%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT182^1 : 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 : n026.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 08:45:03 AM UTC 2026
% Result : Theorem 278.23s 41.19s
% Output : Refutation 278.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT182^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n026.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 06:10:40 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : DAT182^1 : TPTP v9.2.1. Released v7.0.0.
% 0.19/0.45 % Domain : Data Structures
% 0.19/0.45 % Problem : Lazy lists II 857
% 0.19/0.45 % Version : [Bla16] axioms : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Fri04] Friedrich (2004), Lazy Lists II
% 0.19/0.45 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.19/0.45 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bla16]
% 0.19/0.45 % Names : llist2__857.p [Bla16]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.33 v9.1.0, 0.67 v8.1.0, 0.50 v7.5.0, 0.33 v7.2.0, 0.50 v7.1.0
% 0.19/0.45 % Syntax : Number of formulae : 325 ( 82 unt; 45 typ; 0 def)
% 0.19/0.45 % Number of atoms : 880 ( 222 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 13 ( 3 avg)
% 0.19/0.45 % Number of connectives : 3808 ( 93 ~; 22 |; 52 &;3156 @)
% 0.19/0.45 % ( 0 <=>; 485 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 21 ( 9 avg)
% 0.19/0.45 % Number of types : 3 ( 2 usr)
% 0.19/0.45 % Number of type conns : 205 ( 205 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 44 ( 43 usr; 2 con; 0-5 aty)
% 0.19/0.45 % Number of variables : 1053 ( 51 ^; 918 !; 45 ?;1053 :)
% 0.19/0.45 % ( 39 !>; 0 ?*; 0 @-; 0 @+)
% 0.19/0.45 % SPC : TH1_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.19/0.45 % 2016-07-13 14:49:40.110
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 %----Could-be-implicit typings (5)
% 0.19/0.45 thf(ty_t_Coinductive__List_Ollist,type,
% 0.19/0.45 coinductive_llist: $tType > $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_Set_Oset,type,
% 0.19/0.45 set: $tType > $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_Nat_Onat,type,
% 0.19/0.45 nat: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_t_itself,type,
% 0.19/0.45 itself: $tType > $tType ).
% 0.19/0.45
% 0.19/0.45 thf(ty_tf_a,type,
% 0.19/0.45 a: $tType ).
% 0.19/0.45
% 0.19/0.45 %----Explicit typings (40)
% 0.19/0.45 thf(sy_cl_HOL_Otype,type,
% 0.19/0.45 type:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Oord,type,
% 0.19/0.45 ord:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Otop,type,
% 0.19/0.45 top:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Oorder,type,
% 0.19/0.45 order:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Ono__bot,type,
% 0.19/0.45 no_bot:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Ono__top,type,
% 0.19/0.45 no_top:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Olinorder,type,
% 0.19/0.45 linorder:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Opreorder,type,
% 0.19/0.45 preorder:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Oorder__top,type,
% 0.19/0.45 order_top:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Owellorder,type,
% 0.19/0.45 wellorder:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Odense__order,type,
% 0.19/0.45 dense_order:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.19/0.45 dense_linorder:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 0.19/0.45 condit1656338222tinuum:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 0.19/0.45 condit1037483654norder:
% 0.19/0.45 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 0.19/0.45 coindu328551480prefix:
% 0.19/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Coinductive__List_Olappend,type,
% 0.19/0.45 coinductive_lappend:
% 0.19/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.19/0.45 coinductive_LCons:
% 0.19/0.45 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 0.19/0.45 coinductive_LNil:
% 0.19/0.45 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 0.19/0.45 coindu1478340336prefix:
% 0.19/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllstsp,type,
% 0.19/0.45 lList21511617539llstsp:
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts,type,
% 0.19/0.45 lList2236698231inlsts:
% 0.19/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec,type,
% 0.19/0.45 lList21916056377ts_rec:
% 0.19/0.45 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B > B ) > ( coinductive_llist @ A ) > B ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlstsp,type,
% 0.19/0.45 lList2860480441nlstsp:
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts,type,
% 0.19/0.45 lList22096119349pslsts:
% 0.19/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast,type,
% 0.19/0.45 lList2370560421utlast:
% 0.19/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oldrop,type,
% 0.19/0.45 lList2508575361_ldrop:
% 0.19/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast,type,
% 0.19/0.45 lList2170638824_llast:
% 0.19/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollength,type,
% 0.19/0.45 lList21232602520length:
% 0.19/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev,type,
% 0.19/0.45 lList2281150353e_lrev:
% 0.19/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oltake,type,
% 0.19/0.45 lList22119844313_ltake:
% 0.19/0.45 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts,type,
% 0.19/0.45 lList21148268032oslsts:
% 0.19/0.45 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.19/0.45 ord_less:
% 0.19/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.19/0.45 ord_less_eq:
% 0.19/0.45 !>[A: $tType] : ( A > A > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Orderings_Oordering__top,type,
% 0.19/0.45 ordering_top:
% 0.19/0.45 !>[A: $tType] : ( ( A > A > $o ) > ( A > A > $o ) > A > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.19/0.45 top_top:
% 0.19/0.45 !>[A: $tType] : A ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Pure_Otype,type,
% 0.19/0.45 type2:
% 0.19/0.45 !>[A: $tType] : ( itself @ A ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_Set_OCollect,type,
% 0.19/0.45 collect:
% 0.19/0.45 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_c_member,type,
% 0.19/0.45 member:
% 0.19/0.45 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_a,type,
% 0.19/0.45 a2: a ).
% 0.19/0.45
% 0.19/0.45 thf(sy_v_l,type,
% 0.19/0.45 l: coinductive_llist @ a ).
% 0.19/0.45
% 0.19/0.45 %----Relevant facts (256)
% 0.19/0.45 thf(fact_0_llistE,axiom,
% 0.19/0.45 ! [A: $tType,Y: coinductive_llist @ A] :
% 0.19/0.45 ( ( Y
% 0.19/0.45 != ( coinductive_LNil @ A ) )
% 0.19/0.45 => ~ ! [X21: A,X22: coinductive_llist @ A] :
% 0.19/0.45 ( Y
% 0.19/0.45 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % llistE
% 0.19/0.45 thf(fact_1_llist_Oinject,axiom,
% 0.19/0.45 ! [A: $tType,X212: A,X222: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 0.19/0.45 ( ( ( coinductive_LCons @ A @ X212 @ X222 )
% 0.19/0.45 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 0.19/0.45 = ( ( X212 = Y21 )
% 0.19/0.45 & ( X222 = Y22 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % llist.inject
% 0.19/0.45 thf(fact_2_order__refl,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.19/0.45
% 0.19/0.45 % order_refl
% 0.19/0.45 thf(fact_3_llist_Odistinct_I1_J,axiom,
% 0.19/0.45 ! [A: $tType,X212: A,X222: coinductive_llist @ A] :
% 0.19/0.45 ( ( coinductive_LNil @ A )
% 0.19/0.45 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ).
% 0.19/0.45
% 0.19/0.45 % llist.distinct(1)
% 0.19/0.45 thf(fact_4_neq__LNil__conv,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.19/0.45 ( ( Xs
% 0.19/0.45 != ( coinductive_LNil @ A ) )
% 0.19/0.45 = ( ? [X2: A,Xs2: coinductive_llist @ A] :
% 0.19/0.45 ( Xs
% 0.19/0.45 = ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % neq_LNil_conv
% 0.19/0.45 thf(fact_5_llist__less__def,axiom,
% 0.19/0.45 ( ( ord_less @ ( coinductive_llist @ a ) )
% 0.19/0.45 = ( ^ [S: coinductive_llist @ a,T: coinductive_llist @ a] :
% 0.19/0.45 ( ( ord_less_eq @ ( coinductive_llist @ a ) @ S @ T )
% 0.19/0.45 & ( S != T ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % llist_less_def
% 0.19/0.45 thf(fact_6_llist__le__def,axiom,
% 0.19/0.45 ( ( ord_less_eq @ ( coinductive_llist @ a ) )
% 0.19/0.45 = ( ^ [S: coinductive_llist @ a,T: coinductive_llist @ a] :
% 0.19/0.45 ? [D: coinductive_llist @ a] :
% 0.19/0.45 ( T
% 0.19/0.45 = ( coinductive_lappend @ a @ S @ D ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % llist_le_def
% 0.19/0.45 thf(fact_7_lbutlast__LNil,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( lList2370560421utlast @ A @ ( coinductive_LNil @ A ) )
% 0.19/0.45 = ( coinductive_LNil @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 % lbutlast_LNil
% 0.19/0.45 thf(fact_8_fps__induct,axiom,
% 0.19/0.45 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.19/0.45 => ( ! [A3: A] :
% 0.19/0.45 ( ( member @ A @ A3 @ A2 )
% 0.19/0.45 => ( P @ ( coinductive_LCons @ A @ A3 @ ( coinductive_LNil @ A ) ) ) )
% 0.19/0.45 => ( ! [A3: A,L2: coinductive_llist @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.19/0.45 => ( ( P @ L2 )
% 0.19/0.45 => ( ( member @ A @ A3 @ A2 )
% 0.19/0.45 => ( P @ ( coinductive_LCons @ A @ A3 @ L2 ) ) ) ) )
% 0.19/0.45 => ( P @ L ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % fps_induct
% 0.19/0.45 thf(fact_9_alllstsp_Ocases,axiom,
% 0.19/0.45 ! [A: $tType,A2: A > $o,A4: coinductive_llist @ A] :
% 0.19/0.45 ( ( lList21511617539llstsp @ A @ A2 @ A4 )
% 0.19/0.45 => ( ( A4
% 0.19/0.45 != ( coinductive_LNil @ A ) )
% 0.19/0.45 => ~ ! [L2: coinductive_llist @ A,A3: A] :
% 0.19/0.45 ( ( A4
% 0.19/0.45 = ( coinductive_LCons @ A @ A3 @ L2 ) )
% 0.19/0.45 => ( ( lList21511617539llstsp @ A @ A2 @ L2 )
% 0.19/0.45 => ~ ( A2 @ A3 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % alllstsp.cases
% 0.19/0.45 thf(fact_10_alllstsp_Osimps,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( lList21511617539llstsp @ A )
% 0.19/0.45 = ( ^ [A5: A > $o,A6: coinductive_llist @ A] :
% 0.19/0.45 ( ( A6
% 0.19/0.45 = ( coinductive_LNil @ A ) )
% 0.19/0.45 | ? [L3: coinductive_llist @ A,B2: A] :
% 0.19/0.45 ( ( A6
% 0.19/0.45 = ( coinductive_LCons @ A @ B2 @ L3 ) )
% 0.19/0.45 & ( lList21511617539llstsp @ A @ A5 @ L3 )
% 0.19/0.45 & ( A5 @ B2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % alllstsp.simps
% 0.19/0.45 thf(fact_11_finlstsp_Ocases,axiom,
% 0.19/0.45 ! [A: $tType,A2: A > $o,A4: coinductive_llist @ A] :
% 0.19/0.45 ( ( lList2860480441nlstsp @ A @ A2 @ A4 )
% 0.19/0.45 => ( ( A4
% 0.19/0.45 != ( coinductive_LNil @ A ) )
% 0.19/0.45 => ~ ! [L2: coinductive_llist @ A,A3: A] :
% 0.19/0.45 ( ( A4
% 0.19/0.45 = ( coinductive_LCons @ A @ A3 @ L2 ) )
% 0.19/0.45 => ( ( lList2860480441nlstsp @ A @ A2 @ L2 )
% 0.19/0.45 => ~ ( A2 @ A3 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % finlstsp.cases
% 0.19/0.45 thf(fact_12_finlstsp_Osimps,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( lList2860480441nlstsp @ A )
% 0.19/0.45 = ( ^ [A5: A > $o,A6: coinductive_llist @ A] :
% 0.19/0.45 ( ( A6
% 0.19/0.45 = ( coinductive_LNil @ A ) )
% 0.19/0.45 | ? [L3: coinductive_llist @ A,B2: A] :
% 0.19/0.45 ( ( A6
% 0.19/0.45 = ( coinductive_LCons @ A @ B2 @ L3 ) )
% 0.19/0.45 & ( lList2860480441nlstsp @ A @ A5 @ L3 )
% 0.19/0.45 & ( A5 @ B2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % finlstsp.simps
% 0.19/0.45 thf(fact_13_lappend__code_I2_J,axiom,
% 0.19/0.45 ! [A: $tType,Xa: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.19/0.45 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa @ X ) @ Ys )
% 0.19/0.45 = ( coinductive_LCons @ A @ Xa @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lappend_code(2)
% 0.19/0.45 thf(fact_14_lappend__eq__LNil__iff,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.19/0.45 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.19/0.45 = ( coinductive_LNil @ A ) )
% 0.19/0.45 = ( ( Xs
% 0.19/0.45 = ( coinductive_LNil @ A ) )
% 0.19/0.45 & ( Ys
% 0.19/0.45 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lappend_eq_LNil_iff
% 0.19/0.45 thf(fact_15_LNil__eq__lappend__iff,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.19/0.45 ( ( ( coinductive_LNil @ A )
% 0.19/0.45 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.19/0.45 = ( ( Xs
% 0.19/0.45 = ( coinductive_LNil @ A ) )
% 0.19/0.45 & ( Ys
% 0.19/0.45 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % LNil_eq_lappend_iff
% 0.19/0.45 thf(fact_16_lappend__LNil2,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.19/0.45 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.19/0.45 = Xs ) ).
% 0.19/0.45
% 0.19/0.45 % lappend_LNil2
% 0.19/0.45 thf(fact_17_lappend__code_I1_J,axiom,
% 0.19/0.45 ! [A: $tType,Ys: coinductive_llist @ A] :
% 0.19/0.45 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 0.19/0.45 = Ys ) ).
% 0.19/0.45
% 0.19/0.45 % lappend_code(1)
% 0.19/0.45 thf(fact_18_lappend__is__LNil__conv,axiom,
% 0.19/0.45 ! [A: $tType,S2: coinductive_llist @ A,T2: coinductive_llist @ A] :
% 0.19/0.45 ( ( ( coinductive_lappend @ A @ S2 @ T2 )
% 0.19/0.45 = ( coinductive_LNil @ A ) )
% 0.19/0.45 = ( ( S2
% 0.19/0.45 = ( coinductive_LNil @ A ) )
% 0.19/0.45 & ( T2
% 0.19/0.45 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lappend_is_LNil_conv
% 0.19/0.45 thf(fact_19_LNil__is__lappend__conv,axiom,
% 0.19/0.45 ! [A: $tType,S2: coinductive_llist @ A,T2: coinductive_llist @ A] :
% 0.19/0.45 ( ( ( coinductive_LNil @ A )
% 0.19/0.45 = ( coinductive_lappend @ A @ S2 @ T2 ) )
% 0.19/0.45 = ( ( S2
% 0.19/0.45 = ( coinductive_LNil @ A ) )
% 0.19/0.45 & ( T2
% 0.19/0.45 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % LNil_is_lappend_conv
% 0.19/0.45 thf(fact_20_ord__eq__less__subst,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType] :
% 0.19/0.45 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.19/0.45 & ( ord @ A @ ( type2 @ A ) ) )
% 0.19/0.45 => ! [A4: A,F: B > A,B3: B,C: B] :
% 0.19/0.45 ( ( A4
% 0.19/0.45 = ( F @ B3 ) )
% 0.19/0.45 => ( ( ord_less @ B @ B3 @ C )
% 0.19/0.45 => ( ! [X3: B,Y2: B] :
% 0.19/0.45 ( ( ord_less @ B @ X3 @ Y2 )
% 0.19/0.45 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.19/0.45 => ( ord_less @ A @ A4 @ ( F @ C ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ord_eq_less_subst
% 0.19/0.45 thf(fact_21_ord__less__eq__subst,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType] :
% 0.19/0.45 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.19/0.45 & ( ord @ A @ ( type2 @ A ) ) )
% 0.19/0.45 => ! [A4: A,B3: A,F: A > B,C: B] :
% 0.19/0.45 ( ( ord_less @ A @ A4 @ B3 )
% 0.19/0.45 => ( ( ( F @ B3 )
% 0.19/0.45 = C )
% 0.19/0.45 => ( ! [X3: A,Y2: A] :
% 0.19/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.19/0.45 => ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.19/0.45 => ( ord_less @ B @ ( F @ A4 ) @ C ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ord_less_eq_subst
% 0.19/0.45 thf(fact_22_order__less__subst1,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType] :
% 0.19/0.45 ( ( ( order @ B @ ( type2 @ B ) )
% 0.19/0.45 & ( order @ A @ ( type2 @ A ) ) )
% 0.19/0.45 => ! [A4: A,F: B > A,B3: B,C: B] :
% 0.19/0.45 ( ( ord_less @ A @ A4 @ ( F @ B3 ) )
% 0.19/0.45 => ( ( ord_less @ B @ B3 @ C )
% 0.19/0.45 => ( ! [X3: B,Y2: B] :
% 0.19/0.45 ( ( ord_less @ B @ X3 @ Y2 )
% 0.19/0.45 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.19/0.45 => ( ord_less @ A @ A4 @ ( F @ C ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order_less_subst1
% 0.19/0.45 thf(fact_23_order__less__subst2,axiom,
% 0.19/0.45 ! [A: $tType,C2: $tType] :
% 0.19/0.45 ( ( ( order @ C2 @ ( type2 @ C2 ) )
% 0.19/0.45 & ( order @ A @ ( type2 @ A ) ) )
% 0.19/0.45 => ! [A4: A,B3: A,F: A > C2,C: C2] :
% 0.19/0.45 ( ( ord_less @ A @ A4 @ B3 )
% 0.19/0.45 => ( ( ord_less @ C2 @ ( F @ B3 ) @ C )
% 0.19/0.45 => ( ! [X3: A,Y2: A] :
% 0.19/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.19/0.45 => ( ord_less @ C2 @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.19/0.45 => ( ord_less @ C2 @ ( F @ A4 ) @ C ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order_less_subst2
% 0.19/0.45 thf(fact_24_lt__ex,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( no_bot @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A] :
% 0.19/0.45 ? [Y2: A] : ( ord_less @ A @ Y2 @ X ) ) ).
% 0.19/0.45
% 0.19/0.45 % lt_ex
% 0.19/0.45 thf(fact_25_gt__ex,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( no_top @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A] :
% 0.19/0.45 ? [X1: A] : ( ord_less @ A @ X @ X1 ) ) ).
% 0.19/0.45
% 0.19/0.45 % gt_ex
% 0.19/0.45 thf(fact_26_neqE,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( X != Y )
% 0.19/0.45 => ( ~ ( ord_less @ A @ X @ Y )
% 0.19/0.45 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % neqE
% 0.19/0.45 thf(fact_27_lappend__assoc,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.19/0.45 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 0.19/0.45 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lappend_assoc
% 0.19/0.45 thf(fact_28_neq__iff,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( X != Y )
% 0.19/0.45 = ( ( ord_less @ A @ X @ Y )
% 0.19/0.45 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % neq_iff
% 0.19/0.45 thf(fact_29_order_Oasym,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A,B3: A] :
% 0.19/0.45 ( ( ord_less @ A @ A4 @ B3 )
% 0.19/0.45 => ~ ( ord_less @ A @ B3 @ A4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order.asym
% 0.19/0.45 thf(fact_30_dense,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( dense_order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( ord_less @ A @ X @ Y )
% 0.19/0.45 => ? [Z: A] :
% 0.19/0.45 ( ( ord_less @ A @ X @ Z )
% 0.19/0.45 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dense
% 0.19/0.45 thf(fact_31_less__imp__neq,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( ord_less @ A @ X @ Y )
% 0.19/0.45 => ( X != Y ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_imp_neq
% 0.19/0.45 thf(fact_32_less__asym,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( ord_less @ A @ X @ Y )
% 0.19/0.45 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_asym
% 0.19/0.45 thf(fact_33_less__asym_H,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A,B3: A] :
% 0.19/0.45 ( ( ord_less @ A @ A4 @ B3 )
% 0.19/0.45 => ~ ( ord_less @ A @ B3 @ A4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_asym'
% 0.19/0.45 thf(fact_34_less__trans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A,Z2: A] :
% 0.19/0.45 ( ( ord_less @ A @ X @ Y )
% 0.19/0.45 => ( ( ord_less @ A @ Y @ Z2 )
% 0.19/0.45 => ( ord_less @ A @ X @ Z2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_trans
% 0.19/0.45 thf(fact_35_less__linear,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( ord_less @ A @ X @ Y )
% 0.19/0.45 | ( X = Y )
% 0.19/0.45 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_linear
% 0.19/0.45 thf(fact_36_less__irrefl,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A] :
% 0.19/0.45 ~ ( ord_less @ A @ X @ X ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_irrefl
% 0.19/0.45 thf(fact_37_ord__eq__less__trans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( ord @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A,B3: A,C: A] :
% 0.19/0.45 ( ( A4 = B3 )
% 0.19/0.45 => ( ( ord_less @ A @ B3 @ C )
% 0.19/0.45 => ( ord_less @ A @ A4 @ C ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ord_eq_less_trans
% 0.19/0.45 thf(fact_38_ord__less__eq__trans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( ord @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A,B3: A,C: A] :
% 0.19/0.45 ( ( ord_less @ A @ A4 @ B3 )
% 0.19/0.45 => ( ( B3 = C )
% 0.19/0.45 => ( ord_less @ A @ A4 @ C ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ord_less_eq_trans
% 0.19/0.45 thf(fact_39_dual__order_Oasym,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [B3: A,A4: A] :
% 0.19/0.45 ( ( ord_less @ A @ B3 @ A4 )
% 0.19/0.45 => ~ ( ord_less @ A @ A4 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dual_order.asym
% 0.19/0.45 thf(fact_40_less__imp__not__eq,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( ord_less @ A @ X @ Y )
% 0.19/0.45 => ( X != Y ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_imp_not_eq
% 0.19/0.45 thf(fact_41_less__not__sym,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( ord_less @ A @ X @ Y )
% 0.19/0.45 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_not_sym
% 0.19/0.45 thf(fact_42_less__induct,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [P: A > $o,A4: A] :
% 0.19/0.45 ( ! [X3: A] :
% 0.19/0.45 ( ! [Y3: A] :
% 0.19/0.45 ( ( ord_less @ A @ Y3 @ X3 )
% 0.19/0.45 => ( P @ Y3 ) )
% 0.19/0.45 => ( P @ X3 ) )
% 0.19/0.45 => ( P @ A4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_induct
% 0.19/0.45 thf(fact_43_antisym__conv3,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [Y: A,X: A] :
% 0.19/0.45 ( ~ ( ord_less @ A @ Y @ X )
% 0.19/0.45 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.19/0.45 = ( X = Y ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % antisym_conv3
% 0.19/0.45 thf(fact_44_less__imp__not__eq2,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( ord_less @ A @ X @ Y )
% 0.19/0.45 => ( Y != X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_imp_not_eq2
% 0.19/0.45 thf(fact_45_mem__Collect__eq,axiom,
% 0.19/0.45 ! [A: $tType,A4: A,P: A > $o] :
% 0.19/0.45 ( ( member @ A @ A4 @ ( collect @ A @ P ) )
% 0.19/0.45 = ( P @ A4 ) ) ).
% 0.19/0.45
% 0.19/0.45 % mem_Collect_eq
% 0.19/0.45 thf(fact_46_Collect__mem__eq,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A] :
% 0.19/0.45 ( ( collect @ A
% 0.19/0.45 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 0.19/0.45 = A2 ) ).
% 0.19/0.45
% 0.19/0.45 % Collect_mem_eq
% 0.19/0.45 thf(fact_47_Collect__cong,axiom,
% 0.19/0.45 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.45 ( ! [X3: A] :
% 0.19/0.45 ( ( P @ X3 )
% 0.19/0.45 = ( Q @ X3 ) )
% 0.19/0.45 => ( ( collect @ A @ P )
% 0.19/0.45 = ( collect @ A @ Q ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Collect_cong
% 0.19/0.45 thf(fact_48_ext,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.19/0.45 ( ! [X3: A] :
% 0.19/0.45 ( ( F @ X3 )
% 0.19/0.45 = ( G @ X3 ) )
% 0.19/0.45 => ( F = G ) ) ).
% 0.19/0.45
% 0.19/0.45 % ext
% 0.19/0.45 thf(fact_49_less__imp__triv,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A,P: $o] :
% 0.19/0.45 ( ( ord_less @ A @ X @ Y )
% 0.19/0.45 => ( ( ord_less @ A @ Y @ X )
% 0.19/0.45 => P ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_imp_triv
% 0.19/0.45 thf(fact_50_linorder__cases,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ~ ( ord_less @ A @ X @ Y )
% 0.19/0.45 => ( ( X != Y )
% 0.19/0.45 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % linorder_cases
% 0.19/0.45 thf(fact_51_dual__order_Oirrefl,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A] :
% 0.19/0.45 ~ ( ord_less @ A @ A4 @ A4 ) ) ).
% 0.19/0.45
% 0.19/0.45 % dual_order.irrefl
% 0.19/0.45 thf(fact_52_fpslsts__mono,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList22096119349pslsts @ A @ A2 ) @ ( lList22096119349pslsts @ A @ B4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % fpslsts_mono
% 0.19/0.45 thf(fact_53_order_Ostrict__trans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A,B3: A,C: A] :
% 0.19/0.45 ( ( ord_less @ A @ A4 @ B3 )
% 0.19/0.45 => ( ( ord_less @ A @ B3 @ C )
% 0.19/0.45 => ( ord_less @ A @ A4 @ C ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order.strict_trans
% 0.19/0.45 thf(fact_54_alllstsp__mono,axiom,
% 0.19/0.45 ! [A: $tType,A2: A > $o,B4: A > $o] :
% 0.19/0.45 ( ( ord_less_eq @ ( A > $o ) @ A2 @ B4 )
% 0.19/0.45 => ( ord_less_eq @ ( ( coinductive_llist @ A ) > $o ) @ ( lList21511617539llstsp @ A @ A2 ) @ ( lList21511617539llstsp @ A @ B4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % alllstsp_mono
% 0.19/0.45 thf(fact_55_finlstsp__mono,axiom,
% 0.19/0.45 ! [A: $tType,A2: A > $o,B4: A > $o] :
% 0.19/0.45 ( ( ord_less_eq @ ( A > $o ) @ A2 @ B4 )
% 0.19/0.45 => ( ord_less_eq @ ( ( coinductive_llist @ A ) > $o ) @ ( lList2860480441nlstsp @ A @ A2 ) @ ( lList2860480441nlstsp @ A @ B4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % finlstsp_mono
% 0.19/0.45 thf(fact_56_less__imp__not__less,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( ord_less @ A @ X @ Y )
% 0.19/0.45 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_imp_not_less
% 0.19/0.45 thf(fact_57_dual__order_Ostrict__trans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [B3: A,A4: A,C: A] :
% 0.19/0.45 ( ( ord_less @ A @ B3 @ A4 )
% 0.19/0.45 => ( ( ord_less @ A @ C @ B3 )
% 0.19/0.45 => ( ord_less @ A @ C @ A4 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dual_order.strict_trans
% 0.19/0.45 thf(fact_58_not__less__iff__gr__or__eq,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.19/0.45 = ( ( ord_less @ A @ Y @ X )
% 0.19/0.45 | ( X = Y ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % not_less_iff_gr_or_eq
% 0.19/0.45 thf(fact_59_order_Ostrict__implies__not__eq,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A,B3: A] :
% 0.19/0.45 ( ( ord_less @ A @ A4 @ B3 )
% 0.19/0.45 => ( A4 != B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order.strict_implies_not_eq
% 0.19/0.45 thf(fact_60_dual__order_Ostrict__implies__not__eq,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [B3: A,A4: A] :
% 0.19/0.45 ( ( ord_less @ A @ B3 @ A4 )
% 0.19/0.45 => ( A4 != B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dual_order.strict_implies_not_eq
% 0.19/0.45 thf(fact_61_order_Onot__eq__order__implies__strict,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A,B3: A] :
% 0.19/0.45 ( ( A4 != B3 )
% 0.19/0.45 => ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.19/0.45 => ( ord_less @ A @ A4 @ B3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order.not_eq_order_implies_strict
% 0.19/0.45 thf(fact_62_dual__order_Ostrict__implies__order,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [B3: A,A4: A] :
% 0.19/0.45 ( ( ord_less @ A @ B3 @ A4 )
% 0.19/0.45 => ( ord_less_eq @ A @ B3 @ A4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dual_order.strict_implies_order
% 0.19/0.45 thf(fact_63_dual__order_Ostrict__iff__order,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ( ( ord_less @ A )
% 0.19/0.45 = ( ^ [B2: A,A6: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ B2 @ A6 )
% 0.19/0.45 & ( A6 != B2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dual_order.strict_iff_order
% 0.19/0.45 thf(fact_64_dual__order_Oorder__iff__strict,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ( ( ord_less_eq @ A )
% 0.19/0.45 = ( ^ [B2: A,A6: A] :
% 0.19/0.45 ( ( ord_less @ A @ B2 @ A6 )
% 0.19/0.45 | ( A6 = B2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dual_order.order_iff_strict
% 0.19/0.45 thf(fact_65_order_Ostrict__implies__order,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A,B3: A] :
% 0.19/0.45 ( ( ord_less @ A @ A4 @ B3 )
% 0.19/0.45 => ( ord_less_eq @ A @ A4 @ B3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order.strict_implies_order
% 0.19/0.45 thf(fact_66_dense__le__bounded,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A,Z2: A] :
% 0.19/0.45 ( ( ord_less @ A @ X @ Y )
% 0.19/0.45 => ( ! [W: A] :
% 0.19/0.45 ( ( ord_less @ A @ X @ W )
% 0.19/0.45 => ( ( ord_less @ A @ W @ Y )
% 0.19/0.45 => ( ord_less_eq @ A @ W @ Z2 ) ) )
% 0.19/0.45 => ( ord_less_eq @ A @ Y @ Z2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dense_le_bounded
% 0.19/0.45 thf(fact_67_dense__ge__bounded,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [Z2: A,X: A,Y: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z2 @ X )
% 0.19/0.45 => ( ! [W: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z2 @ W )
% 0.19/0.45 => ( ( ord_less @ A @ W @ X )
% 0.19/0.45 => ( ord_less_eq @ A @ Y @ W ) ) )
% 0.19/0.45 => ( ord_less_eq @ A @ Y @ Z2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dense_ge_bounded
% 0.19/0.45 thf(fact_68_dual__order_Ostrict__trans2,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [B3: A,A4: A,C: A] :
% 0.19/0.45 ( ( ord_less @ A @ B3 @ A4 )
% 0.19/0.45 => ( ( ord_less_eq @ A @ C @ B3 )
% 0.19/0.45 => ( ord_less @ A @ C @ A4 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dual_order.strict_trans2
% 0.19/0.45 thf(fact_69_dual__order_Ostrict__trans1,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [B3: A,A4: A,C: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ B3 @ A4 )
% 0.19/0.45 => ( ( ord_less @ A @ C @ B3 )
% 0.19/0.45 => ( ord_less @ A @ C @ A4 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dual_order.strict_trans1
% 0.19/0.45 thf(fact_70_order_Ostrict__iff__order,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ( ( ord_less @ A )
% 0.19/0.45 = ( ^ [A6: A,B2: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A6 @ B2 )
% 0.19/0.45 & ( A6 != B2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order.strict_iff_order
% 0.19/0.45 thf(fact_71_order_Oorder__iff__strict,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ( ( ord_less_eq @ A )
% 0.19/0.45 = ( ^ [A6: A,B2: A] :
% 0.19/0.45 ( ( ord_less @ A @ A6 @ B2 )
% 0.19/0.45 | ( A6 = B2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order.order_iff_strict
% 0.19/0.45 thf(fact_72_order_Ostrict__trans2,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A,B3: A,C: A] :
% 0.19/0.45 ( ( ord_less @ A @ A4 @ B3 )
% 0.19/0.45 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.19/0.45 => ( ord_less @ A @ A4 @ C ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order.strict_trans2
% 0.19/0.45 thf(fact_73_order_Ostrict__trans1,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A,B3: A,C: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.19/0.45 => ( ( ord_less @ A @ B3 @ C )
% 0.19/0.45 => ( ord_less @ A @ A4 @ C ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order.strict_trans1
% 0.19/0.45 thf(fact_74_not__le__imp__less,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [Y: A,X: A] :
% 0.19/0.45 ( ~ ( ord_less_eq @ A @ Y @ X )
% 0.19/0.45 => ( ord_less @ A @ X @ Y ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % not_le_imp_less
% 0.19/0.45 thf(fact_75_less__le__not__le,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ( ( ord_less @ A )
% 0.19/0.45 = ( ^ [X2: A,Y4: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.19/0.45 & ~ ( ord_less_eq @ A @ Y4 @ X2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_le_not_le
% 0.19/0.45 thf(fact_76_le__imp__less__or__eq,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X @ Y )
% 0.19/0.45 => ( ( ord_less @ A @ X @ Y )
% 0.19/0.45 | ( X = Y ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_imp_less_or_eq
% 0.19/0.45 thf(fact_77_le__less__linear,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X @ Y )
% 0.19/0.45 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_less_linear
% 0.19/0.45 thf(fact_78_dense__le,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [Y: A,Z2: A] :
% 0.19/0.45 ( ! [X3: A] :
% 0.19/0.45 ( ( ord_less @ A @ X3 @ Y )
% 0.19/0.45 => ( ord_less_eq @ A @ X3 @ Z2 ) )
% 0.19/0.45 => ( ord_less_eq @ A @ Y @ Z2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dense_le
% 0.19/0.45 thf(fact_79_dense__ge,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [Z2: A,Y: A] :
% 0.19/0.45 ( ! [X3: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z2 @ X3 )
% 0.19/0.45 => ( ord_less_eq @ A @ Y @ X3 ) )
% 0.19/0.45 => ( ord_less_eq @ A @ Y @ Z2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dense_ge
% 0.19/0.45 thf(fact_80_less__le__trans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A,Z2: A] :
% 0.19/0.45 ( ( ord_less @ A @ X @ Y )
% 0.19/0.45 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.19/0.45 => ( ord_less @ A @ X @ Z2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_le_trans
% 0.19/0.45 thf(fact_81_le__less__trans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A,Z2: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X @ Y )
% 0.19/0.45 => ( ( ord_less @ A @ Y @ Z2 )
% 0.19/0.45 => ( ord_less @ A @ X @ Z2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_less_trans
% 0.19/0.45 thf(fact_82_antisym__conv2,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X @ Y )
% 0.19/0.45 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.19/0.45 = ( X = Y ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % antisym_conv2
% 0.19/0.45 thf(fact_83_antisym__conv1,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ~ ( ord_less @ A @ X @ Y )
% 0.19/0.45 => ( ( ord_less_eq @ A @ X @ Y )
% 0.19/0.45 = ( X = Y ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % antisym_conv1
% 0.19/0.45 thf(fact_84_less__imp__le,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( ord_less @ A @ X @ Y )
% 0.19/0.45 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_imp_le
% 0.19/0.45 thf(fact_85_le__neq__trans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A,B3: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.19/0.45 => ( ( A4 != B3 )
% 0.19/0.45 => ( ord_less @ A @ A4 @ B3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_neq_trans
% 0.19/0.45 thf(fact_86_not__less,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.19/0.45 = ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % not_less
% 0.19/0.45 thf(fact_87_not__le,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( ~ ( ord_less_eq @ A @ X @ Y ) )
% 0.19/0.45 = ( ord_less @ A @ Y @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % not_le
% 0.19/0.45 thf(fact_88_order__less__le__subst2,axiom,
% 0.19/0.45 ! [A: $tType,C2: $tType] :
% 0.19/0.45 ( ( ( order @ C2 @ ( type2 @ C2 ) )
% 0.19/0.45 & ( order @ A @ ( type2 @ A ) ) )
% 0.19/0.45 => ! [A4: A,B3: A,F: A > C2,C: C2] :
% 0.19/0.45 ( ( ord_less @ A @ A4 @ B3 )
% 0.19/0.45 => ( ( ord_less_eq @ C2 @ ( F @ B3 ) @ C )
% 0.19/0.45 => ( ! [X3: A,Y2: A] :
% 0.19/0.45 ( ( ord_less @ A @ X3 @ Y2 )
% 0.19/0.45 => ( ord_less @ C2 @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.19/0.45 => ( ord_less @ C2 @ ( F @ A4 ) @ C ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order_less_le_subst2
% 0.19/0.45 thf(fact_89_order__less__le__subst1,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType] :
% 0.19/0.45 ( ( ( order @ B @ ( type2 @ B ) )
% 0.19/0.45 & ( order @ A @ ( type2 @ A ) ) )
% 0.19/0.45 => ! [A4: A,F: B > A,B3: B,C: B] :
% 0.19/0.45 ( ( ord_less @ A @ A4 @ ( F @ B3 ) )
% 0.19/0.45 => ( ( ord_less_eq @ B @ B3 @ C )
% 0.19/0.45 => ( ! [X3: B,Y2: B] :
% 0.19/0.45 ( ( ord_less_eq @ B @ X3 @ Y2 )
% 0.19/0.45 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.19/0.45 => ( ord_less @ A @ A4 @ ( F @ C ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order_less_le_subst1
% 0.19/0.45 thf(fact_90_order__le__less__subst2,axiom,
% 0.19/0.45 ! [A: $tType,C2: $tType] :
% 0.19/0.45 ( ( ( order @ C2 @ ( type2 @ C2 ) )
% 0.19/0.45 & ( order @ A @ ( type2 @ A ) ) )
% 0.19/0.45 => ! [A4: A,B3: A,F: A > C2,C: C2] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.19/0.45 => ( ( ord_less @ C2 @ ( F @ B3 ) @ C )
% 0.19/0.45 => ( ! [X3: A,Y2: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.19/0.45 => ( ord_less_eq @ C2 @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.19/0.45 => ( ord_less @ C2 @ ( F @ A4 ) @ C ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order_le_less_subst2
% 0.19/0.45 thf(fact_91_order__le__less__subst1,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType] :
% 0.19/0.45 ( ( ( order @ B @ ( type2 @ B ) )
% 0.19/0.45 & ( order @ A @ ( type2 @ A ) ) )
% 0.19/0.45 => ! [A4: A,F: B > A,B3: B,C: B] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A4 @ ( F @ B3 ) )
% 0.19/0.45 => ( ( ord_less @ B @ B3 @ C )
% 0.19/0.45 => ( ! [X3: B,Y2: B] :
% 0.19/0.45 ( ( ord_less @ B @ X3 @ Y2 )
% 0.19/0.45 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.19/0.45 => ( ord_less @ A @ A4 @ ( F @ C ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order_le_less_subst1
% 0.19/0.45 thf(fact_92_less__le,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ( ( ord_less @ A )
% 0.19/0.45 = ( ^ [X2: A,Y4: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.19/0.45 & ( X2 != Y4 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_le
% 0.19/0.45 thf(fact_93_le__less,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ( ( ord_less_eq @ A )
% 0.19/0.45 = ( ^ [X2: A,Y4: A] :
% 0.19/0.45 ( ( ord_less @ A @ X2 @ Y4 )
% 0.19/0.45 | ( X2 = Y4 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_less
% 0.19/0.45 thf(fact_94_leI,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ~ ( ord_less @ A @ X @ Y )
% 0.19/0.45 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % leI
% 0.19/0.45 thf(fact_95_leD,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [Y: A,X: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ Y @ X )
% 0.19/0.45 => ~ ( ord_less @ A @ X @ Y ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % leD
% 0.19/0.45 thf(fact_96_lappend__LNil__LNil,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 0.19/0.45 = ( coinductive_LNil @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 % lappend_LNil_LNil
% 0.19/0.45 thf(fact_97_lappend__snocL1__conv__LCons2,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.19/0.45 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 0.19/0.45 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lappend_snocL1_conv_LCons2
% 0.19/0.45 thf(fact_98_LList2__Mirabelle__hamjzmohle_Ollist__le__def,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( ord_less_eq @ ( coinductive_llist @ A ) )
% 0.19/0.45 = ( ^ [S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.19/0.45 ? [D: coinductive_llist @ A] :
% 0.19/0.45 ( T
% 0.19/0.45 = ( coinductive_lappend @ A @ S @ D ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % LList2_Mirabelle_hamjzmohle.llist_le_def
% 0.19/0.45 thf(fact_99_finlstsp_OLCons__fin,axiom,
% 0.19/0.45 ! [A: $tType,A2: A > $o,L: coinductive_llist @ A,A4: A] :
% 0.19/0.45 ( ( lList2860480441nlstsp @ A @ A2 @ L )
% 0.19/0.45 => ( ( A2 @ A4 )
% 0.19/0.45 => ( lList2860480441nlstsp @ A @ A2 @ ( coinductive_LCons @ A @ A4 @ L ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % finlstsp.LCons_fin
% 0.19/0.45 thf(fact_100_alllstsp_OLCons__all,axiom,
% 0.19/0.45 ! [A: $tType,A2: A > $o,L: coinductive_llist @ A,A4: A] :
% 0.19/0.45 ( ( lList21511617539llstsp @ A @ A2 @ L )
% 0.19/0.45 => ( ( A2 @ A4 )
% 0.19/0.45 => ( lList21511617539llstsp @ A @ A2 @ ( coinductive_LCons @ A @ A4 @ L ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % alllstsp.LCons_all
% 0.19/0.45 thf(fact_101_finlstsp_OLNil__fin,axiom,
% 0.19/0.45 ! [A: $tType,A2: A > $o] : ( lList2860480441nlstsp @ A @ A2 @ ( coinductive_LNil @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 % finlstsp.LNil_fin
% 0.19/0.45 thf(fact_102_alllstsp_OLNil__all,axiom,
% 0.19/0.45 ! [A: $tType,A2: A > $o] : ( lList21511617539llstsp @ A @ A2 @ ( coinductive_LNil @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 % alllstsp.LNil_all
% 0.19/0.45 thf(fact_103_LList2__Mirabelle__hamjzmohle_Ollist__less__def,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( ord_less @ ( coinductive_llist @ A ) )
% 0.19/0.45 = ( ^ [S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ T )
% 0.19/0.45 & ( S != T ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % LList2_Mirabelle_hamjzmohle.llist_less_def
% 0.19/0.45 thf(fact_104_dual__order_Oantisym,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [B3: A,A4: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ B3 @ A4 )
% 0.19/0.45 => ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.19/0.45 => ( A4 = B3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dual_order.antisym
% 0.19/0.45 thf(fact_105_dual__order_Otrans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [B3: A,A4: A,C: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ B3 @ A4 )
% 0.19/0.45 => ( ( ord_less_eq @ A @ C @ B3 )
% 0.19/0.45 => ( ord_less_eq @ A @ C @ A4 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % dual_order.trans
% 0.19/0.45 thf(fact_106_linorder__wlog,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [P: A > A > $o,A4: A,B3: A] :
% 0.19/0.45 ( ! [A3: A,B5: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A3 @ B5 )
% 0.19/0.45 => ( P @ A3 @ B5 ) )
% 0.19/0.45 => ( ! [A3: A,B5: A] :
% 0.19/0.45 ( ( P @ B5 @ A3 )
% 0.19/0.45 => ( P @ A3 @ B5 ) )
% 0.19/0.45 => ( P @ A4 @ B3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % linorder_wlog
% 0.19/0.45 thf(fact_107_dual__order_Orefl,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A] : ( ord_less_eq @ A @ A4 @ A4 ) ) ).
% 0.19/0.45
% 0.19/0.45 % dual_order.refl
% 0.19/0.45 thf(fact_108_order__trans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A,Z2: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X @ Y )
% 0.19/0.45 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.19/0.45 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order_trans
% 0.19/0.45 thf(fact_109_order__class_Oorder_Oantisym,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A,B3: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.19/0.45 => ( ( ord_less_eq @ A @ B3 @ A4 )
% 0.19/0.45 => ( A4 = B3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order_class.order.antisym
% 0.19/0.45 thf(fact_110_ord__le__eq__trans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( ord @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A,B3: A,C: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.19/0.45 => ( ( B3 = C )
% 0.19/0.45 => ( ord_less_eq @ A @ A4 @ C ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ord_le_eq_trans
% 0.19/0.45 thf(fact_111_ord__eq__le__trans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( ord @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A,B3: A,C: A] :
% 0.19/0.45 ( ( A4 = B3 )
% 0.19/0.45 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.19/0.45 => ( ord_less_eq @ A @ A4 @ C ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ord_eq_le_trans
% 0.19/0.45 thf(fact_112_antisym__conv,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [Y: A,X: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ Y @ X )
% 0.19/0.45 => ( ( ord_less_eq @ A @ X @ Y )
% 0.19/0.45 = ( X = Y ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % antisym_conv
% 0.19/0.45 thf(fact_113_le__cases3,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A,Z2: A] :
% 0.19/0.45 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.19/0.45 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 0.19/0.45 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.19/0.45 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 0.19/0.45 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 0.19/0.45 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 0.19/0.45 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 0.19/0.45 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.19/0.45 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.19/0.45 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 0.19/0.45 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 0.19/0.45 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_cases3
% 0.19/0.45 thf(fact_114_order_Otrans,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A,B3: A,C: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.19/0.45 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.19/0.45 => ( ord_less_eq @ A @ A4 @ C ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order.trans
% 0.19/0.45 thf(fact_115_le__cases,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.19/0.45 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_cases
% 0.19/0.45 thf(fact_116_wlog__linorder__le,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [P: A > A > $o,B3: A,A4: A] :
% 0.19/0.45 ( ! [A3: A,B5: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A3 @ B5 )
% 0.19/0.45 => ( P @ A3 @ B5 ) )
% 0.19/0.45 => ( ( ( P @ B3 @ A4 )
% 0.19/0.45 => ( P @ A4 @ B3 ) )
% 0.19/0.45 => ( P @ A4 @ B3 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % wlog_linorder_le
% 0.19/0.45 thf(fact_117_eq__refl,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( preorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( X = Y )
% 0.19/0.45 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % eq_refl
% 0.19/0.45 thf(fact_118_linear,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X @ Y )
% 0.19/0.45 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % linear
% 0.19/0.45 thf(fact_119_antisym,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [X: A,Y: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X @ Y )
% 0.19/0.45 => ( ( ord_less_eq @ A @ Y @ X )
% 0.19/0.45 => ( X = Y ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % antisym
% 0.19/0.45 thf(fact_120_eq__iff,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order @ A @ ( type2 @ A ) )
% 0.19/0.45 => ( ( ^ [Y5: A,Z3: A] : ( Y5 = Z3 ) )
% 0.19/0.45 = ( ^ [X2: A,Y4: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.19/0.45 & ( ord_less_eq @ A @ Y4 @ X2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % eq_iff
% 0.19/0.45 thf(fact_121_ord__le__eq__subst,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType] :
% 0.19/0.45 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.19/0.45 & ( ord @ A @ ( type2 @ A ) ) )
% 0.19/0.45 => ! [A4: A,B3: A,F: A > B,C: B] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.19/0.45 => ( ( ( F @ B3 )
% 0.19/0.45 = C )
% 0.19/0.45 => ( ! [X3: A,Y2: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.19/0.45 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.19/0.45 => ( ord_less_eq @ B @ ( F @ A4 ) @ C ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ord_le_eq_subst
% 0.19/0.45 thf(fact_122_ord__eq__le__subst,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType] :
% 0.19/0.45 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.19/0.45 & ( ord @ A @ ( type2 @ A ) ) )
% 0.19/0.45 => ! [A4: A,F: B > A,B3: B,C: B] :
% 0.19/0.45 ( ( A4
% 0.19/0.45 = ( F @ B3 ) )
% 0.19/0.45 => ( ( ord_less_eq @ B @ B3 @ C )
% 0.19/0.45 => ( ! [X3: B,Y2: B] :
% 0.19/0.45 ( ( ord_less_eq @ B @ X3 @ Y2 )
% 0.19/0.45 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.19/0.45 => ( ord_less_eq @ A @ A4 @ ( F @ C ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ord_eq_le_subst
% 0.19/0.45 thf(fact_123_order__subst2,axiom,
% 0.19/0.45 ! [A: $tType,C2: $tType] :
% 0.19/0.45 ( ( ( order @ C2 @ ( type2 @ C2 ) )
% 0.19/0.45 & ( order @ A @ ( type2 @ A ) ) )
% 0.19/0.45 => ! [A4: A,B3: A,F: A > C2,C: C2] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.19/0.45 => ( ( ord_less_eq @ C2 @ ( F @ B3 ) @ C )
% 0.19/0.45 => ( ! [X3: A,Y2: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.19/0.45 => ( ord_less_eq @ C2 @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.19/0.45 => ( ord_less_eq @ C2 @ ( F @ A4 ) @ C ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order_subst2
% 0.19/0.45 thf(fact_124_order__subst1,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType] :
% 0.19/0.45 ( ( ( order @ B @ ( type2 @ B ) )
% 0.19/0.45 & ( order @ A @ ( type2 @ A ) ) )
% 0.19/0.45 => ! [A4: A,F: B > A,B3: B,C: B] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A4 @ ( F @ B3 ) )
% 0.19/0.45 => ( ( ord_less_eq @ B @ B3 @ C )
% 0.19/0.45 => ( ! [X3: B,Y2: B] :
% 0.19/0.45 ( ( ord_less_eq @ B @ X3 @ Y2 )
% 0.19/0.45 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.19/0.45 => ( ord_less_eq @ A @ A4 @ ( F @ C ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % order_subst1
% 0.19/0.45 thf(fact_125_le__fun__def,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType] :
% 0.19/0.45 ( ( ord @ B @ ( type2 @ B ) )
% 0.19/0.45 => ( ( ord_less_eq @ ( A > B ) )
% 0.19/0.45 = ( ^ [F2: A > B,G2: A > B] :
% 0.19/0.45 ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_fun_def
% 0.19/0.45 thf(fact_126_le__funI,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType] :
% 0.19/0.45 ( ( ord @ B @ ( type2 @ B ) )
% 0.19/0.45 => ! [F: A > B,G: A > B] :
% 0.19/0.45 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.19/0.45 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_funI
% 0.19/0.45 thf(fact_127_le__funE,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType] :
% 0.19/0.45 ( ( ord @ B @ ( type2 @ B ) )
% 0.19/0.45 => ! [F: A > B,G: A > B,X: A] :
% 0.19/0.45 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.19/0.45 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_funE
% 0.19/0.45 thf(fact_128_le__funD,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType] :
% 0.19/0.45 ( ( ord @ B @ ( type2 @ B ) )
% 0.19/0.45 => ! [F: A > B,G: A > B,X: A] :
% 0.19/0.45 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.19/0.45 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % le_funD
% 0.19/0.45 thf(fact_129_alllstsp_Ocoinduct,axiom,
% 0.19/0.45 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,A2: A > $o] :
% 0.19/0.45 ( ( X4 @ X )
% 0.19/0.45 => ( ! [X3: coinductive_llist @ A] :
% 0.19/0.45 ( ( X4 @ X3 )
% 0.19/0.45 => ( ( X3
% 0.19/0.45 = ( coinductive_LNil @ A ) )
% 0.19/0.45 | ? [L4: coinductive_llist @ A,A7: A] :
% 0.19/0.45 ( ( X3
% 0.19/0.45 = ( coinductive_LCons @ A @ A7 @ L4 ) )
% 0.19/0.45 & ( ( X4 @ L4 )
% 0.19/0.45 | ( lList21511617539llstsp @ A @ A2 @ L4 ) )
% 0.19/0.45 & ( A2 @ A7 ) ) ) )
% 0.19/0.45 => ( lList21511617539llstsp @ A @ A2 @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % alllstsp.coinduct
% 0.19/0.45 thf(fact_130_finlstsp_Oinducts,axiom,
% 0.19/0.45 ! [A: $tType,A2: A > $o,X: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.19/0.45 ( ( lList2860480441nlstsp @ A @ A2 @ X )
% 0.19/0.45 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.19/0.45 => ( ! [L2: coinductive_llist @ A,A3: A] :
% 0.19/0.45 ( ( lList2860480441nlstsp @ A @ A2 @ L2 )
% 0.19/0.45 => ( ( P @ L2 )
% 0.19/0.45 => ( ( A2 @ A3 )
% 0.19/0.45 => ( P @ ( coinductive_LCons @ A @ A3 @ L2 ) ) ) ) )
% 0.19/0.45 => ( P @ X ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % finlstsp.inducts
% 0.19/0.45 thf(fact_131_lbutlast__lapp__llast,axiom,
% 0.19/0.45 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.19/0.45 => ( L
% 0.19/0.45 = ( coinductive_lappend @ A @ ( lList2370560421utlast @ A @ L ) @ ( coinductive_LCons @ A @ ( lList2170638824_llast @ A @ L ) @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lbutlast_lapp_llast
% 0.19/0.45 thf(fact_132_complete__interval,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( condit1037483654norder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A,B3: A,P: A > $o] :
% 0.19/0.45 ( ( ord_less @ A @ A4 @ B3 )
% 0.19/0.45 => ( ( P @ A4 )
% 0.19/0.45 => ( ~ ( P @ B3 )
% 0.19/0.45 => ? [C3: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ A4 @ C3 )
% 0.19/0.45 & ( ord_less_eq @ A @ C3 @ B3 )
% 0.19/0.45 & ! [X5: A] :
% 0.19/0.45 ( ( ( ord_less_eq @ A @ A4 @ X5 )
% 0.19/0.45 & ( ord_less @ A @ X5 @ C3 ) )
% 0.19/0.45 => ( P @ X5 ) )
% 0.19/0.45 & ! [D2: A] :
% 0.19/0.45 ( ! [X3: A] :
% 0.19/0.45 ( ( ( ord_less_eq @ A @ A4 @ X3 )
% 0.19/0.45 & ( ord_less @ A @ X3 @ D2 ) )
% 0.19/0.45 => ( P @ X3 ) )
% 0.19/0.45 => ( ord_less_eq @ A @ D2 @ C3 ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % complete_interval
% 0.19/0.45 thf(fact_133_pinf_I6_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [T2: A] :
% 0.19/0.45 ? [Z: A] :
% 0.19/0.45 ! [X5: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z @ X5 )
% 0.19/0.45 => ~ ( ord_less_eq @ A @ X5 @ T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % pinf(6)
% 0.19/0.45 thf(fact_134_pinf_I8_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [T2: A] :
% 0.19/0.45 ? [Z: A] :
% 0.19/0.45 ! [X5: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z @ X5 )
% 0.19/0.45 => ( ord_less_eq @ A @ T2 @ X5 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % pinf(8)
% 0.19/0.45 thf(fact_135_minf_I6_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [T2: A] :
% 0.19/0.45 ? [Z: A] :
% 0.19/0.45 ! [X5: A] :
% 0.19/0.45 ( ( ord_less @ A @ X5 @ Z )
% 0.19/0.45 => ( ord_less_eq @ A @ X5 @ T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % minf(6)
% 0.19/0.45 thf(fact_136_minf_I8_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [T2: A] :
% 0.19/0.45 ? [Z: A] :
% 0.19/0.45 ! [X5: A] :
% 0.19/0.45 ( ( ord_less @ A @ X5 @ Z )
% 0.19/0.45 => ~ ( ord_less_eq @ A @ T2 @ X5 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % minf(8)
% 0.19/0.45 thf(fact_137_lbutlast__snoc,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,X: A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( lList2370560421utlast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) )
% 0.19/0.45 = Xs ) ) ).
% 0.19/0.45
% 0.19/0.45 % lbutlast_snoc
% 0.19/0.45 thf(fact_138_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.19/0.45 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.19/0.45 = ( ( Xs
% 0.19/0.45 = ( coinductive_LNil @ A ) )
% 0.19/0.45 | ? [Xs2: coinductive_llist @ A] :
% 0.19/0.45 ( ( Xs
% 0.19/0.45 = ( coinductive_LCons @ A @ Y @ Xs2 ) )
% 0.19/0.45 & ( coindu328551480prefix @ A @ Xs2 @ Ys ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Coinductive_List.finite_lprefix_nitpick_simps(3)
% 0.19/0.45 thf(fact_139_lstrict__prefix__code_I2_J,axiom,
% 0.19/0.45 ! [B: $tType,Y: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y @ Ys ) ) ).
% 0.19/0.45
% 0.19/0.45 % lstrict_prefix_code(2)
% 0.19/0.45 thf(fact_140_lstrict__prefix__code_I3_J,axiom,
% 0.19/0.45 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 0.19/0.45 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 0.19/0.45
% 0.19/0.45 % lstrict_prefix_code(3)
% 0.19/0.45 thf(fact_141_lbutlast__LCons,axiom,
% 0.19/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( ( R
% 0.19/0.45 = ( coinductive_LNil @ A ) )
% 0.19/0.45 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.19/0.45 = ( coinductive_LNil @ A ) ) )
% 0.19/0.45 & ( ( R
% 0.19/0.45 != ( coinductive_LNil @ A ) )
% 0.19/0.45 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.19/0.45 = ( coinductive_LCons @ A @ A4 @ ( lList2370560421utlast @ A @ R ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lbutlast_LCons
% 0.19/0.45 thf(fact_142_predicate1I,axiom,
% 0.19/0.45 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.45 ( ! [X3: A] :
% 0.19/0.45 ( ( P @ X3 )
% 0.19/0.45 => ( Q @ X3 ) )
% 0.19/0.45 => ( ord_less_eq @ ( A > $o ) @ P @ Q ) ) ).
% 0.19/0.45
% 0.19/0.45 % predicate1I
% 0.19/0.45 thf(fact_143_lapp__fin__fin__iff,axiom,
% 0.19/0.45 ! [A: $tType,R: coinductive_llist @ A,S2: coinductive_llist @ A,A2: set @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S2 ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 = ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 & ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lapp_fin_fin_iff
% 0.19/0.45 thf(fact_144_same__lappend__eq,axiom,
% 0.19/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S2: coinductive_llist @ A,T2: coinductive_llist @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( ( coinductive_lappend @ A @ R @ S2 )
% 0.19/0.45 = ( coinductive_lappend @ A @ R @ T2 ) )
% 0.19/0.45 = ( S2 = T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % same_lappend_eq
% 0.19/0.45 thf(fact_145_lstrict__prefix__code_I4_J,axiom,
% 0.19/0.45 ! [B: $tType,X: B,Xs: coinductive_llist @ B,Y: B,Ys: coinductive_llist @ B] :
% 0.19/0.45 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 0.19/0.45 = ( ( X = Y )
% 0.19/0.45 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lstrict_prefix_code(4)
% 0.19/0.45 thf(fact_146_lstrict__prefix__code_I1_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 % lstrict_prefix_code(1)
% 0.19/0.45 thf(fact_147_fpslsts__iff,axiom,
% 0.19/0.45 ! [A: $tType,S2: coinductive_llist @ A,A2: set @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.19/0.45 = ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 & ( S2
% 0.19/0.45 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % fpslsts_iff
% 0.19/0.45 thf(fact_148_LList2__Mirabelle__hamjzmohle_Ollast__LCons,axiom,
% 0.19/0.45 ! [B: $tType,R: coinductive_llist @ B,A2: set @ B,A4: B] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ B ) @ R @ ( lList2236698231inlsts @ B @ A2 ) )
% 0.19/0.45 => ( ( ( R
% 0.19/0.45 = ( coinductive_LNil @ B ) )
% 0.19/0.45 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A4 @ R ) )
% 0.19/0.45 = A4 ) )
% 0.19/0.45 & ( ( R
% 0.19/0.45 != ( coinductive_LNil @ B ) )
% 0.19/0.45 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A4 @ R ) )
% 0.19/0.45 = ( lList2170638824_llast @ B @ R ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % LList2_Mirabelle_hamjzmohle.llast_LCons
% 0.19/0.45 thf(fact_149_llast__snoc,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,X: A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( lList2170638824_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) )
% 0.19/0.45 = X ) ) ).
% 0.19/0.45
% 0.19/0.45 % llast_snoc
% 0.19/0.45 thf(fact_150_predicate1D,axiom,
% 0.19/0.45 ! [A: $tType,P: A > $o,Q: A > $o,X: A] :
% 0.19/0.45 ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 0.19/0.45 => ( ( P @ X )
% 0.19/0.45 => ( Q @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % predicate1D
% 0.19/0.45 thf(fact_151_less__fun__def,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType] :
% 0.19/0.45 ( ( ord @ B @ ( type2 @ B ) )
% 0.19/0.45 => ( ( ord_less @ ( A > B ) )
% 0.19/0.45 = ( ^ [F2: A > B,G2: A > B] :
% 0.19/0.45 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.19/0.45 & ~ ( ord_less_eq @ ( A > B ) @ G2 @ F2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % less_fun_def
% 0.19/0.45 thf(fact_152_rev__predicate1D,axiom,
% 0.19/0.45 ! [A: $tType,P: A > $o,X: A,Q: A > $o] :
% 0.19/0.45 ( ( P @ X )
% 0.19/0.45 => ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 0.19/0.45 => ( Q @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % rev_predicate1D
% 0.19/0.45 thf(fact_153_llist__less__induct,axiom,
% 0.19/0.45 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 0.19/0.45 ( ! [Xs3: coinductive_llist @ A] :
% 0.19/0.45 ( ! [Ys2: coinductive_llist @ A] :
% 0.19/0.45 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs3 )
% 0.19/0.45 => ( P @ Ys2 ) )
% 0.19/0.45 => ( P @ Xs3 ) )
% 0.19/0.45 => ( P @ Xs ) ) ).
% 0.19/0.45
% 0.19/0.45 % llist_less_induct
% 0.19/0.45 thf(fact_154_finlsts__mono,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A2 ) @ ( lList2236698231inlsts @ A @ B4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % finlsts_mono
% 0.19/0.45 thf(fact_155_finlsts_OLCons__fin,axiom,
% 0.19/0.45 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( member @ A @ A4 @ A2 )
% 0.19/0.45 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ L ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % finlsts.LCons_fin
% 0.19/0.45 thf(fact_156_finlsts_OLNil__fin,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2236698231inlsts @ A @ A2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % finlsts.LNil_fin
% 0.19/0.45 thf(fact_157_lapp__fin__fin__lemma,axiom,
% 0.19/0.45 ! [A: $tType,R: coinductive_llist @ A,S2: coinductive_llist @ A,A2: set @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S2 ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lapp_fin_fin_lemma
% 0.19/0.45 thf(fact_158_lappfin__finT,axiom,
% 0.19/0.45 ! [A: $tType,S2: coinductive_llist @ A,A2: set @ A,T2: coinductive_llist @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S2 @ T2 ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lappfin_finT
% 0.19/0.45 thf(fact_159_finlsts_Ocases,axiom,
% 0.19/0.45 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( A4
% 0.19/0.45 != ( coinductive_LNil @ A ) )
% 0.19/0.45 => ~ ! [L2: coinductive_llist @ A,A3: A] :
% 0.19/0.45 ( ( A4
% 0.19/0.45 = ( coinductive_LCons @ A @ A3 @ L2 ) )
% 0.19/0.45 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ~ ( member @ A @ A3 @ A2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % finlsts.cases
% 0.19/0.45 thf(fact_160_finlsts_Osimps,axiom,
% 0.19/0.45 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 = ( ( A4
% 0.19/0.45 = ( coinductive_LNil @ A ) )
% 0.19/0.45 | ? [L3: coinductive_llist @ A,A6: A] :
% 0.19/0.45 ( ( A4
% 0.19/0.45 = ( coinductive_LCons @ A @ A6 @ L3 ) )
% 0.19/0.45 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 & ( member @ A @ A6 @ A2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % finlsts.simps
% 0.19/0.45 thf(fact_161_finlsts__induct,axiom,
% 0.19/0.45 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ! [L2: coinductive_llist @ A] :
% 0.19/0.45 ( ( L2
% 0.19/0.45 = ( coinductive_LNil @ A ) )
% 0.19/0.45 => ( P @ L2 ) )
% 0.19/0.45 => ( ! [A3: A,L2: coinductive_llist @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( P @ L2 )
% 0.19/0.45 => ( ( member @ A @ A3 @ A2 )
% 0.19/0.45 => ( P @ ( coinductive_LCons @ A @ A3 @ L2 ) ) ) ) )
% 0.19/0.45 => ( P @ X ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % finlsts_induct
% 0.19/0.45 thf(fact_162_finlsts_Oinducts,axiom,
% 0.19/0.45 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.19/0.45 => ( ! [L2: coinductive_llist @ A,A3: A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( P @ L2 )
% 0.19/0.45 => ( ( member @ A @ A3 @ A2 )
% 0.19/0.45 => ( P @ ( coinductive_LCons @ A @ A3 @ L2 ) ) ) ) )
% 0.19/0.45 => ( P @ X ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % finlsts.inducts
% 0.19/0.45 thf(fact_163_fpslsts__cases,axiom,
% 0.19/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.19/0.45 => ~ ! [A3: A,Rs: coinductive_llist @ A] :
% 0.19/0.45 ( ( R
% 0.19/0.45 = ( coinductive_LCons @ A @ A3 @ Rs ) )
% 0.19/0.45 => ( ( member @ A @ A3 @ A2 )
% 0.19/0.45 => ~ ( member @ ( coinductive_llist @ A ) @ Rs @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % fpslsts_cases
% 0.19/0.45 thf(fact_164_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 0.19/0.45
% 0.19/0.45 % Coinductive_List.finite_lprefix_nitpick_simps(2)
% 0.19/0.45 thf(fact_165_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.19/0.45 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.19/0.45 = ( Xs
% 0.19/0.45 = ( coinductive_LNil @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Coinductive_List.finite_lprefix_nitpick_simps(1)
% 0.19/0.45 thf(fact_166_lrev__induct,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.19/0.45 => ( ! [X3: A,Xs3: coinductive_llist @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( P @ Xs3 )
% 0.19/0.45 => ( ( member @ A @ X3 @ A2 )
% 0.19/0.45 => ( P @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) ) ) ) ) )
% 0.19/0.45 => ( P @ Xs ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lrev_induct
% 0.19/0.45 thf(fact_167_finlsts__rev__cases,axiom,
% 0.19/0.45 ! [A: $tType,T2: coinductive_llist @ A,A2: set @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( T2
% 0.19/0.45 != ( coinductive_LNil @ A ) )
% 0.19/0.45 => ~ ! [A3: A,L2: coinductive_llist @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( member @ A @ A3 @ A2 )
% 0.19/0.45 => ( T2
% 0.19/0.45 != ( coinductive_lappend @ A @ L2 @ ( coinductive_LCons @ A @ A3 @ ( coinductive_LNil @ A ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % finlsts_rev_cases
% 0.19/0.45 thf(fact_168_ex__gt__or__lt,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( condit1656338222tinuum @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A] :
% 0.19/0.45 ? [B5: A] :
% 0.19/0.45 ( ( ord_less @ A @ A4 @ B5 )
% 0.19/0.45 | ( ord_less @ A @ B5 @ A4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ex_gt_or_lt
% 0.19/0.45 thf(fact_169_pinf_I1_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.19/0.45 ( ? [Z4: A] :
% 0.19/0.45 ! [X3: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z4 @ X3 )
% 0.19/0.45 => ( ( P @ X3 )
% 0.19/0.45 = ( P2 @ X3 ) ) )
% 0.19/0.45 => ( ? [Z4: A] :
% 0.19/0.45 ! [X3: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z4 @ X3 )
% 0.19/0.45 => ( ( Q @ X3 )
% 0.19/0.45 = ( Q2 @ X3 ) ) )
% 0.19/0.45 => ? [Z: A] :
% 0.19/0.45 ! [X5: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z @ X5 )
% 0.19/0.45 => ( ( ( P @ X5 )
% 0.19/0.45 & ( Q @ X5 ) )
% 0.19/0.45 = ( ( P2 @ X5 )
% 0.19/0.45 & ( Q2 @ X5 ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % pinf(1)
% 0.19/0.45 thf(fact_170_pinf_I2_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.19/0.45 ( ? [Z4: A] :
% 0.19/0.45 ! [X3: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z4 @ X3 )
% 0.19/0.45 => ( ( P @ X3 )
% 0.19/0.45 = ( P2 @ X3 ) ) )
% 0.19/0.45 => ( ? [Z4: A] :
% 0.19/0.45 ! [X3: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z4 @ X3 )
% 0.19/0.45 => ( ( Q @ X3 )
% 0.19/0.45 = ( Q2 @ X3 ) ) )
% 0.19/0.45 => ? [Z: A] :
% 0.19/0.45 ! [X5: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z @ X5 )
% 0.19/0.45 => ( ( ( P @ X5 )
% 0.19/0.45 | ( Q @ X5 ) )
% 0.19/0.45 = ( ( P2 @ X5 )
% 0.19/0.45 | ( Q2 @ X5 ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % pinf(2)
% 0.19/0.45 thf(fact_171_pinf_I3_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [T2: A] :
% 0.19/0.45 ? [Z: A] :
% 0.19/0.45 ! [X5: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z @ X5 )
% 0.19/0.45 => ( X5 != T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % pinf(3)
% 0.19/0.45 thf(fact_172_pinf_I4_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [T2: A] :
% 0.19/0.45 ? [Z: A] :
% 0.19/0.45 ! [X5: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z @ X5 )
% 0.19/0.45 => ( X5 != T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % pinf(4)
% 0.19/0.45 thf(fact_173_pinf_I5_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [T2: A] :
% 0.19/0.45 ? [Z: A] :
% 0.19/0.45 ! [X5: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z @ X5 )
% 0.19/0.45 => ~ ( ord_less @ A @ X5 @ T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % pinf(5)
% 0.19/0.45 thf(fact_174_pinf_I7_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [T2: A] :
% 0.19/0.45 ? [Z: A] :
% 0.19/0.45 ! [X5: A] :
% 0.19/0.45 ( ( ord_less @ A @ Z @ X5 )
% 0.19/0.45 => ( ord_less @ A @ T2 @ X5 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % pinf(7)
% 0.19/0.45 thf(fact_175_pinf_I11_J,axiom,
% 0.19/0.45 ! [C2: $tType,D3: $tType] :
% 0.19/0.45 ( ( ord @ C2 @ ( type2 @ C2 ) )
% 0.19/0.45 => ! [F3: D3] :
% 0.19/0.45 ? [Z: C2] :
% 0.19/0.45 ! [X5: C2] :
% 0.19/0.45 ( ( ord_less @ C2 @ Z @ X5 )
% 0.19/0.45 => ( F3 = F3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % pinf(11)
% 0.19/0.45 thf(fact_176_minf_I1_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.19/0.45 ( ? [Z4: A] :
% 0.19/0.45 ! [X3: A] :
% 0.19/0.45 ( ( ord_less @ A @ X3 @ Z4 )
% 0.19/0.45 => ( ( P @ X3 )
% 0.19/0.45 = ( P2 @ X3 ) ) )
% 0.19/0.45 => ( ? [Z4: A] :
% 0.19/0.45 ! [X3: A] :
% 0.19/0.45 ( ( ord_less @ A @ X3 @ Z4 )
% 0.19/0.45 => ( ( Q @ X3 )
% 0.19/0.45 = ( Q2 @ X3 ) ) )
% 0.19/0.45 => ? [Z: A] :
% 0.19/0.45 ! [X5: A] :
% 0.19/0.45 ( ( ord_less @ A @ X5 @ Z )
% 0.19/0.45 => ( ( ( P @ X5 )
% 0.19/0.45 & ( Q @ X5 ) )
% 0.19/0.45 = ( ( P2 @ X5 )
% 0.19/0.45 & ( Q2 @ X5 ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % minf(1)
% 0.19/0.45 thf(fact_177_minf_I2_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.19/0.45 ( ? [Z4: A] :
% 0.19/0.45 ! [X3: A] :
% 0.19/0.45 ( ( ord_less @ A @ X3 @ Z4 )
% 0.19/0.45 => ( ( P @ X3 )
% 0.19/0.45 = ( P2 @ X3 ) ) )
% 0.19/0.45 => ( ? [Z4: A] :
% 0.19/0.45 ! [X3: A] :
% 0.19/0.45 ( ( ord_less @ A @ X3 @ Z4 )
% 0.19/0.45 => ( ( Q @ X3 )
% 0.19/0.45 = ( Q2 @ X3 ) ) )
% 0.19/0.45 => ? [Z: A] :
% 0.19/0.45 ! [X5: A] :
% 0.19/0.45 ( ( ord_less @ A @ X5 @ Z )
% 0.19/0.45 => ( ( ( P @ X5 )
% 0.19/0.45 | ( Q @ X5 ) )
% 0.19/0.45 = ( ( P2 @ X5 )
% 0.19/0.45 | ( Q2 @ X5 ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % minf(2)
% 0.19/0.45 thf(fact_178_minf_I3_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [T2: A] :
% 0.19/0.45 ? [Z: A] :
% 0.19/0.45 ! [X5: A] :
% 0.19/0.45 ( ( ord_less @ A @ X5 @ Z )
% 0.19/0.45 => ( X5 != T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % minf(3)
% 0.19/0.45 thf(fact_179_minf_I4_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [T2: A] :
% 0.19/0.45 ? [Z: A] :
% 0.19/0.45 ! [X5: A] :
% 0.19/0.45 ( ( ord_less @ A @ X5 @ Z )
% 0.19/0.45 => ( X5 != T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % minf(4)
% 0.19/0.45 thf(fact_180_minf_I5_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [T2: A] :
% 0.19/0.45 ? [Z: A] :
% 0.19/0.45 ! [X5: A] :
% 0.19/0.45 ( ( ord_less @ A @ X5 @ Z )
% 0.19/0.45 => ( ord_less @ A @ X5 @ T2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % minf(5)
% 0.19/0.45 thf(fact_181_minf_I7_J,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( linorder @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [T2: A] :
% 0.19/0.45 ? [Z: A] :
% 0.19/0.45 ! [X5: A] :
% 0.19/0.45 ( ( ord_less @ A @ X5 @ Z )
% 0.19/0.45 => ~ ( ord_less @ A @ T2 @ X5 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % minf(7)
% 0.19/0.45 thf(fact_182_minf_I11_J,axiom,
% 0.19/0.45 ! [C2: $tType,D3: $tType] :
% 0.19/0.45 ( ( ord @ C2 @ ( type2 @ C2 ) )
% 0.19/0.45 => ! [F3: D3] :
% 0.19/0.45 ? [Z: C2] :
% 0.19/0.45 ! [X5: C2] :
% 0.19/0.45 ( ( ord_less @ C2 @ X5 @ Z )
% 0.19/0.45 => ( F3 = F3 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % minf(11)
% 0.19/0.45 thf(fact_183_lrev__LCons,axiom,
% 0.19/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( lList2281150353e_lrev @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.19/0.45 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ R ) @ ( coinductive_LCons @ A @ A4 @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lrev_LCons
% 0.19/0.45 thf(fact_184_subsetI,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.19/0.45 ( ! [X3: A] :
% 0.19/0.45 ( ( member @ A @ X3 @ A2 )
% 0.19/0.45 => ( member @ A @ X3 @ B4 ) )
% 0.19/0.45 => ( ord_less_eq @ ( set @ A ) @ A2 @ B4 ) ) ).
% 0.19/0.45
% 0.19/0.45 % subsetI
% 0.19/0.45 thf(fact_185_psubsetI,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( ( A2 != B4 )
% 0.19/0.45 => ( ord_less @ ( set @ A ) @ A2 @ B4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % psubsetI
% 0.19/0.45 thf(fact_186_subset__antisym,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ A2 )
% 0.19/0.45 => ( A2 = B4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_antisym
% 0.19/0.45 thf(fact_187_lrev__LNil,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( lList2281150353e_lrev @ A @ ( coinductive_LNil @ A ) )
% 0.19/0.45 = ( coinductive_LNil @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 % lrev_LNil
% 0.19/0.45 thf(fact_188_lrevT,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( member @ ( coinductive_llist @ A ) @ ( lList2281150353e_lrev @ A @ Xs ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lrevT
% 0.19/0.45 thf(fact_189_psubsetD,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A,C: A] :
% 0.19/0.45 ( ( ord_less @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( ( member @ A @ C @ A2 )
% 0.19/0.45 => ( member @ A @ C @ B4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % psubsetD
% 0.19/0.45 thf(fact_190_psubset__trans,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A,C4: set @ A] :
% 0.19/0.45 ( ( ord_less @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( ( ord_less @ ( set @ A ) @ B4 @ C4 )
% 0.19/0.45 => ( ord_less @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % psubset_trans
% 0.19/0.45 thf(fact_191_subset__iff__psubset__eq,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) )
% 0.19/0.45 = ( ^ [A5: set @ A,B6: set @ A] :
% 0.19/0.45 ( ( ord_less @ ( set @ A ) @ A5 @ B6 )
% 0.19/0.45 | ( A5 = B6 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_iff_psubset_eq
% 0.19/0.45 thf(fact_192_subset__psubset__trans,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A,C4: set @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( ( ord_less @ ( set @ A ) @ B4 @ C4 )
% 0.19/0.45 => ( ord_less @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_psubset_trans
% 0.19/0.45 thf(fact_193_subset__not__subset__eq,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( ord_less @ ( set @ A ) )
% 0.19/0.45 = ( ^ [A5: set @ A,B6: set @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B6 )
% 0.19/0.45 & ~ ( ord_less_eq @ ( set @ A ) @ B6 @ A5 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_not_subset_eq
% 0.19/0.45 thf(fact_194_psubset__subset__trans,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A,C4: set @ A] :
% 0.19/0.45 ( ( ord_less @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C4 )
% 0.19/0.45 => ( ord_less @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % psubset_subset_trans
% 0.19/0.45 thf(fact_195_psubset__imp__subset,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.19/0.45 ( ( ord_less @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( ord_less_eq @ ( set @ A ) @ A2 @ B4 ) ) ).
% 0.19/0.45
% 0.19/0.45 % psubset_imp_subset
% 0.19/0.45 thf(fact_196_Collect__mono__iff,axiom,
% 0.19/0.45 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.19/0.45 = ( ! [X2: A] :
% 0.19/0.45 ( ( P @ X2 )
% 0.19/0.45 => ( Q @ X2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Collect_mono_iff
% 0.19/0.45 thf(fact_197_contra__subsetD,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A,C: A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( ~ ( member @ A @ C @ B4 )
% 0.19/0.45 => ~ ( member @ A @ C @ A2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % contra_subsetD
% 0.19/0.45 thf(fact_198_set__eq__subset,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( ^ [Y5: set @ A,Z3: set @ A] : ( Y5 = Z3 ) )
% 0.19/0.45 = ( ^ [A5: set @ A,B6: set @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B6 )
% 0.19/0.45 & ( ord_less_eq @ ( set @ A ) @ B6 @ A5 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % set_eq_subset
% 0.19/0.45 thf(fact_199_subset__trans,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A,C4: set @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C4 )
% 0.19/0.45 => ( ord_less_eq @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_trans
% 0.19/0.45 thf(fact_200_Collect__mono,axiom,
% 0.19/0.45 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.19/0.45 ( ! [X3: A] :
% 0.19/0.45 ( ( P @ X3 )
% 0.19/0.45 => ( Q @ X3 ) )
% 0.19/0.45 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % Collect_mono
% 0.19/0.45 thf(fact_201_subset__refl,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 0.19/0.45
% 0.19/0.45 % subset_refl
% 0.19/0.45 thf(fact_202_rev__subsetD,axiom,
% 0.19/0.45 ! [A: $tType,C: A,A2: set @ A,B4: set @ A] :
% 0.19/0.45 ( ( member @ A @ C @ A2 )
% 0.19/0.45 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( member @ A @ C @ B4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % rev_subsetD
% 0.19/0.45 thf(fact_203_subset__iff,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) )
% 0.19/0.45 = ( ^ [A5: set @ A,B6: set @ A] :
% 0.19/0.45 ! [T: A] :
% 0.19/0.45 ( ( member @ A @ T @ A5 )
% 0.19/0.45 => ( member @ A @ T @ B6 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_iff
% 0.19/0.45 thf(fact_204_set__rev__mp,axiom,
% 0.19/0.45 ! [A: $tType,X: A,A2: set @ A,B4: set @ A] :
% 0.19/0.45 ( ( member @ A @ X @ A2 )
% 0.19/0.45 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( member @ A @ X @ B4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % set_rev_mp
% 0.19/0.45 thf(fact_205_psubset__eq,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( ord_less @ ( set @ A ) )
% 0.19/0.45 = ( ^ [A5: set @ A,B6: set @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B6 )
% 0.19/0.45 & ( A5 != B6 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % psubset_eq
% 0.19/0.45 thf(fact_206_equalityD2,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.19/0.45 ( ( A2 = B4 )
% 0.19/0.45 => ( ord_less_eq @ ( set @ A ) @ B4 @ A2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % equalityD2
% 0.19/0.45 thf(fact_207_equalityD1,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.19/0.45 ( ( A2 = B4 )
% 0.19/0.45 => ( ord_less_eq @ ( set @ A ) @ A2 @ B4 ) ) ).
% 0.19/0.45
% 0.19/0.45 % equalityD1
% 0.19/0.45 thf(fact_208_subset__eq,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) )
% 0.19/0.45 = ( ^ [A5: set @ A,B6: set @ A] :
% 0.19/0.45 ! [X2: A] :
% 0.19/0.45 ( ( member @ A @ X2 @ A5 )
% 0.19/0.45 => ( member @ A @ X2 @ B6 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_eq
% 0.19/0.45 thf(fact_209_equalityE,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.19/0.45 ( ( A2 = B4 )
% 0.19/0.45 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ~ ( ord_less_eq @ ( set @ A ) @ B4 @ A2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % equalityE
% 0.19/0.45 thf(fact_210_subsetCE,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A,C: A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( ( member @ A @ C @ A2 )
% 0.19/0.45 => ( member @ A @ C @ B4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subsetCE
% 0.19/0.45 thf(fact_211_psubsetE,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.19/0.45 ( ( ord_less @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( ord_less_eq @ ( set @ A ) @ B4 @ A2 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % psubsetE
% 0.19/0.45 thf(fact_212_subsetD,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A,C: A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( ( member @ A @ C @ A2 )
% 0.19/0.45 => ( member @ A @ C @ B4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subsetD
% 0.19/0.45 thf(fact_213_in__mono,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A,X: A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( ( member @ A @ X @ A2 )
% 0.19/0.45 => ( member @ A @ X @ B4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % in_mono
% 0.19/0.45 thf(fact_214_set__mp,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A,X: A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( ( member @ A @ X @ A2 )
% 0.19/0.45 => ( member @ A @ X @ B4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % set_mp
% 0.19/0.45 thf(fact_215_LList2__Mirabelle__hamjzmohle_Ollast__lappend,axiom,
% 0.19/0.45 ! [A: $tType,X: coinductive_llist @ A,Y: coinductive_llist @ A,A4: A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.19/0.45 => ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.19/0.45 => ( ( lList2170638824_llast @ A @ ( coinductive_lappend @ A @ X @ ( coinductive_LCons @ A @ A4 @ Y ) ) )
% 0.19/0.45 = ( lList2170638824_llast @ A @ ( coinductive_LCons @ A @ A4 @ Y ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % LList2_Mirabelle_hamjzmohle.llast_lappend
% 0.19/0.45 thf(fact_216_poslsts__mono,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.19/0.45 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.19/0.45 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList21148268032oslsts @ A @ A2 ) @ ( lList21148268032oslsts @ A @ B4 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % poslsts_mono
% 0.19/0.45 thf(fact_217_lrev__lappend,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.19/0.45 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.19/0.45 => ( ( lList2281150353e_lrev @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.19/0.45 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ Ys ) @ ( lList2281150353e_lrev @ A @ Xs ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lrev_lappend
% 0.19/0.45 thf(fact_218_top__apply,axiom,
% 0.19/0.45 ! [C2: $tType,D3: $tType] :
% 0.19/0.45 ( ( top @ C2 @ ( type2 @ C2 ) )
% 0.19/0.45 => ( ( top_top @ ( D3 > C2 ) )
% 0.19/0.45 = ( ^ [X2: D3] : ( top_top @ C2 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % top_apply
% 0.19/0.45 thf(fact_219_UNIV__I,axiom,
% 0.19/0.45 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % UNIV_I
% 0.19/0.45 thf(fact_220_lrev__lrev__ident,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.19/0.45 => ( ( lList2281150353e_lrev @ A @ ( lList2281150353e_lrev @ A @ Xs ) )
% 0.19/0.45 = Xs ) ) ).
% 0.19/0.45
% 0.19/0.45 % lrev_lrev_ident
% 0.19/0.45 thf(fact_221_lrev__is__lrev__conv,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.19/0.45 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.19/0.45 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 0.19/0.45 = ( lList2281150353e_lrev @ A @ Ys ) )
% 0.19/0.45 = ( Xs = Ys ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lrev_is_lrev_conv
% 0.19/0.45 thf(fact_222_poslsts__UNIV,axiom,
% 0.19/0.45 ! [A: $tType,S2: coinductive_llist @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList21148268032oslsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.19/0.45 = ( S2
% 0.19/0.45 != ( coinductive_LNil @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % poslsts_UNIV
% 0.19/0.45 thf(fact_223_lrev__is__LNil__conv,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.19/0.45 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 0.19/0.45 = ( coinductive_LNil @ A ) )
% 0.19/0.45 = ( Xs
% 0.19/0.45 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % lrev_is_LNil_conv
% 0.19/0.45 thf(fact_224_LNil__is__lrev__conv,axiom,
% 0.19/0.45 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.19/0.45 => ( ( ( coinductive_LNil @ A )
% 0.19/0.45 = ( lList2281150353e_lrev @ A @ Xs ) )
% 0.19/0.45 = ( Xs
% 0.19/0.45 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % LNil_is_lrev_conv
% 0.19/0.45 thf(fact_225_subset__UNIV,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % subset_UNIV
% 0.19/0.45 thf(fact_226_top_Onot__eq__extremum,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order_top @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A] :
% 0.19/0.45 ( ( A4
% 0.19/0.45 != ( top_top @ A ) )
% 0.19/0.45 = ( ord_less @ A @ A4 @ ( top_top @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % top.not_eq_extremum
% 0.19/0.45 thf(fact_227_top_Oextremum__strict,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order_top @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A] :
% 0.19/0.45 ~ ( ord_less @ A @ ( top_top @ A ) @ A4 ) ) ).
% 0.19/0.45
% 0.19/0.45 % top.extremum_strict
% 0.19/0.45 thf(fact_228_UNIV__eq__I,axiom,
% 0.19/0.45 ! [A: $tType,A2: set @ A] :
% 0.19/0.45 ( ! [X3: A] : ( member @ A @ X3 @ A2 )
% 0.19/0.45 => ( ( top_top @ ( set @ A ) )
% 0.19/0.45 = A2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % UNIV_eq_I
% 0.19/0.45 thf(fact_229_UNIV__witness,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % UNIV_witness
% 0.19/0.45 thf(fact_230_top_Oextremum__uniqueI,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order_top @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A4 )
% 0.19/0.45 => ( A4
% 0.19/0.45 = ( top_top @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % top.extremum_uniqueI
% 0.19/0.45 thf(fact_231_top_Oextremum__unique,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order_top @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A] :
% 0.19/0.45 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A4 )
% 0.19/0.45 = ( A4
% 0.19/0.45 = ( top_top @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % top.extremum_unique
% 0.19/0.45 thf(fact_232_top__greatest,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order_top @ A @ ( type2 @ A ) )
% 0.19/0.45 => ! [A4: A] : ( ord_less_eq @ A @ A4 @ ( top_top @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % top_greatest
% 0.19/0.45 thf(fact_233_finT__simp,axiom,
% 0.19/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % finT_simp
% 0.19/0.45 thf(fact_234_fin__finite,axiom,
% 0.19/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % fin_finite
% 0.19/0.45 thf(fact_235_iso__tuple__UNIV__I,axiom,
% 0.19/0.45 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % iso_tuple_UNIV_I
% 0.19/0.45 thf(fact_236_top_Oordering__top__axioms,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( order_top @ A @ ( type2 @ A ) )
% 0.19/0.45 => ( ordering_top @ A @ ( ord_less_eq @ A ) @ ( ord_less @ A ) @ ( top_top @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % top.ordering_top_axioms
% 0.19/0.45 thf(fact_237_top__set__def,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( top_top @ ( set @ A ) )
% 0.19/0.45 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % top_set_def
% 0.19/0.45 thf(fact_238_ordering__top_Oextremum__uniqueI,axiom,
% 0.19/0.45 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,Top: A,A4: A] :
% 0.19/0.45 ( ( ordering_top @ A @ Less_eq @ Less @ Top )
% 0.19/0.45 => ( ( Less_eq @ Top @ A4 )
% 0.19/0.45 => ( A4 = Top ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ordering_top.extremum_uniqueI
% 0.19/0.45 thf(fact_239_ordering__top_Onot__eq__extremum,axiom,
% 0.19/0.45 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,Top: A,A4: A] :
% 0.19/0.45 ( ( ordering_top @ A @ Less_eq @ Less @ Top )
% 0.19/0.45 => ( ( A4 != Top )
% 0.19/0.45 = ( Less @ A4 @ Top ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ordering_top.not_eq_extremum
% 0.19/0.45 thf(fact_240_ordering__top_Oextremum__unique,axiom,
% 0.19/0.45 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,Top: A,A4: A] :
% 0.19/0.45 ( ( ordering_top @ A @ Less_eq @ Less @ Top )
% 0.19/0.45 => ( ( Less_eq @ Top @ A4 )
% 0.19/0.45 = ( A4 = Top ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ordering_top.extremum_unique
% 0.19/0.45 thf(fact_241_ordering__top_Oextremum__strict,axiom,
% 0.19/0.45 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,Top: A,A4: A] :
% 0.19/0.45 ( ( ordering_top @ A @ Less_eq @ Less @ Top )
% 0.19/0.45 => ~ ( Less @ Top @ A4 ) ) ).
% 0.19/0.45
% 0.19/0.45 % ordering_top.extremum_strict
% 0.19/0.45 thf(fact_242_ordering__top_Oextremum,axiom,
% 0.19/0.45 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,Top: A,A4: A] :
% 0.19/0.45 ( ( ordering_top @ A @ Less_eq @ Less @ Top )
% 0.19/0.45 => ( Less_eq @ A4 @ Top ) ) ).
% 0.19/0.45
% 0.19/0.45 % ordering_top.extremum
% 0.19/0.45 thf(fact_243_ltake__fin,axiom,
% 0.19/0.45 ! [A: $tType,R: coinductive_llist @ A,I: nat] : ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ R @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ltake_fin
% 0.19/0.45 thf(fact_244_finlsts__rec__LCons__def,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,F: ( coinductive_llist @ A ) > B,C: B,D4: A > ( coinductive_llist @ A ) > B > B,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.19/0.45 ( ( F
% 0.19/0.45 = ( lList21916056377ts_rec @ B @ A @ C @ D4 ) )
% 0.19/0.45 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( F @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.19/0.45 = ( D4 @ A4 @ R @ ( F @ R ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % finlsts_rec_LCons_def
% 0.19/0.45 thf(fact_245_top1I,axiom,
% 0.19/0.45 ! [A: $tType,X: A] : ( top_top @ ( A > $o ) @ X ) ).
% 0.19/0.45
% 0.19/0.45 % top1I
% 0.19/0.45 thf(fact_246_LList2__Mirabelle__hamjzmohle_Oltake__LNil,axiom,
% 0.19/0.45 ! [A: $tType,I: nat] :
% 0.19/0.45 ( ( lList22119844313_ltake @ A @ ( coinductive_LNil @ A ) @ I )
% 0.19/0.45 = ( coinductive_LNil @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 % LList2_Mirabelle_hamjzmohle.ltake_LNil
% 0.19/0.45 thf(fact_247_finlsts__rec__LNil__def,axiom,
% 0.19/0.45 ! [A: $tType,B: $tType,F: ( coinductive_llist @ A ) > B,C: B,D4: A > ( coinductive_llist @ A ) > B > B] :
% 0.19/0.45 ( ( F
% 0.19/0.45 = ( lList21916056377ts_rec @ B @ A @ C @ D4 ) )
% 0.19/0.45 => ( ( F @ ( coinductive_LNil @ A ) )
% 0.19/0.45 = C ) ) ).
% 0.19/0.45
% 0.19/0.45 % finlsts_rec_LNil_def
% 0.19/0.45 thf(fact_248_finlsts__rec__LNil,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,C: A,D4: B > ( coinductive_llist @ B ) > A > A] :
% 0.19/0.45 ( ( lList21916056377ts_rec @ A @ B @ C @ D4 @ ( coinductive_LNil @ B ) )
% 0.19/0.45 = C ) ).
% 0.19/0.45
% 0.19/0.45 % finlsts_rec_LNil
% 0.19/0.45 thf(fact_249_finlsts__rec__LCons,axiom,
% 0.19/0.45 ! [B: $tType,A: $tType,R: coinductive_llist @ A,A2: set @ A,C: B,D4: A > ( coinductive_llist @ A ) > B > B,A4: A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( lList21916056377ts_rec @ B @ A @ C @ D4 @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.19/0.45 = ( D4 @ A4 @ R @ ( lList21916056377ts_rec @ B @ A @ C @ D4 @ R ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % finlsts_rec_LCons
% 0.19/0.45 thf(fact_250_ltake__lappend__llength,axiom,
% 0.19/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S2: coinductive_llist @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( lList22119844313_ltake @ A @ ( coinductive_lappend @ A @ R @ S2 ) @ ( lList21232602520length @ A @ R ) )
% 0.19/0.45 = R ) ) ).
% 0.19/0.45
% 0.19/0.45 % ltake_lappend_llength
% 0.19/0.45 thf(fact_251_top__empty__eq,axiom,
% 0.19/0.45 ! [A: $tType] :
% 0.19/0.45 ( ( top_top @ ( A > $o ) )
% 0.19/0.45 = ( ^ [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % top_empty_eq
% 0.19/0.45 thf(fact_252_llength__drop__take,axiom,
% 0.19/0.45 ! [A: $tType,T2: coinductive_llist @ A,I: nat] :
% 0.19/0.45 ( ( ( lList2508575361_ldrop @ A @ T2 @ I )
% 0.19/0.45 != ( coinductive_LNil @ A ) )
% 0.19/0.45 => ( ( lList21232602520length @ A @ ( lList22119844313_ltake @ A @ T2 @ I ) )
% 0.19/0.45 = I ) ) ).
% 0.19/0.45
% 0.19/0.45 % llength_drop_take
% 0.19/0.45 thf(fact_253_lapp__suff__llength,axiom,
% 0.19/0.45 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S2: coinductive_llist @ A] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.19/0.45 => ( ( lList2508575361_ldrop @ A @ ( coinductive_lappend @ A @ R @ S2 ) @ ( lList21232602520length @ A @ R ) )
% 0.19/0.45 = S2 ) ) ).
% 0.19/0.45
% 0.19/0.45 % lapp_suff_llength
% 0.19/0.45 thf(fact_254_LList2__Mirabelle__hamjzmohle_Oldrop__LNil,axiom,
% 0.19/0.45 ! [A: $tType,I: nat] :
% 0.19/0.45 ( ( lList2508575361_ldrop @ A @ ( coinductive_LNil @ A ) @ I )
% 0.19/0.45 = ( coinductive_LNil @ A ) ) ).
% 0.19/0.45
% 0.19/0.45 % LList2_Mirabelle_hamjzmohle.ldrop_LNil
% 0.19/0.45 thf(fact_255_ldrop__fin__iffT,axiom,
% 0.19/0.45 ! [A: $tType,T2: coinductive_llist @ A,I: nat] :
% 0.19/0.45 ( ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T2 @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.19/0.45 = ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 % ldrop_fin_iffT
% 0.19/0.45
% 0.19/0.45 %----Type constructors (23)
% 0.19/0.45 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 0.19/0.45 ! [A8: $tType,A9: $tType] :
% 0.19/0.45 ( ( order_top @ A9 @ ( type2 @ A9 ) )
% 0.19/0.45 => ( order_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.19/0.45 ! [A8: $tType,A9: $tType] :
% 0.19/0.45 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 0.19/0.45 => ( preorder @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.19/0.45 ! [A8: $tType,A9: $tType] :
% 0.19/0.45 ( ( order @ A9 @ ( type2 @ A9 ) )
% 0.19/0.45 => ( order @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_fun___Orderings_Otop,axiom,
% 0.19/0.45 ! [A8: $tType,A9: $tType] :
% 0.19/0.45 ( ( top @ A9 @ ( type2 @ A9 ) )
% 0.19/0.45 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_fun___Orderings_Oord,axiom,
% 0.19/0.45 ! [A8: $tType,A9: $tType] :
% 0.19/0.45 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 0.19/0.45 => ( ord @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 0.19/0.45 condit1037483654norder @ nat @ ( type2 @ nat ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.19/0.45 wellorder @ nat @ ( type2 @ nat ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.19/0.45 preorder @ nat @ ( type2 @ nat ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.19/0.45 linorder @ nat @ ( type2 @ nat ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.19/0.45 no_top @ nat @ ( type2 @ nat ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.19/0.45 order @ nat @ ( type2 @ nat ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.19/0.45 ord @ nat @ ( type2 @ nat ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Set_Oset___Orderings_Oorder__top_4,axiom,
% 0.19/0.45 ! [A8: $tType] : ( order_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Set_Oset___Orderings_Opreorder_5,axiom,
% 0.19/0.45 ! [A8: $tType] : ( preorder @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Set_Oset___Orderings_Oorder_6,axiom,
% 0.19/0.45 ! [A8: $tType] : ( order @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Set_Oset___Orderings_Otop_7,axiom,
% 0.19/0.45 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_Set_Oset___Orderings_Oord_8,axiom,
% 0.19/0.45 ! [A8: $tType] : ( ord @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_HOL_Obool___Orderings_Oorder__top_9,axiom,
% 0.19/0.45 order_top @ $o @ ( type2 @ $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_HOL_Obool___Orderings_Opreorder_10,axiom,
% 0.19/0.45 preorder @ $o @ ( type2 @ $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_HOL_Obool___Orderings_Olinorder_11,axiom,
% 0.19/0.45 linorder @ $o @ ( type2 @ $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_HOL_Obool___Orderings_Oorder_12,axiom,
% 0.19/0.45 order @ $o @ ( type2 @ $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_HOL_Obool___Orderings_Otop_13,axiom,
% 0.19/0.45 top @ $o @ ( type2 @ $o ) ).
% 0.19/0.45
% 0.19/0.45 thf(tcon_HOL_Obool___Orderings_Oord_14,axiom,
% 0.19/0.45 ord @ $o @ ( type2 @ $o ) ).
% 0.19/0.45
% 0.19/0.45 %----Conjectures (1)
% 0.19/0.45 thf(conj_0,conjecture,
% 0.19/0.45 ~ ( ord_less_eq @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ a2 @ l ) @ ( coinductive_LNil @ a ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 0.29/1.70 ---- Embedded in THF ---
% 0.29/1.70 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.29/1.70 %%% Generated on Tue Feb 24 06:10:41 EST 2026
% 0.29/1.70 %%% using '$$dhol' embedding, version 1.3.0.
% 0.29/1.70 %%% Logic specification used:
% 0.29/1.70 %%% thf(spec, logic, $$dhol).
% 0.29/1.70
% 0.29/1.70 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.gEkGcnFM62/DTF2DTF9795.p
% 0.29/1.70 thf(ty_t_Coinductive__List_Ollist, type, coinductive_llist: ($tType > $tType)).
% 0.29/1.70 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 0.29/1.70 thf(ty_t_Nat_Onat, type, nat: $tType).
% 0.29/1.70 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 0.29/1.70 thf(ty_tf_a, type, a: $tType).
% 0.29/1.70 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.29/1.70 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.29/1.70 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.29/1.70 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.29/1.70 thf(sy_cl_Orderings_Ono__bot, type, no_bot: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.29/1.70 thf(sy_cl_Orderings_Ono__top, type, no_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.29/1.70 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.29/1.70 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.29/1.70 thf(sy_cl_Orderings_Oorder__top, type, order_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.29/1.70 thf(sy_cl_Orderings_Owellorder, type, wellorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.29/1.70 thf(sy_cl_Orderings_Odense__order, type, dense_order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.29/1.70 thf(sy_cl_Orderings_Odense__linorder, type, dense_linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.29/1.70 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum, type, condit1656338222tinuum: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.29/1.70 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder, type, condit1037483654norder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.29/1.70 thf(sy_c_Coinductive__List_Ofinite__lprefix, type, coindu328551480prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 0.29/1.70 thf(sy_c_Coinductive__List_Olappend, type, coinductive_lappend: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 0.29/1.70 thf(sy_c_Coinductive__List_Ollist_OLCons, type, coinductive_LCons: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 0.29/1.70 thf(sy_c_Coinductive__List_Ollist_OLNil, type, coinductive_LNil: (!> [A:$tType]: ((coinductive_llist @ A)))).
% 0.29/1.70 thf(sy_c_Coinductive__List_Olstrict__prefix, type, coindu1478340336prefix: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > $o))))).
% 0.29/1.70 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllstsp, type, lList21511617539llstsp: (!> [A:$tType]: (((A > $o) > ((coinductive_llist @ A) > $o))))).
% 0.29/1.70 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts, type, lList2236698231inlsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 0.29/1.70 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)))))).
% 0.29/1.70 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlstsp, type, lList2860480441nlstsp: (!> [A:$tType]: (((A > $o) > ((coinductive_llist @ A) > $o))))).
% 0.29/1.70 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts, type, lList22096119349pslsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 0.29/1.70 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast, type, lList2370560421utlast: (!> [A:$tType]: (((coinductive_llist @ A) > (coinductive_llist @ A))))).
% 0.29/1.70 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oldrop, type, lList2508575361_ldrop: (!> [A:$tType]: (((coinductive_llist @ A) > (nat > (coinductive_llist @ A)))))).
% 0.29/1.70 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast, type, lList2170638824_llast: (!> [A:$tType]: (((coinductive_llist @ A) > A)))).
% 0.29/1.70 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollength, type, lList21232602520length: (!> [A:$tType]: (((coinductive_llist @ A) > nat)))).
% 0.29/1.70 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev, type, lList2281150353e_lrev: (!> [A:$tType]: (((coinductive_llist @ A) > (coinductive_llist @ A))))).
% 0.29/1.70 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oltake, type, lList22119844313_ltake: (!> [A:$tType]: (((coinductive_llist @ A) > (nat > (coinductive_llist @ A)))))).
% 0.29/1.70 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts, type, lList21148268032oslsts: (!> [A:$tType]: (((set @ A) > (set @ (coinductive_llist @ A)))))).
% 0.29/1.70 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 0.29/1.70 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 0.29/1.70 thf(sy_c_Orderings_Oordering__top, type, ordering_top: (!> [A:$tType]: (((A > (A > $o)) > ((A > (A > $o)) > (A > $o)))))).
% 0.29/1.70 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 0.29/1.70 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 0.29/1.70 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 0.29/1.70 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 0.29/1.70 thf(sy_v_a, type, a2: a).
% 0.29/1.70 thf(sy_v_l, type, l: (coinductive_llist @ a)).
% 0.29/1.70 thf(fact_0_llistE, axiom, (! [A:$tType,Y:(coinductive_llist @ A)]: (((Y != (coinductive_LNil @ A)) => (~ ((! [X21:A,X22:(coinductive_llist @ A)]: ((Y != (((coinductive_LCons @ A) @ X21) @ X22)))))))))).
% 0.29/1.70 thf(fact_1_llist_Oinject, axiom, (! [A:$tType,X212:A,X222:(coinductive_llist @ A),Y21:A,Y22:(coinductive_llist @ A)]: ((((((coinductive_LCons @ A) @ X212) @ X222) = (((coinductive_LCons @ A) @ Y21) @ Y22)) = ((X212 = Y21) & (X222 = Y22)))))).
% 0.29/1.70 thf(fact_2_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 0.29/1.70 thf(fact_3_llist_Odistinct_I1_J, axiom, (! [A:$tType,X212:A,X222:(coinductive_llist @ A)]: (((coinductive_LNil @ A) != (((coinductive_LCons @ A) @ X212) @ X222))))).
% 0.29/1.70 thf(fact_4_neq__LNil__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((Xs != (coinductive_LNil @ A)) = (? [X2:A,Xs2:(coinductive_llist @ A)]: ((Xs = (((coinductive_LCons @ A) @ X2) @ Xs2)))))))).
% 0.29/1.70 thf(fact_5_llist__less__def, axiom, ((ord_less @ (coinductive_llist @ a)) = (^ [S:(coinductive_llist @ a),T:(coinductive_llist @ a)]: (((((ord_less_eq @ (coinductive_llist @ a)) @ S) @ T) & (S != T)))))).
% 0.29/1.70 thf(fact_6_llist__le__def, axiom, ((ord_less_eq @ (coinductive_llist @ a)) = (^ [S:(coinductive_llist @ a),T:(coinductive_llist @ a)]: ((? [D:(coinductive_llist @ a)]: ((T = (((coinductive_lappend @ a) @ S) @ D)))))))).
% 0.29/1.70 thf(fact_7_lbutlast__LNil, axiom, (! [A:$tType]: ((((lList2370560421utlast @ A) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 0.29/1.70 thf(fact_8_fps__induct, axiom, (! [A:$tType,L:(coinductive_llist @ A),A2:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList22096119349pslsts @ A) @ A2)) => ((! [A3:A]: (((((member @ A) @ A3) @ A2) => (P @ (((coinductive_LCons @ A) @ A3) @ (coinductive_LNil @ A)))))) => ((! [A3:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList22096119349pslsts @ A) @ A2)) => ((P @ L2) => ((((member @ A) @ A3) @ A2) => (P @ (((coinductive_LCons @ A) @ A3) @ L2))))))) => (P @ L))))))).
% 0.29/1.70 thf(fact_9_alllstsp_Ocases, axiom, (! [A:$tType,A2:(A > $o),A4:(coinductive_llist @ A)]: (((((lList21511617539llstsp @ A) @ A2) @ A4) => ((A4 != (coinductive_LNil @ A)) => (~ ((! [L2:(coinductive_llist @ A),A3:A]: (((A4 = (((coinductive_LCons @ A) @ A3) @ L2)) => ((((lList21511617539llstsp @ A) @ A2) @ L2) => (~ ((A2 @ A3)))))))))))))).
% 0.29/1.70 thf(fact_10_alllstsp_Osimps, axiom, (! [A:$tType]: (((lList21511617539llstsp @ A) = (^ [A5:(A > $o),A6:(coinductive_llist @ A)]: (((A6 = (coinductive_LNil @ A)) | (? [L3:(coinductive_llist @ A),B2:A]: (((A6 = (((coinductive_LCons @ A) @ B2) @ L3)) & ((((lList21511617539llstsp @ A) @ A5) @ L3) & (A5 @ B2)))))))))))).
% 0.29/1.70 thf(fact_11_finlstsp_Ocases, axiom, (! [A:$tType,A2:(A > $o),A4:(coinductive_llist @ A)]: (((((lList2860480441nlstsp @ A) @ A2) @ A4) => ((A4 != (coinductive_LNil @ A)) => (~ ((! [L2:(coinductive_llist @ A),A3:A]: (((A4 = (((coinductive_LCons @ A) @ A3) @ L2)) => ((((lList2860480441nlstsp @ A) @ A2) @ L2) => (~ ((A2 @ A3)))))))))))))).
% 0.29/1.70 thf(fact_12_finlstsp_Osimps, axiom, (! [A:$tType]: (((lList2860480441nlstsp @ A) = (^ [A5:(A > $o),A6:(coinductive_llist @ A)]: (((A6 = (coinductive_LNil @ A)) | (? [L3:(coinductive_llist @ A),B2:A]: (((A6 = (((coinductive_LCons @ A) @ B2) @ L3)) & ((((lList2860480441nlstsp @ A) @ A5) @ L3) & (A5 @ B2)))))))))))).
% 0.29/1.70 thf(fact_13_lappend__code_I2_J, axiom, (! [A:$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)))))).
% 0.29/1.70 thf(fact_14_lappend__eq__LNil__iff, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((((coinductive_lappend @ A) @ Xs) @ Ys) = (coinductive_LNil @ A)) = ((Xs = (coinductive_LNil @ A)) & (Ys = (coinductive_LNil @ A))))))).
% 0.29/1.70 thf(fact_15_LNil__eq__lappend__iff, axiom, (! [A:$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))))))).
% 0.29/1.70 thf(fact_16_lappend__LNil2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ Xs) @ (coinductive_LNil @ A)) = Xs)))).
% 0.29/1.70 thf(fact_17_lappend__code_I1_J, axiom, (! [A:$tType,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ Ys) = Ys)))).
% 0.29/1.70 thf(fact_18_lappend__is__LNil__conv, axiom, (! [A:$tType,S2:(coinductive_llist @ A),T2:(coinductive_llist @ A)]: ((((((coinductive_lappend @ A) @ S2) @ T2) = (coinductive_LNil @ A)) = ((S2 = (coinductive_LNil @ A)) & (T2 = (coinductive_LNil @ A))))))).
% 0.29/1.70 thf(fact_19_LNil__is__lappend__conv, axiom, (! [A:$tType,S2:(coinductive_llist @ A),T2:(coinductive_llist @ A)]: ((((coinductive_LNil @ A) = (((coinductive_lappend @ A) @ S2) @ T2)) = ((S2 = (coinductive_LNil @ A)) & (T2 = (coinductive_LNil @ A))))))).
% 0.29/1.70 thf(fact_20_ord__eq__less__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A4:A,F:(B > A),B3:B,C:B]: (((A4 = (F @ B3)) => ((((ord_less @ B) @ B3) @ C) => ((! [X3:B,Y2:B]: (((((ord_less @ B) @ X3) @ Y2) => (((ord_less @ A) @ (F @ X3)) @ (F @ Y2))))) => (((ord_less @ A) @ A4) @ (F @ C))))))))))).
% 0.29/1.70 thf(fact_21_ord__less__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A4:A,B3:A,F:(A > B),C:B]: (((((ord_less @ A) @ A4) @ B3) => (((F @ B3) = C) => ((! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (((ord_less @ B) @ (F @ X3)) @ (F @ Y2))))) => (((ord_less @ B) @ (F @ A4)) @ C)))))))))).
% 0.29/1.70 thf(fact_22_order__less__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A4:A,F:(B > A),B3:B,C:B]: (((((ord_less @ A) @ A4) @ (F @ B3)) => ((((ord_less @ B) @ B3) @ C) => ((! [X3:B,Y2:B]: (((((ord_less @ B) @ X3) @ Y2) => (((ord_less @ A) @ (F @ X3)) @ (F @ Y2))))) => (((ord_less @ A) @ A4) @ (F @ C))))))))))).
% 0.29/1.70 thf(fact_23_order__less__subst2, axiom, (! [A:$tType,C2:$tType]: (((((order @ C2) @ (type2 @ C2)) & ((order @ A) @ (type2 @ A))) => (! [A4:A,B3:A,F:(A > C2),C:C2]: (((((ord_less @ A) @ A4) @ B3) => ((((ord_less @ C2) @ (F @ B3)) @ C) => ((! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (((ord_less @ C2) @ (F @ X3)) @ (F @ Y2))))) => (((ord_less @ C2) @ (F @ A4)) @ C)))))))))).
% 0.29/1.70 thf(fact_24_lt__ex, axiom, (! [A:$tType]: ((((no_bot @ A) @ (type2 @ A)) => (! [X:A]: ((? [Y2:A]: ((((ord_less @ A) @ Y2) @ X))))))))).
% 0.29/1.70 thf(fact_25_gt__ex, axiom, (! [A:$tType]: ((((no_top @ A) @ (type2 @ A)) => (! [X:A]: ((? [X1:A]: ((((ord_less @ A) @ X) @ X1))))))))).
% 0.29/1.70 thf(fact_26_neqE, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X != Y) => ((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less @ A) @ Y) @ X))))))))).
% 0.29/1.70 thf(fact_27_lappend__assoc, axiom, (! [A:$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)))))).
% 0.29/1.70 thf(fact_28_neq__iff, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X != Y) = ((((ord_less @ A) @ X) @ Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 0.29/1.70 thf(fact_29_order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B3:A]: (((((ord_less @ A) @ A4) @ B3) => (~ ((((ord_less @ A) @ B3) @ A4)))))))))).
% 0.29/1.70 thf(fact_30_dense, axiom, (! [A:$tType]: ((((dense_order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (? [Z:A]: (((((ord_less @ A) @ X) @ Z) & (((ord_less @ A) @ Z) @ Y))))))))))).
% 0.29/1.70 thf(fact_31_less__imp__neq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 0.29/1.70 thf(fact_32_less__asym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 0.29/1.70 thf(fact_33_less__asym_H, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [A4:A,B3:A]: (((((ord_less @ A) @ A4) @ B3) => (~ ((((ord_less @ A) @ B3) @ A4)))))))))).
% 0.29/1.70 thf(fact_34_less__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z2:A]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ Z2) => (((ord_less @ A) @ X) @ Z2))))))))).
% 0.29/1.70 thf(fact_35_less__linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) | ((X = Y) | (((ord_less @ A) @ Y) @ X))))))))).
% 0.29/1.70 thf(fact_36_less__irrefl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((~ ((((ord_less @ A) @ X) @ X))))))))).
% 0.29/1.70 thf(fact_37_ord__eq__less__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A4:A,B3:A,C:A]: (((A4 = B3) => ((((ord_less @ A) @ B3) @ C) => (((ord_less @ A) @ A4) @ C))))))))).
% 0.29/1.70 thf(fact_38_ord__less__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A4:A,B3:A,C:A]: (((((ord_less @ A) @ A4) @ B3) => ((B3 = C) => (((ord_less @ A) @ A4) @ C))))))))).
% 0.29/1.70 thf(fact_39_dual__order_Oasym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A4:A]: (((((ord_less @ A) @ B3) @ A4) => (~ ((((ord_less @ A) @ A4) @ B3)))))))))).
% 0.29/1.70 thf(fact_40_less__imp__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (X != Y)))))))).
% 0.29/1.70 thf(fact_41_less__not__sym, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 0.29/1.70 thf(fact_42_less__induct, axiom, (! [A:$tType]: ((((wellorder @ A) @ (type2 @ A)) => (! [P:(A > $o),A4:A]: (((! [X3:A]: (((! [Y3:A]: (((((ord_less @ A) @ Y3) @ X3) => (P @ Y3)))) => (P @ X3)))) => (P @ A4)))))))).
% 0.29/1.70 thf(fact_43_antisym__conv3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((~ ((((ord_less @ A) @ Y) @ X))) => ((~ ((((ord_less @ A) @ X) @ Y))) = (X = Y))))))))).
% 0.29/1.70 thf(fact_44_less__imp__not__eq2, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (Y != X)))))))).
% 0.29/1.70 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A4:A,P:(A > $o)]: (((((member @ A) @ A4) @ ((collect @ A) @ P)) = (P @ A4))))).
% 0.29/1.70 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A2)))) = A2)))).
% 0.29/1.70 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 0.29/1.70 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 0.29/1.70 thf(fact_49_less__imp__triv, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,P:$o]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ X) => P)))))))).
% 0.29/1.70 thf(fact_50_linorder__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) => ((X != Y) => (((ord_less @ A) @ Y) @ X))))))))).
% 0.29/1.70 thf(fact_51_dual__order_Oirrefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A]: ((~ ((((ord_less @ A) @ A4) @ A4))))))))).
% 0.29/1.70 thf(fact_52_fpslsts__mono, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => (((ord_less_eq @ (set @ (coinductive_llist @ A))) @ ((lList22096119349pslsts @ A) @ A2)) @ ((lList22096119349pslsts @ A) @ B4)))))).
% 0.29/1.70 thf(fact_53_order_Ostrict__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B3:A,C:A]: (((((ord_less @ A) @ A4) @ B3) => ((((ord_less @ A) @ B3) @ C) => (((ord_less @ A) @ A4) @ C))))))))).
% 0.29/1.70 thf(fact_54_alllstsp__mono, axiom, (! [A:$tType,A2:(A > $o),B4:(A > $o)]: (((((ord_less_eq @ (A > $o)) @ A2) @ B4) => (((ord_less_eq @ ((coinductive_llist @ A) > $o)) @ ((lList21511617539llstsp @ A) @ A2)) @ ((lList21511617539llstsp @ A) @ B4)))))).
% 0.29/1.70 thf(fact_55_finlstsp__mono, axiom, (! [A:$tType,A2:(A > $o),B4:(A > $o)]: (((((ord_less_eq @ (A > $o)) @ A2) @ B4) => (((ord_less_eq @ ((coinductive_llist @ A) > $o)) @ ((lList2860480441nlstsp @ A) @ A2)) @ ((lList2860480441nlstsp @ A) @ B4)))))).
% 0.29/1.70 thf(fact_56_less__imp__not__less, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (~ ((((ord_less @ A) @ Y) @ X)))))))))).
% 0.29/1.70 thf(fact_57_dual__order_Ostrict__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A4:A,C:A]: (((((ord_less @ A) @ B3) @ A4) => ((((ord_less @ A) @ C) @ B3) => (((ord_less @ A) @ C) @ A4))))))))).
% 0.29/1.70 thf(fact_58_not__less__iff__gr__or__eq, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) = ((((ord_less @ A) @ Y) @ X) | (X = Y))))))))).
% 0.29/1.70 thf(fact_59_order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B3:A]: (((((ord_less @ A) @ A4) @ B3) => (A4 != B3)))))))).
% 0.29/1.70 thf(fact_60_dual__order_Ostrict__implies__not__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A4:A]: (((((ord_less @ A) @ B3) @ A4) => (A4 != B3)))))))).
% 0.29/1.70 thf(fact_61_order_Onot__eq__order__implies__strict, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B3:A]: (((A4 != B3) => ((((ord_less_eq @ A) @ A4) @ B3) => (((ord_less @ A) @ A4) @ B3))))))))).
% 0.29/1.70 thf(fact_62_dual__order_Ostrict__implies__order, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A4:A]: (((((ord_less @ A) @ B3) @ A4) => (((ord_less_eq @ A) @ B3) @ A4)))))))).
% 0.29/1.70 thf(fact_63_dual__order_Ostrict__iff__order, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [B2:A,A6:A]: (((((ord_less_eq @ A) @ B2) @ A6) & (A6 != B2))))))))).
% 0.29/1.70 thf(fact_64_dual__order_Oorder__iff__strict, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [B2:A,A6:A]: (((((ord_less @ A) @ B2) @ A6) | (A6 = B2))))))))).
% 0.29/1.70 thf(fact_65_order_Ostrict__implies__order, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B3:A]: (((((ord_less @ A) @ A4) @ B3) => (((ord_less_eq @ A) @ A4) @ B3)))))))).
% 0.29/1.70 thf(fact_66_dense__le__bounded, axiom, (! [A:$tType]: ((((dense_linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z2:A]: (((((ord_less @ A) @ X) @ Y) => ((! [W:A]: (((((ord_less @ A) @ X) @ W) => ((((ord_less @ A) @ W) @ Y) => (((ord_less_eq @ A) @ W) @ Z2))))) => (((ord_less_eq @ A) @ Y) @ Z2))))))))).
% 0.29/1.70 thf(fact_67_dense__ge__bounded, axiom, (! [A:$tType]: ((((dense_linorder @ A) @ (type2 @ A)) => (! [Z2:A,X:A,Y:A]: (((((ord_less @ A) @ Z2) @ X) => ((! [W:A]: (((((ord_less @ A) @ Z2) @ W) => ((((ord_less @ A) @ W) @ X) => (((ord_less_eq @ A) @ Y) @ W))))) => (((ord_less_eq @ A) @ Y) @ Z2))))))))).
% 0.29/1.70 thf(fact_68_dual__order_Ostrict__trans2, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A4:A,C:A]: (((((ord_less @ A) @ B3) @ A4) => ((((ord_less_eq @ A) @ C) @ B3) => (((ord_less @ A) @ C) @ A4))))))))).
% 0.29/1.70 thf(fact_69_dual__order_Ostrict__trans1, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A4:A,C:A]: (((((ord_less_eq @ A) @ B3) @ A4) => ((((ord_less @ A) @ C) @ B3) => (((ord_less @ A) @ C) @ A4))))))))).
% 0.29/1.70 thf(fact_70_order_Ostrict__iff__order, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [A6:A,B2:A]: (((((ord_less_eq @ A) @ A6) @ B2) & (A6 != B2))))))))).
% 0.29/1.70 thf(fact_71_order_Oorder__iff__strict, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [A6:A,B2:A]: (((((ord_less @ A) @ A6) @ B2) | (A6 = B2))))))))).
% 0.29/1.70 thf(fact_72_order_Ostrict__trans2, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B3:A,C:A]: (((((ord_less @ A) @ A4) @ B3) => ((((ord_less_eq @ A) @ B3) @ C) => (((ord_less @ A) @ A4) @ C))))))))).
% 0.29/1.70 thf(fact_73_order_Ostrict__trans1, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B3:A,C:A]: (((((ord_less_eq @ A) @ A4) @ B3) => ((((ord_less @ A) @ B3) @ C) => (((ord_less @ A) @ A4) @ C))))))))).
% 0.29/1.70 thf(fact_74_not__le__imp__less, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((~ ((((ord_less_eq @ A) @ Y) @ X))) => (((ord_less @ A) @ X) @ Y)))))))).
% 0.29/1.70 thf(fact_75_less__le__not__le, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [X2:A,Y4:A]: (((((ord_less_eq @ A) @ X2) @ Y4) & (~ ((((ord_less_eq @ A) @ Y4) @ X2))))))))))).
% 0.29/1.70 thf(fact_76_le__imp__less__or__eq, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less @ A) @ X) @ Y) | (X = Y))))))))).
% 0.29/1.70 thf(fact_77_le__less__linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less @ A) @ Y) @ X)))))))).
% 0.29/1.70 thf(fact_78_dense__le, axiom, (! [A:$tType]: ((((dense_linorder @ A) @ (type2 @ A)) => (! [Y:A,Z2:A]: (((! [X3:A]: (((((ord_less @ A) @ X3) @ Y) => (((ord_less_eq @ A) @ X3) @ Z2)))) => (((ord_less_eq @ A) @ Y) @ Z2)))))))).
% 0.29/1.70 thf(fact_79_dense__ge, axiom, (! [A:$tType]: ((((dense_linorder @ A) @ (type2 @ A)) => (! [Z2:A,Y:A]: (((! [X3:A]: (((((ord_less @ A) @ Z2) @ X3) => (((ord_less_eq @ A) @ Y) @ X3)))) => (((ord_less_eq @ A) @ Y) @ Z2)))))))).
% 0.29/1.70 thf(fact_80_less__le__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z2:A]: (((((ord_less @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z2) => (((ord_less @ A) @ X) @ Z2))))))))).
% 0.29/1.70 thf(fact_81_le__less__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z2:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less @ A) @ Y) @ Z2) => (((ord_less @ A) @ X) @ Z2))))))))).
% 0.29/1.70 thf(fact_82_antisym__conv2, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((~ ((((ord_less @ A) @ X) @ Y))) = (X = Y))))))))).
% 0.29/1.70 thf(fact_83_antisym__conv1, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 0.29/1.70 thf(fact_84_less__imp__le, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less @ A) @ X) @ Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 0.29/1.70 thf(fact_85_le__neq__trans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B3:A]: (((((ord_less_eq @ A) @ A4) @ B3) => ((A4 != B3) => (((ord_less @ A) @ A4) @ B3))))))))).
% 0.29/1.70 thf(fact_86_not__less, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) = (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.29/1.70 thf(fact_87_not__le, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) = (((ord_less @ A) @ Y) @ X)))))))).
% 0.29/1.70 thf(fact_88_order__less__le__subst2, axiom, (! [A:$tType,C2:$tType]: (((((order @ C2) @ (type2 @ C2)) & ((order @ A) @ (type2 @ A))) => (! [A4:A,B3:A,F:(A > C2),C:C2]: (((((ord_less @ A) @ A4) @ B3) => ((((ord_less_eq @ C2) @ (F @ B3)) @ C) => ((! [X3:A,Y2:A]: (((((ord_less @ A) @ X3) @ Y2) => (((ord_less @ C2) @ (F @ X3)) @ (F @ Y2))))) => (((ord_less @ C2) @ (F @ A4)) @ C)))))))))).
% 0.29/1.70 thf(fact_89_order__less__le__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A4:A,F:(B > A),B3:B,C:B]: (((((ord_less @ A) @ A4) @ (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C) => ((! [X3:B,Y2:B]: (((((ord_less_eq @ B) @ X3) @ Y2) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y2))))) => (((ord_less @ A) @ A4) @ (F @ C))))))))))).
% 0.29/1.70 thf(fact_90_order__le__less__subst2, axiom, (! [A:$tType,C2:$tType]: (((((order @ C2) @ (type2 @ C2)) & ((order @ A) @ (type2 @ A))) => (! [A4:A,B3:A,F:(A > C2),C:C2]: (((((ord_less_eq @ A) @ A4) @ B3) => ((((ord_less @ C2) @ (F @ B3)) @ C) => ((! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => (((ord_less_eq @ C2) @ (F @ X3)) @ (F @ Y2))))) => (((ord_less @ C2) @ (F @ A4)) @ C)))))))))).
% 0.29/1.70 thf(fact_91_order__le__less__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A4:A,F:(B > A),B3:B,C:B]: (((((ord_less_eq @ A) @ A4) @ (F @ B3)) => ((((ord_less @ B) @ B3) @ C) => ((! [X3:B,Y2:B]: (((((ord_less @ B) @ X3) @ Y2) => (((ord_less @ A) @ (F @ X3)) @ (F @ Y2))))) => (((ord_less @ A) @ A4) @ (F @ C))))))))))).
% 0.29/1.70 thf(fact_92_less__le, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less @ A) = (^ [X2:A,Y4:A]: (((((ord_less_eq @ A) @ X2) @ Y4) & (X2 != Y4))))))))).
% 0.29/1.70 thf(fact_93_le__less, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [X2:A,Y4:A]: (((((ord_less @ A) @ X2) @ Y4) | (X2 = Y4))))))))).
% 0.29/1.70 thf(fact_94_leI, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.29/1.70 thf(fact_95_leD, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less @ A) @ X) @ Y)))))))))).
% 0.29/1.70 thf(fact_96_lappend__LNil__LNil, axiom, (! [A:$tType]: (((((coinductive_lappend @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 0.29/1.70 thf(fact_97_lappend__snocL1__conv__LCons2, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coinductive_lappend @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ (coinductive_LNil @ A)))) @ Ys) = (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys)))))).
% 0.29/1.70 thf(fact_98_LList2__Mirabelle__hamjzmohle_Ollist__le__def, axiom, (! [A:$tType]: (((ord_less_eq @ (coinductive_llist @ A)) = (^ [S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: ((? [D:(coinductive_llist @ A)]: ((T = (((coinductive_lappend @ A) @ S) @ D)))))))))).
% 0.29/1.70 thf(fact_99_finlstsp_OLCons__fin, axiom, (! [A:$tType,A2:(A > $o),L:(coinductive_llist @ A),A4:A]: (((((lList2860480441nlstsp @ A) @ A2) @ L) => ((A2 @ A4) => (((lList2860480441nlstsp @ A) @ A2) @ (((coinductive_LCons @ A) @ A4) @ L))))))).
% 0.29/1.70 thf(fact_100_alllstsp_OLCons__all, axiom, (! [A:$tType,A2:(A > $o),L:(coinductive_llist @ A),A4:A]: (((((lList21511617539llstsp @ A) @ A2) @ L) => ((A2 @ A4) => (((lList21511617539llstsp @ A) @ A2) @ (((coinductive_LCons @ A) @ A4) @ L))))))).
% 0.29/1.70 thf(fact_101_finlstsp_OLNil__fin, axiom, (! [A:$tType,A2:(A > $o)]: ((((lList2860480441nlstsp @ A) @ A2) @ (coinductive_LNil @ A))))).
% 0.29/1.70 thf(fact_102_alllstsp_OLNil__all, axiom, (! [A:$tType,A2:(A > $o)]: ((((lList21511617539llstsp @ A) @ A2) @ (coinductive_LNil @ A))))).
% 0.29/1.70 thf(fact_103_LList2__Mirabelle__hamjzmohle_Ollist__less__def, axiom, (! [A:$tType]: (((ord_less @ (coinductive_llist @ A)) = (^ [S:(coinductive_llist @ A),T:(coinductive_llist @ A)]: (((((ord_less_eq @ (coinductive_llist @ A)) @ S) @ T) & (S != T)))))))).
% 0.29/1.70 thf(fact_104_dual__order_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A4:A]: (((((ord_less_eq @ A) @ B3) @ A4) => ((((ord_less_eq @ A) @ A4) @ B3) => (A4 = B3))))))))).
% 0.29/1.70 thf(fact_105_dual__order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B3:A,A4:A,C:A]: (((((ord_less_eq @ A) @ B3) @ A4) => ((((ord_less_eq @ A) @ C) @ B3) => (((ord_less_eq @ A) @ C) @ A4))))))))).
% 0.29/1.70 thf(fact_106_linorder__wlog, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),A4:A,B3:A]: (((! [A3:A,B5:A]: (((((ord_less_eq @ A) @ A3) @ B5) => ((P @ A3) @ B5)))) => ((! [A3:A,B5:A]: ((((P @ B5) @ A3) => ((P @ A3) @ B5)))) => ((P @ A4) @ B3))))))))).
% 0.29/1.70 thf(fact_107_dual__order_Orefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A]: ((((ord_less_eq @ A) @ A4) @ A4))))))).
% 0.29/1.70 thf(fact_108_order__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z2:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z2) => (((ord_less_eq @ A) @ X) @ Z2))))))))).
% 0.29/1.70 thf(fact_109_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B3:A]: (((((ord_less_eq @ A) @ A4) @ B3) => ((((ord_less_eq @ A) @ B3) @ A4) => (A4 = B3))))))))).
% 0.29/1.70 thf(fact_110_ord__le__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A4:A,B3:A,C:A]: (((((ord_less_eq @ A) @ A4) @ B3) => ((B3 = C) => (((ord_less_eq @ A) @ A4) @ C))))))))).
% 0.29/1.70 thf(fact_111_ord__eq__le__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A4:A,B3:A,C:A]: (((A4 = B3) => ((((ord_less_eq @ A) @ B3) @ C) => (((ord_less_eq @ A) @ A4) @ C))))))))).
% 0.29/1.70 thf(fact_112_antisym__conv, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 0.29/1.70 thf(fact_113_le__cases3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z2:A]: ((((((ord_less_eq @ A) @ X) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z2)))) => (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z2)))) => (((((ord_less_eq @ A) @ X) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y)))) => (((((ord_less_eq @ A) @ Z2) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X)))) => (((((ord_less_eq @ A) @ Y) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y))))))))))))))))).
% 0.29/1.70 thf(fact_114_order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A4:A,B3:A,C:A]: (((((ord_less_eq @ A) @ A4) @ B3) => ((((ord_less_eq @ A) @ B3) @ C) => (((ord_less_eq @ A) @ A4) @ C))))))))).
% 0.29/1.70 thf(fact_115_le__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.29/1.70 thf(fact_116_wlog__linorder__le, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),B3:A,A4:A]: (((! [A3:A,B5:A]: (((((ord_less_eq @ A) @ A3) @ B5) => ((P @ A3) @ B5)))) => ((((P @ B3) @ A4) => ((P @ A4) @ B3)) => ((P @ A4) @ B3))))))))).
% 0.29/1.70 thf(fact_117_eq__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X = Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 0.29/1.70 thf(fact_118_linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.29/1.70 thf(fact_119_antisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 0.29/1.70 thf(fact_120_eq__iff, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((^ [Y5:A,Z3:A]: ((Y5 = Z3))) = (^ [X2:A,Y4:A]: (((((ord_less_eq @ A) @ X2) @ Y4) & (((ord_less_eq @ A) @ Y4) @ X2))))))))).
% 0.29/1.70 thf(fact_121_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A4:A,B3:A,F:(A > B),C:B]: (((((ord_less_eq @ A) @ A4) @ B3) => (((F @ B3) = C) => ((! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => (((ord_less_eq @ B) @ (F @ X3)) @ (F @ Y2))))) => (((ord_less_eq @ B) @ (F @ A4)) @ C)))))))))).
% 0.29/1.70 thf(fact_122_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A4:A,F:(B > A),B3:B,C:B]: (((A4 = (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C) => ((! [X3:B,Y2:B]: (((((ord_less_eq @ B) @ X3) @ Y2) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y2))))) => (((ord_less_eq @ A) @ A4) @ (F @ C))))))))))).
% 0.29/1.70 thf(fact_123_order__subst2, axiom, (! [A:$tType,C2:$tType]: (((((order @ C2) @ (type2 @ C2)) & ((order @ A) @ (type2 @ A))) => (! [A4:A,B3:A,F:(A > C2),C:C2]: (((((ord_less_eq @ A) @ A4) @ B3) => ((((ord_less_eq @ C2) @ (F @ B3)) @ C) => ((! [X3:A,Y2:A]: (((((ord_less_eq @ A) @ X3) @ Y2) => (((ord_less_eq @ C2) @ (F @ X3)) @ (F @ Y2))))) => (((ord_less_eq @ C2) @ (F @ A4)) @ C)))))))))).
% 0.29/1.70 thf(fact_124_order__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A4:A,F:(B > A),B3:B,C:B]: (((((ord_less_eq @ A) @ A4) @ (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C) => ((! [X3:B,Y2:B]: (((((ord_less_eq @ B) @ X3) @ Y2) => (((ord_less_eq @ A) @ (F @ X3)) @ (F @ Y2))))) => (((ord_less_eq @ A) @ A4) @ (F @ C))))))))))).
% 0.29/1.70 thf(fact_125_le__fun__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: ((! [X2:A]: ((((ord_less_eq @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))))).
% 0.29/1.70 thf(fact_126_le__funI, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B)]: (((! [X3:A]: ((((ord_less_eq @ B) @ (F @ X3)) @ (G @ X3)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 0.29/1.70 thf(fact_127_le__funE, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 0.29/1.70 thf(fact_128_le__funD, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 0.29/1.70 thf(fact_129_alllstsp_Ocoinduct, axiom, (! [A:$tType,X4:((coinductive_llist @ A) > $o),X:(coinductive_llist @ A),A2:(A > $o)]: (((X4 @ X) => ((! [X3:(coinductive_llist @ A)]: (((X4 @ X3) => ((X3 = (coinductive_LNil @ A)) | (? [L4:(coinductive_llist @ A),A7:A]: (((X3 = (((coinductive_LCons @ A) @ A7) @ L4)) & (((X4 @ L4) | (((lList21511617539llstsp @ A) @ A2) @ L4)) & (A2 @ A7))))))))) => (((lList21511617539llstsp @ A) @ A2) @ X)))))).
% 0.29/1.70 thf(fact_130_finlstsp_Oinducts, axiom, (! [A:$tType,A2:(A > $o),X:(coinductive_llist @ A),P:((coinductive_llist @ A) > $o)]: (((((lList2860480441nlstsp @ A) @ A2) @ X) => ((P @ (coinductive_LNil @ A)) => ((! [L2:(coinductive_llist @ A),A3:A]: (((((lList2860480441nlstsp @ A) @ A2) @ L2) => ((P @ L2) => ((A2 @ A3) => (P @ (((coinductive_LCons @ A) @ A3) @ L2))))))) => (P @ X))))))).
% 0.29/1.70 thf(fact_131_lbutlast__lapp__llast, axiom, (! [A:$tType,L:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList22096119349pslsts @ A) @ A2)) => (L = (((coinductive_lappend @ A) @ ((lList2370560421utlast @ A) @ L)) @ (((coinductive_LCons @ A) @ ((lList2170638824_llast @ A) @ L)) @ (coinductive_LNil @ A)))))))).
% 0.29/1.70 thf(fact_132_complete__interval, axiom, (! [A:$tType]: ((((condit1037483654norder @ A) @ (type2 @ A)) => (! [A4:A,B3:A,P:(A > $o)]: (((((ord_less @ A) @ A4) @ B3) => ((P @ A4) => ((~ ((P @ B3))) => (? [C3:A]: (((((ord_less_eq @ A) @ A4) @ C3) & ((((ord_less_eq @ A) @ C3) @ B3) & ((! [X5:A]: ((((((ord_less_eq @ A) @ A4) @ X5) & (((ord_less @ A) @ X5) @ C3)) => (P @ X5)))) & (! [D2:A]: (((! [X3:A]: ((((((ord_less_eq @ A) @ A4) @ X3) & (((ord_less @ A) @ X3) @ D2)) => (P @ X3)))) => (((ord_less_eq @ A) @ D2) @ C3)))))))))))))))))).
% 0.29/1.70 thf(fact_133_pinf_I6_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ Z) @ X5) => (~ ((((ord_less_eq @ A) @ X5) @ T2)))))))))))))).
% 0.29/1.70 thf(fact_134_pinf_I8_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ Z) @ X5) => (((ord_less_eq @ A) @ T2) @ X5)))))))))))).
% 0.29/1.70 thf(fact_135_minf_I6_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ X5) @ Z) => (((ord_less_eq @ A) @ X5) @ T2)))))))))))).
% 0.29/1.70 thf(fact_136_minf_I8_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ X5) @ Z) => (~ ((((ord_less_eq @ A) @ T2) @ X5)))))))))))))).
% 0.29/1.70 thf(fact_137_lbutlast__snoc, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A2:(set @ A),X:A]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A2)) => (((lList2370560421utlast @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A)))) = Xs))))).
% 0.29/1.70 thf(fact_138_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Y:A,Ys:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (((coinductive_LCons @ A) @ Y) @ Ys)) = ((Xs = (coinductive_LNil @ A)) | (? [Xs2:(coinductive_llist @ A)]: (((Xs = (((coinductive_LCons @ A) @ Y) @ Xs2)) & (((coindu328551480prefix @ A) @ Xs2) @ Ys))))))))).
% 0.29/1.70 thf(fact_139_lstrict__prefix__code_I2_J, axiom, (! [B:$tType,Y:B,Ys:(coinductive_llist @ B)]: ((((coindu1478340336prefix @ B) @ (coinductive_LNil @ B)) @ (((coinductive_LCons @ B) @ Y) @ Ys))))).
% 0.29/1.70 thf(fact_140_lstrict__prefix__code_I3_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B)]: ((~ ((((coindu1478340336prefix @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) @ (coinductive_LNil @ B))))))).
% 0.29/1.70 thf(fact_141_lbutlast__LCons, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),A4:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((R = (coinductive_LNil @ A)) => (((lList2370560421utlast @ A) @ (((coinductive_LCons @ A) @ A4) @ R)) = (coinductive_LNil @ A))) & ((R != (coinductive_LNil @ A)) => (((lList2370560421utlast @ A) @ (((coinductive_LCons @ A) @ A4) @ R)) = (((coinductive_LCons @ A) @ A4) @ ((lList2370560421utlast @ A) @ R))))))))).
% 0.29/1.70 thf(fact_142_predicate1I, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) => (Q @ X3)))) => (((ord_less_eq @ (A > $o)) @ P) @ Q))))).
% 0.29/1.70 thf(fact_143_lapp__fin__fin__iff, axiom, (! [A:$tType,R:(coinductive_llist @ A),S2:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S2)) @ ((lList2236698231inlsts @ A) @ A2)) = ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ (coinductive_llist @ A)) @ S2) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 0.29/1.70 thf(fact_144_same__lappend__eq, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),S2:(coinductive_llist @ A),T2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((((coinductive_lappend @ A) @ R) @ S2) = (((coinductive_lappend @ A) @ R) @ T2)) = (S2 = T2)))))).
% 0.29/1.70 thf(fact_145_lstrict__prefix__code_I4_J, axiom, (! [B:$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)))))).
% 0.29/1.70 thf(fact_146_lstrict__prefix__code_I1_J, axiom, (! [A:$tType]: ((~ ((((coindu1478340336prefix @ A) @ (coinductive_LNil @ A)) @ (coinductive_LNil @ A))))))).
% 0.29/1.70 thf(fact_147_fpslsts__iff, axiom, (! [A:$tType,S2:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ S2) @ ((lList22096119349pslsts @ A) @ A2)) = ((((member @ (coinductive_llist @ A)) @ S2) @ ((lList2236698231inlsts @ A) @ A2)) & (S2 != (coinductive_LNil @ A))))))).
% 0.29/1.70 thf(fact_148_LList2__Mirabelle__hamjzmohle_Ollast__LCons, axiom, (! [B:$tType,R:(coinductive_llist @ B),A2:(set @ B),A4:B]: (((((member @ (coinductive_llist @ B)) @ R) @ ((lList2236698231inlsts @ B) @ A2)) => (((R = (coinductive_LNil @ B)) => (((lList2170638824_llast @ B) @ (((coinductive_LCons @ B) @ A4) @ R)) = A4)) & ((R != (coinductive_LNil @ B)) => (((lList2170638824_llast @ B) @ (((coinductive_LCons @ B) @ A4) @ R)) = ((lList2170638824_llast @ B) @ R)))))))).
% 0.29/1.70 thf(fact_149_llast__snoc, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A2:(set @ A),X:A]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A2)) => (((lList2170638824_llast @ A) @ (((coinductive_lappend @ A) @ Xs) @ (((coinductive_LCons @ A) @ X) @ (coinductive_LNil @ A)))) = X))))).
% 0.29/1.70 thf(fact_150_predicate1D, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o),X:A]: (((((ord_less_eq @ (A > $o)) @ P) @ Q) => ((P @ X) => (Q @ X)))))).
% 0.29/1.70 thf(fact_151_less__fun__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => ((ord_less @ (A > B)) = (^ [F2:(A > B),G2:(A > B)]: (((((ord_less_eq @ (A > B)) @ F2) @ G2) & (~ ((((ord_less_eq @ (A > B)) @ G2) @ F2))))))))))).
% 0.29/1.70 thf(fact_152_rev__predicate1D, axiom, (! [A:$tType,P:(A > $o),X:A,Q:(A > $o)]: (((P @ X) => ((((ord_less_eq @ (A > $o)) @ P) @ Q) => (Q @ X)))))).
% 0.29/1.70 thf(fact_153_llist__less__induct, axiom, (! [A:$tType,P:((coinductive_llist @ A) > $o),Xs:(coinductive_llist @ A)]: (((! [Xs3:(coinductive_llist @ A)]: (((! [Ys2:(coinductive_llist @ A)]: (((((coindu1478340336prefix @ A) @ Ys2) @ Xs3) => (P @ Ys2)))) => (P @ Xs3)))) => (P @ Xs))))).
% 0.29/1.70 thf(fact_154_finlsts__mono, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => (((ord_less_eq @ (set @ (coinductive_llist @ A))) @ ((lList2236698231inlsts @ A) @ A2)) @ ((lList2236698231inlsts @ A) @ B4)))))).
% 0.29/1.70 thf(fact_155_finlsts_OLCons__fin, axiom, (! [A:$tType,L:(coinductive_llist @ A),A2:(set @ A),A4:A]: (((((member @ (coinductive_llist @ A)) @ L) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ A) @ A4) @ A2) => (((member @ (coinductive_llist @ A)) @ (((coinductive_LCons @ A) @ A4) @ L)) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 0.29/1.70 thf(fact_156_finlsts_OLNil__fin, axiom, (! [A:$tType,A2:(set @ A)]: ((((member @ (coinductive_llist @ A)) @ (coinductive_LNil @ A)) @ ((lList2236698231inlsts @ A) @ A2))))).
% 0.29/1.70 thf(fact_157_lapp__fin__fin__lemma, axiom, (! [A:$tType,R:(coinductive_llist @ A),S2:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ R) @ S2)) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)))))).
% 0.29/1.70 thf(fact_158_lappfin__finT, axiom, (! [A:$tType,S2:(coinductive_llist @ A),A2:(set @ A),T2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S2) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ (coinductive_llist @ A)) @ T2) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ (((coinductive_lappend @ A) @ S2) @ T2)) @ ((lList2236698231inlsts @ A) @ A2))))))).
% 0.29/1.70 thf(fact_159_finlsts_Ocases, axiom, (! [A:$tType,A4:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A4) @ ((lList2236698231inlsts @ A) @ A2)) => ((A4 != (coinductive_LNil @ A)) => (~ ((! [L2:(coinductive_llist @ A),A3:A]: (((A4 = (((coinductive_LCons @ A) @ A3) @ L2)) => ((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => (~ ((((member @ A) @ A3) @ A2)))))))))))))).
% 0.29/1.70 thf(fact_160_finlsts_Osimps, axiom, (! [A:$tType,A4:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ A4) @ ((lList2236698231inlsts @ A) @ A2)) = ((A4 = (coinductive_LNil @ A)) | (? [L3:(coinductive_llist @ A),A6:A]: (((A4 = (((coinductive_LCons @ A) @ A6) @ L3)) & ((((member @ (coinductive_llist @ A)) @ L3) @ ((lList2236698231inlsts @ A) @ A2)) & (((member @ A) @ A6) @ A2)))))))))).
% 0.29/1.70 thf(fact_161_finlsts__induct, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => ((! [L2:(coinductive_llist @ A)]: (((L2 = (coinductive_LNil @ A)) => (P @ L2)))) => ((! [A3:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ L2) => ((((member @ A) @ A3) @ A2) => (P @ (((coinductive_LCons @ A) @ A3) @ L2))))))) => (P @ X))))))).
% 0.29/1.70 thf(fact_162_finlsts_Oinducts, axiom, (! [A:$tType,X:(coinductive_llist @ A),A2:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ (coinductive_LNil @ A)) => ((! [L2:(coinductive_llist @ A),A3:A]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ L2) => ((((member @ A) @ A3) @ A2) => (P @ (((coinductive_LCons @ A) @ A3) @ L2))))))) => (P @ X))))))).
% 0.29/1.70 thf(fact_163_fpslsts__cases, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList22096119349pslsts @ A) @ A2)) => (~ ((! [A3:A,Rs:(coinductive_llist @ A)]: (((R = (((coinductive_LCons @ A) @ A3) @ Rs)) => ((((member @ A) @ A3) @ A2) => (~ ((((member @ (coinductive_llist @ A)) @ Rs) @ ((lList2236698231inlsts @ A) @ A2)))))))))))))).
% 0.29/1.70 thf(fact_164_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coindu328551480prefix @ A) @ (coinductive_LNil @ A)) @ Xs)))).
% 0.29/1.70 thf(fact_165_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((coindu328551480prefix @ A) @ Xs) @ (coinductive_LNil @ A)) = (Xs = (coinductive_LNil @ A)))))).
% 0.29/1.70 thf(fact_166_lrev__induct, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A2:(set @ A),P:((coinductive_llist @ A) > $o)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ (coinductive_LNil @ A)) => ((! [X3:A,Xs3:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs3) @ ((lList2236698231inlsts @ A) @ A2)) => ((P @ Xs3) => ((((member @ A) @ X3) @ A2) => (P @ (((coinductive_lappend @ A) @ Xs3) @ (((coinductive_LCons @ A) @ X3) @ (coinductive_LNil @ A))))))))) => (P @ Xs))))))).
% 0.29/1.70 thf(fact_167_finlsts__rev__cases, axiom, (! [A:$tType,T2:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ T2) @ ((lList2236698231inlsts @ A) @ A2)) => ((T2 != (coinductive_LNil @ A)) => (~ ((! [A3:A,L2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ L2) @ ((lList2236698231inlsts @ A) @ A2)) => ((((member @ A) @ A3) @ A2) => (T2 != (((coinductive_lappend @ A) @ L2) @ (((coinductive_LCons @ A) @ A3) @ (coinductive_LNil @ A))))))))))))))).
% 0.29/1.70 thf(fact_168_ex__gt__or__lt, axiom, (! [A:$tType]: ((((condit1656338222tinuum @ A) @ (type2 @ A)) => (! [A4:A]: ((? [B5:A]: (((((ord_less @ A) @ A4) @ B5) | (((ord_less @ A) @ B5) @ A4)))))))))).
% 0.29/1.70 thf(fact_169_pinf_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z4:A]: ((! [X3:A]: (((((ord_less @ A) @ Z4) @ X3) => ((P @ X3) = (P2 @ X3))))))) => ((? [Z4:A]: ((! [X3:A]: (((((ord_less @ A) @ Z4) @ X3) => ((Q @ X3) = (Q2 @ X3))))))) => (? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ Z) @ X5) => (((P @ X5) & (Q @ X5)) = ((P2 @ X5) & (Q2 @ X5)))))))))))))))).
% 0.29/1.70 thf(fact_170_pinf_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z4:A]: ((! [X3:A]: (((((ord_less @ A) @ Z4) @ X3) => ((P @ X3) = (P2 @ X3))))))) => ((? [Z4:A]: ((! [X3:A]: (((((ord_less @ A) @ Z4) @ X3) => ((Q @ X3) = (Q2 @ X3))))))) => (? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ Z) @ X5) => (((P @ X5) | (Q @ X5)) = ((P2 @ X5) | (Q2 @ X5)))))))))))))))).
% 0.29/1.70 thf(fact_171_pinf_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ Z) @ X5) => (X5 != T2)))))))))))).
% 0.29/1.70 thf(fact_172_pinf_I4_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ Z) @ X5) => (X5 != T2)))))))))))).
% 0.29/1.70 thf(fact_173_pinf_I5_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ Z) @ X5) => (~ ((((ord_less @ A) @ X5) @ T2)))))))))))))).
% 0.29/1.70 thf(fact_174_pinf_I7_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ Z) @ X5) => (((ord_less @ A) @ T2) @ X5)))))))))))).
% 0.29/1.70 thf(fact_175_pinf_I11_J, axiom, (! [C2:$tType,D3:$tType]: ((((ord @ C2) @ (type2 @ C2)) => (! [F3:D3]: ((? [Z:C2]: ((! [X5:C2]: (((((ord_less @ C2) @ Z) @ X5) => (F3 = F3)))))))))))).
% 0.29/1.70 thf(fact_176_minf_I1_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z4:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z4) => ((P @ X3) = (P2 @ X3))))))) => ((? [Z4:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z4) => ((Q @ X3) = (Q2 @ X3))))))) => (? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ X5) @ Z) => (((P @ X5) & (Q @ X5)) = ((P2 @ X5) & (Q2 @ X5)))))))))))))))).
% 0.29/1.70 thf(fact_177_minf_I2_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > $o),P2:(A > $o),Q:(A > $o),Q2:(A > $o)]: (((? [Z4:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z4) => ((P @ X3) = (P2 @ X3))))))) => ((? [Z4:A]: ((! [X3:A]: (((((ord_less @ A) @ X3) @ Z4) => ((Q @ X3) = (Q2 @ X3))))))) => (? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ X5) @ Z) => (((P @ X5) | (Q @ X5)) = ((P2 @ X5) | (Q2 @ X5)))))))))))))))).
% 0.29/1.70 thf(fact_178_minf_I3_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ X5) @ Z) => (X5 != T2)))))))))))).
% 0.29/1.70 thf(fact_179_minf_I4_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ X5) @ Z) => (X5 != T2)))))))))))).
% 0.29/1.70 thf(fact_180_minf_I5_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ X5) @ Z) => (((ord_less @ A) @ X5) @ T2)))))))))))).
% 0.29/1.70 thf(fact_181_minf_I7_J, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [T2:A]: ((? [Z:A]: ((! [X5:A]: (((((ord_less @ A) @ X5) @ Z) => (~ ((((ord_less @ A) @ T2) @ X5)))))))))))))).
% 0.29/1.70 thf(fact_182_minf_I11_J, axiom, (! [C2:$tType,D3:$tType]: ((((ord @ C2) @ (type2 @ C2)) => (! [F3:D3]: ((? [Z:C2]: ((! [X5:C2]: (((((ord_less @ C2) @ X5) @ Z) => (F3 = F3)))))))))))).
% 0.29/1.70 thf(fact_183_lrev__LCons, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),A4:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((lList2281150353e_lrev @ A) @ (((coinductive_LCons @ A) @ A4) @ R)) = (((coinductive_lappend @ A) @ ((lList2281150353e_lrev @ A) @ R)) @ (((coinductive_LCons @ A) @ A4) @ (coinductive_LNil @ A)))))))).
% 0.29/1.70 thf(fact_184_subsetI, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A2) => (((member @ A) @ X3) @ B4)))) => (((ord_less_eq @ (set @ A)) @ A2) @ B4))))).
% 0.29/1.70 thf(fact_185_psubsetI, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => ((A2 != B4) => (((ord_less @ (set @ A)) @ A2) @ B4)))))).
% 0.29/1.70 thf(fact_186_subset__antisym, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ A2) => (A2 = B4)))))).
% 0.29/1.70 thf(fact_187_lrev__LNil, axiom, (! [A:$tType]: ((((lList2281150353e_lrev @ A) @ (coinductive_LNil @ A)) = (coinductive_LNil @ A))))).
% 0.29/1.70 thf(fact_188_lrevT, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ ((lList2281150353e_lrev @ A) @ Xs)) @ ((lList2236698231inlsts @ A) @ A2)))))).
% 0.29/1.70 thf(fact_189_psubsetD, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A),C:A]: (((((ord_less @ (set @ A)) @ A2) @ B4) => ((((member @ A) @ C) @ A2) => (((member @ A) @ C) @ B4)))))).
% 0.29/1.70 thf(fact_190_psubset__trans, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A),C4:(set @ A)]: (((((ord_less @ (set @ A)) @ A2) @ B4) => ((((ord_less @ (set @ A)) @ B4) @ C4) => (((ord_less @ (set @ A)) @ A2) @ C4)))))).
% 0.29/1.70 thf(fact_191_subset__iff__psubset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B6:(set @ A)]: (((((ord_less @ (set @ A)) @ A5) @ B6) | (A5 = B6)))))))).
% 0.29/1.70 thf(fact_192_subset__psubset__trans, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => ((((ord_less @ (set @ A)) @ B4) @ C4) => (((ord_less @ (set @ A)) @ A2) @ C4)))))).
% 0.29/1.70 thf(fact_193_subset__not__subset__eq, axiom, (! [A:$tType]: (((ord_less @ (set @ A)) = (^ [A5:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B6) & (~ ((((ord_less_eq @ (set @ A)) @ B6) @ A5)))))))))).
% 0.29/1.70 thf(fact_194_psubset__subset__trans, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A),C4:(set @ A)]: (((((ord_less @ (set @ A)) @ A2) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ C4) => (((ord_less @ (set @ A)) @ A2) @ C4)))))).
% 0.29/1.70 thf(fact_195_psubset__imp__subset, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((((ord_less @ (set @ A)) @ A2) @ B4) => (((ord_less_eq @ (set @ A)) @ A2) @ B4))))).
% 0.29/1.70 thf(fact_196_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X2:A]: (((P @ X2) => (Q @ X2)))))))).
% 0.29/1.70 thf(fact_197_contra__subsetD, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A),C:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => ((~ ((((member @ A) @ C) @ B4))) => (~ ((((member @ A) @ C) @ A2)))))))).
% 0.29/1.70 thf(fact_198_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y5:(set @ A),Z3:(set @ A)]: ((Y5 = Z3))) = (^ [A5:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B6) & (((ord_less_eq @ (set @ A)) @ B6) @ A5)))))))).
% 0.29/1.70 thf(fact_199_subset__trans, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => ((((ord_less_eq @ (set @ A)) @ B4) @ C4) => (((ord_less_eq @ (set @ A)) @ A2) @ C4)))))).
% 0.29/1.70 thf(fact_200_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) => (Q @ X3)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 0.29/1.70 thf(fact_201_subset__refl, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ A2)))).
% 0.29/1.70 thf(fact_202_rev__subsetD, axiom, (! [A:$tType,C:A,A2:(set @ A),B4:(set @ A)]: (((((member @ A) @ C) @ A2) => ((((ord_less_eq @ (set @ A)) @ A2) @ B4) => (((member @ A) @ C) @ B4)))))).
% 0.29/1.70 thf(fact_203_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B6:(set @ A)]: ((! [T:A]: (((((member @ A) @ T) @ A5) => (((member @ A) @ T) @ B6)))))))))).
% 0.29/1.70 thf(fact_204_set__rev__mp, axiom, (! [A:$tType,X:A,A2:(set @ A),B4:(set @ A)]: (((((member @ A) @ X) @ A2) => ((((ord_less_eq @ (set @ A)) @ A2) @ B4) => (((member @ A) @ X) @ B4)))))).
% 0.29/1.70 thf(fact_205_psubset__eq, axiom, (! [A:$tType]: (((ord_less @ (set @ A)) = (^ [A5:(set @ A),B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A5) @ B6) & (A5 != B6)))))))).
% 0.29/1.70 thf(fact_206_equalityD2, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((A2 = B4) => (((ord_less_eq @ (set @ A)) @ B4) @ A2))))).
% 0.29/1.70 thf(fact_207_equalityD1, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((A2 = B4) => (((ord_less_eq @ (set @ A)) @ A2) @ B4))))).
% 0.29/1.70 thf(fact_208_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A5:(set @ A),B6:(set @ A)]: ((! [X2:A]: (((((member @ A) @ X2) @ A5) => (((member @ A) @ X2) @ B6)))))))))).
% 0.29/1.70 thf(fact_209_equalityE, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((A2 = B4) => (~ (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => (~ ((((ord_less_eq @ (set @ A)) @ B4) @ A2)))))))))).
% 0.29/1.70 thf(fact_210_subsetCE, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A),C:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => ((((member @ A) @ C) @ A2) => (((member @ A) @ C) @ B4)))))).
% 0.29/1.70 thf(fact_211_psubsetE, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((((ord_less @ (set @ A)) @ A2) @ B4) => (~ (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => (((ord_less_eq @ (set @ A)) @ B4) @ A2)))))))).
% 0.29/1.70 thf(fact_212_subsetD, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A),C:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => ((((member @ A) @ C) @ A2) => (((member @ A) @ C) @ B4)))))).
% 0.29/1.70 thf(fact_213_in__mono, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => ((((member @ A) @ X) @ A2) => (((member @ A) @ X) @ B4)))))).
% 0.29/1.70 thf(fact_214_set__mp, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => ((((member @ A) @ X) @ A2) => (((member @ A) @ X) @ B4)))))).
% 0.29/1.70 thf(fact_215_LList2__Mirabelle__hamjzmohle_Ollast__lappend, axiom, (! [A:$tType,X:(coinductive_llist @ A),Y:(coinductive_llist @ A),A4:A]: (((((member @ (coinductive_llist @ A)) @ X) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((member @ (coinductive_llist @ A)) @ Y) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => (((lList2170638824_llast @ A) @ (((coinductive_lappend @ A) @ X) @ (((coinductive_LCons @ A) @ A4) @ Y))) = ((lList2170638824_llast @ A) @ (((coinductive_LCons @ A) @ A4) @ Y)))))))).
% 0.29/1.70 thf(fact_216_poslsts__mono, axiom, (! [A:$tType,A2:(set @ A),B4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B4) => (((ord_less_eq @ (set @ (coinductive_llist @ A))) @ ((lList21148268032oslsts @ A) @ A2)) @ ((lList21148268032oslsts @ A) @ B4)))))).
% 0.29/1.70 thf(fact_217_lrev__lappend, axiom, (! [A:$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)))))))).
% 0.29/1.70 thf(fact_218_top__apply, axiom, (! [C2:$tType,D3:$tType]: ((((top @ C2) @ (type2 @ C2)) => ((top_top @ (D3 > C2)) = (^ [X2:D3]: ((top_top @ C2)))))))).
% 0.29/1.70 thf(fact_219_UNIV__I, axiom, (! [A:$tType,X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A)))))).
% 0.29/1.70 thf(fact_220_lrev__lrev__ident, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => (((lList2281150353e_lrev @ A) @ ((lList2281150353e_lrev @ A) @ Xs)) = Xs))))).
% 0.29/1.70 thf(fact_221_lrev__is__lrev__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((member @ (coinductive_llist @ A)) @ Ys) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((lList2281150353e_lrev @ A) @ Xs) = ((lList2281150353e_lrev @ A) @ Ys)) = (Xs = Ys))))))).
% 0.29/1.70 thf(fact_222_poslsts__UNIV, axiom, (! [A:$tType,S2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ S2) @ ((lList21148268032oslsts @ A) @ (top_top @ (set @ A)))) = (S2 != (coinductive_LNil @ A)))))).
% 0.29/1.70 thf(fact_223_lrev__is__LNil__conv, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ Xs) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) => ((((lList2281150353e_lrev @ A) @ Xs) = (coinductive_LNil @ A)) = (Xs = (coinductive_LNil @ A))))))).
% 0.29/1.70 thf(fact_224_LNil__is__lrev__conv, axiom, (! [A:$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))))))).
% 0.29/1.70 thf(fact_225_subset__UNIV, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ (top_top @ (set @ A)))))).
% 0.29/1.70 thf(fact_226_top_Onot__eq__extremum, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A4:A]: (((A4 != (top_top @ A)) = (((ord_less @ A) @ A4) @ (top_top @ A))))))))).
% 0.29/1.70 thf(fact_227_top_Oextremum__strict, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A4:A]: ((~ ((((ord_less @ A) @ (top_top @ A)) @ A4))))))))).
% 0.29/1.70 thf(fact_228_UNIV__eq__I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X3:A]: ((((member @ A) @ X3) @ A2))) => ((top_top @ (set @ A)) = A2))))).
% 0.29/1.70 thf(fact_229_UNIV__witness, axiom, (! [A:$tType]: ((? [X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))))).
% 0.29/1.70 thf(fact_230_top_Oextremum__uniqueI, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A4:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A4) => (A4 = (top_top @ A))))))))).
% 0.29/1.70 thf(fact_231_top_Oextremum__unique, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A4:A]: (((((ord_less_eq @ A) @ (top_top @ A)) @ A4) = (A4 = (top_top @ A))))))))).
% 0.29/1.70 thf(fact_232_top__greatest, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => (! [A4:A]: ((((ord_less_eq @ A) @ A4) @ (top_top @ A)))))))).
% 0.29/1.70 thf(fact_233_finT__simp, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => (((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 0.29/1.70 thf(fact_234_fin__finite, axiom, (! [A:$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)))))))).
% 0.29/1.70 thf(fact_235_iso__tuple__UNIV__I, axiom, (! [A:$tType,X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A)))))).
% 0.29/1.70 thf(fact_236_top_Oordering__top__axioms, axiom, (! [A:$tType]: ((((order_top @ A) @ (type2 @ A)) => ((((ordering_top @ A) @ (ord_less_eq @ A)) @ (ord_less @ A)) @ (top_top @ A)))))).
% 0.29/1.70 thf(fact_237_top__set__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (top_top @ (A > $o))))))).
% 0.29/1.70 thf(fact_238_ordering__top_Oextremum__uniqueI, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),Top:A,A4:A]: ((((((ordering_top @ A) @ Less_eq) @ Less) @ Top) => (((Less_eq @ Top) @ A4) => (A4 = Top)))))).
% 0.29/1.70 thf(fact_239_ordering__top_Onot__eq__extremum, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),Top:A,A4:A]: ((((((ordering_top @ A) @ Less_eq) @ Less) @ Top) => ((A4 != Top) = ((Less @ A4) @ Top)))))).
% 0.29/1.70 thf(fact_240_ordering__top_Oextremum__unique, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),Top:A,A4:A]: ((((((ordering_top @ A) @ Less_eq) @ Less) @ Top) => (((Less_eq @ Top) @ A4) = (A4 = Top)))))).
% 0.29/1.70 thf(fact_241_ordering__top_Oextremum__strict, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),Top:A,A4:A]: ((((((ordering_top @ A) @ Less_eq) @ Less) @ Top) => (~ (((Less @ Top) @ A4))))))).
% 0.29/1.70 thf(fact_242_ordering__top_Oextremum, axiom, (! [A:$tType,Less_eq:(A > (A > $o)),Less:(A > (A > $o)),Top:A,A4:A]: ((((((ordering_top @ A) @ Less_eq) @ Less) @ Top) => ((Less_eq @ A4) @ Top))))).
% 0.29/1.70 thf(fact_243_ltake__fin, axiom, (! [A:$tType,R:(coinductive_llist @ A),I:nat]: ((((member @ (coinductive_llist @ A)) @ (((lList22119844313_ltake @ A) @ R) @ I)) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A))))))).
% 0.29/1.70 thf(fact_244_finlsts__rec__LCons__def, axiom, (! [B:$tType,A:$tType,F:((coinductive_llist @ A) > B),C:B,D4:(A > ((coinductive_llist @ A) > (B > B))),R:(coinductive_llist @ A),A2:(set @ A),A4:A]: (((F = ((((lList21916056377ts_rec @ B) @ A) @ C) @ D4)) => ((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((F @ (((coinductive_LCons @ A) @ A4) @ R)) = (((D4 @ A4) @ R) @ (F @ R)))))))).
% 0.29/1.70 thf(fact_245_top1I, axiom, (! [A:$tType,X:A]: (((top_top @ (A > $o)) @ X)))).
% 0.29/1.70 thf(fact_246_LList2__Mirabelle__hamjzmohle_Oltake__LNil, axiom, (! [A:$tType,I:nat]: (((((lList22119844313_ltake @ A) @ (coinductive_LNil @ A)) @ I) = (coinductive_LNil @ A))))).
% 0.29/1.70 thf(fact_247_finlsts__rec__LNil__def, axiom, (! [A:$tType,B:$tType,F:((coinductive_llist @ A) > B),C:B,D4:(A > ((coinductive_llist @ A) > (B > B)))]: (((F = ((((lList21916056377ts_rec @ B) @ A) @ C) @ D4)) => ((F @ (coinductive_LNil @ A)) = C))))).
% 0.29/1.70 thf(fact_248_finlsts__rec__LNil, axiom, (! [B:$tType,A:$tType,C:A,D4:(B > ((coinductive_llist @ B) > (A > A)))]: (((((((lList21916056377ts_rec @ A) @ B) @ C) @ D4) @ (coinductive_LNil @ B)) = C)))).
% 0.29/1.70 thf(fact_249_finlsts__rec__LCons, axiom, (! [B:$tType,A:$tType,R:(coinductive_llist @ A),A2:(set @ A),C:B,D4:(A > ((coinductive_llist @ A) > (B > B))),A4:A]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((((lList21916056377ts_rec @ B) @ A) @ C) @ D4) @ (((coinductive_LCons @ A) @ A4) @ R)) = (((D4 @ A4) @ R) @ (((((lList21916056377ts_rec @ B) @ A) @ C) @ D4) @ R))))))).
% 0.29/1.70 thf(fact_250_ltake__lappend__llength, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),S2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((lList22119844313_ltake @ A) @ (((coinductive_lappend @ A) @ R) @ S2)) @ ((lList21232602520length @ A) @ R)) = R))))).
% 0.29/1.70 thf(fact_251_top__empty__eq, axiom, (! [A:$tType]: (((top_top @ (A > $o)) = (^ [X2:A]: ((((member @ A) @ X2) @ (top_top @ (set @ A))))))))).
% 0.29/1.70 thf(fact_252_llength__drop__take, axiom, (! [A:$tType,T2:(coinductive_llist @ A),I:nat]: ((((((lList2508575361_ldrop @ A) @ T2) @ I) != (coinductive_LNil @ A)) => (((lList21232602520length @ A) @ (((lList22119844313_ltake @ A) @ T2) @ I)) = I))))).
% 0.29/1.70 thf(fact_253_lapp__suff__llength, axiom, (! [A:$tType,R:(coinductive_llist @ A),A2:(set @ A),S2:(coinductive_llist @ A)]: (((((member @ (coinductive_llist @ A)) @ R) @ ((lList2236698231inlsts @ A) @ A2)) => ((((lList2508575361_ldrop @ A) @ (((coinductive_lappend @ A) @ R) @ S2)) @ ((lList21232602520length @ A) @ R)) = S2))))).
% 0.29/1.70 thf(fact_254_LList2__Mirabelle__hamjzmohle_Oldrop__LNil, axiom, (! [A:$tType,I:nat]: (((((lList2508575361_ldrop @ A) @ (coinductive_LNil @ A)) @ I) = (coinductive_LNil @ A))))).
% 0.29/1.70 thf(fact_255_ldrop__fin__iffT, axiom, (! [A:$tType,T2:(coinductive_llist @ A),I:nat]: (((((member @ (coinductive_llist @ A)) @ (((lList2508575361_ldrop @ A) @ T2) @ I)) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))) = (((member @ (coinductive_llist @ A)) @ T2) @ ((lList2236698231inlsts @ A) @ (top_top @ (set @ A)))))))).
% 0.29/1.70 thf(tcon_fun___Orderings_Oorder__top, axiom, (! [A8:$tType,A9:$tType]: ((((order_top @ A9) @ (type2 @ A9)) => ((order_top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.29/1.70 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: ((((preorder @ A9) @ (type2 @ A9)) => ((preorder @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.29/1.70 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: ((((order @ A9) @ (type2 @ A9)) => ((order @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.29/1.70 thf(tcon_fun___Orderings_Otop, axiom, (! [A8:$tType,A9:$tType]: ((((top @ A9) @ (type2 @ A9)) => ((top @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.29/1.70 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: ((((ord @ A9) @ (type2 @ A9)) => ((ord @ (A8 > A9)) @ (type2 @ (A8 > A9))))))).
% 0.29/1.70 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder, axiom, ((condit1037483654norder @ nat) @ (type2 @ nat))).
% 0.29/1.70 thf(tcon_Nat_Onat___Orderings_Owellorder, axiom, ((wellorder @ nat) @ (type2 @ nat))).
% 0.29/1.70 thf(tcon_Nat_Onat___Orderings_Opreorder_1, axiom, ((preorder @ nat) @ (type2 @ nat))).
% 0.29/1.70 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, ((linorder @ nat) @ (type2 @ nat))).
% 0.29/1.70 thf(tcon_Nat_Onat___Orderings_Ono__top, axiom, ((no_top @ nat) @ (type2 @ nat))).
% 0.29/1.70 thf(tcon_Nat_Onat___Orderings_Oorder_2, axiom, ((order @ nat) @ (type2 @ nat))).
% 0.29/1.70 thf(tcon_Nat_Onat___Orderings_Oord_3, axiom, ((ord @ nat) @ (type2 @ nat))).
% 0.29/1.70 thf(tcon_Set_Oset___Orderings_Oorder__top_4, axiom, (! [A8:$tType]: (((order_top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.29/1.70 thf(tcon_Set_Oset___Orderings_Opreorder_5, axiom, (! [A8:$tType]: (((preorder @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.29/1.70 thf(tcon_Set_Oset___Orderings_Oorder_6, axiom, (! [A8:$tType]: (((order @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.29/1.70 thf(tcon_Set_Oset___Orderings_Otop_7, axiom, (! [A8:$tType]: (((top @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.29/1.70 thf(tcon_Set_Oset___Orderings_Oord_8, axiom, (! [A8:$tType]: (((ord @ (set @ A8)) @ (type2 @ (set @ A8)))))).
% 0.29/1.70 thf(tcon_HOL_Obool___Orderings_Oorder__top_9, axiom, ((order_top @ $o) @ (type2 @ $o))).
% 0.29/1.70 thf(tcon_HOL_Obool___Orderings_Opreorder_10, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 0.29/1.70 thf(tcon_HOL_Obool___Orderings_Olinorder_11, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 0.29/1.70 thf(tcon_HOL_Obool___Orderings_Oorder_12, axiom, ((order @ $o) @ (type2 @ $o))).
% 0.29/1.70 thf(tcon_HOL_Obool___Orderings_Otop_13, axiom, ((top @ $o) @ (type2 @ $o))).
% 0.29/1.70 thf(tcon_HOL_Obool___Orderings_Oord_14, axiom, ((ord @ $o) @ (type2 @ $o))).
% 0.29/1.70 thf(conj_0, conjecture, (~ ((((ord_less_eq @ (coinductive_llist @ a)) @ (((coinductive_LCons @ a) @ a2) @ l)) @ (coinductive_LNil @ a))))).
% 0.29/1.70 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.gEkGcnFM62/DTF2DTF9795.p
% 0.29/1.70 ------------------------
% 0.29/1.75 ---- Cleaned THF ---
% 0.29/1.75 thf(ty_t_Coinductive__List_Ollist,type,
% 0.29/1.75 coinductive_llist: $tType > $tType ).
% 0.29/1.75
% 0.29/1.75 thf(ty_t_Set_Oset,type,
% 0.29/1.75 set: $tType > $tType ).
% 0.29/1.75
% 0.29/1.75 thf(ty_t_Nat_Onat,type,
% 0.29/1.75 nat: $tType ).
% 0.29/1.75
% 0.29/1.75 thf(ty_t_itself,type,
% 0.29/1.75 itself: $tType > $tType ).
% 0.29/1.75
% 0.29/1.75 thf(ty_tf_a,type,
% 0.29/1.75 a: $tType ).
% 0.29/1.75
% 0.29/1.75 thf(sy_cl_HOL_Otype,type,
% 0.29/1.75 type:
% 0.29/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_cl_Orderings_Oord,type,
% 0.29/1.75 ord:
% 0.29/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_cl_Orderings_Otop,type,
% 0.29/1.75 top:
% 0.29/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_cl_Orderings_Oorder,type,
% 0.29/1.75 order:
% 0.29/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_cl_Orderings_Ono__bot,type,
% 0.29/1.75 no_bot:
% 0.29/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_cl_Orderings_Ono__top,type,
% 0.29/1.75 no_top:
% 0.29/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_cl_Orderings_Olinorder,type,
% 0.29/1.75 linorder:
% 0.29/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_cl_Orderings_Opreorder,type,
% 0.29/1.75 preorder:
% 0.29/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_cl_Orderings_Oorder__top,type,
% 0.29/1.75 order_top:
% 0.29/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_cl_Orderings_Owellorder,type,
% 0.29/1.75 wellorder:
% 0.29/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_cl_Orderings_Odense__order,type,
% 0.29/1.75 dense_order:
% 0.29/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_cl_Orderings_Odense__linorder,type,
% 0.29/1.75 dense_linorder:
% 0.29/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_cl_Conditionally__Complete__Lattices_Olinear__continuum,type,
% 0.29/1.75 condit1656338222tinuum:
% 0.29/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_cl_Conditionally__Complete__Lattices_Oconditionally__complete__linorder,type,
% 0.29/1.75 condit1037483654norder:
% 0.29/1.75 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_Coinductive__List_Ofinite__lprefix,type,
% 0.29/1.75 coindu328551480prefix:
% 0.29/1.75 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_Coinductive__List_Olappend,type,
% 0.29/1.75 coinductive_lappend:
% 0.29/1.75 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.29/1.75 coinductive_LCons:
% 0.29/1.75 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_Coinductive__List_Ollist_OLNil,type,
% 0.29/1.75 coinductive_LNil:
% 0.29/1.75 !>[A: $tType] : ( coinductive_llist @ A ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_Coinductive__List_Olstrict__prefix,type,
% 0.29/1.75 coindu1478340336prefix:
% 0.29/1.75 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oalllstsp,type,
% 0.29/1.75 lList21511617539llstsp:
% 0.29/1.75 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts,type,
% 0.29/1.75 lList2236698231inlsts:
% 0.29/1.75 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlsts__rec,type,
% 0.29/1.75 lList21916056377ts_rec:
% 0.29/1.75 !>[B: $tType,A: $tType] : ( B > ( A > ( coinductive_llist @ A ) > B > B ) > ( coinductive_llist @ A ) > B ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofinlstsp,type,
% 0.29/1.75 lList2860480441nlstsp:
% 0.29/1.75 !>[A: $tType] : ( ( A > $o ) > ( coinductive_llist @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ofpslsts,type,
% 0.29/1.75 lList22096119349pslsts:
% 0.29/1.75 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olbutlast,type,
% 0.29/1.75 lList2370560421utlast:
% 0.29/1.75 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oldrop,type,
% 0.29/1.75 lList2508575361_ldrop:
% 0.29/1.75 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollast,type,
% 0.29/1.75 lList2170638824_llast:
% 0.29/1.75 !>[A: $tType] : ( ( coinductive_llist @ A ) > A ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Ollength,type,
% 0.29/1.75 lList21232602520length:
% 0.29/1.75 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Olrev,type,
% 0.29/1.75 lList2281150353e_lrev:
% 0.29/1.75 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oltake,type,
% 0.29/1.75 lList22119844313_ltake:
% 0.29/1.75 !>[A: $tType] : ( ( coinductive_llist @ A ) > nat > ( coinductive_llist @ A ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_LList2__Mirabelle__hamjzmohle_Oposlsts,type,
% 0.29/1.75 lList21148268032oslsts:
% 0.29/1.75 !>[A: $tType] : ( ( set @ A ) > ( set @ ( coinductive_llist @ A ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.29/1.75 ord_less:
% 0.29/1.75 !>[A: $tType] : ( A > A > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.29/1.75 ord_less_eq:
% 0.29/1.75 !>[A: $tType] : ( A > A > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_Orderings_Oordering__top,type,
% 0.29/1.75 ordering_top:
% 0.29/1.75 !>[A: $tType] : ( ( A > A > $o ) > ( A > A > $o ) > A > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.29/1.75 top_top:
% 0.29/1.75 !>[A: $tType] : A ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_Pure_Otype,type,
% 0.29/1.75 type2:
% 0.29/1.75 !>[A: $tType] : ( itself @ A ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_Set_OCollect,type,
% 0.29/1.75 collect:
% 0.29/1.75 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_c_member,type,
% 0.29/1.75 member:
% 0.29/1.75 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(sy_v_a,type,
% 0.29/1.75 a2: a ).
% 0.29/1.75
% 0.29/1.75 thf(sy_v_l,type,
% 0.29/1.75 l: coinductive_llist @ a ).
% 0.29/1.75
% 0.29/1.75 thf(fact_0_llistE,axiom,
% 0.29/1.75 ! [A: $tType,Y: coinductive_llist @ A] :
% 0.29/1.75 ( ( Y
% 0.29/1.75 != ( coinductive_LNil @ A ) )
% 0.29/1.75 => ~ ! [X21: A,X22: coinductive_llist @ A] :
% 0.29/1.75 ( Y
% 0.29/1.75 != ( coinductive_LCons @ A @ X21 @ X22 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_1_llist_Oinject,axiom,
% 0.29/1.75 ! [A: $tType,X212: A,X222: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 0.29/1.75 ( ( ( coinductive_LCons @ A @ X212 @ X222 )
% 0.29/1.75 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 0.29/1.75 = ( ( X212 = Y21 )
% 0.29/1.75 & ( X222 = Y22 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_2_order__refl,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( preorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_3_llist_Odistinct_I1_J,axiom,
% 0.29/1.75 ! [A: $tType,X212: A,X222: coinductive_llist @ A] :
% 0.29/1.75 ( ( coinductive_LNil @ A )
% 0.29/1.75 != ( coinductive_LCons @ A @ X212 @ X222 ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_4_neq__LNil__conv,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.29/1.75 ( ( Xs
% 0.29/1.75 != ( coinductive_LNil @ A ) )
% 0.29/1.75 = ( ? [X2: A,Xs2: coinductive_llist @ A] :
% 0.29/1.75 ( Xs
% 0.29/1.75 = ( coinductive_LCons @ A @ X2 @ Xs2 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_5_llist__less__def,axiom,
% 0.29/1.75 ( ( ord_less @ ( coinductive_llist @ a ) )
% 0.29/1.75 = ( ^ [S: coinductive_llist @ a,T: coinductive_llist @ a] :
% 0.29/1.75 ( ( ord_less_eq @ ( coinductive_llist @ a ) @ S @ T )
% 0.29/1.75 & ( S != T ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_6_llist__le__def,axiom,
% 0.29/1.75 ( ( ord_less_eq @ ( coinductive_llist @ a ) )
% 0.29/1.75 = ( ^ [S: coinductive_llist @ a,T: coinductive_llist @ a] :
% 0.29/1.75 ? [D: coinductive_llist @ a] :
% 0.29/1.75 ( T
% 0.29/1.75 = ( coinductive_lappend @ a @ S @ D ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_7_lbutlast__LNil,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( lList2370560421utlast @ A @ ( coinductive_LNil @ A ) )
% 0.29/1.75 = ( coinductive_LNil @ A ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_8_fps__induct,axiom,
% 0.29/1.75 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.29/1.75 => ( ! [A3: A] :
% 0.29/1.75 ( ( member @ A @ A3 @ A2 )
% 0.29/1.75 => ( P @ ( coinductive_LCons @ A @ A3 @ ( coinductive_LNil @ A ) ) ) )
% 0.29/1.75 => ( ! [A3: A,L2: coinductive_llist @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.29/1.75 => ( ( P @ L2 )
% 0.29/1.75 => ( ( member @ A @ A3 @ A2 )
% 0.29/1.75 => ( P @ ( coinductive_LCons @ A @ A3 @ L2 ) ) ) ) )
% 0.29/1.75 => ( P @ L ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_9_alllstsp_Ocases,axiom,
% 0.29/1.75 ! [A: $tType,A2: A > $o,A4: coinductive_llist @ A] :
% 0.29/1.75 ( ( lList21511617539llstsp @ A @ A2 @ A4 )
% 0.29/1.75 => ( ( A4
% 0.29/1.75 != ( coinductive_LNil @ A ) )
% 0.29/1.75 => ~ ! [L2: coinductive_llist @ A,A3: A] :
% 0.29/1.75 ( ( A4
% 0.29/1.75 = ( coinductive_LCons @ A @ A3 @ L2 ) )
% 0.29/1.75 => ( ( lList21511617539llstsp @ A @ A2 @ L2 )
% 0.29/1.75 => ~ ( A2 @ A3 ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_10_alllstsp_Osimps,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( lList21511617539llstsp @ A )
% 0.29/1.75 = ( ^ [A5: A > $o,A6: coinductive_llist @ A] :
% 0.29/1.75 ( ( A6
% 0.29/1.75 = ( coinductive_LNil @ A ) )
% 0.29/1.75 | ? [L3: coinductive_llist @ A,B2: A] :
% 0.29/1.75 ( ( A6
% 0.29/1.75 = ( coinductive_LCons @ A @ B2 @ L3 ) )
% 0.29/1.75 & ( lList21511617539llstsp @ A @ A5 @ L3 )
% 0.29/1.75 & ( A5 @ B2 ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_11_finlstsp_Ocases,axiom,
% 0.29/1.75 ! [A: $tType,A2: A > $o,A4: coinductive_llist @ A] :
% 0.29/1.75 ( ( lList2860480441nlstsp @ A @ A2 @ A4 )
% 0.29/1.75 => ( ( A4
% 0.29/1.75 != ( coinductive_LNil @ A ) )
% 0.29/1.75 => ~ ! [L2: coinductive_llist @ A,A3: A] :
% 0.29/1.75 ( ( A4
% 0.29/1.75 = ( coinductive_LCons @ A @ A3 @ L2 ) )
% 0.29/1.75 => ( ( lList2860480441nlstsp @ A @ A2 @ L2 )
% 0.29/1.75 => ~ ( A2 @ A3 ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_12_finlstsp_Osimps,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( lList2860480441nlstsp @ A )
% 0.29/1.75 = ( ^ [A5: A > $o,A6: coinductive_llist @ A] :
% 0.29/1.75 ( ( A6
% 0.29/1.75 = ( coinductive_LNil @ A ) )
% 0.29/1.75 | ? [L3: coinductive_llist @ A,B2: A] :
% 0.29/1.75 ( ( A6
% 0.29/1.75 = ( coinductive_LCons @ A @ B2 @ L3 ) )
% 0.29/1.75 & ( lList2860480441nlstsp @ A @ A5 @ L3 )
% 0.29/1.75 & ( A5 @ B2 ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_13_lappend__code_I2_J,axiom,
% 0.29/1.75 ! [A: $tType,Xa: A,X: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.29/1.75 ( ( coinductive_lappend @ A @ ( coinductive_LCons @ A @ Xa @ X ) @ Ys )
% 0.29/1.75 = ( coinductive_LCons @ A @ Xa @ ( coinductive_lappend @ A @ X @ Ys ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_14_lappend__eq__LNil__iff,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.29/1.75 ( ( ( coinductive_lappend @ A @ Xs @ Ys )
% 0.29/1.75 = ( coinductive_LNil @ A ) )
% 0.29/1.75 = ( ( Xs
% 0.29/1.75 = ( coinductive_LNil @ A ) )
% 0.29/1.75 & ( Ys
% 0.29/1.75 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_15_LNil__eq__lappend__iff,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.29/1.75 ( ( ( coinductive_LNil @ A )
% 0.29/1.75 = ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.29/1.75 = ( ( Xs
% 0.29/1.75 = ( coinductive_LNil @ A ) )
% 0.29/1.75 & ( Ys
% 0.29/1.75 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_16_lappend__LNil2,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.29/1.75 ( ( coinductive_lappend @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.29/1.75 = Xs ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_17_lappend__code_I1_J,axiom,
% 0.29/1.75 ! [A: $tType,Ys: coinductive_llist @ A] :
% 0.29/1.75 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ Ys )
% 0.29/1.75 = Ys ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_18_lappend__is__LNil__conv,axiom,
% 0.29/1.75 ! [A: $tType,S2: coinductive_llist @ A,T2: coinductive_llist @ A] :
% 0.29/1.75 ( ( ( coinductive_lappend @ A @ S2 @ T2 )
% 0.29/1.75 = ( coinductive_LNil @ A ) )
% 0.29/1.75 = ( ( S2
% 0.29/1.75 = ( coinductive_LNil @ A ) )
% 0.29/1.75 & ( T2
% 0.29/1.75 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_19_LNil__is__lappend__conv,axiom,
% 0.29/1.75 ! [A: $tType,S2: coinductive_llist @ A,T2: coinductive_llist @ A] :
% 0.29/1.75 ( ( ( coinductive_LNil @ A )
% 0.29/1.75 = ( coinductive_lappend @ A @ S2 @ T2 ) )
% 0.29/1.75 = ( ( S2
% 0.29/1.75 = ( coinductive_LNil @ A ) )
% 0.29/1.75 & ( T2
% 0.29/1.75 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_20_ord__eq__less__subst,axiom,
% 0.29/1.75 ! [A: $tType,B: $tType] :
% 0.29/1.75 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.29/1.75 & ( ord @ A @ ( type2 @ A ) ) )
% 0.29/1.75 => ! [A4: A,F: B > A,B3: B,C: B] :
% 0.29/1.75 ( ( A4
% 0.29/1.75 = ( F @ B3 ) )
% 0.29/1.75 => ( ( ord_less @ B @ B3 @ C )
% 0.29/1.75 => ( ! [X3: B,Y2: B] :
% 0.29/1.75 ( ( ord_less @ B @ X3 @ Y2 )
% 0.29/1.75 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.29/1.75 => ( ord_less @ A @ A4 @ ( F @ C ) ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_21_ord__less__eq__subst,axiom,
% 0.29/1.75 ! [A: $tType,B: $tType] :
% 0.29/1.75 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.29/1.75 & ( ord @ A @ ( type2 @ A ) ) )
% 0.29/1.75 => ! [A4: A,B3: A,F: A > B,C: B] :
% 0.29/1.75 ( ( ord_less @ A @ A4 @ B3 )
% 0.29/1.75 => ( ( ( F @ B3 )
% 0.29/1.75 = C )
% 0.29/1.75 => ( ! [X3: A,Y2: A] :
% 0.29/1.75 ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.75 => ( ord_less @ B @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.29/1.75 => ( ord_less @ B @ ( F @ A4 ) @ C ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_22_order__less__subst1,axiom,
% 0.29/1.75 ! [A: $tType,B: $tType] :
% 0.29/1.75 ( ( ( order @ B @ ( type2 @ B ) )
% 0.29/1.75 & ( order @ A @ ( type2 @ A ) ) )
% 0.29/1.75 => ! [A4: A,F: B > A,B3: B,C: B] :
% 0.29/1.75 ( ( ord_less @ A @ A4 @ ( F @ B3 ) )
% 0.29/1.75 => ( ( ord_less @ B @ B3 @ C )
% 0.29/1.75 => ( ! [X3: B,Y2: B] :
% 0.29/1.75 ( ( ord_less @ B @ X3 @ Y2 )
% 0.29/1.75 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.29/1.75 => ( ord_less @ A @ A4 @ ( F @ C ) ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_23_order__less__subst2,axiom,
% 0.29/1.75 ! [A: $tType,C2: $tType] :
% 0.29/1.75 ( ( ( order @ C2 @ ( type2 @ C2 ) )
% 0.29/1.75 & ( order @ A @ ( type2 @ A ) ) )
% 0.29/1.75 => ! [A4: A,B3: A,F: A > C2,C: C2] :
% 0.29/1.75 ( ( ord_less @ A @ A4 @ B3 )
% 0.29/1.75 => ( ( ord_less @ C2 @ ( F @ B3 ) @ C )
% 0.29/1.75 => ( ! [X3: A,Y2: A] :
% 0.29/1.75 ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.75 => ( ord_less @ C2 @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.29/1.75 => ( ord_less @ C2 @ ( F @ A4 ) @ C ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_24_lt__ex,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( no_bot @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A] :
% 0.29/1.75 ? [Y2: A] : ( ord_less @ A @ Y2 @ X ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_25_gt__ex,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( no_top @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A] :
% 0.29/1.75 ? [X1: A] : ( ord_less @ A @ X @ X1 ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_26_neqE,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( X != Y )
% 0.29/1.75 => ( ~ ( ord_less @ A @ X @ Y )
% 0.29/1.75 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_27_lappend__assoc,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A,Zs: coinductive_llist @ A] :
% 0.29/1.75 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) @ Zs )
% 0.29/1.75 = ( coinductive_lappend @ A @ Xs @ ( coinductive_lappend @ A @ Ys @ Zs ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_28_neq__iff,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( X != Y )
% 0.29/1.75 = ( ( ord_less @ A @ X @ Y )
% 0.29/1.75 | ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_29_order_Oasym,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A,B3: A] :
% 0.29/1.75 ( ( ord_less @ A @ A4 @ B3 )
% 0.29/1.75 => ~ ( ord_less @ A @ B3 @ A4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_30_dense,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( dense_order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( ord_less @ A @ X @ Y )
% 0.29/1.75 => ? [Z: A] :
% 0.29/1.75 ( ( ord_less @ A @ X @ Z )
% 0.29/1.75 & ( ord_less @ A @ Z @ Y ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_31_less__imp__neq,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( ord_less @ A @ X @ Y )
% 0.29/1.75 => ( X != Y ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_32_less__asym,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( preorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( ord_less @ A @ X @ Y )
% 0.29/1.75 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_33_less__asym_H,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( preorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A,B3: A] :
% 0.29/1.75 ( ( ord_less @ A @ A4 @ B3 )
% 0.29/1.75 => ~ ( ord_less @ A @ B3 @ A4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_34_less__trans,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( preorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A,Z2: A] :
% 0.29/1.75 ( ( ord_less @ A @ X @ Y )
% 0.29/1.75 => ( ( ord_less @ A @ Y @ Z2 )
% 0.29/1.75 => ( ord_less @ A @ X @ Z2 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_35_less__linear,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( ord_less @ A @ X @ Y )
% 0.29/1.75 | ( X = Y )
% 0.29/1.75 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_36_less__irrefl,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( preorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A] :
% 0.29/1.75 ~ ( ord_less @ A @ X @ X ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_37_ord__eq__less__trans,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( ord @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A,B3: A,C: A] :
% 0.29/1.75 ( ( A4 = B3 )
% 0.29/1.75 => ( ( ord_less @ A @ B3 @ C )
% 0.29/1.75 => ( ord_less @ A @ A4 @ C ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_38_ord__less__eq__trans,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( ord @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A,B3: A,C: A] :
% 0.29/1.75 ( ( ord_less @ A @ A4 @ B3 )
% 0.29/1.75 => ( ( B3 = C )
% 0.29/1.75 => ( ord_less @ A @ A4 @ C ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_39_dual__order_Oasym,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [B3: A,A4: A] :
% 0.29/1.75 ( ( ord_less @ A @ B3 @ A4 )
% 0.29/1.75 => ~ ( ord_less @ A @ A4 @ B3 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_40_less__imp__not__eq,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( ord_less @ A @ X @ Y )
% 0.29/1.75 => ( X != Y ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_41_less__not__sym,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( preorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( ord_less @ A @ X @ Y )
% 0.29/1.75 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_42_less__induct,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( wellorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [P: A > $o,A4: A] :
% 0.29/1.75 ( ! [X3: A] :
% 0.29/1.75 ( ! [Y3: A] :
% 0.29/1.75 ( ( ord_less @ A @ Y3 @ X3 )
% 0.29/1.75 => ( P @ Y3 ) )
% 0.29/1.75 => ( P @ X3 ) )
% 0.29/1.75 => ( P @ A4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_43_antisym__conv3,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [Y: A,X: A] :
% 0.29/1.75 ( ~ ( ord_less @ A @ Y @ X )
% 0.29/1.75 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.29/1.75 = ( X = Y ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_44_less__imp__not__eq2,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( ord_less @ A @ X @ Y )
% 0.29/1.75 => ( Y != X ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_45_mem__Collect__eq,axiom,
% 0.29/1.75 ! [A: $tType,A4: A,P: A > $o] :
% 0.29/1.75 ( ( member @ A @ A4 @ ( collect @ A @ P ) )
% 0.29/1.75 = ( P @ A4 ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_46_Collect__mem__eq,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A] :
% 0.29/1.75 ( ( collect @ A
% 0.29/1.75 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 0.29/1.75 = A2 ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_47_Collect__cong,axiom,
% 0.29/1.75 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.29/1.75 ( ! [X3: A] :
% 0.29/1.75 ( ( P @ X3 )
% 0.29/1.75 = ( Q @ X3 ) )
% 0.29/1.75 => ( ( collect @ A @ P )
% 0.29/1.75 = ( collect @ A @ Q ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_48_ext,axiom,
% 0.29/1.75 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.29/1.75 ( ! [X3: A] :
% 0.29/1.75 ( ( F @ X3 )
% 0.29/1.75 = ( G @ X3 ) )
% 0.29/1.75 => ( F = G ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_49_less__imp__triv,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( preorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A,P: $o] :
% 0.29/1.75 ( ( ord_less @ A @ X @ Y )
% 0.29/1.75 => ( ( ord_less @ A @ Y @ X )
% 0.29/1.75 => P ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_50_linorder__cases,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ~ ( ord_less @ A @ X @ Y )
% 0.29/1.75 => ( ( X != Y )
% 0.29/1.75 => ( ord_less @ A @ Y @ X ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_51_dual__order_Oirrefl,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A] :
% 0.29/1.75 ~ ( ord_less @ A @ A4 @ A4 ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_52_fpslsts__mono,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList22096119349pslsts @ A @ A2 ) @ ( lList22096119349pslsts @ A @ B4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_53_order_Ostrict__trans,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A,B3: A,C: A] :
% 0.29/1.75 ( ( ord_less @ A @ A4 @ B3 )
% 0.29/1.75 => ( ( ord_less @ A @ B3 @ C )
% 0.29/1.75 => ( ord_less @ A @ A4 @ C ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_54_alllstsp__mono,axiom,
% 0.29/1.75 ! [A: $tType,A2: A > $o,B4: A > $o] :
% 0.29/1.75 ( ( ord_less_eq @ ( A > $o ) @ A2 @ B4 )
% 0.29/1.75 => ( ord_less_eq @ ( ( coinductive_llist @ A ) > $o ) @ ( lList21511617539llstsp @ A @ A2 ) @ ( lList21511617539llstsp @ A @ B4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_55_finlstsp__mono,axiom,
% 0.29/1.75 ! [A: $tType,A2: A > $o,B4: A > $o] :
% 0.29/1.75 ( ( ord_less_eq @ ( A > $o ) @ A2 @ B4 )
% 0.29/1.75 => ( ord_less_eq @ ( ( coinductive_llist @ A ) > $o ) @ ( lList2860480441nlstsp @ A @ A2 ) @ ( lList2860480441nlstsp @ A @ B4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_56_less__imp__not__less,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( preorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( ord_less @ A @ X @ Y )
% 0.29/1.75 => ~ ( ord_less @ A @ Y @ X ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_57_dual__order_Ostrict__trans,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [B3: A,A4: A,C: A] :
% 0.29/1.75 ( ( ord_less @ A @ B3 @ A4 )
% 0.29/1.75 => ( ( ord_less @ A @ C @ B3 )
% 0.29/1.75 => ( ord_less @ A @ C @ A4 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_58_not__less__iff__gr__or__eq,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.29/1.75 = ( ( ord_less @ A @ Y @ X )
% 0.29/1.75 | ( X = Y ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_59_order_Ostrict__implies__not__eq,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A,B3: A] :
% 0.29/1.75 ( ( ord_less @ A @ A4 @ B3 )
% 0.29/1.75 => ( A4 != B3 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_60_dual__order_Ostrict__implies__not__eq,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [B3: A,A4: A] :
% 0.29/1.75 ( ( ord_less @ A @ B3 @ A4 )
% 0.29/1.75 => ( A4 != B3 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_61_order_Onot__eq__order__implies__strict,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A,B3: A] :
% 0.29/1.75 ( ( A4 != B3 )
% 0.29/1.75 => ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.29/1.75 => ( ord_less @ A @ A4 @ B3 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_62_dual__order_Ostrict__implies__order,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [B3: A,A4: A] :
% 0.29/1.75 ( ( ord_less @ A @ B3 @ A4 )
% 0.29/1.75 => ( ord_less_eq @ A @ B3 @ A4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_63_dual__order_Ostrict__iff__order,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ( ( ord_less @ A )
% 0.29/1.75 = ( ^ [B2: A,A6: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ B2 @ A6 )
% 0.29/1.75 & ( A6 != B2 ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_64_dual__order_Oorder__iff__strict,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ( ( ord_less_eq @ A )
% 0.29/1.75 = ( ^ [B2: A,A6: A] :
% 0.29/1.75 ( ( ord_less @ A @ B2 @ A6 )
% 0.29/1.75 | ( A6 = B2 ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_65_order_Ostrict__implies__order,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A,B3: A] :
% 0.29/1.75 ( ( ord_less @ A @ A4 @ B3 )
% 0.29/1.75 => ( ord_less_eq @ A @ A4 @ B3 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_66_dense__le__bounded,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A,Z2: A] :
% 0.29/1.75 ( ( ord_less @ A @ X @ Y )
% 0.29/1.75 => ( ! [W: A] :
% 0.29/1.75 ( ( ord_less @ A @ X @ W )
% 0.29/1.75 => ( ( ord_less @ A @ W @ Y )
% 0.29/1.75 => ( ord_less_eq @ A @ W @ Z2 ) ) )
% 0.29/1.75 => ( ord_less_eq @ A @ Y @ Z2 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_67_dense__ge__bounded,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [Z2: A,X: A,Y: A] :
% 0.29/1.75 ( ( ord_less @ A @ Z2 @ X )
% 0.29/1.75 => ( ! [W: A] :
% 0.29/1.75 ( ( ord_less @ A @ Z2 @ W )
% 0.29/1.75 => ( ( ord_less @ A @ W @ X )
% 0.29/1.75 => ( ord_less_eq @ A @ Y @ W ) ) )
% 0.29/1.75 => ( ord_less_eq @ A @ Y @ Z2 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_68_dual__order_Ostrict__trans2,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [B3: A,A4: A,C: A] :
% 0.29/1.75 ( ( ord_less @ A @ B3 @ A4 )
% 0.29/1.75 => ( ( ord_less_eq @ A @ C @ B3 )
% 0.29/1.75 => ( ord_less @ A @ C @ A4 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_69_dual__order_Ostrict__trans1,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [B3: A,A4: A,C: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ B3 @ A4 )
% 0.29/1.75 => ( ( ord_less @ A @ C @ B3 )
% 0.29/1.75 => ( ord_less @ A @ C @ A4 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_70_order_Ostrict__iff__order,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ( ( ord_less @ A )
% 0.29/1.75 = ( ^ [A6: A,B2: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ A6 @ B2 )
% 0.29/1.75 & ( A6 != B2 ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_71_order_Oorder__iff__strict,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ( ( ord_less_eq @ A )
% 0.29/1.75 = ( ^ [A6: A,B2: A] :
% 0.29/1.75 ( ( ord_less @ A @ A6 @ B2 )
% 0.29/1.75 | ( A6 = B2 ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_72_order_Ostrict__trans2,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A,B3: A,C: A] :
% 0.29/1.75 ( ( ord_less @ A @ A4 @ B3 )
% 0.29/1.75 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.29/1.75 => ( ord_less @ A @ A4 @ C ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_73_order_Ostrict__trans1,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A,B3: A,C: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.29/1.75 => ( ( ord_less @ A @ B3 @ C )
% 0.29/1.75 => ( ord_less @ A @ A4 @ C ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_74_not__le__imp__less,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [Y: A,X: A] :
% 0.29/1.75 ( ~ ( ord_less_eq @ A @ Y @ X )
% 0.29/1.75 => ( ord_less @ A @ X @ Y ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_75_less__le__not__le,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( preorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ( ( ord_less @ A )
% 0.29/1.75 = ( ^ [X2: A,Y4: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.29/1.75 & ~ ( ord_less_eq @ A @ Y4 @ X2 ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_76_le__imp__less__or__eq,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ X @ Y )
% 0.29/1.75 => ( ( ord_less @ A @ X @ Y )
% 0.29/1.75 | ( X = Y ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_77_le__less__linear,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ X @ Y )
% 0.29/1.75 | ( ord_less @ A @ Y @ X ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_78_dense__le,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [Y: A,Z2: A] :
% 0.29/1.75 ( ! [X3: A] :
% 0.29/1.75 ( ( ord_less @ A @ X3 @ Y )
% 0.29/1.75 => ( ord_less_eq @ A @ X3 @ Z2 ) )
% 0.29/1.75 => ( ord_less_eq @ A @ Y @ Z2 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_79_dense__ge,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( dense_linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [Z2: A,Y: A] :
% 0.29/1.75 ( ! [X3: A] :
% 0.29/1.75 ( ( ord_less @ A @ Z2 @ X3 )
% 0.29/1.75 => ( ord_less_eq @ A @ Y @ X3 ) )
% 0.29/1.75 => ( ord_less_eq @ A @ Y @ Z2 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_80_less__le__trans,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( preorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A,Z2: A] :
% 0.29/1.75 ( ( ord_less @ A @ X @ Y )
% 0.29/1.75 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.29/1.75 => ( ord_less @ A @ X @ Z2 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_81_le__less__trans,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( preorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A,Z2: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ X @ Y )
% 0.29/1.75 => ( ( ord_less @ A @ Y @ Z2 )
% 0.29/1.75 => ( ord_less @ A @ X @ Z2 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_82_antisym__conv2,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ X @ Y )
% 0.29/1.75 => ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.29/1.75 = ( X = Y ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_83_antisym__conv1,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ~ ( ord_less @ A @ X @ Y )
% 0.29/1.75 => ( ( ord_less_eq @ A @ X @ Y )
% 0.29/1.75 = ( X = Y ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_84_less__imp__le,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( preorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( ord_less @ A @ X @ Y )
% 0.29/1.75 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_85_le__neq__trans,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A,B3: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.29/1.75 => ( ( A4 != B3 )
% 0.29/1.75 => ( ord_less @ A @ A4 @ B3 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_86_not__less,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( ~ ( ord_less @ A @ X @ Y ) )
% 0.29/1.75 = ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_87_not__le,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( ~ ( ord_less_eq @ A @ X @ Y ) )
% 0.29/1.75 = ( ord_less @ A @ Y @ X ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_88_order__less__le__subst2,axiom,
% 0.29/1.75 ! [A: $tType,C2: $tType] :
% 0.29/1.75 ( ( ( order @ C2 @ ( type2 @ C2 ) )
% 0.29/1.75 & ( order @ A @ ( type2 @ A ) ) )
% 0.29/1.75 => ! [A4: A,B3: A,F: A > C2,C: C2] :
% 0.29/1.75 ( ( ord_less @ A @ A4 @ B3 )
% 0.29/1.75 => ( ( ord_less_eq @ C2 @ ( F @ B3 ) @ C )
% 0.29/1.75 => ( ! [X3: A,Y2: A] :
% 0.29/1.75 ( ( ord_less @ A @ X3 @ Y2 )
% 0.29/1.75 => ( ord_less @ C2 @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.29/1.75 => ( ord_less @ C2 @ ( F @ A4 ) @ C ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_89_order__less__le__subst1,axiom,
% 0.29/1.75 ! [A: $tType,B: $tType] :
% 0.29/1.75 ( ( ( order @ B @ ( type2 @ B ) )
% 0.29/1.75 & ( order @ A @ ( type2 @ A ) ) )
% 0.29/1.75 => ! [A4: A,F: B > A,B3: B,C: B] :
% 0.29/1.75 ( ( ord_less @ A @ A4 @ ( F @ B3 ) )
% 0.29/1.75 => ( ( ord_less_eq @ B @ B3 @ C )
% 0.29/1.75 => ( ! [X3: B,Y2: B] :
% 0.29/1.75 ( ( ord_less_eq @ B @ X3 @ Y2 )
% 0.29/1.75 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.29/1.75 => ( ord_less @ A @ A4 @ ( F @ C ) ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_90_order__le__less__subst2,axiom,
% 0.29/1.75 ! [A: $tType,C2: $tType] :
% 0.29/1.75 ( ( ( order @ C2 @ ( type2 @ C2 ) )
% 0.29/1.75 & ( order @ A @ ( type2 @ A ) ) )
% 0.29/1.75 => ! [A4: A,B3: A,F: A > C2,C: C2] :
% 0.29/1.75 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.29/1.75 => ( ( ord_less @ C2 @ ( F @ B3 ) @ C )
% 0.29/1.75 => ( ! [X3: A,Y2: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.29/1.75 => ( ord_less_eq @ C2 @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.29/1.75 => ( ord_less @ C2 @ ( F @ A4 ) @ C ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_91_order__le__less__subst1,axiom,
% 0.29/1.75 ! [A: $tType,B: $tType] :
% 0.29/1.75 ( ( ( order @ B @ ( type2 @ B ) )
% 0.29/1.75 & ( order @ A @ ( type2 @ A ) ) )
% 0.29/1.75 => ! [A4: A,F: B > A,B3: B,C: B] :
% 0.29/1.75 ( ( ord_less_eq @ A @ A4 @ ( F @ B3 ) )
% 0.29/1.75 => ( ( ord_less @ B @ B3 @ C )
% 0.29/1.75 => ( ! [X3: B,Y2: B] :
% 0.29/1.75 ( ( ord_less @ B @ X3 @ Y2 )
% 0.29/1.75 => ( ord_less @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.29/1.75 => ( ord_less @ A @ A4 @ ( F @ C ) ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_92_less__le,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ( ( ord_less @ A )
% 0.29/1.75 = ( ^ [X2: A,Y4: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.29/1.75 & ( X2 != Y4 ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_93_le__less,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ( ( ord_less_eq @ A )
% 0.29/1.75 = ( ^ [X2: A,Y4: A] :
% 0.29/1.75 ( ( ord_less @ A @ X2 @ Y4 )
% 0.29/1.75 | ( X2 = Y4 ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_94_leI,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ~ ( ord_less @ A @ X @ Y )
% 0.29/1.75 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_95_leD,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [Y: A,X: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ Y @ X )
% 0.29/1.75 => ~ ( ord_less @ A @ X @ Y ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_96_lappend__LNil__LNil,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( coinductive_lappend @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) )
% 0.29/1.75 = ( coinductive_LNil @ A ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_97_lappend__snocL1__conv__LCons2,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.29/1.75 ( ( coinductive_lappend @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ ( coinductive_LNil @ A ) ) ) @ Ys )
% 0.29/1.75 = ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_98_LList2__Mirabelle__hamjzmohle_Ollist__le__def,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( ord_less_eq @ ( coinductive_llist @ A ) )
% 0.29/1.75 = ( ^ [S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.29/1.75 ? [D: coinductive_llist @ A] :
% 0.29/1.75 ( T
% 0.29/1.75 = ( coinductive_lappend @ A @ S @ D ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_99_finlstsp_OLCons__fin,axiom,
% 0.29/1.75 ! [A: $tType,A2: A > $o,L: coinductive_llist @ A,A4: A] :
% 0.29/1.75 ( ( lList2860480441nlstsp @ A @ A2 @ L )
% 0.29/1.75 => ( ( A2 @ A4 )
% 0.29/1.75 => ( lList2860480441nlstsp @ A @ A2 @ ( coinductive_LCons @ A @ A4 @ L ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_100_alllstsp_OLCons__all,axiom,
% 0.29/1.75 ! [A: $tType,A2: A > $o,L: coinductive_llist @ A,A4: A] :
% 0.29/1.75 ( ( lList21511617539llstsp @ A @ A2 @ L )
% 0.29/1.75 => ( ( A2 @ A4 )
% 0.29/1.75 => ( lList21511617539llstsp @ A @ A2 @ ( coinductive_LCons @ A @ A4 @ L ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_101_finlstsp_OLNil__fin,axiom,
% 0.29/1.75 ! [A: $tType,A2: A > $o] : ( lList2860480441nlstsp @ A @ A2 @ ( coinductive_LNil @ A ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_102_alllstsp_OLNil__all,axiom,
% 0.29/1.75 ! [A: $tType,A2: A > $o] : ( lList21511617539llstsp @ A @ A2 @ ( coinductive_LNil @ A ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_103_LList2__Mirabelle__hamjzmohle_Ollist__less__def,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( ord_less @ ( coinductive_llist @ A ) )
% 0.29/1.75 = ( ^ [S: coinductive_llist @ A,T: coinductive_llist @ A] :
% 0.29/1.75 ( ( ord_less_eq @ ( coinductive_llist @ A ) @ S @ T )
% 0.29/1.75 & ( S != T ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_104_dual__order_Oantisym,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [B3: A,A4: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ B3 @ A4 )
% 0.29/1.75 => ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.29/1.75 => ( A4 = B3 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_105_dual__order_Otrans,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [B3: A,A4: A,C: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ B3 @ A4 )
% 0.29/1.75 => ( ( ord_less_eq @ A @ C @ B3 )
% 0.29/1.75 => ( ord_less_eq @ A @ C @ A4 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_106_linorder__wlog,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [P: A > A > $o,A4: A,B3: A] :
% 0.29/1.75 ( ! [A3: A,B5: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ A3 @ B5 )
% 0.29/1.75 => ( P @ A3 @ B5 ) )
% 0.29/1.75 => ( ! [A3: A,B5: A] :
% 0.29/1.75 ( ( P @ B5 @ A3 )
% 0.29/1.75 => ( P @ A3 @ B5 ) )
% 0.29/1.75 => ( P @ A4 @ B3 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_107_dual__order_Orefl,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A] : ( ord_less_eq @ A @ A4 @ A4 ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_108_order__trans,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( preorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A,Z2: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ X @ Y )
% 0.29/1.75 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.29/1.75 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_109_order__class_Oorder_Oantisym,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A,B3: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.29/1.75 => ( ( ord_less_eq @ A @ B3 @ A4 )
% 0.29/1.75 => ( A4 = B3 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_110_ord__le__eq__trans,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( ord @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A,B3: A,C: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.29/1.75 => ( ( B3 = C )
% 0.29/1.75 => ( ord_less_eq @ A @ A4 @ C ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_111_ord__eq__le__trans,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( ord @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A,B3: A,C: A] :
% 0.29/1.75 ( ( A4 = B3 )
% 0.29/1.75 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.29/1.75 => ( ord_less_eq @ A @ A4 @ C ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_112_antisym__conv,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [Y: A,X: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ Y @ X )
% 0.29/1.75 => ( ( ord_less_eq @ A @ X @ Y )
% 0.29/1.75 = ( X = Y ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_113_le__cases3,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A,Z2: A] :
% 0.29/1.75 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.29/1.75 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 0.29/1.75 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.29/1.75 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 0.29/1.75 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 0.29/1.75 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 0.29/1.75 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 0.29/1.75 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.29/1.75 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.29/1.75 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 0.29/1.75 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 0.29/1.75 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_114_order_Otrans,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A,B3: A,C: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.29/1.75 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.29/1.75 => ( ord_less_eq @ A @ A4 @ C ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_115_le__cases,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.29/1.75 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_116_wlog__linorder__le,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [P: A > A > $o,B3: A,A4: A] :
% 0.29/1.75 ( ! [A3: A,B5: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ A3 @ B5 )
% 0.29/1.75 => ( P @ A3 @ B5 ) )
% 0.29/1.75 => ( ( ( P @ B3 @ A4 )
% 0.29/1.75 => ( P @ A4 @ B3 ) )
% 0.29/1.75 => ( P @ A4 @ B3 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_117_eq__refl,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( preorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( X = Y )
% 0.29/1.75 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_118_linear,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ X @ Y )
% 0.29/1.75 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_119_antisym,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [X: A,Y: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ X @ Y )
% 0.29/1.75 => ( ( ord_less_eq @ A @ Y @ X )
% 0.29/1.75 => ( X = Y ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_120_eq__iff,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order @ A @ ( type2 @ A ) )
% 0.29/1.75 => ( ( ^ [Y5: A,Z3: A] : ( Y5 = Z3 ) )
% 0.29/1.75 = ( ^ [X2: A,Y4: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ X2 @ Y4 )
% 0.29/1.75 & ( ord_less_eq @ A @ Y4 @ X2 ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_121_ord__le__eq__subst,axiom,
% 0.29/1.75 ! [A: $tType,B: $tType] :
% 0.29/1.75 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.29/1.75 & ( ord @ A @ ( type2 @ A ) ) )
% 0.29/1.75 => ! [A4: A,B3: A,F: A > B,C: B] :
% 0.29/1.75 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.29/1.75 => ( ( ( F @ B3 )
% 0.29/1.75 = C )
% 0.29/1.75 => ( ! [X3: A,Y2: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.29/1.75 => ( ord_less_eq @ B @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.29/1.75 => ( ord_less_eq @ B @ ( F @ A4 ) @ C ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_122_ord__eq__le__subst,axiom,
% 0.29/1.75 ! [A: $tType,B: $tType] :
% 0.29/1.75 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.29/1.75 & ( ord @ A @ ( type2 @ A ) ) )
% 0.29/1.75 => ! [A4: A,F: B > A,B3: B,C: B] :
% 0.29/1.75 ( ( A4
% 0.29/1.75 = ( F @ B3 ) )
% 0.29/1.75 => ( ( ord_less_eq @ B @ B3 @ C )
% 0.29/1.75 => ( ! [X3: B,Y2: B] :
% 0.29/1.75 ( ( ord_less_eq @ B @ X3 @ Y2 )
% 0.29/1.75 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.29/1.75 => ( ord_less_eq @ A @ A4 @ ( F @ C ) ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_123_order__subst2,axiom,
% 0.29/1.75 ! [A: $tType,C2: $tType] :
% 0.29/1.75 ( ( ( order @ C2 @ ( type2 @ C2 ) )
% 0.29/1.75 & ( order @ A @ ( type2 @ A ) ) )
% 0.29/1.75 => ! [A4: A,B3: A,F: A > C2,C: C2] :
% 0.29/1.75 ( ( ord_less_eq @ A @ A4 @ B3 )
% 0.29/1.75 => ( ( ord_less_eq @ C2 @ ( F @ B3 ) @ C )
% 0.29/1.75 => ( ! [X3: A,Y2: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ X3 @ Y2 )
% 0.29/1.75 => ( ord_less_eq @ C2 @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.29/1.75 => ( ord_less_eq @ C2 @ ( F @ A4 ) @ C ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_124_order__subst1,axiom,
% 0.29/1.75 ! [A: $tType,B: $tType] :
% 0.29/1.75 ( ( ( order @ B @ ( type2 @ B ) )
% 0.29/1.75 & ( order @ A @ ( type2 @ A ) ) )
% 0.29/1.75 => ! [A4: A,F: B > A,B3: B,C: B] :
% 0.29/1.75 ( ( ord_less_eq @ A @ A4 @ ( F @ B3 ) )
% 0.29/1.75 => ( ( ord_less_eq @ B @ B3 @ C )
% 0.29/1.75 => ( ! [X3: B,Y2: B] :
% 0.29/1.75 ( ( ord_less_eq @ B @ X3 @ Y2 )
% 0.29/1.75 => ( ord_less_eq @ A @ ( F @ X3 ) @ ( F @ Y2 ) ) )
% 0.29/1.75 => ( ord_less_eq @ A @ A4 @ ( F @ C ) ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_125_le__fun__def,axiom,
% 0.29/1.75 ! [B: $tType,A: $tType] :
% 0.29/1.75 ( ( ord @ B @ ( type2 @ B ) )
% 0.29/1.75 => ( ( ord_less_eq @ ( A > B ) )
% 0.29/1.75 = ( ^ [F2: A > B,G2: A > B] :
% 0.29/1.75 ! [X2: A] : ( ord_less_eq @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_126_le__funI,axiom,
% 0.29/1.75 ! [B: $tType,A: $tType] :
% 0.29/1.75 ( ( ord @ B @ ( type2 @ B ) )
% 0.29/1.75 => ! [F: A > B,G: A > B] :
% 0.29/1.75 ( ! [X3: A] : ( ord_less_eq @ B @ ( F @ X3 ) @ ( G @ X3 ) )
% 0.29/1.75 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_127_le__funE,axiom,
% 0.29/1.75 ! [B: $tType,A: $tType] :
% 0.29/1.75 ( ( ord @ B @ ( type2 @ B ) )
% 0.29/1.75 => ! [F: A > B,G: A > B,X: A] :
% 0.29/1.75 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.29/1.75 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_128_le__funD,axiom,
% 0.29/1.75 ! [B: $tType,A: $tType] :
% 0.29/1.75 ( ( ord @ B @ ( type2 @ B ) )
% 0.29/1.75 => ! [F: A > B,G: A > B,X: A] :
% 0.29/1.75 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.29/1.75 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_129_alllstsp_Ocoinduct,axiom,
% 0.29/1.75 ! [A: $tType,X4: ( coinductive_llist @ A ) > $o,X: coinductive_llist @ A,A2: A > $o] :
% 0.29/1.75 ( ( X4 @ X )
% 0.29/1.75 => ( ! [X3: coinductive_llist @ A] :
% 0.29/1.75 ( ( X4 @ X3 )
% 0.29/1.75 => ( ( X3
% 0.29/1.75 = ( coinductive_LNil @ A ) )
% 0.29/1.75 | ? [L4: coinductive_llist @ A,A7: A] :
% 0.29/1.75 ( ( X3
% 0.29/1.75 = ( coinductive_LCons @ A @ A7 @ L4 ) )
% 0.29/1.75 & ( ( X4 @ L4 )
% 0.29/1.75 | ( lList21511617539llstsp @ A @ A2 @ L4 ) )
% 0.29/1.75 & ( A2 @ A7 ) ) ) )
% 0.29/1.75 => ( lList21511617539llstsp @ A @ A2 @ X ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_130_finlstsp_Oinducts,axiom,
% 0.29/1.75 ! [A: $tType,A2: A > $o,X: coinductive_llist @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.29/1.75 ( ( lList2860480441nlstsp @ A @ A2 @ X )
% 0.29/1.75 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.29/1.75 => ( ! [L2: coinductive_llist @ A,A3: A] :
% 0.29/1.75 ( ( lList2860480441nlstsp @ A @ A2 @ L2 )
% 0.29/1.75 => ( ( P @ L2 )
% 0.29/1.75 => ( ( A2 @ A3 )
% 0.29/1.75 => ( P @ ( coinductive_LCons @ A @ A3 @ L2 ) ) ) ) )
% 0.29/1.75 => ( P @ X ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_131_lbutlast__lapp__llast,axiom,
% 0.29/1.75 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.29/1.75 => ( L
% 0.29/1.75 = ( coinductive_lappend @ A @ ( lList2370560421utlast @ A @ L ) @ ( coinductive_LCons @ A @ ( lList2170638824_llast @ A @ L ) @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_132_complete__interval,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( condit1037483654norder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A,B3: A,P: A > $o] :
% 0.29/1.75 ( ( ord_less @ A @ A4 @ B3 )
% 0.29/1.75 => ( ( P @ A4 )
% 0.29/1.75 => ( ~ ( P @ B3 )
% 0.29/1.75 => ? [C3: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ A4 @ C3 )
% 0.29/1.75 & ( ord_less_eq @ A @ C3 @ B3 )
% 0.29/1.75 & ! [X5: A] :
% 0.29/1.75 ( ( ( ord_less_eq @ A @ A4 @ X5 )
% 0.29/1.75 & ( ord_less @ A @ X5 @ C3 ) )
% 0.29/1.75 => ( P @ X5 ) )
% 0.29/1.75 & ! [D2: A] :
% 0.29/1.75 ( ! [X3: A] :
% 0.29/1.75 ( ( ( ord_less_eq @ A @ A4 @ X3 )
% 0.29/1.75 & ( ord_less @ A @ X3 @ D2 ) )
% 0.29/1.75 => ( P @ X3 ) )
% 0.29/1.75 => ( ord_less_eq @ A @ D2 @ C3 ) ) ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_133_pinf_I6_J,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [T2: A] :
% 0.29/1.75 ? [Z: A] :
% 0.29/1.75 ! [X5: A] :
% 0.29/1.75 ( ( ord_less @ A @ Z @ X5 )
% 0.29/1.75 => ~ ( ord_less_eq @ A @ X5 @ T2 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_134_pinf_I8_J,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [T2: A] :
% 0.29/1.75 ? [Z: A] :
% 0.29/1.75 ! [X5: A] :
% 0.29/1.75 ( ( ord_less @ A @ Z @ X5 )
% 0.29/1.75 => ( ord_less_eq @ A @ T2 @ X5 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_135_minf_I6_J,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [T2: A] :
% 0.29/1.75 ? [Z: A] :
% 0.29/1.75 ! [X5: A] :
% 0.29/1.75 ( ( ord_less @ A @ X5 @ Z )
% 0.29/1.75 => ( ord_less_eq @ A @ X5 @ T2 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_136_minf_I8_J,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [T2: A] :
% 0.29/1.75 ? [Z: A] :
% 0.29/1.75 ! [X5: A] :
% 0.29/1.75 ( ( ord_less @ A @ X5 @ Z )
% 0.29/1.75 => ~ ( ord_less_eq @ A @ T2 @ X5 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_137_lbutlast__snoc,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,X: A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( lList2370560421utlast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) )
% 0.29/1.75 = Xs ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_138_Coinductive__List_Ofinite__lprefix__nitpick__simps_I3_J,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A,Y: A,Ys: coinductive_llist @ A] :
% 0.29/1.75 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.29/1.75 = ( ( Xs
% 0.29/1.75 = ( coinductive_LNil @ A ) )
% 0.29/1.75 | ? [Xs2: coinductive_llist @ A] :
% 0.29/1.75 ( ( Xs
% 0.29/1.75 = ( coinductive_LCons @ A @ Y @ Xs2 ) )
% 0.29/1.75 & ( coindu328551480prefix @ A @ Xs2 @ Ys ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_139_lstrict__prefix__code_I2_J,axiom,
% 0.29/1.75 ! [B: $tType,Y: B,Ys: coinductive_llist @ B] : ( coindu1478340336prefix @ B @ ( coinductive_LNil @ B ) @ ( coinductive_LCons @ B @ Y @ Ys ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_140_lstrict__prefix__code_I3_J,axiom,
% 0.29/1.75 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 0.29/1.75 ~ ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LNil @ B ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_141_lbutlast__LCons,axiom,
% 0.29/1.75 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( ( R
% 0.29/1.75 = ( coinductive_LNil @ A ) )
% 0.29/1.75 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.29/1.75 = ( coinductive_LNil @ A ) ) )
% 0.29/1.75 & ( ( R
% 0.29/1.75 != ( coinductive_LNil @ A ) )
% 0.29/1.75 => ( ( lList2370560421utlast @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.29/1.75 = ( coinductive_LCons @ A @ A4 @ ( lList2370560421utlast @ A @ R ) ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_142_predicate1I,axiom,
% 0.29/1.75 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.29/1.75 ( ! [X3: A] :
% 0.29/1.75 ( ( P @ X3 )
% 0.29/1.75 => ( Q @ X3 ) )
% 0.29/1.75 => ( ord_less_eq @ ( A > $o ) @ P @ Q ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_143_lapp__fin__fin__iff,axiom,
% 0.29/1.75 ! [A: $tType,R: coinductive_llist @ A,S2: coinductive_llist @ A,A2: set @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S2 ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 = ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 & ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_144_same__lappend__eq,axiom,
% 0.29/1.75 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S2: coinductive_llist @ A,T2: coinductive_llist @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( ( coinductive_lappend @ A @ R @ S2 )
% 0.29/1.75 = ( coinductive_lappend @ A @ R @ T2 ) )
% 0.29/1.75 = ( S2 = T2 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_145_lstrict__prefix__code_I4_J,axiom,
% 0.29/1.75 ! [B: $tType,X: B,Xs: coinductive_llist @ B,Y: B,Ys: coinductive_llist @ B] :
% 0.29/1.75 ( ( coindu1478340336prefix @ B @ ( coinductive_LCons @ B @ X @ Xs ) @ ( coinductive_LCons @ B @ Y @ Ys ) )
% 0.29/1.75 = ( ( X = Y )
% 0.29/1.75 & ( coindu1478340336prefix @ B @ Xs @ Ys ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_146_lstrict__prefix__code_I1_J,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ~ ( coindu1478340336prefix @ A @ ( coinductive_LNil @ A ) @ ( coinductive_LNil @ A ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_147_fpslsts__iff,axiom,
% 0.29/1.75 ! [A: $tType,S2: coinductive_llist @ A,A2: set @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.29/1.75 = ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 & ( S2
% 0.29/1.75 != ( coinductive_LNil @ A ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_148_LList2__Mirabelle__hamjzmohle_Ollast__LCons,axiom,
% 0.29/1.75 ! [B: $tType,R: coinductive_llist @ B,A2: set @ B,A4: B] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ B ) @ R @ ( lList2236698231inlsts @ B @ A2 ) )
% 0.29/1.75 => ( ( ( R
% 0.29/1.75 = ( coinductive_LNil @ B ) )
% 0.29/1.75 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A4 @ R ) )
% 0.29/1.75 = A4 ) )
% 0.29/1.75 & ( ( R
% 0.29/1.75 != ( coinductive_LNil @ B ) )
% 0.29/1.75 => ( ( lList2170638824_llast @ B @ ( coinductive_LCons @ B @ A4 @ R ) )
% 0.29/1.75 = ( lList2170638824_llast @ B @ R ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_149_llast__snoc,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,X: A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( lList2170638824_llast @ A @ ( coinductive_lappend @ A @ Xs @ ( coinductive_LCons @ A @ X @ ( coinductive_LNil @ A ) ) ) )
% 0.29/1.75 = X ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_150_predicate1D,axiom,
% 0.29/1.75 ! [A: $tType,P: A > $o,Q: A > $o,X: A] :
% 0.29/1.75 ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 0.29/1.75 => ( ( P @ X )
% 0.29/1.75 => ( Q @ X ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_151_less__fun__def,axiom,
% 0.29/1.75 ! [B: $tType,A: $tType] :
% 0.29/1.75 ( ( ord @ B @ ( type2 @ B ) )
% 0.29/1.75 => ( ( ord_less @ ( A > B ) )
% 0.29/1.75 = ( ^ [F2: A > B,G2: A > B] :
% 0.29/1.75 ( ( ord_less_eq @ ( A > B ) @ F2 @ G2 )
% 0.29/1.75 & ~ ( ord_less_eq @ ( A > B ) @ G2 @ F2 ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_152_rev__predicate1D,axiom,
% 0.29/1.75 ! [A: $tType,P: A > $o,X: A,Q: A > $o] :
% 0.29/1.75 ( ( P @ X )
% 0.29/1.75 => ( ( ord_less_eq @ ( A > $o ) @ P @ Q )
% 0.29/1.75 => ( Q @ X ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_153_llist__less__induct,axiom,
% 0.29/1.75 ! [A: $tType,P: ( coinductive_llist @ A ) > $o,Xs: coinductive_llist @ A] :
% 0.29/1.75 ( ! [Xs3: coinductive_llist @ A] :
% 0.29/1.75 ( ! [Ys2: coinductive_llist @ A] :
% 0.29/1.75 ( ( coindu1478340336prefix @ A @ Ys2 @ Xs3 )
% 0.29/1.75 => ( P @ Ys2 ) )
% 0.29/1.75 => ( P @ Xs3 ) )
% 0.29/1.75 => ( P @ Xs ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_154_finlsts__mono,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList2236698231inlsts @ A @ A2 ) @ ( lList2236698231inlsts @ A @ B4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_155_finlsts_OLCons__fin,axiom,
% 0.29/1.75 ! [A: $tType,L: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ L @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( member @ A @ A4 @ A2 )
% 0.29/1.75 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_LCons @ A @ A4 @ L ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_156_finlsts_OLNil__fin,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A] : ( member @ ( coinductive_llist @ A ) @ ( coinductive_LNil @ A ) @ ( lList2236698231inlsts @ A @ A2 ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_157_lapp__fin__fin__lemma,axiom,
% 0.29/1.75 ! [A: $tType,R: coinductive_llist @ A,S2: coinductive_llist @ A,A2: set @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ R @ S2 ) @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_158_lappfin__finT,axiom,
% 0.29/1.75 ! [A: $tType,S2: coinductive_llist @ A,A2: set @ A,T2: coinductive_llist @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( member @ ( coinductive_llist @ A ) @ ( coinductive_lappend @ A @ S2 @ T2 ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_159_finlsts_Ocases,axiom,
% 0.29/1.75 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( A4
% 0.29/1.75 != ( coinductive_LNil @ A ) )
% 0.29/1.75 => ~ ! [L2: coinductive_llist @ A,A3: A] :
% 0.29/1.75 ( ( A4
% 0.29/1.75 = ( coinductive_LCons @ A @ A3 @ L2 ) )
% 0.29/1.75 => ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ~ ( member @ A @ A3 @ A2 ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_160_finlsts_Osimps,axiom,
% 0.29/1.75 ! [A: $tType,A4: coinductive_llist @ A,A2: set @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ A4 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 = ( ( A4
% 0.29/1.75 = ( coinductive_LNil @ A ) )
% 0.29/1.75 | ? [L3: coinductive_llist @ A,A6: A] :
% 0.29/1.75 ( ( A4
% 0.29/1.75 = ( coinductive_LCons @ A @ A6 @ L3 ) )
% 0.29/1.75 & ( member @ ( coinductive_llist @ A ) @ L3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 & ( member @ A @ A6 @ A2 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_161_finlsts__induct,axiom,
% 0.29/1.75 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ! [L2: coinductive_llist @ A] :
% 0.29/1.75 ( ( L2
% 0.29/1.75 = ( coinductive_LNil @ A ) )
% 0.29/1.75 => ( P @ L2 ) )
% 0.29/1.75 => ( ! [A3: A,L2: coinductive_llist @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( P @ L2 )
% 0.29/1.75 => ( ( member @ A @ A3 @ A2 )
% 0.29/1.75 => ( P @ ( coinductive_LCons @ A @ A3 @ L2 ) ) ) ) )
% 0.29/1.75 => ( P @ X ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_162_finlsts_Oinducts,axiom,
% 0.29/1.75 ! [A: $tType,X: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.29/1.75 => ( ! [L2: coinductive_llist @ A,A3: A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( P @ L2 )
% 0.29/1.75 => ( ( member @ A @ A3 @ A2 )
% 0.29/1.75 => ( P @ ( coinductive_LCons @ A @ A3 @ L2 ) ) ) ) )
% 0.29/1.75 => ( P @ X ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_163_fpslsts__cases,axiom,
% 0.29/1.75 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList22096119349pslsts @ A @ A2 ) )
% 0.29/1.75 => ~ ! [A3: A,Rs: coinductive_llist @ A] :
% 0.29/1.75 ( ( R
% 0.29/1.75 = ( coinductive_LCons @ A @ A3 @ Rs ) )
% 0.29/1.75 => ( ( member @ A @ A3 @ A2 )
% 0.29/1.75 => ~ ( member @ ( coinductive_llist @ A ) @ Rs @ ( lList2236698231inlsts @ A @ A2 ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_164_Coinductive__List_Ofinite__lprefix__nitpick__simps_I2_J,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A] : ( coindu328551480prefix @ A @ ( coinductive_LNil @ A ) @ Xs ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_165_Coinductive__List_Ofinite__lprefix__nitpick__simps_I1_J,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.29/1.75 ( ( coindu328551480prefix @ A @ Xs @ ( coinductive_LNil @ A ) )
% 0.29/1.75 = ( Xs
% 0.29/1.75 = ( coinductive_LNil @ A ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_166_lrev__induct,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A,P: ( coinductive_llist @ A ) > $o] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( P @ ( coinductive_LNil @ A ) )
% 0.29/1.75 => ( ! [X3: A,Xs3: coinductive_llist @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ Xs3 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( P @ Xs3 )
% 0.29/1.75 => ( ( member @ A @ X3 @ A2 )
% 0.29/1.75 => ( P @ ( coinductive_lappend @ A @ Xs3 @ ( coinductive_LCons @ A @ X3 @ ( coinductive_LNil @ A ) ) ) ) ) ) )
% 0.29/1.75 => ( P @ Xs ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_167_finlsts__rev__cases,axiom,
% 0.29/1.75 ! [A: $tType,T2: coinductive_llist @ A,A2: set @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( T2
% 0.29/1.75 != ( coinductive_LNil @ A ) )
% 0.29/1.75 => ~ ! [A3: A,L2: coinductive_llist @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ L2 @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( member @ A @ A3 @ A2 )
% 0.29/1.75 => ( T2
% 0.29/1.75 != ( coinductive_lappend @ A @ L2 @ ( coinductive_LCons @ A @ A3 @ ( coinductive_LNil @ A ) ) ) ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_168_ex__gt__or__lt,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( condit1656338222tinuum @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A] :
% 0.29/1.75 ? [B5: A] :
% 0.29/1.75 ( ( ord_less @ A @ A4 @ B5 )
% 0.29/1.75 | ( ord_less @ A @ B5 @ A4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_169_pinf_I1_J,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.29/1.75 ( ? [Z4: A] :
% 0.29/1.75 ! [X3: A] :
% 0.29/1.75 ( ( ord_less @ A @ Z4 @ X3 )
% 0.29/1.75 => ( ( P @ X3 )
% 0.29/1.75 = ( P2 @ X3 ) ) )
% 0.29/1.75 => ( ? [Z4: A] :
% 0.29/1.75 ! [X3: A] :
% 0.29/1.75 ( ( ord_less @ A @ Z4 @ X3 )
% 0.29/1.75 => ( ( Q @ X3 )
% 0.29/1.75 = ( Q2 @ X3 ) ) )
% 0.29/1.75 => ? [Z: A] :
% 0.29/1.75 ! [X5: A] :
% 0.29/1.75 ( ( ord_less @ A @ Z @ X5 )
% 0.29/1.75 => ( ( ( P @ X5 )
% 0.29/1.75 & ( Q @ X5 ) )
% 0.29/1.75 = ( ( P2 @ X5 )
% 0.29/1.75 & ( Q2 @ X5 ) ) ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_170_pinf_I2_J,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.29/1.75 ( ? [Z4: A] :
% 0.29/1.75 ! [X3: A] :
% 0.29/1.75 ( ( ord_less @ A @ Z4 @ X3 )
% 0.29/1.75 => ( ( P @ X3 )
% 0.29/1.75 = ( P2 @ X3 ) ) )
% 0.29/1.75 => ( ? [Z4: A] :
% 0.29/1.75 ! [X3: A] :
% 0.29/1.75 ( ( ord_less @ A @ Z4 @ X3 )
% 0.29/1.75 => ( ( Q @ X3 )
% 0.29/1.75 = ( Q2 @ X3 ) ) )
% 0.29/1.75 => ? [Z: A] :
% 0.29/1.75 ! [X5: A] :
% 0.29/1.75 ( ( ord_less @ A @ Z @ X5 )
% 0.29/1.75 => ( ( ( P @ X5 )
% 0.29/1.75 | ( Q @ X5 ) )
% 0.29/1.75 = ( ( P2 @ X5 )
% 0.29/1.75 | ( Q2 @ X5 ) ) ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_171_pinf_I3_J,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [T2: A] :
% 0.29/1.75 ? [Z: A] :
% 0.29/1.75 ! [X5: A] :
% 0.29/1.75 ( ( ord_less @ A @ Z @ X5 )
% 0.29/1.75 => ( X5 != T2 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_172_pinf_I4_J,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [T2: A] :
% 0.29/1.75 ? [Z: A] :
% 0.29/1.75 ! [X5: A] :
% 0.29/1.75 ( ( ord_less @ A @ Z @ X5 )
% 0.29/1.75 => ( X5 != T2 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_173_pinf_I5_J,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [T2: A] :
% 0.29/1.75 ? [Z: A] :
% 0.29/1.75 ! [X5: A] :
% 0.29/1.75 ( ( ord_less @ A @ Z @ X5 )
% 0.29/1.75 => ~ ( ord_less @ A @ X5 @ T2 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_174_pinf_I7_J,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [T2: A] :
% 0.29/1.75 ? [Z: A] :
% 0.29/1.75 ! [X5: A] :
% 0.29/1.75 ( ( ord_less @ A @ Z @ X5 )
% 0.29/1.75 => ( ord_less @ A @ T2 @ X5 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_175_pinf_I11_J,axiom,
% 0.29/1.75 ! [C2: $tType,D3: $tType] :
% 0.29/1.75 ( ( ord @ C2 @ ( type2 @ C2 ) )
% 0.29/1.75 => ! [F3: D3] :
% 0.29/1.75 ? [Z: C2] :
% 0.29/1.75 ! [X5: C2] :
% 0.29/1.75 ( ( ord_less @ C2 @ Z @ X5 )
% 0.29/1.75 => ( F3 = F3 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_176_minf_I1_J,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.29/1.75 ( ? [Z4: A] :
% 0.29/1.75 ! [X3: A] :
% 0.29/1.75 ( ( ord_less @ A @ X3 @ Z4 )
% 0.29/1.75 => ( ( P @ X3 )
% 0.29/1.75 = ( P2 @ X3 ) ) )
% 0.29/1.75 => ( ? [Z4: A] :
% 0.29/1.75 ! [X3: A] :
% 0.29/1.75 ( ( ord_less @ A @ X3 @ Z4 )
% 0.29/1.75 => ( ( Q @ X3 )
% 0.29/1.75 = ( Q2 @ X3 ) ) )
% 0.29/1.75 => ? [Z: A] :
% 0.29/1.75 ! [X5: A] :
% 0.29/1.75 ( ( ord_less @ A @ X5 @ Z )
% 0.29/1.75 => ( ( ( P @ X5 )
% 0.29/1.75 & ( Q @ X5 ) )
% 0.29/1.75 = ( ( P2 @ X5 )
% 0.29/1.75 & ( Q2 @ X5 ) ) ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_177_minf_I2_J,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [P: A > $o,P2: A > $o,Q: A > $o,Q2: A > $o] :
% 0.29/1.75 ( ? [Z4: A] :
% 0.29/1.75 ! [X3: A] :
% 0.29/1.75 ( ( ord_less @ A @ X3 @ Z4 )
% 0.29/1.75 => ( ( P @ X3 )
% 0.29/1.75 = ( P2 @ X3 ) ) )
% 0.29/1.75 => ( ? [Z4: A] :
% 0.29/1.75 ! [X3: A] :
% 0.29/1.75 ( ( ord_less @ A @ X3 @ Z4 )
% 0.29/1.75 => ( ( Q @ X3 )
% 0.29/1.75 = ( Q2 @ X3 ) ) )
% 0.29/1.75 => ? [Z: A] :
% 0.29/1.75 ! [X5: A] :
% 0.29/1.75 ( ( ord_less @ A @ X5 @ Z )
% 0.29/1.75 => ( ( ( P @ X5 )
% 0.29/1.75 | ( Q @ X5 ) )
% 0.29/1.75 = ( ( P2 @ X5 )
% 0.29/1.75 | ( Q2 @ X5 ) ) ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_178_minf_I3_J,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [T2: A] :
% 0.29/1.75 ? [Z: A] :
% 0.29/1.75 ! [X5: A] :
% 0.29/1.75 ( ( ord_less @ A @ X5 @ Z )
% 0.29/1.75 => ( X5 != T2 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_179_minf_I4_J,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [T2: A] :
% 0.29/1.75 ? [Z: A] :
% 0.29/1.75 ! [X5: A] :
% 0.29/1.75 ( ( ord_less @ A @ X5 @ Z )
% 0.29/1.75 => ( X5 != T2 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_180_minf_I5_J,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [T2: A] :
% 0.29/1.75 ? [Z: A] :
% 0.29/1.75 ! [X5: A] :
% 0.29/1.75 ( ( ord_less @ A @ X5 @ Z )
% 0.29/1.75 => ( ord_less @ A @ X5 @ T2 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_181_minf_I7_J,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( linorder @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [T2: A] :
% 0.29/1.75 ? [Z: A] :
% 0.29/1.75 ! [X5: A] :
% 0.29/1.75 ( ( ord_less @ A @ X5 @ Z )
% 0.29/1.75 => ~ ( ord_less @ A @ T2 @ X5 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_182_minf_I11_J,axiom,
% 0.29/1.75 ! [C2: $tType,D3: $tType] :
% 0.29/1.75 ( ( ord @ C2 @ ( type2 @ C2 ) )
% 0.29/1.75 => ! [F3: D3] :
% 0.29/1.75 ? [Z: C2] :
% 0.29/1.75 ! [X5: C2] :
% 0.29/1.75 ( ( ord_less @ C2 @ X5 @ Z )
% 0.29/1.75 => ( F3 = F3 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_183_lrev__LCons,axiom,
% 0.29/1.75 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( lList2281150353e_lrev @ A @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.29/1.75 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ R ) @ ( coinductive_LCons @ A @ A4 @ ( coinductive_LNil @ A ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_184_subsetI,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.29/1.75 ( ! [X3: A] :
% 0.29/1.75 ( ( member @ A @ X3 @ A2 )
% 0.29/1.75 => ( member @ A @ X3 @ B4 ) )
% 0.29/1.75 => ( ord_less_eq @ ( set @ A ) @ A2 @ B4 ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_185_psubsetI,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( ( A2 != B4 )
% 0.29/1.75 => ( ord_less @ ( set @ A ) @ A2 @ B4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_186_subset__antisym,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ A2 )
% 0.29/1.75 => ( A2 = B4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_187_lrev__LNil,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( lList2281150353e_lrev @ A @ ( coinductive_LNil @ A ) )
% 0.29/1.75 = ( coinductive_LNil @ A ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_188_lrevT,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A,A2: set @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( member @ ( coinductive_llist @ A ) @ ( lList2281150353e_lrev @ A @ Xs ) @ ( lList2236698231inlsts @ A @ A2 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_189_psubsetD,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A,C: A] :
% 0.29/1.75 ( ( ord_less @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( ( member @ A @ C @ A2 )
% 0.29/1.75 => ( member @ A @ C @ B4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_190_psubset__trans,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A,C4: set @ A] :
% 0.29/1.75 ( ( ord_less @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( ( ord_less @ ( set @ A ) @ B4 @ C4 )
% 0.29/1.75 => ( ord_less @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_191_subset__iff__psubset__eq,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) )
% 0.29/1.75 = ( ^ [A5: set @ A,B6: set @ A] :
% 0.29/1.75 ( ( ord_less @ ( set @ A ) @ A5 @ B6 )
% 0.29/1.75 | ( A5 = B6 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_192_subset__psubset__trans,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A,C4: set @ A] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( ( ord_less @ ( set @ A ) @ B4 @ C4 )
% 0.29/1.75 => ( ord_less @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_193_subset__not__subset__eq,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( ord_less @ ( set @ A ) )
% 0.29/1.75 = ( ^ [A5: set @ A,B6: set @ A] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B6 )
% 0.29/1.75 & ~ ( ord_less_eq @ ( set @ A ) @ B6 @ A5 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_194_psubset__subset__trans,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A,C4: set @ A] :
% 0.29/1.75 ( ( ord_less @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C4 )
% 0.29/1.75 => ( ord_less @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_195_psubset__imp__subset,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.29/1.75 ( ( ord_less @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( ord_less_eq @ ( set @ A ) @ A2 @ B4 ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_196_Collect__mono__iff,axiom,
% 0.29/1.75 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.29/1.75 = ( ! [X2: A] :
% 0.29/1.75 ( ( P @ X2 )
% 0.29/1.75 => ( Q @ X2 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_197_contra__subsetD,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A,C: A] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( ~ ( member @ A @ C @ B4 )
% 0.29/1.75 => ~ ( member @ A @ C @ A2 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_198_set__eq__subset,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( ^ [Y5: set @ A,Z3: set @ A] : ( Y5 = Z3 ) )
% 0.29/1.75 = ( ^ [A5: set @ A,B6: set @ A] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B6 )
% 0.29/1.75 & ( ord_less_eq @ ( set @ A ) @ B6 @ A5 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_199_subset__trans,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A,C4: set @ A] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( ( ord_less_eq @ ( set @ A ) @ B4 @ C4 )
% 0.29/1.75 => ( ord_less_eq @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_200_Collect__mono,axiom,
% 0.29/1.75 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.29/1.75 ( ! [X3: A] :
% 0.29/1.75 ( ( P @ X3 )
% 0.29/1.75 => ( Q @ X3 ) )
% 0.29/1.75 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_201_subset__refl,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_202_rev__subsetD,axiom,
% 0.29/1.75 ! [A: $tType,C: A,A2: set @ A,B4: set @ A] :
% 0.29/1.75 ( ( member @ A @ C @ A2 )
% 0.29/1.75 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( member @ A @ C @ B4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_203_subset__iff,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) )
% 0.29/1.75 = ( ^ [A5: set @ A,B6: set @ A] :
% 0.29/1.75 ! [T: A] :
% 0.29/1.75 ( ( member @ A @ T @ A5 )
% 0.29/1.75 => ( member @ A @ T @ B6 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_204_set__rev__mp,axiom,
% 0.29/1.75 ! [A: $tType,X: A,A2: set @ A,B4: set @ A] :
% 0.29/1.75 ( ( member @ A @ X @ A2 )
% 0.29/1.75 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( member @ A @ X @ B4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_205_psubset__eq,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( ord_less @ ( set @ A ) )
% 0.29/1.75 = ( ^ [A5: set @ A,B6: set @ A] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) @ A5 @ B6 )
% 0.29/1.75 & ( A5 != B6 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_206_equalityD2,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.29/1.75 ( ( A2 = B4 )
% 0.29/1.75 => ( ord_less_eq @ ( set @ A ) @ B4 @ A2 ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_207_equalityD1,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.29/1.75 ( ( A2 = B4 )
% 0.29/1.75 => ( ord_less_eq @ ( set @ A ) @ A2 @ B4 ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_208_subset__eq,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) )
% 0.29/1.75 = ( ^ [A5: set @ A,B6: set @ A] :
% 0.29/1.75 ! [X2: A] :
% 0.29/1.75 ( ( member @ A @ X2 @ A5 )
% 0.29/1.75 => ( member @ A @ X2 @ B6 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_209_equalityE,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.29/1.75 ( ( A2 = B4 )
% 0.29/1.75 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ~ ( ord_less_eq @ ( set @ A ) @ B4 @ A2 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_210_subsetCE,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A,C: A] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( ( member @ A @ C @ A2 )
% 0.29/1.75 => ( member @ A @ C @ B4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_211_psubsetE,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.29/1.75 ( ( ord_less @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( ord_less_eq @ ( set @ A ) @ B4 @ A2 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_212_subsetD,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A,C: A] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( ( member @ A @ C @ A2 )
% 0.29/1.75 => ( member @ A @ C @ B4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_213_in__mono,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A,X: A] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( ( member @ A @ X @ A2 )
% 0.29/1.75 => ( member @ A @ X @ B4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_214_set__mp,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A,X: A] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( ( member @ A @ X @ A2 )
% 0.29/1.75 => ( member @ A @ X @ B4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_215_LList2__Mirabelle__hamjzmohle_Ollast__lappend,axiom,
% 0.29/1.75 ! [A: $tType,X: coinductive_llist @ A,Y: coinductive_llist @ A,A4: A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ X @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.29/1.75 => ( ( member @ ( coinductive_llist @ A ) @ Y @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.29/1.75 => ( ( lList2170638824_llast @ A @ ( coinductive_lappend @ A @ X @ ( coinductive_LCons @ A @ A4 @ Y ) ) )
% 0.29/1.75 = ( lList2170638824_llast @ A @ ( coinductive_LCons @ A @ A4 @ Y ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_216_poslsts__mono,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A,B4: set @ A] :
% 0.29/1.75 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B4 )
% 0.29/1.75 => ( ord_less_eq @ ( set @ ( coinductive_llist @ A ) ) @ ( lList21148268032oslsts @ A @ A2 ) @ ( lList21148268032oslsts @ A @ B4 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_217_lrev__lappend,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.29/1.75 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.29/1.75 => ( ( lList2281150353e_lrev @ A @ ( coinductive_lappend @ A @ Xs @ Ys ) )
% 0.29/1.75 = ( coinductive_lappend @ A @ ( lList2281150353e_lrev @ A @ Ys ) @ ( lList2281150353e_lrev @ A @ Xs ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_218_top__apply,axiom,
% 0.29/1.75 ! [C2: $tType,D3: $tType] :
% 0.29/1.75 ( ( top @ C2 @ ( type2 @ C2 ) )
% 0.29/1.75 => ( ( top_top @ ( D3 > C2 ) )
% 0.29/1.75 = ( ^ [X2: D3] : ( top_top @ C2 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_219_UNIV__I,axiom,
% 0.29/1.75 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_220_lrev__lrev__ident,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.29/1.75 => ( ( lList2281150353e_lrev @ A @ ( lList2281150353e_lrev @ A @ Xs ) )
% 0.29/1.75 = Xs ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_221_lrev__is__lrev__conv,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.29/1.75 => ( ( member @ ( coinductive_llist @ A ) @ Ys @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.29/1.75 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 0.29/1.75 = ( lList2281150353e_lrev @ A @ Ys ) )
% 0.29/1.75 = ( Xs = Ys ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_222_poslsts__UNIV,axiom,
% 0.29/1.75 ! [A: $tType,S2: coinductive_llist @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ S2 @ ( lList21148268032oslsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.29/1.75 = ( S2
% 0.29/1.75 != ( coinductive_LNil @ A ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_223_lrev__is__LNil__conv,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.29/1.75 => ( ( ( lList2281150353e_lrev @ A @ Xs )
% 0.29/1.75 = ( coinductive_LNil @ A ) )
% 0.29/1.75 = ( Xs
% 0.29/1.75 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_224_LNil__is__lrev__conv,axiom,
% 0.29/1.75 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ Xs @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.29/1.75 => ( ( ( coinductive_LNil @ A )
% 0.29/1.75 = ( lList2281150353e_lrev @ A @ Xs ) )
% 0.29/1.75 = ( Xs
% 0.29/1.75 = ( coinductive_LNil @ A ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_225_subset__UNIV,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_226_top_Onot__eq__extremum,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order_top @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A] :
% 0.29/1.75 ( ( A4
% 0.29/1.75 != ( top_top @ A ) )
% 0.29/1.75 = ( ord_less @ A @ A4 @ ( top_top @ A ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_227_top_Oextremum__strict,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order_top @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A] :
% 0.29/1.75 ~ ( ord_less @ A @ ( top_top @ A ) @ A4 ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_228_UNIV__eq__I,axiom,
% 0.29/1.75 ! [A: $tType,A2: set @ A] :
% 0.29/1.75 ( ! [X3: A] : ( member @ A @ X3 @ A2 )
% 0.29/1.75 => ( ( top_top @ ( set @ A ) )
% 0.29/1.75 = A2 ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_229_UNIV__witness,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_230_top_Oextremum__uniqueI,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order_top @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A4 )
% 0.29/1.75 => ( A4
% 0.29/1.75 = ( top_top @ A ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_231_top_Oextremum__unique,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order_top @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A] :
% 0.29/1.75 ( ( ord_less_eq @ A @ ( top_top @ A ) @ A4 )
% 0.29/1.75 = ( A4
% 0.29/1.75 = ( top_top @ A ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_232_top__greatest,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order_top @ A @ ( type2 @ A ) )
% 0.29/1.75 => ! [A4: A] : ( ord_less_eq @ A @ A4 @ ( top_top @ A ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_233_finT__simp,axiom,
% 0.29/1.75 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_234_fin__finite,axiom,
% 0.29/1.75 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_235_iso__tuple__UNIV__I,axiom,
% 0.29/1.75 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_236_top_Oordering__top__axioms,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( order_top @ A @ ( type2 @ A ) )
% 0.29/1.75 => ( ordering_top @ A @ ( ord_less_eq @ A ) @ ( ord_less @ A ) @ ( top_top @ A ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_237_top__set__def,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( top_top @ ( set @ A ) )
% 0.29/1.75 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_238_ordering__top_Oextremum__uniqueI,axiom,
% 0.29/1.75 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,Top: A,A4: A] :
% 0.29/1.75 ( ( ordering_top @ A @ Less_eq @ Less @ Top )
% 0.29/1.75 => ( ( Less_eq @ Top @ A4 )
% 0.29/1.75 => ( A4 = Top ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_239_ordering__top_Onot__eq__extremum,axiom,
% 0.29/1.75 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,Top: A,A4: A] :
% 0.29/1.75 ( ( ordering_top @ A @ Less_eq @ Less @ Top )
% 0.29/1.75 => ( ( A4 != Top )
% 0.29/1.75 = ( Less @ A4 @ Top ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_240_ordering__top_Oextremum__unique,axiom,
% 0.29/1.75 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,Top: A,A4: A] :
% 0.29/1.75 ( ( ordering_top @ A @ Less_eq @ Less @ Top )
% 0.29/1.75 => ( ( Less_eq @ Top @ A4 )
% 0.29/1.75 = ( A4 = Top ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_241_ordering__top_Oextremum__strict,axiom,
% 0.29/1.75 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,Top: A,A4: A] :
% 0.29/1.75 ( ( ordering_top @ A @ Less_eq @ Less @ Top )
% 0.29/1.75 => ~ ( Less @ Top @ A4 ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_242_ordering__top_Oextremum,axiom,
% 0.29/1.75 ! [A: $tType,Less_eq: A > A > $o,Less: A > A > $o,Top: A,A4: A] :
% 0.29/1.75 ( ( ordering_top @ A @ Less_eq @ Less @ Top )
% 0.29/1.75 => ( Less_eq @ A4 @ Top ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_243_ltake__fin,axiom,
% 0.29/1.75 ! [A: $tType,R: coinductive_llist @ A,I: nat] : ( member @ ( coinductive_llist @ A ) @ ( lList22119844313_ltake @ A @ R @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_244_finlsts__rec__LCons__def,axiom,
% 0.29/1.75 ! [B: $tType,A: $tType,F: ( coinductive_llist @ A ) > B,C: B,D4: A > ( coinductive_llist @ A ) > B > B,R: coinductive_llist @ A,A2: set @ A,A4: A] :
% 0.29/1.75 ( ( F
% 0.29/1.75 = ( lList21916056377ts_rec @ B @ A @ C @ D4 ) )
% 0.29/1.75 => ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( F @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.29/1.75 = ( D4 @ A4 @ R @ ( F @ R ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_245_top1I,axiom,
% 0.29/1.75 ! [A: $tType,X: A] : ( top_top @ ( A > $o ) @ X ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_246_LList2__Mirabelle__hamjzmohle_Oltake__LNil,axiom,
% 0.29/1.75 ! [A: $tType,I: nat] :
% 0.29/1.75 ( ( lList22119844313_ltake @ A @ ( coinductive_LNil @ A ) @ I )
% 0.29/1.75 = ( coinductive_LNil @ A ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_247_finlsts__rec__LNil__def,axiom,
% 0.29/1.75 ! [A: $tType,B: $tType,F: ( coinductive_llist @ A ) > B,C: B,D4: A > ( coinductive_llist @ A ) > B > B] :
% 0.29/1.75 ( ( F
% 0.29/1.75 = ( lList21916056377ts_rec @ B @ A @ C @ D4 ) )
% 0.29/1.75 => ( ( F @ ( coinductive_LNil @ A ) )
% 0.29/1.75 = C ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_248_finlsts__rec__LNil,axiom,
% 0.29/1.75 ! [B: $tType,A: $tType,C: A,D4: B > ( coinductive_llist @ B ) > A > A] :
% 0.29/1.75 ( ( lList21916056377ts_rec @ A @ B @ C @ D4 @ ( coinductive_LNil @ B ) )
% 0.29/1.75 = C ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_249_finlsts__rec__LCons,axiom,
% 0.29/1.75 ! [B: $tType,A: $tType,R: coinductive_llist @ A,A2: set @ A,C: B,D4: A > ( coinductive_llist @ A ) > B > B,A4: A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( lList21916056377ts_rec @ B @ A @ C @ D4 @ ( coinductive_LCons @ A @ A4 @ R ) )
% 0.29/1.75 = ( D4 @ A4 @ R @ ( lList21916056377ts_rec @ B @ A @ C @ D4 @ R ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_250_ltake__lappend__llength,axiom,
% 0.29/1.75 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S2: coinductive_llist @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( lList22119844313_ltake @ A @ ( coinductive_lappend @ A @ R @ S2 ) @ ( lList21232602520length @ A @ R ) )
% 0.29/1.75 = R ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_251_top__empty__eq,axiom,
% 0.29/1.75 ! [A: $tType] :
% 0.29/1.75 ( ( top_top @ ( A > $o ) )
% 0.29/1.75 = ( ^ [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_252_llength__drop__take,axiom,
% 0.29/1.75 ! [A: $tType,T2: coinductive_llist @ A,I: nat] :
% 0.29/1.75 ( ( ( lList2508575361_ldrop @ A @ T2 @ I )
% 0.29/1.75 != ( coinductive_LNil @ A ) )
% 0.29/1.75 => ( ( lList21232602520length @ A @ ( lList22119844313_ltake @ A @ T2 @ I ) )
% 0.29/1.75 = I ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_253_lapp__suff__llength,axiom,
% 0.29/1.75 ! [A: $tType,R: coinductive_llist @ A,A2: set @ A,S2: coinductive_llist @ A] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ R @ ( lList2236698231inlsts @ A @ A2 ) )
% 0.29/1.75 => ( ( lList2508575361_ldrop @ A @ ( coinductive_lappend @ A @ R @ S2 ) @ ( lList21232602520length @ A @ R ) )
% 0.29/1.75 = S2 ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_254_LList2__Mirabelle__hamjzmohle_Oldrop__LNil,axiom,
% 0.29/1.75 ! [A: $tType,I: nat] :
% 0.29/1.75 ( ( lList2508575361_ldrop @ A @ ( coinductive_LNil @ A ) @ I )
% 0.29/1.75 = ( coinductive_LNil @ A ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(fact_255_ldrop__fin__iffT,axiom,
% 0.29/1.75 ! [A: $tType,T2: coinductive_llist @ A,I: nat] :
% 0.29/1.75 ( ( member @ ( coinductive_llist @ A ) @ ( lList2508575361_ldrop @ A @ T2 @ I ) @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) )
% 0.29/1.75 = ( member @ ( coinductive_llist @ A ) @ T2 @ ( lList2236698231inlsts @ A @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_fun___Orderings_Oorder__top,axiom,
% 0.29/1.75 ! [A8: $tType,A9: $tType] :
% 0.29/1.75 ( ( order_top @ A9 @ ( type2 @ A9 ) )
% 0.29/1.75 => ( order_top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.29/1.75 ! [A8: $tType,A9: $tType] :
% 0.29/1.75 ( ( preorder @ A9 @ ( type2 @ A9 ) )
% 0.29/1.75 => ( preorder @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.29/1.75 ! [A8: $tType,A9: $tType] :
% 0.29/1.75 ( ( order @ A9 @ ( type2 @ A9 ) )
% 0.29/1.75 => ( order @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_fun___Orderings_Otop,axiom,
% 0.29/1.75 ! [A8: $tType,A9: $tType] :
% 0.29/1.75 ( ( top @ A9 @ ( type2 @ A9 ) )
% 0.29/1.75 => ( top @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_fun___Orderings_Oord,axiom,
% 0.29/1.75 ! [A8: $tType,A9: $tType] :
% 0.29/1.75 ( ( ord @ A9 @ ( type2 @ A9 ) )
% 0.29/1.75 => ( ord @ ( A8 > A9 ) @ ( type2 @ ( A8 > A9 ) ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder,axiom,
% 0.29/1.75 condit1037483654norder @ nat @ ( type2 @ nat ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_Nat_Onat___Orderings_Owellorder,axiom,
% 0.29/1.75 wellorder @ nat @ ( type2 @ nat ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_Nat_Onat___Orderings_Opreorder_1,axiom,
% 0.29/1.75 preorder @ nat @ ( type2 @ nat ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.29/1.75 linorder @ nat @ ( type2 @ nat ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_Nat_Onat___Orderings_Ono__top,axiom,
% 0.29/1.75 no_top @ nat @ ( type2 @ nat ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_Nat_Onat___Orderings_Oorder_2,axiom,
% 0.29/1.75 order @ nat @ ( type2 @ nat ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_Nat_Onat___Orderings_Oord_3,axiom,
% 0.29/1.75 ord @ nat @ ( type2 @ nat ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_Set_Oset___Orderings_Oorder__top_4,axiom,
% 0.29/1.75 ! [A8: $tType] : ( order_top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_Set_Oset___Orderings_Opreorder_5,axiom,
% 0.29/1.75 ! [A8: $tType] : ( preorder @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_Set_Oset___Orderings_Oorder_6,axiom,
% 0.29/1.75 ! [A8: $tType] : ( order @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_Set_Oset___Orderings_Otop_7,axiom,
% 0.29/1.75 ! [A8: $tType] : ( top @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_Set_Oset___Orderings_Oord_8,axiom,
% 0.29/1.75 ! [A8: $tType] : ( ord @ ( set @ A8 ) @ ( type2 @ ( set @ A8 ) ) ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_HOL_Obool___Orderings_Oorder__top_9,axiom,
% 0.29/1.75 order_top @ $o @ ( type2 @ $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_HOL_Obool___Orderings_Opreorder_10,axiom,
% 0.29/1.75 preorder @ $o @ ( type2 @ $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_HOL_Obool___Orderings_Olinorder_11,axiom,
% 0.29/1.75 linorder @ $o @ ( type2 @ $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_HOL_Obool___Orderings_Oorder_12,axiom,
% 0.29/1.75 order @ $o @ ( type2 @ $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_HOL_Obool___Orderings_Otop_13,axiom,
% 0.29/1.75 top @ $o @ ( type2 @ $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(tcon_HOL_Obool___Orderings_Oord_14,axiom,
% 0.29/1.75 ord @ $o @ ( type2 @ $o ) ).
% 0.29/1.75
% 0.29/1.75 thf(conj_0,conjecture,
% 0.29/1.75 ~ ( ord_less_eq @ ( coinductive_llist @ a ) @ ( coinductive_LCons @ a @ a2 @ l ) @ ( coinductive_LNil @ a ) ) ).
% 0.29/1.75 ------------------------
% 0.29/1.78 % (9895)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/183Mi)
% 0.29/1.78 % (9897)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_9795 for (2999ds/27Mi)
% 0.29/1.78 % (9896)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_9795 for (2999ds/4Mi)
% 0.29/1.78 % (9898)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/2Mi)
% 0.29/1.78 % (9899)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_9795 for (2999ds/2Mi)
% 0.29/1.78 % (9900)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_9795 for (2999ds/275Mi)
% 0.29/1.78 % (9901)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/18Mi)
% 0.29/1.78 % (9898)Instruction limit reached!
% 0.29/1.78 % (9898)------------------------------
% 0.29/1.78 % (9898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.78 % (9898)Termination reason: Unknown
% 0.29/1.78 % (9898)Termination phase: shuffling
% 0.29/1.78 % (9899)Instruction limit reached!
% 0.29/1.78 % (9899)------------------------------
% 0.29/1.78 % (9899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.78
% 0.29/1.78 % (9898)Memory used [KB]: 1279
% 0.29/1.78 % (9898)Time elapsed: 0.003 s
% 0.29/1.78 % (9898)Instructions burned: 3 (million)
% 0.29/1.78 % (9898)------------------------------
% 0.29/1.78 % (9898)------------------------------
% 0.29/1.78 % (9899)Termination reason: Unknown
% 0.29/1.78 % (9899)Termination phase: shuffling
% 0.29/1.78
% 0.29/1.78 % (9899)Memory used [KB]: 1407
% 0.29/1.78 % (9899)Time elapsed: 0.003 s
% 0.29/1.78 % (9899)Instructions burned: 3 (million)
% 0.29/1.78 % (9899)------------------------------
% 0.29/1.78 % (9899)------------------------------
% 0.29/1.79 % (9896)Instruction limit reached!
% 0.29/1.79 % (9896)------------------------------
% 0.29/1.79 % (9896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.79 % (9896)Termination reason: Unknown
% 0.29/1.79 % (9896)Termination phase: shuffling
% 0.29/1.79
% 0.29/1.79 % (9896)Memory used [KB]: 1407
% 0.29/1.79 % (9896)Time elapsed: 0.004 s
% 0.29/1.79 % (9896)Instructions burned: 4 (million)
% 0.29/1.79 % (9896)------------------------------
% 0.29/1.79 % (9896)------------------------------
% 0.29/1.79 % (9901)Instruction limit reached!
% 0.29/1.79 % (9901)------------------------------
% 0.29/1.79 % (9901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.79 % (9901)Termination reason: Unknown
% 0.29/1.79 % (9901)Termination phase: shuffling
% 0.29/1.79
% 0.29/1.79 % (9901)Memory used [KB]: 1663
% 0.29/1.79 % (9901)Time elapsed: 0.011 s
% 0.29/1.79 % (9901)Instructions burned: 18 (million)
% 0.29/1.79 % (9901)------------------------------
% 0.29/1.79 % (9901)------------------------------
% 3.25/1.80 % (9897)Instruction limit reached!
% 3.25/1.80 % (9897)------------------------------
% 3.25/1.80 % (9897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.80 % (9897)Termination reason: Unknown
% 3.25/1.80 % (9897)Termination phase: Property scanning
% 3.25/1.80
% 3.25/1.80 % (9897)Memory used [KB]: 1791
% 3.25/1.80 % (9897)Time elapsed: 0.016 s
% 3.25/1.80 % (9897)Instructions burned: 29 (million)
% 3.25/1.80 % (9897)------------------------------
% 3.25/1.80 % (9897)------------------------------
% 3.25/1.80 % (9902)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/3Mi)
% 3.25/1.80 % (9903)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_9795 for (2999ds/37Mi)
% 3.25/1.80 % (9904)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_9795 for (2999ds/15Mi)
% 3.25/1.80 % (9902)Instruction limit reached!
% 3.25/1.80 % (9902)------------------------------
% 3.25/1.80 % (9902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.80 % (9902)Termination reason: Unknown
% 3.25/1.80 % (9902)Termination phase: shuffling
% 3.25/1.80
% 3.25/1.80 % (9902)Memory used [KB]: 1407
% 3.25/1.80 % (9902)Time elapsed: 0.003 s
% 3.25/1.80 % (9902)Instructions burned: 3 (million)
% 3.25/1.80 % (9902)------------------------------
% 3.25/1.80 % (9902)------------------------------
% 3.25/1.81 % (9900)Refutation not found, incomplete strategy
% 3.25/1.81 % (9900)------------------------------
% 3.25/1.81 % (9900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.81 % (9900)Termination reason: Refutation not found, incomplete strategy
% 3.25/1.81
% 3.25/1.81
% 3.25/1.81 % (9900)Memory used [KB]: 6396
% 3.25/1.81 % (9900)Time elapsed: 0.025 s
% 3.25/1.81 % (9900)Instructions burned: 47 (million)
% 3.25/1.81 % (9900)------------------------------
% 3.25/1.81 % (9900)------------------------------
% 3.25/1.81 % (9904)Instruction limit reached!
% 3.25/1.81 % (9904)------------------------------
% 3.25/1.81 % (9904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.81 % (9904)Termination reason: Unknown
% 3.25/1.81 % (9904)Termination phase: shuffling
% 3.25/1.81
% 3.25/1.81 % (9904)Memory used [KB]: 1663
% 3.25/1.81 % (9904)Time elapsed: 0.009 s
% 3.25/1.81 % (9904)Instructions burned: 15 (million)
% 3.25/1.81 % (9904)------------------------------
% 3.25/1.81 % (9904)------------------------------
% 3.25/1.81 % (9905)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_9795 for (2999ds/3Mi)
% 3.25/1.81 % (9905)Instruction limit reached!
% 3.25/1.81 % (9905)------------------------------
% 3.25/1.81 % (9905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.81 % (9905)Termination reason: Unknown
% 3.25/1.81 % (9905)Termination phase: shuffling
% 3.25/1.81
% 3.25/1.81 % (9905)Memory used [KB]: 1407
% 3.25/1.81 % (9905)Time elapsed: 0.004 s
% 3.25/1.81 % (9905)Instructions burned: 4 (million)
% 3.25/1.81 % (9905)------------------------------
% 3.25/1.81 % (9905)------------------------------
% 3.25/1.81 % (9906)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_9795 for (2999ds/1041Mi)
% 3.25/1.82 % (9907)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/7Mi)
% 3.25/1.82 % (9903)Instruction limit reached!
% 3.25/1.82 % (9903)------------------------------
% 3.25/1.82 % (9903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.82 % (9903)Termination reason: Unknown
% 3.25/1.82 % (9903)Termination phase: shuffling
% 3.25/1.82
% 3.25/1.82 % (9903)Memory used [KB]: 2046
% 3.25/1.82 % (9903)Time elapsed: 0.019 s
% 3.25/1.82 % (9903)Instructions burned: 38 (million)
% 3.25/1.82 % (9903)------------------------------
% 3.25/1.82 % (9903)------------------------------
% 3.25/1.82 % (9907)Instruction limit reached!
% 3.25/1.82 % (9907)------------------------------
% 3.25/1.82 % (9907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.82 % (9907)Termination reason: Unknown
% 3.25/1.82 % (9907)Termination phase: shuffling
% 3.25/1.82
% 3.25/1.82 % (9907)Memory used [KB]: 1407
% 3.25/1.82 % (9907)Time elapsed: 0.005 s
% 3.25/1.82 % (9907)Instructions burned: 7 (million)
% 3.25/1.82 % (9907)------------------------------
% 3.25/1.82 % (9907)------------------------------
% 3.25/1.82 % (9908)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/16Mi)
% 3.25/1.82 % (9909)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_9795 for (2999ds/3Mi)
% 3.25/1.83 % (9909)Instruction limit reached!
% 3.25/1.83 % (9909)------------------------------
% 3.25/1.83 % (9909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.83 % (9909)Termination reason: Unknown
% 3.25/1.83 % (9909)Termination phase: shuffling
% 3.25/1.83
% 3.25/1.83 % (9909)Memory used [KB]: 1279
% 3.25/1.83 % (9909)Time elapsed: 0.003 s
% 3.25/1.83 % (9909)Instructions burned: 3 (million)
% 3.25/1.83 % (9909)------------------------------
% 3.25/1.83 % (9909)------------------------------
% 3.25/1.83 % (9910)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_9795 for (2999ds/3Mi)
% 3.25/1.83 % (9910)Instruction limit reached!
% 3.25/1.83 % (9910)------------------------------
% 3.25/1.83 % (9910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.83 % (9910)Termination reason: Unknown
% 3.25/1.83 % (9910)Termination phase: shuffling
% 3.25/1.83
% 3.25/1.83 % (9910)Memory used [KB]: 1407
% 3.25/1.83 % (9910)Time elapsed: 0.003 s
% 3.25/1.83 % (9910)Instructions burned: 3 (million)
% 3.25/1.83 % (9910)------------------------------
% 3.25/1.83 % (9910)------------------------------
% 3.25/1.83 % (9908)Instruction limit reached!
% 3.25/1.83 % (9908)------------------------------
% 3.25/1.83 % (9908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.83 % (9908)Termination reason: Unknown
% 3.25/1.83 % (9908)Termination phase: shuffling
% 3.25/1.83
% 3.25/1.83 % (9908)Memory used [KB]: 1663
% 3.25/1.83 % (9908)Time elapsed: 0.010 s
% 3.25/1.83 % (9908)Instructions burned: 17 (million)
% 3.25/1.83 % (9908)------------------------------
% 3.25/1.83 % (9908)------------------------------
% 3.25/1.83 % (9911)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/7Mi)
% 3.25/1.84 % (9912)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/3Mi)
% 3.25/1.84 % (9911)Instruction limit reached!
% 3.25/1.84 % (9911)------------------------------
% 3.25/1.84 % (9911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.84 % (9911)Termination reason: Unknown
% 3.25/1.84 % (9911)Termination phase: shuffling
% 3.25/1.84
% 3.25/1.84 % (9911)Memory used [KB]: 1535
% 3.25/1.84 % (9911)Time elapsed: 0.005 s
% 3.25/1.84 % (9911)Instructions burned: 7 (million)
% 3.25/1.84 % (9911)------------------------------
% 3.25/1.84 % (9911)------------------------------
% 3.25/1.84 % (9912)Instruction limit reached!
% 3.25/1.84 % (9912)------------------------------
% 3.25/1.84 % (9912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.84 % (9912)Termination reason: Unknown
% 3.25/1.84 % (9912)Termination phase: shuffling
% 3.25/1.84
% 3.25/1.84 % (9912)Memory used [KB]: 1407
% 3.25/1.84 % (9912)Time elapsed: 0.003 s
% 3.25/1.84 % (9912)Instructions burned: 3 (million)
% 3.25/1.84 % (9912)------------------------------
% 3.25/1.84 % (9912)------------------------------
% 3.25/1.84 % (9913)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/4Mi)
% 3.25/1.84 % (9913)Instruction limit reached!
% 3.25/1.84 % (9913)------------------------------
% 3.25/1.84 % (9913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.84 % (9913)Termination reason: Unknown
% 3.25/1.84 % (9914)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/18Mi)
% 3.25/1.84 % (9913)Termination phase: shuffling
% 3.25/1.84
% 3.25/1.84 % (9913)Memory used [KB]: 1407
% 3.25/1.84 % (9913)Time elapsed: 0.004 s
% 3.25/1.85 % (9913)Instructions burned: 5 (million)
% 3.25/1.85 % (9913)------------------------------
% 3.25/1.85 % (9913)------------------------------
% 3.25/1.85 % (9915)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/710Mi)
% 3.25/1.85 % (9916)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/6Mi)
% 3.25/1.85 % (9914)Instruction limit reached!
% 3.25/1.85 % (9914)------------------------------
% 3.25/1.85 % (9914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.85 % (9914)Termination reason: Unknown
% 3.25/1.85 % (9914)Termination phase: shuffling
% 3.25/1.85
% 3.25/1.85 % (9914)Memory used [KB]: 1663
% 3.25/1.85 % (9914)Time elapsed: 0.011 s
% 3.25/1.85 % (9914)Instructions burned: 19 (million)
% 3.25/1.85 % (9914)------------------------------
% 3.25/1.85 % (9914)------------------------------
% 3.25/1.86 % (9917)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_9795 for (2999ds/902Mi)
% 3.25/1.86 % (9916)Instruction limit reached!
% 3.25/1.86 % (9916)------------------------------
% 3.25/1.86 % (9916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.86 % (9916)Termination reason: Unknown
% 3.25/1.86 % (9916)Termination phase: shuffling
% 3.25/1.86
% 3.25/1.86 % (9916)Memory used [KB]: 1535
% 3.25/1.86 % (9916)Time elapsed: 0.005 s
% 3.25/1.86 % (9916)Instructions burned: 7 (million)
% 3.25/1.86 % (9916)------------------------------
% 3.25/1.86 % (9916)------------------------------
% 3.25/1.86 % (9918)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_9795 for (2999ds/21Mi)
% 3.25/1.87 % (9895)Instruction limit reached!
% 3.25/1.87 % (9895)------------------------------
% 3.25/1.87 % (9895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.87 % (9895)Termination reason: Unknown
% 3.25/1.87 % (9895)Termination phase: Saturation
% 3.25/1.87
% 3.25/1.87 % (9895)Memory used [KB]: 7036
% 3.25/1.87 % (9895)Time elapsed: 0.089 s
% 3.25/1.87 % (9895)Instructions burned: 184 (million)
% 3.25/1.87 % (9895)------------------------------
% 3.25/1.87 % (9895)------------------------------
% 3.25/1.87 % (9919)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/5Mi)
% 3.25/1.87 % (9918)Instruction limit reached!
% 3.25/1.87 % (9918)------------------------------
% 3.25/1.87 % (9918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.87 % (9918)Termination reason: Unknown
% 3.25/1.87 % (9918)Termination phase: shuffling
% 3.25/1.87
% 3.25/1.87 % (9918)Memory used [KB]: 1791
% 3.25/1.87 % (9918)Time elapsed: 0.012 s
% 3.25/1.87 % (9918)Instructions burned: 21 (million)
% 3.25/1.87 % (9918)------------------------------
% 3.25/1.87 % (9918)------------------------------
% 3.25/1.87 % (9919)Instruction limit reached!
% 3.25/1.87 % (9919)------------------------------
% 3.25/1.87 % (9919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.87 % (9919)Termination reason: Unknown
% 3.25/1.87 % (9919)Termination phase: shuffling
% 3.25/1.87
% 3.25/1.87 % (9919)Memory used [KB]: 1407
% 3.25/1.87 % (9919)Time elapsed: 0.004 s
% 3.25/1.87 % (9919)Instructions burned: 5 (million)
% 3.25/1.87 % (9919)------------------------------
% 3.25/1.87 % (9919)------------------------------
% 3.25/1.87 % (9920)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_9795 for (2999ds/6Mi)
% 3.25/1.88 % (9920)Instruction limit reached!
% 3.25/1.88 % (9920)------------------------------
% 3.25/1.88 % (9920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.88 % (9920)Termination reason: Unknown
% 3.25/1.88 % (9920)Termination phase: shuffling
% 3.25/1.88
% 3.25/1.88 % (9920)Memory used [KB]: 1407
% 3.25/1.88 % (9920)Time elapsed: 0.005 s
% 3.25/1.88 % (9920)Instructions burned: 8 (million)
% 3.25/1.88 % (9920)------------------------------
% 3.25/1.88 % (9920)------------------------------
% 3.25/1.89 % (9921)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_9795 for (2998ds/377Mi)
% 3.25/1.89 % (9922)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_9795 for (2998ds/779Mi)
% 3.25/1.89 % (9923)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_9795 for (2998ds/19Mi)
% 3.25/1.89 % (9924)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_9795 for (2998ds/879Mi)
% 3.25/1.90 % (9923)Instruction limit reached!
% 3.25/1.90 % (9923)------------------------------
% 3.25/1.90 % (9923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.90 % (9923)Termination reason: Unknown
% 3.25/1.90 % (9923)Termination phase: shuffling
% 3.25/1.90
% 3.25/1.90 % (9923)Memory used [KB]: 1663
% 3.25/1.90 % (9923)Time elapsed: 0.011 s
% 3.25/1.90 % (9923)Instructions burned: 20 (million)
% 3.25/1.90 % (9923)------------------------------
% 3.25/1.90 % (9923)------------------------------
% 3.25/1.91 % (9925)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_9795 for (2998ds/17Mi)
% 3.25/1.92 % (9925)Instruction limit reached!
% 3.25/1.92 % (9925)------------------------------
% 3.25/1.92 % (9925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.92 % (9925)Termination reason: Unknown
% 3.25/1.92 % (9925)Termination phase: shuffling
% 3.25/1.92
% 3.25/1.92 % (9925)Memory used [KB]: 1663
% 3.25/1.92 % (9925)Time elapsed: 0.010 s
% 3.25/1.92 % (9925)Instructions burned: 17 (million)
% 3.25/1.92 % (9925)------------------------------
% 3.25/1.92 % (9925)------------------------------
% 3.25/1.94 % (9926)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_9795 for (2998ds/3Mi)
% 3.25/1.94 % (9926)Instruction limit reached!
% 3.25/1.94 % (9926)------------------------------
% 3.25/1.94 % (9926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.94 % (9926)Termination reason: Unknown
% 3.25/1.94 % (9926)Termination phase: shuffling
% 3.25/1.94
% 3.25/1.94 % (9926)Memory used [KB]: 1279
% 3.25/1.94 % (9926)Time elapsed: 0.003 s
% 3.25/1.94 % (9926)Instructions burned: 3 (million)
% 3.25/1.94 % (9926)------------------------------
% 3.25/1.94 % (9926)------------------------------
% 3.25/1.96 % (9927)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_9795 for (2998ds/30Mi)
% 3.25/1.97 % (9927)Instruction limit reached!
% 3.25/1.97 % (9927)------------------------------
% 3.25/1.97 % (9927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.25/1.97 % (9927)Termination reason: Unknown
% 3.25/1.97 % (9927)Termination phase: Property scanning
% 3.25/1.97
% 3.25/1.97 % (9927)Memory used [KB]: 1791
% 3.25/1.97 % (9927)Time elapsed: 0.016 s
% 3.25/1.97 % (9927)Instructions burned: 30 (million)
% 3.25/1.97 % (9927)------------------------------
% 3.25/1.97 % (9927)------------------------------
% 3.25/1.99 % (9928)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_9795 for (2997ds/127Mi)
% 4.97/2.05 % (9928)Instruction limit reached!
% 4.97/2.05 % (9928)------------------------------
% 4.97/2.05 % (9928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.97/2.05 % (9928)Termination reason: Unknown
% 4.97/2.05 % (9928)Termination phase: Saturation
% 4.97/2.05
% 4.97/2.05 % (9928)Memory used [KB]: 6908
% 4.97/2.05 % (9928)Time elapsed: 0.062 s
% 4.97/2.05 % (9928)Instructions burned: 128 (million)
% 4.97/2.05 % (9928)------------------------------
% 4.97/2.05 % (9928)------------------------------
% 4.97/2.06 % (9929)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_9795 for (2997ds/100Mi)
% 4.97/2.07 % (9921)Instruction limit reached!
% 4.97/2.07 % (9921)------------------------------
% 4.97/2.07 % (9921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.97/2.07 % (9921)Termination reason: Unknown
% 4.97/2.07 % (9921)Termination phase: Saturation
% 4.97/2.07
% 4.97/2.07 % (9921)Memory used [KB]: 7675
% 4.97/2.07 % (9921)Time elapsed: 0.184 s
% 4.97/2.07 % (9921)Instructions burned: 378 (million)
% 4.97/2.07 % (9921)------------------------------
% 4.97/2.07 % (9921)------------------------------
% 4.97/2.09 % (9930)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_9795 for (2996ds/3Mi)
% 4.97/2.09 % (9930)Instruction limit reached!
% 4.97/2.09 % (9930)------------------------------
% 4.97/2.09 % (9930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.97/2.09 % (9930)Termination reason: Unknown
% 4.97/2.09 % (9930)Termination phase: shuffling
% 4.97/2.09
% 4.97/2.09 % (9930)Memory used [KB]: 1407
% 4.97/2.09 % (9930)Time elapsed: 0.003 s
% 4.97/2.09 % (9930)Instructions burned: 3 (million)
% 4.97/2.09 % (9930)------------------------------
% 4.97/2.09 % (9930)------------------------------
% 4.97/2.10 % (9931)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_9795 for (2996ds/20Mi)
% 4.97/2.11 % (9929)Instruction limit reached!
% 4.97/2.11 % (9929)------------------------------
% 4.97/2.11 % (9929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.97/2.11 % (9929)Termination reason: Unknown
% 4.97/2.11 % (9929)Termination phase: Property scanning
% 4.97/2.11
% 4.97/2.11 % (9929)Memory used [KB]: 2174
% 4.97/2.11 % (9929)Time elapsed: 0.047 s
% 4.97/2.11 % (9929)Instructions burned: 101 (million)
% 4.97/2.11 % (9929)------------------------------
% 4.97/2.11 % (9929)------------------------------
% 4.97/2.11 % (9931)Instruction limit reached!
% 4.97/2.11 % (9931)------------------------------
% 4.97/2.11 % (9931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.97/2.11 % (9931)Termination reason: Unknown
% 4.97/2.11 % (9931)Termination phase: shuffling
% 4.97/2.11
% 4.97/2.11 % (9931)Memory used [KB]: 1791
% 4.97/2.11 % (9931)Time elapsed: 0.012 s
% 4.97/2.11 % (9931)Instructions burned: 20 (million)
% 4.97/2.11 % (9931)------------------------------
% 4.97/2.11 % (9931)------------------------------
% 5.70/2.13 % (9932)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_9795 for (2996ds/86Mi)
% 5.70/2.13 % (9933)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_9795 for (2996ds/107Mi)
% 5.70/2.17 % (9932)Instruction limit reached!
% 5.70/2.17 % (9932)------------------------------
% 5.70/2.17 % (9932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.17 % (9932)Termination reason: Unknown
% 5.70/2.17 % (9932)Termination phase: Saturation
% 5.70/2.17
% 5.70/2.17 % (9932)Memory used [KB]: 2302
% 5.70/2.17 % (9932)Time elapsed: 0.042 s
% 5.70/2.17 % (9932)Instructions burned: 86 (million)
% 5.70/2.17 % (9932)------------------------------
% 5.70/2.17 % (9932)------------------------------
% 5.70/2.18 % (9933)Instruction limit reached!
% 5.70/2.18 % (9933)------------------------------
% 5.70/2.18 % (9933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.18 % (9933)Termination reason: Unknown
% 5.70/2.18 % (9933)Termination phase: Saturation
% 5.70/2.18
% 5.70/2.18 % (9933)Memory used [KB]: 6780
% 5.70/2.18 % (9933)Time elapsed: 0.053 s
% 5.70/2.18 % (9933)Instructions burned: 107 (million)
% 5.70/2.18 % (9933)------------------------------
% 5.70/2.18 % (9933)------------------------------
% 5.70/2.18 % (9934)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_9795 for (2995ds/39Mi)
% 5.70/2.20 % (9915)Instruction limit reached!
% 5.70/2.20 % (9915)------------------------------
% 5.70/2.20 % (9915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.70/2.20 % (9915)Termination reason: Unknown
% 5.70/2.20 % (9915)Termination phase: Saturation
% 5.70/2.20
% 5.70/2.20 % (9915)Memory used [KB]: 7803
% 5.70/2.20 % (9915)Time elapsed: 0.349 s
% 5.70/2.20 % (9915)Instructions burned: 711 (million)
% 5.70/2.20 % (9915)------------------------------
% 5.70/2.20 % (9915)------------------------------
% 5.82/2.20 % (9935)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_9795 for (2995ds/448Mi)
% 5.82/2.20 % (9934)Instruction limit reached!
% 5.82/2.20 % (9934)------------------------------
% 5.82/2.20 % (9934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.20 % (9934)Termination reason: Unknown
% 5.82/2.20 % (9934)Termination phase: Property scanning
% 5.82/2.20
% 5.82/2.20 % (9934)Memory used [KB]: 2046
% 5.82/2.20 % (9934)Time elapsed: 0.020 s
% 5.82/2.20 % (9934)Instructions burned: 40 (million)
% 5.82/2.20 % (9934)------------------------------
% 5.82/2.20 % (9934)------------------------------
% 5.82/2.21 % (9936)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_9795 for (2995ds/46Mi)
% 5.82/2.22 % (9937)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_9795 for (2995ds/98Mi)
% 5.82/2.23 % (9936)Instruction limit reached!
% 5.82/2.23 % (9936)------------------------------
% 5.82/2.23 % (9936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.24 % (9936)Termination reason: Unknown
% 5.82/2.24 % (9936)Termination phase: Preprocessing 3
% 5.82/2.24
% 5.82/2.24 % (9936)Memory used [KB]: 1918
% 5.82/2.24 % (9936)Time elapsed: 0.024 s
% 5.82/2.24 % (9936)Instructions burned: 46 (million)
% 5.82/2.24 % (9936)------------------------------
% 5.82/2.24 % (9936)------------------------------
% 5.82/2.25 % (9938)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_9795 for (2995ds/507Mi)
% 5.82/2.26 % (9937)Instruction limit reached!
% 5.82/2.26 % (9937)------------------------------
% 5.82/2.26 % (9937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.26 % (9937)Termination reason: Unknown
% 5.82/2.26 % (9937)Termination phase: Property scanning
% 5.82/2.26
% 5.82/2.26 % (9937)Memory used [KB]: 2174
% 5.82/2.26 % (9937)Time elapsed: 0.047 s
% 5.82/2.26 % (9937)Instructions burned: 99 (million)
% 5.82/2.26 % (9937)------------------------------
% 5.82/2.26 % (9937)------------------------------
% 5.82/2.27 % (9922)Instruction limit reached!
% 5.82/2.27 % (9922)------------------------------
% 5.82/2.27 % (9922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.27 % (9922)Termination reason: Unknown
% 5.82/2.27 % (9922)Termination phase: Saturation
% 5.82/2.27
% 5.82/2.27 % (9922)Memory used [KB]: 7931
% 5.82/2.27 % (9922)Time elapsed: 0.380 s
% 5.82/2.27 % (9922)Instructions burned: 779 (million)
% 5.82/2.27 % (9922)------------------------------
% 5.82/2.27 % (9922)------------------------------
% 5.82/2.28 % (9917)Instruction limit reached!
% 5.82/2.28 % (9917)------------------------------
% 5.82/2.28 % (9917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.28 % (9917)Termination reason: Unknown
% 5.82/2.28 % (9917)Termination phase: Saturation
% 5.82/2.28
% 5.82/2.28 % (9917)Memory used [KB]: 8699
% 5.82/2.28 % (9917)Time elapsed: 0.422 s
% 5.82/2.28 % (9917)Instructions burned: 902 (million)
% 5.82/2.28 % (9917)------------------------------
% 5.82/2.28 % (9917)------------------------------
% 5.82/2.28 % (9939)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_9795 for (2995ds/149Mi)
% 5.82/2.28 % (9940)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_9795 for (2994ds/39Mi)
% 5.82/2.29 % (9941)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_9795 for (2994ds/6Mi)
% 5.82/2.30 % (9941)Instruction limit reached!
% 5.82/2.30 % (9941)------------------------------
% 5.82/2.30 % (9941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.30 % (9941)Termination reason: Unknown
% 5.82/2.30 % (9941)Termination phase: shuffling
% 5.82/2.30
% 5.82/2.30 % (9941)Memory used [KB]: 1407
% 5.82/2.30 % (9941)Time elapsed: 0.005 s
% 5.82/2.30 % (9941)Instructions burned: 7 (million)
% 5.82/2.30 % (9941)------------------------------
% 5.82/2.30 % (9941)------------------------------
% 6.70/2.30 % (9940)Instruction limit reached!
% 6.70/2.30 % (9940)------------------------------
% 6.70/2.30 % (9940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.30 % (9940)Termination reason: Unknown
% 6.70/2.30 % (9940)Termination phase: Preprocessing 3
% 6.70/2.30
% 6.70/2.30 % (9940)Memory used [KB]: 1918
% 6.70/2.30 % (9940)Time elapsed: 0.021 s
% 6.70/2.30 % (9940)Instructions burned: 40 (million)
% 6.70/2.30 % (9940)------------------------------
% 6.70/2.30 % (9940)------------------------------
% 6.70/2.31 % (9906)Instruction limit reached!
% 6.70/2.31 % (9906)------------------------------
% 6.70/2.31 % (9906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.31 % (9906)Termination reason: Unknown
% 6.70/2.31 % (9906)Termination phase: Saturation
% 6.70/2.31
% 6.70/2.31 % (9906)Memory used [KB]: 9594
% 6.70/2.31 % (9906)Time elapsed: 0.497 s
% 6.70/2.31 % (9906)Instructions burned: 1042 (million)
% 6.70/2.31 % (9906)------------------------------
% 6.70/2.31 % (9906)------------------------------
% 6.70/2.31 % (9924)Refutation not found, non-redundant clauses discarded% (9924)------------------------------
% 6.70/2.31 % (9924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.31 % (9924)Termination reason: Refutation not found, non-redundant clauses discarded
% 6.70/2.31
% 6.70/2.31 % (9924)Memory used [KB]: 7675
% 6.70/2.31 % (9924)Time elapsed: 0.418 s
% 6.70/2.31 % (9924)Instructions burned: 862 (million)
% 6.70/2.31 % (9924)------------------------------
% 6.70/2.31 % (9924)------------------------------
% 6.70/2.31 % (9942)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_9795 for (2994ds/1087Mi)
% 6.70/2.32 % (9943)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_9795 for (2994ds/47Mi)
% 6.70/2.33 % (9944)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_9795 for (2994ds/44Mi)
% 6.70/2.33 % (9945)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_9795 for (2994ds/432Mi)
% 6.70/2.34 % (9943)Instruction limit reached!
% 6.70/2.34 % (9943)------------------------------
% 6.70/2.34 % (9943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.34 % (9943)Termination reason: Unknown
% 6.70/2.34 % (9943)Termination phase: Preprocessing 3
% 6.70/2.34
% 6.70/2.34 % (9943)Memory used [KB]: 2174
% 6.70/2.34 % (9943)Time elapsed: 0.025 s
% 6.70/2.34 % (9943)Instructions burned: 48 (million)
% 6.70/2.34 % (9943)------------------------------
% 6.70/2.34 % (9943)------------------------------
% 6.70/2.35 % (9944)Instruction limit reached!
% 6.70/2.35 % (9944)------------------------------
% 6.70/2.35 % (9944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.35 % (9944)Termination reason: Unknown
% 6.70/2.35 % (9944)Termination phase: Property scanning
% 6.70/2.35
% 6.70/2.35 % (9944)Memory used [KB]: 2046
% 6.70/2.35 % (9944)Time elapsed: 0.022 s
% 6.70/2.35 % (9944)Instructions burned: 45 (million)
% 6.70/2.35 % (9944)------------------------------
% 6.70/2.35 % (9944)------------------------------
% 6.70/2.35 % (9939)Instruction limit reached!
% 6.70/2.35 % (9939)------------------------------
% 6.70/2.35 % (9939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.35 % (9939)Termination reason: Unknown
% 6.70/2.35 % (9939)Termination phase: Saturation
% 6.70/2.35
% 6.70/2.35 % (9939)Memory used [KB]: 6908
% 6.70/2.35 % (9939)Time elapsed: 0.072 s
% 6.70/2.35 % (9939)Instructions burned: 150 (million)
% 6.70/2.35 % (9939)------------------------------
% 6.70/2.35 % (9939)------------------------------
% 6.70/2.36 % (9946)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_9795 for (2994ds/62Mi)
% 6.70/2.36 % (9947)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_9795 for (2994ds/31Mi)
% 6.70/2.37 % (9948)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_9795 for (2994ds/96Mi)
% 6.70/2.38 % (9947)Instruction limit reached!
% 6.70/2.38 % (9947)------------------------------
% 6.70/2.38 % (9947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.38 % (9947)Termination reason: Unknown
% 6.70/2.38 % (9947)Termination phase: Property scanning
% 6.70/2.38
% 6.70/2.38 % (9947)Memory used [KB]: 1791
% 6.70/2.38 % (9947)Time elapsed: 0.017 s
% 6.70/2.38 % (9947)Instructions burned: 32 (million)
% 6.70/2.38 % (9947)------------------------------
% 6.70/2.38 % (9947)------------------------------
% 6.70/2.39 % (9946)Instruction limit reached!
% 6.70/2.39 % (9946)------------------------------
% 6.70/2.39 % (9946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.70/2.39 % (9946)Termination reason: Unknown
% 6.70/2.39 % (9946)Termination phase: Property scanning
% 6.70/2.39
% 6.70/2.39 % (9946)Memory used [KB]: 2046
% 6.70/2.39 % (9946)Time elapsed: 0.030 s
% 6.70/2.39 % (9946)Instructions burned: 63 (million)
% 6.70/2.39 % (9946)------------------------------
% 6.70/2.39 % (9946)------------------------------
% 6.70/2.39 % (9949)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_9795 for (2993ds/453Mi)
% 7.02/2.40 % (9950)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_9795 for (2993ds/71Mi)
% 7.02/2.41 % (9948)Instruction limit reached!
% 7.02/2.41 % (9948)------------------------------
% 7.02/2.41 % (9948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.41 % (9948)Termination reason: Unknown
% 7.02/2.41 % (9948)Termination phase: Saturation
% 7.02/2.41
% 7.02/2.41 % (9948)Memory used [KB]: 6780
% 7.02/2.41 % (9948)Time elapsed: 0.047 s
% 7.02/2.41 % (9948)Instructions burned: 97 (million)
% 7.02/2.41 % (9948)------------------------------
% 7.02/2.41 % (9948)------------------------------
% 7.02/2.42 % (9935)Instruction limit reached!
% 7.02/2.42 % (9935)------------------------------
% 7.02/2.42 % (9935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.42 % (9935)Termination reason: Unknown
% 7.02/2.42 % (9935)Termination phase: Saturation
% 7.02/2.42
% 7.02/2.42 % (9935)Memory used [KB]: 7931
% 7.02/2.42 % (9935)Time elapsed: 0.221 s
% 7.02/2.42 % (9935)Instructions burned: 449 (million)
% 7.02/2.42 % (9935)------------------------------
% 7.02/2.42 % (9935)------------------------------
% 7.02/2.43 % (9951)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_9795 for (2993ds/83Mi)
% 7.02/2.43 % (9952)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_9795 for (2993ds/11Mi)
% 7.02/2.44 % (9950)Instruction limit reached!
% 7.02/2.44 % (9950)------------------------------
% 7.02/2.44 % (9950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.44 % (9950)Termination reason: Unknown
% 7.02/2.44 % (9950)Termination phase: Property scanning
% 7.02/2.44
% 7.02/2.44 % (9950)Memory used [KB]: 2302
% 7.02/2.44 % (9950)Time elapsed: 0.035 s
% 7.02/2.44 % (9950)Instructions burned: 71 (million)
% 7.02/2.44 % (9950)------------------------------
% 7.02/2.44 % (9950)------------------------------
% 7.02/2.44 % (9952)Instruction limit reached!
% 7.02/2.44 % (9952)------------------------------
% 7.02/2.44 % (9952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.44 % (9952)Termination reason: Unknown
% 7.02/2.44 % (9952)Termination phase: shuffling
% 7.02/2.44
% 7.02/2.44 % (9952)Memory used [KB]: 1535
% 7.02/2.44 % (9952)Time elapsed: 0.007 s
% 7.02/2.44 % (9952)Instructions burned: 12 (million)
% 7.02/2.44 % (9952)------------------------------
% 7.02/2.44 % (9952)------------------------------
% 7.02/2.45 % (9953)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_9795 for (2993ds/41Mi)
% 7.02/2.45 % (9954)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_9795 for (2993ds/6Mi)
% 7.02/2.46 % (9954)Instruction limit reached!
% 7.02/2.46 % (9954)------------------------------
% 7.02/2.46 % (9954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.46 % (9954)Termination reason: Unknown
% 7.02/2.46 % (9954)Termination phase: shuffling
% 7.02/2.46
% 7.02/2.46 % (9954)Memory used [KB]: 1535
% 7.02/2.46 % (9954)Time elapsed: 0.005 s
% 7.02/2.46 % (9954)Instructions burned: 7 (million)
% 7.02/2.46 % (9954)------------------------------
% 7.02/2.46 % (9954)------------------------------
% 7.02/2.47 % (9951)Instruction limit reached!
% 7.02/2.47 % (9951)------------------------------
% 7.02/2.47 % (9951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.47 % (9951)Termination reason: Unknown
% 7.02/2.47 % (9951)Termination phase: Saturation
% 7.02/2.47
% 7.02/2.47 % (9951)Memory used [KB]: 6652
% 7.02/2.47 % (9951)Time elapsed: 0.041 s
% 7.02/2.47 % (9951)Instructions burned: 84 (million)
% 7.02/2.47 % (9951)------------------------------
% 7.02/2.47 % (9951)------------------------------
% 7.02/2.47 % (9953)Instruction limit reached!
% 7.02/2.47 % (9953)------------------------------
% 7.02/2.47 % (9953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.02/2.47 % (9953)Termination reason: Unknown
% 7.02/2.47 % (9953)Termination phase: Property scanning
% 7.02/2.47
% 7.02/2.47 % (9953)Memory used [KB]: 2046
% 7.02/2.47 % (9953)Time elapsed: 0.021 s
% 7.02/2.47 % (9953)Instructions burned: 43 (million)
% 7.02/2.47 % (9953)------------------------------
% 7.02/2.47 % (9953)------------------------------
% 7.02/2.47 % (9955)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_9795 for (2992ds/150Mi)
% 7.02/2.48 % (9956)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_9795 for (2992ds/343Mi)
% 7.02/2.49 % (9957)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_9795 for (2992ds/109Mi)
% 7.51/2.50 % (9938)Instruction limit reached!
% 7.51/2.50 % (9938)------------------------------
% 7.51/2.50 % (9938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.50 % (9938)Termination reason: Unknown
% 7.51/2.50 % (9938)Termination phase: Saturation
% 7.51/2.50
% 7.51/2.50 % (9938)Memory used [KB]: 7931
% 7.51/2.50 % (9938)Time elapsed: 0.250 s
% 7.51/2.50 % (9938)Instructions burned: 508 (million)
% 7.51/2.50 % (9938)------------------------------
% 7.51/2.50 % (9938)------------------------------
% 7.51/2.52 % (9958)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_9795 for (2992ds/253Mi)
% 7.51/2.54 % (9945)Instruction limit reached!
% 7.51/2.54 % (9945)------------------------------
% 7.51/2.54 % (9945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.54 % (9945)Termination reason: Unknown
% 7.51/2.54 % (9945)Termination phase: Saturation
% 7.51/2.54
% 7.51/2.54 % (9945)Memory used [KB]: 3709
% 7.51/2.54 % (9945)Time elapsed: 0.212 s
% 7.51/2.54 % (9945)Instructions burned: 433 (million)
% 7.51/2.54 % (9945)------------------------------
% 7.51/2.54 % (9945)------------------------------
% 7.51/2.54 % (9957)Instruction limit reached!
% 7.51/2.54 % (9957)------------------------------
% 7.51/2.54 % (9957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.54 % (9957)Termination reason: Unknown
% 7.51/2.54 % (9957)Termination phase: Saturation
% 7.51/2.54
% 7.51/2.54 % (9957)Memory used [KB]: 6780
% 7.51/2.54 % (9957)Time elapsed: 0.053 s
% 7.51/2.54 % (9957)Instructions burned: 109 (million)
% 7.51/2.54 % (9957)------------------------------
% 7.51/2.54 % (9957)------------------------------
% 7.51/2.55 % (9955)Instruction limit reached!
% 7.51/2.55 % (9955)------------------------------
% 7.51/2.55 % (9955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.55 % (9955)Termination reason: Unknown
% 7.51/2.55 % (9955)Termination phase: Saturation
% 7.51/2.55
% 7.51/2.55 % (9955)Memory used [KB]: 7036
% 7.51/2.55 % (9955)Time elapsed: 0.074 s
% 7.51/2.55 % (9955)Instructions burned: 151 (million)
% 7.51/2.55 % (9955)------------------------------
% 7.51/2.55 % (9955)------------------------------
% 7.51/2.55 % (9959)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_9795 for (2992ds/140Mi)
% 7.51/2.56 % (9960)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_9795 for (2992ds/614Mi)
% 7.51/2.56 % (9961)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_9795 for (2992ds/202Mi)
% 7.51/2.59 % (9961)Refutation not found, incomplete strategy
% 7.51/2.59 % (9961)------------------------------
% 7.51/2.59 % (9961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.51/2.59 % (9961)Termination reason: Refutation not found, incomplete strategy
% 7.51/2.59
% 7.51/2.59
% 7.51/2.59 % (9961)Memory used [KB]: 6524
% 7.51/2.59 % (9961)Time elapsed: 0.030 s
% 7.51/2.59 % (9961)Instructions burned: 58 (million)
% 7.51/2.59 % (9961)------------------------------
% 7.51/2.59 % (9961)------------------------------
% 8.20/2.61 % (9949)Instruction limit reached!
% 8.20/2.61 % (9949)------------------------------
% 8.20/2.61 % (9949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.61 % (9949)Termination reason: Unknown
% 8.20/2.61 % (9949)Termination phase: Saturation
% 8.20/2.61
% 8.20/2.61 % (9949)Memory used [KB]: 7675
% 8.20/2.61 % (9949)Time elapsed: 0.234 s
% 8.20/2.61 % (9949)Instructions burned: 455 (million)
% 8.20/2.61 % (9949)------------------------------
% 8.20/2.61 % (9949)------------------------------
% 8.20/2.61 % (9962)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_9795 for (2991ds/339Mi)
% 8.20/2.62 % (9963)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_9795 for (2991ds/283Mi)
% 8.20/2.62 % (9959)Instruction limit reached!
% 8.20/2.62 % (9959)------------------------------
% 8.20/2.62 % (9959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.62 % (9959)Termination reason: Unknown
% 8.20/2.62 % (9959)Termination phase: Saturation
% 8.20/2.62
% 8.20/2.62 % (9959)Memory used [KB]: 6780
% 8.20/2.62 % (9959)Time elapsed: 0.071 s
% 8.20/2.62 % (9959)Instructions burned: 140 (million)
% 8.20/2.62 % (9959)------------------------------
% 8.20/2.62 % (9959)------------------------------
% 8.20/2.64 % (9964)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_9795 for (2991ds/134Mi)
% 8.20/2.64 % (9958)Instruction limit reached!
% 8.20/2.64 % (9958)------------------------------
% 8.20/2.64 % (9958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.64 % (9958)Termination reason: Unknown
% 8.20/2.64 % (9958)Termination phase: Saturation
% 8.20/2.64
% 8.20/2.64 % (9958)Memory used [KB]: 7291
% 8.20/2.64 % (9958)Time elapsed: 0.127 s
% 8.20/2.64 % (9958)Instructions burned: 254 (million)
% 8.20/2.64 % (9958)------------------------------
% 8.20/2.64 % (9958)------------------------------
% 8.20/2.65 % (9956)Instruction limit reached!
% 8.20/2.65 % (9956)------------------------------
% 8.20/2.65 % (9956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.20/2.65 % (9956)Termination reason: Unknown
% 8.20/2.65 % (9956)Termination phase: Saturation
% 8.20/2.65
% 8.20/2.65 % (9956)Memory used [KB]: 7164
% 8.20/2.65 % (9956)Time elapsed: 0.166 s
% 8.20/2.65 % (9956)Instructions burned: 343 (million)
% 8.20/2.65 % (9956)------------------------------
% 8.20/2.65 % (9956)------------------------------
% 8.20/2.66 % (9965)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_9795 for (2991ds/298Mi)
% 8.20/2.66 % (9966)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_9795 for (2991ds/192Mi)
% 8.83/2.70 % (9964)Instruction limit reached!
% 8.83/2.70 % (9964)------------------------------
% 8.83/2.70 % (9964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.70 % (9964)Termination reason: Unknown
% 8.83/2.70 % (9964)Termination phase: Saturation
% 8.83/2.70
% 8.83/2.70 % (9964)Memory used [KB]: 6908
% 8.83/2.70 % (9964)Time elapsed: 0.064 s
% 8.83/2.70 % (9964)Instructions burned: 134 (million)
% 8.83/2.70 % (9964)------------------------------
% 8.83/2.70 % (9964)------------------------------
% 8.83/2.72 % (9967)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_9795 for (2990ds/258Mi)
% 8.83/2.76 % (9966)Instruction limit reached!
% 8.83/2.76 % (9966)------------------------------
% 8.83/2.76 % (9966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.76 % (9966)Termination reason: Unknown
% 8.83/2.76 % (9966)Termination phase: Saturation
% 8.83/2.76
% 8.83/2.76 % (9966)Memory used [KB]: 7803
% 8.83/2.76 % (9966)Time elapsed: 0.095 s
% 8.83/2.76 % (9966)Instructions burned: 193 (million)
% 8.83/2.76 % (9966)------------------------------
% 8.83/2.76 % (9966)------------------------------
% 8.83/2.76 % (9963)Instruction limit reached!
% 8.83/2.76 % (9963)------------------------------
% 8.83/2.76 % (9963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.76 % (9963)Termination reason: Unknown
% 8.83/2.76 % (9963)Termination phase: Saturation
% 8.83/2.76
% 8.83/2.76 % (9963)Memory used [KB]: 7547
% 8.83/2.76 % (9963)Time elapsed: 0.141 s
% 8.83/2.76 % (9963)Instructions burned: 284 (million)
% 8.83/2.76 % (9963)------------------------------
% 8.83/2.76 % (9963)------------------------------
% 8.83/2.77 % (9962)Instruction limit reached!
% 8.83/2.77 % (9962)------------------------------
% 8.83/2.77 % (9962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.77 % (9962)Termination reason: Unknown
% 8.83/2.77 % (9962)Termination phase: Saturation
% 8.83/2.77
% 8.83/2.77 % (9962)Memory used [KB]: 7291
% 8.83/2.77 % (9962)Time elapsed: 0.159 s
% 8.83/2.77 % (9962)Instructions burned: 341 (million)
% 8.83/2.77 % (9962)------------------------------
% 8.83/2.77 % (9962)------------------------------
% 8.83/2.77 % (9968)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_9795 for (2989ds/90Mi)
% 8.83/2.78 % (9969)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_9795 for (2989ds/231Mi)
% 8.83/2.78 % (9970)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_9795 for (2989ds/458Mi)
% 8.83/2.80 % (9965)Instruction limit reached!
% 8.83/2.80 % (9965)------------------------------
% 8.83/2.80 % (9965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.80 % (9965)Termination reason: Unknown
% 8.83/2.80 % (9965)Termination phase: Saturation
% 8.83/2.80
% 8.83/2.80 % (9965)Memory used [KB]: 7803
% 8.83/2.80 % (9965)Time elapsed: 0.139 s
% 8.83/2.80 % (9965)Instructions burned: 298 (million)
% 8.83/2.80 % (9965)------------------------------
% 8.83/2.80 % (9965)------------------------------
% 9.50/2.81 % (9971)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_9795 for (2989ds/31Mi)
% 9.50/2.82 % (9968)Instruction limit reached!
% 9.50/2.82 % (9968)------------------------------
% 9.50/2.82 % (9968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/2.82 % (9968)Termination reason: Unknown
% 9.50/2.82 % (9968)Termination phase: Saturation
% 9.50/2.82
% 9.50/2.82 % (9968)Memory used [KB]: 6780
% 9.50/2.82 % (9968)Time elapsed: 0.044 s
% 9.50/2.82 % (9968)Instructions burned: 90 (million)
% 9.50/2.82 % (9968)------------------------------
% 9.50/2.82 % (9968)------------------------------
% 9.50/2.83 % (9971)Instruction limit reached!
% 9.50/2.83 % (9971)------------------------------
% 9.50/2.83 % (9971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/2.83 % (9971)Termination reason: Unknown
% 9.50/2.83 % (9971)Termination phase: Property scanning
% 9.50/2.83
% 9.50/2.83 % (9971)Memory used [KB]: 1791
% 9.50/2.83 % (9971)Time elapsed: 0.018 s
% 9.50/2.83 % (9971)Instructions burned: 33 (million)
% 9.50/2.83 % (9971)------------------------------
% 9.50/2.83 % (9971)------------------------------
% 9.50/2.83 % (9972)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_9795 for (2989ds/297Mi)
% 9.50/2.83 % (9942)Instruction limit reached!
% 9.50/2.83 % (9942)------------------------------
% 9.50/2.83 % (9942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/2.83 % (9942)Termination reason: Unknown
% 9.50/2.83 % (9942)Termination phase: Saturation
% 9.50/2.83
% 9.50/2.83 % (9942)Memory used [KB]: 7675
% 9.50/2.83 % (9942)Time elapsed: 0.524 s
% 9.50/2.83 % (9942)Instructions burned: 1088 (million)
% 9.50/2.83 % (9942)------------------------------
% 9.50/2.83 % (9942)------------------------------
% 9.50/2.84 % (9967)Instruction limit reached!
% 9.50/2.84 % (9967)------------------------------
% 9.50/2.84 % (9967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/2.84 % (9967)Termination reason: Unknown
% 9.50/2.84 % (9967)Termination phase: Saturation
% 9.50/2.84
% 9.50/2.84 % (9967)Memory used [KB]: 7036
% 9.50/2.84 % (9967)Time elapsed: 0.127 s
% 9.50/2.84 % (9967)Instructions burned: 259 (million)
% 9.50/2.84 % (9967)------------------------------
% 9.50/2.84 % (9967)------------------------------
% 9.50/2.84 % (9973)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_9795 for (2989ds/987Mi)
% 9.50/2.85 % (9974)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_9795 for (2989ds/182Mi)
% 9.50/2.86 % (9960)Instruction limit reached!
% 9.50/2.86 % (9960)------------------------------
% 9.50/2.86 % (9960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/2.86 % (9960)Termination reason: Unknown
% 9.50/2.86 % (9960)Termination phase: Saturation
% 9.50/2.86
% 9.50/2.86 % (9960)Memory used [KB]: 8059
% 9.50/2.86 % (9960)Time elapsed: 0.302 s
% 9.50/2.86 % (9960)Instructions burned: 614 (million)
% 9.50/2.86 % (9960)------------------------------
% 9.50/2.86 % (9960)------------------------------
% 9.50/2.86 % (9975)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_9795 for (2989ds/182Mi)
% 9.50/2.87 % (9976)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_9795 for (2989ds/154Mi)
% 9.50/2.88 % (9969)Instruction limit reached!
% 9.50/2.88 % (9969)------------------------------
% 9.50/2.88 % (9969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/2.88 % (9969)Termination reason: Unknown
% 9.50/2.88 % (9969)Termination phase: Saturation
% 9.50/2.88
% 9.50/2.88 % (9969)Memory used [KB]: 6780
% 9.50/2.88 % (9969)Time elapsed: 0.103 s
% 9.50/2.88 % (9969)Instructions burned: 232 (million)
% 9.50/2.88 % (9969)------------------------------
% 9.50/2.88 % (9969)------------------------------
% 9.50/2.90 % (9977)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_9795 for (2988ds/79Mi)
% 10.71/2.93 % (9977)Instruction limit reached!
% 10.71/2.93 % (9977)------------------------------
% 10.71/2.93 % (9977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.71/2.93 % (9977)Termination reason: Unknown
% 10.71/2.93 % (9977)Termination phase: Property scanning
% 10.71/2.93
% 10.71/2.93 % (9977)Memory used [KB]: 2302
% 10.71/2.93 % (9977)Time elapsed: 0.039 s
% 10.71/2.93 % (9977)Instructions burned: 79 (million)
% 10.71/2.93 % (9977)------------------------------
% 10.71/2.93 % (9977)------------------------------
% 10.71/2.94 % (9974)Instruction limit reached!
% 10.71/2.94 % (9974)------------------------------
% 10.71/2.94 % (9974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.71/2.94 % (9974)Termination reason: Unknown
% 10.71/2.94 % (9974)Termination phase: Saturation
% 10.71/2.94
% 10.71/2.94 % (9974)Memory used [KB]: 7036
% 10.71/2.94 % (9974)Time elapsed: 0.088 s
% 10.71/2.94 % (9974)Instructions burned: 182 (million)
% 10.71/2.94 % (9974)------------------------------
% 10.71/2.94 % (9974)------------------------------
% 10.71/2.94 % (9976)Instruction limit reached!
% 10.71/2.94 % (9976)------------------------------
% 10.71/2.94 % (9976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.71/2.94 % (9976)Termination reason: Unknown
% 10.71/2.94 % (9976)Termination phase: Saturation
% 10.71/2.94
% 10.71/2.94 % (9976)Memory used [KB]: 2558
% 10.71/2.94 % (9976)Time elapsed: 0.072 s
% 10.71/2.94 % (9976)Instructions burned: 155 (million)
% 10.71/2.94 % (9976)------------------------------
% 10.71/2.94 % (9976)------------------------------
% 10.71/2.95 % (9978)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_9795 for (2988ds/216Mi)
% 10.71/2.95 % (9975)Instruction limit reached!
% 10.71/2.95 % (9975)------------------------------
% 10.71/2.95 % (9975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.71/2.95 % (9975)Termination reason: Unknown
% 10.71/2.95 % (9975)Termination phase: Saturation
% 10.71/2.95
% 10.71/2.95 % (9975)Memory used [KB]: 7164
% 10.71/2.95 % (9975)Time elapsed: 0.091 s
% 10.71/2.95 % (9975)Instructions burned: 183 (million)
% 10.71/2.95 % (9975)------------------------------
% 10.71/2.95 % (9975)------------------------------
% 10.71/2.95 % (9979)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_9795 for (2988ds/114Mi)
% 10.71/2.96 % (9980)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_9795 for (2988ds/922Mi)
% 10.71/2.97 % (9981)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_9795 for (2988ds/182Mi)
% 10.71/2.97 % (9972)Instruction limit reached!
% 10.71/2.97 % (9972)------------------------------
% 10.71/2.97 % (9972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.71/2.97 % (9972)Termination reason: Unknown
% 10.71/2.97 % (9972)Termination phase: Saturation
% 10.71/2.97
% 10.71/2.97 % (9972)Memory used [KB]: 7675
% 10.71/2.97 % (9972)Time elapsed: 0.142 s
% 10.71/2.97 % (9972)Instructions burned: 298 (million)
% 10.71/2.97 % (9972)------------------------------
% 10.71/2.97 % (9972)------------------------------
% 10.71/2.99 % (9982)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_9795 for (2987ds/164Mi)
% 10.71/3.00 % (9970)Instruction limit reached!
% 10.71/3.00 % (9970)------------------------------
% 10.71/3.00 % (9970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.71/3.00 % (9970)Termination reason: Unknown
% 10.71/3.00 % (9970)Termination phase: Saturation
% 10.71/3.00
% 10.71/3.00 % (9970)Memory used [KB]: 7675
% 10.71/3.00 % (9970)Time elapsed: 0.223 s
% 10.71/3.00 % (9970)Instructions burned: 458 (million)
% 10.71/3.00 % (9970)------------------------------
% 10.71/3.00 % (9970)------------------------------
% 10.71/3.01 % (9979)Instruction limit reached!
% 10.71/3.01 % (9979)------------------------------
% 10.71/3.01 % (9979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.71/3.01 % (9979)Termination reason: Unknown
% 10.71/3.01 % (9979)Termination phase: Saturation
% 10.71/3.01
% 10.71/3.01 % (9979)Memory used [KB]: 6780
% 10.71/3.01 % (9979)Time elapsed: 0.055 s
% 10.71/3.01 % (9979)Instructions burned: 114 (million)
% 10.71/3.01 % (9979)------------------------------
% 10.71/3.01 % (9979)------------------------------
% 10.71/3.02 % (9983)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_9795 for (2987ds/50Mi)
% 10.71/3.02 % (9984)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_9795 for (2987ds/368Mi)
% 11.95/3.04 % (9983)Instruction limit reached!
% 11.95/3.04 % (9983)------------------------------
% 11.95/3.04 % (9983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.95/3.04 % (9983)Termination reason: Unknown
% 11.95/3.04 % (9983)Termination phase: Property scanning
% 11.95/3.04
% 11.95/3.04 % (9983)Memory used [KB]: 2046
% 11.95/3.04 % (9983)Time elapsed: 0.025 s
% 11.95/3.04 % (9983)Instructions burned: 50 (million)
% 11.95/3.04 % (9983)------------------------------
% 11.95/3.04 % (9983)------------------------------
% 11.95/3.05 % (9978)Instruction limit reached!
% 11.95/3.05 % (9978)------------------------------
% 11.95/3.05 % (9978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.95/3.05 % (9978)Termination reason: Unknown
% 11.95/3.05 % (9978)Termination phase: Saturation
% 11.95/3.05
% 11.95/3.05 % (9978)Memory used [KB]: 7291
% 11.95/3.05 % (9978)Time elapsed: 0.101 s
% 11.95/3.05 % (9978)Instructions burned: 217 (million)
% 11.95/3.05 % (9978)------------------------------
% 11.95/3.05 % (9978)------------------------------
% 11.95/3.05 % (9981)Instruction limit reached!
% 11.95/3.05 % (9981)------------------------------
% 11.95/3.05 % (9981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.95/3.05 % (9981)Termination reason: Unknown
% 11.95/3.05 % (9981)Termination phase: Saturation
% 11.95/3.05
% 11.95/3.05 % (9981)Memory used [KB]: 6908
% 11.95/3.05 % (9981)Time elapsed: 0.085 s
% 11.95/3.05 % (9981)Instructions burned: 182 (million)
% 11.95/3.05 % (9981)------------------------------
% 11.95/3.05 % (9981)------------------------------
% 11.95/3.06 % (9985)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_9795 for (2987ds/1021Mi)
% 11.95/3.06 % (9986)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_9795 for (2987ds/267Mi)
% 11.95/3.06 % (9982)Instruction limit reached!
% 11.95/3.06 % (9982)------------------------------
% 11.95/3.06 % (9982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.95/3.06 % (9982)Termination reason: Unknown
% 11.95/3.06 % (9982)Termination phase: Saturation
% 11.95/3.06
% 11.95/3.06 % (9982)Memory used [KB]: 2430
% 11.95/3.06 % (9982)Time elapsed: 0.077 s
% 11.95/3.06 % (9982)Instructions burned: 165 (million)
% 11.95/3.06 % (9982)------------------------------
% 11.95/3.06 % (9982)------------------------------
% 11.95/3.07 % (9987)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_9795 for (2987ds/204Mi)
% 11.95/3.08 % (9988)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_9795 for (2987ds/26Mi)
% 11.95/3.09 % (9988)Instruction limit reached!
% 11.95/3.09 % (9988)------------------------------
% 11.95/3.09 % (9988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.95/3.09 % (9988)Termination reason: Unknown
% 11.95/3.09 % (9988)Termination phase: shuffling
% 11.95/3.09
% 11.95/3.09 % (9988)Memory used [KB]: 1791
% 11.95/3.09 % (9988)Time elapsed: 0.014 s
% 11.95/3.09 % (9988)Instructions burned: 27 (million)
% 11.95/3.09 % (9988)------------------------------
% 11.95/3.09 % (9988)------------------------------
% 11.95/3.11 % (9989)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_9795 for (2986ds/53Mi)
% 12.35/3.14 % (9989)Instruction limit reached!
% 12.35/3.14 % (9989)------------------------------
% 12.35/3.14 % (9989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.35/3.14 % (9989)Termination reason: Unknown
% 12.35/3.14 % (9989)Termination phase: Property scanning
% 12.35/3.14
% 12.35/3.14 % (9989)Memory used [KB]: 2046
% 12.35/3.14 % (9989)Time elapsed: 0.027 s
% 12.35/3.14 % (9989)Instructions burned: 55 (million)
% 12.35/3.14 % (9989)------------------------------
% 12.35/3.14 % (9989)------------------------------
% 12.35/3.15 % (9990)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_9795 for (2986ds/4436Mi)
% 12.35/3.16 % (9987)Instruction limit reached!
% 12.35/3.16 % (9987)------------------------------
% 12.35/3.16 % (9987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.35/3.16 % (9987)Termination reason: Unknown
% 12.35/3.16 % (9987)Termination phase: Saturation
% 12.35/3.16
% 12.35/3.16 % (9987)Memory used [KB]: 7291
% 12.35/3.16 % (9987)Time elapsed: 0.100 s
% 12.35/3.16 % (9987)Instructions burned: 204 (million)
% 12.35/3.16 % (9987)------------------------------
% 12.35/3.16 % (9987)------------------------------
% 12.35/3.19 % (9991)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_9795 for (2986ds/1539Mi)
% 12.35/3.20 % (9986)Instruction limit reached!
% 12.35/3.20 % (9986)------------------------------
% 12.35/3.20 % (9986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.35/3.20 % (9986)Termination reason: Unknown
% 12.35/3.20 % (9986)Termination phase: Saturation
% 12.35/3.20
% 12.35/3.20 % (9986)Memory used [KB]: 7419
% 12.35/3.20 % (9986)Time elapsed: 0.133 s
% 12.35/3.20 % (9986)Instructions burned: 268 (million)
% 12.35/3.20 % (9986)------------------------------
% 12.35/3.20 % (9986)------------------------------
% 12.66/3.21 % (9984)Instruction limit reached!
% 12.66/3.21 % (9984)------------------------------
% 12.66/3.21 % (9984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.66/3.21 % (9984)Termination reason: Unknown
% 12.66/3.21 % (9984)Termination phase: Saturation
% 12.66/3.21
% 12.66/3.21 % (9984)Memory used [KB]: 7931
% 12.66/3.21 % (9984)Time elapsed: 0.186 s
% 12.66/3.21 % (9984)Instructions burned: 369 (million)
% 12.66/3.21 % (9984)------------------------------
% 12.66/3.21 % (9984)------------------------------
% 12.66/3.21 % (9992)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_9795 for (2985ds/408Mi)
% 12.66/3.22 % (9993)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_9795 for (2985ds/5205Mi)
% 13.21/3.33 % (9973)Instruction limit reached!
% 13.21/3.33 % (9973)------------------------------
% 13.21/3.33 % (9973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.21/3.33 % (9973)Termination reason: Unknown
% 13.21/3.33 % (9973)Termination phase: Saturation
% 13.21/3.33
% 13.21/3.33 % (9973)Memory used [KB]: 9466
% 13.21/3.33 % (9973)Time elapsed: 0.484 s
% 13.21/3.33 % (9973)Instructions burned: 987 (million)
% 13.21/3.33 % (9973)------------------------------
% 13.21/3.33 % (9973)------------------------------
% 13.21/3.34 % (9994)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_9795 for (2984ds/1913Mi)
% 13.35/3.41 % (9992)Instruction limit reached!
% 13.35/3.41 % (9992)------------------------------
% 13.35/3.41 % (9992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.35/3.41 % (9992)Termination reason: Unknown
% 13.35/3.41 % (9992)Termination phase: Saturation
% 13.35/3.41
% 13.35/3.41 % (9992)Memory used [KB]: 8059
% 13.35/3.41 % (9992)Time elapsed: 0.217 s
% 13.35/3.41 % (9992)Instructions burned: 409 (million)
% 13.35/3.41 % (9992)------------------------------
% 13.35/3.41 % (9992)------------------------------
% 13.35/3.41 % (9980)Instruction limit reached!
% 13.35/3.41 % (9980)------------------------------
% 13.35/3.41 % (9980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.35/3.41 % (9980)Termination reason: Unknown
% 13.35/3.41 % (9980)Termination phase: Saturation
% 13.35/3.41
% 13.35/3.41 % (9980)Memory used [KB]: 7675
% 13.35/3.41 % (9980)Time elapsed: 0.453 s
% 13.35/3.41 % (9980)Instructions burned: 922 (million)
% 13.35/3.41 % (9980)------------------------------
% 13.35/3.41 % (9980)------------------------------
% 13.35/3.42 % (9995)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_9795 for (2983ds/4350Mi)
% 13.35/3.43 % (9996)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_9795 for (2983ds/68Mi)
% 13.35/3.46 % (9996)Instruction limit reached!
% 13.35/3.46 % (9996)------------------------------
% 13.35/3.46 % (9996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.35/3.46 % (9996)Termination reason: Unknown
% 13.35/3.46 % (9996)Termination phase: Property scanning
% 13.35/3.46
% 13.35/3.46 % (9996)Memory used [KB]: 2174
% 13.35/3.46 % (9996)Time elapsed: 0.034 s
% 13.35/3.46 % (9996)Instructions burned: 68 (million)
% 13.35/3.46 % (9996)------------------------------
% 13.35/3.46 % (9996)------------------------------
% 13.35/3.48 % (9997)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_9795 for (2982ds/358Mi)
% 13.63/3.53 % (9985)Instruction limit reached!
% 13.63/3.53 % (9985)------------------------------
% 13.63/3.53 % (9985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.63/3.53 % (9985)Termination reason: Unknown
% 13.63/3.53 % (9985)Termination phase: Saturation
% 13.63/3.53
% 13.63/3.53 % (9985)Memory used [KB]: 8443
% 13.63/3.53 % (9985)Time elapsed: 0.468 s
% 13.63/3.53 % (9985)Instructions burned: 1021 (million)
% 13.63/3.53 % (9985)------------------------------
% 13.63/3.53 % (9985)------------------------------
% 13.63/3.54 % (9998)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_9795 for (2982ds/31Mi)
% 13.63/3.56 % (9998)Instruction limit reached!
% 13.63/3.56 % (9998)------------------------------
% 13.63/3.56 % (9998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.63/3.56 % (9998)Termination reason: Unknown
% 13.63/3.56 % (9998)Termination phase: Property scanning
% 13.63/3.56
% 13.63/3.56 % (9998)Memory used [KB]: 1791
% 13.63/3.56 % (9998)Time elapsed: 0.018 s
% 13.63/3.56 % (9998)Instructions burned: 32 (million)
% 13.63/3.56 % (9998)------------------------------
% 13.63/3.56 % (9998)------------------------------
% 13.63/3.58 % (9999)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_9795 for (2981ds/279Mi)
% 14.14/3.64 % (9999)Refutation not found, incomplete strategy
% 14.14/3.64 % (9999)------------------------------
% 14.14/3.64 % (9999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.14/3.64 % (9999)Termination reason: Refutation not found, incomplete strategy
% 14.14/3.64
% 14.14/3.64
% 14.14/3.64 % (9999)Memory used [KB]: 6908
% 14.14/3.64 % (9999)Time elapsed: 0.062 s
% 14.14/3.64 % (9999)Instructions burned: 129 (million)
% 14.14/3.64 % (9999)------------------------------
% 14.14/3.64 % (9999)------------------------------
% 14.14/3.65 % (9997)Instruction limit reached!
% 14.14/3.65 % (9997)------------------------------
% 14.14/3.65 % (9997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.14/3.65 % (9997)Termination reason: Unknown
% 14.14/3.65 % (9997)Termination phase: Saturation
% 14.14/3.65
% 14.14/3.65 % (9997)Memory used [KB]: 7419
% 14.14/3.65 % (9997)Time elapsed: 0.179 s
% 14.14/3.65 % (9997)Instructions burned: 359 (million)
% 14.14/3.65 % (9997)------------------------------
% 14.14/3.65 % (9997)------------------------------
% 14.14/3.65 % (10000)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_9795 for (2981ds/258Mi)
% 14.14/3.67 % (10001)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_9795 for (2981ds/26Mi)
% 14.14/3.68 % (10001)Instruction limit reached!
% 14.14/3.68 % (10001)------------------------------
% 14.14/3.68 % (10001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.14/3.68 % (10001)Termination reason: Unknown
% 14.14/3.68 % (10001)Termination phase: shuffling
% 14.14/3.68
% 14.14/3.68 % (10001)Memory used [KB]: 1791
% 14.14/3.68 % (10001)Time elapsed: 0.014 s
% 14.14/3.68 % (10001)Instructions burned: 27 (million)
% 14.14/3.68 % (10001)------------------------------
% 14.14/3.68 % (10001)------------------------------
% 14.44/3.70 % (10002)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_9795 for (2980ds/995Mi)
% 14.44/3.78 % (10000)Instruction limit reached!
% 14.44/3.78 % (10000)------------------------------
% 14.44/3.78 % (10000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.44/3.78 % (10000)Termination reason: Unknown
% 14.44/3.78 % (10000)Termination phase: Saturation
% 14.44/3.78
% 14.44/3.78 % (10000)Memory used [KB]: 7164
% 14.44/3.78 % (10000)Time elapsed: 0.124 s
% 14.44/3.78 % (10000)Instructions burned: 258 (million)
% 14.44/3.78 % (10000)------------------------------
% 14.44/3.78 % (10000)------------------------------
% 14.44/3.79 % (10003)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_9795 for (2979ds/373Mi)
% 14.58/3.93 % (9991)Instruction limit reached!
% 14.58/3.93 % (9991)------------------------------
% 14.58/3.93 % (9991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.58/3.93 % (9991)Termination reason: Unknown
% 14.58/3.93 % (9991)Termination phase: Saturation
% 14.58/3.93
% 14.58/3.93 % (9991)Memory used [KB]: 9978
% 14.58/3.93 % (9991)Time elapsed: 0.771 s
% 14.58/3.93 % (9991)Instructions burned: 1539 (million)
% 14.58/3.93 % (9991)------------------------------
% 14.58/3.93 % (9991)------------------------------
% 14.58/3.95 % (10004)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_9795 for (2978ds/253Mi)
% 14.58/3.97 % (10003)Instruction limit reached!
% 14.58/3.97 % (10003)------------------------------
% 14.58/3.97 % (10003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.58/3.97 % (10003)Termination reason: Unknown
% 14.58/3.97 % (10003)Termination phase: Saturation
% 14.58/3.97
% 14.58/3.97 % (10003)Memory used [KB]: 8059
% 14.58/3.97 % (10003)Time elapsed: 0.183 s
% 14.58/3.97 % (10003)Instructions burned: 374 (million)
% 14.58/3.97 % (10003)------------------------------
% 14.58/3.97 % (10003)------------------------------
% 14.58/3.99 % (10005)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_9795 for (2977ds/832Mi)
% 18.93/4.06 % (10004)Instruction limit reached!
% 18.93/4.06 % (10004)------------------------------
% 18.93/4.06 % (10004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.93/4.06 % (10004)Termination reason: Unknown
% 18.93/4.06 % (10004)Termination phase: Saturation
% 18.93/4.06
% 18.93/4.06 % (10004)Memory used [KB]: 7547
% 18.93/4.06 % (10004)Time elapsed: 0.119 s
% 18.93/4.06 % (10004)Instructions burned: 254 (million)
% 18.93/4.06 % (10004)------------------------------
% 18.93/4.06 % (10004)------------------------------
% 18.93/4.08 % (10006)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_9795 for (2976ds/668Mi)
% 19.62/4.17 % (10002)Instruction limit reached!
% 19.62/4.17 % (10002)------------------------------
% 19.62/4.17 % (10002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.62/4.17 % (10002)Termination reason: Unknown
% 19.62/4.17 % (10002)Termination phase: Saturation
% 19.62/4.17
% 19.62/4.17 % (10002)Memory used [KB]: 9210
% 19.62/4.17 % (10002)Time elapsed: 0.478 s
% 19.62/4.17 % (10002)Instructions burned: 996 (million)
% 19.62/4.17 % (10002)------------------------------
% 19.62/4.17 % (10002)------------------------------
% 19.62/4.19 % (10007)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_9795 for (2975ds/40Mi)
% 20.07/4.21 % (10007)Instruction limit reached!
% 20.07/4.21 % (10007)------------------------------
% 20.07/4.21 % (10007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.07/4.21 % (10007)Termination reason: Unknown
% 20.07/4.21 % (10007)Termination phase: Property scanning
% 20.07/4.21
% 20.07/4.21 % (10007)Memory used [KB]: 2046
% 20.07/4.21 % (10007)Time elapsed: 0.021 s
% 20.07/4.21 % (10007)Instructions burned: 41 (million)
% 20.07/4.21 % (10007)------------------------------
% 20.07/4.21 % (10007)------------------------------
% 20.07/4.23 % (10008)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_9795 for (2975ds/294Mi)
% 20.07/4.26 % (9994)Instruction limit reached!
% 20.07/4.26 % (9994)------------------------------
% 20.07/4.26 % (9994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.07/4.26 % (9994)Termination reason: Unknown
% 20.07/4.26 % (9994)Termination phase: Saturation
% 20.07/4.26
% 20.07/4.26 % (9994)Memory used [KB]: 3837
% 20.07/4.26 % (9994)Time elapsed: 0.941 s
% 20.07/4.26 % (9994)Instructions burned: 1913 (million)
% 20.07/4.26 % (9994)------------------------------
% 20.07/4.26 % (9994)------------------------------
% 20.07/4.26 % (10008)Refutation not found, incomplete strategy
% 20.07/4.26 % (10008)------------------------------
% 20.07/4.26 % (10008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.07/4.26 % (10008)Termination reason: Refutation not found, incomplete strategy
% 20.07/4.26
% 20.07/4.26
% 20.07/4.26 % (10008)Memory used [KB]: 6652
% 20.07/4.26 % (10008)Time elapsed: 0.037 s
% 20.07/4.26 % (10008)Instructions burned: 75 (million)
% 20.07/4.26 % (10008)------------------------------
% 20.07/4.26 % (10008)------------------------------
% 20.07/4.28 % (10009)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_9795 for (2974ds/187Mi)
% 20.07/4.28 % (10010)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_9795 for (2974ds/371Mi)
% 20.61/4.37 % (10009)Instruction limit reached!
% 20.61/4.37 % (10009)------------------------------
% 20.61/4.37 % (10009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.61/4.37 % (10009)Termination reason: Unknown
% 20.61/4.37 % (10009)Termination phase: Saturation
% 20.61/4.37
% 20.61/4.37 % (10009)Memory used [KB]: 7291
% 20.61/4.37 % (10009)Time elapsed: 0.094 s
% 20.61/4.37 % (10009)Instructions burned: 188 (million)
% 20.61/4.37 % (10009)------------------------------
% 20.61/4.37 % (10009)------------------------------
% 20.61/4.39 % (10011)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_9795 for (2973ds/1827Mi)
% 20.61/4.40 % (10005)Instruction limit reached!
% 20.61/4.40 % (10005)------------------------------
% 20.61/4.40 % (10005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.61/4.40 % (10005)Termination reason: Unknown
% 21.12/4.40 % (10005)Termination phase: Saturation
% 21.12/4.40
% 21.12/4.40 % (10005)Memory used [KB]: 8187
% 21.12/4.40 % (10005)Time elapsed: 0.408 s
% 21.12/4.40 % (10005)Instructions burned: 832 (million)
% 21.12/4.40 % (10005)------------------------------
% 21.12/4.40 % (10005)------------------------------
% 21.12/4.40 % (10006)Instruction limit reached!
% 21.12/4.40 % (10006)------------------------------
% 21.12/4.40 % (10006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.12/4.40 % (10006)Termination reason: Unknown
% 21.12/4.40 % (10006)Termination phase: Saturation
% 21.12/4.40
% 21.12/4.40 % (10006)Memory used [KB]: 13816
% 21.12/4.40 % (10006)Time elapsed: 0.322 s
% 21.12/4.40 % (10006)Instructions burned: 668 (million)
% 21.12/4.40 % (10006)------------------------------
% 21.12/4.40 % (10006)------------------------------
% 21.12/4.41 % (10012)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_9795 for (2973ds/70Mi)
% 21.12/4.42 % (10013)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_9795 for (2973ds/316Mi)
% 21.12/4.45 % (10012)Instruction limit reached!
% 21.12/4.45 % (10012)------------------------------
% 21.12/4.45 % (10012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.12/4.45 % (10012)Termination reason: Unknown
% 21.12/4.45 % (10012)Termination phase: Preprocessing 3
% 21.12/4.45
% 21.12/4.45 % (10012)Memory used [KB]: 2174
% 21.12/4.45 % (10012)Time elapsed: 0.034 s
% 21.12/4.45 % (10012)Instructions burned: 71 (million)
% 21.12/4.45 % (10012)------------------------------
% 21.12/4.45 % (10012)------------------------------
% 21.12/4.46 % (10010)Instruction limit reached!
% 21.12/4.46 % (10010)------------------------------
% 21.12/4.46 % (10010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.12/4.46 % (10010)Termination reason: Unknown
% 21.12/4.46 % (10010)Termination phase: Saturation
% 21.12/4.46
% 21.12/4.46 % (10010)Memory used [KB]: 7291
% 21.12/4.46 % (10010)Time elapsed: 0.178 s
% 21.12/4.46 % (10010)Instructions burned: 371 (million)
% 21.12/4.46 % (10010)------------------------------
% 21.12/4.46 % (10010)------------------------------
% 21.12/4.46 % (10014)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_9795 for (2973ds/932Mi)
% 21.12/4.47 % (10015)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_9795 for (2973ds/4714Mi)
% 22.01/4.51 % (10013)Refutation not found, incomplete strategy
% 22.01/4.51 % (10013)------------------------------
% 22.01/4.51 % (10013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.01/4.51 % (10013)Termination reason: Refutation not found, incomplete strategy
% 22.01/4.51
% 22.01/4.51
% 22.01/4.51 % (10013)Memory used [KB]: 7419
% 22.01/4.51 % (10013)Time elapsed: 0.094 s
% 22.01/4.51 % (10013)Instructions burned: 201 (million)
% 22.01/4.51 % (10013)------------------------------
% 22.01/4.51 % (10013)------------------------------
% 22.01/4.53 % (10016)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_9795 for (2972ds/8250Mi)
% 22.01/4.57 % (10015)Refutation not found, incomplete strategy
% 22.01/4.57 % (10015)------------------------------
% 22.01/4.57 % (10015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.01/4.57 % (10015)Termination reason: Refutation not found, incomplete strategy
% 22.01/4.57
% 22.01/4.57
% 22.01/4.57 % (10015)Memory used [KB]: 7547
% 22.01/4.57 % (10015)Time elapsed: 0.096 s
% 22.01/4.57 % (10015)Instructions burned: 204 (million)
% 22.01/4.57 % (10015)------------------------------
% 22.01/4.57 % (10015)------------------------------
% 22.01/4.58 % (10017)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_9795 for (2971ds/770Mi)
% 22.53/4.60 % (10017)Refutation not found, incomplete strategy
% 22.53/4.60 % (10017)------------------------------
% 22.53/4.60 % (10017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.53/4.60 % (10017)Termination reason: Refutation not found, incomplete strategy
% 22.53/4.60
% 22.53/4.60
% 22.53/4.60 % (10017)Memory used [KB]: 6396
% 22.53/4.60 % (10017)Time elapsed: 0.022 s
% 22.53/4.60 % (10017)Instructions burned: 39 (million)
% 22.53/4.60 % (10017)------------------------------
% 22.53/4.60 % (10017)------------------------------
% 22.53/4.62 % (10018)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_9795 for (2971ds/794Mi)
% 23.47/4.91 % (10014)Instruction limit reached!
% 23.47/4.91 % (10014)------------------------------
% 23.47/4.91 % (10014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.47/4.91 % (10014)Termination reason: Unknown
% 23.47/4.91 % (10014)Termination phase: Saturation
% 23.47/4.91
% 23.47/4.91 % (10014)Memory used [KB]: 9722
% 23.47/4.91 % (10014)Time elapsed: 0.447 s
% 23.47/4.91 % (10014)Instructions burned: 932 (million)
% 23.47/4.91 % (10014)------------------------------
% 23.47/4.91 % (10014)------------------------------
% 23.47/4.92 % (10019)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_9795 for (2968ds/464Mi)
% 23.47/5.02 % (10018)Instruction limit reached!
% 23.47/5.02 % (10018)------------------------------
% 23.47/5.02 % (10018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.47/5.02 % (10018)Termination reason: Unknown
% 23.47/5.02 % (10018)Termination phase: Saturation
% 23.47/5.02
% 23.47/5.02 % (10018)Memory used [KB]: 4989
% 23.47/5.02 % (10018)Time elapsed: 0.394 s
% 23.47/5.02 % (10018)Instructions burned: 795 (million)
% 23.47/5.02 % (10018)------------------------------
% 23.47/5.02 % (10018)------------------------------
% 25.95/5.04 % (10020)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_9795 for (2967ds/1376Mi)
% 26.59/5.15 % (10019)Instruction limit reached!
% 26.59/5.15 % (10019)------------------------------
% 26.59/5.15 % (10019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.59/5.15 % (10019)Termination reason: Unknown
% 26.59/5.15 % (10019)Termination phase: Saturation
% 26.59/5.15
% 26.59/5.15 % (10019)Memory used [KB]: 7547
% 26.59/5.15 % (10019)Time elapsed: 0.223 s
% 26.59/5.15 % (10019)Instructions burned: 465 (million)
% 26.59/5.15 % (10019)------------------------------
% 26.59/5.15 % (10019)------------------------------
% 26.59/5.16 % (10021)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_9795 for (2966ds/906Mi)
% 26.98/5.28 % (9990)Instruction limit reached!
% 26.98/5.28 % (9990)------------------------------
% 26.98/5.28 % (9990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.98/5.28 % (9990)Termination reason: Unknown
% 26.98/5.28 % (9990)Termination phase: Saturation
% 26.98/5.28
% 26.98/5.28 % (9990)Memory used [KB]: 10618
% 26.98/5.28 % (9990)Time elapsed: 2.153 s
% 26.98/5.28 % (9990)Instructions burned: 4437 (million)
% 26.98/5.28 % (9990)------------------------------
% 26.98/5.28 % (9990)------------------------------
% 27.47/5.30 % (10022)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_9795 for (2964ds/434Mi)
% 27.47/5.30 % (10011)Instruction limit reached!
% 27.47/5.30 % (10011)------------------------------
% 27.47/5.30 % (10011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.47/5.31 % (10011)Termination reason: Unknown
% 27.47/5.31 % (10011)Termination phase: Saturation
% 27.47/5.31
% 27.47/5.31 % (10011)Memory used [KB]: 10234
% 27.47/5.31 % (10011)Time elapsed: 0.921 s
% 27.47/5.31 % (10011)Instructions burned: 1828 (million)
% 27.47/5.31 % (10011)------------------------------
% 27.47/5.31 % (10011)------------------------------
% 27.47/5.32 % (10023)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_9795 for (2964ds/865Mi)
% 27.47/5.36 % (9995)Instruction limit reached!
% 27.47/5.36 % (9995)------------------------------
% 27.47/5.36 % (9995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.47/5.36 % (9995)Termination reason: Unknown
% 27.47/5.36 % (9995)Termination phase: Saturation
% 27.47/5.36
% 27.47/5.36 % (9995)Memory used [KB]: 10874
% 27.47/5.36 % (9995)Time elapsed: 1.958 s
% 27.47/5.36 % (9995)Instructions burned: 4352 (million)
% 27.47/5.36 % (9995)------------------------------
% 27.47/5.36 % (9995)------------------------------
% 27.47/5.37 % (10024)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_9795 for (2964ds/593Mi)
% 27.96/5.50 % (10022)Instruction limit reached!
% 27.96/5.50 % (10022)------------------------------
% 27.96/5.50 % (10022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.96/5.50 % (10022)Termination reason: Unknown
% 27.96/5.50 % (10022)Termination phase: Saturation
% 27.96/5.50
% 27.96/5.50 % (10022)Memory used [KB]: 7547
% 27.96/5.50 % (10022)Time elapsed: 0.205 s
% 27.96/5.50 % (10022)Instructions burned: 435 (million)
% 27.96/5.50 % (10022)------------------------------
% 27.96/5.50 % (10022)------------------------------
% 27.96/5.52 % (10025)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_9795 for (2962ds/443Mi)
% 28.38/5.62 % (9993)Instruction limit reached!
% 28.38/5.62 % (9993)------------------------------
% 28.38/5.62 % (9993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.38/5.62 % (9993)Termination reason: Unknown
% 28.38/5.62 % (9993)Termination phase: Saturation
% 28.38/5.62
% 28.38/5.62 % (9993)Memory used [KB]: 14583
% 28.38/5.62 % (9993)Time elapsed: 2.422 s
% 28.38/5.62 % (9993)Instructions burned: 5206 (million)
% 28.38/5.62 % (9993)------------------------------
% 28.38/5.62 % (9993)------------------------------
% 28.38/5.63 % (10021)Instruction limit reached!
% 28.38/5.63 % (10021)------------------------------
% 28.38/5.63 % (10021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.38/5.63 % (10021)Termination reason: Unknown
% 28.38/5.63 % (10021)Termination phase: Saturation
% 28.38/5.63
% 28.38/5.63 % (10021)Memory used [KB]: 10874
% 28.38/5.63 % (10021)Time elapsed: 0.469 s
% 28.38/5.63 % (10021)Instructions burned: 907 (million)
% 28.38/5.63 % (10021)------------------------------
% 28.38/5.63 % (10021)------------------------------
% 28.38/5.64 % (10026)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_9795 for (2961ds/594Mi)
% 28.38/5.65 % (10027)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_9795 for (2961ds/327Mi)
% 28.38/5.66 % (10024)Instruction limit reached!
% 28.38/5.66 % (10024)------------------------------
% 28.38/5.66 % (10024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.38/5.66 % (10024)Termination reason: Unknown
% 28.38/5.66 % (10024)Termination phase: Saturation
% 28.38/5.66
% 28.38/5.66 % (10024)Memory used [KB]: 8443
% 28.38/5.66 % (10024)Time elapsed: 0.283 s
% 28.38/5.66 % (10024)Instructions burned: 594 (million)
% 28.38/5.66 % (10024)------------------------------
% 28.38/5.66 % (10024)------------------------------
% 28.38/5.67 % (10028)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_9795 for (2961ds/5411Mi)
% 28.38/5.70 % (10028)Refutation not found, incomplete strategy
% 28.38/5.70 % (10028)------------------------------
% 28.38/5.70 % (10028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.38/5.70 % (10028)Termination reason: Refutation not found, incomplete strategy
% 28.38/5.70
% 28.38/5.70
% 28.38/5.70 % (10028)Memory used [KB]: 6396
% 28.38/5.70 % (10028)Time elapsed: 0.025 s
% 28.38/5.70 % (10028)Instructions burned: 48 (million)
% 28.38/5.70 % (10028)------------------------------
% 28.38/5.70 % (10028)------------------------------
% 29.29/5.70 % (10020)Instruction limit reached!
% 29.29/5.70 % (10020)------------------------------
% 29.29/5.70 % (10020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.29/5.70 % (10020)Termination reason: Unknown
% 29.29/5.70 % (10020)Termination phase: Saturation
% 29.29/5.70
% 29.29/5.70 % (10020)Memory used [KB]: 13176
% 29.29/5.70 % (10020)Time elapsed: 0.667 s
% 29.29/5.70 % (10020)Instructions burned: 1377 (million)
% 29.29/5.70 % (10020)------------------------------
% 29.29/5.70 % (10020)------------------------------
% 29.29/5.71 % (10029)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_9795 for (2960ds/1762Mi)
% 29.29/5.72 % (10030)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_9795 for (2960ds/96Mi)
% 29.29/5.73 % (10023)Instruction limit reached!
% 29.29/5.73 % (10023)------------------------------
% 29.29/5.73 % (10023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.29/5.73 % (10023)Termination reason: Unknown
% 29.29/5.73 % (10023)Termination phase: Saturation
% 29.29/5.73
% 29.29/5.73 % (10023)Memory used [KB]: 9083
% 29.29/5.73 % (10023)Time elapsed: 0.406 s
% 29.29/5.73 % (10023)Instructions burned: 866 (million)
% 29.29/5.73 % (10023)------------------------------
% 29.29/5.73 % (10023)------------------------------
% 29.29/5.74 % (10031)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_9795 for (2960ds/503Mi)
% 29.29/5.75 % (10025)Instruction limit reached!
% 29.29/5.75 % (10025)------------------------------
% 29.29/5.75 % (10025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.29/5.75 % (10025)Termination reason: Unknown
% 29.29/5.75 % (10025)Termination phase: Saturation
% 29.29/5.75
% 29.29/5.75 % (10025)Memory used [KB]: 7547
% 29.29/5.75 % (10025)Time elapsed: 0.232 s
% 29.29/5.75 % (10025)Instructions burned: 444 (million)
% 29.29/5.75 % (10025)------------------------------
% 29.29/5.75 % (10025)------------------------------
% 29.29/5.77 % (10030)Instruction limit reached!
% 29.29/5.77 % (10030)------------------------------
% 29.29/5.77 % (10030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.29/5.77 % (10030)Termination reason: Unknown
% 29.29/5.77 % (10030)Termination phase: Property scanning
% 29.29/5.77
% 29.29/5.77 % (10030)Memory used [KB]: 2174
% 29.29/5.77 % (10030)Time elapsed: 0.045 s
% 29.29/5.77 % (10030)Instructions burned: 97 (million)
% 29.29/5.77 % (10030)------------------------------
% 29.29/5.77 % (10030)------------------------------
% 29.29/5.77 % (10032)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_9795 for (2960ds/90Mi)
% 29.29/5.78 % (10033)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_9795 for (2960ds/593Mi)
% 30.83/5.81 % (10027)Instruction limit reached!
% 30.83/5.81 % (10027)------------------------------
% 30.83/5.81 % (10027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.83/5.81 % (10027)Termination reason: Unknown
% 30.83/5.81 % (10027)Termination phase: Saturation
% 30.83/5.81
% 30.83/5.81 % (10027)Memory used [KB]: 7675
% 30.83/5.81 % (10027)Time elapsed: 0.164 s
% 30.83/5.81 % (10027)Instructions burned: 328 (million)
% 30.83/5.81 % (10027)------------------------------
% 30.83/5.81 % (10027)------------------------------
% 30.83/5.81 % (10032)Instruction limit reached!
% 30.83/5.81 % (10032)------------------------------
% 30.83/5.81 % (10032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.83/5.81 % (10032)Termination reason: Unknown
% 30.83/5.81 % (10032)Termination phase: Saturation
% 30.83/5.81
% 30.83/5.81 % (10032)Memory used [KB]: 6780
% 30.83/5.81 % (10032)Time elapsed: 0.044 s
% 30.83/5.81 % (10032)Instructions burned: 91 (million)
% 30.83/5.81 % (10032)------------------------------
% 30.83/5.81 % (10032)------------------------------
% 30.83/5.83 % (10034)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_9795 for (2959ds/1512Mi)
% 30.83/5.83 % (10035)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_9795 for (2959ds/569Mi)
% 31.18/5.93 % (10026)Instruction limit reached!
% 31.18/5.93 % (10026)------------------------------
% 31.18/5.93 % (10026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.18/5.93 % (10026)Termination reason: Unknown
% 31.18/5.93 % (10026)Termination phase: Saturation
% 31.18/5.93
% 31.18/5.93 % (10026)Memory used [KB]: 7931
% 31.18/5.93 % (10026)Time elapsed: 0.293 s
% 31.18/5.93 % (10026)Instructions burned: 594 (million)
% 31.18/5.93 % (10026)------------------------------
% 31.18/5.93 % (10026)------------------------------
% 31.18/5.95 % (10036)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_9795 for (2958ds/501Mi)
% 31.18/5.98 % (10031)Instruction limit reached!
% 31.18/5.98 % (10031)------------------------------
% 31.18/5.98 % (10031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.18/5.98 % (10031)Termination reason: Unknown
% 31.18/5.98 % (10031)Termination phase: Saturation
% 31.18/5.98
% 31.18/5.98 % (10031)Memory used [KB]: 7803
% 31.18/5.98 % (10031)Time elapsed: 0.263 s
% 31.18/5.98 % (10031)Instructions burned: 503 (million)
% 31.18/5.98 % (10031)------------------------------
% 31.18/5.98 % (10031)------------------------------
% 31.18/6.00 % (10037)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_9795 for (2957ds/562Mi)
% 32.95/6.06 % (10033)Instruction limit reached!
% 32.95/6.06 % (10033)------------------------------
% 32.95/6.06 % (10033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.95/6.06 % (10033)Termination reason: Unknown
% 32.95/6.06 % (10033)Termination phase: Saturation
% 32.95/6.06
% 32.95/6.06 % (10033)Memory used [KB]: 7803
% 32.95/6.06 % (10033)Time elapsed: 0.285 s
% 32.95/6.06 % (10033)Instructions burned: 593 (million)
% 32.95/6.06 % (10033)------------------------------
% 32.95/6.06 % (10033)------------------------------
% 32.95/6.08 % (10038)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_9795 for (2956ds/406Mi)
% 32.95/6.09 % (10035)Instruction limit reached!
% 32.95/6.09 % (10035)------------------------------
% 32.95/6.09 % (10035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.95/6.09 % (10035)Termination reason: Unknown
% 32.95/6.09 % (10035)Termination phase: Saturation
% 32.95/6.09
% 32.95/6.09 % (10035)Memory used [KB]: 7803
% 32.95/6.09 % (10035)Time elapsed: 0.269 s
% 32.95/6.09 % (10035)Instructions burned: 570 (million)
% 32.95/6.09 % (10035)------------------------------
% 32.95/6.09 % (10035)------------------------------
% 32.95/6.11 % (10039)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_9795 for (2956ds/582Mi)
% 33.61/6.19 % (10036)Instruction limit reached!
% 33.61/6.19 % (10036)------------------------------
% 33.61/6.19 % (10036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.61/6.19 % (10036)Termination reason: Unknown
% 33.61/6.19 % (10036)Termination phase: Saturation
% 33.61/6.19
% 33.61/6.19 % (10036)Memory used [KB]: 8315
% 33.61/6.19 % (10036)Time elapsed: 0.243 s
% 33.61/6.19 % (10036)Instructions burned: 501 (million)
% 33.61/6.19 % (10036)------------------------------
% 33.61/6.19 % (10036)------------------------------
% 33.97/6.21 % (10040)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_9795 for (2955ds/456Mi)
% 33.97/6.27 % (10037)Instruction limit reached!
% 33.97/6.27 % (10037)------------------------------
% 33.97/6.27 % (10037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.97/6.27 % (10037)Termination reason: Unknown
% 33.97/6.27 % (10037)Termination phase: Saturation
% 33.97/6.27
% 33.97/6.27 % (10037)Memory used [KB]: 7675
% 33.97/6.27 % (10037)Time elapsed: 0.270 s
% 33.97/6.27 % (10037)Instructions burned: 563 (million)
% 33.97/6.27 % (10037)------------------------------
% 33.97/6.27 % (10037)------------------------------
% 33.97/6.28 % (10038)Instruction limit reached!
% 33.97/6.28 % (10038)------------------------------
% 33.97/6.28 % (10038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.97/6.28 % (10038)Termination reason: Unknown
% 33.97/6.28 % (10038)Termination phase: Saturation
% 33.97/6.28
% 33.97/6.28 % (10038)Memory used [KB]: 7803
% 33.97/6.28 % (10038)Time elapsed: 0.204 s
% 33.97/6.28 % (10038)Instructions burned: 406 (million)
% 33.97/6.28 % (10038)------------------------------
% 33.97/6.28 % (10038)------------------------------
% 33.97/6.29 % (10041)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_9795 for (2954ds/393Mi)
% 34.56/6.30 % (10042)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_9795 for (2954ds/1335Mi)
% 34.87/6.40 % (10039)Instruction limit reached!
% 34.87/6.40 % (10039)------------------------------
% 34.87/6.40 % (10039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.87/6.40 % (10039)Termination reason: Unknown
% 34.87/6.40 % (10039)Termination phase: Saturation
% 34.87/6.40
% 34.87/6.40 % (10039)Memory used [KB]: 8059
% 34.87/6.40 % (10039)Time elapsed: 0.293 s
% 34.87/6.40 % (10039)Instructions burned: 582 (million)
% 34.87/6.40 % (10039)------------------------------
% 34.87/6.40 % (10039)------------------------------
% 34.87/6.42 % (10043)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_9795 for (2953ds/3373Mi)
% 34.87/6.42 % (10040)Instruction limit reached!
% 34.87/6.42 % (10040)------------------------------
% 34.87/6.42 % (10040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.87/6.42 % (10040)Termination reason: Unknown
% 34.87/6.42 % (10040)Termination phase: Saturation
% 34.87/6.42
% 34.87/6.42 % (10040)Memory used [KB]: 7547
% 34.87/6.42 % (10040)Time elapsed: 0.220 s
% 34.87/6.42 % (10040)Instructions burned: 456 (million)
% 34.87/6.42 % (10040)------------------------------
% 34.87/6.42 % (10040)------------------------------
% 34.87/6.44 % (10044)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_9795 for (2953ds/474Mi)
% 34.87/6.47 % (10041)Instruction limit reached!
% 34.87/6.47 % (10041)------------------------------
% 34.87/6.47 % (10041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.87/6.47 % (10041)Termination reason: Unknown
% 34.87/6.47 % (10041)Termination phase: Saturation
% 34.87/6.47
% 34.87/6.47 % (10041)Memory used [KB]: 7419
% 34.87/6.47 % (10041)Time elapsed: 0.185 s
% 34.87/6.47 % (10041)Instructions burned: 393 (million)
% 34.87/6.47 % (10041)------------------------------
% 34.87/6.47 % (10041)------------------------------
% 34.87/6.49 % (10045)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_9795 for (2952ds/157Mi)
% 35.91/6.55 % (10029)Instruction limit reached!
% 35.91/6.55 % (10029)------------------------------
% 35.91/6.55 % (10029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.91/6.55 % (10029)Termination reason: Unknown
% 35.91/6.55 % (10029)Termination phase: Saturation
% 35.91/6.55
% 35.91/6.55 % (10029)Memory used [KB]: 10362
% 35.91/6.55 % (10029)Time elapsed: 0.856 s
% 35.91/6.55 % (10029)Instructions burned: 1763 (million)
% 35.91/6.55 % (10029)------------------------------
% 35.91/6.55 % (10029)------------------------------
% 35.91/6.56 % (10045)Instruction limit reached!
% 35.91/6.56 % (10045)------------------------------
% 35.91/6.56 % (10045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.91/6.56 % (10045)Termination reason: Unknown
% 35.91/6.56 % (10045)Termination phase: Saturation
% 35.91/6.56
% 35.91/6.56 % (10045)Memory used [KB]: 6908
% 35.91/6.56 % (10045)Time elapsed: 0.073 s
% 35.91/6.56 % (10045)Instructions burned: 158 (million)
% 35.91/6.56 % (10045)------------------------------
% 35.91/6.56 % (10045)------------------------------
% 35.91/6.56 % (10046)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_9795 for (2952ds/590Mi)
% 35.91/6.56 % (10034)Instruction limit reached!
% 35.91/6.56 % (10034)------------------------------
% 35.91/6.56 % (10034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.91/6.56 % (10034)Termination reason: Unknown
% 35.91/6.56 % (10034)Termination phase: Saturation
% 35.91/6.56
% 35.91/6.56 % (10034)Memory used [KB]: 8699
% 35.91/6.56 % (10034)Time elapsed: 0.740 s
% 35.91/6.56 % (10034)Instructions burned: 1513 (million)
% 35.91/6.56 % (10034)------------------------------
% 35.91/6.56 % (10034)------------------------------
% 35.91/6.57 % (10047)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_9795 for (2952ds/104Mi)
% 35.91/6.58 % (10048)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_9795 for (2951ds/414Mi)
% 36.23/6.62 % (10047)Instruction limit reached!
% 36.23/6.62 % (10047)------------------------------
% 36.23/6.62 % (10047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.23/6.62 % (10047)Termination reason: Unknown
% 36.23/6.62 % (10047)Termination phase: Saturation
% 36.23/6.62
% 36.23/6.62 % (10047)Memory used [KB]: 2558
% 36.23/6.62 % (10047)Time elapsed: 0.051 s
% 36.23/6.62 % (10047)Instructions burned: 104 (million)
% 36.23/6.62 % (10047)------------------------------
% 36.23/6.62 % (10047)------------------------------
% 36.23/6.64 % (10049)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_9795 for (2951ds/715Mi)
% 36.23/6.68 % (10044)Instruction limit reached!
% 36.23/6.68 % (10044)------------------------------
% 36.23/6.68 % (10044)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.23/6.68 % (10044)Termination reason: Unknown
% 36.23/6.68 % (10044)Termination phase: Saturation
% 36.23/6.68
% 36.23/6.68 % (10044)Memory used [KB]: 8059
% 36.23/6.68 % (10044)Time elapsed: 0.236 s
% 36.23/6.68 % (10044)Instructions burned: 476 (million)
% 36.23/6.68 % (10044)------------------------------
% 36.23/6.68 % (10044)------------------------------
% 36.23/6.69 % (10050)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_9795 for (2950ds/961Mi)
% 36.64/6.78 % (10048)Instruction limit reached!
% 36.64/6.78 % (10048)------------------------------
% 36.64/6.78 % (10048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.64/6.78 % (10048)Termination reason: Unknown
% 36.64/6.78 % (10048)Termination phase: Saturation
% 36.64/6.78
% 36.64/6.78 % (10048)Memory used [KB]: 7547
% 36.64/6.78 % (10048)Time elapsed: 0.197 s
% 36.64/6.78 % (10048)Instructions burned: 414 (million)
% 36.64/6.78 % (10048)------------------------------
% 36.64/6.78 % (10048)------------------------------
% 36.64/6.79 % (10051)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_9795 for (2949ds/1213Mi)
% 36.97/6.84 % (10046)Instruction limit reached!
% 36.97/6.84 % (10046)------------------------------
% 36.97/6.84 % (10046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.97/6.84 % (10046)Termination reason: Unknown
% 36.97/6.84 % (10046)Termination phase: Saturation
% 36.97/6.84
% 36.97/6.84 % (10046)Memory used [KB]: 8059
% 36.97/6.84 % (10046)Time elapsed: 0.282 s
% 36.97/6.84 % (10046)Instructions burned: 591 (million)
% 36.97/6.84 % (10046)------------------------------
% 36.97/6.84 % (10046)------------------------------
% 36.97/6.86 % (10052)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_9795 for (2949ds/1979Mi)
% 37.36/6.94 % (10042)Instruction limit reached!
% 37.36/6.94 % (10042)------------------------------
% 37.36/6.94 % (10042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.36/6.94 % (10042)Termination reason: Unknown
% 37.36/6.94 % (10042)Termination phase: Saturation
% 37.36/6.94
% 37.36/6.94 % (10042)Memory used [KB]: 8443
% 37.36/6.94 % (10042)Time elapsed: 0.645 s
% 37.36/6.94 % (10042)Instructions burned: 1335 (million)
% 37.36/6.94 % (10042)------------------------------
% 37.36/6.94 % (10042)------------------------------
% 37.36/6.96 % (10053)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_9795 for (2948ds/481Mi)
% 37.36/6.99 % (10049)Instruction limit reached!
% 37.36/6.99 % (10049)------------------------------
% 37.36/6.99 % (10049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.36/6.99 % (10049)Termination reason: Unknown
% 37.36/6.99 % (10049)Termination phase: Saturation
% 37.36/6.99
% 37.36/6.99 % (10049)Memory used [KB]: 4349
% 37.36/6.99 % (10049)Time elapsed: 0.355 s
% 37.36/6.99 % (10049)Instructions burned: 715 (million)
% 37.36/6.99 % (10049)------------------------------
% 37.36/6.99 % (10049)------------------------------
% 37.36/7.01 % (10054)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_9795 for (2947ds/783Mi)
% 40.66/7.15 % (10050)Instruction limit reached!
% 40.66/7.15 % (10050)------------------------------
% 40.66/7.15 % (10050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.66/7.15 % (10050)Termination reason: Unknown
% 40.66/7.15 % (10050)Termination phase: Saturation
% 40.66/7.15
% 40.66/7.15 % (10050)Memory used [KB]: 8315
% 40.66/7.15 % (10050)Time elapsed: 0.464 s
% 40.66/7.15 % (10050)Instructions burned: 961 (million)
% 40.66/7.15 % (10050)------------------------------
% 40.66/7.15 % (10050)------------------------------
% 40.66/7.17 % (10055)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_9795 for (2946ds/432Mi)
% 41.14/7.20 % (10053)Instruction limit reached!
% 41.14/7.20 % (10053)------------------------------
% 41.14/7.20 % (10053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.14/7.20 % (10053)Termination reason: Unknown
% 41.14/7.20 % (10053)Termination phase: Saturation
% 41.14/7.20
% 41.14/7.20 % (10053)Memory used [KB]: 7803
% 41.14/7.20 % (10053)Time elapsed: 0.243 s
% 41.14/7.20 % (10053)Instructions burned: 481 (million)
% 41.14/7.20 % (10053)------------------------------
% 41.14/7.20 % (10053)------------------------------
% 41.14/7.22 % (10056)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_9795 for (2945ds/1670Mi)
% 41.65/7.37 % (10055)Instruction limit reached!
% 41.65/7.37 % (10055)------------------------------
% 41.65/7.37 % (10055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.65/7.37 % (10055)Termination reason: Unknown
% 41.65/7.37 % (10055)Termination phase: Saturation
% 41.65/7.37
% 41.65/7.37 % (10055)Memory used [KB]: 7803
% 41.65/7.37 % (10055)Time elapsed: 0.203 s
% 41.65/7.37 % (10055)Instructions burned: 432 (million)
% 41.65/7.37 % (10055)------------------------------
% 41.65/7.37 % (10055)------------------------------
% 41.65/7.38 % (10054)Instruction limit reached!
% 41.65/7.38 % (10054)------------------------------
% 41.65/7.38 % (10054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.65/7.38 % (10054)Termination reason: Unknown
% 41.65/7.38 % (10054)Termination phase: Saturation
% 41.65/7.38
% 41.65/7.38 % (10054)Memory used [KB]: 8059
% 41.65/7.38 % (10054)Time elapsed: 0.376 s
% 41.65/7.38 % (10054)Instructions burned: 783 (million)
% 41.65/7.38 % (10054)------------------------------
% 41.65/7.38 % (10054)------------------------------
% 41.65/7.39 % (10057)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_9795 for (2943ds/90Mi)
% 42.36/7.40 % (10051)Instruction limit reached!
% 42.36/7.40 % (10051)------------------------------
% 42.36/7.40 % (10051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.36/7.40 % (10051)Termination reason: Unknown
% 42.36/7.40 % (10051)Termination phase: Saturation
% 42.36/7.40
% 42.36/7.40 % (10051)Memory used [KB]: 9083
% 42.36/7.40 % (10051)Time elapsed: 0.608 s
% 42.36/7.40 % (10051)Instructions burned: 1213 (million)
% 42.36/7.40 % (10051)------------------------------
% 42.36/7.40 % (10051)------------------------------
% 42.36/7.40 % (10058)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_9795 for (2943ds/346Mi)
% 42.36/7.42 % (10059)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_9795 for (2943ds/401Mi)
% 42.36/7.43 % (10057)Instruction limit reached!
% 42.36/7.43 % (10057)------------------------------
% 42.36/7.43 % (10057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.36/7.43 % (10057)Termination reason: Unknown
% 42.36/7.43 % (10057)Termination phase: Saturation
% 42.36/7.43
% 42.36/7.43 % (10057)Memory used [KB]: 6780
% 42.36/7.43 % (10057)Time elapsed: 0.045 s
% 42.36/7.43 % (10057)Instructions burned: 90 (million)
% 42.36/7.43 % (10057)------------------------------
% 42.36/7.43 % (10057)------------------------------
% 42.36/7.45 % (10060)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_9795 for (2943ds/6454Mi)
% 42.73/7.57 % (10058)Instruction limit reached!
% 42.73/7.57 % (10058)------------------------------
% 42.73/7.57 % (10058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.73/7.57 % (10058)Termination reason: Unknown
% 42.73/7.57 % (10058)Termination phase: Saturation
% 42.73/7.57
% 42.73/7.57 % (10058)Memory used [KB]: 7675
% 42.73/7.57 % (10058)Time elapsed: 0.170 s
% 42.73/7.57 % (10058)Instructions burned: 346 (million)
% 42.73/7.57 % (10058)------------------------------
% 42.73/7.57 % (10058)------------------------------
% 42.73/7.58 % (10061)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_9795 for (2941ds/283Mi)
% 43.22/7.60 % (10059)Instruction limit reached!
% 43.22/7.60 % (10059)------------------------------
% 43.22/7.60 % (10059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.22/7.60 % (10059)Termination reason: Unknown
% 43.22/7.60 % (10059)Termination phase: Saturation
% 43.22/7.60
% 43.22/7.60 % (10059)Memory used [KB]: 8059
% 43.22/7.60 % (10059)Time elapsed: 0.190 s
% 43.22/7.60 % (10059)Instructions burned: 401 (million)
% 43.22/7.60 % (10059)------------------------------
% 43.22/7.60 % (10059)------------------------------
% 43.22/7.63 % (10062)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_9795 for (2941ds/865Mi)
% 43.72/7.74 % (10061)Instruction limit reached!
% 43.72/7.74 % (10061)------------------------------
% 43.72/7.74 % (10061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.72/7.74 % (10061)Termination reason: Unknown
% 43.72/7.74 % (10061)Termination phase: Saturation
% 43.72/7.74
% 43.72/7.74 % (10061)Memory used [KB]: 7547
% 43.72/7.74 % (10061)Time elapsed: 0.173 s
% 43.72/7.74 % (10061)Instructions burned: 285 (million)
% 43.72/7.74 % (10061)------------------------------
% 43.72/7.74 % (10061)------------------------------
% 43.72/7.76 % (10063)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_9795 for (2940ds/4528Mi)
% 43.72/7.78 % (10063)Refutation not found, incomplete strategy
% 43.72/7.78 % (10063)------------------------------
% 43.72/7.78 % (10063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.72/7.78 % (10063)Termination reason: Refutation not found, incomplete strategy
% 43.72/7.78
% 43.72/7.78
% 43.72/7.78 % (10063)Memory used [KB]: 1791
% 43.72/7.78 % (10063)Time elapsed: 0.021 s
% 43.72/7.78 % (10063)Instructions burned: 39 (million)
% 43.72/7.78 % (10063)------------------------------
% 43.72/7.78 % (10063)------------------------------
% 44.16/7.81 % (10052)Instruction limit reached!
% 44.16/7.81 % (10052)------------------------------
% 44.16/7.81 % (10052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.16/7.81 % (10052)Termination reason: Unknown
% 44.16/7.81 % (10052)Termination phase: Saturation
% 44.16/7.81
% 44.16/7.81 % (10052)Memory used [KB]: 8571
% 44.16/7.81 % (10052)Time elapsed: 0.952 s
% 44.16/7.81 % (10052)Instructions burned: 1980 (million)
% 44.16/7.81 % (10052)------------------------------
% 44.16/7.81 % (10052)------------------------------
% 44.16/7.81 % (10064)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_9795 for (2939ds/1001Mi)
% 44.16/7.83 % (10065)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_9795 for (2939ds/102Mi)
% 44.16/7.87 % (10065)Instruction limit reached!
% 44.16/7.87 % (10065)------------------------------
% 44.16/7.87 % (10065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.16/7.87 % (10065)Termination reason: Unknown
% 44.16/7.87 % (10065)Termination phase: Saturation
% 44.16/7.87
% 44.16/7.87 % (10065)Memory used [KB]: 2174
% 44.16/7.87 % (10065)Time elapsed: 0.048 s
% 44.16/7.87 % (10065)Instructions burned: 103 (million)
% 44.16/7.87 % (10065)------------------------------
% 44.16/7.87 % (10065)------------------------------
% 44.16/7.89 % (10066)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_9795 for (2938ds/952Mi)
% 44.45/8.01 % (10062)Instruction limit reached!
% 44.45/8.01 % (10062)------------------------------
% 44.45/8.01 % (10062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 44.45/8.01 % (10062)Termination reason: Unknown
% 44.45/8.01 % (10062)Termination phase: Saturation
% 44.45/8.01
% 44.45/8.01 % (10062)Memory used [KB]: 8955
% 44.45/8.01 % (10062)Time elapsed: 0.398 s
% 44.45/8.01 % (10062)Instructions burned: 865 (million)
% 44.45/8.01 % (10062)------------------------------
% 44.45/8.01 % (10062)------------------------------
% 46.62/8.03 % (10067)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_9795 for (2937ds/578Mi)
% 46.62/8.03 % (10056)Instruction limit reached!
% 46.62/8.03 % (10056)------------------------------
% 46.62/8.03 % (10056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.62/8.03 % (10056)Termination reason: Unknown
% 46.62/8.03 % (10056)Termination phase: Saturation
% 46.62/8.03
% 46.62/8.03 % (10056)Memory used [KB]: 9722
% 46.62/8.03 % (10056)Time elapsed: 0.814 s
% 46.62/8.03 % (10056)Instructions burned: 1671 (million)
% 46.62/8.03 % (10056)------------------------------
% 46.62/8.03 % (10056)------------------------------
% 46.62/8.05 % (10068)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_9795 for (2937ds/643Mi)
% 46.62/8.07 % (10043)Instruction limit reached!
% 46.62/8.07 % (10043)------------------------------
% 46.62/8.07 % (10043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 46.62/8.07 % (10043)Termination reason: Unknown
% 46.62/8.07 % (10043)Termination phase: Saturation
% 46.62/8.07
% 46.62/8.07 % (10043)Memory used [KB]: 11769
% 46.62/8.07 % (10043)Time elapsed: 1.652 s
% 46.62/8.07 % (10043)Instructions burned: 3374 (million)
% 46.62/8.07 % (10043)------------------------------
% 46.62/8.07 % (10043)------------------------------
% 46.62/8.09 % (10069)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_9795 for (2937ds/865Mi)
% 47.85/8.30 % (10067)Instruction limit reached!
% 47.85/8.30 % (10067)------------------------------
% 47.85/8.30 % (10067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.85/8.30 % (10067)Termination reason: Unknown
% 47.85/8.30 % (10067)Termination phase: Saturation
% 47.85/8.30
% 47.85/8.30 % (10067)Memory used [KB]: 8827
% 47.85/8.30 % (10067)Time elapsed: 0.273 s
% 47.85/8.30 % (10067)Instructions burned: 579 (million)
% 47.85/8.30 % (10067)------------------------------
% 47.85/8.30 % (10067)------------------------------
% 47.85/8.31 % (10064)Instruction limit reached!
% 47.85/8.31 % (10064)------------------------------
% 47.85/8.31 % (10064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.85/8.31 % (10064)Termination reason: Unknown
% 47.85/8.31 % (10064)Termination phase: Saturation
% 47.85/8.31
% 47.85/8.31 % (10064)Memory used [KB]: 9210
% 47.85/8.31 % (10064)Time elapsed: 0.536 s
% 47.85/8.31 % (10064)Instructions burned: 1001 (million)
% 47.85/8.31 % (10064)------------------------------
% 47.85/8.31 % (10064)------------------------------
% 47.85/8.32 % (10070)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_9795 for (2934ds/1174Mi)
% 47.85/8.33 % (10071)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_9795 for (2934ds/644Mi)
% 47.85/8.35 % (10066)Instruction limit reached!
% 47.85/8.35 % (10066)------------------------------
% 47.85/8.35 % (10066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.85/8.35 % (10066)Termination reason: Unknown
% 47.85/8.35 % (10066)Termination phase: Saturation
% 47.85/8.35
% 47.85/8.35 % (10066)Memory used [KB]: 8443
% 47.85/8.35 % (10066)Time elapsed: 0.466 s
% 47.85/8.35 % (10066)Instructions burned: 953 (million)
% 47.85/8.35 % (10066)------------------------------
% 47.85/8.35 % (10066)------------------------------
% 47.85/8.36 % (10068)Instruction limit reached!
% 47.85/8.36 % (10068)------------------------------
% 47.85/8.36 % (10068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.85/8.36 % (10068)Termination reason: Unknown
% 47.85/8.36 % (10068)Termination phase: Saturation
% 47.85/8.36
% 47.85/8.36 % (10068)Memory used [KB]: 9083
% 47.85/8.36 % (10068)Time elapsed: 0.310 s
% 47.85/8.36 % (10068)Instructions burned: 644 (million)
% 47.85/8.36 % (10068)------------------------------
% 47.85/8.36 % (10068)------------------------------
% 47.85/8.37 % (10072)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_9795 for (2934ds/1201Mi)
% 47.85/8.37 % (10073)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_9795 for (2934ds/1046Mi)
% 48.96/8.51 % (10069)Instruction limit reached!
% 48.96/8.51 % (10069)------------------------------
% 48.96/8.51 % (10069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.96/8.51 % (10069)Termination reason: Unknown
% 48.96/8.51 % (10069)Termination phase: Saturation
% 48.96/8.51
% 48.96/8.51 % (10069)Memory used [KB]: 9083
% 48.96/8.51 % (10069)Time elapsed: 0.443 s
% 48.96/8.51 % (10069)Instructions burned: 865 (million)
% 48.96/8.51 % (10069)------------------------------
% 48.96/8.51 % (10069)------------------------------
% 48.96/8.52 % (10074)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_9795 for (2932ds/222Mi)
% 48.96/8.54 % (10016)Instruction limit reached!
% 48.96/8.54 % (10016)------------------------------
% 48.96/8.54 % (10016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.96/8.54 % (10016)Termination reason: Unknown
% 48.96/8.54 % (10016)Termination phase: Saturation
% 48.96/8.54
% 48.96/8.54 % (10016)Memory used [KB]: 14967
% 48.96/8.54 % (10016)Time elapsed: 4.013 s
% 48.96/8.54 % (10016)Instructions burned: 8251 (million)
% 48.96/8.54 % (10016)------------------------------
% 48.96/8.54 % (10016)------------------------------
% 48.96/8.56 % (10075)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_9795 for (2932ds/68Mi)
% 48.96/8.59 % (10075)Instruction limit reached!
% 48.96/8.59 % (10075)------------------------------
% 48.96/8.59 % (10075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.96/8.59 % (10075)Termination reason: Unknown
% 48.96/8.59 % (10075)Termination phase: Property scanning
% 48.96/8.59
% 48.96/8.59 % (10075)Memory used [KB]: 2174
% 48.96/8.59 % (10075)Time elapsed: 0.035 s
% 48.96/8.59 % (10075)Instructions burned: 69 (million)
% 48.96/8.59 % (10075)------------------------------
% 48.96/8.59 % (10075)------------------------------
% 49.62/8.61 % (10076)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_9795 for (2931ds/454Mi)
% 49.62/8.63 % (10074)Instruction limit reached!
% 49.62/8.63 % (10074)------------------------------
% 49.62/8.63 % (10074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.62/8.63 % (10074)Termination reason: Unknown
% 49.62/8.63 % (10074)Termination phase: Saturation
% 49.62/8.63
% 49.62/8.63 % (10074)Memory used [KB]: 7291
% 49.62/8.63 % (10074)Time elapsed: 0.105 s
% 49.62/8.63 % (10074)Instructions burned: 222 (million)
% 49.62/8.63 % (10074)------------------------------
% 49.62/8.63 % (10074)------------------------------
% 49.62/8.64 % (10077)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_9795 for (2931ds/360Mi)
% 49.62/8.64 % (10071)Instruction limit reached!
% 49.62/8.64 % (10071)------------------------------
% 49.62/8.64 % (10071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.62/8.64 % (10071)Termination reason: Unknown
% 49.62/8.64 % (10071)Termination phase: Saturation
% 49.62/8.64
% 49.62/8.64 % (10071)Memory used [KB]: 8699
% 49.62/8.64 % (10071)Time elapsed: 0.338 s
% 49.62/8.64 % (10071)Instructions burned: 644 (million)
% 49.62/8.64 % (10071)------------------------------
% 49.62/8.64 % (10071)------------------------------
% 49.62/8.66 % (10078)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_9795 for (2931ds/157Mi)
% 50.17/8.73 % (10078)Instruction limit reached!
% 50.17/8.73 % (10078)------------------------------
% 50.17/8.73 % (10078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.17/8.73 % (10078)Termination reason: Unknown
% 50.17/8.73 % (10078)Termination phase: Saturation
% 50.17/8.73
% 50.17/8.73 % (10078)Memory used [KB]: 6908
% 50.17/8.73 % (10078)Time elapsed: 0.074 s
% 50.17/8.73 % (10078)Instructions burned: 157 (million)
% 50.17/8.73 % (10078)------------------------------
% 50.17/8.73 % (10078)------------------------------
% 50.17/8.75 % (10079)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_9795 for (2930ds/5061Mi)
% 50.36/8.81 % (10077)Instruction limit reached!
% 50.36/8.81 % (10077)------------------------------
% 50.36/8.81 % (10077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.36/8.81 % (10077)Termination reason: Unknown
% 50.36/8.81 % (10077)Termination phase: Saturation
% 50.36/8.81
% 50.36/8.81 % (10077)Memory used [KB]: 7931
% 50.36/8.81 % (10077)Time elapsed: 0.170 s
% 50.36/8.81 % (10077)Instructions burned: 360 (million)
% 50.36/8.81 % (10077)------------------------------
% 50.36/8.81 % (10077)------------------------------
% 50.36/8.83 % (10080)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_9795 for (2929ds/2401Mi)
% 50.36/8.83 % (10076)Instruction limit reached!
% 50.36/8.83 % (10076)------------------------------
% 50.36/8.83 % (10076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.36/8.83 % (10076)Termination reason: Unknown
% 50.36/8.83 % (10076)Termination phase: Saturation
% 50.36/8.83
% 50.36/8.83 % (10076)Memory used [KB]: 12537
% 50.36/8.83 % (10076)Time elapsed: 0.220 s
% 50.36/8.83 % (10076)Instructions burned: 455 (million)
% 50.36/8.83 % (10076)------------------------------
% 50.36/8.83 % (10076)------------------------------
% 50.36/8.85 % (10081)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_9795 for (2929ds/5798Mi)
% 50.36/8.87 % (10073)Instruction limit reached!
% 50.36/8.87 % (10073)------------------------------
% 50.36/8.87 % (10073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.36/8.87 % (10073)Termination reason: Unknown
% 50.36/8.87 % (10073)Termination phase: Saturation
% 50.36/8.87
% 50.36/8.87 % (10073)Memory used [KB]: 8699
% 50.36/8.87 % (10073)Time elapsed: 0.499 s
% 50.36/8.87 % (10073)Instructions burned: 1047 (million)
% 50.36/8.87 % (10073)------------------------------
% 50.36/8.87 % (10073)------------------------------
% 50.36/8.89 % (10082)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_9795 for (2928ds/346Mi)
% 50.36/8.89 % (10070)Instruction limit reached!
% 50.36/8.89 % (10070)------------------------------
% 50.36/8.89 % (10070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.36/8.89 % (10070)Termination reason: Unknown
% 50.36/8.89 % (10070)Termination phase: Saturation
% 50.36/8.89
% 50.36/8.89 % (10070)Memory used [KB]: 9338
% 50.36/8.89 % (10070)Time elapsed: 0.574 s
% 50.36/8.89 % (10070)Instructions burned: 1175 (million)
% 50.36/8.89 % (10070)------------------------------
% 50.36/8.89 % (10070)------------------------------
% 51.98/8.91 % (10083)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_9795 for (2928ds/1321Mi)
% 51.98/8.94 % (10072)Instruction limit reached!
% 51.98/8.94 % (10072)------------------------------
% 51.98/8.94 % (10072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.98/8.94 % (10072)Termination reason: Unknown
% 51.98/8.94 % (10072)Termination phase: Saturation
% 51.98/8.94
% 51.98/8.94 % (10072)Memory used [KB]: 8315
% 51.98/8.94 % (10072)Time elapsed: 0.568 s
% 51.98/8.94 % (10072)Instructions burned: 1201 (million)
% 51.98/8.94 % (10072)------------------------------
% 51.98/8.94 % (10072)------------------------------
% 51.98/8.95 % (10084)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_9795 for (2928ds/1312Mi)
% 53.67/9.05 % (10082)Instruction limit reached!
% 53.67/9.05 % (10082)------------------------------
% 53.67/9.05 % (10082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.67/9.05 % (10082)Termination reason: Unknown
% 53.67/9.05 % (10082)Termination phase: Saturation
% 53.67/9.05
% 53.67/9.05 % (10082)Memory used [KB]: 7675
% 53.67/9.06 % (10082)Time elapsed: 0.170 s
% 53.67/9.06 % (10082)Instructions burned: 346 (million)
% 53.67/9.06 % (10082)------------------------------
% 53.67/9.06 % (10082)------------------------------
% 53.67/9.07 % (10085)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_9795 for (2927ds/672Mi)
% 55.98/9.41 % (10085)Instruction limit reached!
% 55.98/9.41 % (10085)------------------------------
% 55.98/9.41 % (10085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.98/9.41 % (10085)Termination reason: Unknown
% 55.98/9.41 % (10085)Termination phase: Saturation
% 55.98/9.41
% 55.98/9.41 % (10085)Memory used [KB]: 8059
% 55.98/9.41 % (10085)Time elapsed: 0.338 s
% 55.98/9.41 % (10085)Instructions burned: 672 (million)
% 55.98/9.41 % (10085)------------------------------
% 55.98/9.41 % (10085)------------------------------
% 55.98/9.43 % (10086)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_9795 for (2923ds/1897Mi)
% 56.92/9.53 % (10083)Instruction limit reached!
% 56.92/9.53 % (10083)------------------------------
% 56.92/9.53 % (10083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.92/9.53 % (10083)Termination reason: Unknown
% 56.92/9.53 % (10083)Termination phase: Saturation
% 56.92/9.53
% 56.92/9.53 % (10083)Memory used [KB]: 3837
% 56.92/9.53 % (10083)Time elapsed: 0.626 s
% 56.92/9.53 % (10083)Instructions burned: 1321 (million)
% 56.92/9.53 % (10083)------------------------------
% 56.92/9.53 % (10083)------------------------------
% 56.92/9.55 % (10087)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_9795 for (2922ds/1202Mi)
% 56.92/9.58 % (10084)Instruction limit reached!
% 56.92/9.58 % (10084)------------------------------
% 56.92/9.58 % (10084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.92/9.58 % (10084)Termination reason: Unknown
% 56.92/9.58 % (10084)Termination phase: Saturation
% 56.92/9.58
% 56.92/9.58 % (10084)Memory used [KB]: 9466
% 56.92/9.58 % (10084)Time elapsed: 0.624 s
% 56.92/9.58 % (10084)Instructions burned: 1313 (million)
% 56.92/9.58 % (10084)------------------------------
% 56.92/9.58 % (10084)------------------------------
% 56.92/9.59 % (10088)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_9795 for (2921ds/1493Mi)
% 57.44/9.65 % (10088)Refutation not found, incomplete strategy
% 57.44/9.65 % (10088)------------------------------
% 57.44/9.65 % (10088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.44/9.65 % (10088)Termination reason: Refutation not found, incomplete strategy
% 57.44/9.65
% 57.44/9.65
% 57.44/9.65 % (10088)Memory used [KB]: 6908
% 57.44/9.65 % (10088)Time elapsed: 0.061 s
% 57.44/9.65 % (10088)Instructions burned: 130 (million)
% 57.44/9.65 % (10088)------------------------------
% 57.44/9.65 % (10088)------------------------------
% 57.44/9.67 % (10089)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_9795 for (2921ds/7679Mi)
% 58.74/9.98 % (10080)Instruction limit reached!
% 58.74/9.98 % (10080)------------------------------
% 58.74/9.98 % (10080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.74/9.98 % (10080)Termination reason: Unknown
% 58.74/9.98 % (10080)Termination phase: Saturation
% 58.74/9.98
% 58.74/9.98 % (10080)Memory used [KB]: 8827
% 58.74/9.98 % (10080)Time elapsed: 1.153 s
% 58.74/9.98 % (10080)Instructions burned: 2401 (million)
% 58.74/9.98 % (10080)------------------------------
% 58.74/9.98 % (10080)------------------------------
% 58.74/10.00 % (10090)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_9795 for (2917ds/340Mi)
% 61.41/10.13 % (10087)Instruction limit reached!
% 61.41/10.13 % (10087)------------------------------
% 61.41/10.13 % (10087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.41/10.13 % (10087)Termination reason: Unknown
% 61.41/10.13 % (10087)Termination phase: Saturation
% 61.41/10.13
% 61.41/10.13 % (10087)Memory used [KB]: 4349
% 61.41/10.13 % (10087)Time elapsed: 0.581 s
% 61.41/10.13 % (10087)Instructions burned: 1202 (million)
% 61.41/10.13 % (10087)------------------------------
% 61.41/10.13 % (10087)------------------------------
% 61.41/10.14 % (10091)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_9795 for (2916ds/3672Mi)
% 61.41/10.16 % (10090)Instruction limit reached!
% 61.41/10.16 % (10090)------------------------------
% 61.41/10.16 % (10090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.41/10.16 % (10090)Termination reason: Unknown
% 61.41/10.16 % (10090)Termination phase: Saturation
% 61.41/10.16
% 61.41/10.16 % (10090)Memory used [KB]: 8443
% 61.41/10.16 % (10090)Time elapsed: 0.167 s
% 61.41/10.16 % (10090)Instructions burned: 340 (million)
% 61.41/10.16 % (10090)------------------------------
% 61.41/10.16 % (10090)------------------------------
% 61.41/10.18 % (10092)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_9795 for (2916ds/1535Mi)
% 62.32/10.36 % (10086)Instruction limit reached!
% 62.32/10.36 % (10086)------------------------------
% 62.32/10.36 % (10086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.32/10.36 % (10086)Termination reason: Unknown
% 62.32/10.36 % (10086)Termination phase: Saturation
% 62.32/10.36
% 62.32/10.36 % (10086)Memory used [KB]: 10618
% 62.32/10.36 % (10086)Time elapsed: 0.932 s
% 62.32/10.36 % (10086)Instructions burned: 1898 (million)
% 62.32/10.36 % (10086)------------------------------
% 62.32/10.36 % (10086)------------------------------
% 62.32/10.37 % (10093)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_9795 for (2914ds/4637Mi)
% 63.58/10.63 % (10060)Instruction limit reached!
% 63.58/10.63 % (10060)------------------------------
% 63.58/10.63 % (10060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.58/10.63 % (10060)Termination reason: Unknown
% 63.58/10.63 % (10060)Termination phase: Saturation
% 63.58/10.63
% 63.58/10.63 % (10060)Memory used [KB]: 11385
% 63.58/10.63 % (10060)Time elapsed: 3.181 s
% 63.58/10.63 % (10060)Instructions burned: 6455 (million)
% 63.58/10.63 % (10060)------------------------------
% 63.58/10.63 % (10060)------------------------------
% 63.58/10.65 % (10094)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_9795 for (2911ds/3174Mi)
% 64.22/10.89 % (10092)Instruction limit reached!
% 64.22/10.89 % (10092)------------------------------
% 64.22/10.89 % (10092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.22/10.89 % (10092)Termination reason: Unknown
% 64.22/10.89 % (10092)Termination phase: Saturation
% 64.22/10.89
% 64.22/10.89 % (10092)Memory used [KB]: 11641
% 64.22/10.89 % (10092)Time elapsed: 0.716 s
% 64.22/10.89 % (10092)Instructions burned: 1535 (million)
% 64.22/10.89 % (10092)------------------------------
% 64.22/10.89 % (10092)------------------------------
% 65.25/10.92 % (10095)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_9795 for (2908ds/307Mi)
% 67.61/11.07 % (10095)Instruction limit reached!
% 67.61/11.07 % (10095)------------------------------
% 67.61/11.07 % (10095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.61/11.07 % (10095)Termination reason: Unknown
% 67.61/11.07 % (10095)Termination phase: Saturation
% 67.61/11.07
% 67.61/11.07 % (10095)Memory used [KB]: 7291
% 67.61/11.07 % (10095)Time elapsed: 0.143 s
% 67.61/11.07 % (10095)Instructions burned: 308 (million)
% 67.61/11.07 % (10095)------------------------------
% 67.61/11.07 % (10095)------------------------------
% 67.61/11.08 % (10096)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_9795 for (2906ds/3619Mi)
% 68.27/11.16 % (10079)Instruction limit reached!
% 68.27/11.16 % (10079)------------------------------
% 68.27/11.16 % (10079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.27/11.16 % (10079)Termination reason: Unknown
% 68.27/11.16 % (10079)Termination phase: Saturation
% 68.27/11.16
% 68.27/11.16 % (10079)Memory used [KB]: 11129
% 68.27/11.16 % (10079)Time elapsed: 2.412 s
% 68.27/11.16 % (10079)Instructions burned: 5061 (million)
% 68.27/11.16 % (10079)------------------------------
% 68.27/11.16 % (10079)------------------------------
% 68.27/11.18 % (10097)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_9795 for (2906ds/2325Mi)
% 70.71/11.64 % (10081)Instruction limit reached!
% 70.71/11.64 % (10081)------------------------------
% 70.71/11.64 % (10081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.71/11.64 % (10081)Termination reason: Unknown
% 70.71/11.64 % (10081)Termination phase: Saturation
% 70.71/11.64
% 70.71/11.64 % (10081)Memory used [KB]: 10362
% 70.71/11.64 % (10081)Time elapsed: 2.788 s
% 70.71/11.64 % (10081)Instructions burned: 5798 (million)
% 70.71/11.64 % (10081)------------------------------
% 70.71/11.64 % (10081)------------------------------
% 70.71/11.66 % (10098)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_9795 for (2901ds/2341Mi)
% 71.98/11.93 % (10091)Instruction limit reached!
% 71.98/11.93 % (10091)------------------------------
% 71.98/11.93 % (10091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.98/11.93 % (10091)Termination reason: Unknown
% 71.98/11.93 % (10091)Termination phase: Saturation
% 71.98/11.93
% 71.98/11.93 % (10091)Memory used [KB]: 11257
% 71.98/11.93 % (10091)Time elapsed: 1.787 s
% 71.98/11.93 % (10091)Instructions burned: 3673 (million)
% 71.98/11.93 % (10091)------------------------------
% 71.98/11.93 % (10091)------------------------------
% 71.98/11.95 % (10099)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_9795 for (2898ds/7257Mi)
% 75.35/12.14 % (10094)Instruction limit reached!
% 75.35/12.14 % (10094)------------------------------
% 75.35/12.14 % (10094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.35/12.14 % (10094)Termination reason: Unknown
% 75.35/12.14 % (10094)Termination phase: Saturation
% 75.35/12.14
% 75.35/12.14 % (10094)Memory used [KB]: 9850
% 75.35/12.14 % (10094)Time elapsed: 1.507 s
% 75.35/12.14 % (10094)Instructions burned: 3174 (million)
% 75.35/12.14 % (10094)------------------------------
% 75.35/12.14 % (10094)------------------------------
% 75.35/12.16 % (10100)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_9795 for (2896ds/3710Mi)
% 75.81/12.29 % (10097)Instruction limit reached!
% 75.81/12.29 % (10097)------------------------------
% 75.81/12.29 % (10097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.81/12.29 % (10097)Termination reason: Unknown
% 75.81/12.29 % (10097)Termination phase: Saturation
% 75.81/12.29
% 75.81/12.29 % (10097)Memory used [KB]: 11769
% 75.81/12.29 % (10097)Time elapsed: 1.117 s
% 75.81/12.29 % (10097)Instructions burned: 2326 (million)
% 75.81/12.29 % (10097)------------------------------
% 75.81/12.29 % (10097)------------------------------
% 76.42/12.31 % (10101)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_9795 for (2894ds/326Mi)
% 76.92/12.47 % (10101)Instruction limit reached!
% 76.92/12.47 % (10101)------------------------------
% 76.92/12.47 % (10101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.92/12.47 % (10101)Termination reason: Unknown
% 76.92/12.47 % (10101)Termination phase: Saturation
% 76.92/12.47
% 76.92/12.47 % (10101)Memory used [KB]: 7164
% 76.92/12.47 % (10101)Time elapsed: 0.162 s
% 76.92/12.47 % (10101)Instructions burned: 326 (million)
% 76.92/12.47 % (10101)------------------------------
% 76.92/12.47 % (10101)------------------------------
% 76.92/12.49 % (10102)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_9795 for (2892ds/1100Mi)
% 78.10/12.61 % (10093)Instruction limit reached!
% 78.10/12.61 % (10093)------------------------------
% 78.10/12.61 % (10093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.10/12.61 % (10093)Termination reason: Unknown
% 78.10/12.61 % (10093)Termination phase: Saturation
% 78.10/12.61
% 78.10/12.61 % (10093)Memory used [KB]: 12409
% 78.10/12.61 % (10093)Time elapsed: 2.235 s
% 78.10/12.61 % (10093)Instructions burned: 4638 (million)
% 78.10/12.61 % (10093)------------------------------
% 78.10/12.61 % (10093)------------------------------
% 78.10/12.63 % (10103)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_9795 for (2891ds/406Mi)
% 78.51/12.77 % (10096)Instruction limit reached!
% 78.51/12.77 % (10096)------------------------------
% 78.51/12.77 % (10096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.51/12.77 % (10096)Termination reason: Unknown
% 78.51/12.77 % (10096)Termination phase: Saturation
% 78.51/12.77
% 78.51/12.77 % (10096)Memory used [KB]: 12025
% 78.51/12.77 % (10096)Time elapsed: 1.702 s
% 78.51/12.77 % (10096)Instructions burned: 3619 (million)
% 78.51/12.77 % (10096)------------------------------
% 78.51/12.77 % (10096)------------------------------
% 78.51/12.79 % (10104)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_9795 for (2889ds/1871Mi)
% 78.89/12.82 % (10098)Instruction limit reached!
% 78.89/12.82 % (10098)------------------------------
% 78.89/12.82 % (10098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.89/12.82 % (10098)Termination reason: Unknown
% 78.89/12.82 % (10098)Termination phase: Saturation
% 78.89/12.82
% 78.89/12.82 % (10098)Memory used [KB]: 9338
% 78.89/12.82 % (10098)Time elapsed: 1.157 s
% 78.89/12.82 % (10098)Instructions burned: 2341 (million)
% 78.89/12.82 % (10098)------------------------------
% 78.89/12.82 % (10098)------------------------------
% 78.89/12.83 % (10105)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_9795 for (2889ds/1194Mi)
% 78.89/12.86 % (10089)Instruction limit reached!
% 78.89/12.86 % (10089)------------------------------
% 78.89/12.86 % (10089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.89/12.86 % (10089)Termination reason: Unknown
% 78.89/12.86 % (10089)Termination phase: Saturation
% 78.89/12.86
% 78.89/12.86 % (10089)Memory used [KB]: 18166
% 78.89/12.86 % (10089)Time elapsed: 3.190 s
% 78.89/12.86 % (10089)Instructions burned: 7679 (million)
% 78.89/12.86 % (10089)------------------------------
% 78.89/12.86 % (10089)------------------------------
% 78.89/12.86 % (10103)Instruction limit reached!
% 78.89/12.86 % (10103)------------------------------
% 78.89/12.86 % (10103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.89/12.86 % (10103)Termination reason: Unknown
% 78.89/12.86 % (10103)Termination phase: Saturation
% 78.89/12.86
% 78.89/12.86 % (10103)Memory used [KB]: 7931
% 78.89/12.86 % (10103)Time elapsed: 0.265 s
% 78.89/12.86 % (10103)Instructions burned: 406 (million)
% 78.89/12.86 % (10103)------------------------------
% 78.89/12.86 % (10103)------------------------------
% 78.89/12.88 % (10107)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_9795 for (2888ds/3115Mi)
% 78.89/12.88 % (10106)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_9795 for (2888ds/474Mi)
% 81.37/13.04 % (10102)Instruction limit reached!
% 81.37/13.04 % (10102)------------------------------
% 81.37/13.04 % (10102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.37/13.04 % (10102)Termination reason: Unknown
% 81.37/13.04 % (10102)Termination phase: Saturation
% 81.37/13.04
% 81.37/13.04 % (10102)Memory used [KB]: 10362
% 81.37/13.04 % (10102)Time elapsed: 0.551 s
% 81.37/13.04 % (10102)Instructions burned: 1101 (million)
% 81.37/13.04 % (10102)------------------------------
% 81.37/13.04 % (10102)------------------------------
% 81.37/13.05 % (10108)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_9795 for (2887ds/831Mi)
% 81.37/13.06 % (10106)Instruction limit reached!
% 81.37/13.06 % (10106)------------------------------
% 81.37/13.06 % (10106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.37/13.06 % (10106)Termination reason: Unknown
% 81.37/13.06 % (10106)Termination phase: Saturation
% 81.37/13.06
% 81.37/13.06 % (10106)Memory used [KB]: 8059
% 81.37/13.06 % (10106)Time elapsed: 0.187 s
% 81.37/13.06 % (10106)Instructions burned: 475 (million)
% 81.37/13.06 % (10106)------------------------------
% 81.37/13.06 % (10106)------------------------------
% 81.37/13.07 % (10109)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_9795 for (2886ds/1188Mi)
% 83.38/13.41 % (10105)Instruction limit reached!
% 83.38/13.41 % (10105)------------------------------
% 83.38/13.41 % (10105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.38/13.41 % (10105)Termination reason: Unknown
% 83.38/13.41 % (10105)Termination phase: Saturation
% 83.38/13.41
% 83.38/13.41 % (10105)Memory used [KB]: 8699
% 83.38/13.41 % (10105)Time elapsed: 0.575 s
% 83.38/13.41 % (10105)Instructions burned: 1194 (million)
% 83.38/13.41 % (10105)------------------------------
% 83.38/13.41 % (10105)------------------------------
% 83.38/13.43 % (10110)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_9795 for (2883ds/2868Mi)
% 83.38/13.46 % (10108)Instruction limit reached!
% 83.38/13.46 % (10108)------------------------------
% 83.38/13.46 % (10108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.38/13.46 % (10108)Termination reason: Unknown
% 83.38/13.46 % (10108)Termination phase: Saturation
% 83.38/13.46
% 83.38/13.46 % (10108)Memory used [KB]: 9722
% 83.38/13.46 % (10108)Time elapsed: 0.412 s
% 83.38/13.46 % (10108)Instructions burned: 833 (million)
% 83.38/13.46 % (10108)------------------------------
% 83.38/13.46 % (10108)------------------------------
% 83.38/13.48 % (10111)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_9795 for (2882ds/1516Mi)
% 84.18/13.52 % (10110)Refutation not found, incomplete strategy
% 84.18/13.52 % (10110)------------------------------
% 84.18/13.52 % (10110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.18/13.52 % (10110)Termination reason: Refutation not found, incomplete strategy
% 84.18/13.52
% 84.18/13.52
% 84.18/13.52 % (10110)Memory used [KB]: 7547
% 84.18/13.52 % (10110)Time elapsed: 0.096 s
% 84.18/13.52 % (10110)Instructions burned: 210 (million)
% 84.18/13.52 % (10110)------------------------------
% 84.18/13.52 % (10110)------------------------------
% 84.18/13.53 % (10112)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_9795 for (2882ds/2321Mi)
% 84.18/13.59 % (10112)Refutation not found, incomplete strategy
% 84.18/13.59 % (10112)------------------------------
% 84.18/13.59 % (10112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.18/13.59 % (10112)Termination reason: Refutation not found, incomplete strategy
% 84.18/13.59
% 84.18/13.59
% 84.18/13.59 % (10112)Memory used [KB]: 7547
% 84.18/13.59 % (10112)Time elapsed: 0.060 s
% 84.18/13.59 % (10112)Instructions burned: 216 (million)
% 84.18/13.59 % (10112)------------------------------
% 84.18/13.59 % (10112)------------------------------
% 84.72/13.60 % (10113)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_9795 for (2881ds/2812Mi)
% 84.72/13.64 % (10109)Instruction limit reached!
% 84.72/13.64 % (10109)------------------------------
% 84.72/13.64 % (10109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.72/13.64 % (10109)Termination reason: Unknown
% 84.72/13.64 % (10109)Termination phase: Saturation
% 84.72/13.64
% 84.72/13.64 % (10109)Memory used [KB]: 8955
% 84.72/13.64 % (10109)Time elapsed: 0.566 s
% 84.72/13.64 % (10109)Instructions burned: 1189 (million)
% 84.72/13.64 % (10109)------------------------------
% 84.72/13.64 % (10109)------------------------------
% 84.72/13.66 % (10114)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_9795 for (2881ds/4604Mi)
% 85.70/13.76 % (10104)Instruction limit reached!
% 85.70/13.76 % (10104)------------------------------
% 85.70/13.76 % (10104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 85.70/13.76 % (10104)Termination reason: Unknown
% 85.70/13.76 % (10104)Termination phase: Saturation
% 85.70/13.76
% 85.70/13.76 % (10104)Memory used [KB]: 10746
% 85.70/13.76 % (10104)Time elapsed: 0.980 s
% 85.70/13.76 % (10104)Instructions burned: 1871 (million)
% 85.70/13.76 % (10104)------------------------------
% 85.70/13.76 % (10104)------------------------------
% 85.70/13.78 % (10115)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_9795 for (2879ds/2678Mi)
% 86.39/13.90 % (10100)Instruction limit reached!
% 86.39/13.90 % (10100)------------------------------
% 86.39/13.90 % (10100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 86.39/13.90 % (10100)Termination reason: Unknown
% 86.39/13.90 % (10100)Termination phase: Saturation
% 86.39/13.90
% 86.39/13.90 % (10100)Memory used [KB]: 16758
% 86.39/13.90 % (10100)Time elapsed: 1.746 s
% 86.39/13.90 % (10100)Instructions burned: 3711 (million)
% 86.39/13.90 % (10100)------------------------------
% 86.39/13.90 % (10100)------------------------------
% 86.39/13.92 % (10116)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_9795 for (2878ds/643Mi)
% 89.57/14.21 % (10111)Instruction limit reached!
% 89.57/14.21 % (10111)------------------------------
% 89.57/14.21 % (10111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.57/14.21 % (10111)Termination reason: Unknown
% 89.57/14.21 % (10111)Termination phase: Saturation
% 89.57/14.21
% 89.57/14.21 % (10111)Memory used [KB]: 8059
% 89.57/14.21 % (10111)Time elapsed: 0.730 s
% 89.57/14.21 % (10111)Instructions burned: 1516 (million)
% 89.57/14.21 % (10111)------------------------------
% 89.57/14.21 % (10111)------------------------------
% 89.57/14.22 % (10116)Instruction limit reached!
% 89.57/14.22 % (10116)------------------------------
% 89.57/14.22 % (10116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 89.57/14.22 % (10116)Termination reason: Unknown
% 89.57/14.22 % (10116)Termination phase: Saturation
% 89.57/14.22
% 89.57/14.22 % (10116)Memory used [KB]: 9083
% 89.57/14.22 % (10116)Time elapsed: 0.311 s
% 89.57/14.22 % (10116)Instructions burned: 643 (million)
% 89.57/14.22 % (10116)------------------------------
% 89.57/14.22 % (10116)------------------------------
% 89.57/14.23 % (10117)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_9795 for (2875ds/458Mi)
% 89.57/14.24 % (10118)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_9795 for (2875ds/2546Mi)
% 90.13/14.31 % (10107)Instruction limit reached!
% 90.13/14.31 % (10107)------------------------------
% 90.13/14.31 % (10107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.13/14.31 % (10107)Termination reason: Unknown
% 90.13/14.31 % (10107)Termination phase: Saturation
% 90.13/14.31
% 90.13/14.31 % (10107)Memory used [KB]: 12665
% 90.13/14.31 % (10107)Time elapsed: 1.439 s
% 90.13/14.31 % (10107)Instructions burned: 3115 (million)
% 90.13/14.31 % (10107)------------------------------
% 90.13/14.31 % (10107)------------------------------
% 90.13/14.34 % (10119)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_9795 for (2874ds/1432Mi)
% 90.55/14.43 % (10117)Instruction limit reached!
% 90.55/14.43 % (10117)------------------------------
% 90.55/14.43 % (10117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.55/14.43 % (10117)Termination reason: Unknown
% 90.55/14.43 % (10117)Termination phase: Saturation
% 90.55/14.43
% 90.55/14.43 % (10117)Memory used [KB]: 7675
% 90.55/14.43 % (10117)Time elapsed: 0.167 s
% 90.55/14.43 % (10117)Instructions burned: 460 (million)
% 90.55/14.43 % (10117)------------------------------
% 90.55/14.43 % (10117)------------------------------
% 90.55/14.44 % (10120)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_9795 for (2873ds/386Mi)
% 91.13/14.55 % (10120)Instruction limit reached!
% 91.13/14.55 % (10120)------------------------------
% 91.13/14.55 % (10120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.13/14.55 % (10120)Termination reason: Unknown
% 91.13/14.55 % (10120)Termination phase: Saturation
% 91.13/14.55
% 91.13/14.55 % (10120)Memory used [KB]: 8059
% 91.13/14.55 % (10120)Time elapsed: 0.115 s
% 91.13/14.55 % (10120)Instructions burned: 388 (million)
% 91.13/14.55 % (10120)------------------------------
% 91.13/14.55 % (10120)------------------------------
% 91.13/14.56 % (10121)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_9795 for (2872ds/360Mi)
% 91.66/14.67 % (10121)Instruction limit reached!
% 91.66/14.67 % (10121)------------------------------
% 91.66/14.67 % (10121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.66/14.67 % (10121)Termination reason: Unknown
% 91.66/14.67 % (10121)Termination phase: Saturation
% 91.66/14.67
% 91.66/14.67 % (10121)Memory used [KB]: 7931
% 91.66/14.67 % (10121)Time elapsed: 0.106 s
% 91.66/14.67 % (10121)Instructions burned: 362 (million)
% 91.66/14.67 % (10121)------------------------------
% 91.66/14.67 % (10121)------------------------------
% 91.66/14.68 % (10122)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_9795 for (2870ds/5446Mi)
% 92.58/14.84 % (10113)Instruction limit reached!
% 92.58/14.84 % (10113)------------------------------
% 92.58/14.84 % (10113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.58/14.84 % (10113)Termination reason: Unknown
% 92.58/14.84 % (10113)Termination phase: Saturation
% 92.58/14.84
% 92.58/14.84 % (10113)Memory used [KB]: 11001
% 92.58/14.84 % (10113)Time elapsed: 1.236 s
% 92.58/14.84 % (10113)Instructions burned: 2812 (million)
% 92.58/14.84 % (10113)------------------------------
% 92.58/14.84 % (10113)------------------------------
% 92.58/14.88 % (10123)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_9795 for (2869ds/2573Mi)
% 92.91/14.99 % (10119)Instruction limit reached!
% 92.91/14.99 % (10119)------------------------------
% 92.91/14.99 % (10119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.91/14.99 % (10119)Termination reason: Unknown
% 92.91/14.99 % (10119)Termination phase: Saturation
% 92.91/14.99
% 92.91/14.99 % (10119)Memory used [KB]: 10746
% 92.91/14.99 % (10119)Time elapsed: 0.676 s
% 92.91/14.99 % (10119)Instructions burned: 1434 (million)
% 92.91/14.99 % (10119)------------------------------
% 92.91/14.99 % (10119)------------------------------
% 92.91/15.01 % (10124)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_9795 for (2867ds/2655Mi)
% 95.16/15.09 % (10115)Instruction limit reached!
% 95.16/15.09 % (10115)------------------------------
% 95.16/15.09 % (10115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 95.16/15.09 % (10115)Termination reason: Unknown
% 95.16/15.09 % (10115)Termination phase: Saturation
% 95.16/15.09
% 95.16/15.09 % (10115)Memory used [KB]: 12281
% 95.16/15.09 % (10115)Time elapsed: 1.316 s
% 95.16/15.09 % (10115)Instructions burned: 2678 (million)
% 95.16/15.09 % (10115)------------------------------
% 95.16/15.09 % (10115)------------------------------
% 95.16/15.11 % (10125)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_9795 for (2866ds/2781Mi)
% 97.54/15.49 % (10099)Instruction limit reached!
% 97.54/15.49 % (10099)------------------------------
% 97.54/15.49 % (10099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 97.54/15.49 % (10099)Termination reason: Unknown
% 97.54/15.49 % (10099)Termination phase: Saturation
% 97.54/15.49
% 97.54/15.49 % (10099)Memory used [KB]: 14072
% 97.54/15.49 % (10099)Time elapsed: 3.559 s
% 97.54/15.49 % (10099)Instructions burned: 7257 (million)
% 97.54/15.49 % (10099)------------------------------
% 97.54/15.49 % (10099)------------------------------
% 98.16/15.51 % (10126)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_9795 for (2862ds/307Mi)
% 98.16/15.53 % (10118)Instruction limit reached!
% 98.16/15.53 % (10118)------------------------------
% 98.16/15.53 % (10118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.16/15.53 % (10118)Termination reason: Unknown
% 98.16/15.53 % (10118)Termination phase: Saturation
% 98.16/15.53
% 98.16/15.53 % (10118)Memory used [KB]: 10746
% 98.16/15.53 % (10118)Time elapsed: 1.287 s
% 98.16/15.53 % (10118)Instructions burned: 2547 (million)
% 98.16/15.53 % (10118)------------------------------
% 98.16/15.53 % (10118)------------------------------
% 98.16/15.54 % (10127)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_9795 for (2862ds/1548Mi)
% 98.60/15.65 % (10126)Instruction limit reached!
% 98.60/15.65 % (10126)------------------------------
% 98.60/15.65 % (10126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 98.60/15.65 % (10126)Termination reason: Unknown
% 98.60/15.65 % (10126)Termination phase: Saturation
% 98.60/15.65
% 98.60/15.65 % (10126)Memory used [KB]: 7419
% 98.60/15.65 % (10126)Time elapsed: 0.143 s
% 98.60/15.65 % (10126)Instructions burned: 307 (million)
% 98.60/15.65 % (10126)------------------------------
% 98.60/15.65 % (10126)------------------------------
% 98.60/15.66 % (10128)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_9795 for (2861ds/5214Mi)
% 99.55/15.89 % (10114)Instruction limit reached!
% 99.55/15.89 % (10114)------------------------------
% 99.55/15.89 % (10114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 99.55/15.89 % (10114)Termination reason: Unknown
% 99.55/15.89 % (10114)Termination phase: Saturation
% 99.55/15.89
% 99.55/15.89 % (10114)Memory used [KB]: 13048
% 99.55/15.89 % (10114)Time elapsed: 2.232 s
% 99.55/15.89 % (10114)Instructions burned: 4604 (million)
% 99.55/15.89 % (10114)------------------------------
% 99.55/15.89 % (10114)------------------------------
% 99.97/15.90 % (10129)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_9795 for (2858ds/3201Mi)
% 102.21/16.09 % (10123)Instruction limit reached!
% 102.21/16.09 % (10123)------------------------------
% 102.21/16.09 % (10123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 102.21/16.09 % (10123)Termination reason: Unknown
% 102.21/16.09 % (10123)Termination phase: Saturation
% 102.21/16.09
% 102.21/16.09 % (10123)Memory used [KB]: 12025
% 102.21/16.09 % (10123)Time elapsed: 1.243 s
% 102.21/16.09 % (10123)Instructions burned: 2573 (million)
% 102.21/16.09 % (10123)------------------------------
% 102.21/16.09 % (10123)------------------------------
% 102.21/16.11 % (10130)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_9795 for (2856ds/454Mi)
% 103.34/16.26 % (10124)Instruction limit reached!
% 103.34/16.26 % (10124)------------------------------
% 103.34/16.26 % (10124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 103.34/16.26 % (10124)Termination reason: Unknown
% 103.34/16.26 % (10124)Termination phase: Saturation
% 103.34/16.26
% 103.34/16.26 % (10124)Memory used [KB]: 12920
% 103.34/16.26 % (10124)Time elapsed: 1.252 s
% 103.34/16.26 % (10124)Instructions burned: 2655 (million)
% 103.34/16.26 % (10124)------------------------------
% 103.34/16.26 % (10124)------------------------------
% 103.34/16.28 % (10127)Instruction limit reached!
% 103.34/16.28 % (10127)------------------------------
% 103.34/16.28 % (10127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 103.34/16.28 % (10127)Termination reason: Unknown
% 103.34/16.28 % (10127)Termination phase: Saturation
% 103.34/16.28
% 103.34/16.28 % (10127)Memory used [KB]: 11385
% 103.34/16.28 % (10127)Time elapsed: 0.738 s
% 103.34/16.28 % (10127)Instructions burned: 1548 (million)
% 103.34/16.28 % (10127)------------------------------
% 103.34/16.28 % (10127)------------------------------
% 103.34/16.28 % (10131)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_9795 for (2855ds/3049Mi)
% 103.34/16.30 % (10132)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_9795 for (2854ds/7311Mi)
% 103.93/16.32 % (10130)Instruction limit reached!
% 103.93/16.32 % (10130)------------------------------
% 103.93/16.32 % (10130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 103.93/16.32 % (10130)Termination reason: Unknown
% 103.93/16.32 % (10130)Termination phase: Saturation
% 103.93/16.32
% 103.93/16.32 % (10130)Memory used [KB]: 12537
% 103.93/16.32 % (10130)Time elapsed: 0.219 s
% 103.93/16.32 % (10130)Instructions burned: 455 (million)
% 103.93/16.33 % (10130)------------------------------
% 103.93/16.33 % (10130)------------------------------
% 103.93/16.34 % (10133)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_9795 for (2854ds/6804Mi)
% 104.96/16.55 % (10125)Instruction limit reached!
% 104.96/16.55 % (10125)------------------------------
% 104.96/16.55 % (10125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 104.96/16.55 % (10125)Termination reason: Unknown
% 104.96/16.55 % (10125)Termination phase: Saturation
% 104.96/16.55
% 104.96/16.55 % (10125)Memory used [KB]: 6012
% 104.96/16.55 % (10125)Time elapsed: 1.436 s
% 104.96/16.55 % (10125)Instructions burned: 2781 (million)
% 104.96/16.55 % (10125)------------------------------
% 104.96/16.55 % (10125)------------------------------
% 104.96/16.56 % (10134)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_9795 for (2852ds/1683Mi)
% 110.44/17.25 % (10122)Instruction limit reached!
% 110.44/17.25 % (10122)------------------------------
% 110.44/17.25 % (10122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 110.44/17.25 % (10122)Termination reason: Unknown
% 110.44/17.25 % (10122)Termination phase: Saturation
% 110.44/17.25
% 110.44/17.25 % (10122)Memory used [KB]: 15351
% 110.44/17.25 % (10122)Time elapsed: 2.589 s
% 110.44/17.25 % (10122)Instructions burned: 5447 (million)
% 110.44/17.25 % (10122)------------------------------
% 110.44/17.25 % (10122)------------------------------
% 110.44/17.27 % (10135)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_9795 for (2845ds/4688Mi)
% 111.71/17.42 % (10134)Instruction limit reached!
% 111.71/17.42 % (10134)------------------------------
% 111.71/17.42 % (10134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 111.71/17.42 % (10134)Termination reason: Unknown
% 111.71/17.42 % (10134)Termination phase: Saturation
% 111.71/17.42
% 111.71/17.42 % (10134)Memory used [KB]: 9978
% 111.71/17.42 % (10134)Time elapsed: 0.859 s
% 111.71/17.42 % (10134)Instructions burned: 1684 (million)
% 111.71/17.42 % (10134)------------------------------
% 111.71/17.42 % (10134)------------------------------
% 111.71/17.44 % (10136)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_9795 for (2843ds/2207Mi)
% 111.71/17.44 % (10129)Instruction limit reached!
% 111.71/17.44 % (10129)------------------------------
% 111.71/17.44 % (10129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 111.71/17.44 % (10129)Termination reason: Unknown
% 111.71/17.44 % (10129)Termination phase: Saturation
% 111.71/17.44
% 111.71/17.44 % (10129)Memory used [KB]: 10746
% 111.71/17.44 % (10129)Time elapsed: 1.539 s
% 111.71/17.44 % (10129)Instructions burned: 3202 (million)
% 111.71/17.44 % (10129)------------------------------
% 111.71/17.44 % (10129)------------------------------
% 111.71/17.46 % (10137)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=8216:si=on:rtra=on_0 on DTF2THF_9795 for (2843ds/8216Mi)
% 112.59/17.66 % (10131)Instruction limit reached!
% 112.59/17.66 % (10131)------------------------------
% 112.59/17.66 % (10131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 112.59/17.66 % (10131)Termination reason: Unknown
% 112.59/17.66 % (10131)Termination phase: Saturation
% 112.59/17.66
% 112.59/17.66 % (10131)Memory used [KB]: 9083
% 112.59/17.66 % (10131)Time elapsed: 1.381 s
% 112.59/17.66 % (10131)Instructions burned: 3049 (million)
% 112.59/17.66 % (10131)------------------------------
% 112.59/17.66 % (10131)------------------------------
% 112.59/17.68 % (10138)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_9795 for (2841ds/430Mi)
% 113.27/17.88 % (10138)Instruction limit reached!
% 113.27/17.88 % (10138)------------------------------
% 113.27/17.88 % (10138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 113.27/17.88 % (10138)Termination reason: Unknown
% 113.27/17.88 % (10138)Termination phase: Saturation
% 113.27/17.88
% 113.27/17.88 % (10138)Memory used [KB]: 7675
% 113.27/17.88 % (10138)Time elapsed: 0.204 s
% 113.27/17.88 % (10138)Instructions burned: 431 (million)
% 113.27/17.88 % (10138)------------------------------
% 113.27/17.88 % (10138)------------------------------
% 113.27/17.90 % (10139)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_9795 for (2838ds/2012Mi)
% 116.92/18.15 % (10128)Instruction limit reached!
% 116.92/18.15 % (10128)------------------------------
% 116.92/18.15 % (10128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 116.92/18.15 % (10128)Termination reason: Unknown
% 116.92/18.15 % (10128)Termination phase: Saturation
% 116.92/18.15
% 116.92/18.15 % (10128)Memory used [KB]: 15735
% 116.92/18.15 % (10128)Time elapsed: 2.484 s
% 116.92/18.15 % (10128)Instructions burned: 5215 (million)
% 116.92/18.15 % (10128)------------------------------
% 116.92/18.15 % (10128)------------------------------
% 116.92/18.17 % (10140)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_9795 for (2836ds/631Mi)
% 118.59/18.48 % (10140)Instruction limit reached!
% 118.59/18.48 % (10140)------------------------------
% 118.59/18.48 % (10140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 118.59/18.48 % (10140)Termination reason: Unknown
% 118.59/18.48 % (10140)Termination phase: Saturation
% 118.59/18.48
% 118.59/18.48 % (10140)Memory used [KB]: 8571
% 118.59/18.48 % (10140)Time elapsed: 0.340 s
% 118.59/18.48 % (10140)Instructions burned: 631 (million)
% 118.59/18.48 % (10140)------------------------------
% 118.59/18.48 % (10140)------------------------------
% 119.52/18.50 % (10141)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_9795 for (2832ds/8785Mi)
% 119.52/18.56 % (10136)Instruction limit reached!
% 119.52/18.56 % (10136)------------------------------
% 119.52/18.56 % (10136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 119.52/18.56 % (10136)Termination reason: Unknown
% 119.52/18.56 % (10136)Termination phase: Saturation
% 119.52/18.56
% 119.52/18.56 % (10136)Memory used [KB]: 10362
% 119.52/18.56 % (10136)Time elapsed: 1.125 s
% 119.52/18.56 % (10136)Instructions burned: 2208 (million)
% 119.52/18.56 % (10136)------------------------------
% 119.52/18.56 % (10136)------------------------------
% 119.52/18.58 % (10142)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_9795 for (2832ds/739Mi)
% 121.11/18.89 % (10139)Instruction limit reached!
% 121.11/18.89 % (10139)------------------------------
% 121.11/18.89 % (10139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 121.11/18.89 % (10139)Termination reason: Unknown
% 121.11/18.89 % (10139)Termination phase: Saturation
% 121.11/18.89
% 121.11/18.89 % (10139)Memory used [KB]: 18677
% 121.11/18.89 % (10139)Time elapsed: 1.014 s
% 121.11/18.89 % (10139)Instructions burned: 2012 (million)
% 121.11/18.89 % (10139)------------------------------
% 121.11/18.89 % (10139)------------------------------
% 121.62/18.90 % (10143)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_9795 for (2828ds/5473Mi)
% 121.62/18.95 % (10142)Instruction limit reached!
% 121.62/18.95 % (10142)------------------------------
% 121.62/18.95 % (10142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 121.62/18.95 % (10142)Termination reason: Unknown
% 121.62/18.95 % (10142)Termination phase: Saturation
% 121.62/18.95
% 121.62/18.95 % (10142)Memory used [KB]: 8315
% 121.62/18.95 % (10142)Time elapsed: 0.393 s
% 121.62/18.95 % (10142)Instructions burned: 740 (million)
% 121.62/18.95 % (10142)------------------------------
% 121.62/18.95 % (10142)------------------------------
% 121.62/18.96 % (10144)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_9795 for (2828ds/43570Mi)
% 121.62/18.99 % (10144)Refutation not found, incomplete strategy
% 121.62/18.99 % (10144)------------------------------
% 121.62/18.99 % (10144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 121.62/18.99 % (10144)Termination reason: Refutation not found, incomplete strategy
% 121.62/18.99
% 121.62/18.99
% 121.62/18.99 % (10144)Memory used [KB]: 6396
% 121.62/18.99 % (10144)Time elapsed: 0.026 s
% 121.62/18.99 % (10144)Instructions burned: 47 (million)
% 121.62/18.99 % (10144)------------------------------
% 121.62/18.99 % (10144)------------------------------
% 121.62/19.01 % (10145)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_9795 for (2827ds/8382Mi)
% 125.84/19.49 % (10135)Instruction limit reached!
% 125.84/19.49 % (10135)------------------------------
% 125.84/19.49 % (10135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 125.84/19.49 % (10135)Termination reason: Unknown
% 125.84/19.49 % (10135)Termination phase: Saturation
% 125.84/19.49
% 125.84/19.49 % (10135)Memory used [KB]: 6396
% 125.84/19.49 % (10135)Time elapsed: 2.221 s
% 125.84/19.49 % (10135)Instructions burned: 4689 (million)
% 125.84/19.49 % (10135)------------------------------
% 125.84/19.49 % (10135)------------------------------
% 126.55/19.51 % (10146)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_9795 for (2822ds/407Mi)
% 126.55/19.54 % (10133)Instruction limit reached!
% 126.55/19.54 % (10133)------------------------------
% 126.55/19.54 % (10133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 126.55/19.54 % (10133)Termination reason: Unknown
% 126.55/19.54 % (10133)Termination phase: Saturation
% 126.55/19.54
% 126.55/19.54 % (10133)Memory used [KB]: 12665
% 126.55/19.54 % (10133)Time elapsed: 3.199 s
% 126.55/19.54 % (10133)Instructions burned: 6805 (million)
% 126.55/19.54 % (10133)------------------------------
% 126.55/19.54 % (10133)------------------------------
% 126.55/19.56 % (10147)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_9795 for (2822ds/2971Mi)
% 127.09/19.65 % (10147)Refutation not found, incomplete strategy
% 127.09/19.65 % (10147)------------------------------
% 127.09/19.65 % (10147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.09/19.65 % (10147)Termination reason: Refutation not found, incomplete strategy
% 127.09/19.65
% 127.09/19.65
% 127.09/19.65 % (10147)Memory used [KB]: 7547
% 127.09/19.65 % (10147)Time elapsed: 0.098 s
% 127.09/19.65 % (10147)Instructions burned: 208 (million)
% 127.09/19.65 % (10147)------------------------------
% 127.09/19.65 % (10147)------------------------------
% 127.09/19.67 % (10148)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_9795 for (2820ds/9822Mi)
% 127.71/19.70 % (10146)Instruction limit reached!
% 127.71/19.70 % (10146)------------------------------
% 127.71/19.70 % (10146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.71/19.70 % (10146)Termination reason: Unknown
% 127.71/19.70 % (10146)Termination phase: Saturation
% 127.71/19.70
% 127.71/19.70 % (10146)Memory used [KB]: 7931
% 127.71/19.70 % (10146)Time elapsed: 0.199 s
% 127.71/19.70 % (10146)Instructions burned: 409 (million)
% 127.71/19.70 % (10146)------------------------------
% 127.71/19.70 % (10146)------------------------------
% 127.71/19.71 % (10149)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_9795 for (2820ds/8425Mi)
% 127.71/19.76 % (10132)Refutation not found, non-redundant clauses discarded% (10132)------------------------------
% 127.71/19.76 % (10132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 127.71/19.76 % (10132)Termination reason: Refutation not found, non-redundant clauses discarded
% 127.71/19.76
% 127.71/19.76 % (10132)Memory used [KB]: 10746
% 127.71/19.76 % (10132)Time elapsed: 3.464 s
% 127.71/19.76 % (10132)Instructions burned: 7155 (million)
% 127.71/19.76 % (10132)------------------------------
% 127.71/19.76 % (10132)------------------------------
% 127.71/19.78 % (10150)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_9795 for (2819ds/3107Mi)
% 138.40/21.26 % (10150)Instruction limit reached!
% 138.40/21.26 % (10150)------------------------------
% 138.40/21.26 % (10150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 138.40/21.26 % (10150)Termination reason: Unknown
% 138.40/21.26 % (10150)Termination phase: Saturation
% 138.40/21.26
% 138.40/21.26 % (10150)Memory used [KB]: 10234
% 138.40/21.26 % (10150)Time elapsed: 1.491 s
% 138.40/21.26 % (10150)Instructions burned: 3107 (million)
% 138.40/21.26 % (10150)------------------------------
% 138.40/21.26 % (10150)------------------------------
% 138.40/21.28 % (10151)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_9795 for (2804ds/7967Mi)
% 139.08/21.37 % (10151)Refutation not found, incomplete strategy
% 139.08/21.37 % (10151)------------------------------
% 139.08/21.37 % (10151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 139.08/21.37 % (10151)Termination reason: Refutation not found, incomplete strategy
% 139.08/21.37
% 139.08/21.37
% 139.08/21.37 % (10151)Memory used [KB]: 7547
% 139.08/21.37 % (10151)Time elapsed: 0.098 s
% 139.08/21.37 % (10151)Instructions burned: 203 (million)
% 139.08/21.37 % (10151)------------------------------
% 139.08/21.37 % (10151)------------------------------
% 139.08/21.39 % (10152)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_9795 for (2803ds/3629Mi)
% 139.78/21.43 % (10137)Instruction limit reached!
% 139.78/21.43 % (10137)------------------------------
% 139.78/21.43 % (10137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 139.78/21.43 % (10137)Termination reason: Unknown
% 139.78/21.43 % (10137)Termination phase: Saturation
% 139.78/21.43
% 139.78/21.43 % (10137)Memory used [KB]: 16630
% 139.78/21.43 % (10137)Time elapsed: 3.970 s
% 139.78/21.43 % (10137)Instructions burned: 8217 (million)
% 139.78/21.43 % (10137)------------------------------
% 139.78/21.43 % (10137)------------------------------
% 139.78/21.44 % (10153)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_9795 for (2803ds/939Mi)
% 140.32/21.58 % (10143)Instruction limit reached!
% 140.32/21.58 % (10143)------------------------------
% 140.32/21.58 % (10143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 140.32/21.58 % (10143)Termination reason: Unknown
% 140.32/21.58 % (10143)Termination phase: Saturation
% 140.32/21.58
% 140.32/21.58 % (10143)Memory used [KB]: 12409
% 140.32/21.58 % (10143)Time elapsed: 2.704 s
% 140.32/21.58 % (10143)Instructions burned: 5474 (million)
% 140.32/21.58 % (10143)------------------------------
% 140.32/21.58 % (10143)------------------------------
% 140.81/21.60 % (10154)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_9795 for (2801ds/1188Mi)
% 141.21/21.73 % (10153)Instruction limit reached!
% 141.21/21.73 % (10153)------------------------------
% 141.21/21.73 % (10153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 141.21/21.73 % (10153)Termination reason: Unknown
% 141.21/21.73 % (10153)Termination phase: Saturation
% 141.21/21.73
% 141.21/21.73 % (10153)Memory used [KB]: 8443
% 141.21/21.73 % (10153)Time elapsed: 0.291 s
% 141.21/21.73 % (10153)Instructions burned: 941 (million)
% 141.21/21.73 % (10153)------------------------------
% 141.21/21.73 % (10153)------------------------------
% 141.21/21.74 % (10155)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_9795 for (2800ds/3205Mi)
% 144.12/22.07 % (10154)Instruction limit reached!
% 144.12/22.07 % (10154)------------------------------
% 144.12/22.07 % (10154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 144.12/22.07 % (10154)Termination reason: Unknown
% 144.12/22.07 % (10154)Termination phase: Saturation
% 144.12/22.07
% 144.12/22.07 % (10154)Memory used [KB]: 8955
% 144.12/22.07 % (10154)Time elapsed: 0.474 s
% 144.12/22.07 % (10154)Instructions burned: 1189 (million)
% 144.12/22.07 % (10154)------------------------------
% 144.12/22.07 % (10154)------------------------------
% 144.12/22.08 % (10170)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_9795 for (2796ds/865Mi)
% 145.27/22.29 % (10170)Refutation not found, non-redundant clauses discarded% (10170)------------------------------
% 145.27/22.29 % (10170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 145.27/22.29 % (10170)Termination reason: Refutation not found, non-redundant clauses discarded
% 145.27/22.29
% 145.27/22.29 % (10170)Memory used [KB]: 8315
% 145.27/22.29 % (10170)Time elapsed: 0.208 s
% 145.27/22.29 % (10170)Instructions burned: 673 (million)
% 145.27/22.29 % (10170)------------------------------
% 145.27/22.29 % (10170)------------------------------
% 146.09/22.30 % (10267)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_9795 for (2794ds/7469Mi)
% 146.70/22.41 % (10141)Instruction limit reached!
% 146.70/22.41 % (10141)------------------------------
% 146.70/22.41 % (10141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 146.70/22.41 % (10141)Termination reason: Unknown
% 146.70/22.41 % (10141)Termination phase: Saturation
% 146.70/22.41
% 146.70/22.41 % (10141)Memory used [KB]: 15991
% 146.70/22.41 % (10141)Time elapsed: 3.931 s
% 146.70/22.41 % (10141)Instructions burned: 8787 (million)
% 146.70/22.41 % (10141)------------------------------
% 146.70/22.41 % (10141)------------------------------
% 146.70/22.42 % (10317)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_9795 for (2793ds/4165Mi)
% 147.73/22.65 % (10145)Instruction limit reached!
% 147.73/22.65 % (10145)------------------------------
% 147.73/22.65 % (10145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 147.73/22.65 % (10145)Termination reason: Unknown
% 147.73/22.65 % (10145)Termination phase: Saturation
% 147.73/22.65
% 147.73/22.65 % (10145)Memory used [KB]: 17014
% 147.73/22.65 % (10145)Time elapsed: 3.651 s
% 147.73/22.65 % (10145)Instructions burned: 8383 (million)
% 147.73/22.65 % (10145)------------------------------
% 147.73/22.65 % (10145)------------------------------
% 147.73/22.67 % (10388)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_9795 for (2791ds/13468Mi)
% 147.73/22.67 % (10152)Instruction limit reached!
% 147.73/22.67 % (10152)------------------------------
% 147.73/22.67 % (10152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 147.73/22.67 % (10152)Termination reason: Unknown
% 147.73/22.67 % (10152)Termination phase: Saturation
% 147.73/22.67
% 147.73/22.67 % (10152)Memory used [KB]: 10746
% 147.73/22.67 % (10152)Time elapsed: 1.277 s
% 147.73/22.67 % (10152)Instructions burned: 3631 (million)
% 147.73/22.67 % (10152)------------------------------
% 147.73/22.67 % (10152)------------------------------
% 147.73/22.68 % (10389)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on DTF2THF_9795 for (2790ds/2635Mi)
% 148.17/22.75 % (10155)Instruction limit reached!
% 148.17/22.75 % (10155)------------------------------
% 148.17/22.75 % (10155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 148.17/22.75 % (10155)Termination reason: Unknown
% 148.17/22.75 % (10155)Termination phase: Saturation
% 148.17/22.75
% 148.17/22.75 % (10155)Memory used [KB]: 13432
% 148.17/22.75 % (10155)Time elapsed: 1.011 s
% 148.17/22.75 % (10155)Instructions burned: 3207 (million)
% 148.17/22.75 % (10155)------------------------------
% 148.17/22.75 % (10155)------------------------------
% 148.17/22.76 % (10390)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=631:si=on:rtra=on_0 on DTF2THF_9795 for (2790ds/631Mi)
% 148.63/22.94 % (10390)Instruction limit reached!
% 148.63/22.94 % (10390)------------------------------
% 148.63/22.94 % (10390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 148.63/22.94 % (10390)Termination reason: Unknown
% 148.63/22.94 % (10390)Termination phase: Saturation
% 148.63/22.94
% 148.63/22.94 % (10390)Memory used [KB]: 9083
% 148.63/22.94 % (10390)Time elapsed: 0.188 s
% 148.63/22.94 % (10390)Instructions burned: 631 (million)
% 148.63/22.94 % (10390)------------------------------
% 148.63/22.94 % (10390)------------------------------
% 148.63/22.95 % (10391)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on DTF2THF_9795 for (2788ds/15557Mi)
% 148.63/23.00 % (10149)Instruction limit reached!
% 148.63/23.00 % (10149)------------------------------
% 148.63/23.00 % (10149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 148.63/23.00 % (10149)Termination reason: Unknown
% 148.63/23.00 % (10149)Termination phase: Saturation
% 148.63/23.00
% 148.63/23.00 % (10149)Memory used [KB]: 13816
% 148.63/23.00 % (10149)Time elapsed: 3.278 s
% 148.63/23.00 % (10149)Instructions burned: 8426 (million)
% 148.63/23.00 % (10149)------------------------------
% 148.63/23.00 % (10149)------------------------------
% 148.63/23.01 % (10392)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on DTF2THF_9795 for (2787ds/2142Mi)
% 152.83/23.31 % (10148)Instruction limit reached!
% 152.83/23.31 % (10148)------------------------------
% 152.83/23.31 % (10148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 152.83/23.31 % (10148)Termination reason: Unknown
% 152.83/23.31 % (10148)Termination phase: Saturation
% 152.83/23.31
% 152.83/23.31 % (10148)Memory used [KB]: 18038
% 152.83/23.31 % (10148)Time elapsed: 3.645 s
% 152.83/23.31 % (10148)Instructions burned: 9824 (million)
% 152.83/23.31 % (10148)------------------------------
% 152.83/23.31 % (10148)------------------------------
% 152.83/23.32 % (10393)dis+1002_1:1_aac=none:au=on:bd=off:cnfonf=conj_eager:nwc=5.0:sgt=5:sp=reverse_arity:ss=axioms:i=5624:si=on:rtra=on_0 on DTF2THF_9795 for (2784ds/5624Mi)
% 153.36/23.49 % (10389)Instruction limit reached!
% 153.36/23.49 % (10389)------------------------------
% 153.36/23.49 % (10389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 153.36/23.49 % (10389)Termination reason: Unknown
% 153.36/23.49 % (10389)Termination phase: Saturation
% 153.36/23.49
% 153.36/23.49 % (10389)Memory used [KB]: 13688
% 153.36/23.49 % (10389)Time elapsed: 0.809 s
% 153.36/23.49 % (10389)Instructions burned: 2636 (million)
% 153.36/23.49 % (10389)------------------------------
% 153.36/23.49 % (10389)------------------------------
% 153.36/23.50 % (10394)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=1665:si=on:rtra=on_0 on DTF2THF_9795 for (2782ds/1665Mi)
% 154.25/23.69 % (10392)Instruction limit reached!
% 154.25/23.69 % (10392)------------------------------
% 154.25/23.69 % (10392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 154.25/23.69 % (10392)Termination reason: Unknown
% 154.25/23.69 % (10392)Termination phase: Saturation
% 154.25/23.69
% 154.25/23.69 % (10392)Memory used [KB]: 9210
% 154.25/23.69 % (10392)Time elapsed: 0.695 s
% 154.25/23.69 % (10392)Instructions burned: 2143 (million)
% 154.25/23.69 % (10392)------------------------------
% 154.25/23.69 % (10392)------------------------------
% 154.25/23.70 % (10395)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=64912:si=on:rtra=on_0 on DTF2THF_9795 for (2780ds/64912Mi)
% 155.33/23.71 % (10395)Refutation not found, incomplete strategy
% 155.33/23.71 % (10395)------------------------------
% 155.33/23.71 % (10395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 155.33/23.71 % (10395)Termination reason: Refutation not found, incomplete strategy
% 155.33/23.71
% 155.33/23.71
% 155.33/23.71 % (10395)Memory used [KB]: 1918
% 155.33/23.71 % (10395)Time elapsed: 0.013 s
% 155.33/23.71 % (10395)Instructions burned: 38 (million)
% 155.33/23.71 % (10395)------------------------------
% 155.33/23.71 % (10395)------------------------------
% 155.33/23.72 % (10317)Instruction limit reached!
% 155.33/23.72 % (10317)------------------------------
% 155.33/23.72 % (10317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 155.33/23.72 % (10317)Termination reason: Unknown
% 155.33/23.72 % (10317)Termination phase: Saturation
% 155.33/23.72
% 155.33/23.72 % (10317)Memory used [KB]: 16502
% 155.33/23.72 % (10317)Time elapsed: 1.301 s
% 155.33/23.72 % (10317)Instructions burned: 4165 (million)
% 155.33/23.72 % (10317)------------------------------
% 155.33/23.72 % (10317)------------------------------
% 155.33/23.72 % (10396)lrs+10_1:32_atotf=0.1:avsq=on:bsr=on:cnfonf=lazy_gen:fde=unused:i=7801:si=on:rtra=on_0 on DTF2THF_9795 for (2780ds/7801Mi)
% 155.33/23.73 % (10397)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15194:si=on:rtra=on_0 on DTF2THF_9795 for (2780ds/15194Mi)
% 156.01/24.00 % (10394)Instruction limit reached!
% 156.01/24.00 % (10394)------------------------------
% 156.01/24.00 % (10394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 156.01/24.00 % (10394)Termination reason: Unknown
% 156.01/24.00 % (10394)Termination phase: Saturation
% 156.01/24.00
% 156.01/24.00 % (10394)Memory used [KB]: 9722
% 156.01/24.00 % (10394)Time elapsed: 0.527 s
% 156.01/24.00 % (10394)Instructions burned: 1666 (million)
% 156.01/24.00 % (10394)------------------------------
% 156.01/24.00 % (10394)------------------------------
% 156.01/24.01 % (10398)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=6753:si=on:rtra=on_0 on DTF2THF_9795 for (2777ds/6753Mi)
% 161.06/24.59 % (10267)Instruction limit reached!
% 161.06/24.59 % (10267)------------------------------
% 161.06/24.59 % (10267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 161.06/24.59 % (10267)Termination reason: Unknown
% 161.06/24.59 % (10267)Termination phase: Saturation
% 161.06/24.59
% 161.06/24.59 % (10267)Memory used [KB]: 14200
% 161.06/24.59 % (10267)Time elapsed: 2.290 s
% 161.06/24.59 % (10267)Instructions burned: 7471 (million)
% 161.06/24.59 % (10267)------------------------------
% 161.06/24.59 % (10267)------------------------------
% 161.66/24.60 % (10399)lrs+1002_1:28_bd=off:cnfonf=lazy_simp:plsq=on:plsqr=1,1:prag=on:i=1003:si=on:rtra=on_0 on DTF2THF_9795 for (2771ds/1003Mi)
% 163.17/24.90 % (10399)Instruction limit reached!
% 163.17/24.90 % (10399)------------------------------
% 163.17/24.90 % (10399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 163.17/24.90 % (10399)Termination reason: Unknown
% 163.17/24.90 % (10399)Termination phase: Saturation
% 163.17/24.90
% 163.17/24.90 % (10399)Memory used [KB]: 8699
% 163.17/24.90 % (10399)Time elapsed: 0.297 s
% 163.17/24.90 % (10399)Instructions burned: 1004 (million)
% 163.17/24.90 % (10399)------------------------------
% 163.17/24.90 % (10399)------------------------------
% 163.17/24.91 % (10400)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=13018:si=on:rtra=on_0 on DTF2THF_9795 for (2768ds/13018Mi)
% 163.17/25.01 % (10393)Instruction limit reached!
% 163.17/25.01 % (10393)------------------------------
% 163.17/25.01 % (10393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 163.17/25.01 % (10393)Termination reason: Unknown
% 163.17/25.01 % (10393)Termination phase: Saturation
% 163.17/25.01
% 163.17/25.01 % (10393)Memory used [KB]: 11257
% 163.17/25.01 % (10393)Time elapsed: 1.709 s
% 163.17/25.01 % (10393)Instructions burned: 5626 (million)
% 163.17/25.01 % (10393)------------------------------
% 163.17/25.01 % (10393)------------------------------
% 163.17/25.02 % (10401)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1267:si=on:rtra=on_0 on DTF2THF_9795 for (2767ds/1267Mi)
% 167.49/25.40 % (10401)Instruction limit reached!
% 167.49/25.40 % (10401)------------------------------
% 167.49/25.40 % (10401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 167.49/25.40 % (10401)Termination reason: Unknown
% 167.49/25.40 % (10401)Termination phase: Saturation
% 167.49/25.40
% 167.49/25.40 % (10401)Memory used [KB]: 8059
% 167.49/25.40 % (10401)Time elapsed: 0.381 s
% 167.49/25.40 % (10401)Instructions burned: 1270 (million)
% 167.49/25.40 % (10401)------------------------------
% 167.49/25.40 % (10401)------------------------------
% 167.49/25.41 % (10402)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=2570:si=on:rtra=on_0 on DTF2THF_9795 for (2763ds/2570Mi)
% 172.23/26.07 % (10396)Instruction limit reached!
% 172.23/26.07 % (10396)------------------------------
% 172.23/26.07 % (10396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 172.23/26.07 % (10396)Termination reason: Unknown
% 172.23/26.07 % (10396)Termination phase: Saturation
% 172.23/26.07
% 172.23/26.07 % (10396)Memory used [KB]: 16247
% 172.23/26.07 % (10396)Time elapsed: 2.348 s
% 172.23/26.07 % (10396)Instructions burned: 7803 (million)
% 172.23/26.07 % (10396)------------------------------
% 172.23/26.07 % (10396)------------------------------
% 172.23/26.08 % (10403)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on DTF2THF_9795 for (2756ds/13163Mi)
% 172.23/26.10 % (10398)Instruction limit reached!
% 172.23/26.10 % (10398)------------------------------
% 172.23/26.10 % (10398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 172.23/26.10 % (10398)Termination reason: Unknown
% 172.23/26.10 % (10398)Termination phase: Saturation
% 172.23/26.10
% 172.23/26.10 % (10398)Memory used [KB]: 12025
% 172.23/26.10 % (10398)Time elapsed: 2.096 s
% 172.23/26.10 % (10398)Instructions burned: 6755 (million)
% 172.23/26.10 % (10398)------------------------------
% 172.23/26.10 % (10398)------------------------------
% 172.23/26.11 % (10404)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on DTF2THF_9795 for (2756ds/5087Mi)
% 172.91/26.17 % (10402)Instruction limit reached!
% 172.91/26.17 % (10402)------------------------------
% 172.91/26.17 % (10402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 172.91/26.17 % (10402)Termination reason: Unknown
% 172.91/26.17 % (10402)Termination phase: Saturation
% 172.91/26.17
% 172.91/26.17 % (10402)Memory used [KB]: 11001
% 172.91/26.17 % (10402)Time elapsed: 0.760 s
% 172.91/26.17 % (10402)Instructions burned: 2571 (million)
% 172.91/26.17 % (10402)------------------------------
% 172.91/26.17 % (10402)------------------------------
% 172.91/26.18 % (10405)lrs+1002_1:1_aac=none:au=on:bd=off:cnfonf=lazy_pi_sigma_gen:s2a=on:sac=on:sd=1:sgt=20:ss=axioms:i=10380:si=on:rtra=on_0 on DTF2THF_9795 for (2755ds/10380Mi)
% 175.68/26.90 % (10388)Instruction limit reached!
% 175.68/26.90 % (10388)------------------------------
% 175.68/26.90 % (10388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 175.68/26.90 % (10388)Termination reason: Unknown
% 175.68/26.90 % (10388)Termination phase: Saturation
% 175.68/26.90
% 175.68/26.90 % (10388)Memory used [KB]: 17526
% 175.68/26.90 % (10388)Time elapsed: 4.231 s
% 175.68/26.90 % (10388)Instructions burned: 13468 (million)
% 175.68/26.90 % (10388)------------------------------
% 175.68/26.90 % (10388)------------------------------
% 171.86/26.91 % (10406)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4218:si=on:rtra=on_0 on DTF2THF_9795 for (2748ds/4218Mi)
% 181.21/27.31 % (10406)Refutation not found, incomplete strategy
% 181.21/27.31 % (10406)------------------------------
% 181.21/27.31 % (10406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 181.21/27.31 % (10406)Termination reason: Refutation not found, incomplete strategy
% 181.21/27.31
% 181.21/27.31
% 181.21/27.31 % (10406)Memory used [KB]: 9594
% 181.21/27.31 % (10406)Time elapsed: 0.399 s
% 181.21/27.31 % (10406)Instructions burned: 1218 (million)
% 181.21/27.31 % (10406)------------------------------
% 181.21/27.31 % (10406)------------------------------
% 181.21/27.32 % (10407)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3971:si=on:rtra=on_0 on DTF2THF_9795 for (2744ds/3971Mi)
% 182.44/27.59 % (10391)Instruction limit reached!
% 182.44/27.59 % (10391)------------------------------
% 182.44/27.59 % (10391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 182.44/27.59 % (10391)Termination reason: Unknown
% 182.44/27.59 % (10391)Termination phase: Saturation
% 182.44/27.59
% 182.44/27.59 % (10391)Memory used [KB]: 35436
% 182.44/27.59 % (10391)Time elapsed: 4.635 s
% 182.44/27.59 % (10391)Instructions burned: 15557 (million)
% 182.44/27.59 % (10391)------------------------------
% 182.44/27.59 % (10391)------------------------------
% 183.05/27.60 % (10408)dis+1010_1:1_anc=all_dependent:au=on:bs=on:sd=5:sp=occurrence:ss=axioms:st=2.0:i=14014:si=on:rtra=on_0 on DTF2THF_9795 for (2741ds/14014Mi)
% 183.05/27.69 % (10404)Instruction limit reached!
% 183.05/27.69 % (10404)------------------------------
% 183.05/27.69 % (10404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 183.05/27.69 % (10404)Termination reason: Unknown
% 183.05/27.69 % (10404)Termination phase: Saturation
% 183.05/27.69
% 183.05/27.69 % (10404)Memory used [KB]: 11129
% 183.05/27.69 % (10404)Time elapsed: 1.576 s
% 183.05/27.69 % (10404)Instructions burned: 5088 (million)
% 183.05/27.69 % (10404)------------------------------
% 183.05/27.69 % (10404)------------------------------
% 183.55/27.70 % (10409)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on DTF2THF_9795 for (2740ds/8517Mi)
% 187.53/28.22 % (10397)Instruction limit reached!
% 187.53/28.22 % (10397)------------------------------
% 187.53/28.22 % (10397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 187.53/28.22 % (10397)Termination reason: Unknown
% 187.53/28.22 % (10397)Termination phase: Saturation
% 187.53/28.22
% 187.53/28.22 % (10397)Memory used [KB]: 15991
% 187.53/28.22 % (10397)Time elapsed: 4.493 s
% 187.53/28.22 % (10397)Instructions burned: 15195 (million)
% 187.53/28.22 % (10397)------------------------------
% 187.53/28.22 % (10397)------------------------------
% 187.53/28.23 % (10410)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on DTF2THF_9795 for (2735ds/10148Mi)
% 189.35/28.54 % (10407)Instruction limit reached!
% 189.35/28.54 % (10407)------------------------------
% 189.35/28.54 % (10407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 189.35/28.54 % (10407)Termination reason: Unknown
% 189.35/28.54 % (10407)Termination phase: Saturation
% 189.35/28.54
% 189.35/28.54 % (10407)Memory used [KB]: 10874
% 189.35/28.54 % (10407)Time elapsed: 1.236 s
% 189.35/28.54 % (10407)Instructions burned: 3972 (million)
% 189.35/28.54 % (10407)------------------------------
% 189.35/28.54 % (10407)------------------------------
% 189.35/28.55 % (10411)lrs+10_1:2_ntd=on:nwc=10.0:plsq=on:plsqc=1:plsqr=2,1:ss=axioms:i=9078:si=on:rtra=on_0 on DTF2THF_9795 for (2732ds/9078Mi)
% 190.92/28.89 % (10400)Instruction limit reached!
% 190.92/28.89 % (10400)------------------------------
% 190.92/28.89 % (10400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 190.92/28.89 % (10400)Termination reason: Unknown
% 190.92/28.89 % (10400)Termination phase: Saturation
% 190.92/28.89
% 190.92/28.89 % (10400)Memory used [KB]: 29807
% 190.92/28.89 % (10400)Time elapsed: 3.984 s
% 190.92/28.89 % (10400)Instructions burned: 13020 (million)
% 190.92/28.89 % (10400)------------------------------
% 190.92/28.89 % (10400)------------------------------
% 191.43/28.90 % (10412)lrs+2_1:1_bet=on:bsr=on:cnfonf=lazy_pi_sigma_gen:er=filter:kws=inv_frequency:ntd=on:sd=3:ss=axioms:i=16164:si=on:rtra=on_0 on DTF2THF_9795 for (2728ds/16164Mi)
% 194.57/29.28 % (10405)Instruction limit reached!
% 194.57/29.28 % (10405)------------------------------
% 194.57/29.28 % (10405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 194.57/29.28 % (10405)Termination reason: Unknown
% 194.57/29.28 % (10405)Termination phase: Saturation
% 194.57/29.28
% 194.57/29.28 % (10405)Memory used [KB]: 9210
% 194.57/29.28 % (10405)Time elapsed: 3.105 s
% 194.57/29.28 % (10405)Instructions burned: 10382 (million)
% 194.57/29.28 % (10405)------------------------------
% 194.57/29.28 % (10405)------------------------------
% 194.57/29.29 % (10415)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on DTF2THF_9795 for (2724ds/6102Mi)
% 201.07/30.16 % (10403)Instruction limit reached!
% 201.07/30.16 % (10403)------------------------------
% 201.07/30.16 % (10403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 201.07/30.16 % (10403)Termination reason: Unknown
% 201.07/30.16 % (10403)Termination phase: Saturation
% 201.07/30.16
% 201.07/30.16 % (10403)Memory used [KB]: 25841
% 201.07/30.16 % (10403)Time elapsed: 4.080 s
% 201.07/30.16 % (10403)Instructions burned: 13163 (million)
% 201.07/30.16 % (10403)------------------------------
% 201.07/30.16 % (10403)------------------------------
% 201.07/30.17 % (10731)lrs+1010_1:1_au=on:bd=off:e2e=on:fde=unused:nm=4:s2a=on:sos=all:sp=const_frequency:i=10308:si=on:rtra=on_0 on DTF2THF_9795 for (2716ds/10308Mi)
% 202.18/30.39 % (10409)Instruction limit reached!
% 202.18/30.39 % (10409)------------------------------
% 202.18/30.39 % (10409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 202.18/30.39 % (10409)Termination reason: Unknown
% 202.18/30.39 % (10409)Termination phase: Saturation
% 202.18/30.39
% 202.18/30.39 % (10409)Memory used [KB]: 19189
% 202.18/30.39 % (10409)Time elapsed: 2.688 s
% 202.18/30.39 % (10409)Instructions burned: 8518 (million)
% 202.18/30.39 % (10409)------------------------------
% 202.18/30.39 % (10409)------------------------------
% 202.76/30.40 % (10783)dis+1010_1:1_au=on:avsq=on:bd=off:cbe=off:cnfonf=off:cs=on:hud=5:nm=0:plsq=on:plsqc=1:plsqr=7,1:ss=axioms:tgt=full:i=4041:si=on:rtra=on_0 on DTF2THF_9795 for (2713ds/4041Mi)
% 208.59/31.23 % (10415)Instruction limit reached!
% 208.59/31.23 % (10415)------------------------------
% 208.59/31.23 % (10415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 208.59/31.23 % (10415)Termination reason: Unknown
% 208.59/31.23 % (10415)Termination phase: Saturation
% 208.59/31.23
% 208.59/31.23 % (10415)Memory used [KB]: 12409
% 208.59/31.23 % (10415)Time elapsed: 1.937 s
% 208.59/31.23 % (10415)Instructions burned: 6104 (million)
% 208.59/31.23 % (10415)------------------------------
% 208.59/31.23 % (10415)------------------------------
% 208.59/31.24 % (11015)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=6901:si=on:rtra=on_0 on DTF2THF_9795 for (2705ds/6901Mi)
% 209.25/31.36 % (10410)Instruction limit reached!
% 209.25/31.36 % (10410)------------------------------
% 209.25/31.36 % (10410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 209.25/31.36 % (10410)Termination reason: Unknown
% 209.25/31.36 % (10410)Termination phase: Saturation
% 209.25/31.36
% 209.25/31.36 % (10410)Memory used [KB]: 15479
% 209.25/31.36 % (10410)Time elapsed: 3.131 s
% 209.25/31.36 % (10410)Instructions burned: 10150 (million)
% 209.25/31.36 % (10410)------------------------------
% 209.25/31.36 % (10410)------------------------------
% 209.25/31.37 % (11016)lrs-1_1:1_au=on:cbe=off:ntd=on:i=5576:si=on:rtra=on_0 on DTF2THF_9795 for (2703ds/5576Mi)
% 209.82/31.41 % (10411)Instruction limit reached!
% 209.82/31.41 % (10411)------------------------------
% 209.82/31.41 % (10411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 209.82/31.41 % (10411)Termination reason: Unknown
% 209.82/31.41 % (10411)Termination phase: Saturation
% 209.82/31.41
% 209.82/31.41 % (10411)Memory used [KB]: 21620
% 209.82/31.41 % (10411)Time elapsed: 2.862 s
% 209.82/31.41 % (10411)Instructions burned: 9078 (million)
% 209.82/31.41 % (10411)------------------------------
% 209.82/31.41 % (10411)------------------------------
% 209.82/31.42 % (11017)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=2014:si=on:rtra=on_0 on DTF2THF_9795 for (2703ds/2014Mi)
% 210.66/31.61 % (10783)Instruction limit reached!
% 210.66/31.61 % (10783)------------------------------
% 210.66/31.61 % (10783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 210.66/31.61 % (10783)Termination reason: Unknown
% 210.66/31.61 % (10783)Termination phase: Saturation
% 210.66/31.61
% 210.66/31.61 % (10783)Memory used [KB]: 11641
% 210.66/31.61 % (10783)Time elapsed: 1.218 s
% 210.66/31.61 % (10783)Instructions burned: 4043 (million)
% 210.66/31.61 % (10783)------------------------------
% 210.66/31.61 % (10783)------------------------------
% 210.66/31.62 % (11018)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=5115:si=on:rtra=on_0 on DTF2THF_9795 for (2701ds/5115Mi)
% 214.37/32.03 % (11017)Instruction limit reached!
% 214.37/32.03 % (11017)------------------------------
% 214.37/32.03 % (11017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 214.37/32.03 % (11017)Termination reason: Unknown
% 214.37/32.03 % (11017)Termination phase: Saturation
% 214.37/32.03
% 214.37/32.03 % (11017)Memory used [KB]: 13304
% 214.37/32.03 % (11017)Time elapsed: 0.615 s
% 214.37/32.03 % (11017)Instructions burned: 2016 (million)
% 214.37/32.03 % (11017)------------------------------
% 214.37/32.03 % (11017)------------------------------
% 214.37/32.04 % (11019)lrs+2_1:1_au=on:cnfonf=lazy_pi_sigma_gen:sos=on:ss=axioms:i=13001:si=on:rtra=on_0 on DTF2THF_9795 for (2697ds/13001Mi)
% 214.37/32.06 % (10408)Instruction limit reached!
% 214.37/32.06 % (10408)------------------------------
% 214.37/32.06 % (10408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 214.37/32.06 % (10408)Termination reason: Unknown
% 214.37/32.06 % (10408)Termination phase: Saturation
% 214.37/32.06
% 214.37/32.06 % (10408)Memory used [KB]: 22515
% 214.37/32.06 % (10408)Time elapsed: 4.464 s
% 214.37/32.06 % (10408)Instructions burned: 14015 (million)
% 214.37/32.06 % (10408)------------------------------
% 214.37/32.06 % (10408)------------------------------
% 214.37/32.07 % (11020)dis+10_1:2_aac=none:acc=on:atotf=0.1:au=on:fde=none:ins=1:ixr=off:nwc=5.0:i=11105:si=on:rtra=on_0 on DTF2THF_9795 for (2697ds/11105Mi)
% 214.37/32.08 % (11019)Refutation not found, incomplete strategy
% 214.37/32.08 % (11019)------------------------------
% 214.37/32.08 % (11019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 214.37/32.08 % (11019)Termination reason: Refutation not found, incomplete strategy
% 214.37/32.08
% 214.37/32.08
% 214.37/32.08 % (11019)Memory used [KB]: 6908
% 214.37/32.08 % (11019)Time elapsed: 0.036 s
% 214.37/32.08 % (11019)Instructions burned: 128 (million)
% 214.37/32.08 % (11019)------------------------------
% 214.37/32.08 % (11019)------------------------------
% 214.37/32.09 % (11021)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=13832:si=on:rtra=on_0 on DTF2THF_9795 for (2696ds/13832Mi)
% 222.11/33.14 % (11016)Instruction limit reached!
% 222.11/33.14 % (11016)------------------------------
% 222.11/33.14 % (11016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 222.11/33.14 % (11016)Termination reason: Unknown
% 222.11/33.14 % (11016)Termination phase: Saturation
% 222.11/33.14
% 222.11/33.14 % (11016)Memory used [KB]: 11897
% 222.11/33.14 % (11016)Time elapsed: 1.774 s
% 222.11/33.14 % (11016)Instructions burned: 5576 (million)
% 222.11/33.14 % (11016)------------------------------
% 222.11/33.14 % (11016)------------------------------
% 222.11/33.16 % (11022)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=32887:si=on:rtra=on_0 on DTF2THF_9795 for (2686ds/32887Mi)
% 222.11/33.17 % (11018)Instruction limit reached!
% 222.11/33.17 % (11018)------------------------------
% 222.11/33.17 % (11018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 222.11/33.17 % (11018)Termination reason: Unknown
% 222.11/33.17 % (11018)Termination phase: Saturation
% 222.11/33.17
% 222.11/33.17 % (11018)Memory used [KB]: 18677
% 222.11/33.17 % (11018)Time elapsed: 1.549 s
% 222.11/33.17 % (11018)Instructions burned: 5118 (million)
% 222.11/33.17 % (11018)------------------------------
% 222.11/33.17 % (11018)------------------------------
% 222.11/33.18 % (11023)dis+1010_2:1_avsq=on:fde=unused:prag=on:i=3362:si=on:rtra=on_0 on DTF2THF_9795 for (2685ds/3362Mi)
% 223.07/33.35 % (10731)Instruction limit reached!
% 223.07/33.35 % (10731)------------------------------
% 223.07/33.35 % (10731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 223.07/33.35 % (10731)Termination reason: Unknown
% 223.07/33.35 % (10731)Termination phase: Saturation
% 223.07/33.35
% 223.07/33.35 % (10731)Memory used [KB]: 16758
% 223.07/33.35 % (10731)Time elapsed: 3.186 s
% 223.07/33.35 % (10731)Instructions burned: 10309 (million)
% 223.07/33.35 % (10731)------------------------------
% 223.07/33.35 % (10731)------------------------------
% 223.07/33.36 % (11024)ott+1002_1:1_au=on:cnfonf=lazy_simp:nwc=5.0:sgt=5:ss=axioms:st=1.5:i=24965:si=on:rtra=on_0 on DTF2THF_9795 for (2684ds/24965Mi)
% 223.07/33.37 % (11015)Instruction limit reached!
% 223.07/33.37 % (11015)------------------------------
% 223.07/33.37 % (11015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 223.07/33.37 % (11015)Termination reason: Unknown
% 223.07/33.37 % (11015)Termination phase: Saturation
% 223.07/33.37
% 223.07/33.37 % (11015)Memory used [KB]: 13816
% 223.07/33.37 % (11015)Time elapsed: 2.133 s
% 223.07/33.37 % (11015)Instructions burned: 6903 (million)
% 223.07/33.37 % (11015)------------------------------
% 223.07/33.37 % (11015)------------------------------
% 223.07/33.38 % (11025)lrs+1010_2:1_amm=off:avsq=on:c=on:cbe=off:e2e=on:fsr=off:ins=3:s2a=on:s2at=-1.0:i=15705:si=on:rtra=on_0 on DTF2THF_9795 for (2683ds/15705Mi)
% 224.43/33.74 % (10412)Instruction limit reached!
% 224.43/33.74 % (10412)------------------------------
% 224.43/33.74 % (10412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 224.43/33.74 % (10412)Termination reason: Unknown
% 224.43/33.74 % (10412)Termination phase: Saturation
% 224.43/33.74
% 224.43/33.74 % (10412)Memory used [KB]: 16630
% 224.43/33.74 % (10412)Time elapsed: 4.838 s
% 224.43/33.74 % (10412)Instructions burned: 16165 (million)
% 224.43/33.74 % (10412)------------------------------
% 224.43/33.74 % (10412)------------------------------
% 224.43/33.75 % (11026)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1536:si=on:rtra=on_0 on DTF2THF_9795 for (2680ds/1536Mi)
% 229.64/34.22 % (11026)Instruction limit reached!
% 229.64/34.22 % (11026)------------------------------
% 229.64/34.22 % (11026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 229.64/34.22 % (11026)Termination reason: Unknown
% 229.64/34.22 % (11026)Termination phase: Saturation
% 229.64/34.22
% 229.64/34.22 % (11026)Memory used [KB]: 8571
% 229.64/34.22 % (11026)Time elapsed: 0.469 s
% 229.64/34.22 % (11026)Instructions burned: 1538 (million)
% 229.64/34.22 % (11026)------------------------------
% 229.64/34.22 % (11026)------------------------------
% 229.64/34.22 % (11023)Instruction limit reached!
% 229.64/34.22 % (11023)------------------------------
% 229.64/34.22 % (11023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 229.64/34.22 % (11023)Termination reason: Unknown
% 229.64/34.22 % (11023)Termination phase: Saturation
% 229.64/34.22
% 229.64/34.22 % (11023)Memory used [KB]: 14328
% 229.64/34.22 % (11023)Time elapsed: 1.036 s
% 229.64/34.22 % (11023)Instructions burned: 3363 (million)
% 229.64/34.22 % (11023)------------------------------
% 229.64/34.22 % (11023)------------------------------
% 229.64/34.23 % (11028)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=4925:si=on:rtra=on_0 on DTF2THF_9795 for (2675ds/4925Mi)
% 229.64/34.24 % (11027)dis+10_1:1_fde=none:kws=precedence:piset=not:prag=on:slsq=on:slsqc=1:sp=unary_frequency:i=23684:si=on:rtra=on_0 on DTF2THF_9795 for (2675ds/23684Mi)
% 238.05/35.49 % (11020)Instruction limit reached!
% 238.05/35.49 % (11020)------------------------------
% 238.05/35.49 % (11020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 238.05/35.49 % (11020)Termination reason: Unknown
% 238.05/35.49 % (11020)Termination phase: Saturation
% 238.05/35.49
% 238.05/35.49 % (11020)Memory used [KB]: 24306
% 238.05/35.49 % (11020)Time elapsed: 3.422 s
% 238.05/35.49 % (11020)Instructions burned: 11107 (million)
% 238.05/35.49 % (11020)------------------------------
% 238.05/35.49 % (11020)------------------------------
% 238.77/35.51 % (11029)lrs-1010_1:50_au=on:awrs=converge:awrsf=430:bet=on:cbe=off:cha=on:nm=20:sac=on:i=14666:si=on:rtra=on_0 on DTF2THF_9795 for (2662ds/14666Mi)
% 239.98/35.73 % (11028)Instruction limit reached!
% 239.98/35.73 % (11028)------------------------------
% 239.98/35.73 % (11028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 239.98/35.73 % (11028)Termination reason: Unknown
% 239.98/35.73 % (11028)Termination phase: Saturation
% 239.98/35.73
% 239.98/35.73 % (11028)Memory used [KB]: 10874
% 239.98/35.73 % (11028)Time elapsed: 1.519 s
% 239.98/35.73 % (11028)Instructions burned: 4927 (million)
% 239.98/35.73 % (11028)------------------------------
% 239.98/35.73 % (11028)------------------------------
% 239.98/35.74 % (11030)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=3322:si=on:rtra=on_0 on DTF2THF_9795 for (2660ds/3322Mi)
% 242.35/36.10 % (11021)Instruction limit reached!
% 242.35/36.10 % (11021)------------------------------
% 242.35/36.10 % (11021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 242.35/36.10 % (11021)Termination reason: Unknown
% 242.35/36.10 % (11021)Termination phase: Saturation
% 242.35/36.10
% 242.35/36.10 % (11021)Memory used [KB]: 30958
% 242.35/36.10 % (11021)Time elapsed: 4.019 s
% 242.35/36.10 % (11021)Instructions burned: 13834 (million)
% 242.35/36.10 % (11021)------------------------------
% 242.35/36.10 % (11021)------------------------------
% 243.07/36.12 % (11031)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1810:si=on:rtra=on_0 on DTF2THF_9795 for (2656ds/1810Mi)
% 244.17/36.34 % (11030)Instruction limit reached!
% 244.17/36.34 % (11030)------------------------------
% 244.17/36.34 % (11030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 244.17/36.34 % (11030)Termination reason: Unknown
% 244.17/36.34 % (11030)Termination phase: Saturation
% 244.17/36.34
% 244.17/36.34 % (11030)Memory used [KB]: 8187
% 244.17/36.34 % (11030)Time elapsed: 0.636 s
% 244.17/36.34 % (11030)Instructions burned: 3324 (million)
% 244.17/36.34 % (11030)------------------------------
% 244.17/36.34 % (11030)------------------------------
% 244.17/36.35 % (11032)dis+1666_1:1_anc=none:bs=on:cbe=off:cha=on:cnfonf=lazy_gen:fe=off:fsr=off:hud=5:kws=precedence:piset=pi_sigma:prag=on:sos=on:sp=frequency:i=2465:si=on:rtra=on_0 on DTF2THF_9795 for (2654ds/2465Mi)
% 244.73/36.42 % (11032)Refutation not found, incomplete strategy
% 244.73/36.42 % (11032)------------------------------
% 244.73/36.42 % (11032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 244.73/36.42 % (11032)Termination reason: Refutation not found, incomplete strategy
% 244.73/36.42
% 244.73/36.42
% 244.73/36.42 % (11032)Memory used [KB]: 7675
% 244.73/36.42 % (11032)Time elapsed: 0.063 s
% 244.73/36.42 % (11032)Instructions burned: 219 (million)
% 244.73/36.42 % (11032)------------------------------
% 244.73/36.42 % (11032)------------------------------
% 244.73/36.43 % (11033)dis+1002_1:1_cbe=off:cnfonf=lazy_pi_sigma_gen:fsr=off:ins=1:kws=inv_precedence:nwc=10.0:ss=axioms:st=2.0:i=41234:si=on:rtra=on_0 on DTF2THF_9795 for (2653ds/41234Mi)
% 245.81/36.65 % (11031)Instruction limit reached!
% 245.81/36.65 % (11031)------------------------------
% 245.81/36.65 % (11031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 245.81/36.65 % (11031)Termination reason: Unknown
% 245.81/36.65 % (11031)Termination phase: Saturation
% 245.81/36.65
% 245.81/36.65 % (11031)Memory used [KB]: 9850
% 245.81/36.65 % (11031)Time elapsed: 0.565 s
% 245.81/36.65 % (11031)Instructions burned: 1810 (million)
% 245.81/36.65 % (11031)------------------------------
% 245.81/36.65 % (11031)------------------------------
% 245.81/36.66 % (11034)dis+1002_1:1_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:nm=0:i=14027:si=on:rtra=on_0 on DTF2THF_9795 for (2651ds/14027Mi)
% 257.18/38.17 % (11025)Instruction limit reached!
% 257.18/38.17 % (11025)------------------------------
% 257.18/38.17 % (11025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 257.18/38.17 % (11025)Termination reason: Unknown
% 257.18/38.17 % (11025)Termination phase: Saturation
% 257.18/38.17
% 257.18/38.17 % (11025)Memory used [KB]: 35564
% 257.18/38.17 % (11025)Time elapsed: 4.792 s
% 257.18/38.17 % (11025)Instructions burned: 15705 (million)
% 257.18/38.17 % (11025)------------------------------
% 257.18/38.17 % (11025)------------------------------
% 257.18/38.19 % (11035)dis+1010_1:1_au=on:cnfonf=conj_eager:nwc=10.0:sac=on:i=27021:si=on:rtra=on_0 on DTF2THF_9795 for (2635ds/27021Mi)
% 270.51/40.07 % (11029)Instruction limit reached!
% 270.51/40.07 % (11029)------------------------------
% 270.51/40.07 % (11029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 270.51/40.07 % (11029)Termination reason: Unknown
% 270.51/40.07 % (11029)Termination phase: Saturation
% 270.51/40.07
% 270.51/40.07 % (11029)Memory used [KB]: 20468
% 270.51/40.07 % (11029)Time elapsed: 4.594 s
% 270.51/40.07 % (11029)Instructions burned: 14667 (million)
% 270.51/40.07 % (11029)------------------------------
% 270.51/40.07 % (11029)------------------------------
% 270.51/40.08 % (11036)dis-1666_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:i=5643:si=on:rtra=on_0 on DTF2THF_9795 for (2616ds/5643Mi)
% 275.26/40.86 % (11034)Instruction limit reached!
% 275.26/40.86 % (11034)------------------------------
% 275.26/40.86 % (11034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 275.26/40.86 % (11034)Termination reason: Unknown
% 275.26/40.86 % (11034)Termination phase: Saturation
% 275.26/40.86
% 275.26/40.86 % (11034)Memory used [KB]: 17910
% 275.26/40.86 % (11034)Time elapsed: 4.193 s
% 275.26/40.86 % (11034)Instructions burned: 14029 (million)
% 275.26/40.86 % (11034)------------------------------
% 275.26/40.86 % (11034)------------------------------
% 275.26/40.87 % (11037)dis+1002_1:1_apa=on:au=on:cnfonf=off:e2e=on:flr=on:nm=4:s2a=on:i=8612:si=on:rtra=on_0 on DTF2THF_9795 for (2608ds/8612Mi)
% 277.52/41.08 % (11024)Instruction limit reached!
% 277.52/41.08 % (11024)------------------------------
% 277.52/41.08 % (11024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 277.52/41.08 % (11024)Termination reason: Unknown
% 277.52/41.08 % (11024)Termination phase: Saturation
% 277.52/41.08
% 277.52/41.08 % (11024)Memory used [KB]: 20852
% 277.52/41.08 % (11024)Time elapsed: 7.719 s
% 277.52/41.08 % (11024)Instructions burned: 24965 (million)
% 277.52/41.08 % (11024)------------------------------
% 277.52/41.08 % (11024)------------------------------
% 277.52/41.09 % (11038)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=3743:si=on:rtra=on_0 on DTF2THF_9795 for (2606ds/3743Mi)
% 278.23/41.19 % (11022)First to succeed.
% 278.23/41.19 % (11022)Refutation found. Thanks to Tanya!
% 278.23/41.19 % SZS status Theorem for DTF2THF_9795
% 278.23/41.19 % SZS output start Proof for DTF2THF_9795
% 278.23/41.19 thf(type_def_5, type, itself: ($tType) > $tType).
% 278.23/41.19 thf(type_def_7, type, coinductive_llist: ($tType) > $tType).
% 278.23/41.19 thf(type_def_8, type, set: ($tType) > $tType).
% 278.23/41.19 thf(type_def_9, type, nat: $tType).
% 278.23/41.19 thf(type_def_10, type, a: $tType).
% 278.23/41.19 thf(func_def_0, type, coinductive_llist: ($tType) > $tType).
% 278.23/41.19 thf(func_def_1, type, set: ($tType) > $tType).
% 278.23/41.19 thf(func_def_2, type, nat: $tType).
% 278.23/41.19 thf(func_def_3, type, itself: ($tType) > $tType).
% 278.23/41.19 thf(func_def_4, type, a: $tType).
% 278.23/41.19 thf(func_def_5, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 278.23/41.19 thf(func_def_6, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 278.23/41.19 thf(func_def_7, type, top: !>[X0: $tType]:(itself @ X0 > $o)).
% 278.23/41.19 thf(func_def_8, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 278.23/41.19 thf(func_def_9, type, no_bot: !>[X0: $tType]:(itself @ X0 > $o)).
% 278.23/41.19 thf(func_def_10, type, no_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 278.23/41.19 thf(func_def_11, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 278.23/41.19 thf(func_def_12, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 278.23/41.19 thf(func_def_13, type, order_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 278.23/41.19 thf(func_def_14, type, wellorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 278.23/41.19 thf(func_def_15, type, dense_order: !>[X0: $tType]:(itself @ X0 > $o)).
% 278.23/41.19 thf(func_def_16, type, dense_linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 278.23/41.19 thf(func_def_17, type, condit1656338222tinuum: !>[X0: $tType]:(itself @ X0 > $o)).
% 278.23/41.19 thf(func_def_18, type, condit1037483654norder: !>[X0: $tType]:(itself @ X0 > $o)).
% 278.23/41.19 thf(func_def_19, type, coindu328551480prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 278.23/41.19 thf(func_def_20, type, coinductive_lappend: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_21, type, coinductive_LCons: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_22, type, coinductive_LNil: !>[X0: $tType]:(coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_23, type, coindu1478340336prefix: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > $o)).
% 278.23/41.19 thf(func_def_24, type, lList21511617539llstsp: !>[X0: $tType]:((X0 > $o) > coinductive_llist @ X0 > $o)).
% 278.23/41.19 thf(func_def_25, type, lList2236698231inlsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_26, type, lList21916056377ts_rec: !>[X0: $tType, X1: $tType]:(X0 > (X1 > coinductive_llist @ X1 > X0 > X0) > coinductive_llist @ X1 > X0)).
% 278.23/41.19 thf(func_def_27, type, lList2860480441nlstsp: !>[X0: $tType]:((X0 > $o) > coinductive_llist @ X0 > $o)).
% 278.23/41.19 thf(func_def_28, type, lList22096119349pslsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_29, type, lList2370560421utlast: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_30, type, lList2508575361_ldrop: !>[X0: $tType]:(coinductive_llist @ X0 > nat > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_31, type, lList2170638824_llast: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 278.23/41.19 thf(func_def_32, type, lList21232602520length: !>[X0: $tType]:(coinductive_llist @ X0 > nat)).
% 278.23/41.19 thf(func_def_33, type, lList2281150353e_lrev: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_34, type, lList22119844313_ltake: !>[X0: $tType]:(coinductive_llist @ X0 > nat > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_35, type, lList21148268032oslsts: !>[X0: $tType]:(set @ X0 > set @ coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_36, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 278.23/41.19 thf(func_def_37, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 278.23/41.19 thf(func_def_38, type, ordering_top: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0 > $o)).
% 278.23/41.19 thf(func_def_39, type, top_top: !>[X0: $tType]:(X0)).
% 278.23/41.19 thf(func_def_40, type, type2: !>[X0: $tType]:(itself @ X0)).
% 278.23/41.19 thf(func_def_41, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 278.23/41.19 thf(func_def_42, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 278.23/41.19 thf(func_def_43, type, a2: a).
% 278.23/41.19 thf(func_def_44, type, l: coinductive_llist @ a).
% 278.23/41.19 thf(func_def_60, type, sK0: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_61, type, sK1: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 278.23/41.19 thf(func_def_62, type, sK2: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 278.23/41.19 thf(func_def_63, type, sK3: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_64, type, sK4: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 278.23/41.19 thf(func_def_65, type, sK5: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_66, type, sK6: !>[X0: $tType]:(coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_67, type, sK7: !>[X0: $tType]:(coinductive_llist @ X0 > (X0 > $o) > X0)).
% 278.23/41.19 thf(func_def_68, type, sK8: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 278.23/41.19 thf(func_def_69, type, sK9: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 278.23/41.19 thf(func_def_70, type, sK10: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_71, type, sK11: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > X0)).
% 278.23/41.19 thf(func_def_72, type, sK12: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > set @ X0 > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_73, type, sK13: !>[X0: $tType]:(coinductive_llist @ X0 > (X0 > $o) > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_74, type, sK14: !>[X0: $tType]:(coinductive_llist @ X0 > (X0 > $o) > X0)).
% 278.23/41.19 thf(func_def_75, type, sK15: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 278.23/41.19 thf(func_def_76, type, sK16: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 278.23/41.19 thf(func_def_77, type, sK17: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_78, type, sK18: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 278.23/41.19 thf(func_def_79, type, sK19: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_80, type, sK20: !>[X0: $tType]:((X0 > $o) > (coinductive_llist @ X0 > $o) > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_81, type, sK21: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_82, type, sK22: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 278.23/41.19 thf(func_def_83, type, sK23: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > (X0 > $o) > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_84, type, sK24: !>[X0: $tType]:((coinductive_llist @ X0 > $o) > (X0 > $o) > X0)).
% 278.23/41.19 thf(func_def_85, type, sK25: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > X0)).
% 278.23/41.19 thf(func_def_86, type, sK26: !>[X0: $tType]:(set @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_88, type, sK28: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > X0 > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_89, type, sK29: !>[X0: $tType]:(coinductive_llist @ X0 > set @ X0 > X0)).
% 278.23/41.19 thf(func_def_90, type, sK30: !>[X0: $tType]:(coinductive_llist @ X0 > set @ X0 > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_91, type, sK31: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 278.23/41.19 thf(func_def_92, type, sK32: !>[X0: $tType]:(coinductive_llist @ X0 > X0)).
% 278.23/41.19 thf(func_def_93, type, ph33: !>[X0: $tType]:(X0)).
% 278.23/41.19 thf(func_def_94, type, sK34: coinductive_llist @ a > coinductive_llist @ a > coinductive_llist @ a).
% 278.23/41.19 thf(f21379,plain,(
% 278.23/41.19 $false),
% 278.23/41.19 inference(subsumption_resolution,[status(thm)],[f21378,f957])).
% 278.23/41.19 thf(f957,plain,(
% 278.23/41.19 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : X0] : ((coinductive_LNil @ X0 != (coinductive_LCons @ X0 @ X1 @ X2))) )),
% 278.23/41.19 inference(cnf_transformation,[status(thm)],[f809])).
% 278.23/41.19 thf(f809,plain,(
% 278.23/41.19 ! [X0 : $tType,X1 : X0,X2 : coinductive_llist @ X0] : (coinductive_LNil @ X0 != (coinductive_LCons @ X0 @ X1 @ X2))),
% 278.23/41.19 inference(rectify,[status(thm)],[f4])).
% 278.23/41.19 thf(f4,axiom,(
% 278.23/41.19 ! [X0 : $tType,X5 : X0,X6 : coinductive_llist @ X0] : (coinductive_LNil @ X0 != (coinductive_LCons @ X0 @ X5 @ X6))),
% 278.23/41.19 file('/export/starexec/sandbox/tmp/tmp.gEkGcnFM62/DTF2THF_9795.p',fact_3_llist_Odistinct_I1_J)).
% 278.23/41.19 thf(f21378,plain,(
% 278.23/41.19 ((coinductive_LCons @ a @ a2 @ l) = coinductive_LNil @ a)),
% 278.23/41.19 inference(trivial_inequality_removal,[status(thm)],[f21352])).
% 278.23/41.19 thf(f21352,plain,(
% 278.23/41.19 ($false = $true) | ((coinductive_LCons @ a @ a2 @ l) = coinductive_LNil @ a)),
% 278.23/41.19 inference(superposition,[status(thm)],[f21349,f924])).
% 278.23/41.19 thf(f924,plain,(
% 278.23/41.19 ((ord_less_eq @ coinductive_llist @ a @ (coinductive_LCons @ a @ a2 @ l) @ coinductive_LNil @ a) = $true)),
% 278.23/41.19 inference(cnf_transformation,[status(thm)],[f803])).
% 278.23/41.19 thf(f803,plain,(
% 278.23/41.19 ((ord_less_eq @ coinductive_llist @ a @ (coinductive_LCons @ a @ a2 @ l) @ coinductive_LNil @ a) = $true)),
% 278.23/41.19 inference(flattening,[status(thm)],[f370])).
% 278.23/41.19 thf(f370,plain,(
% 278.23/41.19 ~~((ord_less_eq @ coinductive_llist @ a @ (coinductive_LCons @ a @ a2 @ l) @ coinductive_LNil @ a) = $true)),
% 278.23/41.19 inference(fool_elimination,[status(thm)],[f369])).
% 278.23/41.19 thf(f369,plain,(
% 278.23/41.19 ~~(ord_less_eq @ coinductive_llist @ a @ (coinductive_LCons @ a @ a2 @ l) @ coinductive_LNil @ a)),
% 278.23/41.19 inference(rectify,[status(thm)],[f281])).
% 278.23/41.19 thf(f281,negated_conjecture,(
% 278.23/41.19 ~~(ord_less_eq @ coinductive_llist @ a @ (coinductive_LCons @ a @ a2 @ l) @ coinductive_LNil @ a)),
% 278.23/41.19 inference(negated_conjecture,[status(cth)],[f280])).
% 278.23/41.19 thf(f280,conjecture,(
% 278.23/41.19 ~(ord_less_eq @ coinductive_llist @ a @ (coinductive_LCons @ a @ a2 @ l) @ coinductive_LNil @ a)),
% 278.23/41.19 file('/export/starexec/sandbox/tmp/tmp.gEkGcnFM62/DTF2THF_9795.p',conj_0)).
% 278.23/41.19 thf(f21349,plain,(
% 278.23/41.19 ( ! [X0 : coinductive_llist @ a] : (($false = (ord_less_eq @ coinductive_llist @ a @ X0 @ coinductive_LNil @ a)) | (coinductive_LNil @ a = X0)) )),
% 278.23/41.19 inference(equality_resolution,[status(thm)],[f20976])).
% 278.23/41.19 thf(f20976,plain,(
% 278.23/41.19 ( ! [X0 : coinductive_llist @ a,X1 : coinductive_llist @ a] : ((coinductive_LNil @ a != X1) | (coinductive_LNil @ a = X0) | ((ord_less_eq @ coinductive_llist @ a @ X0 @ X1) = $false)) )),
% 278.23/41.19 inference(superposition,[status(thm)],[f2316,f1390])).
% 278.23/41.19 thf(f1390,plain,(
% 278.23/41.19 ( ! [X2 : coinductive_llist @ a,X1 : coinductive_llist @ a] : (((coinductive_lappend @ a @ X1 @ (sK34 @ X1 @ X2)) = X2) | ($false = (ord_less_eq @ coinductive_llist @ a @ X1 @ X2))) )),
% 278.23/41.19 inference(equality_proxy_clausification,[status(thm)],[f1389])).
% 278.23/41.19 thf(f1389,plain,(
% 278.23/41.19 ( ! [X2 : coinductive_llist @ a,X1 : coinductive_llist @ a] : (($false = (ord_less_eq @ coinductive_llist @ a @ X1 @ X2)) | ($true = ((coinductive_lappend @ a @ X1 @ (sK34 @ X1 @ X2)) = X2))) )),
% 278.23/41.19 inference(beta_eta_normalization,[status(thm)],[f1388])).
% 278.23/41.19 thf(f1388,plain,(
% 278.23/41.19 ( ! [X2 : coinductive_llist @ a,X1 : coinductive_llist @ a] : (($false = (ord_less_eq @ coinductive_llist @ a @ X1 @ X2)) | (((^[Y0 : coinductive_llist @ a]: ((coinductive_lappend @ a @ X1 @ Y0) = X2)) @ (sK34 @ X1 @ X2)) = $true)) )),
% 278.23/41.19 inference(sigma_clausification,[status(thm)],[f1383])).
% 278.23/41.19 thf(f1383,plain,(
% 278.23/41.19 ( ! [X2 : coinductive_llist @ a,X1 : coinductive_llist @ a] : (((?? @ coinductive_llist @ a @ (^[Y0 : coinductive_llist @ a]: ((coinductive_lappend @ a @ X1 @ Y0) = X2))) = $true) | ($false = (ord_less_eq @ coinductive_llist @ a @ X1 @ X2))) )),
% 278.23/41.19 inference(binary_proxy_clausification,[status(thm)],[f1382])).
% 278.23/41.19 thf(f1382,plain,(
% 278.23/41.19 ( ! [X2 : coinductive_llist @ a,X1 : coinductive_llist @ a] : (((?? @ coinductive_llist @ a @ (^[Y0 : coinductive_llist @ a]: ((coinductive_lappend @ a @ X1 @ Y0) = X2))) = (ord_less_eq @ coinductive_llist @ a @ X1 @ X2))) )),
% 278.23/41.19 inference(beta_eta_normalization,[status(thm)],[f1381])).
% 278.23/41.19 thf(f1381,plain,(
% 278.23/41.19 ( ! [X2 : coinductive_llist @ a,X1 : coinductive_llist @ a] : ((((^[Y0 : coinductive_llist @ a]: (?? @ coinductive_llist @ a @ (^[Y1 : coinductive_llist @ a]: ((coinductive_lappend @ a @ X1 @ Y1) = Y0)))) @ X2) = (ord_less_eq @ coinductive_llist @ a @ X1 @ X2))) )),
% 278.23/41.19 inference(argument_congruence,[status(thm)],[f1095])).
% 278.23/41.19 thf(f1095,plain,(
% 278.23/41.19 ( ! [X1 : coinductive_llist @ a] : (((^[Y0 : coinductive_llist @ a]: (?? @ coinductive_llist @ a @ (^[Y1 : coinductive_llist @ a]: ((coinductive_lappend @ a @ X1 @ Y1) = Y0)))) = (ord_less_eq @ coinductive_llist @ a @ X1))) )),
% 278.23/41.19 inference(beta_eta_normalization,[status(thm)],[f1094])).
% 278.23/41.19 thf(f1094,plain,(
% 278.23/41.19 ( ! [X1 : coinductive_llist @ a] : (((ord_less_eq @ coinductive_llist @ a @ X1) = ((^[Y0 : coinductive_llist @ a]: ((^[Y1 : coinductive_llist @ a]: (?? @ coinductive_llist @ a @ (^[Y2 : coinductive_llist @ a]: ((coinductive_lappend @ a @ Y0 @ Y2) = Y1)))))) @ X1))) )),
% 278.23/41.19 inference(argument_congruence,[status(thm)],[f970])).
% 278.23/41.19 thf(f970,plain,(
% 278.23/41.19 (ord_less_eq @ coinductive_llist @ a = (^[Y0 : coinductive_llist @ a]: ((^[Y1 : coinductive_llist @ a]: (?? @ coinductive_llist @ a @ (^[Y2 : coinductive_llist @ a]: ((coinductive_lappend @ a @ Y0 @ Y2) = Y1)))))))),
% 278.23/41.19 inference(cnf_transformation,[status(thm)],[f330])).
% 278.23/41.19 thf(f330,plain,(
% 278.23/41.19 (ord_less_eq @ coinductive_llist @ a = (^[Y0 : coinductive_llist @ a]: ((^[Y1 : coinductive_llist @ a]: (?? @ coinductive_llist @ a @ (^[Y2 : coinductive_llist @ a]: ((coinductive_lappend @ a @ Y0 @ Y2) = Y1)))))))),
% 278.23/41.19 inference(fool_elimination,[status(thm)],[f329])).
% 278.23/41.19 thf(f329,plain,(
% 278.23/41.19 (ord_less_eq @ coinductive_llist @ a = (^[X0 : coinductive_llist @ a, X1 : coinductive_llist @ a] : (? [X2 : coinductive_llist @ a] : ((coinductive_lappend @ a @ X0 @ X2) = X1))))),
% 278.23/41.19 inference(rectify,[status(thm)],[f7])).
% 278.23/41.19 thf(f7,axiom,(
% 278.23/41.19 (ord_less_eq @ coinductive_llist @ a = (^[X13 : coinductive_llist @ a, X14 : coinductive_llist @ a] : (? [X15 : coinductive_llist @ a] : ((coinductive_lappend @ a @ X13 @ X15) = X14))))),
% 278.23/41.19 file('/export/starexec/sandbox/tmp/tmp.gEkGcnFM62/DTF2THF_9795.p',fact_6_llist__le__def)).
% 278.23/41.19 thf(f2316,plain,(
% 278.23/41.19 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : ((coinductive_LNil @ X0 != (coinductive_lappend @ X0 @ X1 @ X2)) | (coinductive_LNil @ X0 = X1)) )),
% 278.23/41.19 inference(superposition,[status(thm)],[f957,f1248])).
% 278.23/41.19 thf(f1248,plain,(
% 278.23/41.19 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : (((coinductive_lappend @ X0 @ X1 @ X2) = (coinductive_LCons @ X0 @ (sK16 @ X0 @ X1) @ (coinductive_lappend @ X0 @ (sK17 @ X0 @ X1) @ X2))) | (coinductive_LNil @ X0 = X1)) )),
% 278.23/41.19 inference(superposition,[status(thm)],[f944,f936])).
% 278.23/41.19 thf(f936,plain,(
% 278.23/41.19 ( ! [X0 : $tType,X1 : coinductive_llist @ X0] : (((coinductive_LCons @ X0 @ (sK16 @ X0 @ X1) @ (sK17 @ X0 @ X1)) = X1) | (coinductive_LNil @ X0 = X1)) )),
% 278.23/41.19 inference(cnf_transformation,[status(thm)],[f879])).
% 278.23/41.19 thf(f879,plain,(
% 278.23/41.19 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((coinductive_LNil @ X0 = X1) | ((coinductive_LCons @ X0 @ (sK16 @ X0 @ X1) @ (sK17 @ X0 @ X1)) = X1))),
% 278.23/41.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f814,f878])).
% 278.23/41.19 thf(f878,plain,(
% 278.23/41.19 ! [X0 : $tType,X1 : coinductive_llist @ X0] : (? [X2 : X0,X3 : coinductive_llist @ X0] : ((coinductive_LCons @ X0 @ X2 @ X3) = X1) => ((coinductive_LCons @ X0 @ (sK16 @ X0 @ X1) @ (sK17 @ X0 @ X1)) = X1))),
% 278.23/41.19 introduced(definition,[],[choice_axiom])).
% 278.23/41.19 thf(f814,plain,(
% 278.23/41.19 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((coinductive_LNil @ X0 = X1) | ? [X2 : X0,X3 : coinductive_llist @ X0] : ((coinductive_LCons @ X0 @ X2 @ X3) = X1))),
% 278.23/41.19 inference(ennf_transformation,[status(thm)],[f810])).
% 278.23/41.19 thf(f810,plain,(
% 278.23/41.19 ! [X0 : $tType,X1 : coinductive_llist @ X0] : ((coinductive_LNil @ X0 != X1) => ~! [X2 : X0,X3 : coinductive_llist @ X0] : ((coinductive_LCons @ X0 @ X2 @ X3) != X1))),
% 278.23/41.19 inference(rectify,[status(thm)],[f1])).
% 278.23/41.19 thf(f1,axiom,(
% 278.23/41.19 ! [X0 : $tType,X2 : coinductive_llist @ X0] : ((coinductive_LNil @ X0 != X2) => ~! [X3 : X0,X4 : coinductive_llist @ X0] : ((coinductive_LCons @ X0 @ X3 @ X4) != X2))),
% 278.23/41.19 file('/export/starexec/sandbox/tmp/tmp.gEkGcnFM62/DTF2THF_9795.p',fact_0_llistE)).
% 278.23/41.19 thf(f944,plain,(
% 278.23/41.19 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X3 : coinductive_llist @ X0,X1 : X0] : (((coinductive_LCons @ X0 @ X1 @ (coinductive_lappend @ X0 @ X2 @ X3)) = (coinductive_lappend @ X0 @ (coinductive_LCons @ X0 @ X1 @ X2) @ X3))) )),
% 278.23/41.19 inference(cnf_transformation,[status(thm)],[f806])).
% 278.23/41.19 thf(f806,plain,(
% 278.23/41.19 ! [X0 : $tType,X1 : X0,X2 : coinductive_llist @ X0,X3 : coinductive_llist @ X0] : ((coinductive_LCons @ X0 @ X1 @ (coinductive_lappend @ X0 @ X2 @ X3)) = (coinductive_lappend @ X0 @ (coinductive_LCons @ X0 @ X1 @ X2) @ X3))),
% 278.23/41.19 inference(rectify,[status(thm)],[f14])).
% 278.23/41.19 thf(f14,axiom,(
% 278.23/41.19 ! [X0 : $tType,X26 : X0,X9 : coinductive_llist @ X0,X27 : coinductive_llist @ X0] : ((coinductive_lappend @ X0 @ (coinductive_LCons @ X0 @ X26 @ X9) @ X27) = (coinductive_LCons @ X0 @ X26 @ (coinductive_lappend @ X0 @ X9 @ X27)))),
% 278.23/41.19 file('/export/starexec/sandbox/tmp/tmp.gEkGcnFM62/DTF2THF_9795.p',fact_13_lappend__code_I2_J)).
% 278.23/41.19 % SZS output end Proof for DTF2THF_9795
% 278.23/41.19 % (11022)------------------------------
% 278.23/41.19 % (11022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 278.23/41.19 % (11022)Termination reason: Refutation
% 278.23/41.19
% 278.23/41.19 % (11022)Memory used [KB]: 16502
% 278.23/41.19 % (11022)Time elapsed: 8.032 s
% 278.23/41.19 % (11022)Instructions burned: 26330 (million)
% 278.23/41.19 % (11022)------------------------------
% 278.23/41.19 % (11022)------------------------------
% 278.23/41.19 % (9894)Success in time 39.435 s
%------------------------------------------------------------------------------