%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT180^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n021.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 08:45:02 AM UTC 2026
% Result : Theorem 35.67s 6.34s
% Output : Refutation 35.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT180^1 : TPTP v9.2.1. Released v7.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n021.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 06:10:53 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : DAT180^1 : TPTP v9.2.1. Released v7.0.0.
% 0.28/0.46 % Domain : Data Structures
% 0.28/0.46 % Problem : Lazy lists II 676
% 0.28/0.46 % Version : [Bla16] axioms : Especial.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [Fri04] Friedrich (2004), Lazy Lists II
% 0.28/0.46 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.28/0.46 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bla16]
% 0.28/0.46 % Names : llist2__676.p [Bla16]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.00 v7.2.0, 0.25 v7.1.0
% 0.28/0.46 % Syntax : Number of formulae : 343 ( 124 unt; 63 typ; 0 def)
% 0.28/0.46 % Number of atoms : 638 ( 333 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 5 ( 2 avg)
% 0.28/0.46 % Number of connectives : 3409 ( 53 ~; 11 |; 36 &;3076 @)
% 0.28/0.46 % ( 0 <=>; 233 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 19 ( 6 avg)
% 0.28/0.46 % Number of types : 3 ( 2 usr)
% 0.28/0.46 % Number of type conns : 121 ( 121 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 64 ( 61 usr; 5 con; 0-5 aty)
% 0.28/0.46 % Number of variables : 860 ( 16 ^; 774 !; 16 ?; 860 :)
% 0.28/0.46 % ( 54 !>; 0 ?*; 0 @-; 0 @+)
% 0.28/0.46 % SPC : TH1_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.28/0.46 % 2016-07-13 14:48:23.354
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 %----Could-be-implicit typings (5)
% 0.28/0.46 thf(ty_t_Coinductive__List_Ollist,type,
% 0.28/0.46 coinductive_llist: $tType > $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_t_Set_Oset,type,
% 0.28/0.46 set: $tType > $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_t_Nat_Onat,type,
% 0.28/0.46 nat: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_t_itself,type,
% 0.28/0.46 itself: $tType > $tType ).
% 0.28/0.46
% 0.28/0.46 thf(ty_tf_a,type,
% 0.28/0.46 a: $tType ).
% 0.28/0.46
% 0.28/0.46 %----Explicit typings (58)
% 0.28/0.46 thf(sy_cl_HOL_Otype,type,
% 0.28/0.46 type:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Oone,type,
% 0.28/0.46 one:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Ozero,type,
% 0.28/0.46 zero:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Orderings_Otop,type,
% 0.28/0.46 top:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Ogroup__add,type,
% 0.28/0.46 group_add:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Omonoid__add,type,
% 0.28/0.46 monoid_add:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.28/0.46 preorder:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Oab__group__add,type,
% 0.28/0.46 ab_group_add:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.28/0.46 semigroup_add:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 0.28/0.46 comm_semiring_1:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 0.28/0.46 comm_monoid_add:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Fields_Olinordered__field,type,
% 0.28/0.46 linordered_field:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.28/0.46 ab_semigroup_add:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Ocomm__monoid__diff,type,
% 0.28/0.46 comm_monoid_diff:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.28/0.46 cancel_semigroup_add:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.28/0.46 ordered_ab_group_add:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 0.28/0.46 cancel1352612707id_add:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 0.28/0.46 cancel146912293up_add:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 0.28/0.46 linord219039673up_add:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.28/0.46 ordere779506340up_add:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 0.28/0.46 canoni770627133id_add:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 0.28/0.46 ordere236663937imp_le:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 0.28/0.46 ordere516151231imp_le:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
% 0.28/0.46 semiri456707255roduct:
% 0.28/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 0.28/0.46 coindu328551480prefix:
% 0.28/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Coinductive__List_Olappend,type,
% 0.28/0.46 coinductive_lappend:
% 0.28/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.28/0.46 coinductive_LCons:
% 0.28/0.46 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 0.28/0.46 coinductive_LNil:
% 0.28/0.46 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 0.28/0.46 coindu1478340336prefix:
% 0.28/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Coinductive__List_Olsublist,type,
% 0.28/0.46 coinductive_lsublist:
% 0.28/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( set @ nat ) > ( coinductive_llist @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Coinductive__List_Omonoid__add__class_Ollistsum,type,
% 0.28/0.46 coindu780009021istsum:
% 0.28/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 0.28/0.46 minus_minus:
% 0.28/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.28/0.46 one_one:
% 0.28/0.46 !>[A: $tType] : A ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.28/0.46 plus_plus:
% 0.28/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 0.28/0.46 zero_zero:
% 0.28/0.46 !>[A: $tType] : A ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_If,type,
% 0.28/0.46 if:
% 0.28/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts,type,
% 0.28/0.46 lList2435255213lllsts:
% 0.28/0.46 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts,type,
% 0.28/0.46 lList2236698231inlsts:
% 0.28/0.46 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec,type,
% 0.28/0.46 lList21916056377ts_rec:
% 0.28/0.46 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B > B ) > ( coinductive_llist @ A ) > B ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts,type,
% 0.28/0.46 lList22096119349pslsts:
% 0.28/0.46 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts,type,
% 0.28/0.46 lList21612149805nflsts:
% 0.28/0.46 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast,type,
% 0.28/0.46 lList2370560421utlast:
% 0.28/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oldrop,type,
% 0.28/0.46 lList2508575361_ldrop:
% 0.28/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast,type,
% 0.28/0.46 lList2170638824_llast:
% 0.28/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollength,type,
% 0.28/0.46 lList21232602520length:
% 0.28/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev,type,
% 0.28/0.46 lList2281150353e_lrev:
% 0.28/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oltake,type,
% 0.28/0.46 lList22119844313_ltake:
% 0.28/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts,type,
% 0.28/0.46 lList21148268032oslsts:
% 0.28/0.46 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Nat_OSuc,type,
% 0.28/0.46 suc: nat > nat ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Nat__Bijection_Otriangle,type,
% 0.28/0.46 nat_triangle: nat > nat ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.28/0.46 ord_less_eq:
% 0.28/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.28/0.46 top_top:
% 0.28/0.46 !>[A: $tType] : A ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Pure_Otype,type,
% 0.28/0.46 type2:
% 0.28/0.46 !>[A: $tType] : ( itself @ A ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_Set_OCollect,type,
% 0.28/0.46 collect:
% 0.28/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_c_member,type,
% 0.28/0.46 member:
% 0.28/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.28/0.46
% 0.28/0.46 thf(sy_v_A,type,
% 0.28/0.46 a2: set @ a ).
% 0.28/0.46
% 0.28/0.46 thf(sy_v_i,type,
% 0.28/0.46 i: nat ).
% 0.28/0.46
% 0.28/0.46 thf(sy_v_t,type,
% 0.28/0.46 t: coinductive_llist @ a ).
% 0.28/0.46
% 0.28/0.46 %----Relevant facts (252)
% 0.28/0.46 thf(fact_0_lrevT,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ ( lList2281150353e_lrev @ A @ Xs ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lrevT
% 0.28/0.46 thf(fact_1_LList2__Mirabelle__hamjzmohle_Oldrop__LNil,axiom,
% 0.28/0.46 ! [A: $tType,I: nat] :
% 0.28/0.46 ( ( lList2508575361_ldrop @ A @ ( coinductive_LNil @ A ) @ I )
% 0.28/0.46 = ( coinductive_LNil @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 % LList2_Mirabelle_hamjzmohle.ldrop_LNil
% 0.28/0.46 thf(fact_2_ldropT,axiom,
% 0.28/0.46 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ldropT
% 0.28/0.46 thf(fact_3_LList2__Mirabelle__hamjzmohle_Oldrop_Osimps_I1_J,axiom,
% 0.28/0.46 ! [A: $tType,L: coinductive_llist @ A] :
% 0.28/0.46 ( ( lList2508575361_ldrop @ A @ L @ ( zero_zero @ nat ) )
% 0.28/0.46 = L ) ).
% 0.28/0.46
% 0.28/0.46 % LList2_Mirabelle_hamjzmohle.ldrop.simps(1)
% 0.28/0.46 thf(fact_4_ldrop__add,axiom,
% 0.28/0.46 ! [A: $tType,T: coinductive_llist @ A,I: nat,K: nat] :
% 0.28/0.46 ( ( lList2508575361_ldrop @ A @ T @ ( plus_plus @ nat @ I @ K ) )
% 0.28/0.46 = ( lList2508575361_ldrop @ A @ ( lList2508575361_ldrop @ A @ T @ I ) @ K ) ) ).
% 0.28/0.46
% 0.28/0.46 % ldrop_add
% 0.28/0.46 thf(fact_5_finite__lemma,axiom,
% 0.28/0.46 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,B2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ B2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ B2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finite_lemma
% 0.28/0.46 thf(fact_6_finsubsetall,axiom,
% 0.28/0.46 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finsubsetall
% 0.28/0.46 thf(fact_7_same__lappend__eq,axiom,
% 0.28/0.46 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ( ( coinductive_lappend @ A @ R @ S )
% 0.28/0.46 = ( coinductive_lappend @ A @ R @ T ) )
% 0.28/0.46 = ( S = T ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % same_lappend_eq
% 0.28/0.46 thf(fact_8_lapp__fin__fin__iff,axiom,
% 0.28/0.46 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 = ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lapp_fin_fin_iff
% 0.28/0.46 thf(fact_9_finT__simp,axiom,
% 0.28/0.46 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finT_simp
% 0.28/0.46 thf(fact_10_fin__finite,axiom,
% 0.28/0.46 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % fin_finite
% 0.28/0.46 thf(fact_11_finlsts_OLNil__fin,axiom,
% 0.28/0.46 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2236698231inlsts @ A @ A2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % finlsts.LNil_fin
% 0.28/0.46 thf(fact_12_LNil__is__lappend__conv,axiom,
% 0.28/0.46 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.28/0.46 ( ( ( coinductive_LNil @ A )
% 0.28/0.46 = ( coinductive_lappend @ A @ S @ T ) )
% 0.28/0.46 = ( ( S
% 0.28/0.46 = ( coinductive_LNil @ A ) )
% 0.28/0.46 & ( T
% 0.28/0.46 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % LNil_is_lappend_conv
% 0.28/0.46 thf(fact_13_lappend__is__LNil__conv,axiom,
% 0.28/0.46 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.28/0.46 ( ( ( coinductive_lappend @ A @ S @ T )
% 0.28/0.46 = ( coinductive_LNil @ A ) )
% 0.28/0.46 = ( ( S
% 0.28/0.46 = ( coinductive_LNil @ A ) )
% 0.28/0.46 & ( T
% 0.28/0.46 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lappend_is_LNil_conv
% 0.28/0.46 thf(fact_14_alllsts__UNIV,axiom,
% 0.28/0.46 ! [A: $tType,S: coinductive_llist @ A] : ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % alllsts_UNIV
% 0.28/0.46 thf(fact_15_lrev__LNil,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( lList2281150353e_lrev @ A @ ( coinductive_LNil @ A ) )
% 0.28/0.46 = ( coinductive_LNil @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 % lrev_LNil
% 0.28/0.46 thf(fact_16_lrev__is__lrev__conv,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.46 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.46 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 0.28/0.46 = ( lList2281150353e_lrev @ A @ Ys ) )
% 0.28/0.46 = ( Xs = Ys ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lrev_is_lrev_conv
% 0.28/0.46 thf(fact_17_lrev__lrev__ident,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.46 => ( ( lList2281150353e_lrev @ A @ ( lList2281150353e_lrev @ A @ Xs ) )
% 0.28/0.46 = Xs ) ) ).
% 0.28/0.46
% 0.28/0.46 % lrev_lrev_ident
% 0.28/0.46 thf(fact_18_lrev__is__LNil__conv,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.46 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 0.28/0.46 = ( coinductive_LNil @ A ) )
% 0.28/0.46 = ( Xs
% 0.28/0.46 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lrev_is_LNil_conv
% 0.28/0.46 thf(fact_19_LNil__is__lrev__conv,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.46 => ( ( ( coinductive_LNil @ A )
% 0.28/0.46 = ( lList2281150353e_lrev @ A @ Xs ) )
% 0.28/0.46 = ( Xs
% 0.28/0.46 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % LNil_is_lrev_conv
% 0.28/0.46 thf(fact_20_lrev__lappend,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.46 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.46 => ( ( lList2281150353e_lrev @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.28/0.46 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ Ys ) @ ( lList2281150353e_lrev @ A @ Xs ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lrev_lappend
% 0.28/0.46 thf(fact_21_lappT,axiom,
% 0.28/0.46 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.46 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lappT
% 0.28/0.46 thf(fact_22_lapp__all__invT,axiom,
% 0.28/0.46 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lapp_all_invT
% 0.28/0.46 thf(fact_23_alllsts_OLNil__all,axiom,
% 0.28/0.46 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2435255213lllsts @ A @ A2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % alllsts.LNil_all
% 0.28/0.46 thf(fact_24_lapp__fin__fin__lemma,axiom,
% 0.28/0.46 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lapp_fin_fin_lemma
% 0.28/0.46 thf(fact_25_lappfin__finT,axiom,
% 0.28/0.46 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lappfin_finT
% 0.28/0.46 thf(fact_26_lappend__code_I1_J,axiom,
% 0.28/0.46 ! [A: $tType,Ys: coinductive_llist @ A] :
% 0.28/0.46 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 0.28/0.46 = Ys ) ).
% 0.28/0.46
% 0.28/0.46 % lappend_code(1)
% 0.28/0.46 thf(fact_27_lappend__LNil2,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.28/0.46 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.28/0.46 = Xs ) ).
% 0.28/0.46
% 0.28/0.46 % lappend_LNil2
% 0.28/0.46 thf(fact_28_LNil__eq__lappend__iff,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.28/0.46 ( ( ( coinductive_LNil @ A )
% 0.28/0.46 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.28/0.46 = ( ( Xs
% 0.28/0.46 = ( coinductive_LNil @ A ) )
% 0.28/0.46 & ( Ys
% 0.28/0.46 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % LNil_eq_lappend_iff
% 0.28/0.46 thf(fact_29_lappend__eq__LNil__iff,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.28/0.46 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.28/0.46 = ( coinductive_LNil @ A ) )
% 0.28/0.46 = ( ( Xs
% 0.28/0.46 = ( coinductive_LNil @ A ) )
% 0.28/0.46 & ( Ys
% 0.28/0.46 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lappend_eq_LNil_iff
% 0.28/0.46 thf(fact_30_add__is__0,axiom,
% 0.28/0.46 ! [M: nat,N: nat] :
% 0.28/0.46 ( ( ( plus_plus @ nat @ M @ N )
% 0.28/0.46 = ( zero_zero @ nat ) )
% 0.28/0.46 = ( ( M
% 0.28/0.46 = ( zero_zero @ nat ) )
% 0.28/0.46 & ( N
% 0.28/0.46 = ( zero_zero @ nat ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_is_0
% 0.28/0.46 thf(fact_31_Nat_Oadd__0__right,axiom,
% 0.28/0.46 ! [M: nat] :
% 0.28/0.46 ( ( plus_plus @ nat @ M @ ( zero_zero @ nat ) )
% 0.28/0.46 = M ) ).
% 0.28/0.46
% 0.28/0.46 % Nat.add_0_right
% 0.28/0.46 thf(fact_32_add_Oleft__neutral,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( monoid_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A] :
% 0.28/0.46 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A3 )
% 0.28/0.46 = A3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % add.left_neutral
% 0.28/0.46 thf(fact_33_add_Oright__neutral,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( monoid_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A] :
% 0.28/0.46 ( ( plus_plus @ A @ A3 @ ( zero_zero @ A ) )
% 0.28/0.46 = A3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % add.right_neutral
% 0.28/0.46 thf(fact_34_double__zero,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A] :
% 0.28/0.46 ( ( ( plus_plus @ A @ A3 @ A3 )
% 0.28/0.46 = ( zero_zero @ A ) )
% 0.28/0.46 = ( A3
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % double_zero
% 0.28/0.46 thf(fact_35_double__zero__sym,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A] :
% 0.28/0.46 ( ( ( zero_zero @ A )
% 0.28/0.46 = ( plus_plus @ A @ A3 @ A3 ) )
% 0.28/0.46 = ( A3
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % double_zero_sym
% 0.28/0.46 thf(fact_36_add__cancel__left__left,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [B3: A,A3: A] :
% 0.28/0.46 ( ( ( plus_plus @ A @ B3 @ A3 )
% 0.28/0.46 = A3 )
% 0.28/0.46 = ( B3
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_cancel_left_left
% 0.28/0.46 thf(fact_37_add__right__cancel,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [B3: A,A3: A,C: A] :
% 0.28/0.46 ( ( ( plus_plus @ A @ B3 @ A3 )
% 0.28/0.46 = ( plus_plus @ A @ C @ A3 ) )
% 0.28/0.46 = ( B3 = C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_right_cancel
% 0.28/0.46 thf(fact_38_add__left__cancel,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A,C: A] :
% 0.28/0.46 ( ( ( plus_plus @ A @ A3 @ B3 )
% 0.28/0.46 = ( plus_plus @ A @ A3 @ C ) )
% 0.28/0.46 = ( B3 = C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_left_cancel
% 0.28/0.46 thf(fact_39_add__cancel__right__right,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A] :
% 0.28/0.46 ( ( A3
% 0.28/0.46 = ( plus_plus @ A @ A3 @ B3 ) )
% 0.28/0.46 = ( B3
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_cancel_right_right
% 0.28/0.46 thf(fact_40_add__cancel__right__left,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A] :
% 0.28/0.46 ( ( A3
% 0.28/0.46 = ( plus_plus @ A @ B3 @ A3 ) )
% 0.28/0.46 = ( B3
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_cancel_right_left
% 0.28/0.46 thf(fact_41_add__cancel__left__right,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A] :
% 0.28/0.46 ( ( ( plus_plus @ A @ A3 @ B3 )
% 0.28/0.46 = A3 )
% 0.28/0.46 = ( B3
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_cancel_left_right
% 0.28/0.46 thf(fact_42_zero__reorient,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( zero @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [X: A] :
% 0.28/0.46 ( ( ( zero_zero @ A )
% 0.28/0.46 = X )
% 0.28/0.46 = ( X
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % zero_reorient
% 0.28/0.46 thf(fact_43_add__right__imp__eq,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [B3: A,A3: A,C: A] :
% 0.28/0.46 ( ( ( plus_plus @ A @ B3 @ A3 )
% 0.28/0.46 = ( plus_plus @ A @ C @ A3 ) )
% 0.28/0.46 => ( B3 = C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_right_imp_eq
% 0.28/0.46 thf(fact_44_mem__Collect__eq,axiom,
% 0.28/0.46 ! [A: $tType,A3: A,P: A > $o] :
% 0.28/0.46 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.28/0.46 = ( P @ A3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % mem_Collect_eq
% 0.28/0.46 thf(fact_45_Collect__mem__eq,axiom,
% 0.28/0.46 ! [A: $tType,A2: set @ A] :
% 0.28/0.46 ( ( collect @ A
% 0.28/0.46 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 0.28/0.46 = A2 ) ).
% 0.28/0.46
% 0.28/0.46 % Collect_mem_eq
% 0.28/0.46 thf(fact_46_Collect__cong,axiom,
% 0.28/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.28/0.46 ( ! [X3: A] :
% 0.28/0.46 ( ( P @ X3 )
% 0.28/0.46 = ( Q @ X3 ) )
% 0.28/0.46 => ( ( collect @ A @ P )
% 0.28/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Collect_cong
% 0.28/0.46 thf(fact_47_ext,axiom,
% 0.28/0.46 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.28/0.46 ( ! [X3: A] :
% 0.28/0.46 ( ( F @ X3 )
% 0.28/0.46 = ( G @ X3 ) )
% 0.28/0.46 => ( F = G ) ) ).
% 0.28/0.46
% 0.28/0.46 % ext
% 0.28/0.46 thf(fact_48_add__left__imp__eq,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A,C: A] :
% 0.28/0.46 ( ( ( plus_plus @ A @ A3 @ B3 )
% 0.28/0.46 = ( plus_plus @ A @ A3 @ C ) )
% 0.28/0.46 => ( B3 = C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_left_imp_eq
% 0.28/0.46 thf(fact_49_add_Oleft__commute,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [B3: A,A3: A,C: A] :
% 0.28/0.46 ( ( plus_plus @ A @ B3 @ ( plus_plus @ A @ A3 @ C ) )
% 0.28/0.46 = ( plus_plus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add.left_commute
% 0.28/0.46 thf(fact_50_add_Ocommute,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ( ( plus_plus @ A )
% 0.28/0.46 = ( ^ [A4: A,B4: A] : ( plus_plus @ A @ B4 @ A4 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add.commute
% 0.28/0.46 thf(fact_51_add_Oright__cancel,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [B3: A,A3: A,C: A] :
% 0.28/0.46 ( ( ( plus_plus @ A @ B3 @ A3 )
% 0.28/0.46 = ( plus_plus @ A @ C @ A3 ) )
% 0.28/0.46 = ( B3 = C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add.right_cancel
% 0.28/0.46 thf(fact_52_add_Oleft__cancel,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A,C: A] :
% 0.28/0.46 ( ( ( plus_plus @ A @ A3 @ B3 )
% 0.28/0.46 = ( plus_plus @ A @ A3 @ C ) )
% 0.28/0.46 = ( B3 = C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add.left_cancel
% 0.28/0.46 thf(fact_53_add_Oassoc,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( semigroup_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A,C: A] :
% 0.28/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ C )
% 0.28/0.46 = ( plus_plus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add.assoc
% 0.28/0.46 thf(fact_54_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [I: A,J: A,K: A,L: A] :
% 0.28/0.46 ( ( ( I = J )
% 0.28/0.46 & ( K = L ) )
% 0.28/0.46 => ( ( plus_plus @ A @ I @ K )
% 0.28/0.46 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_mono_thms_linordered_semiring(4)
% 0.28/0.46 thf(fact_55_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A,C: A] :
% 0.28/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ C )
% 0.28/0.46 = ( plus_plus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ab_semigroup_add_class.add_ac(1)
% 0.28/0.46 thf(fact_56_nat__add__right__cancel,axiom,
% 0.28/0.46 ! [M: nat,K: nat,N: nat] :
% 0.28/0.46 ( ( ( plus_plus @ nat @ M @ K )
% 0.28/0.46 = ( plus_plus @ nat @ N @ K ) )
% 0.28/0.46 = ( M = N ) ) ).
% 0.28/0.46
% 0.28/0.46 % nat_add_right_cancel
% 0.28/0.46 thf(fact_57_nat__add__left__cancel,axiom,
% 0.28/0.46 ! [K: nat,M: nat,N: nat] :
% 0.28/0.46 ( ( ( plus_plus @ nat @ K @ M )
% 0.28/0.46 = ( plus_plus @ nat @ K @ N ) )
% 0.28/0.46 = ( M = N ) ) ).
% 0.28/0.46
% 0.28/0.46 % nat_add_left_cancel
% 0.28/0.46 thf(fact_58_lappend__assoc,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.28/0.46 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 0.28/0.46 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lappend_assoc
% 0.28/0.46 thf(fact_59_add__eq__0__iff__both__eq__0,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [X: A,Y: A] :
% 0.28/0.46 ( ( ( plus_plus @ A @ X @ Y )
% 0.28/0.46 = ( zero_zero @ A ) )
% 0.28/0.46 = ( ( X
% 0.28/0.46 = ( zero_zero @ A ) )
% 0.28/0.46 & ( Y
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_eq_0_iff_both_eq_0
% 0.28/0.46 thf(fact_60_add_Ogroup__left__neutral,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A] :
% 0.28/0.46 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A3 )
% 0.28/0.46 = A3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % add.group_left_neutral
% 0.28/0.46 thf(fact_61_add_Ocomm__neutral,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( comm_monoid_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A] :
% 0.28/0.46 ( ( plus_plus @ A @ A3 @ ( zero_zero @ A ) )
% 0.28/0.46 = A3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % add.comm_neutral
% 0.28/0.46 thf(fact_62_comm__monoid__add__class_Oadd__0,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( comm_monoid_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A] :
% 0.28/0.46 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A3 )
% 0.28/0.46 = A3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % comm_monoid_add_class.add_0
% 0.28/0.46 thf(fact_63_add__eq__self__zero,axiom,
% 0.28/0.46 ! [M: nat,N: nat] :
% 0.28/0.46 ( ( ( plus_plus @ nat @ M @ N )
% 0.28/0.46 = M )
% 0.28/0.46 => ( N
% 0.28/0.46 = ( zero_zero @ nat ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_eq_self_zero
% 0.28/0.46 thf(fact_64_plus__nat_Oadd__0,axiom,
% 0.28/0.46 ! [N: nat] :
% 0.28/0.46 ( ( plus_plus @ nat @ ( zero_zero @ nat ) @ N )
% 0.28/0.46 = N ) ).
% 0.28/0.46
% 0.28/0.46 % plus_nat.add_0
% 0.28/0.46 thf(fact_65_lappend__LNil__LNil,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 0.28/0.46 = ( coinductive_LNil @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 % lappend_LNil_LNil
% 0.28/0.46 thf(fact_66_iso__tuple__UNIV__I,axiom,
% 0.28/0.46 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % iso_tuple_UNIV_I
% 0.28/0.46 thf(fact_67_UNIV__I,axiom,
% 0.28/0.46 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % UNIV_I
% 0.28/0.46 thf(fact_68_top__apply,axiom,
% 0.28/0.46 ! [C2: $tType,D: $tType] :
% 0.28/0.46 ( ( top @ C2 @ ( type2 @ C2 ) )
% 0.28/0.46 => ( ( top_top @ ( D > C2 ) )
% 0.28/0.46 = ( ^ [X2: D] : ( top_top @ C2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % top_apply
% 0.28/0.46 thf(fact_69_poslsts__iff,axiom,
% 0.28/0.46 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ A2 ) )
% 0.28/0.46 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.46 & ( S
% 0.28/0.46 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % poslsts_iff
% 0.28/0.46 thf(fact_70_fpslsts__iff,axiom,
% 0.28/0.46 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.28/0.46 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 & ( S
% 0.28/0.46 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % fpslsts_iff
% 0.28/0.46 thf(fact_71_poslsts__UNIV,axiom,
% 0.28/0.46 ! [A: $tType,S: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.46 = ( S
% 0.28/0.46 != ( coinductive_LNil @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % poslsts_UNIV
% 0.28/0.46 thf(fact_72_ind__euclid,axiom,
% 0.28/0.46 ! [P: nat > nat > $o,A3: nat,B3: nat] :
% 0.28/0.46 ( ! [A5: nat,B5: nat] :
% 0.28/0.46 ( ( P @ A5 @ B5 )
% 0.28/0.46 = ( P @ B5 @ A5 ) )
% 0.28/0.46 => ( ! [A5: nat] : ( P @ A5 @ ( zero_zero @ nat ) )
% 0.28/0.46 => ( ! [A5: nat,B5: nat] :
% 0.28/0.46 ( ( P @ A5 @ B5 )
% 0.28/0.46 => ( P @ A5 @ ( plus_plus @ nat @ A5 @ B5 ) ) )
% 0.28/0.46 => ( P @ A3 @ B3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ind_euclid
% 0.28/0.46 thf(fact_73_LList2__Mirabelle__hamjzmohle_Ollength__LNil,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( lList21232602520length @ A @ ( coinductive_LNil @ A ) )
% 0.28/0.46 = ( zero_zero @ nat ) ) ).
% 0.28/0.46
% 0.28/0.46 % LList2_Mirabelle_hamjzmohle.llength_LNil
% 0.28/0.46 thf(fact_74_add__0__iff,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( semiri456707255roduct @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [B3: A,A3: A] :
% 0.28/0.46 ( ( B3
% 0.28/0.46 = ( plus_plus @ A @ B3 @ A3 ) )
% 0.28/0.46 = ( A3
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_0_iff
% 0.28/0.46 thf(fact_75_top__set__def,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( top_top @ ( set @ A ) )
% 0.28/0.46 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % top_set_def
% 0.28/0.46 thf(fact_76_semiring__normalization__rules_I25_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,C: A,D2: A] :
% 0.28/0.46 ( ( plus_plus @ A @ A3 @ ( plus_plus @ A @ C @ D2 ) )
% 0.28/0.46 = ( plus_plus @ A @ ( plus_plus @ A @ A3 @ C ) @ D2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % semiring_normalization_rules(25)
% 0.28/0.46 thf(fact_77_semiring__normalization__rules_I24_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.28/0.46 => ( ( plus_plus @ A )
% 0.28/0.46 = ( ^ [A4: A,C3: A] : ( plus_plus @ A @ C3 @ A4 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % semiring_normalization_rules(24)
% 0.28/0.46 thf(fact_78_semiring__normalization__rules_I23_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A,C: A] :
% 0.28/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ C )
% 0.28/0.46 = ( plus_plus @ A @ ( plus_plus @ A @ A3 @ C ) @ B3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % semiring_normalization_rules(23)
% 0.28/0.46 thf(fact_79_semiring__normalization__rules_I22_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,C: A,D2: A] :
% 0.28/0.46 ( ( plus_plus @ A @ A3 @ ( plus_plus @ A @ C @ D2 ) )
% 0.28/0.46 = ( plus_plus @ A @ C @ ( plus_plus @ A @ A3 @ D2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % semiring_normalization_rules(22)
% 0.28/0.46 thf(fact_80_semiring__normalization__rules_I21_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A,C: A] :
% 0.28/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ C )
% 0.28/0.46 = ( plus_plus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % semiring_normalization_rules(21)
% 0.28/0.46 thf(fact_81_semiring__normalization__rules_I20_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A,C: A,D2: A] :
% 0.28/0.46 ( ( plus_plus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ ( plus_plus @ A @ C @ D2 ) )
% 0.28/0.46 = ( plus_plus @ A @ ( plus_plus @ A @ A3 @ C ) @ ( plus_plus @ A @ B3 @ D2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % semiring_normalization_rules(20)
% 0.28/0.46 thf(fact_82_UNIV__eq__I,axiom,
% 0.28/0.46 ! [A: $tType,A2: set @ A] :
% 0.28/0.46 ( ! [X3: A] : ( member @ A @ X3 @ A2 )
% 0.28/0.46 => ( ( top_top @ ( set @ A ) )
% 0.28/0.46 = A2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % UNIV_eq_I
% 0.28/0.46 thf(fact_83_UNIV__witness,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % UNIV_witness
% 0.28/0.46 thf(fact_84_semiring__normalization__rules_I6_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A] :
% 0.28/0.46 ( ( plus_plus @ A @ A3 @ ( zero_zero @ A ) )
% 0.28/0.46 = A3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % semiring_normalization_rules(6)
% 0.28/0.46 thf(fact_85_semiring__normalization__rules_I5_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A] :
% 0.28/0.46 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A3 )
% 0.28/0.46 = A3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % semiring_normalization_rules(5)
% 0.28/0.46 thf(fact_86_lbutlast__LNil,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( lList2370560421utlast @ A @ ( coinductive_LNil @ A ) )
% 0.28/0.46 = ( coinductive_LNil @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 % lbutlast_LNil
% 0.28/0.46 thf(fact_87_take__fin,axiom,
% 0.28/0.46 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % take_fin
% 0.28/0.46 thf(fact_88_lrev__LCons,axiom,
% 0.28/0.46 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A3: A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ( lList2281150353e_lrev @ A @ ( coinductive_LCons @ A @ A3 @ R ) )
% 0.28/0.46 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ R ) @ ( coinductive_LCons @ A @ A3 @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lrev_LCons
% 0.28/0.46 thf(fact_89_ltake__fin,axiom,
% 0.28/0.46 ! [A: $tType,R: coinductive_llist @ A,I: nat] : ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ R @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ltake_fin
% 0.28/0.46 thf(fact_90_inflstsI,axiom,
% 0.28/0.46 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.46 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % inflstsI
% 0.28/0.46 thf(fact_91_llistsum__LNil,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( monoid_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ( ( coindu780009021istsum @ A @ ( coinductive_LNil @ A ) )
% 0.28/0.46 = ( zero_zero @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % llistsum_LNil
% 0.28/0.46 thf(fact_92_llist_Oinject,axiom,
% 0.28/0.46 ! [A: $tType,X21: A,X22: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 0.28/0.46 ( ( ( coinductive_LCons @ A @ X21 @ X22 )
% 0.28/0.46 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 0.28/0.46 = ( ( X21 = Y21 )
% 0.28/0.46 & ( X22 = Y22 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % llist.inject
% 0.28/0.46 thf(fact_93_top1I,axiom,
% 0.28/0.46 ! [A: $tType,X: A] : ( top_top @ ( A > $o ) @ X ) ).
% 0.28/0.46
% 0.28/0.46 % top1I
% 0.28/0.46 thf(fact_94_lappend__code_I2_J,axiom,
% 0.28/0.46 ! [A: $tType,Xa: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.28/0.46 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa @ X ) @ Ys )
% 0.28/0.46 = ( coinductive_LCons @ A @ Xa @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lappend_code(2)
% 0.28/0.46 thf(fact_95_LConsE,axiom,
% 0.28/0.46 ! [A: $tType,X: A,Xs: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X @ Xs ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.46 = ( ( member @ A @ X @ A2 )
% 0.28/0.46 & ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % LConsE
% 0.28/0.46 thf(fact_96_lapp__inf,axiom,
% 0.28/0.46 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.46 => ( ( coinductive_lappend @ A @ S @ T )
% 0.28/0.46 = S ) ) ).
% 0.28/0.46
% 0.28/0.46 % lapp_inf
% 0.28/0.46 thf(fact_97_LList2__Mirabelle__hamjzmohle_Oltake__LNil,axiom,
% 0.28/0.46 ! [A: $tType,I: nat] :
% 0.28/0.46 ( ( lList22119844313_ltake @ A @ ( coinductive_LNil @ A ) @ I )
% 0.28/0.46 = ( coinductive_LNil @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 % LList2_Mirabelle_hamjzmohle.ltake_LNil
% 0.28/0.46 thf(fact_98_notfin__inf,axiom,
% 0.28/0.46 ! [A: $tType,X: coinductive_llist @ A] :
% 0.28/0.46 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 0.28/0.46 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % notfin_inf
% 0.28/0.46 thf(fact_99_notinf__fin,axiom,
% 0.28/0.46 ! [A: $tType,X: coinductive_llist @ A] :
% 0.28/0.46 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 0.28/0.46 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % notinf_fin
% 0.28/0.46 thf(fact_100_llength__take,axiom,
% 0.28/0.46 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.46 => ( ( lList21232602520length @ A @ ( lList22119844313_ltake @ A @ T @ I ) )
% 0.28/0.46 = I ) ) ).
% 0.28/0.46
% 0.28/0.46 % llength_take
% 0.28/0.46 thf(fact_101_lbutlast__LCons,axiom,
% 0.28/0.46 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A3: A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ( ( R
% 0.28/0.46 = ( coinductive_LNil @ A ) )
% 0.28/0.46 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A3 @ R ) )
% 0.28/0.46 = ( coinductive_LNil @ A ) ) )
% 0.28/0.46 & ( ( R
% 0.28/0.46 != ( coinductive_LNil @ A ) )
% 0.28/0.46 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A3 @ R ) )
% 0.28/0.46 = ( coinductive_LCons @ A @ A3 @ ( lList2370560421utlast @ A @ R ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lbutlast_LCons
% 0.28/0.46 thf(fact_102_inflsts__cases,axiom,
% 0.28/0.46 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.46 => ~ ! [A5: A,L2: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.46 => ( ( member @ A @ A5 @ A2 )
% 0.28/0.46 => ( S
% 0.28/0.46 != ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % inflsts_cases
% 0.28/0.46 thf(fact_103_inflstsI2,axiom,
% 0.28/0.46 ! [A: $tType,A3: A,A2: set @ A,T: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ A @ A3 @ A2 )
% 0.28/0.46 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % inflstsI2
% 0.28/0.46 thf(fact_104_neq__LNil__conv,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.28/0.46 ( ( Xs
% 0.28/0.46 != ( coinductive_LNil @ A ) )
% 0.28/0.46 = ( ? [X2: A,Xs2: coinductive_llist @ A] :
% 0.28/0.46 ( Xs
% 0.28/0.46 = ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % neq_LNil_conv
% 0.28/0.46 thf(fact_105_llist_Odistinct_I1_J,axiom,
% 0.28/0.46 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 0.28/0.46 ( ( coinductive_LNil @ A )
% 0.28/0.46 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 0.28/0.46
% 0.28/0.46 % llist.distinct(1)
% 0.28/0.46 thf(fact_106_llistE,axiom,
% 0.28/0.46 ! [A: $tType,Y: coinductive_llist @ A] :
% 0.28/0.46 ( ( Y
% 0.28/0.46 != ( coinductive_LNil @ A ) )
% 0.28/0.46 => ~ ! [X212: A,X222: coinductive_llist @ A] :
% 0.28/0.46 ( Y
% 0.28/0.46 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % llistE
% 0.28/0.46 thf(fact_107_finlsts_OLCons__fin,axiom,
% 0.28/0.46 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A3: A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ( member @ A @ A3 @ A2 )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ L ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finlsts.LCons_fin
% 0.28/0.46 thf(fact_108_alllsts_OLCons__all,axiom,
% 0.28/0.46 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A3: A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.46 => ( ( member @ A @ A3 @ A2 )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ L ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % alllsts.LCons_all
% 0.28/0.46 thf(fact_109_infT__simp,axiom,
% 0.28/0.46 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % infT_simp
% 0.28/0.46 thf(fact_110_infsubsetall,axiom,
% 0.28/0.46 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % infsubsetall
% 0.28/0.46 thf(fact_111_lappend__snocL1__conv__LCons2,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.28/0.46 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 0.28/0.46 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lappend_snocL1_conv_LCons2
% 0.28/0.46 thf(fact_112_finlsts_Ocases,axiom,
% 0.28/0.46 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ( A3
% 0.28/0.46 != ( coinductive_LNil @ A ) )
% 0.28/0.46 => ~ ! [L2: coinductive_llist @ A,A5: A] :
% 0.28/0.46 ( ( A3
% 0.28/0.46 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 0.28/0.46 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ~ ( member @ A @ A5 @ A2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finlsts.cases
% 0.28/0.46 thf(fact_113_finlsts_Osimps,axiom,
% 0.28/0.46 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 = ( ( A3
% 0.28/0.46 = ( coinductive_LNil @ A ) )
% 0.28/0.46 | ? [L3: coinductive_llist @ A,A4: A] :
% 0.28/0.46 ( ( A3
% 0.28/0.46 = ( coinductive_LCons @ A @ A4 @ L3 ) )
% 0.28/0.46 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 & ( member @ A @ A4 @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finlsts.simps
% 0.28/0.46 thf(fact_114_finlsts__induct,axiom,
% 0.28/0.46 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ! [L2: coinductive_llist @ A] :
% 0.28/0.46 ( ( L2
% 0.28/0.46 = ( coinductive_LNil @ A ) )
% 0.28/0.46 => ( P @ L2 ) )
% 0.28/0.46 => ( ! [A5: A,L2: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ( P @ L2 )
% 0.28/0.46 => ( ( member @ A @ A5 @ A2 )
% 0.28/0.46 => ( P @ ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) )
% 0.28/0.46 => ( P @ X ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finlsts_induct
% 0.28/0.46 thf(fact_115_finlsts_Oinducts,axiom,
% 0.28/0.46 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.28/0.46 => ( ! [L2: coinductive_llist @ A,A5: A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ( P @ L2 )
% 0.28/0.46 => ( ( member @ A @ A5 @ A2 )
% 0.28/0.46 => ( P @ ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) )
% 0.28/0.46 => ( P @ X ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finlsts.inducts
% 0.28/0.46 thf(fact_116_alllsts_Ocoinduct,axiom,
% 0.28/0.46 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( X4 @ X )
% 0.28/0.46 => ( ! [X3: coinductive_llist @ A] :
% 0.28/0.46 ( ( X4 @ X3 )
% 0.28/0.46 => ( ( X3
% 0.28/0.46 = ( coinductive_LNil @ A ) )
% 0.28/0.46 | ? [L4: coinductive_llist @ A,A6: A] :
% 0.28/0.46 ( ( X3
% 0.28/0.46 = ( coinductive_LCons @ A @ A6 @ L4 ) )
% 0.28/0.46 & ( ( X4 @ L4 )
% 0.28/0.46 | ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 0.28/0.46 & ( member @ A @ A6 @ A2 ) ) ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % alllsts.coinduct
% 0.28/0.46 thf(fact_117_alllsts_Osimps,axiom,
% 0.28/0.46 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.46 = ( ( A3
% 0.28/0.46 = ( coinductive_LNil @ A ) )
% 0.28/0.46 | ? [L3: coinductive_llist @ A,A4: A] :
% 0.28/0.46 ( ( A3
% 0.28/0.46 = ( coinductive_LCons @ A @ A4 @ L3 ) )
% 0.28/0.46 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.46 & ( member @ A @ A4 @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % alllsts.simps
% 0.28/0.46 thf(fact_118_alllsts_Ocases,axiom,
% 0.28/0.46 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.46 => ( ( A3
% 0.28/0.46 != ( coinductive_LNil @ A ) )
% 0.28/0.46 => ~ ! [L2: coinductive_llist @ A,A5: A] :
% 0.28/0.46 ( ( A3
% 0.28/0.46 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 0.28/0.46 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.46 => ~ ( member @ A @ A5 @ A2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % alllsts.cases
% 0.28/0.46 thf(fact_119_fin__inf__cases,axiom,
% 0.28/0.46 ! [A: $tType,R: coinductive_llist @ A] :
% 0.28/0.46 ( ~ ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % fin_inf_cases
% 0.28/0.46 thf(fact_120_fpslsts__cases,axiom,
% 0.28/0.46 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.28/0.46 => ~ ! [A5: A,Rs: coinductive_llist @ A] :
% 0.28/0.46 ( ( R
% 0.28/0.46 = ( coinductive_LCons @ A @ A5 @ Rs ) )
% 0.28/0.46 => ( ( member @ A @ A5 @ A2 )
% 0.28/0.46 => ~ ( member @ ( coinductive_llist @ A ) @ Rs @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % fpslsts_cases
% 0.28/0.46 thf(fact_121_app__invT,axiom,
% 0.28/0.46 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % app_invT
% 0.28/0.46 thf(fact_122_lapp__infT,axiom,
% 0.28/0.46 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.46 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) )
% 0.28/0.46 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lapp_infT
% 0.28/0.46 thf(fact_123_lapp__inv2T,axiom,
% 0.28/0.46 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.46 => ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) )
% 0.28/0.46 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lapp_inv2T
% 0.28/0.46 thf(fact_124_lapp__fin__infT,axiom,
% 0.28/0.46 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lapp_fin_infT
% 0.28/0.46 thf(fact_125_alllstsE,axiom,
% 0.28/0.46 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.46 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % alllstsE
% 0.28/0.46 thf(fact_126_finlsts__rev__cases,axiom,
% 0.28/0.46 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ( T
% 0.28/0.46 != ( coinductive_LNil @ A ) )
% 0.28/0.46 => ~ ! [A5: A,L2: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ( member @ A @ A5 @ A2 )
% 0.28/0.46 => ( T
% 0.28/0.46 != ( coinductive_lappend @ A @ L2 @ ( coinductive_LCons @ A @ A5 @ ( coinductive_LNil @ A ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % finlsts_rev_cases
% 0.28/0.46 thf(fact_127_lrev__induct,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.28/0.46 => ( ! [X3: A,Xs3: coinductive_llist @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ Xs3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ( P @ Xs3 )
% 0.28/0.46 => ( ( member @ A @ X3 @ A2 )
% 0.28/0.46 => ( P @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) ) ) ) ) )
% 0.28/0.46 => ( P @ Xs ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lrev_induct
% 0.28/0.46 thf(fact_128_LList2__Mirabelle__hamjzmohle_Oltake_Osimps_I1_J,axiom,
% 0.28/0.46 ! [A: $tType,L: coinductive_llist @ A] :
% 0.28/0.46 ( ( lList22119844313_ltake @ A @ L @ ( zero_zero @ nat ) )
% 0.28/0.46 = ( coinductive_LNil @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 % LList2_Mirabelle_hamjzmohle.ltake.simps(1)
% 0.28/0.46 thf(fact_129_inflstsE,axiom,
% 0.28/0.46 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 0.28/0.46 => ~ ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.46 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % inflstsE
% 0.28/0.46 thf(fact_130_lapp__allT__iff,axiom,
% 0.28/0.46 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 0.28/0.46 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 0.28/0.46 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lapp_allT_iff
% 0.28/0.46 thf(fact_131_LList2__Mirabelle__hamjzmohle_Oltake__ldrop,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A,M: nat,N: nat] :
% 0.28/0.46 ( ( lList22119844313_ltake @ A @ ( lList2508575361_ldrop @ A @ Xs @ M ) @ N )
% 0.28/0.46 = ( lList2508575361_ldrop @ A @ ( lList22119844313_ltake @ A @ Xs @ ( plus_plus @ nat @ N @ M ) ) @ M ) ) ).
% 0.28/0.46
% 0.28/0.46 % LList2_Mirabelle_hamjzmohle.ltake_ldrop
% 0.28/0.46 thf(fact_132_ltake__ldrop__id,axiom,
% 0.28/0.46 ! [A: $tType,X: coinductive_llist @ A,I: nat] :
% 0.28/0.46 ( ( coinductive_lappend @ A @ ( lList22119844313_ltake @ A @ X @ I ) @ ( lList2508575361_ldrop @ A @ X @ I ) )
% 0.28/0.46 = X ) ).
% 0.28/0.46
% 0.28/0.46 % ltake_ldrop_id
% 0.28/0.46 thf(fact_133_LList2__Mirabelle__hamjzmohle_Ollast__LCons,axiom,
% 0.28/0.46 ! [B: $tType,R: coinductive_llist @ B,A2: set @ B,A3: B] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ B ) @ R @ ( lList2236698231inlsts @ B @ A2 ) )
% 0.28/0.46 => ( ( ( R
% 0.28/0.46 = ( coinductive_LNil @ B ) )
% 0.28/0.46 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A3 @ R ) )
% 0.28/0.46 = A3 ) )
% 0.28/0.46 & ( ( R
% 0.28/0.46 != ( coinductive_LNil @ B ) )
% 0.28/0.46 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A3 @ R ) )
% 0.28/0.46 = ( lList2170638824_llast @ B @ R ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % LList2_Mirabelle_hamjzmohle.llast_LCons
% 0.28/0.46 thf(fact_134_top__empty__eq,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( top_top @ ( A > $o ) )
% 0.28/0.46 = ( ^ [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % top_empty_eq
% 0.28/0.46 thf(fact_135_lsublist__singleton,axiom,
% 0.28/0.46 ! [A: $tType,A2: set @ nat,X: A] :
% 0.28/0.46 ( ( ( member @ nat @ ( zero_zero @ nat ) @ A2 )
% 0.28/0.46 => ( ( coinductive_lsublist @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) @ A2 )
% 0.28/0.46 = ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) )
% 0.28/0.46 & ( ~ ( member @ nat @ ( zero_zero @ nat ) @ A2 )
% 0.28/0.46 => ( ( coinductive_lsublist @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) @ A2 )
% 0.28/0.46 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lsublist_singleton
% 0.28/0.46 thf(fact_136_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.28/0.46 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.28/0.46 = ( ( Xs
% 0.28/0.46 = ( coinductive_LNil @ A ) )
% 0.28/0.46 | ? [Xs2: coinductive_llist @ A] :
% 0.28/0.46 ( ( Xs
% 0.28/0.46 = ( coinductive_LCons @ A @ Y @ Xs2 ) )
% 0.28/0.46 & ( coindu328551480prefix @ A @ Xs2 @ Ys ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Coinductive_List.finite_lprefix_nitpick_simps(3)
% 0.28/0.46 thf(fact_137_top__conj_I1_J,axiom,
% 0.28/0.46 ! [A: $tType,X: A,P: $o] :
% 0.28/0.46 ( ( ( top_top @ ( A > $o ) @ X )
% 0.28/0.46 & P )
% 0.28/0.46 = P ) ).
% 0.28/0.46
% 0.28/0.46 % top_conj(1)
% 0.28/0.46 thf(fact_138_lsublist__LNil,axiom,
% 0.28/0.46 ! [A: $tType,A2: set @ nat] :
% 0.28/0.46 ( ( coinductive_lsublist @ A @ ( coinductive_LNil @ A ) @ A2 )
% 0.28/0.46 = ( coinductive_LNil @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 % lsublist_LNil
% 0.28/0.46 thf(fact_139_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 0.28/0.46
% 0.28/0.46 % Coinductive_List.finite_lprefix_nitpick_simps(2)
% 0.28/0.46 thf(fact_140_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 0.28/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.28/0.46 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.28/0.46 = ( Xs
% 0.28/0.46 = ( coinductive_LNil @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Coinductive_List.finite_lprefix_nitpick_simps(1)
% 0.28/0.46 thf(fact_141_top__conj_I2_J,axiom,
% 0.28/0.46 ! [A: $tType,P: $o,X: A] :
% 0.28/0.46 ( ( P
% 0.28/0.46 & ( top_top @ ( A > $o ) @ X ) )
% 0.28/0.46 = P ) ).
% 0.28/0.46
% 0.28/0.46 % top_conj(2)
% 0.28/0.46 thf(fact_142_lstrict__prefix__code_I3_J,axiom,
% 0.28/0.46 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 0.28/0.46 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 0.28/0.46
% 0.28/0.46 % lstrict_prefix_code(3)
% 0.28/0.46 thf(fact_143_lstrict__prefix__code_I2_J,axiom,
% 0.28/0.46 ! [B: $tType,Y: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y @ Ys ) ) ).
% 0.28/0.46
% 0.28/0.46 % lstrict_prefix_code(2)
% 0.28/0.46 thf(fact_144_inflsts__def,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( lList21612149805nflsts @ A )
% 0.28/0.46 = ( ^ [A7: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A7 ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % inflsts_def
% 0.28/0.46 thf(fact_145_LList2__Mirabelle__hamjzmohle_Ollength__LCons,axiom,
% 0.28/0.46 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A3: A] :
% 0.28/0.46 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.46 => ( ( lList21232602520length @ A @ ( coinductive_LCons @ A @ A3 @ R ) )
% 0.28/0.46 = ( suc @ ( lList21232602520length @ A @ R ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % LList2_Mirabelle_hamjzmohle.llength_LCons
% 0.28/0.46 thf(fact_146_nat_Oinject,axiom,
% 0.28/0.46 ! [X23: nat,Y2: nat] :
% 0.28/0.46 ( ( ( suc @ X23 )
% 0.28/0.46 = ( suc @ Y2 ) )
% 0.28/0.46 = ( X23 = Y2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % nat.inject
% 0.28/0.46 thf(fact_147_old_Onat_Oinject,axiom,
% 0.28/0.46 ! [Nat: nat,Nat2: nat] :
% 0.28/0.46 ( ( ( suc @ Nat )
% 0.28/0.46 = ( suc @ Nat2 ) )
% 0.28/0.46 = ( Nat = Nat2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % old.nat.inject
% 0.28/0.46 thf(fact_148_DiffI,axiom,
% 0.28/0.46 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.28/0.46 ( ( member @ A @ C @ A2 )
% 0.28/0.46 => ( ~ ( member @ A @ C @ B2 )
% 0.28/0.46 => ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % DiffI
% 0.28/0.46 thf(fact_149_Diff__iff,axiom,
% 0.28/0.46 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.28/0.46 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.28/0.46 = ( ( member @ A @ C @ A2 )
% 0.28/0.46 & ~ ( member @ A @ C @ B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % Diff_iff
% 0.28/0.46 thf(fact_150_Diff__idemp,axiom,
% 0.28/0.46 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.28/0.46 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ B2 )
% 0.28/0.46 = ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % Diff_idemp
% 0.28/0.46 thf(fact_151_diff__self,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A] :
% 0.28/0.46 ( ( minus_minus @ A @ A3 @ A3 )
% 0.28/0.46 = ( zero_zero @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % diff_self
% 0.28/0.46 thf(fact_152_diff__0__right,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A] :
% 0.28/0.46 ( ( minus_minus @ A @ A3 @ ( zero_zero @ A ) )
% 0.28/0.46 = A3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % diff_0_right
% 0.28/0.46 thf(fact_153_zero__diff,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( comm_monoid_diff @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A] :
% 0.28/0.46 ( ( minus_minus @ A @ ( zero_zero @ A ) @ A3 )
% 0.28/0.46 = ( zero_zero @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % zero_diff
% 0.28/0.46 thf(fact_154_diff__zero,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A] :
% 0.28/0.46 ( ( minus_minus @ A @ A3 @ ( zero_zero @ A ) )
% 0.28/0.46 = A3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % diff_zero
% 0.28/0.46 thf(fact_155_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A] :
% 0.28/0.46 ( ( minus_minus @ A @ A3 @ A3 )
% 0.28/0.46 = ( zero_zero @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % cancel_comm_monoid_add_class.diff_cancel
% 0.28/0.46 thf(fact_156_add__diff__cancel,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A] :
% 0.28/0.46 ( ( minus_minus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ B3 )
% 0.28/0.46 = A3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_diff_cancel
% 0.28/0.46 thf(fact_157_diff__add__cancel,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A] :
% 0.28/0.46 ( ( plus_plus @ A @ ( minus_minus @ A @ A3 @ B3 ) @ B3 )
% 0.28/0.46 = A3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % diff_add_cancel
% 0.28/0.46 thf(fact_158_add__diff__cancel__left,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [C: A,A3: A,B3: A] :
% 0.28/0.46 ( ( minus_minus @ A @ ( plus_plus @ A @ C @ A3 ) @ ( plus_plus @ A @ C @ B3 ) )
% 0.28/0.46 = ( minus_minus @ A @ A3 @ B3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_diff_cancel_left
% 0.28/0.46 thf(fact_159_add__diff__cancel__left_H,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A] :
% 0.28/0.46 ( ( minus_minus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ A3 )
% 0.28/0.46 = B3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_diff_cancel_left'
% 0.28/0.46 thf(fact_160_add__diff__cancel__right,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,C: A,B3: A] :
% 0.28/0.46 ( ( minus_minus @ A @ ( plus_plus @ A @ A3 @ C ) @ ( plus_plus @ A @ B3 @ C ) )
% 0.28/0.46 = ( minus_minus @ A @ A3 @ B3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_diff_cancel_right
% 0.28/0.46 thf(fact_161_add__diff__cancel__right_H,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A] :
% 0.28/0.46 ( ( minus_minus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ B3 )
% 0.28/0.46 = A3 ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_diff_cancel_right'
% 0.28/0.46 thf(fact_162_add__Suc__right,axiom,
% 0.28/0.46 ! [M: nat,N: nat] :
% 0.28/0.46 ( ( plus_plus @ nat @ M @ ( suc @ N ) )
% 0.28/0.46 = ( suc @ ( plus_plus @ nat @ M @ N ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_Suc_right
% 0.28/0.46 thf(fact_163_lstrict__prefix__code_I4_J,axiom,
% 0.28/0.46 ! [B: $tType,X: B,Xs: coinductive_llist @ B,Y: B,Ys: coinductive_llist @ B] :
% 0.28/0.46 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 0.28/0.46 = ( ( X = Y )
% 0.28/0.46 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % lstrict_prefix_code(4)
% 0.28/0.46 thf(fact_164_lstrict__prefix__code_I1_J,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 0.28/0.46
% 0.28/0.46 % lstrict_prefix_code(1)
% 0.28/0.46 thf(fact_165_diff__add__zero,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( comm_monoid_diff @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A] :
% 0.28/0.46 ( ( minus_minus @ A @ A3 @ ( plus_plus @ A @ A3 @ B3 ) )
% 0.28/0.46 = ( zero_zero @ A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % diff_add_zero
% 0.28/0.46 thf(fact_166_eq__iff__diff__eq__0,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.28/0.46 = ( ^ [A4: A,B4: A] :
% 0.28/0.46 ( ( minus_minus @ A @ A4 @ B4 )
% 0.28/0.46 = ( zero_zero @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eq_iff_diff_eq_0
% 0.28/0.46 thf(fact_167_diff__eq__eq,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A,C: A] :
% 0.28/0.46 ( ( ( minus_minus @ A @ A3 @ B3 )
% 0.28/0.46 = C )
% 0.28/0.46 = ( A3
% 0.28/0.46 = ( plus_plus @ A @ C @ B3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % diff_eq_eq
% 0.28/0.46 thf(fact_168_eq__diff__eq,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,C: A,B3: A] :
% 0.28/0.46 ( ( A3
% 0.28/0.46 = ( minus_minus @ A @ C @ B3 ) )
% 0.28/0.46 = ( ( plus_plus @ A @ A3 @ B3 )
% 0.28/0.46 = C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % eq_diff_eq
% 0.28/0.46 thf(fact_169_add__diff__eq,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A,C: A] :
% 0.28/0.46 ( ( plus_plus @ A @ A3 @ ( minus_minus @ A @ B3 @ C ) )
% 0.28/0.46 = ( minus_minus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_diff_eq
% 0.28/0.46 thf(fact_170_diff__diff__eq2,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A,C: A] :
% 0.28/0.46 ( ( minus_minus @ A @ A3 @ ( minus_minus @ A @ B3 @ C ) )
% 0.28/0.46 = ( minus_minus @ A @ ( plus_plus @ A @ A3 @ C ) @ B3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % diff_diff_eq2
% 0.28/0.46 thf(fact_171_diff__add__eq,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( ab_group_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A,C: A] :
% 0.28/0.46 ( ( plus_plus @ A @ ( minus_minus @ A @ A3 @ B3 ) @ C )
% 0.28/0.46 = ( minus_minus @ A @ ( plus_plus @ A @ A3 @ C ) @ B3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % diff_add_eq
% 0.28/0.46 thf(fact_172_diff__add__eq__diff__diff__swap,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A,C: A] :
% 0.28/0.46 ( ( minus_minus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) )
% 0.28/0.46 = ( minus_minus @ A @ ( minus_minus @ A @ A3 @ C ) @ B3 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % diff_add_eq_diff_diff_swap
% 0.28/0.46 thf(fact_173_diff__diff__add,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A,C: A] :
% 0.28/0.46 ( ( minus_minus @ A @ ( minus_minus @ A @ A3 @ B3 ) @ C )
% 0.28/0.46 = ( minus_minus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % diff_diff_add
% 0.28/0.46 thf(fact_174_add__implies__diff,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [C: A,B3: A,A3: A] :
% 0.28/0.46 ( ( ( plus_plus @ A @ C @ B3 )
% 0.28/0.46 = A3 )
% 0.28/0.46 => ( C
% 0.28/0.46 = ( minus_minus @ A @ A3 @ B3 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_implies_diff
% 0.28/0.46 thf(fact_175_nat_Odistinct_I1_J,axiom,
% 0.28/0.46 ! [X23: nat] :
% 0.28/0.46 ( ( zero_zero @ nat )
% 0.28/0.46 != ( suc @ X23 ) ) ).
% 0.28/0.46
% 0.28/0.46 % nat.distinct(1)
% 0.28/0.46 thf(fact_176_old_Onat_Odistinct_I2_J,axiom,
% 0.28/0.46 ! [Nat3: nat] :
% 0.28/0.46 ( ( suc @ Nat3 )
% 0.28/0.46 != ( zero_zero @ nat ) ) ).
% 0.28/0.46
% 0.28/0.46 % old.nat.distinct(2)
% 0.28/0.46 thf(fact_177_old_Onat_Odistinct_I1_J,axiom,
% 0.28/0.46 ! [Nat2: nat] :
% 0.28/0.46 ( ( zero_zero @ nat )
% 0.28/0.46 != ( suc @ Nat2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % old.nat.distinct(1)
% 0.28/0.46 thf(fact_178_nat_OdiscI,axiom,
% 0.28/0.46 ! [Nat: nat,X23: nat] :
% 0.28/0.46 ( ( Nat
% 0.28/0.46 = ( suc @ X23 ) )
% 0.28/0.46 => ( Nat
% 0.28/0.46 != ( zero_zero @ nat ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % nat.discI
% 0.28/0.46 thf(fact_179_nat__induct,axiom,
% 0.28/0.46 ! [P: nat > $o,N: nat] :
% 0.28/0.46 ( ( P @ ( zero_zero @ nat ) )
% 0.28/0.46 => ( ! [N2: nat] :
% 0.28/0.46 ( ( P @ N2 )
% 0.28/0.46 => ( P @ ( suc @ N2 ) ) )
% 0.28/0.46 => ( P @ N ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % nat_induct
% 0.28/0.46 thf(fact_180_diff__induct,axiom,
% 0.28/0.46 ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.28/0.46 ( ! [X3: nat] : ( P @ X3 @ ( zero_zero @ nat ) )
% 0.28/0.46 => ( ! [Y4: nat] : ( P @ ( zero_zero @ nat ) @ ( suc @ Y4 ) )
% 0.28/0.46 => ( ! [X3: nat,Y4: nat] :
% 0.28/0.46 ( ( P @ X3 @ Y4 )
% 0.28/0.46 => ( P @ ( suc @ X3 ) @ ( suc @ Y4 ) ) )
% 0.28/0.46 => ( P @ M @ N ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % diff_induct
% 0.28/0.46 thf(fact_181_zero__induct,axiom,
% 0.28/0.46 ! [P: nat > $o,K: nat] :
% 0.28/0.46 ( ( P @ K )
% 0.28/0.46 => ( ! [N2: nat] :
% 0.28/0.46 ( ( P @ ( suc @ N2 ) )
% 0.28/0.46 => ( P @ N2 ) )
% 0.28/0.46 => ( P @ ( zero_zero @ nat ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % zero_induct
% 0.28/0.46 thf(fact_182_Suc__neq__Zero,axiom,
% 0.28/0.46 ! [M: nat] :
% 0.28/0.46 ( ( suc @ M )
% 0.28/0.46 != ( zero_zero @ nat ) ) ).
% 0.28/0.46
% 0.28/0.46 % Suc_neq_Zero
% 0.28/0.46 thf(fact_183_Zero__neq__Suc,axiom,
% 0.28/0.46 ! [M: nat] :
% 0.28/0.46 ( ( zero_zero @ nat )
% 0.28/0.46 != ( suc @ M ) ) ).
% 0.28/0.46
% 0.28/0.46 % Zero_neq_Suc
% 0.28/0.46 thf(fact_184_Zero__not__Suc,axiom,
% 0.28/0.46 ! [M: nat] :
% 0.28/0.46 ( ( zero_zero @ nat )
% 0.28/0.46 != ( suc @ M ) ) ).
% 0.28/0.46
% 0.28/0.46 % Zero_not_Suc
% 0.28/0.46 thf(fact_185_old_Onat_Oexhaust,axiom,
% 0.28/0.46 ! [Y: nat] :
% 0.28/0.46 ( ( Y
% 0.28/0.46 != ( zero_zero @ nat ) )
% 0.28/0.46 => ~ ! [Nat4: nat] :
% 0.28/0.46 ( Y
% 0.28/0.46 != ( suc @ Nat4 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % old.nat.exhaust
% 0.28/0.46 thf(fact_186_old_Onat_Oinducts,axiom,
% 0.28/0.46 ! [P: nat > $o,Nat: nat] :
% 0.28/0.46 ( ( P @ ( zero_zero @ nat ) )
% 0.28/0.46 => ( ! [Nat4: nat] :
% 0.28/0.46 ( ( P @ Nat4 )
% 0.28/0.46 => ( P @ ( suc @ Nat4 ) ) )
% 0.28/0.46 => ( P @ Nat ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % old.nat.inducts
% 0.28/0.46 thf(fact_187_not0__implies__Suc,axiom,
% 0.28/0.46 ! [N: nat] :
% 0.28/0.46 ( ( N
% 0.28/0.46 != ( zero_zero @ nat ) )
% 0.28/0.46 => ? [M2: nat] :
% 0.28/0.46 ( N
% 0.28/0.46 = ( suc @ M2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % not0_implies_Suc
% 0.28/0.46 thf(fact_188_add__Suc__shift,axiom,
% 0.28/0.46 ! [M: nat,N: nat] :
% 0.28/0.46 ( ( plus_plus @ nat @ ( suc @ M ) @ N )
% 0.28/0.46 = ( plus_plus @ nat @ M @ ( suc @ N ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_Suc_shift
% 0.28/0.46 thf(fact_189_add__Suc,axiom,
% 0.28/0.46 ! [M: nat,N: nat] :
% 0.28/0.46 ( ( plus_plus @ nat @ ( suc @ M ) @ N )
% 0.28/0.46 = ( suc @ ( plus_plus @ nat @ M @ N ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_Suc
% 0.28/0.46 thf(fact_190_DiffE,axiom,
% 0.28/0.46 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.28/0.46 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.28/0.46 => ~ ( ( member @ A @ C @ A2 )
% 0.28/0.46 => ( member @ A @ C @ B2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % DiffE
% 0.28/0.46 thf(fact_191_DiffD1,axiom,
% 0.28/0.46 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.28/0.46 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.28/0.46 => ( member @ A @ C @ A2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % DiffD1
% 0.28/0.46 thf(fact_192_DiffD2,axiom,
% 0.28/0.46 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.28/0.46 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 0.28/0.46 => ~ ( member @ A @ C @ B2 ) ) ).
% 0.28/0.46
% 0.28/0.46 % DiffD2
% 0.28/0.46 thf(fact_193_Suc__inject,axiom,
% 0.28/0.46 ! [X: nat,Y: nat] :
% 0.28/0.46 ( ( ( suc @ X )
% 0.28/0.46 = ( suc @ Y ) )
% 0.28/0.46 => ( X = Y ) ) ).
% 0.28/0.46
% 0.28/0.46 % Suc_inject
% 0.28/0.46 thf(fact_194_n__not__Suc__n,axiom,
% 0.28/0.46 ! [N: nat] :
% 0.28/0.46 ( N
% 0.28/0.46 != ( suc @ N ) ) ).
% 0.28/0.46
% 0.28/0.46 % n_not_Suc_n
% 0.28/0.46 thf(fact_195_llist__less__induct,axiom,
% 0.28/0.46 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 0.28/0.46 ( ! [Xs3: coinductive_llist @ A] :
% 0.28/0.46 ( ! [Ys2: coinductive_llist @ A] :
% 0.28/0.46 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs3 )
% 0.28/0.46 => ( P @ Ys2 ) )
% 0.28/0.46 => ( P @ Xs3 ) )
% 0.28/0.46 => ( P @ Xs ) ) ).
% 0.28/0.46
% 0.28/0.46 % llist_less_induct
% 0.28/0.46 thf(fact_196_diff__eq__diff__eq,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( group_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,B3: A,C: A,D2: A] :
% 0.28/0.46 ( ( ( minus_minus @ A @ A3 @ B3 )
% 0.28/0.46 = ( minus_minus @ A @ C @ D2 ) )
% 0.28/0.46 => ( ( A3 = B3 )
% 0.28/0.46 = ( C = D2 ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % diff_eq_diff_eq
% 0.28/0.46 thf(fact_197_diff__right__commute,axiom,
% 0.28/0.46 ! [A: $tType] :
% 0.28/0.46 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 0.28/0.46 => ! [A3: A,C: A,B3: A] :
% 0.28/0.46 ( ( minus_minus @ A @ ( minus_minus @ A @ A3 @ C ) @ B3 )
% 0.28/0.46 = ( minus_minus @ A @ ( minus_minus @ A @ A3 @ B3 ) @ C ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % diff_right_commute
% 0.28/0.46 thf(fact_198_one__is__add,axiom,
% 0.28/0.46 ! [M: nat,N: nat] :
% 0.28/0.46 ( ( ( suc @ ( zero_zero @ nat ) )
% 0.28/0.46 = ( plus_plus @ nat @ M @ N ) )
% 0.28/0.46 = ( ( ( M
% 0.28/0.46 = ( suc @ ( zero_zero @ nat ) ) )
% 0.28/0.46 & ( N
% 0.28/0.46 = ( zero_zero @ nat ) ) )
% 0.28/0.46 | ( ( M
% 0.28/0.46 = ( zero_zero @ nat ) )
% 0.28/0.46 & ( N
% 0.28/0.46 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % one_is_add
% 0.28/0.46 thf(fact_199_add__is__1,axiom,
% 0.28/0.46 ! [M: nat,N: nat] :
% 0.28/0.46 ( ( ( plus_plus @ nat @ M @ N )
% 0.28/0.46 = ( suc @ ( zero_zero @ nat ) ) )
% 0.28/0.46 = ( ( ( M
% 0.28/0.46 = ( suc @ ( zero_zero @ nat ) ) )
% 0.28/0.46 & ( N
% 0.28/0.46 = ( zero_zero @ nat ) ) )
% 0.28/0.46 | ( ( M
% 0.28/0.46 = ( zero_zero @ nat ) )
% 0.28/0.46 & ( N
% 0.28/0.46 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % add_is_1
% 0.28/0.46 thf(fact_200_ltake__LCons__Suc,axiom,
% 0.28/0.46 ! [A: $tType,A3: A,L: coinductive_llist @ A,I: nat] :
% 0.28/0.46 ( ( lList22119844313_ltake @ A @ ( coinductive_LCons @ A @ A3 @ L ) @ ( suc @ I ) )
% 0.28/0.46 = ( coinductive_LCons @ A @ A3 @ ( lList22119844313_ltake @ A @ L @ I ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % ltake_LCons_Suc
% 0.28/0.46 thf(fact_201_list__decode_Ocases,axiom,
% 0.28/0.46 ! [X: nat] :
% 0.28/0.46 ( ( X
% 0.28/0.46 != ( zero_zero @ nat ) )
% 0.28/0.46 => ~ ! [N2: nat] :
% 0.28/0.46 ( X
% 0.28/0.46 != ( suc @ N2 ) ) ) ).
% 0.28/0.46
% 0.28/0.46 % list_decode.cases
% 0.28/0.46 thf(fact_202_dependent__nat__choice,axiom,
% 0.28/0.46 ! [A: $tType,P: nat > A > $o,Q: nat > A > A > $o] :
% 0.28/0.46 ( ? [X1: A] : ( P @ ( zero_zero @ nat ) @ X1 )
% 0.28/0.46 => ( ! [X3: A,N2: nat] :
% 0.28/0.46 ( ( P @ N2 @ X3 )
% 0.28/0.46 => ? [Y5: A] :
% 0.28/0.46 ( ( P @ ( suc @ N2 ) @ Y5 )
% 0.28/0.46 & ( Q @ N2 @ X3 @ Y5 ) ) )
% 0.28/0.46 => ? [F2: nat > A] :
% 0.28/0.47 ! [N3: nat] :
% 0.28/0.47 ( ( P @ N3 @ ( F2 @ N3 ) )
% 0.28/0.47 & ( Q @ N3 @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % dependent_nat_choice
% 0.28/0.47 thf(fact_203_exists__least__lemma,axiom,
% 0.28/0.47 ! [P: nat > $o] :
% 0.28/0.47 ( ~ ( P @ ( zero_zero @ nat ) )
% 0.28/0.47 => ( ? [X1: nat] : ( P @ X1 )
% 0.28/0.47 => ? [N2: nat] :
% 0.28/0.47 ( ~ ( P @ N2 )
% 0.28/0.47 & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % exists_least_lemma
% 0.28/0.47 thf(fact_204_diff__0__eq__0,axiom,
% 0.28/0.47 ! [N: nat] :
% 0.28/0.47 ( ( minus_minus @ nat @ ( zero_zero @ nat ) @ N )
% 0.28/0.47 = ( zero_zero @ nat ) ) ).
% 0.28/0.47
% 0.28/0.47 % diff_0_eq_0
% 0.28/0.47 thf(fact_205_diff__self__eq__0,axiom,
% 0.28/0.47 ! [M: nat] :
% 0.28/0.47 ( ( minus_minus @ nat @ M @ M )
% 0.28/0.47 = ( zero_zero @ nat ) ) ).
% 0.28/0.47
% 0.28/0.47 % diff_self_eq_0
% 0.28/0.47 thf(fact_206_diff__Suc__Suc,axiom,
% 0.28/0.47 ! [M: nat,N: nat] :
% 0.28/0.47 ( ( minus_minus @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 0.28/0.47 = ( minus_minus @ nat @ M @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % diff_Suc_Suc
% 0.28/0.47 thf(fact_207_Suc__diff__diff,axiom,
% 0.28/0.47 ! [M: nat,N: nat,K: nat] :
% 0.28/0.47 ( ( minus_minus @ nat @ ( minus_minus @ nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 0.28/0.47 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ N ) @ K ) ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_diff_diff
% 0.28/0.47 thf(fact_208_diff__diff__left,axiom,
% 0.28/0.47 ! [I: nat,J: nat,K: nat] :
% 0.28/0.47 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I @ J ) @ K )
% 0.28/0.47 = ( minus_minus @ nat @ I @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % diff_diff_left
% 0.28/0.47 thf(fact_209_diffs0__imp__equal,axiom,
% 0.28/0.47 ! [M: nat,N: nat] :
% 0.28/0.47 ( ( ( minus_minus @ nat @ M @ N )
% 0.28/0.47 = ( zero_zero @ nat ) )
% 0.28/0.47 => ( ( ( minus_minus @ nat @ N @ M )
% 0.28/0.47 = ( zero_zero @ nat ) )
% 0.28/0.47 => ( M = N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % diffs0_imp_equal
% 0.28/0.47 thf(fact_210_minus__nat_Odiff__0,axiom,
% 0.28/0.47 ! [M: nat] :
% 0.28/0.47 ( ( minus_minus @ nat @ M @ ( zero_zero @ nat ) )
% 0.28/0.47 = M ) ).
% 0.28/0.47
% 0.28/0.47 % minus_nat.diff_0
% 0.28/0.47 thf(fact_211_Nat_Odiff__cancel,axiom,
% 0.28/0.47 ! [K: nat,M: nat,N: nat] :
% 0.28/0.47 ( ( minus_minus @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 0.28/0.47 = ( minus_minus @ nat @ M @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % Nat.diff_cancel
% 0.28/0.47 thf(fact_212_diff__cancel2,axiom,
% 0.28/0.47 ! [M: nat,K: nat,N: nat] :
% 0.28/0.47 ( ( minus_minus @ nat @ ( plus_plus @ nat @ M @ K ) @ ( plus_plus @ nat @ N @ K ) )
% 0.28/0.47 = ( minus_minus @ nat @ M @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % diff_cancel2
% 0.28/0.47 thf(fact_213_diff__add__inverse,axiom,
% 0.28/0.47 ! [N: nat,M: nat] :
% 0.28/0.47 ( ( minus_minus @ nat @ ( plus_plus @ nat @ N @ M ) @ N )
% 0.28/0.47 = M ) ).
% 0.28/0.47
% 0.28/0.47 % diff_add_inverse
% 0.28/0.47 thf(fact_214_diff__add__inverse2,axiom,
% 0.28/0.47 ! [M: nat,N: nat] :
% 0.28/0.47 ( ( minus_minus @ nat @ ( plus_plus @ nat @ M @ N ) @ N )
% 0.28/0.47 = M ) ).
% 0.28/0.47
% 0.28/0.47 % diff_add_inverse2
% 0.28/0.47 thf(fact_215_zero__induct__lemma,axiom,
% 0.28/0.47 ! [P: nat > $o,K: nat,I: nat] :
% 0.28/0.47 ( ( P @ K )
% 0.28/0.47 => ( ! [N2: nat] :
% 0.28/0.47 ( ( P @ ( suc @ N2 ) )
% 0.28/0.47 => ( P @ N2 ) )
% 0.28/0.47 => ( P @ ( minus_minus @ nat @ K @ I ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % zero_induct_lemma
% 0.28/0.47 thf(fact_216_diff__add__0,axiom,
% 0.28/0.47 ! [N: nat,M: nat] :
% 0.28/0.47 ( ( minus_minus @ nat @ N @ ( plus_plus @ nat @ N @ M ) )
% 0.28/0.47 = ( zero_zero @ nat ) ) ).
% 0.28/0.47
% 0.28/0.47 % diff_add_0
% 0.28/0.47 thf(fact_217_triangle__Suc,axiom,
% 0.28/0.47 ! [N: nat] :
% 0.28/0.47 ( ( nat_triangle @ ( suc @ N ) )
% 0.28/0.47 = ( plus_plus @ nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % triangle_Suc
% 0.28/0.47 thf(fact_218_add__diff__add,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ab_group_add @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [A3: A,C: A,B3: A,D2: A] :
% 0.28/0.47 ( ( minus_minus @ A @ ( plus_plus @ A @ A3 @ C ) @ ( plus_plus @ A @ B3 @ D2 ) )
% 0.28/0.47 = ( plus_plus @ A @ ( minus_minus @ A @ A3 @ B3 ) @ ( minus_minus @ A @ C @ D2 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_diff_add
% 0.28/0.47 thf(fact_219_triangle__0,axiom,
% 0.28/0.47 ( ( nat_triangle @ ( zero_zero @ nat ) )
% 0.28/0.47 = ( zero_zero @ nat ) ) ).
% 0.28/0.47
% 0.28/0.47 % triangle_0
% 0.28/0.47 thf(fact_220_diff__commute,axiom,
% 0.28/0.47 ! [I: nat,J: nat,K: nat] :
% 0.28/0.47 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I @ J ) @ K )
% 0.28/0.47 = ( minus_minus @ nat @ ( minus_minus @ nat @ I @ K ) @ J ) ) ).
% 0.28/0.47
% 0.28/0.47 % diff_commute
% 0.28/0.47 thf(fact_221_linordered__field__class_Osign__simps_I34_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [A3: A,B3: A,C: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( minus_minus @ A @ A3 @ B3 ) @ C )
% 0.28/0.47 = ( minus_minus @ A @ ( plus_plus @ A @ A3 @ C ) @ B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % linordered_field_class.sign_simps(34)
% 0.28/0.47 thf(fact_222_linordered__field__class_Osign__simps_I33_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [A3: A,B3: A,C: A] :
% 0.28/0.47 ( ( minus_minus @ A @ ( minus_minus @ A @ A3 @ B3 ) @ C )
% 0.28/0.47 = ( minus_minus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % linordered_field_class.sign_simps(33)
% 0.28/0.47 thf(fact_223_linordered__field__class_Osign__simps_I28_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [B3: A,A3: A,C: A] :
% 0.28/0.47 ( ( plus_plus @ A @ B3 @ ( plus_plus @ A @ A3 @ C ) )
% 0.28/0.47 = ( plus_plus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % linordered_field_class.sign_simps(28)
% 0.28/0.47 thf(fact_224_linordered__field__class_Osign__simps_I27_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.28/0.47 => ( ( plus_plus @ A )
% 0.28/0.47 = ( ^ [A4: A,B4: A] : ( plus_plus @ A @ B4 @ A4 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % linordered_field_class.sign_simps(27)
% 0.28/0.47 thf(fact_225_linordered__field__class_Osign__simps_I26_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [A3: A,B3: A,C: A] :
% 0.28/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ C )
% 0.28/0.47 = ( plus_plus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % linordered_field_class.sign_simps(26)
% 0.28/0.47 thf(fact_226_linordered__field__class_Osign__simps_I29_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [A3: A,B3: A,C: A] :
% 0.28/0.47 ( ( plus_plus @ A @ A3 @ ( minus_minus @ A @ B3 @ C ) )
% 0.28/0.47 = ( minus_minus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % linordered_field_class.sign_simps(29)
% 0.28/0.47 thf(fact_227_linordered__field__class_Osign__simps_I30_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [A3: A,B3: A,C: A] :
% 0.28/0.47 ( ( ( minus_minus @ A @ A3 @ B3 )
% 0.28/0.47 = C )
% 0.28/0.47 = ( A3
% 0.28/0.47 = ( plus_plus @ A @ C @ B3 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % linordered_field_class.sign_simps(30)
% 0.28/0.47 thf(fact_228_linordered__field__class_Osign__simps_I31_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [A3: A,C: A,B3: A] :
% 0.28/0.47 ( ( A3
% 0.28/0.47 = ( minus_minus @ A @ C @ B3 ) )
% 0.28/0.47 = ( ( plus_plus @ A @ A3 @ B3 )
% 0.28/0.47 = C ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % linordered_field_class.sign_simps(31)
% 0.28/0.47 thf(fact_229_linordered__field__class_Osign__simps_I32_J,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [A3: A,B3: A,C: A] :
% 0.28/0.47 ( ( minus_minus @ A @ A3 @ ( minus_minus @ A @ B3 @ C ) )
% 0.28/0.47 = ( minus_minus @ A @ ( plus_plus @ A @ A3 @ C ) @ B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % linordered_field_class.sign_simps(32)
% 0.28/0.47 thf(fact_230_finlsts__rec__LCons,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,R: coinductive_llist @ A,A2: set @ A,C: B,D2: A > ( coinductive_llist @ A ) > B > B,A3: A] :
% 0.28/0.47 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.47 => ( ( lList21916056377ts_rec @ B @ A @ C @ D2 @ ( coinductive_LCons @ A @ A3 @ R ) )
% 0.28/0.47 = ( D2 @ A3 @ R @ ( lList21916056377ts_rec @ B @ A @ C @ D2 @ R ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finlsts_rec_LCons
% 0.28/0.47 thf(fact_231_finlsts__rec__LCons__def,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,F: ( coinductive_llist @ A ) > B,C: B,D2: A > ( coinductive_llist @ A ) > B > B,R: coinductive_llist @ A,A2: set @ A,A3: A] :
% 0.28/0.47 ( ( F
% 0.28/0.47 = ( lList21916056377ts_rec @ B @ A @ C @ D2 ) )
% 0.28/0.47 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.28/0.47 => ( ( F @ ( coinductive_LCons @ A @ A3 @ R ) )
% 0.28/0.47 = ( D2 @ A3 @ R @ ( F @ R ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % finlsts_rec_LCons_def
% 0.28/0.47 thf(fact_232_finlsts__rec__LNil,axiom,
% 0.28/0.47 ! [B: $tType,A: $tType,C: A,D2: B > ( coinductive_llist @ B ) > A > A] :
% 0.28/0.47 ( ( lList21916056377ts_rec @ A @ B @ C @ D2 @ ( coinductive_LNil @ B ) )
% 0.28/0.47 = C ) ).
% 0.28/0.47
% 0.28/0.47 % finlsts_rec_LNil
% 0.28/0.47 thf(fact_233_finlsts__rec__LNil__def,axiom,
% 0.28/0.47 ! [A: $tType,B: $tType,F: ( coinductive_llist @ A ) > B,C: B,D2: A > ( coinductive_llist @ A ) > B > B] :
% 0.28/0.47 ( ( F
% 0.28/0.47 = ( lList21916056377ts_rec @ B @ A @ C @ D2 ) )
% 0.28/0.47 => ( ( F @ ( coinductive_LNil @ A ) )
% 0.28/0.47 = C ) ) ).
% 0.28/0.47
% 0.28/0.47 % finlsts_rec_LNil_def
% 0.28/0.47 thf(fact_234_add__eq__if,axiom,
% 0.28/0.47 ( ( plus_plus @ nat )
% 0.28/0.47 = ( ^ [M3: nat,N4: nat] :
% 0.28/0.47 ( if @ nat
% 0.28/0.47 @ ( M3
% 0.28/0.47 = ( zero_zero @ nat ) )
% 0.28/0.47 @ N4
% 0.28/0.47 @ ( suc @ ( plus_plus @ nat @ ( minus_minus @ nat @ M3 @ ( one_one @ nat ) ) @ N4 ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_eq_if
% 0.28/0.47 thf(fact_235_diff__Suc__diff__eq1,axiom,
% 0.28/0.47 ! [K: nat,J: nat,I: nat] :
% 0.28/0.47 ( ( ord_less_eq @ nat @ K @ J )
% 0.28/0.47 => ( ( minus_minus @ nat @ I @ ( suc @ ( minus_minus @ nat @ J @ K ) ) )
% 0.28/0.47 = ( minus_minus @ nat @ ( plus_plus @ nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % diff_Suc_diff_eq1
% 0.28/0.47 thf(fact_236_order__refl,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.28/0.47
% 0.28/0.47 % order_refl
% 0.28/0.47 thf(fact_237_le__zero__eq,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [N: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 0.28/0.47 = ( N
% 0.28/0.47 = ( zero_zero @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_zero_eq
% 0.28/0.47 thf(fact_238_add__le__cancel__right,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [A3: A,C: A,B3: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A3 @ C ) @ ( plus_plus @ A @ B3 @ C ) )
% 0.28/0.47 = ( ord_less_eq @ A @ A3 @ B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_le_cancel_right
% 0.28/0.47 thf(fact_239_add__le__cancel__left,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [C: A,A3: A,B3: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A3 ) @ ( plus_plus @ A @ C @ B3 ) )
% 0.28/0.47 = ( ord_less_eq @ A @ A3 @ B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_le_cancel_left
% 0.28/0.47 thf(fact_240_le0,axiom,
% 0.28/0.47 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 0.28/0.47
% 0.28/0.47 % le0
% 0.28/0.47 thf(fact_241_Suc__le__mono,axiom,
% 0.28/0.47 ! [N: nat,M: nat] :
% 0.28/0.47 ( ( ord_less_eq @ nat @ ( suc @ N ) @ ( suc @ M ) )
% 0.28/0.47 = ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.28/0.47
% 0.28/0.47 % Suc_le_mono
% 0.28/0.47 thf(fact_242_nat__add__left__cancel__le,axiom,
% 0.28/0.47 ! [K: nat,M: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 0.28/0.47 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.28/0.47
% 0.28/0.47 % nat_add_left_cancel_le
% 0.28/0.47 thf(fact_243_diff__diff__cancel,axiom,
% 0.28/0.47 ! [I: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_eq @ nat @ I @ N )
% 0.28/0.47 => ( ( minus_minus @ nat @ N @ ( minus_minus @ nat @ N @ I ) )
% 0.28/0.47 = I ) ) ).
% 0.28/0.47
% 0.28/0.47 % diff_diff_cancel
% 0.28/0.47 thf(fact_244_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [A3: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A3 @ A3 ) )
% 0.28/0.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % zero_le_double_add_iff_zero_le_single_add
% 0.28/0.47 thf(fact_245_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [A3: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A3 @ A3 ) @ ( zero_zero @ A ) )
% 0.28/0.47 = ( ord_less_eq @ A @ A3 @ ( zero_zero @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % double_add_le_zero_iff_single_add_le_zero
% 0.28/0.47 thf(fact_246_le__add__same__cancel2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [A3: A,B3: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A3 @ ( plus_plus @ A @ B3 @ A3 ) )
% 0.28/0.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_add_same_cancel2
% 0.28/0.47 thf(fact_247_le__add__same__cancel1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [A3: A,B3: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ A3 @ ( plus_plus @ A @ A3 @ B3 ) )
% 0.28/0.47 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % le_add_same_cancel1
% 0.28/0.47 thf(fact_248_add__le__same__cancel2,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [A3: A,B3: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A3 @ B3 ) @ B3 )
% 0.28/0.47 = ( ord_less_eq @ A @ A3 @ ( zero_zero @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_le_same_cancel2
% 0.28/0.47 thf(fact_249_add__le__same__cancel1,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [B3: A,A3: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B3 @ A3 ) @ B3 )
% 0.28/0.47 = ( ord_less_eq @ A @ A3 @ ( zero_zero @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % add_le_same_cancel1
% 0.28/0.47 thf(fact_250_diff__ge__0__iff__ge,axiom,
% 0.28/0.47 ! [A: $tType] :
% 0.28/0.47 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.28/0.47 => ! [A3: A,B3: A] :
% 0.28/0.47 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A3 @ B3 ) )
% 0.28/0.47 = ( ord_less_eq @ A @ B3 @ A3 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % diff_ge_0_iff_ge
% 0.28/0.47 thf(fact_251_diff__is__0__eq_H,axiom,
% 0.28/0.47 ! [M: nat,N: nat] :
% 0.28/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.28/0.47 => ( ( minus_minus @ nat @ M @ N )
% 0.28/0.47 = ( zero_zero @ nat ) ) ) ).
% 0.28/0.47
% 0.28/0.47 % diff_is_0_eq'
% 0.28/0.47
% 0.28/0.47 %----Type constructors (23)
% 0.28/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 0.28/0.47 => ( preorder @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_fun___Orderings_Otop,axiom,
% 0.28/0.47 ! [A8: $tType,A9: $tType] :
% 0.28/0.47 ( ( top @ A9 @ ( type2 @ A9 ) )
% 0.28/0.47 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 0.28/0.47 semiri456707255roduct @ nat @ ( type2 @ nat ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le,axiom,
% 0.28/0.47 ordere516151231imp_le @ nat @ ( type2 @ nat ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 0.28/0.47 ordere236663937imp_le @ nat @ ( type2 @ nat ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 0.28/0.47 canoni770627133id_add @ nat @ ( type2 @ nat ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 0.28/0.47 ordere779506340up_add @ nat @ ( type2 @ nat ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 0.28/0.47 cancel146912293up_add @ nat @ ( type2 @ nat ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 0.28/0.47 cancel1352612707id_add @ nat @ ( type2 @ nat ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 0.28/0.47 cancel_semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff,axiom,
% 0.28/0.47 comm_monoid_diff @ nat @ ( type2 @ nat ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 0.28/0.47 ab_semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 0.28/0.47 comm_monoid_add @ nat @ ( type2 @ nat ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
% 0.28/0.47 comm_semiring_1 @ nat @ ( type2 @ nat ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 0.28/0.47 semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.28/0.47 preorder @ nat @ ( type2 @ nat ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Omonoid__add,axiom,
% 0.28/0.47 monoid_add @ nat @ ( type2 @ nat ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 0.28/0.47 zero @ nat @ ( type2 @ nat ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.28/0.47 one @ nat @ ( type2 @ nat ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_2,axiom,
% 0.28/0.47 ! [A8: $tType] : ( preorder @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_Set_Oset___Orderings_Otop_3,axiom,
% 0.28/0.47 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_4,axiom,
% 0.28/0.47 preorder @ $o @ ( type2 @ $o ) ).
% 0.28/0.47
% 0.28/0.47 thf(tcon_HOL_Obool___Orderings_Otop_5,axiom,
% 0.28/0.47 top @ $o @ ( type2 @ $o ) ).
% 0.28/0.47
% 0.28/0.47 %----Helper facts (3)
% 0.28/0.47 thf(help_If_3_1_T,axiom,
% 0.28/0.47 ! [P: $o] :
% 0.28/0.47 ( ( P = $true )
% 0.28/0.47 | ( P = $false ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_If_2_1_T,axiom,
% 0.28/0.47 ! [A: $tType,X: A,Y: A] :
% 0.28/0.47 ( ( if @ A @ $false @ X @ Y )
% 0.28/0.47 = Y ) ).
% 0.28/0.47
% 0.28/0.47 thf(help_If_1_1_T,axiom,
% 0.28/0.47 ! [A: $tType,X: A,Y: A] :
% 0.28/0.47 ( ( if @ A @ $true @ X @ Y )
% 0.28/0.47 = X ) ).
% 0.28/0.47
% 0.28/0.47 %----Conjectures (2)
% 0.28/0.47 thf(conj_0,hypothesis,
% 0.28/0.47 member @ ( coinductive_llist @ a ) @ t @ ( lList2236698231inlsts @ a @ a2 ) ).
% 0.28/0.47
% 0.28/0.47 thf(conj_1,conjecture,
% 0.28/0.47 member @ ( coinductive_llist @ a ) @ ( lList2508575361_ldrop @ a @ t @ i ) @ ( lList2236698231inlsts @ a @ a2 ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 2.47/1.49 ---- Embedded in THF ---
% 2.47/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.47/1.49 %%% Generated on Tue Feb 24 06:10:54 EST 2026
% 2.47/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 2.47/1.49 %%% Logic specification used:
% 2.47/1.49 %%% thf(spec, logic, $$dhol).
% 2.47/1.49
% 2.47/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.3cDcvzBLpc/DTF2DTF27050.p
% 2.47/1.49 thf(ty_t_Coinductive__List_Ollist, type, coinductive_llist: ($tType > $tType)).
% 2.47/1.49 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.47/1.49 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.47/1.49 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.47/1.49 thf(ty_tf_a, type, a: $tType).
% 2.47/1.49 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Ozero, type, zero: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Omonoid__add, type, monoid_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Oab__group__add, type, ab_group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Osemigroup__add, type, semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Rings_Ocomm__semiring__1, type, comm_semiring_1: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Ocomm__monoid__add, type, comm_monoid_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Fields_Olinordered__field, type, linordered_field: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Oab__semigroup__add, type, ab_semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Ocomm__monoid__diff, type, comm_monoid_diff: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Ocancel__comm__monoid__add, type, cancel1352612707id_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Ocancel__ab__semigroup__add, type, cancel146912293up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Olinordered__ab__group__add, type, linord219039673up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add, type, canoni770627133id_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le, type, ordere236663937imp_le: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le, type, ordere516151231imp_le: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, type, semiri456707255roduct: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.47/1.49 thf(sy_c_Coinductive__List_Ofinite__lprefix, type, coindu328551480prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.47/1.49 thf(sy_c_Coinductive__List_Olappend, type, coinductive_lappend: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.47/1.49 thf(sy_c_Coinductive__List_Ollist_OLCons, type, coinductive_LCons: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 2.47/1.49 thf(sy_c_Coinductive__List_Ollist_OLNil, type, coinductive_LNil: (!> [A:$tType]: ((coinductive_llist @ A)))).
% 2.47/1.49 thf(sy_c_Coinductive__List_Olstrict__prefix, type, coindu1478340336prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 2.47/1.49 thf(sy_c_Coinductive__List_Olsublist, type, coinductive_lsublist: (!> [A:$tType]: (((coinductive_llist @ A) > ((set @ nat) > (coinductive_llist @ A)))))).
% 2.47/1.49 thf(sy_c_Coinductive__List_Omonoid__add__class_Ollistsum, type, coindu780009021istsum: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 2.47/1.49 thf(sy_c_Groups_Ominus__class_Ominus, type, minus_minus: (!> [A:$tType]: ((A > (A > A))))).
% 2.47/1.49 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 2.47/1.49 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 2.47/1.49 thf(sy_c_Groups_Ozero__class_Ozero, type, zero_zero: (!> [A:$tType]: (A))).
% 2.47/1.49 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.47/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts, type, lList2435255213lllsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.47/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts, type, lList2236698231inlsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.47/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec, type, lList21916056377ts_rec: (!> [B:$tType,A:$tType]: ((B > ((A > ((coinductive_llist @ A) > (B > B))) > ((coinductive_llist @ A) > B)))))).
% 2.47/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts, type, lList22096119349pslsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.47/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts, type, lList21612149805nflsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.47/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast, type, lList2370560421utlast: (!> [A:$tType]: (((coinductive_llist @ A) > (coinductive_llist @ A))))).
% 2.47/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oldrop, type, lList2508575361_ldrop: (!> [A:$tType]: (((coinductive_llist @ A) > (nat > (coinductive_llist @ A)))))).
% 2.47/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast, type, lList2170638824_llast: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 2.47/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollength, type, lList21232602520length: (!> [A:$tType]: (((coinductive_llist @ A) > nat)))).
% 2.47/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev, type, lList2281150353e_lrev: (!> [A:$tType]: (((coinductive_llist @ A) > (coinductive_llist @ A))))).
% 2.47/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oltake, type, lList22119844313_ltake: (!> [A:$tType]: (((coinductive_llist @ A) > (nat > (coinductive_llist @ A)))))).
% 2.47/1.49 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts, type, lList21148268032oslsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 2.47/1.49 thf(sy_c_Nat_OSuc, type, suc: (nat > nat)).
% 2.47/1.49 thf(sy_c_Nat__Bijection_Otriangle, type, nat_triangle: (nat > nat)).
% 2.47/1.49 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.47/1.49 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 2.47/1.49 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.47/1.49 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.47/1.49 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.47/1.49 thf(sy_v_A, type, a2: (set @ a)).
% 2.47/1.49 thf(sy_v_i, type, i: nat).
% 2.47/1.49 thf(sy_v_t, type, t: (coinductive_llist @ a)).
% 2.47/1.49 thf(fact_0_lrevT, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ ((lList2281150353e_lrev @ A) @ Xs)) @ ((lList2236698231inlsts @ A) @ A2)))))).
% 2.47/1.49 thf(fact_1_LList2__Mirabelle__hamjzmohle_Oldrop__LNil, axiom, (! [A:$tType,I:nat]: (((((lList2508575361_ldrop @ A) @ (coinductive_LNil @ A)) @ I) = (coinductive_LNil @ A))))).
% 2.47/1.49 thf(fact_2_ldropT, axiom, (! [A:$tType,T:(coinductive_llist @ A),A2:(set @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList2435255213lllsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((lList2508575361_ldrop @ A) @ T) @ I)) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 2.47/1.49 thf(fact_3_LList2__Mirabelle__hamjzmohle_Oldrop_Osimps_I1_J, axiom, (! [A:$tType,L:(coinductive_llist @ A)]: (((((lList2508575361_ldrop @ A) @ L) @ (zero_zero @ nat)) = L)))).
% 2.47/1.49 thf(fact_4_ldrop__add, axiom, (! [A:$tType,T:(coinductive_llist @ A),I:nat,K:nat]: (((((lList2508575361_ldrop @ A) @ T) @ (((plus_plus @ nat) @ I) @ K)) = (((lList2508575361_ldrop @ A) @ (((lList2508575361_ldrop @ A) @ T) @ I)) @ K))))).
% 2.47/1.49 thf(fact_5_finite__lemma, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),B2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ B2)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ B2))))))).
% 2.47/1.49 thf(fact_6_finsubsetall, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 2.47/1.49 thf(fact_7_same__lappend__eq, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((((coinductive_lappend @ A) @ R) @ S) = (((coinductive_lappend @ A) @ R) @ T)) = (S = T)))))).
% 2.47/1.49 thf(fact_8_lapp__fin__fin__iff, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2236698231inlsts @ A) @ A2)) = ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 2.47/1.49 thf(fact_9_finT__simp, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 2.47/1.49 thf(fact_10_fin__finite, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 2.47/1.49 thf(fact_11_finlsts_OLNil__fin, axiom, (! [A:$tType,A2:(set @ A)]: ((((member @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ ((lList2236698231inlsts @ A) @ A2))))).
% 2.47/1.49 thf(fact_12_LNil__is__lappend__conv, axiom, (! [A:$tType,S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: ((((coinductive_LNil @ A) = (((coinductive_lappend @ A) @ S) @ T)) = ((S = (coinductive_LNil @ A)) & (T = (coinductive_LNil @ A))))))).
% 2.47/1.49 thf(fact_13_lappend__is__LNil__conv, axiom, (! [A:$tType,S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: ((((((coinductive_lappend @ A) @ S) @ T) = (coinductive_LNil @ A)) = ((S = (coinductive_LNil @ A)) & (T = (coinductive_LNil @ A))))))).
% 2.47/1.49 thf(fact_14_alllsts__UNIV, axiom, (! [A:$tType,S:(coinductive_llist @ A)]: ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ (top_top @ (set @ A))))))).
% 2.47/1.49 thf(fact_15_lrev__LNil, axiom, (! [A:$tType]: ((((lList2281150353e_lrev @ A) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.47/1.49 thf(fact_16_lrev__is__lrev__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((member @ (coinductive_llist @ A)) @ Ys) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((lList2281150353e_lrev @ A) @ Xs) = ((lList2281150353e_lrev @ A) @ Ys)) = (Xs = Ys))))))).
% 2.47/1.49 thf(fact_17_lrev__lrev__ident, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => (((lList2281150353e_lrev @ A) @ ((lList2281150353e_lrev @ A) @ Xs)) = Xs))))).
% 2.47/1.49 thf(fact_18_lrev__is__LNil__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((lList2281150353e_lrev @ A) @ Xs) = (coinductive_LNil @ A)) = (Xs = (coinductive_LNil @ A))))))).
% 2.47/1.49 thf(fact_19_LNil__is__lrev__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => (((coinductive_LNil @ A) = ((lList2281150353e_lrev @ A) @ Xs)) = (Xs = (coinductive_LNil @ A))))))).
% 2.47/1.49 thf(fact_20_lrev__lappend, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((member @ (coinductive_llist @ A)) @ Ys) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => (((lList2281150353e_lrev @ A) @ (((coinductive_lappend @ A) @ Xs) @ Ys)) = (((coinductive_lappend @ A) @ ((lList2281150353e_lrev @ A) @ Ys)) @ ((lList2281150353e_lrev @ A) @ Xs)))))))).
% 2.47/1.49 thf(fact_21_lappT, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList2435255213lllsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T)) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 2.47/1.49 thf(fact_22_lapp__all__invT, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2435255213lllsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 2.47/1.49 thf(fact_23_alllsts_OLNil__all, axiom, (! [A:$tType,A2:(set @ A)]: ((((member @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ ((lList2435255213lllsts @ A) @ A2))))).
% 2.47/1.49 thf(fact_24_lapp__fin__fin__lemma, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)))))).
% 2.47/1.49 thf(fact_25_lappfin__finT, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T)) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 2.47/1.49 thf(fact_26_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ Ys) = Ys)))).
% 2.47/1.49 thf(fact_27_lappend__LNil2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ Xs) @ (coinductive_LNil @ A)) = Xs)))).
% 2.47/1.49 thf(fact_28_LNil__eq__lappend__iff, axiom, (! [A:$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))))))).
% 2.47/1.49 thf(fact_29_lappend__eq__LNil__iff, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((((coinductive_lappend @ A) @ Xs) @ Ys) = (coinductive_LNil @ A)) = ((Xs = (coinductive_LNil @ A)) & (Ys = (coinductive_LNil @ A))))))).
% 2.47/1.49 thf(fact_30_add__is__0, axiom, (! [M:nat,N:nat]: ((((((plus_plus @ nat) @ M) @ N) = (zero_zero @ nat)) = ((M = (zero_zero @ nat)) & (N = (zero_zero @ nat))))))).
% 2.47/1.49 thf(fact_31_Nat_Oadd__0__right, axiom, (! [M:nat]: (((((plus_plus @ nat) @ M) @ (zero_zero @ nat)) = M)))).
% 2.47/1.49 thf(fact_32_add_Oleft__neutral, axiom, (! [A:$tType]: ((((monoid_add @ A) @ (type2 @ A)) => (! [A3:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A3) = A3))))))).
% 2.47/1.49 thf(fact_33_add_Oright__neutral, axiom, (! [A:$tType]: ((((monoid_add @ A) @ (type2 @ A)) => (! [A3:A]: (((((plus_plus @ A) @ A3) @ (zero_zero @ A)) = A3))))))).
% 2.47/1.49 thf(fact_34_double__zero, axiom, (! [A:$tType]: ((((linord219039673up_add @ A) @ (type2 @ A)) => (! [A3:A]: ((((((plus_plus @ A) @ A3) @ A3) = (zero_zero @ A)) = (A3 = (zero_zero @ A))))))))).
% 2.47/1.49 thf(fact_35_double__zero__sym, axiom, (! [A:$tType]: ((((linord219039673up_add @ A) @ (type2 @ A)) => (! [A3:A]: ((((zero_zero @ A) = (((plus_plus @ A) @ A3) @ A3)) = (A3 = (zero_zero @ A))))))))).
% 2.47/1.49 thf(fact_36_add__cancel__left__left, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [B3:A,A3:A]: ((((((plus_plus @ A) @ B3) @ A3) = A3) = (B3 = (zero_zero @ A))))))))).
% 2.47/1.49 thf(fact_37_add__right__cancel, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [B3:A,A3:A,C:A]: ((((((plus_plus @ A) @ B3) @ A3) = (((plus_plus @ A) @ C) @ A3)) = (B3 = C)))))))).
% 2.47/1.49 thf(fact_38_add__left__cancel, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: ((((((plus_plus @ A) @ A3) @ B3) = (((plus_plus @ A) @ A3) @ C)) = (B3 = C)))))))).
% 2.47/1.49 thf(fact_39_add__cancel__right__right, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A]: (((A3 = (((plus_plus @ A) @ A3) @ B3)) = (B3 = (zero_zero @ A))))))))).
% 2.47/1.49 thf(fact_40_add__cancel__right__left, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A]: (((A3 = (((plus_plus @ A) @ B3) @ A3)) = (B3 = (zero_zero @ A))))))))).
% 2.47/1.49 thf(fact_41_add__cancel__left__right, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A]: ((((((plus_plus @ A) @ A3) @ B3) = A3) = (B3 = (zero_zero @ A))))))))).
% 2.47/1.49 thf(fact_42_zero__reorient, axiom, (! [A:$tType]: ((((zero @ A) @ (type2 @ A)) => (! [X:A]: ((((zero_zero @ A) = X) = (X = (zero_zero @ A))))))))).
% 2.47/1.49 thf(fact_43_add__right__imp__eq, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [B3:A,A3:A,C:A]: ((((((plus_plus @ A) @ B3) @ A3) = (((plus_plus @ A) @ C) @ A3)) => (B3 = C)))))))).
% 2.47/1.49 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 2.47/1.49 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A2)))) = A2)))).
% 2.47/1.49 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.47/1.49 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.47/1.49 thf(fact_48_add__left__imp__eq, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: ((((((plus_plus @ A) @ A3) @ B3) = (((plus_plus @ A) @ A3) @ C)) => (B3 = C)))))))).
% 2.47/1.49 thf(fact_49_add_Oleft__commute, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => (! [B3:A,A3:A,C:A]: (((((plus_plus @ A) @ B3) @ (((plus_plus @ A) @ A3) @ C)) = (((plus_plus @ A) @ A3) @ (((plus_plus @ A) @ B3) @ C))))))))).
% 2.47/1.49 thf(fact_50_add_Ocommute, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A4:A,B4:A]: ((((plus_plus @ A) @ B4) @ A4)))))))).
% 2.47/1.49 thf(fact_51_add_Oright__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [B3:A,A3:A,C:A]: ((((((plus_plus @ A) @ B3) @ A3) = (((plus_plus @ A) @ C) @ A3)) = (B3 = C)))))))).
% 2.47/1.49 thf(fact_52_add_Oleft__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: ((((((plus_plus @ A) @ A3) @ B3) = (((plus_plus @ A) @ A3) @ C)) = (B3 = C)))))))).
% 2.47/1.49 thf(fact_53_add_Oassoc, axiom, (! [A:$tType]: ((((semigroup_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A3) @ B3)) @ C) = (((plus_plus @ A) @ A3) @ (((plus_plus @ A) @ B3) @ C))))))))).
% 2.47/1.49 thf(fact_54_add__mono__thms__linordered__semiring_I4_J, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (K = L)) => ((((plus_plus @ A) @ I) @ K) = (((plus_plus @ A) @ J) @ L))))))))).
% 2.47/1.49 thf(fact_55_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A3) @ B3)) @ C) = (((plus_plus @ A) @ A3) @ (((plus_plus @ A) @ B3) @ C))))))))).
% 2.47/1.49 thf(fact_56_nat__add__right__cancel, axiom, (! [M:nat,K:nat,N:nat]: ((((((plus_plus @ nat) @ M) @ K) = (((plus_plus @ nat) @ N) @ K)) = (M = N))))).
% 2.47/1.49 thf(fact_57_nat__add__left__cancel, axiom, (! [K:nat,M:nat,N:nat]: ((((((plus_plus @ nat) @ K) @ M) = (((plus_plus @ nat) @ K) @ N)) = (M = N))))).
% 2.47/1.49 thf(fact_58_lappend__assoc, axiom, (! [A:$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)))))).
% 2.47/1.49 thf(fact_59_add__eq__0__iff__both__eq__0, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((((plus_plus @ A) @ X) @ Y) = (zero_zero @ A)) = ((X = (zero_zero @ A)) & (Y = (zero_zero @ A)))))))))).
% 2.47/1.49 thf(fact_60_add_Ogroup__left__neutral, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A3:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A3) = A3))))))).
% 2.47/1.49 thf(fact_61_add_Ocomm__neutral, axiom, (! [A:$tType]: ((((comm_monoid_add @ A) @ (type2 @ A)) => (! [A3:A]: (((((plus_plus @ A) @ A3) @ (zero_zero @ A)) = A3))))))).
% 2.47/1.49 thf(fact_62_comm__monoid__add__class_Oadd__0, axiom, (! [A:$tType]: ((((comm_monoid_add @ A) @ (type2 @ A)) => (! [A3:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A3) = A3))))))).
% 2.47/1.49 thf(fact_63_add__eq__self__zero, axiom, (! [M:nat,N:nat]: ((((((plus_plus @ nat) @ M) @ N) = M) => (N = (zero_zero @ nat)))))).
% 2.47/1.49 thf(fact_64_plus__nat_Oadd__0, axiom, (! [N:nat]: (((((plus_plus @ nat) @ (zero_zero @ nat)) @ N) = N)))).
% 2.47/1.49 thf(fact_65_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.47/1.49 thf(fact_66_iso__tuple__UNIV__I, axiom, (! [A:$tType,X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A)))))).
% 2.47/1.49 thf(fact_67_UNIV__I, axiom, (! [A:$tType,X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A)))))).
% 2.47/1.49 thf(fact_68_top__apply, axiom, (! [C2:$tType,D:$tType]: ((((top @ C2) @ (type2 @ C2)) => ((top_top @ (D > C2)) = (^ [X2:D]: ((top_top @ C2)))))))).
% 2.47/1.49 thf(fact_69_poslsts__iff, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21148268032oslsts @ A) @ A2)) = ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ A2)) & (S != (coinductive_LNil @ A))))))).
% 2.47/1.49 thf(fact_70_fpslsts__iff, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList22096119349pslsts @ A) @ A2)) = ((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2)) & (S != (coinductive_LNil @ A))))))).
% 2.47/1.49 thf(fact_71_poslsts__UNIV, axiom, (! [A:$tType,S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21148268032oslsts @ A) @ (top_top @ (set @ A)))) = (S != (coinductive_LNil @ A)))))).
% 2.47/1.49 thf(fact_72_ind__euclid, axiom, (! [P:(nat > (nat > $o)),A3:nat,B3:nat]: (((! [A5:nat,B5:nat]: ((((P @ A5) @ B5) = ((P @ B5) @ A5)))) => ((! [A5:nat]: (((P @ A5) @ (zero_zero @ nat)))) => ((! [A5:nat,B5:nat]: ((((P @ A5) @ B5) => ((P @ A5) @ (((plus_plus @ nat) @ A5) @ B5))))) => ((P @ A3) @ B3))))))).
% 2.47/1.49 thf(fact_73_LList2__Mirabelle__hamjzmohle_Ollength__LNil, axiom, (! [A:$tType]: ((((lList21232602520length @ A) @ (coinductive_LNil @ A)) = (zero_zero @ nat))))).
% 2.47/1.49 thf(fact_74_add__0__iff, axiom, (! [A:$tType]: ((((semiri456707255roduct @ A) @ (type2 @ A)) => (! [B3:A,A3:A]: (((B3 = (((plus_plus @ A) @ B3) @ A3)) = (A3 = (zero_zero @ A))))))))).
% 2.47/1.49 thf(fact_75_top__set__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (top_top @ (A > $o))))))).
% 2.47/1.49 thf(fact_76_semiring__normalization__rules_I25_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A3:A,C:A,D2:A]: (((((plus_plus @ A) @ A3) @ (((plus_plus @ A) @ C) @ D2)) = (((plus_plus @ A) @ (((plus_plus @ A) @ A3) @ C)) @ D2)))))))).
% 2.47/1.49 thf(fact_77_semiring__normalization__rules_I24_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A4:A,C3:A]: ((((plus_plus @ A) @ C3) @ A4)))))))).
% 2.47/1.49 thf(fact_78_semiring__normalization__rules_I23_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A3) @ B3)) @ C) = (((plus_plus @ A) @ (((plus_plus @ A) @ A3) @ C)) @ B3)))))))).
% 2.47/1.49 thf(fact_79_semiring__normalization__rules_I22_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A3:A,C:A,D2:A]: (((((plus_plus @ A) @ A3) @ (((plus_plus @ A) @ C) @ D2)) = (((plus_plus @ A) @ C) @ (((plus_plus @ A) @ A3) @ D2))))))))).
% 2.47/1.49 thf(fact_80_semiring__normalization__rules_I21_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A3) @ B3)) @ C) = (((plus_plus @ A) @ A3) @ (((plus_plus @ A) @ B3) @ C))))))))).
% 2.47/1.49 thf(fact_81_semiring__normalization__rules_I20_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A,D2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A3) @ B3)) @ (((plus_plus @ A) @ C) @ D2)) = (((plus_plus @ A) @ (((plus_plus @ A) @ A3) @ C)) @ (((plus_plus @ A) @ B3) @ D2))))))))).
% 2.47/1.49 thf(fact_82_UNIV__eq__I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X3:A]: ((((member @ A) @ X3) @ A2))) => ((top_top @ (set @ A)) = A2))))).
% 2.47/1.49 thf(fact_83_UNIV__witness, axiom, (! [A:$tType]: ((? [X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))))).
% 2.47/1.49 thf(fact_84_semiring__normalization__rules_I6_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A3:A]: (((((plus_plus @ A) @ A3) @ (zero_zero @ A)) = A3))))))).
% 2.47/1.49 thf(fact_85_semiring__normalization__rules_I5_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A3:A]: (((((plus_plus @ A) @ (zero_zero @ A)) @ A3) = A3))))))).
% 2.47/1.49 thf(fact_86_lbutlast__LNil, axiom, (! [A:$tType]: ((((lList2370560421utlast @ A) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 2.47/1.49 thf(fact_87_take__fin, axiom, (! [A:$tType,T:(coinductive_llist @ A),A2:(set @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList2435255213lllsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((lList22119844313_ltake @ A) @ T) @ I)) @ ((lList2236698231inlsts @ A) @ A2)))))).
% 2.47/1.49 thf(fact_88_lrev__LCons, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),A3:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((lList2281150353e_lrev @ A) @ (((coinductive_LCons @ A) @ A3) @ R)) = (((coinductive_lappend @ A) @ ((lList2281150353e_lrev @ A) @ R)) @ (((coinductive_LCons @ A) @ A3) @ (coinductive_LNil @ A)))))))).
% 2.47/1.49 thf(fact_89_ltake__fin, axiom, (! [A:$tType,R:(coinductive_llist @ A),I:nat]: ((((member @ (coinductive_llist @ A)) @ (((lList22119844313_ltake @ A) @ R) @ I)) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A))))))).
% 2.47/1.49 thf(fact_90_inflstsI, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)) => ((~ ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.47/1.49 thf(fact_91_llistsum__LNil, axiom, (! [A:$tType]: ((((monoid_add @ A) @ (type2 @ A)) => (((coindu780009021istsum @ A) @ (coinductive_LNil @ A)) = (zero_zero @ A)))))).
% 2.47/1.49 thf(fact_92_llist_Oinject, axiom, (! [A:$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)))))).
% 2.47/1.49 thf(fact_93_top1I, axiom, (! [A:$tType,X:A]: (((top_top @ (A > $o)) @ X)))).
% 2.47/1.49 thf(fact_94_lappend__code_I2_J, axiom, (! [A:$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)))))).
% 2.47/1.49 thf(fact_95_LConsE, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ X) @ Xs)) @ ((lList2435255213lllsts @ A) @ A2)) = ((((member @ A) @ X) @ A2) & (((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 2.47/1.49 thf(fact_96_lapp__inf, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2)) => ((((coinductive_lappend @ A) @ S) @ T) = S))))).
% 2.47/1.49 thf(fact_97_LList2__Mirabelle__hamjzmohle_Oltake__LNil, axiom, (! [A:$tType,I:nat]: (((((lList22119844313_ltake @ A) @ (coinductive_LNil @ A)) @ I) = (coinductive_LNil @ A))))).
% 2.47/1.49 thf(fact_98_notfin__inf, axiom, (! [A:$tType,X:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) = (((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.47/1.49 thf(fact_99_notinf__fin, axiom, (! [A:$tType,X:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))) = (((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 2.47/1.49 thf(fact_100_llength__take, axiom, (! [A:$tType,T:(coinductive_llist @ A),A2:(set @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A2)) => (((lList21232602520length @ A) @ (((lList22119844313_ltake @ A) @ T) @ I)) = I))))).
% 2.47/1.49 thf(fact_101_lbutlast__LCons, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),A3:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((R = (coinductive_LNil @ A)) => (((lList2370560421utlast @ A) @ (((coinductive_LCons @ A) @ A3) @ R)) = (coinductive_LNil @ A))) & ((R != (coinductive_LNil @ A)) => (((lList2370560421utlast @ A) @ (((coinductive_LCons @ A) @ A3) @ R)) = (((coinductive_LCons @ A) @ A3) @ ((lList2370560421utlast @ A) @ R))))))))).
% 2.47/1.49 thf(fact_102_inflsts__cases, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2)) => (~ ((! [A5:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList21612149805nflsts @ A) @ A2)) => ((((member @ A) @ A5) @ A2) => (S != (((coinductive_LCons @ A) @ A5) @ L2)))))))))))).
% 2.47/1.49 thf(fact_103_inflstsI2, axiom, (! [A:$tType,A3:A,A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ A) @ A3) @ A2) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A3) @ T)) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.47/1.49 thf(fact_104_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((Xs != (coinductive_LNil @ A)) = (? [X2:A,Xs2:(coinductive_llist @ A)]: ((Xs = (((coinductive_LCons @ A) @ X2) @ Xs2)))))))).
% 2.47/1.49 thf(fact_105_llist_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(coinductive_llist @ A)]: (((coinductive_LNil @ A) != (((coinductive_LCons @ A) @ X21) @ X22))))).
% 2.47/1.49 thf(fact_106_llistE, axiom, (! [A:$tType,Y:(coinductive_llist @ A)]: (((Y != (coinductive_LNil @ A)) => (~ ((! [X212:A,X222:(coinductive_llist @ A)]: ((Y != (((coinductive_LCons @ A) @ X212) @ X222)))))))))).
% 2.47/1.49 thf(fact_107_finlsts_OLCons__fin, axiom, (! [A:$tType,L:(coinductive_llist @ A),A2:(set @ A),A3:A]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ A) @ A3) @ A2) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A3) @ L)) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 2.47/1.49 thf(fact_108_alllsts_OLCons__all, axiom, (! [A:$tType,L:(coinductive_llist @ A),A2:(set @ A),A3:A]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList2435255213lllsts @ A) @ A2)) => ((((member @ A) @ A3) @ A2) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A3) @ L)) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 2.47/1.49 thf(fact_109_infT__simp, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.47/1.49 thf(fact_110_infsubsetall, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)))))).
% 2.47/1.49 thf(fact_111_lappend__snocL1__conv__LCons2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ (coinductive_LNil @ A)))) @ Ys) = (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys)))))).
% 2.47/1.49 thf(fact_112_finlsts_Ocases, axiom, (! [A:$tType,A3:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A3) @ ((lList2236698231inlsts @ A) @ A2)) => ((A3 != (coinductive_LNil @ A)) => (~ ((! [L2:(coinductive_llist @ A),A5:A]: (((A3 = (((coinductive_LCons @ A) @ A5) @ L2)) => ((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => (~ ((((member @ A) @ A5) @ A2)))))))))))))).
% 2.47/1.49 thf(fact_113_finlsts_Osimps, axiom, (! [A:$tType,A3:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A3) @ ((lList2236698231inlsts @ A) @ A2)) = ((A3 = (coinductive_LNil @ A)) | (? [L3:(coinductive_llist @ A),A4:A]: (((A3 = (((coinductive_LCons @ A) @ A4) @ L3)) & ((((member @ (coinductive_llist @ A)) @ L3) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ A) @ A4) @ A2)))))))))).
% 2.47/1.49 thf(fact_114_finlsts__induct, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => ((! [L2:(coinductive_llist @ A)]: (((L2 = (coinductive_LNil @ A)) => (P @ L2)))) => ((! [A5:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ L2) => ((((member @ A) @ A5) @ A2) => (P @ (((coinductive_LCons @ A) @ A5) @ L2))))))) => (P @ X))))))).
% 2.47/1.49 thf(fact_115_finlsts_Oinducts, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ (coinductive_LNil @ A)) => ((! [L2:(coinductive_llist @ A),A5:A]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ L2) => ((((member @ A) @ A5) @ A2) => (P @ (((coinductive_LCons @ A) @ A5) @ L2))))))) => (P @ X))))))).
% 2.47/1.49 thf(fact_116_alllsts_Ocoinduct, axiom, (! [A:$tType,X4:((coinductive_llist @ A) > $o),X:(coinductive_llist @ A),A2:(set @ A)]: (((X4 @ X) => ((! [X3:(coinductive_llist @ A)]: (((X4 @ X3) => ((X3 = (coinductive_LNil @ A)) | (? [L4:(coinductive_llist @ A),A6:A]: (((X3 = (((coinductive_LCons @ A) @ A6) @ L4)) & (((X4 @ L4) | (((member @ (coinductive_llist @ A)) @ L4) @ ((lList2435255213lllsts @ A) @ A2))) & (((member @ A) @ A6) @ A2))))))))) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2))))))).
% 2.47/1.49 thf(fact_117_alllsts_Osimps, axiom, (! [A:$tType,A3:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A3) @ ((lList2435255213lllsts @ A) @ A2)) = ((A3 = (coinductive_LNil @ A)) | (? [L3:(coinductive_llist @ A),A4:A]: (((A3 = (((coinductive_LCons @ A) @ A4) @ L3)) & ((((member @ (coinductive_llist @ A)) @ L3) @ ((lList2435255213lllsts @ A) @ A2)) & (((member @ A) @ A4) @ A2)))))))))).
% 2.47/1.49 thf(fact_118_alllsts_Ocases, axiom, (! [A:$tType,A3:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A3) @ ((lList2435255213lllsts @ A) @ A2)) => ((A3 != (coinductive_LNil @ A)) => (~ ((! [L2:(coinductive_llist @ A),A5:A]: (((A3 = (((coinductive_LCons @ A) @ A5) @ L2)) => ((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2435255213lllsts @ A) @ A2)) => (~ ((((member @ A) @ A5) @ A2)))))))))))))).
% 2.47/1.49 thf(fact_119_fin__inf__cases, axiom, (! [A:$tType,R:(coinductive_llist @ A)]: (((~ ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ (top_top @ (set @ A)))))))).
% 2.47/1.49 thf(fact_120_fpslsts__cases, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList22096119349pslsts @ A) @ A2)) => (~ ((! [A5:A,Rs:(coinductive_llist @ A)]: (((R = (((coinductive_LCons @ A) @ A5) @ Rs)) => ((((member @ A) @ A5) @ A2) => (~ ((((member @ (coinductive_llist @ A)) @ Rs) @ ((lList2236698231inlsts @ A) @ A2)))))))))))))).
% 2.47/1.49 thf(fact_121_app__invT, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),S:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.47/1.49 thf(fact_122_lapp__infT, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList21612149805nflsts @ A) @ A2)) = (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2))) | (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.47/1.49 thf(fact_123_lapp__inv2T, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList21612149805nflsts @ A) @ A2)) => (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList21612149805nflsts @ A) @ A2))) | (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.47/1.49 thf(fact_124_lapp__fin__infT, axiom, (! [A:$tType,S:(coinductive_llist @ A),A2:(set @ A),T:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T) @ ((lList21612149805nflsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S) @ T)) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.47/1.49 thf(fact_125_alllstsE, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)) => ((~ ((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)))) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.47/1.49 thf(fact_126_finlsts__rev__cases, axiom, (! [A:$tType,T:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ T) @ ((lList2236698231inlsts @ A) @ A2)) => ((T != (coinductive_LNil @ A)) => (~ ((! [A5:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ A) @ A5) @ A2) => (T != (((coinductive_lappend @ A) @ L2) @ (((coinductive_LCons @ A) @ A5) @ (coinductive_LNil @ A))))))))))))))).
% 2.47/1.49 thf(fact_127_lrev__induct, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A2:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ (coinductive_LNil @ A)) => ((! [X3:A,Xs3:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs3) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ Xs3) => ((((member @ A) @ X3) @ A2) => (P @ (((coinductive_lappend @ A) @ Xs3) @ (((coinductive_LCons @ A) @ X3) @ (coinductive_LNil @ A))))))))) => (P @ Xs))))))).
% 2.47/1.49 thf(fact_128_LList2__Mirabelle__hamjzmohle_Oltake_Osimps_I1_J, axiom, (! [A:$tType,L:(coinductive_llist @ A)]: (((((lList22119844313_ltake @ A) @ L) @ (zero_zero @ nat)) = (coinductive_LNil @ A))))).
% 2.47/1.49 thf(fact_129_inflstsE, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList21612149805nflsts @ A) @ A2)) => (~ (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2435255213lllsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A))))))))))).
% 2.47/1.49 thf(fact_130_lapp__allT__iff, axiom, (! [A:$tType,R:(coinductive_llist @ A),S:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S)) @ ((lList2435255213lllsts @ A) @ A2)) = (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ S) @ ((lList2435255213lllsts @ A) @ A2))) | (((member @ (coinductive_llist @ A)) @ R) @ ((lList21612149805nflsts @ A) @ A2))))))).
% 2.47/1.49 thf(fact_131_LList2__Mirabelle__hamjzmohle_Oltake__ldrop, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),M:nat,N:nat]: (((((lList22119844313_ltake @ A) @ (((lList2508575361_ldrop @ A) @ Xs) @ M)) @ N) = (((lList2508575361_ldrop @ A) @ (((lList22119844313_ltake @ A) @ Xs) @ (((plus_plus @ nat) @ N) @ M))) @ M))))).
% 2.47/1.49 thf(fact_132_ltake__ldrop__id, axiom, (! [A:$tType,X:(coinductive_llist @ A),I:nat]: (((((coinductive_lappend @ A) @ (((lList22119844313_ltake @ A) @ X) @ I)) @ (((lList2508575361_ldrop @ A) @ X) @ I)) = X)))).
% 2.47/1.49 thf(fact_133_LList2__Mirabelle__hamjzmohle_Ollast__LCons, axiom, (! [B:$tType,R:(coinductive_llist @ B),A2:(set @ B),A3:B]: (((((member @ (coinductive_llist @ B)) @ R) @ ((lList2236698231inlsts @ B) @ A2)) => (((R = (coinductive_LNil @ B)) => (((lList2170638824_llast @ B) @ (((coinductive_LCons @ B) @ A3) @ R)) = A3)) & ((R != (coinductive_LNil @ B)) => (((lList2170638824_llast @ B) @ (((coinductive_LCons @ B) @ A3) @ R)) = ((lList2170638824_llast @ B) @ R)))))))).
% 2.47/1.49 thf(fact_134_top__empty__eq, axiom, (! [A:$tType]: (((top_top @ (A > $o)) = (^ [X2:A]: ((((member @ A) @ X2) @ (top_top @ (set @ A))))))))).
% 2.47/1.49 thf(fact_135_lsublist__singleton, axiom, (! [A:$tType,A2:(set @ nat),X:A]: ((((((member @ nat) @ (zero_zero @ nat)) @ A2) => ((((coinductive_lsublist @ A) @ (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A))) @ A2) = (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A)))) & ((~ ((((member @ nat) @ (zero_zero @ nat)) @ A2))) => ((((coinductive_lsublist @ A) @ (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A))) @ A2) = (coinductive_LNil @ A))))))).
% 2.47/1.49 thf(fact_136_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = ((Xs = (coinductive_LNil @ A)) | (? [Xs2:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ Y) @ Xs2)) & (((coindu328551480prefix @ A) @ Xs2) @ Ys))))))))).
% 2.47/1.49 thf(fact_137_top__conj_I1_J, axiom, (! [A:$tType,X:A,P:$o]: (((((top_top @ (A > $o)) @ X) & P) = P)))).
% 2.47/1.49 thf(fact_138_lsublist__LNil, axiom, (! [A:$tType,A2:(set @ nat)]: (((((coinductive_lsublist @ A) @ (coinductive_LNil @ A)) @ A2) = (coinductive_LNil @ A))))).
% 2.47/1.49 thf(fact_139_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coindu328551480prefix @ A) @ (coinductive_LNil @ A)) @ Xs)))).
% 2.47/1.49 thf(fact_140_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (coinductive_LNil @ A)) = (Xs = (coinductive_LNil @ A)))))).
% 2.47/1.49 thf(fact_141_top__conj_I2_J, axiom, (! [A:$tType,P:$o,X:A]: (((P & ((top_top @ (A > $o)) @ X)) = P)))).
% 2.47/1.49 thf(fact_142_lstrict__prefix__code_I3_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B)]: ((~ ((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) @ (coinductive_LNil @ B))))))).
% 2.47/1.49 thf(fact_143_lstrict__prefix__code_I2_J, axiom, (! [B:$tType,Y:B,Ys:(coinductive_llist @ B)]: ((((coindu1478340336prefix @ B) @ (coinductive_LNil @ B)) @ (((coinductive_LCons @ B) @ Y) @ Ys))))).
% 2.47/1.49 thf(fact_144_inflsts__def, axiom, (! [A:$tType]: (((lList21612149805nflsts @ A) = (^ [A7:(set @ A)]: ((((minus_minus @ (set @ (coinductive_llist @ A))) @ ((lList2435255213lllsts @ A) @ A7)) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))))).
% 2.47/1.49 thf(fact_145_LList2__Mirabelle__hamjzmohle_Ollength__LCons, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),A3:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((lList21232602520length @ A) @ (((coinductive_LCons @ A) @ A3) @ R)) = (suc @ ((lList21232602520length @ A) @ R))))))).
% 2.47/1.49 thf(fact_146_nat_Oinject, axiom, (! [X23:nat,Y2:nat]: ((((suc @ X23) = (suc @ Y2)) = (X23 = Y2))))).
% 2.47/1.49 thf(fact_147_old_Onat_Oinject, axiom, (! [Nat:nat,Nat2:nat]: ((((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))).
% 2.47/1.49 thf(fact_148_DiffI, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ A2) => ((~ ((((member @ A) @ C) @ B2))) => (((member @ A) @ C) @ (((minus_minus @ (set @ A)) @ A2) @ B2))))))).
% 2.47/1.49 thf(fact_149_Diff__iff, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) = ((((member @ A) @ C) @ A2) & (~ ((((member @ A) @ C) @ B2)))))))).
% 2.47/1.49 thf(fact_150_Diff__idemp, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((minus_minus @ (set @ A)) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) @ B2) = (((minus_minus @ (set @ A)) @ A2) @ B2))))).
% 2.47/1.49 thf(fact_151_diff__self, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A3:A]: (((((minus_minus @ A) @ A3) @ A3) = (zero_zero @ A)))))))).
% 2.47/1.49 thf(fact_152_diff__0__right, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A3:A]: (((((minus_minus @ A) @ A3) @ (zero_zero @ A)) = A3))))))).
% 2.47/1.49 thf(fact_153_zero__diff, axiom, (! [A:$tType]: ((((comm_monoid_diff @ A) @ (type2 @ A)) => (! [A3:A]: (((((minus_minus @ A) @ (zero_zero @ A)) @ A3) = (zero_zero @ A)))))))).
% 2.47/1.49 thf(fact_154_diff__zero, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [A3:A]: (((((minus_minus @ A) @ A3) @ (zero_zero @ A)) = A3))))))).
% 2.47/1.49 thf(fact_155_cancel__comm__monoid__add__class_Odiff__cancel, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [A3:A]: (((((minus_minus @ A) @ A3) @ A3) = (zero_zero @ A)))))))).
% 2.47/1.49 thf(fact_156_add__diff__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A3) @ B3)) @ B3) = A3))))))).
% 2.47/1.49 thf(fact_157_diff__add__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A]: (((((plus_plus @ A) @ (((minus_minus @ A) @ A3) @ B3)) @ B3) = A3))))))).
% 2.47/1.49 thf(fact_158_add__diff__cancel__left, axiom, (! [A:$tType]: ((((cancel146912293up_add @ A) @ (type2 @ A)) => (! [C:A,A3:A,B3:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ C) @ A3)) @ (((plus_plus @ A) @ C) @ B3)) = (((minus_minus @ A) @ A3) @ B3)))))))).
% 2.47/1.49 thf(fact_159_add__diff__cancel__left_H, axiom, (! [A:$tType]: ((((cancel146912293up_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A3) @ B3)) @ A3) = B3))))))).
% 2.47/1.49 thf(fact_160_add__diff__cancel__right, axiom, (! [A:$tType]: ((((cancel146912293up_add @ A) @ (type2 @ A)) => (! [A3:A,C:A,B3:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A3) @ C)) @ (((plus_plus @ A) @ B3) @ C)) = (((minus_minus @ A) @ A3) @ B3)))))))).
% 2.47/1.49 thf(fact_161_add__diff__cancel__right_H, axiom, (! [A:$tType]: ((((cancel146912293up_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A3) @ B3)) @ B3) = A3))))))).
% 2.47/1.49 thf(fact_162_add__Suc__right, axiom, (! [M:nat,N:nat]: (((((plus_plus @ nat) @ M) @ (suc @ N)) = (suc @ (((plus_plus @ nat) @ M) @ N)))))).
% 2.47/1.49 thf(fact_163_lstrict__prefix__code_I4_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B),Y:B,Ys:(coinductive_llist @ B)]: (((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) @ (((coinductive_LCons @ B) @ Y) @ Ys)) = ((X = Y) & (((coindu1478340336prefix @ B) @ Xs) @ Ys)))))).
% 2.47/1.49 thf(fact_164_lstrict__prefix__code_I1_J, axiom, (! [A:$tType]: ((~ ((((coindu1478340336prefix @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A))))))).
% 2.47/1.49 thf(fact_165_diff__add__zero, axiom, (! [A:$tType]: ((((comm_monoid_diff @ A) @ (type2 @ A)) => (! [A3:A,B3:A]: (((((minus_minus @ A) @ A3) @ (((plus_plus @ A) @ A3) @ B3)) = (zero_zero @ A)))))))).
% 2.47/1.49 thf(fact_166_eq__iff__diff__eq__0, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => ((^ [Y3:A,Z:A]: ((Y3 = Z))) = (^ [A4:A,B4:A]: (((((minus_minus @ A) @ A4) @ B4) = (zero_zero @ A))))))))).
% 2.47/1.49 thf(fact_167_diff__eq__eq, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: ((((((minus_minus @ A) @ A3) @ B3) = C) = (A3 = (((plus_plus @ A) @ C) @ B3))))))))).
% 2.47/1.49 thf(fact_168_eq__diff__eq, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A3:A,C:A,B3:A]: (((A3 = (((minus_minus @ A) @ C) @ B3)) = ((((plus_plus @ A) @ A3) @ B3) = C)))))))).
% 2.47/1.49 thf(fact_169_add__diff__eq, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: (((((plus_plus @ A) @ A3) @ (((minus_minus @ A) @ B3) @ C)) = (((minus_minus @ A) @ (((plus_plus @ A) @ A3) @ B3)) @ C)))))))).
% 2.47/1.49 thf(fact_170_diff__diff__eq2, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: (((((minus_minus @ A) @ A3) @ (((minus_minus @ A) @ B3) @ C)) = (((minus_minus @ A) @ (((plus_plus @ A) @ A3) @ C)) @ B3)))))))).
% 2.47/1.49 thf(fact_171_diff__add__eq, axiom, (! [A:$tType]: ((((ab_group_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: (((((plus_plus @ A) @ (((minus_minus @ A) @ A3) @ B3)) @ C) = (((minus_minus @ A) @ (((plus_plus @ A) @ A3) @ C)) @ B3)))))))).
% 2.47/1.49 thf(fact_172_diff__add__eq__diff__diff__swap, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: (((((minus_minus @ A) @ A3) @ (((plus_plus @ A) @ B3) @ C)) = (((minus_minus @ A) @ (((minus_minus @ A) @ A3) @ C)) @ B3)))))))).
% 2.47/1.49 thf(fact_173_diff__diff__add, axiom, (! [A:$tType]: ((((cancel146912293up_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A3) @ B3)) @ C) = (((minus_minus @ A) @ A3) @ (((plus_plus @ A) @ B3) @ C))))))))).
% 2.47/1.49 thf(fact_174_add__implies__diff, axiom, (! [A:$tType]: ((((cancel1352612707id_add @ A) @ (type2 @ A)) => (! [C:A,B3:A,A3:A]: ((((((plus_plus @ A) @ C) @ B3) = A3) => (C = (((minus_minus @ A) @ A3) @ B3))))))))).
% 2.47/1.49 thf(fact_175_nat_Odistinct_I1_J, axiom, (! [X23:nat]: (((zero_zero @ nat) != (suc @ X23))))).
% 2.47/1.49 thf(fact_176_old_Onat_Odistinct_I2_J, axiom, (! [Nat3:nat]: (((suc @ Nat3) != (zero_zero @ nat))))).
% 2.47/1.49 thf(fact_177_old_Onat_Odistinct_I1_J, axiom, (! [Nat2:nat]: (((zero_zero @ nat) != (suc @ Nat2))))).
% 2.47/1.49 thf(fact_178_nat_OdiscI, axiom, (! [Nat:nat,X23:nat]: (((Nat = (suc @ X23)) => (Nat != (zero_zero @ nat)))))).
% 2.47/1.49 thf(fact_179_nat__induct, axiom, (! [P:(nat > $o),N:nat]: (((P @ (zero_zero @ nat)) => ((! [N2:nat]: (((P @ N2) => (P @ (suc @ N2))))) => (P @ N)))))).
% 2.47/1.49 thf(fact_180_diff__induct, axiom, (! [P:(nat > (nat > $o)),M:nat,N:nat]: (((! [X3:nat]: (((P @ X3) @ (zero_zero @ nat)))) => ((! [Y4:nat]: (((P @ (zero_zero @ nat)) @ (suc @ Y4)))) => ((! [X3:nat,Y4:nat]: ((((P @ X3) @ Y4) => ((P @ (suc @ X3)) @ (suc @ Y4))))) => ((P @ M) @ N))))))).
% 2.47/1.49 thf(fact_181_zero__induct, axiom, (! [P:(nat > $o),K:nat]: (((P @ K) => ((! [N2:nat]: (((P @ (suc @ N2)) => (P @ N2)))) => (P @ (zero_zero @ nat))))))).
% 2.47/1.49 thf(fact_182_Suc__neq__Zero, axiom, (! [M:nat]: (((suc @ M) != (zero_zero @ nat))))).
% 2.47/1.49 thf(fact_183_Zero__neq__Suc, axiom, (! [M:nat]: (((zero_zero @ nat) != (suc @ M))))).
% 2.47/1.49 thf(fact_184_Zero__not__Suc, axiom, (! [M:nat]: (((zero_zero @ nat) != (suc @ M))))).
% 2.47/1.49 thf(fact_185_old_Onat_Oexhaust, axiom, (! [Y:nat]: (((Y != (zero_zero @ nat)) => (~ ((! [Nat4:nat]: ((Y != (suc @ Nat4)))))))))).
% 2.47/1.49 thf(fact_186_old_Onat_Oinducts, axiom, (! [P:(nat > $o),Nat:nat]: (((P @ (zero_zero @ nat)) => ((! [Nat4:nat]: (((P @ Nat4) => (P @ (suc @ Nat4))))) => (P @ Nat)))))).
% 2.47/1.49 thf(fact_187_not0__implies__Suc, axiom, (! [N:nat]: (((N != (zero_zero @ nat)) => (? [M2:nat]: ((N = (suc @ M2)))))))).
% 2.47/1.49 thf(fact_188_add__Suc__shift, axiom, (! [M:nat,N:nat]: (((((plus_plus @ nat) @ (suc @ M)) @ N) = (((plus_plus @ nat) @ M) @ (suc @ N)))))).
% 2.47/1.49 thf(fact_189_add__Suc, axiom, (! [M:nat,N:nat]: (((((plus_plus @ nat) @ (suc @ M)) @ N) = (suc @ (((plus_plus @ nat) @ M) @ N)))))).
% 2.47/1.49 thf(fact_190_DiffE, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) => (~ (((((member @ A) @ C) @ A2) => (((member @ A) @ C) @ B2)))))))).
% 2.47/1.49 thf(fact_191_DiffD1, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) => (((member @ A) @ C) @ A2))))).
% 2.47/1.49 thf(fact_192_DiffD2, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((minus_minus @ (set @ A)) @ A2) @ B2)) => (~ ((((member @ A) @ C) @ B2))))))).
% 2.47/1.49 thf(fact_193_Suc__inject, axiom, (! [X:nat,Y:nat]: ((((suc @ X) = (suc @ Y)) => (X = Y))))).
% 2.47/1.49 thf(fact_194_n__not__Suc__n, axiom, (! [N:nat]: ((N != (suc @ N))))).
% 2.47/1.49 thf(fact_195_llist__less__induct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > $o),Xs:(coinductive_llist @ A)]: (((! [Xs3:(coinductive_llist @ A)]: (((! [Ys2:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys2) @ Xs3) => (P @ Ys2)))) => (P @ Xs3)))) => (P @ Xs))))).
% 2.47/1.49 thf(fact_196_diff__eq__diff__eq, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A,D2:A]: ((((((minus_minus @ A) @ A3) @ B3) = (((minus_minus @ A) @ C) @ D2)) => ((A3 = B3) = (C = D2))))))))).
% 2.47/1.49 thf(fact_197_diff__right__commute, axiom, (! [A:$tType]: ((((cancel146912293up_add @ A) @ (type2 @ A)) => (! [A3:A,C:A,B3:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A3) @ C)) @ B3) = (((minus_minus @ A) @ (((minus_minus @ A) @ A3) @ B3)) @ C)))))))).
% 2.47/1.49 thf(fact_198_one__is__add, axiom, (! [M:nat,N:nat]: ((((suc @ (zero_zero @ nat)) = (((plus_plus @ nat) @ M) @ N)) = (((M = (suc @ (zero_zero @ nat))) & (N = (zero_zero @ nat))) | ((M = (zero_zero @ nat)) & (N = (suc @ (zero_zero @ nat))))))))).
% 2.47/1.49 thf(fact_199_add__is__1, axiom, (! [M:nat,N:nat]: ((((((plus_plus @ nat) @ M) @ N) = (suc @ (zero_zero @ nat))) = (((M = (suc @ (zero_zero @ nat))) & (N = (zero_zero @ nat))) | ((M = (zero_zero @ nat)) & (N = (suc @ (zero_zero @ nat))))))))).
% 2.47/1.49 thf(fact_200_ltake__LCons__Suc, axiom, (! [A:$tType,A3:A,L:(coinductive_llist @ A),I:nat]: (((((lList22119844313_ltake @ A) @ (((coinductive_LCons @ A) @ A3) @ L)) @ (suc @ I)) = (((coinductive_LCons @ A) @ A3) @ (((lList22119844313_ltake @ A) @ L) @ I)))))).
% 2.47/1.49 thf(fact_201_list__decode_Ocases, axiom, (! [X:nat]: (((X != (zero_zero @ nat)) => (~ ((! [N2:nat]: ((X != (suc @ N2)))))))))).
% 2.47/1.49 thf(fact_202_dependent__nat__choice, axiom, (! [A:$tType,P:(nat > (A > $o)),Q:(nat > (A > (A > $o)))]: (((? [X1:A]: (((P @ (zero_zero @ nat)) @ X1))) => ((! [X3:A,N2:nat]: ((((P @ N2) @ X3) => (? [Y5:A]: ((((P @ (suc @ N2)) @ Y5) & (((Q @ N2) @ X3) @ Y5))))))) => (? [F2:(nat > A)]: ((! [N3:nat]: ((((P @ N3) @ (F2 @ N3)) & (((Q @ N3) @ (F2 @ N3)) @ (F2 @ (suc @ N3))))))))))))).
% 2.47/1.49 thf(fact_203_exists__least__lemma, axiom, (! [P:(nat > $o)]: (((~ ((P @ (zero_zero @ nat)))) => ((? [X1:nat]: ((P @ X1))) => (? [N2:nat]: (((~ ((P @ N2))) & (P @ (suc @ N2)))))))))).
% 2.47/1.49 thf(fact_204_diff__0__eq__0, axiom, (! [N:nat]: (((((minus_minus @ nat) @ (zero_zero @ nat)) @ N) = (zero_zero @ nat))))).
% 2.47/1.49 thf(fact_205_diff__self__eq__0, axiom, (! [M:nat]: (((((minus_minus @ nat) @ M) @ M) = (zero_zero @ nat))))).
% 2.47/1.49 thf(fact_206_diff__Suc__Suc, axiom, (! [M:nat,N:nat]: (((((minus_minus @ nat) @ (suc @ M)) @ (suc @ N)) = (((minus_minus @ nat) @ M) @ N))))).
% 2.47/1.49 thf(fact_207_Suc__diff__diff, axiom, (! [M:nat,N:nat,K:nat]: (((((minus_minus @ nat) @ (((minus_minus @ nat) @ (suc @ M)) @ N)) @ (suc @ K)) = (((minus_minus @ nat) @ (((minus_minus @ nat) @ M) @ N)) @ K))))).
% 2.47/1.49 thf(fact_208_diff__diff__left, axiom, (! [I:nat,J:nat,K:nat]: (((((minus_minus @ nat) @ (((minus_minus @ nat) @ I) @ J)) @ K) = (((minus_minus @ nat) @ I) @ (((plus_plus @ nat) @ J) @ K)))))).
% 2.47/1.49 thf(fact_209_diffs0__imp__equal, axiom, (! [M:nat,N:nat]: ((((((minus_minus @ nat) @ M) @ N) = (zero_zero @ nat)) => (((((minus_minus @ nat) @ N) @ M) = (zero_zero @ nat)) => (M = N)))))).
% 2.47/1.49 thf(fact_210_minus__nat_Odiff__0, axiom, (! [M:nat]: (((((minus_minus @ nat) @ M) @ (zero_zero @ nat)) = M)))).
% 2.47/1.49 thf(fact_211_Nat_Odiff__cancel, axiom, (! [K:nat,M:nat,N:nat]: (((((minus_minus @ nat) @ (((plus_plus @ nat) @ K) @ M)) @ (((plus_plus @ nat) @ K) @ N)) = (((minus_minus @ nat) @ M) @ N))))).
% 2.47/1.49 thf(fact_212_diff__cancel2, axiom, (! [M:nat,K:nat,N:nat]: (((((minus_minus @ nat) @ (((plus_plus @ nat) @ M) @ K)) @ (((plus_plus @ nat) @ N) @ K)) = (((minus_minus @ nat) @ M) @ N))))).
% 2.47/1.49 thf(fact_213_diff__add__inverse, axiom, (! [N:nat,M:nat]: (((((minus_minus @ nat) @ (((plus_plus @ nat) @ N) @ M)) @ N) = M)))).
% 2.47/1.49 thf(fact_214_diff__add__inverse2, axiom, (! [M:nat,N:nat]: (((((minus_minus @ nat) @ (((plus_plus @ nat) @ M) @ N)) @ N) = M)))).
% 2.47/1.49 thf(fact_215_zero__induct__lemma, axiom, (! [P:(nat > $o),K:nat,I:nat]: (((P @ K) => ((! [N2:nat]: (((P @ (suc @ N2)) => (P @ N2)))) => (P @ (((minus_minus @ nat) @ K) @ I))))))).
% 2.47/1.49 thf(fact_216_diff__add__0, axiom, (! [N:nat,M:nat]: (((((minus_minus @ nat) @ N) @ (((plus_plus @ nat) @ N) @ M)) = (zero_zero @ nat))))).
% 2.47/1.49 thf(fact_217_triangle__Suc, axiom, (! [N:nat]: (((nat_triangle @ (suc @ N)) = (((plus_plus @ nat) @ (nat_triangle @ N)) @ (suc @ N)))))).
% 2.47/1.49 thf(fact_218_add__diff__add, axiom, (! [A:$tType]: ((((ab_group_add @ A) @ (type2 @ A)) => (! [A3:A,C:A,B3:A,D2:A]: (((((minus_minus @ A) @ (((plus_plus @ A) @ A3) @ C)) @ (((plus_plus @ A) @ B3) @ D2)) = (((plus_plus @ A) @ (((minus_minus @ A) @ A3) @ B3)) @ (((minus_minus @ A) @ C) @ D2))))))))).
% 2.47/1.49 thf(fact_219_triangle__0, axiom, ((nat_triangle @ (zero_zero @ nat)) = (zero_zero @ nat))).
% 2.47/1.49 thf(fact_220_diff__commute, axiom, (! [I:nat,J:nat,K:nat]: (((((minus_minus @ nat) @ (((minus_minus @ nat) @ I) @ J)) @ K) = (((minus_minus @ nat) @ (((minus_minus @ nat) @ I) @ K)) @ J))))).
% 2.47/1.49 thf(fact_221_linordered__field__class_Osign__simps_I34_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: (((((plus_plus @ A) @ (((minus_minus @ A) @ A3) @ B3)) @ C) = (((minus_minus @ A) @ (((plus_plus @ A) @ A3) @ C)) @ B3)))))))).
% 2.47/1.49 thf(fact_222_linordered__field__class_Osign__simps_I33_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: (((((minus_minus @ A) @ (((minus_minus @ A) @ A3) @ B3)) @ C) = (((minus_minus @ A) @ A3) @ (((plus_plus @ A) @ B3) @ C))))))))).
% 2.47/1.49 thf(fact_223_linordered__field__class_Osign__simps_I28_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [B3:A,A3:A,C:A]: (((((plus_plus @ A) @ B3) @ (((plus_plus @ A) @ A3) @ C)) = (((plus_plus @ A) @ A3) @ (((plus_plus @ A) @ B3) @ C))))))))).
% 2.47/1.49 thf(fact_224_linordered__field__class_Osign__simps_I27_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A4:A,B4:A]: ((((plus_plus @ A) @ B4) @ A4)))))))).
% 2.47/1.49 thf(fact_225_linordered__field__class_Osign__simps_I26_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A3) @ B3)) @ C) = (((plus_plus @ A) @ A3) @ (((plus_plus @ A) @ B3) @ C))))))))).
% 2.47/1.49 thf(fact_226_linordered__field__class_Osign__simps_I29_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: (((((plus_plus @ A) @ A3) @ (((minus_minus @ A) @ B3) @ C)) = (((minus_minus @ A) @ (((plus_plus @ A) @ A3) @ B3)) @ C)))))))).
% 2.47/1.49 thf(fact_227_linordered__field__class_Osign__simps_I30_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: ((((((minus_minus @ A) @ A3) @ B3) = C) = (A3 = (((plus_plus @ A) @ C) @ B3))))))))).
% 2.47/1.49 thf(fact_228_linordered__field__class_Osign__simps_I31_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [A3:A,C:A,B3:A]: (((A3 = (((minus_minus @ A) @ C) @ B3)) = ((((plus_plus @ A) @ A3) @ B3) = C)))))))).
% 2.47/1.49 thf(fact_229_linordered__field__class_Osign__simps_I32_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [A3:A,B3:A,C:A]: (((((minus_minus @ A) @ A3) @ (((minus_minus @ A) @ B3) @ C)) = (((minus_minus @ A) @ (((plus_plus @ A) @ A3) @ C)) @ B3)))))))).
% 2.47/1.49 thf(fact_230_finlsts__rec__LCons, axiom, (! [B:$tType,A:$tType,R:(coinductive_llist @ A),A2:(set @ A),C:B,D2:(A > ((coinductive_llist @ A) > (B > B))),A3:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((((lList21916056377ts_rec @ B) @ A) @ C) @ D2) @ (((coinductive_LCons @ A) @ A3) @ R)) = (((D2 @ A3) @ R) @ (((((lList21916056377ts_rec @ B) @ A) @ C) @ D2) @ R))))))).
% 2.47/1.49 thf(fact_231_finlsts__rec__LCons__def, axiom, (! [B:$tType,A:$tType,F:((coinductive_llist @ A) > B),C:B,D2:(A > ((coinductive_llist @ A) > (B > B))),R:(coinductive_llist @ A),A2:(set @ A),A3:A]: (((F = ((((lList21916056377ts_rec @ B) @ A) @ C) @ D2)) => ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((F @ (((coinductive_LCons @ A) @ A3) @ R)) = (((D2 @ A3) @ R) @ (F @ R)))))))).
% 2.47/1.49 thf(fact_232_finlsts__rec__LNil, axiom, (! [B:$tType,A:$tType,C:A,D2:(B > ((coinductive_llist @ B) > (A > A)))]: (((((((lList21916056377ts_rec @ A) @ B) @ C) @ D2) @ (coinductive_LNil @ B)) = C)))).
% 2.47/1.49 thf(fact_233_finlsts__rec__LNil__def, axiom, (! [A:$tType,B:$tType,F:((coinductive_llist @ A) > B),C:B,D2:(A > ((coinductive_llist @ A) > (B > B)))]: (((F = ((((lList21916056377ts_rec @ B) @ A) @ C) @ D2)) => ((F @ (coinductive_LNil @ A)) = C))))).
% 2.47/1.49 thf(fact_234_add__eq__if, axiom, ((plus_plus @ nat) = (^ [M3:nat,N4:nat]: (((((if @ nat) @ (M3 = (zero_zero @ nat))) @ N4) @ (suc @ (((plus_plus @ nat) @ (((minus_minus @ nat) @ M3) @ (one_one @ nat))) @ N4))))))).
% 2.47/1.49 thf(fact_235_diff__Suc__diff__eq1, axiom, (! [K:nat,J:nat,I:nat]: (((((ord_less_eq @ nat) @ K) @ J) => ((((minus_minus @ nat) @ I) @ (suc @ (((minus_minus @ nat) @ J) @ K))) = (((minus_minus @ nat) @ (((plus_plus @ nat) @ I) @ K)) @ (suc @ J))))))).
% 2.47/1.49 thf(fact_236_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 2.47/1.49 thf(fact_237_le__zero__eq, axiom, (! [A:$tType]: ((((canoni770627133id_add @ A) @ (type2 @ A)) => (! [N:A]: (((((ord_less_eq @ A) @ N) @ (zero_zero @ A)) = (N = (zero_zero @ A))))))))).
% 2.47/1.49 thf(fact_238_add__le__cancel__right, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [A3:A,C:A,B3:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A3) @ C)) @ (((plus_plus @ A) @ B3) @ C)) = (((ord_less_eq @ A) @ A3) @ B3)))))))).
% 2.47/1.49 thf(fact_239_add__le__cancel__left, axiom, (! [A:$tType]: ((((ordere236663937imp_le @ A) @ (type2 @ A)) => (! [C:A,A3:A,B3:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ C) @ A3)) @ (((plus_plus @ A) @ C) @ B3)) = (((ord_less_eq @ A) @ A3) @ B3)))))))).
% 2.47/1.49 thf(fact_240_le0, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ (zero_zero @ nat)) @ N)))).
% 2.47/1.49 thf(fact_241_Suc__le__mono, axiom, (! [N:nat,M:nat]: (((((ord_less_eq @ nat) @ (suc @ N)) @ (suc @ M)) = (((ord_less_eq @ nat) @ N) @ M))))).
% 2.47/1.49 thf(fact_242_nat__add__left__cancel__le, axiom, (! [K:nat,M:nat,N:nat]: (((((ord_less_eq @ nat) @ (((plus_plus @ nat) @ K) @ M)) @ (((plus_plus @ nat) @ K) @ N)) = (((ord_less_eq @ nat) @ M) @ N))))).
% 2.47/1.49 thf(fact_243_diff__diff__cancel, axiom, (! [I:nat,N:nat]: (((((ord_less_eq @ nat) @ I) @ N) => ((((minus_minus @ nat) @ N) @ (((minus_minus @ nat) @ N) @ I)) = I))))).
% 2.47/1.49 thf(fact_244_zero__le__double__add__iff__zero__le__single__add, axiom, (! [A:$tType]: ((((linord219039673up_add @ A) @ (type2 @ A)) => (! [A3:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((plus_plus @ A) @ A3) @ A3)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ A3)))))))).
% 2.47/1.49 thf(fact_245_double__add__le__zero__iff__single__add__le__zero, axiom, (! [A:$tType]: ((((linord219039673up_add @ A) @ (type2 @ A)) => (! [A3:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A3) @ A3)) @ (zero_zero @ A)) = (((ord_less_eq @ A) @ A3) @ (zero_zero @ A))))))))).
% 2.47/1.49 thf(fact_246_le__add__same__cancel2, axiom, (! [A:$tType]: ((((ordere516151231imp_le @ A) @ (type2 @ A)) => (! [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ (((plus_plus @ A) @ B3) @ A3)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ B3)))))))).
% 2.47/1.49 thf(fact_247_le__add__same__cancel1, axiom, (! [A:$tType]: ((((ordere516151231imp_le @ A) @ (type2 @ A)) => (! [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ (((plus_plus @ A) @ A3) @ B3)) = (((ord_less_eq @ A) @ (zero_zero @ A)) @ B3)))))))).
% 2.47/1.49 thf(fact_248_add__le__same__cancel2, axiom, (! [A:$tType]: ((((ordere516151231imp_le @ A) @ (type2 @ A)) => (! [A3:A,B3:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ A3) @ B3)) @ B3) = (((ord_less_eq @ A) @ A3) @ (zero_zero @ A))))))))).
% 2.47/1.49 thf(fact_249_add__le__same__cancel1, axiom, (! [A:$tType]: ((((ordere516151231imp_le @ A) @ (type2 @ A)) => (! [B3:A,A3:A]: (((((ord_less_eq @ A) @ (((plus_plus @ A) @ B3) @ A3)) @ B3) = (((ord_less_eq @ A) @ A3) @ (zero_zero @ A))))))))).
% 2.47/1.49 thf(fact_250_diff__ge__0__iff__ge, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A3:A,B3:A]: (((((ord_less_eq @ A) @ (zero_zero @ A)) @ (((minus_minus @ A) @ A3) @ B3)) = (((ord_less_eq @ A) @ B3) @ A3)))))))).
% 2.47/1.49 thf(fact_251_diff__is__0__eq_H, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((minus_minus @ nat) @ M) @ N) = (zero_zero @ nat)))))).
% 2.47/1.49 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: ((((preorder @ A9) @ (type2 @ A9)) => ((preorder @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.47/1.49 thf(tcon_fun___Orderings_Otop, axiom, (! [A8:$tType,A9:$tType]: ((((top @ A9) @ (type2 @ A9)) => ((top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 2.47/1.49 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, axiom, ((semiri456707255roduct @ nat) @ (type2 @ nat))).
% 2.47/1.49 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le, axiom, ((ordere516151231imp_le @ nat) @ (type2 @ nat))).
% 2.47/1.49 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, axiom, ((ordere236663937imp_le @ nat) @ (type2 @ nat))).
% 2.47/1.49 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, axiom, ((canoni770627133id_add @ nat) @ (type2 @ nat))).
% 2.47/1.49 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, axiom, ((ordere779506340up_add @ nat) @ (type2 @ nat))).
% 2.47/1.49 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add, axiom, ((cancel146912293up_add @ nat) @ (type2 @ nat))).
% 2.47/1.49 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add, axiom, ((cancel1352612707id_add @ nat) @ (type2 @ nat))).
% 2.47/1.49 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add, axiom, ((cancel_semigroup_add @ nat) @ (type2 @ nat))).
% 2.47/1.49 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff, axiom, ((comm_monoid_diff @ nat) @ (type2 @ nat))).
% 2.47/1.49 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add, axiom, ((ab_semigroup_add @ nat) @ (type2 @ nat))).
% 2.47/1.49 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add, axiom, ((comm_monoid_add @ nat) @ (type2 @ nat))).
% 2.47/1.49 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1, axiom, ((comm_semiring_1 @ nat) @ (type2 @ nat))).
% 2.47/1.49 thf(tcon_Nat_Onat___Groups_Osemigroup__add, axiom, ((semigroup_add @ nat) @ (type2 @ nat))).
% 2.47/1.49 thf(tcon_Nat_Onat___Orderings_Opreorder_1, axiom, ((preorder @ nat) @ (type2 @ nat))).
% 2.47/1.49 thf(tcon_Nat_Onat___Groups_Omonoid__add, axiom, ((monoid_add @ nat) @ (type2 @ nat))).
% 2.47/1.49 thf(tcon_Nat_Onat___Groups_Ozero, axiom, ((zero @ nat) @ (type2 @ nat))).
% 2.47/1.49 thf(tcon_Nat_Onat___Groups_Oone, axiom, ((one @ nat) @ (type2 @ nat))).
% 2.47/1.49 thf(tcon_Set_Oset___Orderings_Opreorder_2, axiom, (! [A8:$tType]: (((preorder @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.47/1.49 thf(tcon_Set_Oset___Orderings_Otop_3, axiom, (! [A8:$tType]: (((top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 2.47/1.49 thf(tcon_HOL_Obool___Orderings_Opreorder_4, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 2.47/1.49 thf(tcon_HOL_Obool___Orderings_Otop_5, axiom, ((top @ $o) @ (type2 @ $o))).
% 2.47/1.49 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.47/1.49 thf(help_If_2_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $false) @ X) @ Y) = Y)))).
% 2.47/1.49 thf(help_If_1_1_T, axiom, (! [A:$tType,X:A,Y:A]: ((((((if @ A) @ $true) @ X) @ Y) = X)))).
% 2.47/1.49 thf(conj_0, hypothesis, (((member @ (coinductive_llist @ a)) @ t) @ ((lList2236698231inlsts @ a) @ a2))).
% 2.47/1.49 thf(conj_1, conjecture, (((member @ (coinductive_llist @ a)) @ (((lList2508575361_ldrop @ a) @ t) @ i)) @ ((lList2236698231inlsts @ a) @ a2))).
% 2.47/1.49 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.3cDcvzBLpc/DTF2DTF27050.p
% 2.47/1.49 ------------------------
% 2.75/1.51 ---- Cleaned THF ---
% 2.75/1.51 thf(ty_t_Coinductive__List_Ollist,type,
% 2.75/1.51 coinductive_llist: $tType > $tType ).
% 2.75/1.51
% 2.75/1.51 thf(ty_t_Set_Oset,type,
% 2.75/1.51 set: $tType > $tType ).
% 2.75/1.51
% 2.75/1.51 thf(ty_t_Nat_Onat,type,
% 2.75/1.51 nat: $tType ).
% 2.75/1.51
% 2.75/1.51 thf(ty_t_itself,type,
% 2.75/1.51 itself: $tType > $tType ).
% 2.75/1.51
% 2.75/1.51 thf(ty_tf_a,type,
% 2.75/1.51 a: $tType ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_HOL_Otype,type,
% 2.75/1.51 type:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Oone,type,
% 2.75/1.51 one:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Ozero,type,
% 2.75/1.51 zero:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Orderings_Otop,type,
% 2.75/1.51 top:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Ogroup__add,type,
% 2.75/1.51 group_add:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Omonoid__add,type,
% 2.75/1.51 monoid_add:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Orderings_Opreorder,type,
% 2.75/1.51 preorder:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Oab__group__add,type,
% 2.75/1.51 ab_group_add:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Osemigroup__add,type,
% 2.75/1.51 semigroup_add:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 2.75/1.51 comm_semiring_1:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Ocomm__monoid__add,type,
% 2.75/1.51 comm_monoid_add:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Fields_Olinordered__field,type,
% 2.75/1.51 linordered_field:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 2.75/1.51 ab_semigroup_add:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Ocomm__monoid__diff,type,
% 2.75/1.51 comm_monoid_diff:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 2.75/1.51 cancel_semigroup_add:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 2.75/1.51 ordered_ab_group_add:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Ocancel__comm__monoid__add,type,
% 2.75/1.51 cancel1352612707id_add:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Ocancel__ab__semigroup__add,type,
% 2.75/1.51 cancel146912293up_add:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Olinordered__ab__group__add,type,
% 2.75/1.51 linord219039673up_add:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 2.75/1.51 ordere779506340up_add:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Ocanonically__ordered__monoid__add,type,
% 2.75/1.51 canoni770627133id_add:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Oordered__ab__semigroup__add__imp__le,type,
% 2.75/1.51 ordere236663937imp_le:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Groups_Oordered__ab__semigroup__monoid__add__imp__le,type,
% 2.75/1.51 ordere516151231imp_le:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
% 2.75/1.51 semiri456707255roduct:
% 2.75/1.51 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 2.75/1.51 coindu328551480prefix:
% 2.75/1.51 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_Coinductive__List_Olappend,type,
% 2.75/1.51 coinductive_lappend:
% 2.75/1.51 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 2.75/1.51 coinductive_LCons:
% 2.75/1.51 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 2.75/1.51 coinductive_LNil:
% 2.75/1.51 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 2.75/1.51 coindu1478340336prefix:
% 2.75/1.51 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_Coinductive__List_Olsublist,type,
% 2.75/1.51 coinductive_lsublist:
% 2.75/1.51 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( set @ nat ) > ( coinductive_llist @ A ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_Coinductive__List_Omonoid__add__class_Ollistsum,type,
% 2.75/1.51 coindu780009021istsum:
% 2.75/1.51 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_Groups_Ominus__class_Ominus,type,
% 2.75/1.51 minus_minus:
% 2.75/1.51 !>[A: $tType] : ( A > A > A ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_Groups_Oone__class_Oone,type,
% 2.75/1.51 one_one:
% 2.75/1.51 !>[A: $tType] : A ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 2.75/1.51 plus_plus:
% 2.75/1.51 !>[A: $tType] : ( A > A > A ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_Groups_Ozero__class_Ozero,type,
% 2.75/1.51 zero_zero:
% 2.75/1.51 !>[A: $tType] : A ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_If,type,
% 2.75/1.51 if:
% 2.75/1.51 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllsts,type,
% 2.75/1.51 lList2435255213lllsts:
% 2.75/1.51 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts,type,
% 2.75/1.51 lList2236698231inlsts:
% 2.75/1.51 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec,type,
% 2.75/1.51 lList21916056377ts_rec:
% 2.75/1.51 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B > B ) > ( coinductive_llist @ A ) > B ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts,type,
% 2.75/1.51 lList22096119349pslsts:
% 2.75/1.51 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oinflsts,type,
% 2.75/1.51 lList21612149805nflsts:
% 2.75/1.51 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast,type,
% 2.75/1.51 lList2370560421utlast:
% 2.75/1.51 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oldrop,type,
% 2.75/1.51 lList2508575361_ldrop:
% 2.75/1.51 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast,type,
% 2.75/1.51 lList2170638824_llast:
% 2.75/1.51 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollength,type,
% 2.75/1.51 lList21232602520length:
% 2.75/1.51 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev,type,
% 2.75/1.51 lList2281150353e_lrev:
% 2.75/1.51 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oltake,type,
% 2.75/1.51 lList22119844313_ltake:
% 2.75/1.51 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts,type,
% 2.75/1.51 lList21148268032oslsts:
% 2.75/1.51 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_Nat_OSuc,type,
% 2.75/1.51 suc: nat > nat ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_Nat__Bijection_Otriangle,type,
% 2.75/1.51 nat_triangle: nat > nat ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.75/1.51 ord_less_eq:
% 2.75/1.51 !>[A: $tType] : ( A > A > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_Orderings_Otop__class_Otop,type,
% 2.75/1.51 top_top:
% 2.75/1.51 !>[A: $tType] : A ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_Pure_Otype,type,
% 2.75/1.51 type2:
% 2.75/1.51 !>[A: $tType] : ( itself @ A ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_Set_OCollect,type,
% 2.75/1.51 collect:
% 2.75/1.51 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_c_member,type,
% 2.75/1.51 member:
% 2.75/1.51 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.75/1.51
% 2.75/1.51 thf(sy_v_A,type,
% 2.75/1.51 a2: set @ a ).
% 2.75/1.51
% 2.75/1.51 thf(sy_v_i,type,
% 2.75/1.51 i: nat ).
% 2.75/1.51
% 2.75/1.51 thf(sy_v_t,type,
% 2.75/1.51 t: coinductive_llist @ a ).
% 2.75/1.51
% 2.75/1.51 thf(fact_0_lrevT,axiom,
% 2.75/1.51 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ ( lList2281150353e_lrev @ A @ Xs ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_1_LList2__Mirabelle__hamjzmohle_Oldrop__LNil,axiom,
% 2.75/1.51 ! [A: $tType,I: nat] :
% 2.75/1.51 ( ( lList2508575361_ldrop @ A @ ( coinductive_LNil @ A ) @ I )
% 2.75/1.51 = ( coinductive_LNil @ A ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_2_ldropT,axiom,
% 2.75/1.51 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T @ I ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_3_LList2__Mirabelle__hamjzmohle_Oldrop_Osimps_I1_J,axiom,
% 2.75/1.51 ! [A: $tType,L: coinductive_llist @ A] :
% 2.75/1.51 ( ( lList2508575361_ldrop @ A @ L @ ( zero_zero @ nat ) )
% 2.75/1.51 = L ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_4_ldrop__add,axiom,
% 2.75/1.51 ! [A: $tType,T: coinductive_llist @ A,I: nat,K: nat] :
% 2.75/1.51 ( ( lList2508575361_ldrop @ A @ T @ ( plus_plus @ nat @ I @ K ) )
% 2.75/1.51 = ( lList2508575361_ldrop @ A @ ( lList2508575361_ldrop @ A @ T @ I ) @ K ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_5_finite__lemma,axiom,
% 2.75/1.51 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,B2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ B2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ B2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_6_finsubsetall,axiom,
% 2.75/1.51 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_7_same__lappend__eq,axiom,
% 2.75/1.51 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( ( ( coinductive_lappend @ A @ R @ S )
% 2.75/1.51 = ( coinductive_lappend @ A @ R @ T ) )
% 2.75/1.51 = ( S = T ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_8_lapp__fin__fin__iff,axiom,
% 2.75/1.51 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 = ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_9_finT__simp,axiom,
% 2.75/1.51 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_10_fin__finite,axiom,
% 2.75/1.51 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_11_finlsts_OLNil__fin,axiom,
% 2.75/1.51 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2236698231inlsts @ A @ A2 ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_12_LNil__is__lappend__conv,axiom,
% 2.75/1.51 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.75/1.51 ( ( ( coinductive_LNil @ A )
% 2.75/1.51 = ( coinductive_lappend @ A @ S @ T ) )
% 2.75/1.51 = ( ( S
% 2.75/1.51 = ( coinductive_LNil @ A ) )
% 2.75/1.51 & ( T
% 2.75/1.51 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_13_lappend__is__LNil__conv,axiom,
% 2.75/1.51 ! [A: $tType,S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 2.75/1.51 ( ( ( coinductive_lappend @ A @ S @ T )
% 2.75/1.51 = ( coinductive_LNil @ A ) )
% 2.75/1.51 = ( ( S
% 2.75/1.51 = ( coinductive_LNil @ A ) )
% 2.75/1.51 & ( T
% 2.75/1.51 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_14_alllsts__UNIV,axiom,
% 2.75/1.51 ! [A: $tType,S: coinductive_llist @ A] : ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_15_lrev__LNil,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( lList2281150353e_lrev @ A @ ( coinductive_LNil @ A ) )
% 2.75/1.51 = ( coinductive_LNil @ A ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_16_lrev__is__lrev__conv,axiom,
% 2.75/1.51 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.75/1.51 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.75/1.51 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 2.75/1.51 = ( lList2281150353e_lrev @ A @ Ys ) )
% 2.75/1.51 = ( Xs = Ys ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_17_lrev__lrev__ident,axiom,
% 2.75/1.51 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.75/1.51 => ( ( lList2281150353e_lrev @ A @ ( lList2281150353e_lrev @ A @ Xs ) )
% 2.75/1.51 = Xs ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_18_lrev__is__LNil__conv,axiom,
% 2.75/1.51 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.75/1.51 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 2.75/1.51 = ( coinductive_LNil @ A ) )
% 2.75/1.51 = ( Xs
% 2.75/1.51 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_19_LNil__is__lrev__conv,axiom,
% 2.75/1.51 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.75/1.51 => ( ( ( coinductive_LNil @ A )
% 2.75/1.51 = ( lList2281150353e_lrev @ A @ Xs ) )
% 2.75/1.51 = ( Xs
% 2.75/1.51 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_20_lrev__lappend,axiom,
% 2.75/1.51 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.75/1.51 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.75/1.51 => ( ( lList2281150353e_lrev @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.75/1.51 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ Ys ) @ ( lList2281150353e_lrev @ A @ Xs ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_21_lappT,axiom,
% 2.75/1.51 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.75/1.51 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_22_lapp__all__invT,axiom,
% 2.75/1.51 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_23_alllsts_OLNil__all,axiom,
% 2.75/1.51 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2435255213lllsts @ A @ A2 ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_24_lapp__fin__fin__lemma,axiom,
% 2.75/1.51 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_25_lappfin__finT,axiom,
% 2.75/1.51 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_26_lappend__code_I1_J,axiom,
% 2.75/1.51 ! [A: $tType,Ys: coinductive_llist @ A] :
% 2.75/1.51 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 2.75/1.51 = Ys ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_27_lappend__LNil2,axiom,
% 2.75/1.51 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.75/1.51 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.75/1.51 = Xs ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_28_LNil__eq__lappend__iff,axiom,
% 2.75/1.51 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.75/1.51 ( ( ( coinductive_LNil @ A )
% 2.75/1.51 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 2.75/1.51 = ( ( Xs
% 2.75/1.51 = ( coinductive_LNil @ A ) )
% 2.75/1.51 & ( Ys
% 2.75/1.51 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_29_lappend__eq__LNil__iff,axiom,
% 2.75/1.51 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.75/1.51 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 2.75/1.51 = ( coinductive_LNil @ A ) )
% 2.75/1.51 = ( ( Xs
% 2.75/1.51 = ( coinductive_LNil @ A ) )
% 2.75/1.51 & ( Ys
% 2.75/1.51 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_30_add__is__0,axiom,
% 2.75/1.51 ! [M: nat,N: nat] :
% 2.75/1.51 ( ( ( plus_plus @ nat @ M @ N )
% 2.75/1.51 = ( zero_zero @ nat ) )
% 2.75/1.51 = ( ( M
% 2.75/1.51 = ( zero_zero @ nat ) )
% 2.75/1.51 & ( N
% 2.75/1.51 = ( zero_zero @ nat ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_31_Nat_Oadd__0__right,axiom,
% 2.75/1.51 ! [M: nat] :
% 2.75/1.51 ( ( plus_plus @ nat @ M @ ( zero_zero @ nat ) )
% 2.75/1.51 = M ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_32_add_Oleft__neutral,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( monoid_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A] :
% 2.75/1.51 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A3 )
% 2.75/1.51 = A3 ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_33_add_Oright__neutral,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( monoid_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A] :
% 2.75/1.51 ( ( plus_plus @ A @ A3 @ ( zero_zero @ A ) )
% 2.75/1.51 = A3 ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_34_double__zero,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A] :
% 2.75/1.51 ( ( ( plus_plus @ A @ A3 @ A3 )
% 2.75/1.51 = ( zero_zero @ A ) )
% 2.75/1.51 = ( A3
% 2.75/1.51 = ( zero_zero @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_35_double__zero__sym,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A] :
% 2.75/1.51 ( ( ( zero_zero @ A )
% 2.75/1.51 = ( plus_plus @ A @ A3 @ A3 ) )
% 2.75/1.51 = ( A3
% 2.75/1.51 = ( zero_zero @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_36_add__cancel__left__left,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [B3: A,A3: A] :
% 2.75/1.51 ( ( ( plus_plus @ A @ B3 @ A3 )
% 2.75/1.51 = A3 )
% 2.75/1.51 = ( B3
% 2.75/1.51 = ( zero_zero @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_37_add__right__cancel,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [B3: A,A3: A,C: A] :
% 2.75/1.51 ( ( ( plus_plus @ A @ B3 @ A3 )
% 2.75/1.51 = ( plus_plus @ A @ C @ A3 ) )
% 2.75/1.51 = ( B3 = C ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_38_add__left__cancel,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A,B3: A,C: A] :
% 2.75/1.51 ( ( ( plus_plus @ A @ A3 @ B3 )
% 2.75/1.51 = ( plus_plus @ A @ A3 @ C ) )
% 2.75/1.51 = ( B3 = C ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_39_add__cancel__right__right,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A,B3: A] :
% 2.75/1.51 ( ( A3
% 2.75/1.51 = ( plus_plus @ A @ A3 @ B3 ) )
% 2.75/1.51 = ( B3
% 2.75/1.51 = ( zero_zero @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_40_add__cancel__right__left,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A,B3: A] :
% 2.75/1.51 ( ( A3
% 2.75/1.51 = ( plus_plus @ A @ B3 @ A3 ) )
% 2.75/1.51 = ( B3
% 2.75/1.51 = ( zero_zero @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_41_add__cancel__left__right,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A,B3: A] :
% 2.75/1.51 ( ( ( plus_plus @ A @ A3 @ B3 )
% 2.75/1.51 = A3 )
% 2.75/1.51 = ( B3
% 2.75/1.51 = ( zero_zero @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_42_zero__reorient,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( zero @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [X: A] :
% 2.75/1.51 ( ( ( zero_zero @ A )
% 2.75/1.51 = X )
% 2.75/1.51 = ( X
% 2.75/1.51 = ( zero_zero @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_43_add__right__imp__eq,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [B3: A,A3: A,C: A] :
% 2.75/1.51 ( ( ( plus_plus @ A @ B3 @ A3 )
% 2.75/1.51 = ( plus_plus @ A @ C @ A3 ) )
% 2.75/1.51 => ( B3 = C ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_44_mem__Collect__eq,axiom,
% 2.75/1.51 ! [A: $tType,A3: A,P: A > $o] :
% 2.75/1.51 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 2.75/1.51 = ( P @ A3 ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_45_Collect__mem__eq,axiom,
% 2.75/1.51 ! [A: $tType,A2: set @ A] :
% 2.75/1.51 ( ( collect @ A
% 2.75/1.51 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 2.75/1.51 = A2 ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_46_Collect__cong,axiom,
% 2.75/1.51 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.75/1.51 ( ! [X3: A] :
% 2.75/1.51 ( ( P @ X3 )
% 2.75/1.51 = ( Q @ X3 ) )
% 2.75/1.51 => ( ( collect @ A @ P )
% 2.75/1.51 = ( collect @ A @ Q ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_47_ext,axiom,
% 2.75/1.51 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.75/1.51 ( ! [X3: A] :
% 2.75/1.51 ( ( F @ X3 )
% 2.75/1.51 = ( G @ X3 ) )
% 2.75/1.51 => ( F = G ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_48_add__left__imp__eq,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A,B3: A,C: A] :
% 2.75/1.51 ( ( ( plus_plus @ A @ A3 @ B3 )
% 2.75/1.51 = ( plus_plus @ A @ A3 @ C ) )
% 2.75/1.51 => ( B3 = C ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_49_add_Oleft__commute,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [B3: A,A3: A,C: A] :
% 2.75/1.51 ( ( plus_plus @ A @ B3 @ ( plus_plus @ A @ A3 @ C ) )
% 2.75/1.51 = ( plus_plus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_50_add_Ocommute,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ( ( plus_plus @ A )
% 2.75/1.51 = ( ^ [A4: A,B4: A] : ( plus_plus @ A @ B4 @ A4 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_51_add_Oright__cancel,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( group_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [B3: A,A3: A,C: A] :
% 2.75/1.51 ( ( ( plus_plus @ A @ B3 @ A3 )
% 2.75/1.51 = ( plus_plus @ A @ C @ A3 ) )
% 2.75/1.51 = ( B3 = C ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_52_add_Oleft__cancel,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( group_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A,B3: A,C: A] :
% 2.75/1.51 ( ( ( plus_plus @ A @ A3 @ B3 )
% 2.75/1.51 = ( plus_plus @ A @ A3 @ C ) )
% 2.75/1.51 = ( B3 = C ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_53_add_Oassoc,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( semigroup_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A,B3: A,C: A] :
% 2.75/1.51 ( ( plus_plus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ C )
% 2.75/1.51 = ( plus_plus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_54_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [I: A,J: A,K: A,L: A] :
% 2.75/1.51 ( ( ( I = J )
% 2.75/1.51 & ( K = L ) )
% 2.75/1.51 => ( ( plus_plus @ A @ I @ K )
% 2.75/1.51 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_55_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A,B3: A,C: A] :
% 2.75/1.51 ( ( plus_plus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ C )
% 2.75/1.51 = ( plus_plus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_56_nat__add__right__cancel,axiom,
% 2.75/1.51 ! [M: nat,K: nat,N: nat] :
% 2.75/1.51 ( ( ( plus_plus @ nat @ M @ K )
% 2.75/1.51 = ( plus_plus @ nat @ N @ K ) )
% 2.75/1.51 = ( M = N ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_57_nat__add__left__cancel,axiom,
% 2.75/1.51 ! [K: nat,M: nat,N: nat] :
% 2.75/1.51 ( ( ( plus_plus @ nat @ K @ M )
% 2.75/1.51 = ( plus_plus @ nat @ K @ N ) )
% 2.75/1.51 = ( M = N ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_58_lappend__assoc,axiom,
% 2.75/1.51 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 2.75/1.51 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 2.75/1.51 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_59_add__eq__0__iff__both__eq__0,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [X: A,Y: A] :
% 2.75/1.51 ( ( ( plus_plus @ A @ X @ Y )
% 2.75/1.51 = ( zero_zero @ A ) )
% 2.75/1.51 = ( ( X
% 2.75/1.51 = ( zero_zero @ A ) )
% 2.75/1.51 & ( Y
% 2.75/1.51 = ( zero_zero @ A ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_60_add_Ogroup__left__neutral,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( group_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A] :
% 2.75/1.51 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A3 )
% 2.75/1.51 = A3 ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_61_add_Ocomm__neutral,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( comm_monoid_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A] :
% 2.75/1.51 ( ( plus_plus @ A @ A3 @ ( zero_zero @ A ) )
% 2.75/1.51 = A3 ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_62_comm__monoid__add__class_Oadd__0,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( comm_monoid_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A] :
% 2.75/1.51 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A3 )
% 2.75/1.51 = A3 ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_63_add__eq__self__zero,axiom,
% 2.75/1.51 ! [M: nat,N: nat] :
% 2.75/1.51 ( ( ( plus_plus @ nat @ M @ N )
% 2.75/1.51 = M )
% 2.75/1.51 => ( N
% 2.75/1.51 = ( zero_zero @ nat ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_64_plus__nat_Oadd__0,axiom,
% 2.75/1.51 ! [N: nat] :
% 2.75/1.51 ( ( plus_plus @ nat @ ( zero_zero @ nat ) @ N )
% 2.75/1.51 = N ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_65_lappend__LNil__LNil,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 2.75/1.51 = ( coinductive_LNil @ A ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_66_iso__tuple__UNIV__I,axiom,
% 2.75/1.51 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_67_UNIV__I,axiom,
% 2.75/1.51 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_68_top__apply,axiom,
% 2.75/1.51 ! [C2: $tType,D: $tType] :
% 2.75/1.51 ( ( top @ C2 @ ( type2 @ C2 ) )
% 2.75/1.51 => ( ( top_top @ ( D > C2 ) )
% 2.75/1.51 = ( ^ [X2: D] : ( top_top @ C2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_69_poslsts__iff,axiom,
% 2.75/1.51 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ A2 ) )
% 2.75/1.51 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.75/1.51 & ( S
% 2.75/1.51 != ( coinductive_LNil @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_70_fpslsts__iff,axiom,
% 2.75/1.51 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList22096119349pslsts @ A @ A2 ) )
% 2.75/1.51 = ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 & ( S
% 2.75/1.51 != ( coinductive_LNil @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_71_poslsts__UNIV,axiom,
% 2.75/1.51 ! [A: $tType,S: coinductive_llist @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21148268032oslsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.75/1.51 = ( S
% 2.75/1.51 != ( coinductive_LNil @ A ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_72_ind__euclid,axiom,
% 2.75/1.51 ! [P: nat > nat > $o,A3: nat,B3: nat] :
% 2.75/1.51 ( ! [A5: nat,B5: nat] :
% 2.75/1.51 ( ( P @ A5 @ B5 )
% 2.75/1.51 = ( P @ B5 @ A5 ) )
% 2.75/1.51 => ( ! [A5: nat] : ( P @ A5 @ ( zero_zero @ nat ) )
% 2.75/1.51 => ( ! [A5: nat,B5: nat] :
% 2.75/1.51 ( ( P @ A5 @ B5 )
% 2.75/1.51 => ( P @ A5 @ ( plus_plus @ nat @ A5 @ B5 ) ) )
% 2.75/1.51 => ( P @ A3 @ B3 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_73_LList2__Mirabelle__hamjzmohle_Ollength__LNil,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( lList21232602520length @ A @ ( coinductive_LNil @ A ) )
% 2.75/1.51 = ( zero_zero @ nat ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_74_add__0__iff,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( semiri456707255roduct @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [B3: A,A3: A] :
% 2.75/1.51 ( ( B3
% 2.75/1.51 = ( plus_plus @ A @ B3 @ A3 ) )
% 2.75/1.51 = ( A3
% 2.75/1.51 = ( zero_zero @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_75_top__set__def,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( top_top @ ( set @ A ) )
% 2.75/1.51 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_76_semiring__normalization__rules_I25_J,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A,C: A,D2: A] :
% 2.75/1.51 ( ( plus_plus @ A @ A3 @ ( plus_plus @ A @ C @ D2 ) )
% 2.75/1.51 = ( plus_plus @ A @ ( plus_plus @ A @ A3 @ C ) @ D2 ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_77_semiring__normalization__rules_I24_J,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.75/1.51 => ( ( plus_plus @ A )
% 2.75/1.51 = ( ^ [A4: A,C3: A] : ( plus_plus @ A @ C3 @ A4 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_78_semiring__normalization__rules_I23_J,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A,B3: A,C: A] :
% 2.75/1.51 ( ( plus_plus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ C )
% 2.75/1.51 = ( plus_plus @ A @ ( plus_plus @ A @ A3 @ C ) @ B3 ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_79_semiring__normalization__rules_I22_J,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A,C: A,D2: A] :
% 2.75/1.51 ( ( plus_plus @ A @ A3 @ ( plus_plus @ A @ C @ D2 ) )
% 2.75/1.51 = ( plus_plus @ A @ C @ ( plus_plus @ A @ A3 @ D2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_80_semiring__normalization__rules_I21_J,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A,B3: A,C: A] :
% 2.75/1.51 ( ( plus_plus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ C )
% 2.75/1.51 = ( plus_plus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_81_semiring__normalization__rules_I20_J,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A,B3: A,C: A,D2: A] :
% 2.75/1.51 ( ( plus_plus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ ( plus_plus @ A @ C @ D2 ) )
% 2.75/1.51 = ( plus_plus @ A @ ( plus_plus @ A @ A3 @ C ) @ ( plus_plus @ A @ B3 @ D2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_82_UNIV__eq__I,axiom,
% 2.75/1.51 ! [A: $tType,A2: set @ A] :
% 2.75/1.51 ( ! [X3: A] : ( member @ A @ X3 @ A2 )
% 2.75/1.51 => ( ( top_top @ ( set @ A ) )
% 2.75/1.51 = A2 ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_83_UNIV__witness,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_84_semiring__normalization__rules_I6_J,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A] :
% 2.75/1.51 ( ( plus_plus @ A @ A3 @ ( zero_zero @ A ) )
% 2.75/1.51 = A3 ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_85_semiring__normalization__rules_I5_J,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.75/1.51 => ! [A3: A] :
% 2.75/1.51 ( ( plus_plus @ A @ ( zero_zero @ A ) @ A3 )
% 2.75/1.51 = A3 ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_86_lbutlast__LNil,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( lList2370560421utlast @ A @ ( coinductive_LNil @ A ) )
% 2.75/1.51 = ( coinductive_LNil @ A ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_87_take__fin,axiom,
% 2.75/1.51 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ T @ I ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_88_lrev__LCons,axiom,
% 2.75/1.51 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A3: A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( ( lList2281150353e_lrev @ A @ ( coinductive_LCons @ A @ A3 @ R ) )
% 2.75/1.51 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ R ) @ ( coinductive_LCons @ A @ A3 @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_89_ltake__fin,axiom,
% 2.75/1.51 ! [A: $tType,R: coinductive_llist @ A,I: nat] : ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ R @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_90_inflstsI,axiom,
% 2.75/1.51 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.75/1.51 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_91_llistsum__LNil,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( monoid_add @ A @ ( type2 @ A ) )
% 2.75/1.51 => ( ( coindu780009021istsum @ A @ ( coinductive_LNil @ A ) )
% 2.75/1.51 = ( zero_zero @ A ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_92_llist_Oinject,axiom,
% 2.75/1.51 ! [A: $tType,X21: A,X22: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 2.75/1.51 ( ( ( coinductive_LCons @ A @ X21 @ X22 )
% 2.75/1.51 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 2.75/1.51 = ( ( X21 = Y21 )
% 2.75/1.51 & ( X22 = Y22 ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_93_top1I,axiom,
% 2.75/1.51 ! [A: $tType,X: A] : ( top_top @ ( A > $o ) @ X ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_94_lappend__code_I2_J,axiom,
% 2.75/1.51 ! [A: $tType,Xa: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 2.75/1.51 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa @ X ) @ Ys )
% 2.75/1.51 = ( coinductive_LCons @ A @ Xa @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_95_LConsE,axiom,
% 2.75/1.51 ! [A: $tType,X: A,Xs: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ X @ Xs ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.75/1.51 = ( ( member @ A @ X @ A2 )
% 2.75/1.51 & ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_96_lapp__inf,axiom,
% 2.75/1.51 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.75/1.51 => ( ( coinductive_lappend @ A @ S @ T )
% 2.75/1.51 = S ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_97_LList2__Mirabelle__hamjzmohle_Oltake__LNil,axiom,
% 2.75/1.51 ! [A: $tType,I: nat] :
% 2.75/1.51 ( ( lList22119844313_ltake @ A @ ( coinductive_LNil @ A ) @ I )
% 2.75/1.51 = ( coinductive_LNil @ A ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_98_notfin__inf,axiom,
% 2.75/1.51 ! [A: $tType,X: coinductive_llist @ A] :
% 2.75/1.51 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 2.75/1.51 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_99_notinf__fin,axiom,
% 2.75/1.51 ! [A: $tType,X: coinductive_llist @ A] :
% 2.75/1.51 ( ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) )
% 2.75/1.51 = ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_100_llength__take,axiom,
% 2.75/1.51 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A,I: nat] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.75/1.51 => ( ( lList21232602520length @ A @ ( lList22119844313_ltake @ A @ T @ I ) )
% 2.75/1.51 = I ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_101_lbutlast__LCons,axiom,
% 2.75/1.51 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A3: A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( ( ( R
% 2.75/1.51 = ( coinductive_LNil @ A ) )
% 2.75/1.51 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A3 @ R ) )
% 2.75/1.51 = ( coinductive_LNil @ A ) ) )
% 2.75/1.51 & ( ( R
% 2.75/1.51 != ( coinductive_LNil @ A ) )
% 2.75/1.51 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A3 @ R ) )
% 2.75/1.51 = ( coinductive_LCons @ A @ A3 @ ( lList2370560421utlast @ A @ R ) ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_102_inflsts__cases,axiom,
% 2.75/1.51 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.75/1.51 => ~ ! [A5: A,L2: coinductive_llist @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.75/1.51 => ( ( member @ A @ A5 @ A2 )
% 2.75/1.51 => ( S
% 2.75/1.51 != ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_103_inflstsI2,axiom,
% 2.75/1.51 ! [A: $tType,A3: A,A2: set @ A,T: coinductive_llist @ A] :
% 2.75/1.51 ( ( member @ A @ A3 @ A2 )
% 2.75/1.51 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_104_neq__LNil__conv,axiom,
% 2.75/1.51 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.75/1.51 ( ( Xs
% 2.75/1.51 != ( coinductive_LNil @ A ) )
% 2.75/1.51 = ( ? [X2: A,Xs2: coinductive_llist @ A] :
% 2.75/1.51 ( Xs
% 2.75/1.51 = ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_105_llist_Odistinct_I1_J,axiom,
% 2.75/1.51 ! [A: $tType,X21: A,X22: coinductive_llist @ A] :
% 2.75/1.51 ( ( coinductive_LNil @ A )
% 2.75/1.51 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_106_llistE,axiom,
% 2.75/1.51 ! [A: $tType,Y: coinductive_llist @ A] :
% 2.75/1.51 ( ( Y
% 2.75/1.51 != ( coinductive_LNil @ A ) )
% 2.75/1.51 => ~ ! [X212: A,X222: coinductive_llist @ A] :
% 2.75/1.51 ( Y
% 2.75/1.51 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_107_finlsts_OLCons__fin,axiom,
% 2.75/1.51 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A3: A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( ( member @ A @ A3 @ A2 )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ L ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_108_alllsts_OLCons__all,axiom,
% 2.75/1.51 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A3: A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.75/1.51 => ( ( member @ A @ A3 @ A2 )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A3 @ L ) @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_109_infT__simp,axiom,
% 2.75/1.51 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_110_infsubsetall,axiom,
% 2.75/1.51 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_111_lappend__snocL1__conv__LCons2,axiom,
% 2.75/1.51 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.75/1.51 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 2.75/1.51 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_112_finlsts_Ocases,axiom,
% 2.75/1.51 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( ( A3
% 2.75/1.51 != ( coinductive_LNil @ A ) )
% 2.75/1.51 => ~ ! [L2: coinductive_llist @ A,A5: A] :
% 2.75/1.51 ( ( A3
% 2.75/1.51 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 2.75/1.51 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ~ ( member @ A @ A5 @ A2 ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_113_finlsts_Osimps,axiom,
% 2.75/1.51 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 = ( ( A3
% 2.75/1.51 = ( coinductive_LNil @ A ) )
% 2.75/1.51 | ? [L3: coinductive_llist @ A,A4: A] :
% 2.75/1.51 ( ( A3
% 2.75/1.51 = ( coinductive_LCons @ A @ A4 @ L3 ) )
% 2.75/1.51 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 & ( member @ A @ A4 @ A2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_114_finlsts__induct,axiom,
% 2.75/1.51 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( ! [L2: coinductive_llist @ A] :
% 2.75/1.51 ( ( L2
% 2.75/1.51 = ( coinductive_LNil @ A ) )
% 2.75/1.51 => ( P @ L2 ) )
% 2.75/1.51 => ( ! [A5: A,L2: coinductive_llist @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( ( P @ L2 )
% 2.75/1.51 => ( ( member @ A @ A5 @ A2 )
% 2.75/1.51 => ( P @ ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) )
% 2.75/1.51 => ( P @ X ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_115_finlsts_Oinducts,axiom,
% 2.75/1.51 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.75/1.51 => ( ! [L2: coinductive_llist @ A,A5: A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( ( P @ L2 )
% 2.75/1.51 => ( ( member @ A @ A5 @ A2 )
% 2.75/1.51 => ( P @ ( coinductive_LCons @ A @ A5 @ L2 ) ) ) ) )
% 2.75/1.51 => ( P @ X ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_116_alllsts_Ocoinduct,axiom,
% 2.75/1.51 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( X4 @ X )
% 2.75/1.51 => ( ! [X3: coinductive_llist @ A] :
% 2.75/1.51 ( ( X4 @ X3 )
% 2.75/1.51 => ( ( X3
% 2.75/1.51 = ( coinductive_LNil @ A ) )
% 2.75/1.51 | ? [L4: coinductive_llist @ A,A6: A] :
% 2.75/1.51 ( ( X3
% 2.75/1.51 = ( coinductive_LCons @ A @ A6 @ L4 ) )
% 2.75/1.51 & ( ( X4 @ L4 )
% 2.75/1.51 | ( member @ ( coinductive_llist @ A ) @ L4 @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 2.75/1.51 & ( member @ A @ A6 @ A2 ) ) ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_117_alllsts_Osimps,axiom,
% 2.75/1.51 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.75/1.51 = ( ( A3
% 2.75/1.51 = ( coinductive_LNil @ A ) )
% 2.75/1.51 | ? [L3: coinductive_llist @ A,A4: A] :
% 2.75/1.51 ( ( A3
% 2.75/1.51 = ( coinductive_LCons @ A @ A4 @ L3 ) )
% 2.75/1.51 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.75/1.51 & ( member @ A @ A4 @ A2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_118_alllsts_Ocases,axiom,
% 2.75/1.51 ! [A: $tType,A3: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ A3 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.75/1.51 => ( ( A3
% 2.75/1.51 != ( coinductive_LNil @ A ) )
% 2.75/1.51 => ~ ! [L2: coinductive_llist @ A,A5: A] :
% 2.75/1.51 ( ( A3
% 2.75/1.51 = ( coinductive_LCons @ A @ A5 @ L2 ) )
% 2.75/1.51 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.75/1.51 => ~ ( member @ A @ A5 @ A2 ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_119_fin__inf__cases,axiom,
% 2.75/1.51 ! [A: $tType,R: coinductive_llist @ A] :
% 2.75/1.51 ( ~ ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_120_fpslsts__cases,axiom,
% 2.75/1.51 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList22096119349pslsts @ A @ A2 ) )
% 2.75/1.51 => ~ ! [A5: A,Rs: coinductive_llist @ A] :
% 2.75/1.51 ( ( R
% 2.75/1.51 = ( coinductive_LCons @ A @ A5 @ Rs ) )
% 2.75/1.51 => ( ( member @ A @ A5 @ A2 )
% 2.75/1.51 => ~ ( member @ ( coinductive_llist @ A ) @ Rs @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_121_app__invT,axiom,
% 2.75/1.51 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S: coinductive_llist @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_122_lapp__infT,axiom,
% 2.75/1.51 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.75/1.51 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) )
% 2.75/1.51 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_123_lapp__inv2T,axiom,
% 2.75/1.51 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.75/1.51 => ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList21612149805nflsts @ A @ A2 ) ) )
% 2.75/1.51 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_124_lapp__fin__infT,axiom,
% 2.75/1.51 ! [A: $tType,S: coinductive_llist @ A,A2: set @ A,T: coinductive_llist @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ S @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S @ T ) @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_125_alllstsE,axiom,
% 2.75/1.51 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.75/1.51 => ( ~ ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_126_finlsts__rev__cases,axiom,
% 2.75/1.51 ! [A: $tType,T: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ T @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( ( T
% 2.75/1.51 != ( coinductive_LNil @ A ) )
% 2.75/1.51 => ~ ! [A5: A,L2: coinductive_llist @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( ( member @ A @ A5 @ A2 )
% 2.75/1.51 => ( T
% 2.75/1.51 != ( coinductive_lappend @ A @ L2 @ ( coinductive_LCons @ A @ A5 @ ( coinductive_LNil @ A ) ) ) ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_127_lrev__induct,axiom,
% 2.75/1.51 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( ( P @ ( coinductive_LNil @ A ) )
% 2.75/1.51 => ( ! [X3: A,Xs3: coinductive_llist @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ Xs3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 => ( ( P @ Xs3 )
% 2.75/1.51 => ( ( member @ A @ X3 @ A2 )
% 2.75/1.51 => ( P @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) ) ) ) ) )
% 2.75/1.51 => ( P @ Xs ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_128_LList2__Mirabelle__hamjzmohle_Oltake_Osimps_I1_J,axiom,
% 2.75/1.51 ! [A: $tType,L: coinductive_llist @ A] :
% 2.75/1.51 ( ( lList22119844313_ltake @ A @ L @ ( zero_zero @ nat ) )
% 2.75/1.51 = ( coinductive_LNil @ A ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_129_inflstsE,axiom,
% 2.75/1.51 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList21612149805nflsts @ A @ A2 ) )
% 2.75/1.51 => ~ ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.75/1.51 => ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_130_lapp__allT__iff,axiom,
% 2.75/1.51 ! [A: $tType,R: coinductive_llist @ A,S: coinductive_llist @ A,A2: set @ A] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S ) @ ( lList2435255213lllsts @ A @ A2 ) )
% 2.75/1.51 = ( ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.51 & ( member @ ( coinductive_llist @ A ) @ S @ ( lList2435255213lllsts @ A @ A2 ) ) )
% 2.75/1.51 | ( member @ ( coinductive_llist @ A ) @ R @ ( lList21612149805nflsts @ A @ A2 ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_131_LList2__Mirabelle__hamjzmohle_Oltake__ldrop,axiom,
% 2.75/1.51 ! [A: $tType,Xs: coinductive_llist @ A,M: nat,N: nat] :
% 2.75/1.51 ( ( lList22119844313_ltake @ A @ ( lList2508575361_ldrop @ A @ Xs @ M ) @ N )
% 2.75/1.51 = ( lList2508575361_ldrop @ A @ ( lList22119844313_ltake @ A @ Xs @ ( plus_plus @ nat @ N @ M ) ) @ M ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_132_ltake__ldrop__id,axiom,
% 2.75/1.51 ! [A: $tType,X: coinductive_llist @ A,I: nat] :
% 2.75/1.51 ( ( coinductive_lappend @ A @ ( lList22119844313_ltake @ A @ X @ I ) @ ( lList2508575361_ldrop @ A @ X @ I ) )
% 2.75/1.51 = X ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_133_LList2__Mirabelle__hamjzmohle_Ollast__LCons,axiom,
% 2.75/1.51 ! [B: $tType,R: coinductive_llist @ B,A2: set @ B,A3: B] :
% 2.75/1.51 ( ( member @ ( coinductive_llist @ B ) @ R @ ( lList2236698231inlsts @ B @ A2 ) )
% 2.75/1.51 => ( ( ( R
% 2.75/1.51 = ( coinductive_LNil @ B ) )
% 2.75/1.51 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A3 @ R ) )
% 2.75/1.51 = A3 ) )
% 2.75/1.51 & ( ( R
% 2.75/1.51 != ( coinductive_LNil @ B ) )
% 2.75/1.51 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A3 @ R ) )
% 2.75/1.51 = ( lList2170638824_llast @ B @ R ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_134_top__empty__eq,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( top_top @ ( A > $o ) )
% 2.75/1.51 = ( ^ [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_135_lsublist__singleton,axiom,
% 2.75/1.51 ! [A: $tType,A2: set @ nat,X: A] :
% 2.75/1.51 ( ( ( member @ nat @ ( zero_zero @ nat ) @ A2 )
% 2.75/1.51 => ( ( coinductive_lsublist @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) @ A2 )
% 2.75/1.51 = ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) )
% 2.75/1.51 & ( ~ ( member @ nat @ ( zero_zero @ nat ) @ A2 )
% 2.75/1.51 => ( ( coinductive_lsublist @ A @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) @ A2 )
% 2.75/1.51 = ( coinductive_LNil @ A ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_136_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 2.75/1.51 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 2.75/1.51 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 2.75/1.51 = ( ( Xs
% 2.75/1.51 = ( coinductive_LNil @ A ) )
% 2.75/1.51 | ? [Xs2: coinductive_llist @ A] :
% 2.75/1.51 ( ( Xs
% 2.75/1.51 = ( coinductive_LCons @ A @ Y @ Xs2 ) )
% 2.75/1.51 & ( coindu328551480prefix @ A @ Xs2 @ Ys ) ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_137_top__conj_I1_J,axiom,
% 2.75/1.51 ! [A: $tType,X: A,P: $o] :
% 2.75/1.51 ( ( ( top_top @ ( A > $o ) @ X )
% 2.75/1.51 & P )
% 2.75/1.51 = P ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_138_lsublist__LNil,axiom,
% 2.75/1.51 ! [A: $tType,A2: set @ nat] :
% 2.75/1.51 ( ( coinductive_lsublist @ A @ ( coinductive_LNil @ A ) @ A2 )
% 2.75/1.51 = ( coinductive_LNil @ A ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_139_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 2.75/1.51 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_140_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 2.75/1.51 ! [A: $tType,Xs: coinductive_llist @ A] :
% 2.75/1.51 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 2.75/1.51 = ( Xs
% 2.75/1.51 = ( coinductive_LNil @ A ) ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_141_top__conj_I2_J,axiom,
% 2.75/1.51 ! [A: $tType,P: $o,X: A] :
% 2.75/1.51 ( ( P
% 2.75/1.51 & ( top_top @ ( A > $o ) @ X ) )
% 2.75/1.51 = P ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_142_lstrict__prefix__code_I3_J,axiom,
% 2.75/1.51 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 2.75/1.51 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_143_lstrict__prefix__code_I2_J,axiom,
% 2.75/1.51 ! [B: $tType,Y: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y @ Ys ) ) ).
% 2.75/1.51
% 2.75/1.51 thf(fact_144_inflsts__def,axiom,
% 2.75/1.51 ! [A: $tType] :
% 2.75/1.51 ( ( lList21612149805nflsts @ A )
% 2.75/1.51 = ( ^ [A7: set @ A] : ( minus_minus @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2435255213lllsts @ A @ A7 ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_145_LList2__Mirabelle__hamjzmohle_Ollength__LCons,axiom,
% 2.75/1.52 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A3: A] :
% 2.75/1.52 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.52 => ( ( lList21232602520length @ A @ ( coinductive_LCons @ A @ A3 @ R ) )
% 2.75/1.52 = ( suc @ ( lList21232602520length @ A @ R ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_146_nat_Oinject,axiom,
% 2.75/1.52 ! [X23: nat,Y2: nat] :
% 2.75/1.52 ( ( ( suc @ X23 )
% 2.75/1.52 = ( suc @ Y2 ) )
% 2.75/1.52 = ( X23 = Y2 ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_147_old_Onat_Oinject,axiom,
% 2.75/1.52 ! [Nat: nat,Nat2: nat] :
% 2.75/1.52 ( ( ( suc @ Nat )
% 2.75/1.52 = ( suc @ Nat2 ) )
% 2.75/1.52 = ( Nat = Nat2 ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_148_DiffI,axiom,
% 2.75/1.52 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.75/1.52 ( ( member @ A @ C @ A2 )
% 2.75/1.52 => ( ~ ( member @ A @ C @ B2 )
% 2.75/1.52 => ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_149_Diff__iff,axiom,
% 2.75/1.52 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.75/1.52 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.75/1.52 = ( ( member @ A @ C @ A2 )
% 2.75/1.52 & ~ ( member @ A @ C @ B2 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_150_Diff__idemp,axiom,
% 2.75/1.52 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.75/1.52 ( ( minus_minus @ ( set @ A ) @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) @ B2 )
% 2.75/1.52 = ( minus_minus @ ( set @ A ) @ A2 @ B2 ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_151_diff__self,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A] :
% 2.75/1.52 ( ( minus_minus @ A @ A3 @ A3 )
% 2.75/1.52 = ( zero_zero @ A ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_152_diff__0__right,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A] :
% 2.75/1.52 ( ( minus_minus @ A @ A3 @ ( zero_zero @ A ) )
% 2.75/1.52 = A3 ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_153_zero__diff,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( comm_monoid_diff @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A] :
% 2.75/1.52 ( ( minus_minus @ A @ ( zero_zero @ A ) @ A3 )
% 2.75/1.52 = ( zero_zero @ A ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_154_diff__zero,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A] :
% 2.75/1.52 ( ( minus_minus @ A @ A3 @ ( zero_zero @ A ) )
% 2.75/1.52 = A3 ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_155_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A] :
% 2.75/1.52 ( ( minus_minus @ A @ A3 @ A3 )
% 2.75/1.52 = ( zero_zero @ A ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_156_add__diff__cancel,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A] :
% 2.75/1.52 ( ( minus_minus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ B3 )
% 2.75/1.52 = A3 ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_157_diff__add__cancel,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A] :
% 2.75/1.52 ( ( plus_plus @ A @ ( minus_minus @ A @ A3 @ B3 ) @ B3 )
% 2.75/1.52 = A3 ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_158_add__diff__cancel__left,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [C: A,A3: A,B3: A] :
% 2.75/1.52 ( ( minus_minus @ A @ ( plus_plus @ A @ C @ A3 ) @ ( plus_plus @ A @ C @ B3 ) )
% 2.75/1.52 = ( minus_minus @ A @ A3 @ B3 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_159_add__diff__cancel__left_H,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A] :
% 2.75/1.52 ( ( minus_minus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ A3 )
% 2.75/1.52 = B3 ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_160_add__diff__cancel__right,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,C: A,B3: A] :
% 2.75/1.52 ( ( minus_minus @ A @ ( plus_plus @ A @ A3 @ C ) @ ( plus_plus @ A @ B3 @ C ) )
% 2.75/1.52 = ( minus_minus @ A @ A3 @ B3 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_161_add__diff__cancel__right_H,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A] :
% 2.75/1.52 ( ( minus_minus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ B3 )
% 2.75/1.52 = A3 ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_162_add__Suc__right,axiom,
% 2.75/1.52 ! [M: nat,N: nat] :
% 2.75/1.52 ( ( plus_plus @ nat @ M @ ( suc @ N ) )
% 2.75/1.52 = ( suc @ ( plus_plus @ nat @ M @ N ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_163_lstrict__prefix__code_I4_J,axiom,
% 2.75/1.52 ! [B: $tType,X: B,Xs: coinductive_llist @ B,Y: B,Ys: coinductive_llist @ B] :
% 2.75/1.52 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 2.75/1.52 = ( ( X = Y )
% 2.75/1.52 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_164_lstrict__prefix__code_I1_J,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_165_diff__add__zero,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( comm_monoid_diff @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A] :
% 2.75/1.52 ( ( minus_minus @ A @ A3 @ ( plus_plus @ A @ A3 @ B3 ) )
% 2.75/1.52 = ( zero_zero @ A ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_166_eq__iff__diff__eq__0,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 2.75/1.52 = ( ^ [A4: A,B4: A] :
% 2.75/1.52 ( ( minus_minus @ A @ A4 @ B4 )
% 2.75/1.52 = ( zero_zero @ A ) ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_167_diff__eq__eq,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A,C: A] :
% 2.75/1.52 ( ( ( minus_minus @ A @ A3 @ B3 )
% 2.75/1.52 = C )
% 2.75/1.52 = ( A3
% 2.75/1.52 = ( plus_plus @ A @ C @ B3 ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_168_eq__diff__eq,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,C: A,B3: A] :
% 2.75/1.52 ( ( A3
% 2.75/1.52 = ( minus_minus @ A @ C @ B3 ) )
% 2.75/1.52 = ( ( plus_plus @ A @ A3 @ B3 )
% 2.75/1.52 = C ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_169_add__diff__eq,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A,C: A] :
% 2.75/1.52 ( ( plus_plus @ A @ A3 @ ( minus_minus @ A @ B3 @ C ) )
% 2.75/1.52 = ( minus_minus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ C ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_170_diff__diff__eq2,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A,C: A] :
% 2.75/1.52 ( ( minus_minus @ A @ A3 @ ( minus_minus @ A @ B3 @ C ) )
% 2.75/1.52 = ( minus_minus @ A @ ( plus_plus @ A @ A3 @ C ) @ B3 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_171_diff__add__eq,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( ab_group_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A,C: A] :
% 2.75/1.52 ( ( plus_plus @ A @ ( minus_minus @ A @ A3 @ B3 ) @ C )
% 2.75/1.52 = ( minus_minus @ A @ ( plus_plus @ A @ A3 @ C ) @ B3 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_172_diff__add__eq__diff__diff__swap,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A,C: A] :
% 2.75/1.52 ( ( minus_minus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) )
% 2.75/1.52 = ( minus_minus @ A @ ( minus_minus @ A @ A3 @ C ) @ B3 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_173_diff__diff__add,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A,C: A] :
% 2.75/1.52 ( ( minus_minus @ A @ ( minus_minus @ A @ A3 @ B3 ) @ C )
% 2.75/1.52 = ( minus_minus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_174_add__implies__diff,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( cancel1352612707id_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [C: A,B3: A,A3: A] :
% 2.75/1.52 ( ( ( plus_plus @ A @ C @ B3 )
% 2.75/1.52 = A3 )
% 2.75/1.52 => ( C
% 2.75/1.52 = ( minus_minus @ A @ A3 @ B3 ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_175_nat_Odistinct_I1_J,axiom,
% 2.75/1.52 ! [X23: nat] :
% 2.75/1.52 ( ( zero_zero @ nat )
% 2.75/1.52 != ( suc @ X23 ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_176_old_Onat_Odistinct_I2_J,axiom,
% 2.75/1.52 ! [Nat3: nat] :
% 2.75/1.52 ( ( suc @ Nat3 )
% 2.75/1.52 != ( zero_zero @ nat ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_177_old_Onat_Odistinct_I1_J,axiom,
% 2.75/1.52 ! [Nat2: nat] :
% 2.75/1.52 ( ( zero_zero @ nat )
% 2.75/1.52 != ( suc @ Nat2 ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_178_nat_OdiscI,axiom,
% 2.75/1.52 ! [Nat: nat,X23: nat] :
% 2.75/1.52 ( ( Nat
% 2.75/1.52 = ( suc @ X23 ) )
% 2.75/1.52 => ( Nat
% 2.75/1.52 != ( zero_zero @ nat ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_179_nat__induct,axiom,
% 2.75/1.52 ! [P: nat > $o,N: nat] :
% 2.75/1.52 ( ( P @ ( zero_zero @ nat ) )
% 2.75/1.52 => ( ! [N2: nat] :
% 2.75/1.52 ( ( P @ N2 )
% 2.75/1.52 => ( P @ ( suc @ N2 ) ) )
% 2.75/1.52 => ( P @ N ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_180_diff__induct,axiom,
% 2.75/1.52 ! [P: nat > nat > $o,M: nat,N: nat] :
% 2.75/1.52 ( ! [X3: nat] : ( P @ X3 @ ( zero_zero @ nat ) )
% 2.75/1.52 => ( ! [Y4: nat] : ( P @ ( zero_zero @ nat ) @ ( suc @ Y4 ) )
% 2.75/1.52 => ( ! [X3: nat,Y4: nat] :
% 2.75/1.52 ( ( P @ X3 @ Y4 )
% 2.75/1.52 => ( P @ ( suc @ X3 ) @ ( suc @ Y4 ) ) )
% 2.75/1.52 => ( P @ M @ N ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_181_zero__induct,axiom,
% 2.75/1.52 ! [P: nat > $o,K: nat] :
% 2.75/1.52 ( ( P @ K )
% 2.75/1.52 => ( ! [N2: nat] :
% 2.75/1.52 ( ( P @ ( suc @ N2 ) )
% 2.75/1.52 => ( P @ N2 ) )
% 2.75/1.52 => ( P @ ( zero_zero @ nat ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_182_Suc__neq__Zero,axiom,
% 2.75/1.52 ! [M: nat] :
% 2.75/1.52 ( ( suc @ M )
% 2.75/1.52 != ( zero_zero @ nat ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_183_Zero__neq__Suc,axiom,
% 2.75/1.52 ! [M: nat] :
% 2.75/1.52 ( ( zero_zero @ nat )
% 2.75/1.52 != ( suc @ M ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_184_Zero__not__Suc,axiom,
% 2.75/1.52 ! [M: nat] :
% 2.75/1.52 ( ( zero_zero @ nat )
% 2.75/1.52 != ( suc @ M ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_185_old_Onat_Oexhaust,axiom,
% 2.75/1.52 ! [Y: nat] :
% 2.75/1.52 ( ( Y
% 2.75/1.52 != ( zero_zero @ nat ) )
% 2.75/1.52 => ~ ! [Nat4: nat] :
% 2.75/1.52 ( Y
% 2.75/1.52 != ( suc @ Nat4 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_186_old_Onat_Oinducts,axiom,
% 2.75/1.52 ! [P: nat > $o,Nat: nat] :
% 2.75/1.52 ( ( P @ ( zero_zero @ nat ) )
% 2.75/1.52 => ( ! [Nat4: nat] :
% 2.75/1.52 ( ( P @ Nat4 )
% 2.75/1.52 => ( P @ ( suc @ Nat4 ) ) )
% 2.75/1.52 => ( P @ Nat ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_187_not0__implies__Suc,axiom,
% 2.75/1.52 ! [N: nat] :
% 2.75/1.52 ( ( N
% 2.75/1.52 != ( zero_zero @ nat ) )
% 2.75/1.52 => ? [M2: nat] :
% 2.75/1.52 ( N
% 2.75/1.52 = ( suc @ M2 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_188_add__Suc__shift,axiom,
% 2.75/1.52 ! [M: nat,N: nat] :
% 2.75/1.52 ( ( plus_plus @ nat @ ( suc @ M ) @ N )
% 2.75/1.52 = ( plus_plus @ nat @ M @ ( suc @ N ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_189_add__Suc,axiom,
% 2.75/1.52 ! [M: nat,N: nat] :
% 2.75/1.52 ( ( plus_plus @ nat @ ( suc @ M ) @ N )
% 2.75/1.52 = ( suc @ ( plus_plus @ nat @ M @ N ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_190_DiffE,axiom,
% 2.75/1.52 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.75/1.52 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.75/1.52 => ~ ( ( member @ A @ C @ A2 )
% 2.75/1.52 => ( member @ A @ C @ B2 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_191_DiffD1,axiom,
% 2.75/1.52 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.75/1.52 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.75/1.52 => ( member @ A @ C @ A2 ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_192_DiffD2,axiom,
% 2.75/1.52 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.75/1.52 ( ( member @ A @ C @ ( minus_minus @ ( set @ A ) @ A2 @ B2 ) )
% 2.75/1.52 => ~ ( member @ A @ C @ B2 ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_193_Suc__inject,axiom,
% 2.75/1.52 ! [X: nat,Y: nat] :
% 2.75/1.52 ( ( ( suc @ X )
% 2.75/1.52 = ( suc @ Y ) )
% 2.75/1.52 => ( X = Y ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_194_n__not__Suc__n,axiom,
% 2.75/1.52 ! [N: nat] :
% 2.75/1.52 ( N
% 2.75/1.52 != ( suc @ N ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_195_llist__less__induct,axiom,
% 2.75/1.52 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 2.75/1.52 ( ! [Xs3: coinductive_llist @ A] :
% 2.75/1.52 ( ! [Ys2: coinductive_llist @ A] :
% 2.75/1.52 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs3 )
% 2.75/1.52 => ( P @ Ys2 ) )
% 2.75/1.52 => ( P @ Xs3 ) )
% 2.75/1.52 => ( P @ Xs ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_196_diff__eq__diff__eq,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( group_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A,C: A,D2: A] :
% 2.75/1.52 ( ( ( minus_minus @ A @ A3 @ B3 )
% 2.75/1.52 = ( minus_minus @ A @ C @ D2 ) )
% 2.75/1.52 => ( ( A3 = B3 )
% 2.75/1.52 = ( C = D2 ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_197_diff__right__commute,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( cancel146912293up_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,C: A,B3: A] :
% 2.75/1.52 ( ( minus_minus @ A @ ( minus_minus @ A @ A3 @ C ) @ B3 )
% 2.75/1.52 = ( minus_minus @ A @ ( minus_minus @ A @ A3 @ B3 ) @ C ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_198_one__is__add,axiom,
% 2.75/1.52 ! [M: nat,N: nat] :
% 2.75/1.52 ( ( ( suc @ ( zero_zero @ nat ) )
% 2.75/1.52 = ( plus_plus @ nat @ M @ N ) )
% 2.75/1.52 = ( ( ( M
% 2.75/1.52 = ( suc @ ( zero_zero @ nat ) ) )
% 2.75/1.52 & ( N
% 2.75/1.52 = ( zero_zero @ nat ) ) )
% 2.75/1.52 | ( ( M
% 2.75/1.52 = ( zero_zero @ nat ) )
% 2.75/1.52 & ( N
% 2.75/1.52 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_199_add__is__1,axiom,
% 2.75/1.52 ! [M: nat,N: nat] :
% 2.75/1.52 ( ( ( plus_plus @ nat @ M @ N )
% 2.75/1.52 = ( suc @ ( zero_zero @ nat ) ) )
% 2.75/1.52 = ( ( ( M
% 2.75/1.52 = ( suc @ ( zero_zero @ nat ) ) )
% 2.75/1.52 & ( N
% 2.75/1.52 = ( zero_zero @ nat ) ) )
% 2.75/1.52 | ( ( M
% 2.75/1.52 = ( zero_zero @ nat ) )
% 2.75/1.52 & ( N
% 2.75/1.52 = ( suc @ ( zero_zero @ nat ) ) ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_200_ltake__LCons__Suc,axiom,
% 2.75/1.52 ! [A: $tType,A3: A,L: coinductive_llist @ A,I: nat] :
% 2.75/1.52 ( ( lList22119844313_ltake @ A @ ( coinductive_LCons @ A @ A3 @ L ) @ ( suc @ I ) )
% 2.75/1.52 = ( coinductive_LCons @ A @ A3 @ ( lList22119844313_ltake @ A @ L @ I ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_201_list__decode_Ocases,axiom,
% 2.75/1.52 ! [X: nat] :
% 2.75/1.52 ( ( X
% 2.75/1.52 != ( zero_zero @ nat ) )
% 2.75/1.52 => ~ ! [N2: nat] :
% 2.75/1.52 ( X
% 2.75/1.52 != ( suc @ N2 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_202_dependent__nat__choice,axiom,
% 2.75/1.52 ! [A: $tType,P: nat > A > $o,Q: nat > A > A > $o] :
% 2.75/1.52 ( ? [X1: A] : ( P @ ( zero_zero @ nat ) @ X1 )
% 2.75/1.52 => ( ! [X3: A,N2: nat] :
% 2.75/1.52 ( ( P @ N2 @ X3 )
% 2.75/1.52 => ? [Y5: A] :
% 2.75/1.52 ( ( P @ ( suc @ N2 ) @ Y5 )
% 2.75/1.52 & ( Q @ N2 @ X3 @ Y5 ) ) )
% 2.75/1.52 => ? [F2: nat > A] :
% 2.75/1.52 ! [N3: nat] :
% 2.75/1.52 ( ( P @ N3 @ ( F2 @ N3 ) )
% 2.75/1.52 & ( Q @ N3 @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_203_exists__least__lemma,axiom,
% 2.75/1.52 ! [P: nat > $o] :
% 2.75/1.52 ( ~ ( P @ ( zero_zero @ nat ) )
% 2.75/1.52 => ( ? [X1: nat] : ( P @ X1 )
% 2.75/1.52 => ? [N2: nat] :
% 2.75/1.52 ( ~ ( P @ N2 )
% 2.75/1.52 & ( P @ ( suc @ N2 ) ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_204_diff__0__eq__0,axiom,
% 2.75/1.52 ! [N: nat] :
% 2.75/1.52 ( ( minus_minus @ nat @ ( zero_zero @ nat ) @ N )
% 2.75/1.52 = ( zero_zero @ nat ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_205_diff__self__eq__0,axiom,
% 2.75/1.52 ! [M: nat] :
% 2.75/1.52 ( ( minus_minus @ nat @ M @ M )
% 2.75/1.52 = ( zero_zero @ nat ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_206_diff__Suc__Suc,axiom,
% 2.75/1.52 ! [M: nat,N: nat] :
% 2.75/1.52 ( ( minus_minus @ nat @ ( suc @ M ) @ ( suc @ N ) )
% 2.75/1.52 = ( minus_minus @ nat @ M @ N ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_207_Suc__diff__diff,axiom,
% 2.75/1.52 ! [M: nat,N: nat,K: nat] :
% 2.75/1.52 ( ( minus_minus @ nat @ ( minus_minus @ nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 2.75/1.52 = ( minus_minus @ nat @ ( minus_minus @ nat @ M @ N ) @ K ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_208_diff__diff__left,axiom,
% 2.75/1.52 ! [I: nat,J: nat,K: nat] :
% 2.75/1.52 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I @ J ) @ K )
% 2.75/1.52 = ( minus_minus @ nat @ I @ ( plus_plus @ nat @ J @ K ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_209_diffs0__imp__equal,axiom,
% 2.75/1.52 ! [M: nat,N: nat] :
% 2.75/1.52 ( ( ( minus_minus @ nat @ M @ N )
% 2.75/1.52 = ( zero_zero @ nat ) )
% 2.75/1.52 => ( ( ( minus_minus @ nat @ N @ M )
% 2.75/1.52 = ( zero_zero @ nat ) )
% 2.75/1.52 => ( M = N ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_210_minus__nat_Odiff__0,axiom,
% 2.75/1.52 ! [M: nat] :
% 2.75/1.52 ( ( minus_minus @ nat @ M @ ( zero_zero @ nat ) )
% 2.75/1.52 = M ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_211_Nat_Odiff__cancel,axiom,
% 2.75/1.52 ! [K: nat,M: nat,N: nat] :
% 2.75/1.52 ( ( minus_minus @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 2.75/1.52 = ( minus_minus @ nat @ M @ N ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_212_diff__cancel2,axiom,
% 2.75/1.52 ! [M: nat,K: nat,N: nat] :
% 2.75/1.52 ( ( minus_minus @ nat @ ( plus_plus @ nat @ M @ K ) @ ( plus_plus @ nat @ N @ K ) )
% 2.75/1.52 = ( minus_minus @ nat @ M @ N ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_213_diff__add__inverse,axiom,
% 2.75/1.52 ! [N: nat,M: nat] :
% 2.75/1.52 ( ( minus_minus @ nat @ ( plus_plus @ nat @ N @ M ) @ N )
% 2.75/1.52 = M ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_214_diff__add__inverse2,axiom,
% 2.75/1.52 ! [M: nat,N: nat] :
% 2.75/1.52 ( ( minus_minus @ nat @ ( plus_plus @ nat @ M @ N ) @ N )
% 2.75/1.52 = M ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_215_zero__induct__lemma,axiom,
% 2.75/1.52 ! [P: nat > $o,K: nat,I: nat] :
% 2.75/1.52 ( ( P @ K )
% 2.75/1.52 => ( ! [N2: nat] :
% 2.75/1.52 ( ( P @ ( suc @ N2 ) )
% 2.75/1.52 => ( P @ N2 ) )
% 2.75/1.52 => ( P @ ( minus_minus @ nat @ K @ I ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_216_diff__add__0,axiom,
% 2.75/1.52 ! [N: nat,M: nat] :
% 2.75/1.52 ( ( minus_minus @ nat @ N @ ( plus_plus @ nat @ N @ M ) )
% 2.75/1.52 = ( zero_zero @ nat ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_217_triangle__Suc,axiom,
% 2.75/1.52 ! [N: nat] :
% 2.75/1.52 ( ( nat_triangle @ ( suc @ N ) )
% 2.75/1.52 = ( plus_plus @ nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_218_add__diff__add,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( ab_group_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,C: A,B3: A,D2: A] :
% 2.75/1.52 ( ( minus_minus @ A @ ( plus_plus @ A @ A3 @ C ) @ ( plus_plus @ A @ B3 @ D2 ) )
% 2.75/1.52 = ( plus_plus @ A @ ( minus_minus @ A @ A3 @ B3 ) @ ( minus_minus @ A @ C @ D2 ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_219_triangle__0,axiom,
% 2.75/1.52 ( ( nat_triangle @ ( zero_zero @ nat ) )
% 2.75/1.52 = ( zero_zero @ nat ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_220_diff__commute,axiom,
% 2.75/1.52 ! [I: nat,J: nat,K: nat] :
% 2.75/1.52 ( ( minus_minus @ nat @ ( minus_minus @ nat @ I @ J ) @ K )
% 2.75/1.52 = ( minus_minus @ nat @ ( minus_minus @ nat @ I @ K ) @ J ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_221_linordered__field__class_Osign__simps_I34_J,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A,C: A] :
% 2.75/1.52 ( ( plus_plus @ A @ ( minus_minus @ A @ A3 @ B3 ) @ C )
% 2.75/1.52 = ( minus_minus @ A @ ( plus_plus @ A @ A3 @ C ) @ B3 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_222_linordered__field__class_Osign__simps_I33_J,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A,C: A] :
% 2.75/1.52 ( ( minus_minus @ A @ ( minus_minus @ A @ A3 @ B3 ) @ C )
% 2.75/1.52 = ( minus_minus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_223_linordered__field__class_Osign__simps_I28_J,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [B3: A,A3: A,C: A] :
% 2.75/1.52 ( ( plus_plus @ A @ B3 @ ( plus_plus @ A @ A3 @ C ) )
% 2.75/1.52 = ( plus_plus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_224_linordered__field__class_Osign__simps_I27_J,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.75/1.52 => ( ( plus_plus @ A )
% 2.75/1.52 = ( ^ [A4: A,B4: A] : ( plus_plus @ A @ B4 @ A4 ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_225_linordered__field__class_Osign__simps_I26_J,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A,C: A] :
% 2.75/1.52 ( ( plus_plus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ C )
% 2.75/1.52 = ( plus_plus @ A @ A3 @ ( plus_plus @ A @ B3 @ C ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_226_linordered__field__class_Osign__simps_I29_J,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A,C: A] :
% 2.75/1.52 ( ( plus_plus @ A @ A3 @ ( minus_minus @ A @ B3 @ C ) )
% 2.75/1.52 = ( minus_minus @ A @ ( plus_plus @ A @ A3 @ B3 ) @ C ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_227_linordered__field__class_Osign__simps_I30_J,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A,C: A] :
% 2.75/1.52 ( ( ( minus_minus @ A @ A3 @ B3 )
% 2.75/1.52 = C )
% 2.75/1.52 = ( A3
% 2.75/1.52 = ( plus_plus @ A @ C @ B3 ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_228_linordered__field__class_Osign__simps_I31_J,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,C: A,B3: A] :
% 2.75/1.52 ( ( A3
% 2.75/1.52 = ( minus_minus @ A @ C @ B3 ) )
% 2.75/1.52 = ( ( plus_plus @ A @ A3 @ B3 )
% 2.75/1.52 = C ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_229_linordered__field__class_Osign__simps_I32_J,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A,C: A] :
% 2.75/1.52 ( ( minus_minus @ A @ A3 @ ( minus_minus @ A @ B3 @ C ) )
% 2.75/1.52 = ( minus_minus @ A @ ( plus_plus @ A @ A3 @ C ) @ B3 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_230_finlsts__rec__LCons,axiom,
% 2.75/1.52 ! [B: $tType,A: $tType,R: coinductive_llist @ A,A2: set @ A,C: B,D2: A > ( coinductive_llist @ A ) > B > B,A3: A] :
% 2.75/1.52 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.52 => ( ( lList21916056377ts_rec @ B @ A @ C @ D2 @ ( coinductive_LCons @ A @ A3 @ R ) )
% 2.75/1.52 = ( D2 @ A3 @ R @ ( lList21916056377ts_rec @ B @ A @ C @ D2 @ R ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_231_finlsts__rec__LCons__def,axiom,
% 2.75/1.52 ! [B: $tType,A: $tType,F: ( coinductive_llist @ A ) > B,C: B,D2: A > ( coinductive_llist @ A ) > B > B,R: coinductive_llist @ A,A2: set @ A,A3: A] :
% 2.75/1.52 ( ( F
% 2.75/1.52 = ( lList21916056377ts_rec @ B @ A @ C @ D2 ) )
% 2.75/1.52 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 2.75/1.52 => ( ( F @ ( coinductive_LCons @ A @ A3 @ R ) )
% 2.75/1.52 = ( D2 @ A3 @ R @ ( F @ R ) ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_232_finlsts__rec__LNil,axiom,
% 2.75/1.52 ! [B: $tType,A: $tType,C: A,D2: B > ( coinductive_llist @ B ) > A > A] :
% 2.75/1.52 ( ( lList21916056377ts_rec @ A @ B @ C @ D2 @ ( coinductive_LNil @ B ) )
% 2.75/1.52 = C ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_233_finlsts__rec__LNil__def,axiom,
% 2.75/1.52 ! [A: $tType,B: $tType,F: ( coinductive_llist @ A ) > B,C: B,D2: A > ( coinductive_llist @ A ) > B > B] :
% 2.75/1.52 ( ( F
% 2.75/1.52 = ( lList21916056377ts_rec @ B @ A @ C @ D2 ) )
% 2.75/1.52 => ( ( F @ ( coinductive_LNil @ A ) )
% 2.75/1.52 = C ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_234_add__eq__if,axiom,
% 2.75/1.52 ( ( plus_plus @ nat )
% 2.75/1.52 = ( ^ [M3: nat,N4: nat] :
% 2.75/1.52 ( if @ nat
% 2.75/1.52 @ ( M3
% 2.75/1.52 = ( zero_zero @ nat ) )
% 2.75/1.52 @ N4
% 2.75/1.52 @ ( suc @ ( plus_plus @ nat @ ( minus_minus @ nat @ M3 @ ( one_one @ nat ) ) @ N4 ) ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_235_diff__Suc__diff__eq1,axiom,
% 2.75/1.52 ! [K: nat,J: nat,I: nat] :
% 2.75/1.52 ( ( ord_less_eq @ nat @ K @ J )
% 2.75/1.52 => ( ( minus_minus @ nat @ I @ ( suc @ ( minus_minus @ nat @ J @ K ) ) )
% 2.75/1.52 = ( minus_minus @ nat @ ( plus_plus @ nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_236_order__refl,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( preorder @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_237_le__zero__eq,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( canoni770627133id_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [N: A] :
% 2.75/1.52 ( ( ord_less_eq @ A @ N @ ( zero_zero @ A ) )
% 2.75/1.52 = ( N
% 2.75/1.52 = ( zero_zero @ A ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_238_add__le__cancel__right,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,C: A,B3: A] :
% 2.75/1.52 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A3 @ C ) @ ( plus_plus @ A @ B3 @ C ) )
% 2.75/1.52 = ( ord_less_eq @ A @ A3 @ B3 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_239_add__le__cancel__left,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( ordere236663937imp_le @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [C: A,A3: A,B3: A] :
% 2.75/1.52 ( ( ord_less_eq @ A @ ( plus_plus @ A @ C @ A3 ) @ ( plus_plus @ A @ C @ B3 ) )
% 2.75/1.52 = ( ord_less_eq @ A @ A3 @ B3 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_240_le0,axiom,
% 2.75/1.52 ! [N: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ N ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_241_Suc__le__mono,axiom,
% 2.75/1.52 ! [N: nat,M: nat] :
% 2.75/1.52 ( ( ord_less_eq @ nat @ ( suc @ N ) @ ( suc @ M ) )
% 2.75/1.52 = ( ord_less_eq @ nat @ N @ M ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_242_nat__add__left__cancel__le,axiom,
% 2.75/1.52 ! [K: nat,M: nat,N: nat] :
% 2.75/1.52 ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ K @ M ) @ ( plus_plus @ nat @ K @ N ) )
% 2.75/1.52 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_243_diff__diff__cancel,axiom,
% 2.75/1.52 ! [I: nat,N: nat] :
% 2.75/1.52 ( ( ord_less_eq @ nat @ I @ N )
% 2.75/1.52 => ( ( minus_minus @ nat @ N @ ( minus_minus @ nat @ N @ I ) )
% 2.75/1.52 = I ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_244_zero__le__double__add__iff__zero__le__single__add,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A] :
% 2.75/1.52 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( plus_plus @ A @ A3 @ A3 ) )
% 2.75/1.52 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ A3 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_245_double__add__le__zero__iff__single__add__le__zero,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( linord219039673up_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A] :
% 2.75/1.52 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A3 @ A3 ) @ ( zero_zero @ A ) )
% 2.75/1.52 = ( ord_less_eq @ A @ A3 @ ( zero_zero @ A ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_246_le__add__same__cancel2,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A] :
% 2.75/1.52 ( ( ord_less_eq @ A @ A3 @ ( plus_plus @ A @ B3 @ A3 ) )
% 2.75/1.52 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B3 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_247_le__add__same__cancel1,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A] :
% 2.75/1.52 ( ( ord_less_eq @ A @ A3 @ ( plus_plus @ A @ A3 @ B3 ) )
% 2.75/1.52 = ( ord_less_eq @ A @ ( zero_zero @ A ) @ B3 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_248_add__le__same__cancel2,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A] :
% 2.75/1.52 ( ( ord_less_eq @ A @ ( plus_plus @ A @ A3 @ B3 ) @ B3 )
% 2.75/1.52 = ( ord_less_eq @ A @ A3 @ ( zero_zero @ A ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_249_add__le__same__cancel1,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( ordere516151231imp_le @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [B3: A,A3: A] :
% 2.75/1.52 ( ( ord_less_eq @ A @ ( plus_plus @ A @ B3 @ A3 ) @ B3 )
% 2.75/1.52 = ( ord_less_eq @ A @ A3 @ ( zero_zero @ A ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_250_diff__ge__0__iff__ge,axiom,
% 2.75/1.52 ! [A: $tType] :
% 2.75/1.52 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 2.75/1.52 => ! [A3: A,B3: A] :
% 2.75/1.52 ( ( ord_less_eq @ A @ ( zero_zero @ A ) @ ( minus_minus @ A @ A3 @ B3 ) )
% 2.75/1.52 = ( ord_less_eq @ A @ B3 @ A3 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(fact_251_diff__is__0__eq_H,axiom,
% 2.75/1.52 ! [M: nat,N: nat] :
% 2.75/1.52 ( ( ord_less_eq @ nat @ M @ N )
% 2.75/1.52 => ( ( minus_minus @ nat @ M @ N )
% 2.75/1.52 = ( zero_zero @ nat ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.75/1.52 ! [A8: $tType,A9: $tType] :
% 2.75/1.52 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 2.75/1.52 => ( preorder @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_fun___Orderings_Otop,axiom,
% 2.75/1.52 ! [A8: $tType,A9: $tType] :
% 2.75/1.52 ( ( top @ A9 @ ( type2 @ A9 ) )
% 2.75/1.52 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 2.75/1.52 semiri456707255roduct @ nat @ ( type2 @ nat ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le,axiom,
% 2.75/1.52 ordere516151231imp_le @ nat @ ( type2 @ nat ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 2.75/1.52 ordere236663937imp_le @ nat @ ( type2 @ nat ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add,axiom,
% 2.75/1.52 canoni770627133id_add @ nat @ ( type2 @ nat ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 2.75/1.52 ordere779506340up_add @ nat @ ( type2 @ nat ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add,axiom,
% 2.75/1.52 cancel146912293up_add @ nat @ ( type2 @ nat ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add,axiom,
% 2.75/1.52 cancel1352612707id_add @ nat @ ( type2 @ nat ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 2.75/1.52 cancel_semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__diff,axiom,
% 2.75/1.52 comm_monoid_diff @ nat @ ( type2 @ nat ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 2.75/1.52 ab_semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__add,axiom,
% 2.75/1.52 comm_monoid_add @ nat @ ( type2 @ nat ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
% 2.75/1.52 comm_semiring_1 @ nat @ ( type2 @ nat ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 2.75/1.52 semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 2.75/1.52 preorder @ nat @ ( type2 @ nat ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Nat_Onat___Groups_Omonoid__add,axiom,
% 2.75/1.52 monoid_add @ nat @ ( type2 @ nat ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Nat_Onat___Groups_Ozero,axiom,
% 2.75/1.52 zero @ nat @ ( type2 @ nat ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 2.75/1.52 one @ nat @ ( type2 @ nat ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Set_Oset___Orderings_Opreorder_2,axiom,
% 2.75/1.52 ! [A8: $tType] : ( preorder @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_Set_Oset___Orderings_Otop_3,axiom,
% 2.75/1.52 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_HOL_Obool___Orderings_Opreorder_4,axiom,
% 2.75/1.52 preorder @ $o @ ( type2 @ $o ) ).
% 2.75/1.52
% 2.75/1.52 thf(tcon_HOL_Obool___Orderings_Otop_5,axiom,
% 2.75/1.52 top @ $o @ ( type2 @ $o ) ).
% 2.75/1.52
% 2.75/1.52 thf(help_If_3_1_T,axiom,
% 2.75/1.52 ! [P: $o] :
% 2.75/1.52 ( ( P = $true )
% 2.75/1.52 | ( P = $false ) ) ).
% 2.75/1.52
% 2.75/1.52 thf(help_If_2_1_T,axiom,
% 2.75/1.52 ! [A: $tType,X: A,Y: A] :
% 2.75/1.52 ( ( if @ A @ $false @ X @ Y )
% 2.75/1.52 = Y ) ).
% 2.75/1.52
% 2.75/1.52 thf(help_If_1_1_T,axiom,
% 2.75/1.52 ! [A: $tType,X: A,Y: A] :
% 2.75/1.52 ( ( if @ A @ $true @ X @ Y )
% 2.75/1.52 = X ) ).
% 2.75/1.52
% 2.75/1.52 thf(conj_0,hypothesis,
% 2.75/1.52 member @ ( coinductive_llist @ a ) @ t @ ( lList2236698231inlsts @ a @ a2 ) ).
% 2.75/1.52
% 2.75/1.52 thf(conj_1,conjecture,
% 2.75/1.52 member @ ( coinductive_llist @ a ) @ ( lList2508575361_ldrop @ a @ t @ i ) @ ( lList2236698231inlsts @ a @ a2 ) ).
% 2.75/1.52 ------------------------
% 2.75/1.54 % (27244)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_27050 for (2999ds/4Mi)
% 2.75/1.54 % (27248)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_27050 for (2999ds/275Mi)
% 2.75/1.54 % (27244)Instruction limit reached!
% 2.75/1.54 % (27244)------------------------------
% 2.75/1.54 % (27244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.54 % (27244)Termination reason: Unknown
% 2.75/1.54 % (27244)Termination phase: shuffling
% 2.75/1.54
% 2.75/1.54 % (27244)Memory used [KB]: 1407
% 2.75/1.54 % (27244)Time elapsed: 0.003 s
% 2.75/1.54 % (27244)Instructions burned: 4 (million)
% 2.75/1.54 % (27244)------------------------------
% 2.75/1.54 % (27244)------------------------------
% 2.75/1.54 % (27249)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27050 for (2999ds/18Mi)
% 2.75/1.54 % (27245)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_27050 for (2999ds/27Mi)
% 2.75/1.54 % (27246)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27050 for (2999ds/2Mi)
% 2.75/1.54 % (27243)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27050 for (2999ds/183Mi)
% 2.75/1.54 % (27246)Instruction limit reached!
% 2.75/1.54 % (27246)------------------------------
% 2.75/1.54 % (27246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.54 % (27246)Termination reason: Unknown
% 2.75/1.54 % (27246)Termination phase: shuffling
% 2.75/1.54
% 2.75/1.54 % (27246)Memory used [KB]: 1279
% 2.75/1.54 % (27246)Time elapsed: 0.003 s
% 2.75/1.54 % (27246)Instructions burned: 2 (million)
% 2.75/1.54 % (27246)------------------------------
% 2.75/1.54 % (27246)------------------------------
% 2.75/1.55 % (27247)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_27050 for (2999ds/2Mi)
% 2.75/1.55 % (27247)Instruction limit reached!
% 2.75/1.55 % (27247)------------------------------
% 2.75/1.55 % (27247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.55 % (27247)Termination reason: Unknown
% 2.75/1.55 % (27247)Termination phase: shuffling
% 2.75/1.55
% 2.75/1.55 % (27247)Memory used [KB]: 1407
% 2.75/1.55 % (27247)Time elapsed: 0.003 s
% 2.75/1.55 % (27247)Instructions burned: 4 (million)
% 2.75/1.55 % (27247)------------------------------
% 2.75/1.55 % (27247)------------------------------
% 2.75/1.55 % (27249)Instruction limit reached!
% 2.75/1.55 % (27249)------------------------------
% 2.75/1.55 % (27249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.55 % (27249)Termination reason: Unknown
% 2.75/1.55 % (27249)Termination phase: Property scanning
% 2.75/1.55
% 2.75/1.55 % (27249)Memory used [KB]: 1663
% 2.75/1.55 % (27249)Time elapsed: 0.009 s
% 2.75/1.55 % (27249)Instructions burned: 20 (million)
% 2.75/1.55 % (27249)------------------------------
% 2.75/1.55 % (27249)------------------------------
% 2.75/1.55 % (27250)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27050 for (2999ds/3Mi)
% 2.75/1.55 % (27250)Instruction limit reached!
% 2.75/1.55 % (27250)------------------------------
% 2.75/1.55 % (27250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.55 % (27250)Termination reason: Unknown
% 2.75/1.55 % (27250)Termination phase: shuffling
% 2.75/1.55
% 2.75/1.55 % (27250)Memory used [KB]: 1279
% 2.75/1.55 % (27250)Time elapsed: 0.002 s
% 2.75/1.55 % (27250)Instructions burned: 3 (million)
% 2.75/1.55 % (27250)------------------------------
% 2.75/1.55 % (27250)------------------------------
% 2.75/1.55 % (27245)Instruction limit reached!
% 2.75/1.55 % (27245)------------------------------
% 2.75/1.55 % (27245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.55 % (27245)Termination reason: Unknown
% 2.75/1.55 % (27245)Termination phase: Property scanning
% 2.75/1.55
% 2.75/1.55 % (27245)Memory used [KB]: 1663
% 2.75/1.55 % (27245)Time elapsed: 0.011 s
% 2.75/1.55 % (27245)Instructions burned: 29 (million)
% 2.75/1.55 % (27245)------------------------------
% 2.75/1.55 % (27245)------------------------------
% 2.75/1.55 % (27251)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_27050 for (2999ds/37Mi)
% 2.75/1.56 % (27252)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_27050 for (2999ds/15Mi)
% 2.75/1.56 % (27253)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_27050 for (2999ds/3Mi)
% 2.75/1.56 % (27254)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_27050 for (2999ds/1041Mi)
% 2.75/1.56 % (27253)Instruction limit reached!
% 2.75/1.56 % (27253)------------------------------
% 2.75/1.56 % (27253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.56 % (27253)Termination reason: Unknown
% 2.75/1.56 % (27253)Termination phase: shuffling
% 2.75/1.56
% 2.75/1.56 % (27253)Memory used [KB]: 1407
% 2.75/1.56 % (27253)Time elapsed: 0.003 s
% 2.75/1.56 % (27253)Instructions burned: 5 (million)
% 2.75/1.56 % (27253)------------------------------
% 2.75/1.56 % (27253)------------------------------
% 2.75/1.56 % (27252)Instruction limit reached!
% 2.75/1.56 % (27252)------------------------------
% 2.75/1.56 % (27252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.56 % (27252)Termination reason: Unknown
% 2.75/1.56 % (27252)Termination phase: shuffling
% 2.75/1.56
% 2.75/1.56 % (27252)Memory used [KB]: 1535
% 2.75/1.56 % (27252)Time elapsed: 0.007 s
% 2.75/1.56 % (27252)Instructions burned: 16 (million)
% 2.75/1.56 % (27252)------------------------------
% 2.75/1.56 % (27252)------------------------------
% 2.75/1.56 % (27255)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27050 for (2999ds/7Mi)
% 2.75/1.56 % (27248)Refutation not found, incomplete strategy
% 2.75/1.56 % (27248)------------------------------
% 2.75/1.56 % (27248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.56 % (27248)Termination reason: Refutation not found, incomplete strategy
% 2.75/1.56
% 2.75/1.56
% 2.75/1.56 % (27248)Memory used [KB]: 6524
% 2.75/1.56 % (27248)Time elapsed: 0.023 s
% 2.75/1.56 % (27248)Instructions burned: 67 (million)
% 2.75/1.56 % (27248)------------------------------
% 2.75/1.56 % (27248)------------------------------
% 2.75/1.57 % (27255)Instruction limit reached!
% 2.75/1.57 % (27255)------------------------------
% 2.75/1.57 % (27255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.57 % (27255)Termination reason: Unknown
% 2.75/1.57 % (27255)Termination phase: shuffling
% 2.75/1.57
% 2.75/1.57 % (27255)Memory used [KB]: 1407
% 2.75/1.57 % (27255)Time elapsed: 0.004 s
% 2.75/1.57 % (27255)Instructions burned: 8 (million)
% 2.75/1.57 % (27255)------------------------------
% 2.75/1.57 % (27255)------------------------------
% 2.75/1.57 % (27251)Instruction limit reached!
% 2.75/1.57 % (27251)------------------------------
% 2.75/1.57 % (27251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.57 % (27251)Termination reason: Unknown
% 2.75/1.57 % (27251)Termination phase: Property scanning
% 2.75/1.57
% 2.75/1.57 % (27251)Memory used [KB]: 2046
% 2.75/1.57 % (27251)Time elapsed: 0.017 s
% 2.75/1.57 % (27251)Instructions burned: 38 (million)
% 2.75/1.57 % (27251)------------------------------
% 2.75/1.57 % (27251)------------------------------
% 2.75/1.57 % (27257)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_27050 for (2999ds/3Mi)
% 2.75/1.57 % (27256)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27050 for (2999ds/16Mi)
% 2.75/1.57 % (27257)Instruction limit reached!
% 2.75/1.57 % (27257)------------------------------
% 2.75/1.57 % (27257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.57 % (27257)Termination reason: Unknown
% 2.75/1.57 % (27257)Termination phase: shuffling
% 2.75/1.57
% 2.75/1.57 % (27257)Memory used [KB]: 1279
% 2.75/1.57 % (27257)Time elapsed: 0.002 s
% 2.75/1.57 % (27257)Instructions burned: 3 (million)
% 2.75/1.57 % (27257)------------------------------
% 2.75/1.57 % (27257)------------------------------
% 2.75/1.57 % (27258)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_27050 for (2999ds/3Mi)
% 2.75/1.57 % (27258)Instruction limit reached!
% 2.75/1.57 % (27258)------------------------------
% 2.75/1.57 % (27258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.57 % (27258)Termination reason: Unknown
% 2.75/1.57 % (27258)Termination phase: shuffling
% 2.75/1.57
% 2.75/1.57 % (27258)Memory used [KB]: 1407
% 2.75/1.57 % (27258)Time elapsed: 0.003 s
% 2.75/1.57 % (27258)Instructions burned: 4 (million)
% 2.75/1.57 % (27258)------------------------------
% 2.75/1.57 % (27258)------------------------------
% 2.75/1.58 % (27259)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27050 for (2999ds/7Mi)
% 2.75/1.58 % (27256)Instruction limit reached!
% 2.75/1.58 % (27256)------------------------------
% 2.75/1.58 % (27256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.58 % (27256)Termination reason: Unknown
% 2.75/1.58 % (27256)Termination phase: shuffling
% 2.75/1.58
% 2.75/1.58 % (27256)Memory used [KB]: 1535
% 2.75/1.58 % (27256)Time elapsed: 0.008 s
% 2.75/1.58 % (27256)Instructions burned: 17 (million)
% 2.75/1.58 % (27256)------------------------------
% 2.75/1.58 % (27256)------------------------------
% 2.75/1.58 % (27259)Instruction limit reached!
% 2.75/1.58 % (27259)------------------------------
% 2.75/1.58 % (27259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.58 % (27259)Termination reason: Unknown
% 2.75/1.58 % (27259)Termination phase: shuffling
% 2.75/1.58
% 2.75/1.58 % (27259)Memory used [KB]: 1407
% 2.75/1.58 % (27259)Time elapsed: 0.004 s
% 2.75/1.58 % (27259)Instructions burned: 9 (million)
% 2.75/1.58 % (27259)------------------------------
% 2.75/1.58 % (27259)------------------------------
% 2.75/1.58 % (27263)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_27050 for (2999ds/3Mi)
% 2.75/1.58 % (27266)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_27050 for (2999ds/4Mi)
% 2.75/1.58 % (27263)Instruction limit reached!
% 2.75/1.58 % (27263)------------------------------
% 2.75/1.58 % (27263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.58 % (27263)Termination reason: Unknown
% 2.75/1.58 % (27263)Termination phase: shuffling
% 2.75/1.58
% 2.75/1.58 % (27263)Memory used [KB]: 1407
% 2.75/1.58 % (27263)Time elapsed: 0.003 s
% 2.75/1.58 % (27263)Instructions burned: 4 (million)
% 2.75/1.58 % (27263)------------------------------
% 2.75/1.58 % (27263)------------------------------
% 2.75/1.58 % (27266)Instruction limit reached!
% 2.75/1.58 % (27266)------------------------------
% 2.75/1.58 % (27266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.58 % (27266)Termination reason: Unknown
% 2.75/1.58 % (27266)Termination phase: shuffling
% 2.75/1.58
% 2.75/1.58 % (27266)Memory used [KB]: 1407
% 2.75/1.58 % (27266)Time elapsed: 0.003 s
% 2.75/1.58 % (27266)Instructions burned: 6 (million)
% 2.75/1.58 % (27266)------------------------------
% 2.75/1.58 % (27266)------------------------------
% 2.75/1.58 % (27267)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_27050 for (2999ds/18Mi)
% 2.75/1.59 % (27268)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_27050 for (2999ds/710Mi)
% 2.75/1.59 % (27269)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27050 for (2999ds/6Mi)
% 2.75/1.59 % (27267)Instruction limit reached!
% 2.75/1.59 % (27267)------------------------------
% 2.75/1.59 % (27267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.59 % (27267)Termination reason: Unknown
% 2.75/1.59 % (27267)Termination phase: shuffling
% 2.75/1.59
% 2.75/1.59 % (27267)Memory used [KB]: 1663
% 2.75/1.59 % (27267)Time elapsed: 0.007 s
% 2.75/1.59 % (27267)Instructions burned: 18 (million)
% 2.75/1.59 % (27267)------------------------------
% 2.75/1.59 % (27267)------------------------------
% 2.75/1.59 % (27269)Instruction limit reached!
% 2.75/1.59 % (27269)------------------------------
% 2.75/1.59 % (27269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.75/1.59 % (27269)Termination reason: Unknown
% 2.75/1.59 % (27269)Termination phase: shuffling
% 2.75/1.59
% 2.75/1.59 % (27269)Memory used [KB]: 1407
% 2.75/1.59 % (27269)Time elapsed: 0.004 s
% 2.75/1.59 % (27269)Instructions burned: 6 (million)
% 2.75/1.59 % (27269)------------------------------
% 2.75/1.59 % (27269)------------------------------
% 2.75/1.59 % (27270)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_27050 for (2999ds/902Mi)
% 2.75/1.59 % (27271)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_27050 for (2999ds/21Mi)
% 2.77/1.60 % (27271)Instruction limit reached!
% 2.77/1.60 % (27271)------------------------------
% 2.77/1.60 % (27271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.60 % (27271)Termination reason: Unknown
% 2.77/1.60 % (27271)Termination phase: shuffling
% 2.77/1.60
% 2.77/1.60 % (27271)Memory used [KB]: 1663
% 2.77/1.60 % (27271)Time elapsed: 0.008 s
% 2.77/1.60 % (27271)Instructions burned: 21 (million)
% 2.77/1.60 % (27271)------------------------------
% 2.77/1.60 % (27271)------------------------------
% 2.77/1.60 % (27273)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_27050 for (2999ds/6Mi)
% 2.77/1.60 % (27272)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_27050 for (2999ds/5Mi)
% 2.77/1.60 % (27272)Instruction limit reached!
% 2.77/1.60 % (27272)------------------------------
% 2.77/1.60 % (27272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.60 % (27272)Termination reason: Unknown
% 2.77/1.60 % (27272)Termination phase: shuffling
% 2.77/1.60
% 2.77/1.60 % (27272)Memory used [KB]: 1407
% 2.77/1.60 % (27272)Time elapsed: 0.004 s
% 2.77/1.60 % (27272)Instructions burned: 6 (million)
% 2.77/1.60 % (27272)------------------------------
% 2.77/1.60 % (27272)------------------------------
% 2.77/1.60 % (27273)Instruction limit reached!
% 2.77/1.60 % (27273)------------------------------
% 2.77/1.60 % (27273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.60 % (27273)Termination reason: Unknown
% 2.77/1.60 % (27273)Termination phase: shuffling
% 2.77/1.60
% 2.77/1.60 % (27273)Memory used [KB]: 1407
% 2.77/1.60 % (27273)Time elapsed: 0.004 s
% 2.77/1.60 % (27273)Instructions burned: 7 (million)
% 2.77/1.60 % (27273)------------------------------
% 2.77/1.60 % (27273)------------------------------
% 2.77/1.60 % (27243)Instruction limit reached!
% 2.77/1.60 % (27243)------------------------------
% 2.77/1.60 % (27243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.60 % (27243)Termination reason: Unknown
% 2.77/1.60 % (27243)Termination phase: Saturation
% 2.77/1.60
% 2.77/1.60 % (27243)Memory used [KB]: 6780
% 2.77/1.60 % (27243)Time elapsed: 0.063 s
% 2.77/1.60 % (27243)Instructions burned: 184 (million)
% 2.77/1.60 % (27243)------------------------------
% 2.77/1.60 % (27243)------------------------------
% 2.77/1.61 % (27276)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_27050 for (2999ds/377Mi)
% 2.77/1.61 % (27277)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_27050 for (2999ds/779Mi)
% 2.77/1.62 % (27278)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_27050 for (2999ds/19Mi)
% 2.77/1.62 % (27279)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_27050 for (2999ds/879Mi)
% 2.77/1.63 % (27278)Instruction limit reached!
% 2.77/1.63 % (27278)------------------------------
% 2.77/1.63 % (27278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.63 % (27278)Termination reason: Unknown
% 2.77/1.63 % (27278)Termination phase: shuffling
% 2.77/1.63
% 2.77/1.63 % (27278)Memory used [KB]: 1663
% 2.77/1.63 % (27278)Time elapsed: 0.012 s
% 2.77/1.63 % (27278)Instructions burned: 20 (million)
% 2.77/1.63 % (27278)------------------------------
% 2.77/1.63 % (27278)------------------------------
% 2.77/1.64 % (27288)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_27050 for (2999ds/17Mi)
% 2.77/1.65 % (27288)Instruction limit reached!
% 2.77/1.65 % (27288)------------------------------
% 2.77/1.65 % (27288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.65 % (27288)Termination reason: Unknown
% 2.77/1.65 % (27288)Termination phase: shuffling
% 2.77/1.65
% 2.77/1.65 % (27288)Memory used [KB]: 1535
% 2.77/1.65 % (27288)Time elapsed: 0.010 s
% 2.77/1.65 % (27288)Instructions burned: 17 (million)
% 2.77/1.65 % (27288)------------------------------
% 2.77/1.65 % (27288)------------------------------
% 2.77/1.67 % (27296)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_27050 for (2998ds/3Mi)
% 2.77/1.67 % (27296)Instruction limit reached!
% 2.77/1.67 % (27296)------------------------------
% 2.77/1.67 % (27296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.67 % (27296)Termination reason: Unknown
% 2.77/1.67 % (27296)Termination phase: shuffling
% 2.77/1.67
% 2.77/1.67 % (27296)Memory used [KB]: 1407
% 2.77/1.67 % (27296)Time elapsed: 0.004 s
% 2.77/1.67 % (27296)Instructions burned: 4 (million)
% 2.77/1.67 % (27296)------------------------------
% 2.77/1.67 % (27296)------------------------------
% 2.77/1.69 % (27301)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_27050 for (2998ds/30Mi)
% 2.77/1.70 % (27301)Instruction limit reached!
% 2.77/1.70 % (27301)------------------------------
% 2.77/1.70 % (27301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.70 % (27301)Termination reason: Unknown
% 2.77/1.70 % (27301)Termination phase: Property scanning
% 2.77/1.70
% 2.77/1.70 % (27301)Memory used [KB]: 1663
% 2.77/1.70 % (27301)Time elapsed: 0.014 s
% 2.77/1.70 % (27301)Instructions burned: 31 (million)
% 2.77/1.70 % (27301)------------------------------
% 2.77/1.70 % (27301)------------------------------
% 2.77/1.71 % (27309)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_27050 for (2998ds/127Mi)
% 2.77/1.77 % (27309)Instruction limit reached!
% 2.77/1.77 % (27309)------------------------------
% 2.77/1.77 % (27309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.77 % (27309)Termination reason: Unknown
% 2.77/1.77 % (27309)Termination phase: Saturation
% 2.77/1.77
% 2.77/1.77 % (27309)Memory used [KB]: 6780
% 2.77/1.77 % (27309)Time elapsed: 0.060 s
% 2.77/1.77 % (27309)Instructions burned: 127 (million)
% 2.77/1.77 % (27309)------------------------------
% 2.77/1.77 % (27309)------------------------------
% 2.77/1.79 % (27315)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_27050 for (2997ds/100Mi)
% 2.77/1.80 % (27276)Instruction limit reached!
% 2.77/1.80 % (27276)------------------------------
% 2.77/1.80 % (27276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.80 % (27276)Termination reason: Unknown
% 2.77/1.80 % (27276)Termination phase: Saturation
% 2.77/1.80
% 2.77/1.80 % (27276)Memory used [KB]: 7547
% 2.77/1.80 % (27276)Time elapsed: 0.189 s
% 2.77/1.80 % (27276)Instructions burned: 377 (million)
% 2.77/1.80 % (27276)------------------------------
% 2.77/1.80 % (27276)------------------------------
% 2.77/1.82 % (27317)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_27050 for (2997ds/3Mi)
% 2.77/1.82 % (27317)Instruction limit reached!
% 2.77/1.82 % (27317)------------------------------
% 2.77/1.82 % (27317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.82 % (27317)Termination reason: Unknown
% 2.77/1.82 % (27317)Termination phase: shuffling
% 2.77/1.82
% 2.77/1.82 % (27317)Memory used [KB]: 1279
% 2.77/1.82 % (27317)Time elapsed: 0.002 s
% 2.77/1.82 % (27317)Instructions burned: 3 (million)
% 2.77/1.82 % (27317)------------------------------
% 2.77/1.82 % (27317)------------------------------
% 2.77/1.83 % (27319)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_27050 for (2997ds/20Mi)
% 2.77/1.83 % (27315)Instruction limit reached!
% 2.77/1.83 % (27315)------------------------------
% 2.77/1.83 % (27315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.83 % (27315)Termination reason: Unknown
% 2.77/1.83 % (27315)Termination phase: Saturation
% 2.77/1.83
% 2.77/1.83 % (27315)Memory used [KB]: 6652
% 2.77/1.83 % (27315)Time elapsed: 0.041 s
% 2.77/1.83 % (27315)Instructions burned: 103 (million)
% 2.77/1.83 % (27315)------------------------------
% 2.77/1.83 % (27315)------------------------------
% 2.77/1.83 % (27319)Instruction limit reached!
% 2.77/1.83 % (27319)------------------------------
% 2.77/1.83 % (27319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.83 % (27319)Termination reason: Unknown
% 2.77/1.83 % (27319)Termination phase: Property scanning
% 2.77/1.83
% 2.77/1.83 % (27319)Memory used [KB]: 1663
% 2.77/1.83 % (27319)Time elapsed: 0.009 s
% 2.77/1.83 % (27319)Instructions burned: 23 (million)
% 2.77/1.83 % (27319)------------------------------
% 2.77/1.83 % (27319)------------------------------
% 2.77/1.84 % (27321)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_27050 for (2997ds/86Mi)
% 2.77/1.84 % (27322)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_27050 for (2996ds/107Mi)
% 2.77/1.86 % (27321)Instruction limit reached!
% 2.77/1.86 % (27321)------------------------------
% 2.77/1.86 % (27321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.86 % (27321)Termination reason: Unknown
% 2.77/1.86 % (27321)Termination phase: Saturation
% 2.77/1.86
% 2.77/1.86 % (27321)Memory used [KB]: 6524
% 2.77/1.86 % (27321)Time elapsed: 0.027 s
% 2.77/1.86 % (27321)Instructions burned: 86 (million)
% 2.77/1.86 % (27321)------------------------------
% 2.77/1.86 % (27321)------------------------------
% 2.77/1.87 % (27323)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_27050 for (2996ds/39Mi)
% 2.77/1.88 % (27322)Instruction limit reached!
% 2.77/1.88 % (27322)------------------------------
% 2.77/1.88 % (27322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.88 % (27322)Termination reason: Unknown
% 2.77/1.88 % (27322)Termination phase: Saturation
% 2.77/1.88
% 2.77/1.88 % (27322)Memory used [KB]: 6652
% 2.77/1.88 % (27322)Time elapsed: 0.034 s
% 2.77/1.88 % (27322)Instructions burned: 108 (million)
% 2.77/1.88 % (27322)------------------------------
% 2.77/1.88 % (27322)------------------------------
% 2.77/1.88 % (27268)Instruction limit reached!
% 2.77/1.88 % (27268)------------------------------
% 2.77/1.88 % (27268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.88 % (27268)Termination reason: Unknown
% 2.77/1.88 % (27268)Termination phase: Saturation
% 2.77/1.88
% 2.77/1.88 % (27268)Memory used [KB]: 7931
% 2.77/1.88 % (27268)Time elapsed: 0.296 s
% 2.77/1.88 % (27268)Instructions burned: 710 (million)
% 2.77/1.88 % (27268)------------------------------
% 2.77/1.88 % (27268)------------------------------
% 2.77/1.88 % (27323)Instruction limit reached!
% 2.77/1.88 % (27323)------------------------------
% 2.77/1.88 % (27323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.88 % (27323)Termination reason: Unknown
% 2.77/1.88 % (27323)Termination phase: Property scanning
% 2.77/1.88
% 2.77/1.88 % (27323)Memory used [KB]: 2046
% 2.77/1.88 % (27323)Time elapsed: 0.012 s
% 2.77/1.88 % (27323)Instructions burned: 41 (million)
% 2.77/1.88 % (27323)------------------------------
% 2.77/1.88 % (27323)------------------------------
% 2.77/1.89 % (27324)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_27050 for (2996ds/448Mi)
% 2.77/1.89 % (27326)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_27050 for (2996ds/98Mi)
% 2.77/1.90 % (27325)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_27050 for (2996ds/46Mi)
% 2.77/1.92 % (27254)Instruction limit reached!
% 2.77/1.92 % (27254)------------------------------
% 2.77/1.92 % (27254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.92 % (27254)Termination reason: Unknown
% 2.77/1.92 % (27254)Termination phase: Saturation
% 2.77/1.92
% 2.77/1.92 % (27254)Memory used [KB]: 9338
% 2.77/1.92 % (27254)Time elapsed: 0.359 s
% 2.77/1.92 % (27254)Instructions burned: 1043 (million)
% 2.77/1.92 % (27254)------------------------------
% 2.77/1.92 % (27254)------------------------------
% 2.77/1.92 % (27325)Instruction limit reached!
% 2.77/1.92 % (27325)------------------------------
% 2.77/1.92 % (27325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.92 % (27325)Termination reason: Unknown
% 2.77/1.92 % (27325)Termination phase: Property scanning
% 2.77/1.92
% 2.77/1.92 % (27325)Memory used [KB]: 1791
% 2.77/1.92 % (27325)Time elapsed: 0.022 s
% 2.77/1.92 % (27325)Instructions burned: 46 (million)
% 2.77/1.92 % (27325)------------------------------
% 2.77/1.92 % (27325)------------------------------
% 2.77/1.92 % (27326)Instruction limit reached!
% 2.77/1.92 % (27326)------------------------------
% 2.77/1.92 % (27326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.92 % (27326)Termination reason: Unknown
% 2.77/1.92 % (27326)Termination phase: Saturation
% 2.77/1.92
% 2.77/1.92 % (27326)Memory used [KB]: 2174
% 2.77/1.92 % (27326)Time elapsed: 0.029 s
% 2.77/1.92 % (27326)Instructions burned: 101 (million)
% 2.77/1.92 % (27326)------------------------------
% 2.77/1.92 % (27326)------------------------------
% 2.77/1.93 % (27277)Instruction limit reached!
% 2.77/1.93 % (27277)------------------------------
% 2.77/1.93 % (27277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.93 % (27277)Termination reason: Unknown
% 2.77/1.93 % (27277)Termination phase: Saturation
% 2.77/1.93
% 2.77/1.93 % (27277)Memory used [KB]: 7419
% 2.77/1.93 % (27277)Time elapsed: 0.312 s
% 2.77/1.93 % (27277)Instructions burned: 781 (million)
% 2.77/1.93 % (27277)------------------------------
% 2.77/1.93 % (27277)------------------------------
% 2.77/1.93 % (27327)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_27050 for (2996ds/507Mi)
% 2.77/1.93 % (27270)Instruction limit reached!
% 2.77/1.93 % (27270)------------------------------
% 2.77/1.93 % (27270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.93 % (27270)Termination reason: Unknown
% 2.77/1.93 % (27270)Termination phase: Saturation
% 2.77/1.93
% 2.77/1.93 % (27270)Memory used [KB]: 7419
% 2.77/1.93 % (27270)Time elapsed: 0.340 s
% 2.77/1.93 % (27270)Instructions burned: 903 (million)
% 2.77/1.93 % (27270)------------------------------
% 2.77/1.93 % (27270)------------------------------
% 2.77/1.93 % (27329)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_27050 for (2996ds/39Mi)
% 2.77/1.93 % (27328)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_27050 for (2996ds/149Mi)
% 2.77/1.94 % (27330)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_27050 for (2996ds/6Mi)
% 2.77/1.94 % (27330)Instruction limit reached!
% 2.77/1.94 % (27330)------------------------------
% 2.77/1.94 % (27330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.94 % (27330)Termination reason: Unknown
% 2.77/1.94 % (27330)Termination phase: shuffling
% 2.77/1.94
% 2.77/1.94 % (27330)Memory used [KB]: 1407
% 2.77/1.94 % (27330)Time elapsed: 0.003 s
% 2.77/1.94 % (27330)Instructions burned: 6 (million)
% 2.77/1.94 % (27330)------------------------------
% 2.77/1.94 % (27330)------------------------------
% 2.77/1.94 % (27331)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_27050 for (2996ds/1087Mi)
% 2.77/1.94 % (27329)Instruction limit reached!
% 2.77/1.94 % (27329)------------------------------
% 2.77/1.94 % (27329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.94 % (27329)Termination reason: Unknown
% 2.77/1.94 % (27329)Termination phase: Property scanning
% 2.77/1.94
% 2.77/1.94 % (27329)Memory used [KB]: 1918
% 2.77/1.94 % (27329)Time elapsed: 0.014 s
% 2.77/1.94 % (27329)Instructions burned: 41 (million)
% 2.77/1.94 % (27329)------------------------------
% 2.77/1.94 % (27329)------------------------------
% 2.77/1.95 % (27332)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_27050 for (2996ds/47Mi)
% 2.77/1.95 % (27333)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_27050 for (2995ds/44Mi)
% 2.77/1.96 % (27332)Instruction limit reached!
% 2.77/1.96 % (27332)------------------------------
% 2.77/1.96 % (27332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.96 % (27332)Termination reason: Unknown
% 2.77/1.96 % (27332)Termination phase: Property scanning
% 2.77/1.96
% 2.77/1.96 % (27332)Memory used [KB]: 1918
% 2.77/1.96 % (27332)Time elapsed: 0.015 s
% 2.77/1.96 % (27332)Instructions burned: 47 (million)
% 2.77/1.96 % (27332)------------------------------
% 2.77/1.96 % (27332)------------------------------
% 2.77/1.96 % (27333)Instruction limit reached!
% 2.77/1.96 % (27333)------------------------------
% 2.77/1.96 % (27333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.96 % (27333)Termination reason: Unknown
% 2.77/1.96 % (27333)Termination phase: Property scanning
% 2.77/1.96
% 2.77/1.96 % (27333)Memory used [KB]: 2046
% 2.77/1.96 % (27333)Time elapsed: 0.013 s
% 2.77/1.96 % (27333)Instructions burned: 45 (million)
% 2.77/1.96 % (27333)------------------------------
% 2.77/1.96 % (27333)------------------------------
% 2.77/1.97 % (27279)Instruction limit reached!
% 2.77/1.97 % (27279)------------------------------
% 2.77/1.97 % (27279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.97 % (27279)Termination reason: Unknown
% 2.77/1.97 % (27279)Termination phase: Saturation
% 2.77/1.97
% 2.77/1.97 % (27279)Memory used [KB]: 7931
% 2.77/1.97 % (27279)Time elapsed: 0.349 s
% 2.77/1.97 % (27279)Instructions burned: 881 (million)
% 2.77/1.97 % (27279)------------------------------
% 2.77/1.97 % (27279)------------------------------
% 2.77/1.97 % (27336)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_27050 for (2995ds/432Mi)
% 2.77/1.97 % (27338)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_27050 for (2995ds/62Mi)
% 2.77/1.98 % (27340)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_27050 for (2995ds/31Mi)
% 2.77/1.99 % (27340)Instruction limit reached!
% 2.77/1.99 % (27340)------------------------------
% 2.77/1.99 % (27340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.99 % (27340)Termination reason: Unknown
% 2.77/1.99 % (27340)Termination phase: Preprocessing 2
% 2.77/1.99
% 2.77/1.99 % (27340)Memory used [KB]: 1663
% 2.77/1.99 % (27340)Time elapsed: 0.011 s
% 2.77/1.99 % (27340)Instructions burned: 32 (million)
% 2.77/1.99 % (27340)------------------------------
% 2.77/1.99 % (27340)------------------------------
% 2.77/1.99 % (27328)Instruction limit reached!
% 2.77/1.99 % (27328)------------------------------
% 2.77/1.99 % (27328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.99 % (27328)Termination reason: Unknown
% 2.77/1.99 % (27328)Termination phase: Saturation
% 2.77/1.99
% 2.77/1.99 % (27328)Memory used [KB]: 6780
% 2.77/1.99 % (27328)Time elapsed: 0.080 s
% 2.77/1.99 % (27328)Instructions burned: 151 (million)
% 2.77/1.99 % (27328)------------------------------
% 2.77/1.99 % (27328)------------------------------
% 2.77/1.99 % (27338)Instruction limit reached!
% 2.77/1.99 % (27338)------------------------------
% 2.77/1.99 % (27338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.99 % (27338)Termination reason: Unknown
% 2.77/1.99 % (27338)Termination phase: Preprocessing 3
% 2.77/1.99
% 2.77/1.99 % (27338)Memory used [KB]: 2046
% 2.77/1.99 % (27338)Time elapsed: 0.018 s
% 2.77/1.99 % (27338)Instructions burned: 63 (million)
% 2.77/1.99 % (27338)------------------------------
% 2.77/1.99 % (27338)------------------------------
% 2.77/2.00 % (27351)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_27050 for (2995ds/96Mi)
% 2.77/2.00 % (27355)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_27050 for (2995ds/71Mi)
% 2.77/2.00 % (27352)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_27050 for (2995ds/453Mi)
% 6.06/2.02 % (27355)Instruction limit reached!
% 6.06/2.02 % (27355)------------------------------
% 6.06/2.02 % (27355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.02 % (27355)Termination reason: Unknown
% 6.06/2.02 % (27355)Termination phase: Saturation
% 6.06/2.02
% 6.06/2.02 % (27355)Memory used [KB]: 6524
% 6.06/2.02 % (27355)Time elapsed: 0.022 s
% 6.06/2.02 % (27355)Instructions burned: 73 (million)
% 6.06/2.02 % (27355)------------------------------
% 6.06/2.02 % (27355)------------------------------
% 6.06/2.02 % (27351)Instruction limit reached!
% 6.06/2.02 % (27351)------------------------------
% 6.06/2.02 % (27351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.02 % (27351)Termination reason: Unknown
% 6.06/2.02 % (27351)Termination phase: Saturation
% 6.06/2.02
% 6.06/2.02 % (27351)Memory used [KB]: 6652
% 6.06/2.02 % (27351)Time elapsed: 0.029 s
% 6.06/2.02 % (27351)Instructions burned: 97 (million)
% 6.06/2.02 % (27351)------------------------------
% 6.06/2.02 % (27351)------------------------------
% 6.06/2.02 % (27324)Instruction limit reached!
% 6.06/2.02 % (27324)------------------------------
% 6.06/2.02 % (27324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.02 % (27324)Termination reason: Unknown
% 6.06/2.02 % (27324)Termination phase: Saturation
% 6.06/2.02
% 6.06/2.02 % (27324)Memory used [KB]: 7675
% 6.06/2.02 % (27324)Time elapsed: 0.140 s
% 6.06/2.02 % (27324)Instructions burned: 450 (million)
% 6.06/2.02 % (27324)------------------------------
% 6.06/2.02 % (27324)------------------------------
% 6.06/2.03 % (27373)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_27050 for (2994ds/83Mi)
% 6.06/2.03 % (27375)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_27050 for (2994ds/11Mi)
% 6.06/2.03 % (27377)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_27050 for (2994ds/41Mi)
% 6.06/2.04 % (27375)Instruction limit reached!
% 6.06/2.04 % (27375)------------------------------
% 6.06/2.04 % (27375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.04 % (27375)Termination reason: Unknown
% 6.06/2.04 % (27375)Termination phase: shuffling
% 6.06/2.04
% 6.06/2.04 % (27375)Memory used [KB]: 1535
% 6.06/2.04 % (27375)Time elapsed: 0.004 s
% 6.06/2.04 % (27375)Instructions burned: 11 (million)
% 6.06/2.04 % (27375)------------------------------
% 6.06/2.04 % (27375)------------------------------
% 6.06/2.05 % (27383)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27050 for (2994ds/6Mi)
% 6.06/2.05 % (27377)Instruction limit reached!
% 6.06/2.05 % (27377)------------------------------
% 6.06/2.05 % (27377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.05 % (27377)Termination reason: Unknown
% 6.06/2.05 % (27377)Termination phase: Property scanning
% 6.06/2.05
% 6.06/2.05 % (27377)Memory used [KB]: 2046
% 6.06/2.05 % (27377)Time elapsed: 0.014 s
% 6.06/2.05 % (27377)Instructions burned: 43 (million)
% 6.06/2.05 % (27377)------------------------------
% 6.06/2.05 % (27377)------------------------------
% 6.06/2.05 % (27383)Instruction limit reached!
% 6.06/2.05 % (27383)------------------------------
% 6.06/2.05 % (27383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.05 % (27383)Termination reason: Unknown
% 6.06/2.05 % (27383)Termination phase: shuffling
% 6.06/2.05
% 6.06/2.05 % (27383)Memory used [KB]: 1407
% 6.06/2.05 % (27383)Time elapsed: 0.003 s
% 6.06/2.05 % (27383)Instructions burned: 6 (million)
% 6.06/2.05 % (27383)------------------------------
% 6.06/2.05 % (27383)------------------------------
% 6.06/2.06 % (27386)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_27050 for (2994ds/150Mi)
% 6.06/2.06 % (27387)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_27050 for (2994ds/343Mi)
% 6.06/2.06 % (27373)Instruction limit reached!
% 6.06/2.06 % (27373)------------------------------
% 6.06/2.06 % (27373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.06 % (27373)Termination reason: Unknown
% 6.06/2.06 % (27373)Termination phase: Saturation
% 6.06/2.06
% 6.06/2.06 % (27373)Memory used [KB]: 6524
% 6.06/2.06 % (27373)Time elapsed: 0.028 s
% 6.06/2.06 % (27373)Instructions burned: 85 (million)
% 6.06/2.06 % (27373)------------------------------
% 6.06/2.06 % (27373)------------------------------
% 6.06/2.07 % (27393)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_27050 for (2994ds/109Mi)
% 6.06/2.08 % (27327)Instruction limit reached!
% 6.06/2.08 % (27327)------------------------------
% 6.06/2.08 % (27327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.08 % (27327)Termination reason: Unknown
% 6.06/2.08 % (27327)Termination phase: Saturation
% 6.06/2.08
% 6.06/2.08 % (27327)Memory used [KB]: 7803
% 6.06/2.08 % (27327)Time elapsed: 0.176 s
% 6.06/2.08 % (27327)Instructions burned: 508 (million)
% 6.06/2.08 % (27327)------------------------------
% 6.06/2.08 % (27327)------------------------------
% 6.06/2.09 % (27404)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_27050 for (2994ds/253Mi)
% 6.06/2.10 % (27393)Instruction limit reached!
% 6.06/2.10 % (27393)------------------------------
% 6.06/2.10 % (27393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.10 % (27393)Termination reason: Unknown
% 6.06/2.10 % (27393)Termination phase: Saturation
% 6.06/2.10
% 6.06/2.10 % (27393)Memory used [KB]: 6652
% 6.06/2.10 % (27393)Time elapsed: 0.035 s
% 6.06/2.10 % (27393)Instructions burned: 112 (million)
% 6.06/2.10 % (27393)------------------------------
% 6.06/2.10 % (27393)------------------------------
% 6.06/2.10 % (27336)Instruction limit reached!
% 6.06/2.10 % (27336)------------------------------
% 6.06/2.10 % (27336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.10 % (27336)Termination reason: Unknown
% 6.06/2.10 % (27336)Termination phase: Saturation
% 6.06/2.10
% 6.06/2.10 % (27336)Memory used [KB]: 3454
% 6.06/2.10 % (27336)Time elapsed: 0.136 s
% 6.06/2.10 % (27336)Instructions burned: 433 (million)
% 6.06/2.10 % (27336)------------------------------
% 6.06/2.10 % (27336)------------------------------
% 6.06/2.11 % (27386)Instruction limit reached!
% 6.06/2.11 % (27386)------------------------------
% 6.06/2.11 % (27386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.06/2.11 % (27386)Termination reason: Unknown
% 6.06/2.11 % (27386)Termination phase: Saturation
% 6.06/2.11
% 6.06/2.11 % (27386)Memory used [KB]: 6908
% 6.06/2.11 % (27386)Time elapsed: 0.050 s
% 6.06/2.11 % (27386)Instructions burned: 152 (million)
% 6.06/2.11 % (27386)------------------------------
% 6.06/2.11 % (27386)------------------------------
% 6.06/2.11 % (27412)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_27050 for (2994ds/140Mi)
% 6.70/2.11 % (27415)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_27050 for (2994ds/614Mi)
% 6.70/2.11 % (27416)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_27050 for (2994ds/202Mi)
% 6.70/2.15 % (27412)Instruction limit reached!
% 6.70/2.15 % (27412)------------------------------
% 6.70/2.15 % (27412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.15 % (27412)Termination reason: Unknown
% 6.70/2.15 % (27412)Termination phase: Saturation
% 6.70/2.15
% 6.70/2.15 % (27412)Memory used [KB]: 6652
% 6.70/2.15 % (27412)Time elapsed: 0.044 s
% 6.70/2.15 % (27412)Instructions burned: 141 (million)
% 6.70/2.15 % (27412)------------------------------
% 6.70/2.15 % (27412)------------------------------
% 6.70/2.15 % (27352)Instruction limit reached!
% 6.70/2.15 % (27352)------------------------------
% 6.70/2.15 % (27352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.15 % (27352)Termination reason: Unknown
% 6.70/2.15 % (27352)Termination phase: Saturation
% 6.70/2.15
% 6.70/2.15 % (27352)Memory used [KB]: 7547
% 6.70/2.15 % (27352)Time elapsed: 0.154 s
% 6.70/2.15 % (27352)Instructions burned: 454 (million)
% 6.70/2.15 % (27352)------------------------------
% 6.70/2.15 % (27352)------------------------------
% 6.70/2.16 % (27438)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_27050 for (2993ds/339Mi)
% 6.70/2.16 % (27439)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_27050 for (2993ds/283Mi)
% 6.70/2.17 % (27387)Instruction limit reached!
% 6.70/2.17 % (27387)------------------------------
% 6.70/2.17 % (27387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.17 % (27387)Termination reason: Unknown
% 6.70/2.17 % (27387)Termination phase: Saturation
% 6.70/2.17
% 6.70/2.17 % (27387)Memory used [KB]: 7419
% 6.70/2.17 % (27387)Time elapsed: 0.109 s
% 6.70/2.17 % (27387)Instructions burned: 343 (million)
% 6.70/2.17 % (27387)------------------------------
% 6.70/2.17 % (27387)------------------------------
% 6.70/2.17 % (27404)Instruction limit reached!
% 6.70/2.17 % (27404)------------------------------
% 6.70/2.17 % (27404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.17 % (27404)Termination reason: Unknown
% 6.70/2.17 % (27404)Termination phase: Saturation
% 6.70/2.17
% 6.70/2.17 % (27404)Memory used [KB]: 7291
% 6.70/2.17 % (27404)Time elapsed: 0.080 s
% 6.70/2.17 % (27404)Instructions burned: 254 (million)
% 6.70/2.17 % (27404)------------------------------
% 6.70/2.17 % (27404)------------------------------
% 6.70/2.17 % (27445)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_27050 for (2993ds/134Mi)
% 6.70/2.18 % (27416)Instruction limit reached!
% 6.70/2.18 % (27416)------------------------------
% 6.70/2.18 % (27416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.18 % (27416)Termination reason: Unknown
% 6.70/2.18 % (27416)Termination phase: Saturation
% 6.70/2.18
% 6.70/2.18 % (27416)Memory used [KB]: 6780
% 6.70/2.18 % (27416)Time elapsed: 0.062 s
% 6.70/2.18 % (27416)Instructions burned: 203 (million)
% 6.70/2.18 % (27416)------------------------------
% 6.70/2.18 % (27416)------------------------------
% 6.70/2.18 % (27451)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_27050 for (2993ds/298Mi)
% 6.70/2.19 % (27456)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_27050 for (2993ds/192Mi)
% 7.16/2.22 % (27445)Instruction limit reached!
% 7.16/2.22 % (27445)------------------------------
% 7.16/2.22 % (27445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.16/2.22 % (27445)Termination reason: Unknown
% 7.16/2.22 % (27445)Termination phase: Saturation
% 7.16/2.22
% 7.16/2.22 % (27445)Memory used [KB]: 6780
% 7.16/2.22 % (27445)Time elapsed: 0.044 s
% 7.16/2.22 % (27445)Instructions burned: 135 (million)
% 7.16/2.22 % (27445)------------------------------
% 7.16/2.22 % (27445)------------------------------
% 7.16/2.23 % (27478)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_27050 for (2993ds/258Mi)
% 7.16/2.25 % (27456)Instruction limit reached!
% 7.16/2.25 % (27456)------------------------------
% 7.16/2.25 % (27456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.16/2.25 % (27456)Termination reason: Unknown
% 7.16/2.25 % (27456)Termination phase: Saturation
% 7.16/2.25
% 7.16/2.25 % (27456)Memory used [KB]: 7675
% 7.16/2.25 % (27456)Time elapsed: 0.061 s
% 7.16/2.25 % (27456)Instructions burned: 192 (million)
% 7.16/2.25 % (27456)------------------------------
% 7.16/2.25 % (27456)------------------------------
% 7.16/2.25 % (27490)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_27050 for (2992ds/90Mi)
% 7.16/2.26 % (27439)Instruction limit reached!
% 7.16/2.26 % (27439)------------------------------
% 7.16/2.26 % (27439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.16/2.26 % (27439)Termination reason: Unknown
% 7.16/2.26 % (27439)Termination phase: Saturation
% 7.16/2.26
% 7.16/2.26 % (27439)Memory used [KB]: 7291
% 7.16/2.26 % (27439)Time elapsed: 0.092 s
% 7.16/2.26 % (27439)Instructions burned: 284 (million)
% 7.16/2.26 % (27439)------------------------------
% 7.16/2.26 % (27439)------------------------------
% 7.16/2.26 % (27497)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_27050 for (2992ds/231Mi)
% 7.16/2.27 % (27438)Instruction limit reached!
% 7.16/2.27 % (27438)------------------------------
% 7.16/2.27 % (27438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.16/2.27 % (27438)Termination reason: Unknown
% 7.16/2.27 % (27438)Termination phase: Saturation
% 7.16/2.27
% 7.16/2.27 % (27438)Memory used [KB]: 7419
% 7.16/2.27 % (27438)Time elapsed: 0.106 s
% 7.16/2.27 % (27438)Instructions burned: 341 (million)
% 7.16/2.27 % (27438)------------------------------
% 7.16/2.27 % (27438)------------------------------
% 7.16/2.27 % (27451)Instruction limit reached!
% 7.16/2.27 % (27451)------------------------------
% 7.16/2.27 % (27451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.16/2.27 % (27451)Termination reason: Unknown
% 7.16/2.27 % (27451)Termination phase: Saturation
% 7.16/2.27
% 7.16/2.27 % (27451)Memory used [KB]: 7675
% 7.16/2.27 % (27451)Time elapsed: 0.093 s
% 7.16/2.27 % (27451)Instructions burned: 300 (million)
% 7.16/2.27 % (27451)------------------------------
% 7.16/2.27 % (27451)------------------------------
% 7.16/2.28 % (27501)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_27050 for (2992ds/458Mi)
% 7.16/2.28 % (27490)Instruction limit reached!
% 7.16/2.28 % (27490)------------------------------
% 7.16/2.28 % (27490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.16/2.28 % (27490)Termination reason: Unknown
% 7.16/2.28 % (27490)Termination phase: Saturation
% 7.16/2.28
% 7.16/2.28 % (27490)Memory used [KB]: 6524
% 7.16/2.28 % (27490)Time elapsed: 0.028 s
% 7.16/2.28 % (27490)Instructions burned: 92 (million)
% 7.16/2.28 % (27490)------------------------------
% 7.16/2.28 % (27490)------------------------------
% 7.16/2.28 % (27505)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_27050 for (2992ds/31Mi)
% 7.16/2.29 % (27331)Instruction limit reached!
% 7.16/2.29 % (27331)------------------------------
% 7.16/2.29 % (27331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.16/2.29 % (27331)Termination reason: Unknown
% 7.16/2.29 % (27331)Termination phase: Saturation
% 7.16/2.29
% 7.16/2.29 % (27331)Memory used [KB]: 7675
% 7.16/2.29 % (27331)Time elapsed: 0.370 s
% 7.16/2.29 % (27331)Instructions burned: 1087 (million)
% 7.16/2.29 % (27331)------------------------------
% 7.16/2.29 % (27331)------------------------------
% 7.16/2.29 % (27509)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_27050 for (2992ds/297Mi)
% 7.16/2.29 % (27505)Instruction limit reached!
% 7.16/2.29 % (27505)------------------------------
% 7.16/2.29 % (27505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.16/2.29 % (27505)Termination reason: Unknown
% 7.16/2.29 % (27505)Termination phase: Preprocessing 1
% 7.16/2.29
% 7.16/2.29 % (27505)Memory used [KB]: 1663
% 7.16/2.29 % (27505)Time elapsed: 0.011 s
% 7.16/2.29 % (27505)Instructions burned: 32 (million)
% 7.16/2.29 % (27505)------------------------------
% 7.16/2.29 % (27505)------------------------------
% 7.16/2.30 % (27511)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_27050 for (2992ds/987Mi)
% 7.75/2.30 % (27515)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_27050 for (2992ds/182Mi)
% 7.75/2.30 % (27415)Instruction limit reached!
% 7.75/2.30 % (27415)------------------------------
% 7.75/2.30 % (27415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.30 % (27415)Termination reason: Unknown
% 7.75/2.30 % (27415)Termination phase: Saturation
% 7.75/2.30
% 7.75/2.30 % (27415)Memory used [KB]: 7931
% 7.75/2.30 % (27415)Time elapsed: 0.190 s
% 7.75/2.30 % (27415)Instructions burned: 614 (million)
% 7.75/2.30 % (27415)------------------------------
% 7.75/2.30 % (27415)------------------------------
% 7.75/2.31 % (27478)Instruction limit reached!
% 7.75/2.31 % (27478)------------------------------
% 7.75/2.31 % (27478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.31 % (27478)Termination reason: Unknown
% 7.75/2.31 % (27478)Termination phase: Saturation
% 7.75/2.31
% 7.75/2.31 % (27478)Memory used [KB]: 7036
% 7.75/2.31 % (27478)Time elapsed: 0.085 s
% 7.75/2.31 % (27478)Instructions burned: 261 (million)
% 7.75/2.31 % (27478)------------------------------
% 7.75/2.31 % (27478)------------------------------
% 7.75/2.31 % (27519)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_27050 for (2992ds/182Mi)
% 7.75/2.32 % (27523)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_27050 for (2992ds/154Mi)
% 7.75/2.33 % (27497)Instruction limit reached!
% 7.75/2.33 % (27497)------------------------------
% 7.75/2.33 % (27497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.33 % (27497)Termination reason: Unknown
% 7.75/2.33 % (27497)Termination phase: Saturation
% 7.75/2.33
% 7.75/2.33 % (27497)Memory used [KB]: 7036
% 7.75/2.33 % (27497)Time elapsed: 0.067 s
% 7.75/2.33 % (27497)Instructions burned: 232 (million)
% 7.75/2.33 % (27497)------------------------------
% 7.75/2.33 % (27497)------------------------------
% 7.75/2.34 % (27534)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_27050 for (2992ds/79Mi)
% 7.75/2.36 % (27515)Instruction limit reached!
% 7.75/2.36 % (27515)------------------------------
% 7.75/2.36 % (27515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.36 % (27515)Termination reason: Unknown
% 7.75/2.36 % (27515)Termination phase: Saturation
% 7.75/2.36
% 7.75/2.36 % (27515)Memory used [KB]: 6908
% 7.75/2.36 % (27515)Time elapsed: 0.059 s
% 7.75/2.36 % (27515)Instructions burned: 182 (million)
% 7.75/2.36 % (27515)------------------------------
% 7.75/2.36 % (27515)------------------------------
% 7.75/2.36 % (27534)Instruction limit reached!
% 7.75/2.36 % (27534)------------------------------
% 7.75/2.36 % (27534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.36 % (27534)Termination reason: Unknown
% 7.75/2.36 % (27534)Termination phase: Saturation
% 7.75/2.36
% 7.75/2.36 % (27534)Memory used [KB]: 6524
% 7.75/2.36 % (27534)Time elapsed: 0.024 s
% 7.75/2.36 % (27534)Instructions burned: 79 (million)
% 7.75/2.36 % (27534)------------------------------
% 7.75/2.36 % (27534)------------------------------
% 7.75/2.36 % (27523)Instruction limit reached!
% 7.75/2.36 % (27523)------------------------------
% 7.75/2.36 % (27523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.36 % (27523)Termination reason: Unknown
% 7.75/2.36 % (27523)Termination phase: Saturation
% 7.75/2.36
% 7.75/2.36 % (27523)Memory used [KB]: 2686
% 7.75/2.36 % (27523)Time elapsed: 0.044 s
% 7.75/2.36 % (27523)Instructions burned: 156 (million)
% 7.75/2.36 % (27523)------------------------------
% 7.75/2.36 % (27523)------------------------------
% 7.75/2.37 % (27542)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_27050 for (2991ds/216Mi)
% 7.75/2.37 % (27519)Instruction limit reached!
% 7.75/2.37 % (27519)------------------------------
% 7.75/2.37 % (27519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.37 % (27519)Termination reason: Unknown
% 7.75/2.37 % (27519)Termination phase: Saturation
% 7.75/2.37
% 7.75/2.37 % (27519)Memory used [KB]: 6908
% 7.75/2.37 % (27519)Time elapsed: 0.060 s
% 7.75/2.37 % (27519)Instructions burned: 183 (million)
% 7.75/2.37 % (27519)------------------------------
% 7.75/2.37 % (27519)------------------------------
% 7.75/2.37 % (27544)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_27050 for (2991ds/114Mi)
% 7.75/2.37 % (27545)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_27050 for (2991ds/922Mi)
% 7.75/2.38 % (27509)Instruction limit reached!
% 7.75/2.38 % (27509)------------------------------
% 7.75/2.38 % (27509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.38 % (27509)Termination reason: Unknown
% 7.75/2.38 % (27509)Termination phase: Saturation
% 7.75/2.38
% 7.75/2.38 % (27509)Memory used [KB]: 7036
% 7.75/2.38 % (27509)Time elapsed: 0.088 s
% 7.75/2.38 % (27509)Instructions burned: 298 (million)
% 7.75/2.38 % (27509)------------------------------
% 7.75/2.38 % (27509)------------------------------
% 7.75/2.38 % (27551)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_27050 for (2991ds/182Mi)
% 7.75/2.39 % (27554)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_27050 for (2991ds/164Mi)
% 8.43/2.41 % (27544)Instruction limit reached!
% 8.43/2.41 % (27544)------------------------------
% 8.43/2.41 % (27544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.41 % (27544)Termination reason: Unknown
% 8.43/2.41 % (27544)Termination phase: Saturation
% 8.43/2.41
% 8.43/2.41 % (27544)Memory used [KB]: 6780
% 8.43/2.41 % (27544)Time elapsed: 0.035 s
% 8.43/2.41 % (27544)Instructions burned: 114 (million)
% 8.43/2.41 % (27544)------------------------------
% 8.43/2.41 % (27544)------------------------------
% 8.43/2.42 % (27564)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_27050 for (2991ds/50Mi)
% 8.43/2.42 % (27501)Refutation not found, non-redundant clauses discarded% (27501)------------------------------
% 8.43/2.42 % (27501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.42 % (27501)Termination reason: Refutation not found, non-redundant clauses discarded
% 8.43/2.42
% 8.43/2.42 % (27501)Memory used [KB]: 7803
% 8.43/2.42 % (27501)Time elapsed: 0.145 s
% 8.43/2.42 % (27501)Instructions burned: 454 (million)
% 8.43/2.42 % (27501)------------------------------
% 8.43/2.42 % (27501)------------------------------
% 8.43/2.43 % (27564)Instruction limit reached!
% 8.43/2.43 % (27564)------------------------------
% 8.43/2.43 % (27564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.43 % (27564)Termination reason: Unknown
% 8.43/2.43 % (27564)Termination phase: Property scanning
% 8.43/2.43
% 8.43/2.43 % (27564)Memory used [KB]: 2046
% 8.43/2.43 % (27564)Time elapsed: 0.015 s
% 8.43/2.43 % (27564)Instructions burned: 52 (million)
% 8.43/2.43 % (27564)------------------------------
% 8.43/2.43 % (27564)------------------------------
% 8.43/2.43 % (27573)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_27050 for (2991ds/368Mi)
% 8.43/2.43 % (27551)Instruction limit reached!
% 8.43/2.43 % (27551)------------------------------
% 8.43/2.43 % (27551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.43 % (27551)Termination reason: Unknown
% 8.43/2.43 % (27551)Termination phase: Saturation
% 8.43/2.43
% 8.43/2.43 % (27551)Memory used [KB]: 6908
% 8.43/2.43 % (27551)Time elapsed: 0.053 s
% 8.43/2.43 % (27551)Instructions burned: 185 (million)
% 8.43/2.43 % (27551)------------------------------
% 8.43/2.43 % (27551)------------------------------
% 8.43/2.43 % (27542)Instruction limit reached!
% 8.43/2.43 % (27542)------------------------------
% 8.43/2.43 % (27542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.43 % (27542)Termination reason: Unknown
% 8.43/2.43 % (27542)Termination phase: Saturation
% 8.43/2.43
% 8.43/2.43 % (27542)Memory used [KB]: 7036
% 8.43/2.43 % (27542)Time elapsed: 0.066 s
% 8.43/2.43 % (27542)Instructions burned: 217 (million)
% 8.43/2.43 % (27542)------------------------------
% 8.43/2.43 % (27542)------------------------------
% 8.43/2.44 % (27554)Instruction limit reached!
% 8.43/2.44 % (27554)------------------------------
% 8.43/2.44 % (27554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.44 % (27554)Termination reason: Unknown
% 8.43/2.44 % (27554)Termination phase: Saturation
% 8.43/2.44
% 8.43/2.44 % (27554)Memory used [KB]: 2302
% 8.43/2.44 % (27554)Time elapsed: 0.050 s
% 8.43/2.44 % (27554)Instructions burned: 167 (million)
% 8.43/2.44 % (27554)------------------------------
% 8.43/2.44 % (27554)------------------------------
% 8.43/2.44 % (27579)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_27050 for (2991ds/1021Mi)
% 8.43/2.44 % (27583)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_27050 for (2990ds/267Mi)
% 8.43/2.44 % (27584)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_27050 for (2990ds/204Mi)
% 8.43/2.45 % (27587)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_27050 for (2990ds/26Mi)
% 8.43/2.45 % (27587)Instruction limit reached!
% 8.43/2.45 % (27587)------------------------------
% 8.43/2.45 % (27587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.45 % (27587)Termination reason: Unknown
% 8.43/2.45 % (27587)Termination phase: shuffling
% 8.43/2.45
% 8.43/2.45 % (27587)Memory used [KB]: 1791
% 8.43/2.45 % (27587)Time elapsed: 0.009 s
% 8.43/2.45 % (27587)Instructions burned: 28 (million)
% 8.43/2.45 % (27587)------------------------------
% 8.43/2.45 % (27587)------------------------------
% 8.43/2.46 % (27601)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_27050 for (2990ds/53Mi)
% 8.43/2.48 % (27601)Instruction limit reached!
% 8.43/2.48 % (27601)------------------------------
% 8.43/2.48 % (27601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.43/2.48 % (27601)Termination reason: Unknown
% 8.43/2.48 % (27601)Termination phase: Property scanning
% 8.43/2.48
% 8.43/2.48 % (27601)Memory used [KB]: 2046
% 8.43/2.48 % (27601)Time elapsed: 0.015 s
% 8.43/2.48 % (27601)Instructions burned: 53 (million)
% 8.43/2.48 % (27601)------------------------------
% 8.43/2.48 % (27601)------------------------------
% 8.43/2.49 % (27610)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_27050 for (2990ds/4436Mi)
% 8.90/2.51 % (27584)Instruction limit reached!
% 8.90/2.51 % (27584)------------------------------
% 8.90/2.51 % (27584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.51 % (27584)Termination reason: Unknown
% 8.90/2.51 % (27584)Termination phase: Saturation
% 8.90/2.51
% 8.90/2.51 % (27584)Memory used [KB]: 6780
% 8.90/2.51 % (27584)Time elapsed: 0.066 s
% 8.90/2.51 % (27584)Instructions burned: 205 (million)
% 8.90/2.51 % (27584)------------------------------
% 8.90/2.51 % (27584)------------------------------
% 8.90/2.52 % (27612)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_27050 for (2990ds/1539Mi)
% 8.90/2.53 % (27583)Instruction limit reached!
% 8.90/2.53 % (27583)------------------------------
% 8.90/2.53 % (27583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.53 % (27583)Termination reason: Unknown
% 8.90/2.53 % (27583)Termination phase: Saturation
% 8.90/2.53
% 8.90/2.53 % (27583)Memory used [KB]: 7291
% 8.90/2.53 % (27583)Time elapsed: 0.085 s
% 8.90/2.53 % (27583)Instructions burned: 267 (million)
% 8.90/2.53 % (27583)------------------------------
% 8.90/2.53 % (27583)------------------------------
% 8.90/2.53 % (27573)Instruction limit reached!
% 8.90/2.53 % (27573)------------------------------
% 8.90/2.53 % (27573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.53 % (27573)Termination reason: Unknown
% 8.90/2.53 % (27573)Termination phase: Saturation
% 8.90/2.53
% 8.90/2.53 % (27573)Memory used [KB]: 7036
% 8.90/2.53 % (27573)Time elapsed: 0.126 s
% 8.90/2.53 % (27573)Instructions burned: 369 (million)
% 8.90/2.53 % (27573)------------------------------
% 8.90/2.53 % (27573)------------------------------
% 8.90/2.54 % (27613)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_27050 for (2989ds/408Mi)
% 8.90/2.54 % (27614)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_27050 for (2989ds/5205Mi)
% 9.17/2.60 % (27511)Instruction limit reached!
% 9.17/2.60 % (27511)------------------------------
% 9.17/2.60 % (27511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.17/2.60 % (27511)Termination reason: Unknown
% 9.17/2.60 % (27511)Termination phase: Saturation
% 9.17/2.60
% 9.17/2.60 % (27511)Memory used [KB]: 8443
% 9.17/2.60 % (27511)Time elapsed: 0.304 s
% 9.17/2.60 % (27511)Instructions burned: 987 (million)
% 9.17/2.60 % (27511)------------------------------
% 9.17/2.60 % (27511)------------------------------
% 9.17/2.61 % (27615)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_27050 for (2989ds/1913Mi)
% 9.17/2.66 % (27613)Instruction limit reached!
% 9.17/2.66 % (27613)------------------------------
% 9.17/2.66 % (27613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.17/2.66 % (27613)Termination reason: Unknown
% 9.17/2.66 % (27613)Termination phase: Saturation
% 9.17/2.66
% 9.17/2.66 % (27613)Memory used [KB]: 7547
% 9.17/2.66 % (27613)Time elapsed: 0.127 s
% 9.17/2.66 % (27613)Instructions burned: 411 (million)
% 9.17/2.66 % (27613)------------------------------
% 9.17/2.66 % (27613)------------------------------
% 9.17/2.67 % (27545)Instruction limit reached!
% 9.17/2.67 % (27545)------------------------------
% 9.17/2.67 % (27545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.17/2.67 % (27545)Termination reason: Unknown
% 9.17/2.67 % (27545)Termination phase: Saturation
% 9.17/2.67
% 9.17/2.67 % (27545)Memory used [KB]: 7419
% 9.17/2.67 % (27545)Time elapsed: 0.314 s
% 9.17/2.67 % (27545)Instructions burned: 923 (million)
% 9.17/2.67 % (27545)------------------------------
% 9.17/2.67 % (27545)------------------------------
% 9.17/2.67 % (27616)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_27050 for (2988ds/4350Mi)
% 9.17/2.67 % (27617)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_27050 for (2988ds/68Mi)
% 9.17/2.68 % (27616)Refutation not found, incomplete strategy
% 9.17/2.68 % (27616)------------------------------
% 9.17/2.68 % (27616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.17/2.68 % (27616)Termination reason: Refutation not found, incomplete strategy
% 9.17/2.68
% 9.17/2.68
% 9.17/2.68 % (27616)Memory used [KB]: 6140
% 9.17/2.68 % (27616)Time elapsed: 0.012 s
% 9.17/2.68 % (27616)Instructions burned: 35 (million)
% 9.17/2.68 % (27616)------------------------------
% 9.17/2.68 % (27616)------------------------------
% 9.17/2.69 % (27618)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_27050 for (2988ds/358Mi)
% 9.17/2.69 % (27617)Instruction limit reached!
% 9.17/2.69 % (27617)------------------------------
% 9.17/2.69 % (27617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.17/2.69 % (27617)Termination reason: Unknown
% 9.17/2.69 % (27617)Termination phase: Saturation
% 9.17/2.69
% 9.17/2.69 % (27617)Memory used [KB]: 1918
% 9.17/2.69 % (27617)Time elapsed: 0.021 s
% 9.17/2.69 % (27617)Instructions burned: 69 (million)
% 9.17/2.69 % (27617)------------------------------
% 9.17/2.69 % (27617)------------------------------
% 9.98/2.70 % (27619)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_27050 for (2988ds/31Mi)
% 9.98/2.71 % (27619)Instruction limit reached!
% 9.98/2.71 % (27619)------------------------------
% 9.98/2.71 % (27619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.71 % (27619)Termination reason: Unknown
% 9.98/2.71 % (27619)Termination phase: Preprocessing 1
% 9.98/2.71
% 9.98/2.71 % (27619)Memory used [KB]: 1663
% 9.98/2.71 % (27619)Time elapsed: 0.011 s
% 9.98/2.71 % (27619)Instructions burned: 32 (million)
% 9.98/2.71 % (27619)------------------------------
% 9.98/2.71 % (27619)------------------------------
% 9.98/2.72 % (27620)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_27050 for (2988ds/279Mi)
% 9.98/2.75 % (27620)Refutation not found, incomplete strategy
% 9.98/2.75 % (27620)------------------------------
% 9.98/2.75 % (27620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.75 % (27620)Termination reason: Refutation not found, incomplete strategy
% 9.98/2.75
% 9.98/2.75
% 9.98/2.75 % (27620)Memory used [KB]: 6780
% 9.98/2.75 % (27620)Time elapsed: 0.027 s
% 9.98/2.75 % (27620)Instructions burned: 97 (million)
% 9.98/2.75 % (27620)------------------------------
% 9.98/2.75 % (27620)------------------------------
% 9.98/2.75 % (27579)Instruction limit reached!
% 9.98/2.75 % (27579)------------------------------
% 9.98/2.75 % (27579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.75 % (27579)Termination reason: Unknown
% 9.98/2.75 % (27579)Termination phase: Saturation
% 9.98/2.75
% 9.98/2.75 % (27579)Memory used [KB]: 8187
% 9.98/2.75 % (27579)Time elapsed: 0.339 s
% 9.98/2.75 % (27579)Instructions burned: 1022 (million)
% 9.98/2.75 % (27579)------------------------------
% 9.98/2.75 % (27579)------------------------------
% 9.98/2.76 % (27621)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_27050 for (2987ds/258Mi)
% 9.98/2.76 % (27622)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_27050 for (2987ds/26Mi)
% 9.98/2.77 % (27622)Instruction limit reached!
% 9.98/2.77 % (27622)------------------------------
% 9.98/2.77 % (27622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.98/2.77 % (27622)Termination reason: Unknown
% 9.98/2.77 % (27622)Termination phase: shuffling
% 9.98/2.77
% 9.98/2.77 % (27622)Memory used [KB]: 1791
% 9.98/2.77 % (27622)Time elapsed: 0.008 s
% 9.98/2.77 % (27622)Instructions burned: 26 (million)
% 9.98/2.77 % (27622)------------------------------
% 9.98/2.77 % (27622)------------------------------
% 9.98/2.79 % (27623)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_27050 for (2987ds/995Mi)
% 10.37/2.81 % (27618)Instruction limit reached!
% 10.37/2.81 % (27618)------------------------------
% 10.37/2.81 % (27618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.37/2.81 % (27618)Termination reason: Unknown
% 10.37/2.81 % (27618)Termination phase: Saturation
% 10.37/2.81
% 10.37/2.81 % (27618)Memory used [KB]: 7164
% 10.37/2.81 % (27618)Time elapsed: 0.114 s
% 10.37/2.81 % (27618)Instructions burned: 359 (million)
% 10.37/2.81 % (27618)------------------------------
% 10.37/2.81 % (27618)------------------------------
% 10.37/2.82 % (27624)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_27050 for (2987ds/373Mi)
% 10.37/2.84 % (27621)Instruction limit reached!
% 10.37/2.84 % (27621)------------------------------
% 10.37/2.84 % (27621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.37/2.84 % (27621)Termination reason: Unknown
% 10.37/2.84 % (27621)Termination phase: Saturation
% 10.37/2.84
% 10.37/2.84 % (27621)Memory used [KB]: 7164
% 10.37/2.84 % (27621)Time elapsed: 0.082 s
% 10.37/2.84 % (27621)Instructions burned: 260 (million)
% 10.37/2.84 % (27621)------------------------------
% 10.37/2.84 % (27621)------------------------------
% 10.37/2.85 % (27625)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_27050 for (2986ds/253Mi)
% 10.58/2.92 % (27625)Instruction limit reached!
% 10.58/2.92 % (27625)------------------------------
% 10.58/2.92 % (27625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.58/2.92 % (27625)Termination reason: Unknown
% 10.58/2.92 % (27625)Termination phase: Saturation
% 10.58/2.92
% 10.58/2.92 % (27625)Memory used [KB]: 7547
% 10.58/2.92 % (27625)Time elapsed: 0.074 s
% 10.58/2.92 % (27625)Instructions burned: 256 (million)
% 10.58/2.92 % (27625)------------------------------
% 10.58/2.92 % (27625)------------------------------
% 10.58/2.93 % (27626)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_27050 for (2986ds/832Mi)
% 10.58/2.93 % (27624)Instruction limit reached!
% 10.58/2.93 % (27624)------------------------------
% 10.58/2.93 % (27624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.58/2.93 % (27624)Termination reason: Unknown
% 10.58/2.93 % (27624)Termination phase: Saturation
% 10.58/2.93
% 10.58/2.93 % (27624)Memory used [KB]: 6908
% 10.58/2.93 % (27624)Time elapsed: 0.120 s
% 10.58/2.93 % (27624)Instructions burned: 375 (million)
% 10.58/2.93 % (27624)------------------------------
% 10.58/2.93 % (27624)------------------------------
% 10.58/2.94 % (27627)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_27050 for (2985ds/668Mi)
% 10.58/2.99 % (27612)Instruction limit reached!
% 10.58/2.99 % (27612)------------------------------
% 10.58/2.99 % (27612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.58/2.99 % (27612)Termination reason: Unknown
% 10.58/2.99 % (27612)Termination phase: Saturation
% 10.58/2.99
% 10.58/2.99 % (27612)Memory used [KB]: 10490
% 10.58/2.99 % (27612)Time elapsed: 0.471 s
% 10.58/2.99 % (27612)Instructions burned: 1540 (million)
% 10.58/2.99 % (27612)------------------------------
% 10.58/2.99 % (27612)------------------------------
% 10.58/3.00 % (27628)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_27050 for (2985ds/40Mi)
% 10.58/3.01 % (27628)Instruction limit reached!
% 10.58/3.01 % (27628)------------------------------
% 10.58/3.01 % (27628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.58/3.01 % (27628)Termination reason: Unknown
% 10.58/3.01 % (27628)Termination phase: Property scanning
% 10.58/3.01
% 10.58/3.01 % (27628)Memory used [KB]: 2046
% 10.58/3.01 % (27628)Time elapsed: 0.013 s
% 10.58/3.01 % (27628)Instructions burned: 43 (million)
% 10.58/3.01 % (27628)------------------------------
% 10.58/3.01 % (27628)------------------------------
% 10.58/3.01 % (27615)Instruction limit reached!
% 10.58/3.01 % (27615)------------------------------
% 10.58/3.01 % (27615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.58/3.01 % (27615)Termination reason: Unknown
% 10.58/3.01 % (27615)Termination phase: Saturation
% 10.58/3.01
% 10.58/3.01 % (27615)Memory used [KB]: 2430
% 10.58/3.01 % (27615)Time elapsed: 0.404 s
% 10.58/3.01 % (27615)Instructions burned: 1917 (million)
% 10.58/3.01 % (27615)------------------------------
% 10.58/3.01 % (27615)------------------------------
% 13.10/3.02 % (27629)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_27050 for (2985ds/294Mi)
% 13.10/3.02 % (27630)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_27050 for (2985ds/187Mi)
% 13.10/3.04 % (27629)Refutation not found, incomplete strategy
% 13.10/3.04 % (27629)------------------------------
% 13.10/3.04 % (27629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.10/3.04 % (27629)Termination reason: Refutation not found, incomplete strategy
% 13.10/3.04
% 13.10/3.04
% 13.10/3.04 % (27629)Memory used [KB]: 6524
% 13.10/3.04 % (27629)Time elapsed: 0.019 s
% 13.10/3.04 % (27629)Instructions burned: 67 (million)
% 13.10/3.04 % (27629)------------------------------
% 13.10/3.04 % (27629)------------------------------
% 13.10/3.05 % (27631)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_27050 for (2984ds/371Mi)
% 13.10/3.08 % (27630)Instruction limit reached!
% 13.10/3.08 % (27630)------------------------------
% 13.10/3.08 % (27630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.10/3.08 % (27630)Termination reason: Unknown
% 13.10/3.08 % (27630)Termination phase: Saturation
% 13.10/3.08
% 13.10/3.08 % (27630)Memory used [KB]: 6780
% 13.10/3.08 % (27630)Time elapsed: 0.079 s
% 13.10/3.08 % (27630)Instructions burned: 190 (million)
% 13.10/3.08 % (27630)------------------------------
% 13.10/3.08 % (27630)------------------------------
% 13.10/3.09 % (27632)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_27050 for (2984ds/1827Mi)
% 13.69/3.15 % (27627)Instruction limit reached!
% 13.69/3.15 % (27627)------------------------------
% 13.69/3.15 % (27627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.15 % (27627)Termination reason: Unknown
% 13.69/3.15 % (27627)Termination phase: Saturation
% 13.69/3.15
% 13.69/3.15 % (27627)Memory used [KB]: 13688
% 13.69/3.15 % (27627)Time elapsed: 0.204 s
% 13.69/3.15 % (27627)Instructions burned: 669 (million)
% 13.69/3.15 % (27627)------------------------------
% 13.69/3.15 % (27627)------------------------------
% 13.69/3.16 % (27633)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_27050 for (2983ds/70Mi)
% 13.69/3.17 % (27631)Instruction limit reached!
% 13.69/3.17 % (27631)------------------------------
% 13.69/3.17 % (27631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.17 % (27631)Termination reason: Unknown
% 13.69/3.17 % (27631)Termination phase: Saturation
% 13.69/3.17
% 13.69/3.17 % (27631)Memory used [KB]: 7164
% 13.69/3.17 % (27631)Time elapsed: 0.146 s
% 13.69/3.17 % (27631)Instructions burned: 371 (million)
% 13.69/3.17 % (27631)------------------------------
% 13.69/3.17 % (27631)------------------------------
% 13.69/3.17 % (27623)Instruction limit reached!
% 13.69/3.17 % (27623)------------------------------
% 13.69/3.17 % (27623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.17 % (27623)Termination reason: Unknown
% 13.69/3.17 % (27623)Termination phase: Saturation
% 13.69/3.17
% 13.69/3.17 % (27623)Memory used [KB]: 9210
% 13.69/3.17 % (27623)Time elapsed: 0.387 s
% 13.69/3.17 % (27623)Instructions burned: 995 (million)
% 13.69/3.17 % (27623)------------------------------
% 13.69/3.17 % (27623)------------------------------
% 13.69/3.18 % (27633)Instruction limit reached!
% 13.69/3.18 % (27633)------------------------------
% 13.69/3.18 % (27633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.18 % (27633)Termination reason: Unknown
% 13.69/3.18 % (27633)Termination phase: Property scanning
% 13.69/3.18
% 13.69/3.18 % (27633)Memory used [KB]: 2174
% 13.69/3.18 % (27633)Time elapsed: 0.020 s
% 13.69/3.18 % (27633)Instructions burned: 70 (million)
% 13.69/3.18 % (27633)------------------------------
% 13.69/3.18 % (27633)------------------------------
% 13.69/3.18 % (27634)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_27050 for (2983ds/316Mi)
% 13.69/3.18 % (27626)Instruction limit reached!
% 13.69/3.18 % (27626)------------------------------
% 13.69/3.18 % (27626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.69/3.18 % (27626)Termination reason: Unknown
% 13.69/3.18 % (27626)Termination phase: Saturation
% 13.69/3.18
% 13.69/3.18 % (27626)Memory used [KB]: 7547
% 13.69/3.18 % (27626)Time elapsed: 0.248 s
% 13.69/3.18 % (27626)Instructions burned: 832 (million)
% 13.69/3.18 % (27626)------------------------------
% 13.69/3.18 % (27626)------------------------------
% 13.69/3.18 % (27635)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_27050 for (2983ds/932Mi)
% 13.69/3.18 % (27636)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_27050 for (2983ds/4714Mi)
% 13.69/3.19 % (27637)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_27050 for (2983ds/8250Mi)
% 14.21/3.23 % (27634)Refutation not found, incomplete strategy
% 14.21/3.23 % (27634)------------------------------
% 14.21/3.23 % (27634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.21/3.23 % (27634)Termination reason: Refutation not found, incomplete strategy
% 14.21/3.23
% 14.21/3.23
% 14.21/3.23 % (27634)Memory used [KB]: 7036
% 14.21/3.23 % (27634)Time elapsed: 0.047 s
% 14.21/3.23 % (27634)Instructions burned: 169 (million)
% 14.21/3.23 % (27634)------------------------------
% 14.21/3.23 % (27634)------------------------------
% 14.21/3.23 % (27636)Refutation not found, incomplete strategy
% 14.21/3.23 % (27636)------------------------------
% 14.21/3.23 % (27636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.21/3.23 % (27636)Termination reason: Refutation not found, incomplete strategy
% 14.21/3.23
% 14.21/3.23
% 14.21/3.23 % (27636)Memory used [KB]: 7164
% 14.21/3.23 % (27636)Time elapsed: 0.048 s
% 14.21/3.23 % (27636)Instructions burned: 167 (million)
% 14.21/3.23 % (27636)------------------------------
% 14.21/3.23 % (27636)------------------------------
% 14.21/3.24 % (27638)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_27050 for (2982ds/770Mi)
% 14.21/3.24 % (27639)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_27050 for (2982ds/794Mi)
% 14.21/3.25 % (27638)Refutation not found, incomplete strategy
% 14.21/3.25 % (27638)------------------------------
% 14.21/3.25 % (27638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.21/3.25 % (27638)Termination reason: Refutation not found, incomplete strategy
% 14.21/3.25
% 14.21/3.25
% 14.21/3.25 % (27638)Memory used [KB]: 6268
% 14.21/3.25 % (27638)Time elapsed: 0.013 s
% 14.21/3.25 % (27638)Instructions burned: 38 (million)
% 14.21/3.25 % (27638)------------------------------
% 14.21/3.25 % (27638)------------------------------
% 14.21/3.26 % (27640)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_27050 for (2982ds/464Mi)
% 14.74/3.40 % (27640)Instruction limit reached!
% 14.74/3.40 % (27640)------------------------------
% 14.74/3.40 % (27640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.74/3.40 % (27640)Termination reason: Unknown
% 14.74/3.40 % (27640)Termination phase: Saturation
% 14.74/3.40
% 14.74/3.40 % (27640)Memory used [KB]: 7291
% 14.74/3.40 % (27640)Time elapsed: 0.146 s
% 14.74/3.40 % (27640)Instructions burned: 465 (million)
% 14.74/3.40 % (27640)------------------------------
% 14.74/3.40 % (27640)------------------------------
% 14.74/3.41 % (27641)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_27050 for (2981ds/1376Mi)
% 14.74/3.47 % (27635)Instruction limit reached!
% 14.74/3.47 % (27635)------------------------------
% 14.74/3.47 % (27635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.74/3.47 % (27635)Termination reason: Unknown
% 14.74/3.47 % (27635)Termination phase: Saturation
% 14.74/3.47
% 14.74/3.47 % (27635)Memory used [KB]: 9338
% 14.74/3.47 % (27635)Time elapsed: 0.287 s
% 14.74/3.47 % (27635)Instructions burned: 934 (million)
% 14.74/3.47 % (27635)------------------------------
% 14.74/3.47 % (27635)------------------------------
% 14.74/3.48 % (27642)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_27050 for (2980ds/906Mi)
% 14.74/3.49 % (27639)Instruction limit reached!
% 14.74/3.49 % (27639)------------------------------
% 14.74/3.49 % (27639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.74/3.49 % (27639)Termination reason: Unknown
% 14.74/3.49 % (27639)Termination phase: Saturation
% 14.74/3.49
% 14.74/3.49 % (27639)Memory used [KB]: 5628
% 14.74/3.49 % (27639)Time elapsed: 0.252 s
% 14.74/3.49 % (27639)Instructions burned: 796 (million)
% 14.74/3.49 % (27639)------------------------------
% 14.74/3.49 % (27639)------------------------------
% 15.65/3.50 % (27643)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_27050 for (2980ds/434Mi)
% 15.65/3.51 % (27632)Instruction limit reached!
% 15.65/3.51 % (27632)------------------------------
% 15.65/3.51 % (27632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.65/3.51 % (27632)Termination reason: Unknown
% 15.65/3.51 % (27632)Termination phase: Saturation
% 15.65/3.51
% 15.65/3.51 % (27632)Memory used [KB]: 7547
% 15.65/3.51 % (27632)Time elapsed: 0.426 s
% 15.65/3.51 % (27632)Instructions burned: 1830 (million)
% 15.65/3.51 % (27632)------------------------------
% 15.65/3.51 % (27632)------------------------------
% 15.65/3.52 % (27644)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_27050 for (2980ds/865Mi)
% 16.30/3.63 % (27643)Instruction limit reached!
% 16.30/3.63 % (27643)------------------------------
% 16.30/3.63 % (27643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.30/3.63 % (27643)Termination reason: Unknown
% 16.30/3.63 % (27643)Termination phase: Saturation
% 16.30/3.63
% 16.30/3.63 % (27643)Memory used [KB]: 7547
% 16.30/3.63 % (27643)Time elapsed: 0.129 s
% 16.30/3.63 % (27643)Instructions burned: 436 (million)
% 16.30/3.63 % (27643)------------------------------
% 16.30/3.63 % (27643)------------------------------
% 16.30/3.64 % (27645)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_27050 for (2978ds/593Mi)
% 16.64/3.79 % (27644)Instruction limit reached!
% 16.64/3.79 % (27644)------------------------------
% 16.64/3.79 % (27644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.64/3.79 % (27644)Termination reason: Unknown
% 16.64/3.79 % (27644)Termination phase: Saturation
% 16.64/3.79
% 16.64/3.79 % (27644)Memory used [KB]: 7931
% 16.64/3.79 % (27644)Time elapsed: 0.268 s
% 16.64/3.79 % (27644)Instructions burned: 866 (million)
% 16.64/3.79 % (27644)------------------------------
% 16.64/3.79 % (27644)------------------------------
% 16.64/3.79 % (27642)Instruction limit reached!
% 16.64/3.79 % (27642)------------------------------
% 16.64/3.79 % (27642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.64/3.79 % (27642)Termination reason: Unknown
% 16.64/3.79 % (27642)Termination phase: Saturation
% 16.64/3.79
% 16.64/3.79 % (27642)Memory used [KB]: 10874
% 16.64/3.79 % (27642)Time elapsed: 0.314 s
% 16.64/3.79 % (27642)Instructions burned: 908 (million)
% 16.64/3.79 % (27642)------------------------------
% 16.64/3.79 % (27642)------------------------------
% 16.64/3.80 % (27646)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_27050 for (2977ds/443Mi)
% 17.44/3.80 % (27647)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_27050 for (2977ds/594Mi)
% 17.44/3.82 % (27645)Instruction limit reached!
% 17.44/3.82 % (27645)------------------------------
% 17.44/3.82 % (27645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.82 % (27645)Termination reason: Unknown
% 17.44/3.82 % (27645)Termination phase: Saturation
% 17.44/3.82
% 17.44/3.82 % (27645)Memory used [KB]: 8187
% 17.44/3.82 % (27645)Time elapsed: 0.185 s
% 17.44/3.82 % (27645)Instructions burned: 595 (million)
% 17.44/3.82 % (27645)------------------------------
% 17.44/3.82 % (27645)------------------------------
% 17.44/3.83 % (27641)Instruction limit reached!
% 17.44/3.83 % (27641)------------------------------
% 17.44/3.83 % (27641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.83 % (27641)Termination reason: Unknown
% 17.44/3.83 % (27641)Termination phase: Saturation
% 17.44/3.83
% 17.44/3.83 % (27641)Memory used [KB]: 10362
% 17.44/3.83 % (27641)Time elapsed: 0.421 s
% 17.44/3.83 % (27641)Instructions burned: 1378 (million)
% 17.44/3.83 % (27641)------------------------------
% 17.44/3.83 % (27641)------------------------------
% 17.44/3.83 % (27648)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_27050 for (2977ds/327Mi)
% 17.44/3.84 % (27649)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_27050 for (2976ds/5411Mi)
% 17.44/3.86 % (27649)Refutation not found, incomplete strategy
% 17.44/3.86 % (27649)------------------------------
% 17.44/3.86 % (27649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.86 % (27649)Termination reason: Refutation not found, incomplete strategy
% 17.44/3.86
% 17.44/3.86
% 17.44/3.86 % (27649)Memory used [KB]: 6524
% 17.44/3.86 % (27649)Time elapsed: 0.024 s
% 17.44/3.86 % (27649)Instructions burned: 74 (million)
% 17.44/3.86 % (27649)------------------------------
% 17.44/3.86 % (27649)------------------------------
% 17.44/3.87 % (27610)Instruction limit reached!
% 17.44/3.87 % (27610)------------------------------
% 17.44/3.87 % (27610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.44/3.87 % (27610)Termination reason: Unknown
% 17.44/3.87 % (27610)Termination phase: Saturation
% 17.44/3.87
% 17.44/3.87 % (27610)Memory used [KB]: 9466
% 17.44/3.87 % (27610)Time elapsed: 1.388 s
% 17.44/3.87 % (27610)Instructions burned: 4438 (million)
% 17.44/3.87 % (27610)------------------------------
% 17.44/3.87 % (27610)------------------------------
% 17.44/3.87 % (27650)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_27050 for (2976ds/1762Mi)
% 17.44/3.88 % (27651)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_27050 for (2976ds/96Mi)
% 18.28/3.91 % (27651)Instruction limit reached!
% 18.28/3.91 % (27651)------------------------------
% 18.28/3.91 % (27651)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.28/3.91 % (27651)Termination reason: Unknown
% 18.28/3.91 % (27651)Termination phase: Saturation
% 18.28/3.91
% 18.28/3.91 % (27651)Memory used [KB]: 6652
% 18.28/3.91 % (27651)Time elapsed: 0.027 s
% 18.28/3.91 % (27651)Instructions burned: 98 (million)
% 18.28/3.91 % (27651)------------------------------
% 18.28/3.91 % (27651)------------------------------
% 18.28/3.92 % (27652)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_27050 for (2976ds/503Mi)
% 18.28/3.93 % (27646)Instruction limit reached!
% 18.28/3.93 % (27646)------------------------------
% 18.28/3.93 % (27646)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.28/3.93 % (27646)Termination reason: Unknown
% 18.28/3.93 % (27646)Termination phase: Saturation
% 18.28/3.93
% 18.28/3.93 % (27646)Memory used [KB]: 7036
% 18.28/3.93 % (27646)Time elapsed: 0.137 s
% 18.28/3.93 % (27646)Instructions burned: 446 (million)
% 18.28/3.93 % (27646)------------------------------
% 18.28/3.93 % (27646)------------------------------
% 18.28/3.94 % (27648)Instruction limit reached!
% 18.28/3.94 % (27648)------------------------------
% 18.28/3.94 % (27648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.28/3.94 % (27648)Termination reason: Unknown
% 18.28/3.94 % (27648)Termination phase: Saturation
% 18.28/3.94
% 18.28/3.94 % (27648)Memory used [KB]: 7419
% 18.28/3.94 % (27648)Time elapsed: 0.104 s
% 18.28/3.94 % (27648)Instructions burned: 327 (million)
% 18.28/3.94 % (27648)------------------------------
% 18.28/3.94 % (27648)------------------------------
% 18.28/3.94 % (27653)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_27050 for (2975ds/90Mi)
% 18.28/3.95 % (27654)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_27050 for (2975ds/593Mi)
% 18.28/3.97 % (27653)Instruction limit reached!
% 18.28/3.97 % (27653)------------------------------
% 18.28/3.97 % (27653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.28/3.97 % (27653)Termination reason: Unknown
% 18.28/3.97 % (27653)Termination phase: Saturation
% 18.28/3.97
% 18.28/3.97 % (27653)Memory used [KB]: 6524
% 18.28/3.97 % (27653)Time elapsed: 0.027 s
% 18.28/3.97 % (27653)Instructions burned: 90 (million)
% 18.28/3.97 % (27653)------------------------------
% 18.28/3.97 % (27653)------------------------------
% 18.28/3.98 % (27655)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_27050 for (2975ds/1512Mi)
% 18.28/3.99 % (27647)Instruction limit reached!
% 18.28/3.99 % (27647)------------------------------
% 18.28/3.99 % (27647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.28/3.99 % (27647)Termination reason: Unknown
% 18.28/3.99 % (27647)Termination phase: Saturation
% 18.28/3.99
% 18.28/3.99 % (27647)Memory used [KB]: 7164
% 18.28/3.99 % (27647)Time elapsed: 0.191 s
% 18.28/3.99 % (27647)Instructions burned: 596 (million)
% 18.28/3.99 % (27647)------------------------------
% 18.28/3.99 % (27647)------------------------------
% 18.28/4.00 % (27656)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_27050 for (2975ds/569Mi)
% 20.19/4.07 % (27652)Instruction limit reached!
% 20.19/4.07 % (27652)------------------------------
% 20.19/4.07 % (27652)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.19/4.07 % (27652)Termination reason: Unknown
% 20.19/4.07 % (27652)Termination phase: Saturation
% 20.19/4.07
% 20.19/4.07 % (27652)Memory used [KB]: 7931
% 20.19/4.07 % (27652)Time elapsed: 0.152 s
% 20.19/4.07 % (27652)Instructions burned: 505 (million)
% 20.19/4.07 % (27652)------------------------------
% 20.19/4.07 % (27652)------------------------------
% 20.19/4.08 % (27657)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_27050 for (2974ds/501Mi)
% 20.19/4.11 % (27654)Instruction limit reached!
% 20.19/4.11 % (27654)------------------------------
% 20.19/4.11 % (27654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.19/4.11 % (27654)Termination reason: Unknown
% 20.19/4.11 % (27654)Termination phase: Saturation
% 20.19/4.11
% 20.19/4.11 % (27654)Memory used [KB]: 7547
% 20.19/4.11 % (27654)Time elapsed: 0.167 s
% 20.19/4.11 % (27654)Instructions burned: 597 (million)
% 20.19/4.11 % (27654)------------------------------
% 20.19/4.11 % (27654)------------------------------
% 20.19/4.12 % (27658)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_27050 for (2974ds/562Mi)
% 20.84/4.15 % (27614)Instruction limit reached!
% 20.84/4.15 % (27614)------------------------------
% 20.84/4.15 % (27614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.84/4.15 % (27614)Termination reason: Unknown
% 20.84/4.15 % (27614)Termination phase: Saturation
% 20.84/4.15
% 20.84/4.15 % (27614)Memory used [KB]: 14328
% 20.84/4.15 % (27614)Time elapsed: 1.608 s
% 20.84/4.15 % (27614)Instructions burned: 5205 (million)
% 20.84/4.15 % (27614)------------------------------
% 20.84/4.15 % (27614)------------------------------
% 20.84/4.16 % (27659)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_27050 for (2973ds/406Mi)
% 20.84/4.17 % (27656)Instruction limit reached!
% 20.84/4.17 % (27656)------------------------------
% 20.84/4.17 % (27656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.84/4.17 % (27656)Termination reason: Unknown
% 20.84/4.17 % (27656)Termination phase: Saturation
% 20.84/4.17
% 20.84/4.17 % (27656)Memory used [KB]: 7931
% 20.84/4.17 % (27656)Time elapsed: 0.169 s
% 20.84/4.17 % (27656)Instructions burned: 571 (million)
% 20.84/4.17 % (27656)------------------------------
% 20.84/4.17 % (27656)------------------------------
% 20.84/4.18 % (27660)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_27050 for (2973ds/582Mi)
% 21.15/4.22 % (27657)Instruction limit reached!
% 21.15/4.22 % (27657)------------------------------
% 21.15/4.22 % (27657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.15/4.22 % (27657)Termination reason: Unknown
% 21.15/4.22 % (27657)Termination phase: Saturation
% 21.15/4.22
% 21.15/4.22 % (27657)Memory used [KB]: 8187
% 21.15/4.22 % (27657)Time elapsed: 0.144 s
% 21.15/4.22 % (27657)Instructions burned: 502 (million)
% 21.15/4.22 % (27657)------------------------------
% 21.15/4.22 % (27657)------------------------------
% 21.15/4.23 % (27661)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_27050 for (2972ds/456Mi)
% 21.15/4.29 % (27659)Instruction limit reached!
% 21.15/4.29 % (27659)------------------------------
% 21.15/4.29 % (27659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.15/4.29 % (27659)Termination reason: Unknown
% 21.15/4.29 % (27659)Termination phase: Saturation
% 21.15/4.29
% 21.15/4.29 % (27659)Memory used [KB]: 7419
% 21.15/4.29 % (27659)Time elapsed: 0.128 s
% 21.15/4.29 % (27659)Instructions burned: 406 (million)
% 21.15/4.29 % (27659)------------------------------
% 21.15/4.29 % (27659)------------------------------
% 21.15/4.30 % (27658)Instruction limit reached!
% 21.15/4.30 % (27658)------------------------------
% 21.15/4.30 % (27658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.15/4.30 % (27658)Termination reason: Unknown
% 21.15/4.30 % (27658)Termination phase: Saturation
% 21.15/4.30
% 21.15/4.30 % (27658)Memory used [KB]: 7547
% 21.15/4.30 % (27658)Time elapsed: 0.175 s
% 21.15/4.30 % (27658)Instructions burned: 564 (million)
% 21.15/4.30 % (27658)------------------------------
% 21.15/4.30 % (27658)------------------------------
% 21.92/4.30 % (27662)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_27050 for (2972ds/393Mi)
% 21.92/4.31 % (27663)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_27050 for (2972ds/1335Mi)
% 21.92/4.36 % (27660)Instruction limit reached!
% 21.92/4.36 % (27660)------------------------------
% 21.92/4.36 % (27660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.92/4.36 % (27660)Termination reason: Unknown
% 21.92/4.36 % (27660)Termination phase: Saturation
% 21.92/4.36
% 21.92/4.36 % (27660)Memory used [KB]: 7164
% 21.92/4.36 % (27660)Time elapsed: 0.184 s
% 21.92/4.36 % (27660)Instructions burned: 585 (million)
% 21.92/4.36 % (27660)------------------------------
% 21.92/4.36 % (27660)------------------------------
% 21.92/4.37 % (27664)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_27050 for (2971ds/3373Mi)
% 21.92/4.37 % (27661)Refutation not found, non-redundant clauses discarded% (27661)------------------------------
% 21.92/4.37 % (27661)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.92/4.37 % (27661)Termination reason: Refutation not found, non-redundant clauses discarded
% 21.92/4.37
% 21.92/4.37 % (27661)Memory used [KB]: 7419
% 21.92/4.37 % (27661)Time elapsed: 0.141 s
% 21.92/4.37 % (27661)Instructions burned: 446 (million)
% 21.92/4.37 % (27661)------------------------------
% 21.92/4.37 % (27661)------------------------------
% 21.92/4.38 % (27665)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_27050 for (2971ds/474Mi)
% 21.92/4.39 % (27650)Instruction limit reached!
% 21.92/4.39 % (27650)------------------------------
% 21.92/4.39 % (27650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.92/4.39 % (27650)Termination reason: Unknown
% 21.92/4.39 % (27650)Termination phase: Saturation
% 21.92/4.39
% 21.92/4.39 % (27650)Memory used [KB]: 9850
% 21.92/4.39 % (27650)Time elapsed: 0.516 s
% 21.92/4.39 % (27650)Instructions burned: 1765 (million)
% 21.92/4.39 % (27650)------------------------------
% 21.92/4.39 % (27650)------------------------------
% 22.57/4.40 % (27666)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_27050 for (2971ds/157Mi)
% 22.57/4.41 % (27662)Instruction limit reached!
% 22.57/4.41 % (27662)------------------------------
% 22.57/4.41 % (27662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.57/4.41 % (27662)Termination reason: Unknown
% 22.57/4.41 % (27662)Termination phase: Saturation
% 22.57/4.41
% 22.57/4.41 % (27662)Memory used [KB]: 7291
% 22.57/4.41 % (27662)Time elapsed: 0.113 s
% 22.57/4.41 % (27662)Instructions burned: 393 (million)
% 22.57/4.41 % (27662)------------------------------
% 22.57/4.41 % (27662)------------------------------
% 22.57/4.42 % (27667)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_27050 for (2971ds/590Mi)
% 22.57/4.43 % (27655)Instruction limit reached!
% 22.57/4.43 % (27655)------------------------------
% 22.57/4.43 % (27655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.57/4.43 % (27655)Termination reason: Unknown
% 22.57/4.43 % (27655)Termination phase: Saturation
% 22.57/4.43
% 22.57/4.43 % (27655)Memory used [KB]: 8443
% 22.57/4.43 % (27655)Time elapsed: 0.454 s
% 22.57/4.43 % (27655)Instructions burned: 1514 (million)
% 22.57/4.43 % (27655)------------------------------
% 22.57/4.43 % (27655)------------------------------
% 22.57/4.44 % (27668)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_27050 for (2970ds/104Mi)
% 22.57/4.44 % (27666)Instruction limit reached!
% 22.57/4.44 % (27666)------------------------------
% 22.57/4.44 % (27666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.57/4.44 % (27666)Termination reason: Unknown
% 22.57/4.44 % (27666)Termination phase: Saturation
% 22.57/4.44
% 22.57/4.44 % (27666)Memory used [KB]: 6908
% 22.57/4.44 % (27666)Time elapsed: 0.045 s
% 22.57/4.44 % (27666)Instructions burned: 159 (million)
% 22.57/4.44 % (27666)------------------------------
% 22.57/4.44 % (27666)------------------------------
% 22.57/4.45 % (27669)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_27050 for (2970ds/414Mi)
% 22.57/4.47 % (27668)Instruction limit reached!
% 22.57/4.47 % (27668)------------------------------
% 22.57/4.47 % (27668)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.57/4.47 % (27668)Termination reason: Unknown
% 22.57/4.47 % (27668)Termination phase: Saturation
% 22.57/4.47
% 22.57/4.47 % (27668)Memory used [KB]: 2430
% 22.57/4.47 % (27668)Time elapsed: 0.032 s
% 22.57/4.47 % (27668)Instructions burned: 105 (million)
% 22.57/4.47 % (27668)------------------------------
% 22.57/4.47 % (27668)------------------------------
% 22.57/4.48 % (27670)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_27050 for (2970ds/715Mi)
% 22.93/4.53 % (27665)Instruction limit reached!
% 22.93/4.53 % (27665)------------------------------
% 22.93/4.53 % (27665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.93/4.53 % (27665)Termination reason: Unknown
% 22.93/4.53 % (27665)Termination phase: Saturation
% 22.93/4.53
% 22.93/4.53 % (27665)Memory used [KB]: 7803
% 22.93/4.53 % (27665)Time elapsed: 0.148 s
% 22.93/4.53 % (27665)Instructions burned: 476 (million)
% 22.93/4.53 % (27665)------------------------------
% 22.93/4.53 % (27665)------------------------------
% 22.93/4.54 % (27671)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_27050 for (2969ds/961Mi)
% 22.93/4.58 % (27669)Instruction limit reached!
% 22.93/4.58 % (27669)------------------------------
% 22.93/4.58 % (27669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.93/4.58 % (27669)Termination reason: Unknown
% 22.93/4.58 % (27669)Termination phase: Saturation
% 22.93/4.58
% 22.93/4.58 % (27669)Memory used [KB]: 7547
% 22.93/4.58 % (27669)Time elapsed: 0.124 s
% 22.93/4.58 % (27669)Instructions burned: 416 (million)
% 22.93/4.58 % (27669)------------------------------
% 22.93/4.58 % (27669)------------------------------
% 22.93/4.59 % (27672)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_27050 for (2969ds/1213Mi)
% 22.93/4.59 % (27667)Instruction limit reached!
% 22.93/4.59 % (27667)------------------------------
% 22.93/4.59 % (27667)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.93/4.59 % (27667)Termination reason: Unknown
% 22.93/4.59 % (27667)Termination phase: Saturation
% 22.93/4.59
% 22.93/4.59 % (27667)Memory used [KB]: 7931
% 22.93/4.59 % (27667)Time elapsed: 0.176 s
% 22.93/4.59 % (27667)Instructions burned: 592 (million)
% 22.93/4.59 % (27667)------------------------------
% 22.93/4.59 % (27667)------------------------------
% 23.52/4.60 % (27673)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_27050 for (2969ds/1979Mi)
% 23.52/4.60 % (27663)Instruction limit reached!
% 23.52/4.60 % (27663)------------------------------
% 23.52/4.60 % (27663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.52/4.60 % (27663)Termination reason: Unknown
% 23.52/4.60 % (27663)Termination phase: Saturation
% 23.52/4.60
% 23.52/4.60 % (27663)Memory used [KB]: 7675
% 23.52/4.60 % (27663)Time elapsed: 0.299 s
% 23.52/4.60 % (27663)Instructions burned: 1338 (million)
% 23.52/4.60 % (27663)------------------------------
% 23.52/4.60 % (27663)------------------------------
% 23.52/4.61 % (27674)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_27050 for (2969ds/481Mi)
% 23.92/4.71 % (27670)Instruction limit reached!
% 23.92/4.71 % (27670)------------------------------
% 23.92/4.71 % (27670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.92/4.71 % (27670)Termination reason: Unknown
% 23.92/4.71 % (27670)Termination phase: Saturation
% 23.92/4.71
% 23.92/4.71 % (27670)Memory used [KB]: 3326
% 23.92/4.71 % (27670)Time elapsed: 0.229 s
% 23.92/4.71 % (27670)Instructions burned: 716 (million)
% 23.92/4.71 % (27670)------------------------------
% 23.92/4.71 % (27670)------------------------------
% 23.92/4.72 % (27675)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_27050 for (2968ds/783Mi)
% 23.92/4.77 % (27671)Instruction limit reached!
% 23.92/4.77 % (27671)------------------------------
% 23.92/4.77 % (27671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.92/4.77 % (27671)Termination reason: Unknown
% 23.92/4.77 % (27671)Termination phase: Saturation
% 23.92/4.77
% 23.92/4.77 % (27671)Memory used [KB]: 6908
% 23.92/4.77 % (27671)Time elapsed: 0.229 s
% 23.92/4.77 % (27671)Instructions burned: 966 (million)
% 23.92/4.77 % (27671)------------------------------
% 23.92/4.77 % (27671)------------------------------
% 23.92/4.77 % (27674)Instruction limit reached!
% 23.92/4.77 % (27674)------------------------------
% 23.92/4.77 % (27674)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.92/4.77 % (27674)Termination reason: Unknown
% 23.92/4.77 % (27674)Termination phase: Saturation
% 23.92/4.77
% 23.92/4.77 % (27674)Memory used [KB]: 7547
% 23.92/4.77 % (27674)Time elapsed: 0.157 s
% 23.92/4.77 % (27674)Instructions burned: 482 (million)
% 23.92/4.77 % (27674)------------------------------
% 23.92/4.77 % (27674)------------------------------
% 23.92/4.78 % (27676)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_27050 for (2967ds/432Mi)
% 23.92/4.78 % (27677)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_27050 for (2967ds/1670Mi)
% 24.67/4.82 % (27637)Instruction limit reached!
% 24.67/4.82 % (27637)------------------------------
% 24.67/4.82 % (27637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.67/4.82 % (27637)Termination reason: Unknown
% 24.67/4.82 % (27637)Termination phase: Saturation
% 24.67/4.82
% 24.67/4.82 % (27637)Memory used [KB]: 8187
% 24.67/4.82 % (27637)Time elapsed: 1.632 s
% 24.67/4.82 % (27637)Instructions burned: 8253 (million)
% 24.67/4.82 % (27637)------------------------------
% 24.67/4.82 % (27637)------------------------------
% 24.67/4.83 % (27678)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_27050 for (2967ds/90Mi)
% 24.67/4.86 % (27678)Instruction limit reached!
% 24.67/4.86 % (27678)------------------------------
% 24.67/4.86 % (27678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.67/4.86 % (27678)Termination reason: Unknown
% 24.67/4.86 % (27678)Termination phase: Saturation
% 24.67/4.86
% 24.67/4.86 % (27678)Memory used [KB]: 6652
% 24.67/4.86 % (27678)Time elapsed: 0.029 s
% 24.67/4.86 % (27678)Instructions burned: 91 (million)
% 24.67/4.86 % (27678)------------------------------
% 24.67/4.86 % (27678)------------------------------
% 24.67/4.87 % (27679)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_27050 for (2966ds/346Mi)
% 24.74/4.91 % (27676)Instruction limit reached!
% 24.74/4.91 % (27676)------------------------------
% 24.74/4.91 % (27676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.74/4.91 % (27676)Termination reason: Unknown
% 24.74/4.91 % (27676)Termination phase: Saturation
% 24.74/4.91
% 24.74/4.91 % (27676)Memory used [KB]: 7803
% 24.74/4.91 % (27676)Time elapsed: 0.132 s
% 24.74/4.91 % (27676)Instructions burned: 434 (million)
% 24.74/4.91 % (27676)------------------------------
% 24.74/4.91 % (27676)------------------------------
% 24.74/4.92 % (27680)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_27050 for (2966ds/401Mi)
% 24.74/4.96 % (27675)Instruction limit reached!
% 24.74/4.96 % (27675)------------------------------
% 24.74/4.96 % (27675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.74/4.96 % (27675)Termination reason: Unknown
% 24.74/4.96 % (27675)Termination phase: Saturation
% 24.74/4.96
% 24.74/4.96 % (27675)Memory used [KB]: 8315
% 24.74/4.96 % (27675)Time elapsed: 0.241 s
% 24.74/4.96 % (27675)Instructions burned: 783 (million)
% 24.74/4.96 % (27675)------------------------------
% 24.74/4.96 % (27675)------------------------------
% 24.74/4.97 % (27672)Instruction limit reached!
% 24.74/4.97 % (27672)------------------------------
% 24.74/4.97 % (27672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.74/4.97 % (27672)Termination reason: Unknown
% 24.74/4.97 % (27672)Termination phase: Saturation
% 24.74/4.97
% 24.74/4.97 % (27672)Memory used [KB]: 8059
% 24.74/4.97 % (27672)Time elapsed: 0.383 s
% 24.74/4.97 % (27672)Instructions burned: 1214 (million)
% 24.74/4.97 % (27672)------------------------------
% 24.74/4.97 % (27672)------------------------------
% 24.74/4.97 % (27681)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_27050 for (2965ds/6454Mi)
% 24.74/4.97 % (27679)Instruction limit reached!
% 24.74/4.97 % (27679)------------------------------
% 24.74/4.97 % (27679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.74/4.97 % (27679)Termination reason: Unknown
% 24.74/4.97 % (27679)Termination phase: Saturation
% 24.74/4.97
% 24.74/4.97 % (27679)Memory used [KB]: 7675
% 24.74/4.97 % (27679)Time elapsed: 0.108 s
% 24.74/4.97 % (27679)Instructions burned: 347 (million)
% 24.74/4.97 % (27679)------------------------------
% 24.74/4.97 % (27679)------------------------------
% 24.74/4.98 % (27682)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_27050 for (2965ds/283Mi)
% 24.74/4.98 % (27683)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_27050 for (2965ds/865Mi)
% 27.22/5.04 % (27680)Instruction limit reached!
% 27.22/5.04 % (27680)------------------------------
% 27.22/5.04 % (27680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.22/5.04 % (27680)Termination reason: Unknown
% 27.22/5.04 % (27680)Termination phase: Saturation
% 27.22/5.04
% 27.22/5.04 % (27680)Memory used [KB]: 7803
% 27.22/5.04 % (27680)Time elapsed: 0.122 s
% 27.22/5.04 % (27680)Instructions burned: 402 (million)
% 27.22/5.04 % (27680)------------------------------
% 27.22/5.04 % (27680)------------------------------
% 27.22/5.05 % (27684)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_27050 for (2964ds/4528Mi)
% 27.22/5.06 % (27684)Refutation not found, incomplete strategy
% 27.22/5.06 % (27684)------------------------------
% 27.22/5.06 % (27684)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.22/5.06 % (27684)Termination reason: Refutation not found, incomplete strategy
% 27.22/5.06
% 27.22/5.06
% 27.22/5.06 % (27684)Memory used [KB]: 1791
% 27.22/5.06 % (27684)Time elapsed: 0.013 s
% 27.22/5.06 % (27684)Instructions burned: 36 (million)
% 27.22/5.06 % (27684)------------------------------
% 27.22/5.06 % (27684)------------------------------
% 27.22/5.07 % (27682)Instruction limit reached!
% 27.22/5.07 % (27682)------------------------------
% 27.22/5.07 % (27682)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.22/5.07 % (27682)Termination reason: Unknown
% 27.22/5.07 % (27682)Termination phase: Saturation
% 27.22/5.07
% 27.22/5.07 % (27682)Memory used [KB]: 7803
% 27.22/5.07 % (27682)Time elapsed: 0.112 s
% 27.22/5.07 % (27682)Instructions burned: 284 (million)
% 27.22/5.07 % (27682)------------------------------
% 27.22/5.07 % (27682)------------------------------
% 27.22/5.07 % (27685)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_27050 for (2964ds/1001Mi)
% 27.22/5.08 % (27686)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_27050 for (2964ds/102Mi)
% 27.22/5.10 % (27686)Instruction limit reached!
% 27.22/5.10 % (27686)------------------------------
% 27.22/5.10 % (27686)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.22/5.10 % (27686)Termination reason: Unknown
% 27.22/5.10 % (27686)Termination phase: Saturation
% 27.22/5.10
% 27.22/5.10 % (27686)Memory used [KB]: 6652
% 27.22/5.10 % (27686)Time elapsed: 0.028 s
% 27.22/5.10 % (27686)Instructions burned: 102 (million)
% 27.22/5.10 % (27686)------------------------------
% 27.22/5.10 % (27686)------------------------------
% 27.22/5.11 % (27687)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_27050 for (2964ds/952Mi)
% 28.21/5.22 % (27673)Instruction limit reached!
% 28.21/5.22 % (27673)------------------------------
% 28.21/5.22 % (27673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.21/5.22 % (27673)Termination reason: Unknown
% 28.21/5.22 % (27673)Termination phase: Saturation
% 28.21/5.22
% 28.21/5.22 % (27673)Memory used [KB]: 7419
% 28.21/5.22 % (27673)Time elapsed: 0.622 s
% 28.21/5.22 % (27673)Instructions burned: 1980 (million)
% 28.21/5.22 % (27673)------------------------------
% 28.21/5.22 % (27673)------------------------------
% 28.21/5.23 % (27688)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_27050 for (2962ds/578Mi)
% 28.21/5.26 % (27683)Instruction limit reached!
% 28.21/5.26 % (27683)------------------------------
% 28.21/5.26 % (27683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.21/5.26 % (27683)Termination reason: Unknown
% 28.21/5.26 % (27683)Termination phase: Saturation
% 28.21/5.26
% 28.21/5.26 % (27683)Memory used [KB]: 8699
% 28.21/5.26 % (27683)Time elapsed: 0.301 s
% 28.21/5.26 % (27683)Instructions burned: 866 (million)
% 28.21/5.26 % (27683)------------------------------
% 28.21/5.26 % (27683)------------------------------
% 28.21/5.27 % (27689)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_27050 for (2962ds/643Mi)
% 28.21/5.28 % (27685)Instruction limit reached!
% 28.21/5.28 % (27685)------------------------------
% 28.21/5.28 % (27685)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.21/5.28 % (27685)Termination reason: Unknown
% 28.21/5.28 % (27685)Termination phase: Saturation
% 28.21/5.28
% 28.21/5.28 % (27685)Memory used [KB]: 7164
% 28.21/5.28 % (27685)Time elapsed: 0.210 s
% 28.21/5.28 % (27685)Instructions burned: 1003 (million)
% 28.21/5.28 % (27685)------------------------------
% 28.21/5.28 % (27685)------------------------------
% 28.21/5.29 % (27677)Instruction limit reached!
% 28.21/5.29 % (27677)------------------------------
% 28.21/5.29 % (27677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.21/5.29 % (27677)Termination reason: Unknown
% 28.21/5.29 % (27677)Termination phase: Saturation
% 28.21/5.29
% 28.21/5.29 % (27677)Memory used [KB]: 9338
% 28.21/5.29 % (27677)Time elapsed: 0.511 s
% 28.21/5.29 % (27677)Instructions burned: 1672 (million)
% 28.21/5.29 % (27677)------------------------------
% 28.21/5.29 % (27677)------------------------------
% 28.21/5.29 % (27690)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_27050 for (2962ds/865Mi)
% 28.84/5.30 % (27691)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_27050 for (2962ds/1174Mi)
% 28.84/5.38 % (27664)Instruction limit reached!
% 28.84/5.38 % (27664)------------------------------
% 28.84/5.38 % (27664)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.84/5.38 % (27664)Termination reason: Unknown
% 28.84/5.38 % (27664)Termination phase: Saturation
% 28.84/5.38
% 28.84/5.38 % (27664)Memory used [KB]: 10874
% 28.84/5.38 % (27664)Time elapsed: 1.012 s
% 28.84/5.38 % (27664)Instructions burned: 3376 (million)
% 28.84/5.38 % (27664)------------------------------
% 28.84/5.38 % (27664)------------------------------
% 28.84/5.39 % (27692)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_27050 for (2961ds/644Mi)
% 29.04/5.41 % (27688)Instruction limit reached!
% 29.04/5.41 % (27688)------------------------------
% 29.04/5.41 % (27688)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.04/5.41 % (27688)Termination reason: Unknown
% 29.04/5.41 % (27688)Termination phase: Saturation
% 29.04/5.41
% 29.04/5.41 % (27688)Memory used [KB]: 8315
% 29.04/5.41 % (27688)Time elapsed: 0.174 s
% 29.04/5.41 % (27688)Instructions burned: 580 (million)
% 29.04/5.41 % (27688)------------------------------
% 29.04/5.41 % (27688)------------------------------
% 29.04/5.42 % (27693)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_27050 for (2961ds/1201Mi)
% 29.04/5.42 % (27687)Instruction limit reached!
% 29.04/5.42 % (27687)------------------------------
% 29.04/5.42 % (27687)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.04/5.42 % (27687)Termination reason: Unknown
% 29.04/5.42 % (27687)Termination phase: Saturation
% 29.04/5.42
% 29.04/5.42 % (27687)Memory used [KB]: 8443
% 29.04/5.42 % (27687)Time elapsed: 0.305 s
% 29.04/5.42 % (27687)Instructions burned: 952 (million)
% 29.04/5.42 % (27687)------------------------------
% 29.04/5.42 % (27687)------------------------------
% 29.04/5.43 % (27694)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_27050 for (2961ds/1046Mi)
% 29.04/5.46 % (27690)Refutation not found, non-redundant clauses discarded% (27690)------------------------------
% 29.04/5.46 % (27690)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.04/5.46 % (27690)Termination reason: Refutation not found, non-redundant clauses discarded
% 29.04/5.46
% 29.04/5.46 % (27690)Memory used [KB]: 7931
% 29.04/5.46 % (27690)Time elapsed: 0.175 s
% 29.04/5.46 % (27690)Instructions burned: 568 (million)
% 29.04/5.46 % (27690)------------------------------
% 29.04/5.46 % (27690)------------------------------
% 29.04/5.47 % (27689)Instruction limit reached!
% 29.04/5.47 % (27689)------------------------------
% 29.04/5.47 % (27689)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.04/5.47 % (27689)Termination reason: Unknown
% 29.04/5.47 % (27689)Termination phase: Saturation
% 29.04/5.47
% 29.04/5.47 % (27689)Memory used [KB]: 8187
% 29.04/5.47 % (27689)Time elapsed: 0.199 s
% 29.04/5.47 % (27689)Instructions burned: 643 (million)
% 29.04/5.47 % (27689)------------------------------
% 29.04/5.47 % (27689)------------------------------
% 29.04/5.47 % (27695)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_27050 for (2960ds/222Mi)
% 29.04/5.48 % (27696)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_27050 for (2960ds/68Mi)
% 30.04/5.50 % (27696)Instruction limit reached!
% 30.04/5.50 % (27696)------------------------------
% 30.04/5.50 % (27696)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.04/5.50 % (27696)Termination reason: Unknown
% 30.04/5.50 % (27696)Termination phase: Saturation
% 30.04/5.50
% 30.04/5.50 % (27696)Memory used [KB]: 1918
% 30.04/5.50 % (27696)Time elapsed: 0.021 s
% 30.04/5.50 % (27696)Instructions burned: 69 (million)
% 30.04/5.50 % (27696)------------------------------
% 30.04/5.50 % (27696)------------------------------
% 30.04/5.51 % (27697)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_27050 for (2960ds/454Mi)
% 30.04/5.54 % (27695)Instruction limit reached!
% 30.04/5.54 % (27695)------------------------------
% 30.04/5.54 % (27695)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.04/5.54 % (27695)Termination reason: Unknown
% 30.04/5.54 % (27695)Termination phase: Saturation
% 30.04/5.54
% 30.04/5.54 % (27695)Memory used [KB]: 7036
% 30.04/5.54 % (27695)Time elapsed: 0.065 s
% 30.04/5.54 % (27695)Instructions burned: 224 (million)
% 30.04/5.54 % (27695)------------------------------
% 30.04/5.54 % (27695)------------------------------
% 30.04/5.55 % (27698)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_27050 for (2959ds/360Mi)
% 30.04/5.59 % (27692)Instruction limit reached!
% 30.04/5.59 % (27692)------------------------------
% 30.04/5.59 % (27692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.04/5.59 % (27692)Termination reason: Unknown
% 30.04/5.59 % (27692)Termination phase: Saturation
% 30.04/5.59
% 30.04/5.59 % (27692)Memory used [KB]: 8315
% 30.04/5.59 % (27692)Time elapsed: 0.203 s
% 30.04/5.59 % (27692)Instructions burned: 644 (million)
% 30.04/5.59 % (27692)------------------------------
% 30.04/5.59 % (27692)------------------------------
% 30.45/5.60 % (27699)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_27050 for (2959ds/157Mi)
% 30.45/5.64 % (27697)Instruction limit reached!
% 30.45/5.64 % (27697)------------------------------
% 30.45/5.64 % (27697)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.45/5.64 % (27697)Termination reason: Unknown
% 30.45/5.64 % (27697)Termination phase: Saturation
% 30.45/5.64
% 30.45/5.64 % (27697)Memory used [KB]: 12665
% 30.45/5.64 % (27697)Time elapsed: 0.136 s
% 30.45/5.64 % (27697)Instructions burned: 455 (million)
% 30.45/5.64 % (27697)------------------------------
% 30.45/5.64 % (27697)------------------------------
% 30.45/5.65 % (27699)Instruction limit reached!
% 30.45/5.65 % (27699)------------------------------
% 30.45/5.65 % (27699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.45/5.65 % (27699)Termination reason: Unknown
% 30.45/5.65 % (27699)Termination phase: Saturation
% 30.45/5.65
% 30.45/5.65 % (27699)Memory used [KB]: 6908
% 30.45/5.65 % (27699)Time elapsed: 0.045 s
% 30.45/5.65 % (27699)Instructions burned: 159 (million)
% 30.45/5.65 % (27699)------------------------------
% 30.45/5.65 % (27699)------------------------------
% 30.45/5.65 % (27700)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_27050 for (2958ds/5061Mi)
% 30.45/5.66 % (27698)Instruction limit reached!
% 30.45/5.66 % (27698)------------------------------
% 30.45/5.66 % (27698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.45/5.66 % (27698)Termination reason: Unknown
% 30.45/5.66 % (27698)Termination phase: Saturation
% 30.45/5.66
% 30.45/5.66 % (27698)Memory used [KB]: 7803
% 30.45/5.66 % (27698)Time elapsed: 0.109 s
% 30.45/5.66 % (27698)Instructions burned: 362 (million)
% 30.45/5.66 % (27698)------------------------------
% 30.45/5.66 % (27698)------------------------------
% 30.45/5.66 % (27701)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_27050 for (2958ds/2401Mi)
% 30.45/5.67 % (27702)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_27050 for (2958ds/5798Mi)
% 30.45/5.67 % (27691)Instruction limit reached!
% 30.45/5.67 % (27691)------------------------------
% 30.45/5.67 % (27691)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.45/5.67 % (27691)Termination reason: Unknown
% 30.45/5.67 % (27691)Termination phase: Saturation
% 30.45/5.67
% 30.45/5.67 % (27691)Memory used [KB]: 8571
% 30.45/5.67 % (27691)Time elapsed: 0.369 s
% 30.45/5.67 % (27691)Instructions burned: 1177 (million)
% 30.45/5.67 % (27691)------------------------------
% 30.45/5.67 % (27691)------------------------------
% 30.45/5.68 % (27703)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_27050 for (2958ds/346Mi)
% 31.25/5.74 % (27694)Instruction limit reached!
% 31.25/5.74 % (27694)------------------------------
% 31.25/5.74 % (27694)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.25/5.74 % (27694)Termination reason: Unknown
% 31.25/5.74 % (27694)Termination phase: Saturation
% 31.25/5.74
% 31.25/5.74 % (27694)Memory used [KB]: 8955
% 31.25/5.74 % (27694)Time elapsed: 0.316 s
% 31.25/5.74 % (27694)Instructions burned: 1046 (million)
% 31.25/5.74 % (27694)------------------------------
% 31.25/5.74 % (27694)------------------------------
% 31.25/5.75 % (27704)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_27050 for (2957ds/1321Mi)
% 31.25/5.79 % (27703)Instruction limit reached!
% 31.25/5.79 % (27703)------------------------------
% 31.25/5.79 % (27703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.25/5.79 % (27703)Termination reason: Unknown
% 31.25/5.79 % (27703)Termination phase: Saturation
% 31.25/5.79
% 31.25/5.79 % (27703)Memory used [KB]: 7675
% 31.25/5.79 % (27703)Time elapsed: 0.111 s
% 31.25/5.79 % (27703)Instructions burned: 346 (million)
% 31.25/5.79 % (27703)------------------------------
% 31.25/5.79 % (27703)------------------------------
% 31.25/5.79 % (27693)Instruction limit reached!
% 31.25/5.79 % (27693)------------------------------
% 31.25/5.79 % (27693)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.25/5.79 % (27693)Termination reason: Unknown
% 31.25/5.79 % (27693)Termination phase: Saturation
% 31.25/5.79
% 31.25/5.79 % (27693)Memory used [KB]: 8315
% 31.25/5.79 % (27693)Time elapsed: 0.375 s
% 31.25/5.79 % (27693)Instructions burned: 1202 (million)
% 31.25/5.79 % (27693)------------------------------
% 31.25/5.79 % (27693)------------------------------
% 31.25/5.80 % (27705)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_27050 for (2957ds/1312Mi)
% 32.17/5.80 % (27706)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_27050 for (2957ds/672Mi)
% 32.28/6.02 % (27706)Instruction limit reached!
% 32.28/6.02 % (27706)------------------------------
% 32.28/6.02 % (27706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.28/6.02 % (27706)Termination reason: Unknown
% 32.28/6.02 % (27706)Termination phase: Saturation
% 32.28/6.02
% 32.28/6.02 % (27706)Memory used [KB]: 8315
% 32.28/6.02 % (27706)Time elapsed: 0.222 s
% 32.28/6.02 % (27706)Instructions burned: 674 (million)
% 32.28/6.02 % (27706)------------------------------
% 32.28/6.02 % (27706)------------------------------
% 34.23/6.03 % (27707)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_27050 for (2955ds/1897Mi)
% 34.83/6.14 % (27704)Instruction limit reached!
% 34.83/6.14 % (27704)------------------------------
% 34.83/6.14 % (27704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.83/6.14 % (27704)Termination reason: Unknown
% 34.83/6.14 % (27704)Termination phase: Saturation
% 34.83/6.14
% 34.83/6.14 % (27704)Memory used [KB]: 3965
% 34.83/6.14 % (27704)Time elapsed: 0.389 s
% 34.83/6.14 % (27704)Instructions burned: 1322 (million)
% 34.83/6.14 % (27704)------------------------------
% 34.83/6.14 % (27704)------------------------------
% 34.83/6.15 % (27708)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_27050 for (2953ds/1202Mi)
% 35.22/6.20 % (27705)Instruction limit reached!
% 35.22/6.20 % (27705)------------------------------
% 35.22/6.20 % (27705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.22/6.20 % (27705)Termination reason: Unknown
% 35.22/6.20 % (27705)Termination phase: Saturation
% 35.22/6.20
% 35.22/6.20 % (27705)Memory used [KB]: 8571
% 35.22/6.20 % (27705)Time elapsed: 0.403 s
% 35.22/6.20 % (27705)Instructions burned: 1313 (million)
% 35.22/6.20 % (27705)------------------------------
% 35.22/6.20 % (27705)------------------------------
% 35.22/6.21 % (27709)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_27050 for (2953ds/1493Mi)
% 35.22/6.23 % (27709)Refutation not found, incomplete strategy
% 35.22/6.23 % (27709)------------------------------
% 35.22/6.23 % (27709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.22/6.23 % (27709)Termination reason: Refutation not found, incomplete strategy
% 35.22/6.23
% 35.22/6.23
% 35.22/6.23 % (27709)Memory used [KB]: 6780
% 35.22/6.23 % (27709)Time elapsed: 0.027 s
% 35.22/6.23 % (27709)Instructions burned: 96 (million)
% 35.22/6.23 % (27709)------------------------------
% 35.22/6.23 % (27709)------------------------------
% 35.22/6.24 % (27710)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_27050 for (2952ds/7679Mi)
% 35.67/6.34 % (27707)First to succeed.
% 35.67/6.34 % (27707)Refutation found. Thanks to Tanya!
% 35.67/6.34 % SZS status Theorem for DTF2THF_27050
% 35.67/6.34 % SZS output start Proof for DTF2THF_27050
% 35.67/6.34 thf(type_def_5, type, itself: ($tType) > $tType).
% 35.67/6.34 thf(type_def_7, type, coinductive_llist: ($tType) > $tType).
% 35.67/6.34 thf(type_def_8, type, nat: $tType).
% 35.67/6.34 thf(type_def_9, type, set: ($tType) > $tType).
% 35.67/6.34 thf(type_def_10, type, a: $tType).
% 35.67/6.34 thf(func_def_0, type, coinductive_llist: ($tType) > $tType).
% 35.67/6.34 thf(func_def_1, type, set: ($tType) > $tType).
% 35.67/6.34 thf(func_def_2, type, nat: $tType).
% 35.67/6.34 thf(func_def_3, type, itself: ($tType) > $tType).
% 35.67/6.34 thf(func_def_4, type, a: $tType).
% 35.67/6.34 thf(func_def_5, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_6, type, one: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_7, type, zero: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_8, type, top: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_9, type, group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_10, type, monoid_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_11, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_12, type, ab_group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_13, type, semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_14, type, comm_semiring_1: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_15, type, comm_monoid_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_16, type, linordered_field: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_17, type, ab_semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_18, type, comm_monoid_diff: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_19, type, cancel_semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_20, type, ordered_ab_group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_21, type, cancel1352612707id_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_22, type, cancel146912293up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_23, type, linord219039673up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_24, type, ordere779506340up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_25, type, canoni770627133id_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_26, type, ordere236663937imp_le: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_27, type, ordere516151231imp_le: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_28, type, semiri456707255roduct: !>[X0: $tType]:(itself @ X0 > $o)).
% 35.67/6.34 thf(func_def_29, type, coindu328551480prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 35.67/6.34 thf(func_def_30, type, coinductive_lappend: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_31, type, coinductive_LCons: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_32, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_33, type, coindu1478340336prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 35.67/6.34 thf(func_def_34, type, coinductive_lsublist: !>[X0: $tType]:(coinductive_llist @ X0 > set @ nat > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_35, type, coindu780009021istsum: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 35.67/6.34 thf(func_def_36, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 35.67/6.34 thf(func_def_37, type, one_one: !>[X0: $tType]:(X0)).
% 35.67/6.34 thf(func_def_38, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 35.67/6.34 thf(func_def_39, type, zero_zero: !>[X0: $tType]:(X0)).
% 35.67/6.34 thf(func_def_40, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 35.67/6.34 thf(func_def_41, type, lList2435255213lllsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_42, type, lList2236698231inlsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_43, type, lList21916056377ts_rec: !>[X0: $tType, X1: $tType]:(X0 > (X1 > coinductive_llist @ X1 > X0 > X0) > coinductive_llist @ X1 > X0)).
% 35.67/6.34 thf(func_def_44, type, lList22096119349pslsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_45, type, lList21612149805nflsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_46, type, lList2370560421utlast: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_47, type, lList2508575361_ldrop: !>[X0: $tType]:(coinductive_llist @ X0 > nat > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_48, type, lList2170638824_llast: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 35.67/6.34 thf(func_def_49, type, lList21232602520length: !>[X0: $tType]:(coinductive_llist @ X0 > nat)).
% 35.67/6.34 thf(func_def_50, type, lList2281150353e_lrev: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_51, type, lList22119844313_ltake: !>[X0: $tType]:(coinductive_llist @ X0 > nat > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_52, type, lList21148268032oslsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_53, type, suc: nat > nat).
% 35.67/6.34 thf(func_def_54, type, nat_triangle: nat > nat).
% 35.67/6.34 thf(func_def_55, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 35.67/6.34 thf(func_def_56, type, top_top: !>[X0: $tType]:(X0)).
% 35.67/6.34 thf(func_def_57, type, type2: !>[X0: $tType]:(itself @ X0)).
% 35.67/6.34 thf(func_def_58, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 35.67/6.34 thf(func_def_59, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 35.67/6.34 thf(func_def_60, type, a2: set @ a).
% 35.67/6.34 thf(func_def_61, type, i: nat).
% 35.67/6.34 thf(func_def_62, type, t: coinductive_llist @ a).
% 35.67/6.34 thf(func_def_70, type, sK0: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 35.67/6.34 thf(func_def_71, type, sK1: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_72, type, sK2: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_73, type, sK3: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 35.67/6.34 thf(func_def_74, type, sK4: nat > nat).
% 35.67/6.34 thf(func_def_75, type, sK5: !>[X0: $tType]:(X0)).
% 35.67/6.34 thf(func_def_76, type, sK6: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 35.67/6.34 thf(func_def_77, type, sK7: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_78, type, sK8: (nat > $o) > nat).
% 35.67/6.34 thf(func_def_79, type, sK9: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat > X0)).
% 35.67/6.34 thf(func_def_80, type, sK10: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > X0)).
% 35.67/6.34 thf(func_def_81, type, sK11: !>[X0: $tType]:((nat > X0 > X0 > $o) > (nat > X0 > $o) > nat)).
% 35.67/6.34 thf(func_def_82, type, sK12: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_83, type, sK13: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 35.67/6.34 thf(func_def_84, type, sK14: nat > nat).
% 35.67/6.34 thf(func_def_85, type, sK15: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_86, type, sK16: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 35.67/6.34 thf(func_def_87, type, sK17: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_88, type, sK18: nat > nat).
% 35.67/6.34 thf(func_def_89, type, sK19: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_90, type, sK20: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 35.67/6.34 thf(func_def_91, type, sK21: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 35.67/6.34 thf(func_def_92, type, sK22: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_93, type, sK23: !>[X0: $tType]:(set @ X0 > X0)).
% 35.67/6.34 thf(func_def_94, type, sK24: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 35.67/6.34 thf(func_def_95, type, sK25: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_96, type, sK26: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 35.67/6.34 thf(func_def_97, type, sK27: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_98, type, sK28: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 35.67/6.34 thf(func_def_99, type, sK29: (nat > nat > $o) > nat).
% 35.67/6.34 thf(func_def_100, type, sK30: (nat > nat > $o) > nat).
% 35.67/6.34 thf(func_def_101, type, sK31: (nat > nat > $o) > nat).
% 35.67/6.34 thf(func_def_102, type, sK32: (nat > nat > $o) > nat).
% 35.67/6.34 thf(func_def_103, type, sK33: (nat > nat > $o) > nat).
% 35.67/6.34 thf(func_def_104, type, sK34: (nat > nat > $o) > nat).
% 35.67/6.34 thf(func_def_105, type, sK35: (nat > nat > $o) > nat).
% 35.67/6.34 thf(func_def_106, type, sK36: (nat > nat > $o) > nat).
% 35.67/6.34 thf(func_def_107, type, sK37: (nat > nat > $o) > nat).
% 35.67/6.34 thf(func_def_108, type, sK38: (nat > $o) > nat).
% 35.67/6.34 thf(func_def_109, type, sK39: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_110, type, sK40: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 35.67/6.34 thf(func_def_111, type, sK41: (nat > $o) > nat).
% 35.67/6.34 thf(func_def_112, type, sK42: !>[X0: $tType]:(set @ X0 > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 35.67/6.34 thf(func_def_113, type, sK43: (nat > $o) > nat).
% 35.67/6.34 thf(func_def_114, type, sK44: (nat > $o) > nat).
% 35.67/6.34 thf(func_def_116, type, ph46: !>[X0: $tType]:(X0)).
% 35.67/6.34 thf(f4291,plain,(
% 35.67/6.34 $false),
% 35.67/6.34 inference(trivial_inequality_removal,[status(thm)],[f4272])).
% 35.67/6.34 thf(f4272,plain,(
% 35.67/6.34 ($true != $true)),
% 35.67/6.34 inference(superposition,[status(thm)],[f4239,f1122])).
% 35.67/6.34 thf(f1122,plain,(
% 35.67/6.34 ((member @ coinductive_llist @ a @ t @ (lList2236698231inlsts @ a @ a2)) = $true)),
% 35.67/6.34 inference(cnf_transformation,[status(thm)],[f304])).
% 35.67/6.34 thf(f304,plain,(
% 35.67/6.34 ((member @ coinductive_llist @ a @ t @ (lList2236698231inlsts @ a @ a2)) = $true)),
% 35.67/6.34 inference(fool_elimination,[status(thm)],[f303])).
% 35.67/6.34 thf(f303,plain,(
% 35.67/6.34 (member @ coinductive_llist @ a @ t @ (lList2236698231inlsts @ a @ a2))),
% 35.67/6.34 inference(rectify,[status(thm)],[f279])).
% 35.67/6.34 thf(f279,axiom,(
% 35.67/6.34 (member @ coinductive_llist @ a @ t @ (lList2236698231inlsts @ a @ a2))),
% 35.67/6.34 file('/export/starexec/sandbox/tmp/tmp.3cDcvzBLpc/DTF2THF_27050.p',conj_0)).
% 35.67/6.34 thf(f4239,plain,(
% 35.67/6.34 ((member @ coinductive_llist @ a @ t @ (lList2236698231inlsts @ a @ a2)) != $true)),
% 35.67/6.34 inference(superposition,[status(thm)],[f1325,f941])).
% 35.67/6.34 thf(f941,plain,(
% 35.67/6.34 ( ! [X0 : $tType,X2 : nat,X1 : coinductive_llist @ X0] : (((coinductive_lappend @ X0 @ (lList22119844313_ltake @ X0 @ X1 @ X2) @ (lList2508575361_ldrop @ X0 @ X1 @ X2)) = X1)) )),
% 35.67/6.34 inference(cnf_transformation,[status(thm)],[f724])).
% 35.67/6.34 thf(f724,plain,(
% 35.67/6.34 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : nat] : ((coinductive_lappend @ X0 @ (lList22119844313_ltake @ X0 @ X1 @ X2) @ (lList2508575361_ldrop @ X0 @ X1 @ X2)) = X1)),
% 35.67/6.34 inference(rectify,[status(thm)],[f133])).
% 35.67/6.34 thf(f133,axiom,(
% 35.67/6.34 ! [X0 : $tType,X8 : coinductive_llist @ X0,X4 : nat] : ((coinductive_lappend @ X0 @ (lList22119844313_ltake @ X0 @ X8 @ X4) @ (lList2508575361_ldrop @ X0 @ X8 @ X4)) = X8)),
% 35.67/6.34 file('/export/starexec/sandbox/tmp/tmp.3cDcvzBLpc/DTF2THF_27050.p',fact_132_ltake__ldrop__id)).
% 35.67/6.34 thf(f1325,plain,(
% 35.67/6.34 ( ! [X0 : coinductive_llist @ a] : (($true != (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ X0 @ (lList2508575361_ldrop @ a @ t @ i)) @ (lList2236698231inlsts @ a @ a2)))) )),
% 35.67/6.34 inference(trivial_inequality_removal,[status(thm)],[f1315])).
% 35.67/6.34 thf(f1315,plain,(
% 35.67/6.34 ( ! [X0 : coinductive_llist @ a] : (($true != $true) | ($true != (member @ coinductive_llist @ a @ (coinductive_lappend @ a @ X0 @ (lList2508575361_ldrop @ a @ t @ i)) @ (lList2236698231inlsts @ a @ a2)))) )),
% 35.67/6.34 inference(superposition,[status(thm)],[f1078,f991])).
% 35.67/6.34 thf(f991,plain,(
% 35.67/6.34 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X3 : set @ X0,X1 : coinductive_llist @ X0] : (($true != (member @ coinductive_llist @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2) @ (lList2236698231inlsts @ X0 @ X3))) | ((member @ coinductive_llist @ X0 @ X2 @ (lList2236698231inlsts @ X0 @ X3)) = $true)) )),
% 35.67/6.34 inference(cnf_transformation,[status(thm)],[f873])).
% 35.67/6.34 thf(f873,plain,(
% 35.67/6.34 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0,X3 : set @ X0] : ((($true = (member @ coinductive_llist @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2) @ (lList2236698231inlsts @ X0 @ X3))) | ((member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ X3)) != $true) | ((member @ coinductive_llist @ X0 @ X2 @ (lList2236698231inlsts @ X0 @ X3)) != $true)) & ((((member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ X3)) = $true) & ((member @ coinductive_llist @ X0 @ X2 @ (lList2236698231inlsts @ X0 @ X3)) = $true)) | ($true != (member @ coinductive_llist @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2) @ (lList2236698231inlsts @ X0 @ X3)))))),
% 35.67/6.34 inference(flattening,[status(thm)],[f872])).
% 35.67/6.34 thf(f872,plain,(
% 35.67/6.34 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0,X3 : set @ X0] : ((($true = (member @ coinductive_llist @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2) @ (lList2236698231inlsts @ X0 @ X3))) | (((member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ X3)) != $true) | ((member @ coinductive_llist @ X0 @ X2 @ (lList2236698231inlsts @ X0 @ X3)) != $true))) & ((((member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ X3)) = $true) & ((member @ coinductive_llist @ X0 @ X2 @ (lList2236698231inlsts @ X0 @ X3)) = $true)) | ($true != (member @ coinductive_llist @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2) @ (lList2236698231inlsts @ X0 @ X3)))))),
% 35.67/6.34 inference(nnf_transformation,[status(thm)],[f500])).
% 35.67/6.34 thf(f500,plain,(
% 35.67/6.34 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0,X3 : set @ X0] : (($true = (member @ coinductive_llist @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2) @ (lList2236698231inlsts @ X0 @ X3))) <=> (((member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ X3)) = $true) & ((member @ coinductive_llist @ X0 @ X2 @ (lList2236698231inlsts @ X0 @ X3)) = $true)))),
% 35.67/6.34 inference(fool_elimination,[status(thm)],[f499])).
% 35.67/6.34 thf(f499,plain,(
% 35.67/6.34 ! [X0 : $tType,X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0,X3 : set @ X0] : ((member @ coinductive_llist @ X0 @ (coinductive_lappend @ X0 @ X1 @ X2) @ (lList2236698231inlsts @ X0 @ X3)) = (member @ coinductive_llist @ X0 @ X1 @ (lList2236698231inlsts @ X0 @ X3)) & (member @ coinductive_llist @ X0 @ X2 @ (lList2236698231inlsts @ X0 @ X3)))),
% 35.67/6.34 inference(rectify,[status(thm)],[f9])).
% 35.67/6.34 thf(f9,axiom,(
% 35.67/6.34 ! [X0 : $tType,X10 : coinductive_llist @ X0,X11 : coinductive_llist @ X0,X3 : set @ X0] : ((member @ coinductive_llist @ X0 @ (coinductive_lappend @ X0 @ X10 @ X11) @ (lList2236698231inlsts @ X0 @ X3)) = (member @ coinductive_llist @ X0 @ X10 @ (lList2236698231inlsts @ X0 @ X3)) & (member @ coinductive_llist @ X0 @ X11 @ (lList2236698231inlsts @ X0 @ X3)))),
% 35.67/6.34 file('/export/starexec/sandbox/tmp/tmp.3cDcvzBLpc/DTF2THF_27050.p',fact_8_lapp__fin__fin__iff)).
% 35.67/6.34 thf(f1078,plain,(
% 35.67/6.34 ((member @ coinductive_llist @ a @ (lList2508575361_ldrop @ a @ t @ i) @ (lList2236698231inlsts @ a @ a2)) != $true)),
% 35.67/6.34 inference(cnf_transformation,[status(thm)],[f719])).
% 35.67/6.34 thf(f719,plain,(
% 35.67/6.34 ((member @ coinductive_llist @ a @ (lList2508575361_ldrop @ a @ t @ i) @ (lList2236698231inlsts @ a @ a2)) != $true)),
% 35.67/6.34 inference(flattening,[status(thm)],[f418])).
% 35.67/6.34 thf(f418,plain,(
% 35.67/6.34 ~((member @ coinductive_llist @ a @ (lList2508575361_ldrop @ a @ t @ i) @ (lList2236698231inlsts @ a @ a2)) = $true)),
% 35.67/6.34 inference(fool_elimination,[status(thm)],[f417])).
% 35.67/6.34 thf(f417,plain,(
% 35.67/6.34 ~(member @ coinductive_llist @ a @ (lList2508575361_ldrop @ a @ t @ i) @ (lList2236698231inlsts @ a @ a2))),
% 35.67/6.34 inference(rectify,[status(thm)],[f281])).
% 35.67/6.34 thf(f281,negated_conjecture,(
% 35.67/6.34 ~(member @ coinductive_llist @ a @ (lList2508575361_ldrop @ a @ t @ i) @ (lList2236698231inlsts @ a @ a2))),
% 35.67/6.34 inference(negated_conjecture,[status(cth)],[f280])).
% 35.67/6.34 thf(f280,conjecture,(
% 35.67/6.34 (member @ coinductive_llist @ a @ (lList2508575361_ldrop @ a @ t @ i) @ (lList2236698231inlsts @ a @ a2))),
% 35.67/6.34 file('/export/starexec/sandbox/tmp/tmp.3cDcvzBLpc/DTF2THF_27050.p',conj_1)).
% 35.67/6.34 % SZS output end Proof for DTF2THF_27050
% 35.67/6.34 % (27707)------------------------------
% 35.67/6.34 % (27707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.67/6.34 % (27707)Termination reason: Refutation
% 35.67/6.34
% 35.67/6.34 % (27707)Memory used [KB]: 8059
% 35.67/6.34 % (27707)Time elapsed: 0.310 s
% 35.67/6.34 % (27707)Instructions burned: 979 (million)
% 35.67/6.34 % (27707)------------------------------
% 35.67/6.34 % (27707)------------------------------
% 35.67/6.34 % (27242)Success in time 4.818 s
%------------------------------------------------------------------------------