_llexord @ A) @ R3) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) @ (((coinductive_lappend @ A) @ Xs) @ Zs)) = ((((coinductive_llexord @ A) @ R3) @ Ys) @ Zs))))))).
% 1.61/1.08 thf(fact_250_llexord__lappend__leftD, axiom, (! [A:$tType,R3:(A > (A > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: ((((((coinductive_llexord @ A) @ R3) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) @ (((coinductive_lappend @ A) @ Xs) @ Zs)) => (((coinductive_lfinite @ A) @ Xs) => ((! [X3:A]: (((((member @ A) @ X3) @ ((coinductive_lset @ A) @ Xs)) => (~ (((R3 @ X3) @ X3)))))) => ((((coinductive_llexord @ A) @ R3) @ Ys) @ Zs))))))).
% 1.61/1.08 thf(fact_251_in__lset__ltlD, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ ((coinductive_ltl @ A) @ Xs))) => (((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)))))).
% 1.61/1.08 thf(fact_252_lset__lmember, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) = (((coinductive_lmember @ A) @ X) @ Xs))))).
% 1.61/1.08 thf(fact_253_in__lset__ldropnD, axiom, (! [A:$tType,X:A,N:nat,Xs:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ (((coinductive_ldropn @ A) @ N) @ Xs))) => (((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)))))).
% 1.61/1.08 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 1.61/1.08 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 1.61/1.08 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 1.61/1.08 thf(conj_0, conjecture, (((coinductive_lfinite @ a) @ xsa) & ((coinductive_lfinite @ a) @ acca))).
% 1.61/1.08 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.tZ0Cg1ODeg/DTF2DTF26636.p
% 1.61/1.08 ------------------------
% 1.61/1.11 ---- Cleaned THF ---
% 1.61/1.11 thf(ty_t_Coinductive__List_Ollist,type,
% 1.61/1.11 coinductive_llist: $tType > $tType ).
% 1.61/1.11
% 1.61/1.11 thf(ty_t_Product__Type_Oprod,type,
% 1.61/1.11 product_prod: $tType > $tType > $tType ).
% 1.61/1.11
% 1.61/1.11 thf(ty_t_Set_Oset,type,
% 1.61/1.11 set: $tType > $tType ).
% 1.61/1.11
% 1.61/1.11 thf(ty_t_Nat_Onat,type,
% 1.61/1.11 nat: $tType ).
% 1.61/1.11
% 1.61/1.11 thf(ty_t_itself,type,
% 1.61/1.11 itself: $tType > $tType ).
% 1.61/1.11
% 1.61/1.11 thf(ty_tf_a,type,
% 1.61/1.11 a: $tType ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 1.61/1.11 coindu328551480prefix:
% 1.61/1.11 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Ogen__lset,type,
% 1.61/1.11 coinductive_gen_lset:
% 1.61/1.11 !>[A: $tType] : ( ( set @ A ) > ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Olappend,type,
% 1.61/1.11 coinductive_lappend:
% 1.61/1.11 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Olconcat,type,
% 1.61/1.11 coinductive_lconcat:
% 1.61/1.11 !>[A: $tType] : ( ( coinductive_llist @ ( coinductive_llist @ A ) ) > ( coinductive_llist @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Oldropn,type,
% 1.61/1.11 coinductive_ldropn:
% 1.61/1.11 !>[A: $tType] : ( nat > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Olfinite,type,
% 1.61/1.11 coinductive_lfinite:
% 1.61/1.11 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Ollast,type,
% 1.61/1.11 coinductive_llast:
% 1.61/1.11 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Ollexord,type,
% 1.61/1.11 coinductive_llexord:
% 1.61/1.11 !>[A: $tType] : ( ( A > A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 1.61/1.11 coinductive_LCons:
% 1.61/1.11 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 1.61/1.11 coinductive_LNil:
% 1.61/1.11 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Ollist_Ocase__llist,type,
% 1.61/1.11 coindu1381640503_llist:
% 1.61/1.11 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B ) > ( coinductive_llist @ A ) > B ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Ollist_Olhd,type,
% 1.61/1.11 coinductive_lhd:
% 1.61/1.11 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Ollist_Olnull,type,
% 1.61/1.11 coinductive_lnull:
% 1.61/1.11 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Ollist_Olset,type,
% 1.61/1.11 coinductive_lset:
% 1.61/1.11 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Ollist_Oltl,type,
% 1.61/1.11 coinductive_ltl:
% 1.61/1.11 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Olmember,type,
% 1.61/1.11 coinductive_lmember:
% 1.61/1.11 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > $o ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Olprefix,type,
% 1.61/1.11 coinductive_lprefix:
% 1.61/1.11 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 1.61/1.11 coindu1478340336prefix:
% 1.61/1.11 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_OltakeWhile,type,
% 1.61/1.11 coindu501562517eWhile:
% 1.61/1.11 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Olzip,type,
% 1.61/1.11 coinductive_lzip:
% 1.61/1.11 !>[A: $tType,B: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ B ) > ( coinductive_llist @ ( product_prod @ A @ B ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Oord_Olsorted,type,
% 1.61/1.11 coinductive_lsorted:
% 1.61/1.11 !>[A: $tType] : ( ( A > A > $o ) > ( coinductive_llist @ A ) > $o ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Coinductive__List_Ounfold__llist,type,
% 1.61/1.11 coindu1441602521_llist:
% 1.61/1.11 !>[A: $tType,B: $tType] : ( ( A > $o ) > ( A > B ) > ( A > A ) > A > ( coinductive_llist @ B ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_HOL_Oundefined,type,
% 1.61/1.11 undefined:
% 1.61/1.11 !>[A: $tType] : A ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_If,type,
% 1.61/1.11 if:
% 1.61/1.11 !>[A: $tType] : ( $o > A > A > A ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_LMirror__Mirabelle__wyovfcktfy_Olmirror,type,
% 1.61/1.11 lMirro427583474mirror:
% 1.61/1.11 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_LMirror__Mirabelle__wyovfcktfy_Olmirror__aux,type,
% 1.61/1.11 lMirro999291890or_aux:
% 1.61/1.11 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Product__Type_OPair,type,
% 1.61/1.11 product_Pair:
% 1.61/1.11 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 1.61/1.11 produc2004651681e_prod:
% 1.61/1.11 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Product__Type_Oold_Oprod_Orec__prod,type,
% 1.61/1.11 product_rec_prod:
% 1.61/1.11 !>[A: $tType,B: $tType,T: $tType] : ( ( A > B > T ) > ( product_prod @ A @ B ) > T ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Pure_Otype,type,
% 1.61/1.11 type:
% 1.61/1.11 !>[A: $tType] : ( itself @ A ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_Set_OCollect,type,
% 1.61/1.11 collect:
% 1.61/1.11 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_c_member,type,
% 1.61/1.11 member:
% 1.61/1.11 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 1.61/1.11
% 1.61/1.11 thf(sy_v_acc,type,
% 1.61/1.11 acc: coinductive_llist @ a ).
% 1.61/1.11
% 1.61/1.11 thf(sy_v_acca____,type,
% 1.61/1.11 acca: coinductive_llist @ a ).
% 1.61/1.11
% 1.61/1.11 thf(sy_v_xs,type,
% 1.61/1.11 xs: coinductive_llist @ a ).
% 1.61/1.11
% 1.61/1.11 thf(sy_v_xsa____,type,
% 1.61/1.11 xsa: coinductive_llist @ a ).
% 1.61/1.11
% 1.61/1.11 thf(fact_0__092_060open_062lfinite_A_Ilmirror__aux_Aacc_Axs_J_092_060close_062,axiom,
% 1.61/1.11 coinductive_lfinite @ a @ ( lMirro999291890or_aux @ a @ acc @ xs ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_1_LCons_Ohyps_I2_J,axiom,
% 1.61/1.11 ~ ( coinductive_lnull @ a @ ( lMirro999291890or_aux @ a @ acca @ xsa ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_2_LCons_Ohyps_I1_J,axiom,
% 1.61/1.11 coinductive_lfinite @ a @ ( lMirro999291890or_aux @ a @ acca @ xsa ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_3_LCons_Ohyps_I3_J,axiom,
% 1.61/1.11 ! [Acc: coinductive_llist @ a,Xs: coinductive_llist @ a] :
% 1.61/1.11 ( ( ( coinductive_ltl @ a @ ( lMirro999291890or_aux @ a @ acca @ xsa ) )
% 1.61/1.11 = ( lMirro999291890or_aux @ a @ Acc @ Xs ) )
% 1.61/1.11 => ( ( coinductive_lfinite @ a @ Xs )
% 1.61/1.11 & ( coinductive_lfinite @ a @ Acc ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_4_lfinite__ltl,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lfinite @ A @ ( coinductive_ltl @ A @ Xs ) )
% 1.61/1.11 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_5_lnull__imp__lfinite,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_6_lmirror__aux_Oexhaust,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Acc: coinductive_llist @ A] :
% 1.61/1.11 ( ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ~ ( coinductive_lnull @ A @ Acc ) )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 | ~ ( coinductive_lnull @ A @ Acc ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_7_lmirror__aux_Odisc__iff_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,Acc: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( ~ ( coinductive_lnull @ A @ ( lMirro999291890or_aux @ A @ Acc @ Xs ) ) )
% 1.61/1.11 = ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 | ~ ( coinductive_lnull @ A @ Acc ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_8_lnull__lmirror__aux,axiom,
% 1.61/1.11 ! [A: $tType,Acc: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ ( lMirro999291890or_aux @ A @ Acc @ Xs ) )
% 1.61/1.11 = ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 & ( coinductive_lnull @ A @ Acc ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_9_lfinite__induct,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 1.61/1.11 ( ( coinductive_lfinite @ A @ Xs )
% 1.61/1.11 => ( ! [Xs2: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ Xs2 )
% 1.61/1.11 => ( P @ Xs2 ) )
% 1.61/1.11 => ( ! [Xs2: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lfinite @ A @ Xs2 )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ Xs2 )
% 1.61/1.11 => ( ( P @ ( coinductive_ltl @ A @ Xs2 ) )
% 1.61/1.11 => ( P @ Xs2 ) ) ) )
% 1.61/1.11 => ( P @ Xs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_10_lstrict__prefix__lfinite1,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coindu1478340336prefix @ A @ Xs @ Ys )
% 1.61/1.11 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_11_lfinite__code_I1_J,axiom,
% 1.61/1.11 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_12_lfinite__ldropn,axiom,
% 1.61/1.11 ! [A: $tType,N: nat,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lfinite @ A @ ( coinductive_ldropn @ A @ N @ Xs ) )
% 1.61/1.11 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_13_lfinite__lzip,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 1.61/1.11 ( ( coinductive_lfinite @ ( product_prod @ A @ B ) @ ( coinductive_lzip @ A @ B @ Xs @ Ys ) )
% 1.61/1.11 = ( ( coinductive_lfinite @ A @ Xs )
% 1.61/1.11 | ( coinductive_lfinite @ B @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_14_lfinite__code_I2_J,axiom,
% 1.61/1.11 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 1.61/1.11 ( ( coinductive_lfinite @ B @ ( coinductive_LCons @ B @ X @ Xs ) )
% 1.61/1.11 = ( coinductive_lfinite @ B @ Xs ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_15_lfinite__LCons,axiom,
% 1.61/1.11 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 1.61/1.11 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_16_llist_Oinject,axiom,
% 1.61/1.11 ! [A: $tType,X21: A,X22: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 1.61/1.11 ( ( ( coinductive_LCons @ A @ X21 @ X22 )
% 1.61/1.11 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 1.61/1.11 = ( ( X21 = Y21 )
% 1.61/1.11 & ( X22 = Y22 ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_17_lzip_Odisc__iff_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 1.61/1.11 ( ( ~ ( coinductive_lnull @ ( product_prod @ A @ B ) @ ( coinductive_lzip @ A @ B @ Xs @ Ys ) ) )
% 1.61/1.11 = ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 & ~ ( coinductive_lnull @ B @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_18_lnull__lzip,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 1.61/1.11 ( ( coinductive_lnull @ ( product_prod @ A @ B ) @ ( coinductive_lzip @ A @ B @ Xs @ Ys ) )
% 1.61/1.11 = ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 | ( coinductive_lnull @ B @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_19_lzip__simps_I2_J,axiom,
% 1.61/1.11 ! [D: $tType,C: $tType,Xs: coinductive_llist @ C] :
% 1.61/1.11 ( ( coinductive_lzip @ C @ D @ Xs @ ( coinductive_LNil @ D ) )
% 1.61/1.11 = ( coinductive_LNil @ ( product_prod @ C @ D ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_20_lzip__simps_I1_J,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,Ys: coinductive_llist @ B] :
% 1.61/1.11 ( ( coinductive_lzip @ A @ B @ ( coinductive_LNil @ A ) @ Ys )
% 1.61/1.11 = ( coinductive_LNil @ ( product_prod @ A @ B ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_21_ldropn__LNil,axiom,
% 1.61/1.11 ! [A: $tType,N: nat] :
% 1.61/1.11 ( ( coinductive_ldropn @ A @ N @ ( coinductive_LNil @ A ) )
% 1.61/1.11 = ( coinductive_LNil @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_22_ldropn__lzip,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,N: nat,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 1.61/1.11 ( ( coinductive_ldropn @ ( product_prod @ A @ B ) @ N @ ( coinductive_lzip @ A @ B @ Xs @ Ys ) )
% 1.61/1.11 = ( coinductive_lzip @ A @ B @ ( coinductive_ldropn @ A @ N @ Xs ) @ ( coinductive_ldropn @ B @ N @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_23_lmirror__aux__simps_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,Acc: coinductive_llist @ A,Xa: A,X: coinductive_llist @ A] :
% 1.61/1.11 ( ( lMirro999291890or_aux @ A @ Acc @ ( coinductive_LCons @ A @ Xa @ X ) )
% 1.61/1.11 = ( coinductive_LCons @ A @ Xa @ ( lMirro999291890or_aux @ A @ ( coinductive_LCons @ A @ Xa @ Acc ) @ X ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_24_lmirror__aux__simps_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,Acc: coinductive_llist @ A] :
% 1.61/1.11 ( ( lMirro999291890or_aux @ A @ Acc @ ( coinductive_LNil @ A ) )
% 1.61/1.11 = Acc ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_25_lstrict__prefix__code_I4_J,axiom,
% 1.61/1.11 ! [B: $tType,X: B,Xs: coinductive_llist @ B,Y: B,Ys: coinductive_llist @ B] :
% 1.61/1.11 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 1.61/1.11 = ( ( X = Y )
% 1.61/1.11 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_26_lstrict__prefix__code_I1_J,axiom,
% 1.61/1.11 ! [A: $tType] :
% 1.61/1.11 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_27_lstrict__prefix__code_I3_J,axiom,
% 1.61/1.11 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 1.61/1.11 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_28_lstrict__prefix__code_I2_J,axiom,
% 1.61/1.11 ! [B: $tType,Y: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y @ Ys ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_29_lzip_Octr_I1_J,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 1.61/1.11 ( ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 | ( coinductive_lnull @ B @ Ys ) )
% 1.61/1.11 => ( ( coinductive_lzip @ A @ B @ Xs @ Ys )
% 1.61/1.11 = ( coinductive_LNil @ ( product_prod @ A @ B ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_30_ltl__simps_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_ltl @ A @ ( coinductive_LCons @ A @ X21 @ X22 ) )
% 1.61/1.11 = X22 ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_31_ltl__simps_I1_J,axiom,
% 1.61/1.11 ! [A: $tType] :
% 1.61/1.11 ( ( coinductive_ltl @ A @ ( coinductive_LNil @ A ) )
% 1.61/1.11 = ( coinductive_LNil @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_32_lzip_Odisc_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 1.61/1.11 ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ B @ Ys )
% 1.61/1.11 => ~ ( coinductive_lnull @ ( product_prod @ A @ B ) @ ( coinductive_lzip @ A @ B @ Xs @ Ys ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_33_lzip_Odisc_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 1.61/1.11 ( ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 | ( coinductive_lnull @ B @ Ys ) )
% 1.61/1.11 => ( coinductive_lnull @ ( product_prod @ A @ B ) @ ( coinductive_lzip @ A @ B @ Xs @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_34_llist_Odisc_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 1.61/1.11 ~ ( coinductive_lnull @ A @ ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_35_llist_Odisc_I1_J,axiom,
% 1.61/1.11 ! [A: $tType] : ( coinductive_lnull @ A @ ( coinductive_LNil @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_36_llist_OdiscI_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,Llist: coinductive_llist @ A,X21: A,X22: coinductive_llist @ A] :
% 1.61/1.11 ( ( Llist
% 1.61/1.11 = ( coinductive_LCons @ A @ X21 @ X22 ) )
% 1.61/1.11 => ~ ( coinductive_lnull @ A @ Llist ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_37_llist_OdiscI_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,Llist: coinductive_llist @ A] :
% 1.61/1.11 ( ( Llist
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 => ( coinductive_lnull @ A @ Llist ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_38_llist_Ocollapse_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,Llist: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ Llist )
% 1.61/1.11 => ( Llist
% 1.61/1.11 = ( coinductive_LNil @ A ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_39_llist_Odistinct_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_LNil @ A )
% 1.61/1.11 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_40_lmirror__aux_Octr_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Acc: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_lnull @ A @ Acc )
% 1.61/1.11 => ( ( lMirro999291890or_aux @ A @ Acc @ Xs )
% 1.61/1.11 = ( coinductive_LNil @ A ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_41_ltl__lzip,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 1.61/1.11 ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ B @ Ys )
% 1.61/1.11 => ( ( coinductive_ltl @ ( product_prod @ A @ B ) @ ( coinductive_lzip @ A @ B @ Xs @ Ys ) )
% 1.61/1.11 = ( coinductive_lzip @ A @ B @ ( coinductive_ltl @ A @ Xs ) @ ( coinductive_ltl @ B @ Ys ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_42_lnull__ltlI,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( coinductive_lnull @ A @ ( coinductive_ltl @ A @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_43_ltl__ldropn,axiom,
% 1.61/1.11 ! [A: $tType,N: nat,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_ltl @ A @ ( coinductive_ldropn @ A @ N @ Xs ) )
% 1.61/1.11 = ( coinductive_ldropn @ A @ N @ ( coinductive_ltl @ A @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_44_mem__Collect__eq,axiom,
% 1.61/1.11 ! [A: $tType,A2: A,P: A > $o] :
% 1.61/1.11 ( ( member @ A @ A2 @ ( collect @ A @ P ) )
% 1.61/1.11 = ( P @ A2 ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_45_Collect__mem__eq,axiom,
% 1.61/1.11 ! [A: $tType,A3: set @ A] :
% 1.61/1.11 ( ( collect @ A
% 1.61/1.11 @ ^ [X2: A] : ( member @ A @ X2 @ A3 ) )
% 1.61/1.11 = A3 ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_46_Collect__cong,axiom,
% 1.61/1.11 ! [A: $tType,P: A > $o,Q: A > $o] :
% 1.61/1.11 ( ! [X3: A] :
% 1.61/1.11 ( ( P @ X3 )
% 1.61/1.11 = ( Q @ X3 ) )
% 1.61/1.11 => ( ( collect @ A @ P )
% 1.61/1.11 = ( collect @ A @ Q ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_47_ext,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 1.61/1.11 ( ! [X3: A] :
% 1.61/1.11 ( ( F @ X3 )
% 1.61/1.11 = ( G @ X3 ) )
% 1.61/1.11 => ( F = G ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_48_ldropn__lnull,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,N: nat] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_ldropn @ A @ N @ Xs )
% 1.61/1.11 = ( coinductive_LNil @ A ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_49_lzip_Oexhaust,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 1.61/1.11 ( ~ ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 | ( coinductive_lnull @ B @ Ys ) )
% 1.61/1.11 => ~ ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( coinductive_lnull @ B @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_50_lfinite_Ocases,axiom,
% 1.61/1.11 ! [A: $tType,A2: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lfinite @ A @ A2 )
% 1.61/1.11 => ( ( A2
% 1.61/1.11 != ( coinductive_LNil @ A ) )
% 1.61/1.11 => ~ ! [Xs2: coinductive_llist @ A] :
% 1.61/1.11 ( ? [X3: A] :
% 1.61/1.11 ( A2
% 1.61/1.11 = ( coinductive_LCons @ A @ X3 @ Xs2 ) )
% 1.61/1.11 => ~ ( coinductive_lfinite @ A @ Xs2 ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_51_lfinite_Osimps,axiom,
% 1.61/1.11 ! [A: $tType] :
% 1.61/1.11 ( ( coinductive_lfinite @ A )
% 1.61/1.11 = ( ^ [A4: coinductive_llist @ A] :
% 1.61/1.11 ( ( A4
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 | ? [Xs3: coinductive_llist @ A,X2: A] :
% 1.61/1.11 ( ( A4
% 1.61/1.11 = ( coinductive_LCons @ A @ X2 @ Xs3 ) )
% 1.61/1.11 & ( coinductive_lfinite @ A @ Xs3 ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_52_llimit__induct,axiom,
% 1.61/1.11 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( P @ ( coinductive_LNil @ A ) )
% 1.61/1.11 => ( ! [X3: A,Xs2: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lfinite @ A @ Xs2 )
% 1.61/1.11 => ( ( P @ Xs2 )
% 1.61/1.11 => ( P @ ( coinductive_LCons @ A @ X3 @ Xs2 ) ) ) )
% 1.61/1.11 => ( ( ! [Ys2: coinductive_llist @ A] :
% 1.61/1.11 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs )
% 1.61/1.11 => ( P @ Ys2 ) )
% 1.61/1.11 => ( P @ Xs ) )
% 1.61/1.11 => ( P @ Xs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_53_llist_Oexhaust,axiom,
% 1.61/1.11 ! [A: $tType,Y: coinductive_llist @ A] :
% 1.61/1.11 ( ( Y
% 1.61/1.11 != ( coinductive_LNil @ A ) )
% 1.61/1.11 => ~ ! [X212: A,X222: coinductive_llist @ A] :
% 1.61/1.11 ( Y
% 1.61/1.11 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_54_neq__LNil__conv,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( Xs
% 1.61/1.11 != ( coinductive_LNil @ A ) )
% 1.61/1.11 = ( ? [X2: A,Xs4: coinductive_llist @ A] :
% 1.61/1.11 ( Xs
% 1.61/1.11 = ( coinductive_LCons @ A @ X2 @ Xs4 ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_55_not__lnull__conv,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( ~ ( coinductive_lnull @ A @ Xs ) )
% 1.61/1.11 = ( ? [X2: A,Xs4: coinductive_llist @ A] :
% 1.61/1.11 ( Xs
% 1.61/1.11 = ( coinductive_LCons @ A @ X2 @ Xs4 ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_56_lappend_Oexhaust,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ~ ( coinductive_lnull @ A @ Ys ) )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_57_lfinite_Oinducts,axiom,
% 1.61/1.11 ! [A: $tType,X: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 1.61/1.11 ( ( coinductive_lfinite @ A @ X )
% 1.61/1.11 => ( ( P @ ( coinductive_LNil @ A ) )
% 1.61/1.11 => ( ! [Xs2: coinductive_llist @ A,X3: A] :
% 1.61/1.11 ( ( coinductive_lfinite @ A @ Xs2 )
% 1.61/1.11 => ( ( P @ Xs2 )
% 1.61/1.11 => ( P @ ( coinductive_LCons @ A @ X3 @ Xs2 ) ) ) )
% 1.61/1.11 => ( P @ X ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_58_lnull__def,axiom,
% 1.61/1.11 ! [A: $tType] :
% 1.61/1.11 ( ( coinductive_lnull @ A )
% 1.61/1.11 = ( ^ [Llist2: coinductive_llist @ A] :
% 1.61/1.11 ( Llist2
% 1.61/1.11 = ( coinductive_LNil @ A ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_59_llist__less__induct,axiom,
% 1.61/1.11 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ! [Xs2: coinductive_llist @ A] :
% 1.61/1.11 ( ! [Ys2: coinductive_llist @ A] :
% 1.61/1.11 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs2 )
% 1.61/1.11 => ( P @ Ys2 ) )
% 1.61/1.11 => ( P @ Xs2 ) )
% 1.61/1.11 => ( P @ Xs ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_60_lzip__eq__LNil__conv,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 1.61/1.11 ( ( ( coinductive_lzip @ A @ B @ Xs @ Ys )
% 1.61/1.11 = ( coinductive_LNil @ ( product_prod @ A @ B ) ) )
% 1.61/1.11 = ( ( Xs
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 | ( Ys
% 1.61/1.11 = ( coinductive_LNil @ B ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_61_lfinite__LConsI,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 1.61/1.11 ( ( coinductive_lfinite @ A @ Xs )
% 1.61/1.11 => ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_62_lfinite__LNil,axiom,
% 1.61/1.11 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_63_lmirror__aux_Odisc_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Acc: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_lnull @ A @ Acc )
% 1.61/1.11 => ( coinductive_lnull @ A @ ( lMirro999291890or_aux @ A @ Acc @ Xs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_64_lmirror__aux_Odisc_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Acc: coinductive_llist @ A] :
% 1.61/1.11 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 | ~ ( coinductive_lnull @ A @ Acc ) )
% 1.61/1.11 => ~ ( coinductive_lnull @ A @ ( lMirro999291890or_aux @ A @ Acc @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_65_lmirror__def,axiom,
% 1.61/1.11 ! [A: $tType] :
% 1.61/1.11 ( ( lMirro427583474mirror @ A )
% 1.61/1.11 = ( lMirro999291890or_aux @ A @ ( coinductive_LNil @ A ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_66_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 1.61/1.11 = ( ( Xs
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 | ? [Xs4: coinductive_llist @ A] :
% 1.61/1.11 ( ( Xs
% 1.61/1.11 = ( coinductive_LCons @ A @ Y @ Xs4 ) )
% 1.61/1.11 & ( coindu328551480prefix @ A @ Xs4 @ Ys ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_67_ltl__lmirror__aux,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Acc: coinductive_llist @ A] :
% 1.61/1.11 ( ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_ltl @ A @ ( lMirro999291890or_aux @ A @ Acc @ Xs ) )
% 1.61/1.11 = ( coinductive_ltl @ A @ Acc ) ) )
% 1.61/1.11 & ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_ltl @ A @ ( lMirro999291890or_aux @ A @ Acc @ Xs ) )
% 1.61/1.11 = ( lMirro999291890or_aux @ A @ ( coinductive_LCons @ A @ ( coinductive_lhd @ A @ Xs ) @ Acc ) @ ( coinductive_ltl @ A @ Xs ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_68_llast__singleton,axiom,
% 1.61/1.11 ! [A: $tType,X: A] :
% 1.61/1.11 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) )
% 1.61/1.11 = X ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_69_lhd__LCons__ltl,axiom,
% 1.61/1.11 ! [A: $tType,Llist: coinductive_llist @ A] :
% 1.61/1.11 ( ~ ( coinductive_lnull @ A @ Llist )
% 1.61/1.11 => ( ( coinductive_LCons @ A @ ( coinductive_lhd @ A @ Llist ) @ ( coinductive_ltl @ A @ Llist ) )
% 1.61/1.11 = Llist ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_70_lmember__code_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,X: A] :
% 1.61/1.11 ~ ( coinductive_lmember @ A @ X @ ( coinductive_LNil @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_71_lmember__code_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,X: A,Y: A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lmember @ A @ X @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 1.61/1.11 = ( ( X = Y )
% 1.61/1.11 | ( coinductive_lmember @ A @ X @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_72_lstrict__prefix__lappend__conv,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coindu1478340336prefix @ A @ Xs @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 1.61/1.11 = ( ( coinductive_lfinite @ A @ Xs )
% 1.61/1.11 & ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_73_gen__lset__code_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,A3: set @ A] :
% 1.61/1.11 ( ( coinductive_gen_lset @ A @ A3 @ ( coinductive_LNil @ A ) )
% 1.61/1.11 = A3 ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_74_llast__LCons,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 1.61/1.11 ( ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 1.61/1.11 = X ) )
% 1.61/1.11 & ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 1.61/1.11 = ( coinductive_llast @ A @ Xs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_75_lappend__code_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,Xa: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa @ X ) @ Ys )
% 1.61/1.11 = ( coinductive_LCons @ A @ Xa @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_76_lnull__lappend,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 1.61/1.11 = ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 & ( coinductive_lnull @ A @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_77_lappend_Odisc__iff_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) )
% 1.61/1.11 = ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_78_lappend__LNil2,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 1.61/1.11 = Xs ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_79_lappend__code_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 1.61/1.11 = Ys ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_80_lfinite__lappend,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lfinite @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 1.61/1.11 = ( ( coinductive_lfinite @ A @ Xs )
% 1.61/1.11 & ( coinductive_lfinite @ A @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_81_llast__LCons2,axiom,
% 1.61/1.11 ! [A: $tType,X: A,Y: A,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs ) ) )
% 1.61/1.11 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_82_ltl__lappend,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_ltl @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 1.61/1.11 = ( coinductive_ltl @ A @ Ys ) ) )
% 1.61/1.11 & ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_ltl @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 1.61/1.11 = ( coinductive_lappend @ A @ ( coinductive_ltl @ A @ Xs ) @ Ys ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_83_lhd__lappend,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_lhd @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 1.61/1.11 = ( coinductive_lhd @ A @ Ys ) ) )
% 1.61/1.11 & ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_lhd @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 1.61/1.11 = ( coinductive_lhd @ A @ Xs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_84_llast__lappend__LCons,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lfinite @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) )
% 1.61/1.11 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_85_lappend__assoc,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 1.61/1.11 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_86_lhd__LCons,axiom,
% 1.61/1.11 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lhd @ A @ ( coinductive_LCons @ A @ X21 @ X22 ) )
% 1.61/1.11 = X21 ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_87_ltakeWhile_Oexhaust,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 1.61/1.11 ( ~ ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 | ~ ( P @ ( coinductive_lhd @ A @ Xs ) ) )
% 1.61/1.11 => ~ ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ~ ( P @ ( coinductive_lhd @ A @ Xs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_88_lappend__lnull2,axiom,
% 1.61/1.11 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ Ys )
% 1.61/1.11 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 1.61/1.11 = Xs ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_89_lappend__lnull1,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 1.61/1.11 = Ys ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_90_lappend_Odisc_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_lnull @ A @ Ys )
% 1.61/1.11 => ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_91_lappend_Odisc_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 | ~ ( coinductive_lnull @ A @ Ys ) )
% 1.61/1.11 => ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_92_lappend__eq__LNil__iff,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 = ( ( Xs
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 & ( Ys
% 1.61/1.11 = ( coinductive_LNil @ A ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_93_LNil__eq__lappend__iff,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( ( coinductive_LNil @ A )
% 1.61/1.11 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 1.61/1.11 = ( ( Xs
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 & ( Ys
% 1.61/1.11 = ( coinductive_LNil @ A ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_94_lappend__LNil__LNil,axiom,
% 1.61/1.11 ! [A: $tType] :
% 1.61/1.11 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 1.61/1.11 = ( coinductive_LNil @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_95_lappend__inf,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ~ ( coinductive_lfinite @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 1.61/1.11 = Xs ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_96_lappend__snocL1__conv__LCons2,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 1.61/1.11 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_97_lappend_Octr_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_lnull @ A @ Ys )
% 1.61/1.11 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 1.61/1.11 = ( coinductive_LNil @ A ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_98_llist_Ocoinduct__strong,axiom,
% 1.61/1.11 ! [A: $tType,R: ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o,Llist: coinductive_llist @ A,Llist3: coinductive_llist @ A] :
% 1.61/1.11 ( ( R @ Llist @ Llist3 )
% 1.61/1.11 => ( ! [Llist4: coinductive_llist @ A,Llist5: coinductive_llist @ A] :
% 1.61/1.11 ( ( R @ Llist4 @ Llist5 )
% 1.61/1.11 => ( ( ( coinductive_lnull @ A @ Llist4 )
% 1.61/1.11 = ( coinductive_lnull @ A @ Llist5 ) )
% 1.61/1.11 & ( ~ ( coinductive_lnull @ A @ Llist4 )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ Llist5 )
% 1.61/1.11 => ( ( ( coinductive_lhd @ A @ Llist4 )
% 1.61/1.11 = ( coinductive_lhd @ A @ Llist5 ) )
% 1.61/1.11 & ( ( R @ ( coinductive_ltl @ A @ Llist4 ) @ ( coinductive_ltl @ A @ Llist5 ) )
% 1.61/1.11 | ( ( coinductive_ltl @ A @ Llist4 )
% 1.61/1.11 = ( coinductive_ltl @ A @ Llist5 ) ) ) ) ) ) ) )
% 1.61/1.11 => ( Llist = Llist3 ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_99_llist_Ocoinduct,axiom,
% 1.61/1.11 ! [A: $tType,R: ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o,Llist: coinductive_llist @ A,Llist3: coinductive_llist @ A] :
% 1.61/1.11 ( ( R @ Llist @ Llist3 )
% 1.61/1.11 => ( ! [Llist4: coinductive_llist @ A,Llist5: coinductive_llist @ A] :
% 1.61/1.11 ( ( R @ Llist4 @ Llist5 )
% 1.61/1.11 => ( ( ( coinductive_lnull @ A @ Llist4 )
% 1.61/1.11 = ( coinductive_lnull @ A @ Llist5 ) )
% 1.61/1.11 & ( ~ ( coinductive_lnull @ A @ Llist4 )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ Llist5 )
% 1.61/1.11 => ( ( ( coinductive_lhd @ A @ Llist4 )
% 1.61/1.11 = ( coinductive_lhd @ A @ Llist5 ) )
% 1.61/1.11 & ( R @ ( coinductive_ltl @ A @ Llist4 ) @ ( coinductive_ltl @ A @ Llist5 ) ) ) ) ) ) )
% 1.61/1.11 => ( Llist = Llist3 ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_100_llist_Oexpand,axiom,
% 1.61/1.11 ! [A: $tType,Llist: coinductive_llist @ A,Llist3: coinductive_llist @ A] :
% 1.61/1.11 ( ( ( coinductive_lnull @ A @ Llist )
% 1.61/1.11 = ( coinductive_lnull @ A @ Llist3 ) )
% 1.61/1.11 => ( ( ~ ( coinductive_lnull @ A @ Llist )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ Llist3 )
% 1.61/1.11 => ( ( ( coinductive_lhd @ A @ Llist )
% 1.61/1.11 = ( coinductive_lhd @ A @ Llist3 ) )
% 1.61/1.11 & ( ( coinductive_ltl @ A @ Llist )
% 1.61/1.11 = ( coinductive_ltl @ A @ Llist3 ) ) ) ) )
% 1.61/1.11 => ( Llist = Llist3 ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_101_lappend__ltl,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_lappend @ A @ ( coinductive_ltl @ A @ Xs ) @ Ys )
% 1.61/1.11 = ( coinductive_ltl @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_102_lhd__lmirror__aux,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Acc: coinductive_llist @ A] :
% 1.61/1.11 ( ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_lhd @ A @ ( lMirro999291890or_aux @ A @ Acc @ Xs ) )
% 1.61/1.11 = ( coinductive_lhd @ A @ Acc ) ) )
% 1.61/1.11 & ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_lhd @ A @ ( lMirro999291890or_aux @ A @ Acc @ Xs ) )
% 1.61/1.11 = ( coinductive_lhd @ A @ Xs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_103_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 1.61/1.11 = ( Xs
% 1.61/1.11 = ( coinductive_LNil @ A ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_104_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_105_llist_Oexhaust__sel,axiom,
% 1.61/1.11 ! [A: $tType,Llist: coinductive_llist @ A] :
% 1.61/1.11 ( ( Llist
% 1.61/1.11 != ( coinductive_LNil @ A ) )
% 1.61/1.11 => ( Llist
% 1.61/1.11 = ( coinductive_LCons @ A @ ( coinductive_lhd @ A @ Llist ) @ ( coinductive_ltl @ A @ Llist ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_106_eq__LConsD,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( Xs
% 1.61/1.11 = ( coinductive_LCons @ A @ Y @ Ys ) )
% 1.61/1.11 => ( ( Xs
% 1.61/1.11 != ( coinductive_LNil @ A ) )
% 1.61/1.11 & ( ( coinductive_lhd @ A @ Xs )
% 1.61/1.11 = Y )
% 1.61/1.11 & ( ( coinductive_ltl @ A @ Xs )
% 1.61/1.11 = Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_107_lfinite__rev__induct,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 1.61/1.11 ( ( coinductive_lfinite @ A @ Xs )
% 1.61/1.11 => ( ( P @ ( coinductive_LNil @ A ) )
% 1.61/1.11 => ( ! [X3: A,Xs2: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lfinite @ A @ Xs2 )
% 1.61/1.11 => ( ( P @ Xs2 )
% 1.61/1.11 => ( P @ ( coinductive_lappend @ A @ Xs2 @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) ) ) ) )
% 1.61/1.11 => ( P @ Xs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_108_lzip_Ocode,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType] :
% 1.61/1.11 ( ( coinductive_lzip @ A @ B )
% 1.61/1.11 = ( ^ [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ B] :
% 1.61/1.11 ( if @ ( coinductive_llist @ ( product_prod @ A @ B ) )
% 1.61/1.11 @ ( ( coinductive_lnull @ A @ Xs3 )
% 1.61/1.11 | ( coinductive_lnull @ B @ Ys3 ) )
% 1.61/1.11 @ ( coinductive_LNil @ ( product_prod @ A @ B ) )
% 1.61/1.11 @ ( coinductive_LCons @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ ( coinductive_lhd @ A @ Xs3 ) @ ( coinductive_lhd @ B @ Ys3 ) ) @ ( coinductive_lzip @ A @ B @ ( coinductive_ltl @ A @ Xs3 ) @ ( coinductive_ltl @ B @ Ys3 ) ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_109_llexord__conv,axiom,
% 1.61/1.11 ! [A: $tType] :
% 1.61/1.11 ( ( coinductive_llexord @ A )
% 1.61/1.11 = ( ^ [R2: A > A > $o,Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A] :
% 1.61/1.11 ( ( Xs3 = Ys3 )
% 1.61/1.11 | ? [Zs2: coinductive_llist @ A,Xs4: coinductive_llist @ A,Y2: A,Ys4: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lfinite @ A @ Zs2 )
% 1.61/1.11 & ( Xs3
% 1.61/1.11 = ( coinductive_lappend @ A @ Zs2 @ Xs4 ) )
% 1.61/1.11 & ( Ys3
% 1.61/1.11 = ( coinductive_lappend @ A @ Zs2 @ ( coinductive_LCons @ A @ Y2 @ Ys4 ) ) )
% 1.61/1.11 & ( ( Xs4
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 | ( R2 @ ( coinductive_lhd @ A @ Xs4 ) @ Y2 ) ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_110_llist_Osplit__sel__asm,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( coinductive_llist @ A ) > B,Llist: coinductive_llist @ A] :
% 1.61/1.11 ( ( P @ ( coindu1381640503_llist @ B @ A @ F1 @ F2 @ Llist ) )
% 1.61/1.11 = ( ~ ( ( ( Llist
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 & ~ ( P @ F1 ) )
% 1.61/1.11 | ( ( Llist
% 1.61/1.11 = ( coinductive_LCons @ A @ ( coinductive_lhd @ A @ Llist ) @ ( coinductive_ltl @ A @ Llist ) ) )
% 1.61/1.11 & ~ ( P @ ( F2 @ ( coinductive_lhd @ A @ Llist ) @ ( coinductive_ltl @ A @ Llist ) ) ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_111_llist_Osplit__sel,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( coinductive_llist @ A ) > B,Llist: coinductive_llist @ A] :
% 1.61/1.11 ( ( P @ ( coindu1381640503_llist @ B @ A @ F1 @ F2 @ Llist ) )
% 1.61/1.11 = ( ( ( Llist
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 => ( P @ F1 ) )
% 1.61/1.11 & ( ( Llist
% 1.61/1.11 = ( coinductive_LCons @ A @ ( coinductive_lhd @ A @ Llist ) @ ( coinductive_ltl @ A @ Llist ) ) )
% 1.61/1.11 => ( P @ ( F2 @ ( coinductive_lhd @ A @ Llist ) @ ( coinductive_ltl @ A @ Llist ) ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_112_unfold__llist__id,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coindu1441602521_llist @ ( coinductive_llist @ A ) @ A @ ( coinductive_lnull @ A ) @ ( coinductive_lhd @ A ) @ ( coinductive_ltl @ A ) @ Xs )
% 1.61/1.11 = Xs ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_113_ltakeWhile_Ocode,axiom,
% 1.61/1.11 ! [A: $tType] :
% 1.61/1.11 ( ( coindu501562517eWhile @ A )
% 1.61/1.11 = ( ^ [P2: A > $o,Xs3: coinductive_llist @ A] :
% 1.61/1.11 ( if @ ( coinductive_llist @ A )
% 1.61/1.11 @ ( ( coinductive_lnull @ A @ Xs3 )
% 1.61/1.11 | ~ ( P2 @ ( coinductive_lhd @ A @ Xs3 ) ) )
% 1.61/1.11 @ ( coinductive_LNil @ A )
% 1.61/1.11 @ ( coinductive_LCons @ A @ ( coinductive_lhd @ A @ Xs3 ) @ ( coindu501562517eWhile @ A @ P2 @ ( coinductive_ltl @ A @ Xs3 ) ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_114_llexord__refl,axiom,
% 1.61/1.11 ! [A: $tType,R3: A > A > $o,Xs: coinductive_llist @ A] : ( coinductive_llexord @ A @ R3 @ Xs @ Xs ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_115_ltakeWhile__LNil,axiom,
% 1.61/1.11 ! [A: $tType,P: A > $o] :
% 1.61/1.11 ( ( coindu501562517eWhile @ A @ P @ ( coinductive_LNil @ A ) )
% 1.61/1.11 = ( coinductive_LNil @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_116_llexord__LCons__LCons,axiom,
% 1.61/1.11 ! [A: $tType,R3: A > A > $o,X: A,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_llexord @ A @ R3 @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 1.61/1.11 = ( ( ( X = Y )
% 1.61/1.11 & ( coinductive_llexord @ A @ R3 @ Xs @ Ys ) )
% 1.61/1.11 | ( R3 @ X @ Y ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_117_llexord__LNil__right,axiom,
% 1.61/1.11 ! [A: $tType,Ys: coinductive_llist @ A,R3: A > A > $o,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ Ys )
% 1.61/1.11 => ( ( coinductive_llexord @ A @ R3 @ Xs @ Ys )
% 1.61/1.11 = ( coinductive_lnull @ A @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_118_llexord__code_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,R3: A > A > $o,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R3 @ ( coinductive_LNil @ A ) @ Ys ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_119_unfold__llist__eq__LCons,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,IS_LNIL: B > $o,LHD: B > A,LTL: B > B,B2: B,X: A,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ B2 )
% 1.61/1.11 = ( coinductive_LCons @ A @ X @ Xs ) )
% 1.61/1.11 = ( ~ ( IS_LNIL @ B2 )
% 1.61/1.11 & ( X
% 1.61/1.11 = ( LHD @ B2 ) )
% 1.61/1.11 & ( Xs
% 1.61/1.11 = ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ B2 ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_120_unfold__llist_Odisc__iff_I2_J,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,P3: A > $o,G21: A > B,G22: A > A,A2: A] :
% 1.61/1.11 ( ( ~ ( coinductive_lnull @ B @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) ) )
% 1.61/1.11 = ( ~ ( P3 @ A2 ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_121_unfold__llist_Odisc__iff_I1_J,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,P3: A > $o,G21: A > B,G22: A > A,A2: A] :
% 1.61/1.11 ( ( coinductive_lnull @ B @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) )
% 1.61/1.11 = ( P3 @ A2 ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_122_ltakeWhile__LCons,axiom,
% 1.61/1.11 ! [A: $tType,P: A > $o,X: A,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( ( P @ X )
% 1.61/1.11 => ( ( coindu501562517eWhile @ A @ P @ ( coinductive_LCons @ A @ X @ Xs ) )
% 1.61/1.11 = ( coinductive_LCons @ A @ X @ ( coindu501562517eWhile @ A @ P @ Xs ) ) ) )
% 1.61/1.11 & ( ~ ( P @ X )
% 1.61/1.11 => ( ( coindu501562517eWhile @ A @ P @ ( coinductive_LCons @ A @ X @ Xs ) )
% 1.61/1.11 = ( coinductive_LNil @ A ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_123_ltakeWhile_Odisc__iff_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( ~ ( coinductive_lnull @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) ) )
% 1.61/1.11 = ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 & ( P @ ( coinductive_lhd @ A @ Xs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_124_ltakeWhile_Odisc__iff_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) )
% 1.61/1.11 = ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 | ~ ( P @ ( coinductive_lhd @ A @ Xs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_125_lnull__ltakeWhile,axiom,
% 1.61/1.11 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) )
% 1.61/1.11 = ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ~ ( P @ ( coinductive_lhd @ A @ Xs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_126_lzip__simps_I3_J,axiom,
% 1.61/1.11 ! [C: $tType,B: $tType,X: C,Xs: coinductive_llist @ C,Y: B,Ys: coinductive_llist @ B] :
% 1.61/1.11 ( ( coinductive_lzip @ C @ B @ ( coinductive_LCons @ C @ X @ Xs ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 1.61/1.11 = ( coinductive_LCons @ ( product_prod @ C @ B ) @ ( product_Pair @ C @ B @ X @ Y ) @ ( coinductive_lzip @ C @ B @ Xs @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_127_llexord__antisym,axiom,
% 1.61/1.11 ! [A: $tType,R3: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_llexord @ A @ R3 @ Xs @ Ys )
% 1.61/1.11 => ( ( coinductive_llexord @ A @ R3 @ Ys @ Xs )
% 1.61/1.11 => ( ! [A5: A,B3: A] :
% 1.61/1.11 ( ( R3 @ A5 @ B3 )
% 1.61/1.11 => ~ ( R3 @ B3 @ A5 ) )
% 1.61/1.11 => ( Xs = Ys ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_128_llexord__linear,axiom,
% 1.61/1.11 ! [A: $tType,R3: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ! [X3: A,Y3: A] :
% 1.61/1.11 ( ( R3 @ X3 @ Y3 )
% 1.61/1.11 | ( X3 = Y3 )
% 1.61/1.11 | ( R3 @ Y3 @ X3 ) )
% 1.61/1.11 => ( ( coinductive_llexord @ A @ R3 @ Xs @ Ys )
% 1.61/1.11 | ( coinductive_llexord @ A @ R3 @ Ys @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_129_llexord__trans,axiom,
% 1.61/1.11 ! [A: $tType,R3: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_llexord @ A @ R3 @ Xs @ Ys )
% 1.61/1.11 => ( ( coinductive_llexord @ A @ R3 @ Ys @ Zs )
% 1.61/1.11 => ( ! [A5: A,B3: A,C2: A] :
% 1.61/1.11 ( ( R3 @ A5 @ B3 )
% 1.61/1.11 => ( ( R3 @ B3 @ C2 )
% 1.61/1.11 => ( R3 @ A5 @ C2 ) ) )
% 1.61/1.11 => ( coinductive_llexord @ A @ R3 @ Xs @ Zs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_130_llexord__code_I3_J,axiom,
% 1.61/1.11 ! [A: $tType,R3: A > A > $o,X: A,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_llexord @ A @ R3 @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 1.61/1.11 = ( ( R3 @ X @ Y )
% 1.61/1.11 | ( ( X = Y )
% 1.61/1.11 & ( coinductive_llexord @ A @ R3 @ Xs @ Ys ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_131_llexord__LCons__left,axiom,
% 1.61/1.11 ! [A: $tType,R3: A > A > $o,X: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_llexord @ A @ R3 @ ( coinductive_LCons @ A @ X @ Xs ) @ Ys )
% 1.61/1.11 = ( ? [Y2: A,Ys4: coinductive_llist @ A] :
% 1.61/1.11 ( ( Ys
% 1.61/1.11 = ( coinductive_LCons @ A @ Y2 @ Ys4 ) )
% 1.61/1.11 & ( ( ( X = Y2 )
% 1.61/1.11 & ( coinductive_llexord @ A @ R3 @ Xs @ Ys4 ) )
% 1.61/1.11 | ( R3 @ X @ Y2 ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_132_llexord__LCons__eq,axiom,
% 1.61/1.11 ! [A: $tType,R3: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,X: A] :
% 1.61/1.11 ( ( coinductive_llexord @ A @ R3 @ Xs @ Ys )
% 1.61/1.11 => ( coinductive_llexord @ A @ R3 @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ X @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_133_llexord__LCons__less,axiom,
% 1.61/1.11 ! [A: $tType,R3: A > A > $o,X: A,Y: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( R3 @ X @ Y )
% 1.61/1.11 => ( coinductive_llexord @ A @ R3 @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_134_lnull__llexord,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,R3: A > A > $o,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( coinductive_llexord @ A @ R3 @ Xs @ Ys ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_135_llexord__LNil,axiom,
% 1.61/1.11 ! [A: $tType,R3: A > A > $o,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R3 @ ( coinductive_LNil @ A ) @ Ys ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_136_llexord__lappend__leftI,axiom,
% 1.61/1.11 ! [A: $tType,R3: A > A > $o,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_llexord @ A @ R3 @ Ys @ Zs )
% 1.61/1.11 => ( coinductive_llexord @ A @ R3 @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( coinductive_lappend @ A @ Xs @ Zs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_137_llexord__append__right,axiom,
% 1.61/1.11 ! [A: $tType,R3: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] : ( coinductive_llexord @ A @ R3 @ Xs @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_138_unfold__llist_Octr_I2_J,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 1.61/1.11 ( ~ ( P3 @ A2 )
% 1.61/1.11 => ( ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A2 )
% 1.61/1.11 = ( coinductive_LCons @ B @ ( G21 @ A2 ) @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ ( G22 @ A2 ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_139_unfold__llist_Odisc_I2_J,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 1.61/1.11 ( ~ ( P3 @ A2 )
% 1.61/1.11 => ~ ( coinductive_lnull @ B @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_140_unfold__llist_Odisc_I1_J,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 1.61/1.11 ( ( P3 @ A2 )
% 1.61/1.11 => ( coinductive_lnull @ B @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_141_unfold__llist_Octr_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 1.61/1.11 ( ( P3 @ A2 )
% 1.61/1.11 => ( ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A2 )
% 1.61/1.11 = ( coinductive_LNil @ B ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_142_llist_Osimps_I5_J,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,F1: B,F2: A > ( coinductive_llist @ A ) > B,X21: A,X22: coinductive_llist @ A] :
% 1.61/1.11 ( ( coindu1381640503_llist @ B @ A @ F1 @ F2 @ ( coinductive_LCons @ A @ X21 @ X22 ) )
% 1.61/1.11 = ( F2 @ X21 @ X22 ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_143_llist_Osimps_I4_J,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,F1: B,F2: A > ( coinductive_llist @ A ) > B] :
% 1.61/1.11 ( ( coindu1381640503_llist @ B @ A @ F1 @ F2 @ ( coinductive_LNil @ A ) )
% 1.61/1.11 = F1 ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_144_unfold__llist_Osimps_I4_J,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 1.61/1.11 ( ~ ( P3 @ A2 )
% 1.61/1.11 => ( ( coinductive_ltl @ B @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) )
% 1.61/1.11 = ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ ( G22 @ A2 ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_145_unfold__llist_Osimps_I3_J,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,P3: A > $o,A2: A,G21: A > B,G22: A > A] :
% 1.61/1.11 ( ~ ( P3 @ A2 )
% 1.61/1.11 => ( ( coinductive_lhd @ B @ ( coindu1441602521_llist @ A @ B @ P3 @ G21 @ G22 @ A2 ) )
% 1.61/1.11 = ( G21 @ A2 ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_146_lhd__ltakeWhile,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 1.61/1.11 ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( P @ ( coinductive_lhd @ A @ Xs ) )
% 1.61/1.11 => ( ( coinductive_lhd @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) )
% 1.61/1.11 = ( coinductive_lhd @ A @ Xs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_147_ltakeWhile_Odisc_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 1.61/1.11 ( ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 | ~ ( P @ ( coinductive_lhd @ A @ Xs ) ) )
% 1.61/1.11 => ( coinductive_lnull @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_148_ltakeWhile_Odisc_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 1.61/1.11 ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( P @ ( coinductive_lhd @ A @ Xs ) )
% 1.61/1.11 => ~ ( coinductive_lnull @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_149_ltakeWhile__eq__LNil__iff,axiom,
% 1.61/1.11 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( ( coindu501562517eWhile @ A @ P @ Xs )
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 = ( ( Xs
% 1.61/1.11 != ( coinductive_LNil @ A ) )
% 1.61/1.11 => ~ ( P @ ( coinductive_lhd @ A @ Xs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_150_lzip__eq__LCons__conv,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,Z: product_prod @ A @ B,Zs: coinductive_llist @ ( product_prod @ A @ B )] :
% 1.61/1.11 ( ( ( coinductive_lzip @ A @ B @ Xs @ Ys )
% 1.61/1.11 = ( coinductive_LCons @ ( product_prod @ A @ B ) @ Z @ Zs ) )
% 1.61/1.11 = ( ? [X2: A,Xs4: coinductive_llist @ A,Y2: B,Ys4: coinductive_llist @ B] :
% 1.61/1.11 ( ( Xs
% 1.61/1.11 = ( coinductive_LCons @ A @ X2 @ Xs4 ) )
% 1.61/1.11 & ( Ys
% 1.61/1.11 = ( coinductive_LCons @ B @ Y2 @ Ys4 ) )
% 1.61/1.11 & ( Z
% 1.61/1.11 = ( product_Pair @ A @ B @ X2 @ Y2 ) )
% 1.61/1.11 & ( Zs
% 1.61/1.11 = ( coinductive_lzip @ A @ B @ Xs4 @ Ys4 ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_151_llexord__code_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,R3: A > A > $o,X: A,Xs: coinductive_llist @ A] :
% 1.61/1.11 ~ ( coinductive_llexord @ A @ R3 @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LNil @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_152_llexord_Ocases,axiom,
% 1.61/1.11 ! [A: $tType,R3: A > A > $o,A1: coinductive_llist @ A,A22: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_llexord @ A @ R3 @ A1 @ A22 )
% 1.61/1.11 => ( ! [Xs2: coinductive_llist @ A,Ys5: coinductive_llist @ A,X3: A] :
% 1.61/1.11 ( ( A1
% 1.61/1.11 = ( coinductive_LCons @ A @ X3 @ Xs2 ) )
% 1.61/1.11 => ( ( A22
% 1.61/1.11 = ( coinductive_LCons @ A @ X3 @ Ys5 ) )
% 1.61/1.11 => ~ ( coinductive_llexord @ A @ R3 @ Xs2 @ Ys5 ) ) )
% 1.61/1.11 => ( ! [X3: A] :
% 1.61/1.11 ( ? [Xs2: coinductive_llist @ A] :
% 1.61/1.11 ( A1
% 1.61/1.11 = ( coinductive_LCons @ A @ X3 @ Xs2 ) )
% 1.61/1.11 => ! [Y3: A] :
% 1.61/1.11 ( ? [Ys5: coinductive_llist @ A] :
% 1.61/1.11 ( A22
% 1.61/1.11 = ( coinductive_LCons @ A @ Y3 @ Ys5 ) )
% 1.61/1.11 => ~ ( R3 @ X3 @ Y3 ) ) )
% 1.61/1.11 => ~ ( ( A1
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 => ! [Ys5: coinductive_llist @ A] : ( A22 != Ys5 ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_153_llexord_Osimps,axiom,
% 1.61/1.11 ! [A: $tType] :
% 1.61/1.11 ( ( coinductive_llexord @ A )
% 1.61/1.11 = ( ^ [R2: A > A > $o,A12: coinductive_llist @ A,A23: coinductive_llist @ A] :
% 1.61/1.11 ( ? [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A,X2: A] :
% 1.61/1.11 ( ( A12
% 1.61/1.11 = ( coinductive_LCons @ A @ X2 @ Xs3 ) )
% 1.61/1.11 & ( A23
% 1.61/1.11 = ( coinductive_LCons @ A @ X2 @ Ys3 ) )
% 1.61/1.11 & ( coinductive_llexord @ A @ R2 @ Xs3 @ Ys3 ) )
% 1.61/1.11 | ? [X2: A,Y2: A,Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A] :
% 1.61/1.11 ( ( A12
% 1.61/1.11 = ( coinductive_LCons @ A @ X2 @ Xs3 ) )
% 1.61/1.11 & ( A23
% 1.61/1.11 = ( coinductive_LCons @ A @ Y2 @ Ys3 ) )
% 1.61/1.11 & ( R2 @ X2 @ Y2 ) )
% 1.61/1.11 | ? [Ys3: coinductive_llist @ A] :
% 1.61/1.11 ( ( A12
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 & ( A23 = Ys3 ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_154_llexord_Ocoinduct,axiom,
% 1.61/1.11 ! [A: $tType,X4: ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,Xa: coinductive_llist @ A,R3: A > A > $o] :
% 1.61/1.11 ( ( X4 @ X @ Xa )
% 1.61/1.11 => ( ! [X3: coinductive_llist @ A,Xa2: coinductive_llist @ A] :
% 1.61/1.11 ( ( X4 @ X3 @ Xa2 )
% 1.61/1.11 => ( ? [Xs5: coinductive_llist @ A,Ys2: coinductive_llist @ A,Xb: A] :
% 1.61/1.11 ( ( X3
% 1.61/1.11 = ( coinductive_LCons @ A @ Xb @ Xs5 ) )
% 1.61/1.11 & ( Xa2
% 1.61/1.11 = ( coinductive_LCons @ A @ Xb @ Ys2 ) )
% 1.61/1.11 & ( ( X4 @ Xs5 @ Ys2 )
% 1.61/1.11 | ( coinductive_llexord @ A @ R3 @ Xs5 @ Ys2 ) ) )
% 1.61/1.11 | ? [Xb: A,Y4: A,Xs5: coinductive_llist @ A,Ys2: coinductive_llist @ A] :
% 1.61/1.11 ( ( X3
% 1.61/1.11 = ( coinductive_LCons @ A @ Xb @ Xs5 ) )
% 1.61/1.11 & ( Xa2
% 1.61/1.11 = ( coinductive_LCons @ A @ Y4 @ Ys2 ) )
% 1.61/1.11 & ( R3 @ Xb @ Y4 ) )
% 1.61/1.11 | ? [Ys2: coinductive_llist @ A] :
% 1.61/1.11 ( ( X3
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 & ( Xa2 = Ys2 ) ) ) )
% 1.61/1.11 => ( coinductive_llexord @ A @ R3 @ X @ Xa ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_155_unfold__llist_Ocode,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType] :
% 1.61/1.11 ( ( coindu1441602521_llist @ A @ B )
% 1.61/1.11 = ( ^ [P4: A > $o,G212: A > B,G222: A > A,A4: A] : ( if @ ( coinductive_llist @ B ) @ ( P4 @ A4 ) @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ ( G212 @ A4 ) @ ( coindu1441602521_llist @ A @ B @ P4 @ G212 @ G222 @ ( G222 @ A4 ) ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_156_ltl__unfold__llist,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,IS_LNIL: B > $o,A2: B,LHD: B > A,LTL: B > B] :
% 1.61/1.11 ( ( ( IS_LNIL @ A2 )
% 1.61/1.11 => ( ( coinductive_ltl @ A @ ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 1.61/1.11 = ( coinductive_LNil @ A ) ) )
% 1.61/1.11 & ( ~ ( IS_LNIL @ A2 )
% 1.61/1.11 => ( ( coinductive_ltl @ A @ ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ A2 ) )
% 1.61/1.11 = ( coindu1441602521_llist @ B @ A @ IS_LNIL @ LHD @ LTL @ ( LTL @ A2 ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_157_ltakeWhile_Octr_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 1.61/1.11 ( ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 | ~ ( P @ ( coinductive_lhd @ A @ Xs ) ) )
% 1.61/1.11 => ( ( coindu501562517eWhile @ A @ P @ Xs )
% 1.61/1.11 = ( coinductive_LNil @ A ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_158_ltakeWhile_Osimps_I4_J,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 1.61/1.11 ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( P @ ( coinductive_lhd @ A @ Xs ) )
% 1.61/1.11 => ( ( coinductive_ltl @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) )
% 1.61/1.11 = ( coindu501562517eWhile @ A @ P @ ( coinductive_ltl @ A @ Xs ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_159_ltl__ltakeWhile,axiom,
% 1.61/1.11 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( ( P @ ( coinductive_lhd @ A @ Xs ) )
% 1.61/1.11 => ( ( coinductive_ltl @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) )
% 1.61/1.11 = ( coindu501562517eWhile @ A @ P @ ( coinductive_ltl @ A @ Xs ) ) ) )
% 1.61/1.11 & ( ~ ( P @ ( coinductive_lhd @ A @ Xs ) )
% 1.61/1.11 => ( ( coinductive_ltl @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) )
% 1.61/1.11 = ( coinductive_LNil @ A ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_160_lhd__lzip,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 1.61/1.11 ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ B @ Ys )
% 1.61/1.11 => ( ( coinductive_lhd @ ( product_prod @ A @ B ) @ ( coinductive_lzip @ A @ B @ Xs @ Ys ) )
% 1.61/1.11 = ( product_Pair @ A @ B @ ( coinductive_lhd @ A @ Xs ) @ ( coinductive_lhd @ B @ Ys ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_161_llexord__coinduct,axiom,
% 1.61/1.11 ! [A: $tType,X4: ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,R3: A > A > $o] :
% 1.61/1.11 ( ( X4 @ Xs @ Ys )
% 1.61/1.11 => ( ! [Xs2: coinductive_llist @ A,Ys5: coinductive_llist @ A] :
% 1.61/1.11 ( ( X4 @ Xs2 @ Ys5 )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ Xs2 )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ Ys5 )
% 1.61/1.11 & ( ~ ( coinductive_lnull @ A @ Ys5 )
% 1.61/1.11 => ( ( R3 @ ( coinductive_lhd @ A @ Xs2 ) @ ( coinductive_lhd @ A @ Ys5 ) )
% 1.61/1.11 | ( ( ( coinductive_lhd @ A @ Xs2 )
% 1.61/1.11 = ( coinductive_lhd @ A @ Ys5 ) )
% 1.61/1.11 & ( ( X4 @ ( coinductive_ltl @ A @ Xs2 ) @ ( coinductive_ltl @ A @ Ys5 ) )
% 1.61/1.11 | ( coinductive_llexord @ A @ R3 @ ( coinductive_ltl @ A @ Xs2 ) @ ( coinductive_ltl @ A @ Ys5 ) ) ) ) ) ) ) ) )
% 1.61/1.11 => ( coinductive_llexord @ A @ R3 @ Xs @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_162_ltakeWhile_Octr_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 1.61/1.11 ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( P @ ( coinductive_lhd @ A @ Xs ) )
% 1.61/1.11 => ( ( coindu501562517eWhile @ A @ P @ Xs )
% 1.61/1.11 = ( coinductive_LCons @ A @ ( coinductive_lhd @ A @ Xs ) @ ( coindu501562517eWhile @ A @ P @ ( coinductive_ltl @ A @ Xs ) ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_163_llist_Ocase__eq__if,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType] :
% 1.61/1.11 ( ( coindu1381640503_llist @ B @ A )
% 1.61/1.11 = ( ^ [F12: B,F22: A > ( coinductive_llist @ A ) > B,Llist2: coinductive_llist @ A] : ( if @ B @ ( coinductive_lnull @ A @ Llist2 ) @ F12 @ ( F22 @ ( coinductive_lhd @ A @ Llist2 ) @ ( coinductive_ltl @ A @ Llist2 ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_164_lzip_Octr_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 1.61/1.11 ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ B @ Ys )
% 1.61/1.11 => ( ( coinductive_lzip @ A @ B @ Xs @ Ys )
% 1.61/1.11 = ( coinductive_LCons @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ ( coinductive_lhd @ A @ Xs ) @ ( coinductive_lhd @ B @ Ys ) ) @ ( coinductive_lzip @ A @ B @ ( coinductive_ltl @ A @ Xs ) @ ( coinductive_ltl @ B @ Ys ) ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_165_prod_Oinject,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,X1: A,X23: B,Y1: A,Y23: B] :
% 1.61/1.11 ( ( ( product_Pair @ A @ B @ X1 @ X23 )
% 1.61/1.11 = ( product_Pair @ A @ B @ Y1 @ Y23 ) )
% 1.61/1.11 = ( ( X1 = Y1 )
% 1.61/1.11 & ( X23 = Y23 ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_166_old_Oprod_Oinject,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B4: B] :
% 1.61/1.11 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 1.61/1.11 = ( product_Pair @ A @ B @ A6 @ B4 ) )
% 1.61/1.11 = ( ( A2 = A6 )
% 1.61/1.11 & ( B2 = B4 ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_167_llast__lappend,axiom,
% 1.61/1.11 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( ( coinductive_lnull @ A @ Ys )
% 1.61/1.11 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 1.61/1.11 = ( coinductive_llast @ A @ Xs ) ) )
% 1.61/1.11 & ( ~ ( coinductive_lnull @ A @ Ys )
% 1.61/1.11 => ( ( ( coinductive_lfinite @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 1.61/1.11 = ( coinductive_llast @ A @ Ys ) ) )
% 1.61/1.11 & ( ~ ( coinductive_lfinite @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 1.61/1.11 = ( undefined @ A ) ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_168_ltl__lconcat,axiom,
% 1.61/1.11 ! [A: $tType,Xss: coinductive_llist @ ( coinductive_llist @ A )] :
% 1.61/1.11 ( ~ ( coinductive_lnull @ ( coinductive_llist @ A ) @ Xss )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ ( coinductive_lhd @ ( coinductive_llist @ A ) @ Xss ) )
% 1.61/1.11 => ( ( coinductive_ltl @ A @ ( coinductive_lconcat @ A @ Xss ) )
% 1.61/1.11 = ( coinductive_lappend @ A @ ( coinductive_ltl @ A @ ( coinductive_lhd @ ( coinductive_llist @ A ) @ Xss ) ) @ ( coinductive_lconcat @ A @ ( coinductive_ltl @ ( coinductive_llist @ A ) @ Xss ) ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_169_lconcat__LNil,axiom,
% 1.61/1.11 ! [A: $tType] :
% 1.61/1.11 ( ( coinductive_lconcat @ A @ ( coinductive_LNil @ ( coinductive_llist @ A ) ) )
% 1.61/1.11 = ( coinductive_LNil @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_170_lconcat__LCons,axiom,
% 1.61/1.11 ! [B: $tType,Xs: coinductive_llist @ B,Xss: coinductive_llist @ ( coinductive_llist @ B )] :
% 1.61/1.11 ( ( coinductive_lconcat @ B @ ( coinductive_LCons @ ( coinductive_llist @ B ) @ Xs @ Xss ) )
% 1.61/1.11 = ( coinductive_lappend @ B @ Xs @ ( coinductive_lconcat @ B @ Xss ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_171_lconcat__lappend,axiom,
% 1.61/1.11 ! [A: $tType,Xss: coinductive_llist @ ( coinductive_llist @ A ),Yss: coinductive_llist @ ( coinductive_llist @ A )] :
% 1.61/1.11 ( ( coinductive_lfinite @ ( coinductive_llist @ A ) @ Xss )
% 1.61/1.11 => ( ( coinductive_lconcat @ A @ ( coinductive_lappend @ ( coinductive_llist @ A ) @ Xss @ Yss ) )
% 1.61/1.11 = ( coinductive_lappend @ A @ ( coinductive_lconcat @ A @ Xss ) @ ( coinductive_lconcat @ A @ Yss ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_172_lhd__lconcat,axiom,
% 1.61/1.11 ! [A: $tType,Xss: coinductive_llist @ ( coinductive_llist @ A )] :
% 1.61/1.11 ( ~ ( coinductive_lnull @ ( coinductive_llist @ A ) @ Xss )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ ( coinductive_lhd @ ( coinductive_llist @ A ) @ Xss ) )
% 1.61/1.11 => ( ( coinductive_lhd @ A @ ( coinductive_lconcat @ A @ Xss ) )
% 1.61/1.11 = ( coinductive_lhd @ A @ ( coinductive_lhd @ ( coinductive_llist @ A ) @ Xss ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_173_llast__LNil,axiom,
% 1.61/1.11 ! [A: $tType] :
% 1.61/1.11 ( ( coinductive_llast @ A @ ( coinductive_LNil @ A ) )
% 1.61/1.11 = ( undefined @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_174_llast__linfinite,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ~ ( coinductive_lfinite @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_llast @ A @ Xs )
% 1.61/1.11 = ( undefined @ A ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_175_old_Oprod_Oinducts,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 1.61/1.11 ( ! [A5: A,B3: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B3 ) )
% 1.61/1.11 => ( P @ Prod ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_176_old_Oprod_Oexhaust,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,Y: product_prod @ A @ B] :
% 1.61/1.11 ~ ! [A5: A,B3: B] :
% 1.61/1.11 ( Y
% 1.61/1.11 != ( product_Pair @ A @ B @ A5 @ B3 ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_177_prod__induct7,axiom,
% 1.61/1.11 ! [G2: $tType,F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) ) )] :
% 1.61/1.11 ( ! [A5: A,B3: B,C2: C,D2: D,E2: E,F4: F3,G3: G2] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) ) @ B3 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F3 @ G2 ) @ E2 @ ( product_Pair @ F3 @ G2 @ F4 @ G3 ) ) ) ) ) ) )
% 1.61/1.11 => ( P @ X ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_178_prod__induct6,axiom,
% 1.61/1.11 ! [F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 1.61/1.11 ( ! [A5: A,B3: B,C2: C,D2: D,E2: E,F4: F3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B3 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D2 @ ( product_Pair @ E @ F3 @ E2 @ F4 ) ) ) ) ) )
% 1.61/1.11 => ( P @ X ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_179_prod__induct5,axiom,
% 1.61/1.11 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 1.61/1.11 ( ! [A5: A,B3: B,C2: C,D2: D,E2: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B3 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) )
% 1.61/1.11 => ( P @ X ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_180_prod__induct4,axiom,
% 1.61/1.11 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 1.61/1.11 ( ! [A5: A,B3: B,C2: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B3 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) )
% 1.61/1.11 => ( P @ X ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_181_prod__induct3,axiom,
% 1.61/1.11 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 1.61/1.11 ( ! [A5: A,B3: B,C2: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B3 @ C2 ) ) )
% 1.61/1.11 => ( P @ X ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_182_prod__cases7,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,G2: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) ) )] :
% 1.61/1.11 ~ ! [A5: A,B3: B,C2: C,D2: D,E2: E,F4: F3,G3: G2] :
% 1.61/1.11 ( Y
% 1.61/1.11 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) ) @ B3 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G2 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F3 @ G2 ) @ E2 @ ( product_Pair @ F3 @ G2 @ F4 @ G3 ) ) ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_183_prod__cases6,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 1.61/1.11 ~ ! [A5: A,B3: B,C2: C,D2: D,E2: E,F4: F3] :
% 1.61/1.11 ( Y
% 1.61/1.11 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B3 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C2 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D2 @ ( product_Pair @ E @ F3 @ E2 @ F4 ) ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_184_prod__cases5,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 1.61/1.11 ~ ! [A5: A,B3: B,C2: C,D2: D,E2: E] :
% 1.61/1.11 ( Y
% 1.61/1.11 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B3 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C2 @ ( product_Pair @ D @ E @ D2 @ E2 ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_185_prod__cases4,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 1.61/1.11 ~ ! [A5: A,B3: B,C2: C,D2: D] :
% 1.61/1.11 ( Y
% 1.61/1.11 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A5 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B3 @ ( product_Pair @ C @ D @ C2 @ D2 ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_186_prod__cases3,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,C: $tType,Y: product_prod @ A @ ( product_prod @ B @ C )] :
% 1.61/1.11 ~ ! [A5: A,B3: B,C2: C] :
% 1.61/1.11 ( Y
% 1.61/1.11 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A5 @ ( product_Pair @ B @ C @ B3 @ C2 ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_187_Pair__inject,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,A2: A,B2: B,A6: A,B4: B] :
% 1.61/1.11 ( ( ( product_Pair @ A @ B @ A2 @ B2 )
% 1.61/1.11 = ( product_Pair @ A @ B @ A6 @ B4 ) )
% 1.61/1.11 => ~ ( ( A2 = A6 )
% 1.61/1.11 => ( B2 != B4 ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_188_prod__cases,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 1.61/1.11 ( ! [A5: A,B3: B] : ( P @ ( product_Pair @ A @ B @ A5 @ B3 ) )
% 1.61/1.11 => ( P @ P3 ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_189_surj__pair,axiom,
% 1.61/1.11 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 1.61/1.11 ? [X3: A,Y3: B] :
% 1.61/1.11 ( P3
% 1.61/1.11 = ( product_Pair @ A @ B @ X3 @ Y3 ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_190_old_Oprod_Orec,axiom,
% 1.61/1.11 ! [A: $tType,T: $tType,B: $tType,F1: A > B > T,A2: A,B2: B] :
% 1.61/1.11 ( ( product_rec_prod @ A @ B @ T @ F1 @ ( product_Pair @ A @ B @ A2 @ B2 ) )
% 1.61/1.11 = ( F1 @ A2 @ B2 ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_191_internal__case__prod__conv,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A2: B,B2: C] :
% 1.61/1.11 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A2 @ B2 ) )
% 1.61/1.11 = ( C3 @ A2 @ B2 ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_192_ord_Olsorted__coinduct_H,axiom,
% 1.61/1.11 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A,Less_eq: A > A > $o] :
% 1.61/1.11 ( ( X4 @ Xs )
% 1.61/1.11 => ( ! [Xs2: coinductive_llist @ A] :
% 1.61/1.11 ( ( X4 @ Xs2 )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ Xs2 )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ ( coinductive_ltl @ A @ Xs2 ) )
% 1.61/1.11 => ( ( Less_eq @ ( coinductive_lhd @ A @ Xs2 ) @ ( coinductive_lhd @ A @ ( coinductive_ltl @ A @ Xs2 ) ) )
% 1.61/1.11 & ( ( X4 @ ( coinductive_ltl @ A @ Xs2 ) )
% 1.61/1.11 | ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_ltl @ A @ Xs2 ) ) ) ) ) ) )
% 1.61/1.11 => ( coinductive_lsorted @ A @ Less_eq @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_193_ord_Olsorted__LCons__LCons,axiom,
% 1.61/1.11 ! [A: $tType,Less_eq: A > A > $o,X: A,Y: A,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs ) ) )
% 1.61/1.11 = ( ( Less_eq @ X @ Y )
% 1.61/1.11 & ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ Y @ Xs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_194_ord_OLCons__LCons,axiom,
% 1.61/1.11 ! [A: $tType,Less_eq: A > A > $o,X: A,Y: A,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( Less_eq @ X @ Y )
% 1.61/1.11 => ( ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ Y @ Xs ) )
% 1.61/1.11 => ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y @ Xs ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_195_ord_OLNil,axiom,
% 1.61/1.11 ! [A: $tType,Less_eq: A > A > $o] : ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LNil @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_196_ord_Olsorted__code_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,Less_eq: A > A > $o] : ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LNil @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_197_ord_Olsorted__ltlI,axiom,
% 1.61/1.11 ! [A: $tType,Less_eq: A > A > $o,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lsorted @ A @ Less_eq @ Xs )
% 1.61/1.11 => ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_ltl @ A @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_198_ord_Olsorted__ldropn,axiom,
% 1.61/1.11 ! [A: $tType,Less_eq: A > A > $o,Xs: coinductive_llist @ A,N: nat] :
% 1.61/1.11 ( ( coinductive_lsorted @ A @ Less_eq @ Xs )
% 1.61/1.11 => ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_ldropn @ A @ N @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_199_ord_Olsorted__code_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,Less_eq: A > A > $o,X: A] : ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_200_ord_Olsorted_Ocases,axiom,
% 1.61/1.11 ! [A: $tType,Less_eq: A > A > $o,A2: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lsorted @ A @ Less_eq @ A2 )
% 1.61/1.11 => ( ( A2
% 1.61/1.11 != ( coinductive_LNil @ A ) )
% 1.61/1.11 => ( ! [X3: A] :
% 1.61/1.11 ( A2
% 1.61/1.11 != ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) )
% 1.61/1.11 => ~ ! [X3: A,Y3: A,Xs2: coinductive_llist @ A] :
% 1.61/1.11 ( ( A2
% 1.61/1.11 = ( coinductive_LCons @ A @ X3 @ ( coinductive_LCons @ A @ Y3 @ Xs2 ) ) )
% 1.61/1.11 => ( ( Less_eq @ X3 @ Y3 )
% 1.61/1.11 => ~ ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ Y3 @ Xs2 ) ) ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_201_ord_Olsorted_Osimps,axiom,
% 1.61/1.11 ! [A: $tType] :
% 1.61/1.11 ( ( coinductive_lsorted @ A )
% 1.61/1.11 = ( ^ [Less_eq2: A > A > $o,A4: coinductive_llist @ A] :
% 1.61/1.11 ( ( A4
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 | ? [X2: A] :
% 1.61/1.11 ( A4
% 1.61/1.11 = ( coinductive_LCons @ A @ X2 @ ( coinductive_LNil @ A ) ) )
% 1.61/1.11 | ? [X2: A,Y2: A,Xs3: coinductive_llist @ A] :
% 1.61/1.11 ( ( A4
% 1.61/1.11 = ( coinductive_LCons @ A @ X2 @ ( coinductive_LCons @ A @ Y2 @ Xs3 ) ) )
% 1.61/1.11 & ( Less_eq2 @ X2 @ Y2 )
% 1.61/1.11 & ( coinductive_lsorted @ A @ Less_eq2 @ ( coinductive_LCons @ A @ Y2 @ Xs3 ) ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_202_ord_Olsorted_Ocoinduct,axiom,
% 1.61/1.11 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,Less_eq: A > A > $o] :
% 1.61/1.11 ( ( X4 @ X )
% 1.61/1.11 => ( ! [X3: coinductive_llist @ A] :
% 1.61/1.11 ( ( X4 @ X3 )
% 1.61/1.11 => ( ( X3
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 | ? [Xa3: A] :
% 1.61/1.11 ( X3
% 1.61/1.11 = ( coinductive_LCons @ A @ Xa3 @ ( coinductive_LNil @ A ) ) )
% 1.61/1.11 | ? [Xa3: A,Y4: A,Xs5: coinductive_llist @ A] :
% 1.61/1.11 ( ( X3
% 1.61/1.11 = ( coinductive_LCons @ A @ Xa3 @ ( coinductive_LCons @ A @ Y4 @ Xs5 ) ) )
% 1.61/1.11 & ( Less_eq @ Xa3 @ Y4 )
% 1.61/1.11 & ( ( X4 @ ( coinductive_LCons @ A @ Y4 @ Xs5 ) )
% 1.61/1.11 | ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ Y4 @ Xs5 ) ) ) ) ) )
% 1.61/1.11 => ( coinductive_lsorted @ A @ Less_eq @ X ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_203_ord_OSingleton,axiom,
% 1.61/1.11 ! [A: $tType,Less_eq: A > A > $o,X: A] : ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_204_ord_Olsorted__LCons_H,axiom,
% 1.61/1.11 ! [A: $tType,Less_eq: A > A > $o,X: A,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lsorted @ A @ Less_eq @ ( coinductive_LCons @ A @ X @ Xs ) )
% 1.61/1.11 = ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( Less_eq @ X @ ( coinductive_lhd @ A @ Xs ) )
% 1.61/1.11 & ( coinductive_lsorted @ A @ Less_eq @ Xs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_205_ord_Olsorted__lhdD,axiom,
% 1.61/1.11 ! [A: $tType,Less_eq: A > A > $o,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lsorted @ A @ Less_eq @ Xs )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ ( coinductive_ltl @ A @ Xs ) )
% 1.61/1.11 => ( Less_eq @ ( coinductive_lhd @ A @ Xs ) @ ( coinductive_lhd @ A @ ( coinductive_ltl @ A @ Xs ) ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_206_ssubst__Pair__rhs,axiom,
% 1.61/1.11 ! [B: $tType,A: $tType,R3: A,S: B,R: set @ ( product_prod @ A @ B ),S2: B] :
% 1.61/1.11 ( ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S ) @ R )
% 1.61/1.11 => ( ( S2 = S )
% 1.61/1.11 => ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ R3 @ S2 ) @ R ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_207_lprefix__expand,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ Ys )
% 1.61/1.11 & ( ( coinductive_lhd @ A @ Xs )
% 1.61/1.11 = ( coinductive_lhd @ A @ Ys ) )
% 1.61/1.11 & ( coinductive_lprefix @ A @ ( coinductive_ltl @ A @ Xs ) @ ( coinductive_ltl @ A @ Ys ) ) ) )
% 1.61/1.11 => ( coinductive_lprefix @ A @ Xs @ Ys ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_208_lprefix__refl,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A] : ( coinductive_lprefix @ A @ Xs @ Xs ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_209_llist_Oleq__refl,axiom,
% 1.61/1.11 ! [A: $tType,X: coinductive_llist @ A] : ( coinductive_lprefix @ A @ X @ X ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_210_LCons__lprefix__LCons,axiom,
% 1.61/1.11 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 1.61/1.11 = ( ( X = Y )
% 1.61/1.11 & ( coinductive_lprefix @ A @ Xs @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_211_lprefix__code_I1_J,axiom,
% 1.61/1.11 ! [A: $tType,Ys: coinductive_llist @ A] : ( coinductive_lprefix @ A @ ( coinductive_LNil @ A ) @ Ys ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_212_lprefix__LNil,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 1.61/1.11 = ( coinductive_lnull @ A @ Xs ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_213_lprefix__lappend__same,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( coinductive_lappend @ A @ Xs @ Zs ) )
% 1.61/1.11 = ( ( coinductive_lfinite @ A @ Xs )
% 1.61/1.11 => ( coinductive_lprefix @ A @ Ys @ Zs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_214_ord_Olsorted__lprefixD,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Less_eq: A > A > $o] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 1.61/1.11 => ( ( coinductive_lsorted @ A @ Less_eq @ Ys )
% 1.61/1.11 => ( coinductive_lsorted @ A @ Less_eq @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_215_lprefix__lappend,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] : ( coinductive_lprefix @ A @ Xs @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_216_lappend__lprefixE,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 1.61/1.11 => ~ ! [Zs3: coinductive_llist @ A] :
% 1.61/1.11 ( Zs
% 1.61/1.11 != ( coinductive_lappend @ A @ Xs @ Zs3 ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_217_lprefix__lappendD,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) )
% 1.61/1.11 => ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 1.61/1.11 | ( coinductive_lprefix @ A @ Ys @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_218_lprefix__conv__lappend,axiom,
% 1.61/1.11 ! [A: $tType] :
% 1.61/1.11 ( ( coinductive_lprefix @ A )
% 1.61/1.11 = ( ^ [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A] :
% 1.61/1.11 ? [Zs2: coinductive_llist @ A] :
% 1.61/1.11 ( Ys3
% 1.61/1.11 = ( coinductive_lappend @ A @ Xs3 @ Zs2 ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_219_lprefix__lappend__sameI,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 1.61/1.11 => ( coinductive_lprefix @ A @ ( coinductive_lappend @ A @ Zs @ Xs ) @ ( coinductive_lappend @ A @ Zs @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_220_lprefix__lfiniteD,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 1.61/1.11 => ( ( coinductive_lfinite @ A @ Ys )
% 1.61/1.11 => ( coinductive_lfinite @ A @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_221_not__lfinite__lprefix__conv__eq,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ~ ( coinductive_lfinite @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 1.61/1.11 = ( Xs = Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_222_LNil__lprefix,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A] : ( coinductive_lprefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_223_LCons__lprefix__conv,axiom,
% 1.61/1.11 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ ( coinductive_LCons @ A @ X @ Xs ) @ Ys )
% 1.61/1.11 = ( ? [Ys4: coinductive_llist @ A] :
% 1.61/1.11 ( ( Ys
% 1.61/1.11 = ( coinductive_LCons @ A @ X @ Ys4 ) )
% 1.61/1.11 & ( coinductive_lprefix @ A @ Xs @ Ys4 ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_224_Le__LCons,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,X: A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 1.61/1.11 => ( coinductive_lprefix @ A @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ X @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_225_lprefixI,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,X4: set @ ( product_prod @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) )] :
% 1.61/1.11 ( ( member @ ( product_prod @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) ) @ ( product_Pair @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) @ Xs @ Ys ) @ X4 )
% 1.61/1.11 => ( ! [Xs2: coinductive_llist @ A,Ys5: coinductive_llist @ A] :
% 1.61/1.11 ( ( member @ ( product_prod @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) ) @ ( product_Pair @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) @ Xs2 @ Ys5 ) @ X4 )
% 1.61/1.11 => ( ( coinductive_lnull @ A @ Xs2 )
% 1.61/1.11 | ? [X5: A,Xs6: coinductive_llist @ A,Ys6: coinductive_llist @ A] :
% 1.61/1.11 ( ( Xs2
% 1.61/1.11 = ( coinductive_LCons @ A @ X5 @ Xs6 ) )
% 1.61/1.11 & ( Ys5
% 1.61/1.11 = ( coinductive_LCons @ A @ X5 @ Ys6 ) )
% 1.61/1.11 & ( ( member @ ( product_prod @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) ) @ ( product_Pair @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) @ Xs6 @ Ys6 ) @ X4 )
% 1.61/1.11 | ( coinductive_lprefix @ A @ Xs6 @ Ys6 ) ) ) ) )
% 1.61/1.11 => ( coinductive_lprefix @ A @ Xs @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_226_lprefix__code_I2_J,axiom,
% 1.61/1.11 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 1.61/1.11 ~ ( coinductive_lprefix @ A @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LNil @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_227_lprefix_Ocases,axiom,
% 1.61/1.11 ! [A: $tType,A1: coinductive_llist @ A,A22: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ A1 @ A22 )
% 1.61/1.11 => ( ( ( A1
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 => ! [Xs2: coinductive_llist @ A] : ( A22 != Xs2 ) )
% 1.61/1.11 => ~ ! [Xs2: coinductive_llist @ A,Ys5: coinductive_llist @ A,X3: A] :
% 1.61/1.11 ( ( A1
% 1.61/1.11 = ( coinductive_LCons @ A @ X3 @ Xs2 ) )
% 1.61/1.11 => ( ( A22
% 1.61/1.11 = ( coinductive_LCons @ A @ X3 @ Ys5 ) )
% 1.61/1.11 => ~ ( coinductive_lprefix @ A @ Xs2 @ Ys5 ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_228_lprefix_Osimps,axiom,
% 1.61/1.11 ! [A: $tType] :
% 1.61/1.11 ( ( coinductive_lprefix @ A )
% 1.61/1.11 = ( ^ [A12: coinductive_llist @ A,A23: coinductive_llist @ A] :
% 1.61/1.11 ( ? [Xs3: coinductive_llist @ A] :
% 1.61/1.11 ( ( A12
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 & ( A23 = Xs3 ) )
% 1.61/1.11 | ? [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A,X2: A] :
% 1.61/1.11 ( ( A12
% 1.61/1.11 = ( coinductive_LCons @ A @ X2 @ Xs3 ) )
% 1.61/1.11 & ( A23
% 1.61/1.11 = ( coinductive_LCons @ A @ X2 @ Ys3 ) )
% 1.61/1.11 & ( coinductive_lprefix @ A @ Xs3 @ Ys3 ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_229_lprefix_Ocoinduct,axiom,
% 1.61/1.11 ! [A: $tType,X4: ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,Xa: coinductive_llist @ A] :
% 1.61/1.11 ( ( X4 @ X @ Xa )
% 1.61/1.11 => ( ! [X3: coinductive_llist @ A,Xa2: coinductive_llist @ A] :
% 1.61/1.11 ( ( X4 @ X3 @ Xa2 )
% 1.61/1.11 => ( ? [Xs5: coinductive_llist @ A] :
% 1.61/1.11 ( ( X3
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 & ( Xa2 = Xs5 ) )
% 1.61/1.11 | ? [Xs5: coinductive_llist @ A,Ys2: coinductive_llist @ A,Xb: A] :
% 1.61/1.11 ( ( X3
% 1.61/1.11 = ( coinductive_LCons @ A @ Xb @ Xs5 ) )
% 1.61/1.11 & ( Xa2
% 1.61/1.11 = ( coinductive_LCons @ A @ Xb @ Ys2 ) )
% 1.61/1.11 & ( ( X4 @ Xs5 @ Ys2 )
% 1.61/1.11 | ( coinductive_lprefix @ A @ Xs5 @ Ys2 ) ) ) ) )
% 1.61/1.11 => ( coinductive_lprefix @ A @ X @ Xa ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_230_lprefix__LCons__conv,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 1.61/1.11 = ( ( Xs
% 1.61/1.11 = ( coinductive_LNil @ A ) )
% 1.61/1.11 | ? [Xs4: coinductive_llist @ A] :
% 1.61/1.11 ( ( Xs
% 1.61/1.11 = ( coinductive_LCons @ A @ Y @ Xs4 ) )
% 1.61/1.11 & ( coinductive_lprefix @ A @ Xs4 @ Ys ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_231_lprefix__lhdD,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( ( coinductive_lhd @ A @ Xs )
% 1.61/1.11 = ( coinductive_lhd @ A @ Ys ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_232_lprefix__imp__llexord,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,R3: A > A > $o] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 1.61/1.11 => ( coinductive_llexord @ A @ R3 @ Xs @ Ys ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_233_lprefix__ltakeWhile,axiom,
% 1.61/1.11 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] : ( coinductive_lprefix @ A @ ( coindu501562517eWhile @ A @ P @ Xs ) @ Xs ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_234_lprefix__trans,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 1.61/1.11 => ( ( coinductive_lprefix @ A @ Ys @ Zs )
% 1.61/1.11 => ( coinductive_lprefix @ A @ Xs @ Zs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_235_llist_Oleq__trans,axiom,
% 1.61/1.11 ! [A: $tType,X: coinductive_llist @ A,Y: coinductive_llist @ A,Z: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ X @ Y )
% 1.61/1.11 => ( ( coinductive_lprefix @ A @ Y @ Z )
% 1.61/1.11 => ( coinductive_lprefix @ A @ X @ Z ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_236_lprefix__antisym,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 1.61/1.11 => ( ( coinductive_lprefix @ A @ Ys @ Xs )
% 1.61/1.11 => ( Xs = Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_237_llist_Oleq__antisym,axiom,
% 1.61/1.11 ! [A: $tType,X: coinductive_llist @ A,Y: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ X @ Y )
% 1.61/1.11 => ( ( coinductive_lprefix @ A @ Y @ X )
% 1.61/1.11 => ( X = Y ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_238_lprefix__down__linear,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Zs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ Xs @ Zs )
% 1.61/1.11 => ( ( coinductive_lprefix @ A @ Ys @ Zs )
% 1.61/1.11 => ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 1.61/1.11 | ( coinductive_lprefix @ A @ Ys @ Xs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_239_Coinductive__List_Ofinite__lprefix__def,axiom,
% 1.61/1.11 ! [A: $tType] :
% 1.61/1.11 ( ( coindu328551480prefix @ A )
% 1.61/1.11 = ( coinductive_lprefix @ A ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_240_lstrict__prefix__def,axiom,
% 1.61/1.11 ! [A: $tType] :
% 1.61/1.11 ( ( coindu1478340336prefix @ A )
% 1.61/1.11 = ( ^ [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ Xs3 @ Ys3 )
% 1.61/1.11 & ( Xs3 != Ys3 ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_241_lprefix__lconcatI,axiom,
% 1.61/1.11 ! [A: $tType,Xss: coinductive_llist @ ( coinductive_llist @ A ),Yss: coinductive_llist @ ( coinductive_llist @ A )] :
% 1.61/1.11 ( ( coinductive_lprefix @ ( coinductive_llist @ A ) @ Xss @ Yss )
% 1.61/1.11 => ( coinductive_lprefix @ A @ ( coinductive_lconcat @ A @ Xss ) @ ( coinductive_lconcat @ A @ Yss ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_242_lprefix__ltlI,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 1.61/1.11 => ( coinductive_lprefix @ A @ ( coinductive_ltl @ A @ Xs ) @ ( coinductive_ltl @ A @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_243_lprefix__not__lnullD,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_244_lprefix__lnullD,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 1.61/1.11 => ( ( coinductive_lnull @ A @ Ys )
% 1.61/1.11 => ( coinductive_lnull @ A @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_245_lprefix__lnull,axiom,
% 1.61/1.11 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ Ys )
% 1.61/1.11 => ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 1.61/1.11 = ( coinductive_lnull @ A @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_246_lnull__lprefix,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lnull @ A @ Xs )
% 1.61/1.11 => ( coinductive_lprefix @ A @ Xs @ Ys ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_247_Coinductive__List_Olprefix__nitpick__simps,axiom,
% 1.61/1.11 ! [A: $tType] :
% 1.61/1.11 ( ( coinductive_lprefix @ A )
% 1.61/1.11 = ( ^ [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A] :
% 1.61/1.11 ( ( ( coinductive_lfinite @ A @ Xs3 )
% 1.61/1.11 => ( coindu328551480prefix @ A @ Xs3 @ Ys3 ) )
% 1.61/1.11 & ( ~ ( coinductive_lfinite @ A @ Xs3 )
% 1.61/1.11 => ( Xs3 = Ys3 ) ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_248_lprefix__coinduct,axiom,
% 1.61/1.11 ! [A: $tType,P: ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 1.61/1.11 ( ( P @ Xs @ Ys )
% 1.61/1.11 => ( ! [Xs2: coinductive_llist @ A,Ys5: coinductive_llist @ A] :
% 1.61/1.11 ( ( P @ Xs2 @ Ys5 )
% 1.61/1.11 => ( ( ( coinductive_lnull @ A @ Ys5 )
% 1.61/1.11 => ( coinductive_lnull @ A @ Xs2 ) )
% 1.61/1.11 & ( ~ ( coinductive_lnull @ A @ Xs2 )
% 1.61/1.11 => ( ~ ( coinductive_lnull @ A @ Ys5 )
% 1.61/1.11 => ( ( ( coinductive_lhd @ A @ Xs2 )
% 1.61/1.11 = ( coinductive_lhd @ A @ Ys5 ) )
% 1.61/1.11 & ( ( P @ ( coinductive_ltl @ A @ Xs2 ) @ ( coinductive_ltl @ A @ Ys5 ) )
% 1.61/1.11 | ( coinductive_lprefix @ A @ ( coinductive_ltl @ A @ Xs2 ) @ ( coinductive_ltl @ A @ Ys5 ) ) ) ) ) ) ) )
% 1.61/1.11 => ( coinductive_lprefix @ A @ Xs @ Ys ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_249_llexord__lappend__left,axiom,
% 1.61/1.11 ! [A: $tType,Xs: coinductive_llist @ A,R3: A > A > $o,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_lfinite @ A @ Xs )
% 1.61/1.11 => ( ! [X3: A] :
% 1.61/1.11 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 1.61/1.11 => ~ ( R3 @ X3 @ X3 ) )
% 1.61/1.11 => ( ( coinductive_llexord @ A @ R3 @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( coinductive_lappend @ A @ Xs @ Zs ) )
% 1.61/1.11 = ( coinductive_llexord @ A @ R3 @ Ys @ Zs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_250_llexord__lappend__leftD,axiom,
% 1.61/1.11 ! [A: $tType,R3: A > A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 1.61/1.11 ( ( coinductive_llexord @ A @ R3 @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( coinductive_lappend @ A @ Xs @ Zs ) )
% 1.61/1.11 => ( ( coinductive_lfinite @ A @ Xs )
% 1.61/1.11 => ( ! [X3: A] :
% 1.61/1.11 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 1.61/1.11 => ~ ( R3 @ X3 @ X3 ) )
% 1.61/1.11 => ( coinductive_llexord @ A @ R3 @ Ys @ Zs ) ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_251_in__lset__ltlD,axiom,
% 1.61/1.11 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_ltl @ A @ Xs ) ) )
% 1.61/1.11 => ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_252_lset__lmember,axiom,
% 1.61/1.11 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 1.61/1.11 = ( coinductive_lmember @ A @ X @ Xs ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(fact_253_in__lset__ldropnD,axiom,
% 1.61/1.11 ! [A: $tType,X: A,N: nat,Xs: coinductive_llist @ A] :
% 1.61/1.11 ( ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_ldropn @ A @ N @ Xs ) ) )
% 1.61/1.11 => ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(help_If_3_1_T,axiom,
% 1.61/1.11 ! [P: $o] :
% 1.61/1.11 ( ( P = $true )
% 1.61/1.11 | ( P = $false ) ) ).
% 1.61/1.11
% 1.61/1.11 thf(help_If_2_1_T,axiom,
% 1.61/1.11 ! [A: $tType,X: A,Y: A] :
% 1.61/1.11 ( ( if @ A @ $false @ X @ Y )
% 1.61/1.11 = Y ) ).
% 1.61/1.11
% 1.61/1.11 thf(help_If_1_1_T,axiom,
% 1.61/1.11 ! [A: $tType,X: A,Y: A] :
% 1.61/1.11 ( ( if @ A @ $true @ X @ Y )
% 1.61/1.11 = X ) ).
% 1.61/1.11
% 1.61/1.11 thf(conj_0,conjecture,
% 1.61/1.11 ( ( coinductive_lfinite @ a @ xsa )
% 1.61/1.11 & ( coinductive_lfinite @ a @ acca ) ) ).
% 1.61/1.11 ------------------------
% 1.82/1.13 % (26966)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_26636 for (2999ds/4Mi)
% 1.82/1.13 % (26965)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/183Mi)
% 1.82/1.13 % (26967)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_26636 for (2999ds/27Mi)
% 1.82/1.13 % (26968)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/2Mi)
% 1.82/1.13 % (26969)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_26636 for (2999ds/2Mi)
% 1.82/1.13 % (26970)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_26636 for (2999ds/275Mi)
% 1.82/1.13 % (26971)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/18Mi)
% 1.82/1.13 % (26969)Instruction limit reached!
% 1.82/1.13 % (26969)------------------------------
% 1.82/1.13 % (26969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.13 % (26969)Termination reason: Unknown
% 1.82/1.13 % (26969)Termination phase: shuffling
% 1.82/1.13
% 1.82/1.13 % (26969)Memory used [KB]: 1279
% 1.82/1.13 % (26969)Time elapsed: 0.002 s
% 1.82/1.13 % (26969)Instructions burned: 2 (million)
% 1.82/1.13 % (26969)------------------------------
% 1.82/1.13 % (26969)------------------------------
% 1.82/1.13 % (26966)Instruction limit reached!
% 1.82/1.13 % (26966)------------------------------
% 1.82/1.13 % (26966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.13 % (26966)Termination reason: Unknown
% 1.82/1.13 % (26966)Termination phase: shuffling
% 1.82/1.13
% 1.82/1.13 % (26966)Memory used [KB]: 1407
% 1.82/1.13 % (26966)Time elapsed: 0.003 s
% 1.82/1.13 % (26966)Instructions burned: 5 (million)
% 1.82/1.13 % (26966)------------------------------
% 1.82/1.13 % (26966)------------------------------
% 1.82/1.13 % (26968)Instruction limit reached!
% 1.82/1.13 % (26968)------------------------------
% 1.82/1.13 % (26968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.13 % (26968)Termination reason: Unknown
% 1.82/1.13 % (26968)Termination phase: shuffling
% 1.82/1.13
% 1.82/1.13 % (26968)Memory used [KB]: 1407
% 1.82/1.13 % (26968)Time elapsed: 0.003 s
% 1.82/1.13 % (26968)Instructions burned: 4 (million)
% 1.82/1.13 % (26968)------------------------------
% 1.82/1.13 % (26968)------------------------------
% 1.82/1.14 % (26971)Instruction limit reached!
% 1.82/1.14 % (26971)------------------------------
% 1.82/1.14 % (26971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.14 % (26971)Termination reason: Unknown
% 1.82/1.14 % (26971)Termination phase: shuffling
% 1.82/1.14
% 1.82/1.14 % (26971)Memory used [KB]: 1663
% 1.82/1.14 % (26971)Time elapsed: 0.008 s
% 1.82/1.14 % (26971)Instructions burned: 20 (million)
% 1.82/1.14 % (26971)------------------------------
% 1.82/1.14 % (26971)------------------------------
% 1.82/1.14 % (26967)Instruction limit reached!
% 1.82/1.14 % (26967)------------------------------
% 1.82/1.14 % (26967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.14 % (26967)Termination reason: Unknown
% 1.82/1.14 % (26967)Termination phase: Property scanning
% 1.82/1.14
% 1.82/1.14 % (26967)Memory used [KB]: 1918
% 1.82/1.14 % (26967)Time elapsed: 0.011 s
% 1.82/1.14 % (26967)Instructions burned: 30 (million)
% 1.82/1.14 % (26967)------------------------------
% 1.82/1.14 % (26967)------------------------------
% 1.82/1.14 % (26972)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/3Mi)
% 1.82/1.14 % (26973)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_26636 for (2999ds/37Mi)
% 1.82/1.14 % (26974)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_26636 for (2999ds/15Mi)
% 1.82/1.14 % (26972)Instruction limit reached!
% 1.82/1.14 % (26972)------------------------------
% 1.82/1.14 % (26972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.14 % (26972)Termination reason: Unknown
% 1.82/1.14 % (26972)Termination phase: shuffling
% 1.82/1.14
% 1.82/1.14 % (26972)Memory used [KB]: 1407
% 1.82/1.14 % (26972)Time elapsed: 0.002 s
% 1.82/1.14 % (26972)Instructions burned: 3 (million)
% 1.82/1.14 % (26972)------------------------------
% 1.82/1.14 % (26972)------------------------------
% 1.82/1.14 % (26974)Instruction limit reached!
% 1.82/1.14 % (26974)------------------------------
% 1.82/1.14 % (26974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.14 % (26974)Termination reason: Unknown
% 1.82/1.14 % (26974)Termination phase: shuffling
% 1.82/1.14
% 1.82/1.14 % (26974)Memory used [KB]: 1663
% 1.82/1.14 % (26974)Time elapsed: 0.006 s
% 1.82/1.14 % (26974)Instructions burned: 15 (million)
% 1.82/1.14 % (26974)------------------------------
% 1.82/1.14 % (26974)------------------------------
% 1.82/1.14 % (26975)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_26636 for (2999ds/3Mi)
% 1.82/1.15 % (26975)Instruction limit reached!
% 1.82/1.15 % (26975)------------------------------
% 1.82/1.15 % (26975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.15 % (26975)Termination reason: Unknown
% 1.82/1.15 % (26975)Termination phase: shuffling
% 1.82/1.15
% 1.82/1.15 % (26975)Memory used [KB]: 1407
% 1.82/1.15 % (26975)Time elapsed: 0.002 s
% 1.82/1.15 % (26975)Instructions burned: 3 (million)
% 1.82/1.15 % (26975)------------------------------
% 1.82/1.15 % (26975)------------------------------
% 1.82/1.15 % (26976)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_26636 for (2999ds/1041Mi)
% 1.82/1.15 % (26977)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/7Mi)
% 1.82/1.15 % (26973)Instruction limit reached!
% 1.82/1.15 % (26973)------------------------------
% 1.82/1.15 % (26973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.15 % (26973)Termination reason: Unknown
% 1.82/1.15 % (26973)Termination phase: shuffling
% 1.82/1.15
% 1.82/1.15 % (26973)Memory used [KB]: 2174
% 1.82/1.15 % (26973)Time elapsed: 0.012 s
% 1.82/1.15 % (26973)Instructions burned: 40 (million)
% 1.82/1.15 % (26973)------------------------------
% 1.82/1.15 % (26973)------------------------------
% 1.82/1.15 % (26970)Refutation not found, incomplete strategy
% 1.82/1.15 % (26970)------------------------------
% 1.82/1.15 % (26970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.15 % (26970)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.15
% 1.82/1.15
% 1.82/1.15 % (26970)Memory used [KB]: 6652
% 1.82/1.15 % (26970)Time elapsed: 0.023 s
% 1.82/1.15 % (26970)Instructions burned: 71 (million)
% 1.82/1.15 % (26970)------------------------------
% 1.82/1.15 % (26970)------------------------------
% 1.82/1.15 % (26977)Instruction limit reached!
% 1.82/1.15 % (26977)------------------------------
% 1.82/1.15 % (26977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.15 % (26977)Termination reason: Unknown
% 1.82/1.15 % (26977)Termination phase: shuffling
% 1.82/1.15
% 1.82/1.15 % (26977)Memory used [KB]: 1535
% 1.82/1.15 % (26977)Time elapsed: 0.004 s
% 1.82/1.15 % (26977)Instructions burned: 9 (million)
% 1.82/1.15 % (26977)------------------------------
% 1.82/1.15 % (26977)------------------------------
% 1.82/1.15 % (26978)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/16Mi)
% 1.82/1.15 % (26979)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_26636 for (2999ds/3Mi)
% 1.82/1.16 % (26979)Instruction limit reached!
% 1.82/1.16 % (26979)------------------------------
% 1.82/1.16 % (26979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.16 % (26979)Termination reason: Unknown
% 1.82/1.16 % (26979)Termination phase: shuffling
% 1.82/1.16
% 1.82/1.16 % (26979)Memory used [KB]: 1407
% 1.82/1.16 % (26979)Time elapsed: 0.002 s
% 1.82/1.16 % (26979)Instructions burned: 3 (million)
% 1.82/1.16 % (26979)------------------------------
% 1.82/1.16 % (26979)------------------------------
% 1.82/1.16 % (26978)Instruction limit reached!
% 1.82/1.16 % (26978)------------------------------
% 1.82/1.16 % (26978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.16 % (26978)Termination reason: Unknown
% 1.82/1.16 % (26978)Termination phase: shuffling
% 1.82/1.16
% 1.82/1.16 % (26978)Memory used [KB]: 1663
% 1.82/1.16 % (26978)Time elapsed: 0.007 s
% 1.82/1.16 % (26978)Instructions burned: 18 (million)
% 1.82/1.16 % (26978)------------------------------
% 1.82/1.16 % (26978)------------------------------
% 1.82/1.16 % (26980)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_26636 for (2999ds/3Mi)
% 1.82/1.16 % (26981)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/7Mi)
% 1.82/1.16 % (26982)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/3Mi)
% 1.82/1.16 % (26980)Instruction limit reached!
% 1.82/1.16 % (26980)------------------------------
% 1.82/1.16 % (26980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.16 % (26980)Termination reason: Unknown
% 1.82/1.16 % (26980)Termination phase: shuffling
% 1.82/1.16
% 1.82/1.16 % (26980)Memory used [KB]: 1407
% 1.82/1.16 % (26980)Time elapsed: 0.003 s
% 1.82/1.16 % (26980)Instructions burned: 6 (million)
% 1.82/1.16 % (26980)------------------------------
% 1.82/1.16 % (26980)------------------------------
% 1.82/1.16 % (26982)Instruction limit reached!
% 1.82/1.16 % (26982)------------------------------
% 1.82/1.16 % (26982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.16 % (26982)Termination reason: Unknown
% 1.82/1.16 % (26982)Termination phase: shuffling
% 1.82/1.16
% 1.82/1.16 % (26982)Memory used [KB]: 1407
% 1.82/1.16 % (26982)Time elapsed: 0.002 s
% 1.82/1.16 % (26982)Instructions burned: 3 (million)
% 1.82/1.16 % (26982)------------------------------
% 1.82/1.16 % (26982)------------------------------
% 1.82/1.16 % (26981)Instruction limit reached!
% 1.82/1.16 % (26981)------------------------------
% 1.82/1.16 % (26981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.16 % (26981)Termination reason: Unknown
% 1.82/1.16 % (26981)Termination phase: shuffling
% 1.82/1.16
% 1.82/1.16 % (26981)Memory used [KB]: 1535
% 1.82/1.16 % (26981)Time elapsed: 0.004 s
% 1.82/1.16 % (26981)Instructions burned: 8 (million)
% 1.82/1.16 % (26981)------------------------------
% 1.82/1.16 % (26981)------------------------------
% 1.82/1.17 % (26983)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/4Mi)
% 1.82/1.17 % (26983)Instruction limit reached!
% 1.82/1.17 % (26983)------------------------------
% 1.82/1.17 % (26983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.17 % (26983)Termination reason: Unknown
% 1.82/1.17 % (26983)Termination phase: shuffling
% 1.82/1.17
% 1.82/1.17 % (26983)Memory used [KB]: 1407
% 1.82/1.17 % (26983)Time elapsed: 0.003 s
% 1.82/1.17 % (26983)Instructions burned: 6 (million)
% 1.82/1.17 % (26983)------------------------------
% 1.82/1.17 % (26983)------------------------------
% 1.82/1.17 % (26984)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/18Mi)
% 1.82/1.17 % (26985)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/710Mi)
% 1.82/1.17 % (26986)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/6Mi)
% 1.82/1.17 % (26987)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_26636 for (2999ds/902Mi)
% 1.82/1.17 % (26986)Instruction limit reached!
% 1.82/1.17 % (26986)------------------------------
% 1.82/1.17 % (26986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.17 % (26986)Termination reason: Unknown
% 1.82/1.17 % (26986)Termination phase: shuffling
% 1.82/1.17
% 1.82/1.17 % (26986)Memory used [KB]: 1407
% 1.82/1.17 % (26986)Time elapsed: 0.003 s
% 1.82/1.17 % (26986)Instructions burned: 6 (million)
% 1.82/1.17 % (26986)------------------------------
% 1.82/1.17 % (26986)------------------------------
% 1.82/1.17 % (26984)Instruction limit reached!
% 1.82/1.17 % (26984)------------------------------
% 1.82/1.17 % (26984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.17 % (26984)Termination reason: Unknown
% 1.82/1.17 % (26984)Termination phase: shuffling
% 1.82/1.17
% 1.82/1.17 % (26984)Memory used [KB]: 1663
% 1.82/1.17 % (26984)Time elapsed: 0.007 s
% 1.82/1.17 % (26984)Instructions burned: 18 (million)
% 1.82/1.17 % (26984)------------------------------
% 1.82/1.17 % (26984)------------------------------
% 1.82/1.18 % (26988)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_26636 for (2999ds/21Mi)
% 1.82/1.18 % (26965)Instruction limit reached!
% 1.82/1.18 % (26965)------------------------------
% 1.82/1.18 % (26965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.18 % (26965)Termination reason: Unknown
% 1.82/1.18 % (26965)Termination phase: Saturation
% 1.82/1.18
% 1.82/1.18 % (26965)Memory used [KB]: 7164
% 1.82/1.18 % (26965)Time elapsed: 0.053 s
% 1.82/1.18 % (26965)Instructions burned: 185 (million)
% 1.82/1.18 % (26965)------------------------------
% 1.82/1.18 % (26965)------------------------------
% 1.82/1.18 % (26989)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/5Mi)
% 1.82/1.18 % (26988)Instruction limit reached!
% 1.82/1.18 % (26988)------------------------------
% 1.82/1.18 % (26988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.18 % (26988)Termination reason: Unknown
% 1.82/1.18 % (26988)Termination phase: shuffling
% 1.82/1.18
% 1.82/1.18 % (26988)Memory used [KB]: 1791
% 1.82/1.18 % (26988)Time elapsed: 0.009 s
% 1.82/1.18 % (26988)Instructions burned: 24 (million)
% 1.82/1.18 % (26988)------------------------------
% 1.82/1.18 % (26988)------------------------------
% 1.82/1.18 % (26990)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_26636 for (2999ds/6Mi)
% 1.82/1.18 % (26989)Instruction limit reached!
% 1.82/1.18 % (26989)------------------------------
% 1.82/1.18 % (26989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.18 % (26989)Termination reason: Unknown
% 1.82/1.18 % (26989)Termination phase: shuffling
% 1.82/1.18
% 1.82/1.18 % (26989)Memory used [KB]: 1407
% 1.82/1.18 % (26989)Time elapsed: 0.003 s
% 1.82/1.18 % (26989)Instructions burned: 7 (million)
% 1.82/1.18 % (26989)------------------------------
% 1.82/1.18 % (26989)------------------------------
% 1.82/1.19 % (26990)Instruction limit reached!
% 1.82/1.19 % (26990)------------------------------
% 1.82/1.19 % (26990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.19 % (26990)Termination reason: Unknown
% 1.82/1.19 % (26990)Termination phase: shuffling
% 1.82/1.19
% 1.82/1.19 % (26990)Memory used [KB]: 1407
% 1.82/1.19 % (26990)Time elapsed: 0.003 s
% 1.82/1.19 % (26990)Instructions burned: 6 (million)
% 1.82/1.19 % (26990)------------------------------
% 1.82/1.19 % (26990)------------------------------
% 1.82/1.19 % (26991)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/377Mi)
% 1.82/1.19 % (26992)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_26636 for (2999ds/779Mi)
% 1.82/1.19 % (26993)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_26636 for (2999ds/19Mi)
% 1.82/1.20 % (26994)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/879Mi)
% 1.82/1.20 % (26993)Instruction limit reached!
% 1.82/1.20 % (26993)------------------------------
% 1.82/1.20 % (26993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.20 % (26993)Termination reason: Unknown
% 1.82/1.20 % (26993)Termination phase: shuffling
% 1.82/1.20
% 1.82/1.20 % (26993)Memory used [KB]: 1791
% 1.82/1.20 % (26993)Time elapsed: 0.007 s
% 1.82/1.20 % (26993)Instructions burned: 22 (million)
% 1.82/1.20 % (26993)------------------------------
% 1.82/1.20 % (26993)------------------------------
% 1.82/1.21 % (26995)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/17Mi)
% 1.82/1.22 % (26987)Refutation not found, incomplete strategy
% 1.82/1.22 % (26987)------------------------------
% 1.82/1.22 % (26987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.22 % (26987)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.22
% 1.82/1.22
% 1.82/1.22 % (26987)Memory used [KB]: 7419
% 1.82/1.22 % (26987)Time elapsed: 0.043 s
% 1.82/1.22 % (26987)Instructions burned: 140 (million)
% 1.82/1.22 % (26987)------------------------------
% 1.82/1.22 % (26987)------------------------------
% 1.82/1.22 % (26995)Instruction limit reached!
% 1.82/1.22 % (26995)------------------------------
% 1.82/1.22 % (26995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.22 % (26995)Termination reason: Unknown
% 1.82/1.22 % (26995)Termination phase: shuffling
% 1.82/1.22
% 1.82/1.22 % (26995)Memory used [KB]: 1663
% 1.82/1.22 % (26995)Time elapsed: 0.007 s
% 1.82/1.22 % (26995)Instructions burned: 17 (million)
% 1.82/1.22 % (26995)------------------------------
% 1.82/1.22 % (26995)------------------------------
% 1.82/1.22 % (26996)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/3Mi)
% 1.82/1.23 % (26997)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_26636 for (2999ds/30Mi)
% 1.82/1.23 % (26996)Instruction limit reached!
% 1.82/1.23 % (26996)------------------------------
% 1.82/1.23 % (26996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.23 % (26996)Termination reason: Unknown
% 1.82/1.23 % (26996)Termination phase: shuffling
% 1.82/1.23
% 1.82/1.23 % (26996)Memory used [KB]: 1407
% 1.82/1.23 % (26996)Time elapsed: 0.003 s
% 1.82/1.23 % (26996)Instructions burned: 5 (million)
% 1.82/1.23 % (26996)------------------------------
% 1.82/1.23 % (26996)------------------------------
% 1.82/1.24 % (26998)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_26636 for (2998ds/127Mi)
% 1.82/1.24 % (26997)Instruction limit reached!
% 1.82/1.24 % (26997)------------------------------
% 1.82/1.24 % (26997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.24 % (26997)Termination reason: Unknown
% 1.82/1.24 % (26997)Termination phase: Property scanning
% 1.82/1.24
% 1.82/1.24 % (26997)Memory used [KB]: 1918
% 1.82/1.24 % (26997)Time elapsed: 0.012 s
% 1.82/1.24 % (26997)Instructions burned: 34 (million)
% 1.82/1.24 % (26997)------------------------------
% 1.82/1.24 % (26997)------------------------------
% 1.82/1.25 % (26999)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_26636 for (2998ds/100Mi)
% 1.82/1.27 % (26998)Instruction limit reached!
% 1.82/1.27 % (26998)------------------------------
% 1.82/1.27 % (26998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.27 % (26998)Termination reason: Unknown
% 1.82/1.27 % (26998)Termination phase: Saturation
% 1.82/1.27
% 1.82/1.27 % (26998)Memory used [KB]: 6780
% 1.82/1.27 % (26998)Time elapsed: 0.037 s
% 1.82/1.27 % (26998)Instructions burned: 129 (million)
% 1.82/1.27 % (26998)------------------------------
% 1.82/1.27 % (26998)------------------------------
% 1.82/1.27 % (26999)Instruction limit reached!
% 1.82/1.27 % (26999)------------------------------
% 1.82/1.27 % (26999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.27 % (26999)Termination reason: Unknown
% 1.82/1.27 % (26999)Termination phase: Property scanning
% 1.82/1.27
% 1.82/1.27 % (26999)Memory used [KB]: 2430
% 1.82/1.27 % (26999)Time elapsed: 0.029 s
% 1.82/1.27 % (26999)Instructions burned: 103 (million)
% 1.82/1.27 % (26999)------------------------------
% 1.82/1.27 % (26999)------------------------------
% 1.82/1.28 % (27000)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_26636 for (2998ds/3Mi)
% 1.82/1.28 % (27000)Instruction limit reached!
% 1.82/1.28 % (27000)------------------------------
% 1.82/1.28 % (27000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.28 % (27000)Termination reason: Unknown
% 1.82/1.28 % (27000)Termination phase: shuffling
% 1.82/1.28
% 1.82/1.28 % (27000)Memory used [KB]: 1407
% 1.82/1.28 % (27000)Time elapsed: 0.002 s
% 1.82/1.28 % (27000)Instructions burned: 3 (million)
% 1.82/1.28 % (27000)------------------------------
% 1.82/1.28 % (27000)------------------------------
% 1.82/1.28 % (27001)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_26636 for (2998ds/20Mi)
% 1.82/1.29 % (27001)Instruction limit reached!
% 1.82/1.29 % (27001)------------------------------
% 1.82/1.29 % (27001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.29 % (27001)Termination reason: Unknown
% 1.82/1.29 % (27001)Termination phase: shuffling
% 1.82/1.29
% 1.82/1.29 % (27001)Memory used [KB]: 1791
% 1.82/1.29 % (27001)Time elapsed: 0.008 s
% 1.82/1.29 % (27001)Instructions burned: 21 (million)
% 1.82/1.29 % (27001)------------------------------
% 1.82/1.29 % (27001)------------------------------
% 1.82/1.29 % (27002)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_26636 for (2998ds/86Mi)
% 1.82/1.29 % (26991)Instruction limit reached!
% 1.82/1.29 % (26991)------------------------------
% 1.82/1.29 % (26991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.29 % (26991)Termination reason: Unknown
% 1.82/1.29 % (26991)Termination phase: Saturation
% 1.82/1.29
% 1.82/1.29 % (26991)Memory used [KB]: 8059
% 1.82/1.29 % (26991)Time elapsed: 0.105 s
% 1.82/1.29 % (26991)Instructions burned: 380 (million)
% 1.82/1.29 % (26991)------------------------------
% 1.82/1.29 % (26991)------------------------------
% 1.82/1.30 % (27003)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_26636 for (2998ds/107Mi)
% 1.82/1.30 % (27004)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_26636 for (2998ds/39Mi)
% 1.82/1.31 % (27004)Instruction limit reached!
% 1.82/1.31 % (27004)------------------------------
% 1.82/1.31 % (27004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.31 % (27004)Termination reason: Unknown
% 1.82/1.31 % (27004)Termination phase: shuffling
% 1.82/1.31
% 1.82/1.31 % (27004)Memory used [KB]: 2174
% 1.82/1.31 % (27004)Time elapsed: 0.012 s
% 1.82/1.31 % (27004)Instructions burned: 41 (million)
% 1.82/1.31 % (27004)------------------------------
% 1.82/1.31 % (27004)------------------------------
% 1.82/1.32 % (27002)Instruction limit reached!
% 1.82/1.32 % (27002)------------------------------
% 1.82/1.32 % (27002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.32 % (27002)Termination reason: Unknown
% 1.82/1.32 % (27002)Termination phase: Property scanning
% 1.82/1.32
% 1.82/1.32 % (27002)Memory used [KB]: 2302
% 1.82/1.32 % (27002)Time elapsed: 0.026 s
% 1.82/1.32 % (27002)Instructions burned: 87 (million)
% 1.82/1.32 % (27002)------------------------------
% 1.82/1.32 % (27002)------------------------------
% 1.82/1.32 % (27005)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_26636 for (2997ds/448Mi)
% 1.82/1.33 % (27006)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_26636 for (2997ds/46Mi)
% 1.82/1.33 % (27003)Instruction limit reached!
% 1.82/1.33 % (27003)------------------------------
% 1.82/1.33 % (27003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.33 % (27003)Termination reason: Unknown
% 1.82/1.33 % (27003)Termination phase: Property scanning
% 1.82/1.33
% 1.82/1.33 % (27003)Memory used [KB]: 2302
% 1.82/1.33 % (27003)Time elapsed: 0.031 s
% 1.82/1.33 % (27003)Instructions burned: 107 (million)
% 1.82/1.33 % (27003)------------------------------
% 1.82/1.33 % (27003)------------------------------
% 1.82/1.34 % (27007)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_26636 for (2997ds/98Mi)
% 1.82/1.34 % (27006)Instruction limit reached!
% 1.82/1.34 % (27006)------------------------------
% 1.82/1.34 % (27006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.34 % (27006)Termination reason: Unknown
% 1.82/1.34 % (27006)Termination phase: Preprocessing 1
% 1.82/1.34
% 1.82/1.34 % (27006)Memory used [KB]: 1918
% 1.82/1.34 % (27006)Time elapsed: 0.015 s
% 1.82/1.34 % (27006)Instructions burned: 47 (million)
% 1.82/1.34 % (27006)------------------------------
% 1.82/1.34 % (27006)------------------------------
% 1.82/1.35 % (27008)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_26636 for (2997ds/507Mi)
% 1.82/1.36 % (27007)Instruction limit reached!
% 1.82/1.36 % (27007)------------------------------
% 1.82/1.36 % (27007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.36 % (27007)Termination reason: Unknown
% 1.82/1.36 % (27007)Termination phase: Property scanning
% 1.82/1.36
% 1.82/1.36 % (27007)Memory used [KB]: 2430
% 1.82/1.36 % (27007)Time elapsed: 0.027 s
% 1.82/1.36 % (27007)Instructions burned: 98 (million)
% 1.82/1.36 % (27007)------------------------------
% 1.82/1.36 % (27007)------------------------------
% 1.82/1.37 % (27009)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_26636 for (2997ds/149Mi)
% 1.82/1.38 % (26985)Instruction limit reached!
% 1.82/1.38 % (26985)------------------------------
% 1.82/1.38 % (26985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.38 % (26985)Termination reason: Unknown
% 1.82/1.38 % (26985)Termination phase: Saturation
% 1.82/1.38
% 1.82/1.38 % (26985)Memory used [KB]: 7803
% 1.82/1.38 % (26985)Time elapsed: 0.215 s
% 1.82/1.38 % (26985)Instructions burned: 712 (million)
% 1.82/1.38 % (26985)------------------------------
% 1.82/1.38 % (26985)------------------------------
% 1.82/1.39 % (27010)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_26636 for (2997ds/39Mi)
% 1.82/1.41 % (27010)Instruction limit reached!
% 1.82/1.41 % (27010)------------------------------
% 1.82/1.41 % (27010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.41 % (27010)Termination reason: Unknown
% 1.82/1.41 % (27010)Termination phase: Preprocessing 1
% 1.82/1.41
% 1.82/1.41 % (27010)Memory used [KB]: 1918
% 1.82/1.41 % (27010)Time elapsed: 0.013 s
% 1.82/1.41 % (27010)Instructions burned: 39 (million)
% 1.82/1.41 % (27010)------------------------------
% 1.82/1.41 % (27010)------------------------------
% 1.82/1.41 % (27009)Instruction limit reached!
% 1.82/1.41 % (27009)------------------------------
% 1.82/1.41 % (27009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.41 % (27009)Termination reason: Unknown
% 1.82/1.41 % (27009)Termination phase: Saturation
% 1.82/1.41
% 1.82/1.41 % (27009)Memory used [KB]: 7036
% 1.82/1.41 % (27009)Time elapsed: 0.042 s
% 1.82/1.41 % (27009)Instructions burned: 150 (million)
% 1.82/1.41 % (27009)------------------------------
% 1.82/1.41 % (27009)------------------------------
% 1.82/1.42 % (27011)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_26636 for (2997ds/6Mi)
% 1.82/1.42 % (27011)Instruction limit reached!
% 1.82/1.42 % (27011)------------------------------
% 1.82/1.42 % (27011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.42 % (27011)Termination reason: Unknown
% 1.82/1.42 % (27011)Termination phase: shuffling
% 1.82/1.42
% 1.82/1.42 % (27011)Memory used [KB]: 1407
% 1.82/1.42 % (27011)Time elapsed: 0.003 s
% 1.82/1.42 % (27011)Instructions burned: 7 (million)
% 1.82/1.42 % (27011)------------------------------
% 1.82/1.42 % (27011)------------------------------
% 1.82/1.42 % (27012)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_26636 for (2996ds/1087Mi)
% 1.82/1.43 % (27013)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_26636 for (2996ds/47Mi)
% 1.82/1.44 % (26992)Instruction limit reached!
% 1.82/1.44 % (26992)------------------------------
% 1.82/1.44 % (26992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.44 % (26992)Termination reason: Unknown
% 1.82/1.44 % (26992)Termination phase: Saturation
% 1.82/1.44
% 1.82/1.44 % (26992)Memory used [KB]: 7675
% 1.82/1.44 % (26992)Time elapsed: 0.265 s
% 1.82/1.44 % (26992)Instructions burned: 779 (million)
% 1.82/1.44 % (26992)------------------------------
% 1.82/1.44 % (26992)------------------------------
% 1.82/1.44 % (27013)Instruction limit reached!
% 1.82/1.44 % (27013)------------------------------
% 1.82/1.44 % (27013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.44 % (27013)Termination reason: Unknown
% 1.82/1.44 % (27013)Termination phase: Preprocessing 3
% 1.82/1.44
% 1.82/1.44 % (27013)Memory used [KB]: 2174
% 1.82/1.44 % (27013)Time elapsed: 0.017 s
% 1.82/1.44 % (27013)Instructions burned: 49 (million)
% 1.82/1.44 % (27013)------------------------------
% 1.82/1.44 % (27013)------------------------------
% 1.82/1.45 % (27014)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_26636 for (2996ds/44Mi)
% 1.82/1.45 % (27015)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_26636 for (2996ds/432Mi)
% 1.82/1.46 % (27014)Instruction limit reached!
% 1.82/1.46 % (27014)------------------------------
% 1.82/1.46 % (27014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.46 % (27014)Termination reason: Unknown
% 1.82/1.46 % (27014)Termination phase: Property scanning
% 1.82/1.46
% 1.82/1.46 % (27014)Memory used [KB]: 2174
% 1.82/1.46 % (27014)Time elapsed: 0.014 s
% 1.82/1.46 % (27014)Instructions burned: 47 (million)
% 1.82/1.46 % (27014)------------------------------
% 1.82/1.46 % (27014)------------------------------
% 1.82/1.46 % (27005)Instruction limit reached!
% 1.82/1.46 % (27005)------------------------------
% 1.82/1.46 % (27005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.46 % (27005)Termination reason: Unknown
% 1.82/1.46 % (27005)Termination phase: Saturation
% 1.82/1.46
% 1.82/1.46 % (27005)Memory used [KB]: 7675
% 1.82/1.46 % (27005)Time elapsed: 0.138 s
% 1.82/1.46 % (27005)Instructions burned: 449 (million)
% 1.82/1.46 % (27005)------------------------------
% 1.82/1.46 % (27005)------------------------------
% 1.82/1.46 % (26976)Instruction limit reached!
% 1.82/1.46 % (26976)------------------------------
% 1.82/1.46 % (26976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.46 % (26976)Termination reason: Unknown
% 1.82/1.46 % (26976)Termination phase: Saturation
% 1.82/1.46
% 1.82/1.46 % (26976)Memory used [KB]: 9466
% 1.82/1.46 % (26976)Time elapsed: 0.314 s
% 1.82/1.46 % (26976)Instructions burned: 1042 (million)
% 1.82/1.46 % (26976)------------------------------
% 1.82/1.46 % (26976)------------------------------
% 1.82/1.47 % (26994)Instruction limit reached!
% 1.82/1.47 % (26994)------------------------------
% 1.82/1.47 % (26994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.47 % (26994)Termination reason: Unknown
% 1.82/1.47 % (26994)Termination phase: Saturation
% 1.82/1.47
% 1.82/1.47 % (26994)Memory used [KB]: 7931
% 1.82/1.47 % (26994)Time elapsed: 0.292 s
% 1.82/1.47 % (26994)Instructions burned: 881 (million)
% 1.82/1.47 % (26994)------------------------------
% 1.82/1.47 % (26994)------------------------------
% 1.82/1.47 % (27016)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_26636 for (2996ds/62Mi)
% 1.82/1.47 % (27017)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_26636 for (2996ds/31Mi)
% 1.82/1.47 % (27018)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_26636 for (2996ds/96Mi)
% 1.82/1.48 % (27019)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_26636 for (2996ds/453Mi)
% 1.82/1.48 % (27017)Instruction limit reached!
% 1.82/1.48 % (27017)------------------------------
% 1.82/1.48 % (27017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.48 % (27017)Termination reason: Unknown
% 1.82/1.48 % (27017)Termination phase: Property scanning
% 1.82/1.48
% 1.82/1.48 % (27017)Memory used [KB]: 1918
% 1.82/1.48 % (27017)Time elapsed: 0.012 s
% 1.82/1.48 % (27017)Instructions burned: 33 (million)
% 1.82/1.48 % (27017)------------------------------
% 1.82/1.48 % (27017)------------------------------
% 1.82/1.49 % (27016)Instruction limit reached!
% 1.82/1.49 % (27016)------------------------------
% 1.82/1.49 % (27016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.49 % (27016)Termination reason: Unknown
% 1.82/1.49 % (27016)Termination phase: Property scanning
% 1.82/1.49
% 1.82/1.49 % (27016)Memory used [KB]: 2174
% 1.82/1.49 % (27016)Time elapsed: 0.019 s
% 1.82/1.49 % (27016)Instructions burned: 64 (million)
% 1.82/1.49 % (27016)------------------------------
% 1.82/1.49 % (27016)------------------------------
% 1.82/1.49 % (27020)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_26636 for (2996ds/71Mi)
% 1.82/1.50 % (27021)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_26636 for (2996ds/83Mi)
% 1.82/1.50 % (27018)Instruction limit reached!
% 1.82/1.50 % (27018)------------------------------
% 1.82/1.50 % (27018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.50 % (27018)Termination reason: Unknown
% 1.82/1.50 % (27018)Termination phase: Property scanning
% 1.82/1.50
% 1.82/1.50 % (27018)Memory used [KB]: 2174
% 1.82/1.50 % (27018)Time elapsed: 0.030 s
% 1.82/1.50 % (27018)Instructions burned: 97 (million)
% 1.82/1.50 % (27018)------------------------------
% 1.82/1.50 % (27018)------------------------------
% 1.82/1.50 % (27008)Instruction limit reached!
% 1.82/1.50 % (27008)------------------------------
% 1.82/1.50 % (27008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.50 % (27008)Termination reason: Unknown
% 1.82/1.50 % (27008)Termination phase: Saturation
% 1.82/1.50
% 1.82/1.50 % (27008)Memory used [KB]: 8699
% 1.82/1.50 % (27008)Time elapsed: 0.153 s
% 1.82/1.50 % (27008)Instructions burned: 508 (million)
% 1.82/1.50 % (27008)------------------------------
% 1.82/1.50 % (27008)------------------------------
% 1.82/1.51 % (27022)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_26636 for (2996ds/11Mi)
% 1.82/1.51 % (27023)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_26636 for (2996ds/41Mi)
% 1.82/1.51 % (27020)Instruction limit reached!
% 1.82/1.51 % (27020)------------------------------
% 1.82/1.51 % (27020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.51 % (27020)Termination reason: Unknown
% 1.82/1.51 % (27020)Termination phase: Property scanning
% 1.82/1.51
% 1.82/1.51 % (27020)Memory used [KB]: 2174
% 1.82/1.51 % (27020)Time elapsed: 0.023 s
% 1.82/1.51 % (27020)Instructions burned: 73 (million)
% 1.82/1.51 % (27020)------------------------------
% 1.82/1.51 % (27020)------------------------------
% 1.82/1.51 % (27022)Instruction limit reached!
% 1.82/1.51 % (27022)------------------------------
% 1.82/1.51 % (27022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.51 % (27022)Termination reason: Unknown
% 1.82/1.51 % (27022)Termination phase: shuffling
% 1.82/1.51
% 1.82/1.51 % (27022)Memory used [KB]: 1663
% 1.82/1.51 % (27022)Time elapsed: 0.005 s
% 1.82/1.51 % (27022)Instructions burned: 14 (million)
% 1.82/1.51 % (27022)------------------------------
% 1.82/1.51 % (27022)------------------------------
% 1.82/1.52 % (27021)Instruction limit reached!
% 1.82/1.52 % (27021)------------------------------
% 1.82/1.52 % (27021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.52 % (27021)Termination reason: Unknown
% 1.82/1.52 % (27021)Termination phase: Saturation
% 1.82/1.52
% 1.82/1.52 % (27021)Memory used [KB]: 6652
% 1.82/1.52 % (27021)Time elapsed: 0.026 s
% 1.82/1.52 % (27021)Instructions burned: 83 (million)
% 1.82/1.52 % (27021)------------------------------
% 1.82/1.52 % (27021)------------------------------
% 1.82/1.52 % (27024)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26636 for (2996ds/6Mi)
% 1.82/1.52 % (27025)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_26636 for (2996ds/150Mi)
% 1.82/1.52 % (27023)Instruction limit reached!
% 1.82/1.52 % (27023)------------------------------
% 1.82/1.52 % (27023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.52 % (27023)Termination reason: Unknown
% 1.82/1.52 % (27023)Termination phase: shuffling
% 1.82/1.52
% 1.82/1.52 % (27023)Memory used [KB]: 2174
% 1.82/1.52 % (27023)Time elapsed: 0.013 s
% 1.82/1.52 % (27023)Instructions burned: 44 (million)
% 1.82/1.52 % (27023)------------------------------
% 1.82/1.52 % (27023)------------------------------
% 1.82/1.52 % (27024)Instruction limit reached!
% 1.82/1.52 % (27024)------------------------------
% 1.82/1.52 % (27024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.52 % (27024)Termination reason: Unknown
% 1.82/1.52 % (27024)Termination phase: shuffling
% 1.82/1.52
% 1.82/1.52 % (27024)Memory used [KB]: 1407
% 1.82/1.52 % (27024)Time elapsed: 0.003 s
% 1.82/1.52 % (27024)Instructions burned: 6 (million)
% 1.82/1.52 % (27024)------------------------------
% 1.82/1.52 % (27024)------------------------------
% 1.82/1.53 % (27026)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_26636 for (2995ds/343Mi)
% 1.82/1.53 % (27027)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_26636 for (2995ds/109Mi)
% 1.82/1.53 % (27028)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_26636 for (2995ds/253Mi)
% 1.82/1.56 % (27027)Instruction limit reached!
% 1.82/1.56 % (27027)------------------------------
% 1.82/1.56 % (27027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.56 % (27027)Termination reason: Unknown
% 1.82/1.56 % (27027)Termination phase: Property scanning
% 1.82/1.56
% 1.82/1.56 % (27027)Memory used [KB]: 2174
% 1.82/1.56 % (27027)Time elapsed: 0.032 s
% 1.82/1.56 % (27027)Instructions burned: 110 (million)
% 1.82/1.56 % (27027)------------------------------
% 1.82/1.56 % (27027)------------------------------
% 1.82/1.56 % (27025)Instruction limit reached!
% 1.82/1.56 % (27025)------------------------------
% 1.82/1.56 % (27025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.56 % (27025)Termination reason: Unknown
% 1.82/1.56 % (27025)Termination phase: Saturation
% 1.82/1.56
% 1.82/1.56 % (27025)Memory used [KB]: 7036
% 1.82/1.56 % (27025)Time elapsed: 0.043 s
% 1.82/1.56 % (27025)Instructions burned: 153 (million)
% 1.82/1.56 % (27025)------------------------------
% 1.82/1.56 % (27025)------------------------------
% 1.82/1.57 % (27029)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_26636 for (2995ds/140Mi)
% 1.82/1.57 % (27030)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_26636 for (2995ds/614Mi)
% 1.82/1.59 % (27015)Instruction limit reached!
% 1.82/1.59 % (27015)------------------------------
% 1.82/1.59 % (27015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.59 % (27015)Termination reason: Unknown
% 1.82/1.59 % (27015)Termination phase: Saturation
% 1.82/1.59
% 1.82/1.59 % (27015)Memory used [KB]: 3326
% 1.82/1.59 % (27015)Time elapsed: 0.134 s
% 1.82/1.59 % (27015)Instructions burned: 434 (million)
% 1.82/1.59 % (27015)------------------------------
% 1.82/1.59 % (27015)------------------------------
% 1.82/1.60 % (27031)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_26636 for (2995ds/202Mi)
% 1.82/1.61 % (27019)Instruction limit reached!
% 1.82/1.61 % (27019)------------------------------
% 1.82/1.61 % (27019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.61 % (27019)Termination reason: Unknown
% 1.82/1.61 % (27019)Termination phase: Saturation
% 1.82/1.61
% 1.82/1.61 % (27019)Memory used [KB]: 8443
% 1.82/1.61 % (27019)Time elapsed: 0.135 s
% 1.82/1.61 % (27019)Instructions burned: 455 (million)
% 1.82/1.61 % (27019)------------------------------
% 1.82/1.61 % (27019)------------------------------
% 1.82/1.61 % (27028)Instruction limit reached!
% 1.82/1.61 % (27028)------------------------------
% 1.82/1.61 % (27028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.61 % (27028)Termination reason: Unknown
% 1.82/1.61 % (27028)Termination phase: Saturation
% 1.82/1.61
% 1.82/1.61 % (27028)Memory used [KB]: 7419
% 1.82/1.61 % (27028)Time elapsed: 0.082 s
% 1.82/1.61 % (27028)Instructions burned: 255 (million)
% 1.82/1.61 % (27028)------------------------------
% 1.82/1.61 % (27028)------------------------------
% 1.82/1.61 % (27031)Refutation not found, incomplete strategy
% 1.82/1.61 % (27031)------------------------------
% 1.82/1.61 % (27031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.61 % (27031)Termination reason: Refutation not found, incomplete strategy
% 1.82/1.61
% 1.82/1.61
% 1.82/1.61 % (27031)Memory used [KB]: 6524
% 1.82/1.61 % (27031)Time elapsed: 0.020 s
% 1.82/1.61 % (27031)Instructions burned: 58 (million)
% 1.82/1.61 % (27031)------------------------------
% 1.82/1.61 % (27031)------------------------------
% 1.82/1.62 % (27032)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_26636 for (2995ds/339Mi)
% 1.82/1.62 % (27029)Instruction limit reached!
% 1.82/1.62 % (27029)------------------------------
% 1.82/1.62 % (27029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.62 % (27029)Termination reason: Unknown
% 1.82/1.62 % (27029)Termination phase: Saturation
% 1.82/1.62
% 1.82/1.62 % (27029)Memory used [KB]: 6780
% 1.82/1.62 % (27029)Time elapsed: 0.048 s
% 1.82/1.62 % (27029)Instructions burned: 142 (million)
% 1.82/1.62 % (27029)------------------------------
% 1.82/1.62 % (27029)------------------------------
% 1.82/1.62 % (27033)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_26636 for (2995ds/283Mi)
% 1.82/1.62 % (27034)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_26636 for (2995ds/134Mi)
% 1.82/1.63 % (27035)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_26636 for (2995ds/298Mi)
% 1.82/1.64 % (27026)Instruction limit reached!
% 1.82/1.64 % (27026)------------------------------
% 1.82/1.64 % (27026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.64 % (27026)Termination reason: Unknown
% 1.82/1.64 % (27026)Termination phase: Saturation
% 1.82/1.64
% 1.82/1.64 % (27026)Memory used [KB]: 8187
% 1.82/1.64 % (27026)Time elapsed: 0.106 s
% 1.82/1.64 % (27026)Instructions burned: 344 (million)
% 1.82/1.64 % (27026)------------------------------
% 1.82/1.64 % (27026)------------------------------
% 1.82/1.65 % (27036)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_26636 for (2994ds/192Mi)
% 1.82/1.66 % (27034)Instruction limit reached!
% 1.82/1.66 % (27034)------------------------------
% 1.82/1.66 % (27034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.66 % (27034)Termination reason: Unknown
% 1.82/1.66 % (27034)Termination phase: Saturation
% 1.82/1.66
% 1.82/1.66 % (27034)Memory used [KB]: 6908
% 1.82/1.66 % (27034)Time elapsed: 0.040 s
% 1.82/1.66 % (27034)Instructions burned: 136 (million)
% 1.82/1.66 % (27034)------------------------------
% 1.82/1.66 % (27034)------------------------------
% 1.82/1.67 % (27037)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_26636 for (2994ds/258Mi)
% 1.82/1.70 % (27036)Instruction limit reached!
% 1.82/1.70 % (27036)------------------------------
% 1.82/1.70 % (27036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.70 % (27036)Termination reason: Unknown
% 1.82/1.70 % (27036)Termination phase: Saturation
% 1.82/1.70
% 1.82/1.70 % (27036)Memory used [KB]: 3198
% 1.82/1.70 % (27036)Time elapsed: 0.059 s
% 1.82/1.70 % (27036)Instructions burned: 193 (million)
% 1.82/1.70 % (27036)------------------------------
% 1.82/1.70 % (27036)------------------------------
% 1.82/1.71 % (27033)Instruction limit reached!
% 1.82/1.71 % (27033)------------------------------
% 1.82/1.71 % (27033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.71 % (27033)Termination reason: Unknown
% 1.82/1.71 % (27033)Termination phase: Saturation
% 1.82/1.71
% 1.82/1.71 % (27033)Memory used [KB]: 7419
% 1.82/1.71 % (27033)Time elapsed: 0.111 s
% 1.82/1.71 % (27033)Instructions burned: 284 (million)
% 1.82/1.71 % (27033)------------------------------
% 1.82/1.71 % (27033)------------------------------
% 1.82/1.71 % (27038)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_26636 for (2994ds/90Mi)
% 1.82/1.71 % (27032)Instruction limit reached!
% 1.82/1.71 % (27032)------------------------------
% 1.82/1.71 % (27032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.71 % (27032)Termination reason: Unknown
% 1.82/1.71 % (27032)Termination phase: Saturation
% 1.82/1.71
% 1.82/1.71 % (27032)Memory used [KB]: 7419
% 1.82/1.71 % (27032)Time elapsed: 0.097 s
% 1.82/1.71 % (27032)Instructions burned: 340 (million)
% 1.82/1.71 % (27032)------------------------------
% 1.82/1.71 % (27032)------------------------------
% 1.82/1.71 % (27035)Instruction limit reached!
% 1.82/1.71 % (27035)------------------------------
% 1.82/1.71 % (27035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.71 % (27035)Termination reason: Unknown
% 1.82/1.71 % (27035)Termination phase: Saturation
% 1.82/1.71
% 1.82/1.71 % (27035)Memory used [KB]: 8571
% 1.82/1.71 % (27035)Time elapsed: 0.087 s
% 1.82/1.71 % (27035)Instructions burned: 298 (million)
% 1.82/1.71 % (27035)------------------------------
% 1.82/1.71 % (27035)------------------------------
% 1.82/1.72 % (27039)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_26636 for (2993ds/231Mi)
% 1.82/1.72 % (27040)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_26636 for (2993ds/458Mi)
% 1.82/1.72 % (27041)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_26636 for (2993ds/31Mi)
% 1.82/1.73 % (27041)Instruction limit reached!
% 1.82/1.73 % (27041)------------------------------
% 1.82/1.73 % (27041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.73 % (27041)Termination reason: Unknown
% 1.82/1.73 % (27041)Termination phase: Property scanning
% 1.82/1.73
% 1.82/1.73 % (27041)Memory used [KB]: 1918
% 1.82/1.73 % (27041)Time elapsed: 0.011 s
% 1.82/1.73 % (27041)Instructions burned: 32 (million)
% 1.82/1.73 % (27041)------------------------------
% 1.82/1.73 % (27041)------------------------------
% 1.82/1.74 % (27038)Instruction limit reached!
% 1.82/1.74 % (27038)------------------------------
% 1.82/1.74 % (27038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.74 % (27038)Termination reason: Unknown
% 1.82/1.74 % (27038)Termination phase: Property scanning
% 1.82/1.74
% 1.82/1.74 % (27038)Memory used [KB]: 2174
% 1.82/1.74 % (27038)Time elapsed: 0.027 s
% 1.82/1.74 % (27038)Instructions burned: 90 (million)
% 1.82/1.74 % (27038)------------------------------
% 1.82/1.74 % (27038)------------------------------
% 1.82/1.74 % (27030)Instruction limit reached!
% 1.82/1.74 % (27030)------------------------------
% 1.82/1.74 % (27030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.74 % (27030)Termination reason: Unknown
% 1.82/1.74 % (27030)Termination phase: Saturation
% 1.82/1.74
% 1.82/1.74 % (27030)Memory used [KB]: 8571
% 1.82/1.74 % (27030)Time elapsed: 0.170 s
% 1.82/1.74 % (27030)Instructions burned: 617 (million)
% 1.82/1.74 % (27030)------------------------------
% 1.82/1.74 % (27030)------------------------------
% 1.82/1.74 % (27042)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_26636 for (2993ds/297Mi)
% 1.82/1.75 % (27043)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_26636 for (2993ds/987Mi)
% 1.82/1.75 % (27044)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_26636 for (2993ds/182Mi)
% 1.82/1.75 % (27037)Instruction limit reached!
% 1.82/1.75 % (27037)------------------------------
% 1.82/1.75 % (27037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.75 % (27037)Termination reason: Unknown
% 1.82/1.75 % (27037)Termination phase: Saturation
% 1.82/1.75
% 1.82/1.75 % (27037)Memory used [KB]: 7036
% 1.82/1.75 % (27037)Time elapsed: 0.103 s
% 1.82/1.75 % (27037)Instructions burned: 260 (million)
% 1.82/1.75 % (27037)------------------------------
% 1.82/1.75 % (27037)------------------------------
% 1.82/1.76 % (27012)Instruction limit reached!
% 1.82/1.76 % (27012)------------------------------
% 1.82/1.76 % (27012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.76 % (27012)Termination reason: Unknown
% 1.82/1.76 % (27012)Termination phase: Saturation
% 1.82/1.76
% 1.82/1.76 % (27012)Memory used [KB]: 7547
% 1.82/1.76 % (27012)Time elapsed: 0.337 s
% 1.82/1.76 % (27012)Instructions burned: 1089 (million)
% 1.82/1.76 % (27012)------------------------------
% 1.82/1.76 % (27012)------------------------------
% 1.82/1.76 % (27045)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_26636 for (2993ds/182Mi)
% 1.82/1.77 % (27046)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_26636 for (2993ds/154Mi)
% 1.82/1.79 % (27039)Instruction limit reached!
% 1.82/1.79 % (27039)------------------------------
% 1.82/1.79 % (27039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.79 % (27039)Termination reason: Unknown
% 1.82/1.79 % (27039)Termination phase: Saturation
% 1.82/1.79
% 1.82/1.79 % (27039)Memory used [KB]: 7164
% 1.82/1.79 % (27039)Time elapsed: 0.065 s
% 1.82/1.79 % (27039)Instructions burned: 231 (million)
% 1.82/1.79 % (27039)------------------------------
% 1.82/1.79 % (27039)------------------------------
% 1.82/1.79 % (27047)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_26636 for (2993ds/79Mi)
% 1.82/1.80 % (27044)Instruction limit reached!
% 1.82/1.80 % (27044)------------------------------
% 1.82/1.80 % (27044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.80 % (27044)Termination reason: Unknown
% 1.82/1.80 % (27044)Termination phase: Saturation
% 1.82/1.80
% 1.82/1.80 % (27044)Memory used [KB]: 7164
% 1.82/1.80 % (27044)Time elapsed: 0.051 s
% 1.82/1.80 % (27044)Instructions burned: 185 (million)
% 1.82/1.80 % (27044)------------------------------
% 1.82/1.80 % (27044)------------------------------
% 1.82/1.81 % (27046)Instruction limit reached!
% 1.82/1.81 % (27046)------------------------------
% 1.82/1.81 % (27046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.81 % (27046)Termination reason: Unknown
% 1.82/1.81 % (27046)Termination phase: Saturation
% 1.82/1.81
% 1.82/1.81 % (27046)Memory used [KB]: 2814
% 1.82/1.81 % (27046)Time elapsed: 0.042 s
% 1.82/1.81 % (27046)Instructions burned: 154 (million)
% 1.82/1.81 % (27046)------------------------------
% 1.82/1.81 % (27046)------------------------------
% 1.82/1.81 % (27048)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_26636 for (2993ds/216Mi)
% 1.82/1.82 % (27045)Instruction limit reached!
% 1.82/1.82 % (27045)------------------------------
% 1.82/1.82 % (27045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.82 % (27045)Termination reason: Unknown
% 1.82/1.82 % (27045)Termination phase: Saturation
% 1.82/1.82
% 1.82/1.82 % (27045)Memory used [KB]: 7036
% 1.82/1.82 % (27045)Time elapsed: 0.056 s
% 1.82/1.82 % (27045)Instructions burned: 183 (million)
% 1.82/1.82 % (27045)------------------------------
% 1.82/1.82 % (27045)------------------------------
% 1.82/1.82 % (27047)Instruction limit reached!
% 1.82/1.82 % (27047)------------------------------
% 1.82/1.82 % (27047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.82 % (27047)Termination reason: Unknown
% 1.82/1.82 % (27047)Termination phase: Function definition elimination
% 1.82/1.82
% 1.82/1.82 % (27047)Memory used [KB]: 2174
% 1.82/1.82 % (27047)Time elapsed: 0.024 s
% 1.82/1.82 % (27047)Instructions burned: 80 (million)
% 1.82/1.82 % (27047)------------------------------
% 1.82/1.82 % (27047)------------------------------
% 1.82/1.82 % (27049)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_26636 for (2992ds/114Mi)
% 1.82/1.83 % (27050)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_26636 for (2992ds/922Mi)
% 1.82/1.83 % (27051)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_26636 for (2992ds/182Mi)
% 1.82/1.83 % (27042)Instruction limit reached!
% 1.82/1.83 % (27042)------------------------------
% 1.82/1.83 % (27042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.83 % (27042)Termination reason: Unknown
% 1.82/1.83 % (27042)Termination phase: Saturation
% 1.82/1.83
% 1.82/1.83 % (27042)Memory used [KB]: 7419
% 1.82/1.83 % (27042)Time elapsed: 0.087 s
% 1.82/1.83 % (27042)Instructions burned: 298 (million)
% 1.82/1.83 % (27042)------------------------------
% 1.82/1.83 % (27042)------------------------------
% 1.82/1.84 % (27052)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_26636 for (2992ds/164Mi)
% 1.82/1.85 % (27040)Instruction limit reached!
% 1.82/1.85 % (27040)------------------------------
% 1.82/1.85 % (27040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.85 % (27040)Termination reason: Unknown
% 1.82/1.85 % (27040)Termination phase: Saturation
% 1.82/1.85
% 1.82/1.85 % (27040)Memory used [KB]: 8187
% 1.82/1.85 % (27040)Time elapsed: 0.125 s
% 1.82/1.85 % (27040)Instructions burned: 458 (million)
% 1.82/1.85 % (27040)------------------------------
% 1.82/1.85 % (27040)------------------------------
% 1.82/1.85 % (27049)Instruction limit reached!
% 1.82/1.85 % (27049)------------------------------
% 1.82/1.85 % (27049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.85 % (27049)Termination reason: Unknown
% 1.82/1.85 % (27049)Termination phase: Property scanning
% 1.82/1.85
% 1.82/1.85 % (27049)Memory used [KB]: 2302
% 1.82/1.85 % (27049)Time elapsed: 0.034 s
% 1.82/1.85 % (27049)Instructions burned: 117 (million)
% 1.82/1.85 % (27049)------------------------------
% 1.82/1.85 % (27049)------------------------------
% 1.82/1.86 % (27053)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_26636 for (2992ds/50Mi)
% 1.82/1.86 % (27054)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_26636 for (2992ds/368Mi)
% 1.82/1.87 % (27053)Instruction limit reached!
% 1.82/1.87 % (27053)------------------------------
% 1.82/1.87 % (27053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.87 % (27053)Termination reason: Unknown
% 1.82/1.87 % (27053)Termination phase: Property scanning
% 1.82/1.87
% 1.82/1.87 % (27053)Memory used [KB]: 2174
% 1.82/1.87 % (27053)Time elapsed: 0.015 s
% 1.82/1.87 % (27053)Instructions burned: 51 (million)
% 1.82/1.87 % (27053)------------------------------
% 1.82/1.87 % (27053)------------------------------
% 1.82/1.87 % (27048)Instruction limit reached!
% 1.82/1.87 % (27048)------------------------------
% 1.82/1.87 % (27048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.87 % (27048)Termination reason: Unknown
% 1.82/1.87 % (27048)Termination phase: Saturation
% 1.82/1.87
% 1.82/1.87 % (27048)Memory used [KB]: 7291
% 1.82/1.87 % (27048)Time elapsed: 0.064 s
% 1.82/1.87 % (27048)Instructions burned: 217 (million)
% 1.82/1.87 % (27048)------------------------------
% 1.82/1.87 % (27048)------------------------------
% 1.82/1.88 % (27051)Instruction limit reached!
% 1.82/1.88 % (27051)------------------------------
% 1.82/1.88 % (27051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.88 % (27051)Termination reason: Unknown
% 1.82/1.88 % (27051)Termination phase: Saturation
% 1.82/1.88
% 1.82/1.88 % (27051)Memory used [KB]: 7291
% 1.82/1.88 % (27051)Time elapsed: 0.052 s
% 1.82/1.88 % (27051)Instructions burned: 182 (million)
% 1.82/1.88 % (27051)------------------------------
% 1.82/1.88 % (27051)------------------------------
% 1.82/1.88 % (27055)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_26636 for (2992ds/1021Mi)
% 1.82/1.88 % (27056)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_26636 for (2992ds/267Mi)
% 1.82/1.89 % (27052)Instruction limit reached!
% 1.82/1.89 % (27052)------------------------------
% 1.82/1.89 % (27052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.89 % (27052)Termination reason: Unknown
% 1.82/1.89 % (27052)Termination phase: Saturation
% 1.82/1.89
% 1.82/1.89 % (27052)Memory used [KB]: 2430
% 1.82/1.89 % (27052)Time elapsed: 0.048 s
% 1.82/1.89 % (27052)Instructions burned: 167 (million)
% 1.82/1.89 % (27052)------------------------------
% 1.82/1.89 % (27052)------------------------------
% 1.82/1.89 % (27057)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_26636 for (2992ds/204Mi)
% 1.82/1.90 % (27058)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_26636 for (2992ds/26Mi)
% 1.82/1.90 % (27058)Instruction limit reached!
% 1.82/1.90 % (27058)------------------------------
% 1.82/1.90 % (27058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.90 % (27058)Termination reason: Unknown
% 1.82/1.90 % (27058)Termination phase: shuffling
% 1.82/1.90
% 1.82/1.90 % (27058)Memory used [KB]: 1918
% 1.82/1.90 % (27058)Time elapsed: 0.009 s
% 1.82/1.90 % (27058)Instructions burned: 29 (million)
% 1.82/1.90 % (27058)------------------------------
% 1.82/1.90 % (27058)------------------------------
% 1.82/1.91 % (27059)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_26636 for (2992ds/53Mi)
% 1.82/1.93 % (27059)Instruction limit reached!
% 1.82/1.93 % (27059)------------------------------
% 1.82/1.93 % (27059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.93 % (27059)Termination reason: Unknown
% 1.82/1.93 % (27059)Termination phase: Property scanning
% 1.82/1.93
% 1.82/1.93 % (27059)Memory used [KB]: 2174
% 1.82/1.93 % (27059)Time elapsed: 0.017 s
% 1.82/1.93 % (27059)Instructions burned: 56 (million)
% 1.82/1.93 % (27059)------------------------------
% 1.82/1.93 % (27059)------------------------------
% 1.82/1.94 % (27060)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_26636 for (2991ds/4436Mi)
% 1.82/1.95 % (27057)Instruction limit reached!
% 1.82/1.95 % (27057)------------------------------
% 1.82/1.95 % (27057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.95 % (27057)Termination reason: Unknown
% 1.82/1.95 % (27057)Termination phase: Saturation
% 1.82/1.95
% 1.82/1.95 % (27057)Memory used [KB]: 7164
% 1.82/1.95 % (27057)Time elapsed: 0.059 s
% 1.82/1.95 % (27057)Instructions burned: 207 (million)
% 1.82/1.95 % (27057)------------------------------
% 1.82/1.95 % (27057)------------------------------
% 1.82/1.96 % (27061)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_26636 for (2991ds/1539Mi)
% 1.82/1.96 % (27054)Instruction limit reached!
% 1.82/1.96 % (27054)------------------------------
% 1.82/1.96 % (27054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.96 % (27054)Termination reason: Unknown
% 1.82/1.96 % (27054)Termination phase: Saturation
% 1.82/1.96
% 1.82/1.96 % (27054)Memory used [KB]: 7931
% 1.82/1.96 % (27054)Time elapsed: 0.102 s
% 1.82/1.96 % (27054)Instructions burned: 369 (million)
% 1.82/1.96 % (27054)------------------------------
% 1.82/1.96 % (27054)------------------------------
% 1.82/1.97 % (27056)Instruction limit reached!
% 1.82/1.97 % (27056)------------------------------
% 1.82/1.97 % (27056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.82/1.97 % (27056)Termination reason: Unknown
% 1.82/1.97 % (27056)Termination phase: Saturation
% 1.82/1.97
% 1.82/1.97 % (27056)Memory used [KB]: 7419
% 1.82/1.97 % (27056)Time elapsed: 0.083 s
% 1.82/1.97 % (27056)Instructions burned: 269 (million)
% 1.82/1.97 % (27056)------------------------------
% 1.82/1.97 % (27056)------------------------------
% 1.82/1.97 % (27062)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_26636 for (2991ds/408Mi)
% 1.82/1.97 % (27063)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_26636 for (2991ds/5205Mi)
% 8.02/2.04 % (27043)Instruction limit reached!
% 8.02/2.04 % (27043)------------------------------
% 8.02/2.04 % (27043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.04 % (27043)Termination reason: Unknown
% 8.02/2.04 % (27043)Termination phase: Saturation
% 8.02/2.04
% 8.02/2.04 % (27043)Memory used [KB]: 8443
% 8.02/2.04 % (27043)Time elapsed: 0.294 s
% 8.02/2.04 % (27043)Instructions burned: 987 (million)
% 8.02/2.04 % (27043)------------------------------
% 8.02/2.04 % (27043)------------------------------
% 8.02/2.05 % (27064)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_26636 for (2990ds/1913Mi)
% 8.02/2.10 % (27062)Instruction limit reached!
% 8.02/2.10 % (27062)------------------------------
% 8.02/2.10 % (27062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.02/2.10 % (27062)Termination reason: Unknown
% 8.02/2.10 % (27062)Termination phase: Saturation
% 8.02/2.10
% 8.02/2.10 % (27062)Memory used [KB]: 8187
% 8.02/2.10 % (27062)Time elapsed: 0.125 s
% 8.02/2.10 % (27062)Instructions burned: 410 (million)
% 8.02/2.10 % (27062)------------------------------
% 8.02/2.10 % (27062)------------------------------
% 8.02/2.11 % (27065)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_26636 for (2990ds/4350Mi)
% 8.65/2.12 % (27050)Instruction limit reached!
% 8.65/2.12 % (27050)------------------------------
% 8.65/2.12 % (27050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.65/2.12 % (27050)Termination reason: Unknown
% 8.65/2.12 % (27050)Termination phase: Saturation
% 8.65/2.12
% 8.65/2.12 % (27050)Memory used [KB]: 7931
% 8.65/2.12 % (27050)Time elapsed: 0.291 s
% 8.65/2.12 % (27050)Instructions burned: 925 (million)
% 8.65/2.12 % (27050)------------------------------
% 8.65/2.12 % (27050)------------------------------
% 8.65/2.13 % (27066)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_26636 for (2989ds/68Mi)
% 8.65/2.15 % (27066)Instruction limit reached!
% 8.65/2.15 % (27066)------------------------------
% 8.65/2.15 % (27066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.65/2.15 % (27066)Termination reason: Unknown
% 8.65/2.15 % (27066)Termination phase: Property scanning
% 8.65/2.15
% 8.65/2.15 % (27066)Memory used [KB]: 2174
% 8.65/2.15 % (27066)Time elapsed: 0.022 s
% 8.65/2.15 % (27066)Instructions burned: 70 (million)
% 8.65/2.15 % (27066)------------------------------
% 8.65/2.15 % (27066)------------------------------
% 8.65/2.16 % (27067)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_26636 for (2989ds/358Mi)
% 8.65/2.19 % (27055)Instruction limit reached!
% 8.65/2.19 % (27055)------------------------------
% 8.65/2.19 % (27055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.65/2.19 % (27055)Termination reason: Unknown
% 8.65/2.19 % (27055)Termination phase: Saturation
% 8.65/2.19
% 8.65/2.19 % (27055)Memory used [KB]: 9722
% 8.65/2.19 % (27055)Time elapsed: 0.306 s
% 8.65/2.19 % (27055)Instructions burned: 1023 (million)
% 8.65/2.19 % (27055)------------------------------
% 8.65/2.19 % (27055)------------------------------
% 8.65/2.20 % (27068)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_26636 for (2989ds/31Mi)
% 9.03/2.21 % (27068)Instruction limit reached!
% 9.03/2.21 % (27068)------------------------------
% 9.03/2.21 % (27068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.03/2.21 % (27068)Termination reason: Unknown
% 9.03/2.21 % (27068)Termination phase: Property scanning
% 9.03/2.21
% 9.03/2.21 % (27068)Memory used [KB]: 1918
% 9.03/2.21 % (27068)Time elapsed: 0.011 s
% 9.03/2.21 % (27068)Instructions burned: 32 (million)
% 9.03/2.21 % (27068)------------------------------
% 9.03/2.21 % (27068)------------------------------
% 9.03/2.22 % (27069)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_26636 for (2988ds/279Mi)
% 9.03/2.25 % (27069)Refutation not found, incomplete strategy
% 9.03/2.25 % (27069)------------------------------
% 9.03/2.25 % (27069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.03/2.25 % (27069)Termination reason: Refutation not found, incomplete strategy
% 9.03/2.25
% 9.03/2.25
% 9.03/2.25 % (27069)Memory used [KB]: 6908
% 9.03/2.25 % (27069)Time elapsed: 0.035 s
% 9.03/2.25 % (27069)Instructions burned: 120 (million)
% 9.03/2.25 % (27069)------------------------------
% 9.03/2.25 % (27069)------------------------------
% 9.03/2.26 % (27067)Instruction limit reached!
% 9.03/2.26 % (27067)------------------------------
% 9.03/2.26 % (27067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.03/2.26 % (27067)Termination reason: Unknown
% 9.03/2.26 % (27067)Termination phase: Saturation
% 9.03/2.26
% 9.03/2.26 % (27067)Memory used [KB]: 7931
% 9.03/2.26 % (27067)Time elapsed: 0.103 s
% 9.03/2.26 % (27067)Instructions burned: 358 (million)
% 9.03/2.26 % (27067)------------------------------
% 9.03/2.26 % (27067)------------------------------
% 9.03/2.26 % (27070)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_26636 for (2988ds/258Mi)
% 9.03/2.27 % (27071)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_26636 for (2988ds/26Mi)
% 9.03/2.28 % (27071)Instruction limit reached!
% 9.03/2.28 % (27071)------------------------------
% 9.03/2.28 % (27071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.03/2.28 % (27071)Termination reason: Unknown
% 9.03/2.28 % (27071)Termination phase: shuffling
% 9.03/2.28
% 9.03/2.28 % (27071)Memory used [KB]: 1918
% 9.03/2.28 % (27071)Time elapsed: 0.009 s
% 9.03/2.28 % (27071)Instructions burned: 29 (million)
% 9.03/2.28 % (27071)------------------------------
% 9.03/2.28 % (27071)------------------------------
% 9.03/2.29 % (27072)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_26636 for (2988ds/995Mi)
% 9.52/2.34 % (27070)Instruction limit reached!
% 9.52/2.34 % (27070)------------------------------
% 9.52/2.34 % (27070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.52/2.34 % (27070)Termination reason: Unknown
% 9.52/2.34 % (27070)Termination phase: Saturation
% 9.52/2.34
% 9.52/2.34 % (27070)Memory used [KB]: 7547
% 9.52/2.34 % (27070)Time elapsed: 0.079 s
% 9.52/2.34 % (27070)Instructions burned: 260 (million)
% 9.52/2.34 % (27070)------------------------------
% 9.52/2.34 % (27070)------------------------------
% 9.52/2.35 % (27073)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_26636 for (2987ds/373Mi)
% 9.90/2.42 % (27061)Instruction limit reached!
% 9.90/2.42 % (27061)------------------------------
% 9.90/2.42 % (27061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.90/2.42 % (27061)Termination reason: Unknown
% 9.90/2.42 % (27061)Termination phase: Saturation
% 9.90/2.42
% 9.90/2.42 % (27061)Memory used [KB]: 10618
% 9.90/2.42 % (27061)Time elapsed: 0.462 s
% 9.90/2.42 % (27061)Instructions burned: 1539 (million)
% 9.90/2.42 % (27061)------------------------------
% 9.90/2.42 % (27061)------------------------------
% 9.90/2.43 % (27074)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_26636 for (2986ds/253Mi)
% 9.90/2.45 % (27073)Instruction limit reached!
% 9.90/2.45 % (27073)------------------------------
% 9.90/2.45 % (27073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.90/2.45 % (27073)Termination reason: Unknown
% 9.90/2.45 % (27073)Termination phase: Saturation
% 9.90/2.45
% 9.90/2.45 % (27073)Memory used [KB]: 8187
% 9.90/2.45 % (27073)Time elapsed: 0.108 s
% 9.90/2.45 % (27073)Instructions burned: 374 (million)
% 9.90/2.45 % (27073)------------------------------
% 9.90/2.45 % (27073)------------------------------
% 9.90/2.46 % (27075)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_26636 for (2986ds/832Mi)
% 10.26/2.50 % (27074)Instruction limit reached!
% 10.26/2.50 % (27074)------------------------------
% 10.26/2.50 % (27074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.50 % (27074)Termination reason: Unknown
% 10.26/2.50 % (27074)Termination phase: Saturation
% 10.26/2.50
% 10.26/2.50 % (27074)Memory used [KB]: 7675
% 10.26/2.50 % (27074)Time elapsed: 0.073 s
% 10.26/2.50 % (27074)Instructions burned: 256 (million)
% 10.26/2.50 % (27074)------------------------------
% 10.26/2.50 % (27074)------------------------------
% 10.26/2.51 % (27076)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_26636 for (2986ds/668Mi)
% 10.26/2.51 % (27075)Refutation not found, incomplete strategy
% 10.26/2.51 % (27075)------------------------------
% 10.26/2.51 % (27075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.51 % (27075)Termination reason: Refutation not found, incomplete strategy
% 10.26/2.51
% 10.26/2.51
% 10.26/2.51 % (27075)Memory used [KB]: 7547
% 10.26/2.51 % (27075)Time elapsed: 0.047 s
% 10.26/2.51 % (27075)Instructions burned: 157 (million)
% 10.26/2.51 % (27075)------------------------------
% 10.26/2.51 % (27075)------------------------------
% 10.26/2.52 % (27077)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_26636 for (2985ds/40Mi)
% 10.26/2.53 % (27077)Instruction limit reached!
% 10.26/2.53 % (27077)------------------------------
% 10.26/2.53 % (27077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.53 % (27077)Termination reason: Unknown
% 10.26/2.53 % (27077)Termination phase: shuffling
% 10.26/2.53
% 10.26/2.53 % (27077)Memory used [KB]: 2174
% 10.26/2.53 % (27077)Time elapsed: 0.012 s
% 10.26/2.53 % (27077)Instructions burned: 41 (million)
% 10.26/2.53 % (27077)------------------------------
% 10.26/2.53 % (27077)------------------------------
% 10.26/2.54 % (27078)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_26636 for (2985ds/294Mi)
% 10.26/2.56 % (27078)Refutation not found, incomplete strategy
% 10.26/2.56 % (27078)------------------------------
% 10.26/2.56 % (27078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.56 % (27078)Termination reason: Refutation not found, incomplete strategy
% 10.26/2.56
% 10.26/2.56
% 10.26/2.56 % (27078)Memory used [KB]: 6780
% 10.26/2.56 % (27078)Time elapsed: 0.024 s
% 10.26/2.56 % (27078)Instructions burned: 86 (million)
% 10.26/2.56 % (27078)------------------------------
% 10.26/2.56 % (27078)------------------------------
% 10.26/2.57 % (27079)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_26636 for (2985ds/187Mi)
% 10.26/2.58 % (27072)Instruction limit reached!
% 10.26/2.58 % (27072)------------------------------
% 10.26/2.58 % (27072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.26/2.58 % (27072)Termination reason: Unknown
% 10.26/2.58 % (27072)Termination phase: Saturation
% 10.26/2.58
% 10.26/2.58 % (27072)Memory used [KB]: 9594
% 10.26/2.58 % (27072)Time elapsed: 0.298 s
% 10.26/2.58 % (27072)Instructions burned: 996 (million)
% 10.26/2.58 % (27072)------------------------------
% 10.26/2.58 % (27072)------------------------------
% 10.26/2.59 % (27080)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_26636 for (2985ds/371Mi)
% 10.96/2.62 % (27079)Instruction limit reached!
% 10.96/2.62 % (27079)------------------------------
% 10.96/2.62 % (27079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.96/2.62 % (27079)Termination reason: Unknown
% 10.96/2.62 % (27079)Termination phase: Saturation
% 10.96/2.62
% 10.96/2.62 % (27079)Memory used [KB]: 7164
% 10.96/2.62 % (27079)Time elapsed: 0.052 s
% 10.96/2.62 % (27079)Instructions burned: 189 (million)
% 10.96/2.62 % (27079)------------------------------
% 10.96/2.62 % (27079)------------------------------
% 10.96/2.63 % (27064)Instruction limit reached!
% 10.96/2.63 % (27064)------------------------------
% 10.96/2.63 % (27064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.96/2.63 % (27064)Termination reason: Unknown
% 10.96/2.63 % (27064)Termination phase: Saturation
% 10.96/2.63
% 10.96/2.63 % (27064)Memory used [KB]: 4861
% 10.96/2.63 % (27064)Time elapsed: 0.577 s
% 10.96/2.63 % (27064)Instructions burned: 1913 (million)
% 10.96/2.63 % (27064)------------------------------
% 10.96/2.63 % (27064)------------------------------
% 10.96/2.63 % (27081)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_26636 for (2984ds/1827Mi)
% 10.96/2.64 % (27082)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_26636 for (2984ds/70Mi)
% 10.96/2.66 % (27082)Instruction limit reached!
% 10.96/2.66 % (27082)------------------------------
% 10.96/2.66 % (27082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.96/2.66 % (27082)Termination reason: Unknown
% 10.96/2.66 % (27082)Termination phase: Preprocessing 1
% 10.96/2.66
% 10.96/2.66 % (27082)Memory used [KB]: 2174
% 10.96/2.66 % (27082)Time elapsed: 0.020 s
% 10.96/2.66 % (27082)Instructions burned: 73 (million)
% 10.96/2.66 % (27082)------------------------------
% 10.96/2.66 % (27082)------------------------------
% 10.96/2.66 % (27083)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_26636 for (2984ds/316Mi)
% 11.83/2.70 % (27076)Instruction limit reached!
% 11.83/2.70 % (27076)------------------------------
% 11.83/2.70 % (27076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.83/2.70 % (27076)Termination reason: Unknown
% 11.83/2.70 % (27076)Termination phase: Saturation
% 11.83/2.70
% 11.83/2.70 % (27076)Memory used [KB]: 13560
% 11.83/2.70 % (27076)Time elapsed: 0.195 s
% 11.83/2.70 % (27076)Instructions burned: 668 (million)
% 11.83/2.70 % (27076)------------------------------
% 11.83/2.70 % (27076)------------------------------
% 11.83/2.71 % (27080)Instruction limit reached!
% 11.83/2.71 % (27080)------------------------------
% 11.83/2.71 % (27080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.83/2.71 % (27080)Termination reason: Unknown
% 11.83/2.71 % (27080)Termination phase: Saturation
% 11.83/2.71
% 11.83/2.71 % (27080)Memory used [KB]: 7931
% 11.83/2.71 % (27080)Time elapsed: 0.114 s
% 11.83/2.71 % (27080)Instructions burned: 372 (million)
% 11.83/2.71 % (27080)------------------------------
% 11.83/2.71 % (27080)------------------------------
% 11.83/2.71 % (27084)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_26636 for (2984ds/932Mi)
% 11.83/2.71 % (27085)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_26636 for (2984ds/4714Mi)
% 11.83/2.72 % (27083)Refutation not found, incomplete strategy
% 11.83/2.72 % (27083)------------------------------
% 11.83/2.72 % (27083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.83/2.72 % (27083)Termination reason: Refutation not found, incomplete strategy
% 11.83/2.72
% 11.83/2.72
% 11.83/2.72 % (27083)Memory used [KB]: 7547
% 11.83/2.72 % (27083)Time elapsed: 0.059 s
% 11.83/2.72 % (27083)Instructions burned: 219 (million)
% 11.83/2.72 % (27083)------------------------------
% 11.83/2.72 % (27083)------------------------------
% 11.83/2.73 % (27086)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_26636 for (2983ds/8250Mi)
% 11.83/2.77 % (27085)Refutation not found, incomplete strategy
% 11.83/2.77 % (27085)------------------------------
% 11.83/2.77 % (27085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.83/2.77 % (27085)Termination reason: Refutation not found, incomplete strategy
% 11.83/2.77
% 11.83/2.77
% 11.83/2.77 % (27085)Memory used [KB]: 7547
% 11.83/2.77 % (27085)Time elapsed: 0.060 s
% 11.83/2.77 % (27085)Instructions burned: 220 (million)
% 11.83/2.77 % (27085)------------------------------
% 11.83/2.77 % (27085)------------------------------
% 11.83/2.78 % (27087)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_26636 for (2983ds/770Mi)
% 12.49/2.80 % (27087)Refutation not found, incomplete strategy
% 12.49/2.80 % (27087)------------------------------
% 12.49/2.80 % (27087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.49/2.80 % (27087)Termination reason: Refutation not found, incomplete strategy
% 12.49/2.80
% 12.49/2.80
% 12.49/2.80 % (27087)Memory used [KB]: 6524
% 12.49/2.80 % (27087)Time elapsed: 0.017 s
% 12.49/2.80 % (27087)Instructions burned: 50 (million)
% 12.49/2.80 % (27087)------------------------------
% 12.49/2.80 % (27087)------------------------------
% 12.49/2.81 % (27088)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_26636 for (2983ds/794Mi)
% 12.72/2.98 % (27084)Instruction limit reached!
% 12.72/2.98 % (27084)------------------------------
% 12.72/2.98 % (27084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.72/2.98 % (27084)Termination reason: Unknown
% 12.72/2.98 % (27084)Termination phase: Saturation
% 12.72/2.98
% 12.72/2.98 % (27084)Memory used [KB]: 9978
% 12.72/2.98 % (27084)Time elapsed: 0.268 s
% 12.72/2.98 % (27084)Instructions burned: 933 (million)
% 12.72/2.98 % (27084)------------------------------
% 12.72/2.98 % (27084)------------------------------
% 12.72/2.99 % (27089)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_26636 for (2981ds/464Mi)
% 15.01/3.04 % (27088)Instruction limit reached!
% 15.01/3.04 % (27088)------------------------------
% 15.01/3.04 % (27088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.01/3.04 % (27088)Termination reason: Unknown
% 15.01/3.04 % (27088)Termination phase: Saturation
% 15.01/3.04
% 15.01/3.04 % (27088)Memory used [KB]: 5628
% 15.01/3.04 % (27088)Time elapsed: 0.226 s
% 15.01/3.04 % (27088)Instructions burned: 794 (million)
% 15.01/3.04 % (27088)------------------------------
% 15.01/3.04 % (27088)------------------------------
% 15.01/3.05 % (27090)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_26636 for (2980ds/1376Mi)
% 15.65/3.12 % (27089)Instruction limit reached!
% 15.65/3.12 % (27089)------------------------------
% 15.65/3.12 % (27089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.65/3.12 % (27089)Termination reason: Unknown
% 15.65/3.12 % (27089)Termination phase: Saturation
% 15.65/3.12
% 15.65/3.12 % (27089)Memory used [KB]: 7931
% 15.65/3.12 % (27089)Time elapsed: 0.135 s
% 15.65/3.12 % (27089)Instructions burned: 465 (million)
% 15.65/3.12 % (27089)------------------------------
% 15.65/3.12 % (27089)------------------------------
% 15.65/3.13 % (27091)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_26636 for (2979ds/906Mi)
% 16.10/3.20 % (27081)Instruction limit reached!
% 16.10/3.20 % (27081)------------------------------
% 16.10/3.20 % (27081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.10/3.20 % (27081)Termination reason: Unknown
% 16.10/3.20 % (27081)Termination phase: Saturation
% 16.10/3.20
% 16.10/3.20 % (27081)Memory used [KB]: 8955
% 16.10/3.20 % (27081)Time elapsed: 0.569 s
% 16.10/3.20 % (27081)Instructions burned: 1829 (million)
% 16.10/3.20 % (27081)------------------------------
% 16.10/3.20 % (27081)------------------------------
% 16.10/3.21 % (27092)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_26636 for (2979ds/434Mi)
% 16.10/3.26 % (27060)Instruction limit reached!
% 16.10/3.26 % (27060)------------------------------
% 16.10/3.26 % (27060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.10/3.26 % (27060)Termination reason: Unknown
% 16.10/3.26 % (27060)Termination phase: Saturation
% 16.10/3.26
% 16.10/3.26 % (27060)Memory used [KB]: 9594
% 16.10/3.26 % (27060)Time elapsed: 1.326 s
% 16.10/3.26 % (27060)Instructions burned: 4436 (million)
% 16.10/3.26 % (27060)------------------------------
% 16.10/3.26 % (27060)------------------------------
% 16.10/3.27 % (27093)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_26636 for (2978ds/865Mi)
% 16.50/3.34 % (27092)Instruction limit reached!
% 16.50/3.34 % (27092)------------------------------
% 16.50/3.34 % (27092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.50/3.34 % (27092)Termination reason: Unknown
% 16.50/3.34 % (27092)Termination phase: Saturation
% 16.50/3.34
% 16.50/3.34 % (27092)Memory used [KB]: 7291
% 16.50/3.34 % (27092)Time elapsed: 0.132 s
% 16.50/3.34 % (27092)Instructions burned: 434 (million)
% 16.50/3.34 % (27092)------------------------------
% 16.50/3.34 % (27092)------------------------------
% 16.50/3.35 % (27094)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_26636 for (2977ds/593Mi)
% 16.50/3.36 % (27065)Refutation not found, non-redundant clauses discarded% (27065)------------------------------
% 16.50/3.36 % (27065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.50/3.36 % (27065)Termination reason: Refutation not found, non-redundant clauses discarded
% 16.50/3.36
% 16.50/3.36 % (27065)Memory used [KB]: 9850
% 16.50/3.36 % (27065)Time elapsed: 1.258 s
% 16.50/3.36 % (27065)Instructions burned: 4140 (million)
% 16.50/3.36 % (27065)------------------------------
% 16.50/3.36 % (27065)------------------------------
% 16.50/3.37 % (27095)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_26636 for (2977ds/443Mi)
% 16.92/3.45 % (27091)Instruction limit reached!
% 16.92/3.45 % (27091)------------------------------
% 16.92/3.45 % (27091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.92/3.45 % (27091)Termination reason: Unknown
% 16.92/3.45 % (27091)Termination phase: Saturation
% 16.92/3.45
% 16.92/3.45 % (27091)Memory used [KB]: 12025
% 16.92/3.45 % (27091)Time elapsed: 0.318 s
% 16.92/3.45 % (27091)Instructions burned: 906 (million)
% 16.92/3.45 % (27091)------------------------------
% 16.92/3.45 % (27091)------------------------------
% 16.92/3.46 % (27096)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_26636 for (2976ds/594Mi)
% 16.92/3.46 % (27090)Instruction limit reached!
% 16.92/3.46 % (27090)------------------------------
% 16.92/3.46 % (27090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.92/3.46 % (27090)Termination reason: Unknown
% 16.92/3.46 % (27090)Termination phase: Saturation
% 16.92/3.46
% 16.92/3.46 % (27090)Memory used [KB]: 12920
% 16.92/3.46 % (27090)Time elapsed: 0.419 s
% 16.92/3.46 % (27090)Instructions burned: 1377 (million)
% 16.92/3.46 % (27090)------------------------------
% 16.92/3.46 % (27090)------------------------------
% 16.92/3.47 % (27097)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_26636 for (2976ds/327Mi)
% 17.87/3.50 % (27095)Instruction limit reached!
% 17.87/3.50 % (27095)------------------------------
% 17.87/3.50 % (27095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.87/3.50 % (27095)Termination reason: Unknown
% 17.87/3.50 % (27095)Termination phase: Saturation
% 17.87/3.50
% 17.87/3.50 % (27095)Memory used [KB]: 8187
% 17.87/3.50 % (27095)Time elapsed: 0.128 s
% 17.87/3.50 % (27095)Instructions burned: 444 (million)
% 17.87/3.50 % (27095)------------------------------
% 17.87/3.50 % (27095)------------------------------
% 17.87/3.51 % (27098)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_26636 for (2976ds/5411Mi)
% 17.87/3.53 % (27094)Instruction limit reached!
% 17.87/3.53 % (27094)------------------------------
% 17.87/3.53 % (27094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.87/3.53 % (27094)Termination reason: Unknown
% 17.87/3.53 % (27094)Termination phase: Saturation
% 17.87/3.53
% 17.87/3.53 % (27094)Memory used [KB]: 9466
% 17.87/3.53 % (27094)Time elapsed: 0.175 s
% 17.87/3.53 % (27094)Instructions burned: 594 (million)
% 17.87/3.53 % (27094)------------------------------
% 17.87/3.53 % (27094)------------------------------
% 17.87/3.53 % (27098)Refutation not found, incomplete strategy
% 17.87/3.53 % (27098)------------------------------
% 17.87/3.53 % (27098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.87/3.53 % (27098)Termination reason: Refutation not found, incomplete strategy
% 17.87/3.53
% 17.87/3.53
% 17.87/3.53 % (27098)Memory used [KB]: 6652
% 17.87/3.53 % (27098)Time elapsed: 0.024 s
% 17.87/3.53 % (27098)Instructions burned: 71 (million)
% 17.87/3.53 % (27098)------------------------------
% 17.87/3.53 % (27098)------------------------------
% 17.87/3.53 % (27093)Instruction limit reached!
% 17.87/3.53 % (27093)------------------------------
% 17.87/3.53 % (27093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.87/3.53 % (27093)Termination reason: Unknown
% 17.87/3.53 % (27093)Termination phase: Saturation
% 17.87/3.53
% 17.87/3.53 % (27093)Memory used [KB]: 8187
% 17.87/3.53 % (27093)Time elapsed: 0.263 s
% 17.87/3.53 % (27093)Instructions burned: 865 (million)
% 17.87/3.53 % (27093)------------------------------
% 17.87/3.53 % (27093)------------------------------
% 17.87/3.54 % (27099)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_26636 for (2975ds/1762Mi)
% 17.87/3.54 % (27063)Instruction limit reached!
% 17.87/3.54 % (27063)------------------------------
% 17.87/3.54 % (27063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.87/3.54 % (27063)Termination reason: Unknown
% 17.87/3.54 % (27063)Termination phase: Saturation
% 17.87/3.54
% 17.87/3.54 % (27063)Memory used [KB]: 15351
% 17.87/3.54 % (27063)Time elapsed: 1.564 s
% 17.87/3.54 % (27063)Instructions burned: 5207 (million)
% 17.87/3.54 % (27063)------------------------------
% 17.87/3.54 % (27063)------------------------------
% 17.87/3.54 % (27100)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_26636 for (2975ds/96Mi)
% 17.87/3.54 % (27101)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_26636 for (2975ds/503Mi)
% 17.87/3.55 % (27102)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_26636 for (2975ds/90Mi)
% 17.87/3.57 % (27100)Instruction limit reached!
% 17.87/3.57 % (27100)------------------------------
% 17.87/3.57 % (27100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.87/3.57 % (27100)Termination reason: Unknown
% 17.87/3.57 % (27100)Termination phase: Property scanning
% 17.87/3.57
% 17.87/3.57 % (27100)Memory used [KB]: 2430
% 17.87/3.57 % (27100)Time elapsed: 0.029 s
% 17.87/3.57 % (27100)Instructions burned: 97 (million)
% 17.87/3.57 % (27100)------------------------------
% 17.87/3.57 % (27100)------------------------------
% 17.87/3.57 % (27097)Instruction limit reached!
% 17.87/3.57 % (27097)------------------------------
% 17.87/3.57 % (27097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.87/3.57 % (27097)Termination reason: Unknown
% 17.87/3.57 % (27097)Termination phase: Saturation
% 17.87/3.57
% 17.87/3.57 % (27097)Memory used [KB]: 7675
% 17.87/3.57 % (27097)Time elapsed: 0.103 s
% 17.87/3.57 % (27097)Instructions burned: 327 (million)
% 17.87/3.57 % (27097)------------------------------
% 17.87/3.57 % (27097)------------------------------
% 17.87/3.58 % (27102)Instruction limit reached!
% 17.87/3.58 % (27102)------------------------------
% 17.87/3.58 % (27102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.87/3.58 % (27102)Termination reason: Unknown
% 17.87/3.58 % (27102)Termination phase: Property scanning
% 17.87/3.58
% 17.87/3.58 % (27102)Memory used [KB]: 2302
% 17.87/3.58 % (27102)Time elapsed: 0.029 s
% 17.87/3.58 % (27102)Instructions burned: 92 (million)
% 17.87/3.58 % (27102)------------------------------
% 17.87/3.58 % (27102)------------------------------
% 17.87/3.58 % (27103)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_26636 for (2975ds/593Mi)
% 17.87/3.58 % (27104)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_26636 for (2975ds/1512Mi)
% 17.87/3.59 % (27105)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_26636 for (2975ds/569Mi)
% 18.82/3.63 % (27104)Refutation not found, incomplete strategy
% 18.82/3.63 % (27104)------------------------------
% 18.82/3.63 % (27104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.82/3.63 % (27104)Termination reason: Refutation not found, incomplete strategy
% 18.82/3.63
% 18.82/3.63
% 18.82/3.63 % (27104)Memory used [KB]: 7675
% 18.82/3.63 % (27104)Time elapsed: 0.048 s
% 18.82/3.63 % (27104)Instructions burned: 159 (million)
% 18.82/3.63 % (27104)------------------------------
% 18.82/3.63 % (27104)------------------------------
% 18.82/3.64 % (27106)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_26636 for (2974ds/501Mi)
% 18.82/3.64 % (27096)Instruction limit reached!
% 18.82/3.64 % (27096)------------------------------
% 18.82/3.64 % (27096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.82/3.64 % (27096)Termination reason: Unknown
% 18.82/3.64 % (27096)Termination phase: Saturation
% 18.82/3.64
% 18.82/3.64 % (27096)Memory used [KB]: 7547
% 18.82/3.64 % (27096)Time elapsed: 0.187 s
% 18.82/3.64 % (27096)Instructions burned: 595 (million)
% 18.82/3.64 % (27096)------------------------------
% 18.82/3.64 % (27096)------------------------------
% 18.82/3.65 % (27107)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_26636 for (2974ds/562Mi)
% 19.19/3.70 % (27101)Instruction limit reached!
% 19.19/3.70 % (27101)------------------------------
% 19.19/3.70 % (27101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.19/3.70 % (27101)Termination reason: Unknown
% 19.19/3.70 % (27101)Termination phase: Saturation
% 19.19/3.70
% 19.19/3.70 % (27101)Memory used [KB]: 7547
% 19.19/3.70 % (27101)Time elapsed: 0.154 s
% 19.19/3.70 % (27101)Instructions burned: 505 (million)
% 19.19/3.70 % (27101)------------------------------
% 19.19/3.70 % (27101)------------------------------
% 19.19/3.71 % (27108)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_26636 for (2974ds/406Mi)
% 19.19/3.75 % (27103)Instruction limit reached!
% 19.19/3.75 % (27103)------------------------------
% 19.19/3.75 % (27103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.19/3.75 % (27103)Termination reason: Unknown
% 19.19/3.75 % (27103)Termination phase: Saturation
% 19.19/3.75
% 19.19/3.75 % (27103)Memory used [KB]: 8955
% 19.19/3.75 % (27103)Time elapsed: 0.168 s
% 19.19/3.75 % (27103)Instructions burned: 593 (million)
% 19.19/3.75 % (27103)------------------------------
% 19.19/3.75 % (27103)------------------------------
% 19.19/3.75 % (27105)Instruction limit reached!
% 19.19/3.75 % (27105)------------------------------
% 19.19/3.75 % (27105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.19/3.75 % (27105)Termination reason: Unknown
% 19.19/3.75 % (27105)Termination phase: Saturation
% 19.19/3.75
% 19.19/3.75 % (27105)Memory used [KB]: 8571
% 19.19/3.75 % (27105)Time elapsed: 0.170 s
% 19.19/3.75 % (27105)Instructions burned: 570 (million)
% 19.19/3.75 % (27105)------------------------------
% 19.19/3.75 % (27105)------------------------------
% 19.19/3.76 % (27109)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_26636 for (2973ds/582Mi)
% 19.19/3.76 % (27110)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_26636 for (2973ds/456Mi)
% 19.19/3.79 % (27106)Instruction limit reached!
% 19.19/3.79 % (27106)------------------------------
% 19.19/3.79 % (27106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.19/3.79 % (27106)Termination reason: Unknown
% 19.19/3.79 % (27106)Termination phase: Saturation
% 19.19/3.79
% 19.19/3.79 % (27106)Memory used [KB]: 8571
% 19.19/3.79 % (27106)Time elapsed: 0.153 s
% 19.19/3.79 % (27106)Instructions burned: 503 (million)
% 19.19/3.79 % (27106)------------------------------
% 19.19/3.79 % (27106)------------------------------
% 19.95/3.80 % (27111)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_26636 for (2973ds/393Mi)
% 19.95/3.83 % (27107)Instruction limit reached!
% 19.95/3.83 % (27107)------------------------------
% 19.95/3.83 % (27107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.95/3.83 % (27107)Termination reason: Unknown
% 19.95/3.83 % (27107)Termination phase: Saturation
% 19.95/3.83
% 19.95/3.83 % (27107)Memory used [KB]: 7675
% 19.95/3.83 % (27107)Time elapsed: 0.175 s
% 19.95/3.83 % (27107)Instructions burned: 562 (million)
% 19.95/3.83 % (27107)------------------------------
% 19.95/3.83 % (27107)------------------------------
% 19.95/3.83 % (27108)Instruction limit reached!
% 19.95/3.83 % (27108)------------------------------
% 19.95/3.83 % (27108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.95/3.83 % (27108)Termination reason: Unknown
% 19.95/3.83 % (27108)Termination phase: Saturation
% 19.95/3.83
% 19.95/3.83 % (27108)Memory used [KB]: 8315
% 19.95/3.83 % (27108)Time elapsed: 0.128 s
% 19.95/3.83 % (27108)Instructions burned: 408 (million)
% 19.95/3.83 % (27108)------------------------------
% 19.95/3.83 % (27108)------------------------------
% 19.95/3.84 % (27112)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_26636 for (2972ds/1335Mi)
% 19.95/3.84 % (27113)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_26636 for (2972ds/3373Mi)
% 20.38/3.91 % (27110)Instruction limit reached!
% 20.38/3.91 % (27110)------------------------------
% 20.38/3.91 % (27110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.38/3.91 % (27110)Termination reason: Unknown
% 20.38/3.91 % (27110)Termination phase: Saturation
% 20.38/3.91
% 20.38/3.91 % (27110)Memory used [KB]: 7419
% 20.38/3.91 % (27110)Time elapsed: 0.143 s
% 20.38/3.91 % (27110)Instructions burned: 457 (million)
% 20.38/3.91 % (27110)------------------------------
% 20.38/3.91 % (27110)------------------------------
% 20.38/3.91 % (27111)Instruction limit reached!
% 20.38/3.91 % (27111)------------------------------
% 20.38/3.91 % (27111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.38/3.91 % (27111)Termination reason: Unknown
% 20.38/3.91 % (27111)Termination phase: Saturation
% 20.38/3.91
% 20.38/3.91 % (27111)Memory used [KB]: 7675
% 20.38/3.91 % (27111)Time elapsed: 0.109 s
% 20.38/3.91 % (27111)Instructions burned: 393 (million)
% 20.38/3.91 % (27111)------------------------------
% 20.38/3.91 % (27111)------------------------------
% 20.38/3.92 % (27114)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_26636 for (2972ds/474Mi)
% 20.38/3.92 % (27109)Instruction limit reached!
% 20.38/3.92 % (27109)------------------------------
% 20.38/3.92 % (27109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.38/3.92 % (27109)Termination reason: Unknown
% 20.38/3.92 % (27109)Termination phase: Saturation
% 20.38/3.92
% 20.38/3.92 % (27109)Memory used [KB]: 8827
% 20.38/3.92 % (27109)Time elapsed: 0.162 s
% 20.38/3.92 % (27109)Instructions burned: 582 (million)
% 20.38/3.92 % (27109)------------------------------
% 20.38/3.92 % (27109)------------------------------
% 20.38/3.92 % (27115)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_26636 for (2972ds/157Mi)
% 20.38/3.93 % (27116)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_26636 for (2972ds/590Mi)
% 20.38/3.97 % (27115)Instruction limit reached!
% 20.38/3.97 % (27115)------------------------------
% 20.38/3.97 % (27115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.38/3.97 % (27115)Termination reason: Unknown
% 20.38/3.97 % (27115)Termination phase: Saturation
% 20.38/3.97
% 20.38/3.97 % (27115)Memory used [KB]: 7164
% 20.38/3.97 % (27115)Time elapsed: 0.047 s
% 20.38/3.97 % (27115)Instructions burned: 159 (million)
% 20.38/3.97 % (27115)------------------------------
% 20.38/3.97 % (27115)------------------------------
% 20.38/3.98 % (27117)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_26636 for (2971ds/104Mi)
% 20.38/4.01 % (27117)Instruction limit reached!
% 20.38/4.01 % (27117)------------------------------
% 20.38/4.01 % (27117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.38/4.01 % (27117)Termination reason: Unknown
% 20.38/4.01 % (27117)Termination phase: Property scanning
% 20.38/4.01
% 20.38/4.01 % (27117)Memory used [KB]: 2302
% 20.38/4.01 % (27117)Time elapsed: 0.031 s
% 20.38/4.01 % (27117)Instructions burned: 108 (million)
% 20.38/4.01 % (27117)------------------------------
% 20.38/4.01 % (27117)------------------------------
% 22.05/4.02 % (27118)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_26636 for (2971ds/414Mi)
% 22.05/4.06 % (27099)Instruction limit reached!
% 22.05/4.06 % (27099)------------------------------
% 22.05/4.06 % (27099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.05/4.06 % (27099)Termination reason: Unknown
% 22.05/4.06 % (27099)Termination phase: Saturation
% 22.05/4.06
% 22.05/4.06 % (27099)Memory used [KB]: 8955
% 22.05/4.06 % (27099)Time elapsed: 0.529 s
% 22.05/4.06 % (27099)Instructions burned: 1764 (million)
% 22.05/4.06 % (27099)------------------------------
% 22.05/4.06 % (27099)------------------------------
% 22.05/4.06 % (27114)Instruction limit reached!
% 22.05/4.06 % (27114)------------------------------
% 22.05/4.06 % (27114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.05/4.06 % (27114)Termination reason: Unknown
% 22.05/4.06 % (27114)Termination phase: Saturation
% 22.05/4.06
% 22.05/4.06 % (27114)Memory used [KB]: 7547
% 22.05/4.06 % (27114)Time elapsed: 0.149 s
% 22.05/4.06 % (27114)Instructions burned: 474 (million)
% 22.05/4.06 % (27114)------------------------------
% 22.05/4.06 % (27114)------------------------------
% 22.05/4.07 % (27119)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_26636 for (2970ds/715Mi)
% 22.05/4.07 % (27120)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_26636 for (2970ds/961Mi)
% 22.05/4.10 % (27116)Instruction limit reached!
% 22.05/4.10 % (27116)------------------------------
% 22.05/4.10 % (27116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.05/4.10 % (27116)Termination reason: Unknown
% 22.05/4.10 % (27116)Termination phase: Saturation
% 22.05/4.10
% 22.05/4.10 % (27116)Memory used [KB]: 7803
% 22.05/4.10 % (27116)Time elapsed: 0.172 s
% 22.05/4.10 % (27116)Instructions burned: 592 (million)
% 22.05/4.10 % (27116)------------------------------
% 22.05/4.10 % (27116)------------------------------
% 22.05/4.11 % (27121)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_26636 for (2970ds/1213Mi)
% 22.55/4.14 % (27118)Instruction limit reached!
% 22.55/4.14 % (27118)------------------------------
% 22.55/4.14 % (27118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.55/4.14 % (27118)Termination reason: Unknown
% 22.55/4.14 % (27118)Termination phase: Saturation
% 22.55/4.14
% 22.55/4.14 % (27118)Memory used [KB]: 8443
% 22.55/4.14 % (27118)Time elapsed: 0.125 s
% 22.55/4.14 % (27118)Instructions burned: 414 (million)
% 22.55/4.14 % (27118)------------------------------
% 22.55/4.14 % (27118)------------------------------
% 22.55/4.15 % (27122)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_26636 for (2969ds/1979Mi)
% 22.94/4.24 % (27112)Instruction limit reached!
% 22.94/4.24 % (27112)------------------------------
% 22.94/4.24 % (27112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.94/4.24 % (27112)Termination reason: Unknown
% 22.94/4.24 % (27112)Termination phase: Saturation
% 22.94/4.24
% 22.94/4.24 % (27112)Memory used [KB]: 7803
% 22.94/4.24 % (27112)Time elapsed: 0.408 s
% 22.94/4.24 % (27112)Instructions burned: 1337 (million)
% 22.94/4.24 % (27112)------------------------------
% 22.94/4.24 % (27112)------------------------------
% 22.94/4.25 % (27123)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_26636 for (2968ds/481Mi)
% 22.94/4.28 % (27119)Instruction limit reached!
% 22.94/4.28 % (27119)------------------------------
% 22.94/4.28 % (27119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.94/4.28 % (27119)Termination reason: Unknown
% 22.94/4.28 % (27119)Termination phase: Saturation
% 22.94/4.28
% 22.94/4.28 % (27119)Memory used [KB]: 5117
% 22.94/4.28 % (27119)Time elapsed: 0.206 s
% 22.94/4.28 % (27119)Instructions burned: 715 (million)
% 22.94/4.28 % (27119)------------------------------
% 22.94/4.28 % (27119)------------------------------
% 22.94/4.29 % (27124)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_26636 for (2968ds/783Mi)
% 23.41/4.36 % (27120)Instruction limit reached!
% 23.41/4.36 % (27120)------------------------------
% 23.41/4.36 % (27120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.41/4.36 % (27120)Termination reason: Unknown
% 23.41/4.36 % (27120)Termination phase: Saturation
% 23.41/4.36
% 23.41/4.36 % (27120)Memory used [KB]: 9083
% 23.41/4.36 % (27120)Time elapsed: 0.286 s
% 23.41/4.36 % (27120)Instructions burned: 962 (million)
% 23.41/4.36 % (27120)------------------------------
% 23.41/4.36 % (27120)------------------------------
% 23.41/4.37 % (27125)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_26636 for (2967ds/432Mi)
% 23.91/4.40 % (27123)Instruction limit reached!
% 23.91/4.40 % (27123)------------------------------
% 23.91/4.40 % (27123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.91/4.40 % (27123)Termination reason: Unknown
% 23.91/4.40 % (27123)Termination phase: Saturation
% 23.91/4.40
% 23.91/4.40 % (27123)Memory used [KB]: 7547
% 23.91/4.40 % (27123)Time elapsed: 0.150 s
% 23.91/4.40 % (27123)Instructions burned: 482 (million)
% 23.91/4.40 % (27123)------------------------------
% 23.91/4.40 % (27123)------------------------------
% 23.91/4.41 % (27126)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_26636 for (2967ds/1670Mi)
% 23.91/4.49 % (27121)Instruction limit reached!
% 23.91/4.49 % (27121)------------------------------
% 23.91/4.49 % (27121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.91/4.49 % (27121)Termination reason: Unknown
% 23.91/4.49 % (27121)Termination phase: Saturation
% 23.91/4.49
% 23.91/4.49 % (27121)Memory used [KB]: 8571
% 23.91/4.49 % (27121)Time elapsed: 0.379 s
% 23.91/4.49 % (27121)Instructions burned: 1214 (million)
% 23.91/4.49 % (27121)------------------------------
% 23.91/4.49 % (27121)------------------------------
% 24.65/4.50 % (27127)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_26636 for (2966ds/90Mi)
% 24.65/4.50 % (27125)Instruction limit reached!
% 24.65/4.50 % (27125)------------------------------
% 24.65/4.50 % (27125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.65/4.50 % (27125)Termination reason: Unknown
% 24.65/4.50 % (27125)Termination phase: Saturation
% 24.65/4.50
% 24.65/4.50 % (27125)Memory used [KB]: 7419
% 24.65/4.50 % (27125)Time elapsed: 0.132 s
% 24.65/4.50 % (27125)Instructions burned: 432 (million)
% 24.65/4.50 % (27125)------------------------------
% 24.65/4.50 % (27125)------------------------------
% 24.65/4.51 % (27128)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_26636 for (2966ds/346Mi)
% 24.65/4.52 % (27124)Instruction limit reached!
% 24.65/4.52 % (27124)------------------------------
% 24.65/4.52 % (27124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.65/4.52 % (27124)Termination reason: Unknown
% 24.65/4.52 % (27124)Termination phase: Saturation
% 24.65/4.52
% 24.65/4.52 % (27124)Memory used [KB]: 7931
% 24.65/4.52 % (27124)Time elapsed: 0.236 s
% 24.65/4.52 % (27124)Instructions burned: 783 (million)
% 24.65/4.52 % (27124)------------------------------
% 24.65/4.52 % (27124)------------------------------
% 24.65/4.52 % (27127)Instruction limit reached!
% 24.65/4.52 % (27127)------------------------------
% 24.65/4.52 % (27127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.65/4.52 % (27127)Termination reason: Unknown
% 24.65/4.52 % (27127)Termination phase: Property scanning
% 24.65/4.52
% 24.65/4.52 % (27127)Memory used [KB]: 2302
% 24.65/4.52 % (27127)Time elapsed: 0.028 s
% 24.65/4.52 % (27127)Instructions burned: 92 (million)
% 24.65/4.52 % (27127)------------------------------
% 24.65/4.52 % (27127)------------------------------
% 24.65/4.53 % (27129)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_26636 for (2965ds/401Mi)
% 24.65/4.53 % (27130)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_26636 for (2965ds/6454Mi)
% 25.29/4.61 % (27128)Instruction limit reached!
% 25.29/4.61 % (27128)------------------------------
% 25.29/4.61 % (27128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.29/4.61 % (27128)Termination reason: Unknown
% 25.29/4.61 % (27128)Termination phase: Saturation
% 25.29/4.61
% 25.29/4.61 % (27128)Memory used [KB]: 7419
% 25.29/4.61 % (27128)Time elapsed: 0.106 s
% 25.29/4.61 % (27128)Instructions burned: 348 (million)
% 25.29/4.61 % (27128)------------------------------
% 25.29/4.61 % (27128)------------------------------
% 25.29/4.62 % (27131)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_26636 for (2965ds/283Mi)
% 25.29/4.65 % (27129)Instruction limit reached!
% 25.29/4.65 % (27129)------------------------------
% 25.29/4.65 % (27129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.29/4.65 % (27129)Termination reason: Unknown
% 25.29/4.65 % (27129)Termination phase: Saturation
% 25.29/4.65
% 25.29/4.65 % (27129)Memory used [KB]: 9210
% 25.29/4.65 % (27129)Time elapsed: 0.116 s
% 25.29/4.65 % (27129)Instructions burned: 403 (million)
% 25.29/4.65 % (27129)------------------------------
% 25.29/4.65 % (27129)------------------------------
% 25.29/4.66 % (27132)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_26636 for (2964ds/865Mi)
% 25.72/4.70 % (27131)Instruction limit reached!
% 25.72/4.70 % (27131)------------------------------
% 25.72/4.70 % (27131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.72/4.70 % (27131)Termination reason: Unknown
% 25.72/4.70 % (27131)Termination phase: Saturation
% 25.72/4.70
% 25.72/4.70 % (27131)Memory used [KB]: 7803
% 25.72/4.70 % (27131)Time elapsed: 0.078 s
% 25.72/4.70 % (27131)Instructions burned: 283 (million)
% 25.72/4.70 % (27131)------------------------------
% 25.72/4.70 % (27131)------------------------------
% 25.72/4.71 % (27133)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_26636 for (2964ds/4528Mi)
% 25.72/4.73 % (27133)Refutation not found, incomplete strategy
% 25.72/4.73 % (27133)------------------------------
% 25.72/4.73 % (27133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.72/4.73 % (27133)Termination reason: Refutation not found, incomplete strategy
% 25.72/4.73
% 25.72/4.73
% 25.72/4.73 % (27133)Memory used [KB]: 2046
% 25.72/4.73 % (27133)Time elapsed: 0.017 s
% 25.72/4.73 % (27133)Instructions burned: 52 (million)
% 25.72/4.73 % (27133)------------------------------
% 25.72/4.73 % (27133)------------------------------
% 25.72/4.74 % (27134)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_26636 for (2963ds/1001Mi)
% 25.72/4.74 % (27122)Instruction limit reached!
% 25.72/4.74 % (27122)------------------------------
% 25.72/4.74 % (27122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.72/4.74 % (27122)Termination reason: Unknown
% 25.72/4.74 % (27122)Termination phase: Saturation
% 25.72/4.74
% 25.72/4.74 % (27122)Memory used [KB]: 10490
% 25.72/4.74 % (27122)Time elapsed: 0.593 s
% 25.72/4.74 % (27122)Instructions burned: 1979 (million)
% 25.72/4.74 % (27122)------------------------------
% 25.72/4.74 % (27122)------------------------------
% 25.72/4.75 % (27135)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_26636 for (2963ds/102Mi)
% 25.72/4.78 % (27135)Instruction limit reached!
% 25.72/4.78 % (27135)------------------------------
% 25.72/4.78 % (27135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.72/4.78 % (27135)Termination reason: Unknown
% 25.72/4.78 % (27135)Termination phase: Property scanning
% 25.72/4.78
% 25.72/4.78 % (27135)Memory used [KB]: 2430
% 25.72/4.78 % (27135)Time elapsed: 0.029 s
% 25.72/4.78 % (27135)Instructions burned: 104 (million)
% 25.72/4.78 % (27135)------------------------------
% 25.72/4.78 % (27135)------------------------------
% 25.72/4.79 % (27136)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_26636 for (2963ds/952Mi)
% 26.67/4.89 % (27113)Instruction limit reached!
% 26.67/4.89 % (27113)------------------------------
% 26.67/4.89 % (27113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.67/4.89 % (27113)Termination reason: Unknown
% 26.67/4.89 % (27113)Termination phase: Saturation
% 26.67/4.89
% 26.67/4.89 % (27113)Memory used [KB]: 12281
% 26.67/4.89 % (27113)Time elapsed: 1.044 s
% 26.67/4.89 % (27113)Instructions burned: 3373 (million)
% 26.67/4.89 % (27113)------------------------------
% 26.67/4.89 % (27113)------------------------------
% 26.86/4.90 % (27137)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_26636 for (2962ds/578Mi)
% 26.86/4.91 % (27126)Instruction limit reached!
% 26.86/4.91 % (27126)------------------------------
% 26.86/4.91 % (27126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.86/4.91 % (27126)Termination reason: Unknown
% 26.86/4.91 % (27126)Termination phase: Saturation
% 26.86/4.91
% 26.86/4.91 % (27126)Memory used [KB]: 10234
% 26.86/4.91 % (27126)Time elapsed: 0.499 s
% 26.86/4.91 % (27126)Instructions burned: 1672 (million)
% 26.86/4.91 % (27126)------------------------------
% 26.86/4.91 % (27126)------------------------------
% 26.86/4.92 % (27132)Instruction limit reached!
% 26.86/4.92 % (27132)------------------------------
% 26.86/4.92 % (27132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.86/4.92 % (27132)Termination reason: Unknown
% 26.86/4.92 % (27132)Termination phase: Saturation
% 26.86/4.92
% 26.86/4.92 % (27132)Memory used [KB]: 10874
% 26.86/4.92 % (27132)Time elapsed: 0.262 s
% 26.86/4.92 % (27132)Instructions burned: 866 (million)
% 26.86/4.92 % (27132)------------------------------
% 26.86/4.92 % (27132)------------------------------
% 26.86/4.92 % (27138)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_26636 for (2962ds/643Mi)
% 26.86/4.93 % (27139)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_26636 for (2962ds/865Mi)
% 26.86/4.99 % (27134)Instruction limit reached!
% 26.86/4.99 % (27134)------------------------------
% 26.86/4.99 % (27134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.86/4.99 % (27134)Termination reason: Unknown
% 26.86/4.99 % (27134)Termination phase: Saturation
% 26.86/4.99
% 26.86/4.99 % (27134)Memory used [KB]: 9083
% 26.86/4.99 % (27134)Time elapsed: 0.255 s
% 26.86/4.99 % (27134)Instructions burned: 1005 (million)
% 26.86/4.99 % (27134)------------------------------
% 26.86/4.99 % (27134)------------------------------
% 26.86/5.00 % (27140)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_26636 for (2961ds/1174Mi)
% 29.02/5.06 % (27136)Instruction limit reached!
% 29.02/5.06 % (27136)------------------------------
% 29.02/5.06 % (27136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.02/5.06 % (27136)Termination reason: Unknown
% 29.02/5.06 % (27136)Termination phase: Saturation
% 29.02/5.06
% 29.02/5.06 % (27136)Memory used [KB]: 10106
% 29.02/5.06 % (27136)Time elapsed: 0.269 s
% 29.02/5.06 % (27136)Instructions burned: 954 (million)
% 29.02/5.06 % (27136)------------------------------
% 29.02/5.06 % (27136)------------------------------
% 29.02/5.07 % (27137)Instruction limit reached!
% 29.02/5.07 % (27137)------------------------------
% 29.02/5.07 % (27137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.02/5.07 % (27137)Termination reason: Unknown
% 29.02/5.07 % (27137)Termination phase: Saturation
% 29.02/5.07
% 29.02/5.07 % (27137)Memory used [KB]: 8699
% 29.02/5.07 % (27137)Time elapsed: 0.170 s
% 29.02/5.07 % (27137)Instructions burned: 578 (million)
% 29.02/5.07 % (27137)------------------------------
% 29.02/5.07 % (27137)------------------------------
% 29.02/5.07 % (27141)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_26636 for (2960ds/644Mi)
% 29.02/5.08 % (27142)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_26636 for (2960ds/1201Mi)
% 29.64/5.11 % (27138)Instruction limit reached!
% 29.64/5.11 % (27138)------------------------------
% 29.64/5.11 % (27138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.64/5.11 % (27138)Termination reason: Unknown
% 29.64/5.11 % (27138)Termination phase: Saturation
% 29.64/5.11
% 29.64/5.11 % (27138)Memory used [KB]: 9338
% 29.64/5.11 % (27138)Time elapsed: 0.195 s
% 29.64/5.11 % (27138)Instructions burned: 645 (million)
% 29.64/5.11 % (27138)------------------------------
% 29.64/5.11 % (27138)------------------------------
% 29.64/5.12 % (27143)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_26636 for (2960ds/1046Mi)
% 29.64/5.16 % (27139)Refutation not found, non-redundant clauses discarded% (27139)------------------------------
% 29.64/5.16 % (27139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.64/5.16 % (27139)Termination reason: Refutation not found, non-redundant clauses discarded
% 29.64/5.16
% 29.64/5.16 % (27139)Memory used [KB]: 8443
% 29.64/5.16 % (27139)Time elapsed: 0.235 s
% 29.64/5.16 % (27139)Instructions burned: 769 (million)
% 29.64/5.16 % (27139)------------------------------
% 29.64/5.16 % (27139)------------------------------
% 29.64/5.17 % (27144)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_26636 for (2959ds/222Mi)
% 29.97/5.23 % (27144)Instruction limit reached!
% 29.97/5.23 % (27144)------------------------------
% 29.97/5.23 % (27144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.97/5.23 % (27144)Termination reason: Unknown
% 29.97/5.23 % (27144)Termination phase: Saturation
% 29.97/5.23
% 29.97/5.23 % (27144)Memory used [KB]: 7547
% 29.97/5.23 % (27144)Time elapsed: 0.063 s
% 29.97/5.23 % (27144)Instructions burned: 223 (million)
% 29.97/5.23 % (27144)------------------------------
% 29.97/5.23 % (27144)------------------------------
% 29.97/5.24 % (27145)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_26636 for (2958ds/68Mi)
% 29.97/5.26 % (27141)Instruction limit reached!
% 29.97/5.26 % (27141)------------------------------
% 29.97/5.26 % (27141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.97/5.26 % (27141)Termination reason: Unknown
% 29.97/5.26 % (27141)Termination phase: Saturation
% 29.97/5.26
% 29.97/5.26 % (27141)Memory used [KB]: 9850
% 29.97/5.26 % (27141)Time elapsed: 0.199 s
% 29.97/5.26 % (27141)Instructions burned: 645 (million)
% 29.97/5.26 % (27141)------------------------------
% 29.97/5.26 % (27141)------------------------------
% 29.97/5.26 % (27145)Instruction limit reached!
% 29.97/5.26 % (27145)------------------------------
% 29.97/5.26 % (27145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.97/5.26 % (27145)Termination reason: Unknown
% 29.97/5.27 % (27145)Termination phase: Property scanning
% 29.97/5.27
% 29.97/5.27 % (27145)Memory used [KB]: 2174
% 29.97/5.27 % (27145)Time elapsed: 0.023 s
% 29.97/5.27 % (27145)Instructions burned: 69 (million)
% 29.97/5.27 % (27145)------------------------------
% 29.97/5.27 % (27145)------------------------------
% 29.97/5.27 % (27146)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_26636 for (2958ds/454Mi)
% 29.97/5.27 % (27147)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_26636 for (2958ds/360Mi)
% 30.59/5.33 % (27086)Instruction limit reached!
% 30.59/5.33 % (27086)------------------------------
% 30.59/5.33 % (27086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.59/5.33 % (27086)Termination reason: Unknown
% 30.59/5.33 % (27086)Termination phase: Saturation
% 30.59/5.33
% 30.59/5.33 % (27086)Memory used [KB]: 14967
% 30.59/5.33 % (27086)Time elapsed: 2.598 s
% 30.59/5.33 % (27086)Instructions burned: 8252 (million)
% 30.59/5.33 % (27086)------------------------------
% 30.59/5.33 % (27086)------------------------------
% 30.59/5.34 % (27148)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_26636 for (2957ds/157Mi)
% 30.59/5.36 % (27140)Instruction limit reached!
% 30.59/5.36 % (27140)------------------------------
% 30.59/5.36 % (27140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.59/5.36 % (27140)Termination reason: Unknown
% 30.59/5.36 % (27140)Termination phase: Saturation
% 30.59/5.36
% 30.59/5.36 % (27140)Memory used [KB]: 9978
% 30.59/5.36 % (27140)Time elapsed: 0.362 s
% 30.59/5.36 % (27140)Instructions burned: 1174 (million)
% 30.59/5.36 % (27140)------------------------------
% 30.59/5.36 % (27140)------------------------------
% 30.59/5.37 % (27149)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_26636 for (2957ds/5061Mi)
% 30.59/5.38 % (27147)Instruction limit reached!
% 30.59/5.38 % (27147)------------------------------
% 30.59/5.38 % (27147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.59/5.38 % (27147)Termination reason: Unknown
% 30.59/5.38 % (27147)Termination phase: Saturation
% 30.59/5.38
% 30.59/5.38 % (27147)Memory used [KB]: 8955
% 30.59/5.38 % (27147)Time elapsed: 0.102 s
% 30.59/5.38 % (27147)Instructions burned: 363 (million)
% 30.59/5.38 % (27147)------------------------------
% 30.59/5.38 % (27147)------------------------------
% 30.59/5.38 % (27148)Instruction limit reached!
% 30.59/5.38 % (27148)------------------------------
% 30.59/5.38 % (27148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.59/5.38 % (27148)Termination reason: Unknown
% 30.59/5.38 % (27148)Termination phase: Saturation
% 30.59/5.38
% 30.59/5.38 % (27148)Memory used [KB]: 7164
% 30.59/5.38 % (27148)Time elapsed: 0.044 s
% 30.59/5.38 % (27148)Instructions burned: 158 (million)
% 30.59/5.38 % (27148)------------------------------
% 30.59/5.38 % (27148)------------------------------
% 30.59/5.38 % (27150)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_26636 for (2957ds/2401Mi)
% 30.59/5.39 % (27151)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_26636 for (2957ds/5798Mi)
% 30.98/5.41 % (27146)Instruction limit reached!
% 30.98/5.41 % (27146)------------------------------
% 30.98/5.41 % (27146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.98/5.41 % (27146)Termination reason: Unknown
% 30.98/5.41 % (27146)Termination phase: Saturation
% 30.98/5.41
% 30.98/5.41 % (27146)Memory used [KB]: 13176
% 30.98/5.41 % (27146)Time elapsed: 0.133 s
% 30.98/5.41 % (27146)Instructions burned: 455 (million)
% 30.98/5.41 % (27146)------------------------------
% 30.98/5.41 % (27146)------------------------------
% 30.98/5.42 % (27152)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_26636 for (2956ds/346Mi)
% 30.98/5.42 % (27142)Instruction limit reached!
% 30.98/5.42 % (27142)------------------------------
% 30.98/5.42 % (27142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.98/5.42 % (27142)Termination reason: Unknown
% 30.98/5.42 % (27142)Termination phase: Saturation
% 30.98/5.42
% 30.98/5.42 % (27142)Memory used [KB]: 8699
% 30.98/5.42 % (27142)Time elapsed: 0.344 s
% 30.98/5.42 % (27142)Instructions burned: 1204 (million)
% 30.98/5.42 % (27142)------------------------------
% 30.98/5.42 % (27142)------------------------------
% 30.98/5.43 % (27153)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_26636 for (2956ds/1321Mi)
% 30.98/5.43 % (27143)Instruction limit reached!
% 30.98/5.43 % (27143)------------------------------
% 30.98/5.43 % (27143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.98/5.43 % (27143)Termination reason: Unknown
% 30.98/5.43 % (27143)Termination phase: Saturation
% 30.98/5.43
% 30.98/5.43 % (27143)Memory used [KB]: 9210
% 30.98/5.43 % (27143)Time elapsed: 0.307 s
% 30.98/5.43 % (27143)Instructions burned: 1047 (million)
% 30.98/5.43 % (27143)------------------------------
% 30.98/5.43 % (27143)------------------------------
% 30.98/5.44 % (27154)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_26636 for (2956ds/1312Mi)
% 31.88/5.52 % (27152)Instruction limit reached!
% 31.88/5.52 % (27152)------------------------------
% 31.88/5.52 % (27152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.88/5.52 % (27152)Termination reason: Unknown
% 31.88/5.52 % (27152)Termination phase: Saturation
% 31.88/5.52
% 31.88/5.52 % (27152)Memory used [KB]: 7419
% 31.88/5.52 % (27152)Time elapsed: 0.105 s
% 31.88/5.52 % (27152)Instructions burned: 347 (million)
% 31.88/5.52 % (27152)------------------------------
% 31.88/5.52 % (27152)------------------------------
% 31.88/5.53 % (27155)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_26636 for (2955ds/672Mi)
% 32.19/5.74 % (27155)Instruction limit reached!
% 32.19/5.74 % (27155)------------------------------
% 32.19/5.74 % (27155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.19/5.74 % (27155)Termination reason: Unknown
% 32.19/5.74 % (27155)Termination phase: Saturation
% 32.19/5.74
% 32.19/5.74 % (27155)Memory used [KB]: 7675
% 32.19/5.74 % (27155)Time elapsed: 0.211 s
% 32.19/5.74 % (27155)Instructions burned: 673 (million)
% 32.19/5.74 % (27155)------------------------------
% 32.19/5.74 % (27155)------------------------------
% 32.19/5.75 % (27156)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_26636 for (2953ds/1897Mi)
% 32.52/5.82 % (27153)Instruction limit reached!
% 32.52/5.82 % (27153)------------------------------
% 32.52/5.82 % (27153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.52/5.82 % (27153)Termination reason: Unknown
% 32.52/5.82 % (27153)Termination phase: Saturation
% 32.52/5.82
% 32.52/5.82 % (27153)Memory used [KB]: 5245
% 32.52/5.82 % (27153)Time elapsed: 0.396 s
% 32.52/5.82 % (27153)Instructions burned: 1321 (million)
% 32.52/5.82 % (27153)------------------------------
% 32.52/5.82 % (27153)------------------------------
% 32.52/5.82 % (27154)Instruction limit reached!
% 32.52/5.82 % (27154)------------------------------
% 32.52/5.82 % (27154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.52/5.82 % (27154)Termination reason: Unknown
% 32.52/5.82 % (27154)Termination phase: Saturation
% 32.52/5.82
% 32.52/5.82 % (27154)Memory used [KB]: 9083
% 32.52/5.82 % (27154)Time elapsed: 0.385 s
% 32.52/5.82 % (27154)Instructions burned: 1314 (million)
% 32.52/5.82 % (27154)------------------------------
% 32.52/5.82 % (27154)------------------------------
% 32.52/5.83 % (27157)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_26636 for (2952ds/1202Mi)
% 32.52/5.83 % (27158)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_26636 for (2952ds/1493Mi)
% 32.52/5.87 % (27158)Refutation not found, incomplete strategy
% 32.52/5.87 % (27158)------------------------------
% 32.52/5.87 % (27158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.52/5.87 % (27158)Termination reason: Refutation not found, incomplete strategy
% 32.52/5.87
% 32.52/5.87
% 32.52/5.87 % (27158)Memory used [KB]: 6908
% 32.52/5.87 % (27158)Time elapsed: 0.033 s
% 32.52/5.87 % (27158)Instructions burned: 120 (million)
% 32.52/5.87 % (27158)------------------------------
% 32.52/5.87 % (27158)------------------------------
% 32.52/5.88 % (27159)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_26636 for (2952ds/7679Mi)
% 36.03/6.09 % (27150)Instruction limit reached!
% 36.03/6.09 % (27150)------------------------------
% 36.03/6.09 % (27150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.03/6.09 % (27150)Termination reason: Unknown
% 36.03/6.09 % (27150)Termination phase: Saturation
% 36.03/6.09
% 36.03/6.09 % (27150)Memory used [KB]: 7419
% 36.03/6.09 % (27150)Time elapsed: 0.710 s
% 36.03/6.09 % (27150)Instructions burned: 2401 (million)
% 36.03/6.09 % (27150)------------------------------
% 36.03/6.09 % (27150)------------------------------
% 36.03/6.10 % (27160)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_26636 for (2950ds/340Mi)
% 37.24/6.20 % (27160)Instruction limit reached!
% 37.24/6.20 % (27160)------------------------------
% 37.24/6.20 % (27160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.24/6.20 % (27160)Termination reason: Unknown
% 37.24/6.20 % (27160)Termination phase: Saturation
% 37.24/6.20
% 37.24/6.20 % (27160)Memory used [KB]: 7291
% 37.24/6.20 % (27160)Time elapsed: 0.097 s
% 37.24/6.20 % (27160)Instructions burned: 341 (million)
% 37.24/6.20 % (27160)------------------------------
% 37.24/6.20 % (27160)------------------------------
% 37.24/6.21 % (27157)Instruction limit reached!
% 37.24/6.21 % (27157)------------------------------
% 37.24/6.21 % (27157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.24/6.21 % (27157)Termination reason: Unknown
% 37.24/6.21 % (27157)Termination phase: Saturation
% 37.24/6.21
% 37.24/6.21 % (27157)Memory used [KB]: 4477
% 37.24/6.21 % (27157)Time elapsed: 0.374 s
% 37.24/6.21 % (27157)Instructions burned: 1203 (million)
% 37.24/6.21 % (27157)------------------------------
% 37.24/6.21 % (27157)------------------------------
% 37.24/6.21 % (27161)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_26636 for (2949ds/3672Mi)
% 37.24/6.22 % (27162)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_26636 for (2949ds/1535Mi)
% 37.86/6.35 % (27156)Instruction limit reached!
% 37.86/6.35 % (27156)------------------------------
% 37.86/6.35 % (27156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.86/6.35 % (27156)Termination reason: Unknown
% 37.86/6.35 % (27156)Termination phase: Saturation
% 37.86/6.35
% 37.86/6.35 % (27156)Memory used [KB]: 9466
% 37.86/6.35 % (27156)Time elapsed: 0.599 s
% 37.86/6.35 % (27156)Instructions burned: 1897 (million)
% 37.86/6.35 % (27156)------------------------------
% 37.86/6.35 % (27156)------------------------------
% 37.86/6.36 % (27163)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_26636 for (2947ds/4637Mi)
% 38.32/6.48 % (27130)Instruction limit reached!
% 38.32/6.48 % (27130)------------------------------
% 38.32/6.48 % (27130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.32/6.48 % (27130)Termination reason: Unknown
% 38.32/6.48 % (27130)Termination phase: Saturation
% 38.32/6.48
% 38.32/6.48 % (27130)Memory used [KB]: 10874
% 38.32/6.48 % (27130)Time elapsed: 1.953 s
% 38.32/6.48 % (27130)Instructions burned: 6455 (million)
% 38.32/6.48 % (27130)------------------------------
% 38.32/6.48 % (27130)------------------------------
% 38.32/6.49 % (27164)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_26636 for (2946ds/3174Mi)
% 39.03/6.67 % (27162)Instruction limit reached!
% 39.03/6.67 % (27162)------------------------------
% 39.03/6.67 % (27162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.03/6.67 % (27162)Termination reason: Unknown
% 39.03/6.67 % (27162)Termination phase: Saturation
% 39.03/6.67
% 39.03/6.67 % (27162)Memory used [KB]: 12153
% 39.03/6.67 % (27162)Time elapsed: 0.457 s
% 39.03/6.67 % (27162)Instructions burned: 1537 (million)
% 39.03/6.67 % (27162)------------------------------
% 39.03/6.67 % (27162)------------------------------
% 39.03/6.68 % (27165)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_26636 for (2944ds/307Mi)
% 39.80/6.77 % (27165)Instruction limit reached!
% 39.80/6.77 % (27165)------------------------------
% 39.80/6.77 % (27165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.80/6.77 % (27165)Termination reason: Unknown
% 39.80/6.77 % (27165)Termination phase: Saturation
% 39.80/6.77
% 39.80/6.77 % (27165)Memory used [KB]: 7675
% 39.80/6.77 % (27165)Time elapsed: 0.085 s
% 39.80/6.77 % (27165)Instructions burned: 308 (million)
% 39.80/6.77 % (27165)------------------------------
% 39.80/6.77 % (27165)------------------------------
% 39.80/6.77 % (27166)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_26636 for (2943ds/3619Mi)
% 40.19/6.82 % (27166)Refutation not found, incomplete strategy
% 40.19/6.82 % (27166)------------------------------
% 40.19/6.82 % (27166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.19/6.82 % (27166)Termination reason: Refutation not found, incomplete strategy
% 40.19/6.82
% 40.19/6.82
% 40.19/6.82 % (27166)Memory used [KB]: 7291
% 40.19/6.82 % (27166)Time elapsed: 0.041 s
% 40.19/6.82 % (27166)Instructions burned: 139 (million)
% 40.19/6.82 % (27166)------------------------------
% 40.19/6.82 % (27166)------------------------------
% 40.19/6.82 % (27167)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_26636 for (2942ds/2325Mi)
% 40.54/6.91 % (27161)Instruction limit reached!
% 40.54/6.91 % (27161)------------------------------
% 40.54/6.91 % (27161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.54/6.91 % (27161)Termination reason: Unknown
% 40.54/6.91 % (27161)Termination phase: Saturation
% 40.54/6.91
% 40.54/6.91 % (27161)Memory used [KB]: 9083
% 40.54/6.91 % (27161)Time elapsed: 0.698 s
% 40.54/6.91 % (27161)Instructions burned: 3674 (million)
% 40.54/6.91 % (27161)------------------------------
% 40.54/6.91 % (27161)------------------------------
% 40.54/6.92 % (27168)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_26636 for (2942ds/2341Mi)
% 40.54/6.93 % (27149)Instruction limit reached!
% 40.54/6.93 % (27149)------------------------------
% 40.54/6.93 % (27149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.54/6.93 % (27149)Termination reason: Unknown
% 40.54/6.93 % (27149)Termination phase: Saturation
% 40.54/6.93
% 40.54/6.93 % (27149)Memory used [KB]: 14711
% 40.54/6.93 % (27149)Time elapsed: 1.561 s
% 40.54/6.93 % (27149)Instructions burned: 5062 (million)
% 40.54/6.93 % (27149)------------------------------
% 40.54/6.93 % (27149)------------------------------
% 40.54/6.94 % (27169)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_26636 for (2941ds/7257Mi)
% 40.54/6.97 % (27169)Refutation not found, incomplete strategy
% 40.54/6.97 % (27169)------------------------------
% 40.54/6.97 % (27169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.54/6.97 % (27169)Termination reason: Refutation not found, incomplete strategy
% 40.54/6.97
% 40.54/6.97
% 40.54/6.97 % (27169)Memory used [KB]: 7036
% 40.54/6.97 % (27169)Time elapsed: 0.032 s
% 40.54/6.97 % (27169)Instructions burned: 107 (million)
% 40.54/6.97 % (27169)------------------------------
% 40.54/6.97 % (27169)------------------------------
% 40.54/6.98 % (27170)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_26636 for (2941ds/3710Mi)
% 43.74/7.13 % (27151)Instruction limit reached!
% 43.74/7.13 % (27151)------------------------------
% 43.74/7.13 % (27151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.74/7.13 % (27151)Termination reason: Unknown
% 43.74/7.13 % (27151)Termination phase: Saturation
% 43.74/7.13
% 43.74/7.13 % (27151)Memory used [KB]: 10106
% 43.74/7.13 % (27151)Time elapsed: 1.737 s
% 43.74/7.13 % (27151)Instructions burned: 5799 (million)
% 43.74/7.13 % (27151)------------------------------
% 43.74/7.13 % (27151)------------------------------
% 43.74/7.14 % (27171)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_26636 for (2939ds/326Mi)
% 44.28/7.22 % (27167)Refutation not found, non-redundant clauses discarded% (27167)------------------------------
% 44.28/7.22 % (27167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.28/7.22 % (27167)Termination reason: Refutation not found, non-redundant clauses discarded
% 44.28/7.22
% 44.28/7.22 % (27167)Memory used [KB]: 9210
% 44.28/7.22 % (27167)Time elapsed: 0.398 s
% 44.28/7.22 % (27167)Instructions burned: 1328 (million)
% 44.28/7.22 % (27167)------------------------------
% 44.28/7.22 % (27167)------------------------------
% 44.28/7.23 % (27172)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_26636 for (2938ds/1100Mi)
% 44.28/7.24 % (27171)Instruction limit reached!
% 44.28/7.24 % (27171)------------------------------
% 44.28/7.24 % (27171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.28/7.24 % (27171)Termination reason: Unknown
% 44.28/7.24 % (27171)Termination phase: Saturation
% 44.28/7.24
% 44.28/7.24 % (27171)Memory used [KB]: 7164
% 44.28/7.24 % (27171)Time elapsed: 0.101 s
% 44.28/7.24 % (27171)Instructions burned: 327 (million)
% 44.28/7.24 % (27171)------------------------------
% 44.28/7.24 % (27171)------------------------------
% 44.28/7.25 % (27173)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_26636 for (2938ds/406Mi)
% 44.93/7.37 % (27173)Instruction limit reached!
% 44.93/7.37 % (27173)------------------------------
% 44.93/7.37 % (27173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.93/7.37 % (27173)Termination reason: Unknown
% 44.93/7.37 % (27173)Termination phase: Saturation
% 44.93/7.37
% 44.93/7.37 % (27173)Memory used [KB]: 8059
% 44.93/7.37 % (27173)Time elapsed: 0.125 s
% 44.93/7.37 % (27173)Instructions burned: 407 (million)
% 44.93/7.37 % (27173)------------------------------
% 44.93/7.37 % (27173)------------------------------
% 44.93/7.38 % (27174)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_26636 for (2937ds/1871Mi)
% 45.56/7.44 % (27168)Instruction limit reached!
% 45.56/7.44 % (27168)------------------------------
% 45.56/7.44 % (27168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.56/7.44 % (27168)Termination reason: Unknown
% 45.56/7.44 % (27168)Termination phase: Saturation
% 45.56/7.44
% 45.56/7.44 % (27168)Memory used [KB]: 7803
% 45.56/7.44 % (27168)Time elapsed: 0.520 s
% 45.56/7.44 % (27168)Instructions burned: 2342 (million)
% 45.56/7.44 % (27168)------------------------------
% 45.56/7.44 % (27168)------------------------------
% 45.56/7.44 % (27175)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_26636 for (2936ds/1194Mi)
% 45.56/7.45 % (27164)Instruction limit reached!
% 45.56/7.45 % (27164)------------------------------
% 45.56/7.45 % (27164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.56/7.45 % (27164)Termination reason: Unknown
% 45.56/7.45 % (27164)Termination phase: Saturation
% 45.56/7.45
% 45.56/7.45 % (27164)Memory used [KB]: 9978
% 45.56/7.45 % (27164)Time elapsed: 0.956 s
% 45.56/7.45 % (27164)Instructions burned: 3174 (million)
% 45.56/7.45 % (27164)------------------------------
% 45.56/7.45 % (27164)------------------------------
% 45.56/7.46 % (27176)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_26636 for (2936ds/474Mi)
% 45.97/7.55 % (27172)Instruction limit reached!
% 45.97/7.55 % (27172)------------------------------
% 45.97/7.55 % (27172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 45.97/7.55 % (27172)Termination reason: Unknown
% 45.97/7.55 % (27172)Termination phase: Saturation
% 45.97/7.55
% 45.97/7.55 % (27172)Memory used [KB]: 11001
% 45.97/7.55 % (27172)Time elapsed: 0.322 s
% 45.97/7.55 % (27172)Instructions burned: 1100 (million)
% 45.97/7.55 % (27172)------------------------------
% 45.97/7.55 % (27172)------------------------------
% 45.97/7.56 % (27177)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_26636 for (2935ds/3115Mi)
% 46.60/7.61 % (27176)Instruction limit reached!
% 46.60/7.61 % (27176)------------------------------
% 46.60/7.61 % (27176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.60/7.61 % (27176)Termination reason: Unknown
% 46.60/7.61 % (27176)Termination phase: Saturation
% 46.60/7.61
% 46.60/7.61 % (27176)Memory used [KB]: 7547
% 46.60/7.61 % (27176)Time elapsed: 0.147 s
% 46.60/7.61 % (27176)Instructions burned: 474 (million)
% 46.60/7.61 % (27176)------------------------------
% 46.60/7.61 % (27176)------------------------------
% 46.60/7.61 % (27178)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_26636 for (2935ds/831Mi)
% 47.05/7.74 % (27163)Instruction limit reached!
% 47.05/7.74 % (27163)------------------------------
% 47.05/7.74 % (27163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.05/7.74 % (27163)Termination reason: Unknown
% 47.05/7.74 % (27163)Termination phase: Saturation
% 47.05/7.74
% 47.05/7.74 % (27163)Memory used [KB]: 11129
% 47.05/7.74 % (27163)Time elapsed: 1.387 s
% 47.05/7.74 % (27163)Instructions burned: 4637 (million)
% 47.05/7.74 % (27163)------------------------------
% 47.05/7.74 % (27163)------------------------------
% 47.05/7.75 % (27179)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_26636 for (2933ds/1188Mi)
% 47.34/7.80 % (27175)Instruction limit reached!
% 47.34/7.80 % (27175)------------------------------
% 47.34/7.80 % (27175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.34/7.80 % (27175)Termination reason: Unknown
% 47.34/7.80 % (27175)Termination phase: Saturation
% 47.34/7.80
% 47.34/7.80 % (27175)Memory used [KB]: 9850
% 47.34/7.80 % (27175)Time elapsed: 0.360 s
% 47.34/7.80 % (27175)Instructions burned: 1195 (million)
% 47.34/7.80 % (27175)------------------------------
% 47.34/7.80 % (27175)------------------------------
% 47.34/7.81 % (27180)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_26636 for (2933ds/2868Mi)
% 47.34/7.85 % (27178)Instruction limit reached!
% 47.34/7.85 % (27178)------------------------------
% 47.34/7.85 % (27178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.34/7.85 % (27178)Termination reason: Unknown
% 47.34/7.85 % (27178)Termination phase: Saturation
% 47.34/7.85
% 47.34/7.85 % (27178)Memory used [KB]: 10618
% 47.34/7.85 % (27178)Time elapsed: 0.239 s
% 47.34/7.85 % (27178)Instructions burned: 832 (million)
% 47.34/7.85 % (27178)------------------------------
% 47.34/7.85 % (27178)------------------------------
% 47.34/7.86 % (27181)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_26636 for (2932ds/1516Mi)
% 47.34/7.87 % (27180)Refutation not found, incomplete strategy
% 47.34/7.87 % (27180)------------------------------
% 47.34/7.87 % (27180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.34/7.87 % (27180)Termination reason: Refutation not found, incomplete strategy
% 47.34/7.87
% 47.34/7.87
% 47.34/7.87 % (27180)Memory used [KB]: 7675
% 47.34/7.87 % (27180)Time elapsed: 0.061 s
% 47.34/7.87 % (27180)Instructions burned: 219 (million)
% 47.34/7.87 % (27180)------------------------------
% 47.34/7.87 % (27180)------------------------------
% 47.34/7.88 % (27182)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_26636 for (2932ds/2321Mi)
% 48.21/7.95 % (27182)Refutation not found, incomplete strategy
% 48.21/7.95 % (27182)------------------------------
% 48.21/7.95 % (27182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.21/7.95 % (27182)Termination reason: Refutation not found, incomplete strategy
% 48.21/7.95
% 48.21/7.95
% 48.21/7.95 % (27182)Memory used [KB]: 7675
% 48.21/7.95 % (27182)Time elapsed: 0.065 s
% 48.21/7.95 % (27182)Instructions burned: 236 (million)
% 48.21/7.95 % (27182)------------------------------
% 48.21/7.95 % (27182)------------------------------
% 48.21/7.96 % (27183)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_26636 for (2931ds/2812Mi)
% 48.21/7.97 % (27174)Instruction limit reached!
% 48.21/7.97 % (27174)------------------------------
% 48.21/7.97 % (27174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.21/7.97 % (27174)Termination reason: Unknown
% 48.21/7.97 % (27174)Termination phase: Saturation
% 48.21/7.97
% 48.21/7.97 % (27174)Memory used [KB]: 10106
% 48.21/7.97 % (27174)Time elapsed: 0.594 s
% 48.21/7.97 % (27174)Instructions burned: 1871 (million)
% 48.21/7.97 % (27174)------------------------------
% 48.21/7.97 % (27174)------------------------------
% 48.21/7.98 % (27184)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_26636 for (2931ds/4604Mi)
% 50.06/8.08 % (27170)Instruction limit reached!
% 50.06/8.08 % (27170)------------------------------
% 50.06/8.08 % (27170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.06/8.08 % (27170)Termination reason: Unknown
% 50.06/8.08 % (27170)Termination phase: Saturation
% 50.06/8.08
% 50.06/8.08 % (27170)Memory used [KB]: 18038
% 50.06/8.08 % (27170)Time elapsed: 1.101 s
% 50.06/8.08 % (27170)Instructions burned: 3712 (million)
% 50.06/8.08 % (27170)------------------------------
% 50.06/8.08 % (27170)------------------------------
% 50.06/8.09 % (27185)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_26636 for (2930ds/2678Mi)
% 50.74/8.11 % (27179)Instruction limit reached!
% 50.74/8.11 % (27179)------------------------------
% 50.74/8.11 % (27179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.74/8.11 % (27179)Termination reason: Unknown
% 50.74/8.11 % (27179)Termination phase: Saturation
% 50.74/8.11
% 50.74/8.11 % (27179)Memory used [KB]: 9466
% 50.74/8.11 % (27179)Time elapsed: 0.360 s
% 50.74/8.11 % (27179)Instructions burned: 1189 (million)
% 50.74/8.11 % (27179)------------------------------
% 50.74/8.11 % (27179)------------------------------
% 50.74/8.12 % (27186)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_26636 for (2929ds/643Mi)
% 50.74/8.16 % (27159)Instruction limit reached!
% 50.74/8.16 % (27159)------------------------------
% 50.74/8.16 % (27159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.74/8.16 % (27159)Termination reason: Unknown
% 50.74/8.16 % (27159)Termination phase: Saturation
% 50.74/8.16
% 50.74/8.16 % (27159)Memory used [KB]: 13048
% 50.74/8.16 % (27159)Time elapsed: 2.290 s
% 50.74/8.16 % (27159)Instructions burned: 7680 (million)
% 50.74/8.16 % (27159)------------------------------
% 50.74/8.16 % (27159)------------------------------
% 50.74/8.17 % (27187)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_26636 for (2929ds/458Mi)
% 51.56/8.30 % (27187)Instruction limit reached!
% 51.56/8.30 % (27187)------------------------------
% 51.56/8.30 % (27187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.56/8.30 % (27187)Termination reason: Unknown
% 51.56/8.30 % (27187)Termination phase: Saturation
% 51.56/8.30
% 51.56/8.30 % (27187)Memory used [KB]: 7803
% 51.56/8.30 % (27187)Time elapsed: 0.131 s
% 51.56/8.30 % (27187)Instructions burned: 460 (million)
% 51.56/8.30 % (27187)------------------------------
% 51.56/8.30 % (27187)------------------------------
% 51.56/8.31 % (27181)Instruction limit reached!
% 51.56/8.31 % (27181)------------------------------
% 51.56/8.31 % (27181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.56/8.31 % (27181)Termination reason: Unknown
% 51.56/8.31 % (27181)Termination phase: Saturation
% 51.56/8.31
% 51.56/8.31 % (27181)Memory used [KB]: 8187
% 51.56/8.31 % (27181)Time elapsed: 0.469 s
% 51.56/8.31 % (27181)Instructions burned: 1518 (million)
% 51.56/8.31 % (27181)------------------------------
% 51.56/8.31 % (27181)------------------------------
% 51.56/8.31 % (27186)Instruction limit reached!
% 51.56/8.31 % (27186)------------------------------
% 51.56/8.31 % (27186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.56/8.31 % (27186)Termination reason: Unknown
% 51.56/8.31 % (27186)Termination phase: Saturation
% 51.56/8.31
% 51.56/8.31 % (27186)Memory used [KB]: 9338
% 51.56/8.31 % (27186)Time elapsed: 0.192 s
% 51.56/8.31 % (27186)Instructions burned: 645 (million)
% 51.56/8.31 % (27186)------------------------------
% 51.56/8.31 % (27186)------------------------------
% 51.56/8.31 % (27188)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_26636 for (2927ds/2546Mi)
% 51.56/8.32 % (27189)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_26636 for (2927ds/1432Mi)
% 51.56/8.32 % (27190)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_26636 for (2927ds/386Mi)
% 52.22/8.43 % (27190)Instruction limit reached!
% 52.22/8.43 % (27190)------------------------------
% 52.22/8.43 % (27190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.22/8.43 % (27190)Termination reason: Unknown
% 52.22/8.43 % (27190)Termination phase: Saturation
% 52.22/8.43
% 52.22/8.43 % (27190)Memory used [KB]: 9083
% 52.22/8.43 % (27190)Time elapsed: 0.110 s
% 52.22/8.43 % (27190)Instructions burned: 387 (million)
% 52.22/8.43 % (27190)------------------------------
% 52.22/8.43 % (27190)------------------------------
% 52.22/8.44 % (27191)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_26636 for (2926ds/360Mi)
% 52.22/8.48 % (27177)Instruction limit reached!
% 52.22/8.48 % (27177)------------------------------
% 52.22/8.48 % (27177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.22/8.48 % (27177)Termination reason: Unknown
% 52.22/8.48 % (27177)Termination phase: Saturation
% 52.22/8.48
% 52.22/8.48 % (27177)Memory used [KB]: 12281
% 52.22/8.48 % (27177)Time elapsed: 0.914 s
% 52.22/8.48 % (27177)Instructions burned: 3116 (million)
% 52.22/8.48 % (27177)------------------------------
% 52.22/8.48 % (27177)------------------------------
% 52.22/8.49 % (27192)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_26636 for (2926ds/5446Mi)
% 52.63/8.54 % (27191)Instruction limit reached!
% 52.63/8.54 % (27191)------------------------------
% 52.63/8.54 % (27191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.63/8.54 % (27191)Termination reason: Unknown
% 52.63/8.54 % (27191)Termination phase: Saturation
% 52.63/8.54
% 52.63/8.54 % (27191)Memory used [KB]: 8827
% 52.63/8.54 % (27191)Time elapsed: 0.101 s
% 52.63/8.54 % (27191)Instructions burned: 361 (million)
% 52.63/8.54 % (27191)------------------------------
% 52.63/8.54 % (27191)------------------------------
% 52.63/8.55 % (27193)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_26636 for (2925ds/2573Mi)
% 53.14/8.75 % (27189)Instruction limit reached!
% 53.14/8.75 % (27189)------------------------------
% 53.14/8.75 % (27189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.14/8.75 % (27189)Termination reason: Unknown
% 53.14/8.75 % (27189)Termination phase: Saturation
% 53.14/8.75
% 53.14/8.75 % (27189)Memory used [KB]: 9594
% 53.14/8.75 % (27189)Time elapsed: 0.429 s
% 53.14/8.75 % (27189)Instructions burned: 1432 (million)
% 53.14/8.75 % (27189)------------------------------
% 53.14/8.75 % (27189)------------------------------
% 53.14/8.76 % (27194)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_26636 for (2923ds/2655Mi)
% 53.77/8.81 % (27183)Instruction limit reached!
% 53.77/8.81 % (27183)------------------------------
% 53.77/8.81 % (27183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.77/8.81 % (27183)Termination reason: Unknown
% 53.77/8.81 % (27183)Termination phase: Saturation
% 53.77/8.81
% 53.77/8.81 % (27183)Memory used [KB]: 11513
% 53.77/8.81 % (27183)Time elapsed: 0.879 s
% 53.77/8.81 % (27183)Instructions burned: 2813 (million)
% 53.77/8.81 % (27183)------------------------------
% 53.77/8.81 % (27183)------------------------------
% 53.77/8.82 % (27195)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_26636 for (2922ds/2781Mi)
% 53.77/8.90 % (27185)Instruction limit reached!
% 53.77/8.90 % (27185)------------------------------
% 53.77/8.90 % (27185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.77/8.90 % (27185)Termination reason: Unknown
% 53.77/8.90 % (27185)Termination phase: Saturation
% 53.77/8.90
% 53.77/8.90 % (27185)Memory used [KB]: 10746
% 53.77/8.90 % (27185)Time elapsed: 0.804 s
% 53.77/8.90 % (27185)Instructions burned: 2680 (million)
% 53.77/8.90 % (27185)------------------------------
% 53.77/8.90 % (27185)------------------------------
% 53.90/8.91 % (27196)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_26636 for (2922ds/307Mi)
% 53.90/8.99 % (27196)Instruction limit reached!
% 53.90/8.99 % (27196)------------------------------
% 53.90/8.99 % (27196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.90/8.99 % (27196)Termination reason: Unknown
% 53.90/8.99 % (27196)Termination phase: Saturation
% 53.90/8.99
% 53.90/8.99 % (27196)Memory used [KB]: 7803
% 53.90/8.99 % (27196)Time elapsed: 0.086 s
% 53.90/8.99 % (27196)Instructions burned: 309 (million)
% 53.90/8.99 % (27196)------------------------------
% 53.90/8.99 % (27196)------------------------------
% 57.06/9.01 % (27197)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_26636 for (2921ds/1548Mi)
% 57.06/9.10 % (27188)Instruction limit reached!
% 57.06/9.10 % (27188)------------------------------
% 57.06/9.10 % (27188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.06/9.10 % (27188)Termination reason: Unknown
% 57.06/9.10 % (27188)Termination phase: Saturation
% 57.06/9.10
% 57.06/9.10 % (27188)Memory used [KB]: 10874
% 57.06/9.10 % (27188)Time elapsed: 0.787 s
% 57.06/9.10 % (27188)Instructions burned: 2546 (million)
% 57.06/9.10 % (27188)------------------------------
% 57.06/9.10 % (27188)------------------------------
% 57.06/9.11 % (27198)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_26636 for (2920ds/5214Mi)
% 58.84/9.31 % (27193)Instruction limit reached!
% 58.84/9.31 % (27193)------------------------------
% 58.84/9.31 % (27193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.84/9.31 % (27193)Termination reason: Unknown
% 58.84/9.31 % (27193)Termination phase: Saturation
% 58.84/9.31
% 58.84/9.31 % (27193)Memory used [KB]: 10234
% 58.84/9.31 % (27193)Time elapsed: 0.757 s
% 58.84/9.31 % (27193)Instructions burned: 2575 (million)
% 58.84/9.31 % (27193)------------------------------
% 58.84/9.31 % (27193)------------------------------
% 58.84/9.32 % (27199)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_26636 for (2918ds/3201Mi)
% 58.84/9.34 % (27184)Instruction limit reached!
% 58.84/9.34 % (27184)------------------------------
% 58.84/9.34 % (27184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.84/9.34 % (27184)Termination reason: Unknown
% 58.84/9.34 % (27184)Termination phase: Saturation
% 58.84/9.34
% 58.84/9.34 % (27184)Memory used [KB]: 12537
% 58.84/9.34 % (27184)Time elapsed: 1.380 s
% 58.84/9.34 % (27184)Instructions burned: 4604 (million)
% 58.84/9.34 % (27184)------------------------------
% 58.84/9.34 % (27184)------------------------------
% 58.84/9.35 % (27200)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_26636 for (2917ds/454Mi)
% 59.33/9.47 % (27197)Instruction limit reached!
% 59.33/9.47 % (27197)------------------------------
% 59.33/9.47 % (27197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.33/9.47 % (27197)Termination reason: Unknown
% 59.33/9.47 % (27197)Termination phase: Saturation
% 59.33/9.47
% 59.33/9.47 % (27197)Memory used [KB]: 8955
% 59.33/9.47 % (27197)Time elapsed: 0.481 s
% 59.33/9.47 % (27197)Instructions burned: 1549 (million)
% 59.33/9.47 % (27197)------------------------------
% 59.33/9.47 % (27197)------------------------------
% 59.33/9.48 % (27200)Instruction limit reached!
% 59.33/9.48 % (27200)------------------------------
% 59.33/9.48 % (27200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.33/9.48 % (27200)Termination reason: Unknown
% 59.33/9.48 % (27200)Termination phase: Saturation
% 59.33/9.48
% 59.33/9.48 % (27200)Memory used [KB]: 13304
% 59.33/9.48 % (27200)Time elapsed: 0.132 s
% 59.33/9.48 % (27200)Instructions burned: 457 (million)
% 59.33/9.48 % (27200)------------------------------
% 59.33/9.48 % (27200)------------------------------
% 59.33/9.48 % (27201)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_26636 for (2916ds/3049Mi)
% 59.33/9.49 % (27202)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_26636 for (2916ds/7311Mi)
% 59.86/9.54 % (27194)Instruction limit reached!
% 59.86/9.54 % (27194)------------------------------
% 59.86/9.54 % (27194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.86/9.54 % (27194)Termination reason: Unknown
% 59.86/9.54 % (27194)Termination phase: Saturation
% 59.86/9.54
% 59.86/9.54 % (27194)Memory used [KB]: 16886
% 59.86/9.54 % (27194)Time elapsed: 0.783 s
% 59.86/9.54 % (27194)Instructions burned: 2658 (million)
% 59.86/9.54 % (27194)------------------------------
% 59.86/9.54 % (27194)------------------------------
% 59.86/9.55 % (27203)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_26636 for (2915ds/6804Mi)
% 59.86/9.60 % (27203)Refutation not found, incomplete strategy
% 59.86/9.60 % (27203)------------------------------
% 59.86/9.60 % (27203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.86/9.60 % (27203)Termination reason: Refutation not found, incomplete strategy
% 59.86/9.60
% 59.86/9.60
% 59.86/9.60 % (27203)Memory used [KB]: 7547
% 59.86/9.60 % (27203)Time elapsed: 0.047 s
% 59.86/9.60 % (27203)Instructions burned: 156 (million)
% 59.86/9.60 % (27203)------------------------------
% 59.86/9.60 % (27203)------------------------------
% 60.10/9.61 % (27204)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_26636 for (2915ds/1683Mi)
% 60.10/9.67 % (27195)Instruction limit reached!
% 60.10/9.67 % (27195)------------------------------
% 60.10/9.67 % (27195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.10/9.67 % (27195)Termination reason: Unknown
% 60.10/9.67 % (27195)Termination phase: Saturation
% 60.10/9.67
% 60.10/9.67 % (27195)Memory used [KB]: 4861
% 60.10/9.67 % (27195)Time elapsed: 0.852 s
% 60.10/9.67 % (27195)Instructions burned: 2782 (million)
% 60.10/9.67 % (27195)------------------------------
% 60.10/9.67 % (27195)------------------------------
% 60.10/9.68 % (27205)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_26636 for (2914ds/4688Mi)
% 60.45/9.89 % (27198)Refutation not found, non-redundant clauses discarded% (27198)------------------------------
% 60.45/9.89 % (27198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.45/9.89 % (27198)Termination reason: Refutation not found, non-redundant clauses discarded
% 60.45/9.89
% 60.45/9.89 % (27198)Memory used [KB]: 12153
% 60.45/9.89 % (27198)Time elapsed: 0.785 s
% 60.45/9.89 % (27198)Instructions burned: 2606 (million)
% 60.45/9.89 % (27198)------------------------------
% 60.45/9.89 % (27198)------------------------------
% 60.55/9.91 % (27206)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_26636 for (2912ds/2207Mi)
% 64.76/10.13 % (27192)Instruction limit reached!
% 64.76/10.13 % (27192)------------------------------
% 64.76/10.13 % (27192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.76/10.13 % (27192)Termination reason: Unknown
% 64.76/10.13 % (27192)Termination phase: Saturation
% 64.76/10.13
% 64.76/10.13 % (27192)Memory used [KB]: 16502
% 64.76/10.13 % (27192)Time elapsed: 1.641 s
% 64.76/10.13 % (27192)Instructions burned: 5448 (million)
% 64.76/10.13 % (27192)------------------------------
% 64.76/10.13 % (27192)------------------------------
% 64.76/10.13 % (27204)Instruction limit reached!
% 64.76/10.13 % (27204)------------------------------
% 64.76/10.13 % (27204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.76/10.13 % (27204)Termination reason: Unknown
% 64.76/10.13 % (27204)Termination phase: Saturation
% 64.76/10.13
% 64.76/10.13 % (27204)Memory used [KB]: 8827
% 64.76/10.13 % (27204)Time elapsed: 0.526 s
% 64.76/10.13 % (27204)Instructions burned: 1684 (million)
% 64.76/10.13 % (27204)------------------------------
% 64.76/10.13 % (27204)------------------------------
% 64.76/10.14 % (27207)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=8216:si=on:rtra=on_0 on DTF2THF_26636 for (2909ds/8216Mi)
% 64.76/10.14 % (27208)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_26636 for (2909ds/430Mi)
% 65.22/10.26 % (27208)Instruction limit reached!
% 65.22/10.26 % (27208)------------------------------
% 65.22/10.26 % (27208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.22/10.26 % (27208)Termination reason: Unknown
% 65.22/10.26 % (27208)Termination phase: Saturation
% 65.22/10.26
% 65.22/10.26 % (27208)Memory used [KB]: 7931
% 65.22/10.26 % (27208)Time elapsed: 0.123 s
% 65.22/10.26 % (27208)Instructions burned: 430 (million)
% 65.22/10.26 % (27208)------------------------------
% 65.22/10.26 % (27208)------------------------------
% 65.22/10.27 % (27209)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_26636 for (2908ds/2012Mi)
% 65.22/10.28 % (27199)Instruction limit reached!
% 65.22/10.28 % (27199)------------------------------
% 65.22/10.28 % (27199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.22/10.28 % (27199)Termination reason: Unknown
% 65.22/10.28 % (27199)Termination phase: Saturation
% 65.22/10.28
% 65.22/10.28 % (27199)Memory used [KB]: 12281
% 65.22/10.28 % (27199)Time elapsed: 0.965 s
% 65.22/10.28 % (27199)Instructions burned: 3202 (million)
% 65.22/10.28 % (27199)------------------------------
% 65.22/10.28 % (27199)------------------------------
% 65.22/10.29 % (27210)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_26636 for (2908ds/631Mi)
% 66.25/10.40 % (27201)Instruction limit reached!
% 66.25/10.40 % (27201)------------------------------
% 66.25/10.40 % (27201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.25/10.40 % (27201)Termination reason: Unknown
% 66.25/10.40 % (27201)Termination phase: Saturation
% 66.25/10.40
% 66.25/10.40 % (27201)Memory used [KB]: 11641
% 66.25/10.40 % (27201)Time elapsed: 0.914 s
% 66.25/10.40 % (27201)Instructions burned: 3051 (million)
% 66.25/10.40 % (27201)------------------------------
% 66.25/10.40 % (27201)------------------------------
% 66.25/10.41 % (27211)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_26636 for (2907ds/8785Mi)
% 66.25/10.48 % (27210)Instruction limit reached!
% 66.25/10.48 % (27210)------------------------------
% 66.25/10.48 % (27210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.25/10.48 % (27210)Termination reason: Unknown
% 66.25/10.48 % (27210)Termination phase: Saturation
% 66.25/10.48
% 66.25/10.48 % (27210)Memory used [KB]: 9722
% 66.25/10.48 % (27210)Time elapsed: 0.191 s
% 66.25/10.48 % (27210)Instructions burned: 632 (million)
% 66.25/10.48 % (27210)------------------------------
% 66.25/10.48 % (27210)------------------------------
% 66.25/10.49 % (27212)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_26636 for (2906ds/739Mi)
% 66.76/10.58 % (27206)Instruction limit reached!
% 66.76/10.58 % (27206)------------------------------
% 66.76/10.58 % (27206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.76/10.58 % (27206)Termination reason: Unknown
% 66.76/10.58 % (27206)Termination phase: Saturation
% 66.76/10.58
% 66.76/10.58 % (27206)Memory used [KB]: 10746
% 66.76/10.58 % (27206)Time elapsed: 0.672 s
% 66.76/10.58 % (27206)Instructions burned: 2209 (million)
% 66.76/10.58 % (27206)------------------------------
% 66.76/10.58 % (27206)------------------------------
% 66.76/10.59 % (27213)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_26636 for (2905ds/5473Mi)
% 67.25/10.71 % (27212)Instruction limit reached!
% 67.25/10.71 % (27212)------------------------------
% 67.25/10.71 % (27212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.25/10.71 % (27212)Termination reason: Unknown
% 67.25/10.71 % (27212)Termination phase: Saturation
% 67.25/10.71
% 67.25/10.71 % (27212)Memory used [KB]: 8443
% 67.25/10.71 % (27212)Time elapsed: 0.226 s
% 67.25/10.71 % (27212)Instructions burned: 740 (million)
% 67.25/10.71 % (27212)------------------------------
% 67.25/10.71 % (27212)------------------------------
% 67.25/10.72 % (27214)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_26636 for (2903ds/43570Mi)
% 67.25/10.75 % (27214)Refutation not found, incomplete strategy
% 67.25/10.75 % (27214)------------------------------
% 67.25/10.75 % (27214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.25/10.75 % (27214)Termination reason: Refutation not found, incomplete strategy
% 67.25/10.75
% 67.25/10.75
% 67.25/10.75 % (27214)Memory used [KB]: 6652
% 67.25/10.75 % (27214)Time elapsed: 0.022 s
% 67.25/10.75 % (27214)Instructions burned: 71 (million)
% 67.25/10.75 % (27214)------------------------------
% 67.25/10.75 % (27214)------------------------------
% 67.25/10.76 % (27215)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_26636 for (2903ds/8382Mi)
% 67.72/10.87 % (27209)Instruction limit reached!
% 67.72/10.87 % (27209)------------------------------
% 67.72/10.87 % (27209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.72/10.87 % (27209)Termination reason: Unknown
% 67.72/10.87 % (27209)Termination phase: Saturation
% 67.72/10.87
% 67.72/10.87 % (27209)Memory used [KB]: 17270
% 67.72/10.87 % (27209)Time elapsed: 0.596 s
% 67.72/10.87 % (27209)Instructions burned: 2014 (million)
% 67.72/10.87 % (27209)------------------------------
% 67.72/10.87 % (27209)------------------------------
% 67.72/10.88 % (27216)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_26636 for (2902ds/407Mi)
% 68.52/10.97 % (27205)Instruction limit reached!
% 68.52/10.97 % (27205)------------------------------
% 68.52/10.97 % (27205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.52/10.97 % (27205)Termination reason: Unknown
% 68.52/10.97 % (27205)Termination phase: Saturation
% 68.52/10.97
% 68.52/10.97 % (27205)Memory used [KB]: 12281
% 68.52/10.97 % (27205)Time elapsed: 1.291 s
% 68.52/10.97 % (27205)Instructions burned: 4688 (million)
% 68.52/10.97 % (27205)------------------------------
% 68.52/10.97 % (27205)------------------------------
% 68.52/10.98 % (27217)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_26636 for (2901ds/2971Mi)
% 68.52/10.99 % (27216)Instruction limit reached!
% 68.52/10.99 % (27216)------------------------------
% 68.52/10.99 % (27216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.52/10.99 % (27216)Termination reason: Unknown
% 68.52/10.99 % (27216)Termination phase: Saturation
% 68.52/10.99
% 68.52/10.99 % (27216)Memory used [KB]: 8059
% 68.52/10.99 % (27216)Time elapsed: 0.110 s
% 68.52/10.99 % (27216)Instructions burned: 407 (million)
% 68.52/10.99 % (27216)------------------------------
% 68.52/10.99 % (27216)------------------------------
% 68.52/11.00 % (27218)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_26636 for (2901ds/9822Mi)
% 71.07/11.04 % (27217)Refutation not found, incomplete strategy
% 71.07/11.04 % (27217)------------------------------
% 71.07/11.04 % (27217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.07/11.04 % (27217)Termination reason: Refutation not found, incomplete strategy
% 71.07/11.04
% 71.07/11.04
% 71.07/11.04 % (27217)Memory used [KB]: 7675
% 71.07/11.04 % (27217)Time elapsed: 0.061 s
% 71.07/11.04 % (27217)Instructions burned: 221 (million)
% 71.07/11.04 % (27217)------------------------------
% 71.07/11.04 % (27217)------------------------------
% 71.07/11.05 % (27219)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_26636 for (2900ds/8425Mi)
% 74.60/11.66 % (27202)First to succeed.
% 74.60/11.67 % (27202)Refutation found. Thanks to Tanya!
% 74.60/11.67 % SZS status Theorem for DTF2THF_26636
% 74.60/11.67 % SZS output start Proof for DTF2THF_26636
% 74.60/11.67 thf(type_def_5, type, coinductive_llist: ($tType) > $tType).
% 74.60/11.67 thf(type_def_7, type, set: ($tType) > $tType).
% 74.60/11.67 thf(type_def_8, type, nat: $tType).
% 74.60/11.67 thf(type_def_9, type, product_prod: ($tType * $tType) > $tType).
% 74.60/11.67 thf(type_def_10, type, itself: ($tType) > $tType).
% 74.60/11.67 thf(type_def_11, type, a: $tType).
% 74.60/11.67 thf(func_def_0, type, coinductive_llist: ($tType) > $tType).
% 74.60/11.67 thf(func_def_1, type, product_prod: ($tType * $tType) > $tType).
% 74.60/11.67 thf(func_def_2, type, set: ($tType) > $tType).
% 74.60/11.67 thf(func_def_3, type, nat: $tType).
% 74.60/11.67 thf(func_def_4, type, itself: ($tType) > $tType).
% 74.60/11.67 thf(func_def_5, type, a: $tType).
% 74.60/11.67 thf(func_def_6, type, coindu328551480prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 74.60/11.67 thf(func_def_7, type, coinductive_gen_lset: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > set @ X0)).
% 74.60/11.67 thf(func_def_8, type, coinductive_lappend: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_9, type, coinductive_lconcat: !>[X0: $tType]:(coinductive_llist @ coinductive_llist @ X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_10, type, coinductive_ldropn: !>[X0: $tType]:(nat > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_11, type, coinductive_lfinite: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 74.60/11.67 thf(func_def_12, type, coinductive_llast: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 74.60/11.67 thf(func_def_13, type, coinductive_llexord: !>[X0: $tType]:((X0 > X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 74.60/11.67 thf(func_def_14, type, coinductive_LCons: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_15, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_16, type, coindu1381640503_llist: !>[X0: $tType, X1: $tType]:(X0 > (X1 > coinductive_llist @ X1 > X0) > coinductive_llist @ X1 > X0)).
% 74.60/11.67 thf(func_def_17, type, coinductive_lhd: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 74.60/11.67 thf(func_def_18, type, coinductive_lnull: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 74.60/11.67 thf(func_def_19, type, coinductive_lset: !>[X0: $tType]:(coinductive_llist @ X0 > set @ X0)).
% 74.60/11.67 thf(func_def_20, type, coinductive_ltl: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_21, type, coinductive_lmember: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > $o)).
% 74.60/11.67 thf(func_def_22, type, coinductive_lprefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 74.60/11.67 thf(func_def_23, type, coindu1478340336prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 74.60/11.67 thf(func_def_24, type, coindu501562517eWhile: !>[X0: $tType]:((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_25, type, coinductive_lzip: !>[X0: $tType, X1: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X1 > coinductive_llist @ product_prod @ X0 @ X1)).
% 74.60/11.67 thf(func_def_26, type, coinductive_lsorted: !>[X0: $tType]:((X0 > X0 > $o) > coinductive_llist @ X0 > $o)).
% 74.60/11.67 thf(func_def_27, type, coindu1441602521_llist: !>[X0: $tType, X1: $tType]:((X0 > $o) > (X0 > X1) > (X0 > X0) > X0 > coinductive_llist @ X1)).
% 74.60/11.67 thf(func_def_28, type, undefined: !>[X0: $tType]:(X0)).
% 74.60/11.67 thf(func_def_29, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 74.60/11.67 thf(func_def_30, type, lMirro427583474mirror: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_31, type, lMirro999291890or_aux: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_32, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 74.60/11.67 thf(func_def_33, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 74.60/11.67 thf(func_def_34, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 74.60/11.67 thf(func_def_35, type, type: !>[X0: $tType]:(itself @ X0)).
% 74.60/11.67 thf(func_def_36, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 74.60/11.67 thf(func_def_37, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 74.60/11.67 thf(func_def_38, type, acc: coinductive_llist @ a).
% 74.60/11.67 thf(func_def_39, type, acca: coinductive_llist @ a).
% 74.60/11.67 thf(func_def_40, type, xs: coinductive_llist @ a).
% 74.60/11.67 thf(func_def_41, type, xsa: coinductive_llist @ a).
% 74.60/11.67 thf(func_def_59, type, sP0: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 74.60/11.67 thf(func_def_60, type, sK1: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_61, type, sK2: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_62, type, sK3: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 74.60/11.67 thf(func_def_63, type, sK4: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_64, type, sK5: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_65, type, sK6: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_66, type, sK7: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 74.60/11.67 thf(func_def_67, type, sK8: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_68, type, sK9: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_69, type, sK10: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > X0)).
% 74.60/11.67 thf(func_def_70, type, sK11: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 74.60/11.67 thf(func_def_71, type, sK12: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_72, type, sK13: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_73, type, sK14: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_74, type, sK15: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_75, type, sK16: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_76, type, sK17: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_77, type, sK18: !>[X0: $tType]:((coinductive_llist @ X0 > coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_78, type, sK19: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_79, type, sK20: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_80, type, sK21: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > X0)).
% 74.60/11.67 thf(func_def_81, type, sK22: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_82, type, sK23: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 74.60/11.67 thf(func_def_83, type, sK24: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_84, type, sK25: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > X0)).
% 74.60/11.67 thf(func_def_85, type, sK26: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_86, type, sK27: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_87, type, sK28: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 74.60/11.67 thf(func_def_88, type, sK29: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_89, type, sK30: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 74.60/11.67 thf(func_def_91, type, ph32: !>[X0: $tType]:(X0)).
% 74.60/11.67 thf(f11666,plain,(
% 74.60/11.67 $false),
% 74.60/11.67 inference(avatar_sat_refutation,[status(thm)],[f1163,f5182,f5228,f11503,f11516,f11600,f11602,f11665])).
% 74.60/11.67 thf(f11665,plain,(
% 74.60/11.67 spl31_2 | ~spl31_53),
% 74.60/11.67 inference(avatar_contradiction_clause,[status(thm)],[f11664])).
% 74.60/11.67 thf(f11664,plain,(
% 74.60/11.67 $false | (spl31_2 | ~spl31_53)),
% 74.60/11.67 inference(subsumption_resolution,[status(thm)],[f11638,f1162])).
% 74.60/11.67 thf(f1162,plain,(
% 74.60/11.67 ((coinductive_lfinite @ a @ xsa) != $true) | spl31_2),
% 74.60/11.67 inference(avatar_component_clause,[status(thm)],[f1160])).
% 74.60/11.67 thf(f1160,definition,(
% 74.60/11.67 spl31_2 <=> ((coinductive_lfinite @ a @ xsa) = $true)),
% 74.60/11.67 introduced(definition,[new_symbols(naming,[spl31_2])],[avatar_definition])).
% 74.60/11.67 thf(f11638,plain,(
% 74.60/11.67 ((coinductive_lfinite @ a @ xsa) = $true) | ~spl31_53),
% 74.60/11.67 inference(trivial_inequality_removal,[status(thm)],[f11628])).
% 74.60/11.67 thf(f11628,plain,(
% 74.60/11.67 ((coinductive_lfinite @ a @ xsa) = $true) | ($true != $true) | ~spl31_53),
% 74.60/11.67 inference(superposition,[status(thm)],[f6764,f11515])).
% 74.60/11.67 thf(f11515,plain,(
% 74.60/11.67 ($true = (coinductive_lfinite @ a @ (coinductive_ltl @ a @ xsa))) | ~spl31_53),
% 74.60/11.67 inference(avatar_component_clause,[status(thm)],[f11513])).
% 74.60/11.67 thf(f11513,definition,(
% 74.60/11.67 spl31_53 <=> ($true = (coinductive_lfinite @ a @ (coinductive_ltl @ a @ xsa)))),
% 74.60/11.67 introduced(definition,[new_symbols(naming,[spl31_53])],[avatar_definition])).
% 74.60/11.67 thf(f6764,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((coinductive_lfinite @ X0 @ (coinductive_ltl @ X0 @ X1)) != $true) | ((coinductive_lfinite @ X0 @ X1) = $true)) )),
% 74.60/11.67 inference(duplicate_literal_removal,[status(thm)],[f6745])).
% 74.60/11.67 thf(f6745,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((coinductive_lfinite @ X0 @ X1) = $true) | ((coinductive_lfinite @ X0 @ (coinductive_ltl @ X0 @ X1)) != $true) | ((coinductive_lfinite @ X0 @ X1) = $true)) )),
% 74.60/11.67 inference(superposition,[status(thm)],[f2747,f1068])).
% 74.60/11.67 thf(f1068,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : (((coinductive_lappend @ X0 @ X1 @ X2) = X1) | ((coinductive_lfinite @ X0 @ X1) = $true)) )),
% 74.60/11.67 inference(cnf_transformation,[status(thm)],[f807])).
% 74.60/11.67 thf(f807,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : (((coinductive_lfinite @ X0 @ X1) = $true) | ((coinductive_lappend @ X0 @ X1 @ X2) = X1))),
% 74.60/11.67 inference(ennf_transformation,[status(thm)],[f771])).
% 74.60/11.67 thf(f771,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : (((coinductive_lfinite @ X0 @ X1) != $true) => ((coinductive_lappend @ X0 @ X1 @ X2) = X1))),
% 74.60/11.67 inference(flattening,[status(thm)],[f743])).
% 74.60/11.67 thf(f743,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : (~((coinductive_lfinite @ X0 @ X1) = $true) => ((coinductive_lappend @ X0 @ X1 @ X2) = X1))),
% 74.60/11.67 inference(fool_elimination,[status(thm)],[f742])).
% 74.60/11.67 thf(f742,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : (~(coinductive_lfinite @ X0 @ X1) => ((coinductive_lappend @ X0 @ X1 @ X2) = X1))),
% 74.60/11.67 inference(rectify,[status(thm)],[f96])).
% 74.60/11.67 thf(f96,axiom,(
% 74.60/11.67 ! [X0 : $tType,X5 : coinductive_llist @ X0,X8 : coinductive_llist @ X0] : (~(coinductive_lfinite @ X0 @ X5) => ((coinductive_lappend @ X0 @ X5 @ X8) = X5))),
% 74.60/11.67 file('/export/starexec/sandbox/tmp/tmp.tZ0Cg1ODeg/DTF2THF_26636.p',fact_95_lappend__inf)).
% 74.60/11.67 thf(f2747,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : (((coinductive_lfinite @ X0 @ (coinductive_ltl @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2))) != $true) | ((coinductive_lfinite @ X0 @ X1) = $true)) )),
% 74.60/11.67 inference(subsumption_resolution,[status(thm)],[f2746,f970])).
% 74.60/11.67 thf(f970,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((coinductive_lnull @ X0 @ X1) != $true) | ((coinductive_lfinite @ X0 @ X1) = $true)) )),
% 74.60/11.67 inference(cnf_transformation,[status(thm)],[f803])).
% 74.60/11.67 thf(f803,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((coinductive_lfinite @ X0 @ X1) = $true) | ((coinductive_lnull @ X0 @ X1) != $true))),
% 74.60/11.67 inference(ennf_transformation,[status(thm)],[f422])).
% 74.60/11.67 thf(f422,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((coinductive_lnull @ X0 @ X1) = $true) => ((coinductive_lfinite @ X0 @ X1) = $true))),
% 74.60/11.67 inference(fool_elimination,[status(thm)],[f421])).
% 74.60/11.67 thf(f421,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((coinductive_lnull @ X0 @ X1) => (coinductive_lfinite @ X0 @ X1))),
% 74.60/11.67 inference(rectify,[status(thm)],[f6])).
% 74.60/11.67 thf(f6,axiom,(
% 74.60/11.67 ! [X0 : $tType,X5 : coinductive_llist @ X0] : ((coinductive_lnull @ X0 @ X5) => (coinductive_lfinite @ X0 @ X5))),
% 74.60/11.67 file('/export/starexec/sandbox/tmp/tmp.tZ0Cg1ODeg/DTF2THF_26636.p',fact_5_lnull__imp__lfinite)).
% 74.60/11.67 thf(f2746,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : (((coinductive_lnull @ X0 @ X1) = $true) | ((coinductive_lfinite @ X0 @ (coinductive_ltl @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2))) != $true) | ((coinductive_lfinite @ X0 @ X1) = $true)) )),
% 74.60/11.67 inference(forward_demodulation,[status(thm)],[f2733,f1025])).
% 74.60/11.67 thf(f1025,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((coinductive_lfinite @ X0 @ X1) = (coinductive_lfinite @ X0 @ (coinductive_ltl @ X0 @ X1)))) )),
% 74.60/11.67 inference(cnf_transformation,[status(thm)],[f523])).
% 74.60/11.67 thf(f523,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((coinductive_lfinite @ X0 @ X1) = (coinductive_lfinite @ X0 @ (coinductive_ltl @ X0 @ X1)))),
% 74.60/11.67 inference(fool_elimination,[status(thm)],[f522])).
% 74.60/11.67 thf(f522,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((coinductive_lfinite @ X0 @ X1) = (coinductive_lfinite @ X0 @ (coinductive_ltl @ X0 @ X1)))),
% 74.60/11.67 inference(rectify,[status(thm)],[f5])).
% 74.60/11.67 thf(f5,axiom,(
% 74.60/11.67 ! [X0 : $tType,X5 : coinductive_llist @ X0] : ((coinductive_lfinite @ X0 @ (coinductive_ltl @ X0 @ X5)) = (coinductive_lfinite @ X0 @ X5))),
% 74.60/11.67 file('/export/starexec/sandbox/tmp/tmp.tZ0Cg1ODeg/DTF2THF_26636.p',fact_4_lfinite__ltl)).
% 74.60/11.67 thf(f2733,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : (((coinductive_lfinite @ X0 @ (coinductive_ltl @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2))) != $true) | ((coinductive_lnull @ X0 @ X1) = $true) | ((coinductive_lfinite @ X0 @ (coinductive_ltl @ X0 @ X1)) = $true)) )),
% 74.60/11.67 inference(superposition,[status(thm)],[f963,f961])).
% 74.60/11.67 thf(f961,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : (((coinductive_lappend @ X0 @ (coinductive_ltl @ X0 @ X1) @ X2) = (coinductive_ltl @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2))) | ((coinductive_lnull @ X0 @ X1) = $true)) )),
% 74.60/11.67 inference(cnf_transformation,[status(thm)],[f862])).
% 74.60/11.67 thf(f862,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : ((((coinductive_lnull @ X0 @ X1) = $true) | ((coinductive_lappend @ X0 @ (coinductive_ltl @ X0 @ X1) @ X2) = (coinductive_ltl @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2)))) & (((coinductive_lnull @ X0 @ X1) != $true) | ((coinductive_ltl @ X0 @ X2) = (coinductive_ltl @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2)))))),
% 74.60/11.67 inference(ennf_transformation,[status(thm)],[f783])).
% 74.60/11.67 thf(f783,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : ((((coinductive_lnull @ X0 @ X1) = $true) => ((coinductive_ltl @ X0 @ X2) = (coinductive_ltl @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2)))) & (((coinductive_lnull @ X0 @ X1) != $true) => ((coinductive_lappend @ X0 @ (coinductive_ltl @ X0 @ X1) @ X2) = (coinductive_ltl @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2)))))),
% 74.60/11.67 inference(flattening,[status(thm)],[f466])).
% 74.60/11.67 thf(f466,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : ((~((coinductive_lnull @ X0 @ X1) = $true) => ((coinductive_lappend @ X0 @ (coinductive_ltl @ X0 @ X1) @ X2) = (coinductive_ltl @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2)))) & (((coinductive_lnull @ X0 @ X1) = $true) => ((coinductive_ltl @ X0 @ X2) = (coinductive_ltl @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2)))))),
% 74.60/11.67 inference(fool_elimination,[status(thm)],[f465])).
% 74.60/11.67 thf(f465,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : ((~(coinductive_lnull @ X0 @ X1) => ((coinductive_lappend @ X0 @ (coinductive_ltl @ X0 @ X1) @ X2) = (coinductive_ltl @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2)))) & ((coinductive_lnull @ X0 @ X1) => ((coinductive_ltl @ X0 @ X2) = (coinductive_ltl @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2)))))),
% 74.60/11.67 inference(rectify,[status(thm)],[f83])).
% 74.60/11.67 thf(f83,axiom,(
% 74.60/11.67 ! [X0 : $tType,X5 : coinductive_llist @ X0,X8 : coinductive_llist @ X0] : ((~(coinductive_lnull @ X0 @ X5) => ((coinductive_ltl @ X0 @ (coinductive_lappend @ X0 @ X5 @ X8)) = (coinductive_lappend @ X0 @ (coinductive_ltl @ X0 @ X5) @ X8))) & ((coinductive_lnull @ X0 @ X5) => ((coinductive_ltl @ X0 @ (coinductive_lappend @ X0 @ X5 @ X8)) = (coinductive_ltl @ X0 @ X8))))),
% 74.60/11.67 file('/export/starexec/sandbox/tmp/tmp.tZ0Cg1ODeg/DTF2THF_26636.p',fact_82_ltl__lappend)).
% 74.60/11.67 thf(f963,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : (($true != (coinductive_lfinite @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2))) | ((coinductive_lfinite @ X0 @ X1) = $true)) )),
% 74.60/11.67 inference(cnf_transformation,[status(thm)],[f891])).
% 74.60/11.67 thf(f891,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : (((((coinductive_lfinite @ X0 @ X2) = $true) & ((coinductive_lfinite @ X0 @ X1) = $true)) | ($true != (coinductive_lfinite @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2)))) & (($true = (coinductive_lfinite @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2))) | ((coinductive_lfinite @ X0 @ X2) != $true) | ((coinductive_lfinite @ X0 @ X1) != $true)))),
% 74.60/11.67 inference(flattening,[status(thm)],[f890])).
% 74.60/11.67 thf(f890,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : (((((coinductive_lfinite @ X0 @ X2) = $true) & ((coinductive_lfinite @ X0 @ X1) = $true)) | ($true != (coinductive_lfinite @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2)))) & (($true = (coinductive_lfinite @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2))) | (((coinductive_lfinite @ X0 @ X2) != $true) | ((coinductive_lfinite @ X0 @ X1) != $true))))),
% 74.60/11.67 inference(nnf_transformation,[status(thm)],[f450])).
% 74.60/11.67 thf(f450,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : ((((coinductive_lfinite @ X0 @ X2) = $true) & ((coinductive_lfinite @ X0 @ X1) = $true)) <=> ($true = (coinductive_lfinite @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2))))),
% 74.60/11.67 inference(fool_elimination,[status(thm)],[f449])).
% 74.60/11.67 thf(f449,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : ((coinductive_lfinite @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2)) = (coinductive_lfinite @ X0 @ X1) & (coinductive_lfinite @ X0 @ X2))),
% 74.60/11.67 inference(rectify,[status(thm)],[f81])).
% 74.60/11.67 thf(f81,axiom,(
% 74.60/11.67 ! [X0 : $tType,X5 : coinductive_llist @ X0,X8 : coinductive_llist @ X0] : ((coinductive_lfinite @ X0 @ (coinductive_lappend @ X0 @ X5 @ X8)) = (coinductive_lfinite @ X0 @ X5) & (coinductive_lfinite @ X0 @ X8))),
% 74.60/11.67 file('/export/starexec/sandbox/tmp/tmp.tZ0Cg1ODeg/DTF2THF_26636.p',fact_80_lfinite__lappend)).
% 74.60/11.67 thf(f11602,plain,(
% 74.60/11.67 spl31_2 | ~spl31_52),
% 74.60/11.67 inference(avatar_contradiction_clause,[status(thm)],[f11601])).
% 74.60/11.67 thf(f11601,plain,(
% 74.60/11.67 $false | (spl31_2 | ~spl31_52)),
% 74.60/11.67 inference(subsumption_resolution,[status(thm)],[f11552,f1162])).
% 74.60/11.67 thf(f11552,plain,(
% 74.60/11.67 ((coinductive_lfinite @ a @ xsa) = $true) | ~spl31_52),
% 74.60/11.67 inference(trivial_inequality_removal,[status(thm)],[f11529])).
% 74.60/11.67 thf(f11529,plain,(
% 74.60/11.67 ($true != $true) | ((coinductive_lfinite @ a @ xsa) = $true) | ~spl31_52),
% 74.60/11.67 inference(superposition,[status(thm)],[f970,f11511])).
% 74.60/11.67 thf(f11511,plain,(
% 74.60/11.67 ((coinductive_lnull @ a @ xsa) = $true) | ~spl31_52),
% 74.60/11.67 inference(avatar_component_clause,[status(thm)],[f11509])).
% 74.60/11.67 thf(f11509,definition,(
% 74.60/11.67 spl31_52 <=> ((coinductive_lnull @ a @ xsa) = $true)),
% 74.60/11.67 introduced(definition,[new_symbols(naming,[spl31_52])],[avatar_definition])).
% 74.60/11.67 thf(f11600,plain,(
% 74.60/11.67 spl31_16 | ~spl31_52),
% 74.60/11.67 inference(avatar_contradiction_clause,[status(thm)],[f11599])).
% 74.60/11.67 thf(f11599,plain,(
% 74.60/11.67 $false | (spl31_16 | ~spl31_52)),
% 74.60/11.67 inference(subsumption_resolution,[status(thm)],[f11557,f5140])).
% 74.60/11.67 thf(f5140,plain,(
% 74.60/11.67 (xsa != coinductive_LNil @ a) | spl31_16),
% 74.60/11.67 inference(avatar_component_clause,[status(thm)],[f5139])).
% 74.60/11.67 thf(f5139,definition,(
% 74.60/11.67 spl31_16 <=> (xsa = coinductive_LNil @ a)),
% 74.60/11.67 introduced(definition,[new_symbols(naming,[spl31_16])],[avatar_definition])).
% 74.60/11.67 thf(f11557,plain,(
% 74.60/11.67 (xsa = coinductive_LNil @ a) | ~spl31_52),
% 74.60/11.67 inference(trivial_inequality_removal,[status(thm)],[f11540])).
% 74.60/11.67 thf(f11540,plain,(
% 74.60/11.67 ($true != $true) | (xsa = coinductive_LNil @ a) | ~spl31_52),
% 74.60/11.67 inference(superposition,[status(thm)],[f1102,f11511])).
% 74.60/11.67 thf(f1102,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((coinductive_lnull @ X0 @ X1) != $true) | (coinductive_LNil @ X0 = X1)) )),
% 74.60/11.67 inference(cnf_transformation,[status(thm)],[f883])).
% 74.60/11.67 thf(f883,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((coinductive_LNil @ X0 = X1) | ((coinductive_lnull @ X0 @ X1) != $true))),
% 74.60/11.67 inference(ennf_transformation,[status(thm)],[f635])).
% 74.60/11.67 thf(f635,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((coinductive_lnull @ X0 @ X1) = $true) => (coinductive_LNil @ X0 = X1))),
% 74.60/11.67 inference(fool_elimination,[status(thm)],[f634])).
% 74.60/11.67 thf(f634,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((coinductive_lnull @ X0 @ X1) => (coinductive_LNil @ X0 = X1))),
% 74.60/11.67 inference(rectify,[status(thm)],[f39])).
% 74.60/11.67 thf(f39,axiom,(
% 74.60/11.67 ! [X0 : $tType,X18 : coinductive_llist @ X0] : ((coinductive_lnull @ X0 @ X18) => (coinductive_LNil @ X0 = X18))),
% 74.60/11.67 file('/export/starexec/sandbox/tmp/tmp.tZ0Cg1ODeg/DTF2THF_26636.p',fact_38_llist_Ocollapse_I1_J)).
% 74.60/11.67 thf(f11516,plain,(
% 74.60/11.67 spl31_52 | spl31_53),
% 74.60/11.67 inference(avatar_split_clause,[status(thm)],[f11322,f11513,f11509])).
% 74.60/11.67 thf(f11322,plain,(
% 74.60/11.67 ((coinductive_lnull @ a @ xsa) = $true) | ($true = (coinductive_lfinite @ a @ (coinductive_ltl @ a @ xsa)))),
% 74.60/11.67 inference(equality_resolution,[status(thm)],[f11271])).
% 74.60/11.67 thf(f11271,plain,(
% 74.60/11.67 ( ! [X0 : coinductive_llist @ a,X1 : coinductive_llist @ a] : (((coinductive_ltl @ a @ (lMirro999291890or_aux @ a @ acca @ xsa)) != (coinductive_ltl @ a @ (lMirro999291890or_aux @ a @ X1 @ X0))) | ((coinductive_lnull @ a @ X0) = $true) | ((coinductive_lfinite @ a @ (coinductive_ltl @ a @ X0)) = $true)) )),
% 74.60/11.67 inference(superposition,[status(thm)],[f1126,f995])).
% 74.60/11.67 thf(f995,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : (((coinductive_ltl @ X0 @ (lMirro999291890or_aux @ X0 @ X2 @ X1)) = (lMirro999291890or_aux @ X0 @ (coinductive_LCons @ X0 @ (coinductive_lhd @ X0 @ X1) @ X2) @ (coinductive_ltl @ X0 @ X1))) | ((coinductive_lnull @ X0 @ X1) = $true)) )),
% 74.60/11.67 inference(cnf_transformation,[status(thm)],[f881])).
% 74.60/11.67 thf(f881,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : ((((coinductive_ltl @ X0 @ (lMirro999291890or_aux @ X0 @ X2 @ X1)) = (lMirro999291890or_aux @ X0 @ (coinductive_LCons @ X0 @ (coinductive_lhd @ X0 @ X1) @ X2) @ (coinductive_ltl @ X0 @ X1))) | ((coinductive_lnull @ X0 @ X1) = $true)) & (((coinductive_lnull @ X0 @ X1) != $true) | ((coinductive_ltl @ X0 @ (lMirro999291890or_aux @ X0 @ X2 @ X1)) = (coinductive_ltl @ X0 @ X2))))),
% 74.60/11.67 inference(ennf_transformation,[status(thm)],[f799])).
% 74.60/11.67 thf(f799,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : ((((coinductive_lnull @ X0 @ X1) != $true) => ((coinductive_ltl @ X0 @ (lMirro999291890or_aux @ X0 @ X2 @ X1)) = (lMirro999291890or_aux @ X0 @ (coinductive_LCons @ X0 @ (coinductive_lhd @ X0 @ X1) @ X2) @ (coinductive_ltl @ X0 @ X1)))) & (((coinductive_lnull @ X0 @ X1) = $true) => ((coinductive_ltl @ X0 @ (lMirro999291890or_aux @ X0 @ X2 @ X1)) = (coinductive_ltl @ X0 @ X2))))),
% 74.60/11.67 inference(flattening,[status(thm)],[f577])).
% 74.60/11.67 thf(f577,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : ((((coinductive_lnull @ X0 @ X1) = $true) => ((coinductive_ltl @ X0 @ (lMirro999291890or_aux @ X0 @ X2 @ X1)) = (coinductive_ltl @ X0 @ X2))) & (~((coinductive_lnull @ X0 @ X1) = $true) => ((coinductive_ltl @ X0 @ (lMirro999291890or_aux @ X0 @ X2 @ X1)) = (lMirro999291890or_aux @ X0 @ (coinductive_LCons @ X0 @ (coinductive_lhd @ X0 @ X1) @ X2) @ (coinductive_ltl @ X0 @ X1)))))),
% 74.60/11.67 inference(fool_elimination,[status(thm)],[f576])).
% 74.60/11.67 thf(f576,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : (((coinductive_lnull @ X0 @ X1) => ((coinductive_ltl @ X0 @ (lMirro999291890or_aux @ X0 @ X2 @ X1)) = (coinductive_ltl @ X0 @ X2))) & (~(coinductive_lnull @ X0 @ X1) => ((coinductive_ltl @ X0 @ (lMirro999291890or_aux @ X0 @ X2 @ X1)) = (lMirro999291890or_aux @ X0 @ (coinductive_LCons @ X0 @ (coinductive_lhd @ X0 @ X1) @ X2) @ (coinductive_ltl @ X0 @ X1)))))),
% 74.60/11.67 inference(rectify,[status(thm)],[f68])).
% 74.60/11.67 thf(f68,axiom,(
% 74.60/11.67 ! [X0 : $tType,X5 : coinductive_llist @ X0,X4 : coinductive_llist @ X0] : (((coinductive_lnull @ X0 @ X5) => ((coinductive_ltl @ X0 @ (lMirro999291890or_aux @ X0 @ X4 @ X5)) = (coinductive_ltl @ X0 @ X4))) & (~(coinductive_lnull @ X0 @ X5) => ((coinductive_ltl @ X0 @ (lMirro999291890or_aux @ X0 @ X4 @ X5)) = (lMirro999291890or_aux @ X0 @ (coinductive_LCons @ X0 @ (coinductive_lhd @ X0 @ X5) @ X4) @ (coinductive_ltl @ X0 @ X5)))))),
% 74.60/11.67 file('/export/starexec/sandbox/tmp/tmp.tZ0Cg1ODeg/DTF2THF_26636.p',fact_67_ltl__lmirror__aux)).
% 74.60/11.67 thf(f1126,plain,(
% 74.60/11.67 ( ! [X0 : coinductive_llist @ a,X1 : coinductive_llist @ a] : (((coinductive_ltl @ a @ (lMirro999291890or_aux @ a @ acca @ xsa)) != (lMirro999291890or_aux @ a @ X0 @ X1)) | ($true = (coinductive_lfinite @ a @ X1))) )),
% 74.60/11.67 inference(cnf_transformation,[status(thm)],[f863])).
% 74.60/11.67 thf(f863,plain,(
% 74.60/11.67 ! [X0 : coinductive_llist @ a,X1 : coinductive_llist @ a] : ((($true = (coinductive_lfinite @ a @ X1)) & ((coinductive_lfinite @ a @ X0) = $true)) | ((coinductive_ltl @ a @ (lMirro999291890or_aux @ a @ acca @ xsa)) != (lMirro999291890or_aux @ a @ X0 @ X1)))),
% 74.60/11.67 inference(ennf_transformation,[status(thm)],[f314])).
% 74.60/11.67 thf(f314,plain,(
% 74.60/11.67 ! [X0 : coinductive_llist @ a,X1 : coinductive_llist @ a] : (((coinductive_ltl @ a @ (lMirro999291890or_aux @ a @ acca @ xsa)) = (lMirro999291890or_aux @ a @ X0 @ X1)) => (($true = (coinductive_lfinite @ a @ X1)) & ((coinductive_lfinite @ a @ X0) = $true)))),
% 74.60/11.67 inference(fool_elimination,[status(thm)],[f313])).
% 74.60/11.67 thf(f313,plain,(
% 74.60/11.67 ! [X0 : coinductive_llist @ a,X1 : coinductive_llist @ a] : (((coinductive_ltl @ a @ (lMirro999291890or_aux @ a @ acca @ xsa)) = (lMirro999291890or_aux @ a @ X0 @ X1)) => ((coinductive_lfinite @ a @ X0) & (coinductive_lfinite @ a @ X1)))),
% 74.60/11.67 inference(rectify,[status(thm)],[f4])).
% 74.60/11.67 thf(f4,axiom,(
% 74.60/11.67 ! [X4 : coinductive_llist @ a,X5 : coinductive_llist @ a] : (((coinductive_ltl @ a @ (lMirro999291890or_aux @ a @ acca @ xsa)) = (lMirro999291890or_aux @ a @ X4 @ X5)) => ((coinductive_lfinite @ a @ X4) & (coinductive_lfinite @ a @ X5)))),
% 74.60/11.67 file('/export/starexec/sandbox/tmp/tmp.tZ0Cg1ODeg/DTF2THF_26636.p',fact_3_LCons_Ohyps_I3_J)).
% 74.60/11.67 thf(f11503,plain,(
% 74.60/11.67 spl31_1 | ~spl31_20),
% 74.60/11.67 inference(avatar_contradiction_clause,[status(thm)],[f11502])).
% 74.60/11.67 thf(f11502,plain,(
% 74.60/11.67 $false | (spl31_1 | ~spl31_20)),
% 74.60/11.67 inference(subsumption_resolution,[status(thm)],[f11419,f1158])).
% 74.60/11.67 thf(f1158,plain,(
% 74.60/11.67 ((coinductive_lfinite @ a @ acca) != $true) | spl31_1),
% 74.60/11.67 inference(avatar_component_clause,[status(thm)],[f1156])).
% 74.60/11.67 thf(f1156,definition,(
% 74.60/11.67 spl31_1 <=> ((coinductive_lfinite @ a @ acca) = $true)),
% 74.60/11.67 introduced(definition,[new_symbols(naming,[spl31_1])],[avatar_definition])).
% 74.60/11.67 thf(f11419,plain,(
% 74.60/11.67 ((coinductive_lfinite @ a @ acca) = $true) | ~spl31_20),
% 74.60/11.67 inference(superposition,[status(thm)],[f11407,f1086])).
% 74.60/11.67 thf(f1086,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : X0] : (((coinductive_lfinite @ X0 @ (coinductive_LCons @ X0 @ X1 @ X2)) = (coinductive_lfinite @ X0 @ X2))) )),
% 74.60/11.67 inference(cnf_transformation,[status(thm)],[f764])).
% 74.60/11.67 thf(f764,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : X0,X2 : coinductive_llist @ X0] : ((coinductive_lfinite @ X0 @ (coinductive_LCons @ X0 @ X1 @ X2)) = (coinductive_lfinite @ X0 @ X2))),
% 74.60/11.67 inference(fool_elimination,[status(thm)],[f763])).
% 74.60/11.67 thf(f763,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : X0,X2 : coinductive_llist @ X0] : ((coinductive_lfinite @ X0 @ (coinductive_LCons @ X0 @ X1 @ X2)) = (coinductive_lfinite @ X0 @ X2))),
% 74.60/11.67 inference(rectify,[status(thm)],[f15])).
% 74.60/11.67 thf(f15,axiom,(
% 74.60/11.67 ! [X1 : $tType,X10 : X1,X5 : coinductive_llist @ X1] : ((coinductive_lfinite @ X1 @ (coinductive_LCons @ X1 @ X10 @ X5)) = (coinductive_lfinite @ X1 @ X5))),
% 74.60/11.67 file('/export/starexec/sandbox/tmp/tmp.tZ0Cg1ODeg/DTF2THF_26636.p',fact_14_lfinite__code_I2_J)).
% 74.60/11.67 thf(f11407,plain,(
% 74.60/11.67 ((coinductive_lfinite @ a @ (coinductive_LCons @ a @ (sK28 @ a @ xsa) @ acca)) = $true) | ~spl31_20),
% 74.60/11.67 inference(forward_demodulation,[status(thm)],[f11406,f9101])).
% 74.60/11.67 thf(f9101,plain,(
% 74.60/11.67 ((coinductive_lhd @ a @ xsa) = (sK28 @ a @ xsa)) | ~spl31_20),
% 74.60/11.67 inference(superposition,[status(thm)],[f1144,f5181])).
% 74.60/11.67 thf(f5181,plain,(
% 74.60/11.67 (xsa = (coinductive_LCons @ a @ (sK28 @ a @ xsa) @ (sK27 @ a @ xsa))) | ~spl31_20),
% 74.60/11.67 inference(avatar_component_clause,[status(thm)],[f5179])).
% 74.60/11.67 thf(f5179,definition,(
% 74.60/11.67 spl31_20 <=> (xsa = (coinductive_LCons @ a @ (sK28 @ a @ xsa) @ (sK27 @ a @ xsa)))),
% 74.60/11.67 introduced(definition,[new_symbols(naming,[spl31_20])],[avatar_definition])).
% 74.60/11.67 thf(f1144,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X2 : X0,X3 : coinductive_llist @ X0] : (((coinductive_lhd @ X0 @ (coinductive_LCons @ X0 @ X2 @ X3)) = X2)) )),
% 74.60/11.67 inference(equality_resolution,[status(thm)],[f1038])).
% 74.60/11.67 thf(f1038,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X2 : X0,X3 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : (((coinductive_lhd @ X0 @ X1) = X2) | ((coinductive_LCons @ X0 @ X2 @ X3) != X1)) )),
% 74.60/11.67 inference(cnf_transformation,[status(thm)],[f841])).
% 74.60/11.67 thf(f841,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : X0,X3 : coinductive_llist @ X0] : ((((coinductive_lhd @ X0 @ X1) = X2) & (coinductive_LNil @ X0 != X1) & ((coinductive_ltl @ X0 @ X1) = X3)) | ((coinductive_LCons @ X0 @ X2 @ X3) != X1))),
% 74.60/11.67 inference(ennf_transformation,[status(thm)],[f756])).
% 74.60/11.67 thf(f756,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : X0,X3 : coinductive_llist @ X0] : (((coinductive_LCons @ X0 @ X2 @ X3) = X1) => (((coinductive_lhd @ X0 @ X1) = X2) & (coinductive_LNil @ X0 != X1) & ((coinductive_ltl @ X0 @ X1) = X3)))),
% 74.60/11.67 inference(fool_elimination,[status(thm)],[f755])).
% 74.60/11.67 thf(f755,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : X0,X3 : coinductive_llist @ X0] : (((coinductive_LCons @ X0 @ X2 @ X3) = X1) => ((coinductive_LNil @ X0 != X1) & ((coinductive_ltl @ X0 @ X1) = X3) & ((coinductive_lhd @ X0 @ X1) = X2)))),
% 74.60/11.67 inference(rectify,[status(thm)],[f107])).
% 74.60/11.67 thf(f107,axiom,(
% 74.60/11.67 ! [X0 : $tType,X5 : coinductive_llist @ X0,X17 : X0,X8 : coinductive_llist @ X0] : (((coinductive_LCons @ X0 @ X17 @ X8) = X5) => ((coinductive_LNil @ X0 != X5) & ((coinductive_ltl @ X0 @ X5) = X8) & ((coinductive_lhd @ X0 @ X5) = X17)))),
% 74.60/11.67 file('/export/starexec/sandbox/tmp/tmp.tZ0Cg1ODeg/DTF2THF_26636.p',fact_106_eq__LConsD)).
% 74.60/11.67 thf(f11406,plain,(
% 74.60/11.67 ((coinductive_lfinite @ a @ (coinductive_LCons @ a @ (coinductive_lhd @ a @ xsa) @ acca)) = $true) | ~spl31_20),
% 74.60/11.67 inference(subsumption_resolution,[status(thm)],[f11386,f9100])).
% 74.60/11.67 thf(f9100,plain,(
% 74.60/11.67 ((coinductive_lnull @ a @ xsa) != $true) | ~spl31_20),
% 74.60/11.67 inference(superposition,[status(thm)],[f1143,f5181])).
% 74.60/11.67 thf(f1143,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X4 : X0,X5 : coinductive_llist @ X0] : (((coinductive_lnull @ X0 @ (coinductive_LCons @ X0 @ X4 @ X5)) != $true)) )),
% 74.60/11.67 inference(equality_resolution,[status(thm)],[f1027])).
% 74.60/11.67 thf(f1027,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X1 : coinductive_llist @ X0,X4 : X0,X5 : coinductive_llist @ X0] : (((coinductive_lnull @ X0 @ X1) != $true) | ((coinductive_LCons @ X0 @ X4 @ X5) != X1)) )),
% 74.60/11.67 inference(cnf_transformation,[status(thm)],[f915])).
% 74.60/11.67 thf(f915,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((((coinductive_LCons @ X0 @ (sK7 @ X0 @ X1) @ (sK8 @ X0 @ X1)) = X1) | ((coinductive_lnull @ X0 @ X1) = $true)) & (((coinductive_lnull @ X0 @ X1) != $true) | ! [X4 : X0,X5 : coinductive_llist @ X0] : ((coinductive_LCons @ X0 @ X4 @ X5) != X1)))),
% 74.60/11.67 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f913,f914])).
% 74.60/11.67 thf(f914,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (? [X2 : X0,X3 : coinductive_llist @ X0] : ((coinductive_LCons @ X0 @ X2 @ X3) = X1) => ((coinductive_LCons @ X0 @ (sK7 @ X0 @ X1) @ (sK8 @ X0 @ X1)) = X1))),
% 74.60/11.67 introduced(definition,[],[choice_axiom])).
% 74.60/11.67 thf(f913,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((? [X2 : X0,X3 : coinductive_llist @ X0] : ((coinductive_LCons @ X0 @ X2 @ X3) = X1) | ((coinductive_lnull @ X0 @ X1) = $true)) & (((coinductive_lnull @ X0 @ X1) != $true) | ! [X4 : X0,X5 : coinductive_llist @ X0] : ((coinductive_LCons @ X0 @ X4 @ X5) != X1)))),
% 74.60/11.67 inference(rectify,[status(thm)],[f912])).
% 74.60/11.67 thf(f912,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((? [X2 : X0,X3 : coinductive_llist @ X0] : ((coinductive_LCons @ X0 @ X2 @ X3) = X1) | ((coinductive_lnull @ X0 @ X1) = $true)) & (((coinductive_lnull @ X0 @ X1) != $true) | ! [X2 : X0,X3 : coinductive_llist @ X0] : ((coinductive_LCons @ X0 @ X2 @ X3) != X1)))),
% 74.60/11.67 inference(nnf_transformation,[status(thm)],[f779])).
% 74.60/11.67 thf(f779,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (? [X2 : X0,X3 : coinductive_llist @ X0] : ((coinductive_LCons @ X0 @ X2 @ X3) = X1) <=> ((coinductive_lnull @ X0 @ X1) != $true))),
% 74.60/11.67 inference(flattening,[status(thm)],[f575])).
% 74.60/11.67 thf(f575,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (? [X2 : X0,X3 : coinductive_llist @ X0] : ((coinductive_LCons @ X0 @ X2 @ X3) = X1) <=> ~((coinductive_lnull @ X0 @ X1) = $true))),
% 74.60/11.67 inference(fool_elimination,[status(thm)],[f574])).
% 74.60/11.67 thf(f574,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (? [X2 : X0,X3 : coinductive_llist @ X0] : ((coinductive_LCons @ X0 @ X2 @ X3) = X1) = ~(coinductive_lnull @ X0 @ X1))),
% 74.60/11.67 inference(rectify,[status(thm)],[f56])).
% 74.60/11.67 thf(f56,axiom,(
% 74.60/11.67 ! [X0 : $tType,X5 : coinductive_llist @ X0] : (? [X21 : X0,X31 : coinductive_llist @ X0] : ((coinductive_LCons @ X0 @ X21 @ X31) = X5) = ~(coinductive_lnull @ X0 @ X5))),
% 74.60/11.67 file('/export/starexec/sandbox/tmp/tmp.tZ0Cg1ODeg/DTF2THF_26636.p',fact_55_not__lnull__conv)).
% 74.60/11.67 thf(f11386,plain,(
% 74.60/11.67 ((coinductive_lnull @ a @ xsa) = $true) | ((coinductive_lfinite @ a @ (coinductive_LCons @ a @ (coinductive_lhd @ a @ xsa) @ acca)) = $true)),
% 74.60/11.67 inference(equality_resolution,[status(thm)],[f11219])).
% 74.60/11.67 thf(f11219,plain,(
% 74.60/11.67 ( ! [X0 : coinductive_llist @ a,X1 : coinductive_llist @ a] : (((coinductive_ltl @ a @ (lMirro999291890or_aux @ a @ acca @ xsa)) != (coinductive_ltl @ a @ (lMirro999291890or_aux @ a @ X1 @ X0))) | ((coinductive_lnull @ a @ X0) = $true) | ((coinductive_lfinite @ a @ (coinductive_LCons @ a @ (coinductive_lhd @ a @ X0) @ X1)) = $true)) )),
% 74.60/11.67 inference(superposition,[status(thm)],[f1125,f995])).
% 74.60/11.67 thf(f1125,plain,(
% 74.60/11.67 ( ! [X0 : coinductive_llist @ a,X1 : coinductive_llist @ a] : (((coinductive_ltl @ a @ (lMirro999291890or_aux @ a @ acca @ xsa)) != (lMirro999291890or_aux @ a @ X0 @ X1)) | ((coinductive_lfinite @ a @ X0) = $true)) )),
% 74.60/11.67 inference(cnf_transformation,[status(thm)],[f863])).
% 74.60/11.67 thf(f5228,plain,(
% 74.60/11.67 spl31_1 | ~spl31_16),
% 74.60/11.67 inference(avatar_contradiction_clause,[status(thm)],[f5227])).
% 74.60/11.67 thf(f5227,plain,(
% 74.60/11.67 $false | (spl31_1 | ~spl31_16)),
% 74.60/11.67 inference(subsumption_resolution,[status(thm)],[f5226,f1158])).
% 74.60/11.67 thf(f5226,plain,(
% 74.60/11.67 ((coinductive_lfinite @ a @ acca) = $true) | ~spl31_16),
% 74.60/11.67 inference(forward_demodulation,[status(thm)],[f5184,f1117])).
% 74.60/11.67 thf(f1117,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((lMirro999291890or_aux @ X0 @ X1 @ coinductive_LNil @ X0) = X1)) )),
% 74.60/11.67 inference(cnf_transformation,[status(thm)],[f752])).
% 74.60/11.67 thf(f752,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((lMirro999291890or_aux @ X0 @ X1 @ coinductive_LNil @ X0) = X1)),
% 74.60/11.67 inference(fool_elimination,[status(thm)],[f751])).
% 74.60/11.67 thf(f751,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((lMirro999291890or_aux @ X0 @ X1 @ coinductive_LNil @ X0) = X1)),
% 74.60/11.67 inference(rectify,[status(thm)],[f25])).
% 74.60/11.67 thf(f25,axiom,(
% 74.60/11.67 ! [X0 : $tType,X4 : coinductive_llist @ X0] : ((lMirro999291890or_aux @ X0 @ X4 @ coinductive_LNil @ X0) = X4)),
% 74.60/11.67 file('/export/starexec/sandbox/tmp/tmp.tZ0Cg1ODeg/DTF2THF_26636.p',fact_24_lmirror__aux__simps_I1_J)).
% 74.60/11.67 thf(f5184,plain,(
% 74.60/11.67 ($true = (coinductive_lfinite @ a @ (lMirro999291890or_aux @ a @ acca @ coinductive_LNil @ a))) | ~spl31_16),
% 74.60/11.67 inference(backward_demodulation,[status(thm)],[f1043,f5141])).
% 74.60/11.67 thf(f5141,plain,(
% 74.60/11.67 (xsa = coinductive_LNil @ a) | ~spl31_16),
% 74.60/11.67 inference(avatar_component_clause,[status(thm)],[f5139])).
% 74.60/11.67 thf(f1043,plain,(
% 74.60/11.67 ((coinductive_lfinite @ a @ (lMirro999291890or_aux @ a @ acca @ xsa)) = $true)),
% 74.60/11.67 inference(cnf_transformation,[status(thm)],[f282])).
% 74.60/11.67 thf(f282,plain,(
% 74.60/11.67 ((coinductive_lfinite @ a @ (lMirro999291890or_aux @ a @ acca @ xsa)) = $true)),
% 74.60/11.67 inference(fool_elimination,[status(thm)],[f281])).
% 74.60/11.67 thf(f281,plain,(
% 74.60/11.67 (coinductive_lfinite @ a @ (lMirro999291890or_aux @ a @ acca @ xsa))),
% 74.60/11.67 inference(rectify,[status(thm)],[f3])).
% 74.60/11.67 thf(f3,axiom,(
% 74.60/11.67 (coinductive_lfinite @ a @ (lMirro999291890or_aux @ a @ acca @ xsa))),
% 74.60/11.67 file('/export/starexec/sandbox/tmp/tmp.tZ0Cg1ODeg/DTF2THF_26636.p',fact_2_LCons_Ohyps_I1_J)).
% 74.60/11.67 thf(f5182,plain,(
% 74.60/11.67 spl31_20 | spl31_16 | ~spl31_2),
% 74.60/11.67 inference(avatar_split_clause,[status(thm)],[f5161,f1160,f5139,f5179])).
% 74.60/11.67 thf(f5161,plain,(
% 74.60/11.67 (xsa = (coinductive_LCons @ a @ (sK28 @ a @ xsa) @ (sK27 @ a @ xsa))) | (xsa = coinductive_LNil @ a) | ~spl31_2),
% 74.60/11.67 inference(trivial_inequality_removal,[status(thm)],[f5155])).
% 74.60/11.67 thf(f5155,plain,(
% 74.60/11.67 (xsa = (coinductive_LCons @ a @ (sK28 @ a @ xsa) @ (sK27 @ a @ xsa))) | ($true != $true) | (xsa = coinductive_LNil @ a) | ~spl31_2),
% 74.60/11.67 inference(superposition,[status(thm)],[f1115,f1161])).
% 74.60/11.67 thf(f1161,plain,(
% 74.60/11.67 ((coinductive_lfinite @ a @ xsa) = $true) | ~spl31_2),
% 74.60/11.67 inference(avatar_component_clause,[status(thm)],[f1160])).
% 74.60/11.67 thf(f1115,plain,(
% 74.60/11.67 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((coinductive_lfinite @ X0 @ X1) != $true) | ((coinductive_LCons @ X0 @ (sK28 @ X0 @ X1) @ (sK27 @ X0 @ X1)) = X1) | (coinductive_LNil @ X0 = X1)) )),
% 74.60/11.67 inference(cnf_transformation,[status(thm)],[f949])).
% 74.60/11.67 thf(f949,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((coinductive_LNil @ X0 = X1) | ((coinductive_lfinite @ X0 @ X1) != $true) | (($true = (coinductive_lfinite @ X0 @ (sK27 @ X0 @ X1))) & ((coinductive_LCons @ X0 @ (sK28 @ X0 @ X1) @ (sK27 @ X0 @ X1)) = X1)))),
% 74.60/11.67 inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28])],[f834,f948,f947])).
% 74.60/11.67 thf(f947,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (? [X2 : coinductive_llist @ X0] : (((coinductive_lfinite @ X0 @ X2) = $true) & ? [X3 : X0] : ((coinductive_LCons @ X0 @ X3 @ X2) = X1)) => (($true = (coinductive_lfinite @ X0 @ (sK27 @ X0 @ X1))) & ? [X3 : X0] : ((coinductive_LCons @ X0 @ X3 @ (sK27 @ X0 @ X1)) = X1)))),
% 74.60/11.67 introduced(definition,[],[choice_axiom])).
% 74.60/11.67 thf(f948,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (? [X3 : X0] : ((coinductive_LCons @ X0 @ X3 @ (sK27 @ X0 @ X1)) = X1) => ((coinductive_LCons @ X0 @ (sK28 @ X0 @ X1) @ (sK27 @ X0 @ X1)) = X1))),
% 74.60/11.67 introduced(definition,[],[choice_axiom])).
% 74.60/11.67 thf(f834,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((coinductive_LNil @ X0 = X1) | ((coinductive_lfinite @ X0 @ X1) != $true) | ? [X2 : coinductive_llist @ X0] : (((coinductive_lfinite @ X0 @ X2) = $true) & ? [X3 : X0] : ((coinductive_LCons @ X0 @ X3 @ X2) = X1)))),
% 74.60/11.67 inference(flattening,[status(thm)],[f833])).
% 74.60/11.67 thf(f833,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((? [X2 : coinductive_llist @ X0] : (((coinductive_lfinite @ X0 @ X2) = $true) & ? [X3 : X0] : ((coinductive_LCons @ X0 @ X3 @ X2) = X1)) | (coinductive_LNil @ X0 = X1)) | ((coinductive_lfinite @ X0 @ X1) != $true))),
% 74.60/11.67 inference(ennf_transformation,[status(thm)],[f774])).
% 74.60/11.67 thf(f774,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((coinductive_lfinite @ X0 @ X1) = $true) => ((coinductive_LNil @ X0 != X1) => ~! [X2 : coinductive_llist @ X0] : (? [X3 : X0] : ((coinductive_LCons @ X0 @ X3 @ X2) = X1) => ((coinductive_lfinite @ X0 @ X2) != $true))))),
% 74.60/11.67 inference(flattening,[status(thm)],[f355])).
% 74.60/11.67 thf(f355,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((coinductive_lfinite @ X0 @ X1) = $true) => ((coinductive_LNil @ X0 != X1) => ~! [X2 : coinductive_llist @ X0] : (? [X3 : X0] : ((coinductive_LCons @ X0 @ X3 @ X2) = X1) => ~((coinductive_lfinite @ X0 @ X2) = $true))))),
% 74.60/11.67 inference(fool_elimination,[status(thm)],[f354])).
% 74.60/11.67 thf(f354,plain,(
% 74.60/11.67 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((coinductive_lfinite @ X0 @ X1) => ((coinductive_LNil @ X0 != X1) => ~! [X2 : coinductive_llist @ X0] : (? [X3 : X0] : ((coinductive_LCons @ X0 @ X3 @ X2) = X1) => ~(coinductive_lfinite @ X0 @ X2))))),
% 74.60/11.67 inference(rectify,[status(thm)],[f51])).
% 74.60/11.67 thf(f51,axiom,(
% 74.60/11.67 ! [X0 : $tType,X19 : coinductive_llist @ X0] : ((coinductive_lfinite @ X0 @ X19) => ((coinductive_LNil @ X0 != X19) => ~! [X7 : coinductive_llist @ X0] : (? [X23 : X0] : ((coinductive_LCons @ X0 @ X23 @ X7) = X19) => ~(coinductive_lfinite @ X0 @ X7))))),
% 74.60/11.67 file('/export/starexec/sandbox/tmp/tmp.tZ0Cg1ODeg/DTF2THF_26636.p',fact_50_lfinite_Ocases)).
% 74.60/11.67 thf(f1163,plain,(
% 74.60/11.67 ~spl31_1 | ~spl31_2),
% 74.60/11.67 inference(avatar_split_clause,[status(thm)],[f1042,f1160,f1156])).
% 74.60/11.67 thf(f1042,plain,(
% 74.60/11.67 ((coinductive_lfinite @ a @ acca) != $true) | ((coinductive_lfinite @ a @ xsa) != $true)),
% 74.60/11.67 inference(cnf_transformation,[status(thm)],[f821])).
% 74.60/11.67 thf(f821,plain,(
% 74.60/11.67 ((coinductive_lfinite @ a @ xsa) != $true) | ((coinductive_lfinite @ a @ acca) != $true)),
% 74.60/11.67 inference(ennf_transformation,[status(thm)],[f357])).
% 74.60/11.67 thf(f357,plain,(
% 74.60/11.67 ~(((coinductive_lfinite @ a @ acca) = $true) & ((coinductive_lfinite @ a @ xsa) = $true))),
% 74.60/11.67 inference(fool_elimination,[status(thm)],[f356])).
% 74.60/11.67 thf(f356,plain,(
% 74.60/11.67 ~((coinductive_lfinite @ a @ acca) & (coinductive_lfinite @ a @ xsa))),
% 74.60/11.67 inference(rectify,[status(thm)],[f259])).
% 74.60/11.67 thf(f259,negated_conjecture,(
% 74.60/11.67 ~((coinductive_lfinite @ a @ acca) & (coinductive_lfinite @ a @ xsa))),
% 74.60/11.67 inference(negated_conjecture,[status(cth)],[f258])).
% 74.60/11.67 thf(f258,conjecture,(
% 74.60/11.67 (coinductive_lfinite @ a @ acca) & (coinductive_lfinite @ a @ xsa)),
% 74.60/11.67 file('/export/starexec/sandbox/tmp/tmp.tZ0Cg1ODeg/DTF2THF_26636.p',conj_0)).
% 74.60/11.67 % SZS output end Proof for DTF2THF_26636
% 74.60/11.67 % (27202)------------------------------
% 74.60/11.67 % (27202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.60/11.67 % (27202)Termination reason: Refutation
% 74.60/11.67
% 74.60/11.67 % (27202)Memory used [KB]: 11769
% 74.60/11.67 % (27202)Time elapsed: 2.175 s
% 74.60/11.67 % (27202)Instructions burned: 6975 (million)
% 74.60/11.67 % (27202)------------------------------
% 74.60/11.67 % (27202)------------------------------
% 74.60/11.67 % (26964)Success in time 10.56 s
%------------------------------------------------------------------------------