%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT225^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 08:45:12 AM UTC 2026
% Result : Theorem 20.67s 4.15s
% Output : Refutation 20.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : DAT225^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n002.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 06:11:18 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.42 ---- Original DTF file ---
% 0.15/0.42 thf(spec,logic,$$dhol).
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 % File : DAT225^1 : TPTP v9.2.1. Released v7.0.0.
% 0.15/0.42 % Domain : Data Structures
% 0.15/0.42 % Problem : Tllist 693
% 0.15/0.42 % Version : [Bla16] axioms : Especial.
% 0.15/0.42 % English :
% 0.15/0.42
% 0.15/0.42 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.15/0.42 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.15/0.42 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.15/0.42 % Source : [Bla16]
% 0.15/0.42 % Names : tllist__693.p [Bla16]
% 0.15/0.42
% 0.15/0.42 % Status : Theorem
% 0.15/0.42 % Rating : 0.67 v8.1.0, 1.00 v7.1.0
% 0.15/0.42 % Syntax : Number of formulae : 308 ( 152 unt; 49 typ; 0 def)
% 0.15/0.42 % Number of atoms : 596 ( 292 equ; 0 cnn)
% 0.15/0.42 % Maximal formula atoms : 11 ( 2 avg)
% 0.15/0.42 % Number of connectives : 4175 ( 92 ~; 14 |; 64 &;3764 @)
% 0.15/0.42 % ( 0 <=>; 241 =>; 0 <=; 0 <~>)
% 0.15/0.42 % Maximal formula depth : 28 ( 8 avg)
% 0.15/0.42 % Number of types : 7 ( 6 usr)
% 0.15/0.42 % Number of type conns : 317 ( 317 >; 0 *; 0 +; 0 <<)
% 0.15/0.42 % Number of symbols : 46 ( 43 usr; 4 con; 0-7 aty)
% 0.15/0.42 % Number of variables : 1329 ( 124 ^;1118 !; 39 ?;1329 :)
% 0.15/0.42 % ( 48 !>; 0 ?*; 0 @-; 0 @+)
% 0.15/0.42 % SPC : TH1_THM_EQU_NAR
% 0.15/0.42
% 0.15/0.42 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.15/0.42 % 2016-07-13 14:53:24.453
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 %----Could-be-implicit typings (11)
% 0.15/0.42 thf(ty_t_TLList__Mirabelle__qhjoikztpd_Otllist,type,
% 0.15/0.42 tLList446370796tllist: $tType > $tType > $tType ).
% 0.15/0.42
% 0.15/0.42 thf(ty_t_Coinductive__List_Ollist,type,
% 0.15/0.42 coinductive_llist: $tType > $tType ).
% 0.15/0.42
% 0.15/0.42 thf(ty_t_Product__Type_Oprod,type,
% 0.15/0.42 product_prod: $tType > $tType > $tType ).
% 0.15/0.42
% 0.15/0.42 thf(ty_t_Set_Oset,type,
% 0.15/0.42 set: $tType > $tType ).
% 0.15/0.42
% 0.15/0.42 thf(ty_t_itself,type,
% 0.15/0.42 itself: $tType > $tType ).
% 0.15/0.42
% 0.15/0.42 thf(ty_tf_f,type,
% 0.15/0.42 f: $tType ).
% 0.15/0.42
% 0.15/0.42 thf(ty_tf_e,type,
% 0.15/0.42 e: $tType ).
% 0.15/0.42
% 0.15/0.42 thf(ty_tf_d,type,
% 0.15/0.42 d: $tType ).
% 0.15/0.42
% 0.15/0.42 thf(ty_tf_c,type,
% 0.15/0.42 c: $tType ).
% 0.15/0.42
% 0.15/0.42 thf(ty_tf_b,type,
% 0.15/0.42 b: $tType ).
% 0.15/0.42
% 0.15/0.42 thf(ty_tf_a,type,
% 0.15/0.42 a: $tType ).
% 0.15/0.42
% 0.15/0.42 %----Explicit typings (38)
% 0.15/0.42 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 0.15/0.42 coindu328551480prefix:
% 0.15/0.42 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Coinductive__List_Olappend,type,
% 0.15/0.42 coinductive_lappend:
% 0.15/0.42 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Coinductive__List_Olfilter,type,
% 0.15/0.42 coinductive_lfilter:
% 0.15/0.42 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Coinductive__List_Olfinite,type,
% 0.15/0.42 coinductive_lfinite:
% 0.15/0.42 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Coinductive__List_Ollast,type,
% 0.15/0.42 coinductive_llast:
% 0.15/0.42 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.15/0.42 coinductive_LCons:
% 0.15/0.42 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 0.15/0.42 coinductive_LNil:
% 0.15/0.42 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Coinductive__List_Ollist_Ollist__all2,type,
% 0.15/0.42 coindu1486289336t_all2:
% 0.15/0.42 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ B ) > $o ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Coinductive__List_Ollist_Olnull,type,
% 0.15/0.42 coinductive_lnull:
% 0.15/0.42 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Coinductive__List_Ollist_Olset,type,
% 0.15/0.42 coinductive_lset:
% 0.15/0.42 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Coinductive__List_Olprefix,type,
% 0.15/0.42 coinductive_lprefix:
% 0.15/0.42 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 0.15/0.42 coindu1478340336prefix:
% 0.15/0.42 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_HOL_OThe,type,
% 0.15/0.42 the:
% 0.15/0.42 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_HOL_Oundefined,type,
% 0.15/0.42 undefined:
% 0.15/0.42 !>[A: $tType] : A ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_If,type,
% 0.15/0.42 if:
% 0.15/0.42 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.15/0.42 sup_sup:
% 0.15/0.42 !>[A: $tType] : ( A > A > A ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Product__Type_OPair,type,
% 0.15/0.42 product_Pair:
% 0.15/0.42 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Product__Type_Oapfst,type,
% 0.15/0.42 product_apfst:
% 0.15/0.42 !>[A: $tType,C: $tType,B: $tType] : ( ( A > C ) > ( product_prod @ A @ B ) > ( product_prod @ C @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 0.15/0.42 produc2004651681e_prod:
% 0.15/0.42 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Product__Type_Oprod_Ocase__prod,type,
% 0.15/0.42 product_case_prod:
% 0.15/0.42 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Product__Type_Oprod_Ofst,type,
% 0.15/0.42 product_fst:
% 0.15/0.42 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > A ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Product__Type_Oprod_Osnd,type,
% 0.15/0.42 product_snd:
% 0.15/0.42 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > B ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Product__Type_Oprod_Oswap,type,
% 0.15/0.42 product_swap:
% 0.15/0.42 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > ( product_prod @ B @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Product__Type_Oscomp,type,
% 0.15/0.42 product_scomp:
% 0.15/0.42 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( A > ( product_prod @ B @ C ) ) > ( B > C > D ) > A > D ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Pure_Otype,type,
% 0.15/0.42 type:
% 0.15/0.42 !>[A: $tType] : ( itself @ A ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Relation_Oreflp,type,
% 0.15/0.42 reflp:
% 0.15/0.42 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_Set_OCollect,type,
% 0.15/0.42 collect:
% 0.15/0.42 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Ocr__tllist,type,
% 0.15/0.42 tLList47617868tllist:
% 0.15/0.42 !>[A: $tType,B: $tType] : ( ( product_prod @ ( coinductive_llist @ A ) @ B ) > ( tLList446370796tllist @ A @ B ) > $o ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Olappendt,type,
% 0.15/0.42 tLList98099029ppendt:
% 0.15/0.42 !>[A: $tType,B: $tType] : ( ( coinductive_llist @ A ) > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist__of__llist,type,
% 0.15/0.42 tLList1672613558_llist:
% 0.15/0.42 !>[B: $tType,A: $tType] : ( B > ( coinductive_llist @ A ) > ( tLList446370796tllist @ A @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_c_member,type,
% 0.15/0.42 member:
% 0.15/0.42 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_v_Pa,type,
% 0.15/0.42 pa: a > b > $o ).
% 0.15/0.42
% 0.15/0.42 thf(sy_v_Qa,type,
% 0.15/0.42 qa: c > d > $o ).
% 0.15/0.42
% 0.15/0.42 thf(sy_v_Ra,type,
% 0.15/0.42 ra: e > f > $o ).
% 0.15/0.42
% 0.15/0.42 thf(sy_v_xs_Ha,type,
% 0.15/0.42 xs_a: c > ( product_prod @ ( coinductive_llist @ a ) @ e ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_v_xsa,type,
% 0.15/0.42 xsa: product_prod @ ( coinductive_llist @ a ) @ c ).
% 0.15/0.42
% 0.15/0.42 thf(sy_v_ys_Ha,type,
% 0.15/0.42 ys_a: d > ( product_prod @ ( coinductive_llist @ b ) @ f ) ).
% 0.15/0.42
% 0.15/0.42 thf(sy_v_ysa,type,
% 0.15/0.42 ysa: product_prod @ ( coinductive_llist @ b ) @ d ).
% 0.15/0.42
% 0.15/0.42 %----Relevant facts (253)
% 0.15/0.42 thf(fact_0_fst__apfst,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,C: $tType,F: C > A,X: product_prod @ C @ B] :
% 0.15/0.42 ( ( product_fst @ A @ B @ ( product_apfst @ C @ A @ B @ F @ X ) )
% 0.15/0.42 = ( F @ ( product_fst @ C @ B @ X ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % fst_apfst
% 0.15/0.42 thf(fact_1_apfst__eq__conv,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,C: $tType,F: C > A,X: product_prod @ C @ B,G: C > A] :
% 0.15/0.42 ( ( ( product_apfst @ C @ A @ B @ F @ X )
% 0.15/0.42 = ( product_apfst @ C @ A @ B @ G @ X ) )
% 0.15/0.42 = ( ( F @ ( product_fst @ C @ B @ X ) )
% 0.15/0.42 = ( G @ ( product_fst @ C @ B @ X ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % apfst_eq_conv
% 0.15/0.42 thf(fact_2_lfinite__lappend,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lfinite @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.15/0.42 = ( ( coinductive_lfinite @ A @ Xs )
% 0.15/0.42 & ( coinductive_lfinite @ A @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfinite_lappend
% 0.15/0.42 thf(fact_3_split__part,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,P: $o,Q: A > B > $o] :
% 0.15/0.42 ( ( product_case_prod @ A @ B @ $o
% 0.15/0.42 @ ^ [A2: A,B2: B] :
% 0.15/0.42 ( P
% 0.15/0.42 & ( Q @ A2 @ B2 ) ) )
% 0.15/0.42 = ( ^ [Ab: product_prod @ A @ B] :
% 0.15/0.42 ( P
% 0.15/0.42 & ( product_case_prod @ A @ B @ $o @ Q @ Ab ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % split_part
% 0.15/0.42 thf(fact_4_llist__all2__lappendI,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,Xs2: coinductive_llist @ A,Ys2: coinductive_llist @ B] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.15/0.42 => ( ( ( coinductive_lfinite @ A @ Xs )
% 0.15/0.42 => ( ( coinductive_lfinite @ B @ Ys )
% 0.15/0.42 => ( coindu1486289336t_all2 @ A @ B @ P @ Xs2 @ Ys2 ) ) )
% 0.15/0.42 => ( coindu1486289336t_all2 @ A @ B @ P @ ( coinductive_lappend @ A @ Xs @ Xs2 ) @ ( coinductive_lappend @ B @ Ys @ Ys2 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_lappendI
% 0.15/0.42 thf(fact_5_fst__def,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType] :
% 0.15/0.42 ( ( product_fst @ A @ B )
% 0.15/0.42 = ( product_case_prod @ A @ B @ A
% 0.15/0.42 @ ^ [X1: A,X2: B] : X1 ) ) ).
% 0.15/0.42
% 0.15/0.42 % fst_def
% 0.15/0.42 thf(fact_6_case__prod__app,axiom,
% 0.15/0.42 ! [A: $tType,D: $tType,C: $tType,B: $tType] :
% 0.15/0.42 ( ( product_case_prod @ B @ C @ ( D > A ) )
% 0.15/0.42 = ( ^ [F2: B > C > D > A,X3: product_prod @ B @ C,Y: D] :
% 0.15/0.42 ( product_case_prod @ B @ C @ A
% 0.15/0.42 @ ^ [L: B,R: C] : ( F2 @ L @ R @ Y )
% 0.15/0.42 @ X3 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % case_prod_app
% 0.15/0.42 thf(fact_7_lappend__inf,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.15/0.42 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.15/0.42 = Xs ) ) ).
% 0.15/0.42
% 0.15/0.42 % lappend_inf
% 0.15/0.42 thf(fact_8_llist__all2__lfiniteD,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.15/0.42 => ( ( coinductive_lfinite @ A @ Xs )
% 0.15/0.42 = ( coinductive_lfinite @ B @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_lfiniteD
% 0.15/0.42 thf(fact_9_llist__all2__conj,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ B
% 0.15/0.42 @ ^ [X3: A,Y: B] :
% 0.15/0.42 ( ( P @ X3 @ Y )
% 0.15/0.42 & ( Q @ X3 @ Y ) )
% 0.15/0.42 @ Xs
% 0.15/0.42 @ Ys )
% 0.15/0.42 = ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.15/0.42 & ( coindu1486289336t_all2 @ A @ B @ Q @ Xs @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_conj
% 0.15/0.42 thf(fact_10_prod_Odisc__eq__case,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 0.15/0.42 ( product_case_prod @ A @ B @ $o
% 0.15/0.42 @ ^ [Uu: A,Uv: B] : $true
% 0.15/0.42 @ Prod ) ).
% 0.15/0.42
% 0.15/0.42 % prod.disc_eq_case
% 0.15/0.42 thf(fact_11_prod_Ocase__distrib,axiom,
% 0.15/0.42 ! [C: $tType,D: $tType,B: $tType,A: $tType,H: C > D,F: A > B > C,Prod: product_prod @ A @ B] :
% 0.15/0.42 ( ( H @ ( product_case_prod @ A @ B @ C @ F @ Prod ) )
% 0.15/0.42 = ( product_case_prod @ A @ B @ D
% 0.15/0.42 @ ^ [X1: A,X2: B] : ( H @ ( F @ X1 @ X2 ) )
% 0.15/0.42 @ Prod ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod.case_distrib
% 0.15/0.42 thf(fact_12_llist_Orel__refl,axiom,
% 0.15/0.42 ! [B: $tType,Ra: B > B > $o,X: coinductive_llist @ B] :
% 0.15/0.42 ( ! [X4: B] : ( Ra @ X4 @ X4 )
% 0.15/0.42 => ( coindu1486289336t_all2 @ B @ B @ Ra @ X @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.rel_refl
% 0.15/0.42 thf(fact_13_llist_Orel__eq,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ A
% 0.15/0.42 @ ^ [Y2: A,Z: A] : ( Y2 = Z ) )
% 0.15/0.42 = ( ^ [Y2: coinductive_llist @ A,Z: coinductive_llist @ A] : ( Y2 = Z ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.rel_eq
% 0.15/0.42 thf(fact_14_llist__all2__mono,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,P2: A > B > $o] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.15/0.42 => ( ! [X4: A,Y3: B] :
% 0.15/0.42 ( ( P @ X4 @ Y3 )
% 0.15/0.42 => ( P2 @ X4 @ Y3 ) )
% 0.15/0.42 => ( coindu1486289336t_all2 @ A @ B @ P2 @ Xs @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_mono
% 0.15/0.42 thf(fact_15_llist__all2__rsp,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,R2: A > B > $o,S: A > A > $o,T: B > B > $o,X: coinductive_llist @ A,Y4: coinductive_llist @ B,A3: coinductive_llist @ A,B3: coinductive_llist @ B] :
% 0.15/0.42 ( ! [X4: A,Y3: B] :
% 0.15/0.42 ( ( R2 @ X4 @ Y3 )
% 0.15/0.42 => ! [A4: A,B4: B] :
% 0.15/0.42 ( ( R2 @ A4 @ B4 )
% 0.15/0.42 => ( ( S @ X4 @ A4 )
% 0.15/0.42 = ( T @ Y3 @ B4 ) ) ) )
% 0.15/0.42 => ( ( coindu1486289336t_all2 @ A @ B @ R2 @ X @ Y4 )
% 0.15/0.42 => ( ( coindu1486289336t_all2 @ A @ B @ R2 @ A3 @ B3 )
% 0.15/0.42 => ( ( coindu1486289336t_all2 @ A @ A @ S @ X @ A3 )
% 0.15/0.42 = ( coindu1486289336t_all2 @ B @ B @ T @ Y4 @ B3 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_rsp
% 0.15/0.42 thf(fact_16_lappend__assoc,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 0.15/0.42 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lappend_assoc
% 0.15/0.42 thf(fact_17_internal__case__prod__def,axiom,
% 0.15/0.42 ! [C: $tType,B: $tType,A: $tType] :
% 0.15/0.42 ( ( produc2004651681e_prod @ A @ B @ C )
% 0.15/0.42 = ( product_case_prod @ A @ B @ C ) ) ).
% 0.15/0.42
% 0.15/0.42 % internal_case_prod_def
% 0.15/0.42 thf(fact_18_reflp__tllist,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType] :
% 0.15/0.42 ( reflp @ ( product_prod @ ( coinductive_llist @ A ) @ B )
% 0.15/0.42 @ ( product_case_prod @ ( coinductive_llist @ A ) @ B @ ( ( product_prod @ ( coinductive_llist @ A ) @ B ) > $o )
% 0.15/0.42 @ ^ [Xs3: coinductive_llist @ A,A2: B] :
% 0.15/0.42 ( product_case_prod @ ( coinductive_llist @ A ) @ B @ $o
% 0.15/0.42 @ ^ [Ys3: coinductive_llist @ A,B2: B] :
% 0.15/0.42 ( ( Xs3 = Ys3 )
% 0.15/0.42 & ( ( coinductive_lfinite @ A @ Ys3 )
% 0.15/0.42 => ( A2 = B2 ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % reflp_tllist
% 0.15/0.42 thf(fact_19_tllist_Oabs__eq__iff,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,X: product_prod @ ( coinductive_llist @ A ) @ B,Y4: product_prod @ ( coinductive_llist @ A ) @ B] :
% 0.15/0.42 ( ( ( product_case_prod @ ( coinductive_llist @ A ) @ B @ ( tLList446370796tllist @ A @ B )
% 0.15/0.42 @ ^ [Xs3: coinductive_llist @ A,A2: B] : ( tLList1672613558_llist @ B @ A @ A2 @ Xs3 )
% 0.15/0.42 @ X )
% 0.15/0.42 = ( product_case_prod @ ( coinductive_llist @ A ) @ B @ ( tLList446370796tllist @ A @ B )
% 0.15/0.42 @ ^ [Xs3: coinductive_llist @ A,A2: B] : ( tLList1672613558_llist @ B @ A @ A2 @ Xs3 )
% 0.15/0.42 @ Y4 ) )
% 0.15/0.42 = ( product_case_prod @ ( coinductive_llist @ A ) @ B @ ( ( product_prod @ ( coinductive_llist @ A ) @ B ) > $o )
% 0.15/0.42 @ ^ [Xs3: coinductive_llist @ A,A2: B] :
% 0.15/0.42 ( product_case_prod @ ( coinductive_llist @ A ) @ B @ $o
% 0.15/0.42 @ ^ [Ys3: coinductive_llist @ A,B2: B] :
% 0.15/0.42 ( ( Xs3 = Ys3 )
% 0.15/0.42 & ( ( coinductive_lfinite @ A @ Ys3 )
% 0.15/0.42 => ( A2 = B2 ) ) ) )
% 0.15/0.42 @ X
% 0.15/0.42 @ Y4 ) ) ).
% 0.15/0.42
% 0.15/0.42 % tllist.abs_eq_iff
% 0.15/0.42 thf(fact_20_case__swap,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,C: $tType,F: C > B > A,P3: product_prod @ C @ B] :
% 0.15/0.42 ( ( product_case_prod @ B @ C @ A
% 0.15/0.42 @ ^ [Y: B,X3: C] : ( F @ X3 @ Y )
% 0.15/0.42 @ ( product_swap @ C @ B @ P3 ) )
% 0.15/0.42 = ( product_case_prod @ C @ B @ A @ F @ P3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % case_swap
% 0.15/0.42 thf(fact_21_llast__linfinite,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.15/0.42 => ( ( coinductive_llast @ A @ Xs )
% 0.15/0.42 = ( undefined @ A ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llast_linfinite
% 0.15/0.42 thf(fact_22_scomp__apply,axiom,
% 0.15/0.42 ! [A: $tType,D: $tType,C: $tType,B: $tType] :
% 0.15/0.42 ( ( product_scomp @ B @ C @ D @ A )
% 0.15/0.42 = ( ^ [F2: B > ( product_prod @ C @ D ),G2: C > D > A,X3: B] : ( product_case_prod @ C @ D @ A @ G2 @ ( F2 @ X3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % scomp_apply
% 0.15/0.42 thf(fact_23_lprefix__lappend__same,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( coinductive_lappend @ A @ Xs @ Zs ) )
% 0.15/0.42 = ( ( coinductive_lfinite @ A @ Xs )
% 0.15/0.42 => ( coinductive_lprefix @ A @ Ys @ Zs ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_lappend_same
% 0.15/0.42 thf(fact_24_lfilter__lappend__lfinite,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lfinite @ A @ Xs )
% 0.15/0.42 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.15/0.42 = ( coinductive_lappend @ A @ ( coinductive_lfilter @ A @ P @ Xs ) @ ( coinductive_lfilter @ A @ P @ Ys ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfilter_lappend_lfinite
% 0.15/0.42 thf(fact_25_case__prod__unfold,axiom,
% 0.15/0.42 ! [C: $tType,B: $tType,A: $tType] :
% 0.15/0.42 ( ( product_case_prod @ A @ B @ C )
% 0.15/0.42 = ( ^ [C2: A > B > C,P4: product_prod @ A @ B] : ( C2 @ ( product_fst @ A @ B @ P4 ) @ ( product_snd @ A @ B @ P4 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % case_prod_unfold
% 0.15/0.42 thf(fact_26_case__prod__beta_H,axiom,
% 0.15/0.42 ! [C: $tType,B: $tType,A: $tType] :
% 0.15/0.42 ( ( product_case_prod @ A @ B @ C )
% 0.15/0.42 = ( ^ [F2: A > B > C,X3: product_prod @ A @ B] : ( F2 @ ( product_fst @ A @ B @ X3 ) @ ( product_snd @ A @ B @ X3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % case_prod_beta'
% 0.15/0.42 thf(fact_27_split__comp__eq,axiom,
% 0.15/0.42 ! [A: $tType,C: $tType,B: $tType,D: $tType,F: A > B > C,G: D > A] :
% 0.15/0.42 ( ( ^ [U: product_prod @ D @ B] : ( F @ ( G @ ( product_fst @ D @ B @ U ) ) @ ( product_snd @ D @ B @ U ) ) )
% 0.15/0.42 = ( product_case_prod @ D @ B @ C
% 0.15/0.42 @ ^ [X3: D] : ( F @ ( G @ X3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % split_comp_eq
% 0.15/0.42 thf(fact_28_lprefix__refl,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A] : ( coinductive_lprefix @ A @ Xs @ Xs ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_refl
% 0.15/0.42 thf(fact_29_llist_Oleq__refl,axiom,
% 0.15/0.42 ! [A: $tType,X: coinductive_llist @ A] : ( coinductive_lprefix @ A @ X @ X ) ).
% 0.15/0.42
% 0.15/0.42 % llist.leq_refl
% 0.15/0.42 thf(fact_30_lfilter__idem,axiom,
% 0.15/0.42 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lfilter @ A @ P @ ( coinductive_lfilter @ A @ P @ Xs ) )
% 0.15/0.42 = ( coinductive_lfilter @ A @ P @ Xs ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfilter_idem
% 0.15/0.42 thf(fact_31_swap__swap,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,P3: product_prod @ A @ B] :
% 0.15/0.42 ( ( product_swap @ B @ A @ ( product_swap @ A @ B @ P3 ) )
% 0.15/0.42 = P3 ) ).
% 0.15/0.42
% 0.15/0.42 % swap_swap
% 0.15/0.42 thf(fact_32_lfilter__K__True,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lfilter @ A
% 0.15/0.42 @ ^ [Uu: A] : $true
% 0.15/0.42 @ Xs )
% 0.15/0.42 = Xs ) ).
% 0.15/0.42
% 0.15/0.42 % lfilter_K_True
% 0.15/0.42 thf(fact_33_tllist__of__llist__inject,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,B3: B,Xs: coinductive_llist @ A,C3: B,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( ( tLList1672613558_llist @ B @ A @ B3 @ Xs )
% 0.15/0.42 = ( tLList1672613558_llist @ B @ A @ C3 @ Ys ) )
% 0.15/0.42 = ( ( Xs = Ys )
% 0.15/0.42 & ( ( coinductive_lfinite @ A @ Ys )
% 0.15/0.42 => ( B3 = C3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % tllist_of_llist_inject
% 0.15/0.42 thf(fact_34_snd__apfst,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,C: $tType,F: C > B,X: product_prod @ C @ A] :
% 0.15/0.42 ( ( product_snd @ B @ A @ ( product_apfst @ C @ B @ A @ F @ X ) )
% 0.15/0.42 = ( product_snd @ C @ A @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % snd_apfst
% 0.15/0.42 thf(fact_35_snd__swap,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,X: product_prod @ A @ B] :
% 0.15/0.42 ( ( product_snd @ B @ A @ ( product_swap @ A @ B @ X ) )
% 0.15/0.42 = ( product_fst @ A @ B @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % snd_swap
% 0.15/0.42 thf(fact_36_fst__swap,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,X: product_prod @ B @ A] :
% 0.15/0.42 ( ( product_fst @ A @ B @ ( product_swap @ B @ A @ X ) )
% 0.15/0.42 = ( product_snd @ B @ A @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % fst_swap
% 0.15/0.42 thf(fact_37_scomp__scomp,axiom,
% 0.15/0.42 ! [A: $tType,C: $tType,D: $tType,B: $tType,F3: $tType,E: $tType,F: A > ( product_prod @ E @ F3 ),G: E > F3 > ( product_prod @ C @ D ),H: C > D > B] :
% 0.15/0.42 ( ( product_scomp @ A @ C @ D @ B @ ( product_scomp @ A @ E @ F3 @ ( product_prod @ C @ D ) @ F @ G ) @ H )
% 0.15/0.42 = ( product_scomp @ A @ E @ F3 @ B @ F
% 0.15/0.42 @ ^ [X3: E] : ( product_scomp @ F3 @ C @ D @ B @ ( G @ X3 ) @ H ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % scomp_scomp
% 0.15/0.42 thf(fact_38_lprefix__trans,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.15/0.42 => ( ( coinductive_lprefix @ A @ Ys @ Zs )
% 0.15/0.42 => ( coinductive_lprefix @ A @ Xs @ Zs ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_trans
% 0.15/0.42 thf(fact_39_llist_Oleq__trans,axiom,
% 0.15/0.42 ! [A: $tType,X: coinductive_llist @ A,Y4: coinductive_llist @ A,Z2: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ X @ Y4 )
% 0.15/0.42 => ( ( coinductive_lprefix @ A @ Y4 @ Z2 )
% 0.15/0.42 => ( coinductive_lprefix @ A @ X @ Z2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.leq_trans
% 0.15/0.42 thf(fact_40_lprefix__antisym,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.15/0.42 => ( ( coinductive_lprefix @ A @ Ys @ Xs )
% 0.15/0.42 => ( Xs = Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_antisym
% 0.15/0.42 thf(fact_41_lprefix__lfilterI,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,P: A > $o] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.15/0.42 => ( coinductive_lprefix @ A @ ( coinductive_lfilter @ A @ P @ Xs ) @ ( coinductive_lfilter @ A @ P @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_lfilterI
% 0.15/0.42 thf(fact_42_llist_Oleq__antisym,axiom,
% 0.15/0.42 ! [A: $tType,X: coinductive_llist @ A,Y4: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ X @ Y4 )
% 0.15/0.42 => ( ( coinductive_lprefix @ A @ Y4 @ X )
% 0.15/0.42 => ( X = Y4 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.leq_antisym
% 0.15/0.42 thf(fact_43_lprefix__down__linear,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Zs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ Xs @ Zs )
% 0.15/0.42 => ( ( coinductive_lprefix @ A @ Ys @ Zs )
% 0.15/0.42 => ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.15/0.42 | ( coinductive_lprefix @ A @ Ys @ Xs ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_down_linear
% 0.15/0.42 thf(fact_44_lfilter__lfilter,axiom,
% 0.15/0.42 ! [A: $tType,P: A > $o,Q: A > $o,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lfilter @ A @ P @ ( coinductive_lfilter @ A @ Q @ Xs ) )
% 0.15/0.42 = ( coinductive_lfilter @ A
% 0.15/0.42 @ ^ [X3: A] :
% 0.15/0.42 ( ( P @ X3 )
% 0.15/0.42 & ( Q @ X3 ) )
% 0.15/0.42 @ Xs ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfilter_lfilter
% 0.15/0.42 thf(fact_45_mem__Collect__eq,axiom,
% 0.15/0.42 ! [A: $tType,A3: A,P: A > $o] :
% 0.15/0.42 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.15/0.42 = ( P @ A3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % mem_Collect_eq
% 0.15/0.42 thf(fact_46_Collect__mem__eq,axiom,
% 0.15/0.42 ! [A: $tType,A5: set @ A] :
% 0.15/0.42 ( ( collect @ A
% 0.15/0.42 @ ^ [X3: A] : ( member @ A @ X3 @ A5 ) )
% 0.15/0.42 = A5 ) ).
% 0.15/0.42
% 0.15/0.42 % Collect_mem_eq
% 0.15/0.42 thf(fact_47_Collect__cong,axiom,
% 0.15/0.42 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.15/0.42 ( ! [X4: A] :
% 0.15/0.42 ( ( P @ X4 )
% 0.15/0.42 = ( Q @ X4 ) )
% 0.15/0.42 => ( ( collect @ A @ P )
% 0.15/0.42 = ( collect @ A @ Q ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % Collect_cong
% 0.15/0.42 thf(fact_48_ext,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.15/0.42 ( ! [X4: A] :
% 0.15/0.42 ( ( F @ X4 )
% 0.15/0.42 = ( G @ X4 ) )
% 0.15/0.42 => ( F = G ) ) ).
% 0.15/0.42
% 0.15/0.42 % ext
% 0.15/0.42 thf(fact_49_llist_Orel__reflp,axiom,
% 0.15/0.42 ! [A: $tType,R2: A > A > $o] :
% 0.15/0.42 ( ( reflp @ A @ R2 )
% 0.15/0.42 => ( reflp @ ( coinductive_llist @ A ) @ ( coindu1486289336t_all2 @ A @ A @ R2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.rel_reflp
% 0.15/0.42 thf(fact_50_tllist_Oabs__induct,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,P: ( tLList446370796tllist @ A @ B ) > $o,X: tLList446370796tllist @ A @ B] :
% 0.15/0.42 ( ! [Y3: product_prod @ ( coinductive_llist @ A ) @ B] :
% 0.15/0.42 ( P
% 0.15/0.42 @ ( product_case_prod @ ( coinductive_llist @ A ) @ B @ ( tLList446370796tllist @ A @ B )
% 0.15/0.42 @ ^ [Xs3: coinductive_llist @ A,A2: B] : ( tLList1672613558_llist @ B @ A @ A2 @ Xs3 )
% 0.15/0.42 @ Y3 ) )
% 0.15/0.42 => ( P @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % tllist.abs_induct
% 0.15/0.42 thf(fact_51_scomp__unfold,axiom,
% 0.15/0.42 ! [D: $tType,C: $tType,B: $tType,A: $tType] :
% 0.15/0.42 ( ( product_scomp @ A @ B @ C @ D )
% 0.15/0.42 = ( ^ [F2: A > ( product_prod @ B @ C ),G2: B > C > D,X3: A] : ( G2 @ ( product_fst @ B @ C @ ( F2 @ X3 ) ) @ ( product_snd @ B @ C @ ( F2 @ X3 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % scomp_unfold
% 0.15/0.42 thf(fact_52_prod__eqI,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,P3: product_prod @ A @ B,Q2: product_prod @ A @ B] :
% 0.15/0.42 ( ( ( product_fst @ A @ B @ P3 )
% 0.15/0.42 = ( product_fst @ A @ B @ Q2 ) )
% 0.15/0.42 => ( ( ( product_snd @ A @ B @ P3 )
% 0.15/0.42 = ( product_snd @ A @ B @ Q2 ) )
% 0.15/0.42 => ( P3 = Q2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod_eqI
% 0.15/0.42 thf(fact_53_prod_Oexpand,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B,Prod2: product_prod @ A @ B] :
% 0.15/0.42 ( ( ( ( product_fst @ A @ B @ Prod )
% 0.15/0.42 = ( product_fst @ A @ B @ Prod2 ) )
% 0.15/0.42 & ( ( product_snd @ A @ B @ Prod )
% 0.15/0.42 = ( product_snd @ A @ B @ Prod2 ) ) )
% 0.15/0.42 => ( Prod = Prod2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod.expand
% 0.15/0.42 thf(fact_54_prod__eq__iff,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType] :
% 0.15/0.42 ( ( ^ [Y2: product_prod @ A @ B,Z: product_prod @ A @ B] : ( Y2 = Z ) )
% 0.15/0.42 = ( ^ [S2: product_prod @ A @ B,T2: product_prod @ A @ B] :
% 0.15/0.42 ( ( ( product_fst @ A @ B @ S2 )
% 0.15/0.42 = ( product_fst @ A @ B @ T2 ) )
% 0.15/0.42 & ( ( product_snd @ A @ B @ S2 )
% 0.15/0.42 = ( product_snd @ A @ B @ T2 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod_eq_iff
% 0.15/0.42 thf(fact_55_lfinite__lfilterI,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 0.15/0.42 ( ( coinductive_lfinite @ A @ Xs )
% 0.15/0.42 => ( coinductive_lfinite @ A @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfinite_lfilterI
% 0.15/0.42 thf(fact_56_llist__all2__lfilterI,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,Q1: A > $o,Q22: B > $o] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.15/0.42 => ( ! [X4: A,Y3: B] :
% 0.15/0.42 ( ( P @ X4 @ Y3 )
% 0.15/0.42 => ( ( Q1 @ X4 )
% 0.15/0.42 = ( Q22 @ Y3 ) ) )
% 0.15/0.42 => ( coindu1486289336t_all2 @ A @ B @ P @ ( coinductive_lfilter @ A @ Q1 @ Xs ) @ ( coinductive_lfilter @ B @ Q22 @ Ys ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_lfilterI
% 0.15/0.42 thf(fact_57_lprefix__lfiniteD,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.15/0.42 => ( ( coinductive_lfinite @ A @ Ys )
% 0.15/0.42 => ( coinductive_lfinite @ A @ Xs ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_lfiniteD
% 0.15/0.42 thf(fact_58_not__lfinite__lprefix__conv__eq,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.15/0.42 => ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.15/0.42 = ( Xs = Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % not_lfinite_lprefix_conv_eq
% 0.15/0.42 thf(fact_59_lprefix__lappend,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] : ( coinductive_lprefix @ A @ Xs @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_lappend
% 0.15/0.42 thf(fact_60_lappend__lprefixE,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 0.15/0.42 => ~ ! [Zs2: coinductive_llist @ A] :
% 0.15/0.42 ( Zs
% 0.15/0.42 != ( coinductive_lappend @ A @ Xs @ Zs2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lappend_lprefixE
% 0.15/0.42 thf(fact_61_lprefix__lappendD,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) )
% 0.15/0.42 => ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.15/0.42 | ( coinductive_lprefix @ A @ Ys @ Xs ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_lappendD
% 0.15/0.42 thf(fact_62_lprefix__conv__lappend,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( coinductive_lprefix @ A )
% 0.15/0.42 = ( ^ [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A] :
% 0.15/0.42 ? [Zs3: coinductive_llist @ A] :
% 0.15/0.42 ( Ys3
% 0.15/0.42 = ( coinductive_lappend @ A @ Xs3 @ Zs3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_conv_lappend
% 0.15/0.42 thf(fact_63_lprefix__lappend__sameI,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.15/0.42 => ( coinductive_lprefix @ A @ ( coinductive_lappend @ A @ Zs @ Xs ) @ ( coinductive_lappend @ A @ Zs @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_lappend_sameI
% 0.15/0.42 thf(fact_64_tllist__of__llist__cong,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,Xs2: coinductive_llist @ A,B3: B,B5: B] :
% 0.15/0.42 ( ( Xs = Xs2 )
% 0.15/0.42 => ( ( ( coinductive_lfinite @ A @ Xs2 )
% 0.15/0.42 => ( B3 = B5 ) )
% 0.15/0.42 => ( ( tLList1672613558_llist @ B @ A @ B3 @ Xs )
% 0.15/0.42 = ( tLList1672613558_llist @ B @ A @ B5 @ Xs2 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % tllist_of_llist_cong
% 0.15/0.42 thf(fact_65_snd__def,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType] :
% 0.15/0.42 ( ( product_snd @ A @ B )
% 0.15/0.42 = ( product_case_prod @ A @ B @ B
% 0.15/0.42 @ ^ [X1: A,X2: B] : X2 ) ) ).
% 0.15/0.42
% 0.15/0.42 % snd_def
% 0.15/0.42 thf(fact_66_scomp__def,axiom,
% 0.15/0.42 ! [D: $tType,C: $tType,B: $tType,A: $tType] :
% 0.15/0.42 ( ( product_scomp @ A @ B @ C @ D )
% 0.15/0.42 = ( ^ [F2: A > ( product_prod @ B @ C ),G2: B > C > D,X3: A] : ( product_case_prod @ B @ C @ D @ G2 @ ( F2 @ X3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % scomp_def
% 0.15/0.42 thf(fact_67_case__prod__beta,axiom,
% 0.15/0.42 ! [A: $tType,C: $tType,B: $tType] :
% 0.15/0.42 ( ( product_case_prod @ B @ C @ A )
% 0.15/0.42 = ( ^ [F2: B > C > A,P4: product_prod @ B @ C] : ( F2 @ ( product_fst @ B @ C @ P4 ) @ ( product_snd @ B @ C @ P4 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % case_prod_beta
% 0.15/0.42 thf(fact_68_prod_Ocase__eq__if,axiom,
% 0.15/0.42 ! [C: $tType,B: $tType,A: $tType] :
% 0.15/0.42 ( ( product_case_prod @ A @ B @ C )
% 0.15/0.42 = ( ^ [F2: A > B > C,Prod3: product_prod @ A @ B] : ( F2 @ ( product_fst @ A @ B @ Prod3 ) @ ( product_snd @ A @ B @ Prod3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod.case_eq_if
% 0.15/0.42 thf(fact_69_Product__Type_OCollect__case__prodD,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,X: product_prod @ A @ B,A5: A > B > $o] :
% 0.15/0.42 ( ( member @ ( product_prod @ A @ B ) @ X @ ( collect @ ( product_prod @ A @ B ) @ ( product_case_prod @ A @ B @ $o @ A5 ) ) )
% 0.15/0.42 => ( A5 @ ( product_fst @ A @ B @ X ) @ ( product_snd @ A @ B @ X ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % Product_Type.Collect_case_prodD
% 0.15/0.42 thf(fact_70_lfilter__eq__lappend__lfiniteD,axiom,
% 0.15/0.42 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.15/0.42 ( ( ( coinductive_lfilter @ A @ P @ Xs )
% 0.15/0.42 = ( coinductive_lappend @ A @ Ys @ Zs ) )
% 0.15/0.42 => ( ( coinductive_lfinite @ A @ Ys )
% 0.15/0.42 => ? [Us: coinductive_llist @ A,Vs: coinductive_llist @ A] :
% 0.15/0.42 ( ( Xs
% 0.15/0.42 = ( coinductive_lappend @ A @ Us @ Vs ) )
% 0.15/0.42 & ( coinductive_lfinite @ A @ Us )
% 0.15/0.42 & ( Ys
% 0.15/0.42 = ( coinductive_lfilter @ A @ P @ Us ) )
% 0.15/0.42 & ( Zs
% 0.15/0.42 = ( coinductive_lfilter @ A @ P @ Vs ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfilter_eq_lappend_lfiniteD
% 0.15/0.42 thf(fact_71_exE__realizer,axiom,
% 0.15/0.42 ! [C: $tType,A: $tType,B: $tType,P: A > B > $o,P3: product_prod @ B @ A,Q: C > $o,F: B > A > C] :
% 0.15/0.42 ( ( P @ ( product_snd @ B @ A @ P3 ) @ ( product_fst @ B @ A @ P3 ) )
% 0.15/0.42 => ( ! [X4: B,Y3: A] :
% 0.15/0.42 ( ( P @ Y3 @ X4 )
% 0.15/0.42 => ( Q @ ( F @ X4 @ Y3 ) ) )
% 0.15/0.42 => ( Q @ ( product_case_prod @ B @ A @ C @ F @ P3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % exE_realizer
% 0.15/0.42 thf(fact_72_lappendt_Oabs__eq,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,Xa: coinductive_llist @ A,X: product_prod @ ( coinductive_llist @ A ) @ B] :
% 0.15/0.42 ( ( tLList98099029ppendt @ A @ B @ Xa
% 0.15/0.42 @ ( product_case_prod @ ( coinductive_llist @ A ) @ B @ ( tLList446370796tllist @ A @ B )
% 0.15/0.42 @ ^ [Xs3: coinductive_llist @ A,A2: B] : ( tLList1672613558_llist @ B @ A @ A2 @ Xs3 )
% 0.15/0.42 @ X ) )
% 0.15/0.42 = ( product_case_prod @ ( coinductive_llist @ A ) @ B @ ( tLList446370796tllist @ A @ B )
% 0.15/0.42 @ ^ [Xs3: coinductive_llist @ A,A2: B] : ( tLList1672613558_llist @ B @ A @ A2 @ Xs3 )
% 0.15/0.42 @ ( product_apfst @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) @ B @ ( coinductive_lappend @ A @ Xa ) @ X ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lappendt.abs_eq
% 0.15/0.42 thf(fact_73_exE__realizer_H,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,P: A > B > $o,P3: product_prod @ B @ A] :
% 0.15/0.42 ( ( P @ ( product_snd @ B @ A @ P3 ) @ ( product_fst @ B @ A @ P3 ) )
% 0.15/0.42 => ~ ! [X4: B,Y3: A] :
% 0.15/0.42 ~ ( P @ Y3 @ X4 ) ) ).
% 0.15/0.42
% 0.15/0.42 % exE_realizer'
% 0.15/0.42 thf(fact_74_tllist__of__llist__eq__lappendt__conv,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,A3: B,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: tLList446370796tllist @ A @ B] :
% 0.15/0.42 ( ( ( tLList1672613558_llist @ B @ A @ A3 @ Xs )
% 0.15/0.42 = ( tLList98099029ppendt @ A @ B @ Ys @ Zs ) )
% 0.15/0.42 = ( ? [Xs4: coinductive_llist @ A,A6: B] :
% 0.15/0.42 ( ( Xs
% 0.15/0.42 = ( coinductive_lappend @ A @ Ys @ Xs4 ) )
% 0.15/0.42 & ( Zs
% 0.15/0.42 = ( tLList1672613558_llist @ B @ A @ A6 @ Xs4 ) )
% 0.15/0.42 & ( ( coinductive_lfinite @ A @ Ys )
% 0.15/0.42 => ( A3 = A6 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % tllist_of_llist_eq_lappendt_conv
% 0.15/0.42 thf(fact_75_Coinductive__List_Olprefix__nitpick__simps,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( coinductive_lprefix @ A )
% 0.15/0.42 = ( ^ [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A] :
% 0.15/0.42 ( ( ( coinductive_lfinite @ A @ Xs3 )
% 0.15/0.42 => ( coindu328551480prefix @ A @ Xs3 @ Ys3 ) )
% 0.15/0.42 & ( ~ ( coinductive_lfinite @ A @ Xs3 )
% 0.15/0.42 => ( Xs3 = Ys3 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % Coinductive_List.lprefix_nitpick_simps
% 0.15/0.42 thf(fact_76_cr__tllist__def,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType] :
% 0.15/0.42 ( ( tLList47617868tllist @ A @ B )
% 0.15/0.42 = ( product_case_prod @ ( coinductive_llist @ A ) @ B @ ( ( tLList446370796tllist @ A @ B ) > $o )
% 0.15/0.42 @ ^ [Xs3: coinductive_llist @ A,B2: B] :
% 0.15/0.42 ( ^ [Y2: tLList446370796tllist @ A @ B,Z: tLList446370796tllist @ A @ B] : ( Y2 = Z )
% 0.15/0.42 @ ( tLList1672613558_llist @ B @ A @ B2 @ Xs3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % cr_tllist_def
% 0.15/0.42 thf(fact_77_llast__lappend,axiom,
% 0.15/0.42 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( ( coinductive_lnull @ A @ Ys )
% 0.15/0.42 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.15/0.42 = ( coinductive_llast @ A @ Xs ) ) )
% 0.15/0.42 & ( ~ ( coinductive_lnull @ A @ Ys )
% 0.15/0.42 => ( ( ( coinductive_lfinite @ A @ Xs )
% 0.15/0.42 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.15/0.42 = ( coinductive_llast @ A @ Ys ) ) )
% 0.15/0.42 & ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.15/0.42 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.15/0.42 = ( undefined @ A ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llast_lappend
% 0.15/0.42 thf(fact_78_llast__lappend__LCons,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Y4: A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lfinite @ A @ Xs )
% 0.15/0.42 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y4 @ Ys ) ) )
% 0.15/0.42 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y4 @ Ys ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llast_lappend_LCons
% 0.15/0.42 thf(fact_79_DEADID_Orel__reflp,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( reflp @ A
% 0.15/0.42 @ ^ [Y2: A,Z: A] : ( Y2 = Z ) ) ).
% 0.15/0.42
% 0.15/0.42 % DEADID.rel_reflp
% 0.15/0.42 thf(fact_80_llist_Oinject,axiom,
% 0.15/0.42 ! [A: $tType,X21: A,X22: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 0.15/0.42 ( ( ( coinductive_LCons @ A @ X21 @ X22 )
% 0.15/0.42 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 0.15/0.42 = ( ( X21 = Y21 )
% 0.15/0.42 & ( X22 = Y22 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.inject
% 0.15/0.42 thf(fact_81_LCons__lprefix__LCons,axiom,
% 0.15/0.42 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Y4: A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y4 @ Ys ) )
% 0.15/0.42 = ( ( X = Y4 )
% 0.15/0.42 & ( coinductive_lprefix @ A @ Xs @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % LCons_lprefix_LCons
% 0.15/0.42 thf(fact_82_lfinite__LCons,axiom,
% 0.15/0.42 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.15/0.42 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfinite_LCons
% 0.15/0.42 thf(fact_83_lfinite__code_I2_J,axiom,
% 0.15/0.42 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 0.15/0.42 ( ( coinductive_lfinite @ B @ ( coinductive_LCons @ B @ X @ Xs ) )
% 0.15/0.42 = ( coinductive_lfinite @ B @ Xs ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfinite_code(2)
% 0.15/0.42 thf(fact_84_llist__all2__LCons__LCons,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,R2: A > B > $o,X21: A,X22: coinductive_llist @ A,Y21: B,Y22: coinductive_llist @ B] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ B @ R2 @ ( coinductive_LCons @ A @ X21 @ X22 ) @ ( coinductive_LCons @ B @ Y21 @ Y22 ) )
% 0.15/0.42 = ( ( R2 @ X21 @ Y21 )
% 0.15/0.42 & ( coindu1486289336t_all2 @ A @ B @ R2 @ X22 @ Y22 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_LCons_LCons
% 0.15/0.42 thf(fact_85_lappend__code_I2_J,axiom,
% 0.15/0.42 ! [A: $tType,Xa: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa @ X ) @ Ys )
% 0.15/0.42 = ( coinductive_LCons @ A @ Xa @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lappend_code(2)
% 0.15/0.42 thf(fact_86_lnull__lappend,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.15/0.42 = ( ( coinductive_lnull @ A @ Xs )
% 0.15/0.42 & ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lnull_lappend
% 0.15/0.42 thf(fact_87_lappend_Odisc__iff_I2_J,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) )
% 0.15/0.42 = ( ~ ( coinductive_lnull @ A @ Xs )
% 0.15/0.42 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lappend.disc_iff(2)
% 0.15/0.42 thf(fact_88_lfilter__LCons,axiom,
% 0.15/0.42 ! [A: $tType,P: A > $o,X: A,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( ( P @ X )
% 0.15/0.42 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.15/0.42 = ( coinductive_LCons @ A @ X @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) )
% 0.15/0.42 & ( ~ ( P @ X )
% 0.15/0.42 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.15/0.42 = ( coinductive_lfilter @ A @ P @ Xs ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfilter_LCons
% 0.15/0.42 thf(fact_89_llast__LCons2,axiom,
% 0.15/0.42 ! [A: $tType,X: A,Y4: A,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y4 @ Xs ) ) )
% 0.15/0.42 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y4 @ Xs ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llast_LCons2
% 0.15/0.42 thf(fact_90_lappend_Oexhaust,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( ( coinductive_lnull @ A @ Xs )
% 0.15/0.42 => ~ ( coinductive_lnull @ A @ Ys ) )
% 0.15/0.42 => ( ~ ( coinductive_lnull @ A @ Xs )
% 0.15/0.42 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lappend.exhaust
% 0.15/0.42 thf(fact_91_not__lnull__conv,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( ~ ( coinductive_lnull @ A @ Xs ) )
% 0.15/0.42 = ( ? [X3: A,Xs4: coinductive_llist @ A] :
% 0.15/0.42 ( Xs
% 0.15/0.42 = ( coinductive_LCons @ A @ X3 @ Xs4 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % not_lnull_conv
% 0.15/0.42 thf(fact_92_lzip_Oexhaust,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.15/0.42 ( ~ ( ( coinductive_lnull @ A @ Xs )
% 0.15/0.42 | ( coinductive_lnull @ B @ Ys ) )
% 0.15/0.42 => ~ ( ~ ( coinductive_lnull @ A @ Xs )
% 0.15/0.42 => ( coinductive_lnull @ B @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lzip.exhaust
% 0.15/0.42 thf(fact_93_llist_OdiscI_I2_J,axiom,
% 0.15/0.42 ! [A: $tType,Llist: coinductive_llist @ A,X21: A,X22: coinductive_llist @ A] :
% 0.15/0.42 ( ( Llist
% 0.15/0.42 = ( coinductive_LCons @ A @ X21 @ X22 ) )
% 0.15/0.42 => ~ ( coinductive_lnull @ A @ Llist ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.discI(2)
% 0.15/0.42 thf(fact_94_llist_Odisc_I2_J,axiom,
% 0.15/0.42 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 0.15/0.42 ~ ( coinductive_lnull @ A @ ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.disc(2)
% 0.15/0.42 thf(fact_95_llast__LCons,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 0.15/0.42 ( ( ( coinductive_lnull @ A @ Xs )
% 0.15/0.42 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.15/0.42 = X ) )
% 0.15/0.42 & ( ~ ( coinductive_lnull @ A @ Xs )
% 0.15/0.42 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.15/0.42 = ( coinductive_llast @ A @ Xs ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llast_LCons
% 0.15/0.42 thf(fact_96_lprefix__not__lnullD,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.15/0.42 => ( ~ ( coinductive_lnull @ A @ Xs )
% 0.15/0.42 => ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_not_lnullD
% 0.15/0.42 thf(fact_97_lprefix__lnullD,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.15/0.42 => ( ( coinductive_lnull @ A @ Ys )
% 0.15/0.42 => ( coinductive_lnull @ A @ Xs ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_lnullD
% 0.15/0.42 thf(fact_98_lprefix__lnull,axiom,
% 0.15/0.42 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lnull @ A @ Ys )
% 0.15/0.42 => ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.15/0.42 = ( coinductive_lnull @ A @ Xs ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_lnull
% 0.15/0.42 thf(fact_99_lnull__lprefix,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lnull @ A @ Xs )
% 0.15/0.42 => ( coinductive_lprefix @ A @ Xs @ Ys ) ) ).
% 0.15/0.42
% 0.15/0.42 % lnull_lprefix
% 0.15/0.42 thf(fact_100_LCons__lprefix__conv,axiom,
% 0.15/0.42 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ ( coinductive_LCons @ A @ X @ Xs ) @ Ys )
% 0.15/0.42 = ( ? [Ys4: coinductive_llist @ A] :
% 0.15/0.42 ( ( Ys
% 0.15/0.42 = ( coinductive_LCons @ A @ X @ Ys4 ) )
% 0.15/0.42 & ( coinductive_lprefix @ A @ Xs @ Ys4 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % LCons_lprefix_conv
% 0.15/0.42 thf(fact_101_Le__LCons,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,X: A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 0.15/0.42 => ( coinductive_lprefix @ A @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ X @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % Le_LCons
% 0.15/0.42 thf(fact_102_lnull__imp__lfinite,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lnull @ A @ Xs )
% 0.15/0.42 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.15/0.42
% 0.15/0.42 % lnull_imp_lfinite
% 0.15/0.42 thf(fact_103_llist__all2__lnullD,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.15/0.42 => ( ( coinductive_lnull @ A @ Xs )
% 0.15/0.42 = ( coinductive_lnull @ B @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_lnullD
% 0.15/0.42 thf(fact_104_lfinite__LConsI,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 0.15/0.42 ( ( coinductive_lfinite @ A @ Xs )
% 0.15/0.42 => ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfinite_LConsI
% 0.15/0.42 thf(fact_105_llist__all2__LCons2,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Y4: B,Ys: coinductive_llist @ B] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ ( coinductive_LCons @ B @ Y4 @ Ys ) )
% 0.15/0.42 = ( ? [X3: A,Xs4: coinductive_llist @ A] :
% 0.15/0.42 ( ( Xs
% 0.15/0.42 = ( coinductive_LCons @ A @ X3 @ Xs4 ) )
% 0.15/0.42 & ( P @ X3 @ Y4 )
% 0.15/0.42 & ( coindu1486289336t_all2 @ A @ B @ P @ Xs4 @ Ys ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_LCons2
% 0.15/0.42 thf(fact_106_llist__all2__LCons1,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,P: A > B > $o,X: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ B @ P @ ( coinductive_LCons @ A @ X @ Xs ) @ Ys )
% 0.15/0.42 = ( ? [Y: B,Ys4: coinductive_llist @ B] :
% 0.15/0.42 ( ( Ys
% 0.15/0.42 = ( coinductive_LCons @ B @ Y @ Ys4 ) )
% 0.15/0.42 & ( P @ X @ Y )
% 0.15/0.42 & ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys4 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_LCons1
% 0.15/0.42 thf(fact_107_llist_Orel__intros_I2_J,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,R2: A > B > $o,X21: A,Y21: B,X22: coinductive_llist @ A,Y22: coinductive_llist @ B] :
% 0.15/0.42 ( ( R2 @ X21 @ Y21 )
% 0.15/0.42 => ( ( coindu1486289336t_all2 @ A @ B @ R2 @ X22 @ Y22 )
% 0.15/0.42 => ( coindu1486289336t_all2 @ A @ B @ R2 @ ( coinductive_LCons @ A @ X21 @ X22 ) @ ( coinductive_LCons @ B @ Y21 @ Y22 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.rel_intros(2)
% 0.15/0.42 thf(fact_108_lappend__lnull2,axiom,
% 0.15/0.42 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lnull @ A @ Ys )
% 0.15/0.42 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.15/0.42 = Xs ) ) ).
% 0.15/0.42
% 0.15/0.42 % lappend_lnull2
% 0.15/0.42 thf(fact_109_lappend__lnull1,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lnull @ A @ Xs )
% 0.15/0.42 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.15/0.42 = Ys ) ) ).
% 0.15/0.42
% 0.15/0.42 % lappend_lnull1
% 0.15/0.42 thf(fact_110_lappend_Odisc_I1_J,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lnull @ A @ Xs )
% 0.15/0.42 => ( ( coinductive_lnull @ A @ Ys )
% 0.15/0.42 => ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lappend.disc(1)
% 0.15/0.42 thf(fact_111_lappend_Odisc_I2_J,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 0.15/0.42 | ~ ( coinductive_lnull @ A @ Ys ) )
% 0.15/0.42 => ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lappend.disc(2)
% 0.15/0.42 thf(fact_112_lfilter__LCons__found,axiom,
% 0.15/0.42 ! [A: $tType,P: A > $o,X: A,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( P @ X )
% 0.15/0.42 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.15/0.42 = ( coinductive_LCons @ A @ X @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfilter_LCons_found
% 0.15/0.42 thf(fact_113_lfilter__LCons__seek,axiom,
% 0.15/0.42 ! [A: $tType,P3: A > $o,X: A,L2: coinductive_llist @ A] :
% 0.15/0.42 ( ~ ( P3 @ X )
% 0.15/0.42 => ( ( coinductive_lfilter @ A @ P3 @ ( coinductive_LCons @ A @ X @ L2 ) )
% 0.15/0.42 = ( coinductive_lfilter @ A @ P3 @ L2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfilter_LCons_seek
% 0.15/0.42 thf(fact_114_Coinductive__List_Ofinite__lprefix__def,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( coindu328551480prefix @ A )
% 0.15/0.42 = ( coinductive_lprefix @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % Coinductive_List.finite_lprefix_def
% 0.15/0.42 thf(fact_115_lstrict__prefix__lappend__conv,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coindu1478340336prefix @ A @ Xs @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.15/0.42 = ( ( coinductive_lfinite @ A @ Xs )
% 0.15/0.42 & ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lstrict_prefix_lappend_conv
% 0.15/0.42 thf(fact_116_lfilter__eq__LConsD,axiom,
% 0.15/0.42 ! [A: $tType,P: A > $o,Ys: coinductive_llist @ A,X: A,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( ( coinductive_lfilter @ A @ P @ Ys )
% 0.15/0.42 = ( coinductive_LCons @ A @ X @ Xs ) )
% 0.15/0.42 => ? [Us: coinductive_llist @ A,Vs: coinductive_llist @ A] :
% 0.15/0.42 ( ( Ys
% 0.15/0.42 = ( coinductive_lappend @ A @ Us @ ( coinductive_LCons @ A @ X @ Vs ) ) )
% 0.15/0.42 & ( coinductive_lfinite @ A @ Us )
% 0.15/0.42 & ! [X5: A] :
% 0.15/0.42 ( ( member @ A @ X5 @ ( coinductive_lset @ A @ Us ) )
% 0.15/0.42 => ~ ( P @ X5 ) )
% 0.15/0.42 & ( P @ X )
% 0.15/0.42 & ( Xs
% 0.15/0.42 = ( coinductive_lfilter @ A @ P @ Vs ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfilter_eq_LConsD
% 0.15/0.42 thf(fact_117_reflpD,axiom,
% 0.15/0.42 ! [A: $tType,R3: A > A > $o,X: A] :
% 0.15/0.42 ( ( reflp @ A @ R3 )
% 0.15/0.42 => ( R3 @ X @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % reflpD
% 0.15/0.42 thf(fact_118_reflpE,axiom,
% 0.15/0.42 ! [A: $tType,R3: A > A > $o,X: A] :
% 0.15/0.42 ( ( reflp @ A @ R3 )
% 0.15/0.42 => ( R3 @ X @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % reflpE
% 0.15/0.42 thf(fact_119_reflpI,axiom,
% 0.15/0.42 ! [A: $tType,R3: A > A > $o] :
% 0.15/0.42 ( ! [X4: A] : ( R3 @ X4 @ X4 )
% 0.15/0.42 => ( reflp @ A @ R3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % reflpI
% 0.15/0.42 thf(fact_120_reflp__def,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( reflp @ A )
% 0.15/0.42 = ( ^ [R: A > A > $o] :
% 0.15/0.42 ! [X3: A] : ( R @ X3 @ X3 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % reflp_def
% 0.15/0.42 thf(fact_121_llist__all2__same,axiom,
% 0.15/0.42 ! [A: $tType,P: A > A > $o,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ A @ P @ Xs @ Xs )
% 0.15/0.42 = ( ! [X3: A] :
% 0.15/0.42 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 0.15/0.42 => ( P @ X3 @ X3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_same
% 0.15/0.42 thf(fact_122_lstrict__prefix__code_I4_J,axiom,
% 0.15/0.42 ! [B: $tType,X: B,Xs: coinductive_llist @ B,Y4: B,Ys: coinductive_llist @ B] :
% 0.15/0.42 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LCons @ B @ Y4 @ Ys ) )
% 0.15/0.42 = ( ( X = Y4 )
% 0.15/0.42 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lstrict_prefix_code(4)
% 0.15/0.42 thf(fact_123_lset__lfilter,axiom,
% 0.15/0.42 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lset @ A @ ( coinductive_lfilter @ A @ P @ Xs ) )
% 0.15/0.42 = ( collect @ A
% 0.15/0.42 @ ^ [X3: A] :
% 0.15/0.42 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 0.15/0.42 & ( P @ X3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lset_lfilter
% 0.15/0.42 thf(fact_124_lnull__lfilter,axiom,
% 0.15/0.42 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lnull @ A @ ( coinductive_lfilter @ A @ P @ Xs ) )
% 0.15/0.42 = ( ! [X3: A] :
% 0.15/0.42 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 0.15/0.42 => ~ ( P @ X3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lnull_lfilter
% 0.15/0.42 thf(fact_125_llist__less__induct,axiom,
% 0.15/0.42 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ! [Xs5: coinductive_llist @ A] :
% 0.15/0.42 ( ! [Ys5: coinductive_llist @ A] :
% 0.15/0.42 ( ( coindu1478340336prefix @ A @ Ys5 @ Xs5 )
% 0.15/0.42 => ( P @ Ys5 ) )
% 0.15/0.42 => ( P @ Xs5 ) )
% 0.15/0.42 => ( P @ Xs ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_less_induct
% 0.15/0.42 thf(fact_126_lset__intros_I2_J,axiom,
% 0.15/0.42 ! [A: $tType,X: A,Xs: coinductive_llist @ A,X6: A] :
% 0.15/0.42 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.15/0.42 => ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ X6 @ Xs ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lset_intros(2)
% 0.15/0.42 thf(fact_127_lset__intros_I1_J,axiom,
% 0.15/0.42 ! [A: $tType,X: A,Xs: coinductive_llist @ A] : ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lset_intros(1)
% 0.15/0.42 thf(fact_128_llist_Oset__intros_I2_J,axiom,
% 0.15/0.42 ! [A: $tType,X: A,A22: coinductive_llist @ A,A1: A] :
% 0.15/0.42 ( ( member @ A @ X @ ( coinductive_lset @ A @ A22 ) )
% 0.15/0.42 => ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ A1 @ A22 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.set_intros(2)
% 0.15/0.42 thf(fact_129_llist_Oset__intros_I1_J,axiom,
% 0.15/0.42 ! [A: $tType,A1: A,A22: coinductive_llist @ A] : ( member @ A @ A1 @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ A1 @ A22 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.set_intros(1)
% 0.15/0.42 thf(fact_130_lset__cases,axiom,
% 0.15/0.42 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.15/0.42 => ( ! [Xs6: coinductive_llist @ A] :
% 0.15/0.42 ( Xs
% 0.15/0.42 != ( coinductive_LCons @ A @ X @ Xs6 ) )
% 0.15/0.42 => ~ ! [X7: A,Xs6: coinductive_llist @ A] :
% 0.15/0.42 ( ( Xs
% 0.15/0.42 = ( coinductive_LCons @ A @ X7 @ Xs6 ) )
% 0.15/0.42 => ~ ( member @ A @ X @ ( coinductive_lset @ A @ Xs6 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lset_cases
% 0.15/0.42 thf(fact_131_lset__induct,axiom,
% 0.15/0.42 ! [A: $tType,X: A,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.15/0.42 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.15/0.42 => ( ! [Xs5: coinductive_llist @ A] : ( P @ ( coinductive_LCons @ A @ X @ Xs5 ) )
% 0.15/0.42 => ( ! [X7: A,Xs5: coinductive_llist @ A] :
% 0.15/0.42 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs5 ) )
% 0.15/0.42 => ( ( X != X7 )
% 0.15/0.42 => ( ( P @ Xs5 )
% 0.15/0.42 => ( P @ ( coinductive_LCons @ A @ X7 @ Xs5 ) ) ) ) )
% 0.15/0.42 => ( P @ Xs ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lset_induct
% 0.15/0.42 thf(fact_132_lset__induct_H,axiom,
% 0.15/0.42 ! [A: $tType,X: A,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.15/0.42 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.15/0.42 => ( ! [Xs5: coinductive_llist @ A] : ( P @ ( coinductive_LCons @ A @ X @ Xs5 ) )
% 0.15/0.42 => ( ! [X7: A,Xs5: coinductive_llist @ A] :
% 0.15/0.42 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs5 ) )
% 0.15/0.42 => ( ( P @ Xs5 )
% 0.15/0.42 => ( P @ ( coinductive_LCons @ A @ X7 @ Xs5 ) ) ) )
% 0.15/0.42 => ( P @ Xs ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lset_induct'
% 0.15/0.42 thf(fact_133_llist_Oset__cases,axiom,
% 0.15/0.42 ! [A: $tType,E2: A,A3: coinductive_llist @ A] :
% 0.15/0.42 ( ( member @ A @ E2 @ ( coinductive_lset @ A @ A3 ) )
% 0.15/0.42 => ( ! [Z22: coinductive_llist @ A] :
% 0.15/0.42 ( A3
% 0.15/0.42 != ( coinductive_LCons @ A @ E2 @ Z22 ) )
% 0.15/0.42 => ~ ! [Z1: A,Z22: coinductive_llist @ A] :
% 0.15/0.42 ( ( A3
% 0.15/0.42 = ( coinductive_LCons @ A @ Z1 @ Z22 ) )
% 0.15/0.42 => ~ ( member @ A @ E2 @ ( coinductive_lset @ A @ Z22 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.set_cases
% 0.15/0.42 thf(fact_134_llist_Oset__induct,axiom,
% 0.15/0.42 ! [A: $tType,X: A,A3: coinductive_llist @ A,P: A > ( coinductive_llist @ A ) > $o] :
% 0.15/0.42 ( ( member @ A @ X @ ( coinductive_lset @ A @ A3 ) )
% 0.15/0.42 => ( ! [Z1: A,Z22: coinductive_llist @ A] : ( P @ Z1 @ ( coinductive_LCons @ A @ Z1 @ Z22 ) )
% 0.15/0.42 => ( ! [Z1: A,Z22: coinductive_llist @ A,Xa2: A] :
% 0.15/0.42 ( ( member @ A @ Xa2 @ ( coinductive_lset @ A @ Z22 ) )
% 0.15/0.42 => ( ( P @ Xa2 @ Z22 )
% 0.15/0.42 => ( P @ Xa2 @ ( coinductive_LCons @ A @ Z1 @ Z22 ) ) ) )
% 0.15/0.42 => ( P @ X @ A3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.set_induct
% 0.15/0.42 thf(fact_135_llist__all2__reflI,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,P: A > A > $o] :
% 0.15/0.42 ( ! [X4: A] :
% 0.15/0.42 ( ( member @ A @ X4 @ ( coinductive_lset @ A @ Xs ) )
% 0.15/0.42 => ( P @ X4 @ X4 ) )
% 0.15/0.42 => ( coindu1486289336t_all2 @ A @ A @ P @ Xs @ Xs ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_reflI
% 0.15/0.42 thf(fact_136_llist__all2__lsetD1,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,X: A] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.15/0.42 => ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.15/0.42 => ? [X4: B] :
% 0.15/0.42 ( ( member @ B @ X4 @ ( coinductive_lset @ B @ Ys ) )
% 0.15/0.42 & ( P @ X @ X4 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_lsetD1
% 0.15/0.42 thf(fact_137_llist__all2__lsetD2,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,Y4: B] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.15/0.42 => ( ( member @ B @ Y4 @ ( coinductive_lset @ B @ Ys ) )
% 0.15/0.42 => ? [X4: A] :
% 0.15/0.42 ( ( member @ A @ X4 @ ( coinductive_lset @ A @ Xs ) )
% 0.15/0.42 & ( P @ X4 @ Y4 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_lsetD2
% 0.15/0.42 thf(fact_138_llist_Orel__cong,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,X: coinductive_llist @ A,Ya: coinductive_llist @ A,Y4: coinductive_llist @ B,Xa: coinductive_llist @ B,R2: A > B > $o,Ra: A > B > $o] :
% 0.15/0.42 ( ( X = Ya )
% 0.15/0.42 => ( ( Y4 = Xa )
% 0.15/0.42 => ( ! [Z3: A,Yb: B] :
% 0.15/0.42 ( ( member @ A @ Z3 @ ( coinductive_lset @ A @ Ya ) )
% 0.15/0.42 => ( ( member @ B @ Yb @ ( coinductive_lset @ B @ Xa ) )
% 0.15/0.42 => ( ( R2 @ Z3 @ Yb )
% 0.15/0.42 = ( Ra @ Z3 @ Yb ) ) ) )
% 0.15/0.42 => ( ( coindu1486289336t_all2 @ A @ B @ R2 @ X @ Y4 )
% 0.15/0.42 = ( coindu1486289336t_all2 @ A @ B @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.rel_cong
% 0.15/0.42 thf(fact_139_llist_Orel__mono__strong,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,R2: A > B > $o,X: coinductive_llist @ A,Y4: coinductive_llist @ B,Ra: A > B > $o] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ B @ R2 @ X @ Y4 )
% 0.15/0.42 => ( ! [Z3: A,Yb: B] :
% 0.15/0.42 ( ( member @ A @ Z3 @ ( coinductive_lset @ A @ X ) )
% 0.15/0.42 => ( ( member @ B @ Yb @ ( coinductive_lset @ B @ Y4 ) )
% 0.15/0.42 => ( ( R2 @ Z3 @ Yb )
% 0.15/0.42 => ( Ra @ Z3 @ Yb ) ) ) )
% 0.15/0.42 => ( coindu1486289336t_all2 @ A @ B @ Ra @ X @ Y4 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.rel_mono_strong
% 0.15/0.42 thf(fact_140_llist_Orel__refl__strong,axiom,
% 0.15/0.42 ! [A: $tType,X: coinductive_llist @ A,Ra: A > A > $o] :
% 0.15/0.42 ( ! [Z3: A] :
% 0.15/0.42 ( ( member @ A @ Z3 @ ( coinductive_lset @ A @ X ) )
% 0.15/0.42 => ( Ra @ Z3 @ Z3 ) )
% 0.15/0.42 => ( coindu1486289336t_all2 @ A @ A @ Ra @ X @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.rel_refl_strong
% 0.15/0.42 thf(fact_141_lfilter__cong,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,P: A > $o,Q: A > $o] :
% 0.15/0.42 ( ( Xs = Ys )
% 0.15/0.42 => ( ! [X4: A] :
% 0.15/0.42 ( ( member @ A @ X4 @ ( coinductive_lset @ A @ Ys ) )
% 0.15/0.42 => ( ( P @ X4 )
% 0.15/0.42 = ( Q @ X4 ) ) )
% 0.15/0.42 => ( ( coinductive_lfilter @ A @ P @ Xs )
% 0.15/0.42 = ( coinductive_lfilter @ A @ Q @ Ys ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfilter_cong
% 0.15/0.42 thf(fact_142_lfilter__id__conv,axiom,
% 0.15/0.42 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( ( coinductive_lfilter @ A @ P @ Xs )
% 0.15/0.42 = Xs )
% 0.15/0.42 = ( ! [X3: A] :
% 0.15/0.42 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 0.15/0.42 => ( P @ X3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfilter_id_conv
% 0.15/0.42 thf(fact_143_lstrict__prefix__def,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( coindu1478340336prefix @ A )
% 0.15/0.42 = ( ^ [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ Xs3 @ Ys3 )
% 0.15/0.42 & ( Xs3 != Ys3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lstrict_prefix_def
% 0.15/0.42 thf(fact_144_lstrict__prefix__lfinite1,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coindu1478340336prefix @ A @ Xs @ Ys )
% 0.15/0.42 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.15/0.42
% 0.15/0.42 % lstrict_prefix_lfinite1
% 0.15/0.42 thf(fact_145_in__lset__lappend__iff,axiom,
% 0.15/0.42 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) )
% 0.15/0.42 = ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.15/0.42 | ( ( coinductive_lfinite @ A @ Xs )
% 0.15/0.42 & ( member @ A @ X @ ( coinductive_lset @ A @ Ys ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % in_lset_lappend_iff
% 0.15/0.42 thf(fact_146_split__llist,axiom,
% 0.15/0.42 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.15/0.42 => ? [Ys6: coinductive_llist @ A,Zs4: coinductive_llist @ A] :
% 0.15/0.42 ( ( Xs
% 0.15/0.42 = ( coinductive_lappend @ A @ Ys6 @ ( coinductive_LCons @ A @ X @ Zs4 ) ) )
% 0.15/0.42 & ( coinductive_lfinite @ A @ Ys6 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % split_llist
% 0.15/0.42 thf(fact_147_split__llist__first,axiom,
% 0.15/0.42 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 0.15/0.42 => ? [Ys6: coinductive_llist @ A,Zs4: coinductive_llist @ A] :
% 0.15/0.42 ( ( Xs
% 0.15/0.42 = ( coinductive_lappend @ A @ Ys6 @ ( coinductive_LCons @ A @ X @ Zs4 ) ) )
% 0.15/0.42 & ( coinductive_lfinite @ A @ Ys6 )
% 0.15/0.42 & ~ ( member @ A @ X @ ( coinductive_lset @ A @ Ys6 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % split_llist_first
% 0.15/0.42 thf(fact_148_reflp__mono,axiom,
% 0.15/0.42 ! [A: $tType,R2: A > A > $o,Q: A > A > $o] :
% 0.15/0.42 ( ( reflp @ A @ R2 )
% 0.15/0.42 => ( ! [X4: A,Y3: A] :
% 0.15/0.42 ( ( R2 @ X4 @ Y3 )
% 0.15/0.42 => ( Q @ X4 @ Y3 ) )
% 0.15/0.42 => ( reflp @ A @ Q ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % reflp_mono
% 0.15/0.42 thf(fact_149_lset__lappend__lfinite,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lfinite @ A @ Xs )
% 0.15/0.42 => ( ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.15/0.42 = ( sup_sup @ ( set @ A ) @ ( coinductive_lset @ A @ Xs ) @ ( coinductive_lset @ A @ Ys ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lset_lappend_lfinite
% 0.15/0.42 thf(fact_150_The__case__prod,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,P: A > B > $o] :
% 0.15/0.42 ( ( the @ ( product_prod @ A @ B ) @ ( product_case_prod @ A @ B @ $o @ P ) )
% 0.15/0.42 = ( the @ ( product_prod @ A @ B )
% 0.15/0.42 @ ^ [Xy: product_prod @ A @ B] : ( P @ ( product_fst @ A @ B @ Xy ) @ ( product_snd @ A @ B @ Xy ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % The_case_prod
% 0.15/0.42 thf(fact_151_llimit__induct,axiom,
% 0.15/0.42 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( P @ ( coinductive_LNil @ A ) )
% 0.15/0.42 => ( ! [X4: A,Xs5: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lfinite @ A @ Xs5 )
% 0.15/0.42 => ( ( P @ Xs5 )
% 0.15/0.42 => ( P @ ( coinductive_LCons @ A @ X4 @ Xs5 ) ) ) )
% 0.15/0.42 => ( ( ! [Ys5: coinductive_llist @ A] :
% 0.15/0.42 ( ( coindu1478340336prefix @ A @ Ys5 @ Xs )
% 0.15/0.42 => ( P @ Ys5 ) )
% 0.15/0.42 => ( P @ Xs ) )
% 0.15/0.42 => ( P @ Xs ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llimit_induct
% 0.15/0.42 thf(fact_152_prod_Oswap__def,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType] :
% 0.15/0.42 ( ( product_swap @ A @ B )
% 0.15/0.42 = ( ^ [P4: product_prod @ A @ B] : ( product_Pair @ B @ A @ ( product_snd @ A @ B @ P4 ) @ ( product_fst @ A @ B @ P4 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod.swap_def
% 0.15/0.42 thf(fact_153_old_Oprod_Oinject,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,A3: A,B3: B,A7: A,B5: B] :
% 0.15/0.42 ( ( ( product_Pair @ A @ B @ A3 @ B3 )
% 0.15/0.42 = ( product_Pair @ A @ B @ A7 @ B5 ) )
% 0.15/0.42 = ( ( A3 = A7 )
% 0.15/0.42 & ( B3 = B5 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % old.prod.inject
% 0.15/0.42 thf(fact_154_prod_Oinject,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,X12: A,X23: B,Y1: A,Y23: B] :
% 0.15/0.42 ( ( ( product_Pair @ A @ B @ X12 @ X23 )
% 0.15/0.42 = ( product_Pair @ A @ B @ Y1 @ Y23 ) )
% 0.15/0.42 = ( ( X12 = Y1 )
% 0.15/0.42 & ( X23 = Y23 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod.inject
% 0.15/0.42 thf(fact_155_mem__case__prodI2,axiom,
% 0.15/0.42 ! [C: $tType,B: $tType,A: $tType,P3: product_prod @ A @ B,Z2: C,C3: A > B > ( set @ C )] :
% 0.15/0.42 ( ! [A4: A,B4: B] :
% 0.15/0.42 ( ( P3
% 0.15/0.42 = ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.15/0.42 => ( member @ C @ Z2 @ ( C3 @ A4 @ B4 ) ) )
% 0.15/0.42 => ( member @ C @ Z2 @ ( product_case_prod @ A @ B @ ( set @ C ) @ C3 @ P3 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % mem_case_prodI2
% 0.15/0.42 thf(fact_156_mem__case__prodI,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,C: $tType,Z2: A,C3: B > C > ( set @ A ),A3: B,B3: C] :
% 0.15/0.42 ( ( member @ A @ Z2 @ ( C3 @ A3 @ B3 ) )
% 0.15/0.42 => ( member @ A @ Z2 @ ( product_case_prod @ B @ C @ ( set @ A ) @ C3 @ ( product_Pair @ B @ C @ A3 @ B3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % mem_case_prodI
% 0.15/0.42 thf(fact_157_lprefix__code_I1_J,axiom,
% 0.15/0.42 ! [A: $tType,Ys: coinductive_llist @ A] : ( coinductive_lprefix @ A @ ( coinductive_LNil @ A ) @ Ys ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_code(1)
% 0.15/0.42 thf(fact_158_lfinite__code_I1_J,axiom,
% 0.15/0.42 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfinite_code(1)
% 0.15/0.42 thf(fact_159_llist__all2__LNil2,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,P: A > B > $o,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ ( coinductive_LNil @ B ) )
% 0.15/0.42 = ( Xs
% 0.15/0.42 = ( coinductive_LNil @ A ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_LNil2
% 0.15/0.42 thf(fact_160_llist__all2__LNil1,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ B] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ B @ P @ ( coinductive_LNil @ A ) @ Xs )
% 0.15/0.42 = ( Xs
% 0.15/0.42 = ( coinductive_LNil @ B ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_LNil1
% 0.15/0.42 thf(fact_161_lappend__LNil2,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.15/0.42 = Xs ) ).
% 0.15/0.42
% 0.15/0.42 % lappend_LNil2
% 0.15/0.42 thf(fact_162_lappend__code_I1_J,axiom,
% 0.15/0.42 ! [A: $tType,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 0.15/0.42 = Ys ) ).
% 0.15/0.42
% 0.15/0.42 % lappend_code(1)
% 0.15/0.42 thf(fact_163_apfst__conv,axiom,
% 0.15/0.42 ! [C: $tType,A: $tType,B: $tType,F: C > A,X: C,Y4: B] :
% 0.15/0.42 ( ( product_apfst @ C @ A @ B @ F @ ( product_Pair @ C @ B @ X @ Y4 ) )
% 0.15/0.42 = ( product_Pair @ A @ B @ ( F @ X ) @ Y4 ) ) ).
% 0.15/0.42
% 0.15/0.42 % apfst_conv
% 0.15/0.42 thf(fact_164_lfilter__LNil,axiom,
% 0.15/0.42 ! [A: $tType,P: A > $o] :
% 0.15/0.42 ( ( coinductive_lfilter @ A @ P @ ( coinductive_LNil @ A ) )
% 0.15/0.42 = ( coinductive_LNil @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfilter_LNil
% 0.15/0.42 thf(fact_165_swap__simp,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,X: B,Y4: A] :
% 0.15/0.42 ( ( product_swap @ B @ A @ ( product_Pair @ B @ A @ X @ Y4 ) )
% 0.15/0.42 = ( product_Pair @ A @ B @ Y4 @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % swap_simp
% 0.15/0.42 thf(fact_166_case__prod__conv,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,C: $tType,F: B > C > A,A3: B,B3: C] :
% 0.15/0.42 ( ( product_case_prod @ B @ C @ A @ F @ ( product_Pair @ B @ C @ A3 @ B3 ) )
% 0.15/0.42 = ( F @ A3 @ B3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % case_prod_conv
% 0.15/0.42 thf(fact_167_lstrict__prefix__code_I1_J,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % lstrict_prefix_code(1)
% 0.15/0.42 thf(fact_168_case__prodI2,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,P3: product_prod @ A @ B,C3: A > B > $o] :
% 0.15/0.42 ( ! [A4: A,B4: B] :
% 0.15/0.42 ( ( P3
% 0.15/0.42 = ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.15/0.42 => ( C3 @ A4 @ B4 ) )
% 0.15/0.42 => ( product_case_prod @ A @ B @ $o @ C3 @ P3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % case_prodI2
% 0.15/0.42 thf(fact_169_case__prodI,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,F: A > B > $o,A3: A,B3: B] :
% 0.15/0.42 ( ( F @ A3 @ B3 )
% 0.15/0.42 => ( product_case_prod @ A @ B @ $o @ F @ ( product_Pair @ A @ B @ A3 @ B3 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % case_prodI
% 0.15/0.42 thf(fact_170_lappendt__LNil,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,Tr: tLList446370796tllist @ A @ B] :
% 0.15/0.42 ( ( tLList98099029ppendt @ A @ B @ ( coinductive_LNil @ A ) @ Tr )
% 0.15/0.42 = Tr ) ).
% 0.15/0.42
% 0.15/0.42 % lappendt_LNil
% 0.15/0.42 thf(fact_171_case__prodI2_H,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,C: $tType,P3: product_prod @ A @ B,C3: A > B > C > $o,X: C] :
% 0.15/0.42 ( ! [A4: A,B4: B] :
% 0.15/0.42 ( ( ( product_Pair @ A @ B @ A4 @ B4 )
% 0.15/0.42 = P3 )
% 0.15/0.42 => ( C3 @ A4 @ B4 @ X ) )
% 0.15/0.42 => ( product_case_prod @ A @ B @ ( C > $o ) @ C3 @ P3 @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % case_prodI2'
% 0.15/0.42 thf(fact_172_lfitler__K__False,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lfilter @ A
% 0.15/0.42 @ ^ [Uu: A] : $false
% 0.15/0.42 @ Xs )
% 0.15/0.42 = ( coinductive_LNil @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfitler_K_False
% 0.15/0.42 thf(fact_173_prod_Ocollapse,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 0.15/0.42 ( ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) )
% 0.15/0.42 = Prod ) ).
% 0.15/0.42
% 0.15/0.42 % prod.collapse
% 0.15/0.42 thf(fact_174_lprefix__LNil,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.15/0.42 = ( coinductive_lnull @ A @ Xs ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_LNil
% 0.15/0.42 thf(fact_175_diverge__lfilter__LNil,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 0.15/0.42 ( ! [X4: A] :
% 0.15/0.42 ( ( member @ A @ X4 @ ( coinductive_lset @ A @ Xs ) )
% 0.15/0.42 => ~ ( P @ X4 ) )
% 0.15/0.42 => ( ( coinductive_lfilter @ A @ P @ Xs )
% 0.15/0.42 = ( coinductive_LNil @ A ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % diverge_lfilter_LNil
% 0.15/0.42 thf(fact_176_llast__singleton,axiom,
% 0.15/0.42 ! [A: $tType,X: A] :
% 0.15/0.42 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) )
% 0.15/0.42 = X ) ).
% 0.15/0.42
% 0.15/0.42 % llast_singleton
% 0.15/0.42 thf(fact_177_lstrict__prefix__code_I3_J,axiom,
% 0.15/0.42 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 0.15/0.42 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % lstrict_prefix_code(3)
% 0.15/0.42 thf(fact_178_lstrict__prefix__code_I2_J,axiom,
% 0.15/0.42 ! [B: $tType,Y4: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y4 @ Ys ) ) ).
% 0.15/0.42
% 0.15/0.42 % lstrict_prefix_code(2)
% 0.15/0.42 thf(fact_179_The__split__eq,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,X: A,Y4: B] :
% 0.15/0.42 ( ( the @ ( product_prod @ A @ B )
% 0.15/0.42 @ ( product_case_prod @ A @ B @ $o
% 0.15/0.42 @ ^ [X8: A,Y5: B] :
% 0.15/0.42 ( ( X = X8 )
% 0.15/0.42 & ( Y4 = Y5 ) ) ) )
% 0.15/0.42 = ( product_Pair @ A @ B @ X @ Y4 ) ) ).
% 0.15/0.42
% 0.15/0.42 % The_split_eq
% 0.15/0.42 thf(fact_180_pred__equals__eq2,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,R2: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 0.15/0.42 ( ( ( ^ [X3: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y ) @ R2 ) )
% 0.15/0.42 = ( ^ [X3: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y ) @ S ) ) )
% 0.15/0.42 = ( R2 = S ) ) ).
% 0.15/0.42
% 0.15/0.42 % pred_equals_eq2
% 0.15/0.42 thf(fact_181_old_Oprod_Ocase,axiom,
% 0.15/0.42 ! [A: $tType,C: $tType,B: $tType,F: A > B > C,X12: A,X23: B] :
% 0.15/0.42 ( ( product_case_prod @ A @ B @ C @ F @ ( product_Pair @ A @ B @ X12 @ X23 ) )
% 0.15/0.42 = ( F @ X12 @ X23 ) ) ).
% 0.15/0.42
% 0.15/0.42 % old.prod.case
% 0.15/0.42 thf(fact_182_LNil__lprefix,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A] : ( coinductive_lprefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 0.15/0.42
% 0.15/0.42 % LNil_lprefix
% 0.15/0.42 thf(fact_183_llist_Odistinct_I1_J,axiom,
% 0.15/0.42 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_LNil @ A )
% 0.15/0.42 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.distinct(1)
% 0.15/0.42 thf(fact_184_llist_Oexhaust,axiom,
% 0.15/0.42 ! [A: $tType,Y4: coinductive_llist @ A] :
% 0.15/0.42 ( ( Y4
% 0.15/0.42 != ( coinductive_LNil @ A ) )
% 0.15/0.42 => ~ ! [X212: A,X222: coinductive_llist @ A] :
% 0.15/0.42 ( Y4
% 0.15/0.42 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.exhaust
% 0.15/0.42 thf(fact_185_neq__LNil__conv,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( Xs
% 0.15/0.42 != ( coinductive_LNil @ A ) )
% 0.15/0.42 = ( ? [X3: A,Xs4: coinductive_llist @ A] :
% 0.15/0.42 ( Xs
% 0.15/0.42 = ( coinductive_LCons @ A @ X3 @ Xs4 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % neq_LNil_conv
% 0.15/0.42 thf(fact_186_split__fst,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,R2: A > $o,P3: product_prod @ A @ B] :
% 0.15/0.42 ( ( R2 @ ( product_fst @ A @ B @ P3 ) )
% 0.15/0.42 = ( ! [X3: A,Y: B] :
% 0.15/0.42 ( ( P3
% 0.15/0.42 = ( product_Pair @ A @ B @ X3 @ Y ) )
% 0.15/0.42 => ( R2 @ X3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % split_fst
% 0.15/0.42 thf(fact_187_split__fst__asm,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,R2: A > $o,P3: product_prod @ A @ B] :
% 0.15/0.42 ( ( R2 @ ( product_fst @ A @ B @ P3 ) )
% 0.15/0.42 = ( ~ ? [X3: A,Y: B] :
% 0.15/0.42 ( ( P3
% 0.15/0.42 = ( product_Pair @ A @ B @ X3 @ Y ) )
% 0.15/0.42 & ~ ( R2 @ X3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % split_fst_asm
% 0.15/0.42 thf(fact_188_fst__eqD,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,X: A,Y4: B,A3: A] :
% 0.15/0.42 ( ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X @ Y4 ) )
% 0.15/0.42 = A3 )
% 0.15/0.42 => ( X = A3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % fst_eqD
% 0.15/0.42 thf(fact_189_fst__conv,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,X12: A,X23: B] :
% 0.15/0.42 ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X12 @ X23 ) )
% 0.15/0.42 = X12 ) ).
% 0.15/0.42
% 0.15/0.42 % fst_conv
% 0.15/0.42 thf(fact_190_llist_Odisc_I1_J,axiom,
% 0.15/0.42 ! [A: $tType] : ( coinductive_lnull @ A @ ( coinductive_LNil @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.disc(1)
% 0.15/0.42 thf(fact_191_llist_OdiscI_I1_J,axiom,
% 0.15/0.42 ! [A: $tType,Llist: coinductive_llist @ A] :
% 0.15/0.42 ( ( Llist
% 0.15/0.42 = ( coinductive_LNil @ A ) )
% 0.15/0.42 => ( coinductive_lnull @ A @ Llist ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.discI(1)
% 0.15/0.42 thf(fact_192_llist_Ocollapse_I1_J,axiom,
% 0.15/0.42 ! [A: $tType,Llist: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lnull @ A @ Llist )
% 0.15/0.42 => ( Llist
% 0.15/0.42 = ( coinductive_LNil @ A ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.collapse(1)
% 0.15/0.42 thf(fact_193_lnull__def,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( coinductive_lnull @ A )
% 0.15/0.42 = ( ^ [Llist2: coinductive_llist @ A] :
% 0.15/0.42 ( Llist2
% 0.15/0.42 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lnull_def
% 0.15/0.42 thf(fact_194_snd__eqD,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,X: B,Y4: A,A3: A] :
% 0.15/0.42 ( ( ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X @ Y4 ) )
% 0.15/0.42 = A3 )
% 0.15/0.42 => ( Y4 = A3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % snd_eqD
% 0.15/0.42 thf(fact_195_snd__conv,axiom,
% 0.15/0.42 ! [Aa: $tType,A: $tType,X12: Aa,X23: A] :
% 0.15/0.42 ( ( product_snd @ Aa @ A @ ( product_Pair @ Aa @ A @ X12 @ X23 ) )
% 0.15/0.42 = X23 ) ).
% 0.15/0.42
% 0.15/0.42 % snd_conv
% 0.15/0.42 thf(fact_196_lfinite__LNil,axiom,
% 0.15/0.42 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfinite_LNil
% 0.15/0.42 thf(fact_197_LNil__transfer,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,P: A > B > $o] : ( coindu1486289336t_all2 @ A @ B @ P @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % LNil_transfer
% 0.15/0.42 thf(fact_198_llist__all2__LNil__LNil,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,R2: A > B > $o] : ( coindu1486289336t_all2 @ A @ B @ R2 @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_LNil_LNil
% 0.15/0.42 thf(fact_199_lappend__LNil__LNil,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 0.15/0.42 = ( coinductive_LNil @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % lappend_LNil_LNil
% 0.15/0.42 thf(fact_200_LNil__eq__lappend__iff,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( ( coinductive_LNil @ A )
% 0.15/0.42 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.15/0.42 = ( ( Xs
% 0.15/0.42 = ( coinductive_LNil @ A ) )
% 0.15/0.42 & ( Ys
% 0.15/0.42 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % LNil_eq_lappend_iff
% 0.15/0.42 thf(fact_201_lappend__eq__LNil__iff,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.15/0.42 = ( coinductive_LNil @ A ) )
% 0.15/0.42 = ( ( Xs
% 0.15/0.42 = ( coinductive_LNil @ A ) )
% 0.15/0.42 & ( Ys
% 0.15/0.42 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lappend_eq_LNil_iff
% 0.15/0.42 thf(fact_202_old_Oprod_Oinducts,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 0.15/0.42 ( ! [A4: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.15/0.42 => ( P @ Prod ) ) ).
% 0.15/0.42
% 0.15/0.42 % old.prod.inducts
% 0.15/0.42 thf(fact_203_old_Oprod_Oexhaust,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,Y4: product_prod @ A @ B] :
% 0.15/0.42 ~ ! [A4: A,B4: B] :
% 0.15/0.42 ( Y4
% 0.15/0.42 != ( product_Pair @ A @ B @ A4 @ B4 ) ) ).
% 0.15/0.42
% 0.15/0.42 % old.prod.exhaust
% 0.15/0.42 thf(fact_204_prod__induct7,axiom,
% 0.15/0.42 ! [G3: $tType,F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) )] :
% 0.15/0.42 ( ! [A4: A,B4: B,C4: C,D2: D,E3: E,F4: F3,G4: G3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F3 @ G3 ) @ E3 @ ( product_Pair @ F3 @ G3 @ F4 @ G4 ) ) ) ) ) ) )
% 0.15/0.42 => ( P @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod_induct7
% 0.15/0.42 thf(fact_205_prod__induct6,axiom,
% 0.15/0.42 ! [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 ) ) ) )] :
% 0.15/0.42 ( ! [A4: A,B4: B,C4: C,D2: D,E3: E,F4: F3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D2 @ ( product_Pair @ E @ F3 @ E3 @ F4 ) ) ) ) ) )
% 0.15/0.42 => ( P @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod_induct6
% 0.15/0.42 thf(fact_206_prod__induct5,axiom,
% 0.15/0.42 ! [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 ) ) )] :
% 0.15/0.42 ( ! [A4: A,B4: B,C4: C,D2: D,E3: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C4 @ ( product_Pair @ D @ E @ D2 @ E3 ) ) ) ) )
% 0.15/0.42 => ( P @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod_induct5
% 0.15/0.42 thf(fact_207_prod__induct4,axiom,
% 0.15/0.42 ! [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 ) )] :
% 0.15/0.42 ( ! [A4: A,B4: B,C4: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C4 @ D2 ) ) ) )
% 0.15/0.42 => ( P @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod_induct4
% 0.15/0.42 thf(fact_208_prod__induct3,axiom,
% 0.15/0.42 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.15/0.42 ( ! [A4: A,B4: B,C4: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C4 ) ) )
% 0.15/0.42 => ( P @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod_induct3
% 0.15/0.42 thf(fact_209_prod__cases7,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,G3: $tType,Y4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) )] :
% 0.15/0.42 ~ ! [A4: A,B4: B,C4: C,D2: D,E3: E,F4: F3,G4: G3] :
% 0.15/0.42 ( Y4
% 0.15/0.42 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F3 @ G3 ) @ E3 @ ( product_Pair @ F3 @ G3 @ F4 @ G4 ) ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod_cases7
% 0.15/0.42 thf(fact_210_prod__cases6,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,Y4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 0.15/0.42 ~ ! [A4: A,B4: B,C4: C,D2: D,E3: E,F4: F3] :
% 0.15/0.42 ( Y4
% 0.15/0.42 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D2 @ ( product_Pair @ E @ F3 @ E3 @ F4 ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod_cases6
% 0.15/0.42 thf(fact_211_prod__cases5,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 0.15/0.42 ~ ! [A4: A,B4: B,C4: C,D2: D,E3: E] :
% 0.15/0.42 ( Y4
% 0.15/0.42 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C4 @ ( product_Pair @ D @ E @ D2 @ E3 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod_cases5
% 0.15/0.42 thf(fact_212_prod__cases4,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 0.15/0.42 ~ ! [A4: A,B4: B,C4: C,D2: D] :
% 0.15/0.42 ( Y4
% 0.15/0.42 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C4 @ D2 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod_cases4
% 0.15/0.42 thf(fact_213_prod__cases3,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,C: $tType,Y4: product_prod @ A @ ( product_prod @ B @ C )] :
% 0.15/0.42 ~ ! [A4: A,B4: B,C4: C] :
% 0.15/0.42 ( Y4
% 0.15/0.42 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C4 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod_cases3
% 0.15/0.42 thf(fact_214_Pair__inject,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,A3: A,B3: B,A7: A,B5: B] :
% 0.15/0.42 ( ( ( product_Pair @ A @ B @ A3 @ B3 )
% 0.15/0.42 = ( product_Pair @ A @ B @ A7 @ B5 ) )
% 0.15/0.42 => ~ ( ( A3 = A7 )
% 0.15/0.42 => ( B3 != B5 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % Pair_inject
% 0.15/0.42 thf(fact_215_prod__cases,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 0.15/0.42 ( ! [A4: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 0.15/0.42 => ( P @ P3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod_cases
% 0.15/0.42 thf(fact_216_surj__pair,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 0.15/0.42 ? [X4: A,Y3: B] :
% 0.15/0.42 ( P3
% 0.15/0.42 = ( product_Pair @ A @ B @ X4 @ Y3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % surj_pair
% 0.15/0.42 thf(fact_217_case__prod__Pair__iden,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,P3: product_prod @ A @ B] :
% 0.15/0.42 ( ( product_case_prod @ A @ B @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B ) @ P3 )
% 0.15/0.42 = P3 ) ).
% 0.15/0.42
% 0.15/0.42 % case_prod_Pair_iden
% 0.15/0.42 thf(fact_218_mem__case__prodE,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,C: $tType,Z2: A,C3: B > C > ( set @ A ),P3: product_prod @ B @ C] :
% 0.15/0.42 ( ( member @ A @ Z2 @ ( product_case_prod @ B @ C @ ( set @ A ) @ C3 @ P3 ) )
% 0.15/0.42 => ~ ! [X4: B,Y3: C] :
% 0.15/0.42 ( ( P3
% 0.15/0.42 = ( product_Pair @ B @ C @ X4 @ Y3 ) )
% 0.15/0.42 => ~ ( member @ A @ Z2 @ ( C3 @ X4 @ Y3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % mem_case_prodE
% 0.15/0.42 thf(fact_219_Pair__scomp,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,C: $tType,X: C,F: C > A > B] :
% 0.15/0.42 ( ( product_scomp @ A @ C @ A @ B @ ( product_Pair @ C @ A @ X ) @ F )
% 0.15/0.42 = ( F @ X ) ) ).
% 0.15/0.42
% 0.15/0.42 % Pair_scomp
% 0.15/0.42 thf(fact_220_cond__case__prod__eta,axiom,
% 0.15/0.42 ! [C: $tType,B: $tType,A: $tType,F: A > B > C,G: ( product_prod @ A @ B ) > C] :
% 0.15/0.42 ( ! [X4: A,Y3: B] :
% 0.15/0.42 ( ( F @ X4 @ Y3 )
% 0.15/0.42 = ( G @ ( product_Pair @ A @ B @ X4 @ Y3 ) ) )
% 0.15/0.42 => ( ( product_case_prod @ A @ B @ C @ F )
% 0.15/0.42 = G ) ) ).
% 0.15/0.42
% 0.15/0.42 % cond_case_prod_eta
% 0.15/0.42 thf(fact_221_case__prod__eta,axiom,
% 0.15/0.42 ! [C: $tType,B: $tType,A: $tType,F: ( product_prod @ A @ B ) > C] :
% 0.15/0.42 ( ( product_case_prod @ A @ B @ C
% 0.15/0.42 @ ^ [X3: A,Y: B] : ( F @ ( product_Pair @ A @ B @ X3 @ Y ) ) )
% 0.15/0.42 = F ) ).
% 0.15/0.42
% 0.15/0.42 % case_prod_eta
% 0.15/0.42 thf(fact_222_case__prodE2,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,C: $tType,Q: A > $o,P: B > C > A,Z2: product_prod @ B @ C] :
% 0.15/0.42 ( ( Q @ ( product_case_prod @ B @ C @ A @ P @ Z2 ) )
% 0.15/0.42 => ~ ! [X4: B,Y3: C] :
% 0.15/0.42 ( ( Z2
% 0.15/0.42 = ( product_Pair @ B @ C @ X4 @ Y3 ) )
% 0.15/0.42 => ~ ( Q @ ( P @ X4 @ Y3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % case_prodE2
% 0.15/0.42 thf(fact_223_scomp__Pair,axiom,
% 0.15/0.42 ! [C: $tType,B: $tType,A: $tType,X: A > ( product_prod @ B @ C )] :
% 0.15/0.42 ( ( product_scomp @ A @ B @ C @ ( product_prod @ B @ C ) @ X @ ( product_Pair @ B @ C ) )
% 0.15/0.42 = X ) ).
% 0.15/0.42
% 0.15/0.42 % scomp_Pair
% 0.15/0.42 thf(fact_224_case__prodE,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,C3: A > B > $o,P3: product_prod @ A @ B] :
% 0.15/0.42 ( ( product_case_prod @ A @ B @ $o @ C3 @ P3 )
% 0.15/0.42 => ~ ! [X4: A,Y3: B] :
% 0.15/0.42 ( ( P3
% 0.15/0.42 = ( product_Pair @ A @ B @ X4 @ Y3 ) )
% 0.15/0.42 => ~ ( C3 @ X4 @ Y3 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % case_prodE
% 0.15/0.42 thf(fact_225_case__prodD,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,F: A > B > $o,A3: A,B3: B] :
% 0.15/0.42 ( ( product_case_prod @ A @ B @ $o @ F @ ( product_Pair @ A @ B @ A3 @ B3 ) )
% 0.15/0.42 => ( F @ A3 @ B3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % case_prodD
% 0.15/0.42 thf(fact_226_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.15/0.42 = ( Xs
% 0.15/0.42 = ( coinductive_LNil @ A ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % Coinductive_List.finite_lprefix_nitpick_simps(1)
% 0.15/0.42 thf(fact_227_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 0.15/0.42
% 0.15/0.42 % Coinductive_List.finite_lprefix_nitpick_simps(2)
% 0.15/0.42 thf(fact_228_case__prodE_H,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,C: $tType,C3: A > B > C > $o,P3: product_prod @ A @ B,Z2: C] :
% 0.15/0.42 ( ( product_case_prod @ A @ B @ ( C > $o ) @ C3 @ P3 @ Z2 )
% 0.15/0.42 => ~ ! [X4: A,Y3: B] :
% 0.15/0.42 ( ( P3
% 0.15/0.42 = ( product_Pair @ A @ B @ X4 @ Y3 ) )
% 0.15/0.42 => ~ ( C3 @ X4 @ Y3 @ Z2 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % case_prodE'
% 0.15/0.42 thf(fact_229_case__prodD_H,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,C: $tType,R2: A > B > C > $o,A3: A,B3: B,C3: C] :
% 0.15/0.42 ( ( product_case_prod @ A @ B @ ( C > $o ) @ R2 @ ( product_Pair @ A @ B @ A3 @ B3 ) @ C3 )
% 0.15/0.42 => ( R2 @ A3 @ B3 @ C3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % case_prodD'
% 0.15/0.42 thf(fact_230_lprefix__code_I2_J,axiom,
% 0.15/0.42 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.15/0.42 ~ ( coinductive_lprefix @ A @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LNil @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_code(2)
% 0.15/0.42 thf(fact_231_lprefix_Ocases,axiom,
% 0.15/0.42 ! [A: $tType,A1: coinductive_llist @ A,A22: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ A1 @ A22 )
% 0.15/0.42 => ( ( ( A1
% 0.15/0.42 = ( coinductive_LNil @ A ) )
% 0.15/0.42 => ! [Xs5: coinductive_llist @ A] : ( A22 != Xs5 ) )
% 0.15/0.42 => ~ ! [Xs5: coinductive_llist @ A,Ys6: coinductive_llist @ A,X4: A] :
% 0.15/0.42 ( ( A1
% 0.15/0.42 = ( coinductive_LCons @ A @ X4 @ Xs5 ) )
% 0.15/0.42 => ( ( A22
% 0.15/0.42 = ( coinductive_LCons @ A @ X4 @ Ys6 ) )
% 0.15/0.42 => ~ ( coinductive_lprefix @ A @ Xs5 @ Ys6 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix.cases
% 0.15/0.42 thf(fact_232_lprefix_Osimps,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( coinductive_lprefix @ A )
% 0.15/0.42 = ( ^ [A12: coinductive_llist @ A,A23: coinductive_llist @ A] :
% 0.15/0.42 ( ? [Xs3: coinductive_llist @ A] :
% 0.15/0.42 ( ( A12
% 0.15/0.42 = ( coinductive_LNil @ A ) )
% 0.15/0.42 & ( A23 = Xs3 ) )
% 0.15/0.42 | ? [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A,X3: A] :
% 0.15/0.42 ( ( A12
% 0.15/0.42 = ( coinductive_LCons @ A @ X3 @ Xs3 ) )
% 0.15/0.42 & ( A23
% 0.15/0.42 = ( coinductive_LCons @ A @ X3 @ Ys3 ) )
% 0.15/0.42 & ( coinductive_lprefix @ A @ Xs3 @ Ys3 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix.simps
% 0.15/0.42 thf(fact_233_lprefix_Ocoinduct,axiom,
% 0.15/0.42 ! [A: $tType,X9: ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,Xa: coinductive_llist @ A] :
% 0.15/0.42 ( ( X9 @ X @ Xa )
% 0.15/0.42 => ( ! [X4: coinductive_llist @ A,Xa2: coinductive_llist @ A] :
% 0.15/0.42 ( ( X9 @ X4 @ Xa2 )
% 0.15/0.42 => ( ? [Xs7: coinductive_llist @ A] :
% 0.15/0.42 ( ( X4
% 0.15/0.42 = ( coinductive_LNil @ A ) )
% 0.15/0.42 & ( Xa2 = Xs7 ) )
% 0.15/0.42 | ? [Xs7: coinductive_llist @ A,Ys5: coinductive_llist @ A,Xb: A] :
% 0.15/0.42 ( ( X4
% 0.15/0.42 = ( coinductive_LCons @ A @ Xb @ Xs7 ) )
% 0.15/0.42 & ( Xa2
% 0.15/0.42 = ( coinductive_LCons @ A @ Xb @ Ys5 ) )
% 0.15/0.42 & ( ( X9 @ Xs7 @ Ys5 )
% 0.15/0.42 | ( coinductive_lprefix @ A @ Xs7 @ Ys5 ) ) ) ) )
% 0.15/0.42 => ( coinductive_lprefix @ A @ X @ Xa ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix.coinduct
% 0.15/0.42 thf(fact_234_lprefix__LCons__conv,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Y4: A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lprefix @ A @ Xs @ ( coinductive_LCons @ A @ Y4 @ Ys ) )
% 0.15/0.42 = ( ( Xs
% 0.15/0.42 = ( coinductive_LNil @ A ) )
% 0.15/0.42 | ? [Xs4: coinductive_llist @ A] :
% 0.15/0.42 ( ( Xs
% 0.15/0.42 = ( coinductive_LCons @ A @ Y4 @ Xs4 ) )
% 0.15/0.42 & ( coinductive_lprefix @ A @ Xs4 @ Ys ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lprefix_LCons_conv
% 0.15/0.42 thf(fact_235_conjI__realizer,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,P: A > $o,P3: A,Q: B > $o,Q2: B] :
% 0.15/0.42 ( ( P @ P3 )
% 0.15/0.42 => ( ( Q @ Q2 )
% 0.15/0.42 => ( ( P @ ( product_fst @ A @ B @ ( product_Pair @ A @ B @ P3 @ Q2 ) ) )
% 0.15/0.42 & ( Q @ ( product_snd @ A @ B @ ( product_Pair @ A @ B @ P3 @ Q2 ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % conjI_realizer
% 0.15/0.42 thf(fact_236_exI__realizer,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,P: A > B > $o,Y4: A,X: B] :
% 0.15/0.42 ( ( P @ Y4 @ X )
% 0.15/0.42 => ( P @ ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X @ Y4 ) ) @ ( product_fst @ B @ A @ ( product_Pair @ B @ A @ X @ Y4 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % exI_realizer
% 0.15/0.42 thf(fact_237_prod_Oexhaust__sel,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 0.15/0.42 ( Prod
% 0.15/0.42 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod.exhaust_sel
% 0.15/0.42 thf(fact_238_surjective__pairing,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,T3: product_prod @ A @ B] :
% 0.15/0.42 ( T3
% 0.15/0.42 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ T3 ) @ ( product_snd @ A @ B @ T3 ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % surjective_pairing
% 0.15/0.42 thf(fact_239_lfinite_Oinducts,axiom,
% 0.15/0.42 ! [A: $tType,X: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.15/0.42 ( ( coinductive_lfinite @ A @ X )
% 0.15/0.42 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.15/0.42 => ( ! [Xs5: coinductive_llist @ A,X4: A] :
% 0.15/0.42 ( ( coinductive_lfinite @ A @ Xs5 )
% 0.15/0.42 => ( ( P @ Xs5 )
% 0.15/0.42 => ( P @ ( coinductive_LCons @ A @ X4 @ Xs5 ) ) ) )
% 0.15/0.42 => ( P @ X ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfinite.inducts
% 0.15/0.42 thf(fact_240_lfinite_Osimps,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( coinductive_lfinite @ A )
% 0.15/0.42 = ( ^ [A2: coinductive_llist @ A] :
% 0.15/0.42 ( ( A2
% 0.15/0.42 = ( coinductive_LNil @ A ) )
% 0.15/0.42 | ? [Xs3: coinductive_llist @ A,X3: A] :
% 0.15/0.42 ( ( A2
% 0.15/0.42 = ( coinductive_LCons @ A @ X3 @ Xs3 ) )
% 0.15/0.42 & ( coinductive_lfinite @ A @ Xs3 ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfinite.simps
% 0.15/0.42 thf(fact_241_lfinite_Ocases,axiom,
% 0.15/0.42 ! [A: $tType,A3: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lfinite @ A @ A3 )
% 0.15/0.42 => ( ( A3
% 0.15/0.42 != ( coinductive_LNil @ A ) )
% 0.15/0.42 => ~ ! [Xs5: coinductive_llist @ A] :
% 0.15/0.42 ( ? [X4: A] :
% 0.15/0.42 ( A3
% 0.15/0.42 = ( coinductive_LCons @ A @ X4 @ Xs5 ) )
% 0.15/0.42 => ~ ( coinductive_lfinite @ A @ Xs5 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfinite.cases
% 0.15/0.42 thf(fact_242_llist__all2__LNil__LCons,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,R2: A > B > $o,Y21: B,Y22: coinductive_llist @ B] :
% 0.15/0.42 ~ ( coindu1486289336t_all2 @ A @ B @ R2 @ ( coinductive_LNil @ A ) @ ( coinductive_LCons @ B @ Y21 @ Y22 ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_LNil_LCons
% 0.15/0.42 thf(fact_243_llist__all2__LCons__LNil,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,R2: A > B > $o,Y21: A,Y22: coinductive_llist @ A] :
% 0.15/0.42 ~ ( coindu1486289336t_all2 @ A @ B @ R2 @ ( coinductive_LCons @ A @ Y21 @ Y22 ) @ ( coinductive_LNil @ B ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_LCons_LNil
% 0.15/0.42 thf(fact_244_llist__all2__cases,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 0.15/0.42 => ( ( ( Xs
% 0.15/0.42 = ( coinductive_LNil @ A ) )
% 0.15/0.42 => ( Ys
% 0.15/0.42 != ( coinductive_LNil @ B ) ) )
% 0.15/0.42 => ~ ! [X4: A,Xs6: coinductive_llist @ A] :
% 0.15/0.42 ( ( Xs
% 0.15/0.42 = ( coinductive_LCons @ A @ X4 @ Xs6 ) )
% 0.15/0.42 => ! [Y3: B,Ys7: coinductive_llist @ B] :
% 0.15/0.42 ( ( Ys
% 0.15/0.42 = ( coinductive_LCons @ B @ Y3 @ Ys7 ) )
% 0.15/0.42 => ( ( P @ X4 @ Y3 )
% 0.15/0.42 => ~ ( coindu1486289336t_all2 @ A @ B @ P @ Xs6 @ Ys7 ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist_all2_cases
% 0.15/0.42 thf(fact_245_llist_Orel__cases,axiom,
% 0.15/0.42 ! [A: $tType,B: $tType,R2: A > B > $o,A3: coinductive_llist @ A,B3: coinductive_llist @ B] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ A @ B @ R2 @ A3 @ B3 )
% 0.15/0.42 => ( ( ( A3
% 0.15/0.42 = ( coinductive_LNil @ A ) )
% 0.15/0.42 => ( B3
% 0.15/0.42 != ( coinductive_LNil @ B ) ) )
% 0.15/0.42 => ~ ! [X13: A,X24: coinductive_llist @ A] :
% 0.15/0.42 ( ( A3
% 0.15/0.42 = ( coinductive_LCons @ A @ X13 @ X24 ) )
% 0.15/0.42 => ! [Y12: B,Y24: coinductive_llist @ B] :
% 0.15/0.42 ( ( B3
% 0.15/0.42 = ( coinductive_LCons @ B @ Y12 @ Y24 ) )
% 0.15/0.42 => ( ( R2 @ X13 @ Y12 )
% 0.15/0.42 => ~ ( coindu1486289336t_all2 @ A @ B @ R2 @ X24 @ Y24 ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % llist.rel_cases
% 0.15/0.42 thf(fact_246_lappend__snocL1__conv__LCons2,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Y4: A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y4 @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 0.15/0.42 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y4 @ Ys ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lappend_snocL1_conv_LCons2
% 0.15/0.42 thf(fact_247_lappend_Octr_I1_J,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coinductive_lnull @ A @ Xs )
% 0.15/0.42 => ( ( coinductive_lnull @ A @ Ys )
% 0.15/0.42 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.15/0.42 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lappend.ctr(1)
% 0.15/0.42 thf(fact_248_internal__case__prod__conv,axiom,
% 0.15/0.42 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A3: B,B3: C] :
% 0.15/0.42 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A3 @ B3 ) )
% 0.15/0.42 = ( C3 @ A3 @ B3 ) ) ).
% 0.15/0.42
% 0.15/0.42 % internal_case_prod_conv
% 0.15/0.42 thf(fact_249_lfilter__empty__conv,axiom,
% 0.15/0.42 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 0.15/0.42 ( ( ( coinductive_lfilter @ A @ P @ Xs )
% 0.15/0.42 = ( coinductive_LNil @ A ) )
% 0.15/0.42 = ( ! [X3: A] :
% 0.15/0.42 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 0.15/0.42 => ~ ( P @ X3 ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % lfilter_empty_conv
% 0.15/0.42 thf(fact_250_llast__LNil,axiom,
% 0.15/0.42 ! [A: $tType] :
% 0.15/0.42 ( ( coinductive_llast @ A @ ( coinductive_LNil @ A ) )
% 0.15/0.42 = ( undefined @ A ) ) ).
% 0.15/0.42
% 0.15/0.42 % llast_LNil
% 0.15/0.42 thf(fact_251_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 0.15/0.42 ! [A: $tType,Xs: coinductive_llist @ A,Y4: A,Ys: coinductive_llist @ A] :
% 0.15/0.42 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y4 @ Ys ) )
% 0.15/0.42 = ( ( Xs
% 0.15/0.42 = ( coinductive_LNil @ A ) )
% 0.15/0.42 | ? [Xs4: coinductive_llist @ A] :
% 0.15/0.42 ( ( Xs
% 0.15/0.42 = ( coinductive_LCons @ A @ Y4 @ Xs4 ) )
% 0.15/0.42 & ( coindu328551480prefix @ A @ Xs4 @ Ys ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % Coinductive_List.finite_lprefix_nitpick_simps(3)
% 0.15/0.42 thf(fact_252_prod_Osplit__sel__asm,axiom,
% 0.15/0.42 ! [C: $tType,B: $tType,A: $tType,P: C > $o,F: A > B > C,Prod: product_prod @ A @ B] :
% 0.15/0.42 ( ( P @ ( product_case_prod @ A @ B @ C @ F @ Prod ) )
% 0.15/0.42 = ( ~ ( ( Prod
% 0.15/0.42 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) )
% 0.15/0.42 & ~ ( P @ ( F @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 % prod.split_sel_asm
% 0.15/0.42
% 0.15/0.42 %----Helper facts (3)
% 0.15/0.42 thf(help_If_3_1_T,axiom,
% 0.15/0.42 ! [P: $o] :
% 0.15/0.42 ( ( P = $true )
% 0.15/0.42 | ( P = $false ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(help_If_2_1_T,axiom,
% 0.15/0.42 ! [A: $tType,X: A,Y4: A] :
% 0.15/0.42 ( ( if @ A @ $false @ X @ Y4 )
% 0.15/0.42 = Y4 ) ).
% 0.15/0.42
% 0.15/0.42 thf(help_If_1_1_T,axiom,
% 0.15/0.42 ! [A: $tType,X: A,Y4: A] :
% 0.15/0.42 ( ( if @ A @ $true @ X @ Y4 )
% 0.15/0.42 = X ) ).
% 0.15/0.42
% 0.15/0.42 %----Conjectures (3)
% 0.15/0.42 thf(conj_0,hypothesis,
% 0.15/0.42 ( product_case_prod @ ( coinductive_llist @ a ) @ c @ ( ( product_prod @ ( coinductive_llist @ b ) @ d ) > $o )
% 0.15/0.42 @ ^ [Xs3: coinductive_llist @ a,B2: c] :
% 0.15/0.42 ( product_case_prod @ ( coinductive_llist @ b ) @ d @ $o
% 0.15/0.42 @ ^ [Ys3: coinductive_llist @ b,B6: d] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ a @ b @ pa @ Xs3 @ Ys3 )
% 0.15/0.42 & ( ( coinductive_lfinite @ a @ Xs3 )
% 0.15/0.42 => ( qa @ B2 @ B6 ) ) ) )
% 0.15/0.42 @ xsa
% 0.15/0.42 @ ysa ) ).
% 0.15/0.42
% 0.15/0.42 thf(conj_1,hypothesis,
% 0.15/0.42 ( ( coinductive_lfinite @ a @ ( product_fst @ ( coinductive_llist @ a ) @ c @ xsa ) )
% 0.15/0.42 => ( ( coinductive_lfinite @ b @ ( product_fst @ ( coinductive_llist @ b ) @ d @ ysa ) )
% 0.15/0.42 => ( ( qa
% 0.15/0.42 @ ( product_case_prod @ ( coinductive_llist @ a ) @ c @ c
% 0.15/0.42 @ ^ [Xs3: coinductive_llist @ a,B2: c] : ( if @ c @ ( coinductive_lfinite @ a @ Xs3 ) @ B2 @ ( undefined @ c ) )
% 0.15/0.42 @ xsa )
% 0.15/0.42 @ ( product_case_prod @ ( coinductive_llist @ b ) @ d @ d
% 0.15/0.42 @ ^ [Xs3: coinductive_llist @ b,B2: d] : ( if @ d @ ( coinductive_lfinite @ b @ Xs3 ) @ B2 @ ( undefined @ d ) )
% 0.15/0.42 @ ysa ) )
% 0.15/0.42 => ( product_case_prod @ ( coinductive_llist @ a ) @ e @ ( ( product_prod @ ( coinductive_llist @ b ) @ f ) > $o )
% 0.15/0.42 @ ^ [Xs3: coinductive_llist @ a,B2: e] :
% 0.15/0.42 ( product_case_prod @ ( coinductive_llist @ b ) @ f @ $o
% 0.15/0.42 @ ^ [Ys3: coinductive_llist @ b,B6: f] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ a @ b @ pa @ Xs3 @ Ys3 )
% 0.15/0.42 & ( ( coinductive_lfinite @ a @ Xs3 )
% 0.15/0.42 => ( ra @ B2 @ B6 ) ) ) )
% 0.15/0.42 @ ( xs_a
% 0.15/0.42 @ ( product_case_prod @ ( coinductive_llist @ a ) @ c @ c
% 0.15/0.42 @ ^ [Xs3: coinductive_llist @ a,B2: c] : ( if @ c @ ( coinductive_lfinite @ a @ Xs3 ) @ B2 @ ( undefined @ c ) )
% 0.15/0.42 @ xsa ) )
% 0.15/0.42 @ ( ys_a
% 0.15/0.42 @ ( product_case_prod @ ( coinductive_llist @ b ) @ d @ d
% 0.15/0.42 @ ^ [Xs3: coinductive_llist @ b,B2: d] : ( if @ d @ ( coinductive_lfinite @ b @ Xs3 ) @ B2 @ ( undefined @ d ) )
% 0.15/0.42 @ ysa ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(conj_2,conjecture,
% 0.15/0.42 ( product_case_prod @ ( coinductive_llist @ a ) @ e @ ( ( product_prod @ ( coinductive_llist @ b ) @ f ) > $o )
% 0.15/0.42 @ ^ [Xs3: coinductive_llist @ a,B2: e] :
% 0.15/0.42 ( product_case_prod @ ( coinductive_llist @ b ) @ f @ $o
% 0.15/0.42 @ ^ [Ys3: coinductive_llist @ b,B6: f] :
% 0.15/0.42 ( ( coindu1486289336t_all2 @ a @ b @ pa @ Xs3 @ Ys3 )
% 0.15/0.42 & ( ( coinductive_lfinite @ a @ Xs3 )
% 0.15/0.42 => ( ra @ B2 @ B6 ) ) ) )
% 0.15/0.42 @ ( product_case_prod @ ( coinductive_llist @ a ) @ c @ ( ( c > ( product_prod @ ( coinductive_llist @ a ) @ e ) ) > ( product_prod @ ( coinductive_llist @ a ) @ e ) )
% 0.15/0.42 @ ^ [Xs3: coinductive_llist @ a,B2: c,F2: c > ( product_prod @ ( coinductive_llist @ a ) @ e )] : ( product_apfst @ ( coinductive_llist @ a ) @ ( coinductive_llist @ a ) @ e @ ( coinductive_lappend @ a @ Xs3 ) @ ( F2 @ B2 ) )
% 0.15/0.42 @ xsa
% 0.15/0.42 @ xs_a )
% 0.15/0.42 @ ( product_case_prod @ ( coinductive_llist @ b ) @ d @ ( ( d > ( product_prod @ ( coinductive_llist @ b ) @ f ) ) > ( product_prod @ ( coinductive_llist @ b ) @ f ) )
% 0.15/0.42 @ ^ [Xs3: coinductive_llist @ b,B2: d,F2: d > ( product_prod @ ( coinductive_llist @ b ) @ f )] : ( product_apfst @ ( coinductive_llist @ b ) @ ( coinductive_llist @ b ) @ f @ ( coinductive_lappend @ b @ Xs3 ) @ ( F2 @ B2 ) )
% 0.15/0.42 @ ysa
% 0.15/0.42 @ ys_a ) ) ).
% 0.15/0.42
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.43 ------------------------
% 2.48/1.45 ---- Embedded in THF ---
% 2.48/1.45 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.48/1.45 %%% Generated on Tue Feb 24 06:11:19 EST 2026
% 2.48/1.45 %%% using '$$dhol' embedding, version 1.3.0.
% 2.48/1.45 %%% Logic specification used:
% 2.48/1.45 %%% thf(spec, logic, $$dhol).
% 2.48/1.45
% 2.48/1.45 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.mqKFzRPNcN/DTF2DTF23357.p
% 2.48/1.45 thf(ty_t_TLList__Mirabelle__qhjoikztpd_Otllist, type, tLList446370796tllist: ($tType > ($tType > $tType))).
% 2.48/1.45 thf(ty_t_Coinductive__List_Ollist, type, coinductive_llist: ($tType > $tType)).
% 2.48/1.45 thf(ty_t_Product__Type_Oprod, type, product_prod: ($tType > ($tType > $tType))).
% 2.48/1.45 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.48/1.45 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.48/1.45 thf(ty_tf_f, type, f: $tType).
% 2.48/1.45 thf(ty_tf_e, type, e: $tType).
% 2.48/1.45 thf(ty_tf_d, type, d: $tType).
% 2.48/1.45 thf(ty_tf_c, type, c: $tType).
% 2.48/1.45 thf(ty_tf_b, type, b: $tType).
% 2.48/1.45 thf(ty_tf_a, type, a: $tType).
% 2.48/1.45 thf(sy_c_Coinductive__List_Ofinite__lprefix, type, coindu328551480prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.48/1.45 thf(sy_c_Coinductive__List_Olappend, type, coinductive_lappend: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.48/1.45 thf(sy_c_Coinductive__List_Olfilter, type, coinductive_lfilter: (!> [A:$tType]: (((A > $o) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.48/1.45 thf(sy_c_Coinductive__List_Olfinite, type, coinductive_lfinite: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 2.48/1.45 thf(sy_c_Coinductive__List_Ollast, type, coinductive_llast: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 2.48/1.45 thf(sy_c_Coinductive__List_Ollist_OLCons, type, coinductive_LCons: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.48/1.45 thf(sy_c_Coinductive__List_Ollist_OLNil, type, coinductive_LNil: (!> [A:$tType]: ((coinductive_llist @ A)))).
% 2.48/1.45 thf(sy_c_Coinductive__List_Ollist_Ollist__all2, type, coindu1486289336t_all2: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((coinductive_llist @ A) > ((coinductive_llist @ B) > $o)))))).
% 2.48/1.45 thf(sy_c_Coinductive__List_Ollist_Olnull, type, coinductive_lnull: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 2.48/1.45 thf(sy_c_Coinductive__List_Ollist_Olset, type, coinductive_lset: (!> [A:$tType]: (((coinductive_llist @ A) > (set @ A))))).
% 2.48/1.45 thf(sy_c_Coinductive__List_Olprefix, type, coinductive_lprefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.48/1.45 thf(sy_c_Coinductive__List_Olstrict__prefix, type, coindu1478340336prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.48/1.45 thf(sy_c_HOL_OThe, type, the: (!> [A:$tType]: (((A > $o) > A)))).
% 2.48/1.45 thf(sy_c_HOL_Oundefined, type, undefined: (!> [A:$tType]: (A))).
% 2.48/1.45 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.48/1.45 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.48/1.45 thf(sy_c_Product__Type_OPair, type, product_Pair: (!> [A:$tType,B:$tType]: ((A > (B > ((product_prod @ A) @ B)))))).
% 2.48/1.45 thf(sy_c_Product__Type_Oapfst, type, product_apfst: (!> [A:$tType,C:$tType,B:$tType]: (((A > C) > (((product_prod @ A) @ B) > ((product_prod @ C) @ B)))))).
% 2.48/1.45 thf(sy_c_Product__Type_Ointernal__case__prod, type, produc2004651681e_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.48/1.45 thf(sy_c_Product__Type_Oprod_Ocase__prod, type, product_case_prod: (!> [A:$tType,B:$tType,C:$tType]: (((A > (B > C)) > (((product_prod @ A) @ B) > C))))).
% 2.48/1.45 thf(sy_c_Product__Type_Oprod_Ofst, type, product_fst: (!> [A:$tType,B:$tType]: ((((product_prod @ A) @ B) > A)))).
% 2.48/1.45 thf(sy_c_Product__Type_Oprod_Osnd, type, product_snd: (!> [A:$tType,B:$tType]: ((((product_prod @ A) @ B) > B)))).
% 2.48/1.45 thf(sy_c_Product__Type_Oprod_Oswap, type, product_swap: (!> [A:$tType,B:$tType]: ((((product_prod @ A) @ B) > ((product_prod @ B) @ A))))).
% 2.48/1.45 thf(sy_c_Product__Type_Oscomp, type, product_scomp: (!> [A:$tType,B:$tType,C:$tType,D:$tType]: (((A > ((product_prod @ B) @ C)) > ((B > (C > D)) > (A > D)))))).
% 2.48/1.45 thf(sy_c_Pure_Otype, type, type: (!> [A:$tType]: ((itself @ A)))).
% 2.48/1.45 thf(sy_c_Relation_Oreflp, type, reflp: (!> [A:$tType]: (((A > (A > $o)) > $o)))).
% 2.48/1.45 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.48/1.45 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Ocr__tllist, type, tLList47617868tllist: (!> [A:$tType,B:$tType]: ((((product_prod @ (coinductive_llist @ A)) @ B) > (((tLList446370796tllist @ A) @ B) > $o))))).
% 2.48/1.45 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Olappendt, type, tLList98099029ppendt: (!> [A:$tType,B:$tType]: (((coinductive_llist @ A) > (((tLList446370796tllist @ A) @ B) > ((tLList446370796tllist @ A) @ B)))))).
% 2.48/1.45 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist__of__llist, type, tLList1672613558_llist: (!> [B:$tType,A:$tType]: ((B > ((coinductive_llist @ A) > ((tLList446370796tllist @ A) @ B)))))).
% 2.48/1.45 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.48/1.45 thf(sy_v_Pa, type, pa: (a > (b > $o))).
% 2.48/1.45 thf(sy_v_Qa, type, qa: (c > (d > $o))).
% 2.48/1.45 thf(sy_v_Ra, type, ra: (e > (f > $o))).
% 2.48/1.45 thf(sy_v_xs_Ha, type, xs_a: (c > ((product_prod @ (coinductive_llist @ a)) @ e))).
% 2.48/1.45 thf(sy_v_xsa, type, xsa: ((product_prod @ (coinductive_llist @ a)) @ c)).
% 2.48/1.45 thf(sy_v_ys_Ha, type, ys_a: (d > ((product_prod @ (coinductive_llist @ b)) @ f))).
% 2.48/1.45 thf(sy_v_ysa, type, ysa: ((product_prod @ (coinductive_llist @ b)) @ d)).
% 2.48/1.45 thf(fact_0_fst__apfst, axiom, (! [A:$tType,B:$tType,C:$tType,F:(C > A),X:((product_prod @ C) @ B)]: (((((product_fst @ A) @ B) @ (((((product_apfst @ C) @ A) @ B) @ F) @ X)) = (F @ (((product_fst @ C) @ B) @ X)))))).
% 2.48/1.45 thf(fact_1_apfst__eq__conv, axiom, (! [A:$tType,B:$tType,C:$tType,F:(C > A),X:((product_prod @ C) @ B),G:(C > A)]: ((((((((product_apfst @ C) @ A) @ B) @ F) @ X) = (((((product_apfst @ C) @ A) @ B) @ G) @ X)) = ((F @ (((product_fst @ C) @ B) @ X)) = (G @ (((product_fst @ C) @ B) @ X))))))).
% 2.48/1.45 thf(fact_2_lfinite__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lfinite @ A) @ Xs) & ((coinductive_lfinite @ A) @ Ys)))))).
% 2.48/1.45 thf(fact_3_split__part, axiom, (! [B:$tType,A:$tType,P:$o,Q:(A > (B > $o))]: ((((((product_case_prod @ A) @ B) @ $o) @ (^ [A2:A,B2:B]: ((P & ((Q @ A2) @ B2))))) = (^ [Ab:((product_prod @ A) @ B)]: ((P & (((((product_case_prod @ A) @ B) @ $o) @ Q) @ Ab)))))))).
% 2.48/1.45 thf(fact_4_llist__all2__lappendI, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B),Xs2:(coinductive_llist @ A),Ys2:(coinductive_llist @ B)]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_lfinite @ B) @ Ys) => (((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs2) @ Ys2))) => (((((coindu1486289336t_all2 @ A) @ B) @ P) @ (((coinductive_lappend @ A) @ Xs) @ Xs2)) @ (((coinductive_lappend @ B) @ Ys) @ Ys2))))))).
% 2.48/1.45 thf(fact_5_fst__def, axiom, (! [B:$tType,A:$tType]: ((((product_fst @ A) @ B) = ((((product_case_prod @ A) @ B) @ A) @ (^ [X1:A,X2:B]: (X1))))))).
% 2.48/1.45 thf(fact_6_case__prod__app, axiom, (! [A:$tType,D:$tType,C:$tType,B:$tType]: (((((product_case_prod @ B) @ C) @ (D > A)) = (^ [F2:(B > (C > (D > A))),X3:((product_prod @ B) @ C),Y:D]: ((((((product_case_prod @ B) @ C) @ A) @ (^ [L:B,R:C]: ((((F2 @ L) @ R) @ Y)))) @ X3))))))).
% 2.48/1.45 thf(fact_7_lappend__inf, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((~ (((coinductive_lfinite @ A) @ Xs))) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = Xs))))).
% 2.48/1.45 thf(fact_8_llist__all2__lfiniteD, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => (((coinductive_lfinite @ A) @ Xs) = ((coinductive_lfinite @ B) @ Ys)))))).
% 2.48/1.45 thf(fact_9_llist__all2__conj, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Q:(A > (B > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((((((coindu1486289336t_all2 @ A) @ B) @ (^ [X3:A,Y:B]: ((((P @ X3) @ Y) & ((Q @ X3) @ Y))))) @ Xs) @ Ys) = ((((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ Ys) & (((((coindu1486289336t_all2 @ A) @ B) @ Q) @ Xs) @ Ys)))))).
% 2.48/1.45 thf(fact_10_prod_Odisc__eq__case, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B)]: ((((((product_case_prod @ A) @ B) @ $o) @ (^ [Uu:A,Uv:B]: ($true))) @ Prod)))).
% 2.48/1.45 thf(fact_11_prod_Ocase__distrib, axiom, (! [C:$tType,D:$tType,B:$tType,A:$tType,H:(C > D),F:(A > (B > C)),Prod:((product_prod @ A) @ B)]: (((H @ (((((product_case_prod @ A) @ B) @ C) @ F) @ Prod)) = (((((product_case_prod @ A) @ B) @ D) @ (^ [X1:A,X2:B]: ((H @ ((F @ X1) @ X2))))) @ Prod))))).
% 2.48/1.45 thf(fact_12_llist_Orel__refl, axiom, (! [B:$tType,Ra:(B > (B > $o)),X:(coinductive_llist @ B)]: (((! [X4:B]: (((Ra @ X4) @ X4))) => (((((coindu1486289336t_all2 @ B) @ B) @ Ra) @ X) @ X))))).
% 2.48/1.45 thf(fact_13_llist_Orel__eq, axiom, (! [A:$tType]: (((((coindu1486289336t_all2 @ A) @ A) @ (^ [Y2:A,Z:A]: ((Y2 = Z)))) = (^ [Y2:(coinductive_llist @ A),Z:(coinductive_llist @ A)]: ((Y2 = Z))))))).
% 2.48/1.45 thf(fact_14_llist__all2__mono, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B),P2:(A > (B > $o))]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => ((! [X4:A,Y3:B]: ((((P @ X4) @ Y3) => ((P2 @ X4) @ Y3)))) => (((((coindu1486289336t_all2 @ A) @ B) @ P2) @ Xs) @ Ys)))))).
% 2.48/1.45 thf(fact_15_llist__all2__rsp, axiom, (! [A:$tType,B:$tType,R2:(A > (B > $o)),S:(A > (A > $o)),T:(B > (B > $o)),X:(coinductive_llist @ A),Y4:(coinductive_llist @ B),A3:(coinductive_llist @ A),B3:(coinductive_llist @ B)]: (((! [X4:A,Y3:B]: ((((R2 @ X4) @ Y3) => (! [A4:A,B4:B]: ((((R2 @ A4) @ B4) => (((S @ X4) @ A4) = ((T @ Y3) @ B4)))))))) => ((((((coindu1486289336t_all2 @ A) @ B) @ R2) @ X) @ Y4) => ((((((coindu1486289336t_all2 @ A) @ B) @ R2) @ A3) @ B3) => ((((((coindu1486289336t_all2 @ A) @ A) @ S) @ X) @ A3) = (((((coindu1486289336t_all2 @ B) @ B) @ T) @ Y4) @ B3)))))))).
% 2.48/1.45 thf(fact_16_lappend__assoc, axiom, (! [A:$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)))))).
% 2.48/1.45 thf(fact_17_internal__case__prod__def, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((produc2004651681e_prod @ A) @ B) @ C) = (((product_case_prod @ A) @ B) @ C))))).
% 2.48/1.45 thf(fact_18_reflp__tllist, axiom, (! [B:$tType,A:$tType]: (((reflp @ ((product_prod @ (coinductive_llist @ A)) @ B)) @ ((((product_case_prod @ (coinductive_llist @ A)) @ B) @ (((product_prod @ (coinductive_llist @ A)) @ B) > $o)) @ (^ [Xs3:(coinductive_llist @ A),A2:B]: (((((product_case_prod @ (coinductive_llist @ A)) @ B) @ $o) @ (^ [Ys3:(coinductive_llist @ A),B2:B]: (((Xs3 = Ys3) & (((coinductive_lfinite @ A) @ Ys3) => (A2 = B2))))))))))))).
% 2.48/1.45 thf(fact_19_tllist_Oabs__eq__iff, axiom, (! [B:$tType,A:$tType,X:((product_prod @ (coinductive_llist @ A)) @ B),Y4:((product_prod @ (coinductive_llist @ A)) @ B)]: ((((((((product_case_prod @ (coinductive_llist @ A)) @ B) @ ((tLList446370796tllist @ A) @ B)) @ (^ [Xs3:(coinductive_llist @ A),A2:B]: (((((tLList1672613558_llist @ B) @ A) @ A2) @ Xs3)))) @ X) = (((((product_case_prod @ (coinductive_llist @ A)) @ B) @ ((tLList446370796tllist @ A) @ B)) @ (^ [Xs3:(coinductive_llist @ A),A2:B]: (((((tLList1672613558_llist @ B) @ A) @ A2) @ Xs3)))) @ Y4)) = ((((((product_case_prod @ (coinductive_llist @ A)) @ B) @ (((product_prod @ (coinductive_llist @ A)) @ B) > $o)) @ (^ [Xs3:(coinductive_llist @ A),A2:B]: (((((product_case_prod @ (coinductive_llist @ A)) @ B) @ $o) @ (^ [Ys3:(coinductive_llist @ A),B2:B]: (((Xs3 = Ys3) & (((coinductive_lfinite @ A) @ Ys3) => (A2 = B2))))))))) @ X) @ Y4))))).
% 2.48/1.45 thf(fact_20_case__swap, axiom, (! [A:$tType,B:$tType,C:$tType,F:(C > (B > A)),P3:((product_prod @ C) @ B)]: (((((((product_case_prod @ B) @ C) @ A) @ (^ [Y:B,X3:C]: (((F @ X3) @ Y)))) @ (((product_swap @ C) @ B) @ P3)) = (((((product_case_prod @ C) @ B) @ A) @ F) @ P3))))).
% 2.48/1.45 thf(fact_21_llast__linfinite, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((~ (((coinductive_lfinite @ A) @ Xs))) => (((coinductive_llast @ A) @ Xs) = (undefined @ A)))))).
% 2.48/1.45 thf(fact_22_scomp__apply, axiom, (! [A:$tType,D:$tType,C:$tType,B:$tType]: ((((((product_scomp @ B) @ C) @ D) @ A) = (^ [F2:(B > ((product_prod @ C) @ D)),G2:(C > (D > A)),X3:B]: ((((((product_case_prod @ C) @ D) @ A) @ G2) @ (F2 @ X3)))))))).
% 2.48/1.45 thf(fact_23_lprefix__lappend__same, axiom, (! [A:$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)))))).
% 2.48/1.45 thf(fact_24_lfilter__lappend__lfinite, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:(A > $o),Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => ((((coinductive_lfilter @ A) @ P) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lappend @ A) @ (((coinductive_lfilter @ A) @ P) @ Xs)) @ (((coinductive_lfilter @ A) @ P) @ Ys))))))).
% 2.48/1.45 thf(fact_25_case__prod__unfold, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((product_case_prod @ A) @ B) @ C) = (^ [C2:(A > (B > C)),P4:((product_prod @ A) @ B)]: (((C2 @ (((product_fst @ A) @ B) @ P4)) @ (((product_snd @ A) @ B) @ P4)))))))).
% 2.48/1.45 thf(fact_26_case__prod__beta_H, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((product_case_prod @ A) @ B) @ C) = (^ [F2:(A > (B > C)),X3:((product_prod @ A) @ B)]: (((F2 @ (((product_fst @ A) @ B) @ X3)) @ (((product_snd @ A) @ B) @ X3)))))))).
% 2.48/1.45 thf(fact_27_split__comp__eq, axiom, (! [A:$tType,C:$tType,B:$tType,D:$tType,F:(A > (B > C)),G:(D > A)]: (((^ [U:((product_prod @ D) @ B)]: (((F @ (G @ (((product_fst @ D) @ B) @ U))) @ (((product_snd @ D) @ B) @ U)))) = ((((product_case_prod @ D) @ B) @ C) @ (^ [X3:D]: ((F @ (G @ X3))))))))).
% 2.48/1.45 thf(fact_28_lprefix__refl, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coinductive_lprefix @ A) @ Xs) @ Xs)))).
% 2.48/1.45 thf(fact_29_llist_Oleq__refl, axiom, (! [A:$tType,X:(coinductive_llist @ A)]: ((((coinductive_lprefix @ A) @ X) @ X)))).
% 2.48/1.45 thf(fact_30_lfilter__idem, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: (((((coinductive_lfilter @ A) @ P) @ (((coinductive_lfilter @ A) @ P) @ Xs)) = (((coinductive_lfilter @ A) @ P) @ Xs))))).
% 2.48/1.45 thf(fact_31_swap__swap, axiom, (! [B:$tType,A:$tType,P3:((product_prod @ A) @ B)]: (((((product_swap @ B) @ A) @ (((product_swap @ A) @ B) @ P3)) = P3)))).
% 2.48/1.45 thf(fact_32_lfilter__K__True, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coinductive_lfilter @ A) @ (^ [Uu:A]: ($true))) @ Xs) = Xs)))).
% 2.48/1.45 thf(fact_33_tllist__of__llist__inject, axiom, (! [A:$tType,B:$tType,B3:B,Xs:(coinductive_llist @ A),C3:B,Ys:(coinductive_llist @ A)]: (((((((tLList1672613558_llist @ B) @ A) @ B3) @ Xs) = ((((tLList1672613558_llist @ B) @ A) @ C3) @ Ys)) = ((Xs = Ys) & (((coinductive_lfinite @ A) @ Ys) => (B3 = C3))))))).
% 2.48/1.45 thf(fact_34_snd__apfst, axiom, (! [B:$tType,A:$tType,C:$tType,F:(C > B),X:((product_prod @ C) @ A)]: (((((product_snd @ B) @ A) @ (((((product_apfst @ C) @ B) @ A) @ F) @ X)) = (((product_snd @ C) @ A) @ X))))).
% 2.48/1.45 thf(fact_35_snd__swap, axiom, (! [B:$tType,A:$tType,X:((product_prod @ A) @ B)]: (((((product_snd @ B) @ A) @ (((product_swap @ A) @ B) @ X)) = (((product_fst @ A) @ B) @ X))))).
% 2.48/1.45 thf(fact_36_fst__swap, axiom, (! [A:$tType,B:$tType,X:((product_prod @ B) @ A)]: (((((product_fst @ A) @ B) @ (((product_swap @ B) @ A) @ X)) = (((product_snd @ B) @ A) @ X))))).
% 2.48/1.45 thf(fact_37_scomp__scomp, axiom, (! [A:$tType,C:$tType,D:$tType,B:$tType,F3:$tType,E:$tType,F:(A > ((product_prod @ E) @ F3)),G:(E > (F3 > ((product_prod @ C) @ D))),H:(C > (D > B))]: ((((((((product_scomp @ A) @ C) @ D) @ B) @ ((((((product_scomp @ A) @ E) @ F3) @ ((product_prod @ C) @ D)) @ F) @ G)) @ H) = ((((((product_scomp @ A) @ E) @ F3) @ B) @ F) @ (^ [X3:E]: (((((((product_scomp @ F3) @ C) @ D) @ B) @ (G @ X3)) @ H)))))))).
% 2.48/1.45 thf(fact_38_lprefix__trans, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => ((((coinductive_lprefix @ A) @ Ys) @ Zs) => (((coinductive_lprefix @ A) @ Xs) @ Zs)))))).
% 2.48/1.45 thf(fact_39_llist_Oleq__trans, axiom, (! [A:$tType,X:(coinductive_llist @ A),Y4:(coinductive_llist @ A),Z2:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ X) @ Y4) => ((((coinductive_lprefix @ A) @ Y4) @ Z2) => (((coinductive_lprefix @ A) @ X) @ Z2)))))).
% 2.48/1.45 thf(fact_40_lprefix__antisym, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => ((((coinductive_lprefix @ A) @ Ys) @ Xs) => (Xs = Ys)))))).
% 2.48/1.45 thf(fact_41_lprefix__lfilterI, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),P:(A > $o)]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => (((coinductive_lprefix @ A) @ (((coinductive_lfilter @ A) @ P) @ Xs)) @ (((coinductive_lfilter @ A) @ P) @ Ys)))))).
% 2.48/1.45 thf(fact_42_llist_Oleq__antisym, axiom, (! [A:$tType,X:(coinductive_llist @ A),Y4:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ X) @ Y4) => ((((coinductive_lprefix @ A) @ Y4) @ X) => (X = Y4)))))).
% 2.48/1.45 thf(fact_43_lprefix__down__linear, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Zs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ Zs) => ((((coinductive_lprefix @ A) @ Ys) @ Zs) => ((((coinductive_lprefix @ A) @ Xs) @ Ys) | (((coinductive_lprefix @ A) @ Ys) @ Xs))))))).
% 2.48/1.45 thf(fact_44_lfilter__lfilter, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o),Xs:(coinductive_llist @ A)]: (((((coinductive_lfilter @ A) @ P) @ (((coinductive_lfilter @ A) @ Q) @ Xs)) = (((coinductive_lfilter @ A) @ (^ [X3:A]: (((P @ X3) & (Q @ X3))))) @ Xs))))).
% 2.48/1.45 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 2.48/1.45 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A5:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A5)))) = A5)))).
% 2.48/1.45 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.48/1.45 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X4:A]: (((F @ X4) = (G @ X4)))) => (F = G))))).
% 2.48/1.45 thf(fact_49_llist_Orel__reflp, axiom, (! [A:$tType,R2:(A > (A > $o))]: ((((reflp @ A) @ R2) => ((reflp @ (coinductive_llist @ A)) @ (((coindu1486289336t_all2 @ A) @ A) @ R2)))))).
% 2.48/1.45 thf(fact_50_tllist_Oabs__induct, axiom, (! [B:$tType,A:$tType,P:(((tLList446370796tllist @ A) @ B) > $o),X:((tLList446370796tllist @ A) @ B)]: (((! [Y3:((product_prod @ (coinductive_llist @ A)) @ B)]: ((P @ (((((product_case_prod @ (coinductive_llist @ A)) @ B) @ ((tLList446370796tllist @ A) @ B)) @ (^ [Xs3:(coinductive_llist @ A),A2:B]: (((((tLList1672613558_llist @ B) @ A) @ A2) @ Xs3)))) @ Y3)))) => (P @ X))))).
% 2.48/1.45 thf(fact_51_scomp__unfold, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType]: ((((((product_scomp @ A) @ B) @ C) @ D) = (^ [F2:(A > ((product_prod @ B) @ C)),G2:(B > (C > D)),X3:A]: (((G2 @ (((product_fst @ B) @ C) @ (F2 @ X3))) @ (((product_snd @ B) @ C) @ (F2 @ X3))))))))).
% 2.48/1.45 thf(fact_52_prod__eqI, axiom, (! [B:$tType,A:$tType,P3:((product_prod @ A) @ B),Q2:((product_prod @ A) @ B)]: ((((((product_fst @ A) @ B) @ P3) = (((product_fst @ A) @ B) @ Q2)) => (((((product_snd @ A) @ B) @ P3) = (((product_snd @ A) @ B) @ Q2)) => (P3 = Q2)))))).
% 2.48/1.45 thf(fact_53_prod_Oexpand, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B),Prod2:((product_prod @ A) @ B)]: (((((((product_fst @ A) @ B) @ Prod) = (((product_fst @ A) @ B) @ Prod2)) & ((((product_snd @ A) @ B) @ Prod) = (((product_snd @ A) @ B) @ Prod2))) => (Prod = Prod2))))).
% 2.48/1.45 thf(fact_54_prod__eq__iff, axiom, (! [B:$tType,A:$tType]: (((^ [Y2:((product_prod @ A) @ B),Z:((product_prod @ A) @ B)]: ((Y2 = Z))) = (^ [S2:((product_prod @ A) @ B),T2:((product_prod @ A) @ B)]: ((((((product_fst @ A) @ B) @ S2) = (((product_fst @ A) @ B) @ T2)) & ((((product_snd @ A) @ B) @ S2) = (((product_snd @ A) @ B) @ T2))))))))).
% 2.48/1.45 thf(fact_55_lfinite__lfilterI, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:(A > $o)]: ((((coinductive_lfinite @ A) @ Xs) => ((coinductive_lfinite @ A) @ (((coinductive_lfilter @ A) @ P) @ Xs)))))).
% 2.48/1.45 thf(fact_56_llist__all2__lfilterI, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B),Q1:(A > $o),Q22:(B > $o)]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => ((! [X4:A,Y3:B]: ((((P @ X4) @ Y3) => ((Q1 @ X4) = (Q22 @ Y3))))) => (((((coindu1486289336t_all2 @ A) @ B) @ P) @ (((coinductive_lfilter @ A) @ Q1) @ Xs)) @ (((coinductive_lfilter @ B) @ Q22) @ Ys))))))).
% 2.48/1.45 thf(fact_57_lprefix__lfiniteD, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => (((coinductive_lfinite @ A) @ Ys) => ((coinductive_lfinite @ A) @ Xs)))))).
% 2.48/1.45 thf(fact_58_not__lfinite__lprefix__conv__eq, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((~ (((coinductive_lfinite @ A) @ Xs))) => ((((coinductive_lprefix @ A) @ Xs) @ Ys) = (Xs = Ys)))))).
% 2.48/1.45 thf(fact_59_lprefix__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lprefix @ A) @ Xs) @ (((coinductive_lappend @ A) @ Xs) @ Ys))))).
% 2.48/1.45 thf(fact_60_lappend__lprefixE, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) @ Zs) => (~ ((! [Zs2:(coinductive_llist @ A)]: ((Zs != (((coinductive_lappend @ A) @ Xs) @ Zs2)))))))))).
% 2.48/1.45 thf(fact_61_lprefix__lappendD, axiom, (! [A:$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)))))).
% 2.48/1.45 thf(fact_62_lprefix__conv__lappend, axiom, (! [A:$tType]: (((coinductive_lprefix @ A) = (^ [Xs3:(coinductive_llist @ A),Ys3:(coinductive_llist @ A)]: ((? [Zs3:(coinductive_llist @ A)]: ((Ys3 = (((coinductive_lappend @ A) @ Xs3) @ Zs3)))))))))).
% 2.48/1.45 thf(fact_63_lprefix__lappend__sameI, axiom, (! [A:$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)))))).
% 2.48/1.45 thf(fact_64_tllist__of__llist__cong, axiom, (! [B:$tType,A:$tType,Xs:(coinductive_llist @ A),Xs2:(coinductive_llist @ A),B3:B,B5:B]: (((Xs = Xs2) => ((((coinductive_lfinite @ A) @ Xs2) => (B3 = B5)) => (((((tLList1672613558_llist @ B) @ A) @ B3) @ Xs) = ((((tLList1672613558_llist @ B) @ A) @ B5) @ Xs2))))))).
% 2.48/1.45 thf(fact_65_snd__def, axiom, (! [B:$tType,A:$tType]: ((((product_snd @ A) @ B) = ((((product_case_prod @ A) @ B) @ B) @ (^ [X1:A,X2:B]: (X2))))))).
% 2.48/1.45 thf(fact_66_scomp__def, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType]: ((((((product_scomp @ A) @ B) @ C) @ D) = (^ [F2:(A > ((product_prod @ B) @ C)),G2:(B > (C > D)),X3:A]: ((((((product_case_prod @ B) @ C) @ D) @ G2) @ (F2 @ X3)))))))).
% 2.48/1.45 thf(fact_67_case__prod__beta, axiom, (! [A:$tType,C:$tType,B:$tType]: (((((product_case_prod @ B) @ C) @ A) = (^ [F2:(B > (C > A)),P4:((product_prod @ B) @ C)]: (((F2 @ (((product_fst @ B) @ C) @ P4)) @ (((product_snd @ B) @ C) @ P4)))))))).
% 2.48/1.45 thf(fact_68_prod_Ocase__eq__if, axiom, (! [C:$tType,B:$tType,A:$tType]: (((((product_case_prod @ A) @ B) @ C) = (^ [F2:(A > (B > C)),Prod3:((product_prod @ A) @ B)]: (((F2 @ (((product_fst @ A) @ B) @ Prod3)) @ (((product_snd @ A) @ B) @ Prod3)))))))).
% 2.48/1.45 thf(fact_69_Product__Type_OCollect__case__prodD, axiom, (! [B:$tType,A:$tType,X:((product_prod @ A) @ B),A5:(A > (B > $o))]: (((((member @ ((product_prod @ A) @ B)) @ X) @ ((collect @ ((product_prod @ A) @ B)) @ ((((product_case_prod @ A) @ B) @ $o) @ A5))) => ((A5 @ (((product_fst @ A) @ B) @ X)) @ (((product_snd @ A) @ B) @ X)))))).
% 2.48/1.45 thf(fact_70_lfilter__eq__lappend__lfiniteD, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:(coinductive_llist @ A)]: ((((((coinductive_lfilter @ A) @ P) @ Xs) = (((coinductive_lappend @ A) @ Ys) @ Zs)) => (((coinductive_lfinite @ A) @ Ys) => (? [Us:(coinductive_llist @ A),Vs:(coinductive_llist @ A)]: (((Xs = (((coinductive_lappend @ A) @ Us) @ Vs)) & (((coinductive_lfinite @ A) @ Us) & ((Ys = (((coinductive_lfilter @ A) @ P) @ Us)) & (Zs = (((coinductive_lfilter @ A) @ P) @ Vs)))))))))))).
% 2.48/1.45 thf(fact_71_exE__realizer, axiom, (! [C:$tType,A:$tType,B:$tType,P:(A > (B > $o)),P3:((product_prod @ B) @ A),Q:(C > $o),F:(B > (A > C))]: ((((P @ (((product_snd @ B) @ A) @ P3)) @ (((product_fst @ B) @ A) @ P3)) => ((! [X4:B,Y3:A]: ((((P @ Y3) @ X4) => (Q @ ((F @ X4) @ Y3))))) => (Q @ (((((product_case_prod @ B) @ A) @ C) @ F) @ P3))))))).
% 2.48/1.45 thf(fact_72_lappendt_Oabs__eq, axiom, (! [B:$tType,A:$tType,Xa:(coinductive_llist @ A),X:((product_prod @ (coinductive_llist @ A)) @ B)]: ((((((tLList98099029ppendt @ A) @ B) @ Xa) @ (((((product_case_prod @ (coinductive_llist @ A)) @ B) @ ((tLList446370796tllist @ A) @ B)) @ (^ [Xs3:(coinductive_llist @ A),A2:B]: (((((tLList1672613558_llist @ B) @ A) @ A2) @ Xs3)))) @ X)) = (((((product_case_prod @ (coinductive_llist @ A)) @ B) @ ((tLList446370796tllist @ A) @ B)) @ (^ [Xs3:(coinductive_llist @ A),A2:B]: (((((tLList1672613558_llist @ B) @ A) @ A2) @ Xs3)))) @ (((((product_apfst @ (coinductive_llist @ A)) @ (coinductive_llist @ A)) @ B) @ ((coinductive_lappend @ A) @ Xa)) @ X)))))).
% 2.48/1.45 thf(fact_73_exE__realizer_H, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),P3:((product_prod @ B) @ A)]: ((((P @ (((product_snd @ B) @ A) @ P3)) @ (((product_fst @ B) @ A) @ P3)) => (~ ((! [X4:B,Y3:A]: ((~ (((P @ Y3) @ X4))))))))))).
% 2.48/1.45 thf(fact_74_tllist__of__llist__eq__lappendt__conv, axiom, (! [B:$tType,A:$tType,A3:B,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),Zs:((tLList446370796tllist @ A) @ B)]: (((((((tLList1672613558_llist @ B) @ A) @ A3) @ Xs) = ((((tLList98099029ppendt @ A) @ B) @ Ys) @ Zs)) = (? [Xs4:(coinductive_llist @ A),A6:B]: (((Xs = (((coinductive_lappend @ A) @ Ys) @ Xs4)) & ((Zs = ((((tLList1672613558_llist @ B) @ A) @ A6) @ Xs4)) & (((coinductive_lfinite @ A) @ Ys) => (A3 = A6)))))))))).
% 2.48/1.45 thf(fact_75_Coinductive__List_Olprefix__nitpick__simps, axiom, (! [A:$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))))))))).
% 2.48/1.45 thf(fact_76_cr__tllist__def, axiom, (! [B:$tType,A:$tType]: ((((tLList47617868tllist @ A) @ B) = ((((product_case_prod @ (coinductive_llist @ A)) @ B) @ (((tLList446370796tllist @ A) @ B) > $o)) @ (^ [Xs3:(coinductive_llist @ A),B2:B]: (((^ [Y2:((tLList446370796tllist @ A) @ B),Z:((tLList446370796tllist @ A) @ B)]: ((Y2 = Z))) @ ((((tLList1672613558_llist @ B) @ A) @ B2) @ Xs3))))))))).
% 2.48/1.45 thf(fact_77_llast__lappend, axiom, (! [A:$tType,Ys:(coinductive_llist @ A),Xs:(coinductive_llist @ A)]: (((((coinductive_lnull @ A) @ Ys) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((coinductive_llast @ A) @ Xs))) & ((~ (((coinductive_lnull @ A) @ Ys))) => ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((coinductive_llast @ A) @ Ys))) & ((~ (((coinductive_lfinite @ A) @ Xs))) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (undefined @ A))))))))).
% 2.48/1.45 thf(fact_78_llast__lappend__LCons, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y4:A,Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y4) @ Ys))) = ((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ Y4) @ Ys))))))).
% 2.48/1.45 thf(fact_79_DEADID_Orel__reflp, axiom, (! [A:$tType]: (((reflp @ A) @ (^ [Y2:A,Z:A]: ((Y2 = Z))))))).
% 2.48/1.45 thf(fact_80_llist_Oinject, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A),Y21:A,Y22:(coinductive_llist @ A)]: ((((((coinductive_LCons @ A) @ X21) @ X22) = (((coinductive_LCons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.48/1.45 thf(fact_81_LCons__lprefix__LCons, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),Y4:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ (((coinductive_LCons @ A) @ Y4) @ Ys)) = ((X = Y4) & (((coinductive_lprefix @ A) @ Xs) @ Ys)))))).
% 2.48/1.45 thf(fact_82_lfinite__LCons, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = ((coinductive_lfinite @ A) @ Xs))))).
% 2.48/1.45 thf(fact_83_lfinite__code_I2_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B)]: ((((coinductive_lfinite @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) = ((coinductive_lfinite @ B) @ Xs))))).
% 2.48/1.45 thf(fact_84_llist__all2__LCons__LCons, axiom, (! [A:$tType,B:$tType,R2:(A > (B > $o)),X21:A,X22:(coinductive_llist @ A),Y21:B,Y22:(coinductive_llist @ B)]: (((((((coindu1486289336t_all2 @ A) @ B) @ R2) @ (((coinductive_LCons @ A) @ X21) @ X22)) @ (((coinductive_LCons @ B) @ Y21) @ Y22)) = (((R2 @ X21) @ Y21) & (((((coindu1486289336t_all2 @ A) @ B) @ R2) @ X22) @ Y22)))))).
% 2.48/1.45 thf(fact_85_lappend__code_I2_J, axiom, (! [A:$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)))))).
% 2.48/1.45 thf(fact_86_lnull__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lnull @ A) @ Xs) & ((coinductive_lnull @ A) @ Ys)))))).
% 2.48/1.45 thf(fact_87_lappend_Odisc__iff_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((~ (((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)))) = ((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))))))).
% 2.48/1.45 thf(fact_88_lfilter__LCons, axiom, (! [A:$tType,P:(A > $o),X:A,Xs:(coinductive_llist @ A)]: ((((P @ X) => ((((coinductive_lfilter @ A) @ P) @ (((coinductive_LCons @ A) @ X) @ Xs)) = (((coinductive_LCons @ A) @ X) @ (((coinductive_lfilter @ A) @ P) @ Xs)))) & ((~ ((P @ X))) => ((((coinductive_lfilter @ A) @ P) @ (((coinductive_LCons @ A) @ X) @ Xs)) = (((coinductive_lfilter @ A) @ P) @ Xs))))))).
% 2.48/1.45 thf(fact_89_llast__LCons2, axiom, (! [A:$tType,X:A,Y4:A,Xs:(coinductive_llist @ A)]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ (((coinductive_LCons @ A) @ Y4) @ Xs))) = ((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ Y4) @ Xs)))))).
% 2.48/1.45 thf(fact_90_lappend_Oexhaust, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lnull @ A) @ Xs) => (~ (((coinductive_lnull @ A) @ Ys)))) => ((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))))))).
% 2.48/1.45 thf(fact_91_not__lnull__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((~ (((coinductive_lnull @ A) @ Xs))) = (? [X3:A,Xs4:(coinductive_llist @ A)]: ((Xs = (((coinductive_LCons @ A) @ X3) @ Xs4)))))))).
% 2.48/1.45 thf(fact_92_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)))))))).
% 2.48/1.45 thf(fact_93_llist_OdiscI_I2_J, axiom, (! [A:$tType,Llist:(coinductive_llist @ A),X21:A,X22:(coinductive_llist @ A)]: (((Llist = (((coinductive_LCons @ A) @ X21) @ X22)) => (~ (((coinductive_lnull @ A) @ Llist))))))).
% 2.48/1.45 thf(fact_94_llist_Odisc_I2_J, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A)]: ((~ (((coinductive_lnull @ A) @ (((coinductive_LCons @ A) @ X21) @ X22))))))).
% 2.48/1.45 thf(fact_95_llast__LCons, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),X:A]: (((((coinductive_lnull @ A) @ Xs) => (((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = X)) & ((~ (((coinductive_lnull @ A) @ Xs))) => (((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = ((coinductive_llast @ A) @ Xs))))))).
% 2.48/1.45 thf(fact_96_lprefix__not__lnullD, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => ((~ (((coinductive_lnull @ A) @ Xs))) => (~ (((coinductive_lnull @ A) @ Ys)))))))).
% 2.48/1.45 thf(fact_97_lprefix__lnullD, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => (((coinductive_lnull @ A) @ Ys) => ((coinductive_lnull @ A) @ Xs)))))).
% 2.48/1.45 thf(fact_98_lprefix__lnull, axiom, (! [A:$tType,Ys:(coinductive_llist @ A),Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Ys) => ((((coinductive_lprefix @ A) @ Xs) @ Ys) = ((coinductive_lnull @ A) @ Xs)))))).
% 2.48/1.45 thf(fact_99_lnull__lprefix, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => (((coinductive_lprefix @ A) @ Xs) @ Ys))))).
% 2.48/1.45 thf(fact_100_LCons__lprefix__conv, axiom, (! [A:$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)))))))).
% 2.48/1.45 thf(fact_101_Le__LCons, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),X:A]: (((((coinductive_lprefix @ A) @ Xs) @ Ys) => (((coinductive_lprefix @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ (((coinductive_LCons @ A) @ X) @ Ys)))))).
% 2.48/1.45 thf(fact_102_lnull__imp__lfinite, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => ((coinductive_lfinite @ A) @ Xs))))).
% 2.48/1.45 thf(fact_103_llist__all2__lnullD, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => (((coinductive_lnull @ A) @ Xs) = ((coinductive_lnull @ B) @ Ys)))))).
% 2.48/1.45 thf(fact_104_lfinite__LConsI, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),X:A]: ((((coinductive_lfinite @ A) @ Xs) => ((coinductive_lfinite @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)))))).
% 2.48/1.45 thf(fact_105_llist__all2__LCons2, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ A),Y4:B,Ys:(coinductive_llist @ B)]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ (((coinductive_LCons @ B) @ Y4) @ Ys)) = (? [X3:A,Xs4:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ X3) @ Xs4)) & (((P @ X3) @ Y4) & (((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs4) @ Ys))))))))).
% 2.48/1.45 thf(fact_106_llist__all2__LCons1, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),X:A,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ Ys) = (? [Y:B,Ys4:(coinductive_llist @ B)]: (((Ys = (((coinductive_LCons @ B) @ Y) @ Ys4)) & (((P @ X) @ Y) & (((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ Ys4))))))))).
% 2.48/1.45 thf(fact_107_llist_Orel__intros_I2_J, axiom, (! [A:$tType,B:$tType,R2:(A > (B > $o)),X21:A,Y21:B,X22:(coinductive_llist @ A),Y22:(coinductive_llist @ B)]: ((((R2 @ X21) @ Y21) => ((((((coindu1486289336t_all2 @ A) @ B) @ R2) @ X22) @ Y22) => (((((coindu1486289336t_all2 @ A) @ B) @ R2) @ (((coinductive_LCons @ A) @ X21) @ X22)) @ (((coinductive_LCons @ B) @ Y21) @ Y22))))))).
% 2.48/1.45 thf(fact_108_lappend__lnull2, axiom, (! [A:$tType,Ys:(coinductive_llist @ A),Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Ys) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = Xs))))).
% 2.48/1.45 thf(fact_109_lappend__lnull1, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = Ys))))).
% 2.48/1.45 thf(fact_110_lappend_Odisc_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => (((coinductive_lnull @ A) @ Ys) => ((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys))))))).
% 2.48/1.45 thf(fact_111_lappend_Odisc_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((~ (((coinductive_lnull @ A) @ Xs))) | (~ (((coinductive_lnull @ A) @ Ys)))) => (~ (((coinductive_lnull @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)))))))).
% 2.48/1.45 thf(fact_112_lfilter__LCons__found, axiom, (! [A:$tType,P:(A > $o),X:A,Xs:(coinductive_llist @ A)]: (((P @ X) => ((((coinductive_lfilter @ A) @ P) @ (((coinductive_LCons @ A) @ X) @ Xs)) = (((coinductive_LCons @ A) @ X) @ (((coinductive_lfilter @ A) @ P) @ Xs))))))).
% 2.48/1.45 thf(fact_113_lfilter__LCons__seek, axiom, (! [A:$tType,P3:(A > $o),X:A,L2:(coinductive_llist @ A)]: (((~ ((P3 @ X))) => ((((coinductive_lfilter @ A) @ P3) @ (((coinductive_LCons @ A) @ X) @ L2)) = (((coinductive_lfilter @ A) @ P3) @ L2)))))).
% 2.48/1.45 thf(fact_114_Coinductive__List_Ofinite__lprefix__def, axiom, (! [A:$tType]: (((coindu328551480prefix @ A) = (coinductive_lprefix @ A))))).
% 2.48/1.45 thf(fact_115_lstrict__prefix__lappend__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Xs) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lfinite @ A) @ Xs) & (~ (((coinductive_lnull @ A) @ Ys)))))))).
% 2.48/1.45 thf(fact_116_lfilter__eq__LConsD, axiom, (! [A:$tType,P:(A > $o),Ys:(coinductive_llist @ A),X:A,Xs:(coinductive_llist @ A)]: ((((((coinductive_lfilter @ A) @ P) @ Ys) = (((coinductive_LCons @ A) @ X) @ Xs)) => (? [Us:(coinductive_llist @ A),Vs:(coinductive_llist @ A)]: (((Ys = (((coinductive_lappend @ A) @ Us) @ (((coinductive_LCons @ A) @ X) @ Vs))) & (((coinductive_lfinite @ A) @ Us) & ((! [X5:A]: (((((member @ A) @ X5) @ ((coinductive_lset @ A) @ Us)) => (~ ((P @ X5)))))) & ((P @ X) & (Xs = (((coinductive_lfilter @ A) @ P) @ Vs)))))))))))).
% 2.48/1.45 thf(fact_117_reflpD, axiom, (! [A:$tType,R3:(A > (A > $o)),X:A]: ((((reflp @ A) @ R3) => ((R3 @ X) @ X))))).
% 2.48/1.45 thf(fact_118_reflpE, axiom, (! [A:$tType,R3:(A > (A > $o)),X:A]: ((((reflp @ A) @ R3) => ((R3 @ X) @ X))))).
% 2.48/1.45 thf(fact_119_reflpI, axiom, (! [A:$tType,R3:(A > (A > $o))]: (((! [X4:A]: (((R3 @ X4) @ X4))) => ((reflp @ A) @ R3))))).
% 2.48/1.45 thf(fact_120_reflp__def, axiom, (! [A:$tType]: (((reflp @ A) = (^ [R:(A > (A > $o))]: ((! [X3:A]: (((R @ X3) @ X3))))))))).
% 2.48/1.45 thf(fact_121_llist__all2__same, axiom, (! [A:$tType,P:(A > (A > $o)),Xs:(coinductive_llist @ A)]: (((((((coindu1486289336t_all2 @ A) @ A) @ P) @ Xs) @ Xs) = (! [X3:A]: (((((member @ A) @ X3) @ ((coinductive_lset @ A) @ Xs)) => ((P @ X3) @ X3)))))))).
% 2.48/1.45 thf(fact_122_lstrict__prefix__code_I4_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B),Y4:B,Ys:(coinductive_llist @ B)]: (((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) @ (((coinductive_LCons @ B) @ Y4) @ Ys)) = ((X = Y4) & (((coindu1478340336prefix @ B) @ Xs) @ Ys)))))).
% 2.48/1.45 thf(fact_123_lset__lfilter, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: ((((coinductive_lset @ A) @ (((coinductive_lfilter @ A) @ P) @ Xs)) = ((collect @ A) @ (^ [X3:A]: (((((member @ A) @ X3) @ ((coinductive_lset @ A) @ Xs)) & (P @ X3))))))))).
% 2.48/1.45 thf(fact_124_lnull__lfilter, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ (((coinductive_lfilter @ A) @ P) @ Xs)) = (! [X3:A]: (((((member @ A) @ X3) @ ((coinductive_lset @ A) @ Xs)) => (~ ((P @ X3)))))))))).
% 2.48/1.45 thf(fact_125_llist__less__induct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > $o),Xs:(coinductive_llist @ A)]: (((! [Xs5:(coinductive_llist @ A)]: (((! [Ys5:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys5) @ Xs5) => (P @ Ys5)))) => (P @ Xs5)))) => (P @ Xs))))).
% 2.48/1.45 thf(fact_126_lset__intros_I2_J, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),X6:A]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => (((member @ A) @ X) @ ((coinductive_lset @ A) @ (((coinductive_LCons @ A) @ X6) @ Xs))))))).
% 2.48/1.45 thf(fact_127_lset__intros_I1_J, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: ((((member @ A) @ X) @ ((coinductive_lset @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)))))).
% 2.48/1.45 thf(fact_128_llist_Oset__intros_I2_J, axiom, (! [A:$tType,X:A,A22:(coinductive_llist @ A),A1:A]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ A22)) => (((member @ A) @ X) @ ((coinductive_lset @ A) @ (((coinductive_LCons @ A) @ A1) @ A22))))))).
% 2.48/1.45 thf(fact_129_llist_Oset__intros_I1_J, axiom, (! [A:$tType,A1:A,A22:(coinductive_llist @ A)]: ((((member @ A) @ A1) @ ((coinductive_lset @ A) @ (((coinductive_LCons @ A) @ A1) @ A22)))))).
% 2.48/1.45 thf(fact_130_lset__cases, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => ((! [Xs6:(coinductive_llist @ A)]: ((Xs != (((coinductive_LCons @ A) @ X) @ Xs6)))) => (~ ((! [X7:A,Xs6:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ X7) @ Xs6)) => (~ ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs6)))))))))))))).
% 2.48/1.45 thf(fact_131_lset__induct, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => ((! [Xs5:(coinductive_llist @ A)]: ((P @ (((coinductive_LCons @ A) @ X) @ Xs5)))) => ((! [X7:A,Xs5:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs5)) => ((X != X7) => ((P @ Xs5) => (P @ (((coinductive_LCons @ A) @ X7) @ Xs5))))))) => (P @ Xs))))))).
% 2.48/1.45 thf(fact_132_lset__induct_H, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => ((! [Xs5:(coinductive_llist @ A)]: ((P @ (((coinductive_LCons @ A) @ X) @ Xs5)))) => ((! [X7:A,Xs5:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs5)) => ((P @ Xs5) => (P @ (((coinductive_LCons @ A) @ X7) @ Xs5)))))) => (P @ Xs))))))).
% 2.48/1.45 thf(fact_133_llist_Oset__cases, axiom, (! [A:$tType,E2:A,A3:(coinductive_llist @ A)]: (((((member @ A) @ E2) @ ((coinductive_lset @ A) @ A3)) => ((! [Z22:(coinductive_llist @ A)]: ((A3 != (((coinductive_LCons @ A) @ E2) @ Z22)))) => (~ ((! [Z1:A,Z22:(coinductive_llist @ A)]: (((A3 = (((coinductive_LCons @ A) @ Z1) @ Z22)) => (~ ((((member @ A) @ E2) @ ((coinductive_lset @ A) @ Z22)))))))))))))).
% 2.48/1.45 thf(fact_134_llist_Oset__induct, axiom, (! [A:$tType,X:A,A3:(coinductive_llist @ A),P:(A > ((coinductive_llist @ A) > $o))]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ A3)) => ((! [Z1:A,Z22:(coinductive_llist @ A)]: (((P @ Z1) @ (((coinductive_LCons @ A) @ Z1) @ Z22)))) => ((! [Z1:A,Z22:(coinductive_llist @ A),Xa2:A]: (((((member @ A) @ Xa2) @ ((coinductive_lset @ A) @ Z22)) => (((P @ Xa2) @ Z22) => ((P @ Xa2) @ (((coinductive_LCons @ A) @ Z1) @ Z22)))))) => ((P @ X) @ A3))))))).
% 2.48/1.45 thf(fact_135_llist__all2__reflI, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:(A > (A > $o))]: (((! [X4:A]: (((((member @ A) @ X4) @ ((coinductive_lset @ A) @ Xs)) => ((P @ X4) @ X4)))) => (((((coindu1486289336t_all2 @ A) @ A) @ P) @ Xs) @ Xs))))).
% 2.48/1.45 thf(fact_136_llist__all2__lsetD1, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B),X:A]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => (? [X4:B]: (((((member @ B) @ X4) @ ((coinductive_lset @ B) @ Ys)) & ((P @ X) @ X4))))))))).
% 2.48/1.45 thf(fact_137_llist__all2__lsetD2, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B),Y4:B]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => ((((member @ B) @ Y4) @ ((coinductive_lset @ B) @ Ys)) => (? [X4:A]: (((((member @ A) @ X4) @ ((coinductive_lset @ A) @ Xs)) & ((P @ X4) @ Y4))))))))).
% 2.48/1.45 thf(fact_138_llist_Orel__cong, axiom, (! [A:$tType,B:$tType,X:(coinductive_llist @ A),Ya:(coinductive_llist @ A),Y4:(coinductive_llist @ B),Xa:(coinductive_llist @ B),R2:(A > (B > $o)),Ra:(A > (B > $o))]: (((X = Ya) => ((Y4 = Xa) => ((! [Z3:A,Yb:B]: (((((member @ A) @ Z3) @ ((coinductive_lset @ A) @ Ya)) => ((((member @ B) @ Yb) @ ((coinductive_lset @ B) @ Xa)) => (((R2 @ Z3) @ Yb) = ((Ra @ Z3) @ Yb)))))) => ((((((coindu1486289336t_all2 @ A) @ B) @ R2) @ X) @ Y4) = (((((coindu1486289336t_all2 @ A) @ B) @ Ra) @ Ya) @ Xa)))))))).
% 2.48/1.45 thf(fact_139_llist_Orel__mono__strong, axiom, (! [A:$tType,B:$tType,R2:(A > (B > $o)),X:(coinductive_llist @ A),Y4:(coinductive_llist @ B),Ra:(A > (B > $o))]: (((((((coindu1486289336t_all2 @ A) @ B) @ R2) @ X) @ Y4) => ((! [Z3:A,Yb:B]: (((((member @ A) @ Z3) @ ((coinductive_lset @ A) @ X)) => ((((member @ B) @ Yb) @ ((coinductive_lset @ B) @ Y4)) => (((R2 @ Z3) @ Yb) => ((Ra @ Z3) @ Yb)))))) => (((((coindu1486289336t_all2 @ A) @ B) @ Ra) @ X) @ Y4)))))).
% 2.48/1.45 thf(fact_140_llist_Orel__refl__strong, axiom, (! [A:$tType,X:(coinductive_llist @ A),Ra:(A > (A > $o))]: (((! [Z3:A]: (((((member @ A) @ Z3) @ ((coinductive_lset @ A) @ X)) => ((Ra @ Z3) @ Z3)))) => (((((coindu1486289336t_all2 @ A) @ A) @ Ra) @ X) @ X))))).
% 2.48/1.45 thf(fact_141_lfilter__cong, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A),P:(A > $o),Q:(A > $o)]: (((Xs = Ys) => ((! [X4:A]: (((((member @ A) @ X4) @ ((coinductive_lset @ A) @ Ys)) => ((P @ X4) = (Q @ X4))))) => ((((coinductive_lfilter @ A) @ P) @ Xs) = (((coinductive_lfilter @ A) @ Q) @ Ys))))))).
% 2.48/1.45 thf(fact_142_lfilter__id__conv, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: ((((((coinductive_lfilter @ A) @ P) @ Xs) = Xs) = (! [X3:A]: (((((member @ A) @ X3) @ ((coinductive_lset @ A) @ Xs)) => (P @ X3)))))))).
% 2.48/1.45 thf(fact_143_lstrict__prefix__def, axiom, (! [A:$tType]: (((coindu1478340336prefix @ A) = (^ [Xs3:(coinductive_llist @ A),Ys3:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs3) @ Ys3) & (Xs3 != Ys3)))))))).
% 2.48/1.45 thf(fact_144_lstrict__prefix__lfinite1, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Xs) @ Ys) => ((coinductive_lfinite @ A) @ Xs))))).
% 2.48/1.45 thf(fact_145_in__lset__lappend__iff, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys))) = ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) | (((coinductive_lfinite @ A) @ Xs) & (((member @ A) @ X) @ ((coinductive_lset @ A) @ Ys)))))))).
% 2.48/1.45 thf(fact_146_split__llist, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => (? [Ys6:(coinductive_llist @ A),Zs4:(coinductive_llist @ A)]: (((Xs = (((coinductive_lappend @ A) @ Ys6) @ (((coinductive_LCons @ A) @ X) @ Zs4))) & ((coinductive_lfinite @ A) @ Ys6)))))))).
% 2.48/1.45 thf(fact_147_split__llist__first, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: (((((member @ A) @ X) @ ((coinductive_lset @ A) @ Xs)) => (? [Ys6:(coinductive_llist @ A),Zs4:(coinductive_llist @ A)]: (((Xs = (((coinductive_lappend @ A) @ Ys6) @ (((coinductive_LCons @ A) @ X) @ Zs4))) & (((coinductive_lfinite @ A) @ Ys6) & (~ ((((member @ A) @ X) @ ((coinductive_lset @ A) @ Ys6)))))))))))).
% 2.48/1.45 thf(fact_148_reflp__mono, axiom, (! [A:$tType,R2:(A > (A > $o)),Q:(A > (A > $o))]: ((((reflp @ A) @ R2) => ((! [X4:A,Y3:A]: ((((R2 @ X4) @ Y3) => ((Q @ X4) @ Y3)))) => ((reflp @ A) @ Q)))))).
% 2.48/1.45 thf(fact_149_lset__lappend__lfinite, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_lset @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((sup_sup @ (set @ A)) @ ((coinductive_lset @ A) @ Xs)) @ ((coinductive_lset @ A) @ Ys))))))).
% 2.48/1.45 thf(fact_150_The__case__prod, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o))]: ((((the @ ((product_prod @ A) @ B)) @ ((((product_case_prod @ A) @ B) @ $o) @ P)) = ((the @ ((product_prod @ A) @ B)) @ (^ [Xy:((product_prod @ A) @ B)]: (((P @ (((product_fst @ A) @ B) @ Xy)) @ (((product_snd @ A) @ B) @ Xy))))))))).
% 2.48/1.45 thf(fact_151_llimit__induct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > $o),Xs:(coinductive_llist @ A)]: (((P @ (coinductive_LNil @ A)) => ((! [X4:A,Xs5:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs5) => ((P @ Xs5) => (P @ (((coinductive_LCons @ A) @ X4) @ Xs5)))))) => (((! [Ys5:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys5) @ Xs) => (P @ Ys5)))) => (P @ Xs)) => (P @ Xs))))))).
% 2.48/1.45 thf(fact_152_prod_Oswap__def, axiom, (! [B:$tType,A:$tType]: ((((product_swap @ A) @ B) = (^ [P4:((product_prod @ A) @ B)]: (((((product_Pair @ B) @ A) @ (((product_snd @ A) @ B) @ P4)) @ (((product_fst @ A) @ B) @ P4)))))))).
% 2.48/1.45 thf(fact_153_old_Oprod_Oinject, axiom, (! [A:$tType,B:$tType,A3:A,B3:B,A7:A,B5:B]: (((((((product_Pair @ A) @ B) @ A3) @ B3) = ((((product_Pair @ A) @ B) @ A7) @ B5)) = ((A3 = A7) & (B3 = B5)))))).
% 2.48/1.45 thf(fact_154_prod_Oinject, axiom, (! [A:$tType,B:$tType,X12:A,X23:B,Y1:A,Y23:B]: (((((((product_Pair @ A) @ B) @ X12) @ X23) = ((((product_Pair @ A) @ B) @ Y1) @ Y23)) = ((X12 = Y1) & (X23 = Y23)))))).
% 2.48/1.45 thf(fact_155_mem__case__prodI2, axiom, (! [C:$tType,B:$tType,A:$tType,P3:((product_prod @ A) @ B),Z2:C,C3:(A > (B > (set @ C)))]: (((! [A4:A,B4:B]: (((P3 = ((((product_Pair @ A) @ B) @ A4) @ B4)) => (((member @ C) @ Z2) @ ((C3 @ A4) @ B4))))) => (((member @ C) @ Z2) @ (((((product_case_prod @ A) @ B) @ (set @ C)) @ C3) @ P3)))))).
% 2.48/1.45 thf(fact_156_mem__case__prodI, axiom, (! [A:$tType,B:$tType,C:$tType,Z2:A,C3:(B > (C > (set @ A))),A3:B,B3:C]: (((((member @ A) @ Z2) @ ((C3 @ A3) @ B3)) => (((member @ A) @ Z2) @ (((((product_case_prod @ B) @ C) @ (set @ A)) @ C3) @ ((((product_Pair @ B) @ C) @ A3) @ B3))))))).
% 2.48/1.45 thf(fact_157_lprefix__code_I1_J, axiom, (! [A:$tType,Ys:(coinductive_llist @ A)]: ((((coinductive_lprefix @ A) @ (coinductive_LNil @ A)) @ Ys)))).
% 2.48/1.45 thf(fact_158_lfinite__code_I1_J, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) @ (coinductive_LNil @ A))))).
% 2.48/1.45 thf(fact_159_llist__all2__LNil2, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ A)]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ (coinductive_LNil @ B)) = (Xs = (coinductive_LNil @ A)))))).
% 2.48/1.45 thf(fact_160_llist__all2__LNil1, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ B)]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ (coinductive_LNil @ A)) @ Xs) = (Xs = (coinductive_LNil @ B)))))).
% 2.48/1.45 thf(fact_161_lappend__LNil2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ Xs) @ (coinductive_LNil @ A)) = Xs)))).
% 2.48/1.45 thf(fact_162_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ Ys) = Ys)))).
% 2.48/1.45 thf(fact_163_apfst__conv, axiom, (! [C:$tType,A:$tType,B:$tType,F:(C > A),X:C,Y4:B]: (((((((product_apfst @ C) @ A) @ B) @ F) @ ((((product_Pair @ C) @ B) @ X) @ Y4)) = ((((product_Pair @ A) @ B) @ (F @ X)) @ Y4))))).
% 2.48/1.45 thf(fact_164_lfilter__LNil, axiom, (! [A:$tType,P:(A > $o)]: (((((coinductive_lfilter @ A) @ P) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.48/1.45 thf(fact_165_swap__simp, axiom, (! [A:$tType,B:$tType,X:B,Y4:A]: (((((product_swap @ B) @ A) @ ((((product_Pair @ B) @ A) @ X) @ Y4)) = ((((product_Pair @ A) @ B) @ Y4) @ X))))).
% 2.48/1.45 thf(fact_166_case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,F:(B > (C > A)),A3:B,B3:C]: (((((((product_case_prod @ B) @ C) @ A) @ F) @ ((((product_Pair @ B) @ C) @ A3) @ B3)) = ((F @ A3) @ B3))))).
% 2.48/1.45 thf(fact_167_lstrict__prefix__code_I1_J, axiom, (! [A:$tType]: ((~ ((((coindu1478340336prefix @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A))))))).
% 2.48/1.45 thf(fact_168_case__prodI2, axiom, (! [B:$tType,A:$tType,P3:((product_prod @ A) @ B),C3:(A > (B > $o))]: (((! [A4:A,B4:B]: (((P3 = ((((product_Pair @ A) @ B) @ A4) @ B4)) => ((C3 @ A4) @ B4)))) => (((((product_case_prod @ A) @ B) @ $o) @ C3) @ P3))))).
% 2.48/1.45 thf(fact_169_case__prodI, axiom, (! [A:$tType,B:$tType,F:(A > (B > $o)),A3:A,B3:B]: ((((F @ A3) @ B3) => (((((product_case_prod @ A) @ B) @ $o) @ F) @ ((((product_Pair @ A) @ B) @ A3) @ B3)))))).
% 2.48/1.45 thf(fact_170_lappendt__LNil, axiom, (! [B:$tType,A:$tType,Tr:((tLList446370796tllist @ A) @ B)]: ((((((tLList98099029ppendt @ A) @ B) @ (coinductive_LNil @ A)) @ Tr) = Tr)))).
% 2.48/1.45 thf(fact_171_case__prodI2_H, axiom, (! [A:$tType,B:$tType,C:$tType,P3:((product_prod @ A) @ B),C3:(A > (B > (C > $o))),X:C]: (((! [A4:A,B4:B]: (((((((product_Pair @ A) @ B) @ A4) @ B4) = P3) => (((C3 @ A4) @ B4) @ X)))) => ((((((product_case_prod @ A) @ B) @ (C > $o)) @ C3) @ P3) @ X))))).
% 2.48/1.45 thf(fact_172_lfitler__K__False, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coinductive_lfilter @ A) @ (^ [Uu:A]: ($false))) @ Xs) = (coinductive_LNil @ A))))).
% 2.48/1.45 thf(fact_173_prod_Ocollapse, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B)]: ((((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod)) = Prod)))).
% 2.48/1.45 thf(fact_174_lprefix__LNil, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ (coinductive_LNil @ A)) = ((coinductive_lnull @ A) @ Xs))))).
% 2.48/1.45 thf(fact_175_diverge__lfilter__LNil, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),P:(A > $o)]: (((! [X4:A]: (((((member @ A) @ X4) @ ((coinductive_lset @ A) @ Xs)) => (~ ((P @ X4)))))) => ((((coinductive_lfilter @ A) @ P) @ Xs) = (coinductive_LNil @ A)))))).
% 2.48/1.45 thf(fact_176_llast__singleton, axiom, (! [A:$tType,X:A]: ((((coinductive_llast @ A) @ (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A))) = X)))).
% 2.48/1.45 thf(fact_177_lstrict__prefix__code_I3_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B)]: ((~ ((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) @ (coinductive_LNil @ B))))))).
% 2.48/1.45 thf(fact_178_lstrict__prefix__code_I2_J, axiom, (! [B:$tType,Y4:B,Ys:(coinductive_llist @ B)]: ((((coindu1478340336prefix @ B) @ (coinductive_LNil @ B)) @ (((coinductive_LCons @ B) @ Y4) @ Ys))))).
% 2.48/1.45 thf(fact_179_The__split__eq, axiom, (! [A:$tType,B:$tType,X:A,Y4:B]: ((((the @ ((product_prod @ A) @ B)) @ ((((product_case_prod @ A) @ B) @ $o) @ (^ [X8:A,Y5:B]: (((X = X8) & (Y4 = Y5)))))) = ((((product_Pair @ A) @ B) @ X) @ Y4))))).
% 2.48/1.45 thf(fact_180_pred__equals__eq2, axiom, (! [B:$tType,A:$tType,R2:(set @ ((product_prod @ A) @ B)),S:(set @ ((product_prod @ A) @ B))]: ((((^ [X3:A,Y:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y)) @ R2))) = (^ [X3:A,Y:B]: ((((member @ ((product_prod @ A) @ B)) @ ((((product_Pair @ A) @ B) @ X3) @ Y)) @ S)))) = (R2 = S))))).
% 2.48/1.45 thf(fact_181_old_Oprod_Ocase, axiom, (! [A:$tType,C:$tType,B:$tType,F:(A > (B > C)),X12:A,X23:B]: (((((((product_case_prod @ A) @ B) @ C) @ F) @ ((((product_Pair @ A) @ B) @ X12) @ X23)) = ((F @ X12) @ X23))))).
% 2.48/1.45 thf(fact_182_LNil__lprefix, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coinductive_lprefix @ A) @ (coinductive_LNil @ A)) @ Xs)))).
% 2.48/1.45 thf(fact_183_llist_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A)]: (((coinductive_LNil @ A) != (((coinductive_LCons @ A) @ X21) @ X22))))).
% 2.48/1.45 thf(fact_184_llist_Oexhaust, axiom, (! [A:$tType,Y4:(coinductive_llist @ A)]: (((Y4 != (coinductive_LNil @ A)) => (~ ((! [X212:A,X222:(coinductive_llist @ A)]: ((Y4 != (((coinductive_LCons @ A) @ X212) @ X222)))))))))).
% 2.48/1.45 thf(fact_185_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((Xs != (coinductive_LNil @ A)) = (? [X3:A,Xs4:(coinductive_llist @ A)]: ((Xs = (((coinductive_LCons @ A) @ X3) @ Xs4)))))))).
% 2.48/1.45 thf(fact_186_split__fst, axiom, (! [B:$tType,A:$tType,R2:(A > $o),P3:((product_prod @ A) @ B)]: (((R2 @ (((product_fst @ A) @ B) @ P3)) = (! [X3:A,Y:B]: (((P3 = ((((product_Pair @ A) @ B) @ X3) @ Y)) => (R2 @ X3)))))))).
% 2.48/1.45 thf(fact_187_split__fst__asm, axiom, (! [B:$tType,A:$tType,R2:(A > $o),P3:((product_prod @ A) @ B)]: (((R2 @ (((product_fst @ A) @ B) @ P3)) = (~ ((? [X3:A,Y:B]: (((P3 = ((((product_Pair @ A) @ B) @ X3) @ Y)) & (~ ((R2 @ X3)))))))))))).
% 2.48/1.45 thf(fact_188_fst__eqD, axiom, (! [B:$tType,A:$tType,X:A,Y4:B,A3:A]: ((((((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ X) @ Y4)) = A3) => (X = A3))))).
% 2.48/1.45 thf(fact_189_fst__conv, axiom, (! [B:$tType,A:$tType,X12:A,X23:B]: (((((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ X12) @ X23)) = X12)))).
% 2.48/1.45 thf(fact_190_llist_Odisc_I1_J, axiom, (! [A:$tType]: (((coinductive_lnull @ A) @ (coinductive_LNil @ A))))).
% 2.48/1.45 thf(fact_191_llist_OdiscI_I1_J, axiom, (! [A:$tType,Llist:(coinductive_llist @ A)]: (((Llist = (coinductive_LNil @ A)) => ((coinductive_lnull @ A) @ Llist))))).
% 2.48/1.45 thf(fact_192_llist_Ocollapse_I1_J, axiom, (! [A:$tType,Llist:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Llist) => (Llist = (coinductive_LNil @ A)))))).
% 2.48/1.45 thf(fact_193_lnull__def, axiom, (! [A:$tType]: (((coinductive_lnull @ A) = (^ [Llist2:(coinductive_llist @ A)]: ((Llist2 = (coinductive_LNil @ A)))))))).
% 2.48/1.45 thf(fact_194_snd__eqD, axiom, (! [B:$tType,A:$tType,X:B,Y4:A,A3:A]: ((((((product_snd @ B) @ A) @ ((((product_Pair @ B) @ A) @ X) @ Y4)) = A3) => (Y4 = A3))))).
% 2.48/1.45 thf(fact_195_snd__conv, axiom, (! [Aa:$tType,A:$tType,X12:Aa,X23:A]: (((((product_snd @ Aa) @ A) @ ((((product_Pair @ Aa) @ A) @ X12) @ X23)) = X23)))).
% 2.48/1.45 thf(fact_196_lfinite__LNil, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) @ (coinductive_LNil @ A))))).
% 2.48/1.45 thf(fact_197_LNil__transfer, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o))]: ((((((coindu1486289336t_all2 @ A) @ B) @ P) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ B))))).
% 2.48/1.45 thf(fact_198_llist__all2__LNil__LNil, axiom, (! [A:$tType,B:$tType,R2:(A > (B > $o))]: ((((((coindu1486289336t_all2 @ A) @ B) @ R2) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ B))))).
% 2.48/1.45 thf(fact_199_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.48/1.45 thf(fact_200_LNil__eq__lappend__iff, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_LNil @ A) = (((coinductive_lappend @ A) @ Xs) @ Ys)) = ((Xs = (coinductive_LNil @ A)) & (Ys = (coinductive_LNil @ A))))))).
% 2.48/1.45 thf(fact_201_lappend__eq__LNil__iff, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((((coinductive_lappend @ A) @ Xs) @ Ys) = (coinductive_LNil @ A)) = ((Xs = (coinductive_LNil @ A)) & (Ys = (coinductive_LNil @ A))))))).
% 2.48/1.45 thf(fact_202_old_Oprod_Oinducts, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),Prod:((product_prod @ A) @ B)]: (((! [A4:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A4) @ B4)))) => (P @ Prod))))).
% 2.48/1.45 thf(fact_203_old_Oprod_Oexhaust, axiom, (! [A:$tType,B:$tType,Y4:((product_prod @ A) @ B)]: ((~ ((! [A4:A,B4:B]: ((Y4 != ((((product_Pair @ A) @ B) @ A4) @ B4))))))))).
% 2.48/1.45 thf(fact_204_prod__induct7, axiom, (! [G3:$tType,F3:$tType,E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))))))]: (((! [A4:A,B4:B,C4:C,D2:D,E3:E,F4:F3,G4:G3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))) @ C4) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F3) @ G3)) @ E3) @ ((((product_Pair @ F3) @ G3) @ F4) @ G4))))))))) => (P @ X))))).
% 2.48/1.45 thf(fact_205_prod__induct6, axiom, (! [F3:$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))))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))))]: (((! [A4:A,B4:B,C4:C,D2:D,E3:E,F4:F3]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))) @ C4) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F3)) @ D2) @ ((((product_Pair @ E) @ F3) @ E3) @ F4)))))))) => (P @ X))))).
% 2.48/1.45 thf(fact_206_prod__induct5, axiom, (! [E:$tType,D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: (((! [A4:A,B4:B,C4:C,D2:D,E3:E]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C4) @ ((((product_Pair @ D) @ E) @ D2) @ E3))))))) => (P @ X))))).
% 2.48/1.45 thf(fact_207_prod__induct4, axiom, (! [D:$tType,C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: (((! [A4:A,B4:B,C4:C,D2:D]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C4) @ D2)))))) => (P @ X))))).
% 2.48/1.45 thf(fact_208_prod__induct3, axiom, (! [C:$tType,B:$tType,A:$tType,P:(((product_prod @ A) @ ((product_prod @ B) @ C)) > $o),X:((product_prod @ A) @ ((product_prod @ B) @ C))]: (((! [A4:A,B4:B,C4:C]: ((P @ ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A4) @ ((((product_Pair @ B) @ C) @ B4) @ C4))))) => (P @ X))))).
% 2.48/1.45 thf(fact_209_prod__cases7, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F3:$tType,G3:$tType,Y4:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))))))]: ((~ ((! [A4:A,B4:B,C4:C,D2:D,E3:E,F4:F3,G4:G3]: ((Y4 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3)))) @ C4) @ ((((product_Pair @ D) @ ((product_prod @ E) @ ((product_prod @ F3) @ G3))) @ D2) @ ((((product_Pair @ E) @ ((product_prod @ F3) @ G3)) @ E3) @ ((((product_Pair @ F3) @ G3) @ F4) @ G4)))))))))))))).
% 2.48/1.45 thf(fact_210_prod__cases6, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,F3:$tType,Y4:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))))]: ((~ ((! [A4:A,B4:B,C4:C,D2:D,E3:E,F4:F3]: ((Y4 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3)))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ ((product_prod @ E) @ F3))) @ C4) @ ((((product_Pair @ D) @ ((product_prod @ E) @ F3)) @ D2) @ ((((product_Pair @ E) @ F3) @ E3) @ F4))))))))))))).
% 2.48/1.45 thf(fact_211_prod__cases5, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,E:$tType,Y4:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))))]: ((~ ((! [A4:A,B4:B,C4:C,D2:D,E3:E]: ((Y4 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E)))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ ((product_prod @ D) @ E))) @ B4) @ ((((product_Pair @ C) @ ((product_prod @ D) @ E)) @ C4) @ ((((product_Pair @ D) @ E) @ D2) @ E3)))))))))))).
% 2.48/1.45 thf(fact_212_prod__cases4, axiom, (! [A:$tType,B:$tType,C:$tType,D:$tType,Y4:((product_prod @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D)))]: ((~ ((! [A4:A,B4:B,C4:C,D2:D]: ((Y4 != ((((product_Pair @ A) @ ((product_prod @ B) @ ((product_prod @ C) @ D))) @ A4) @ ((((product_Pair @ B) @ ((product_prod @ C) @ D)) @ B4) @ ((((product_Pair @ C) @ D) @ C4) @ D2))))))))))).
% 2.48/1.45 thf(fact_213_prod__cases3, axiom, (! [A:$tType,B:$tType,C:$tType,Y4:((product_prod @ A) @ ((product_prod @ B) @ C))]: ((~ ((! [A4:A,B4:B,C4:C]: ((Y4 != ((((product_Pair @ A) @ ((product_prod @ B) @ C)) @ A4) @ ((((product_Pair @ B) @ C) @ B4) @ C4)))))))))).
% 2.48/1.45 thf(fact_214_Pair__inject, axiom, (! [A:$tType,B:$tType,A3:A,B3:B,A7:A,B5:B]: (((((((product_Pair @ A) @ B) @ A3) @ B3) = ((((product_Pair @ A) @ B) @ A7) @ B5)) => (~ (((A3 = A7) => (B3 != B5)))))))).
% 2.48/1.45 thf(fact_215_prod__cases, axiom, (! [B:$tType,A:$tType,P:(((product_prod @ A) @ B) > $o),P3:((product_prod @ A) @ B)]: (((! [A4:A,B4:B]: ((P @ ((((product_Pair @ A) @ B) @ A4) @ B4)))) => (P @ P3))))).
% 2.48/1.45 thf(fact_216_surj__pair, axiom, (! [A:$tType,B:$tType,P3:((product_prod @ A) @ B)]: ((? [X4:A,Y3:B]: ((P3 = ((((product_Pair @ A) @ B) @ X4) @ Y3))))))).
% 2.48/1.45 thf(fact_217_case__prod__Pair__iden, axiom, (! [B:$tType,A:$tType,P3:((product_prod @ A) @ B)]: (((((((product_case_prod @ A) @ B) @ ((product_prod @ A) @ B)) @ ((product_Pair @ A) @ B)) @ P3) = P3)))).
% 2.48/1.45 thf(fact_218_mem__case__prodE, axiom, (! [B:$tType,A:$tType,C:$tType,Z2:A,C3:(B > (C > (set @ A))),P3:((product_prod @ B) @ C)]: (((((member @ A) @ Z2) @ (((((product_case_prod @ B) @ C) @ (set @ A)) @ C3) @ P3)) => (~ ((! [X4:B,Y3:C]: (((P3 = ((((product_Pair @ B) @ C) @ X4) @ Y3)) => (~ ((((member @ A) @ Z2) @ ((C3 @ X4) @ Y3))))))))))))).
% 2.48/1.45 thf(fact_219_Pair__scomp, axiom, (! [A:$tType,B:$tType,C:$tType,X:C,F:(C > (A > B))]: ((((((((product_scomp @ A) @ C) @ A) @ B) @ (((product_Pair @ C) @ A) @ X)) @ F) = (F @ X))))).
% 2.48/1.45 thf(fact_220_cond__case__prod__eta, axiom, (! [C:$tType,B:$tType,A:$tType,F:(A > (B > C)),G:(((product_prod @ A) @ B) > C)]: (((! [X4:A,Y3:B]: ((((F @ X4) @ Y3) = (G @ ((((product_Pair @ A) @ B) @ X4) @ Y3))))) => (((((product_case_prod @ A) @ B) @ C) @ F) = G))))).
% 2.48/1.45 thf(fact_221_case__prod__eta, axiom, (! [C:$tType,B:$tType,A:$tType,F:(((product_prod @ A) @ B) > C)]: ((((((product_case_prod @ A) @ B) @ C) @ (^ [X3:A,Y:B]: ((F @ ((((product_Pair @ A) @ B) @ X3) @ Y))))) = F)))).
% 2.48/1.45 thf(fact_222_case__prodE2, axiom, (! [B:$tType,A:$tType,C:$tType,Q:(A > $o),P:(B > (C > A)),Z2:((product_prod @ B) @ C)]: (((Q @ (((((product_case_prod @ B) @ C) @ A) @ P) @ Z2)) => (~ ((! [X4:B,Y3:C]: (((Z2 = ((((product_Pair @ B) @ C) @ X4) @ Y3)) => (~ ((Q @ ((P @ X4) @ Y3))))))))))))).
% 2.48/1.45 thf(fact_223_scomp__Pair, axiom, (! [C:$tType,B:$tType,A:$tType,X:(A > ((product_prod @ B) @ C))]: ((((((((product_scomp @ A) @ B) @ C) @ ((product_prod @ B) @ C)) @ X) @ ((product_Pair @ B) @ C)) = X)))).
% 2.48/1.45 thf(fact_224_case__prodE, axiom, (! [A:$tType,B:$tType,C3:(A > (B > $o)),P3:((product_prod @ A) @ B)]: (((((((product_case_prod @ A) @ B) @ $o) @ C3) @ P3) => (~ ((! [X4:A,Y3:B]: (((P3 = ((((product_Pair @ A) @ B) @ X4) @ Y3)) => (~ (((C3 @ X4) @ Y3)))))))))))).
% 2.48/1.45 thf(fact_225_case__prodD, axiom, (! [A:$tType,B:$tType,F:(A > (B > $o)),A3:A,B3:B]: (((((((product_case_prod @ A) @ B) @ $o) @ F) @ ((((product_Pair @ A) @ B) @ A3) @ B3)) => ((F @ A3) @ B3))))).
% 2.48/1.45 thf(fact_226_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (coinductive_LNil @ A)) = (Xs = (coinductive_LNil @ A)))))).
% 2.48/1.45 thf(fact_227_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coindu328551480prefix @ A) @ (coinductive_LNil @ A)) @ Xs)))).
% 2.48/1.45 thf(fact_228_case__prodE_H, axiom, (! [B:$tType,A:$tType,C:$tType,C3:(A > (B > (C > $o))),P3:((product_prod @ A) @ B),Z2:C]: ((((((((product_case_prod @ A) @ B) @ (C > $o)) @ C3) @ P3) @ Z2) => (~ ((! [X4:A,Y3:B]: (((P3 = ((((product_Pair @ A) @ B) @ X4) @ Y3)) => (~ ((((C3 @ X4) @ Y3) @ Z2)))))))))))).
% 2.48/1.45 thf(fact_229_case__prodD_H, axiom, (! [B:$tType,A:$tType,C:$tType,R2:(A > (B > (C > $o))),A3:A,B3:B,C3:C]: ((((((((product_case_prod @ A) @ B) @ (C > $o)) @ R2) @ ((((product_Pair @ A) @ B) @ A3) @ B3)) @ C3) => (((R2 @ A3) @ B3) @ C3))))).
% 2.48/1.45 thf(fact_230_lprefix__code_I2_J, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: ((~ ((((coinductive_lprefix @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ (coinductive_LNil @ A))))))).
% 2.48/1.45 thf(fact_231_lprefix_Ocases, axiom, (! [A:$tType,A1:(coinductive_llist @ A),A22:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ A1) @ A22) => (((A1 = (coinductive_LNil @ A)) => (! [Xs5:(coinductive_llist @ A)]: ((A22 != Xs5)))) => (~ ((! [Xs5:(coinductive_llist @ A),Ys6:(coinductive_llist @ A),X4:A]: (((A1 = (((coinductive_LCons @ A) @ X4) @ Xs5)) => ((A22 = (((coinductive_LCons @ A) @ X4) @ Ys6)) => (~ ((((coinductive_lprefix @ A) @ Xs5) @ Ys6)))))))))))))).
% 2.48/1.45 thf(fact_232_lprefix_Osimps, axiom, (! [A:$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),X3:A]: (((A12 = (((coinductive_LCons @ A) @ X3) @ Xs3)) & ((A23 = (((coinductive_LCons @ A) @ X3) @ Ys3)) & (((coinductive_lprefix @ A) @ Xs3) @ Ys3)))))))))))).
% 2.48/1.45 thf(fact_233_lprefix_Ocoinduct, axiom, (! [A:$tType,X9:((coinductive_llist @ A) > ((coinductive_llist @ A) > $o)),X:(coinductive_llist @ A),Xa:(coinductive_llist @ A)]: ((((X9 @ X) @ Xa) => ((! [X4:(coinductive_llist @ A),Xa2:(coinductive_llist @ A)]: ((((X9 @ X4) @ Xa2) => ((? [Xs7:(coinductive_llist @ A)]: (((X4 = (coinductive_LNil @ A)) & (Xa2 = Xs7)))) | (? [Xs7:(coinductive_llist @ A),Ys5:(coinductive_llist @ A),Xb:A]: (((X4 = (((coinductive_LCons @ A) @ Xb) @ Xs7)) & ((Xa2 = (((coinductive_LCons @ A) @ Xb) @ Ys5)) & (((X9 @ Xs7) @ Ys5) | (((coinductive_lprefix @ A) @ Xs7) @ Ys5)))))))))) => (((coinductive_lprefix @ A) @ X) @ Xa)))))).
% 2.48/1.45 thf(fact_234_lprefix__LCons__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y4:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lprefix @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y4) @ Ys)) = ((Xs = (coinductive_LNil @ A)) | (? [Xs4:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ Y4) @ Xs4)) & (((coinductive_lprefix @ A) @ Xs4) @ Ys))))))))).
% 2.48/1.45 thf(fact_235_conjI__realizer, axiom, (! [A:$tType,B:$tType,P:(A > $o),P3:A,Q:(B > $o),Q2:B]: (((P @ P3) => ((Q @ Q2) => ((P @ (((product_fst @ A) @ B) @ ((((product_Pair @ A) @ B) @ P3) @ Q2))) & (Q @ (((product_snd @ A) @ B) @ ((((product_Pair @ A) @ B) @ P3) @ Q2))))))))).
% 2.48/1.45 thf(fact_236_exI__realizer, axiom, (! [B:$tType,A:$tType,P:(A > (B > $o)),Y4:A,X:B]: ((((P @ Y4) @ X) => ((P @ (((product_snd @ B) @ A) @ ((((product_Pair @ B) @ A) @ X) @ Y4))) @ (((product_fst @ B) @ A) @ ((((product_Pair @ B) @ A) @ X) @ Y4))))))).
% 2.48/1.45 thf(fact_237_prod_Oexhaust__sel, axiom, (! [B:$tType,A:$tType,Prod:((product_prod @ A) @ B)]: ((Prod = ((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod)))))).
% 2.48/1.45 thf(fact_238_surjective__pairing, axiom, (! [B:$tType,A:$tType,T3:((product_prod @ A) @ B)]: ((T3 = ((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ T3)) @ (((product_snd @ A) @ B) @ T3)))))).
% 2.48/1.45 thf(fact_239_lfinite_Oinducts, axiom, (! [A:$tType,X:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: ((((coinductive_lfinite @ A) @ X) => ((P @ (coinductive_LNil @ A)) => ((! [Xs5:(coinductive_llist @ A),X4:A]: ((((coinductive_lfinite @ A) @ Xs5) => ((P @ Xs5) => (P @ (((coinductive_LCons @ A) @ X4) @ Xs5)))))) => (P @ X))))))).
% 2.48/1.45 thf(fact_240_lfinite_Osimps, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) = (^ [A2:(coinductive_llist @ A)]: (((A2 = (coinductive_LNil @ A)) | (? [Xs3:(coinductive_llist @ A),X3:A]: (((A2 = (((coinductive_LCons @ A) @ X3) @ Xs3)) & ((coinductive_lfinite @ A) @ Xs3))))))))))).
% 2.48/1.45 thf(fact_241_lfinite_Ocases, axiom, (! [A:$tType,A3:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ A3) => ((A3 != (coinductive_LNil @ A)) => (~ ((! [Xs5:(coinductive_llist @ A)]: (((? [X4:A]: ((A3 = (((coinductive_LCons @ A) @ X4) @ Xs5)))) => (~ (((coinductive_lfinite @ A) @ Xs5))))))))))))).
% 2.48/1.45 thf(fact_242_llist__all2__LNil__LCons, axiom, (! [A:$tType,B:$tType,R2:(A > (B > $o)),Y21:B,Y22:(coinductive_llist @ B)]: ((~ ((((((coindu1486289336t_all2 @ A) @ B) @ R2) @ (coinductive_LNil @ A)) @ (((coinductive_LCons @ B) @ Y21) @ Y22))))))).
% 2.48/1.45 thf(fact_243_llist__all2__LCons__LNil, axiom, (! [A:$tType,B:$tType,R2:(A > (B > $o)),Y21:A,Y22:(coinductive_llist @ A)]: ((~ ((((((coindu1486289336t_all2 @ A) @ B) @ R2) @ (((coinductive_LCons @ A) @ Y21) @ Y22)) @ (coinductive_LNil @ B))))))).
% 2.48/1.45 thf(fact_244_llist__all2__cases, axiom, (! [A:$tType,B:$tType,P:(A > (B > $o)),Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ B)]: (((((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs) @ Ys) => (((Xs = (coinductive_LNil @ A)) => (Ys != (coinductive_LNil @ B))) => (~ ((! [X4:A,Xs6:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ X4) @ Xs6)) => (! [Y3:B,Ys7:(coinductive_llist @ B)]: (((Ys = (((coinductive_LCons @ B) @ Y3) @ Ys7)) => (((P @ X4) @ Y3) => (~ ((((((coindu1486289336t_all2 @ A) @ B) @ P) @ Xs6) @ Ys7))))))))))))))))).
% 2.48/1.45 thf(fact_245_llist_Orel__cases, axiom, (! [A:$tType,B:$tType,R2:(A > (B > $o)),A3:(coinductive_llist @ A),B3:(coinductive_llist @ B)]: (((((((coindu1486289336t_all2 @ A) @ B) @ R2) @ A3) @ B3) => (((A3 = (coinductive_LNil @ A)) => (B3 != (coinductive_LNil @ B))) => (~ ((! [X13:A,X24:(coinductive_llist @ A)]: (((A3 = (((coinductive_LCons @ A) @ X13) @ X24)) => (! [Y12:B,Y24:(coinductive_llist @ B)]: (((B3 = (((coinductive_LCons @ B) @ Y12) @ Y24)) => (((R2 @ X13) @ Y12) => (~ ((((((coindu1486289336t_all2 @ A) @ B) @ R2) @ X24) @ Y24))))))))))))))))).
% 2.48/1.45 thf(fact_246_lappend__snocL1__conv__LCons2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y4:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y4) @ (coinductive_LNil @ A)))) @ Ys) = (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y4) @ Ys)))))).
% 2.48/1.45 thf(fact_247_lappend_Octr_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lnull @ A) @ Xs) => (((coinductive_lnull @ A) @ Ys) => ((((coinductive_lappend @ A) @ Xs) @ Ys) = (coinductive_LNil @ A))))))).
% 2.48/1.45 thf(fact_248_internal__case__prod__conv, axiom, (! [B:$tType,A:$tType,C:$tType,C3:(B > (C > A)),A3:B,B3:C]: (((((((produc2004651681e_prod @ B) @ C) @ A) @ C3) @ ((((product_Pair @ B) @ C) @ A3) @ B3)) = ((C3 @ A3) @ B3))))).
% 2.48/1.45 thf(fact_249_lfilter__empty__conv, axiom, (! [A:$tType,P:(A > $o),Xs:(coinductive_llist @ A)]: ((((((coinductive_lfilter @ A) @ P) @ Xs) = (coinductive_LNil @ A)) = (! [X3:A]: (((((member @ A) @ X3) @ ((coinductive_lset @ A) @ Xs)) => (~ ((P @ X3)))))))))).
% 2.48/1.45 thf(fact_250_llast__LNil, axiom, (! [A:$tType]: ((((coinductive_llast @ A) @ (coinductive_LNil @ A)) = (undefined @ A))))).
% 2.48/1.45 thf(fact_251_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y4:A,Ys:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y4) @ Ys)) = ((Xs = (coinductive_LNil @ A)) | (? [Xs4:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ Y4) @ Xs4)) & (((coindu328551480prefix @ A) @ Xs4) @ Ys))))))))).
% 2.48/1.45 thf(fact_252_prod_Osplit__sel__asm, axiom, (! [C:$tType,B:$tType,A:$tType,P:(C > $o),F:(A > (B > C)),Prod:((product_prod @ A) @ B)]: (((P @ (((((product_case_prod @ A) @ B) @ C) @ F) @ Prod)) = (~ (((Prod = ((((product_Pair @ A) @ B) @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod))) & (~ ((P @ ((F @ (((product_fst @ A) @ B) @ Prod)) @ (((product_snd @ A) @ B) @ Prod)))))))))))).
% 2.48/1.45 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.48/1.45 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y4:A]: ((((((if @ A) @ $false) @ X) @ Y4) = Y4)))).
% 2.48/1.45 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y4:A]: ((((((if @ A) @ $true) @ X) @ Y4) = X)))).
% 2.48/1.45 thf(conj_0, hypothesis, ((((((product_case_prod @ (coinductive_llist @ a)) @ c) @ (((product_prod @ (coinductive_llist @ b)) @ d) > $o)) @ (^ [Xs3:(coinductive_llist @ a),B2:c]: (((((product_case_prod @ (coinductive_llist @ b)) @ d) @ $o) @ (^ [Ys3:(coinductive_llist @ b),B6:d]: (((((((coindu1486289336t_all2 @ a) @ b) @ pa) @ Xs3) @ Ys3) & (((coinductive_lfinite @ a) @ Xs3) => ((qa @ B2) @ B6))))))))) @ xsa) @ ysa)).
% 2.48/1.45 thf(conj_1, hypothesis, (((coinductive_lfinite @ a) @ (((product_fst @ (coinductive_llist @ a)) @ c) @ xsa)) => (((coinductive_lfinite @ b) @ (((product_fst @ (coinductive_llist @ b)) @ d) @ ysa)) => (((qa @ (((((product_case_prod @ (coinductive_llist @ a)) @ c) @ c) @ (^ [Xs3:(coinductive_llist @ a),B2:c]: (((((if @ c) @ ((coinductive_lfinite @ a) @ Xs3)) @ B2) @ (undefined @ c))))) @ xsa)) @ (((((product_case_prod @ (coinductive_llist @ b)) @ d) @ d) @ (^ [Xs3:(coinductive_llist @ b),B2:d]: (((((if @ d) @ ((coinductive_lfinite @ b) @ Xs3)) @ B2) @ (undefined @ d))))) @ ysa)) => ((((((product_case_prod @ (coinductive_llist @ a)) @ e) @ (((product_prod @ (coinductive_llist @ b)) @ f) > $o)) @ (^ [Xs3:(coinductive_llist @ a),B2:e]: (((((product_case_prod @ (coinductive_llist @ b)) @ f) @ $o) @ (^ [Ys3:(coinductive_llist @ b),B6:f]: (((((((coindu1486289336t_all2 @ a) @ b) @ pa) @ Xs3) @ Ys3) & (((coinductive_lfinite @ a) @ Xs3) => ((ra @ B2) @ B6))))))))) @ (xs_a @ (((((product_case_prod @ (coinductive_llist @ a)) @ c) @ c) @ (^ [Xs3:(coinductive_llist @ a),B2:c]: (((((if @ c) @ ((coinductive_lfinite @ a) @ Xs3)) @ B2) @ (undefined @ c))))) @ xsa))) @ (ys_a @ (((((product_case_prod @ (coinductive_llist @ b)) @ d) @ d) @ (^ [Xs3:(coinductive_llist @ b),B2:d]: (((((if @ d) @ ((coinductive_lfinite @ b) @ Xs3)) @ B2) @ (undefined @ d))))) @ ysa))))))).
% 2.48/1.45 thf(conj_2, conjecture, ((((((product_case_prod @ (coinductive_llist @ a)) @ e) @ (((product_prod @ (coinductive_llist @ b)) @ f) > $o)) @ (^ [Xs3:(coinductive_llist @ a),B2:e]: (((((product_case_prod @ (coinductive_llist @ b)) @ f) @ $o) @ (^ [Ys3:(coinductive_llist @ b),B6:f]: (((((((coindu1486289336t_all2 @ a) @ b) @ pa) @ Xs3) @ Ys3) & (((coinductive_lfinite @ a) @ Xs3) => ((ra @ B2) @ B6))))))))) @ ((((((product_case_prod @ (coinductive_llist @ a)) @ c) @ ((c > ((product_prod @ (coinductive_llist @ a)) @ e)) > ((product_prod @ (coinductive_llist @ a)) @ e))) @ (^ [Xs3:(coinductive_llist @ a),B2:c,F2:(c > ((product_prod @ (coinductive_llist @ a)) @ e))]: ((((((product_apfst @ (coinductive_llist @ a)) @ (coinductive_llist @ a)) @ e) @ ((coinductive_lappend @ a) @ Xs3)) @ (F2 @ B2))))) @ xsa) @ xs_a)) @ ((((((product_case_prod @ (coinductive_llist @ b)) @ d) @ ((d > ((product_prod @ (coinductive_llist @ b)) @ f)) > ((product_prod @ (coinductive_llist @ b)) @ f))) @ (^ [Xs3:(coinductive_llist @ b),B2:d,F2:(d > ((product_prod @ (coinductive_llist @ b)) @ f))]: ((((((product_apfst @ (coinductive_llist @ b)) @ (coinductive_llist @ b)) @ f) @ ((coinductive_lappend @ b) @ Xs3)) @ (F2 @ B2))))) @ ysa) @ ys_a))).
% 2.48/1.45 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.mqKFzRPNcN/DTF2DTF23357.p
% 2.48/1.45 ------------------------
% 2.48/1.47 ---- Cleaned THF ---
% 2.48/1.48 thf(ty_t_TLList__Mirabelle__qhjoikztpd_Otllist,type,
% 2.48/1.48 tLList446370796tllist: $tType > $tType > $tType ).
% 2.48/1.48
% 2.48/1.48 thf(ty_t_Coinductive__List_Ollist,type,
% 2.48/1.48 coinductive_llist: $tType > $tType ).
% 2.48/1.48
% 2.48/1.48 thf(ty_t_Product__Type_Oprod,type,
% 2.48/1.48 product_prod: $tType > $tType > $tType ).
% 2.48/1.48
% 2.48/1.48 thf(ty_t_Set_Oset,type,
% 2.48/1.48 set: $tType > $tType ).
% 2.48/1.48
% 2.48/1.48 thf(ty_t_itself,type,
% 2.48/1.48 itself: $tType > $tType ).
% 2.48/1.48
% 2.48/1.48 thf(ty_tf_f,type,
% 2.48/1.48 f: $tType ).
% 2.48/1.48
% 2.48/1.48 thf(ty_tf_e,type,
% 2.48/1.48 e: $tType ).
% 2.48/1.48
% 2.48/1.48 thf(ty_tf_d,type,
% 2.48/1.48 d: $tType ).
% 2.48/1.48
% 2.48/1.48 thf(ty_tf_c,type,
% 2.48/1.48 c: $tType ).
% 2.48/1.48
% 2.48/1.48 thf(ty_tf_b,type,
% 2.48/1.48 b: $tType ).
% 2.48/1.48
% 2.48/1.48 thf(ty_tf_a,type,
% 2.48/1.48 a: $tType ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 2.48/1.48 coindu328551480prefix:
% 2.48/1.48 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Coinductive__List_Olappend,type,
% 2.48/1.48 coinductive_lappend:
% 2.48/1.48 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Coinductive__List_Olfilter,type,
% 2.48/1.48 coinductive_lfilter:
% 2.48/1.48 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Coinductive__List_Olfinite,type,
% 2.48/1.48 coinductive_lfinite:
% 2.48/1.48 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Coinductive__List_Ollast,type,
% 2.48/1.48 coinductive_llast:
% 2.48/1.48 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 2.48/1.48 coinductive_LCons:
% 2.48/1.48 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 2.48/1.48 coinductive_LNil:
% 2.48/1.48 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Coinductive__List_Ollist_Ollist__all2,type,
% 2.48/1.48 coindu1486289336t_all2:
% 2.48/1.48 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( coinductive_llist @ A ) > ( coinductive_llist @ B ) > $o ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Coinductive__List_Ollist_Olnull,type,
% 2.48/1.48 coinductive_lnull:
% 2.48/1.48 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Coinductive__List_Ollist_Olset,type,
% 2.48/1.48 coinductive_lset:
% 2.48/1.48 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( set @ A ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Coinductive__List_Olprefix,type,
% 2.48/1.48 coinductive_lprefix:
% 2.48/1.48 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 2.48/1.48 coindu1478340336prefix:
% 2.48/1.48 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_HOL_OThe,type,
% 2.48/1.48 the:
% 2.48/1.48 !>[A: $tType] : ( ( A > $o ) > A ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_HOL_Oundefined,type,
% 2.48/1.48 undefined:
% 2.48/1.48 !>[A: $tType] : A ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_If,type,
% 2.48/1.48 if:
% 2.48/1.48 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.48/1.48 sup_sup:
% 2.48/1.48 !>[A: $tType] : ( A > A > A ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Product__Type_OPair,type,
% 2.48/1.48 product_Pair:
% 2.48/1.48 !>[A: $tType,B: $tType] : ( A > B > ( product_prod @ A @ B ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Product__Type_Oapfst,type,
% 2.48/1.48 product_apfst:
% 2.48/1.48 !>[A: $tType,C: $tType,B: $tType] : ( ( A > C ) > ( product_prod @ A @ B ) > ( product_prod @ C @ B ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Product__Type_Ointernal__case__prod,type,
% 2.48/1.48 produc2004651681e_prod:
% 2.48/1.48 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Product__Type_Oprod_Ocase__prod,type,
% 2.48/1.48 product_case_prod:
% 2.48/1.48 !>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( product_prod @ A @ B ) > C ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Product__Type_Oprod_Ofst,type,
% 2.48/1.48 product_fst:
% 2.48/1.48 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > A ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Product__Type_Oprod_Osnd,type,
% 2.48/1.48 product_snd:
% 2.48/1.48 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > B ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Product__Type_Oprod_Oswap,type,
% 2.48/1.48 product_swap:
% 2.48/1.48 !>[A: $tType,B: $tType] : ( ( product_prod @ A @ B ) > ( product_prod @ B @ A ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Product__Type_Oscomp,type,
% 2.48/1.48 product_scomp:
% 2.48/1.48 !>[A: $tType,B: $tType,C: $tType,D: $tType] : ( ( A > ( product_prod @ B @ C ) ) > ( B > C > D ) > A > D ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Pure_Otype,type,
% 2.48/1.48 type:
% 2.48/1.48 !>[A: $tType] : ( itself @ A ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Relation_Oreflp,type,
% 2.48/1.48 reflp:
% 2.48/1.48 !>[A: $tType] : ( ( A > A > $o ) > $o ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_Set_OCollect,type,
% 2.48/1.48 collect:
% 2.48/1.48 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Ocr__tllist,type,
% 2.48/1.48 tLList47617868tllist:
% 2.48/1.48 !>[A: $tType,B: $tType] : ( ( product_prod @ ( coinductive_llist @ A ) @ B ) > ( tLList446370796tllist @ A @ B ) > $o ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Olappendt,type,
% 2.48/1.48 tLList98099029ppendt:
% 2.48/1.48 !>[A: $tType,B: $tType] : ( ( coinductive_llist @ A ) > ( tLList446370796tllist @ A @ B ) > ( tLList446370796tllist @ A @ B ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_TLList__Mirabelle__qhjoikztpd_Otllist__of__llist,type,
% 2.48/1.48 tLList1672613558_llist:
% 2.48/1.48 !>[B: $tType,A: $tType] : ( B > ( coinductive_llist @ A ) > ( tLList446370796tllist @ A @ B ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_c_member,type,
% 2.48/1.48 member:
% 2.48/1.48 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_v_Pa,type,
% 2.48/1.48 pa: a > b > $o ).
% 2.48/1.48
% 2.48/1.48 thf(sy_v_Qa,type,
% 2.48/1.48 qa: c > d > $o ).
% 2.48/1.48
% 2.48/1.48 thf(sy_v_Ra,type,
% 2.48/1.48 ra: e > f > $o ).
% 2.48/1.48
% 2.48/1.48 thf(sy_v_xs_Ha,type,
% 2.48/1.48 xs_a: c > ( product_prod @ ( coinductive_llist @ a ) @ e ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_v_xsa,type,
% 2.48/1.48 xsa: product_prod @ ( coinductive_llist @ a ) @ c ).
% 2.48/1.48
% 2.48/1.48 thf(sy_v_ys_Ha,type,
% 2.48/1.48 ys_a: d > ( product_prod @ ( coinductive_llist @ b ) @ f ) ).
% 2.48/1.48
% 2.48/1.48 thf(sy_v_ysa,type,
% 2.48/1.48 ysa: product_prod @ ( coinductive_llist @ b ) @ d ).
% 2.48/1.48
% 2.48/1.48 thf(fact_0_fst__apfst,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,C: $tType,F: C > A,X: product_prod @ C @ B] :
% 2.48/1.48 ( ( product_fst @ A @ B @ ( product_apfst @ C @ A @ B @ F @ X ) )
% 2.48/1.48 = ( F @ ( product_fst @ C @ B @ X ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_1_apfst__eq__conv,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,C: $tType,F: C > A,X: product_prod @ C @ B,G: C > A] :
% 2.48/1.48 ( ( ( product_apfst @ C @ A @ B @ F @ X )
% 2.48/1.48 = ( product_apfst @ C @ A @ B @ G @ X ) )
% 2.48/1.48 = ( ( F @ ( product_fst @ C @ B @ X ) )
% 2.48/1.48 = ( G @ ( product_fst @ C @ B @ X ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_2_lfinite__lappend,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lfinite @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.48/1.48 = ( ( coinductive_lfinite @ A @ Xs )
% 2.48/1.48 & ( coinductive_lfinite @ A @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_3_split__part,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,P: $o,Q: A > B > $o] :
% 2.48/1.48 ( ( product_case_prod @ A @ B @ $o
% 2.48/1.48 @ ^ [A2: A,B2: B] :
% 2.48/1.48 ( P
% 2.48/1.48 & ( Q @ A2 @ B2 ) ) )
% 2.48/1.48 = ( ^ [Ab: product_prod @ A @ B] :
% 2.48/1.48 ( P
% 2.48/1.48 & ( product_case_prod @ A @ B @ $o @ Q @ Ab ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_4_llist__all2__lappendI,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,Xs2: coinductive_llist @ A,Ys2: coinductive_llist @ B] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 2.48/1.48 => ( ( ( coinductive_lfinite @ A @ Xs )
% 2.48/1.48 => ( ( coinductive_lfinite @ B @ Ys )
% 2.48/1.48 => ( coindu1486289336t_all2 @ A @ B @ P @ Xs2 @ Ys2 ) ) )
% 2.48/1.48 => ( coindu1486289336t_all2 @ A @ B @ P @ ( coinductive_lappend @ A @ Xs @ Xs2 ) @ ( coinductive_lappend @ B @ Ys @ Ys2 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_5_fst__def,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType] :
% 2.48/1.48 ( ( product_fst @ A @ B )
% 2.48/1.48 = ( product_case_prod @ A @ B @ A
% 2.48/1.48 @ ^ [X1: A,X2: B] : X1 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_6_case__prod__app,axiom,
% 2.48/1.48 ! [A: $tType,D: $tType,C: $tType,B: $tType] :
% 2.48/1.48 ( ( product_case_prod @ B @ C @ ( D > A ) )
% 2.48/1.48 = ( ^ [F2: B > C > D > A,X3: product_prod @ B @ C,Y: D] :
% 2.48/1.48 ( product_case_prod @ B @ C @ A
% 2.48/1.48 @ ^ [L: B,R: C] : ( F2 @ L @ R @ Y )
% 2.48/1.48 @ X3 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_7_lappend__inf,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ~ ( coinductive_lfinite @ A @ Xs )
% 2.48/1.48 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.48/1.48 = Xs ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_8_llist__all2__lfiniteD,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 2.48/1.48 => ( ( coinductive_lfinite @ A @ Xs )
% 2.48/1.48 = ( coinductive_lfinite @ B @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_9_llist__all2__conj,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,P: A > B > $o,Q: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ B
% 2.48/1.48 @ ^ [X3: A,Y: B] :
% 2.48/1.48 ( ( P @ X3 @ Y )
% 2.48/1.48 & ( Q @ X3 @ Y ) )
% 2.48/1.48 @ Xs
% 2.48/1.48 @ Ys )
% 2.48/1.48 = ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 2.48/1.48 & ( coindu1486289336t_all2 @ A @ B @ Q @ Xs @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_10_prod_Odisc__eq__case,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 2.48/1.48 ( product_case_prod @ A @ B @ $o
% 2.48/1.48 @ ^ [Uu: A,Uv: B] : $true
% 2.48/1.48 @ Prod ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_11_prod_Ocase__distrib,axiom,
% 2.48/1.48 ! [C: $tType,D: $tType,B: $tType,A: $tType,H: C > D,F: A > B > C,Prod: product_prod @ A @ B] :
% 2.48/1.48 ( ( H @ ( product_case_prod @ A @ B @ C @ F @ Prod ) )
% 2.48/1.48 = ( product_case_prod @ A @ B @ D
% 2.48/1.48 @ ^ [X1: A,X2: B] : ( H @ ( F @ X1 @ X2 ) )
% 2.48/1.48 @ Prod ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_12_llist_Orel__refl,axiom,
% 2.48/1.48 ! [B: $tType,Ra: B > B > $o,X: coinductive_llist @ B] :
% 2.48/1.48 ( ! [X4: B] : ( Ra @ X4 @ X4 )
% 2.48/1.48 => ( coindu1486289336t_all2 @ B @ B @ Ra @ X @ X ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_13_llist_Orel__eq,axiom,
% 2.48/1.48 ! [A: $tType] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ A
% 2.48/1.48 @ ^ [Y2: A,Z: A] : ( Y2 = Z ) )
% 2.48/1.48 = ( ^ [Y2: coinductive_llist @ A,Z: coinductive_llist @ A] : ( Y2 = Z ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_14_llist__all2__mono,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,P2: A > B > $o] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 2.48/1.48 => ( ! [X4: A,Y3: B] :
% 2.48/1.48 ( ( P @ X4 @ Y3 )
% 2.48/1.48 => ( P2 @ X4 @ Y3 ) )
% 2.48/1.48 => ( coindu1486289336t_all2 @ A @ B @ P2 @ Xs @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_15_llist__all2__rsp,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,R2: A > B > $o,S: A > A > $o,T: B > B > $o,X: coinductive_llist @ A,Y4: coinductive_llist @ B,A3: coinductive_llist @ A,B3: coinductive_llist @ B] :
% 2.48/1.48 ( ! [X4: A,Y3: B] :
% 2.48/1.48 ( ( R2 @ X4 @ Y3 )
% 2.48/1.48 => ! [A4: A,B4: B] :
% 2.48/1.48 ( ( R2 @ A4 @ B4 )
% 2.48/1.48 => ( ( S @ X4 @ A4 )
% 2.48/1.48 = ( T @ Y3 @ B4 ) ) ) )
% 2.48/1.48 => ( ( coindu1486289336t_all2 @ A @ B @ R2 @ X @ Y4 )
% 2.48/1.48 => ( ( coindu1486289336t_all2 @ A @ B @ R2 @ A3 @ B3 )
% 2.48/1.48 => ( ( coindu1486289336t_all2 @ A @ A @ S @ X @ A3 )
% 2.48/1.48 = ( coindu1486289336t_all2 @ B @ B @ T @ Y4 @ B3 ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_16_lappend__assoc,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 2.48/1.48 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_17_internal__case__prod__def,axiom,
% 2.48/1.48 ! [C: $tType,B: $tType,A: $tType] :
% 2.48/1.48 ( ( produc2004651681e_prod @ A @ B @ C )
% 2.48/1.48 = ( product_case_prod @ A @ B @ C ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_18_reflp__tllist,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType] :
% 2.48/1.48 ( reflp @ ( product_prod @ ( coinductive_llist @ A ) @ B )
% 2.48/1.48 @ ( product_case_prod @ ( coinductive_llist @ A ) @ B @ ( ( product_prod @ ( coinductive_llist @ A ) @ B ) > $o )
% 2.48/1.48 @ ^ [Xs3: coinductive_llist @ A,A2: B] :
% 2.48/1.48 ( product_case_prod @ ( coinductive_llist @ A ) @ B @ $o
% 2.48/1.48 @ ^ [Ys3: coinductive_llist @ A,B2: B] :
% 2.48/1.48 ( ( Xs3 = Ys3 )
% 2.48/1.48 & ( ( coinductive_lfinite @ A @ Ys3 )
% 2.48/1.48 => ( A2 = B2 ) ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_19_tllist_Oabs__eq__iff,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,X: product_prod @ ( coinductive_llist @ A ) @ B,Y4: product_prod @ ( coinductive_llist @ A ) @ B] :
% 2.48/1.48 ( ( ( product_case_prod @ ( coinductive_llist @ A ) @ B @ ( tLList446370796tllist @ A @ B )
% 2.48/1.48 @ ^ [Xs3: coinductive_llist @ A,A2: B] : ( tLList1672613558_llist @ B @ A @ A2 @ Xs3 )
% 2.48/1.48 @ X )
% 2.48/1.48 = ( product_case_prod @ ( coinductive_llist @ A ) @ B @ ( tLList446370796tllist @ A @ B )
% 2.48/1.48 @ ^ [Xs3: coinductive_llist @ A,A2: B] : ( tLList1672613558_llist @ B @ A @ A2 @ Xs3 )
% 2.48/1.48 @ Y4 ) )
% 2.48/1.48 = ( product_case_prod @ ( coinductive_llist @ A ) @ B @ ( ( product_prod @ ( coinductive_llist @ A ) @ B ) > $o )
% 2.48/1.48 @ ^ [Xs3: coinductive_llist @ A,A2: B] :
% 2.48/1.48 ( product_case_prod @ ( coinductive_llist @ A ) @ B @ $o
% 2.48/1.48 @ ^ [Ys3: coinductive_llist @ A,B2: B] :
% 2.48/1.48 ( ( Xs3 = Ys3 )
% 2.48/1.48 & ( ( coinductive_lfinite @ A @ Ys3 )
% 2.48/1.48 => ( A2 = B2 ) ) ) )
% 2.48/1.48 @ X
% 2.48/1.48 @ Y4 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_20_case__swap,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,C: $tType,F: C > B > A,P3: product_prod @ C @ B] :
% 2.48/1.48 ( ( product_case_prod @ B @ C @ A
% 2.48/1.48 @ ^ [Y: B,X3: C] : ( F @ X3 @ Y )
% 2.48/1.48 @ ( product_swap @ C @ B @ P3 ) )
% 2.48/1.48 = ( product_case_prod @ C @ B @ A @ F @ P3 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_21_llast__linfinite,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ~ ( coinductive_lfinite @ A @ Xs )
% 2.48/1.48 => ( ( coinductive_llast @ A @ Xs )
% 2.48/1.48 = ( undefined @ A ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_22_scomp__apply,axiom,
% 2.48/1.48 ! [A: $tType,D: $tType,C: $tType,B: $tType] :
% 2.48/1.48 ( ( product_scomp @ B @ C @ D @ A )
% 2.48/1.48 = ( ^ [F2: B > ( product_prod @ C @ D ),G2: C > D > A,X3: B] : ( product_case_prod @ C @ D @ A @ G2 @ ( F2 @ X3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_23_lprefix__lappend__same,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ ( coinductive_lappend @ A @ Xs @ Zs ) )
% 2.48/1.48 = ( ( coinductive_lfinite @ A @ Xs )
% 2.48/1.48 => ( coinductive_lprefix @ A @ Ys @ Zs ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_24_lfilter__lappend__lfinite,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lfinite @ A @ Xs )
% 2.48/1.48 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.48/1.48 = ( coinductive_lappend @ A @ ( coinductive_lfilter @ A @ P @ Xs ) @ ( coinductive_lfilter @ A @ P @ Ys ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_25_case__prod__unfold,axiom,
% 2.48/1.48 ! [C: $tType,B: $tType,A: $tType] :
% 2.48/1.48 ( ( product_case_prod @ A @ B @ C )
% 2.48/1.48 = ( ^ [C2: A > B > C,P4: product_prod @ A @ B] : ( C2 @ ( product_fst @ A @ B @ P4 ) @ ( product_snd @ A @ B @ P4 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_26_case__prod__beta_H,axiom,
% 2.48/1.48 ! [C: $tType,B: $tType,A: $tType] :
% 2.48/1.48 ( ( product_case_prod @ A @ B @ C )
% 2.48/1.48 = ( ^ [F2: A > B > C,X3: product_prod @ A @ B] : ( F2 @ ( product_fst @ A @ B @ X3 ) @ ( product_snd @ A @ B @ X3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_27_split__comp__eq,axiom,
% 2.48/1.48 ! [A: $tType,C: $tType,B: $tType,D: $tType,F: A > B > C,G: D > A] :
% 2.48/1.48 ( ( ^ [U: product_prod @ D @ B] : ( F @ ( G @ ( product_fst @ D @ B @ U ) ) @ ( product_snd @ D @ B @ U ) ) )
% 2.48/1.48 = ( product_case_prod @ D @ B @ C
% 2.48/1.48 @ ^ [X3: D] : ( F @ ( G @ X3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_28_lprefix__refl,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A] : ( coinductive_lprefix @ A @ Xs @ Xs ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_29_llist_Oleq__refl,axiom,
% 2.48/1.48 ! [A: $tType,X: coinductive_llist @ A] : ( coinductive_lprefix @ A @ X @ X ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_30_lfilter__idem,axiom,
% 2.48/1.48 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lfilter @ A @ P @ ( coinductive_lfilter @ A @ P @ Xs ) )
% 2.48/1.48 = ( coinductive_lfilter @ A @ P @ Xs ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_31_swap__swap,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,P3: product_prod @ A @ B] :
% 2.48/1.48 ( ( product_swap @ B @ A @ ( product_swap @ A @ B @ P3 ) )
% 2.48/1.48 = P3 ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_32_lfilter__K__True,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lfilter @ A
% 2.48/1.48 @ ^ [Uu: A] : $true
% 2.48/1.48 @ Xs )
% 2.48/1.48 = Xs ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_33_tllist__of__llist__inject,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,B3: B,Xs: coinductive_llist @ A,C3: B,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( ( tLList1672613558_llist @ B @ A @ B3 @ Xs )
% 2.48/1.48 = ( tLList1672613558_llist @ B @ A @ C3 @ Ys ) )
% 2.48/1.48 = ( ( Xs = Ys )
% 2.48/1.48 & ( ( coinductive_lfinite @ A @ Ys )
% 2.48/1.48 => ( B3 = C3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_34_snd__apfst,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,C: $tType,F: C > B,X: product_prod @ C @ A] :
% 2.48/1.48 ( ( product_snd @ B @ A @ ( product_apfst @ C @ B @ A @ F @ X ) )
% 2.48/1.48 = ( product_snd @ C @ A @ X ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_35_snd__swap,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,X: product_prod @ A @ B] :
% 2.48/1.48 ( ( product_snd @ B @ A @ ( product_swap @ A @ B @ X ) )
% 2.48/1.48 = ( product_fst @ A @ B @ X ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_36_fst__swap,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,X: product_prod @ B @ A] :
% 2.48/1.48 ( ( product_fst @ A @ B @ ( product_swap @ B @ A @ X ) )
% 2.48/1.48 = ( product_snd @ B @ A @ X ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_37_scomp__scomp,axiom,
% 2.48/1.48 ! [A: $tType,C: $tType,D: $tType,B: $tType,F3: $tType,E: $tType,F: A > ( product_prod @ E @ F3 ),G: E > F3 > ( product_prod @ C @ D ),H: C > D > B] :
% 2.48/1.48 ( ( product_scomp @ A @ C @ D @ B @ ( product_scomp @ A @ E @ F3 @ ( product_prod @ C @ D ) @ F @ G ) @ H )
% 2.48/1.48 = ( product_scomp @ A @ E @ F3 @ B @ F
% 2.48/1.48 @ ^ [X3: E] : ( product_scomp @ F3 @ C @ D @ B @ ( G @ X3 ) @ H ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_38_lprefix__trans,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 2.48/1.48 => ( ( coinductive_lprefix @ A @ Ys @ Zs )
% 2.48/1.48 => ( coinductive_lprefix @ A @ Xs @ Zs ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_39_llist_Oleq__trans,axiom,
% 2.48/1.48 ! [A: $tType,X: coinductive_llist @ A,Y4: coinductive_llist @ A,Z2: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ X @ Y4 )
% 2.48/1.48 => ( ( coinductive_lprefix @ A @ Y4 @ Z2 )
% 2.48/1.48 => ( coinductive_lprefix @ A @ X @ Z2 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_40_lprefix__antisym,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 2.48/1.48 => ( ( coinductive_lprefix @ A @ Ys @ Xs )
% 2.48/1.48 => ( Xs = Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_41_lprefix__lfilterI,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,P: A > $o] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 2.48/1.48 => ( coinductive_lprefix @ A @ ( coinductive_lfilter @ A @ P @ Xs ) @ ( coinductive_lfilter @ A @ P @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_42_llist_Oleq__antisym,axiom,
% 2.48/1.48 ! [A: $tType,X: coinductive_llist @ A,Y4: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ X @ Y4 )
% 2.48/1.48 => ( ( coinductive_lprefix @ A @ Y4 @ X )
% 2.48/1.48 => ( X = Y4 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_43_lprefix__down__linear,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Zs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ Xs @ Zs )
% 2.48/1.48 => ( ( coinductive_lprefix @ A @ Ys @ Zs )
% 2.48/1.48 => ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 2.48/1.48 | ( coinductive_lprefix @ A @ Ys @ Xs ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_44_lfilter__lfilter,axiom,
% 2.48/1.48 ! [A: $tType,P: A > $o,Q: A > $o,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lfilter @ A @ P @ ( coinductive_lfilter @ A @ Q @ Xs ) )
% 2.48/1.48 = ( coinductive_lfilter @ A
% 2.48/1.48 @ ^ [X3: A] :
% 2.48/1.48 ( ( P @ X3 )
% 2.48/1.48 & ( Q @ X3 ) )
% 2.48/1.48 @ Xs ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_45_mem__Collect__eq,axiom,
% 2.48/1.48 ! [A: $tType,A3: A,P: A > $o] :
% 2.48/1.48 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 2.48/1.48 = ( P @ A3 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_46_Collect__mem__eq,axiom,
% 2.48/1.48 ! [A: $tType,A5: set @ A] :
% 2.48/1.48 ( ( collect @ A
% 2.48/1.48 @ ^ [X3: A] : ( member @ A @ X3 @ A5 ) )
% 2.48/1.48 = A5 ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_47_Collect__cong,axiom,
% 2.48/1.48 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.48/1.48 ( ! [X4: A] :
% 2.48/1.48 ( ( P @ X4 )
% 2.48/1.48 = ( Q @ X4 ) )
% 2.48/1.48 => ( ( collect @ A @ P )
% 2.48/1.48 = ( collect @ A @ Q ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_48_ext,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.48/1.48 ( ! [X4: A] :
% 2.48/1.48 ( ( F @ X4 )
% 2.48/1.48 = ( G @ X4 ) )
% 2.48/1.48 => ( F = G ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_49_llist_Orel__reflp,axiom,
% 2.48/1.48 ! [A: $tType,R2: A > A > $o] :
% 2.48/1.48 ( ( reflp @ A @ R2 )
% 2.48/1.48 => ( reflp @ ( coinductive_llist @ A ) @ ( coindu1486289336t_all2 @ A @ A @ R2 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_50_tllist_Oabs__induct,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,P: ( tLList446370796tllist @ A @ B ) > $o,X: tLList446370796tllist @ A @ B] :
% 2.48/1.48 ( ! [Y3: product_prod @ ( coinductive_llist @ A ) @ B] :
% 2.48/1.48 ( P
% 2.48/1.48 @ ( product_case_prod @ ( coinductive_llist @ A ) @ B @ ( tLList446370796tllist @ A @ B )
% 2.48/1.48 @ ^ [Xs3: coinductive_llist @ A,A2: B] : ( tLList1672613558_llist @ B @ A @ A2 @ Xs3 )
% 2.48/1.48 @ Y3 ) )
% 2.48/1.48 => ( P @ X ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_51_scomp__unfold,axiom,
% 2.48/1.48 ! [D: $tType,C: $tType,B: $tType,A: $tType] :
% 2.48/1.48 ( ( product_scomp @ A @ B @ C @ D )
% 2.48/1.48 = ( ^ [F2: A > ( product_prod @ B @ C ),G2: B > C > D,X3: A] : ( G2 @ ( product_fst @ B @ C @ ( F2 @ X3 ) ) @ ( product_snd @ B @ C @ ( F2 @ X3 ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_52_prod__eqI,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,P3: product_prod @ A @ B,Q2: product_prod @ A @ B] :
% 2.48/1.48 ( ( ( product_fst @ A @ B @ P3 )
% 2.48/1.48 = ( product_fst @ A @ B @ Q2 ) )
% 2.48/1.48 => ( ( ( product_snd @ A @ B @ P3 )
% 2.48/1.48 = ( product_snd @ A @ B @ Q2 ) )
% 2.48/1.48 => ( P3 = Q2 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_53_prod_Oexpand,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B,Prod2: product_prod @ A @ B] :
% 2.48/1.48 ( ( ( ( product_fst @ A @ B @ Prod )
% 2.48/1.48 = ( product_fst @ A @ B @ Prod2 ) )
% 2.48/1.48 & ( ( product_snd @ A @ B @ Prod )
% 2.48/1.48 = ( product_snd @ A @ B @ Prod2 ) ) )
% 2.48/1.48 => ( Prod = Prod2 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_54_prod__eq__iff,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType] :
% 2.48/1.48 ( ( ^ [Y2: product_prod @ A @ B,Z: product_prod @ A @ B] : ( Y2 = Z ) )
% 2.48/1.48 = ( ^ [S2: product_prod @ A @ B,T2: product_prod @ A @ B] :
% 2.48/1.48 ( ( ( product_fst @ A @ B @ S2 )
% 2.48/1.48 = ( product_fst @ A @ B @ T2 ) )
% 2.48/1.48 & ( ( product_snd @ A @ B @ S2 )
% 2.48/1.48 = ( product_snd @ A @ B @ T2 ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_55_lfinite__lfilterI,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 2.48/1.48 ( ( coinductive_lfinite @ A @ Xs )
% 2.48/1.48 => ( coinductive_lfinite @ A @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_56_llist__all2__lfilterI,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,Q1: A > $o,Q22: B > $o] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 2.48/1.48 => ( ! [X4: A,Y3: B] :
% 2.48/1.48 ( ( P @ X4 @ Y3 )
% 2.48/1.48 => ( ( Q1 @ X4 )
% 2.48/1.48 = ( Q22 @ Y3 ) ) )
% 2.48/1.48 => ( coindu1486289336t_all2 @ A @ B @ P @ ( coinductive_lfilter @ A @ Q1 @ Xs ) @ ( coinductive_lfilter @ B @ Q22 @ Ys ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_57_lprefix__lfiniteD,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 2.48/1.48 => ( ( coinductive_lfinite @ A @ Ys )
% 2.48/1.48 => ( coinductive_lfinite @ A @ Xs ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_58_not__lfinite__lprefix__conv__eq,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ~ ( coinductive_lfinite @ A @ Xs )
% 2.48/1.48 => ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 2.48/1.48 = ( Xs = Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_59_lprefix__lappend,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] : ( coinductive_lprefix @ A @ Xs @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_60_lappend__lprefixE,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 2.48/1.48 => ~ ! [Zs2: coinductive_llist @ A] :
% 2.48/1.48 ( Zs
% 2.48/1.48 != ( coinductive_lappend @ A @ Xs @ Zs2 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_61_lprefix__lappendD,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) )
% 2.48/1.48 => ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 2.48/1.48 | ( coinductive_lprefix @ A @ Ys @ Xs ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_62_lprefix__conv__lappend,axiom,
% 2.48/1.48 ! [A: $tType] :
% 2.48/1.48 ( ( coinductive_lprefix @ A )
% 2.48/1.48 = ( ^ [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A] :
% 2.48/1.48 ? [Zs3: coinductive_llist @ A] :
% 2.48/1.48 ( Ys3
% 2.48/1.48 = ( coinductive_lappend @ A @ Xs3 @ Zs3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_63_lprefix__lappend__sameI,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 2.48/1.48 => ( coinductive_lprefix @ A @ ( coinductive_lappend @ A @ Zs @ Xs ) @ ( coinductive_lappend @ A @ Zs @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_64_tllist__of__llist__cong,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,Xs: coinductive_llist @ A,Xs2: coinductive_llist @ A,B3: B,B5: B] :
% 2.48/1.48 ( ( Xs = Xs2 )
% 2.48/1.48 => ( ( ( coinductive_lfinite @ A @ Xs2 )
% 2.48/1.48 => ( B3 = B5 ) )
% 2.48/1.48 => ( ( tLList1672613558_llist @ B @ A @ B3 @ Xs )
% 2.48/1.48 = ( tLList1672613558_llist @ B @ A @ B5 @ Xs2 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_65_snd__def,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType] :
% 2.48/1.48 ( ( product_snd @ A @ B )
% 2.48/1.48 = ( product_case_prod @ A @ B @ B
% 2.48/1.48 @ ^ [X1: A,X2: B] : X2 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_66_scomp__def,axiom,
% 2.48/1.48 ! [D: $tType,C: $tType,B: $tType,A: $tType] :
% 2.48/1.48 ( ( product_scomp @ A @ B @ C @ D )
% 2.48/1.48 = ( ^ [F2: A > ( product_prod @ B @ C ),G2: B > C > D,X3: A] : ( product_case_prod @ B @ C @ D @ G2 @ ( F2 @ X3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_67_case__prod__beta,axiom,
% 2.48/1.48 ! [A: $tType,C: $tType,B: $tType] :
% 2.48/1.48 ( ( product_case_prod @ B @ C @ A )
% 2.48/1.48 = ( ^ [F2: B > C > A,P4: product_prod @ B @ C] : ( F2 @ ( product_fst @ B @ C @ P4 ) @ ( product_snd @ B @ C @ P4 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_68_prod_Ocase__eq__if,axiom,
% 2.48/1.48 ! [C: $tType,B: $tType,A: $tType] :
% 2.48/1.48 ( ( product_case_prod @ A @ B @ C )
% 2.48/1.48 = ( ^ [F2: A > B > C,Prod3: product_prod @ A @ B] : ( F2 @ ( product_fst @ A @ B @ Prod3 ) @ ( product_snd @ A @ B @ Prod3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_69_Product__Type_OCollect__case__prodD,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,X: product_prod @ A @ B,A5: A > B > $o] :
% 2.48/1.48 ( ( member @ ( product_prod @ A @ B ) @ X @ ( collect @ ( product_prod @ A @ B ) @ ( product_case_prod @ A @ B @ $o @ A5 ) ) )
% 2.48/1.48 => ( A5 @ ( product_fst @ A @ B @ X ) @ ( product_snd @ A @ B @ X ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_70_lfilter__eq__lappend__lfiniteD,axiom,
% 2.48/1.48 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.48/1.48 ( ( ( coinductive_lfilter @ A @ P @ Xs )
% 2.48/1.48 = ( coinductive_lappend @ A @ Ys @ Zs ) )
% 2.48/1.48 => ( ( coinductive_lfinite @ A @ Ys )
% 2.48/1.48 => ? [Us: coinductive_llist @ A,Vs: coinductive_llist @ A] :
% 2.48/1.48 ( ( Xs
% 2.48/1.48 = ( coinductive_lappend @ A @ Us @ Vs ) )
% 2.48/1.48 & ( coinductive_lfinite @ A @ Us )
% 2.48/1.48 & ( Ys
% 2.48/1.48 = ( coinductive_lfilter @ A @ P @ Us ) )
% 2.48/1.48 & ( Zs
% 2.48/1.48 = ( coinductive_lfilter @ A @ P @ Vs ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_71_exE__realizer,axiom,
% 2.48/1.48 ! [C: $tType,A: $tType,B: $tType,P: A > B > $o,P3: product_prod @ B @ A,Q: C > $o,F: B > A > C] :
% 2.48/1.48 ( ( P @ ( product_snd @ B @ A @ P3 ) @ ( product_fst @ B @ A @ P3 ) )
% 2.48/1.48 => ( ! [X4: B,Y3: A] :
% 2.48/1.48 ( ( P @ Y3 @ X4 )
% 2.48/1.48 => ( Q @ ( F @ X4 @ Y3 ) ) )
% 2.48/1.48 => ( Q @ ( product_case_prod @ B @ A @ C @ F @ P3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_72_lappendt_Oabs__eq,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,Xa: coinductive_llist @ A,X: product_prod @ ( coinductive_llist @ A ) @ B] :
% 2.48/1.48 ( ( tLList98099029ppendt @ A @ B @ Xa
% 2.48/1.48 @ ( product_case_prod @ ( coinductive_llist @ A ) @ B @ ( tLList446370796tllist @ A @ B )
% 2.48/1.48 @ ^ [Xs3: coinductive_llist @ A,A2: B] : ( tLList1672613558_llist @ B @ A @ A2 @ Xs3 )
% 2.48/1.48 @ X ) )
% 2.48/1.48 = ( product_case_prod @ ( coinductive_llist @ A ) @ B @ ( tLList446370796tllist @ A @ B )
% 2.48/1.48 @ ^ [Xs3: coinductive_llist @ A,A2: B] : ( tLList1672613558_llist @ B @ A @ A2 @ Xs3 )
% 2.48/1.48 @ ( product_apfst @ ( coinductive_llist @ A ) @ ( coinductive_llist @ A ) @ B @ ( coinductive_lappend @ A @ Xa ) @ X ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_73_exE__realizer_H,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,P: A > B > $o,P3: product_prod @ B @ A] :
% 2.48/1.48 ( ( P @ ( product_snd @ B @ A @ P3 ) @ ( product_fst @ B @ A @ P3 ) )
% 2.48/1.48 => ~ ! [X4: B,Y3: A] :
% 2.48/1.48 ~ ( P @ Y3 @ X4 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_74_tllist__of__llist__eq__lappendt__conv,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,A3: B,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: tLList446370796tllist @ A @ B] :
% 2.48/1.48 ( ( ( tLList1672613558_llist @ B @ A @ A3 @ Xs )
% 2.48/1.48 = ( tLList98099029ppendt @ A @ B @ Ys @ Zs ) )
% 2.48/1.48 = ( ? [Xs4: coinductive_llist @ A,A6: B] :
% 2.48/1.48 ( ( Xs
% 2.48/1.48 = ( coinductive_lappend @ A @ Ys @ Xs4 ) )
% 2.48/1.48 & ( Zs
% 2.48/1.48 = ( tLList1672613558_llist @ B @ A @ A6 @ Xs4 ) )
% 2.48/1.48 & ( ( coinductive_lfinite @ A @ Ys )
% 2.48/1.48 => ( A3 = A6 ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_75_Coinductive__List_Olprefix__nitpick__simps,axiom,
% 2.48/1.48 ! [A: $tType] :
% 2.48/1.48 ( ( coinductive_lprefix @ A )
% 2.48/1.48 = ( ^ [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A] :
% 2.48/1.48 ( ( ( coinductive_lfinite @ A @ Xs3 )
% 2.48/1.48 => ( coindu328551480prefix @ A @ Xs3 @ Ys3 ) )
% 2.48/1.48 & ( ~ ( coinductive_lfinite @ A @ Xs3 )
% 2.48/1.48 => ( Xs3 = Ys3 ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_76_cr__tllist__def,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType] :
% 2.48/1.48 ( ( tLList47617868tllist @ A @ B )
% 2.48/1.48 = ( product_case_prod @ ( coinductive_llist @ A ) @ B @ ( ( tLList446370796tllist @ A @ B ) > $o )
% 2.48/1.48 @ ^ [Xs3: coinductive_llist @ A,B2: B] :
% 2.48/1.48 ( ^ [Y2: tLList446370796tllist @ A @ B,Z: tLList446370796tllist @ A @ B] : ( Y2 = Z )
% 2.48/1.48 @ ( tLList1672613558_llist @ B @ A @ B2 @ Xs3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_77_llast__lappend,axiom,
% 2.48/1.48 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( ( coinductive_lnull @ A @ Ys )
% 2.48/1.48 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.48/1.48 = ( coinductive_llast @ A @ Xs ) ) )
% 2.48/1.48 & ( ~ ( coinductive_lnull @ A @ Ys )
% 2.48/1.48 => ( ( ( coinductive_lfinite @ A @ Xs )
% 2.48/1.48 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.48/1.48 = ( coinductive_llast @ A @ Ys ) ) )
% 2.48/1.48 & ( ~ ( coinductive_lfinite @ A @ Xs )
% 2.48/1.48 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.48/1.48 = ( undefined @ A ) ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_78_llast__lappend__LCons,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Y4: A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lfinite @ A @ Xs )
% 2.48/1.48 => ( ( coinductive_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y4 @ Ys ) ) )
% 2.48/1.48 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y4 @ Ys ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_79_DEADID_Orel__reflp,axiom,
% 2.48/1.48 ! [A: $tType] :
% 2.48/1.48 ( reflp @ A
% 2.48/1.48 @ ^ [Y2: A,Z: A] : ( Y2 = Z ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_80_llist_Oinject,axiom,
% 2.48/1.48 ! [A: $tType,X21: A,X22: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 2.48/1.48 ( ( ( coinductive_LCons @ A @ X21 @ X22 )
% 2.48/1.48 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 2.48/1.48 = ( ( X21 = Y21 )
% 2.48/1.48 & ( X22 = Y22 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_81_LCons__lprefix__LCons,axiom,
% 2.48/1.48 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Y4: A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ Y4 @ Ys ) )
% 2.48/1.48 = ( ( X = Y4 )
% 2.48/1.48 & ( coinductive_lprefix @ A @ Xs @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_82_lfinite__LCons,axiom,
% 2.48/1.48 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.48/1.48 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_83_lfinite__code_I2_J,axiom,
% 2.48/1.48 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 2.48/1.48 ( ( coinductive_lfinite @ B @ ( coinductive_LCons @ B @ X @ Xs ) )
% 2.48/1.48 = ( coinductive_lfinite @ B @ Xs ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_84_llist__all2__LCons__LCons,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,R2: A > B > $o,X21: A,X22: coinductive_llist @ A,Y21: B,Y22: coinductive_llist @ B] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ B @ R2 @ ( coinductive_LCons @ A @ X21 @ X22 ) @ ( coinductive_LCons @ B @ Y21 @ Y22 ) )
% 2.48/1.48 = ( ( R2 @ X21 @ Y21 )
% 2.48/1.48 & ( coindu1486289336t_all2 @ A @ B @ R2 @ X22 @ Y22 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_85_lappend__code_I2_J,axiom,
% 2.48/1.48 ! [A: $tType,Xa: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa @ X ) @ Ys )
% 2.48/1.48 = ( coinductive_LCons @ A @ Xa @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_86_lnull__lappend,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.48/1.48 = ( ( coinductive_lnull @ A @ Xs )
% 2.48/1.48 & ( coinductive_lnull @ A @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_87_lappend_Odisc__iff_I2_J,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) )
% 2.48/1.48 = ( ~ ( coinductive_lnull @ A @ Xs )
% 2.48/1.48 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_88_lfilter__LCons,axiom,
% 2.48/1.48 ! [A: $tType,P: A > $o,X: A,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( ( P @ X )
% 2.48/1.48 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.48/1.48 = ( coinductive_LCons @ A @ X @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) )
% 2.48/1.48 & ( ~ ( P @ X )
% 2.48/1.48 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.48/1.48 = ( coinductive_lfilter @ A @ P @ Xs ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_89_llast__LCons2,axiom,
% 2.48/1.48 ! [A: $tType,X: A,Y4: A,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LCons @ A @ Y4 @ Xs ) ) )
% 2.48/1.48 = ( coinductive_llast @ A @ ( coinductive_LCons @ A @ Y4 @ Xs ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_90_lappend_Oexhaust,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( ( coinductive_lnull @ A @ Xs )
% 2.48/1.48 => ~ ( coinductive_lnull @ A @ Ys ) )
% 2.48/1.48 => ( ~ ( coinductive_lnull @ A @ Xs )
% 2.48/1.48 | ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_91_not__lnull__conv,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( ~ ( coinductive_lnull @ A @ Xs ) )
% 2.48/1.48 = ( ? [X3: A,Xs4: coinductive_llist @ A] :
% 2.48/1.48 ( Xs
% 2.48/1.48 = ( coinductive_LCons @ A @ X3 @ Xs4 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_92_lzip_Oexhaust,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 2.48/1.48 ( ~ ( ( coinductive_lnull @ A @ Xs )
% 2.48/1.48 | ( coinductive_lnull @ B @ Ys ) )
% 2.48/1.48 => ~ ( ~ ( coinductive_lnull @ A @ Xs )
% 2.48/1.48 => ( coinductive_lnull @ B @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_93_llist_OdiscI_I2_J,axiom,
% 2.48/1.48 ! [A: $tType,Llist: coinductive_llist @ A,X21: A,X22: coinductive_llist @ A] :
% 2.48/1.48 ( ( Llist
% 2.48/1.48 = ( coinductive_LCons @ A @ X21 @ X22 ) )
% 2.48/1.48 => ~ ( coinductive_lnull @ A @ Llist ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_94_llist_Odisc_I2_J,axiom,
% 2.48/1.48 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 2.48/1.48 ~ ( coinductive_lnull @ A @ ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_95_llast__LCons,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 2.48/1.48 ( ( ( coinductive_lnull @ A @ Xs )
% 2.48/1.48 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.48/1.48 = X ) )
% 2.48/1.48 & ( ~ ( coinductive_lnull @ A @ Xs )
% 2.48/1.48 => ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.48/1.48 = ( coinductive_llast @ A @ Xs ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_96_lprefix__not__lnullD,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 2.48/1.48 => ( ~ ( coinductive_lnull @ A @ Xs )
% 2.48/1.48 => ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_97_lprefix__lnullD,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 2.48/1.48 => ( ( coinductive_lnull @ A @ Ys )
% 2.48/1.48 => ( coinductive_lnull @ A @ Xs ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_98_lprefix__lnull,axiom,
% 2.48/1.48 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lnull @ A @ Ys )
% 2.48/1.48 => ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 2.48/1.48 = ( coinductive_lnull @ A @ Xs ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_99_lnull__lprefix,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lnull @ A @ Xs )
% 2.48/1.48 => ( coinductive_lprefix @ A @ Xs @ Ys ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_100_LCons__lprefix__conv,axiom,
% 2.48/1.48 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ ( coinductive_LCons @ A @ X @ Xs ) @ Ys )
% 2.48/1.48 = ( ? [Ys4: coinductive_llist @ A] :
% 2.48/1.48 ( ( Ys
% 2.48/1.48 = ( coinductive_LCons @ A @ X @ Ys4 ) )
% 2.48/1.48 & ( coinductive_lprefix @ A @ Xs @ Ys4 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_101_Le__LCons,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,X: A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ Xs @ Ys )
% 2.48/1.48 => ( coinductive_lprefix @ A @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LCons @ A @ X @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_102_lnull__imp__lfinite,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lnull @ A @ Xs )
% 2.48/1.48 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_103_llist__all2__lnullD,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 2.48/1.48 => ( ( coinductive_lnull @ A @ Xs )
% 2.48/1.48 = ( coinductive_lnull @ B @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_104_lfinite__LConsI,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 2.48/1.48 ( ( coinductive_lfinite @ A @ Xs )
% 2.48/1.48 => ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_105_llist__all2__LCons2,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Y4: B,Ys: coinductive_llist @ B] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ ( coinductive_LCons @ B @ Y4 @ Ys ) )
% 2.48/1.48 = ( ? [X3: A,Xs4: coinductive_llist @ A] :
% 2.48/1.48 ( ( Xs
% 2.48/1.48 = ( coinductive_LCons @ A @ X3 @ Xs4 ) )
% 2.48/1.48 & ( P @ X3 @ Y4 )
% 2.48/1.48 & ( coindu1486289336t_all2 @ A @ B @ P @ Xs4 @ Ys ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_106_llist__all2__LCons1,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,P: A > B > $o,X: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ B @ P @ ( coinductive_LCons @ A @ X @ Xs ) @ Ys )
% 2.48/1.48 = ( ? [Y: B,Ys4: coinductive_llist @ B] :
% 2.48/1.48 ( ( Ys
% 2.48/1.48 = ( coinductive_LCons @ B @ Y @ Ys4 ) )
% 2.48/1.48 & ( P @ X @ Y )
% 2.48/1.48 & ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys4 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_107_llist_Orel__intros_I2_J,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,R2: A > B > $o,X21: A,Y21: B,X22: coinductive_llist @ A,Y22: coinductive_llist @ B] :
% 2.48/1.48 ( ( R2 @ X21 @ Y21 )
% 2.48/1.48 => ( ( coindu1486289336t_all2 @ A @ B @ R2 @ X22 @ Y22 )
% 2.48/1.48 => ( coindu1486289336t_all2 @ A @ B @ R2 @ ( coinductive_LCons @ A @ X21 @ X22 ) @ ( coinductive_LCons @ B @ Y21 @ Y22 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_108_lappend__lnull2,axiom,
% 2.48/1.48 ! [A: $tType,Ys: coinductive_llist @ A,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lnull @ A @ Ys )
% 2.48/1.48 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.48/1.48 = Xs ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_109_lappend__lnull1,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lnull @ A @ Xs )
% 2.48/1.48 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.48/1.48 = Ys ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_110_lappend_Odisc_I1_J,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lnull @ A @ Xs )
% 2.48/1.48 => ( ( coinductive_lnull @ A @ Ys )
% 2.48/1.48 => ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_111_lappend_Odisc_I2_J,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( ~ ( coinductive_lnull @ A @ Xs )
% 2.48/1.48 | ~ ( coinductive_lnull @ A @ Ys ) )
% 2.48/1.48 => ~ ( coinductive_lnull @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_112_lfilter__LCons__found,axiom,
% 2.48/1.48 ! [A: $tType,P: A > $o,X: A,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( P @ X )
% 2.48/1.48 => ( ( coinductive_lfilter @ A @ P @ ( coinductive_LCons @ A @ X @ Xs ) )
% 2.48/1.48 = ( coinductive_LCons @ A @ X @ ( coinductive_lfilter @ A @ P @ Xs ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_113_lfilter__LCons__seek,axiom,
% 2.48/1.48 ! [A: $tType,P3: A > $o,X: A,L2: coinductive_llist @ A] :
% 2.48/1.48 ( ~ ( P3 @ X )
% 2.48/1.48 => ( ( coinductive_lfilter @ A @ P3 @ ( coinductive_LCons @ A @ X @ L2 ) )
% 2.48/1.48 = ( coinductive_lfilter @ A @ P3 @ L2 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_114_Coinductive__List_Ofinite__lprefix__def,axiom,
% 2.48/1.48 ! [A: $tType] :
% 2.48/1.48 ( ( coindu328551480prefix @ A )
% 2.48/1.48 = ( coinductive_lprefix @ A ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_115_lstrict__prefix__lappend__conv,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coindu1478340336prefix @ A @ Xs @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.48/1.48 = ( ( coinductive_lfinite @ A @ Xs )
% 2.48/1.48 & ~ ( coinductive_lnull @ A @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_116_lfilter__eq__LConsD,axiom,
% 2.48/1.48 ! [A: $tType,P: A > $o,Ys: coinductive_llist @ A,X: A,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( ( coinductive_lfilter @ A @ P @ Ys )
% 2.48/1.48 = ( coinductive_LCons @ A @ X @ Xs ) )
% 2.48/1.48 => ? [Us: coinductive_llist @ A,Vs: coinductive_llist @ A] :
% 2.48/1.48 ( ( Ys
% 2.48/1.48 = ( coinductive_lappend @ A @ Us @ ( coinductive_LCons @ A @ X @ Vs ) ) )
% 2.48/1.48 & ( coinductive_lfinite @ A @ Us )
% 2.48/1.48 & ! [X5: A] :
% 2.48/1.48 ( ( member @ A @ X5 @ ( coinductive_lset @ A @ Us ) )
% 2.48/1.48 => ~ ( P @ X5 ) )
% 2.48/1.48 & ( P @ X )
% 2.48/1.48 & ( Xs
% 2.48/1.48 = ( coinductive_lfilter @ A @ P @ Vs ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_117_reflpD,axiom,
% 2.48/1.48 ! [A: $tType,R3: A > A > $o,X: A] :
% 2.48/1.48 ( ( reflp @ A @ R3 )
% 2.48/1.48 => ( R3 @ X @ X ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_118_reflpE,axiom,
% 2.48/1.48 ! [A: $tType,R3: A > A > $o,X: A] :
% 2.48/1.48 ( ( reflp @ A @ R3 )
% 2.48/1.48 => ( R3 @ X @ X ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_119_reflpI,axiom,
% 2.48/1.48 ! [A: $tType,R3: A > A > $o] :
% 2.48/1.48 ( ! [X4: A] : ( R3 @ X4 @ X4 )
% 2.48/1.48 => ( reflp @ A @ R3 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_120_reflp__def,axiom,
% 2.48/1.48 ! [A: $tType] :
% 2.48/1.48 ( ( reflp @ A )
% 2.48/1.48 = ( ^ [R: A > A > $o] :
% 2.48/1.48 ! [X3: A] : ( R @ X3 @ X3 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_121_llist__all2__same,axiom,
% 2.48/1.48 ! [A: $tType,P: A > A > $o,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ A @ P @ Xs @ Xs )
% 2.48/1.48 = ( ! [X3: A] :
% 2.48/1.48 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 2.48/1.48 => ( P @ X3 @ X3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_122_lstrict__prefix__code_I4_J,axiom,
% 2.48/1.48 ! [B: $tType,X: B,Xs: coinductive_llist @ B,Y4: B,Ys: coinductive_llist @ B] :
% 2.48/1.48 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LCons @ B @ Y4 @ Ys ) )
% 2.48/1.48 = ( ( X = Y4 )
% 2.48/1.48 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_123_lset__lfilter,axiom,
% 2.48/1.48 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lset @ A @ ( coinductive_lfilter @ A @ P @ Xs ) )
% 2.48/1.48 = ( collect @ A
% 2.48/1.48 @ ^ [X3: A] :
% 2.48/1.48 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 2.48/1.48 & ( P @ X3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_124_lnull__lfilter,axiom,
% 2.48/1.48 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lnull @ A @ ( coinductive_lfilter @ A @ P @ Xs ) )
% 2.48/1.48 = ( ! [X3: A] :
% 2.48/1.48 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 2.48/1.48 => ~ ( P @ X3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_125_llist__less__induct,axiom,
% 2.48/1.48 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ! [Xs5: coinductive_llist @ A] :
% 2.48/1.48 ( ! [Ys5: coinductive_llist @ A] :
% 2.48/1.48 ( ( coindu1478340336prefix @ A @ Ys5 @ Xs5 )
% 2.48/1.48 => ( P @ Ys5 ) )
% 2.48/1.48 => ( P @ Xs5 ) )
% 2.48/1.48 => ( P @ Xs ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_126_lset__intros_I2_J,axiom,
% 2.48/1.48 ! [A: $tType,X: A,Xs: coinductive_llist @ A,X6: A] :
% 2.48/1.48 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.48/1.48 => ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ X6 @ Xs ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_127_lset__intros_I1_J,axiom,
% 2.48/1.48 ! [A: $tType,X: A,Xs: coinductive_llist @ A] : ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_128_llist_Oset__intros_I2_J,axiom,
% 2.48/1.48 ! [A: $tType,X: A,A22: coinductive_llist @ A,A1: A] :
% 2.48/1.48 ( ( member @ A @ X @ ( coinductive_lset @ A @ A22 ) )
% 2.48/1.48 => ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ A1 @ A22 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_129_llist_Oset__intros_I1_J,axiom,
% 2.48/1.48 ! [A: $tType,A1: A,A22: coinductive_llist @ A] : ( member @ A @ A1 @ ( coinductive_lset @ A @ ( coinductive_LCons @ A @ A1 @ A22 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_130_lset__cases,axiom,
% 2.48/1.48 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.48/1.48 => ( ! [Xs6: coinductive_llist @ A] :
% 2.48/1.48 ( Xs
% 2.48/1.48 != ( coinductive_LCons @ A @ X @ Xs6 ) )
% 2.48/1.48 => ~ ! [X7: A,Xs6: coinductive_llist @ A] :
% 2.48/1.48 ( ( Xs
% 2.48/1.48 = ( coinductive_LCons @ A @ X7 @ Xs6 ) )
% 2.48/1.48 => ~ ( member @ A @ X @ ( coinductive_lset @ A @ Xs6 ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_131_lset__induct,axiom,
% 2.48/1.48 ! [A: $tType,X: A,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.48/1.48 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.48/1.48 => ( ! [Xs5: coinductive_llist @ A] : ( P @ ( coinductive_LCons @ A @ X @ Xs5 ) )
% 2.48/1.48 => ( ! [X7: A,Xs5: coinductive_llist @ A] :
% 2.48/1.48 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs5 ) )
% 2.48/1.48 => ( ( X != X7 )
% 2.48/1.48 => ( ( P @ Xs5 )
% 2.48/1.48 => ( P @ ( coinductive_LCons @ A @ X7 @ Xs5 ) ) ) ) )
% 2.48/1.48 => ( P @ Xs ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_132_lset__induct_H,axiom,
% 2.48/1.48 ! [A: $tType,X: A,Xs: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.48/1.48 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.48/1.48 => ( ! [Xs5: coinductive_llist @ A] : ( P @ ( coinductive_LCons @ A @ X @ Xs5 ) )
% 2.48/1.48 => ( ! [X7: A,Xs5: coinductive_llist @ A] :
% 2.48/1.48 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs5 ) )
% 2.48/1.48 => ( ( P @ Xs5 )
% 2.48/1.48 => ( P @ ( coinductive_LCons @ A @ X7 @ Xs5 ) ) ) )
% 2.48/1.48 => ( P @ Xs ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_133_llist_Oset__cases,axiom,
% 2.48/1.48 ! [A: $tType,E2: A,A3: coinductive_llist @ A] :
% 2.48/1.48 ( ( member @ A @ E2 @ ( coinductive_lset @ A @ A3 ) )
% 2.48/1.48 => ( ! [Z22: coinductive_llist @ A] :
% 2.48/1.48 ( A3
% 2.48/1.48 != ( coinductive_LCons @ A @ E2 @ Z22 ) )
% 2.48/1.48 => ~ ! [Z1: A,Z22: coinductive_llist @ A] :
% 2.48/1.48 ( ( A3
% 2.48/1.48 = ( coinductive_LCons @ A @ Z1 @ Z22 ) )
% 2.48/1.48 => ~ ( member @ A @ E2 @ ( coinductive_lset @ A @ Z22 ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_134_llist_Oset__induct,axiom,
% 2.48/1.48 ! [A: $tType,X: A,A3: coinductive_llist @ A,P: A > ( coinductive_llist @ A ) > $o] :
% 2.48/1.48 ( ( member @ A @ X @ ( coinductive_lset @ A @ A3 ) )
% 2.48/1.48 => ( ! [Z1: A,Z22: coinductive_llist @ A] : ( P @ Z1 @ ( coinductive_LCons @ A @ Z1 @ Z22 ) )
% 2.48/1.48 => ( ! [Z1: A,Z22: coinductive_llist @ A,Xa2: A] :
% 2.48/1.48 ( ( member @ A @ Xa2 @ ( coinductive_lset @ A @ Z22 ) )
% 2.48/1.48 => ( ( P @ Xa2 @ Z22 )
% 2.48/1.48 => ( P @ Xa2 @ ( coinductive_LCons @ A @ Z1 @ Z22 ) ) ) )
% 2.48/1.48 => ( P @ X @ A3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_135_llist__all2__reflI,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,P: A > A > $o] :
% 2.48/1.48 ( ! [X4: A] :
% 2.48/1.48 ( ( member @ A @ X4 @ ( coinductive_lset @ A @ Xs ) )
% 2.48/1.48 => ( P @ X4 @ X4 ) )
% 2.48/1.48 => ( coindu1486289336t_all2 @ A @ A @ P @ Xs @ Xs ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_136_llist__all2__lsetD1,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,X: A] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 2.48/1.48 => ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.48/1.48 => ? [X4: B] :
% 2.48/1.48 ( ( member @ B @ X4 @ ( coinductive_lset @ B @ Ys ) )
% 2.48/1.48 & ( P @ X @ X4 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_137_llist__all2__lsetD2,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B,Y4: B] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 2.48/1.48 => ( ( member @ B @ Y4 @ ( coinductive_lset @ B @ Ys ) )
% 2.48/1.48 => ? [X4: A] :
% 2.48/1.48 ( ( member @ A @ X4 @ ( coinductive_lset @ A @ Xs ) )
% 2.48/1.48 & ( P @ X4 @ Y4 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_138_llist_Orel__cong,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,X: coinductive_llist @ A,Ya: coinductive_llist @ A,Y4: coinductive_llist @ B,Xa: coinductive_llist @ B,R2: A > B > $o,Ra: A > B > $o] :
% 2.48/1.48 ( ( X = Ya )
% 2.48/1.48 => ( ( Y4 = Xa )
% 2.48/1.48 => ( ! [Z3: A,Yb: B] :
% 2.48/1.48 ( ( member @ A @ Z3 @ ( coinductive_lset @ A @ Ya ) )
% 2.48/1.48 => ( ( member @ B @ Yb @ ( coinductive_lset @ B @ Xa ) )
% 2.48/1.48 => ( ( R2 @ Z3 @ Yb )
% 2.48/1.48 = ( Ra @ Z3 @ Yb ) ) ) )
% 2.48/1.48 => ( ( coindu1486289336t_all2 @ A @ B @ R2 @ X @ Y4 )
% 2.48/1.48 = ( coindu1486289336t_all2 @ A @ B @ Ra @ Ya @ Xa ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_139_llist_Orel__mono__strong,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,R2: A > B > $o,X: coinductive_llist @ A,Y4: coinductive_llist @ B,Ra: A > B > $o] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ B @ R2 @ X @ Y4 )
% 2.48/1.48 => ( ! [Z3: A,Yb: B] :
% 2.48/1.48 ( ( member @ A @ Z3 @ ( coinductive_lset @ A @ X ) )
% 2.48/1.48 => ( ( member @ B @ Yb @ ( coinductive_lset @ B @ Y4 ) )
% 2.48/1.48 => ( ( R2 @ Z3 @ Yb )
% 2.48/1.48 => ( Ra @ Z3 @ Yb ) ) ) )
% 2.48/1.48 => ( coindu1486289336t_all2 @ A @ B @ Ra @ X @ Y4 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_140_llist_Orel__refl__strong,axiom,
% 2.48/1.48 ! [A: $tType,X: coinductive_llist @ A,Ra: A > A > $o] :
% 2.48/1.48 ( ! [Z3: A] :
% 2.48/1.48 ( ( member @ A @ Z3 @ ( coinductive_lset @ A @ X ) )
% 2.48/1.48 => ( Ra @ Z3 @ Z3 ) )
% 2.48/1.48 => ( coindu1486289336t_all2 @ A @ A @ Ra @ X @ X ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_141_lfilter__cong,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,P: A > $o,Q: A > $o] :
% 2.48/1.48 ( ( Xs = Ys )
% 2.48/1.48 => ( ! [X4: A] :
% 2.48/1.48 ( ( member @ A @ X4 @ ( coinductive_lset @ A @ Ys ) )
% 2.48/1.48 => ( ( P @ X4 )
% 2.48/1.48 = ( Q @ X4 ) ) )
% 2.48/1.48 => ( ( coinductive_lfilter @ A @ P @ Xs )
% 2.48/1.48 = ( coinductive_lfilter @ A @ Q @ Ys ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_142_lfilter__id__conv,axiom,
% 2.48/1.48 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( ( coinductive_lfilter @ A @ P @ Xs )
% 2.48/1.48 = Xs )
% 2.48/1.48 = ( ! [X3: A] :
% 2.48/1.48 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 2.48/1.48 => ( P @ X3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_143_lstrict__prefix__def,axiom,
% 2.48/1.48 ! [A: $tType] :
% 2.48/1.48 ( ( coindu1478340336prefix @ A )
% 2.48/1.48 = ( ^ [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ Xs3 @ Ys3 )
% 2.48/1.48 & ( Xs3 != Ys3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_144_lstrict__prefix__lfinite1,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coindu1478340336prefix @ A @ Xs @ Ys )
% 2.48/1.48 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_145_in__lset__lappend__iff,axiom,
% 2.48/1.48 ! [A: $tType,X: A,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( member @ A @ X @ ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) ) )
% 2.48/1.48 = ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.48/1.48 | ( ( coinductive_lfinite @ A @ Xs )
% 2.48/1.48 & ( member @ A @ X @ ( coinductive_lset @ A @ Ys ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_146_split__llist,axiom,
% 2.48/1.48 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.48/1.48 => ? [Ys6: coinductive_llist @ A,Zs4: coinductive_llist @ A] :
% 2.48/1.48 ( ( Xs
% 2.48/1.48 = ( coinductive_lappend @ A @ Ys6 @ ( coinductive_LCons @ A @ X @ Zs4 ) ) )
% 2.48/1.48 & ( coinductive_lfinite @ A @ Ys6 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_147_split__llist__first,axiom,
% 2.48/1.48 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( member @ A @ X @ ( coinductive_lset @ A @ Xs ) )
% 2.48/1.48 => ? [Ys6: coinductive_llist @ A,Zs4: coinductive_llist @ A] :
% 2.48/1.48 ( ( Xs
% 2.48/1.48 = ( coinductive_lappend @ A @ Ys6 @ ( coinductive_LCons @ A @ X @ Zs4 ) ) )
% 2.48/1.48 & ( coinductive_lfinite @ A @ Ys6 )
% 2.48/1.48 & ~ ( member @ A @ X @ ( coinductive_lset @ A @ Ys6 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_148_reflp__mono,axiom,
% 2.48/1.48 ! [A: $tType,R2: A > A > $o,Q: A > A > $o] :
% 2.48/1.48 ( ( reflp @ A @ R2 )
% 2.48/1.48 => ( ! [X4: A,Y3: A] :
% 2.48/1.48 ( ( R2 @ X4 @ Y3 )
% 2.48/1.48 => ( Q @ X4 @ Y3 ) )
% 2.48/1.48 => ( reflp @ A @ Q ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_149_lset__lappend__lfinite,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lfinite @ A @ Xs )
% 2.48/1.48 => ( ( coinductive_lset @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.48/1.48 = ( sup_sup @ ( set @ A ) @ ( coinductive_lset @ A @ Xs ) @ ( coinductive_lset @ A @ Ys ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_150_The__case__prod,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,P: A > B > $o] :
% 2.48/1.48 ( ( the @ ( product_prod @ A @ B ) @ ( product_case_prod @ A @ B @ $o @ P ) )
% 2.48/1.48 = ( the @ ( product_prod @ A @ B )
% 2.48/1.48 @ ^ [Xy: product_prod @ A @ B] : ( P @ ( product_fst @ A @ B @ Xy ) @ ( product_snd @ A @ B @ Xy ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_151_llimit__induct,axiom,
% 2.48/1.48 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( P @ ( coinductive_LNil @ A ) )
% 2.48/1.48 => ( ! [X4: A,Xs5: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lfinite @ A @ Xs5 )
% 2.48/1.48 => ( ( P @ Xs5 )
% 2.48/1.48 => ( P @ ( coinductive_LCons @ A @ X4 @ Xs5 ) ) ) )
% 2.48/1.48 => ( ( ! [Ys5: coinductive_llist @ A] :
% 2.48/1.48 ( ( coindu1478340336prefix @ A @ Ys5 @ Xs )
% 2.48/1.48 => ( P @ Ys5 ) )
% 2.48/1.48 => ( P @ Xs ) )
% 2.48/1.48 => ( P @ Xs ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_152_prod_Oswap__def,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType] :
% 2.48/1.48 ( ( product_swap @ A @ B )
% 2.48/1.48 = ( ^ [P4: product_prod @ A @ B] : ( product_Pair @ B @ A @ ( product_snd @ A @ B @ P4 ) @ ( product_fst @ A @ B @ P4 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_153_old_Oprod_Oinject,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,A3: A,B3: B,A7: A,B5: B] :
% 2.48/1.48 ( ( ( product_Pair @ A @ B @ A3 @ B3 )
% 2.48/1.48 = ( product_Pair @ A @ B @ A7 @ B5 ) )
% 2.48/1.48 = ( ( A3 = A7 )
% 2.48/1.48 & ( B3 = B5 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_154_prod_Oinject,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,X12: A,X23: B,Y1: A,Y23: B] :
% 2.48/1.48 ( ( ( product_Pair @ A @ B @ X12 @ X23 )
% 2.48/1.48 = ( product_Pair @ A @ B @ Y1 @ Y23 ) )
% 2.48/1.48 = ( ( X12 = Y1 )
% 2.48/1.48 & ( X23 = Y23 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_155_mem__case__prodI2,axiom,
% 2.48/1.48 ! [C: $tType,B: $tType,A: $tType,P3: product_prod @ A @ B,Z2: C,C3: A > B > ( set @ C )] :
% 2.48/1.48 ( ! [A4: A,B4: B] :
% 2.48/1.48 ( ( P3
% 2.48/1.48 = ( product_Pair @ A @ B @ A4 @ B4 ) )
% 2.48/1.48 => ( member @ C @ Z2 @ ( C3 @ A4 @ B4 ) ) )
% 2.48/1.48 => ( member @ C @ Z2 @ ( product_case_prod @ A @ B @ ( set @ C ) @ C3 @ P3 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_156_mem__case__prodI,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,C: $tType,Z2: A,C3: B > C > ( set @ A ),A3: B,B3: C] :
% 2.48/1.48 ( ( member @ A @ Z2 @ ( C3 @ A3 @ B3 ) )
% 2.48/1.48 => ( member @ A @ Z2 @ ( product_case_prod @ B @ C @ ( set @ A ) @ C3 @ ( product_Pair @ B @ C @ A3 @ B3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_157_lprefix__code_I1_J,axiom,
% 2.48/1.48 ! [A: $tType,Ys: coinductive_llist @ A] : ( coinductive_lprefix @ A @ ( coinductive_LNil @ A ) @ Ys ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_158_lfinite__code_I1_J,axiom,
% 2.48/1.48 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_159_llist__all2__LNil2,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,P: A > B > $o,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ ( coinductive_LNil @ B ) )
% 2.48/1.48 = ( Xs
% 2.48/1.48 = ( coinductive_LNil @ A ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_160_llist__all2__LNil1,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ B] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ B @ P @ ( coinductive_LNil @ A ) @ Xs )
% 2.48/1.48 = ( Xs
% 2.48/1.48 = ( coinductive_LNil @ B ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_161_lappend__LNil2,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.48/1.48 = Xs ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_162_lappend__code_I1_J,axiom,
% 2.48/1.48 ! [A: $tType,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 2.48/1.48 = Ys ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_163_apfst__conv,axiom,
% 2.48/1.48 ! [C: $tType,A: $tType,B: $tType,F: C > A,X: C,Y4: B] :
% 2.48/1.48 ( ( product_apfst @ C @ A @ B @ F @ ( product_Pair @ C @ B @ X @ Y4 ) )
% 2.48/1.48 = ( product_Pair @ A @ B @ ( F @ X ) @ Y4 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_164_lfilter__LNil,axiom,
% 2.48/1.48 ! [A: $tType,P: A > $o] :
% 2.48/1.48 ( ( coinductive_lfilter @ A @ P @ ( coinductive_LNil @ A ) )
% 2.48/1.48 = ( coinductive_LNil @ A ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_165_swap__simp,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,X: B,Y4: A] :
% 2.48/1.48 ( ( product_swap @ B @ A @ ( product_Pair @ B @ A @ X @ Y4 ) )
% 2.48/1.48 = ( product_Pair @ A @ B @ Y4 @ X ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_166_case__prod__conv,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,C: $tType,F: B > C > A,A3: B,B3: C] :
% 2.48/1.48 ( ( product_case_prod @ B @ C @ A @ F @ ( product_Pair @ B @ C @ A3 @ B3 ) )
% 2.48/1.48 = ( F @ A3 @ B3 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_167_lstrict__prefix__code_I1_J,axiom,
% 2.48/1.48 ! [A: $tType] :
% 2.48/1.48 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_168_case__prodI2,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,P3: product_prod @ A @ B,C3: A > B > $o] :
% 2.48/1.48 ( ! [A4: A,B4: B] :
% 2.48/1.48 ( ( P3
% 2.48/1.48 = ( product_Pair @ A @ B @ A4 @ B4 ) )
% 2.48/1.48 => ( C3 @ A4 @ B4 ) )
% 2.48/1.48 => ( product_case_prod @ A @ B @ $o @ C3 @ P3 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_169_case__prodI,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,F: A > B > $o,A3: A,B3: B] :
% 2.48/1.48 ( ( F @ A3 @ B3 )
% 2.48/1.48 => ( product_case_prod @ A @ B @ $o @ F @ ( product_Pair @ A @ B @ A3 @ B3 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_170_lappendt__LNil,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,Tr: tLList446370796tllist @ A @ B] :
% 2.48/1.48 ( ( tLList98099029ppendt @ A @ B @ ( coinductive_LNil @ A ) @ Tr )
% 2.48/1.48 = Tr ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_171_case__prodI2_H,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,C: $tType,P3: product_prod @ A @ B,C3: A > B > C > $o,X: C] :
% 2.48/1.48 ( ! [A4: A,B4: B] :
% 2.48/1.48 ( ( ( product_Pair @ A @ B @ A4 @ B4 )
% 2.48/1.48 = P3 )
% 2.48/1.48 => ( C3 @ A4 @ B4 @ X ) )
% 2.48/1.48 => ( product_case_prod @ A @ B @ ( C > $o ) @ C3 @ P3 @ X ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_172_lfitler__K__False,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lfilter @ A
% 2.48/1.48 @ ^ [Uu: A] : $false
% 2.48/1.48 @ Xs )
% 2.48/1.48 = ( coinductive_LNil @ A ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_173_prod_Ocollapse,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 2.48/1.48 ( ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) )
% 2.48/1.48 = Prod ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_174_lprefix__LNil,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.48/1.48 = ( coinductive_lnull @ A @ Xs ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_175_diverge__lfilter__LNil,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,P: A > $o] :
% 2.48/1.48 ( ! [X4: A] :
% 2.48/1.48 ( ( member @ A @ X4 @ ( coinductive_lset @ A @ Xs ) )
% 2.48/1.48 => ~ ( P @ X4 ) )
% 2.48/1.48 => ( ( coinductive_lfilter @ A @ P @ Xs )
% 2.48/1.48 = ( coinductive_LNil @ A ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_176_llast__singleton,axiom,
% 2.48/1.48 ! [A: $tType,X: A] :
% 2.48/1.48 ( ( coinductive_llast @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) )
% 2.48/1.48 = X ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_177_lstrict__prefix__code_I3_J,axiom,
% 2.48/1.48 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 2.48/1.48 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_178_lstrict__prefix__code_I2_J,axiom,
% 2.48/1.48 ! [B: $tType,Y4: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y4 @ Ys ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_179_The__split__eq,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,X: A,Y4: B] :
% 2.48/1.48 ( ( the @ ( product_prod @ A @ B )
% 2.48/1.48 @ ( product_case_prod @ A @ B @ $o
% 2.48/1.48 @ ^ [X8: A,Y5: B] :
% 2.48/1.48 ( ( X = X8 )
% 2.48/1.48 & ( Y4 = Y5 ) ) ) )
% 2.48/1.48 = ( product_Pair @ A @ B @ X @ Y4 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_180_pred__equals__eq2,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,R2: set @ ( product_prod @ A @ B ),S: set @ ( product_prod @ A @ B )] :
% 2.48/1.48 ( ( ( ^ [X3: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y ) @ R2 ) )
% 2.48/1.48 = ( ^ [X3: A,Y: B] : ( member @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B @ X3 @ Y ) @ S ) ) )
% 2.48/1.48 = ( R2 = S ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_181_old_Oprod_Ocase,axiom,
% 2.48/1.48 ! [A: $tType,C: $tType,B: $tType,F: A > B > C,X12: A,X23: B] :
% 2.48/1.48 ( ( product_case_prod @ A @ B @ C @ F @ ( product_Pair @ A @ B @ X12 @ X23 ) )
% 2.48/1.48 = ( F @ X12 @ X23 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_182_LNil__lprefix,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A] : ( coinductive_lprefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_183_llist_Odistinct_I1_J,axiom,
% 2.48/1.48 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_LNil @ A )
% 2.48/1.48 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_184_llist_Oexhaust,axiom,
% 2.48/1.48 ! [A: $tType,Y4: coinductive_llist @ A] :
% 2.48/1.48 ( ( Y4
% 2.48/1.48 != ( coinductive_LNil @ A ) )
% 2.48/1.48 => ~ ! [X212: A,X222: coinductive_llist @ A] :
% 2.48/1.48 ( Y4
% 2.48/1.48 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_185_neq__LNil__conv,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( Xs
% 2.48/1.48 != ( coinductive_LNil @ A ) )
% 2.48/1.48 = ( ? [X3: A,Xs4: coinductive_llist @ A] :
% 2.48/1.48 ( Xs
% 2.48/1.48 = ( coinductive_LCons @ A @ X3 @ Xs4 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_186_split__fst,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,R2: A > $o,P3: product_prod @ A @ B] :
% 2.48/1.48 ( ( R2 @ ( product_fst @ A @ B @ P3 ) )
% 2.48/1.48 = ( ! [X3: A,Y: B] :
% 2.48/1.48 ( ( P3
% 2.48/1.48 = ( product_Pair @ A @ B @ X3 @ Y ) )
% 2.48/1.48 => ( R2 @ X3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_187_split__fst__asm,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,R2: A > $o,P3: product_prod @ A @ B] :
% 2.48/1.48 ( ( R2 @ ( product_fst @ A @ B @ P3 ) )
% 2.48/1.48 = ( ~ ? [X3: A,Y: B] :
% 2.48/1.48 ( ( P3
% 2.48/1.48 = ( product_Pair @ A @ B @ X3 @ Y ) )
% 2.48/1.48 & ~ ( R2 @ X3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_188_fst__eqD,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,X: A,Y4: B,A3: A] :
% 2.48/1.48 ( ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X @ Y4 ) )
% 2.48/1.48 = A3 )
% 2.48/1.48 => ( X = A3 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_189_fst__conv,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,X12: A,X23: B] :
% 2.48/1.48 ( ( product_fst @ A @ B @ ( product_Pair @ A @ B @ X12 @ X23 ) )
% 2.48/1.48 = X12 ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_190_llist_Odisc_I1_J,axiom,
% 2.48/1.48 ! [A: $tType] : ( coinductive_lnull @ A @ ( coinductive_LNil @ A ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_191_llist_OdiscI_I1_J,axiom,
% 2.48/1.48 ! [A: $tType,Llist: coinductive_llist @ A] :
% 2.48/1.48 ( ( Llist
% 2.48/1.48 = ( coinductive_LNil @ A ) )
% 2.48/1.48 => ( coinductive_lnull @ A @ Llist ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_192_llist_Ocollapse_I1_J,axiom,
% 2.48/1.48 ! [A: $tType,Llist: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lnull @ A @ Llist )
% 2.48/1.48 => ( Llist
% 2.48/1.48 = ( coinductive_LNil @ A ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_193_lnull__def,axiom,
% 2.48/1.48 ! [A: $tType] :
% 2.48/1.48 ( ( coinductive_lnull @ A )
% 2.48/1.48 = ( ^ [Llist2: coinductive_llist @ A] :
% 2.48/1.48 ( Llist2
% 2.48/1.48 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_194_snd__eqD,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,X: B,Y4: A,A3: A] :
% 2.48/1.48 ( ( ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X @ Y4 ) )
% 2.48/1.48 = A3 )
% 2.48/1.48 => ( Y4 = A3 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_195_snd__conv,axiom,
% 2.48/1.48 ! [Aa: $tType,A: $tType,X12: Aa,X23: A] :
% 2.48/1.48 ( ( product_snd @ Aa @ A @ ( product_Pair @ Aa @ A @ X12 @ X23 ) )
% 2.48/1.48 = X23 ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_196_lfinite__LNil,axiom,
% 2.48/1.48 ! [A: $tType] : ( coinductive_lfinite @ A @ ( coinductive_LNil @ A ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_197_LNil__transfer,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,P: A > B > $o] : ( coindu1486289336t_all2 @ A @ B @ P @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ B ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_198_llist__all2__LNil__LNil,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,R2: A > B > $o] : ( coindu1486289336t_all2 @ A @ B @ R2 @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ B ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_199_lappend__LNil__LNil,axiom,
% 2.48/1.48 ! [A: $tType] :
% 2.48/1.48 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 2.48/1.48 = ( coinductive_LNil @ A ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_200_LNil__eq__lappend__iff,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( ( coinductive_LNil @ A )
% 2.48/1.48 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.48/1.48 = ( ( Xs
% 2.48/1.48 = ( coinductive_LNil @ A ) )
% 2.48/1.48 & ( Ys
% 2.48/1.48 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_201_lappend__eq__LNil__iff,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.48/1.48 = ( coinductive_LNil @ A ) )
% 2.48/1.48 = ( ( Xs
% 2.48/1.48 = ( coinductive_LNil @ A ) )
% 2.48/1.48 & ( Ys
% 2.48/1.48 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_202_old_Oprod_Oinducts,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,Prod: product_prod @ A @ B] :
% 2.48/1.48 ( ! [A4: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 2.48/1.48 => ( P @ Prod ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_203_old_Oprod_Oexhaust,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,Y4: product_prod @ A @ B] :
% 2.48/1.48 ~ ! [A4: A,B4: B] :
% 2.48/1.48 ( Y4
% 2.48/1.48 != ( product_Pair @ A @ B @ A4 @ B4 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_204_prod__induct7,axiom,
% 2.48/1.48 ! [G3: $tType,F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) )] :
% 2.48/1.48 ( ! [A4: A,B4: B,C4: C,D2: D,E3: E,F4: F3,G4: G3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F3 @ G3 ) @ E3 @ ( product_Pair @ F3 @ G3 @ F4 @ G4 ) ) ) ) ) ) )
% 2.48/1.48 => ( P @ X ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_205_prod__induct6,axiom,
% 2.48/1.48 ! [F3: $tType,E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 2.48/1.48 ( ! [A4: A,B4: B,C4: C,D2: D,E3: E,F4: F3] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D2 @ ( product_Pair @ E @ F3 @ E3 @ F4 ) ) ) ) ) )
% 2.48/1.48 => ( P @ X ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_206_prod__induct5,axiom,
% 2.48/1.48 ! [E: $tType,D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 2.48/1.48 ( ! [A4: A,B4: B,C4: C,D2: D,E3: E] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C4 @ ( product_Pair @ D @ E @ D2 @ E3 ) ) ) ) )
% 2.48/1.48 => ( P @ X ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_207_prod__induct4,axiom,
% 2.48/1.48 ! [D: $tType,C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.48/1.48 ( ! [A4: A,B4: B,C4: C,D2: D] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C4 @ D2 ) ) ) )
% 2.48/1.48 => ( P @ X ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_208_prod__induct3,axiom,
% 2.48/1.48 ! [C: $tType,B: $tType,A: $tType,P: ( product_prod @ A @ ( product_prod @ B @ C ) ) > $o,X: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.48/1.48 ( ! [A4: A,B4: B,C4: C] : ( P @ ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C4 ) ) )
% 2.48/1.48 => ( P @ X ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_209_prod__cases7,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,G3: $tType,Y4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) )] :
% 2.48/1.48 ~ ! [A4: A,B4: B,C4: C,D2: D,E3: E,F4: F3,G4: G3] :
% 2.48/1.48 ( Y4
% 2.48/1.48 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ ( product_prod @ F3 @ G3 ) ) @ D2 @ ( product_Pair @ E @ ( product_prod @ F3 @ G3 ) @ E3 @ ( product_Pair @ F3 @ G3 @ F4 @ G4 ) ) ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_210_prod__cases6,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,F3: $tType,Y4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) )] :
% 2.48/1.48 ~ ! [A4: A,B4: B,C4: C,D2: D,E3: E,F4: F3] :
% 2.48/1.48 ( Y4
% 2.48/1.48 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ ( product_prod @ E @ F3 ) ) @ C4 @ ( product_Pair @ D @ ( product_prod @ E @ F3 ) @ D2 @ ( product_Pair @ E @ F3 @ E3 @ F4 ) ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_211_prod__cases5,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,C: $tType,D: $tType,E: $tType,Y4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) )] :
% 2.48/1.48 ~ ! [A4: A,B4: B,C4: C,D2: D,E3: E] :
% 2.48/1.48 ( Y4
% 2.48/1.48 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ ( product_prod @ D @ E ) ) @ B4 @ ( product_Pair @ C @ ( product_prod @ D @ E ) @ C4 @ ( product_Pair @ D @ E @ D2 @ E3 ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_212_prod__cases4,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,C: $tType,D: $tType,Y4: product_prod @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) )] :
% 2.48/1.48 ~ ! [A4: A,B4: B,C4: C,D2: D] :
% 2.48/1.48 ( Y4
% 2.48/1.48 != ( product_Pair @ A @ ( product_prod @ B @ ( product_prod @ C @ D ) ) @ A4 @ ( product_Pair @ B @ ( product_prod @ C @ D ) @ B4 @ ( product_Pair @ C @ D @ C4 @ D2 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_213_prod__cases3,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,C: $tType,Y4: product_prod @ A @ ( product_prod @ B @ C )] :
% 2.48/1.48 ~ ! [A4: A,B4: B,C4: C] :
% 2.48/1.48 ( Y4
% 2.48/1.48 != ( product_Pair @ A @ ( product_prod @ B @ C ) @ A4 @ ( product_Pair @ B @ C @ B4 @ C4 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_214_Pair__inject,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,A3: A,B3: B,A7: A,B5: B] :
% 2.48/1.48 ( ( ( product_Pair @ A @ B @ A3 @ B3 )
% 2.48/1.48 = ( product_Pair @ A @ B @ A7 @ B5 ) )
% 2.48/1.48 => ~ ( ( A3 = A7 )
% 2.48/1.48 => ( B3 != B5 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_215_prod__cases,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,P: ( product_prod @ A @ B ) > $o,P3: product_prod @ A @ B] :
% 2.48/1.48 ( ! [A4: A,B4: B] : ( P @ ( product_Pair @ A @ B @ A4 @ B4 ) )
% 2.48/1.48 => ( P @ P3 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_216_surj__pair,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,P3: product_prod @ A @ B] :
% 2.48/1.48 ? [X4: A,Y3: B] :
% 2.48/1.48 ( P3
% 2.48/1.48 = ( product_Pair @ A @ B @ X4 @ Y3 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_217_case__prod__Pair__iden,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,P3: product_prod @ A @ B] :
% 2.48/1.48 ( ( product_case_prod @ A @ B @ ( product_prod @ A @ B ) @ ( product_Pair @ A @ B ) @ P3 )
% 2.48/1.48 = P3 ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_218_mem__case__prodE,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,C: $tType,Z2: A,C3: B > C > ( set @ A ),P3: product_prod @ B @ C] :
% 2.48/1.48 ( ( member @ A @ Z2 @ ( product_case_prod @ B @ C @ ( set @ A ) @ C3 @ P3 ) )
% 2.48/1.48 => ~ ! [X4: B,Y3: C] :
% 2.48/1.48 ( ( P3
% 2.48/1.48 = ( product_Pair @ B @ C @ X4 @ Y3 ) )
% 2.48/1.48 => ~ ( member @ A @ Z2 @ ( C3 @ X4 @ Y3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_219_Pair__scomp,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,C: $tType,X: C,F: C > A > B] :
% 2.48/1.48 ( ( product_scomp @ A @ C @ A @ B @ ( product_Pair @ C @ A @ X ) @ F )
% 2.48/1.48 = ( F @ X ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_220_cond__case__prod__eta,axiom,
% 2.48/1.48 ! [C: $tType,B: $tType,A: $tType,F: A > B > C,G: ( product_prod @ A @ B ) > C] :
% 2.48/1.48 ( ! [X4: A,Y3: B] :
% 2.48/1.48 ( ( F @ X4 @ Y3 )
% 2.48/1.48 = ( G @ ( product_Pair @ A @ B @ X4 @ Y3 ) ) )
% 2.48/1.48 => ( ( product_case_prod @ A @ B @ C @ F )
% 2.48/1.48 = G ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_221_case__prod__eta,axiom,
% 2.48/1.48 ! [C: $tType,B: $tType,A: $tType,F: ( product_prod @ A @ B ) > C] :
% 2.48/1.48 ( ( product_case_prod @ A @ B @ C
% 2.48/1.48 @ ^ [X3: A,Y: B] : ( F @ ( product_Pair @ A @ B @ X3 @ Y ) ) )
% 2.48/1.48 = F ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_222_case__prodE2,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,C: $tType,Q: A > $o,P: B > C > A,Z2: product_prod @ B @ C] :
% 2.48/1.48 ( ( Q @ ( product_case_prod @ B @ C @ A @ P @ Z2 ) )
% 2.48/1.48 => ~ ! [X4: B,Y3: C] :
% 2.48/1.48 ( ( Z2
% 2.48/1.48 = ( product_Pair @ B @ C @ X4 @ Y3 ) )
% 2.48/1.48 => ~ ( Q @ ( P @ X4 @ Y3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_223_scomp__Pair,axiom,
% 2.48/1.48 ! [C: $tType,B: $tType,A: $tType,X: A > ( product_prod @ B @ C )] :
% 2.48/1.48 ( ( product_scomp @ A @ B @ C @ ( product_prod @ B @ C ) @ X @ ( product_Pair @ B @ C ) )
% 2.48/1.48 = X ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_224_case__prodE,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,C3: A > B > $o,P3: product_prod @ A @ B] :
% 2.48/1.48 ( ( product_case_prod @ A @ B @ $o @ C3 @ P3 )
% 2.48/1.48 => ~ ! [X4: A,Y3: B] :
% 2.48/1.48 ( ( P3
% 2.48/1.48 = ( product_Pair @ A @ B @ X4 @ Y3 ) )
% 2.48/1.48 => ~ ( C3 @ X4 @ Y3 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_225_case__prodD,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,F: A > B > $o,A3: A,B3: B] :
% 2.48/1.48 ( ( product_case_prod @ A @ B @ $o @ F @ ( product_Pair @ A @ B @ A3 @ B3 ) )
% 2.48/1.48 => ( F @ A3 @ B3 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_226_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.48/1.48 = ( Xs
% 2.48/1.48 = ( coinductive_LNil @ A ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_227_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_228_case__prodE_H,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,C: $tType,C3: A > B > C > $o,P3: product_prod @ A @ B,Z2: C] :
% 2.48/1.48 ( ( product_case_prod @ A @ B @ ( C > $o ) @ C3 @ P3 @ Z2 )
% 2.48/1.48 => ~ ! [X4: A,Y3: B] :
% 2.48/1.48 ( ( P3
% 2.48/1.48 = ( product_Pair @ A @ B @ X4 @ Y3 ) )
% 2.48/1.48 => ~ ( C3 @ X4 @ Y3 @ Z2 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_229_case__prodD_H,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,C: $tType,R2: A > B > C > $o,A3: A,B3: B,C3: C] :
% 2.48/1.48 ( ( product_case_prod @ A @ B @ ( C > $o ) @ R2 @ ( product_Pair @ A @ B @ A3 @ B3 ) @ C3 )
% 2.48/1.48 => ( R2 @ A3 @ B3 @ C3 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_230_lprefix__code_I2_J,axiom,
% 2.48/1.48 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 2.48/1.48 ~ ( coinductive_lprefix @ A @ ( coinductive_LCons @ A @ X @ Xs ) @ ( coinductive_LNil @ A ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_231_lprefix_Ocases,axiom,
% 2.48/1.48 ! [A: $tType,A1: coinductive_llist @ A,A22: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ A1 @ A22 )
% 2.48/1.48 => ( ( ( A1
% 2.48/1.48 = ( coinductive_LNil @ A ) )
% 2.48/1.48 => ! [Xs5: coinductive_llist @ A] : ( A22 != Xs5 ) )
% 2.48/1.48 => ~ ! [Xs5: coinductive_llist @ A,Ys6: coinductive_llist @ A,X4: A] :
% 2.48/1.48 ( ( A1
% 2.48/1.48 = ( coinductive_LCons @ A @ X4 @ Xs5 ) )
% 2.48/1.48 => ( ( A22
% 2.48/1.48 = ( coinductive_LCons @ A @ X4 @ Ys6 ) )
% 2.48/1.48 => ~ ( coinductive_lprefix @ A @ Xs5 @ Ys6 ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_232_lprefix_Osimps,axiom,
% 2.48/1.48 ! [A: $tType] :
% 2.48/1.48 ( ( coinductive_lprefix @ A )
% 2.48/1.48 = ( ^ [A12: coinductive_llist @ A,A23: coinductive_llist @ A] :
% 2.48/1.48 ( ? [Xs3: coinductive_llist @ A] :
% 2.48/1.48 ( ( A12
% 2.48/1.48 = ( coinductive_LNil @ A ) )
% 2.48/1.48 & ( A23 = Xs3 ) )
% 2.48/1.48 | ? [Xs3: coinductive_llist @ A,Ys3: coinductive_llist @ A,X3: A] :
% 2.48/1.48 ( ( A12
% 2.48/1.48 = ( coinductive_LCons @ A @ X3 @ Xs3 ) )
% 2.48/1.48 & ( A23
% 2.48/1.48 = ( coinductive_LCons @ A @ X3 @ Ys3 ) )
% 2.48/1.48 & ( coinductive_lprefix @ A @ Xs3 @ Ys3 ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_233_lprefix_Ocoinduct,axiom,
% 2.48/1.48 ! [A: $tType,X9: ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,Xa: coinductive_llist @ A] :
% 2.48/1.48 ( ( X9 @ X @ Xa )
% 2.48/1.48 => ( ! [X4: coinductive_llist @ A,Xa2: coinductive_llist @ A] :
% 2.48/1.48 ( ( X9 @ X4 @ Xa2 )
% 2.48/1.48 => ( ? [Xs7: coinductive_llist @ A] :
% 2.48/1.48 ( ( X4
% 2.48/1.48 = ( coinductive_LNil @ A ) )
% 2.48/1.48 & ( Xa2 = Xs7 ) )
% 2.48/1.48 | ? [Xs7: coinductive_llist @ A,Ys5: coinductive_llist @ A,Xb: A] :
% 2.48/1.48 ( ( X4
% 2.48/1.48 = ( coinductive_LCons @ A @ Xb @ Xs7 ) )
% 2.48/1.48 & ( Xa2
% 2.48/1.48 = ( coinductive_LCons @ A @ Xb @ Ys5 ) )
% 2.48/1.48 & ( ( X9 @ Xs7 @ Ys5 )
% 2.48/1.48 | ( coinductive_lprefix @ A @ Xs7 @ Ys5 ) ) ) ) )
% 2.48/1.48 => ( coinductive_lprefix @ A @ X @ Xa ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_234_lprefix__LCons__conv,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Y4: A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lprefix @ A @ Xs @ ( coinductive_LCons @ A @ Y4 @ Ys ) )
% 2.48/1.48 = ( ( Xs
% 2.48/1.48 = ( coinductive_LNil @ A ) )
% 2.48/1.48 | ? [Xs4: coinductive_llist @ A] :
% 2.48/1.48 ( ( Xs
% 2.48/1.48 = ( coinductive_LCons @ A @ Y4 @ Xs4 ) )
% 2.48/1.48 & ( coinductive_lprefix @ A @ Xs4 @ Ys ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_235_conjI__realizer,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,P: A > $o,P3: A,Q: B > $o,Q2: B] :
% 2.48/1.48 ( ( P @ P3 )
% 2.48/1.48 => ( ( Q @ Q2 )
% 2.48/1.48 => ( ( P @ ( product_fst @ A @ B @ ( product_Pair @ A @ B @ P3 @ Q2 ) ) )
% 2.48/1.48 & ( Q @ ( product_snd @ A @ B @ ( product_Pair @ A @ B @ P3 @ Q2 ) ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_236_exI__realizer,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,P: A > B > $o,Y4: A,X: B] :
% 2.48/1.48 ( ( P @ Y4 @ X )
% 2.48/1.48 => ( P @ ( product_snd @ B @ A @ ( product_Pair @ B @ A @ X @ Y4 ) ) @ ( product_fst @ B @ A @ ( product_Pair @ B @ A @ X @ Y4 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_237_prod_Oexhaust__sel,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,Prod: product_prod @ A @ B] :
% 2.48/1.48 ( Prod
% 2.48/1.48 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_238_surjective__pairing,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,T3: product_prod @ A @ B] :
% 2.48/1.48 ( T3
% 2.48/1.48 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ T3 ) @ ( product_snd @ A @ B @ T3 ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_239_lfinite_Oinducts,axiom,
% 2.48/1.48 ! [A: $tType,X: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.48/1.48 ( ( coinductive_lfinite @ A @ X )
% 2.48/1.48 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.48/1.48 => ( ! [Xs5: coinductive_llist @ A,X4: A] :
% 2.48/1.48 ( ( coinductive_lfinite @ A @ Xs5 )
% 2.48/1.48 => ( ( P @ Xs5 )
% 2.48/1.48 => ( P @ ( coinductive_LCons @ A @ X4 @ Xs5 ) ) ) )
% 2.48/1.48 => ( P @ X ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_240_lfinite_Osimps,axiom,
% 2.48/1.48 ! [A: $tType] :
% 2.48/1.48 ( ( coinductive_lfinite @ A )
% 2.48/1.48 = ( ^ [A2: coinductive_llist @ A] :
% 2.48/1.48 ( ( A2
% 2.48/1.48 = ( coinductive_LNil @ A ) )
% 2.48/1.48 | ? [Xs3: coinductive_llist @ A,X3: A] :
% 2.48/1.48 ( ( A2
% 2.48/1.48 = ( coinductive_LCons @ A @ X3 @ Xs3 ) )
% 2.48/1.48 & ( coinductive_lfinite @ A @ Xs3 ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_241_lfinite_Ocases,axiom,
% 2.48/1.48 ! [A: $tType,A3: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lfinite @ A @ A3 )
% 2.48/1.48 => ( ( A3
% 2.48/1.48 != ( coinductive_LNil @ A ) )
% 2.48/1.48 => ~ ! [Xs5: coinductive_llist @ A] :
% 2.48/1.48 ( ? [X4: A] :
% 2.48/1.48 ( A3
% 2.48/1.48 = ( coinductive_LCons @ A @ X4 @ Xs5 ) )
% 2.48/1.48 => ~ ( coinductive_lfinite @ A @ Xs5 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_242_llist__all2__LNil__LCons,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,R2: A > B > $o,Y21: B,Y22: coinductive_llist @ B] :
% 2.48/1.48 ~ ( coindu1486289336t_all2 @ A @ B @ R2 @ ( coinductive_LNil @ A ) @ ( coinductive_LCons @ B @ Y21 @ Y22 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_243_llist__all2__LCons__LNil,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,R2: A > B > $o,Y21: A,Y22: coinductive_llist @ A] :
% 2.48/1.48 ~ ( coindu1486289336t_all2 @ A @ B @ R2 @ ( coinductive_LCons @ A @ Y21 @ Y22 ) @ ( coinductive_LNil @ B ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_244_llist__all2__cases,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,P: A > B > $o,Xs: coinductive_llist @ A,Ys: coinductive_llist @ B] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ B @ P @ Xs @ Ys )
% 2.48/1.48 => ( ( ( Xs
% 2.48/1.48 = ( coinductive_LNil @ A ) )
% 2.48/1.48 => ( Ys
% 2.48/1.48 != ( coinductive_LNil @ B ) ) )
% 2.48/1.48 => ~ ! [X4: A,Xs6: coinductive_llist @ A] :
% 2.48/1.48 ( ( Xs
% 2.48/1.48 = ( coinductive_LCons @ A @ X4 @ Xs6 ) )
% 2.48/1.48 => ! [Y3: B,Ys7: coinductive_llist @ B] :
% 2.48/1.48 ( ( Ys
% 2.48/1.48 = ( coinductive_LCons @ B @ Y3 @ Ys7 ) )
% 2.48/1.48 => ( ( P @ X4 @ Y3 )
% 2.48/1.48 => ~ ( coindu1486289336t_all2 @ A @ B @ P @ Xs6 @ Ys7 ) ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_245_llist_Orel__cases,axiom,
% 2.48/1.48 ! [A: $tType,B: $tType,R2: A > B > $o,A3: coinductive_llist @ A,B3: coinductive_llist @ B] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ A @ B @ R2 @ A3 @ B3 )
% 2.48/1.48 => ( ( ( A3
% 2.48/1.48 = ( coinductive_LNil @ A ) )
% 2.48/1.48 => ( B3
% 2.48/1.48 != ( coinductive_LNil @ B ) ) )
% 2.48/1.48 => ~ ! [X13: A,X24: coinductive_llist @ A] :
% 2.48/1.48 ( ( A3
% 2.48/1.48 = ( coinductive_LCons @ A @ X13 @ X24 ) )
% 2.48/1.48 => ! [Y12: B,Y24: coinductive_llist @ B] :
% 2.48/1.48 ( ( B3
% 2.48/1.48 = ( coinductive_LCons @ B @ Y12 @ Y24 ) )
% 2.48/1.48 => ( ( R2 @ X13 @ Y12 )
% 2.48/1.48 => ~ ( coindu1486289336t_all2 @ A @ B @ R2 @ X24 @ Y24 ) ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_246_lappend__snocL1__conv__LCons2,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Y4: A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y4 @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 2.48/1.48 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y4 @ Ys ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_247_lappend_Octr_I1_J,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coinductive_lnull @ A @ Xs )
% 2.48/1.48 => ( ( coinductive_lnull @ A @ Ys )
% 2.48/1.48 => ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.48/1.48 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_248_internal__case__prod__conv,axiom,
% 2.48/1.48 ! [B: $tType,A: $tType,C: $tType,C3: B > C > A,A3: B,B3: C] :
% 2.48/1.48 ( ( produc2004651681e_prod @ B @ C @ A @ C3 @ ( product_Pair @ B @ C @ A3 @ B3 ) )
% 2.48/1.48 = ( C3 @ A3 @ B3 ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_249_lfilter__empty__conv,axiom,
% 2.48/1.48 ! [A: $tType,P: A > $o,Xs: coinductive_llist @ A] :
% 2.48/1.48 ( ( ( coinductive_lfilter @ A @ P @ Xs )
% 2.48/1.48 = ( coinductive_LNil @ A ) )
% 2.48/1.48 = ( ! [X3: A] :
% 2.48/1.48 ( ( member @ A @ X3 @ ( coinductive_lset @ A @ Xs ) )
% 2.48/1.48 => ~ ( P @ X3 ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_250_llast__LNil,axiom,
% 2.48/1.48 ! [A: $tType] :
% 2.48/1.48 ( ( coinductive_llast @ A @ ( coinductive_LNil @ A ) )
% 2.48/1.48 = ( undefined @ A ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_251_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 2.48/1.48 ! [A: $tType,Xs: coinductive_llist @ A,Y4: A,Ys: coinductive_llist @ A] :
% 2.48/1.48 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y4 @ Ys ) )
% 2.48/1.48 = ( ( Xs
% 2.48/1.48 = ( coinductive_LNil @ A ) )
% 2.48/1.48 | ? [Xs4: coinductive_llist @ A] :
% 2.48/1.48 ( ( Xs
% 2.48/1.48 = ( coinductive_LCons @ A @ Y4 @ Xs4 ) )
% 2.48/1.48 & ( coindu328551480prefix @ A @ Xs4 @ Ys ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(fact_252_prod_Osplit__sel__asm,axiom,
% 2.48/1.48 ! [C: $tType,B: $tType,A: $tType,P: C > $o,F: A > B > C,Prod: product_prod @ A @ B] :
% 2.48/1.48 ( ( P @ ( product_case_prod @ A @ B @ C @ F @ Prod ) )
% 2.48/1.48 = ( ~ ( ( Prod
% 2.48/1.48 = ( product_Pair @ A @ B @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) )
% 2.48/1.48 & ~ ( P @ ( F @ ( product_fst @ A @ B @ Prod ) @ ( product_snd @ A @ B @ Prod ) ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(help_If_3_1_T,axiom,
% 2.48/1.48 ! [P: $o] :
% 2.48/1.48 ( ( P = $true )
% 2.48/1.48 | ( P = $false ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(help_If_2_1_T,axiom,
% 2.48/1.48 ! [A: $tType,X: A,Y4: A] :
% 2.48/1.48 ( ( if @ A @ $false @ X @ Y4 )
% 2.48/1.48 = Y4 ) ).
% 2.48/1.48
% 2.48/1.48 thf(help_If_1_1_T,axiom,
% 2.48/1.48 ! [A: $tType,X: A,Y4: A] :
% 2.48/1.48 ( ( if @ A @ $true @ X @ Y4 )
% 2.48/1.48 = X ) ).
% 2.48/1.48
% 2.48/1.48 thf(conj_0,hypothesis,
% 2.48/1.48 ( product_case_prod @ ( coinductive_llist @ a ) @ c @ ( ( product_prod @ ( coinductive_llist @ b ) @ d ) > $o )
% 2.48/1.48 @ ^ [Xs3: coinductive_llist @ a,B2: c] :
% 2.48/1.48 ( product_case_prod @ ( coinductive_llist @ b ) @ d @ $o
% 2.48/1.48 @ ^ [Ys3: coinductive_llist @ b,B6: d] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ a @ b @ pa @ Xs3 @ Ys3 )
% 2.48/1.48 & ( ( coinductive_lfinite @ a @ Xs3 )
% 2.48/1.48 => ( qa @ B2 @ B6 ) ) ) )
% 2.48/1.48 @ xsa
% 2.48/1.48 @ ysa ) ).
% 2.48/1.48
% 2.48/1.48 thf(conj_1,hypothesis,
% 2.48/1.48 ( ( coinductive_lfinite @ a @ ( product_fst @ ( coinductive_llist @ a ) @ c @ xsa ) )
% 2.48/1.48 => ( ( coinductive_lfinite @ b @ ( product_fst @ ( coinductive_llist @ b ) @ d @ ysa ) )
% 2.48/1.48 => ( ( qa
% 2.48/1.48 @ ( product_case_prod @ ( coinductive_llist @ a ) @ c @ c
% 2.48/1.48 @ ^ [Xs3: coinductive_llist @ a,B2: c] : ( if @ c @ ( coinductive_lfinite @ a @ Xs3 ) @ B2 @ ( undefined @ c ) )
% 2.48/1.48 @ xsa )
% 2.48/1.48 @ ( product_case_prod @ ( coinductive_llist @ b ) @ d @ d
% 2.48/1.48 @ ^ [Xs3: coinductive_llist @ b,B2: d] : ( if @ d @ ( coinductive_lfinite @ b @ Xs3 ) @ B2 @ ( undefined @ d ) )
% 2.48/1.48 @ ysa ) )
% 2.48/1.48 => ( product_case_prod @ ( coinductive_llist @ a ) @ e @ ( ( product_prod @ ( coinductive_llist @ b ) @ f ) > $o )
% 2.48/1.48 @ ^ [Xs3: coinductive_llist @ a,B2: e] :
% 2.48/1.48 ( product_case_prod @ ( coinductive_llist @ b ) @ f @ $o
% 2.48/1.48 @ ^ [Ys3: coinductive_llist @ b,B6: f] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ a @ b @ pa @ Xs3 @ Ys3 )
% 2.48/1.48 & ( ( coinductive_lfinite @ a @ Xs3 )
% 2.48/1.48 => ( ra @ B2 @ B6 ) ) ) )
% 2.48/1.48 @ ( xs_a
% 2.48/1.48 @ ( product_case_prod @ ( coinductive_llist @ a ) @ c @ c
% 2.48/1.48 @ ^ [Xs3: coinductive_llist @ a,B2: c] : ( if @ c @ ( coinductive_lfinite @ a @ Xs3 ) @ B2 @ ( undefined @ c ) )
% 2.48/1.48 @ xsa ) )
% 2.48/1.48 @ ( ys_a
% 2.48/1.48 @ ( product_case_prod @ ( coinductive_llist @ b ) @ d @ d
% 2.48/1.48 @ ^ [Xs3: coinductive_llist @ b,B2: d] : ( if @ d @ ( coinductive_lfinite @ b @ Xs3 ) @ B2 @ ( undefined @ d ) )
% 2.48/1.48 @ ysa ) ) ) ) ) ) ).
% 2.48/1.48
% 2.48/1.48 thf(conj_2,conjecture,
% 2.48/1.48 ( product_case_prod @ ( coinductive_llist @ a ) @ e @ ( ( product_prod @ ( coinductive_llist @ b ) @ f ) > $o )
% 2.48/1.48 @ ^ [Xs3: coinductive_llist @ a,B2: e] :
% 2.48/1.48 ( product_case_prod @ ( coinductive_llist @ b ) @ f @ $o
% 2.48/1.48 @ ^ [Ys3: coinductive_llist @ b,B6: f] :
% 2.48/1.48 ( ( coindu1486289336t_all2 @ a @ b @ pa @ Xs3 @ Ys3 )
% 2.48/1.48 & ( ( coinductive_lfinite @ a @ Xs3 )
% 2.48/1.48 => ( ra @ B2 @ B6 ) ) ) )
% 2.48/1.48 @ ( product_case_prod @ ( coinductive_llist @ a ) @ c @ ( ( c > ( product_prod @ ( coinductive_llist @ a ) @ e ) ) > ( product_prod @ ( coinductive_llist @ a ) @ e ) )
% 2.48/1.48 @ ^ [Xs3: coinductive_llist @ a,B2: c,F2: c > ( product_prod @ ( coinductive_llist @ a ) @ e )] : ( product_apfst @ ( coinductive_llist @ a ) @ ( coinductive_llist @ a ) @ e @ ( coinductive_lappend @ a @ Xs3 ) @ ( F2 @ B2 ) )
% 2.48/1.48 @ xsa
% 2.48/1.48 @ xs_a )
% 2.48/1.48 @ ( product_case_prod @ ( coinductive_llist @ b ) @ d @ ( ( d > ( product_prod @ ( coinductive_llist @ b ) @ f ) ) > ( product_prod @ ( coinductive_llist @ b ) @ f ) )
% 2.48/1.48 @ ^ [Xs3: coinductive_llist @ b,B2: d,F2: d > ( product_prod @ ( coinductive_llist @ b ) @ f )] : ( product_apfst @ ( coinductive_llist @ b ) @ ( coinductive_llist @ b ) @ f @ ( coinductive_lappend @ b @ Xs3 ) @ ( F2 @ B2 ) )
% 2.48/1.48 @ ysa
% 2.48/1.48 @ ys_a ) ) ).
% 2.48/1.48 ------------------------
% 2.61/1.51 % (23576)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_23357 for (2999ds/27Mi)
% 2.61/1.51 % (23577)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23357 for (2999ds/2Mi)
% 2.61/1.51 % (23575)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_23357 for (2999ds/4Mi)
% 2.61/1.51 % (23578)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_23357 for (2999ds/2Mi)
% 2.61/1.51 % (23574)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23357 for (2999ds/183Mi)
% 2.61/1.51 % (23579)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_23357 for (2999ds/275Mi)
% 2.61/1.51 % (23577)Instruction limit reached!
% 2.61/1.51 % (23577)------------------------------
% 2.61/1.51 % (23577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.51 % (23577)Termination reason: Unknown
% 2.61/1.51 % (23577)Termination phase: shuffling
% 2.61/1.51
% 2.61/1.51 % (23577)Memory used [KB]: 1407
% 2.61/1.51 % (23577)Time elapsed: 0.003 s
% 2.61/1.51 % (23577)Instructions burned: 3 (million)
% 2.61/1.51 % (23577)------------------------------
% 2.61/1.51 % (23577)------------------------------
% 2.61/1.51 % (23578)Instruction limit reached!
% 2.61/1.51 % (23578)------------------------------
% 2.61/1.51 % (23578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.51 % (23578)Termination reason: Unknown
% 2.61/1.51 % (23578)Termination phase: shuffling
% 2.61/1.51
% 2.61/1.51 % (23578)Memory used [KB]: 1407
% 2.61/1.51 % (23578)Time elapsed: 0.003 s
% 2.61/1.51 % (23578)Instructions burned: 4 (million)
% 2.61/1.51 % (23578)------------------------------
% 2.61/1.51 % (23578)------------------------------
% 2.61/1.51 % (23575)Instruction limit reached!
% 2.61/1.51 % (23575)------------------------------
% 2.61/1.51 % (23575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.51 % (23575)Termination reason: Unknown
% 2.61/1.51 % (23575)Termination phase: shuffling
% 2.61/1.51
% 2.61/1.51 % (23575)Memory used [KB]: 1535
% 2.61/1.51 % (23575)Time elapsed: 0.004 s
% 2.61/1.51 % (23575)Instructions burned: 7 (million)
% 2.61/1.51 % (23575)------------------------------
% 2.61/1.51 % (23575)------------------------------
% 2.61/1.52 % (23580)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23357 for (2999ds/18Mi)
% 2.61/1.52 % (23576)Instruction limit reached!
% 2.61/1.52 % (23576)------------------------------
% 2.61/1.52 % (23576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.52 % (23576)Termination reason: Unknown
% 2.61/1.52 % (23576)Termination phase: Property scanning
% 2.61/1.52
% 2.61/1.52 % (23576)Memory used [KB]: 1918
% 2.61/1.52 % (23576)Time elapsed: 0.011 s
% 2.61/1.52 % (23576)Instructions burned: 27 (million)
% 2.61/1.52 % (23576)------------------------------
% 2.61/1.52 % (23576)------------------------------
% 2.61/1.52 % (23583)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23357 for (2999ds/3Mi)
% 2.61/1.52 % (23584)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_23357 for (2999ds/37Mi)
% 2.61/1.52 % (23587)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_23357 for (2999ds/15Mi)
% 2.61/1.52 % (23583)Instruction limit reached!
% 2.61/1.52 % (23583)------------------------------
% 2.61/1.52 % (23583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.52 % (23583)Termination reason: Unknown
% 2.61/1.52 % (23583)Termination phase: shuffling
% 2.61/1.52
% 2.61/1.52 % (23583)Memory used [KB]: 1407
% 2.61/1.52 % (23583)Time elapsed: 0.003 s
% 2.61/1.52 % (23583)Instructions burned: 5 (million)
% 2.61/1.52 % (23583)------------------------------
% 2.61/1.52 % (23583)------------------------------
% 2.61/1.53 % (23587)Instruction limit reached!
% 2.61/1.53 % (23587)------------------------------
% 2.61/1.53 % (23587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.53 % (23587)Termination reason: Unknown
% 2.61/1.53 % (23587)Termination phase: shuffling
% 2.61/1.53
% 2.61/1.53 % (23587)Memory used [KB]: 1791
% 2.61/1.53 % (23587)Time elapsed: 0.007 s
% 2.61/1.53 % (23587)Instructions burned: 17 (million)
% 2.61/1.53 % (23587)------------------------------
% 2.61/1.53 % (23587)------------------------------
% 2.61/1.53 % (23594)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_23357 for (2999ds/3Mi)
% 2.61/1.53 % (23580)Instruction limit reached!
% 2.61/1.53 % (23580)------------------------------
% 2.61/1.53 % (23580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.53 % (23594)Instruction limit reached!
% 2.61/1.53 % (23594)------------------------------
% 2.61/1.53 % (23594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.53 % (23594)Termination reason: Unknown
% 2.61/1.53 % (23580)Termination reason: Unknown
% 2.61/1.53 % (23594)Termination phase: shuffling
% 2.61/1.53
% 2.61/1.53 % (23594)Memory used [KB]: 1407
% 2.61/1.53 % (23594)Time elapsed: 0.002 s
% 2.61/1.53 % (23580)Termination phase: shuffling
% 2.61/1.53
% 2.61/1.53 % (23580)Memory used [KB]: 1791
% 2.61/1.53 % (23580)Time elapsed: 0.014 s
% 2.61/1.53 % (23580)Instructions burned: 18 (million)
% 2.61/1.53 % (23594)Instructions burned: 3 (million)
% 2.61/1.53 % (23594)------------------------------
% 2.61/1.53 % (23594)------------------------------
% 2.61/1.53 % (23580)------------------------------
% 2.61/1.53 % (23580)------------------------------
% 2.61/1.53 % (23584)Instruction limit reached!
% 2.61/1.53 % (23584)------------------------------
% 2.61/1.53 % (23584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.53 % (23584)Termination reason: Unknown
% 2.61/1.53 % (23584)Termination phase: shuffling
% 2.61/1.53
% 2.61/1.53 % (23584)Memory used [KB]: 2174
% 2.61/1.53 % (23584)Time elapsed: 0.012 s
% 2.61/1.53 % (23584)Instructions burned: 38 (million)
% 2.61/1.53 % (23584)------------------------------
% 2.61/1.53 % (23584)------------------------------
% 2.61/1.54 % (23601)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23357 for (2999ds/7Mi)
% 2.61/1.54 % (23598)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_23357 for (2999ds/1041Mi)
% 2.61/1.54 % (23602)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23357 for (2999ds/16Mi)
% 2.61/1.54 % (23601)Instruction limit reached!
% 2.61/1.54 % (23601)------------------------------
% 2.61/1.54 % (23601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.54 % (23601)Termination reason: Unknown
% 2.61/1.54 % (23601)Termination phase: shuffling
% 2.61/1.54
% 2.61/1.54 % (23601)Memory used [KB]: 1535
% 2.61/1.54 % (23601)Time elapsed: 0.004 s
% 2.61/1.54 % (23601)Instructions burned: 9 (million)
% 2.61/1.54 % (23601)------------------------------
% 2.61/1.54 % (23601)------------------------------
% 2.61/1.54 % (23605)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_23357 for (2999ds/3Mi)
% 2.61/1.54 % (23605)Instruction limit reached!
% 2.61/1.54 % (23605)------------------------------
% 2.61/1.54 % (23605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.54 % (23605)Termination reason: Unknown
% 2.61/1.54 % (23605)Termination phase: shuffling
% 2.61/1.54
% 2.61/1.54 % (23605)Memory used [KB]: 1407
% 2.61/1.54 % (23605)Time elapsed: 0.002 s
% 2.61/1.54 % (23605)Instructions burned: 3 (million)
% 2.61/1.54 % (23605)------------------------------
% 2.61/1.54 % (23605)------------------------------
% 2.61/1.55 % (23602)Instruction limit reached!
% 2.61/1.55 % (23602)------------------------------
% 2.61/1.55 % (23602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.55 % (23602)Termination reason: Unknown
% 2.61/1.55 % (23602)Termination phase: shuffling
% 2.61/1.55
% 2.61/1.55 % (23602)Memory used [KB]: 1791
% 2.61/1.55 % (23602)Time elapsed: 0.007 s
% 2.61/1.55 % (23602)Instructions burned: 18 (million)
% 2.61/1.55 % (23602)------------------------------
% 2.61/1.55 % (23602)------------------------------
% 2.61/1.55 % (23603)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_23357 for (2999ds/3Mi)
% 2.61/1.55 % (23603)Instruction limit reached!
% 2.61/1.55 % (23603)------------------------------
% 2.61/1.55 % (23603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.55 % (23603)Termination reason: Unknown
% 2.61/1.55 % (23603)Termination phase: shuffling
% 2.61/1.55
% 2.61/1.55 % (23603)Memory used [KB]: 1407
% 2.61/1.55 % (23603)Time elapsed: 0.004 s
% 2.61/1.55 % (23603)Instructions burned: 3 (million)
% 2.61/1.55 % (23603)------------------------------
% 2.61/1.55 % (23603)------------------------------
% 2.61/1.55 % (23608)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_23357 for (2999ds/7Mi)
% 2.61/1.55 % (23610)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_23357 for (2999ds/3Mi)
% 2.61/1.55 % (23608)Instruction limit reached!
% 2.61/1.55 % (23608)------------------------------
% 2.61/1.55 % (23608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.55 % (23608)Termination reason: Unknown
% 2.61/1.55 % (23608)Termination phase: shuffling
% 2.61/1.55
% 2.61/1.55 % (23608)Memory used [KB]: 1535
% 2.61/1.55 % (23608)Time elapsed: 0.004 s
% 2.61/1.55 % (23608)Instructions burned: 9 (million)
% 2.61/1.55 % (23608)------------------------------
% 2.61/1.55 % (23608)------------------------------
% 2.61/1.55 % (23610)Instruction limit reached!
% 2.61/1.55 % (23610)------------------------------
% 2.61/1.55 % (23610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.55 % (23610)Termination reason: Unknown
% 2.61/1.55 % (23610)Termination phase: shuffling
% 2.61/1.55
% 2.61/1.55 % (23610)Memory used [KB]: 1407
% 2.61/1.55 % (23610)Time elapsed: 0.002 s
% 2.61/1.55 % (23610)Instructions burned: 3 (million)
% 2.61/1.55 % (23610)------------------------------
% 2.61/1.55 % (23610)------------------------------
% 2.61/1.55 % (23613)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_23357 for (2999ds/4Mi)
% 2.61/1.56 % (23579)Refutation not found, incomplete strategy
% 2.61/1.56 % (23579)------------------------------
% 2.61/1.56 % (23579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.56 % (23579)Termination reason: Refutation not found, incomplete strategy
% 2.61/1.56
% 2.61/1.56
% 2.61/1.56 % (23579)Memory used [KB]: 7547
% 2.61/1.56 % (23579)Time elapsed: 0.047 s
% 2.61/1.56 % (23579)Instructions burned: 144 (million)
% 2.61/1.56 % (23579)------------------------------
% 2.61/1.56 % (23579)------------------------------
% 2.61/1.56 % (23613)Instruction limit reached!
% 2.61/1.56 % (23613)------------------------------
% 2.61/1.56 % (23613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.56 % (23613)Termination reason: Unknown
% 2.61/1.56 % (23613)Termination phase: shuffling
% 2.61/1.56
% 2.61/1.56 % (23613)Memory used [KB]: 1535
% 2.61/1.56 % (23613)Time elapsed: 0.003 s
% 2.61/1.56 % (23613)Instructions burned: 6 (million)
% 2.61/1.56 % (23613)------------------------------
% 2.61/1.56 % (23613)------------------------------
% 2.61/1.56 % (23619)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_23357 for (2999ds/710Mi)
% 2.61/1.56 % (23620)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23357 for (2999ds/6Mi)
% 2.61/1.56 % (23574)Instruction limit reached!
% 2.61/1.56 % (23574)------------------------------
% 2.61/1.56 % (23574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.56 % (23574)Termination reason: Unknown
% 2.61/1.56 % (23574)Termination phase: Saturation
% 2.61/1.56
% 2.61/1.56 % (23574)Memory used [KB]: 7291
% 2.61/1.56 % (23574)Time elapsed: 0.055 s
% 2.61/1.56 % (23574)Instructions burned: 184 (million)
% 2.61/1.56 % (23574)------------------------------
% 2.61/1.56 % (23574)------------------------------
% 2.61/1.56 % (23620)Instruction limit reached!
% 2.61/1.56 % (23620)------------------------------
% 2.61/1.56 % (23620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.56 % (23620)Termination reason: Unknown
% 2.61/1.56 % (23620)Termination phase: shuffling
% 2.61/1.56
% 2.61/1.56 % (23620)Memory used [KB]: 1535
% 2.61/1.56 % (23620)Time elapsed: 0.004 s
% 2.61/1.56 % (23620)Instructions burned: 8 (million)
% 2.61/1.56 % (23620)------------------------------
% 2.61/1.56 % (23620)------------------------------
% 2.61/1.57 % (23623)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_23357 for (2999ds/902Mi)
% 2.61/1.57 % (23624)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_23357 for (2999ds/21Mi)
% 2.61/1.57 % (23616)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_23357 for (2999ds/18Mi)
% 2.61/1.57 % (23624)Instruction limit reached!
% 2.61/1.57 % (23624)------------------------------
% 2.61/1.57 % (23624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.57 % (23624)Termination reason: Unknown
% 2.61/1.57 % (23624)Termination phase: shuffling
% 2.61/1.57
% 2.61/1.57 % (23624)Memory used [KB]: 1918
% 2.61/1.57 % (23624)Time elapsed: 0.009 s
% 2.61/1.57 % (23624)Instructions burned: 23 (million)
% 2.61/1.57 % (23624)------------------------------
% 2.61/1.57 % (23624)------------------------------
% 2.61/1.57 % (23629)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_23357 for (2999ds/5Mi)
% 2.61/1.57 % (23616)Instruction limit reached!
% 2.61/1.57 % (23616)------------------------------
% 2.61/1.57 % (23616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.57 % (23616)Termination reason: Unknown
% 2.61/1.57 % (23616)Termination phase: shuffling
% 2.61/1.57
% 2.61/1.57 % (23616)Memory used [KB]: 1791
% 2.61/1.57 % (23616)Time elapsed: 0.009 s
% 2.61/1.57 % (23616)Instructions burned: 18 (million)
% 2.61/1.57 % (23616)------------------------------
% 2.61/1.57 % (23616)------------------------------
% 2.61/1.57 % (23630)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_23357 for (2999ds/6Mi)
% 2.61/1.58 % (23629)Instruction limit reached!
% 2.61/1.58 % (23629)------------------------------
% 2.61/1.58 % (23629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.58 % (23629)Termination reason: Unknown
% 2.61/1.58 % (23629)Termination phase: shuffling
% 2.61/1.58
% 2.61/1.58 % (23629)Memory used [KB]: 1535
% 2.61/1.58 % (23629)Time elapsed: 0.003 s
% 2.61/1.58 % (23629)Instructions burned: 7 (million)
% 2.61/1.58 % (23629)------------------------------
% 2.61/1.58 % (23629)------------------------------
% 2.61/1.58 % (23630)Instruction limit reached!
% 2.61/1.58 % (23630)------------------------------
% 2.61/1.58 % (23630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.58 % (23630)Termination reason: Unknown
% 2.61/1.58 % (23630)Termination phase: shuffling
% 2.61/1.58
% 2.61/1.58 % (23630)Memory used [KB]: 1535
% 2.61/1.58 % (23630)Time elapsed: 0.003 s
% 2.61/1.58 % (23630)Instructions burned: 7 (million)
% 2.61/1.58 % (23630)------------------------------
% 2.61/1.58 % (23630)------------------------------
% 2.61/1.58 % (23634)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_23357 for (2999ds/377Mi)
% 2.61/1.58 % (23635)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_23357 for (2999ds/779Mi)
% 2.61/1.59 % (23637)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_23357 for (2999ds/19Mi)
% 2.61/1.59 % (23638)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_23357 for (2999ds/879Mi)
% 2.61/1.59 % (23637)Instruction limit reached!
% 2.61/1.59 % (23637)------------------------------
% 2.61/1.59 % (23637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.59 % (23637)Termination reason: Unknown
% 2.61/1.59 % (23637)Termination phase: shuffling
% 2.61/1.59
% 2.61/1.59 % (23637)Memory used [KB]: 1791
% 2.61/1.59 % (23637)Time elapsed: 0.007 s
% 2.61/1.59 % (23637)Instructions burned: 20 (million)
% 2.61/1.59 % (23637)------------------------------
% 2.61/1.59 % (23637)------------------------------
% 2.61/1.60 % (23645)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_23357 for (2998ds/17Mi)
% 2.61/1.61 % (23645)Instruction limit reached!
% 2.61/1.61 % (23645)------------------------------
% 2.61/1.61 % (23645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.61 % (23645)Termination reason: Unknown
% 2.61/1.61 % (23645)Termination phase: shuffling
% 2.61/1.61
% 2.61/1.61 % (23645)Memory used [KB]: 1791
% 2.61/1.61 % (23645)Time elapsed: 0.008 s
% 2.61/1.61 % (23645)Instructions burned: 18 (million)
% 2.61/1.61 % (23645)------------------------------
% 2.61/1.61 % (23645)------------------------------
% 2.61/1.61 % (23623)Refutation not found, incomplete strategy
% 2.61/1.61 % (23623)------------------------------
% 2.61/1.61 % (23623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.61 % (23623)Termination reason: Refutation not found, incomplete strategy
% 2.61/1.61
% 2.61/1.61
% 2.61/1.61 % (23623)Memory used [KB]: 7547
% 2.61/1.61 % (23623)Time elapsed: 0.049 s
% 2.61/1.61 % (23623)Instructions burned: 160 (million)
% 2.61/1.61 % (23623)------------------------------
% 2.61/1.61 % (23623)------------------------------
% 2.61/1.62 % (23649)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_23357 for (2998ds/3Mi)
% 2.61/1.62 % (23649)Instruction limit reached!
% 2.61/1.62 % (23649)------------------------------
% 2.61/1.62 % (23649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.62 % (23649)Termination reason: Unknown
% 2.61/1.62 % (23649)Termination phase: shuffling
% 2.61/1.62
% 2.61/1.62 % (23649)Memory used [KB]: 1407
% 2.61/1.62 % (23649)Time elapsed: 0.003 s
% 2.61/1.62 % (23649)Instructions burned: 6 (million)
% 2.61/1.62 % (23649)------------------------------
% 2.61/1.62 % (23649)------------------------------
% 2.61/1.62 % (23654)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_23357 for (2998ds/30Mi)
% 2.61/1.63 % (23657)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_23357 for (2998ds/127Mi)
% 2.61/1.63 % (23654)Instruction limit reached!
% 2.61/1.63 % (23654)------------------------------
% 2.61/1.63 % (23654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.63 % (23654)Termination reason: Unknown
% 2.61/1.63 % (23654)Termination phase: Property scanning
% 2.61/1.63
% 2.61/1.63 % (23654)Memory used [KB]: 2046
% 2.61/1.63 % (23654)Time elapsed: 0.011 s
% 2.61/1.63 % (23654)Instructions burned: 30 (million)
% 2.61/1.63 % (23654)------------------------------
% 2.61/1.63 % (23654)------------------------------
% 2.61/1.64 % (23664)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_23357 for (2998ds/100Mi)
% 2.61/1.67 % (23657)Instruction limit reached!
% 2.61/1.67 % (23657)------------------------------
% 2.61/1.67 % (23657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.67 % (23657)Termination reason: Unknown
% 2.61/1.67 % (23657)Termination phase: Saturation
% 2.61/1.67
% 2.61/1.67 % (23657)Memory used [KB]: 7036
% 2.61/1.67 % (23657)Time elapsed: 0.039 s
% 2.61/1.67 % (23657)Instructions burned: 128 (million)
% 2.61/1.67 % (23657)------------------------------
% 2.61/1.67 % (23657)------------------------------
% 2.61/1.67 % (23664)Instruction limit reached!
% 2.61/1.67 % (23664)------------------------------
% 2.61/1.67 % (23664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.67 % (23664)Termination reason: Unknown
% 2.61/1.67 % (23664)Termination phase: Property scanning
% 2.61/1.67
% 2.61/1.67 % (23664)Memory used [KB]: 2686
% 2.61/1.67 % (23664)Time elapsed: 0.030 s
% 2.61/1.67 % (23664)Instructions burned: 103 (million)
% 2.61/1.67 % (23664)------------------------------
% 2.61/1.67 % (23664)------------------------------
% 2.61/1.68 % (23675)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_23357 for (2998ds/3Mi)
% 2.61/1.68 % (23675)Instruction limit reached!
% 2.61/1.68 % (23675)------------------------------
% 2.61/1.68 % (23675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.68 % (23675)Termination reason: Unknown
% 2.61/1.68 % (23675)Termination phase: shuffling
% 2.61/1.68
% 2.61/1.68 % (23675)Memory used [KB]: 1407
% 2.61/1.68 % (23675)Time elapsed: 0.002 s
% 2.61/1.68 % (23675)Instructions burned: 3 (million)
% 2.61/1.68 % (23675)------------------------------
% 2.61/1.68 % (23675)------------------------------
% 2.61/1.68 % (23678)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_23357 for (2998ds/20Mi)
% 2.61/1.69 % (23679)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_23357 for (2997ds/86Mi)
% 2.61/1.69 % (23678)Instruction limit reached!
% 2.61/1.69 % (23678)------------------------------
% 2.61/1.69 % (23678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.69 % (23678)Termination reason: Unknown
% 2.61/1.69 % (23678)Termination phase: shuffling
% 2.61/1.69
% 2.61/1.69 % (23678)Memory used [KB]: 1918
% 2.61/1.69 % (23678)Time elapsed: 0.008 s
% 2.61/1.69 % (23678)Instructions burned: 21 (million)
% 2.61/1.69 % (23678)------------------------------
% 2.61/1.69 % (23678)------------------------------
% 2.61/1.70 % (23634)Instruction limit reached!
% 2.61/1.70 % (23634)------------------------------
% 2.61/1.70 % (23634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.70 % (23634)Termination reason: Unknown
% 2.61/1.70 % (23634)Termination phase: Saturation
% 2.61/1.70
% 2.61/1.70 % (23634)Memory used [KB]: 8443
% 2.61/1.70 % (23634)Time elapsed: 0.115 s
% 2.61/1.70 % (23634)Instructions burned: 378 (million)
% 2.61/1.70 % (23634)------------------------------
% 2.61/1.70 % (23634)------------------------------
% 2.61/1.70 % (23686)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_23357 for (2997ds/107Mi)
% 2.61/1.71 % (23689)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_23357 for (2997ds/39Mi)
% 2.61/1.71 % (23679)Instruction limit reached!
% 2.61/1.71 % (23679)------------------------------
% 2.61/1.71 % (23679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.71 % (23679)Termination reason: Unknown
% 2.61/1.71 % (23679)Termination phase: Property scanning
% 2.61/1.71
% 2.61/1.71 % (23679)Memory used [KB]: 2558
% 2.61/1.71 % (23679)Time elapsed: 0.028 s
% 2.61/1.71 % (23679)Instructions burned: 87 (million)
% 2.61/1.71 % (23679)------------------------------
% 2.61/1.71 % (23679)------------------------------
% 2.61/1.72 % (23689)Instruction limit reached!
% 2.61/1.72 % (23689)------------------------------
% 2.61/1.72 % (23689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.72 % (23689)Termination reason: Unknown
% 2.61/1.72 % (23689)Termination phase: shuffling
% 2.61/1.72
% 2.61/1.72 % (23689)Memory used [KB]: 2174
% 2.61/1.72 % (23689)Time elapsed: 0.013 s
% 2.61/1.72 % (23689)Instructions burned: 40 (million)
% 2.61/1.72 % (23689)------------------------------
% 2.61/1.72 % (23689)------------------------------
% 2.61/1.72 % (23696)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_23357 for (2997ds/448Mi)
% 2.61/1.73 % (23700)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_23357 for (2997ds/46Mi)
% 2.61/1.73 % (23686)Instruction limit reached!
% 2.61/1.73 % (23686)------------------------------
% 2.61/1.73 % (23686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.73 % (23686)Termination reason: Unknown
% 2.61/1.73 % (23686)Termination phase: Property scanning
% 2.61/1.73
% 2.61/1.73 % (23686)Memory used [KB]: 2558
% 2.61/1.73 % (23686)Time elapsed: 0.034 s
% 2.61/1.73 % (23686)Instructions burned: 109 (million)
% 2.61/1.73 % (23686)------------------------------
% 2.61/1.73 % (23686)------------------------------
% 2.61/1.74 % (23706)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_23357 for (2997ds/98Mi)
% 2.61/1.74 % (23700)Instruction limit reached!
% 2.61/1.74 % (23700)------------------------------
% 2.61/1.74 % (23700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.74 % (23700)Termination reason: Unknown
% 2.61/1.74 % (23700)Termination phase: Preprocessing 1
% 2.61/1.74
% 2.61/1.74 % (23700)Memory used [KB]: 1918
% 2.61/1.74 % (23700)Time elapsed: 0.015 s
% 2.61/1.74 % (23700)Instructions burned: 46 (million)
% 2.61/1.74 % (23700)------------------------------
% 2.61/1.74 % (23700)------------------------------
% 2.61/1.75 % (23714)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_23357 for (2997ds/507Mi)
% 2.61/1.77 % (23706)Instruction limit reached!
% 2.61/1.77 % (23706)------------------------------
% 2.61/1.77 % (23706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.77 % (23706)Termination reason: Unknown
% 2.61/1.77 % (23706)Termination phase: Property scanning
% 2.61/1.77
% 2.61/1.77 % (23706)Memory used [KB]: 2686
% 2.61/1.77 % (23706)Time elapsed: 0.029 s
% 2.61/1.77 % (23706)Instructions burned: 98 (million)
% 2.61/1.77 % (23706)------------------------------
% 2.61/1.77 % (23706)------------------------------
% 2.61/1.78 % (23734)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_23357 for (2997ds/149Mi)
% 2.61/1.79 % (23619)Instruction limit reached!
% 2.61/1.79 % (23619)------------------------------
% 2.61/1.79 % (23619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.79 % (23619)Termination reason: Unknown
% 2.61/1.79 % (23619)Termination phase: Saturation
% 2.61/1.79
% 2.61/1.79 % (23619)Memory used [KB]: 8315
% 2.61/1.79 % (23619)Time elapsed: 0.225 s
% 2.61/1.79 % (23619)Instructions burned: 711 (million)
% 2.61/1.79 % (23619)------------------------------
% 2.61/1.79 % (23619)------------------------------
% 2.61/1.80 % (23740)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_23357 for (2996ds/39Mi)
% 2.61/1.81 % (23740)Instruction limit reached!
% 2.61/1.81 % (23740)------------------------------
% 2.61/1.81 % (23740)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.81 % (23740)Termination reason: Unknown
% 2.61/1.81 % (23740)Termination phase: Preprocessing 1
% 2.61/1.81
% 2.61/1.81 % (23740)Memory used [KB]: 1918
% 2.61/1.81 % (23740)Time elapsed: 0.013 s
% 2.61/1.81 % (23740)Instructions burned: 39 (million)
% 2.61/1.81 % (23740)------------------------------
% 2.61/1.81 % (23740)------------------------------
% 2.61/1.82 % (23745)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_23357 for (2996ds/6Mi)
% 2.61/1.82 % (23745)Instruction limit reached!
% 2.61/1.82 % (23745)------------------------------
% 2.61/1.82 % (23745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.82 % (23745)Termination reason: Unknown
% 2.61/1.82 % (23745)Termination phase: shuffling
% 2.61/1.82
% 2.61/1.82 % (23745)Memory used [KB]: 1535
% 2.61/1.82 % (23745)Time elapsed: 0.004 s
% 2.61/1.82 % (23745)Instructions burned: 9 (million)
% 2.61/1.82 % (23745)------------------------------
% 2.61/1.82 % (23745)------------------------------
% 2.61/1.82 % (23734)Instruction limit reached!
% 2.61/1.82 % (23734)------------------------------
% 2.61/1.82 % (23734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.82 % (23734)Termination reason: Unknown
% 2.61/1.82 % (23734)Termination phase: Saturation
% 2.61/1.82
% 2.61/1.82 % (23734)Memory used [KB]: 7164
% 2.61/1.82 % (23734)Time elapsed: 0.045 s
% 2.61/1.82 % (23734)Instructions burned: 150 (million)
% 2.61/1.82 % (23734)------------------------------
% 2.61/1.82 % (23734)------------------------------
% 2.61/1.83 % (23635)Instruction limit reached!
% 2.61/1.83 % (23635)------------------------------
% 2.61/1.83 % (23635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.83 % (23635)Termination reason: Unknown
% 2.61/1.83 % (23635)Termination phase: Saturation
% 2.61/1.83
% 2.61/1.83 % (23635)Memory used [KB]: 9466
% 2.61/1.83 % (23635)Time elapsed: 0.244 s
% 2.61/1.83 % (23635)Instructions burned: 781 (million)
% 2.61/1.83 % (23635)------------------------------
% 2.61/1.83 % (23635)------------------------------
% 2.61/1.83 % (23746)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_23357 for (2996ds/1087Mi)
% 2.61/1.83 % (23747)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_23357 for (2996ds/47Mi)
% 2.61/1.84 % (23748)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_23357 for (2996ds/44Mi)
% 2.61/1.85 % (23747)Instruction limit reached!
% 2.61/1.85 % (23747)------------------------------
% 2.61/1.85 % (23747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.85 % (23747)Termination reason: Unknown
% 2.61/1.85 % (23747)Termination phase: Preprocessing 3
% 2.61/1.85
% 2.61/1.85 % (23747)Memory used [KB]: 2174
% 2.61/1.85 % (23747)Time elapsed: 0.016 s
% 2.61/1.85 % (23747)Instructions burned: 48 (million)
% 2.61/1.85 % (23747)------------------------------
% 2.61/1.85 % (23747)------------------------------
% 2.61/1.85 % (23748)Instruction limit reached!
% 2.61/1.85 % (23748)------------------------------
% 2.61/1.85 % (23748)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.85 % (23748)Termination reason: Unknown
% 2.61/1.85 % (23748)Termination phase: Property scanning
% 2.61/1.85
% 2.61/1.85 % (23748)Memory used [KB]: 2302
% 2.61/1.85 % (23748)Time elapsed: 0.014 s
% 2.61/1.85 % (23748)Instructions burned: 46 (million)
% 2.61/1.85 % (23748)------------------------------
% 2.61/1.85 % (23748)------------------------------
% 2.61/1.86 % (23749)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_23357 for (2996ds/432Mi)
% 2.61/1.86 % (23750)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_23357 for (2996ds/62Mi)
% 2.61/1.86 % (23638)Instruction limit reached!
% 2.61/1.86 % (23638)------------------------------
% 2.61/1.86 % (23638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.86 % (23638)Termination reason: Unknown
% 2.61/1.86 % (23638)Termination phase: Saturation
% 2.61/1.86
% 2.61/1.86 % (23638)Memory used [KB]: 8443
% 2.61/1.86 % (23638)Time elapsed: 0.298 s
% 2.61/1.86 % (23638)Instructions burned: 879 (million)
% 2.61/1.86 % (23638)------------------------------
% 2.61/1.86 % (23638)------------------------------
% 2.61/1.86 % (23696)Instruction limit reached!
% 2.61/1.86 % (23696)------------------------------
% 2.61/1.86 % (23696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.86 % (23696)Termination reason: Unknown
% 2.61/1.86 % (23696)Termination phase: Saturation
% 2.61/1.86
% 2.61/1.86 % (23696)Memory used [KB]: 9466
% 2.61/1.86 % (23696)Time elapsed: 0.140 s
% 2.61/1.86 % (23696)Instructions burned: 450 (million)
% 2.61/1.86 % (23696)------------------------------
% 2.61/1.86 % (23696)------------------------------
% 2.61/1.86 % (23598)Instruction limit reached!
% 2.61/1.86 % (23598)------------------------------
% 2.61/1.86 % (23598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.86 % (23598)Termination reason: Unknown
% 2.61/1.86 % (23598)Termination phase: Saturation
% 2.61/1.86
% 2.61/1.86 % (23598)Memory used [KB]: 9594
% 2.61/1.86 % (23598)Time elapsed: 0.327 s
% 2.61/1.86 % (23598)Instructions burned: 1043 (million)
% 2.61/1.86 % (23598)------------------------------
% 2.61/1.86 % (23598)------------------------------
% 2.61/1.87 % (23751)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_23357 for (2996ds/31Mi)
% 2.61/1.87 % (23752)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_23357 for (2996ds/96Mi)
% 2.61/1.87 % (23753)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_23357 for (2996ds/453Mi)
% 2.61/1.88 % (23750)Instruction limit reached!
% 2.61/1.88 % (23750)------------------------------
% 2.61/1.88 % (23750)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.88 % (23750)Termination reason: Unknown
% 2.61/1.88 % (23750)Termination phase: Property scanning
% 2.61/1.88
% 2.61/1.88 % (23750)Memory used [KB]: 2302
% 2.61/1.88 % (23750)Time elapsed: 0.018 s
% 2.61/1.88 % (23750)Instructions burned: 62 (million)
% 2.61/1.88 % (23750)------------------------------
% 2.61/1.88 % (23750)------------------------------
% 2.61/1.88 % (23751)Instruction limit reached!
% 2.61/1.88 % (23751)------------------------------
% 2.61/1.88 % (23751)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.88 % (23751)Termination reason: Unknown
% 2.61/1.88 % (23751)Termination phase: Property scanning
% 2.61/1.88
% 2.61/1.88 % (23751)Memory used [KB]: 1918
% 2.61/1.88 % (23751)Time elapsed: 0.011 s
% 2.61/1.88 % (23751)Instructions burned: 31 (million)
% 2.61/1.88 % (23751)------------------------------
% 2.61/1.88 % (23751)------------------------------
% 2.61/1.89 % (23754)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_23357 for (2996ds/71Mi)
% 2.61/1.89 % (23755)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_23357 for (2996ds/83Mi)
% 2.61/1.90 % (23752)Instruction limit reached!
% 2.61/1.90 % (23752)------------------------------
% 2.61/1.90 % (23752)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.90 % (23752)Termination reason: Unknown
% 2.61/1.90 % (23752)Termination phase: Property scanning
% 2.61/1.90
% 2.61/1.90 % (23752)Memory used [KB]: 2558
% 2.61/1.90 % (23752)Time elapsed: 0.030 s
% 2.61/1.90 % (23752)Instructions burned: 96 (million)
% 2.61/1.90 % (23752)------------------------------
% 2.61/1.90 % (23752)------------------------------
% 2.61/1.90 % (23714)Instruction limit reached!
% 2.61/1.90 % (23714)------------------------------
% 2.61/1.90 % (23714)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.90 % (23714)Termination reason: Unknown
% 2.61/1.90 % (23714)Termination phase: Saturation
% 2.61/1.90
% 2.61/1.90 % (23714)Memory used [KB]: 8443
% 2.61/1.90 % (23714)Time elapsed: 0.151 s
% 2.61/1.90 % (23714)Instructions burned: 509 (million)
% 2.61/1.90 % (23714)------------------------------
% 2.61/1.90 % (23714)------------------------------
% 2.61/1.91 % (23754)Instruction limit reached!
% 2.61/1.91 % (23754)------------------------------
% 2.61/1.91 % (23754)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.91 % (23754)Termination reason: Unknown
% 2.61/1.91 % (23754)Termination phase: Property scanning
% 2.61/1.91
% 2.61/1.91 % (23754)Memory used [KB]: 2302
% 2.61/1.91 % (23754)Time elapsed: 0.023 s
% 2.61/1.91 % (23754)Instructions burned: 71 (million)
% 2.61/1.91 % (23754)------------------------------
% 2.61/1.91 % (23754)------------------------------
% 2.61/1.91 % (23756)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_23357 for (2995ds/11Mi)
% 2.61/1.91 % (23757)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_23357 for (2995ds/41Mi)
% 2.61/1.91 % (23756)Instruction limit reached!
% 2.61/1.91 % (23756)------------------------------
% 2.61/1.91 % (23756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.91 % (23756)Termination reason: Unknown
% 2.61/1.91 % (23756)Termination phase: shuffling
% 2.61/1.91
% 2.61/1.91 % (23756)Memory used [KB]: 1663
% 2.61/1.91 % (23756)Time elapsed: 0.005 s
% 2.61/1.91 % (23756)Instructions burned: 14 (million)
% 2.61/1.91 % (23756)------------------------------
% 2.61/1.91 % (23756)------------------------------
% 2.61/1.92 % (23755)Instruction limit reached!
% 2.61/1.92 % (23755)------------------------------
% 2.61/1.92 % (23755)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.92 % (23755)Termination reason: Unknown
% 2.61/1.92 % (23755)Termination phase: Property scanning
% 2.61/1.92
% 2.61/1.92 % (23755)Memory used [KB]: 2302
% 2.61/1.92 % (23755)Time elapsed: 0.027 s
% 2.61/1.92 % (23755)Instructions burned: 84 (million)
% 2.61/1.92 % (23755)------------------------------
% 2.61/1.92 % (23755)------------------------------
% 2.61/1.92 % (23758)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23357 for (2995ds/6Mi)
% 2.61/1.92 % (23758)Instruction limit reached!
% 2.61/1.92 % (23758)------------------------------
% 2.61/1.92 % (23758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.92 % (23758)Termination reason: Unknown
% 2.61/1.92 % (23758)Termination phase: shuffling
% 2.61/1.92
% 2.61/1.92 % (23758)Memory used [KB]: 1535
% 2.61/1.92 % (23758)Time elapsed: 0.003 s
% 2.61/1.92 % (23758)Instructions burned: 6 (million)
% 2.61/1.92 % (23758)------------------------------
% 2.61/1.92 % (23758)------------------------------
% 2.61/1.92 % (23757)Instruction limit reached!
% 2.61/1.92 % (23757)------------------------------
% 2.61/1.92 % (23757)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.92 % (23757)Termination reason: Unknown
% 2.61/1.92 % (23757)Termination phase: shuffling
% 2.61/1.92
% 2.61/1.92 % (23757)Memory used [KB]: 2302
% 2.61/1.92 % (23757)Time elapsed: 0.013 s
% 2.61/1.92 % (23757)Instructions burned: 42 (million)
% 2.61/1.92 % (23757)------------------------------
% 2.61/1.92 % (23757)------------------------------
% 2.61/1.92 % (23759)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_23357 for (2995ds/150Mi)
% 2.61/1.93 % (23760)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_23357 for (2995ds/343Mi)
% 2.61/1.93 % (23761)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_23357 for (2995ds/109Mi)
% 2.61/1.93 % (23762)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_23357 for (2995ds/253Mi)
% 2.61/1.96 % (23761)Instruction limit reached!
% 2.61/1.96 % (23761)------------------------------
% 2.61/1.96 % (23761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.96 % (23761)Termination reason: Unknown
% 2.61/1.96 % (23761)Termination phase: Saturation
% 2.61/1.96
% 2.61/1.96 % (23761)Memory used [KB]: 7036
% 2.61/1.96 % (23761)Time elapsed: 0.035 s
% 2.61/1.96 % (23761)Instructions burned: 111 (million)
% 2.61/1.96 % (23761)------------------------------
% 2.61/1.96 % (23761)------------------------------
% 2.61/1.97 % (23759)Instruction limit reached!
% 2.61/1.97 % (23759)------------------------------
% 2.61/1.97 % (23759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.97 % (23759)Termination reason: Unknown
% 2.61/1.97 % (23759)Termination phase: Saturation
% 2.61/1.97
% 2.61/1.97 % (23759)Memory used [KB]: 7291
% 2.61/1.97 % (23759)Time elapsed: 0.048 s
% 2.61/1.97 % (23759)Instructions burned: 152 (million)
% 2.61/1.97 % (23759)------------------------------
% 2.61/1.97 % (23759)------------------------------
% 2.61/1.97 % (23763)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_23357 for (2995ds/140Mi)
% 2.61/1.98 % (23764)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_23357 for (2995ds/614Mi)
% 2.61/1.99 % (23749)Instruction limit reached!
% 2.61/1.99 % (23749)------------------------------
% 2.61/1.99 % (23749)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/1.99 % (23749)Termination reason: Unknown
% 2.61/1.99 % (23749)Termination phase: Saturation
% 2.61/1.99
% 2.61/1.99 % (23749)Memory used [KB]: 4221
% 2.61/1.99 % (23749)Time elapsed: 0.137 s
% 2.61/1.99 % (23749)Instructions burned: 433 (million)
% 2.61/1.99 % (23749)------------------------------
% 2.61/1.99 % (23749)------------------------------
% 2.61/2.00 % (23765)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_23357 for (2994ds/202Mi)
% 2.61/2.01 % (23753)Instruction limit reached!
% 2.61/2.01 % (23753)------------------------------
% 2.61/2.01 % (23753)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.61/2.01 % (23753)Termination reason: Unknown
% 2.61/2.01 % (23753)Termination phase: Saturation
% 2.61/2.01
% 2.61/2.01 % (23753)Memory used [KB]: 8827
% 2.61/2.01 % (23753)Time elapsed: 0.134 s
% 2.61/2.01 % (23753)Instructions burned: 455 (million)
% 2.61/2.01 % (23753)------------------------------
% 2.61/2.01 % (23753)------------------------------
% 6.14/2.02 % (23763)Instruction limit reached!
% 6.14/2.02 % (23763)------------------------------
% 6.14/2.02 % (23763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.14/2.02 % (23763)Termination reason: Unknown
% 6.14/2.02 % (23763)Termination phase: Saturation
% 6.14/2.02
% 6.14/2.02 % (23763)Memory used [KB]: 7291
% 6.14/2.02 % (23763)Time elapsed: 0.045 s
% 6.14/2.02 % (23763)Instructions burned: 142 (million)
% 6.14/2.02 % (23763)------------------------------
% 6.14/2.02 % (23763)------------------------------
% 6.14/2.02 % (23766)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_23357 for (2994ds/339Mi)
% 6.14/2.03 % (23767)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_23357 for (2994ds/283Mi)
% 6.14/2.03 % (23762)Instruction limit reached!
% 6.14/2.03 % (23762)------------------------------
% 6.14/2.03 % (23762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.14/2.03 % (23762)Termination reason: Unknown
% 6.14/2.03 % (23762)Termination phase: Saturation
% 6.14/2.03
% 6.14/2.03 % (23762)Memory used [KB]: 8699
% 6.14/2.03 % (23762)Time elapsed: 0.094 s
% 6.14/2.03 % (23762)Instructions burned: 254 (million)
% 6.14/2.03 % (23762)------------------------------
% 6.14/2.03 % (23762)------------------------------
% 6.14/2.03 % (23760)Instruction limit reached!
% 6.14/2.03 % (23760)------------------------------
% 6.14/2.03 % (23760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.14/2.03 % (23760)Termination reason: Unknown
% 6.14/2.03 % (23760)Termination phase: Saturation
% 6.14/2.03
% 6.14/2.03 % (23760)Memory used [KB]: 8315
% 6.14/2.03 % (23760)Time elapsed: 0.109 s
% 6.14/2.03 % (23760)Instructions burned: 345 (million)
% 6.14/2.03 % (23760)------------------------------
% 6.14/2.03 % (23760)------------------------------
% 6.14/2.04 % (23769)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_23357 for (2994ds/298Mi)
% 6.14/2.05 % (23768)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_23357 for (2994ds/134Mi)
% 6.14/2.06 % (23765)Instruction limit reached!
% 6.14/2.06 % (23765)------------------------------
% 6.14/2.06 % (23765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.14/2.06 % (23765)Termination reason: Unknown
% 6.14/2.06 % (23765)Termination phase: Saturation
% 6.14/2.06
% 6.14/2.06 % (23765)Memory used [KB]: 8443
% 6.14/2.06 % (23765)Time elapsed: 0.063 s
% 6.14/2.06 % (23765)Instructions burned: 202 (million)
% 6.14/2.06 % (23765)------------------------------
% 6.14/2.06 % (23765)------------------------------
% 6.14/2.07 % (23770)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_23357 for (2994ds/192Mi)
% 6.47/2.11 % (23767)Instruction limit reached!
% 6.47/2.11 % (23767)------------------------------
% 6.47/2.11 % (23767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.11 % (23767)Termination reason: Unknown
% 6.47/2.11 % (23767)Termination phase: Saturation
% 6.47/2.11
% 6.47/2.11 % (23767)Memory used [KB]: 7675
% 6.47/2.11 % (23767)Time elapsed: 0.089 s
% 6.47/2.11 % (23767)Instructions burned: 283 (million)
% 6.47/2.11 % (23767)------------------------------
% 6.47/2.11 % (23767)------------------------------
% 6.47/2.11 % (23768)Instruction limit reached!
% 6.47/2.11 % (23768)------------------------------
% 6.47/2.11 % (23768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.11 % (23768)Termination reason: Unknown
% 6.47/2.11 % (23768)Termination phase: Saturation
% 6.47/2.11
% 6.47/2.11 % (23768)Memory used [KB]: 7164
% 6.47/2.11 % (23768)Time elapsed: 0.070 s
% 6.47/2.11 % (23768)Instructions burned: 134 (million)
% 6.47/2.11 % (23768)------------------------------
% 6.47/2.11 % (23768)------------------------------
% 6.47/2.12 % (23766)Instruction limit reached!
% 6.47/2.12 % (23766)------------------------------
% 6.47/2.12 % (23766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.12 % (23766)Termination reason: Unknown
% 6.47/2.12 % (23766)Termination phase: Saturation
% 6.47/2.12
% 6.47/2.12 % (23766)Memory used [KB]: 7419
% 6.47/2.12 % (23766)Time elapsed: 0.106 s
% 6.47/2.12 % (23766)Instructions burned: 339 (million)
% 6.47/2.12 % (23766)------------------------------
% 6.47/2.12 % (23766)------------------------------
% 6.47/2.12 % (23772)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_23357 for (2993ds/90Mi)
% 6.47/2.12 % (23771)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_23357 for (2993ds/258Mi)
% 6.47/2.13 % (23769)Instruction limit reached!
% 6.47/2.13 % (23769)------------------------------
% 6.47/2.13 % (23769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.13 % (23769)Termination reason: Unknown
% 6.47/2.13 % (23769)Termination phase: Saturation
% 6.47/2.13
% 6.47/2.13 % (23769)Memory used [KB]: 8955
% 6.47/2.13 % (23769)Time elapsed: 0.087 s
% 6.47/2.13 % (23769)Instructions burned: 298 (million)
% 6.47/2.13 % (23769)------------------------------
% 6.47/2.13 % (23769)------------------------------
% 6.47/2.13 % (23773)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_23357 for (2993ds/231Mi)
% 6.47/2.13 % (23770)Instruction limit reached!
% 6.47/2.13 % (23770)------------------------------
% 6.47/2.13 % (23770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.13 % (23770)Termination reason: Unknown
% 6.47/2.13 % (23770)Termination phase: Saturation
% 6.47/2.13
% 6.47/2.13 % (23770)Memory used [KB]: 3837
% 6.47/2.13 % (23770)Time elapsed: 0.059 s
% 6.47/2.13 % (23770)Instructions burned: 192 (million)
% 6.47/2.13 % (23770)------------------------------
% 6.47/2.13 % (23770)------------------------------
% 6.47/2.14 % (23774)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_23357 for (2993ds/458Mi)
% 6.47/2.14 % (23775)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_23357 for (2993ds/31Mi)
% 6.47/2.15 % (23772)Instruction limit reached!
% 6.47/2.15 % (23772)------------------------------
% 6.47/2.15 % (23772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.15 % (23772)Termination reason: Unknown
% 6.47/2.15 % (23772)Termination phase: Property scanning
% 6.47/2.15
% 6.47/2.15 % (23772)Memory used [KB]: 2558
% 6.47/2.15 % (23772)Time elapsed: 0.028 s
% 6.47/2.15 % (23772)Instructions burned: 91 (million)
% 6.47/2.15 % (23772)------------------------------
% 6.47/2.15 % (23772)------------------------------
% 6.47/2.15 % (23775)Instruction limit reached!
% 6.47/2.15 % (23775)------------------------------
% 6.47/2.15 % (23775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.15 % (23775)Termination reason: Unknown
% 6.47/2.15 % (23775)Termination phase: Property scanning
% 6.47/2.15
% 6.47/2.15 % (23775)Memory used [KB]: 1918
% 6.47/2.15 % (23775)Time elapsed: 0.011 s
% 6.47/2.15 % (23775)Instructions burned: 31 (million)
% 6.47/2.15 % (23775)------------------------------
% 6.47/2.15 % (23775)------------------------------
% 6.47/2.16 % (23776)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_23357 for (2993ds/297Mi)
% 6.47/2.16 % (23778)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_23357 for (2993ds/987Mi)
% 6.47/2.17 % (23764)Instruction limit reached!
% 6.47/2.17 % (23764)------------------------------
% 6.47/2.17 % (23764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.17 % (23764)Termination reason: Unknown
% 6.47/2.17 % (23764)Termination phase: Saturation
% 6.47/2.17
% 6.47/2.17 % (23764)Memory used [KB]: 8699
% 6.47/2.17 % (23764)Time elapsed: 0.189 s
% 6.47/2.17 % (23764)Instructions burned: 615 (million)
% 6.47/2.17 % (23764)------------------------------
% 6.47/2.17 % (23764)------------------------------
% 6.47/2.17 % (23746)Instruction limit reached!
% 6.47/2.17 % (23746)------------------------------
% 6.47/2.17 % (23746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.17 % (23746)Termination reason: Unknown
% 6.47/2.17 % (23746)Termination phase: Saturation
% 6.47/2.17
% 6.47/2.17 % (23746)Memory used [KB]: 8699
% 6.47/2.17 % (23746)Time elapsed: 0.346 s
% 6.47/2.17 % (23746)Instructions burned: 1089 (million)
% 6.47/2.17 % (23746)------------------------------
% 6.47/2.17 % (23746)------------------------------
% 6.47/2.18 % (23779)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_23357 for (2993ds/182Mi)
% 6.47/2.18 % (23780)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_23357 for (2993ds/182Mi)
% 6.47/2.20 % (23773)Instruction limit reached!
% 6.47/2.20 % (23773)------------------------------
% 6.47/2.20 % (23773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.20 % (23773)Termination reason: Unknown
% 6.47/2.20 % (23773)Termination phase: Saturation
% 6.47/2.20
% 6.47/2.20 % (23773)Memory used [KB]: 7291
% 6.47/2.20 % (23773)Time elapsed: 0.065 s
% 6.47/2.20 % (23773)Instructions burned: 232 (million)
% 6.47/2.20 % (23773)------------------------------
% 6.47/2.20 % (23773)------------------------------
% 7.20/2.20 % (23771)Instruction limit reached!
% 7.20/2.20 % (23771)------------------------------
% 7.20/2.20 % (23771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.20/2.20 % (23771)Termination reason: Unknown
% 7.20/2.20 % (23771)Termination phase: Saturation
% 7.20/2.20
% 7.20/2.20 % (23771)Memory used [KB]: 8315
% 7.20/2.20 % (23771)Time elapsed: 0.081 s
% 7.20/2.20 % (23771)Instructions burned: 258 (million)
% 7.20/2.20 % (23771)------------------------------
% 7.20/2.20 % (23771)------------------------------
% 7.20/2.21 % (23781)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_23357 for (2992ds/154Mi)
% 7.20/2.21 % (23782)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_23357 for (2992ds/79Mi)
% 7.20/2.23 % (23779)Instruction limit reached!
% 7.20/2.23 % (23779)------------------------------
% 7.20/2.23 % (23779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.20/2.23 % (23779)Termination reason: Unknown
% 7.20/2.23 % (23779)Termination phase: Saturation
% 7.20/2.23
% 7.20/2.23 % (23779)Memory used [KB]: 7419
% 7.20/2.23 % (23779)Time elapsed: 0.058 s
% 7.20/2.23 % (23779)Instructions burned: 183 (million)
% 7.20/2.23 % (23779)------------------------------
% 7.20/2.23 % (23779)------------------------------
% 7.20/2.24 % (23782)Instruction limit reached!
% 7.20/2.24 % (23782)------------------------------
% 7.20/2.24 % (23782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.20/2.24 % (23782)Termination reason: Unknown
% 7.20/2.24 % (23782)Termination phase: Function definition elimination
% 7.20/2.24
% 7.20/2.24 % (23782)Memory used [KB]: 2430
% 7.20/2.24 % (23782)Time elapsed: 0.025 s
% 7.20/2.24 % (23782)Instructions burned: 79 (million)
% 7.20/2.24 % (23782)------------------------------
% 7.20/2.24 % (23782)------------------------------
% 7.20/2.24 % (23780)Instruction limit reached!
% 7.20/2.24 % (23780)------------------------------
% 7.20/2.24 % (23780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.20/2.24 % (23780)Termination reason: Unknown
% 7.20/2.24 % (23780)Termination phase: Saturation
% 7.20/2.24
% 7.20/2.24 % (23780)Memory used [KB]: 7419
% 7.20/2.24 % (23780)Time elapsed: 0.058 s
% 7.20/2.24 % (23780)Instructions burned: 182 (million)
% 7.20/2.24 % (23780)------------------------------
% 7.20/2.24 % (23780)------------------------------
% 7.20/2.24 % (23783)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_23357 for (2992ds/216Mi)
% 7.20/2.24 % (23776)Instruction limit reached!
% 7.20/2.24 % (23776)------------------------------
% 7.20/2.24 % (23776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.20/2.24 % (23776)Termination reason: Unknown
% 7.20/2.24 % (23776)Termination phase: Saturation
% 7.20/2.24
% 7.20/2.24 % (23776)Memory used [KB]: 7931
% 7.20/2.24 % (23776)Time elapsed: 0.087 s
% 7.20/2.24 % (23776)Instructions burned: 299 (million)
% 7.20/2.24 % (23776)------------------------------
% 7.20/2.24 % (23776)------------------------------
% 7.20/2.25 % (23784)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_23357 for (2992ds/114Mi)
% 7.20/2.25 % (23781)Instruction limit reached!
% 7.20/2.25 % (23781)------------------------------
% 7.20/2.25 % (23781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.20/2.25 % (23781)Termination reason: Unknown
% 7.20/2.25 % (23781)Termination phase: Saturation
% 7.20/2.25
% 7.20/2.25 % (23781)Memory used [KB]: 2942
% 7.20/2.25 % (23781)Time elapsed: 0.044 s
% 7.20/2.25 % (23781)Instructions burned: 155 (million)
% 7.20/2.25 % (23781)------------------------------
% 7.20/2.25 % (23781)------------------------------
% 7.20/2.25 % (23785)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_23357 for (2992ds/922Mi)
% 7.20/2.25 % (23786)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_23357 for (2992ds/182Mi)
% 7.20/2.26 % (23787)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_23357 for (2992ds/164Mi)
% 7.20/2.28 % (23784)Instruction limit reached!
% 7.20/2.28 % (23784)------------------------------
% 7.20/2.28 % (23784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.20/2.28 % (23784)Termination reason: Unknown
% 7.20/2.28 % (23784)Termination phase: Saturation
% 7.20/2.28
% 7.20/2.28 % (23784)Memory used [KB]: 7036
% 7.20/2.28 % (23784)Time elapsed: 0.035 s
% 7.20/2.28 % (23784)Instructions burned: 115 (million)
% 7.20/2.28 % (23784)------------------------------
% 7.20/2.28 % (23784)------------------------------
% 7.20/2.28 % (23774)Instruction limit reached!
% 7.20/2.28 % (23774)------------------------------
% 7.20/2.28 % (23774)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.20/2.28 % (23774)Termination reason: Unknown
% 7.20/2.28 % (23774)Termination phase: Saturation
% 7.20/2.28
% 7.20/2.28 % (23774)Memory used [KB]: 8699
% 7.20/2.28 % (23774)Time elapsed: 0.144 s
% 7.20/2.28 % (23774)Instructions burned: 460 (million)
% 7.20/2.28 % (23774)------------------------------
% 7.20/2.28 % (23774)------------------------------
% 7.20/2.29 % (23788)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_23357 for (2992ds/50Mi)
% 7.20/2.29 % (23789)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_23357 for (2992ds/368Mi)
% 7.81/2.30 % (23788)Instruction limit reached!
% 7.81/2.30 % (23788)------------------------------
% 7.81/2.30 % (23788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.30 % (23788)Termination reason: Unknown
% 7.81/2.30 % (23788)Termination phase: Property scanning
% 7.81/2.30
% 7.81/2.30 % (23788)Memory used [KB]: 2302
% 7.81/2.30 % (23788)Time elapsed: 0.015 s
% 7.81/2.30 % (23788)Instructions burned: 50 (million)
% 7.81/2.30 % (23788)------------------------------
% 7.81/2.30 % (23788)------------------------------
% 7.81/2.30 % (23787)Instruction limit reached!
% 7.81/2.30 % (23787)------------------------------
% 7.81/2.30 % (23787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.30 % (23787)Termination reason: Unknown
% 7.81/2.30 % (23787)Termination phase: Saturation
% 7.81/2.30
% 7.81/2.30 % (23787)Memory used [KB]: 2814
% 7.81/2.30 % (23787)Time elapsed: 0.047 s
% 7.81/2.30 % (23787)Instructions burned: 165 (million)
% 7.81/2.30 % (23787)------------------------------
% 7.81/2.30 % (23787)------------------------------
% 7.81/2.31 % (23783)Instruction limit reached!
% 7.81/2.31 % (23783)------------------------------
% 7.81/2.31 % (23783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.31 % (23783)Termination reason: Unknown
% 7.81/2.31 % (23783)Termination phase: Saturation
% 7.81/2.31
% 7.81/2.31 % (23783)Memory used [KB]: 7675
% 7.81/2.31 % (23783)Time elapsed: 0.062 s
% 7.81/2.31 % (23783)Instructions burned: 217 (million)
% 7.81/2.31 % (23783)------------------------------
% 7.81/2.31 % (23783)------------------------------
% 7.81/2.31 % (23786)Instruction limit reached!
% 7.81/2.31 % (23786)------------------------------
% 7.81/2.31 % (23786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.31 % (23786)Termination reason: Unknown
% 7.81/2.31 % (23786)Termination phase: Saturation
% 7.81/2.31
% 7.81/2.31 % (23786)Memory used [KB]: 7419
% 7.81/2.31 % (23786)Time elapsed: 0.052 s
% 7.81/2.31 % (23786)Instructions burned: 183 (million)
% 7.81/2.31 % (23786)------------------------------
% 7.81/2.31 % (23786)------------------------------
% 7.81/2.31 % (23790)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_23357 for (2991ds/1021Mi)
% 7.81/2.31 % (23791)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_23357 for (2991ds/267Mi)
% 7.81/2.31 % (23792)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_23357 for (2991ds/204Mi)
% 7.81/2.32 % (23793)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_23357 for (2991ds/26Mi)
% 7.81/2.32 % (23793)Instruction limit reached!
% 7.81/2.32 % (23793)------------------------------
% 7.81/2.32 % (23793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.32 % (23793)Termination reason: Unknown
% 7.81/2.32 % (23793)Termination phase: shuffling
% 7.81/2.32
% 7.81/2.32 % (23793)Memory used [KB]: 2046
% 7.81/2.32 % (23793)Time elapsed: 0.009 s
% 7.81/2.32 % (23793)Instructions burned: 28 (million)
% 7.81/2.32 % (23793)------------------------------
% 7.81/2.32 % (23793)------------------------------
% 7.81/2.33 % (23794)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_23357 for (2991ds/53Mi)
% 7.81/2.35 % (23794)Instruction limit reached!
% 7.81/2.35 % (23794)------------------------------
% 7.81/2.35 % (23794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.35 % (23794)Termination reason: Unknown
% 7.81/2.35 % (23794)Termination phase: Property scanning
% 7.81/2.35
% 7.81/2.35 % (23794)Memory used [KB]: 2302
% 7.81/2.35 % (23794)Time elapsed: 0.016 s
% 7.81/2.35 % (23794)Instructions burned: 55 (million)
% 7.81/2.35 % (23794)------------------------------
% 7.81/2.35 % (23794)------------------------------
% 7.81/2.36 % (23795)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_23357 for (2991ds/4436Mi)
% 7.81/2.37 % (23792)Instruction limit reached!
% 7.81/2.37 % (23792)------------------------------
% 7.81/2.37 % (23792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.37 % (23792)Termination reason: Unknown
% 7.81/2.37 % (23792)Termination phase: Saturation
% 7.81/2.37
% 7.81/2.37 % (23792)Memory used [KB]: 7291
% 7.81/2.37 % (23792)Time elapsed: 0.061 s
% 7.81/2.37 % (23792)Instructions burned: 204 (million)
% 7.81/2.37 % (23792)------------------------------
% 7.81/2.37 % (23792)------------------------------
% 7.81/2.38 % (23796)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_23357 for (2991ds/1539Mi)
% 7.81/2.40 % (23791)Instruction limit reached!
% 7.81/2.40 % (23791)------------------------------
% 7.81/2.40 % (23791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.40 % (23791)Termination reason: Unknown
% 7.81/2.40 % (23791)Termination phase: Saturation
% 7.81/2.40
% 7.81/2.40 % (23791)Memory used [KB]: 7675
% 7.81/2.40 % (23791)Time elapsed: 0.083 s
% 7.81/2.40 % (23791)Instructions burned: 268 (million)
% 7.81/2.40 % (23791)------------------------------
% 7.81/2.40 % (23791)------------------------------
% 8.22/2.40 % (23789)Instruction limit reached!
% 8.22/2.40 % (23789)------------------------------
% 8.22/2.40 % (23789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/2.40 % (23789)Termination reason: Unknown
% 8.22/2.40 % (23789)Termination phase: Saturation
% 8.22/2.40
% 8.22/2.40 % (23789)Memory used [KB]: 8187
% 8.22/2.40 % (23789)Time elapsed: 0.113 s
% 8.22/2.40 % (23789)Instructions burned: 371 (million)
% 8.22/2.40 % (23789)------------------------------
% 8.22/2.40 % (23789)------------------------------
% 8.22/2.40 % (23797)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_23357 for (2990ds/408Mi)
% 8.22/2.41 % (23798)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_23357 for (2990ds/5205Mi)
% 8.22/2.47 % (23778)Instruction limit reached!
% 8.22/2.47 % (23778)------------------------------
% 8.22/2.47 % (23778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.22/2.47 % (23778)Termination reason: Unknown
% 8.22/2.47 % (23778)Termination phase: Saturation
% 8.22/2.47
% 8.22/2.47 % (23778)Memory used [KB]: 8443
% 8.22/2.47 % (23778)Time elapsed: 0.306 s
% 8.22/2.47 % (23778)Instructions burned: 988 (million)
% 8.22/2.47 % (23778)------------------------------
% 8.22/2.47 % (23778)------------------------------
% 8.22/2.48 % (23799)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_23357 for (2990ds/1913Mi)
% 8.66/2.53 % (23797)Instruction limit reached!
% 8.66/2.53 % (23797)------------------------------
% 8.66/2.53 % (23797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.66/2.53 % (23797)Termination reason: Unknown
% 8.66/2.53 % (23797)Termination phase: Saturation
% 8.66/2.53
% 8.66/2.53 % (23797)Memory used [KB]: 8827
% 8.66/2.53 % (23797)Time elapsed: 0.124 s
% 8.66/2.53 % (23797)Instructions burned: 410 (million)
% 8.66/2.53 % (23797)------------------------------
% 8.66/2.53 % (23797)------------------------------
% 8.66/2.54 % (23800)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_23357 for (2989ds/4350Mi)
% 8.66/2.54 % (23785)Instruction limit reached!
% 8.66/2.54 % (23785)------------------------------
% 8.66/2.54 % (23785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.66/2.54 % (23785)Termination reason: Unknown
% 8.66/2.54 % (23785)Termination phase: Saturation
% 8.66/2.54
% 8.66/2.54 % (23785)Memory used [KB]: 8699
% 8.66/2.54 % (23785)Time elapsed: 0.294 s
% 8.66/2.54 % (23785)Instructions burned: 922 (million)
% 8.66/2.54 % (23785)------------------------------
% 8.66/2.54 % (23785)------------------------------
% 8.66/2.55 % (23801)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_23357 for (2989ds/68Mi)
% 8.66/2.57 % (23801)Instruction limit reached!
% 8.66/2.57 % (23801)------------------------------
% 8.66/2.57 % (23801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.66/2.57 % (23801)Termination reason: Unknown
% 8.66/2.57 % (23801)Termination phase: Property scanning
% 8.66/2.57
% 8.66/2.57 % (23801)Memory used [KB]: 2302
% 8.66/2.57 % (23801)Time elapsed: 0.022 s
% 8.66/2.57 % (23801)Instructions burned: 68 (million)
% 8.66/2.57 % (23801)------------------------------
% 8.66/2.57 % (23801)------------------------------
% 8.66/2.58 % (23802)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_23357 for (2989ds/358Mi)
% 9.12/2.63 % (23790)Instruction limit reached!
% 9.12/2.63 % (23790)------------------------------
% 9.12/2.63 % (23790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.12/2.63 % (23790)Termination reason: Unknown
% 9.12/2.63 % (23790)Termination phase: Saturation
% 9.12/2.63
% 9.12/2.63 % (23790)Memory used [KB]: 10106
% 9.12/2.63 % (23790)Time elapsed: 0.320 s
% 9.12/2.63 % (23790)Instructions burned: 1021 (million)
% 9.12/2.63 % (23790)------------------------------
% 9.12/2.63 % (23790)------------------------------
% 9.12/2.64 % (23803)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_23357 for (2988ds/31Mi)
% 9.12/2.65 % (23803)Instruction limit reached!
% 9.12/2.65 % (23803)------------------------------
% 9.12/2.65 % (23803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.12/2.65 % (23803)Termination reason: Unknown
% 9.12/2.65 % (23803)Termination phase: Property scanning
% 9.12/2.65
% 9.12/2.65 % (23803)Memory used [KB]: 1918
% 9.12/2.65 % (23803)Time elapsed: 0.011 s
% 9.12/2.65 % (23803)Instructions burned: 31 (million)
% 9.12/2.65 % (23803)------------------------------
% 9.12/2.65 % (23803)------------------------------
% 9.12/2.66 % (23804)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_23357 for (2988ds/279Mi)
% 9.47/2.70 % (23802)Instruction limit reached!
% 9.47/2.70 % (23802)------------------------------
% 9.47/2.70 % (23802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.47/2.70 % (23802)Termination reason: Unknown
% 9.47/2.70 % (23802)Termination phase: Saturation
% 9.47/2.70
% 9.47/2.70 % (23802)Memory used [KB]: 7675
% 9.47/2.70 % (23802)Time elapsed: 0.115 s
% 9.47/2.70 % (23802)Instructions burned: 360 (million)
% 9.47/2.70 % (23802)------------------------------
% 9.47/2.70 % (23802)------------------------------
% 9.47/2.71 % (23805)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_23357 for (2987ds/258Mi)
% 9.47/2.72 % (23804)Refutation not found, incomplete strategy
% 9.47/2.72 % (23804)------------------------------
% 9.47/2.72 % (23804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.47/2.72 % (23804)Termination reason: Refutation not found, incomplete strategy
% 9.47/2.72
% 9.47/2.72
% 9.47/2.72 % (23804)Memory used [KB]: 7675
% 9.47/2.72 % (23804)Time elapsed: 0.057 s
% 9.47/2.72 % (23804)Instructions burned: 194 (million)
% 9.47/2.72 % (23804)------------------------------
% 9.47/2.72 % (23804)------------------------------
% 9.47/2.73 % (23806)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_23357 for (2987ds/26Mi)
% 9.47/2.74 % (23806)Instruction limit reached!
% 9.47/2.74 % (23806)------------------------------
% 9.47/2.74 % (23806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.47/2.74 % (23806)Termination reason: Unknown
% 9.47/2.74 % (23806)Termination phase: shuffling
% 9.47/2.74
% 9.47/2.74 % (23806)Memory used [KB]: 2046
% 9.47/2.74 % (23806)Time elapsed: 0.009 s
% 9.47/2.74 % (23806)Instructions burned: 28 (million)
% 9.47/2.74 % (23806)------------------------------
% 9.47/2.74 % (23806)------------------------------
% 9.47/2.74 % (23807)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_23357 for (2987ds/995Mi)
% 9.47/2.79 % (23805)Instruction limit reached!
% 9.47/2.79 % (23805)------------------------------
% 9.47/2.79 % (23805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.47/2.79 % (23805)Termination reason: Unknown
% 9.47/2.79 % (23805)Termination phase: Saturation
% 9.47/2.79
% 9.47/2.79 % (23805)Memory used [KB]: 7803
% 9.47/2.79 % (23805)Time elapsed: 0.079 s
% 9.47/2.79 % (23805)Instructions burned: 258 (million)
% 9.47/2.79 % (23805)------------------------------
% 9.47/2.79 % (23805)------------------------------
% 9.47/2.80 % (23808)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_23357 for (2987ds/373Mi)
% 9.77/2.86 % (23796)Instruction limit reached!
% 9.77/2.86 % (23796)------------------------------
% 9.77/2.86 % (23796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.77/2.86 % (23796)Termination reason: Unknown
% 9.77/2.86 % (23796)Termination phase: Saturation
% 9.77/2.86
% 9.77/2.86 % (23796)Memory used [KB]: 11129
% 9.77/2.86 % (23796)Time elapsed: 0.478 s
% 9.77/2.86 % (23796)Instructions burned: 1539 (million)
% 9.77/2.86 % (23796)------------------------------
% 9.77/2.86 % (23796)------------------------------
% 9.77/2.87 % (23809)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_23357 for (2986ds/253Mi)
% 10.27/2.91 % (23808)Instruction limit reached!
% 10.27/2.91 % (23808)------------------------------
% 10.27/2.91 % (23808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.27/2.91 % (23808)Termination reason: Unknown
% 10.27/2.91 % (23808)Termination phase: Saturation
% 10.27/2.91
% 10.27/2.91 % (23808)Memory used [KB]: 8187
% 10.27/2.91 % (23808)Time elapsed: 0.138 s
% 10.27/2.91 % (23808)Instructions burned: 375 (million)
% 10.27/2.91 % (23808)------------------------------
% 10.27/2.91 % (23808)------------------------------
% 10.27/2.92 % (23810)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_23357 for (2985ds/832Mi)
% 10.27/2.94 % (23809)Instruction limit reached!
% 10.27/2.94 % (23809)------------------------------
% 10.27/2.94 % (23809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.27/2.94 % (23809)Termination reason: Unknown
% 10.27/2.94 % (23809)Termination phase: Saturation
% 10.27/2.94
% 10.27/2.94 % (23809)Memory used [KB]: 7931
% 10.27/2.94 % (23809)Time elapsed: 0.072 s
% 10.27/2.94 % (23809)Instructions burned: 254 (million)
% 10.27/2.94 % (23809)------------------------------
% 10.27/2.94 % (23809)------------------------------
% 10.27/2.95 % (23811)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_23357 for (2985ds/668Mi)
% 10.27/2.98 % (23810)Refutation not found, incomplete strategy
% 10.27/2.98 % (23810)------------------------------
% 10.27/2.98 % (23810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.27/2.98 % (23810)Termination reason: Refutation not found, incomplete strategy
% 10.27/2.98
% 10.27/2.98
% 10.27/2.98 % (23810)Memory used [KB]: 7931
% 10.27/2.98 % (23810)Time elapsed: 0.057 s
% 10.27/2.98 % (23810)Instructions burned: 182 (million)
% 10.27/2.98 % (23810)------------------------------
% 10.27/2.98 % (23810)------------------------------
% 10.27/2.99 % (23812)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_23357 for (2984ds/40Mi)
% 10.27/3.00 % (23812)Instruction limit reached!
% 10.27/3.00 % (23812)------------------------------
% 10.27/3.00 % (23812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.27/3.00 % (23812)Termination reason: Unknown
% 10.27/3.00 % (23812)Termination phase: shuffling
% 10.27/3.00
% 10.27/3.00 % (23812)Memory used [KB]: 2302
% 10.27/3.00 % (23812)Time elapsed: 0.013 s
% 10.27/3.00 % (23812)Instructions burned: 42 (million)
% 10.27/3.00 % (23812)------------------------------
% 10.27/3.00 % (23812)------------------------------
% 10.27/3.01 % (23813)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_23357 for (2984ds/294Mi)
% 13.22/3.04 % (23807)Instruction limit reached!
% 13.22/3.04 % (23807)------------------------------
% 13.22/3.04 % (23807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.22/3.04 % (23807)Termination reason: Unknown
% 13.22/3.04 % (23807)Termination phase: Saturation
% 13.22/3.04
% 13.22/3.04 % (23807)Memory used [KB]: 10106
% 13.22/3.04 % (23807)Time elapsed: 0.301 s
% 13.22/3.04 % (23807)Instructions burned: 995 (million)
% 13.22/3.04 % (23807)------------------------------
% 13.22/3.04 % (23807)------------------------------
% 13.22/3.05 % (23813)Refutation not found, incomplete strategy
% 13.22/3.05 % (23813)------------------------------
% 13.22/3.05 % (23813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.22/3.05 % (23813)Termination reason: Refutation not found, incomplete strategy
% 13.22/3.05
% 13.22/3.05
% 13.22/3.05 % (23813)Memory used [KB]: 7419
% 13.22/3.05 % (23813)Time elapsed: 0.040 s
% 13.22/3.05 % (23813)Instructions burned: 136 (million)
% 13.22/3.05 % (23813)------------------------------
% 13.22/3.05 % (23813)------------------------------
% 13.22/3.05 % (23814)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_23357 for (2984ds/187Mi)
% 13.22/3.06 % (23815)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_23357 for (2984ds/371Mi)
% 13.22/3.07 % (23799)Instruction limit reached!
% 13.22/3.07 % (23799)------------------------------
% 13.22/3.07 % (23799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.22/3.07 % (23799)Termination reason: Unknown
% 13.22/3.07 % (23799)Termination phase: Saturation
% 13.22/3.07
% 13.22/3.07 % (23799)Memory used [KB]: 4605
% 13.22/3.07 % (23799)Time elapsed: 0.597 s
% 13.22/3.07 % (23799)Instructions burned: 1914 (million)
% 13.22/3.07 % (23799)------------------------------
% 13.22/3.07 % (23799)------------------------------
% 13.22/3.08 % (23816)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_23357 for (2984ds/1827Mi)
% 13.22/3.11 % (23814)Instruction limit reached!
% 13.22/3.11 % (23814)------------------------------
% 13.22/3.11 % (23814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.22/3.11 % (23814)Termination reason: Unknown
% 13.22/3.11 % (23814)Termination phase: Saturation
% 13.22/3.11
% 13.22/3.11 % (23814)Memory used [KB]: 7291
% 13.22/3.11 % (23814)Time elapsed: 0.056 s
% 13.22/3.11 % (23814)Instructions burned: 190 (million)
% 13.22/3.11 % (23814)------------------------------
% 13.22/3.11 % (23814)------------------------------
% 13.22/3.12 % (23817)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_23357 for (2983ds/70Mi)
% 13.82/3.14 % (23817)Instruction limit reached!
% 13.82/3.14 % (23817)------------------------------
% 13.82/3.14 % (23817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.82/3.14 % (23817)Termination reason: Unknown
% 13.82/3.14 % (23817)Termination phase: Preprocessing 1
% 13.82/3.14
% 13.82/3.14 % (23817)Memory used [KB]: 2302
% 13.82/3.14 % (23817)Time elapsed: 0.021 s
% 13.82/3.14 % (23817)Instructions burned: 72 (million)
% 13.82/3.14 % (23817)------------------------------
% 13.82/3.14 % (23817)------------------------------
% 13.82/3.15 % (23818)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_23357 for (2983ds/316Mi)
% 13.82/3.15 % (23811)Instruction limit reached!
% 13.82/3.15 % (23811)------------------------------
% 13.82/3.15 % (23811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.82/3.15 % (23811)Termination reason: Unknown
% 13.82/3.15 % (23811)Termination phase: Saturation
% 13.82/3.15
% 13.82/3.15 % (23811)Memory used [KB]: 14328
% 13.82/3.15 % (23811)Time elapsed: 0.199 s
% 13.82/3.15 % (23811)Instructions burned: 670 (million)
% 13.82/3.15 % (23811)------------------------------
% 13.82/3.15 % (23811)------------------------------
% 13.82/3.16 % (23819)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_23357 for (2983ds/932Mi)
% 13.82/3.17 % (23815)Instruction limit reached!
% 13.82/3.17 % (23815)------------------------------
% 13.82/3.17 % (23815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.82/3.17 % (23815)Termination reason: Unknown
% 13.82/3.17 % (23815)Termination phase: Saturation
% 13.82/3.17
% 13.82/3.17 % (23815)Memory used [KB]: 8571
% 13.82/3.17 % (23815)Time elapsed: 0.116 s
% 13.82/3.17 % (23815)Instructions burned: 371 (million)
% 13.82/3.17 % (23815)------------------------------
% 13.82/3.17 % (23815)------------------------------
% 13.82/3.18 % (23820)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_23357 for (2983ds/4714Mi)
% 14.25/3.21 % (23818)Refutation not found, incomplete strategy
% 14.25/3.21 % (23818)------------------------------
% 14.25/3.21 % (23818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.25/3.21 % (23818)Termination reason: Refutation not found, incomplete strategy
% 14.25/3.21
% 14.25/3.21
% 14.25/3.21 % (23818)Memory used [KB]: 7803
% 14.25/3.21 % (23818)Time elapsed: 0.066 s
% 14.25/3.21 % (23818)Instructions burned: 225 (million)
% 14.25/3.21 % (23818)------------------------------
% 14.25/3.21 % (23818)------------------------------
% 14.25/3.22 % (23821)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_23357 for (2982ds/8250Mi)
% 14.25/3.25 % (23820)Refutation not found, incomplete strategy
% 14.25/3.25 % (23820)------------------------------
% 14.25/3.25 % (23820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.25/3.25 % (23820)Termination reason: Refutation not found, incomplete strategy
% 14.25/3.25
% 14.25/3.25
% 14.25/3.25 % (23820)Memory used [KB]: 7931
% 14.25/3.25 % (23820)Time elapsed: 0.066 s
% 14.25/3.25 % (23820)Instructions burned: 224 (million)
% 14.25/3.25 % (23820)------------------------------
% 14.25/3.25 % (23820)------------------------------
% 14.25/3.26 % (23822)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_23357 for (2982ds/770Mi)
% 14.99/3.44 % (23819)Instruction limit reached!
% 14.99/3.44 % (23819)------------------------------
% 14.99/3.44 % (23819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.99/3.44 % (23819)Termination reason: Unknown
% 14.99/3.44 % (23819)Termination phase: Saturation
% 14.99/3.44
% 14.99/3.44 % (23819)Memory used [KB]: 11513
% 14.99/3.44 % (23819)Time elapsed: 0.285 s
% 14.99/3.44 % (23819)Instructions burned: 934 (million)
% 14.99/3.44 % (23819)------------------------------
% 14.99/3.44 % (23819)------------------------------
% 14.99/3.45 % (23823)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_23357 for (2980ds/794Mi)
% 14.99/3.49 % (23822)Instruction limit reached!
% 14.99/3.49 % (23822)------------------------------
% 14.99/3.49 % (23822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.99/3.49 % (23822)Termination reason: Unknown
% 14.99/3.49 % (23822)Termination phase: Saturation
% 14.99/3.49
% 14.99/3.49 % (23822)Memory used [KB]: 10234
% 14.99/3.49 % (23822)Time elapsed: 0.236 s
% 14.99/3.49 % (23822)Instructions burned: 772 (million)
% 14.99/3.49 % (23822)------------------------------
% 14.99/3.49 % (23822)------------------------------
% 15.83/3.50 % (23824)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_23357 for (2979ds/464Mi)
% 16.13/3.65 % (23824)Instruction limit reached!
% 16.13/3.65 % (23824)------------------------------
% 16.13/3.65 % (23824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.13/3.65 % (23824)Termination reason: Unknown
% 16.13/3.65 % (23824)Termination phase: Saturation
% 16.13/3.65
% 16.13/3.65 % (23824)Memory used [KB]: 7675
% 16.13/3.65 % (23824)Time elapsed: 0.147 s
% 16.13/3.65 % (23824)Instructions burned: 465 (million)
% 16.13/3.65 % (23824)------------------------------
% 16.13/3.65 % (23824)------------------------------
% 16.13/3.65 % (23816)Instruction limit reached!
% 16.13/3.65 % (23816)------------------------------
% 16.13/3.65 % (23816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.13/3.65 % (23816)Termination reason: Unknown
% 16.13/3.65 % (23816)Termination phase: Saturation
% 16.13/3.65
% 16.13/3.65 % (23816)Memory used [KB]: 9978
% 16.13/3.65 % (23816)Time elapsed: 0.573 s
% 16.13/3.65 % (23816)Instructions burned: 1827 (million)
% 16.13/3.65 % (23816)------------------------------
% 16.13/3.65 % (23816)------------------------------
% 16.13/3.66 % (23825)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_23357 for (2978ds/1376Mi)
% 16.13/3.66 % (23826)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_23357 for (2978ds/906Mi)
% 17.19/3.70 % (23823)Instruction limit reached!
% 17.19/3.70 % (23823)------------------------------
% 17.19/3.70 % (23823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.19/3.70 % (23823)Termination reason: Unknown
% 17.19/3.70 % (23823)Termination phase: Saturation
% 17.19/3.70
% 17.19/3.70 % (23823)Memory used [KB]: 6268
% 17.19/3.70 % (23823)Time elapsed: 0.246 s
% 17.19/3.70 % (23823)Instructions burned: 796 (million)
% 17.19/3.70 % (23823)------------------------------
% 17.19/3.70 % (23823)------------------------------
% 17.19/3.71 % (23827)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_23357 for (2977ds/434Mi)
% 17.19/3.73 % (23795)Instruction limit reached!
% 17.19/3.73 % (23795)------------------------------
% 17.19/3.73 % (23795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.19/3.73 % (23795)Termination reason: Unknown
% 17.19/3.73 % (23795)Termination phase: Saturation
% 17.19/3.73
% 17.19/3.73 % (23795)Memory used [KB]: 12792
% 17.19/3.73 % (23795)Time elapsed: 1.379 s
% 17.19/3.73 % (23795)Instructions burned: 4438 (million)
% 17.19/3.73 % (23795)------------------------------
% 17.19/3.73 % (23795)------------------------------
% 17.19/3.75 % (23828)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_23357 for (2977ds/865Mi)
% 17.69/3.84 % (23827)Instruction limit reached!
% 17.69/3.84 % (23827)------------------------------
% 17.69/3.84 % (23827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.69/3.84 % (23827)Termination reason: Unknown
% 17.69/3.84 % (23827)Termination phase: Saturation
% 17.69/3.84
% 17.69/3.84 % (23827)Memory used [KB]: 8571
% 17.69/3.84 % (23827)Time elapsed: 0.130 s
% 17.69/3.84 % (23827)Instructions burned: 437 (million)
% 17.69/3.84 % (23827)------------------------------
% 17.69/3.84 % (23827)------------------------------
% 17.69/3.84 % (23800)Instruction limit reached!
% 17.69/3.84 % (23800)------------------------------
% 17.69/3.84 % (23800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.69/3.84 % (23800)Termination reason: Unknown
% 17.69/3.84 % (23800)Termination phase: Saturation
% 17.69/3.84
% 17.69/3.84 % (23800)Memory used [KB]: 13688
% 17.69/3.84 % (23800)Time elapsed: 1.305 s
% 17.69/3.84 % (23800)Instructions burned: 4351 (million)
% 17.69/3.84 % (23800)------------------------------
% 17.69/3.84 % (23800)------------------------------
% 17.69/3.85 % (23829)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_23357 for (2976ds/593Mi)
% 17.69/3.85 % (23830)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_23357 for (2976ds/443Mi)
% 17.98/3.99 % (23830)Instruction limit reached!
% 17.98/3.99 % (23830)------------------------------
% 17.98/3.99 % (23830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.98/3.99 % (23830)Termination reason: Unknown
% 17.98/3.99 % (23830)Termination phase: Saturation
% 17.98/3.99
% 17.98/3.99 % (23830)Memory used [KB]: 8059
% 17.98/3.99 % (23830)Time elapsed: 0.142 s
% 17.98/3.99 % (23830)Instructions burned: 444 (million)
% 17.98/3.99 % (23830)------------------------------
% 17.98/3.99 % (23830)------------------------------
% 17.98/4.00 % (23798)Instruction limit reached!
% 17.98/4.00 % (23798)------------------------------
% 17.98/4.00 % (23798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.98/4.00 % (23798)Termination reason: Unknown
% 17.98/4.00 % (23798)Termination phase: Saturation
% 17.98/4.00
% 17.98/4.00 % (23798)Memory used [KB]: 13560
% 17.98/4.00 % (23798)Time elapsed: 1.585 s
% 17.98/4.00 % (23798)Instructions burned: 5205 (million)
% 17.98/4.00 % (23798)------------------------------
% 17.98/4.00 % (23798)------------------------------
% 17.98/4.00 % (23826)Instruction limit reached!
% 17.98/4.00 % (23826)------------------------------
% 17.98/4.00 % (23826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.98/4.00 % (23826)Termination reason: Unknown
% 17.98/4.00 % (23826)Termination phase: Saturation
% 17.98/4.00
% 17.98/4.00 % (23826)Memory used [KB]: 12153
% 17.98/4.00 % (23826)Time elapsed: 0.337 s
% 17.98/4.00 % (23826)Instructions burned: 906 (million)
% 17.98/4.00 % (23826)------------------------------
% 17.98/4.00 % (23826)------------------------------
% 17.98/4.00 % (23831)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_23357 for (2974ds/594Mi)
% 17.98/4.01 % (23828)Instruction limit reached!
% 17.98/4.01 % (23828)------------------------------
% 17.98/4.01 % (23828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.98/4.01 % (23828)Termination reason: Unknown
% 17.98/4.01 % (23828)Termination phase: Saturation
% 17.98/4.01
% 17.98/4.01 % (23828)Memory used [KB]: 9594
% 17.98/4.01 % (23828)Time elapsed: 0.263 s
% 17.98/4.01 % (23828)Instructions burned: 865 (million)
% 17.98/4.01 % (23828)------------------------------
% 17.98/4.01 % (23828)------------------------------
% 17.98/4.01 % (23832)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_23357 for (2974ds/327Mi)
% 17.98/4.01 % (23833)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_23357 for (2974ds/5411Mi)
% 17.98/4.02 % (23834)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_23357 for (2974ds/1762Mi)
% 20.22/4.03 % (23829)Instruction limit reached!
% 20.22/4.03 % (23829)------------------------------
% 20.22/4.03 % (23829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.22/4.03 % (23829)Termination reason: Unknown
% 20.22/4.03 % (23829)Termination phase: Saturation
% 20.22/4.03
% 20.22/4.03 % (23829)Memory used [KB]: 9850
% 20.22/4.03 % (23829)Time elapsed: 0.182 s
% 20.22/4.03 % (23829)Instructions burned: 594 (million)
% 20.22/4.03 % (23829)------------------------------
% 20.22/4.03 % (23829)------------------------------
% 20.22/4.04 % (23835)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_23357 for (2974ds/96Mi)
% 20.22/4.07 % (23835)Instruction limit reached!
% 20.22/4.07 % (23835)------------------------------
% 20.22/4.07 % (23835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.22/4.07 % (23835)Termination reason: Unknown
% 20.22/4.07 % (23835)Termination phase: Property scanning
% 20.22/4.07
% 20.22/4.07 % (23835)Memory used [KB]: 2686
% 20.22/4.07 % (23835)Time elapsed: 0.028 s
% 20.22/4.07 % (23835)Instructions burned: 96 (million)
% 20.22/4.07 % (23835)------------------------------
% 20.22/4.07 % (23835)------------------------------
% 20.22/4.08 % (23836)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_23357 for (2974ds/503Mi)
% 20.22/4.09 % (23825)Instruction limit reached!
% 20.22/4.09 % (23825)------------------------------
% 20.22/4.09 % (23825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.22/4.09 % (23825)Termination reason: Unknown
% 20.22/4.09 % (23825)Termination phase: Saturation
% 20.22/4.09
% 20.22/4.09 % (23825)Memory used [KB]: 11001
% 20.22/4.09 % (23825)Time elapsed: 0.434 s
% 20.22/4.09 % (23825)Instructions burned: 1378 (million)
% 20.22/4.09 % (23825)------------------------------
% 20.22/4.09 % (23825)------------------------------
% 20.22/4.10 % (23837)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_23357 for (2973ds/90Mi)
% 20.22/4.11 % (23832)Instruction limit reached!
% 20.22/4.11 % (23832)------------------------------
% 20.22/4.11 % (23832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.22/4.11 % (23832)Termination reason: Unknown
% 20.22/4.11 % (23832)Termination phase: Saturation
% 20.22/4.11
% 20.22/4.11 % (23832)Memory used [KB]: 8187
% 20.22/4.11 % (23832)Time elapsed: 0.105 s
% 20.22/4.11 % (23832)Instructions burned: 328 (million)
% 20.22/4.11 % (23832)------------------------------
% 20.22/4.11 % (23832)------------------------------
% 20.22/4.12 % (23838)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_23357 for (2973ds/593Mi)
% 20.67/4.13 % (23837)Instruction limit reached!
% 20.67/4.13 % (23837)------------------------------
% 20.67/4.13 % (23837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.67/4.13 % (23837)Termination reason: Unknown
% 20.67/4.13 % (23837)Termination phase: Property scanning
% 20.67/4.13
% 20.67/4.13 % (23837)Memory used [KB]: 2558
% 20.67/4.13 % (23837)Time elapsed: 0.029 s
% 20.67/4.13 % (23837)Instructions burned: 90 (million)
% 20.67/4.13 % (23837)------------------------------
% 20.67/4.13 % (23837)------------------------------
% 20.67/4.14 % (23839)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_23357 for (2973ds/1512Mi)
% 20.67/4.15 % (23833)First to succeed.
% 20.67/4.15 % (23833)Refutation found. Thanks to Tanya!
% 20.67/4.15 % SZS status Theorem for DTF2THF_23357
% 20.67/4.15 % SZS output start Proof for DTF2THF_23357
% 20.67/4.15 thf(type_def_5, type, coinductive_llist: ($tType) > $tType).
% 20.67/4.15 thf(type_def_7, type, set: ($tType) > $tType).
% 20.67/4.15 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 20.67/4.15 thf(type_def_9, type, itself: ($tType) > $tType).
% 20.67/4.15 thf(type_def_10, type, tLList446370796tllist: ($tType * $tType) > $tType).
% 20.67/4.15 thf(type_def_11, type, a: $tType).
% 20.67/4.15 thf(type_def_12, type, b: $tType).
% 20.67/4.15 thf(type_def_13, type, c: $tType).
% 20.67/4.15 thf(type_def_14, type, d: $tType).
% 20.67/4.15 thf(type_def_15, type, e: $tType).
% 20.67/4.15 thf(type_def_16, type, f: $tType).
% 20.67/4.15 thf(func_def_0, type, tLList446370796tllist: ($tType * $tType) > $tType).
% 20.67/4.15 thf(func_def_1, type, coinductive_llist: ($tType) > $tType).
% 20.67/4.15 thf(func_def_2, type, product_prod: ($tType * $tType) > $tType).
% 20.67/4.15 thf(func_def_3, type, set: ($tType) > $tType).
% 20.67/4.15 thf(func_def_4, type, itself: ($tType) > $tType).
% 20.67/4.15 thf(func_def_5, type, f: $tType).
% 20.67/4.15 thf(func_def_6, type, e: $tType).
% 20.67/4.15 thf(func_def_7, type, d: $tType).
% 20.67/4.15 thf(func_def_8, type, c: $tType).
% 20.67/4.15 thf(func_def_9, type, b: $tType).
% 20.67/4.15 thf(func_def_10, type, a: $tType).
% 20.67/4.15 thf(func_def_11, type, coindu328551480prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 20.67/4.15 thf(func_def_12, type, coinductive_lappend: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 20.67/4.15 thf(func_def_13, type, coinductive_lfilter: !>[X0: $tType]:((X0 > $o) > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 20.67/4.15 thf(func_def_14, type, coinductive_lfinite: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 20.67/4.15 thf(func_def_15, type, coinductive_llast: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 20.67/4.15 thf(func_def_16, type, coinductive_LCons: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 20.67/4.15 thf(func_def_17, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 20.67/4.15 thf(func_def_18, type, coindu1486289336t_all2: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > coinductive_llist @ X0 > coinductive_llist @ X1 > $o)).
% 20.67/4.15 thf(func_def_19, type, coinductive_lnull: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 20.67/4.15 thf(func_def_20, type, coinductive_lset: !>[X0: $tType]:(coinductive_llist @ X0 > set @ X0)).
% 20.67/4.15 thf(func_def_21, type, coinductive_lprefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 20.67/4.15 thf(func_def_22, type, coindu1478340336prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 20.67/4.15 thf(func_def_23, type, the: !>[X0: $tType]:((X0 > $o) > X0)).
% 20.67/4.15 thf(func_def_24, type, undefined: !>[X0: $tType]:(X0)).
% 20.67/4.15 thf(func_def_25, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 20.67/4.15 thf(func_def_26, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 20.67/4.15 thf(func_def_27, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod @ X0 @ X1)).
% 20.67/4.15 thf(func_def_28, type, product_apfst: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1) > product_prod @ X0 @ X2 > product_prod @ X1 @ X2)).
% 20.67/4.15 thf(func_def_29, type, produc2004651681e_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 20.67/4.15 thf(func_def_30, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod @ X0 @ X1 > X2)).
% 20.67/4.15 thf(func_def_31, type, product_fst: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 20.67/4.15 thf(func_def_32, type, product_snd: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 20.67/4.15 thf(func_def_33, type, product_swap: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > product_prod @ X1 @ X0)).
% 20.67/4.15 thf(func_def_34, type, product_scomp: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((X0 > product_prod @ X1 @ X2) > (X1 > X2 > X3) > X0 > X3)).
% 20.67/4.15 thf(func_def_35, type, type: !>[X0: $tType]:(itself @ X0)).
% 20.67/4.15 thf(func_def_36, type, reflp: !>[X0: $tType]:((X0 > X0 > $o) > $o)).
% 20.67/4.15 thf(func_def_37, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 20.67/4.15 thf(func_def_38, type, tLList47617868tllist: !>[X0: $tType, X1: $tType]:(product_prod @ coinductive_llist @ X0 @ X1 > tLList446370796tllist @ X0 @ X1 > $o)).
% 20.67/4.15 thf(func_def_39, type, tLList98099029ppendt: !>[X0: $tType, X1: $tType]:(coinductive_llist @ X0 > tLList446370796tllist @ X0 @ X1 > tLList446370796tllist @ X0 @ X1)).
% 20.67/4.15 thf(func_def_40, type, tLList1672613558_llist: !>[X0: $tType, X1: $tType]:(X0 > coinductive_llist @ X1 > tLList446370796tllist @ X1 @ X0)).
% 20.67/4.15 thf(func_def_41, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 20.67/4.15 thf(func_def_42, type, pa: a > b > $o).
% 20.67/4.15 thf(func_def_43, type, qa: c > d > $o).
% 20.67/4.15 thf(func_def_44, type, ra: e > f > $o).
% 20.67/4.15 thf(func_def_45, type, xs_a: c > product_prod @ coinductive_llist @ a @ e).
% 20.67/4.15 thf(func_def_46, type, xsa: product_prod @ coinductive_llist @ a @ c).
% 20.67/4.15 thf(func_def_47, type, ys_a: d > product_prod @ coinductive_llist @ b @ f).
% 20.67/4.15 thf(func_def_48, type, ysa: product_prod @ coinductive_llist @ b @ d).
% 20.67/4.15 thf(func_def_65, type, sK0: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X0 > $o) > (X0 > X1 > $o) > X0)).
% 20.67/4.15 thf(func_def_66, type, sK1: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X0 > $o) > (X0 > X1 > $o) > X1)).
% 20.67/4.15 thf(func_def_67, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X0)).
% 20.67/4.15 thf(func_def_68, type, sK3: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > (X0 > X1 > X2 > $o) > product_prod @ X0 @ X1 > X1)).
% 20.67/4.15 thf(func_def_69, type, sK4: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > product_prod @ X1 @ X0 > (X1 > X0 > X2 > $o) > X1)).
% 20.67/4.15 thf(func_def_70, type, sK5: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > product_prod @ X1 @ X0 > (X1 > X0 > X2 > $o) > X0)).
% 20.67/4.15 thf(func_def_71, type, sK6: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > product_prod @ X1 @ X0 > X1)).
% 20.67/4.15 thf(func_def_72, type, sK7: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > product_prod @ X1 @ X0 > X0)).
% 20.67/4.15 thf(func_def_73, type, sK8: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 20.67/4.15 thf(func_def_74, type, sK9: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 20.67/4.15 thf(func_def_75, type, sK10: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > (X1 > $o) > X1)).
% 20.67/4.15 thf(func_def_76, type, sK11: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > (X1 > $o) > X0)).
% 20.67/4.15 thf(func_def_77, type, sK12: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X0)).
% 20.67/4.15 thf(func_def_78, type, sK13: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > (X0 > X1 > $o) > X1)).
% 20.67/4.15 thf(func_def_79, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X6)).
% 20.67/4.15 thf(func_def_80, type, sK15: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 20.67/4.15 thf(func_def_81, type, sK16: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 20.67/4.15 thf(func_def_82, type, sK17: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 20.67/4.15 thf(func_def_83, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 20.67/4.15 thf(func_def_84, type, sK19: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 20.67/4.15 thf(func_def_85, type, sK20: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod @ X6 @ product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 20.67/4.15 thf(func_def_86, type, sK21: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 20.67/4.15 thf(func_def_87, type, sK22: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 20.67/4.15 thf(func_def_88, type, sK23: !>[X0: $tType, X1: $tType]:(coinductive_llist @ X1 > coinductive_llist @ X0 > (X0 > X1 > $o) > X0)).
% 20.67/4.15 thf(func_def_89, type, sK24: !>[X0: $tType, X1: $tType]:(coinductive_llist @ X1 > coinductive_llist @ X0 > (X0 > X1 > $o) > coinductive_llist @ X0)).
% 20.67/4.15 thf(func_def_90, type, sK25: !>[X0: $tType, X1: $tType]:(coinductive_llist @ X1 > coinductive_llist @ X0 > (X0 > X1 > $o) > X1)).
% 20.67/4.15 thf(func_def_91, type, sK26: !>[X0: $tType, X1: $tType]:(coinductive_llist @ X1 > coinductive_llist @ X0 > (X0 > X1 > $o) > coinductive_llist @ X1)).
% 20.67/4.15 thf(func_def_92, type, sK27: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 20.67/4.15 thf(func_def_93, type, sK28: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 20.67/4.15 thf(func_def_94, type, sK29: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > X0)).
% 20.67/4.15 thf(func_def_95, type, sK30: !>[X0: $tType]:((X0 > $o) > coinductive_llist @ X0 > X0)).
% 20.67/4.15 thf(func_def_96, type, sK31: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 20.67/4.15 thf(func_def_97, type, sK32: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 20.67/4.15 thf(func_def_98, type, sK33: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X0)).
% 20.67/4.15 thf(func_def_99, type, sK34: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X1)).
% 20.67/4.15 thf(func_def_100, type, sK35: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ product_prod @ X1 @ X2 > X2)).
% 20.67/4.15 thf(func_def_101, type, sK36: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 20.67/4.15 thf(func_def_102, type, sK37: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 20.67/4.15 thf(func_def_103, type, sK38: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 20.67/4.15 thf(func_def_104, type, sK39: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 20.67/4.15 thf(func_def_105, type, sK40: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X0)).
% 20.67/4.15 thf(func_def_106, type, sK41: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X1)).
% 20.67/4.15 thf(func_def_107, type, sK42: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X2)).
% 20.67/4.15 thf(func_def_108, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ X3 > X3)).
% 20.67/4.15 thf(func_def_109, type, sK44: !>[X0: $tType, X1: $tType]:(coinductive_llist @ X1 > coinductive_llist @ X0 > (X0 > X1 > $o) > X0)).
% 20.67/4.15 thf(func_def_110, type, sK45: !>[X0: $tType, X1: $tType]:(coinductive_llist @ X1 > coinductive_llist @ X0 > (X0 > X1 > $o) > coinductive_llist @ X0)).
% 20.67/4.15 thf(func_def_111, type, sK46: !>[X0: $tType, X1: $tType]:(coinductive_llist @ X1 > coinductive_llist @ X0 > (X0 > X1 > $o) > X1)).
% 20.67/4.15 thf(func_def_112, type, sK47: !>[X0: $tType, X1: $tType]:(coinductive_llist @ X1 > coinductive_llist @ X0 > (X0 > X1 > $o) > coinductive_llist @ X1)).
% 20.67/4.15 thf(func_def_113, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X2)).
% 20.67/4.15 thf(func_def_114, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ X1 > X0) > (X2 > X1 > X0) > X1)).
% 20.67/4.15 thf(func_def_115, type, sK50: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 20.67/4.15 thf(func_def_116, type, sK51: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 20.67/4.15 thf(func_def_117, type, sK52: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 20.67/4.15 thf(func_def_118, type, sK53: !>[X0: $tType, X1: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X1 > (X1 > X0 > $o) > X1)).
% 20.67/4.15 thf(func_def_119, type, sK54: !>[X0: $tType, X1: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X1 > (X1 > X0 > $o) > coinductive_llist @ X1)).
% 20.67/4.15 thf(func_def_120, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X0)).
% 20.67/4.15 thf(func_def_121, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X1)).
% 20.67/4.15 thf(func_def_122, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X2)).
% 20.67/4.15 thf(func_def_123, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X3)).
% 20.67/4.15 thf(func_def_124, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ X4 > X4)).
% 20.67/4.15 thf(func_def_125, type, sK60: !>[X0: $tType]:(coinductive_llist @ X0 > (X0 > $o) > X0)).
% 20.67/4.15 thf(func_def_126, type, sK61: !>[X0: $tType, X1: $tType]:((tLList446370796tllist @ X1 @ X0 > $o) > product_prod @ coinductive_llist @ X1 @ X0)).
% 20.67/4.15 thf(func_def_127, type, sK62: !>[X0: $tType]:(coinductive_llist @ X0 > (X0 > $o) > X0)).
% 20.67/4.15 thf(func_def_128, type, sK63: !>[X0: $tType, X1: $tType]:(coinductive_llist @ X1 > coinductive_llist @ X0 > X0 > (X0 > X1 > $o) > X1)).
% 20.67/4.15 thf(func_def_129, type, sK64: !>[X0: $tType, X1: $tType]:(coinductive_llist @ X1 > coinductive_llist @ X0 > X0 > (X0 > X1 > $o) > coinductive_llist @ X1)).
% 20.67/4.15 thf(func_def_130, type, sK65: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 20.67/4.15 thf(func_def_131, type, sK66: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0)).
% 20.67/4.15 thf(func_def_132, type, sK67: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0)).
% 20.67/4.15 thf(func_def_133, type, sK68: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0)).
% 20.67/4.15 thf(func_def_134, type, sK69: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 20.67/4.15 thf(func_def_135, type, sK70: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 20.67/4.15 thf(func_def_136, type, sK71: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 20.67/4.15 thf(func_def_137, type, sK72: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 20.67/4.15 thf(func_def_138, type, sK73: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > (X1 > $o) > X1)).
% 20.67/4.15 thf(func_def_139, type, sK74: !>[X0: $tType, X1: $tType]:(product_prod @ X1 @ X0 > (X1 > $o) > X0)).
% 20.67/4.15 thf(func_def_140, type, sK75: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 20.67/4.15 thf(func_def_141, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X0)).
% 20.67/4.15 thf(func_def_142, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ X2 > (X0 > X2 > set @ X1) > X1 > X2)).
% 20.67/4.15 thf(func_def_143, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X5)).
% 20.67/4.15 thf(func_def_144, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 20.67/4.15 thf(func_def_145, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 20.67/4.15 thf(func_def_146, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 20.67/4.15 thf(func_def_147, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 20.67/4.15 thf(func_def_148, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod @ X5 @ product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 20.67/4.15 thf(func_def_149, type, sK84: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X0)).
% 20.67/4.15 thf(func_def_150, type, sK85: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > X1)).
% 20.67/4.15 thf(func_def_151, type, sK86: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X1)).
% 20.67/4.15 thf(func_def_152, type, sK87: !>[X0: $tType, X1: $tType]:((product_prod @ X1 @ X0 > $o) > X0)).
% 20.67/4.15 thf(func_def_153, type, sK88: !>[X0: $tType]:(coinductive_llist @ X0 > (X0 > $o) > X0)).
% 20.67/4.15 thf(func_def_154, type, sK89: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > (X0 > X1 > $o) > X0)).
% 20.67/4.15 thf(func_def_155, type, sK90: !>[X0: $tType, X1: $tType]:(product_prod @ X0 @ X1 > (X0 > X1 > $o) > X1)).
% 20.67/4.15 thf(func_def_156, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1 > set @ X0) > X0 > product_prod @ X2 @ X1 > X2)).
% 20.67/4.15 thf(func_def_157, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1 > set @ X0) > X0 > product_prod @ X2 @ X1 > X1)).
% 20.67/4.15 thf(func_def_158, type, sK93: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X4)).
% 20.67/4.15 thf(func_def_159, type, sK94: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X3)).
% 20.67/4.15 thf(func_def_160, type, sK95: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 20.67/4.15 thf(func_def_161, type, sK96: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 20.67/4.15 thf(func_def_162, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod @ X4 @ product_prod @ X3 @ product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 20.67/4.15 thf(func_def_163, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X2)).
% 20.67/4.15 thf(func_def_164, type, sK99: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X1)).
% 20.67/4.15 thf(func_def_165, type, sK100: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod @ X2 @ product_prod @ X1 @ X0 > $o) > X0)).
% 20.67/4.15 thf(func_def_166, type, sK101: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > coinductive_llist @ X0 > X0)).
% 20.67/4.15 thf(func_def_167, type, sK102: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X1 > $o) > X0)).
% 20.67/4.15 thf(func_def_168, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod @ X0 @ X2 > (X0 > X2 > X1) > (X1 > $o) > X2)).
% 20.67/4.15 thf(func_def_169, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X0)).
% 20.67/4.15 thf(func_def_170, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X1)).
% 20.67/4.15 thf(func_def_171, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X2)).
% 20.67/4.15 thf(func_def_172, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X3)).
% 20.67/4.15 thf(func_def_173, type, sK108: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X4)).
% 20.67/4.15 thf(func_def_174, type, sK109: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X5)).
% 20.67/4.15 thf(func_def_175, type, sK110: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ product_prod @ X5 @ X6 > X6)).
% 20.67/4.15 thf(func_def_176, type, sK111: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0)).
% 20.67/4.15 thf(func_def_177, type, sK112: !>[X0: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0)).
% 20.67/4.15 thf(func_def_178, type, sK113: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X1)).
% 20.67/4.15 thf(func_def_179, type, sK114: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > X0)).
% 20.67/4.15 thf(func_def_180, type, sK115: !>[X0: $tType, X1: $tType]:((X1 > X1 > $o) > (X0 > X0 > $o) > (X0 > X1 > $o) > X0)).
% 20.67/4.15 thf(func_def_181, type, sK116: !>[X0: $tType, X1: $tType]:((X1 > X1 > $o) > (X0 > X0 > $o) > (X0 > X1 > $o) > X1)).
% 20.67/4.15 thf(func_def_182, type, sK117: !>[X0: $tType, X1: $tType]:((X1 > X1 > $o) > (X0 > X0 > $o) > (X0 > X1 > $o) > X0)).
% 20.67/4.15 thf(func_def_183, type, sK118: !>[X0: $tType, X1: $tType]:((X1 > X1 > $o) > (X0 > X0 > $o) > (X0 > X1 > $o) > X1)).
% 20.67/4.15 thf(func_def_184, type, sK119: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1 > X0) > (X0 > $o) > (X1 > X2 > $o) > X2)).
% 20.67/4.15 thf(func_def_185, type, sK120: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1 > X0) > (X0 > $o) > (X1 > X2 > $o) > X1)).
% 20.67/4.15 thf(func_def_186, type, sK121: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X0)).
% 20.67/4.15 thf(func_def_187, type, sK122: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X1)).
% 20.67/4.15 thf(func_def_188, type, sK123: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X2)).
% 20.67/4.15 thf(func_def_189, type, sK124: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X3)).
% 20.67/4.15 thf(func_def_190, type, sK125: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X4)).
% 20.67/4.15 thf(func_def_191, type, sK126: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod @ X0 @ product_prod @ X1 @ product_prod @ X2 @ product_prod @ X3 @ product_prod @ X4 @ X5 > X5)).
% 20.67/4.15 thf(func_def_193, type, ph128: !>[X0: $tType]:(X0)).
% 20.67/4.15 thf(f1983,plain,(
% 20.67/4.15 $false),
% 20.67/4.15 inference(avatar_sat_refutation,[status(thm)],[f1510,f1515,f1528,f1536,f1545,f1554,f1555,f1622,f1766,f1770,f1799,f1802,f1807,f1879,f1900,f1976])).
% 20.67/4.15 thf(f1976,plain,(
% 20.67/4.15 ~spl127_3 | ~spl127_4 | ~spl127_6 | ~spl127_8),
% 20.67/4.15 inference(avatar_contradiction_clause,[status(thm)],[f1975])).
% 20.67/4.15 thf(f1975,plain,(
% 20.67/4.15 $false | (~spl127_3 | ~spl127_4 | ~spl127_6 | ~spl127_8)),
% 20.67/4.15 inference(subsumption_resolution,[status(thm)],[f1974,f1940])).
% 20.67/4.15 thf(f1940,plain,(
% 20.67/4.15 ($true != (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))) @ (product_fst @ coinductive_llist @ b @ f @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) | ~spl127_8),
% 20.67/4.15 inference(subsumption_resolution,[status(thm)],[f1938,f1479])).
% 20.67/4.15 thf(f1479,plain,(
% 20.67/4.15 ($true = (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ b @ d @ ysa)))),
% 20.67/4.15 inference(binary_proxy_clausification,[status(thm)],[f1478])).
% 20.67/4.15 thf(f1478,plain,(
% 20.67/4.15 ($true = (((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) => (qa @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (product_snd @ coinductive_llist @ b @ d @ ysa))) & (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ b @ d @ ysa))))),
% 20.67/4.15 inference(beta_eta_normalization,[status(thm)],[f1366])).
% 20.67/4.15 thf(f1366,plain,(
% 20.67/4.15 ($true = ((^[Y0 : coinductive_llist @ a > c > product_prod @ coinductive_llist @ b @ d > $o]: ((^[Y1 : product_prod @ coinductive_llist @ a @ c]: (Y0 @ (product_fst @ coinductive_llist @ a @ c @ Y1) @ (product_snd @ coinductive_llist @ a @ c @ Y1))))) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : c]: ((^[Y2 : coinductive_llist @ b > d > $o]: ((^[Y3 : product_prod @ coinductive_llist @ b @ d]: (Y2 @ (product_fst @ coinductive_llist @ b @ d @ Y3) @ (product_snd @ coinductive_llist @ b @ d @ Y3))))) @ (^[Y2 : coinductive_llist @ b]: ((^[Y3 : d]: (((coinductive_lfinite @ a @ Y0) => (qa @ Y1 @ Y3)) & (coindu1486289336t_all2 @ a @ b @ pa @ Y0 @ Y2))))))))) @ xsa @ ysa))),
% 20.67/4.15 inference(definition_unfolding,[status(thm)],[f1277,f1018,f1018])).
% 20.67/4.15 thf(f1018,plain,(
% 20.67/4.15 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : ((product_case_prod @ X2 @ X1 @ X0 = (^[Y0 : X2 > X1 > X0]: ((^[Y1 : product_prod @ X2 @ X1]: (Y0 @ (product_fst @ X2 @ X1 @ Y1) @ (product_snd @ X2 @ X1 @ Y1))))))) )),
% 20.67/4.15 inference(cnf_transformation,[status(thm)],[f317])).
% 20.67/4.15 thf(f317,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (product_case_prod @ X2 @ X1 @ X0 = (^[Y0 : X2 > X1 > X0]: ((^[Y1 : product_prod @ X2 @ X1]: (Y0 @ (product_fst @ X2 @ X1 @ Y1) @ (product_snd @ X2 @ X1 @ Y1))))))),
% 20.67/4.15 inference(fool_elimination,[status(thm)],[f316])).
% 20.67/4.15 thf(f316,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : $tType,X2 : $tType] : (product_case_prod @ X2 @ X1 @ X0 = (^[X3 : X2 > X1 > X0, X4 : product_prod @ X2 @ X1] : (X3 @ (product_fst @ X2 @ X1 @ X4) @ (product_snd @ X2 @ X1 @ X4))))),
% 20.67/4.15 inference(rectify,[status(thm)],[f69])).
% 20.67/4.15 thf(f69,axiom,(
% 20.67/4.15 ! [X2 : $tType,X1 : $tType,X0 : $tType] : (product_case_prod @ X0 @ X1 @ X2 = (^[X18 : X0 > X1 > X2, X63 : product_prod @ X0 @ X1] : (X18 @ (product_fst @ X0 @ X1 @ X63) @ (product_snd @ X0 @ X1 @ X63))))),
% 20.67/4.15 file('/export/starexec/sandbox2/tmp/tmp.mqKFzRPNcN/DTF2THF_23357.p',fact_68_prod_Ocase__eq__if)).
% 20.67/4.15 thf(f1277,plain,(
% 20.67/4.15 ($true = (product_case_prod @ coinductive_llist @ a @ c @ (product_prod @ coinductive_llist @ b @ d > $o) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : c]: (product_case_prod @ coinductive_llist @ b @ d @ $o @ (^[Y2 : coinductive_llist @ b]: ((^[Y3 : d]: (((coinductive_lfinite @ a @ Y0) => (qa @ Y1 @ Y3)) & (coindu1486289336t_all2 @ a @ b @ pa @ Y0 @ Y2))))))))) @ xsa @ ysa))),
% 20.67/4.15 inference(cnf_transformation,[status(thm)],[f341])).
% 20.67/4.15 thf(f341,plain,(
% 20.67/4.15 ($true = (product_case_prod @ coinductive_llist @ a @ c @ (product_prod @ coinductive_llist @ b @ d > $o) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : c]: (product_case_prod @ coinductive_llist @ b @ d @ $o @ (^[Y2 : coinductive_llist @ b]: ((^[Y3 : d]: (((coinductive_lfinite @ a @ Y0) => (qa @ Y1 @ Y3)) & (coindu1486289336t_all2 @ a @ b @ pa @ Y0 @ Y2))))))))) @ xsa @ ysa))),
% 20.67/4.15 inference(fool_elimination,[status(thm)],[f340])).
% 20.67/4.15 thf(f340,plain,(
% 20.67/4.15 (product_case_prod @ coinductive_llist @ a @ c @ (product_prod @ coinductive_llist @ b @ d > $o) @ (^[X0 : coinductive_llist @ a, X1 : c] : (product_case_prod @ coinductive_llist @ b @ d @ $o @ (^[X2 : coinductive_llist @ b, X3 : d] : ((coindu1486289336t_all2 @ a @ b @ pa @ X0 @ X2) & ((coinductive_lfinite @ a @ X0) => (qa @ X1 @ X3)))))) @ xsa @ ysa)),
% 20.67/4.15 inference(rectify,[status(thm)],[f257])).
% 20.67/4.15 thf(f257,axiom,(
% 20.67/4.15 (product_case_prod @ coinductive_llist @ a @ c @ (product_prod @ coinductive_llist @ b @ d > $o) @ (^[X42 : coinductive_llist @ a, X12 : c] : (product_case_prod @ coinductive_llist @ b @ d @ $o @ (^[X43 : coinductive_llist @ b, X124 : d] : ((coindu1486289336t_all2 @ a @ b @ pa @ X42 @ X43) & ((coinductive_lfinite @ a @ X42) => (qa @ X12 @ X124)))))) @ xsa @ ysa)),
% 20.67/4.15 file('/export/starexec/sandbox2/tmp/tmp.mqKFzRPNcN/DTF2THF_23357.p',conj_0)).
% 20.67/4.15 thf(f1938,plain,(
% 20.67/4.15 ($true != (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ b @ d @ ysa))) | ($true != (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))) @ (product_fst @ coinductive_llist @ b @ f @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) | ~spl127_8),
% 20.67/4.15 inference(trivial_inequality_removal,[status(thm)],[f1918])).
% 20.67/4.15 thf(f1918,plain,(
% 20.67/4.15 ($true != (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))) @ (product_fst @ coinductive_llist @ b @ f @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) | ($true = $false) | ($true != (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ b @ d @ ysa))) | ~spl127_8),
% 20.67/4.15 inference(superposition,[status(thm)],[f1527,f1041])).
% 20.67/4.15 thf(f1041,plain,(
% 20.67/4.15 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : coinductive_llist @ X0,X6 : coinductive_llist @ X1,X4 : coinductive_llist @ X1,X5 : coinductive_llist @ X0] : (($true = (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ (coinductive_lappend @ X0 @ X3 @ X5) @ (coinductive_lappend @ X1 @ X4 @ X6))) | ($true != (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X5 @ X6)) | ($true != (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4))) )),
% 20.67/4.15 inference(cnf_transformation,[status(thm)],[f766])).
% 20.67/4.15 thf(f766,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1,X5 : coinductive_llist @ X0,X6 : coinductive_llist @ X1] : ((($true = (coinductive_lfinite @ X1 @ X4)) & ($true = (coinductive_lfinite @ X0 @ X3)) & ($true != (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X5 @ X6))) | ($true != (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4)) | ($true = (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ (coinductive_lappend @ X0 @ X3 @ X5) @ (coinductive_lappend @ X1 @ X4 @ X6))))),
% 20.67/4.15 inference(flattening,[status(thm)],[f765])).
% 20.67/4.15 thf(f765,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1,X5 : coinductive_llist @ X0,X6 : coinductive_llist @ X1] : ((($true = (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ (coinductive_lappend @ X0 @ X3 @ X5) @ (coinductive_lappend @ X1 @ X4 @ X6))) | ((($true != (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X5 @ X6)) & ($true = (coinductive_lfinite @ X1 @ X4))) & ($true = (coinductive_lfinite @ X0 @ X3)))) | ($true != (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4)))),
% 20.67/4.15 inference(ennf_transformation,[status(thm)],[f513])).
% 20.67/4.15 thf(f513,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1,X5 : coinductive_llist @ X0,X6 : coinductive_llist @ X1] : (($true = (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4)) => ((($true = (coinductive_lfinite @ X0 @ X3)) => (($true = (coinductive_lfinite @ X1 @ X4)) => ($true = (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X5 @ X6)))) => ($true = (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ (coinductive_lappend @ X0 @ X3 @ X5) @ (coinductive_lappend @ X1 @ X4 @ X6)))))),
% 20.67/4.15 inference(fool_elimination,[status(thm)],[f512])).
% 20.67/4.15 thf(f512,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1,X5 : coinductive_llist @ X0,X6 : coinductive_llist @ X1] : ((coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4) => (((coinductive_lfinite @ X0 @ X3) => ((coinductive_lfinite @ X1 @ X4) => (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X5 @ X6))) => (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ (coinductive_lappend @ X0 @ X3 @ X5) @ (coinductive_lappend @ X1 @ X4 @ X6))))),
% 20.67/4.15 inference(rectify,[status(thm)],[f5])).
% 20.67/4.15 thf(f5,axiom,(
% 20.67/4.15 ! [X0 : $tType,X1 : $tType,X9 : X0 > X1 > $o,X7 : coinductive_llist @ X0,X8 : coinductive_llist @ X1,X14 : coinductive_llist @ X0,X15 : coinductive_llist @ X1] : ((coindu1486289336t_all2 @ X0 @ X1 @ X9 @ X7 @ X8) => (((coinductive_lfinite @ X0 @ X7) => ((coinductive_lfinite @ X1 @ X8) => (coindu1486289336t_all2 @ X0 @ X1 @ X9 @ X14 @ X15))) => (coindu1486289336t_all2 @ X0 @ X1 @ X9 @ (coinductive_lappend @ X0 @ X7 @ X14) @ (coinductive_lappend @ X1 @ X8 @ X15))))),
% 20.67/4.15 file('/export/starexec/sandbox2/tmp/tmp.mqKFzRPNcN/DTF2THF_23357.p',fact_4_llist__all2__lappendI)).
% 20.67/4.15 thf(f1527,plain,(
% 20.67/4.15 ((coindu1486289336t_all2 @ a @ b @ pa @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa) @ (product_fst @ coinductive_llist @ b @ f @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) = $false) | ~spl127_8),
% 20.67/4.15 inference(avatar_component_clause,[status(thm)],[f1525])).
% 20.67/4.15 thf(f1525,definition,(
% 20.67/4.15 spl127_8 <=> ((coindu1486289336t_all2 @ a @ b @ pa @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa) @ (product_fst @ coinductive_llist @ b @ f @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) = $false)),
% 20.67/4.15 introduced(definition,[new_symbols(naming,[spl127_8])],[avatar_definition])).
% 20.67/4.15 thf(f1974,plain,(
% 20.67/4.15 ($true = (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))) @ (product_fst @ coinductive_llist @ b @ f @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) | (~spl127_3 | ~spl127_4 | ~spl127_6)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1973,f1227])).
% 20.67/4.15 thf(f1227,plain,(
% 20.67/4.15 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (((if @ X0 @ $true @ X1 @ X2) = X1)) )),
% 20.67/4.15 inference(cnf_transformation,[status(thm)],[f435])).
% 20.67/4.15 thf(f435,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : X0,X2 : X0] : ((if @ X0 @ $true @ X1 @ X2) = X1)),
% 20.67/4.15 inference(fool_elimination,[status(thm)],[f434])).
% 20.67/4.15 thf(f434,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : X0,X2 : X0] : ((if @ X0 @ $true @ X1 @ X2) = X1)),
% 20.67/4.15 inference(rectify,[status(thm)],[f256])).
% 20.67/4.15 thf(f256,axiom,(
% 20.67/4.15 ! [X0 : $tType,X5 : X0,X36 : X0] : ((if @ X0 @ $true @ X5 @ X36) = X5)),
% 20.67/4.15 file('/export/starexec/sandbox2/tmp/tmp.mqKFzRPNcN/DTF2THF_23357.p',help_If_1_1_T)).
% 20.67/4.15 thf(f1973,plain,(
% 20.67/4.15 ($true = (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))) @ (product_fst @ coinductive_llist @ b @ f @ (ys_a @ (if @ d @ $true @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d)))))) | (~spl127_3 | ~spl127_4 | ~spl127_6)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1972,f1504])).
% 20.67/4.15 thf(f1504,plain,(
% 20.67/4.15 ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) = $true) | ~spl127_4),
% 20.67/4.15 inference(avatar_component_clause,[status(thm)],[f1503])).
% 20.67/4.15 thf(f1503,definition,(
% 20.67/4.15 spl127_4 <=> ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) = $true)),
% 20.67/4.15 introduced(definition,[new_symbols(naming,[spl127_4])],[avatar_definition])).
% 20.67/4.15 thf(f1972,plain,(
% 20.67/4.15 ($true = (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))) @ (product_fst @ coinductive_llist @ b @ f @ (ys_a @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d)))))) | (~spl127_3 | ~spl127_6)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1949,f1227])).
% 20.67/4.15 thf(f1949,plain,(
% 20.67/4.15 ($true = (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ $true @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)))) @ (product_fst @ coinductive_llist @ b @ f @ (ys_a @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d)))))) | (~spl127_3 | ~spl127_6)),
% 20.67/4.15 inference(superposition,[status(thm)],[f1514,f1500])).
% 20.67/4.15 thf(f1500,plain,(
% 20.67/4.15 ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = $true) | ~spl127_3),
% 20.67/4.15 inference(avatar_component_clause,[status(thm)],[f1499])).
% 20.67/4.15 thf(f1499,definition,(
% 20.67/4.15 spl127_3 <=> ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = $true)),
% 20.67/4.15 introduced(definition,[new_symbols(naming,[spl127_3])],[avatar_definition])).
% 20.67/4.15 thf(f1514,plain,(
% 20.67/4.15 ($true = (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)))) @ (product_fst @ coinductive_llist @ b @ f @ (ys_a @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d)))))) | ~spl127_6),
% 20.67/4.15 inference(avatar_component_clause,[status(thm)],[f1512])).
% 20.67/4.15 thf(f1512,definition,(
% 20.67/4.15 spl127_6 <=> ($true = (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)))) @ (product_fst @ coinductive_llist @ b @ f @ (ys_a @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d))))))),
% 20.67/4.15 introduced(definition,[new_symbols(naming,[spl127_6])],[avatar_definition])).
% 20.67/4.15 thf(f1900,plain,(
% 20.67/4.15 ~spl127_1 | ~spl127_3 | ~spl127_24),
% 20.67/4.15 inference(avatar_contradiction_clause,[status(thm)],[f1899])).
% 20.67/4.15 thf(f1899,plain,(
% 20.67/4.15 $false | (~spl127_1 | ~spl127_3 | ~spl127_24)),
% 20.67/4.15 inference(trivial_inequality_removal,[status(thm)],[f1887])).
% 20.67/4.15 thf(f1887,plain,(
% 20.67/4.15 ($true = $false) | (~spl127_1 | ~spl127_3 | ~spl127_24)),
% 20.67/4.15 inference(superposition,[status(thm)],[f1881,f1797])).
% 20.67/4.15 thf(f1797,plain,(
% 20.67/4.15 ($true = (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))))) | ~spl127_24),
% 20.67/4.15 inference(avatar_component_clause,[status(thm)],[f1795])).
% 20.67/4.15 thf(f1795,definition,(
% 20.67/4.15 spl127_24 <=> ($true = (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))))),
% 20.67/4.15 introduced(definition,[new_symbols(naming,[spl127_24])],[avatar_definition])).
% 20.67/4.15 thf(f1881,plain,(
% 20.67/4.15 ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) = $false) | (~spl127_1 | ~spl127_3)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1880,f1227])).
% 20.67/4.15 thf(f1880,plain,(
% 20.67/4.15 ($false = (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ $true @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)))))) | (~spl127_1 | ~spl127_3)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1493,f1500])).
% 20.67/4.15 thf(f1493,plain,(
% 20.67/4.15 ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c))))) = $false) | ~spl127_1),
% 20.67/4.15 inference(avatar_component_clause,[status(thm)],[f1491])).
% 20.67/4.15 thf(f1491,definition,(
% 20.67/4.15 spl127_1 <=> ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c))))) = $false)),
% 20.67/4.15 introduced(definition,[new_symbols(naming,[spl127_1])],[avatar_definition])).
% 20.67/4.15 thf(f1879,plain,(
% 20.67/4.15 ~spl127_3 | ~spl127_4 | ~spl127_5 | ~spl127_7),
% 20.67/4.15 inference(avatar_contradiction_clause,[status(thm)],[f1878])).
% 20.67/4.15 thf(f1878,plain,(
% 20.67/4.15 $false | (~spl127_3 | ~spl127_4 | ~spl127_5 | ~spl127_7)),
% 20.67/4.15 inference(trivial_inequality_removal,[status(thm)],[f1877])).
% 20.67/4.15 thf(f1877,plain,(
% 20.67/4.15 ($true = $false) | (~spl127_3 | ~spl127_4 | ~spl127_5 | ~spl127_7)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1876,f1523])).
% 20.67/4.15 thf(f1523,plain,(
% 20.67/4.15 ($false = (ra @ (product_snd @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))) @ (product_snd @ coinductive_llist @ b @ f @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) | ~spl127_7),
% 20.67/4.15 inference(avatar_component_clause,[status(thm)],[f1521])).
% 20.67/4.15 thf(f1521,definition,(
% 20.67/4.15 spl127_7 <=> ($false = (ra @ (product_snd @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))) @ (product_snd @ coinductive_llist @ b @ f @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa)))))),
% 20.67/4.15 introduced(definition,[new_symbols(naming,[spl127_7])],[avatar_definition])).
% 20.67/4.15 thf(f1876,plain,(
% 20.67/4.15 ($true = (ra @ (product_snd @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))) @ (product_snd @ coinductive_llist @ b @ f @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) | (~spl127_3 | ~spl127_4 | ~spl127_5)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1870,f1227])).
% 20.67/4.15 thf(f1870,plain,(
% 20.67/4.15 ($true = (ra @ (product_snd @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ $true @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)))) @ (product_snd @ coinductive_llist @ b @ f @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) | (~spl127_3 | ~spl127_4 | ~spl127_5)),
% 20.67/4.15 inference(superposition,[status(thm)],[f1809,f1500])).
% 20.67/4.15 thf(f1809,plain,(
% 20.67/4.15 ($true = (ra @ (product_snd @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)))) @ (product_snd @ coinductive_llist @ b @ f @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) | (~spl127_4 | ~spl127_5)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1808,f1227])).
% 20.67/4.15 thf(f1808,plain,(
% 20.67/4.15 ($true = (ra @ (product_snd @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)))) @ (product_snd @ coinductive_llist @ b @ f @ (ys_a @ (if @ d @ $true @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d)))))) | (~spl127_4 | ~spl127_5)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1509,f1504])).
% 20.67/4.15 thf(f1509,plain,(
% 20.67/4.15 ($true = (ra @ (product_snd @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)))) @ (product_snd @ coinductive_llist @ b @ f @ (ys_a @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d)))))) | ~spl127_5),
% 20.67/4.15 inference(avatar_component_clause,[status(thm)],[f1507])).
% 20.67/4.15 thf(f1507,definition,(
% 20.67/4.15 spl127_5 <=> ($true = (ra @ (product_snd @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)))) @ (product_snd @ coinductive_llist @ b @ f @ (ys_a @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d))))))),
% 20.67/4.15 introduced(definition,[new_symbols(naming,[spl127_5])],[avatar_definition])).
% 20.67/4.15 thf(f1807,plain,(
% 20.67/4.15 spl127_3 | ~spl127_9),
% 20.67/4.15 inference(avatar_split_clause,[status(thm)],[f1790,f1533,f1499])).
% 20.67/4.15 thf(f1533,definition,(
% 20.67/4.15 spl127_9 <=> ($true = (coinductive_lfinite @ a @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))))))),
% 20.67/4.15 introduced(definition,[new_symbols(naming,[spl127_9])],[avatar_definition])).
% 20.67/4.15 thf(f1790,plain,(
% 20.67/4.15 ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = $true) | ~spl127_9),
% 20.67/4.15 inference(duplicate_literal_removal,[status(thm)],[f1781])).
% 20.67/4.15 thf(f1781,plain,(
% 20.67/4.15 ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = $true) | ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = $true) | ~spl127_9),
% 20.67/4.15 inference(superposition,[status(thm)],[f1535,f1090])).
% 20.67/4.15 thf(f1090,plain,(
% 20.67/4.15 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : (((coinductive_lappend @ X0 @ X1 @ X2) = X1) | ($true = (coinductive_lfinite @ X0 @ X1))) )),
% 20.67/4.15 inference(cnf_transformation,[status(thm)],[f832])).
% 20.67/4.15 thf(f832,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : (((coinductive_lappend @ X0 @ X1 @ X2) = X1) | ($true = (coinductive_lfinite @ X0 @ X1)))),
% 20.67/4.15 inference(ennf_transformation,[status(thm)],[f677])).
% 20.67/4.15 thf(f677,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : (($true != (coinductive_lfinite @ X0 @ X1)) => ((coinductive_lappend @ X0 @ X1 @ X2) = X1))),
% 20.67/4.15 inference(flattening,[status(thm)],[f581])).
% 20.67/4.15 thf(f581,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : (~($true = (coinductive_lfinite @ X0 @ X1)) => ((coinductive_lappend @ X0 @ X1 @ X2) = X1))),
% 20.67/4.15 inference(fool_elimination,[status(thm)],[f580])).
% 20.67/4.15 thf(f580,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : (~(coinductive_lfinite @ X0 @ X1) => ((coinductive_lappend @ X0 @ X1 @ X2) = X1))),
% 20.67/4.15 inference(rectify,[status(thm)],[f8])).
% 20.67/4.15 thf(f8,axiom,(
% 20.67/4.15 ! [X0 : $tType,X7 : coinductive_llist @ X0,X8 : coinductive_llist @ X0] : (~(coinductive_lfinite @ X0 @ X7) => ((coinductive_lappend @ X0 @ X7 @ X8) = X7))),
% 20.67/4.15 file('/export/starexec/sandbox2/tmp/tmp.mqKFzRPNcN/DTF2THF_23357.p',fact_7_lappend__inf)).
% 20.67/4.15 thf(f1535,plain,(
% 20.67/4.15 ($true = (coinductive_lfinite @ a @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))))) | ~spl127_9),
% 20.67/4.15 inference(avatar_component_clause,[status(thm)],[f1533])).
% 20.67/4.15 thf(f1802,plain,(
% 20.67/4.15 ~spl127_9 | ~spl127_11),
% 20.67/4.15 inference(avatar_contradiction_clause,[status(thm)],[f1801])).
% 20.67/4.15 thf(f1801,plain,(
% 20.67/4.15 $false | (~spl127_9 | ~spl127_11)),
% 20.67/4.15 inference(trivial_inequality_removal,[status(thm)],[f1800])).
% 20.67/4.15 thf(f1800,plain,(
% 20.67/4.15 ($true = $false) | (~spl127_9 | ~spl127_11)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1787,f1544])).
% 20.67/4.15 thf(f1544,plain,(
% 20.67/4.15 ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = $false) | ~spl127_11),
% 20.67/4.15 inference(avatar_component_clause,[status(thm)],[f1542])).
% 20.67/4.15 thf(f1542,definition,(
% 20.67/4.15 spl127_11 <=> ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = $false)),
% 20.67/4.15 introduced(definition,[new_symbols(naming,[spl127_11])],[avatar_definition])).
% 20.67/4.15 thf(f1787,plain,(
% 20.67/4.15 ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = $true) | ~spl127_9),
% 20.67/4.15 inference(trivial_inequality_removal,[status(thm)],[f1783])).
% 20.67/4.15 thf(f1783,plain,(
% 20.67/4.15 ($true != $true) | ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = $true) | ~spl127_9),
% 20.67/4.15 inference(superposition,[status(thm)],[f1200,f1535])).
% 20.67/4.15 thf(f1200,plain,(
% 20.67/4.15 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : (($true != (coinductive_lfinite @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2))) | ($true = (coinductive_lfinite @ X0 @ X1))) )),
% 20.67/4.15 inference(cnf_transformation,[status(thm)],[f967])).
% 20.67/4.15 thf(f967,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : ((($true = (coinductive_lfinite @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2))) | ($true != (coinductive_lfinite @ X0 @ X1)) | ($true != (coinductive_lfinite @ X0 @ X2))) & ((($true = (coinductive_lfinite @ X0 @ X1)) & ($true = (coinductive_lfinite @ X0 @ X2))) | ($true != (coinductive_lfinite @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2)))))),
% 20.67/4.15 inference(flattening,[status(thm)],[f966])).
% 20.67/4.15 thf(f966,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : ((($true = (coinductive_lfinite @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2))) | (($true != (coinductive_lfinite @ X0 @ X1)) | ($true != (coinductive_lfinite @ X0 @ X2)))) & ((($true = (coinductive_lfinite @ X0 @ X1)) & ($true = (coinductive_lfinite @ X0 @ X2))) | ($true != (coinductive_lfinite @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2)))))),
% 20.67/4.15 inference(nnf_transformation,[status(thm)],[f571])).
% 20.67/4.15 thf(f571,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : (($true = (coinductive_lfinite @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2))) <=> (($true = (coinductive_lfinite @ X0 @ X1)) & ($true = (coinductive_lfinite @ X0 @ X2))))),
% 20.67/4.15 inference(fool_elimination,[status(thm)],[f570])).
% 20.67/4.15 thf(f570,plain,(
% 20.67/4.15 ! [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))),
% 20.67/4.15 inference(rectify,[status(thm)],[f3])).
% 20.67/4.15 thf(f3,axiom,(
% 20.67/4.15 ! [X0 : $tType,X7 : coinductive_llist @ X0,X8 : coinductive_llist @ X0] : ((coinductive_lfinite @ X0 @ (coinductive_lappend @ X0 @ X7 @ X8)) = (coinductive_lfinite @ X0 @ X7) & (coinductive_lfinite @ X0 @ X8))),
% 20.67/4.15 file('/export/starexec/sandbox2/tmp/tmp.mqKFzRPNcN/DTF2THF_23357.p',fact_2_lfinite__lappend)).
% 20.67/4.15 thf(f1799,plain,(
% 20.67/4.15 spl127_24 | ~spl127_9),
% 20.67/4.15 inference(avatar_split_clause,[status(thm)],[f1788,f1533,f1795])).
% 20.67/4.15 thf(f1788,plain,(
% 20.67/4.15 ($true = (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))))) | ~spl127_9),
% 20.67/4.15 inference(trivial_inequality_removal,[status(thm)],[f1782])).
% 20.67/4.15 thf(f1782,plain,(
% 20.67/4.15 ($true != $true) | ($true = (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))))) | ~spl127_9),
% 20.67/4.15 inference(superposition,[status(thm)],[f1199,f1535])).
% 20.67/4.15 thf(f1199,plain,(
% 20.67/4.15 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : (($true != (coinductive_lfinite @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2))) | ($true = (coinductive_lfinite @ X0 @ X2))) )),
% 20.67/4.15 inference(cnf_transformation,[status(thm)],[f967])).
% 20.67/4.15 thf(f1770,plain,(
% 20.67/4.15 ~spl127_8 | ~spl127_12),
% 20.67/4.15 inference(avatar_contradiction_clause,[status(thm)],[f1769])).
% 20.67/4.15 thf(f1769,plain,(
% 20.67/4.15 $false | (~spl127_8 | ~spl127_12)),
% 20.67/4.15 inference(trivial_inequality_removal,[status(thm)],[f1768])).
% 20.67/4.15 thf(f1768,plain,(
% 20.67/4.15 ($true = $false) | (~spl127_8 | ~spl127_12)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1767,f1553])).
% 20.67/4.15 thf(f1553,plain,(
% 20.67/4.15 ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) = $false) | ~spl127_12),
% 20.67/4.15 inference(avatar_component_clause,[status(thm)],[f1551])).
% 20.67/4.15 thf(f1551,definition,(
% 20.67/4.15 spl127_12 <=> ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) = $false)),
% 20.67/4.15 introduced(definition,[new_symbols(naming,[spl127_12])],[avatar_definition])).
% 20.67/4.15 thf(f1767,plain,(
% 20.67/4.15 ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) = $true) | ~spl127_8),
% 20.67/4.15 inference(subsumption_resolution,[status(thm)],[f1698,f1479])).
% 20.67/4.15 thf(f1698,plain,(
% 20.67/4.15 ($true != (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ b @ d @ ysa))) | ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) = $true) | ~spl127_8),
% 20.67/4.15 inference(trivial_inequality_removal,[status(thm)],[f1695])).
% 20.67/4.15 thf(f1695,plain,(
% 20.67/4.15 ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) = $true) | ($true = $false) | ($true != (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ b @ d @ ysa))) | ~spl127_8),
% 20.67/4.15 inference(superposition,[status(thm)],[f1043,f1527])).
% 20.67/4.15 thf(f1043,plain,(
% 20.67/4.15 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : coinductive_llist @ X0,X6 : coinductive_llist @ X1,X4 : coinductive_llist @ X1,X5 : coinductive_llist @ X0] : (($true = (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ (coinductive_lappend @ X0 @ X3 @ X5) @ (coinductive_lappend @ X1 @ X4 @ X6))) | ($true != (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4)) | ($true = (coinductive_lfinite @ X1 @ X4))) )),
% 20.67/4.15 inference(cnf_transformation,[status(thm)],[f766])).
% 20.67/4.15 thf(f1766,plain,(
% 20.67/4.15 ~spl127_8 | ~spl127_11),
% 20.67/4.15 inference(avatar_contradiction_clause,[status(thm)],[f1765])).
% 20.67/4.15 thf(f1765,plain,(
% 20.67/4.15 $false | (~spl127_8 | ~spl127_11)),
% 20.67/4.15 inference(trivial_inequality_removal,[status(thm)],[f1764])).
% 20.67/4.15 thf(f1764,plain,(
% 20.67/4.15 ($true = $false) | (~spl127_8 | ~spl127_11)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1763,f1544])).
% 20.67/4.15 thf(f1763,plain,(
% 20.67/4.15 ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = $true) | ~spl127_8),
% 20.67/4.15 inference(subsumption_resolution,[status(thm)],[f1700,f1479])).
% 20.67/4.15 thf(f1700,plain,(
% 20.67/4.15 ($true != (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ b @ d @ ysa))) | ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = $true) | ~spl127_8),
% 20.67/4.15 inference(trivial_inequality_removal,[status(thm)],[f1693])).
% 20.67/4.15 thf(f1693,plain,(
% 20.67/4.15 ($true = $false) | ($true != (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ b @ d @ ysa))) | ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = $true) | ~spl127_8),
% 20.67/4.15 inference(superposition,[status(thm)],[f1042,f1527])).
% 20.67/4.15 thf(f1042,plain,(
% 20.67/4.15 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : coinductive_llist @ X0,X6 : coinductive_llist @ X1,X4 : coinductive_llist @ X1,X5 : coinductive_llist @ X0] : (($true = (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ (coinductive_lappend @ X0 @ X3 @ X5) @ (coinductive_lappend @ X1 @ X4 @ X6))) | ($true != (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4)) | ($true = (coinductive_lfinite @ X0 @ X3))) )),
% 20.67/4.15 inference(cnf_transformation,[status(thm)],[f766])).
% 20.67/4.15 thf(f1622,plain,(
% 20.67/4.15 ~spl127_10 | spl127_2 | ~spl127_3 | ~spl127_4),
% 20.67/4.15 inference(avatar_split_clause,[status(thm)],[f1618,f1503,f1499,f1495,f1538])).
% 20.67/4.15 thf(f1538,definition,(
% 20.67/4.15 spl127_10 <=> ($true = (qa @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (product_snd @ coinductive_llist @ b @ d @ ysa)))),
% 20.67/4.15 introduced(definition,[new_symbols(naming,[spl127_10])],[avatar_definition])).
% 20.67/4.15 thf(f1495,definition,(
% 20.67/4.15 spl127_2 <=> ($true = (qa @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)) @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d))))),
% 20.67/4.15 introduced(definition,[new_symbols(naming,[spl127_2])],[avatar_definition])).
% 20.67/4.15 thf(f1618,plain,(
% 20.67/4.15 ($true != (qa @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (product_snd @ coinductive_llist @ b @ d @ ysa))) | (spl127_2 | ~spl127_3 | ~spl127_4)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1617,f1227])).
% 20.67/4.15 thf(f1617,plain,(
% 20.67/4.15 ($true != (qa @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (if @ d @ $true @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d)))) | (spl127_2 | ~spl127_3 | ~spl127_4)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1616,f1504])).
% 20.67/4.15 thf(f1616,plain,(
% 20.67/4.15 ($true != (qa @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d)))) | (spl127_2 | ~spl127_3)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1600,f1227])).
% 20.67/4.15 thf(f1600,plain,(
% 20.67/4.15 ($true != (qa @ (if @ c @ $true @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)) @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d)))) | (spl127_2 | ~spl127_3)),
% 20.67/4.15 inference(superposition,[status(thm)],[f1497,f1500])).
% 20.67/4.15 thf(f1497,plain,(
% 20.67/4.15 ($true != (qa @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)) @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d)))) | spl127_2),
% 20.67/4.15 inference(avatar_component_clause,[status(thm)],[f1495])).
% 20.67/4.15 thf(f1555,plain,(
% 20.67/4.15 spl127_4 | spl127_11),
% 20.67/4.15 inference(avatar_split_clause,[status(thm)],[f1549,f1542,f1503])).
% 20.67/4.15 thf(f1549,plain,(
% 20.67/4.15 ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) = $true) | ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = $false)),
% 20.67/4.15 inference(binary_proxy_clausification,[status(thm)],[f1547])).
% 20.67/4.15 thf(f1547,plain,(
% 20.67/4.15 ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)))),
% 20.67/4.15 inference(trivial_inequality_removal,[status(thm)],[f1546])).
% 20.67/4.15 thf(f1546,plain,(
% 20.67/4.15 ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa))) | ($true != $true)),
% 20.67/4.15 inference(superposition,[status(thm)],[f1283,f1479])).
% 20.67/4.15 thf(f1283,plain,(
% 20.67/4.15 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1] : (($true != (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4)) | ((coinductive_lfinite @ X1 @ X4) = (coinductive_lfinite @ X0 @ X3))) )),
% 20.67/4.15 inference(cnf_transformation,[status(thm)],[f862])).
% 20.67/4.15 thf(f862,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1] : (($true != (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4)) | ((coinductive_lfinite @ X1 @ X4) = (coinductive_lfinite @ X0 @ X3)))),
% 20.67/4.15 inference(ennf_transformation,[status(thm)],[f493])).
% 20.67/4.15 thf(f493,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1] : (($true = (coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4)) => ((coinductive_lfinite @ X1 @ X4) = (coinductive_lfinite @ X0 @ X3)))),
% 20.67/4.15 inference(fool_elimination,[status(thm)],[f492])).
% 20.67/4.15 thf(f492,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X1] : ((coindu1486289336t_all2 @ X0 @ X1 @ X2 @ X3 @ X4) => ((coinductive_lfinite @ X1 @ X4) = (coinductive_lfinite @ X0 @ X3)))),
% 20.67/4.15 inference(rectify,[status(thm)],[f9])).
% 20.67/4.15 thf(f9,axiom,(
% 20.67/4.15 ! [X0 : $tType,X1 : $tType,X9 : X0 > X1 > $o,X7 : coinductive_llist @ X0,X8 : coinductive_llist @ X1] : ((coindu1486289336t_all2 @ X0 @ X1 @ X9 @ X7 @ X8) => ((coinductive_lfinite @ X0 @ X7) = (coinductive_lfinite @ X1 @ X8)))),
% 20.67/4.15 file('/export/starexec/sandbox2/tmp/tmp.mqKFzRPNcN/DTF2THF_23357.p',fact_8_llist__all2__lfiniteD)).
% 20.67/4.15 thf(f1554,plain,(
% 20.67/4.15 spl127_12 | spl127_3),
% 20.67/4.15 inference(avatar_split_clause,[status(thm)],[f1548,f1499,f1551])).
% 20.67/4.15 thf(f1548,plain,(
% 20.67/4.15 ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = $true) | ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) = $false)),
% 20.67/4.15 inference(binary_proxy_clausification,[status(thm)],[f1547])).
% 20.67/4.15 thf(f1545,plain,(
% 20.67/4.15 spl127_10 | spl127_11),
% 20.67/4.15 inference(avatar_split_clause,[status(thm)],[f1481,f1542,f1538])).
% 20.67/4.15 thf(f1481,plain,(
% 20.67/4.15 ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = $false) | ($true = (qa @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (product_snd @ coinductive_llist @ b @ d @ ysa)))),
% 20.67/4.15 inference(binary_proxy_clausification,[status(thm)],[f1480])).
% 20.67/4.15 thf(f1480,plain,(
% 20.67/4.15 ($true = ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) => (qa @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (product_snd @ coinductive_llist @ b @ d @ ysa))))),
% 20.67/4.15 inference(binary_proxy_clausification,[status(thm)],[f1478])).
% 20.67/4.15 thf(f1536,plain,(
% 20.67/4.15 spl127_8 | spl127_9),
% 20.67/4.15 inference(avatar_split_clause,[status(thm)],[f1531,f1533,f1525])).
% 20.67/4.15 thf(f1531,plain,(
% 20.67/4.15 ($true = (coinductive_lfinite @ a @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))))) | ((coindu1486289336t_all2 @ a @ b @ pa @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa) @ (product_fst @ coinductive_llist @ b @ f @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) = $false)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1530,f1261])).
% 20.67/4.15 thf(f1261,plain,(
% 20.67/4.15 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2 > X0,X4 : product_prod @ X2 @ X1] : (((X3 @ (product_fst @ X2 @ X1 @ X4)) = (product_fst @ X0 @ X1 @ (product_apfst @ X2 @ X0 @ X1 @ X3 @ X4)))) )),
% 20.67/4.15 inference(cnf_transformation,[status(thm)],[f690])).
% 20.67/4.15 thf(f690,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2 > X0,X4 : product_prod @ X2 @ X1] : ((X3 @ (product_fst @ X2 @ X1 @ X4)) = (product_fst @ X0 @ X1 @ (product_apfst @ X2 @ X0 @ X1 @ X3 @ X4)))),
% 20.67/4.15 inference(rectify,[status(thm)],[f1])).
% 20.67/4.15 thf(f1,axiom,(
% 20.67/4.15 ! [X0 : $tType,X1 : $tType,X2 : $tType,X4 : X2 > X0,X5 : product_prod @ X2 @ X1] : ((product_fst @ X0 @ X1 @ (product_apfst @ X2 @ X0 @ X1 @ X4 @ X5)) = (X4 @ (product_fst @ X2 @ X1 @ X5)))),
% 20.67/4.15 file('/export/starexec/sandbox2/tmp/tmp.mqKFzRPNcN/DTF2THF_23357.p',fact_0_fst__apfst)).
% 20.67/4.15 thf(f1530,plain,(
% 20.67/4.15 ($true = (coinductive_lfinite @ a @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))))) | ((coindu1486289336t_all2 @ a @ b @ pa @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) @ (product_fst @ coinductive_llist @ b @ f @ (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) = $false)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1529,f1261])).
% 20.67/4.15 thf(f1529,plain,(
% 20.67/4.15 ($true = (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ e @ (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))))) | ((coindu1486289336t_all2 @ a @ b @ pa @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) @ (product_fst @ coinductive_llist @ b @ f @ (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) = $false)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1485,f1261])).
% 20.67/4.15 thf(f1485,plain,(
% 20.67/4.15 ((coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ e @ (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) @ (product_fst @ coinductive_llist @ b @ f @ (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) = $false) | ($true = (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ e @ (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))))))),
% 20.67/4.15 inference(binary_proxy_clausification,[status(thm)],[f1483])).
% 20.67/4.15 thf(f1483,plain,(
% 20.67/4.15 ($false = ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ e @ (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))))) => (ra @ (product_snd @ coinductive_llist @ a @ e @ (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) @ (product_snd @ coinductive_llist @ b @ f @ (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))))) | ((coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ e @ (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) @ (product_fst @ coinductive_llist @ b @ f @ (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) = $false)),
% 20.67/4.15 inference(binary_proxy_clausification,[status(thm)],[f1482])).
% 20.67/4.15 thf(f1482,plain,(
% 20.67/4.15 ($true != (((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ e @ (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))))) => (ra @ (product_snd @ coinductive_llist @ a @ e @ (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) @ (product_snd @ coinductive_llist @ b @ f @ (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa)))))) & (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ e @ (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) @ (product_fst @ coinductive_llist @ b @ f @ (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa)))))))),
% 20.67/4.15 inference(beta_eta_normalization,[status(thm)],[f1325])).
% 20.67/4.15 thf(f1325,plain,(
% 20.67/4.15 ($true != ((^[Y0 : coinductive_llist @ a > e > product_prod @ coinductive_llist @ b @ f > $o]: ((^[Y1 : product_prod @ coinductive_llist @ a @ e]: (Y0 @ (product_fst @ coinductive_llist @ a @ e @ Y1) @ (product_snd @ coinductive_llist @ a @ e @ Y1))))) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : e]: ((^[Y2 : coinductive_llist @ b > f > $o]: ((^[Y3 : product_prod @ coinductive_llist @ b @ f]: (Y2 @ (product_fst @ coinductive_llist @ b @ f @ Y3) @ (product_snd @ coinductive_llist @ b @ f @ Y3))))) @ (^[Y2 : coinductive_llist @ b]: ((^[Y3 : f]: (((coinductive_lfinite @ a @ Y0) => (ra @ Y1 @ Y3)) & (coindu1486289336t_all2 @ a @ b @ pa @ Y0 @ Y2))))))))) @ ((^[Y0 : coinductive_llist @ a > c > (c > product_prod @ coinductive_llist @ a @ e) > product_prod @ coinductive_llist @ a @ e]: ((^[Y1 : product_prod @ coinductive_llist @ a @ c]: (Y0 @ (product_fst @ coinductive_llist @ a @ c @ Y1) @ (product_snd @ coinductive_llist @ a @ c @ Y1))))) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : c]: ((^[Y2 : c > product_prod @ coinductive_llist @ a @ e]: (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ Y0) @ (Y2 @ Y1))))))) @ xsa @ xs_a) @ ((^[Y0 : coinductive_llist @ b > d > (d > product_prod @ coinductive_llist @ b @ f) > product_prod @ coinductive_llist @ b @ f]: ((^[Y1 : product_prod @ coinductive_llist @ b @ d]: (Y0 @ (product_fst @ coinductive_llist @ b @ d @ Y1) @ (product_snd @ coinductive_llist @ b @ d @ Y1))))) @ (^[Y0 : coinductive_llist @ b]: ((^[Y1 : d]: ((^[Y2 : d > product_prod @ coinductive_llist @ b @ f]: (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ Y0) @ (Y2 @ Y1))))))) @ ysa @ ys_a)))),
% 20.67/4.15 inference(definition_unfolding,[status(thm)],[f1142,f1018,f1018,f1018,f1018])).
% 20.67/4.15 thf(f1142,plain,(
% 20.67/4.15 ($true != (product_case_prod @ coinductive_llist @ a @ e @ (product_prod @ coinductive_llist @ b @ f > $o) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : e]: (product_case_prod @ coinductive_llist @ b @ f @ $o @ (^[Y2 : coinductive_llist @ b]: ((^[Y3 : f]: (((coinductive_lfinite @ a @ Y0) => (ra @ Y1 @ Y3)) & (coindu1486289336t_all2 @ a @ b @ pa @ Y0 @ Y2))))))))) @ (product_case_prod @ coinductive_llist @ a @ c @ ((c > product_prod @ coinductive_llist @ a @ e) > product_prod @ coinductive_llist @ a @ e) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : c]: ((^[Y2 : c > product_prod @ coinductive_llist @ a @ e]: (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ Y0) @ (Y2 @ Y1))))))) @ xsa @ xs_a) @ (product_case_prod @ coinductive_llist @ b @ d @ ((d > product_prod @ coinductive_llist @ b @ f) > product_prod @ coinductive_llist @ b @ f) @ (^[Y0 : coinductive_llist @ b]: ((^[Y1 : d]: ((^[Y2 : d > product_prod @ coinductive_llist @ b @ f]: (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ Y0) @ (Y2 @ Y1))))))) @ ysa @ ys_a)))),
% 20.67/4.15 inference(cnf_transformation,[status(thm)],[f674])).
% 20.67/4.15 thf(f674,plain,(
% 20.67/4.15 ($true != (product_case_prod @ coinductive_llist @ a @ e @ (product_prod @ coinductive_llist @ b @ f > $o) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : e]: (product_case_prod @ coinductive_llist @ b @ f @ $o @ (^[Y2 : coinductive_llist @ b]: ((^[Y3 : f]: (((coinductive_lfinite @ a @ Y0) => (ra @ Y1 @ Y3)) & (coindu1486289336t_all2 @ a @ b @ pa @ Y0 @ Y2))))))))) @ (product_case_prod @ coinductive_llist @ a @ c @ ((c > product_prod @ coinductive_llist @ a @ e) > product_prod @ coinductive_llist @ a @ e) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : c]: ((^[Y2 : c > product_prod @ coinductive_llist @ a @ e]: (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ Y0) @ (Y2 @ Y1))))))) @ xsa @ xs_a) @ (product_case_prod @ coinductive_llist @ b @ d @ ((d > product_prod @ coinductive_llist @ b @ f) > product_prod @ coinductive_llist @ b @ f) @ (^[Y0 : coinductive_llist @ b]: ((^[Y1 : d]: ((^[Y2 : d > product_prod @ coinductive_llist @ b @ f]: (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ Y0) @ (Y2 @ Y1))))))) @ ysa @ ys_a)))),
% 20.67/4.15 inference(flattening,[status(thm)],[f289])).
% 20.67/4.15 thf(f289,plain,(
% 20.67/4.15 ~($true = (product_case_prod @ coinductive_llist @ a @ e @ (product_prod @ coinductive_llist @ b @ f > $o) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : e]: (product_case_prod @ coinductive_llist @ b @ f @ $o @ (^[Y2 : coinductive_llist @ b]: ((^[Y3 : f]: (((coinductive_lfinite @ a @ Y0) => (ra @ Y1 @ Y3)) & (coindu1486289336t_all2 @ a @ b @ pa @ Y0 @ Y2))))))))) @ (product_case_prod @ coinductive_llist @ a @ c @ ((c > product_prod @ coinductive_llist @ a @ e) > product_prod @ coinductive_llist @ a @ e) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : c]: ((^[Y2 : c > product_prod @ coinductive_llist @ a @ e]: (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ Y0) @ (Y2 @ Y1))))))) @ xsa @ xs_a) @ (product_case_prod @ coinductive_llist @ b @ d @ ((d > product_prod @ coinductive_llist @ b @ f) > product_prod @ coinductive_llist @ b @ f) @ (^[Y0 : coinductive_llist @ b]: ((^[Y1 : d]: ((^[Y2 : d > product_prod @ coinductive_llist @ b @ f]: (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ Y0) @ (Y2 @ Y1))))))) @ ysa @ ys_a)))),
% 20.67/4.15 inference(fool_elimination,[status(thm)],[f288])).
% 20.67/4.15 thf(f288,plain,(
% 20.67/4.15 ~(product_case_prod @ coinductive_llist @ a @ e @ (product_prod @ coinductive_llist @ b @ f > $o) @ (^[X0 : coinductive_llist @ a, X1 : e] : (product_case_prod @ coinductive_llist @ b @ f @ $o @ (^[X2 : coinductive_llist @ b, X3 : f] : ((coindu1486289336t_all2 @ a @ b @ pa @ X0 @ X2) & ((coinductive_lfinite @ a @ X0) => (ra @ X1 @ X3)))))) @ (product_case_prod @ coinductive_llist @ a @ c @ ((c > product_prod @ coinductive_llist @ a @ e) > product_prod @ coinductive_llist @ a @ e) @ (^[X4 : coinductive_llist @ a, X5 : c, X6 : c > product_prod @ coinductive_llist @ a @ e] : (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ X4) @ (X6 @ X5))) @ xsa @ xs_a) @ (product_case_prod @ coinductive_llist @ b @ d @ ((d > product_prod @ coinductive_llist @ b @ f) > product_prod @ coinductive_llist @ b @ f) @ (^[X7 : coinductive_llist @ b, X8 : d, X9 : d > product_prod @ coinductive_llist @ b @ f] : (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ X7) @ (X9 @ X8))) @ ysa @ ys_a))),
% 20.67/4.15 inference(rectify,[status(thm)],[f260])).
% 20.67/4.15 thf(f260,negated_conjecture,(
% 20.67/4.15 ~(product_case_prod @ coinductive_llist @ a @ e @ (product_prod @ coinductive_llist @ b @ f > $o) @ (^[X42 : coinductive_llist @ a, X12 : e] : (product_case_prod @ coinductive_llist @ b @ f @ $o @ (^[X43 : coinductive_llist @ b, X124 : f] : ((coindu1486289336t_all2 @ a @ b @ pa @ X42 @ X43) & ((coinductive_lfinite @ a @ X42) => (ra @ X12 @ X124)))))) @ (product_case_prod @ coinductive_llist @ a @ c @ ((c > product_prod @ coinductive_llist @ a @ e) > product_prod @ coinductive_llist @ a @ e) @ (^[X42 : coinductive_llist @ a, X12 : c, X18 : c > product_prod @ coinductive_llist @ a @ e] : (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ X42) @ (X18 @ X12))) @ xsa @ xs_a) @ (product_case_prod @ coinductive_llist @ b @ d @ ((d > product_prod @ coinductive_llist @ b @ f) > product_prod @ coinductive_llist @ b @ f) @ (^[X42 : coinductive_llist @ b, X12 : d, X18 : d > product_prod @ coinductive_llist @ b @ f] : (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ X42) @ (X18 @ X12))) @ ysa @ ys_a))),
% 20.67/4.15 inference(negated_conjecture,[status(cth)],[f259])).
% 20.67/4.15 thf(f259,conjecture,(
% 20.67/4.15 (product_case_prod @ coinductive_llist @ a @ e @ (product_prod @ coinductive_llist @ b @ f > $o) @ (^[X42 : coinductive_llist @ a, X12 : e] : (product_case_prod @ coinductive_llist @ b @ f @ $o @ (^[X43 : coinductive_llist @ b, X124 : f] : ((coindu1486289336t_all2 @ a @ b @ pa @ X42 @ X43) & ((coinductive_lfinite @ a @ X42) => (ra @ X12 @ X124)))))) @ (product_case_prod @ coinductive_llist @ a @ c @ ((c > product_prod @ coinductive_llist @ a @ e) > product_prod @ coinductive_llist @ a @ e) @ (^[X42 : coinductive_llist @ a, X12 : c, X18 : c > product_prod @ coinductive_llist @ a @ e] : (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ X42) @ (X18 @ X12))) @ xsa @ xs_a) @ (product_case_prod @ coinductive_llist @ b @ d @ ((d > product_prod @ coinductive_llist @ b @ f) > product_prod @ coinductive_llist @ b @ f) @ (^[X42 : coinductive_llist @ b, X12 : d, X18 : d > product_prod @ coinductive_llist @ b @ f] : (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ X42) @ (X18 @ X12))) @ ysa @ ys_a))),
% 20.67/4.15 file('/export/starexec/sandbox2/tmp/tmp.mqKFzRPNcN/DTF2THF_23357.p',conj_2)).
% 20.67/4.15 thf(f1528,plain,(
% 20.67/4.15 spl127_7 | spl127_8),
% 20.67/4.15 inference(avatar_split_clause,[status(thm)],[f1519,f1525,f1521])).
% 20.67/4.15 thf(f1519,plain,(
% 20.67/4.15 ($false = (ra @ (product_snd @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))) @ (product_snd @ coinductive_llist @ b @ f @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) | ((coindu1486289336t_all2 @ a @ b @ pa @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa) @ (product_fst @ coinductive_llist @ b @ f @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) = $false)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1518,f1261])).
% 20.67/4.15 thf(f1518,plain,(
% 20.67/4.15 ((coindu1486289336t_all2 @ a @ b @ pa @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) @ (product_fst @ coinductive_llist @ b @ f @ (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) = $false) | ($false = (ra @ (product_snd @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))) @ (product_snd @ coinductive_llist @ b @ f @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa)))))),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1517,f1263])).
% 20.67/4.15 thf(f1263,plain,(
% 20.67/4.15 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X2 > X0,X4 : product_prod @ X2 @ X1] : (((product_snd @ X0 @ X1 @ (product_apfst @ X2 @ X0 @ X1 @ X3 @ X4)) = (product_snd @ X2 @ X1 @ X4))) )),
% 20.67/4.15 inference(cnf_transformation,[status(thm)],[f689])).
% 20.67/4.15 thf(f689,plain,(
% 20.67/4.15 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X2 > X0,X4 : product_prod @ X2 @ X1] : ((product_snd @ X0 @ X1 @ (product_apfst @ X2 @ X0 @ X1 @ X3 @ X4)) = (product_snd @ X2 @ X1 @ X4))),
% 20.67/4.15 inference(rectify,[status(thm)],[f35])).
% 20.67/4.15 thf(f35,axiom,(
% 20.67/4.15 ! [X1 : $tType,X0 : $tType,X2 : $tType,X4 : X2 > X1,X5 : product_prod @ X2 @ X0] : ((product_snd @ X1 @ X0 @ (product_apfst @ X2 @ X1 @ X0 @ X4 @ X5)) = (product_snd @ X2 @ X0 @ X5))),
% 20.67/4.15 file('/export/starexec/sandbox2/tmp/tmp.mqKFzRPNcN/DTF2THF_23357.p',fact_34_snd__apfst)).
% 20.67/4.15 thf(f1517,plain,(
% 20.67/4.15 ($false = (ra @ (product_snd @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa))) @ (product_snd @ coinductive_llist @ b @ f @ (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa)))))) | ((coindu1486289336t_all2 @ a @ b @ pa @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) @ (product_fst @ coinductive_llist @ b @ f @ (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) = $false)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1516,f1263])).
% 20.67/4.15 thf(f1516,plain,(
% 20.67/4.15 ((ra @ (product_snd @ coinductive_llist @ a @ e @ (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) @ (product_snd @ coinductive_llist @ b @ f @ (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) = $false) | ((coindu1486289336t_all2 @ a @ b @ pa @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa) @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) @ (product_fst @ coinductive_llist @ b @ f @ (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) = $false)),
% 20.67/4.15 inference(forward_demodulation,[status(thm)],[f1484,f1261])).
% 20.67/4.15 thf(f1484,plain,(
% 20.67/4.15 ((coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ e @ (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) @ (product_fst @ coinductive_llist @ b @ f @ (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) = $false) | ((ra @ (product_snd @ coinductive_llist @ a @ e @ (product_apfst @ coinductive_llist @ a @ coinductive_llist @ a @ e @ (coinductive_lappend @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (xs_a @ (product_snd @ coinductive_llist @ a @ c @ xsa)))) @ (product_snd @ coinductive_llist @ b @ f @ (product_apfst @ coinductive_llist @ b @ coinductive_llist @ b @ f @ (coinductive_lappend @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (ys_a @ (product_snd @ coinductive_llist @ b @ d @ ysa))))) = $false)),
% 20.67/4.15 inference(binary_proxy_clausification,[status(thm)],[f1483])).
% 20.67/4.15 thf(f1515,plain,(
% 20.67/4.15 ~spl127_4 | ~spl127_3 | spl127_6 | ~spl127_2),
% 20.67/4.15 inference(avatar_split_clause,[status(thm)],[f1488,f1495,f1512,f1499,f1503])).
% 20.67/4.15 thf(f1488,plain,(
% 20.67/4.15 ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) != $true) | ($true != (qa @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)) @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d)))) | ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) != $true) | ($true = (coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)))) @ (product_fst @ coinductive_llist @ b @ f @ (ys_a @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d))))))),
% 20.67/4.15 inference(binary_proxy_clausification,[status(thm)],[f1486])).
% 20.67/4.15 thf(f1486,plain,(
% 20.67/4.15 ($true = ((coindu1486289336t_all2 @ a @ b @ pa @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)))) @ (product_fst @ coinductive_llist @ b @ f @ (ys_a @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d))))) & ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c))))) => (ra @ (product_snd @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)))) @ (product_snd @ coinductive_llist @ b @ f @ (ys_a @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d)))))))) | ($true != (qa @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)) @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d)))) | ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) != $true) | ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) != $true)),
% 20.67/4.15 inference(beta_eta_normalization,[status(thm)],[f1289])).
% 20.67/4.15 thf(f1289,plain,(
% 20.67/4.15 ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) != $true) | ($true != (qa @ ((^[Y0 : coinductive_llist @ a > c > c]: ((^[Y1 : product_prod @ coinductive_llist @ a @ c]: (Y0 @ (product_fst @ coinductive_llist @ a @ c @ Y1) @ (product_snd @ coinductive_llist @ a @ c @ Y1))))) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : c]: (if @ c @ (coinductive_lfinite @ a @ Y0) @ Y1 @ (coinductive_llast @ c @ coinductive_LNil @ c))))) @ xsa) @ ((^[Y0 : coinductive_llist @ b > d > d]: ((^[Y1 : product_prod @ coinductive_llist @ b @ d]: (Y0 @ (product_fst @ coinductive_llist @ b @ d @ Y1) @ (product_snd @ coinductive_llist @ b @ d @ Y1))))) @ (^[Y0 : coinductive_llist @ b]: ((^[Y1 : d]: (if @ d @ (coinductive_lfinite @ b @ Y0) @ Y1 @ (coinductive_llast @ d @ coinductive_LNil @ d))))) @ ysa))) | ($true = ((^[Y0 : coinductive_llist @ a > e > product_prod @ coinductive_llist @ b @ f > $o]: ((^[Y1 : product_prod @ coinductive_llist @ a @ e]: (Y0 @ (product_fst @ coinductive_llist @ a @ e @ Y1) @ (product_snd @ coinductive_llist @ a @ e @ Y1))))) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : e]: ((^[Y2 : coinductive_llist @ b > f > $o]: ((^[Y3 : product_prod @ coinductive_llist @ b @ f]: (Y2 @ (product_fst @ coinductive_llist @ b @ f @ Y3) @ (product_snd @ coinductive_llist @ b @ f @ Y3))))) @ (^[Y2 : coinductive_llist @ b]: ((^[Y3 : f]: ((coindu1486289336t_all2 @ a @ b @ pa @ Y0 @ Y2) & ((coinductive_lfinite @ a @ Y0) => (ra @ Y1 @ Y3)))))))))) @ (xs_a @ ((^[Y0 : coinductive_llist @ a > c > c]: ((^[Y1 : product_prod @ coinductive_llist @ a @ c]: (Y0 @ (product_fst @ coinductive_llist @ a @ c @ Y1) @ (product_snd @ coinductive_llist @ a @ c @ Y1))))) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : c]: (if @ c @ (coinductive_lfinite @ a @ Y0) @ Y1 @ (coinductive_llast @ c @ coinductive_LNil @ c))))) @ xsa)) @ (ys_a @ ((^[Y0 : coinductive_llist @ b > d > d]: ((^[Y1 : product_prod @ coinductive_llist @ b @ d]: (Y0 @ (product_fst @ coinductive_llist @ b @ d @ Y1) @ (product_snd @ coinductive_llist @ b @ d @ Y1))))) @ (^[Y0 : coinductive_llist @ b]: ((^[Y1 : d]: (if @ d @ (coinductive_lfinite @ b @ Y0) @ Y1 @ (coinductive_llast @ d @ coinductive_LNil @ d))))) @ ysa)))) | ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) != $true)),
% 20.67/4.15 inference(definition_unfolding,[status(thm)],[f1020,f1018,f1018,f1018,f1153,f1018,f1153,f1018,f1153,f1018,f1153])).
% 20.67/4.15 thf(f1153,plain,(
% 20.67/4.15 ( ! [X0 : $tType] : ((undefined @ X0 = (coinductive_llast @ X0 @ coinductive_LNil @ X0))) )),
% 20.67/4.15 inference(cnf_transformation,[status(thm)],[f251])).
% 20.67/4.15 thf(f251,axiom,(
% 20.67/4.15 ! [X0 : $tType] : (undefined @ X0 = (coinductive_llast @ X0 @ coinductive_LNil @ X0))),
% 20.67/4.15 file('/export/starexec/sandbox2/tmp/tmp.mqKFzRPNcN/DTF2THF_23357.p',fact_250_llast__LNil)).
% 20.67/4.15 thf(f1020,plain,(
% 20.67/4.15 ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) != $true) | ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) != $true) | ($true = (product_case_prod @ coinductive_llist @ a @ e @ (product_prod @ coinductive_llist @ b @ f > $o) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : e]: (product_case_prod @ coinductive_llist @ b @ f @ $o @ (^[Y2 : coinductive_llist @ b]: ((^[Y3 : f]: ((coindu1486289336t_all2 @ a @ b @ pa @ Y0 @ Y2) & ((coinductive_lfinite @ a @ Y0) => (ra @ Y1 @ Y3)))))))))) @ (xs_a @ (product_case_prod @ coinductive_llist @ a @ c @ c @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : c]: (if @ c @ (coinductive_lfinite @ a @ Y0) @ Y1 @ undefined @ c)))) @ xsa)) @ (ys_a @ (product_case_prod @ coinductive_llist @ b @ d @ d @ (^[Y0 : coinductive_llist @ b]: ((^[Y1 : d]: (if @ d @ (coinductive_lfinite @ b @ Y0) @ Y1 @ undefined @ d)))) @ ysa)))) | ($true != (qa @ (product_case_prod @ coinductive_llist @ a @ c @ c @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : c]: (if @ c @ (coinductive_lfinite @ a @ Y0) @ Y1 @ undefined @ c)))) @ xsa) @ (product_case_prod @ coinductive_llist @ b @ d @ d @ (^[Y0 : coinductive_llist @ b]: ((^[Y1 : d]: (if @ d @ (coinductive_lfinite @ b @ Y0) @ Y1 @ undefined @ d)))) @ ysa)))),
% 20.67/4.15 inference(cnf_transformation,[status(thm)],[f773])).
% 20.67/4.15 thf(f773,plain,(
% 20.67/4.15 ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) != $true) | ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) != $true) | ($true = (product_case_prod @ coinductive_llist @ a @ e @ (product_prod @ coinductive_llist @ b @ f > $o) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : e]: (product_case_prod @ coinductive_llist @ b @ f @ $o @ (^[Y2 : coinductive_llist @ b]: ((^[Y3 : f]: ((coindu1486289336t_all2 @ a @ b @ pa @ Y0 @ Y2) & ((coinductive_lfinite @ a @ Y0) => (ra @ Y1 @ Y3)))))))))) @ (xs_a @ (product_case_prod @ coinductive_llist @ a @ c @ c @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : c]: (if @ c @ (coinductive_lfinite @ a @ Y0) @ Y1 @ undefined @ c)))) @ xsa)) @ (ys_a @ (product_case_prod @ coinductive_llist @ b @ d @ d @ (^[Y0 : coinductive_llist @ b]: ((^[Y1 : d]: (if @ d @ (coinductive_lfinite @ b @ Y0) @ Y1 @ undefined @ d)))) @ ysa)))) | ($true != (qa @ (product_case_prod @ coinductive_llist @ a @ c @ c @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : c]: (if @ c @ (coinductive_lfinite @ a @ Y0) @ Y1 @ undefined @ c)))) @ xsa) @ (product_case_prod @ coinductive_llist @ b @ d @ d @ (^[Y0 : coinductive_llist @ b]: ((^[Y1 : d]: (if @ d @ (coinductive_lfinite @ b @ Y0) @ Y1 @ undefined @ d)))) @ ysa)))),
% 20.67/4.15 inference(flattening,[status(thm)],[f772])).
% 20.67/4.15 thf(f772,plain,(
% 20.67/4.15 ((($true = (product_case_prod @ coinductive_llist @ a @ e @ (product_prod @ coinductive_llist @ b @ f > $o) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : e]: (product_case_prod @ coinductive_llist @ b @ f @ $o @ (^[Y2 : coinductive_llist @ b]: ((^[Y3 : f]: ((coindu1486289336t_all2 @ a @ b @ pa @ Y0 @ Y2) & ((coinductive_lfinite @ a @ Y0) => (ra @ Y1 @ Y3)))))))))) @ (xs_a @ (product_case_prod @ coinductive_llist @ a @ c @ c @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : c]: (if @ c @ (coinductive_lfinite @ a @ Y0) @ Y1 @ undefined @ c)))) @ xsa)) @ (ys_a @ (product_case_prod @ coinductive_llist @ b @ d @ d @ (^[Y0 : coinductive_llist @ b]: ((^[Y1 : d]: (if @ d @ (coinductive_lfinite @ b @ Y0) @ Y1 @ undefined @ d)))) @ ysa)))) | ($true != (qa @ (product_case_prod @ coinductive_llist @ a @ c @ c @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : c]: (if @ c @ (coinductive_lfinite @ a @ Y0) @ Y1 @ undefined @ c)))) @ xsa) @ (product_case_prod @ coinductive_llist @ b @ d @ d @ (^[Y0 : coinductive_llist @ b]: ((^[Y1 : d]: (if @ d @ (coinductive_lfinite @ b @ Y0) @ Y1 @ undefined @ d)))) @ ysa)))) | ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) != $true)) | ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) != $true)),
% 20.67/4.15 inference(ennf_transformation,[status(thm)],[f337])).
% 20.67/4.15 thf(f337,plain,(
% 20.67/4.15 ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) = $true) => (((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) = $true) => (($true = (qa @ (product_case_prod @ coinductive_llist @ a @ c @ c @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : c]: (if @ c @ (coinductive_lfinite @ a @ Y0) @ Y1 @ undefined @ c)))) @ xsa) @ (product_case_prod @ coinductive_llist @ b @ d @ d @ (^[Y0 : coinductive_llist @ b]: ((^[Y1 : d]: (if @ d @ (coinductive_lfinite @ b @ Y0) @ Y1 @ undefined @ d)))) @ ysa))) => ($true = (product_case_prod @ coinductive_llist @ a @ e @ (product_prod @ coinductive_llist @ b @ f > $o) @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : e]: (product_case_prod @ coinductive_llist @ b @ f @ $o @ (^[Y2 : coinductive_llist @ b]: ((^[Y3 : f]: ((coindu1486289336t_all2 @ a @ b @ pa @ Y0 @ Y2) & ((coinductive_lfinite @ a @ Y0) => (ra @ Y1 @ Y3)))))))))) @ (xs_a @ (product_case_prod @ coinductive_llist @ a @ c @ c @ (^[Y0 : coinductive_llist @ a]: ((^[Y1 : c]: (if @ c @ (coinductive_lfinite @ a @ Y0) @ Y1 @ undefined @ c)))) @ xsa)) @ (ys_a @ (product_case_prod @ coinductive_llist @ b @ d @ d @ (^[Y0 : coinductive_llist @ b]: ((^[Y1 : d]: (if @ d @ (coinductive_lfinite @ b @ Y0) @ Y1 @ undefined @ d)))) @ ysa))))))),
% 20.67/4.15 inference(fool_elimination,[status(thm)],[f336])).
% 20.67/4.15 thf(f336,plain,(
% 20.67/4.15 (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) => ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) => ((qa @ (product_case_prod @ coinductive_llist @ a @ c @ c @ (^[X0 : coinductive_llist @ a, X1 : c] : (if @ c @ (coinductive_lfinite @ a @ X0) @ X1 @ undefined @ c)) @ xsa) @ (product_case_prod @ coinductive_llist @ b @ d @ d @ (^[X2 : coinductive_llist @ b, X3 : d] : (if @ d @ (coinductive_lfinite @ b @ X2) @ X3 @ undefined @ d)) @ ysa)) => (product_case_prod @ coinductive_llist @ a @ e @ (product_prod @ coinductive_llist @ b @ f > $o) @ (^[X4 : coinductive_llist @ a, X5 : e] : (product_case_prod @ coinductive_llist @ b @ f @ $o @ (^[X6 : coinductive_llist @ b, X7 : f] : (((coinductive_lfinite @ a @ X4) => (ra @ X5 @ X7)) & (coindu1486289336t_all2 @ a @ b @ pa @ X4 @ X6))))) @ (xs_a @ (product_case_prod @ coinductive_llist @ a @ c @ c @ (^[X8 : coinductive_llist @ a, X9 : c] : (if @ c @ (coinductive_lfinite @ a @ X8) @ X9 @ undefined @ c)) @ xsa)) @ (ys_a @ (product_case_prod @ coinductive_llist @ b @ d @ d @ (^[X10 : coinductive_llist @ b, X11 : d] : (if @ d @ (coinductive_lfinite @ b @ X10) @ X11 @ undefined @ d)) @ ysa)))))),
% 20.67/4.15 inference(rectify,[status(thm)],[f258])).
% 20.67/4.15 thf(f258,axiom,(
% 20.67/4.15 (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) => ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) => ((qa @ (product_case_prod @ coinductive_llist @ a @ c @ c @ (^[X42 : coinductive_llist @ a, X12 : c] : (if @ c @ (coinductive_lfinite @ a @ X42) @ X12 @ undefined @ c)) @ xsa) @ (product_case_prod @ coinductive_llist @ b @ d @ d @ (^[X42 : coinductive_llist @ b, X12 : d] : (if @ d @ (coinductive_lfinite @ b @ X42) @ X12 @ undefined @ d)) @ ysa)) => (product_case_prod @ coinductive_llist @ a @ e @ (product_prod @ coinductive_llist @ b @ f > $o) @ (^[X42 : coinductive_llist @ a, X12 : e] : (product_case_prod @ coinductive_llist @ b @ f @ $o @ (^[X43 : coinductive_llist @ b, X124 : f] : (((coinductive_lfinite @ a @ X42) => (ra @ X12 @ X124)) & (coindu1486289336t_all2 @ a @ b @ pa @ X42 @ X43))))) @ (xs_a @ (product_case_prod @ coinductive_llist @ a @ c @ c @ (^[X42 : coinductive_llist @ a, X12 : c] : (if @ c @ (coinductive_lfinite @ a @ X42) @ X12 @ undefined @ c)) @ xsa)) @ (ys_a @ (product_case_prod @ coinductive_llist @ b @ d @ d @ (^[X42 : coinductive_llist @ b, X12 : d] : (if @ d @ (coinductive_lfinite @ b @ X42) @ X12 @ undefined @ d)) @ ysa)))))),
% 20.67/4.15 file('/export/starexec/sandbox2/tmp/tmp.mqKFzRPNcN/DTF2THF_23357.p',conj_1)).
% 20.67/4.15 thf(f1510,plain,(
% 20.67/4.15 spl127_1 | ~spl127_2 | ~spl127_3 | ~spl127_4 | spl127_5),
% 20.67/4.15 inference(avatar_split_clause,[status(thm)],[f1489,f1507,f1503,f1499,f1495,f1491])).
% 20.67/4.15 thf(f1489,plain,(
% 20.67/4.15 ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) != $true) | ($true != (qa @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)) @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d)))) | ($true = (ra @ (product_snd @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)))) @ (product_snd @ coinductive_llist @ b @ f @ (ys_a @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d)))))) | ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c))))) = $false) | ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) != $true)),
% 20.67/4.15 inference(binary_proxy_clausification,[status(thm)],[f1487])).
% 20.67/4.15 thf(f1487,plain,(
% 20.67/4.15 ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) != $true) | ($true != (qa @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)) @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d)))) | ($true = ((coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c))))) => (ra @ (product_snd @ coinductive_llist @ a @ e @ (xs_a @ (if @ c @ (coinductive_lfinite @ a @ (product_fst @ coinductive_llist @ a @ c @ xsa)) @ (product_snd @ coinductive_llist @ a @ c @ xsa) @ (coinductive_llast @ c @ coinductive_LNil @ c)))) @ (product_snd @ coinductive_llist @ b @ f @ (ys_a @ (if @ d @ (coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) @ (product_snd @ coinductive_llist @ b @ d @ ysa) @ (coinductive_llast @ d @ coinductive_LNil @ d))))))) | ((coinductive_lfinite @ b @ (product_fst @ coinductive_llist @ b @ d @ ysa)) != $true)),
% 20.67/4.15 inference(binary_proxy_clausification,[status(thm)],[f1486])).
% 20.67/4.15 % SZS output end Proof for DTF2THF_23357
% 20.67/4.15 % (23833)------------------------------
% 20.67/4.15 % (23833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.67/4.15 % (23833)Termination reason: Refutation
% 20.67/4.15
% 20.67/4.15 % (23833)Memory used [KB]: 8059
% 20.67/4.15 % (23833)Time elapsed: 0.142 s
% 20.67/4.15 % (23833)Instructions burned: 448 (million)
% 20.67/4.15 % (23833)------------------------------
% 20.67/4.15 % (23833)------------------------------
% 20.67/4.15 % (23564)Success in time 2.664 s
%------------------------------------------------------------------------------